Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 281.6 | ||
Root | \(1.47393 + 0.909692i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.c.239.6 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||
\(3\) | −1.68547 | + | 0.398975i | −0.973108 | + | 0.230348i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.559062 | + | 0.559062i | −0.250020 | + | 0.250020i | −0.820979 | − | 0.570959i | \(-0.806572\pi\) |
0.570959 | + | 0.820979i | \(0.306572\pi\) | |||||||
\(6\) | −0.909692 | + | 1.47393i | −0.371380 | + | 0.601728i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 2.68164 | − | 1.34492i | 0.893879 | − | 0.448307i | ||||
\(10\) | 0.790633i | 0.250020i | ||||||||
\(11\) | −0.347057 | − | 0.347057i | −0.104642 | − | 0.104642i | 0.652848 | − | 0.757489i | \(-0.273574\pi\) |
−0.757489 | + | 0.652848i | \(0.773574\pi\) | |||||||
\(12\) | 0.398975 | + | 1.68547i | 0.115174 | + | 0.486554i | ||||
\(13\) | −3.45365 | − | 1.03551i | −0.957871 | − | 0.287199i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 0.719233 | − | 1.16534i | 0.185705 | − | 0.300888i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.50042 | −1.09151 | −0.545756 | − | 0.837944i | \(-0.683757\pi\) | ||||
−0.545756 | + | 0.837944i | \(0.683757\pi\) | |||||||
\(18\) | 0.945201 | − | 2.84721i | 0.222786 | − | 0.671093i | ||||
\(19\) | −3.86509 | − | 3.86509i | −0.886712 | − | 0.886712i | 0.107494 | − | 0.994206i | \(-0.465717\pi\) |
−0.994206 | + | 0.107494i | \(0.965717\pi\) | |||||||
\(20\) | 0.559062 | + | 0.559062i | 0.125010 | + | 0.125010i | ||||
\(21\) | 0.909692 | − | 1.47393i | 0.198511 | − | 0.321637i | ||||
\(22\) | −0.490813 | −0.104642 | ||||||||
\(23\) | −5.27970 | −1.10089 | −0.550447 | − | 0.834870i | \(-0.685543\pi\) | ||||
−0.550447 | + | 0.834870i | \(0.685543\pi\) | |||||||
\(24\) | 1.47393 | + | 0.909692i | 0.300864 | + | 0.185690i | ||||
\(25\) | 4.37490i | 0.874980i | ||||||||
\(26\) | −3.17432 | + | 1.70989i | −0.622535 | + | 0.335336i | ||||
\(27\) | −3.98324 | + | 3.33674i | −0.766575 | + | 0.642155i | ||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | 10.6966i | 1.98630i | 0.116833 | + | 0.993152i | \(0.462726\pi\) | ||||
−0.116833 | + | 0.993152i | \(0.537274\pi\) | |||||||
\(30\) | −0.315443 | − | 1.33259i | −0.0575917 | − | 0.243297i | ||||
\(31\) | −2.47731 | − | 2.47731i | −0.444938 | − | 0.444938i | 0.448730 | − | 0.893667i | \(-0.351877\pi\) |
−0.893667 | + | 0.448730i | \(0.851877\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0.723423 | + | 0.446489i | 0.125932 | + | 0.0777237i | ||||
\(34\) | −3.18228 | + | 3.18228i | −0.545756 | + | 0.545756i | ||||
\(35\) | − | 0.790633i | − | 0.133641i | ||||||
\(36\) | −1.34492 | − | 2.68164i | −0.224154 | − | 0.446940i | ||||
\(37\) | 6.92111 | − | 6.92111i | 1.13782 | − | 1.13782i | 0.148984 | − | 0.988840i | \(-0.452400\pi\) |
0.988840 | − | 0.148984i | \(-0.0476004\pi\) | |||||||
\(38\) | −5.46606 | −0.886712 | ||||||||
\(39\) | 6.23418 | + | 0.367403i | 0.998268 | + | 0.0588315i | ||||
\(40\) | 0.790633 | 0.125010 | ||||||||
\(41\) | −7.31477 | + | 7.31477i | −1.14237 | + | 1.14237i | −0.154360 | + | 0.988015i | \(0.549332\pi\) |
−0.988015 | + | 0.154360i | \(0.950668\pi\) | |||||||
\(42\) | −0.398975 | − | 1.68547i | −0.0615631 | − | 0.260074i | ||||
\(43\) | − | 7.24514i | − | 1.10487i | −0.833555 | − | 0.552437i | \(-0.813698\pi\) | ||
0.833555 | − | 0.552437i | \(-0.186302\pi\) | |||||||
\(44\) | −0.347057 | + | 0.347057i | −0.0523209 | + | 0.0523209i | ||||
\(45\) | −0.747308 | + | 2.25110i | −0.111402 | + | 0.335574i | ||||
\(46\) | −3.73331 | + | 3.73331i | −0.550447 | + | 0.550447i | ||||
\(47\) | −2.49319 | − | 2.49319i | −0.363669 | − | 0.363669i | 0.501493 | − | 0.865162i | \(-0.332784\pi\) |
−0.865162 | + | 0.501493i | \(0.832784\pi\) | |||||||
\(48\) | 1.68547 | − | 0.398975i | 0.243277 | − | 0.0575870i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 3.09352 | + | 3.09352i | 0.437490 | + | 0.437490i | ||||
\(51\) | 7.58533 | − | 1.79555i | 1.06216 | − | 0.251428i | ||||
\(52\) | −1.03551 | + | 3.45365i | −0.143599 | + | 0.478936i | ||||
\(53\) | − | 12.0607i | − | 1.65667i | −0.560236 | − | 0.828333i | \(-0.689290\pi\) | ||
0.560236 | − | 0.828333i | \(-0.310710\pi\) | |||||||
\(54\) | −0.457147 | + | 5.17600i | −0.0622098 | + | 0.704365i | ||||
\(55\) | 0.388054 | 0.0523251 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 8.05657 | + | 4.97243i | 1.06712 | + | 0.658614i | ||||
\(58\) | 7.56362 | + | 7.56362i | 0.993152 | + | 0.993152i | ||||
\(59\) | 3.41247 | + | 3.41247i | 0.444266 | + | 0.444266i | 0.893443 | − | 0.449177i | \(-0.148283\pi\) |
−0.449177 | + | 0.893443i | \(0.648283\pi\) | |||||||
\(60\) | −1.16534 | − | 0.719233i | −0.150444 | − | 0.0928525i | ||||
\(61\) | 6.42464 | 0.822591 | 0.411296 | − | 0.911502i | \(-0.365076\pi\) | ||||
0.411296 | + | 0.911502i | \(0.365076\pi\) | |||||||
\(62\) | −3.50344 | −0.444938 | ||||||||
\(63\) | −0.945201 | + | 2.84721i | −0.119084 | + | 0.358715i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 2.50972 | − | 1.35189i | 0.311293 | − | 0.167682i | ||||
\(66\) | 0.827253 | − | 0.195822i | 0.101828 | − | 0.0241040i | ||||
\(67\) | −2.43437 | − | 2.43437i | −0.297405 | − | 0.297405i | 0.542592 | − | 0.839997i | \(-0.317443\pi\) |
−0.839997 | + | 0.542592i | \(0.817443\pi\) | |||||||
\(68\) | 4.50042i | 0.545756i | ||||||||
\(69\) | 8.89880 | − | 2.10647i | 1.07129 | − | 0.253589i | ||||
\(70\) | −0.559062 | − | 0.559062i | −0.0668207 | − | 0.0668207i | ||||
\(71\) | −8.49611 | + | 8.49611i | −1.00830 | + | 1.00830i | −0.00833786 | + | 0.999965i | \(0.502654\pi\) |
−0.999965 | + | 0.00833786i | \(0.997346\pi\) | |||||||
\(72\) | −2.84721 | − | 0.945201i | −0.335547 | − | 0.111393i | ||||
\(73\) | 5.93236 | − | 5.93236i | 0.694330 | − | 0.694330i | −0.268851 | − | 0.963182i | \(-0.586644\pi\) |
0.963182 | + | 0.268851i | \(0.0866440\pi\) | |||||||
\(74\) | − | 9.78793i | − | 1.13782i | ||||||
\(75\) | −1.74547 | − | 7.37377i | −0.201550 | − | 0.851450i | ||||
\(76\) | −3.86509 | + | 3.86509i | −0.443356 | + | 0.443356i | ||||
\(77\) | 0.490813 | 0.0559334 | ||||||||
\(78\) | 4.66802 | − | 4.14844i | 0.528550 | − | 0.469718i | ||||
\(79\) | −13.2235 | −1.48776 | −0.743882 | − | 0.668311i | \(-0.767017\pi\) | ||||
−0.743882 | + | 0.668311i | \(0.767017\pi\) | |||||||
\(80\) | 0.559062 | − | 0.559062i | 0.0625051 | − | 0.0625051i | ||||
\(81\) | 5.38237 | − | 7.21319i | 0.598041 | − | 0.801466i | ||||
\(82\) | 10.3446i | 1.14237i | ||||||||
\(83\) | 6.31304 | − | 6.31304i | 0.692946 | − | 0.692946i | −0.269933 | − | 0.962879i | \(-0.587002\pi\) |
0.962879 | + | 0.269933i | \(0.0870016\pi\) | |||||||
\(84\) | −1.47393 | − | 0.909692i | −0.160819 | − | 0.0992555i | ||||
\(85\) | 2.51601 | − | 2.51601i | 0.272900 | − | 0.272900i | ||||
\(86\) | −5.12309 | − | 5.12309i | −0.552437 | − | 0.552437i | ||||
\(87\) | −4.26766 | − | 18.0288i | −0.457541 | − | 1.93289i | ||||
\(88\) | 0.490813i | 0.0523209i | ||||||||
\(89\) | 12.2569 | + | 12.2569i | 1.29923 | + | 1.29923i | 0.928898 | + | 0.370335i | \(0.120757\pi\) |
0.370335 | + | 0.928898i | \(0.379243\pi\) | |||||||
\(90\) | 1.06334 | + | 2.12019i | 0.112086 | + | 0.223488i | ||||
\(91\) | 3.17432 | − | 1.70989i | 0.332759 | − | 0.179245i | ||||
\(92\) | 5.27970i | 0.550447i | ||||||||
\(93\) | 5.16382 | + | 3.18705i | 0.535463 | + | 0.330482i | ||||
\(94\) | −3.52590 | −0.363669 | ||||||||
\(95\) | 4.32165 | 0.443392 | ||||||||
\(96\) | 0.909692 | − | 1.47393i | 0.0928450 | − | 0.150432i | ||||
\(97\) | −0.867358 | − | 0.867358i | −0.0880669 | − | 0.0880669i | 0.661701 | − | 0.749768i | \(-0.269835\pi\) |
−0.749768 | + | 0.661701i | \(0.769835\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | −1.39745 | − | 0.463917i | −0.140449 | − | 0.0466254i | ||||
\(100\) | 4.37490 | 0.437490 | ||||||||
\(101\) | 3.42487 | 0.340787 | 0.170393 | − | 0.985376i | \(-0.445496\pi\) | ||||
0.170393 | + | 0.985376i | \(0.445496\pi\) | |||||||
\(102\) | 4.09399 | − | 6.63329i | 0.405366 | − | 0.656794i | ||||
\(103\) | 0.0883069i | 0.00870114i | 0.999991 | + | 0.00435057i | \(0.00138483\pi\) | ||||
−0.999991 | + | 0.00435057i | \(0.998615\pi\) | |||||||
\(104\) | 1.70989 | + | 3.17432i | 0.167668 | + | 0.311267i | ||||
\(105\) | 0.315443 | + | 1.33259i | 0.0307841 | + | 0.130048i | ||||
\(106\) | −8.52821 | − | 8.52821i | −0.828333 | − | 0.828333i | ||||
\(107\) | − | 5.08715i | − | 0.491794i | −0.969296 | − | 0.245897i | \(-0.920918\pi\) | ||
0.969296 | − | 0.245897i | \(-0.0790824\pi\) | |||||||
\(108\) | 3.33674 | + | 3.98324i | 0.321078 | + | 0.383287i | ||||
\(109\) | 5.92580 | + | 5.92580i | 0.567589 | + | 0.567589i | 0.931452 | − | 0.363863i | \(-0.118542\pi\) |
−0.363863 | + | 0.931452i | \(0.618542\pi\) | |||||||
\(110\) | 0.274395 | − | 0.274395i | 0.0261626 | − | 0.0261626i | ||||
\(111\) | −8.90400 | + | 14.4267i | −0.845130 | + | 1.36932i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | − | 2.88604i | − | 0.271496i | −0.990743 | − | 0.135748i | \(-0.956656\pi\) | ||
0.990743 | − | 0.135748i | \(-0.0433438\pi\) | |||||||
\(114\) | 9.21290 | − | 2.18082i | 0.862867 | − | 0.204252i | ||||
\(115\) | 2.95168 | − | 2.95168i | 0.275246 | − | 0.275246i | ||||
\(116\) | 10.6966 | 0.993152 | ||||||||
\(117\) | −10.6541 | + | 1.86803i | −0.984975 | + | 0.172700i | ||||
\(118\) | 4.82596 | 0.444266 | ||||||||
\(119\) | 3.18228 | − | 3.18228i | 0.291719 | − | 0.291719i | ||||
\(120\) | −1.33259 | + | 0.315443i | −0.121648 | + | 0.0287959i | ||||
\(121\) | − | 10.7591i | − | 0.978100i | ||||||
