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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.10 | ||
Root | \(-0.332438i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.e.694.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.332438i | − | 0.235069i | −0.993069 | − | 0.117535i | \(-0.962501\pi\) | ||
0.993069 | − | 0.117535i | \(-0.0374991\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.88948 | 0.944742 | ||||||||
\(5\) | −0.370655 | − | 2.20513i | −0.165762 | − | 0.986166i | ||||
\(6\) | 0.332438 | 0.135717 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 1.29301i | − | 0.457149i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.733071 | + | 0.123220i | −0.231817 | + | 0.0389656i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.88948i | 0.545447i | ||||||||
\(13\) | − | 5.50702i | − | 1.52737i | −0.645587 | − | 0.763686i | \(-0.723387\pi\) | ||
0.645587 | − | 0.763686i | \(-0.276613\pi\) | |||||||
\(14\) | −0.332438 | −0.0888479 | ||||||||
\(15\) | 2.20513 | − | 0.370655i | 0.569363 | − | 0.0957027i | ||||
\(16\) | 3.34912 | 0.837281 | ||||||||
\(17\) | 6.85571i | 1.66275i | 0.555710 | + | 0.831376i | \(0.312447\pi\) | ||||
−0.555710 | + | 0.831376i | \(0.687553\pi\) | |||||||
\(18\) | 0.332438i | 0.0783565i | ||||||||
\(19\) | 3.55629 | 0.815868 | 0.407934 | − | 0.913011i | \(-0.366249\pi\) | ||||
0.407934 | + | 0.913011i | \(0.366249\pi\) | |||||||
\(20\) | −0.700347 | − | 4.16657i | −0.156602 | − | 0.931673i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.332438i | 0.0708761i | ||||||||
\(23\) | − | 8.38198i | − | 1.74776i | −0.486138 | − | 0.873882i | \(-0.661595\pi\) | ||
0.486138 | − | 0.873882i | \(-0.338405\pi\) | |||||||
\(24\) | 1.29301 | 0.263935 | ||||||||
\(25\) | −4.72523 | + | 1.63469i | −0.945046 | + | 0.326938i | ||||
\(26\) | −1.83074 | −0.359039 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 1.88948i | − | 0.357079i | ||||||
\(29\) | −8.24013 | −1.53015 | −0.765077 | − | 0.643939i | \(-0.777299\pi\) | ||||
−0.765077 | + | 0.643939i | \(0.777299\pi\) | |||||||
\(30\) | −0.123220 | − | 0.733071i | −0.0224968 | − | 0.133840i | ||||
\(31\) | 0.582000 | 0.104530 | 0.0522651 | − | 0.998633i | \(-0.483356\pi\) | ||||
0.0522651 | + | 0.998633i | \(0.483356\pi\) | |||||||
\(32\) | − | 3.69940i | − | 0.653968i | ||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | 2.27910 | 0.390862 | ||||||||
\(35\) | −2.20513 | + | 0.370655i | −0.372736 | + | 0.0626521i | ||||
\(36\) | −1.88948 | −0.314914 | ||||||||
\(37\) | − | 9.80818i | − | 1.61246i | −0.591605 | − | 0.806228i | \(-0.701506\pi\) | ||
0.591605 | − | 0.806228i | \(-0.298494\pi\) | |||||||
\(38\) | − | 1.18225i | − | 0.191786i | ||||||
\(39\) | 5.50702 | 0.881829 | ||||||||
\(40\) | −2.85127 | + | 0.479262i | −0.450825 | + | 0.0757780i | ||||
\(41\) | 6.19751 | 0.967888 | 0.483944 | − | 0.875099i | \(-0.339204\pi\) | ||||
0.483944 | + | 0.875099i | \(0.339204\pi\) | |||||||