\(122\) | 4.54291 | − | 4.54291i | 0.411296 | − | 0.411296i | ||||
\(123\) | 9.41044 | − | 15.2473i | 0.848511 | − | 1.37480i | ||||
\(124\) | −2.47731 | + | 2.47731i | −0.222469 | + | 0.222469i | ||||
\(125\) | −5.24115 | − | 5.24115i | −0.468783 | − | 0.468783i | ||||
\(126\) | 1.34492 | + | 2.68164i | 0.119815 | + | 0.238899i | ||||
\(127\) | 21.1044i | 1.87271i | 0.351053 | + | 0.936356i | \(0.385824\pi\) | ||||
−0.351053 | + | 0.936356i | \(0.614176\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 2.89063 | + | 12.2115i | 0.254506 | + | 1.07516i | ||||
\(130\) | 0.818708 | − | 2.73057i | 0.0718055 | − | 0.239487i | ||||
\(131\) | 7.76803i | 0.678696i | 0.940661 | + | 0.339348i | \(0.110206\pi\) | ||||
−0.940661 | + | 0.339348i | \(0.889794\pi\) | |||||||
\(132\) | 0.446489 | − | 0.723423i | 0.0388619 | − | 0.0629659i | ||||
\(133\) | 5.46606 | 0.473967 | ||||||||
\(134\) | −3.44271 | −0.297405 | ||||||||
\(135\) | 0.361436 | − | 4.09232i | 0.0311074 | − | 0.352211i | ||||
\(136\) | 3.18228 | + | 3.18228i | 0.272878 | + | 0.272878i | ||||
\(137\) | −2.35653 | − | 2.35653i | −0.201332 | − | 0.201332i | 0.599239 | − | 0.800570i | \(-0.295470\pi\) |
−0.800570 | + | 0.599239i | \(0.795470\pi\) | |||||||
\(138\) | 4.80290 | − | 7.78190i | 0.408850 | − | 0.662439i | ||||
\(139\) | 1.53895 | 0.130532 | 0.0652659 | − | 0.997868i | \(-0.479210\pi\) | ||||
0.0652659 | + | 0.997868i | \(0.479210\pi\) | |||||||
\(140\) | −0.790633 | −0.0668207 | ||||||||
\(141\) | 5.19692 | + | 3.20748i | 0.437660 | + | 0.270119i | ||||
\(142\) | 12.0153i | 1.00830i | ||||||||
\(143\) | 0.839235 | + | 1.55800i | 0.0701803 | + | 0.130286i | ||||
\(144\) | −2.68164 | + | 1.34492i | −0.223470 | + | 0.112077i | ||||
\(145\) | −5.98005 | − | 5.98005i | −0.496616 | − | 0.496616i | ||||
\(146\) | − | 8.38963i | − | 0.694330i | ||||||
\(147\) | 0.398975 | + | 1.68547i | 0.0329069 | + | 0.139015i | ||||
\(148\) | −6.92111 | − | 6.92111i | −0.568912 | − | 0.568912i | ||||
\(149\) | 6.80987 | − | 6.80987i | 0.557887 | − | 0.557887i | −0.370819 | − | 0.928705i | \(-0.620923\pi\) |
0.928705 | + | 0.370819i | \(0.120923\pi\) | |||||||
\(150\) | −6.44828 | − | 3.97981i | −0.526500 | − | 0.324950i | ||||
\(151\) | 1.21937 | − | 1.21937i | 0.0992308 | − | 0.0992308i | −0.655749 | − | 0.754979i | \(-0.727647\pi\) |
0.754979 | + | 0.655749i | \(0.227647\pi\) | |||||||
\(152\) | 5.46606i | 0.443356i | ||||||||
\(153\) | −12.0685 | + | 6.05271i | −0.975680 | + | 0.489333i | ||||
\(154\) | 0.347057 | − | 0.347057i | 0.0279667 | − | 0.0279667i | ||||
\(155\) | 2.76994 | 0.222487 | ||||||||
\(156\) | 0.367403 | − | 6.23418i | 0.0294158 | − | 0.499134i | ||||
\(157\) | −5.63769 | −0.449936 | −0.224968 | − | 0.974366i | \(-0.572228\pi\) | ||||
−0.224968 | + | 0.974366i | \(0.572228\pi\) | |||||||
\(158\) | −9.35045 | + | 9.35045i | −0.743882 | + | 0.743882i | ||||
\(159\) | 4.81192 | + | 20.3280i | 0.381610 | + | 1.61211i | ||||
\(160\) | − | 0.790633i | − | 0.0625051i | ||||||
\(161\) | 3.73331 | − | 3.73331i | 0.294226 | − | 0.294226i | ||||
\(162\) | −1.29459 | − | 8.90640i | −0.101712 | − | 0.699753i | ||||
\(163\) | 3.47849 | − | 3.47849i | 0.272456 | − | 0.272456i | −0.557632 | − | 0.830088i | \(-0.688290\pi\) |
0.830088 | + | 0.557632i | \(0.188290\pi\) | |||||||
\(164\) | 7.31477 | + | 7.31477i | 0.571187 | + | 0.571187i | ||||
\(165\) | −0.654054 | + | 0.154824i | −0.0509180 | + | 0.0120530i | ||||
\(166\) | − | 8.92798i | − | 0.692946i | ||||||
\(167\) | 2.49027 | + | 2.49027i | 0.192703 | + | 0.192703i | 0.796863 | − | 0.604160i | \(-0.206491\pi\) |
−0.604160 | + | 0.796863i | \(0.706491\pi\) | |||||||
\(168\) | −1.68547 | + | 0.398975i | −0.130037 | + | 0.0307816i | ||||
\(169\) | 10.8554 | + | 7.15258i | 0.835034 | + | 0.550199i | ||||
\(170\) | − | 3.55818i | − | 0.272900i | ||||||
\(171\) | −15.5630 | − | 5.16653i | −1.19013 | − | 0.395094i | ||||
\(172\) | −7.24514 | −0.552437 | ||||||||
\(173\) | −13.1775 | −1.00187 | −0.500934 | − | 0.865486i | \(-0.667010\pi\) | ||||
−0.500934 | + | 0.865486i | \(0.667010\pi\) | |||||||
\(174\) | −15.7660 | − | 9.73058i | −1.19521 | − | 0.737673i | ||||
\(175\) | −3.09352 | − | 3.09352i | −0.233848 | − | 0.233848i | ||||
\(176\) | 0.347057 | + | 0.347057i | 0.0261604 | + | 0.0261604i | ||||
\(177\) | −7.11311 | − | 4.39013i | −0.534654 | − | 0.329983i | ||||
\(178\) | 17.3339 | 1.29923 | ||||||||
\(179\) | −13.9967 | −1.04616 | −0.523081 | − | 0.852283i | \(-0.675217\pi\) | ||||
−0.523081 | + | 0.852283i | \(0.675217\pi\) | |||||||
\(180\) | 2.25110 | + | 0.747308i | 0.167787 | + | 0.0557010i | ||||
\(181\) | 3.47621i | 0.258385i | 0.991620 | + | 0.129192i | \(0.0412384\pi\) | ||||
−0.991620 | + | 0.129192i | \(0.958762\pi\) | |||||||
\(182\) | 1.03551 | − | 3.45365i | 0.0767571 | − | 0.256002i | ||||
\(183\) | −10.8286 | + | 2.56327i | −0.800471 | + | 0.189482i | ||||
\(184\) | 3.73331 | + | 3.73331i | 0.275224 | + | 0.275224i | ||||
\(185\) | 7.73867i | 0.568958i | ||||||||
\(186\) | 5.90496 | − | 1.39779i | 0.432973 | − | 0.102491i | ||||
\(187\) | 1.56190 | + | 1.56190i | 0.114218 | + | 0.114218i | ||||
\(188\) | −2.49319 | + | 2.49319i | −0.181834 | + | 0.181834i | ||||
\(189\) | 0.457147 | − | 5.17600i | 0.0332525 | − | 0.376499i | ||||
\(190\) | 3.05587 | − | 3.05587i | 0.221696 | − | 0.221696i | ||||
\(191\) | − | 26.9246i | − | 1.94820i | −0.226120 | − | 0.974099i | \(-0.572604\pi\) | ||
0.226120 | − | 0.974099i | \(-0.427396\pi\) | |||||||
\(192\) | −0.398975 | − | 1.68547i | −0.0287935 | − | 0.121639i | ||||
\(193\) | −15.1725 | + | 15.1725i | −1.09214 | + | 1.09214i | −0.0968371 | + | 0.995300i | \(0.530873\pi\) |
−0.995300 | + | 0.0968371i | \(0.969127\pi\) | |||||||
\(194\) | −1.22663 | −0.0880669 | ||||||||
\(195\) | −3.69070 | + | 3.27989i | −0.264296 | + | 0.234878i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −15.8927 | + | 15.8927i | −1.13231 | + | 1.13231i | −0.142517 | + | 0.989792i | \(0.545520\pi\) |
−0.989792 | + | 0.142517i | \(0.954480\pi\) | |||||||
\(198\) | −1.31618 | + | 0.660106i | −0.0935371 | + | 0.0469117i | ||||
\(199\) | − | 4.30765i | − | 0.305361i | −0.988276 | − | 0.152681i | \(-0.951209\pi\) | ||
0.988276 | − | 0.152681i | \(-0.0487905\pi\) | |||||||
\(200\) | 3.09352 | − | 3.09352i | 0.218745 | − | 0.218745i | ||||
\(201\) | 5.07431 | + | 3.13181i | 0.357914 | + | 0.220901i | ||||
\(202\) | 2.42175 | − | 2.42175i | 0.170393 | − | 0.170393i | ||||
\(203\) | −7.56362 | − | 7.56362i | −0.530862 | − | 0.530862i | ||||
\(204\) | −1.79555 | − | 7.58533i | −0.125714 | − | 0.531080i | ||||
\(205\) | − | 8.17882i | − | 0.571234i | ||||||
\(206\) | 0.0624424 | + | 0.0624424i | 0.00435057 | + | 0.00435057i | ||||
\(207\) | −14.1583 | + | 7.10079i | −0.984067 | + | 0.493539i | ||||
\(208\) | 3.45365 | + | 1.03551i | 0.239468 | + | 0.0717997i | ||||
\(209\) | 2.68282i | 0.185574i | ||||||||
\(210\) | 1.16534 | + | 0.719233i | 0.0804158 | + | 0.0496318i | ||||
\(211\) | 9.69453 | 0.667399 | 0.333700 | − | 0.942679i | \(-0.391703\pi\) | ||||
0.333700 | + | 0.942679i | \(0.391703\pi\) | |||||||
\(212\) | −12.0607 | −0.828333 | ||||||||
\(213\) | 10.9302 | − | 17.7097i | 0.748927 | − | 1.21345i | ||||
\(214\) | −3.59716 | − | 3.59716i | −0.245897 | − | 0.245897i | ||||
\(215\) | 4.05049 | + | 4.05049i | 0.276241 | + | 0.276241i | ||||
\(216\) | 5.17600 | + | 0.457147i | 0.352182 | + | 0.0311049i | ||||
\(217\) | 3.50344 | 0.237829 | ||||||||
\(218\) | 8.38035 | 0.567589 | ||||||||
\(219\) | −7.63197 | + | 12.3657i | −0.515721 | + | 0.835596i | ||||
\(220\) | − | 0.388054i | − | 0.0261626i | ||||||
\(221\) | 15.5429 | + | 4.66023i | 1.04553 | + | 0.313481i | ||||
\(222\) | 3.90514 | + | 16.4973i | 0.262096 | + | 1.10723i | ||||
\(223\) | −7.49728 | − | 7.49728i | −0.502055 | − | 0.502055i | 0.410021 | − | 0.912076i | \(-0.365521\pi\) |
−0.912076 | + | 0.410021i | \(0.865521\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 5.88390 | + | 11.7319i | 0.392260 | + | 0.782126i | ||||
\(226\) | −2.04074 | − | 2.04074i | −0.135748 | − | 0.135748i | ||||
\(227\) | 17.5224 | − | 17.5224i | 1.16300 | − | 1.16300i | 0.179185 | − | 0.983815i | \(-0.442654\pi\) |
0.983815 | − | 0.179185i | \(-0.0573459\pi\) | |||||||
\(228\) | 4.97243 | − | 8.05657i | 0.329307 | − | 0.533560i | ||||
\(229\) | −13.8742 | + | 13.8742i | −0.916834 | + | 0.916834i | −0.996798 | − | 0.0799635i | \(-0.974520\pi\) |
0.0799635 | + | 0.996798i | \(0.474520\pi\) | |||||||
\(230\) | − | 4.17431i | − | 0.275246i | ||||||
\(231\) | −0.827253 | + | 0.195822i | −0.0544292 | + | 0.0128842i | ||||
\(232\) | 7.56362 | − | 7.56362i | 0.496576 | − | 0.496576i | ||||
\(233\) | 4.80094 | 0.314520 | 0.157260 | − | 0.987557i | \(-0.449734\pi\) | ||||
0.157260 | + | 0.987557i | \(0.449734\pi\) | |||||||
\(234\) | −6.21271 | + | 8.85451i | −0.406137 | + | 0.578837i | ||||
\(235\) | 2.78770 | 0.181849 | ||||||||
\(236\) | 3.41247 | − | 3.41247i | 0.222133 | − | 0.222133i | ||||
\(237\) | 22.2879 | − | 5.27585i | 1.44775 | − | 0.342703i | ||||
\(238\) | − | 4.50042i | − | 0.291719i | ||||||
\(239\) | −8.85356 | + | 8.85356i | −0.572689 | + | 0.572689i | −0.932879 | − | 0.360190i | \(-0.882712\pi\) |
0.360190 | + | 0.932879i | \(0.382712\pi\) | |||||||
\(240\) | −0.719233 | + | 1.16534i | −0.0464263 | + | 0.0752221i | ||||
\(241\) | 8.79467 | − | 8.79467i | 0.566515 | − | 0.566515i | −0.364636 | − | 0.931150i | \(-0.618806\pi\) |
0.931150 | + | 0.364636i | \(0.118806\pi\) | |||||||
\(242\) | −7.60783 | − | 7.60783i | −0.489050 | − | 0.489050i | ||||
\(243\) | −6.19396 | + | 14.3051i | −0.397343 | + | 0.917670i | ||||
\(244\) | − | 6.42464i | − | 0.411296i | ||||||
\(245\) | 0.559062 | + | 0.559062i | 0.0357172 | + | 0.0357172i | ||||
\(246\) | −4.12725 | − | 17.4356i | −0.263144 | − | 1.11165i | ||||
\(247\) | 9.34634 | + | 17.3510i | 0.594693 | + | 1.10402i | ||||
\(248\) | 3.50344i | 0.222469i | ||||||||
\(249\) | −8.12171 | + | 13.1592i | −0.514693 | + | 0.833930i | ||||
\(250\) | −7.41211 | −0.468783 | ||||||||
\(251\) | −13.6883 | −0.863998 | −0.431999 | − | 0.901874i | \(-0.642192\pi\) | ||||
−0.431999 | + | 0.901874i | \(0.642192\pi\) | |||||||
\(252\) | 2.84721 | + | 0.945201i | 0.179357 | + | 0.0595421i | ||||
\(253\) | 1.83236 | + | 1.83236i | 0.115200 | + | 0.115200i | ||||
\(254\) | 14.9231 | + | 14.9231i | 0.936356 | + | 0.936356i | ||||
\(255\) | −3.23685 | + | 5.24450i | −0.202699 | + | 0.328423i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.2988 | −1.14145 | −0.570723 | − | 0.821142i | \(-0.693337\pi\) | ||||
−0.570723 | + | 0.821142i | \(0.693337\pi\) | |||||||
\(258\) | 10.6788 | + | 6.59085i | 0.664834 | + | 0.410328i | ||||
\(259\) | 9.78793i | 0.608192i | ||||||||
\(260\) | −1.35189 | − | 2.50972i | −0.0838408 | − | 0.155646i | ||||
\(261\) | 14.3861 | + | 28.6843i | 0.890474 | + | 1.77552i | ||||
\(262\) | 5.49282 | + | 5.49282i | 0.339348 | + | 0.339348i | ||||
\(263\) | 16.5203i | 1.01868i | 0.860564 | + | 0.509342i | \(0.170111\pi\) | ||||
−0.860564 | + | 0.509342i | \(0.829889\pi\) | |||||||
\(264\) | −0.195822 | − | 0.827253i | −0.0120520 | − | 0.0509139i | ||||
\(265\) | 6.74269 | + | 6.74269i | 0.414200 | + | 0.414200i | ||||
\(266\) | 3.86509 | − | 3.86509i | 0.236984 | − | 0.236984i | ||||
\(267\) | −25.5490 | − | 15.7685i | −1.56357 | − | 0.965019i | ||||
\(268\) | −2.43437 | + | 2.43437i | −0.148703 | + | 0.148703i | ||||
\(269\) | − | 11.7448i | − | 0.716091i | −0.933704 | − | 0.358046i | \(-0.883443\pi\) | ||
0.933704 | − | 0.358046i | \(-0.116557\pi\) | |||||||
\(270\) | −2.63814 | − | 3.14928i | −0.160552 | − | 0.191659i | ||||
\(271\) | 9.75803 | − | 9.75803i | 0.592758 | − | 0.592758i | −0.345618 | − | 0.938375i | \(-0.612331\pi\) |
0.938375 | + | 0.345618i | \(0.112331\pi\) | |||||||
\(272\) | 4.50042 | 0.272878 | ||||||||
\(273\) | −4.66802 | + | 4.14844i | −0.282522 | + | 0.251075i | ||||
\(274\) | −3.33263 | −0.201332 | ||||||||
\(275\) | 1.51834 | − | 1.51834i | 0.0915594 | − | 0.0915594i | ||||
\(276\) | −2.10647 | − | 8.89880i | −0.126794 | − | 0.535645i | ||||
\(277\) | 1.88463i | 0.113236i | 0.998396 | + | 0.0566181i | \(0.0180318\pi\) | ||||
−0.998396 | + | 0.0566181i | \(0.981968\pi\) | |||||||
\(278\) | 1.08820 | − | 1.08820i | 0.0652659 | − | 0.0652659i | ||||
\(279\) | −9.97503 | − | 3.31146i | −0.597190 | − | 0.198252i | ||||
\(280\) | −0.559062 | + | 0.559062i | −0.0334104 | + | 0.0334104i | ||||
\(281\) | −2.85196 | − | 2.85196i | −0.170134 | − | 0.170134i | 0.616904 | − | 0.787038i | \(-0.288387\pi\) |
−0.787038 | + | 0.616904i | \(0.788387\pi\) | |||||||
\(282\) | 5.94281 | − | 1.40675i | 0.353889 | − | 0.0837705i | ||||
\(283\) | 15.2599i | 0.907107i | 0.891229 | + | 0.453553i | \(0.149844\pi\) | ||||
−0.891229 | + | 0.453553i | \(0.850156\pi\) | |||||||
\(284\) | 8.49611 | + | 8.49611i | 0.504152 | + | 0.504152i | ||||
\(285\) | −7.28402 | + | 1.72423i | −0.431468 | + | 0.102134i | ||||
\(286\) | 1.69510 | + | 0.508242i | 0.100233 | + | 0.0300530i | ||||
\(287\) | − | 10.3446i | − | 0.610625i | ||||||
\(288\) | −0.945201 | + | 2.84721i | −0.0556965 | + | 0.167773i | ||||
\(289\) | 3.25377 | 0.191398 | ||||||||
\(290\) | −8.45707 | −0.496616 | ||||||||
\(291\) | 1.80796 | + | 1.11585i | 0.105985 | + | 0.0654126i | ||||
\(292\) | −5.93236 | − | 5.93236i | −0.347165 | − | 0.347165i | ||||
\(293\) | 13.4365 | + | 13.4365i | 0.784968 | + | 0.784968i | 0.980665 | − | 0.195696i | \(-0.0626967\pi\) |
−0.195696 | + | 0.980665i | \(0.562697\pi\) | |||||||
\(294\) | 1.47393 | + | 0.909692i | 0.0859612 | + | 0.0530543i | ||||
\(295\) | −3.81556 | −0.222151 | ||||||||
\(296\) | −9.78793 | −0.568912 | ||||||||
\(297\) | 2.54045 | + | 0.224374i | 0.147412 | + | 0.0130195i | ||||
\(298\) | − | 9.63062i | − | 0.557887i | ||||||
\(299\) | 18.2343 | + | 5.46718i | 1.05451 | + | 0.316175i | ||||
\(300\) | −7.37377 | + | 1.74547i | −0.425725 | + | 0.100775i | ||||
\(301\) | 5.12309 | + | 5.12309i | 0.295290 | + | 0.295290i | ||||
\(302\) | − | 1.72445i | − | 0.0992308i | ||||||
\(303\) | −5.77252 | + | 1.36644i | −0.331623 | + | 0.0784997i | ||||
\(304\) | 3.86509 | + | 3.86509i | 0.221678 | + | 0.221678i | ||||
\(305\) | −3.59178 | + | 3.59178i | −0.205665 | + | 0.205665i | ||||
\(306\) | −4.25380 | + | 12.8136i | −0.243174 | + | 0.732506i | ||||
\(307\) | 14.1492 | − | 14.1492i | 0.807539 | − | 0.807539i | −0.176722 | − | 0.984261i | \(-0.556549\pi\) |
0.984261 | + | 0.176722i | \(0.0565493\pi\) | |||||||
\(308\) | − | 0.490813i | − | 0.0279667i | ||||||
\(309\) | −0.0352322 | − | 0.148839i | −0.00200429 | − | 0.00846715i | ||||
\(310\) | 1.95864 | − | 1.95864i | 0.111243 | − | 0.111243i | ||||
\(311\) | −33.2959 | −1.88804 | −0.944019 | − | 0.329890i | \(-0.892988\pi\) | ||||
−0.944019 | + | 0.329890i | \(0.892988\pi\) | |||||||
\(312\) | −4.14844 | − | 4.66802i | −0.234859 | − | 0.264275i | ||||
\(313\) | −23.5153 | −1.32917 | −0.664583 | − | 0.747214i | \(-0.731391\pi\) | ||||
−0.664583 | + | 0.747214i | \(0.731391\pi\) | |||||||
\(314\) | −3.98645 | + | 3.98645i | −0.224968 | + | 0.224968i | ||||
\(315\) | −1.06334 | − | 2.12019i | −0.0599124 | − | 0.119459i | ||||
\(316\) | 13.2235i | 0.743882i | ||||||||
\(317\) | 2.21672 | − | 2.21672i | 0.124503 | − | 0.124503i | −0.642110 | − | 0.766613i | \(-0.721941\pi\) |
0.766613 | + | 0.642110i | \(0.221941\pi\) | |||||||
\(318\) | 17.7766 | + | 10.9715i | 0.996862 | + | 0.615253i | ||||
\(319\) | 3.71232 | − | 3.71232i | 0.207850 | − | 0.207850i | ||||
\(320\) | −0.559062 | − | 0.559062i | −0.0312525 | − | 0.0312525i | ||||
\(321\) | 2.02965 | + | 8.57426i | 0.113284 | + | 0.478568i | ||||
\(322\) | − | 5.27970i | − | 0.294226i | ||||||
\(323\) | 17.3945 | + | 17.3945i | 0.967857 | + | 0.967857i | ||||
\(324\) | −7.21319 | − | 5.38237i | −0.400733 | − | 0.299020i | ||||
\(325\) | 4.53025 | − | 15.1094i | 0.251293 | − | 0.838118i | ||||
\(326\) | − | 4.91933i | − | 0.272456i | ||||||
\(327\) | −12.3520 | − | 7.62354i | −0.683069 | − | 0.421583i | ||||
\(328\) | 10.3446 | 0.571187 | ||||||||
\(329\) | 3.52590 | 0.194389 | ||||||||
\(330\) | −0.353009 | + | 0.571963i | −0.0194325 | + | 0.0314855i | ||||
\(331\) | −21.9301 | − | 21.9301i | −1.20539 | − | 1.20539i | −0.972505 | − | 0.232882i | \(-0.925184\pi\) |
−0.232882 | − | 0.972505i | \(-0.574816\pi\) | |||||||
\(332\) | −6.31304 | − | 6.31304i | −0.346473 | − | 0.346473i | ||||
\(333\) | 9.25156 | − | 27.8683i | 0.506983 | − | 1.52717i | ||||
\(334\) | 3.52177 | 0.192703 | ||||||||
\(335\) | 2.72192 | 0.148715 | ||||||||
\(336\) | −0.909692 | + | 1.47393i | −0.0496277 | + | 0.0804093i | ||||
\(337\) | − | 12.0386i | − | 0.655785i | −0.944715 | − | 0.327892i | \(-0.893662\pi\) | ||
0.944715 | − | 0.327892i | \(-0.106338\pi\) | |||||||
\(338\) | 12.7336 | − | 2.61832i | 0.692616 | − | 0.142418i | ||||
\(339\) | 1.15146 | + | 4.86435i | 0.0625387 | + | 0.264195i | ||||
\(340\) | −2.51601 | − | 2.51601i | −0.136450 | − | 0.136450i | ||||
\(341\) | 1.71954i | 0.0931181i | ||||||||
\(342\) | −14.6580 | + | 7.35142i | −0.792614 | + | 0.397519i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −5.12309 | + | 5.12309i | −0.276219 | + | 0.276219i | ||||
\(345\) | −3.79734 | + | 6.15263i | −0.204442 | + | 0.331246i | ||||
\(346\) | −9.31790 | + | 9.31790i | −0.500934 | + | 0.500934i | ||||
\(347\) | 4.91439i | 0.263819i | 0.991262 | + | 0.131909i | \(0.0421108\pi\) | ||||
−0.991262 | + | 0.131909i | \(0.957889\pi\) | |||||||
\(348\) | −18.0288 | + | 4.26766i | −0.966444 | + | 0.228771i | ||||
\(349\) | −3.33670 | + | 3.33670i | −0.178609 | + | 0.178609i | −0.790749 | − | 0.612140i | \(-0.790309\pi\) |
0.612140 | + | 0.790749i | \(0.290309\pi\) | |||||||
\(350\) | −4.37490 | −0.233848 | ||||||||
\(351\) | 17.2119 | − | 7.39925i | 0.918706 | − | 0.394943i | ||||
\(352\) | 0.490813 | 0.0261604 | ||||||||
\(353\) | 4.61015 | − | 4.61015i | 0.245374 | − | 0.245374i | −0.573695 | − | 0.819069i | \(-0.694491\pi\) |
0.819069 | + | 0.573695i | \(0.194491\pi\) | |||||||
\(354\) | −8.13402 | + | 1.92544i | −0.432318 | + | 0.102336i | ||||
\(355\) | − | 9.49971i | − | 0.504192i | ||||||
\(356\) | 12.2569 | − | 12.2569i | 0.649617 | − | 0.649617i | ||||
\(357\) | −4.09399 | + | 6.63329i | −0.216677 | + | 0.351071i | ||||
\(358\) | −9.89715 | + | 9.89715i | −0.523081 | + | 0.523081i | ||||
\(359\) | 8.91675 | + | 8.91675i | 0.470608 | + | 0.470608i | 0.902111 | − | 0.431503i | \(-0.142017\pi\) |
−0.431503 | + | 0.902111i | \(0.642017\pi\) | |||||||
\(360\) | 2.12019 | − | 1.06334i | 0.111744 | − | 0.0560430i | ||||
\(361\) | 10.8778i | 0.572516i | ||||||||
\(362\) | 2.45805 | + | 2.45805i | 0.129192 | + | 0.129192i | ||||
\(363\) | 4.29261 | + | 18.1342i | 0.225304 | + | 0.951797i | ||||
\(364\) | −1.70989 | − | 3.17432i | −0.0896224 | − | 0.166379i | ||||
\(365\) | 6.63312i | 0.347193i | ||||||||
\(366\) | −5.84445 | + | 9.46946i | −0.305494 | + | 0.494976i | ||||
\(367\) | −25.6357 | −1.33817 | −0.669087 | − | 0.743184i | \(-0.733315\pi\) | ||||
−0.669087 | + | 0.743184i | \(0.733315\pi\) | |||||||
\(368\) | 5.27970 | 0.275224 | ||||||||
\(369\) | −9.77777 | + | 29.4534i | −0.509010 | + | 1.53328i | ||||