\(42\) | − | 0.332438i | − | 0.0512963i | ||||||
\(43\) | − | 3.22504i | − | 0.491815i | −0.969293 | − | 0.245907i | \(-0.920914\pi\) | ||
0.969293 | − | 0.245907i | \(-0.0790859\pi\) | |||||||
\(44\) | −1.88948 | −0.284851 | ||||||||
\(45\) | 0.370655 | + | 2.20513i | 0.0552540 | + | 0.328722i | ||||
\(46\) | −2.78649 | −0.410846 | ||||||||
\(47\) | − | 6.73820i | − | 0.982867i | −0.870915 | − | 0.491434i | \(-0.836473\pi\) | ||
0.870915 | − | 0.491434i | \(-0.163527\pi\) | |||||||
\(48\) | 3.34912i | 0.483404i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0.543433 | + | 1.57085i | 0.0768530 | + | 0.222151i | ||||
\(51\) | −6.85571 | −0.959991 | ||||||||
\(52\) | − | 10.4054i | − | 1.44297i | ||||||
\(53\) | 14.0460i | 1.92937i | 0.263407 | + | 0.964685i | \(0.415154\pi\) | ||||
−0.263407 | + | 0.964685i | \(0.584846\pi\) | |||||||
\(54\) | −0.332438 | −0.0452391 | ||||||||
\(55\) | 0.370655 | + | 2.20513i | 0.0499791 | + | 0.297340i | ||||
\(56\) | −1.29301 | −0.172786 | ||||||||
\(57\) | 3.55629i | 0.471042i | ||||||||
\(58\) | 2.73933i | 0.359692i | ||||||||
\(59\) | −2.05642 | −0.267723 | −0.133861 | − | 0.991000i | \(-0.542738\pi\) | ||||
−0.133861 | + | 0.991000i | \(0.542738\pi\) | |||||||
\(60\) | 4.16657 | − | 0.700347i | 0.537901 | − | 0.0904144i | ||||
\(61\) | 11.2070 | 1.43491 | 0.717454 | − | 0.696605i | \(-0.245307\pi\) | ||||
0.717454 | + | 0.696605i | \(0.245307\pi\) | |||||||
\(62\) | − | 0.193479i | − | 0.0245719i | ||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 5.46842 | 0.683553 | ||||||||
\(65\) | −12.1437 | + | 2.04120i | −1.50624 | + | 0.253180i | ||||
\(66\) | −0.332438 | −0.0409203 | ||||||||
\(67\) | 1.52881i | 0.186774i | 0.995630 | + | 0.0933868i | \(0.0297693\pi\) | ||||
−0.995630 | + | 0.0933868i | \(0.970231\pi\) | |||||||
\(68\) | 12.9538i | 1.57087i | ||||||||
\(69\) | 8.38198 | 1.00907 | ||||||||
\(70\) | 0.123220 | + | 0.733071i | 0.0147276 | + | 0.0876187i | ||||
\(71\) | −2.12361 | −0.252026 | −0.126013 | − | 0.992029i | \(-0.540218\pi\) | ||||
−0.126013 | + | 0.992029i | \(0.540218\pi\) | |||||||
\(72\) | 1.29301i | 0.152383i | ||||||||
\(73\) | 1.03179i | 0.120762i | 0.998175 | + | 0.0603809i | \(0.0192315\pi\) | ||||
−0.998175 | + | 0.0603809i | \(0.980768\pi\) | |||||||
\(74\) | −3.26062 | −0.379039 | ||||||||
\(75\) | −1.63469 | − | 4.72523i | −0.188758 | − | 0.545623i | ||||
\(76\) | 6.71955 | 0.770785 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | − | 1.83074i | − | 0.207291i | ||||||
\(79\) | 1.77494 | 0.199697 | 0.0998483 | − | 0.995003i | \(-0.468164\pi\) | ||||
0.0998483 | + | 0.995003i | \(0.468164\pi\) | |||||||
\(80\) | −1.24137 | − | 7.38526i | −0.138789 | − | 0.825697i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 2.06029i | − | 0.227521i | ||||||
\(83\) | 4.43704i | 0.487028i | 0.969897 | + | 0.243514i | \(0.0783002\pi\) | ||||
−0.969897 | + | 0.243514i | \(0.921700\pi\) | |||||||
\(84\) | 1.88948 | 0.206160 | ||||||||