\(370\) | 5.47206 | + | 5.47206i | 0.284479 | + | 0.284479i | ||||
\(371\) | 8.52821 | + | 8.52821i | 0.442762 | + | 0.442762i | ||||
\(372\) | 3.18705 | − | 5.16382i | 0.165241 | − | 0.267732i | ||||
\(373\) | −27.6030 | −1.42923 | −0.714614 | − | 0.699519i | \(-0.753398\pi\) | ||||
−0.714614 | + | 0.699519i | \(0.753398\pi\) | |||||||
\(374\) | 2.20887 | 0.114218 | ||||||||
\(375\) | 10.9249 | + | 6.74273i | 0.564160 | + | 0.348193i | ||||
\(376\) | 3.52590i | 0.181834i | ||||||||
\(377\) | 11.0764 | − | 36.9422i | 0.570464 | − | 1.90262i | ||||
\(378\) | −3.33674 | − | 3.98324i | −0.171623 | − | 0.204876i | ||||
\(379\) | −15.2188 | − | 15.2188i | −0.781739 | − | 0.781739i | 0.198385 | − | 0.980124i | \(-0.436430\pi\) |
−0.980124 | + | 0.198385i | \(0.936430\pi\) | |||||||
\(380\) | − | 4.32165i | − | 0.221696i | ||||||
\(381\) | −8.42012 | − | 35.5709i | −0.431376 | − | 1.82235i | ||||
\(382\) | −19.0386 | − | 19.0386i | −0.974099 | − | 0.974099i | ||||
\(383\) | 7.48783 | − | 7.48783i | 0.382610 | − | 0.382610i | −0.489431 | − | 0.872042i | \(-0.662796\pi\) |
0.872042 | + | 0.489431i | \(0.162796\pi\) | |||||||
\(384\) | −1.47393 | − | 0.909692i | −0.0752160 | − | 0.0464225i | ||||
\(385\) | −0.274395 | + | 0.274395i | −0.0139845 | + | 0.0139845i | ||||
\(386\) | 21.4571i | 1.09214i | ||||||||
\(387\) | −9.74415 | − | 19.4289i | −0.495323 | − | 0.987624i | ||||
\(388\) | −0.867358 | + | 0.867358i | −0.0440334 | + | 0.0440334i | ||||
\(389\) | −7.00656 | −0.355247 | −0.177623 | − | 0.984099i | \(-0.556841\pi\) | ||||
−0.177623 | + | 0.984099i | \(0.556841\pi\) | |||||||
\(390\) | −0.290481 | + | 4.92895i | −0.0147091 | + | 0.249587i | ||||
\(391\) | 23.7609 | 1.20164 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | −3.09925 | − | 13.0928i | −0.156336 | − | 0.660444i | ||||
\(394\) | 22.4757i | 1.13231i | ||||||||
\(395\) | 7.39278 | − | 7.39278i | 0.371971 | − | 0.371971i | ||||
\(396\) | −0.463917 | + | 1.39745i | −0.0233127 | + | 0.0702244i | ||||
\(397\) | −5.42804 | + | 5.42804i | −0.272425 | + | 0.272425i | −0.830076 | − | 0.557650i | \(-0.811703\pi\) |
0.557650 | + | 0.830076i | \(0.311703\pi\) | |||||||
\(398\) | −3.04597 | − | 3.04597i | −0.152681 | − | 0.152681i | ||||
\(399\) | −9.21290 | + | 2.18082i | −0.461222 | + | 0.109178i | ||||
\(400\) | − | 4.37490i | − | 0.218745i | ||||||
\(401\) | −22.7703 | − | 22.7703i | −1.13709 | − | 1.13709i | −0.988969 | − | 0.148126i | \(-0.952676\pi\) |
−0.148126 | − | 0.988969i | \(-0.547324\pi\) | |||||||
\(402\) | 5.80260 | − | 1.37356i | 0.289407 | − | 0.0685067i | ||||
\(403\) | 5.99049 | + | 11.1210i | 0.298407 | + | 0.553978i | ||||
\(404\) | − | 3.42487i | − | 0.170393i | ||||||
\(405\) | 1.02354 | + | 7.04170i | 0.0508603 | + | 0.349905i | ||||
\(406\) | −10.6966 | −0.530862 | ||||||||
\(407\) | −4.80405 | −0.238128 | ||||||||
\(408\) | −6.63329 | − | 4.09399i | −0.328397 | − | 0.202683i | ||||
\(409\) | 5.64482 | + | 5.64482i | 0.279118 | + | 0.279118i | 0.832757 | − | 0.553639i | \(-0.186761\pi\) |
−0.553639 | + | 0.832757i | \(0.686761\pi\) | |||||||
\(410\) | −5.78330 | − | 5.78330i | −0.285617 | − | 0.285617i | ||||
\(411\) | 4.91206 | + | 3.03167i | 0.242294 | + | 0.149541i | ||||
\(412\) | 0.0883069 | 0.00435057 | ||||||||
\(413\) | −4.82596 | −0.237470 | ||||||||
\(414\) | −4.99038 | + | 15.0324i | −0.245264 | + | 0.738803i | ||||
\(415\) | 7.05876i | 0.346501i | ||||||||
\(416\) | 3.17432 | − | 1.70989i | 0.155634 | − | 0.0838341i | ||||
\(417\) | −2.59385 | + | 0.614001i | −0.127022 | + | 0.0300678i | ||||
\(418\) | 1.89704 | + | 1.89704i | 0.0927871 | + | 0.0927871i | ||||
\(419\) | − | 9.00273i | − | 0.439812i | −0.975521 | − | 0.219906i | \(-0.929425\pi\) | ||
0.975521 | − | 0.219906i | \(-0.0705751\pi\) | |||||||
\(420\) | 1.33259 | − | 0.315443i | 0.0650238 | − | 0.0153920i | ||||
\(421\) | −1.90886 | − | 1.90886i | −0.0930321 | − | 0.0930321i | 0.659059 | − | 0.752091i | \(-0.270955\pi\) |
−0.752091 | + | 0.659059i | \(0.770955\pi\) | |||||||
\(422\) | 6.85507 | − | 6.85507i | 0.333700 | − | 0.333700i | ||||
\(423\) | −10.0390 | − | 3.33269i | −0.488112 | − | 0.162041i | ||||
\(424\) | −8.52821 | + | 8.52821i | −0.414166 | + | 0.414166i | ||||
\(425\) | − | 19.6889i | − | 0.955051i | ||||||
\(426\) | −4.79381 | − | 20.2515i | −0.232261 | − | 0.981188i | ||||
\(427\) | −4.54291 | + | 4.54291i | −0.219847 | + | 0.219847i | ||||
\(428\) | −5.08715 | −0.245897 | ||||||||
\(429\) | −2.03611 | − | 2.29113i | −0.0983043 | − | 0.110617i | ||||
\(430\) | 5.72825 | 0.276241 | ||||||||
\(431\) | 11.7362 | − | 11.7362i | 0.565312 | − | 0.565312i | −0.365500 | − | 0.930811i | \(-0.619102\pi\) |
0.930811 | + | 0.365500i | \(0.119102\pi\) | |||||||
\(432\) | 3.98324 | − | 3.33674i | 0.191644 | − | 0.160539i | ||||
\(433\) | − | 13.9122i | − | 0.668577i | −0.942471 | − | 0.334289i | \(-0.891504\pi\) | ||
0.942471 | − | 0.334289i | \(-0.108496\pi\) | |||||||
\(434\) | 2.47731 | − | 2.47731i | 0.118915 | − | 0.118915i | ||||
\(435\) | 12.4651 | + | 7.69332i | 0.597656 | + | 0.368867i | ||||
\(436\) | 5.92580 | − | 5.92580i | 0.283795 | − | 0.283795i | ||||
\(437\) | 20.4065 | + | 20.4065i | 0.976176 | + | 0.976176i | ||||
\(438\) | 3.34725 | + | 14.1405i | 0.159938 | + | 0.675659i | ||||
\(439\) | 8.24651i | 0.393584i | 0.980445 | + | 0.196792i | \(0.0630524\pi\) | ||||
−0.980445 | + | 0.196792i | \(0.936948\pi\) | |||||||
\(440\) | −0.274395 | − | 0.274395i | −0.0130813 | − | 0.0130813i | ||||
\(441\) | −1.34492 | − | 2.68164i | −0.0640439 | − | 0.127697i | ||||
\(442\) | 14.2858 | − | 7.69520i | 0.679504 | − | 0.366023i | ||||
\(443\) | 9.44990i | 0.448978i | 0.974477 | + | 0.224489i | \(0.0720713\pi\) | ||||
−0.974477 | + | 0.224489i | \(0.927929\pi\) | |||||||
\(444\) | 14.4267 | + | 8.90400i | 0.684661 | + | 0.422565i | ||||
\(445\) | −13.7048 | −0.649669 | ||||||||
\(446\) | −10.6028 | −0.502055 | ||||||||
\(447\) | −8.76089 | + | 14.1948i | −0.414376 | + | 0.671392i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | 22.9219 | + | 22.9219i | 1.08175 | + | 1.08175i | 0.996346 | + | 0.0854053i | \(0.0272185\pi\) |
0.0854053 | + | 0.996346i | \(0.472781\pi\) | |||||||
\(450\) | 12.4562 | + | 4.13516i | 0.587193 | + | 0.194933i | ||||
\(451\) | 5.07729 | 0.239080 | ||||||||
\(452\) | −2.88604 | −0.135748 | ||||||||
\(453\) | −1.56872 | + | 2.54171i | −0.0737047 | + | 0.119420i | ||||
\(454\) | − | 24.7804i | − | 1.16300i | ||||||
\(455\) | −0.818708 | + | 2.73057i | −0.0383816 | + | 0.128011i | ||||
\(456\) | −2.18082 | − | 9.21290i | −0.102126 | − | 0.431433i | ||||
\(457\) | −2.72508 | − | 2.72508i | −0.127474 | − | 0.127474i | 0.640492 | − | 0.767965i | \(-0.278731\pi\) |
−0.767965 | + | 0.640492i | \(0.778731\pi\) | |||||||
\(458\) | 19.6211i | 0.916834i | ||||||||
\(459\) | 17.9262 | − | 15.0167i | 0.836725 | − | 0.700920i | ||||
\(460\) | −2.95168 | − | 2.95168i | −0.137623 | − | 0.137623i | ||||
\(461\) | 17.0514 | − | 17.0514i | 0.794161 | − | 0.794161i | −0.188007 | − | 0.982168i | \(-0.560203\pi\) |
0.982168 | + | 0.188007i | \(0.0602026\pi\) | |||||||
\(462\) | −0.446489 | + | 0.723423i | −0.0207725 | + | 0.0336567i | ||||
\(463\) | −7.20273 | + | 7.20273i | −0.334739 | + | 0.334739i | −0.854383 | − | 0.519644i | \(-0.826065\pi\) |
0.519644 | + | 0.854383i | \(0.326065\pi\) | |||||||
\(464\) | − | 10.6966i | − | 0.496576i | ||||||
\(465\) | −4.66866 | + | 1.10514i | −0.216504 | + | 0.0512494i | ||||
\(466\) | 3.39478 | − | 3.39478i | 0.157260 | − | 0.157260i | ||||
\(467\) | −19.1716 | −0.887156 | −0.443578 | − | 0.896236i | \(-0.646291\pi\) | ||||
−0.443578 | + | 0.896236i | \(0.646291\pi\) | |||||||
\(468\) | 1.86803 | + | 10.6541i | 0.0863499 | + | 0.492487i | ||||
\(469\) | 3.44271 | 0.158970 | ||||||||
\(470\) | 1.97120 | − | 1.97120i | 0.0909246 | − | 0.0909246i | ||||
\(471\) | 9.50217 | − | 2.24929i | 0.437837 | − | 0.103642i | ||||
\(472\) | − | 4.82596i | − | 0.222133i | ||||||
\(473\) | −2.51448 | + | 2.51448i | −0.115616 | + | 0.115616i | ||||
\(474\) | 12.0293 | − | 19.4905i | 0.552526 | − | 0.895229i | ||||
\(475\) | 16.9094 | − | 16.9094i | 0.775855 | − | 0.775855i | ||||
\(476\) | −3.18228 | − | 3.18228i | −0.145859 | − | 0.145859i | ||||
\(477\) | −16.2207 | − | 32.3425i | −0.742695 | − | 1.48086i | ||||
\(478\) | 12.5208i | 0.572689i | ||||||||
\(479\) | 21.3865 | + | 21.3865i | 0.977174 | + | 0.977174i | 0.999745 | − | 0.0225708i | \(-0.00718511\pi\) |
−0.0225708 | + | 0.999745i | \(0.507185\pi\) | |||||||
\(480\) | 0.315443 | + | 1.33259i | 0.0143979 | + | 0.0608242i | ||||
\(481\) | −31.0700 | + | 16.7362i | −1.41667 | + | 0.763107i | ||||
\(482\) | − | 12.4375i | − | 0.566515i | ||||||
\(483\) | −4.80290 | + | 7.78190i | −0.218540 | + | 0.354089i | ||||
\(484\) | −10.7591 | −0.489050 | ||||||||
\(485\) | 0.969814 | 0.0440370 | ||||||||
\(486\) | 5.73542 | + | 14.4950i | 0.260164 | + | 0.657506i | ||||
\(487\) | 24.0755 | + | 24.0755i | 1.09096 | + | 1.09096i | 0.995426 | + | 0.0955392i | \(0.0304575\pi\) |
0.0955392 | + | 0.995426i | \(0.469542\pi\) | |||||||
\(488\) | −4.54291 | − | 4.54291i | −0.205648 | − | 0.205648i | ||||
\(489\) | −4.47507 | + | 7.25073i | −0.202370 | + | 0.327889i | ||||
\(490\) | 0.790633 | 0.0357172 | ||||||||
\(491\) | −10.3827 | −0.468565 | −0.234283 | − | 0.972169i | \(-0.575274\pi\) | ||||
−0.234283 | + | 0.972169i | \(0.575274\pi\) | |||||||
\(492\) | −15.2473 | − | 9.41044i | −0.687399 | − | 0.424255i | ||||
\(493\) | − | 48.1390i | − | 2.16807i | ||||||
\(494\) | 18.8779 | + | 5.66016i | 0.849356 | + | 0.254662i | ||||
\(495\) | 1.04062 | − | 0.521902i | 0.0467724 | − | 0.0234577i | ||||
\(496\) | 2.47731 | + | 2.47731i | 0.111234 | + | 0.111234i | ||||
\(497\) | − | 12.0153i | − | 0.538961i | ||||||
\(498\) | 3.56204 | + | 15.0479i | 0.159619 | + | 0.674311i | ||||
\(499\) | 3.48978 | + | 3.48978i | 0.156224 | + | 0.156224i | 0.780891 | − | 0.624667i | \(-0.214765\pi\) |
−0.624667 | + | 0.780891i | \(0.714765\pi\) | |||||||
\(500\) | −5.24115 | + | 5.24115i | −0.234391 | + | 0.234391i | ||||
\(501\) | −5.19084 | − | 3.20373i | −0.231910 | − | 0.143132i | ||||
\(502\) | −9.67910 | + | 9.67910i | −0.431999 | + | 0.431999i | ||||
\(503\) | − | 0.584892i | − | 0.0260790i | −0.999915 | − | 0.0130395i | \(-0.995849\pi\) | ||
0.999915 | − | 0.0130395i | \(-0.00415073\pi\) | |||||||
\(504\) | 2.68164 | − | 1.34492i | 0.119450 | − | 0.0599076i | ||||
\(505\) | −1.91471 | + | 1.91471i | −0.0852037 | + | 0.0852037i | ||||
\(506\) | 2.59135 | 0.115200 | ||||||||
\(507\) | −21.1503 | − | 7.72444i | −0.939316 | − | 0.343054i | ||||
\(508\) | 21.1044 | 0.936356 | ||||||||
\(509\) | 14.6995 | − | 14.6995i | 0.651544 | − | 0.651544i | −0.301821 | − | 0.953365i | \(-0.597594\pi\) |
0.953365 | + | 0.301821i | \(0.0975944\pi\) | |||||||
\(510\) | 1.41962 | + | 5.99722i | 0.0628620 | + | 0.265561i | ||||
\(511\) | 8.38963i | 0.371135i | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 28.2923 | + | 2.49879i | 1.24914 | + | 0.110324i | ||||
\(514\) | −12.9392 | + | 12.9392i | −0.570723 | + | 0.570723i | ||||
\(515\) | −0.0493691 | − | 0.0493691i | −0.00217546 | − | 0.00217546i | ||||
\(516\) | 12.2115 | − | 2.89063i | 0.537581 | − | 0.127253i | ||||
\(517\) | 1.73056i | 0.0761099i | ||||||||
\(518\) | 6.92111 | + | 6.92111i | 0.304096 | + | 0.304096i | ||||
\(519\) | 22.2103 | − | 5.25749i | 0.974925 | − | 0.230778i | ||||
\(520\) | −2.73057 | − | 0.818708i | −0.119744 | − | 0.0359027i | ||||
\(521\) | − | 2.40567i | − | 0.105394i | −0.998611 | − | 0.0526972i | \(-0.983218\pi\) | ||
0.998611 | − | 0.0526972i | \(-0.0167818\pi\) | |||||||
\(522\) | 30.4554 | + | 10.1104i | 1.33299 | + | 0.442521i | ||||
\(523\) | 30.2590 | 1.32313 | 0.661567 | − | 0.749886i | \(-0.269892\pi\) | ||||
0.661567 | + | 0.749886i | \(0.269892\pi\) | |||||||
\(524\) | 7.76803 | 0.339348 | ||||||||
\(525\) | 6.44828 | + | 3.97981i | 0.281426 | + | 0.173693i | ||||
\(526\) | 11.6816 | + | 11.6816i | 0.509342 | + | 0.509342i | ||||
\(527\) | 11.1489 | + | 11.1489i | 0.485655 | + | 0.485655i | ||||
\(528\) | −0.723423 | − | 0.446489i | −0.0314830 | − | 0.0194309i | ||||
\(529\) | 4.87527 | 0.211968 | ||||||||
\(530\) | 9.53560 | 0.414200 | ||||||||
\(531\) | 13.7405 | + | 4.56150i | 0.596287 | + | 0.197952i | ||||
\(532\) | − | 5.46606i | − | 0.236984i | ||||||
\(533\) | 32.8372 | − | 17.6882i | 1.42234 | − | 0.766159i | ||||
\(534\) | −29.2159 | + | 6.91580i | −1.26429 | + | 0.299276i | ||||
\(535\) | 2.84404 | + | 2.84404i | 0.122958 | + | 0.122958i | ||||
\(536\) | 3.44271i | 0.148703i | ||||||||
\(537\) | 23.5910 | − | 5.58432i | 1.01803 | − | 0.240981i | ||||
\(538\) | −8.30481 | − | 8.30481i | −0.358046 | − | 0.358046i | ||||
\(539\) | −0.347057 | + | 0.347057i | −0.0149488 | + | 0.0149488i | ||||
\(540\) | −4.09232 | − | 0.361436i | −0.176105 | − | 0.0155537i | ||||
\(541\) | −11.6253 | + | 11.6253i | −0.499812 | + | 0.499812i | −0.911379 | − | 0.411567i | \(-0.864981\pi\) |
0.411567 | + | 0.911379i | \(0.364981\pi\) | |||||||
\(542\) | − | 13.7999i | − | 0.592758i | ||||||
\(543\) | −1.38692 | − | 5.85906i | −0.0595184 | − | 0.251436i | ||||
\(544\) | 3.18228 | − | 3.18228i | 0.136439 | − | 0.136439i | ||||
\(545\) | −6.62579 | −0.283818 | ||||||||
\(546\) | −0.367403 | + | 6.23418i | −0.0157234 | + | 0.266798i | ||||
\(547\) | 16.5437 | 0.707359 | 0.353680 | − | 0.935367i | \(-0.384930\pi\) | ||||
0.353680 | + | 0.935367i | \(0.384930\pi\) | |||||||
\(548\) | −2.35653 | + | 2.35653i | −0.100666 | + | 0.100666i | ||||
\(549\) | 17.2286 | − | 8.64065i | 0.735298 | − | 0.368774i | ||||
\(550\) | − | 2.14726i | − | 0.0915594i | ||||||
\(551\) | 41.3432 | − | 41.3432i | 1.76128 | − | 1.76128i | ||||
\(552\) | −7.78190 | − | 4.80290i | −0.331220 | − | 0.204425i | ||||
\(553\) | 9.35045 | − | 9.35045i | 0.397621 | − | 0.397621i | ||||
\(554\) | 1.33263 | + | 1.33263i | 0.0566181 | + | 0.0566181i | ||||
\(555\) | −3.08753 | − | 13.0433i | −0.131058 | − | 0.553658i | ||||
\(556\) | − | 1.53895i | − | 0.0652659i | ||||||
\(557\) | 3.77844 | + | 3.77844i | 0.160098 | + | 0.160098i | 0.782610 | − | 0.622512i | \(-0.213888\pi\) |
−0.622512 | + | 0.782610i | \(0.713888\pi\) | |||||||
\(558\) | −9.39497 | + | 4.71186i | −0.397721 | + | 0.199469i | ||||
\(559\) | −7.50241 | + | 25.0222i | −0.317318 | + | 1.05833i | ||||
\(560\) | 0.790633i | 0.0334104i | ||||||||
\(561\) | −3.25571 | − | 2.00939i | −0.137456 | − | 0.0848364i | ||||
\(562\) | −4.03328 | −0.170134 | ||||||||
\(563\) | −37.3621 | −1.57462 | −0.787312 | − | 0.616555i | \(-0.788528\pi\) | ||||
−0.787312 | + | 0.616555i | \(0.788528\pi\) | |||||||
\(564\) | 3.20748 | − | 5.19692i | 0.135059 | − | 0.218830i | ||||
\(565\) | 1.61348 | + | 1.61348i | 0.0678796 | + | 0.0678796i | ||||
\(566\) | 10.7904 | + | 10.7904i | 0.453553 | + | 0.453553i | ||||
\(567\) | 1.29459 | + | 8.90640i | 0.0543675 | + | 0.374034i | ||||
\(568\) | 12.0153 | 0.504152 | ||||||||
\(569\) | 2.27928 | 0.0955524 | 0.0477762 | − | 0.998858i | \(-0.484787\pi\) | ||||
0.0477762 | + | 0.998858i | \(0.484787\pi\) | |||||||
\(570\) | −3.93137 | + | 6.36980i | −0.164667 | + | 0.266801i | ||||
\(571\) | − | 8.84959i | − | 0.370344i | −0.982706 | − | 0.185172i | \(-0.940716\pi\) | ||
0.982706 | − | 0.185172i | \(-0.0592842\pi\) | |||||||
\(572\) | 1.55800 | − | 0.839235i | 0.0651431 | − | 0.0350902i | ||||
\(573\) | 10.7423 | + | 45.3808i | 0.448764 | + | 1.89581i | ||||
\(574\) | −7.31477 | − | 7.31477i | −0.305313 | − | 0.305313i | ||||
\(575\) | − | 23.0982i | − | 0.963260i | ||||||
\(576\) | 1.34492 | + | 2.68164i | 0.0560384 | + | 0.111735i | ||||
\(577\) | 19.6466 | + | 19.6466i | 0.817899 | + | 0.817899i | 0.985803 | − | 0.167904i | \(-0.0536999\pi\) |
−0.167904 | + | 0.985803i | \(0.553700\pi\) | |||||||
\(578\) | 2.30076 | − | 2.30076i | 0.0956991 | − | 0.0956991i | ||||
\(579\) | 19.5193 | − | 31.6262i | 0.811196 | − | 1.31434i | ||||
\(580\) | −5.98005 | + | 5.98005i | −0.248308 | + | 0.248308i | ||||
\(581\) | 8.92798i | 0.370395i | ||||||||
\(582\) | 2.06745 | − | 0.489394i | 0.0856986 | − | 0.0202860i | ||||
\(583\) | −4.18576 | + | 4.18576i | −0.173356 | + | 0.173356i | ||||
\(584\) | −8.38963 | −0.347165 | ||||||||
\(585\) | 4.91197 | − | 7.00067i | 0.203085 | − | 0.289442i | ||||
\(586\) | 19.0021 | 0.784968 | ||||||||
\(587\) | 11.1009 | − | 11.1009i | 0.458182 | − | 0.458182i | −0.439877 | − | 0.898058i | \(-0.644978\pi\) |
0.898058 | + | 0.439877i | \(0.144978\pi\) | |||||||
\(588\) | 1.68547 | − | 0.398975i | 0.0695077 | − | 0.0164534i | ||||
\(589\) | 19.1500i | 0.789063i | ||||||||
\(590\) | −2.69801 | + | 2.69801i | −0.111075 | + | 0.111075i | ||||
\(591\) | 20.4460 | − | 33.1275i | 0.841034 | − | 1.36269i | ||||
\(592\) | −6.92111 | + | 6.92111i | −0.284456 | + | 0.284456i | ||||
\(593\) | −7.19619 | − | 7.19619i | −0.295512 | − | 0.295512i | 0.543741 | − | 0.839253i | \(-0.317007\pi\) |
−0.839253 | + | 0.543741i | \(0.817007\pi\) | |||||||
\(594\) | 1.95503 | − | 1.63771i | 0.0802157 | − | 0.0671962i | ||||
\(595\) | 3.55818i | 0.145871i | ||||||||
\(596\) | −6.80987 | − | 6.80987i | −0.278943 | − | 0.278943i | ||||
\(597\) | 1.71864 | + | 7.26042i | 0.0703394 | + | 0.297149i | ||||
\(598\) | 16.7595 | − | 9.02769i | 0.685345 | − | 0.369170i | ||||
\(599\) | − | 3.19761i | − | 0.130651i | −0.997864 | − | 0.0653253i | \(-0.979191\pi\) | ||
0.997864 | − | 0.0653253i | \(-0.0208085\pi\) | |||||||
\(600\) | −3.97981 | + | 6.44828i | −0.162475 | + | 0.263250i | ||||
\(601\) | −2.82987 | −0.115433 | −0.0577165 | − | 0.998333i | \(-0.518382\pi\) | ||||
−0.0577165 | + | 0.998333i | \(0.518382\pi\) | |||||||
\(602\) | 7.24514 | 0.295290 | ||||||||
\(603\) | −9.80212 | − | 3.25406i | −0.399173 | − | 0.132515i | ||||
\(604\) | −1.21937 | − | 1.21937i | −0.0496154 | − | 0.0496154i | ||||
\(605\) | 6.01501 | + | 6.01501i | 0.244545 | + | 0.244545i | ||||
\(606\) | −3.11557 | + | 5.04800i | −0.126561 | + | 0.205061i | ||||
\(607\) | 31.5745 | 1.28157 | 0.640784 | − | 0.767721i | \(-0.278609\pi\) | ||||
0.640784 | + | 0.767721i | \(0.278609\pi\) | |||||||
\(608\) | 5.46606 | 0.221678 | ||||||||
\(609\) | 15.7660 | + | 9.73058i | 0.638869 | + | 0.394303i | ||||
\(610\) | 5.07954i | 0.205665i | ||||||||
\(611\) | 6.02889 | + | 11.1923i | 0.243903 | + | 0.452793i | ||||
\(612\) | 6.05271 | + | 12.0685i | 0.244666 | + | 0.487840i | ||||
\(613\) | −9.86043 | − | 9.86043i | −0.398259 | − | 0.398259i | 0.479360 | − | 0.877619i | \(-0.340869\pi\) |
−0.877619 | + | 0.479360i | \(0.840869\pi\) | |||||||
\(614\) | − | 20.0100i | − | 0.807539i | ||||||
\(615\) | 3.26314 | + | 13.7852i | 0.131583 | + | 0.555872i | ||||
\(616\) | −0.347057 | − | 0.347057i | −0.0139833 | − | 0.0139833i | ||||
\(617\) | −23.5386 | + | 23.5386i | −0.947630 | + | 0.947630i | −0.998695 | − | 0.0510654i | \(-0.983738\pi\) |
0.0510654 | + | 0.998695i | \(0.483738\pi\) | |||||||
\(618\) | −0.130158 | − | 0.0803321i | −0.00523572 | − | 0.00323143i | ||||
\(619\) | −6.25762 | + | 6.25762i | −0.251515 | + | 0.251515i | −0.821592 | − | 0.570077i | \(-0.806914\pi\) |
0.570077 | + | 0.821592i | \(0.306914\pi\) | |||||||
\(620\) | − | 2.76994i | − | 0.111243i | ||||||