\(85\) | 15.1177 | − | 2.54110i | 1.63975 | − | 0.275621i | ||||
\(86\) | −1.07213 | −0.115611 | ||||||||
\(87\) | − | 8.24013i | − | 0.883434i | ||||||
\(88\) | 1.29301i | 0.137836i | ||||||||
\(89\) | −2.23530 | −0.236942 | −0.118471 | − | 0.992958i | \(-0.537799\pi\) | ||||
−0.118471 | + | 0.992958i | \(0.537799\pi\) | |||||||
\(90\) | 0.733071 | − | 0.123220i | 0.0772725 | − | 0.0129885i | ||||
\(91\) | −5.50702 | −0.577293 | ||||||||
\(92\) | − | 15.8376i | − | 1.65119i | ||||||
\(93\) | 0.582000i | 0.0603506i | ||||||||
\(94\) | −2.24004 | −0.231042 | ||||||||
\(95\) | −1.31816 | − | 7.84209i | −0.135240 | − | 0.804581i | ||||
\(96\) | 3.69940 | 0.377569 | ||||||||
\(97\) | − | 11.2496i | − | 1.14223i | −0.820871 | − | 0.571114i | \(-0.806511\pi\) | ||
0.820871 | − | 0.571114i | \(-0.193489\pi\) | |||||||
\(98\) | 0.332438i | 0.0335813i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −8.92825 | + | 3.08872i | −0.892825 | + | 0.308872i | ||||
\(101\) | 15.7132 | 1.56352 | 0.781762 | − | 0.623576i | \(-0.214321\pi\) | ||||
0.781762 | + | 0.623576i | \(0.214321\pi\) | |||||||
\(102\) | 2.27910i | 0.225664i | ||||||||
\(103\) | 9.00401i | 0.887192i | 0.896227 | + | 0.443596i | \(0.146297\pi\) | ||||
−0.896227 | + | 0.443596i | \(0.853703\pi\) | |||||||
\(104\) | −7.12065 | −0.698237 | ||||||||
\(105\) | −0.370655 | − | 2.20513i | −0.0361722 | − | 0.215199i | ||||
\(106\) | 4.66944 | 0.453536 | ||||||||
\(107\) | 7.11539i | 0.687871i | 0.938993 | + | 0.343935i | \(0.111760\pi\) | ||||
−0.938993 | + | 0.343935i | \(0.888240\pi\) | |||||||
\(108\) | − | 1.88948i | − | 0.181816i | ||||||
\(109\) | 1.84137 | 0.176372 | 0.0881858 | − | 0.996104i | \(-0.471893\pi\) | ||||
0.0881858 | + | 0.996104i | \(0.471893\pi\) | |||||||
\(110\) | 0.733071 | − | 0.123220i | 0.0698956 | − | 0.0117486i | ||||
\(111\) | 9.80818 | 0.930952 | ||||||||
\(112\) | − | 3.34912i | − | 0.316462i | ||||||
\(113\) | − | 17.2295i | − | 1.62082i | −0.585866 | − | 0.810408i | \(-0.699246\pi\) | ||
0.585866 | − | 0.810408i | \(-0.300754\pi\) | |||||||
\(114\) | 1.18225 | 0.110727 | ||||||||
\(115\) | −18.4834 | + | 3.10682i | −1.72359 | + | 0.289713i | ||||
\(116\) | −15.5696 | −1.44560 | ||||||||
\(117\) | 5.50702i | 0.509124i | ||||||||
\(118\) | 0.683632i | 0.0629334i | ||||||||
\(119\) | 6.85571 | 0.628462 | ||||||||
\(120\) | −0.479262 | − | 2.85127i | −0.0437504 | − | 0.260284i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 3.72563i | − | 0.337303i | ||||||
\(123\) | 6.19751i | 0.558810i | ||||||||
\(124\) | 1.09968 | 0.0987542 | ||||||||
\(125\) | 5.35614 | + | 9.81386i | 0.479067 | + | 0.877778i | ||||
\(126\) | 0.332438 | 0.0296160 | ||||||||
\(127\) | 21.8825i | 1.94176i | 0.239562 | + | 0.970881i | \(0.422996\pi\) | ||||
−0.239562 | + | 0.970881i | \(0.577004\pi\) | |||||||
\(128\) | − | 9.21672i | − | 0.814651i | ||||||
\(129\) | 3.22504 | 0.283949 | ||||||||
\(130\) | 0.678575 | + | 4.03704i | 0.0595149 | + | 0.354072i | ||||
\(131\) | −2.60035 | −0.227193 | −0.113597 | − | 0.993527i | \(-0.536237\pi\) | ||||
−0.113597 | + | 0.993527i | \(0.536237\pi\) | |||||||
\(132\) | − | 1.88948i | − | 0.164459i | ||||||
\(133\) | − | 3.55629i | − | 0.308369i | ||||||
\(134\) | 0.508234 | 0.0439048 | ||||||||
\(135\) | −2.20513 | + | 0.370655i | −0.189788 | + | 0.0319009i | ||||
\(136\) | 8.86452 | 0.760126 | ||||||||
\(137\) | − | 16.2047i | − | 1.38446i | −0.721678 | − | 0.692229i | \(-0.756629\pi\) | ||
0.721678 | − | 0.692229i | \(-0.243371\pi\) | |||||||
\(138\) | − | 2.78649i | − | 0.237202i | ||||||
\(139\) | 6.94911 | 0.589416 | 0.294708 | − | 0.955587i | \(-0.404778\pi\) | ||||
0.294708 | + | 0.955587i | \(0.404778\pi\) | |||||||
\(140\) | −4.16657 | + | 0.700347i | −0.352139 | + | 0.0591901i | ||||
\(141\) | 6.73820 | 0.567459 | ||||||||
\(142\) | 0.705968i | 0.0592435i | ||||||||
\(143\) | 5.50702i | 0.460520i | ||||||||
\(144\) | −3.34912 | −0.279094 | ||||||||
\(145\) | 3.05424 | + | 18.1706i | 0.253641 | + | 1.50898i | ||||
\(146\) | 0.343006 | 0.0283874 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | − | 18.5324i | − | 1.52336i | ||||||
\(149\) | 1.33816 | 0.109626 | 0.0548130 | − | 0.998497i | \(-0.482544\pi\) | ||||
0.0548130 | + | 0.998497i | \(0.482544\pi\) | |||||||
\(150\) | −1.57085 | + | 0.543433i | −0.128259 | + | 0.0443711i | ||||
\(151\) | 7.67483 | 0.624569 | 0.312284 | − | 0.949989i | \(-0.398906\pi\) | ||||
0.312284 | + | 0.949989i | \(0.398906\pi\) | |||||||
\(152\) | − | 4.59833i | − | 0.372974i | ||||||
\(153\) | − | 6.85571i | − | 0.554251i | ||||||
\(154\) | 0.332438 | 0.0267886 | ||||||||
\(155\) | −0.215721 | − | 1.28339i | −0.0173271 | − | 0.103084i | ||||
\(156\) | 10.4054 | 0.833101 | ||||||||
\(157\) | 14.3690i | 1.14677i | 0.819287 | + | 0.573384i | \(0.194370\pi\) | ||||
−0.819287 | + | 0.573384i | \(0.805630\pi\) | |||||||
\(158\) | − | 0.590059i | − | 0.0469426i | ||||||
\(159\) | −14.0460 | −1.11392 | ||||||||
\(160\) | −8.15768 | + | 1.37120i | −0.644921 | + | 0.108403i | ||||
\(161\) | −8.38198 | −0.660593 | ||||||||
\(162\) | − | 0.332438i | − | 0.0261188i | ||||||
\(163\) | 12.5382i | 0.982070i | 0.871140 | + | 0.491035i | \(0.163381\pi\) | ||||
−0.871140 | + | 0.491035i | \(0.836619\pi\) | |||||||
\(164\) | 11.7101 | 0.914405 | ||||||||
\(165\) | −2.20513 | + | 0.370655i | −0.171669 | + | 0.0288555i | ||||
\(166\) | 1.47504 | 0.114485 | ||||||||
\(167\) | 4.04140i | 0.312733i | 0.987699 | + | 0.156366i | \(0.0499780\pi\) | ||||
−0.987699 | + | 0.156366i | \(0.950022\pi\) | |||||||
\(168\) | − | 1.29301i | − | 0.0997582i | ||||||
\(169\) | −17.3273 | −1.33287 | ||||||||
\(170\) | −0.844760 | − | 5.02572i | −0.0647901 | − | 0.385455i | ||||
\(171\) | −3.55629 | −0.271956 | ||||||||
\(172\) | − | 6.09367i | − | 0.464638i | ||||||
\(173\) | 15.8667i | 1.20632i | 0.797620 | + | 0.603161i | \(0.206092\pi\) | ||||
−0.797620 | + | 0.603161i | \(0.793908\pi\) | |||||||