\(621\) | 21.0303 | − | 17.6170i | 0.843918 | − | 0.706945i | ||||
\(622\) | −23.5438 | + | 23.5438i | −0.944019 | + | 0.944019i | ||||
\(623\) | −17.3339 | −0.694469 | ||||||||
\(624\) | −6.23418 | − | 0.367403i | −0.249567 | − | 0.0147079i | ||||
\(625\) | −16.0142 | −0.640569 | ||||||||
\(626\) | −16.6279 | + | 16.6279i | −0.664583 | + | 0.664583i | ||||
\(627\) | −1.07038 | − | 4.52181i | −0.0427467 | − | 0.180584i | ||||
\(628\) | 5.63769i | 0.224968i | ||||||||
\(629\) | −31.1479 | + | 31.1479i | −1.24195 | + | 1.24195i | ||||
\(630\) | −2.25110 | − | 0.747308i | −0.0896859 | − | 0.0297734i | ||||
\(631\) | −1.59821 | + | 1.59821i | −0.0636237 | + | 0.0636237i | −0.738203 | − | 0.674579i | \(-0.764325\pi\) |
0.674579 | + | 0.738203i | \(0.264325\pi\) | |||||||
\(632\) | 9.35045 | + | 9.35045i | 0.371941 | + | 0.371941i | ||||
\(633\) | −16.3399 | + | 3.86787i | −0.649452 | + | 0.153734i | ||||
\(634\) | − | 3.13491i | − | 0.124503i | ||||||
\(635\) | −11.7987 | − | 11.7987i | −0.468216 | − | 0.468216i | ||||
\(636\) | 20.3280 | − | 4.81192i | 0.806057 | − | 0.190805i | ||||
\(637\) | −1.03551 | + | 3.45365i | −0.0410284 | + | 0.136839i | ||||
\(638\) | − | 5.25002i | − | 0.207850i | ||||||
\(639\) | −11.3569 | + | 34.2101i | −0.449272 | + | 1.35333i | ||||
\(640\) | −0.790633 | −0.0312525 | ||||||||
\(641\) | 22.4925 | 0.888400 | 0.444200 | − | 0.895928i | \(-0.353488\pi\) | ||||
0.444200 | + | 0.895928i | \(0.353488\pi\) | |||||||
\(642\) | 7.49809 | + | 4.62774i | 0.295926 | + | 0.182642i | ||||
\(643\) | −12.9119 | − | 12.9119i | −0.509196 | − | 0.509196i | 0.405083 | − | 0.914280i | \(-0.367242\pi\) |
−0.914280 | + | 0.405083i | \(0.867242\pi\) | |||||||
\(644\) | −3.73331 | − | 3.73331i | −0.147113 | − | 0.147113i | ||||
\(645\) | −8.44303 | − | 5.21094i | −0.332444 | − | 0.205181i | ||||
\(646\) | 24.5996 | 0.967857 | ||||||||
\(647\) | −4.76406 | −0.187295 | −0.0936473 | − | 0.995605i | \(-0.529853\pi\) | ||||
−0.0936473 | + | 0.995605i | \(0.529853\pi\) | |||||||
\(648\) | −8.90640 | + | 1.29459i | −0.349877 | + | 0.0508561i | ||||
\(649\) | − | 2.36865i | − | 0.0929775i | ||||||
\(650\) | −7.48058 | − | 13.8873i | −0.293412 | − | 0.544705i | ||||
\(651\) | −5.90496 | + | 1.39779i | −0.231434 | + | 0.0547835i | ||||
\(652\) | −3.47849 | − | 3.47849i | −0.136228 | − | 0.136228i | ||||
\(653\) | − | 13.9182i | − | 0.544660i | −0.962204 | − | 0.272330i | \(-0.912206\pi\) | ||
0.962204 | − | 0.272330i | \(-0.0877942\pi\) | |||||||
\(654\) | −14.1249 | + | 3.34355i | −0.552326 | + | 0.130743i | ||||
\(655\) | −4.34281 | − | 4.34281i | −0.169688 | − | 0.169688i | ||||
\(656\) | 7.31477 | − | 7.31477i | 0.285594 | − | 0.285594i | ||||
\(657\) | 7.92988 | − | 23.8870i | 0.309374 | − | 0.931921i | ||||
\(658\) | 2.49319 | − | 2.49319i | 0.0971946 | − | 0.0971946i | ||||
\(659\) | 22.7816i | 0.887447i | 0.896164 | + | 0.443724i | \(0.146343\pi\) | ||||
−0.896164 | + | 0.443724i | \(0.853657\pi\) | |||||||
\(660\) | 0.154824 | + | 0.654054i | 0.00602650 | + | 0.0254590i | ||||
\(661\) | −3.75702 | + | 3.75702i | −0.146131 | + | 0.146131i | −0.776387 | − | 0.630256i | \(-0.782950\pi\) |
0.630256 | + | 0.776387i | \(0.282950\pi\) | |||||||
\(662\) | −31.0138 | −1.20539 | ||||||||
\(663\) | −28.0564 | − | 1.65347i | −1.08962 | − | 0.0642153i | ||||
\(664\) | −8.92798 | −0.346473 | ||||||||
\(665\) | −3.05587 | + | 3.05587i | −0.118501 | + | 0.118501i | ||||
\(666\) | −13.1640 | − | 26.2477i | −0.510095 | − | 1.01708i | ||||
\(667\) | − | 56.4747i | − | 2.18671i | ||||||
\(668\) | 2.49027 | − | 2.49027i | 0.0963515 | − | 0.0963515i | ||||
\(669\) | 15.6277 | + | 9.64523i | 0.604201 | + | 0.372906i | ||||
\(670\) | 1.92469 | − | 1.92469i | 0.0743573 | − | 0.0743573i | ||||
\(671\) | −2.22972 | − | 2.22972i | −0.0860774 | − | 0.0860774i | ||||
\(672\) | 0.398975 | + | 1.68547i | 0.0153908 | + | 0.0650185i | ||||
\(673\) | − | 17.2981i | − | 0.666792i | −0.942787 | − | 0.333396i | \(-0.891805\pi\) | ||
0.942787 | − | 0.333396i | \(-0.108195\pi\) | |||||||
\(674\) | −8.51258 | − | 8.51258i | −0.327892 | − | 0.327892i | ||||
\(675\) | −14.5979 | − | 17.4263i | −0.561873 | − | 0.670737i | ||||
\(676\) | 7.15258 | − | 10.8554i | 0.275099 | − | 0.417517i | ||||
\(677\) | − | 38.4320i | − | 1.47706i | −0.674219 | − | 0.738531i | \(-0.735520\pi\) | ||
0.674219 | − | 0.738531i | \(-0.264480\pi\) | |||||||
\(678\) | 4.25382 | + | 2.62541i | 0.163367 | + | 0.100828i | ||||
\(679\) | 1.22663 | 0.0470737 | ||||||||
\(680\) | −3.55818 | −0.136450 | ||||||||
\(681\) | −22.5425 | + | 36.5244i | −0.863830 | + | 1.39962i | ||||
\(682\) | 1.21590 | + | 1.21590i | 0.0465591 | + | 0.0465591i | ||||
\(683\) | 3.33543 | + | 3.33543i | 0.127627 | + | 0.127627i | 0.768035 | − | 0.640408i | \(-0.221235\pi\) |
−0.640408 | + | 0.768035i | \(0.721235\pi\) | |||||||
\(684\) | −5.16653 | + | 15.5630i | −0.197547 | + | 0.595067i | ||||
\(685\) | 2.63489 | 0.100674 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 17.8492 | − | 28.9201i | 0.680988 | − | 1.10337i | ||||
\(688\) | 7.24514i | 0.276219i | ||||||||
\(689\) | −12.4890 | + | 41.6535i | −0.475792 | + | 1.58687i | ||||
\(690\) | 1.66544 | + | 7.03569i | 0.0634024 | + | 0.267844i | ||||
\(691\) | 11.0166 | + | 11.0166i | 0.419092 | + | 0.419092i | 0.884891 | − | 0.465799i | \(-0.154233\pi\) |
−0.465799 | + | 0.884891i | \(0.654233\pi\) | |||||||
\(692\) | 13.1775i | 0.500934i | ||||||||
\(693\) | 1.31618 | − | 0.660106i | 0.0499977 | − | 0.0250753i | ||||
\(694\) | 3.47500 | + | 3.47500i | 0.131909 | + | 0.131909i | ||||
\(695\) | −0.860367 | + | 0.860367i | −0.0326356 | + | 0.0326356i | ||||
\(696\) | −9.73058 | + | 15.7660i | −0.368837 | + | 0.597607i | ||||
\(697\) | 32.9195 | − | 32.9195i | 1.24692 | − | 1.24692i | ||||
\(698\) | 4.71881i | 0.178609i | ||||||||
\(699\) | −8.09186 | + | 1.91545i | −0.306062 | + | 0.0724491i | ||||
\(700\) | −3.09352 | + | 3.09352i | −0.116924 | + | 0.116924i | ||||
\(701\) | −11.4796 | −0.433579 | −0.216790 | − | 0.976218i | \(-0.569559\pi\) | ||||
−0.216790 | + | 0.976218i | \(0.569559\pi\) | |||||||
\(702\) | 6.93863 | − | 17.4027i | 0.261882 | − | 0.656824i | ||||
\(703\) | −53.5014 | −2.01784 | ||||||||
\(704\) | 0.347057 | − | 0.347057i | 0.0130802 | − | 0.0130802i | ||||
\(705\) | −4.69859 | + | 1.11222i | −0.176959 | + | 0.0418886i | ||||
\(706\) | − | 6.51974i | − | 0.245374i | ||||||
\(707\) | −2.42175 | + | 2.42175i | −0.0910792 | + | 0.0910792i | ||||
\(708\) | −4.39013 | + | 7.11311i | −0.164991 | + | 0.267327i | ||||
\(709\) | 18.4081 | − | 18.4081i | 0.691331 | − | 0.691331i | −0.271193 | − | 0.962525i | \(-0.587418\pi\) |
0.962525 | + | 0.271193i | \(0.0874183\pi\) | |||||||
\(710\) | −6.71731 | − | 6.71731i | −0.252096 | − | 0.252096i | ||||
\(711\) | −35.4607 | + | 17.7846i | −1.32988 | + | 0.666975i | ||||
\(712\) | − | 17.3339i | − | 0.649617i | ||||||
\(713\) | 13.0795 | + | 13.0795i | 0.489829 | + | 0.489829i | ||||
\(714\) | 1.79555 | + | 7.58533i | 0.0671969 | + | 0.283874i | ||||
\(715\) | −1.34020 | − | 0.401833i | −0.0501207 | − | 0.0150277i | ||||
\(716\) | 13.9967i | 0.523081i | ||||||||
\(717\) | 11.3901 | − | 18.4548i | 0.425371 | − | 0.689207i | ||||
\(718\) | 12.6102 | 0.470608 | ||||||||
\(719\) | −4.45696 | −0.166217 | −0.0831084 | − | 0.996541i | \(-0.526485\pi\) | ||||
−0.0831084 | + | 0.996541i | \(0.526485\pi\) | |||||||
\(720\) | 0.747308 | − | 2.25110i | 0.0278505 | − | 0.0838935i | ||||
\(721\) | −0.0624424 | − | 0.0624424i | −0.00232548 | − | 0.00232548i | ||||
\(722\) | 7.69177 | + | 7.69177i | 0.286258 | + | 0.286258i | ||||
\(723\) | −11.3143 | + | 18.3320i | −0.420784 | + | 0.681776i | ||||
\(724\) | 3.47621 | 0.129192 | ||||||||
\(725\) | −46.7964 | −1.73797 | ||||||||
\(726\) | 15.8581 | + | 9.78747i | 0.588550 | + | 0.363247i | ||||
\(727\) | 48.0910i | 1.78360i | 0.452432 | + | 0.891799i | \(0.350557\pi\) | ||||
−0.452432 | + | 0.891799i | \(0.649443\pi\) | |||||||
\(728\) | −3.45365 | − | 1.03551i | −0.128001 | − | 0.0383785i | ||||
\(729\) | 4.73239 | − | 26.5820i | 0.175274 | − | 0.984520i | ||||
\(730\) | 4.69032 | + | 4.69032i | 0.173597 | + | 0.173597i | ||||
\(731\) | 32.6062i | 1.20598i | ||||||||
\(732\) | 2.56327 | + | 10.8286i | 0.0947412 | + | 0.400235i | ||||
\(733\) | 12.2239 | + | 12.2239i | 0.451499 | + | 0.451499i | 0.895852 | − | 0.444353i | \(-0.146566\pi\) |
−0.444353 | + | 0.895852i | \(0.646566\pi\) | |||||||
\(734\) | −18.1272 | + | 18.1272i | −0.669087 | + | 0.669087i | ||||
\(735\) | −1.16534 | − | 0.719233i | −0.0429841 | − | 0.0265293i | ||||
\(736\) | 3.73331 | − | 3.73331i | 0.137612 | − | 0.137612i | ||||
\(737\) | 1.68973i | 0.0622420i | ||||||||
\(738\) | 13.9127 | + | 27.7406i | 0.512135 | + | 1.02115i | ||||
\(739\) | −0.378213 | + | 0.378213i | −0.0139128 | + | 0.0139128i | −0.714029 | − | 0.700116i | \(-0.753132\pi\) |
0.700116 | + | 0.714029i | \(0.253132\pi\) | |||||||
\(740\) | 7.73867 | 0.284479 | ||||||||
\(741\) | −22.6756 | − | 25.5157i | −0.833009 | − | 0.937343i | ||||
\(742\) | 12.0607 | 0.442762 | ||||||||
\(743\) | −13.1510 | + | 13.1510i | −0.482465 | + | 0.482465i | −0.905918 | − | 0.423453i | \(-0.860818\pi\) |
0.423453 | + | 0.905918i | \(0.360818\pi\) | |||||||
\(744\) | −1.39779 | − | 5.90496i | −0.0512453 | − | 0.216486i | ||||
\(745\) | 7.61429i | 0.278966i | ||||||||
\(746\) | −19.5183 | + | 19.5183i | −0.714614 | + | 0.714614i | ||||
\(747\) | 8.43874 | − | 25.4198i | 0.308757 | − | 0.930063i | ||||
\(748\) | 1.56190 | − | 1.56190i | 0.0571089 | − | 0.0571089i | ||||