\(174\) | −2.73933 | −0.207668 | ||||||||
\(175\) | 1.63469 | + | 4.72523i | 0.123571 | + | 0.357194i | ||||
\(176\) | −3.34912 | −0.252450 | ||||||||
\(177\) | − | 2.05642i | − | 0.154570i | ||||||
\(178\) | 0.743101i | 0.0556978i | ||||||||
\(179\) | 0.737568 | 0.0551285 | 0.0275642 | − | 0.999620i | \(-0.491225\pi\) | ||||
0.0275642 | + | 0.999620i | \(0.491225\pi\) | |||||||
\(180\) | 0.700347 | + | 4.16657i | 0.0522008 | + | 0.310558i | ||||
\(181\) | 16.1942 | 1.20370 | 0.601852 | − | 0.798608i | \(-0.294430\pi\) | ||||
0.601852 | + | 0.798608i | \(0.294430\pi\) | |||||||
\(182\) | 1.83074i | 0.135704i | ||||||||
\(183\) | 11.2070i | 0.828445i | ||||||||
\(184\) | −10.8380 | −0.798989 | ||||||||
\(185\) | −21.6284 | + | 3.63545i | −1.59015 | + | 0.267284i | ||||
\(186\) | 0.193479 | 0.0141866 | ||||||||
\(187\) | − | 6.85571i | − | 0.501339i | ||||||
\(188\) | − | 12.7317i | − | 0.928557i | ||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −2.60701 | + | 0.438205i | −0.189132 | + | 0.0317908i | ||||
\(191\) | −14.0663 | −1.01780 | −0.508901 | − | 0.860825i | \(-0.669948\pi\) | ||||
−0.508901 | + | 0.860825i | \(0.669948\pi\) | |||||||
\(192\) | 5.46842i | 0.394649i | ||||||||
\(193\) | 1.40939i | 0.101450i | 0.998713 | + | 0.0507249i | \(0.0161532\pi\) | ||||
−0.998713 | + | 0.0507249i | \(0.983847\pi\) | |||||||
\(194\) | −3.73981 | −0.268503 | ||||||||
\(195\) | −2.04120 | − | 12.1437i | −0.146174 | − | 0.869630i | ||||
\(196\) | −1.88948 | −0.134963 | ||||||||
\(197\) | − | 2.36583i | − | 0.168558i | −0.996442 | − | 0.0842791i | \(-0.973141\pi\) | ||
0.996442 | − | 0.0842791i | \(-0.0268587\pi\) | |||||||
\(198\) | − | 0.332438i | − | 0.0236254i | ||||||
\(199\) | −7.68972 | −0.545110 | −0.272555 | − | 0.962140i | \(-0.587869\pi\) | ||||
−0.272555 | + | 0.962140i | \(0.587869\pi\) | |||||||
\(200\) | 2.11367 | + | 6.10979i | 0.149459 | + | 0.432027i | ||||
\(201\) | −1.52881 | −0.107834 | ||||||||
\(202\) | − | 5.22368i | − | 0.367537i | ||||||
\(203\) | 8.24013i | 0.578344i | ||||||||
\(204\) | −12.9538 | −0.906944 | ||||||||
\(205\) | −2.29714 | − | 13.6663i | −0.160439 | − | 0.954498i | ||||
\(206\) | 2.99328 | 0.208552 | ||||||||
\(207\) | 8.38198i | 0.582588i | ||||||||
\(208\) | − | 18.4437i | − | 1.27884i | ||||||
\(209\) | −3.55629 | −0.245994 | ||||||||
\(210\) | −0.733071 | + | 0.123220i | −0.0505867 | + | 0.00850298i | ||||
\(211\) | −24.9194 | −1.71552 | −0.857762 | − | 0.514047i | \(-0.828146\pi\) | ||||
−0.857762 | + | 0.514047i | \(0.828146\pi\) | |||||||
\(212\) | 26.5397i | 1.82276i | ||||||||
\(213\) | − | 2.12361i | − | 0.145507i | ||||||
\(214\) | 2.36543 | 0.161697 | ||||||||
\(215\) | −7.11166 | + | 1.19538i | −0.485011 | + | 0.0815242i | ||||
\(216\) | −1.29301 | −0.0879784 | ||||||||
\(217\) | − | 0.582000i | − | 0.0395087i | ||||||
\(218\) | − | 0.612143i | − | 0.0414596i | ||||||
\(219\) | −1.03179 | −0.0697218 | ||||||||
\(220\) | 0.700347 | + | 4.16657i | 0.0472174 | + | 0.280910i | ||||
\(221\) | 37.7545 | 2.53964 | ||||||||
\(222\) | − | 3.26062i | − | 0.218838i | ||||||
\(223\) | 12.7387i | 0.853047i | 0.904477 | + | 0.426523i | \(0.140262\pi\) | ||||
−0.904477 | + | 0.426523i | \(0.859738\pi\) | |||||||
\(224\) | −3.69940 | −0.247177 | ||||||||
\(225\) | 4.72523 | − | 1.63469i | 0.315015 | − | 0.108979i | ||||
\(226\) | −5.72775 | −0.381004 | ||||||||
\(227\) | 19.9513i | 1.32421i | 0.749409 | + | 0.662107i | \(0.230338\pi\) | ||||
−0.749409 | + | 0.662107i | \(0.769662\pi\) | |||||||
\(228\) | 6.71955i | 0.445013i | ||||||||
\(229\) | 3.18850 | 0.210702 | 0.105351 | − | 0.994435i | \(-0.466403\pi\) | ||||
0.105351 | + | 0.994435i | \(0.466403\pi\) | |||||||
\(230\) | 1.03283 | + | 6.14459i | 0.0681026 | + | 0.405162i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 10.6546i | 0.699509i | ||||||||
\(233\) | − | 7.68450i | − | 0.503428i | −0.967802 | − | 0.251714i | \(-0.919006\pi\) | ||
0.967802 | − | 0.251714i | \(-0.0809943\pi\) | |||||||
\(234\) | 1.83074 | 0.119680 | ||||||||
\(235\) | −14.8586 | + | 2.49755i | −0.969270 | + | 0.162922i | ||||
\(236\) | −3.88557 | −0.252929 | ||||||||
\(237\) | 1.77494i | 0.115295i | ||||||||
\(238\) | − | 2.27910i | − | 0.147732i | ||||||
\(239\) | −11.5466 | −0.746887 | −0.373444 | − | 0.927653i | \(-0.621823\pi\) | ||||
−0.373444 | + | 0.927653i | \(0.621823\pi\) | |||||||
\(240\) | 7.38526 | − | 1.24137i | 0.476717 | − | 0.0801300i | ||||
\(241\) | 2.94329 | 0.189594 | 0.0947969 | − | 0.995497i | \(-0.469780\pi\) | ||||
0.0947969 | + | 0.995497i | \(0.469780\pi\) | |||||||
\(242\) | − | 0.332438i | − | 0.0213699i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 21.1754 | 1.35562 | ||||||||
\(245\) | 0.370655 | + | 2.20513i | 0.0236803 | + | 0.140881i | ||||
\(246\) | 2.06029 | 0.131359 | ||||||||
\(247\) | − | 19.5845i | − | 1.24613i | ||||||
\(248\) | − | 0.752534i | − | 0.0477859i | ||||||
\(249\) | −4.43704 | −0.281186 | ||||||||
\(250\) | 3.26250 | − | 1.78058i | 0.206339 | − | 0.112614i | ||||
\(251\) | 19.3563 | 1.22176 | 0.610879 | − | 0.791724i | \(-0.290816\pi\) | ||||
0.610879 | + | 0.791724i | \(0.290816\pi\) | |||||||
\(252\) | 1.88948i | 0.119026i | ||||||||
\(253\) | 8.38198i | 0.526971i | ||||||||
\(254\) | 7.27460 | 0.456449 | ||||||||
\(255\) | 2.54110 | + | 15.1177i | 0.159130 | + | 0.946710i | ||||
\(256\) | 7.87285 | 0.492053 | ||||||||
\(257\) | 11.3301i | 0.706755i | 0.935481 | + | 0.353378i | \(0.114967\pi\) | ||||
−0.935481 | + | 0.353378i | \(0.885033\pi\) | |||||||
\(258\) | − | 1.07213i | − | 0.0667478i | ||||||
\(259\) | −9.80818 | −0.609451 | ||||||||
\(260\) | −22.9454 | + | 3.85683i | −1.42301 | + | 0.239190i | ||||
\(261\) | 8.24013 | 0.510051 | ||||||||
\(262\) | 0.864455i | 0.0534062i | ||||||||
\(263\) | 3.36193i | 0.207306i | 0.994614 | + | 0.103653i | \(0.0330531\pi\) | ||||
−0.994614 | + | 0.103653i | \(0.966947\pi\) | |||||||
\(264\) | −1.29301 | −0.0795795 | ||||||||