\(749\) | 3.59716 | + | 3.59716i | 0.131437 | + | 0.131437i | ||||
\(750\) | 12.4929 | − | 2.95724i | 0.456177 | − | 0.107983i | ||||
\(751\) | 21.7792i | 0.794735i | 0.917660 | + | 0.397367i | \(0.130076\pi\) | ||||
−0.917660 | + | 0.397367i | \(0.869924\pi\) | |||||||
\(752\) | 2.49319 | + | 2.49319i | 0.0909172 | + | 0.0909172i | ||||
\(753\) | 23.0713 | − | 5.46129i | 0.840764 | − | 0.199020i | ||||
\(754\) | −18.2899 | − | 33.9543i | −0.666079 | − | 1.23654i | ||||
\(755\) | 1.36341i | 0.0496194i | ||||||||
\(756\) | −5.17600 | − | 0.457147i | −0.188249 | − | 0.0166263i | ||||
\(757\) | −7.96654 | −0.289549 | −0.144774 | − | 0.989465i | \(-0.546246\pi\) | ||||
−0.144774 | + | 0.989465i | \(0.546246\pi\) | |||||||
\(758\) | −21.5227 | −0.781739 | ||||||||
\(759\) | −3.81946 | − | 2.35733i | −0.138638 | − | 0.0855656i | ||||
\(760\) | −3.05587 | − | 3.05587i | −0.110848 | − | 0.110848i | ||||
\(761\) | −26.2245 | − | 26.2245i | −0.950637 | − | 0.950637i | 0.0482010 | − | 0.998838i | \(-0.484651\pi\) |
−0.998838 | + | 0.0482010i | \(0.984651\pi\) | |||||||
\(762\) | −31.1063 | − | 19.1985i | −1.12686 | − | 0.695488i | ||||
\(763\) | −8.38035 | −0.303389 | ||||||||
\(764\) | −26.9246 | −0.974099 | ||||||||
\(765\) | 3.36320 | − | 10.1309i | 0.121597 | − | 0.366283i | ||||
\(766\) | − | 10.5894i | − | 0.382610i | ||||||
\(767\) | −8.25184 | − | 15.3191i | −0.297957 | − | 0.553142i | ||||
\(768\) | −1.68547 | + | 0.398975i | −0.0608193 | + | 0.0143968i | ||||
\(769\) | 4.82224 | + | 4.82224i | 0.173894 | + | 0.173894i | 0.788688 | − | 0.614794i | \(-0.210761\pi\) |
−0.614794 | + | 0.788688i | \(0.710761\pi\) | |||||||
\(770\) | 0.388054i | 0.0139845i | ||||||||
\(771\) | 30.8421 | − | 7.30075i | 1.11075 | − | 0.262930i | ||||
\(772\) | 15.1725 | + | 15.1725i | 0.546069 | + | 0.546069i | ||||
\(773\) | −25.9691 | + | 25.9691i | −0.934044 | + | 0.934044i | −0.997956 | − | 0.0639117i | \(-0.979642\pi\) |
0.0639117 | + | 0.997956i | \(0.479642\pi\) | |||||||
\(774\) | −20.6284 | − | 6.84812i | −0.741474 | − | 0.246151i | ||||
\(775\) | 10.8380 | − | 10.8380i | 0.389311 | − | 0.389311i | ||||
\(776\) | 1.22663i | 0.0440334i | ||||||||
\(777\) | −3.90514 | − | 16.4973i | −0.140096 | − | 0.591837i | ||||
\(778\) | −4.95439 | + | 4.95439i | −0.177623 | + | 0.177623i | ||||
\(779\) | 56.5444 | 2.02592 | ||||||||
\(780\) | 3.27989 | + | 3.69070i | 0.117439 | + | 0.132148i | ||||
\(781\) | 5.89728 | 0.211021 | ||||||||
\(782\) | 16.8015 | − | 16.8015i | 0.600820 | − | 0.600820i | ||||
\(783\) | −35.6916 | − | 42.6070i | −1.27551 | − | 1.52265i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 3.15182 | − | 3.15182i | 0.112493 | − | 0.112493i | ||||
\(786\) | −11.4495 | − | 7.06651i | −0.408390 | − | 0.252054i | ||||
\(787\) | 11.4728 | − | 11.4728i | 0.408961 | − | 0.408961i | −0.472415 | − | 0.881376i | \(-0.656618\pi\) |
0.881376 | + | 0.472415i | \(0.156618\pi\) | |||||||
\(788\) | 15.8927 | + | 15.8927i | 0.566155 | + | 0.566155i | ||||
\(789\) | −6.59117 | − | 27.8445i | −0.234652 | − | 0.991289i | ||||
\(790\) | − | 10.4550i | − | 0.371971i | ||||||
\(791\) | 2.04074 | + | 2.04074i | 0.0725604 | + | 0.0725604i | ||||
\(792\) | 0.660106 | + | 1.31618i | 0.0234558 | + | 0.0467686i | ||||
\(793\) | −22.1885 | − | 6.65278i | −0.787936 | − | 0.236247i | ||||
\(794\) | 7.67641i | 0.272425i | ||||||||
\(795\) | −14.0548 | − | 8.67445i | −0.498472 | − | 0.307651i | ||||
\(796\) | −4.30765 | −0.152681 | ||||||||
\(797\) | −24.6190 | −0.872049 | −0.436024 | − | 0.899935i | \(-0.643614\pi\) | ||||
−0.436024 | + | 0.899935i | \(0.643614\pi\) | |||||||
\(798\) | −4.97243 | + | 8.05657i | −0.176022 | + | 0.285200i | ||||
\(799\) | 11.2204 | + | 11.2204i | 0.396949 | + | 0.396949i | ||||
\(800\) | −3.09352 | − | 3.09352i | −0.109372 | − | 0.109372i | ||||
\(801\) | 49.3533 | + | 16.3841i | 1.74381 | + | 0.578902i | ||||
\(802\) | −32.2021 | −1.13709 | ||||||||
\(803\) | −4.11774 | −0.145312 | ||||||||
\(804\) | 3.13181 | − | 5.07431i | 0.110450 | − | 0.178957i | ||||
\(805\) | 4.17431i | 0.147125i | ||||||||
\(806\) | 12.0997 | + | 3.62785i | 0.426193 | + | 0.127786i | ||||
\(807\) | 4.68587 | + | 19.7955i | 0.164950 | + | 0.696834i | ||||
\(808\) | −2.42175 | − | 2.42175i | −0.0851967 | − | 0.0851967i | ||||
\(809\) | 27.4026i | 0.963423i | 0.876330 | + | 0.481712i | \(0.159985\pi\) | ||||
−0.876330 | + | 0.481712i | \(0.840015\pi\) | |||||||
\(810\) | 5.70299 | + | 4.25548i | 0.200383 | + | 0.149522i | ||||
\(811\) | −18.7220 | − | 18.7220i | −0.657418 | − | 0.657418i | 0.297351 | − | 0.954768i | \(-0.403897\pi\) |
−0.954768 | + | 0.297351i | \(0.903897\pi\) | |||||||
\(812\) | −7.56362 | + | 7.56362i | −0.265431 | + | 0.265431i | ||||
\(813\) | −12.5537 | + | 20.3401i | −0.440277 | + | 0.713358i | ||||
\(814\) | −3.39697 | + | 3.39697i | −0.119064 | + | 0.119064i | ||||
\(815\) | 3.88938i | 0.136239i | ||||||||
\(816\) | −7.58533 | + | 1.79555i | −0.265540 | + | 0.0628569i | ||||
\(817\) | −28.0031 | + | 28.0031i | −0.979705 | + | 0.979705i | ||||
\(818\) | 7.98298 | 0.279118 | ||||||||
\(819\) | 6.21271 | − | 8.85451i | 0.217090 | − | 0.309401i | ||||
\(820\) | −8.17882 | −0.285617 | ||||||||
\(821\) | −19.3107 | + | 19.3107i | −0.673947 | + | 0.673947i | −0.958624 | − | 0.284676i | \(-0.908114\pi\) |
0.284676 | + | 0.958624i | \(0.408114\pi\) | |||||||
\(822\) | 5.61707 | − | 1.32964i | 0.195918 | − | 0.0463764i | ||||
\(823\) | 44.6167i | 1.55524i | 0.628735 | + | 0.777620i | \(0.283573\pi\) | ||||
−0.628735 | + | 0.777620i | \(0.716427\pi\) | |||||||
\(824\) | 0.0624424 | − | 0.0624424i | 0.00217528 | − | 0.00217528i | ||||
\(825\) | −1.95334 | + | 3.16490i | −0.0680067 | + | 0.110188i | ||||
\(826\) | −3.41247 | + | 3.41247i | −0.118735 | + | 0.118735i | ||||
\(827\) | −8.17009 | − | 8.17009i | −0.284102 | − | 0.284102i | 0.550640 | − | 0.834743i | \(-0.314384\pi\) |
−0.834743 | + | 0.550640i | \(0.814384\pi\) | |||||||
\(828\) | 7.10079 | + | 14.1583i | 0.246770 | + | 0.492033i | ||||
\(829\) | 14.0314i | 0.487331i | 0.969859 | + | 0.243665i | \(0.0783499\pi\) | ||||
−0.969859 | + | 0.243665i | \(0.921650\pi\) | |||||||
\(830\) | 4.99130 | + | 4.99130i | 0.173251 | + | 0.173251i | ||||
\(831\) | −0.751918 | − | 3.17649i | −0.0260838 | − | 0.110191i | ||||
\(832\) | 1.03551 | − | 3.45365i | 0.0358998 | − | 0.119734i | ||||
\(833\) | 4.50042i | 0.155930i | ||||||||
\(834\) | −1.39997 | + | 2.26830i | −0.0484769 | + | 0.0785447i | ||||
\(835\) | −2.78443 | −0.0963593 | ||||||||
\(836\) | 2.68282 | 0.0927871 | ||||||||
\(837\) | 18.1338 | + | 1.60159i | 0.626797 | + | 0.0553590i | ||||
\(838\) | −6.36589 | − | 6.36589i | −0.219906 | − | 0.219906i | ||||
\(839\) | −21.3877 | − | 21.3877i | −0.738387 | − | 0.738387i | 0.233879 | − | 0.972266i | \(-0.424858\pi\) |
−0.972266 | + | 0.233879i | \(0.924858\pi\) | |||||||
\(840\) | 0.719233 | − | 1.16534i | 0.0248159 | − | 0.0402079i | ||||
\(841\) | −85.4166 | −2.94540 | ||||||||
\(842\) | −2.69953 | −0.0930321 | ||||||||
\(843\) | 5.94476 | + | 3.66904i | 0.204749 | + | 0.126369i | ||||
\(844\) | − | 9.69453i | − | 0.333700i | ||||||
\(845\) | −10.0676 | + | 2.07013i | −0.346336 | + | 0.0712146i | ||||
\(846\) | −9.45519 | + | 4.74206i | −0.325076 | + | 0.163035i | ||||
\(847\) | 7.60783 | + | 7.60783i | 0.261408 | + | 0.261408i | ||||
\(848\) | 12.0607i | 0.414166i | ||||||||
\(849\) | −6.08831 | − | 25.7201i | −0.208950 | − | 0.882713i | ||||
\(850\) | −13.9221 | − | 13.9221i | −0.477525 | − | 0.477525i | ||||
\(851\) | −36.5414 | + | 36.5414i | −1.25262 | + | 1.25262i | ||||
\(852\) | −17.7097 | − | 10.9302i | −0.606724 | − | 0.374464i | ||||
\(853\) | 1.29289 | − | 1.29289i | 0.0442677 | − | 0.0442677i | −0.684626 | − | 0.728894i | \(-0.740035\pi\) |
0.728894 | + | 0.684626i | \(0.240035\pi\) | |||||||
\(854\) | 6.42464i | 0.219847i | ||||||||
\(855\) | 11.5891 | − | 5.81228i | 0.396339 | − | 0.198776i | ||||
\(856\) | −3.59716 | + | 3.59716i | −0.122948 | + | 0.122948i | ||||
\(857\) | −13.6228 | −0.465345 | −0.232672 | − | 0.972555i | \(-0.574747\pi\) | ||||
−0.232672 | + | 0.972555i | \(0.574747\pi\) | |||||||
\(858\) | −3.05982 | − | 0.180326i | −0.104461 | − | 0.00615624i | ||||
\(859\) | 51.0261 | 1.74099 | 0.870494 | − | 0.492180i | \(-0.163800\pi\) | ||||
0.870494 | + | 0.492180i | \(0.163800\pi\) | |||||||
\(860\) | 4.05049 | − | 4.05049i | 0.138120 | − | 0.138120i | ||||
\(861\) | 4.12725 | + | 17.4356i | 0.140656 | + | 0.594204i | ||||
\(862\) | − | 16.5975i | − | 0.565312i | ||||||
\(863\) | −32.5612 | + | 32.5612i | −1.10839 | + | 1.10839i | −0.115033 | + | 0.993362i | \(0.536697\pi\) |
−0.993362 | + | 0.115033i | \(0.963303\pi\) | |||||||
\(864\) | 0.457147 | − | 5.17600i | 0.0155525 | − | 0.176091i | ||||
\(865\) | 7.36705 | − | 7.36705i | 0.250487 | − | 0.250487i | ||||
\(866\) | −9.83740 | − | 9.83740i | −0.334289 | − | 0.334289i | ||||
\(867\) | −5.48414 | + | 1.29817i | −0.186251 | + | 0.0440882i | ||||
\(868\) | − | 3.50344i | − | 0.118915i | ||||||
\(869\) | 4.58932 | + | 4.58932i | 0.155682 | + | 0.155682i | ||||
\(870\) | 14.2542 | − | 3.37416i | 0.483261 | − | 0.114395i | ||||
\(871\) | 5.88665 | + | 10.9283i | 0.199461 | + | 0.370290i | ||||
\(872\) | − | 8.38035i | − | 0.283795i | ||||||
\(873\) | −3.49247 | − | 1.15941i | −0.118202 | − | 0.0392401i | ||||
\(874\) | 28.8592 | 0.976176 | ||||||||
\(875\) | 7.41211 | 0.250575 | ||||||||
\(876\) | 12.3657 | + | 7.63197i | 0.417798 | + | 0.257860i | ||||
\(877\) | 4.82932 | + | 4.82932i | 0.163075 | + | 0.163075i | 0.783927 | − | 0.620853i | \(-0.213213\pi\) |