\(265\) | 30.9734 | − | 5.20623i | 1.90268 | − | 0.319816i | ||||
\(266\) | −1.18225 | −0.0724882 | ||||||||
\(267\) | − | 2.23530i | − | 0.136798i | ||||||
\(268\) | 2.88866i | 0.176453i | ||||||||
\(269\) | 6.35047 | 0.387195 | 0.193598 | − | 0.981081i | \(-0.437984\pi\) | ||||
0.193598 | + | 0.981081i | \(0.437984\pi\) | |||||||
\(270\) | 0.123220 | + | 0.733071i | 0.00749893 | + | 0.0446133i | ||||
\(271\) | 14.2641 | 0.866485 | 0.433242 | − | 0.901277i | \(-0.357369\pi\) | ||||
0.433242 | + | 0.901277i | \(0.357369\pi\) | |||||||
\(272\) | 22.9606i | 1.39219i | ||||||||
\(273\) | − | 5.50702i | − | 0.333300i | ||||||
\(274\) | −5.38705 | −0.325443 | ||||||||
\(275\) | 4.72523 | − | 1.63469i | 0.284942 | − | 0.0985754i | ||||
\(276\) | 15.8376 | 0.953313 | ||||||||
\(277\) | 24.0288i | 1.44375i | 0.692024 | + | 0.721875i | \(0.256719\pi\) | ||||
−0.692024 | + | 0.721875i | \(0.743281\pi\) | |||||||
\(278\) | − | 2.31015i | − | 0.138554i | ||||||
\(279\) | −0.582000 | −0.0348434 | ||||||||
\(280\) | 0.479262 | + | 2.85127i | 0.0286414 | + | 0.170396i | ||||
\(281\) | 11.6299 | 0.693779 | 0.346890 | − | 0.937906i | \(-0.387238\pi\) | ||||
0.346890 | + | 0.937906i | \(0.387238\pi\) | |||||||
\(282\) | − | 2.24004i | − | 0.133392i | ||||||
\(283\) | 7.02079i | 0.417343i | 0.977986 | + | 0.208671i | \(0.0669139\pi\) | ||||
−0.977986 | + | 0.208671i | \(0.933086\pi\) | |||||||
\(284\) | −4.01252 | −0.238099 | ||||||||
\(285\) | 7.84209 | − | 1.31816i | 0.464525 | − | 0.0780808i | ||||
\(286\) | 1.83074 | 0.108254 | ||||||||
\(287\) | − | 6.19751i | − | 0.365827i | ||||||
\(288\) | 3.69940i | 0.217989i | ||||||||
\(289\) | −30.0007 | −1.76475 | ||||||||
\(290\) | 6.04060 | − | 1.01535i | 0.354716 | − | 0.0596233i | ||||
\(291\) | 11.2496 | 0.659466 | ||||||||
\(292\) | 1.94955i | 0.114089i | ||||||||
\(293\) | 12.3870i | 0.723657i | 0.932245 | + | 0.361829i | \(0.117847\pi\) | ||||
−0.932245 | + | 0.361829i | \(0.882153\pi\) | |||||||
\(294\) | −0.332438 | −0.0193882 | ||||||||
\(295\) | 0.762221 | + | 4.53467i | 0.0443782 | + | 0.264019i | ||||
\(296\) | −12.6821 | −0.737133 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | − | 0.444854i | − | 0.0257697i | ||||||
\(299\) | −46.1597 | −2.66949 | ||||||||
\(300\) | −3.08872 | − | 8.92825i | −0.178327 | − | 0.515473i | ||||
\(301\) | −3.22504 | −0.185888 | ||||||||
\(302\) | − | 2.55141i | − | 0.146817i | ||||||
\(303\) | 15.7132i | 0.902701i | ||||||||
\(304\) | 11.9104 | 0.683111 | ||||||||
\(305\) | −4.15393 | − | 24.7129i | −0.237853 | − | 1.41506i | ||||
\(306\) | −2.27910 | −0.130287 | ||||||||
\(307\) | 8.76620i | 0.500314i | 0.968205 | + | 0.250157i | \(0.0804822\pi\) | ||||
−0.968205 | + | 0.250157i | \(0.919518\pi\) | |||||||
\(308\) | 1.88948i | 0.107663i | ||||||||
\(309\) | −9.00401 | −0.512220 | ||||||||
\(310\) | −0.426647 | + | 0.0717140i | −0.0242319 | + | 0.00407308i | ||||
\(311\) | −13.6554 | −0.774328 | −0.387164 | − | 0.922011i | \(-0.626545\pi\) | ||||