−0.620853 | + | 0.783927i | \(0.713213\pi\) | |||||||
\(878\) | 5.83116 | + | 5.83116i | 0.196792 | + | 0.196792i | ||||
\(879\) | −28.0077 | − | 17.2860i | −0.944675 | − | 0.583043i | ||||
\(880\) | −0.388054 | −0.0130813 | ||||||||
\(881\) | 36.4849 | 1.22921 | 0.614604 | − | 0.788836i | \(-0.289316\pi\) | ||||
0.614604 | + | 0.788836i | \(0.289316\pi\) | |||||||
\(882\) | −2.84721 | − | 0.945201i | −0.0958705 | − | 0.0318266i | ||||
\(883\) | − | 51.3777i | − | 1.72900i | −0.502636 | − | 0.864498i | \(-0.667636\pi\) | ||
0.502636 | − | 0.864498i | \(-0.332364\pi\) | |||||||
\(884\) | 4.66023 | − | 15.5429i | 0.156740 | − | 0.522764i | ||||
\(885\) | 6.43103 | − | 1.52231i | 0.216177 | − | 0.0511720i | ||||
\(886\) | 6.68209 | + | 6.68209i | 0.224489 | + | 0.224489i | ||||
\(887\) | 36.4498i | 1.22387i | 0.790910 | + | 0.611933i | \(0.209608\pi\) | ||||
−0.790910 | + | 0.611933i | \(0.790392\pi\) | |||||||
\(888\) | 16.4973 | − | 3.90514i | 0.553613 | − | 0.131048i | ||||
\(889\) | −14.9231 | − | 14.9231i | −0.500503 | − | 0.500503i | ||||
\(890\) | −9.69075 | + | 9.69075i | −0.324835 | + | 0.324835i | ||||
\(891\) | −4.37138 | + | 0.635400i | −0.146447 | + | 0.0212867i | ||||
\(892\) | −7.49728 | + | 7.49728i | −0.251027 | + | 0.251027i | ||||
\(893\) | 19.2728i | 0.644939i | ||||||||
\(894\) | 3.84237 | + | 16.2321i | 0.128508 | + | 0.542884i | ||||
\(895\) | 7.82502 | − | 7.82502i | 0.261561 | − | 0.261561i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −32.9146 | − | 1.93978i | −1.09899 | − | 0.0647673i | ||||
\(898\) | 32.4165 | 1.08175 | ||||||||
\(899\) | 26.4987 | − | 26.4987i | 0.883781 | − | 0.883781i | ||||
\(900\) | 11.7319 | − | 5.88390i | 0.391063 | − | 0.196130i | ||||
\(901\) | 54.2782i | 1.80827i | ||||||||
\(902\) | 3.59019 | − | 3.59019i | 0.119540 | − | 0.119540i | ||||
\(903\) | −10.6788 | − | 6.59085i | −0.355369 | − | 0.219330i | ||||
\(904\) | −2.04074 | + | 2.04074i | −0.0678741 | + | 0.0678741i | ||||
\(905\) | −1.94342 | − | 1.94342i | −0.0646014 | − | 0.0646014i | ||||
\(906\) | 0.688011 | + | 2.90651i | 0.0228576 | + | 0.0965623i | ||||
\(907\) | 9.19731i | 0.305392i | 0.988273 | + | 0.152696i | \(0.0487955\pi\) | ||||
−0.988273 | + | 0.152696i | \(0.951204\pi\) | |||||||
\(908\) | −17.5224 | − | 17.5224i | −0.581500 | − | 0.581500i | ||||
\(909\) | 9.18425 | − | 4.60618i | 0.304622 | − | 0.152777i | ||||
\(910\) | 1.35189 | + | 2.50972i | 0.0448148 | + | 0.0831965i | ||||
\(911\) | − | 13.7738i | − | 0.456347i | −0.973620 | − | 0.228173i | \(-0.926725\pi\) | ||
0.973620 | − | 0.228173i | \(-0.0732753\pi\) | |||||||
\(912\) | −8.05657 | − | 4.97243i | −0.266780 | − | 0.164654i | ||||
\(913\) | −4.38197 | −0.145022 | ||||||||
\(914\) | −3.85384 | −0.127474 | ||||||||
\(915\) | 4.62081 | − | 7.48687i | 0.152759 | − | 0.247508i | ||||
\(916\) | 13.8742 | + | 13.8742i | 0.458417 | + | 0.458417i | ||||
\(917\) | −5.49282 | − | 5.49282i | −0.181389 | − | 0.181389i | ||||
\(918\) | 2.05735 | − | 23.2942i | 0.0679027 | − | 0.768823i | ||||
\(919\) | 43.2369 | 1.42625 | 0.713127 | − | 0.701035i | \(-0.247278\pi\) | ||||
0.713127 | + | 0.701035i | \(0.247278\pi\) | |||||||
\(920\) | −4.17431 | −0.137623 | ||||||||
\(921\) | −18.2030 | + | 29.4933i | −0.599808 | + | 0.971838i | ||||
\(922\) | − | 24.1143i | − | 0.794161i | ||||||
\(923\) | 38.1404 | − | 20.5448i | 1.25541 | − | 0.676241i | ||||
\(924\) | 0.195822 | + | 0.827253i | 0.00644208 | + | 0.0272146i | ||||
\(925\) | 30.2792 | + | 30.2792i | 0.995573 | + | 0.995573i | ||||
\(926\) | 10.1862i | 0.334739i | ||||||||
\(927\) | 0.118766 | + | 0.236807i | 0.00390079 | + | 0.00777777i | ||||
\(928\) | −7.56362 | − | 7.56362i | −0.248288 | − | 0.248288i | ||||
\(929\) | 16.0965 | − | 16.0965i | 0.528110 | − | 0.528110i | −0.391899 | − | 0.920008i | \(-0.628182\pi\) |
0.920008 | + | 0.391899i | \(0.128182\pi\) | |||||||
\(930\) | −2.51979 | + | 4.08269i | −0.0826272 | + | 0.133877i | ||||
\(931\) | −3.86509 | + | 3.86509i | −0.126673 | + | 0.126673i | ||||
\(932\) | − | 4.80094i | − | 0.157260i | ||||||
\(933\) | 56.1194 | − | 13.2842i | 1.83727 | − | 0.434906i | ||||
\(934\) | −13.5564 | + | 13.5564i | −0.443578 | + | 0.443578i | ||||
\(935\) | −1.74640 | −0.0571135 | ||||||||
\(936\) | 8.85451 | + | 6.21271i | 0.289419 | + | 0.203069i | ||||
\(937\) | −19.1143 | −0.624438 | −0.312219 | − | 0.950010i | \(-0.601072\pi\) | ||||
−0.312219 | + | 0.950010i | \(0.601072\pi\) | |||||||
\(938\) | 2.43437 | − | 2.43437i | 0.0794849 | − | 0.0794849i | ||||
\(939\) | 39.6345 | − | 9.38203i | 1.29342 | − | 0.306171i | ||||
\(940\) | − | 2.78770i | − | 0.0909246i | ||||||
\(941\) | 21.9202 | − | 21.9202i | 0.714579 | − | 0.714579i | −0.252911 | − | 0.967490i | \(-0.581388\pi\) |
0.967490 | + | 0.252911i | \(0.0813880\pi\) | |||||||
\(942\) | 5.12856 | − | 8.30954i | 0.167097 | − | 0.270739i | ||||
\(943\) | 38.6198 | − | 38.6198i | 1.25763 | − | 1.25763i | ||||
\(944\) | −3.41247 | − | 3.41247i | −0.111066 | − | 0.111066i | ||||
\(945\) | 2.63814 | + | 3.14928i | 0.0858185 | + | 0.102446i | ||||
\(946\) | 3.55601i | 0.115616i | ||||||||
\(947\) | −27.5307 | − | 27.5307i | −0.894627 | − | 0.894627i | 0.100328 | − | 0.994954i | \(-0.468011\pi\) |
−0.994954 | + | 0.100328i | \(0.968011\pi\) | |||||||
\(948\) | −5.27585 | − | 22.2879i | −0.171352 | − | 0.723877i | ||||
\(949\) | −26.6313 | + | 14.3453i | −0.864490 | + | 0.465668i | ||||
\(950\) | − | 23.9135i | − | 0.775855i | ||||||
\(951\) | −2.85180 | + | 4.62063i | −0.0924761 | + | 0.149834i | ||||
\(952\) | −4.50042 | −0.145859 | ||||||||
\(953\) | −1.66813 | −0.0540361 | −0.0270181 | − | 0.999635i | \(-0.508601\pi\) | ||||
−0.0270181 | + | 0.999635i | \(0.508601\pi\) | |||||||
\(954\) | −34.3393 | − | 11.3998i | −1.11178 | − | 0.369082i | ||||
\(955\) | 15.0526 | + | 15.0526i | 0.487089 | + | 0.487089i | ||||
\(956\) | 8.85356 | + | 8.85356i | 0.286345 | + | 0.286345i | ||||
\(957\) | −4.77590 | + | 7.73815i | −0.154383 | + | 0.250139i | ||||
\(958\) | 30.2451 | 0.977174 | ||||||||
\(959\) | 3.33263 | 0.107616 | ||||||||
\(960\) | 1.16534 | + | 0.719233i | 0.0376111 | + | 0.0232131i | ||||
\(961\) | − | 18.7259i | − | 0.604061i | ||||||
\(962\) | −10.1355 | + | 33.8041i | −0.326781 | + | 1.08989i | ||||
\(963\) | −6.84183 | − | 13.6419i | −0.220475 | − | 0.439604i | ||||
\(964\) | −8.79467 | − | 8.79467i | −0.283257 | − | 0.283257i | ||||
\(965\) | − | 16.9647i | − | 0.546113i | ||||||
\(966\) | 2.10647 | + | 8.89880i | 0.0677745 | + | 0.286314i | ||||
\(967\) | 31.0792 | + | 31.0792i | 0.999438 | + | 0.999438i | 1.00000 | 0.000561611i | \(-0.000178766\pi\) | |
−0.000561611 | 1.00000i | \(0.500179\pi\) | ||||||||
\(968\) | −7.60783 | + | 7.60783i | −0.244525 | + | 0.244525i | ||||
\(969\) | −36.2580 | − | 22.3780i | −1.16477 | − | 0.718885i | ||||
\(970\) | 0.685762 | − | 0.685762i | 0.0220185 | − | 0.0220185i | ||||
\(971\) | − | 1.88008i | − | 0.0603345i | −0.999545 | − | 0.0301672i | \(-0.990396\pi\) | ||
0.999545 | − | 0.0301672i | \(-0.00960399\pi\) | |||||||
\(972\) | 14.3051 | + | 6.19396i | 0.458835 | + | 0.198671i | ||||
\(973\) | −1.08820 | + | 1.08820i | −0.0348861 | + | 0.0348861i | ||||
\(974\) | 34.0479 | 1.09096 | ||||||||
\(975\) | −1.60735 | + | 27.2739i | −0.0514764 | + | 0.873464i | ||||
\(976\) | −6.42464 | −0.205648 | ||||||||
\(977\) | −3.46359 | + | 3.46359i | −0.110810 | + | 0.110810i | −0.760338 | − | 0.649528i | \(-0.774967\pi\) |
0.649528 | + | 0.760338i | \(0.274967\pi\) | |||||||
\(978\) | 1.96269 | + | 8.29139i | 0.0627598 | + | 0.265129i | ||||
\(979\) | − | 8.50773i | − | 0.271908i | ||||||
\(980\) | 0.559062 | − | 0.559062i | 0.0178586 | − | 0.0178586i | ||||
\(981\) | 23.8606 | + | 7.92112i | 0.761811 | + | 0.252902i | ||||
\(982\) | −7.34168 | + | 7.34168i | −0.234283 | + | 0.234283i | ||||
\(983\) | 8.07529 | + | 8.07529i | 0.257562 | + | 0.257562i | 0.824062 | − | 0.566500i | \(-0.191703\pi\) |
−0.566500 | + | 0.824062i | \(0.691703\pi\) | |||||||
\(984\) | −17.4356 | + | 4.12725i | −0.555827 | + | 0.131572i | ||||
\(985\) | − | 17.7700i | − | 0.566201i | ||||||
\(986\) | −34.0394 | − | 34.0394i | −1.08404 | − | 1.08404i | ||||
\(987\) | −5.94281 | + | 1.40675i | −0.189162 | + | 0.0447772i | ||||
\(988\) | 17.3510 | − | 9.34634i | 0.552009 | − | 0.297347i | ||||
\(989\) | 38.2522i | 1.21635i | ||||||||
\(990\) | 0.366789 | − | 1.10487i | 0.0116573 | − | 0.0351150i | ||||
\(991\) | −22.5280 | −0.715624 | −0.357812 | − | 0.933794i | \(-0.616477\pi\) | ||||
−0.357812 | + | 0.933794i | \(0.616477\pi\) | |||||||
\(992\) | 3.50344 | 0.111234 | ||||||||
\(993\) | 45.7121 | + | 28.2130i | 1.45063 | + | 0.895313i | ||||
\(994\) | −8.49611 | − | 8.49611i | −0.269480 | − | 0.269480i | ||||
\(995\) | 2.40824 | + | 2.40824i | 0.0763464 | + | 0.0763464i | ||||
\(996\) | 13.1592 | + | 8.12171i | 0.416965 | + | 0.257346i | ||||
\(997\) | −53.8521 | −1.70551 | −0.852757 | − | 0.522309i | \(-0.825071\pi\) | ||||
−0.852757 | + | 0.522309i | \(0.825071\pi\) | |||||||
\(998\) | 4.93530 | 0.156224 | ||||||||
\(999\) | −4.47452 | + | 50.6624i | −0.141568 | + | 1.60289i |
(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 | 546.2.p.c.281.6 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.d.281.1 | yes | 20 | ||
13.5 | odd | 4 | 546.2.p.d.239.1 | yes | 20 | ||
39.5 | even | 4 | inner | 546.2.p.c.239.6 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.6 | ✓ | 20 | 39.5 | even | 4 | inner | |
546.2.p.c.281.6 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.p.d.239.1 | yes | 20 | 13.5 | odd | 4 | ||
546.2.p.d.281.1 | yes | 20 | 3.2 | odd | 2 |