−0.387164 | + | 0.922011i | \(0.626545\pi\) | |||||||
\(312\) | − | 7.12065i | − | 0.403128i | ||||||
\(313\) | 20.7806i | 1.17459i | 0.809373 | + | 0.587295i | \(0.199807\pi\) | ||||
−0.809373 | + | 0.587295i | \(0.800193\pi\) | |||||||
\(314\) | 4.77679 | 0.269570 | ||||||||
\(315\) | 2.20513 | − | 0.370655i | 0.124245 | − | 0.0208840i | ||||
\(316\) | 3.35373 | 0.188662 | ||||||||
\(317\) | − | 10.4361i | − | 0.586148i | −0.956090 | − | 0.293074i | \(-0.905322\pi\) | ||
0.956090 | − | 0.293074i | \(-0.0946783\pi\) | |||||||
\(318\) | 4.66944i | 0.261849i | ||||||||
\(319\) | 8.24013 | 0.461359 | ||||||||
\(320\) | −2.02690 | − | 12.0586i | −0.113307 | − | 0.674096i | ||||
\(321\) | −7.11539 | −0.397142 | ||||||||
\(322\) | 2.78649i | 0.155285i | ||||||||
\(323\) | 24.3809i | 1.35659i | ||||||||
\(324\) | 1.88948 | 0.104971 | ||||||||
\(325\) | 9.00226 | + | 26.0219i | 0.499356 | + | 1.44344i | ||||
\(326\) | 4.16819 | 0.230854 | ||||||||
\(327\) | 1.84137i | 0.101828i | ||||||||
\(328\) | − | 8.01346i | − | 0.442469i | ||||||
\(329\) | −6.73820 | −0.371489 | ||||||||
\(330\) | 0.123220 | + | 0.733071i | 0.00678303 | + | 0.0403542i | ||||
\(331\) | −6.63873 | −0.364897 | −0.182449 | − | 0.983215i | \(-0.558402\pi\) | ||||
−0.182449 | + | 0.983215i | \(0.558402\pi\) | |||||||
\(332\) | 8.38371i | 0.460116i | ||||||||
\(333\) | 9.80818i | 0.537485i | ||||||||
\(334\) | 1.34351 | 0.0735139 | ||||||||
\(335\) | 3.37123 | − | 0.566660i | 0.184190 | − | 0.0309600i | ||||
\(336\) | 3.34912 | 0.182710 | ||||||||
\(337\) | 16.2216i | 0.883644i | 0.897103 | + | 0.441822i | \(0.145668\pi\) | ||||
−0.897103 | + | 0.441822i | \(0.854332\pi\) | |||||||
\(338\) | 5.76025i | 0.313316i | ||||||||
\(339\) | 17.2295 | 0.935778 | ||||||||
\(340\) | 28.5648 | − | 4.80137i | 1.54914 | − | 0.260391i | ||||
\(341\) | −0.582000 | −0.0315171 | ||||||||
\(342\) | 1.18225i | 0.0639285i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −4.17003 | −0.224833 | ||||||||
\(345\) | −3.10682 | − | 18.4834i | −0.167266 | − | 0.995112i | ||||
\(346\) | 5.27469 | 0.283569 | ||||||||
\(347\) | − | 26.5268i | − | 1.42403i | −0.702162 | − | 0.712017i | \(-0.747782\pi\) | ||
0.702162 | − | 0.712017i | \(-0.252218\pi\) | |||||||
\(348\) | − | 15.5696i | − | 0.834618i | ||||||
\(349\) | −29.4038 | −1.57395 | −0.786975 | − | 0.616985i | \(-0.788354\pi\) | ||||
−0.786975 | + | 0.616985i | \(0.788354\pi\) | |||||||
\(350\) | 1.57085 | − | 0.543433i | 0.0839653 | − | 0.0290477i | ||||
\(351\) | −5.50702 | −0.293943 | ||||||||
\(352\) | 3.69940i | 0.197179i | ||||||||
\(353\) | − | 2.61496i | − | 0.139180i | −0.997576 | − | 0.0695901i | \(-0.977831\pi\) | ||
0.997576 | − | 0.0695901i | \(-0.0221691\pi\) | |||||||
\(354\) | −0.683632 | −0.0363346 | ||||||||
\(355\) | 0.787125 | + | 4.68283i | 0.0417763 | + | 0.248539i | ||||
\(356\) | −4.22357 | −0.223849 | ||||||||
\(357\) | 6.85571i | 0.362842i | ||||||||
\(358\) | − | 0.245196i | − | 0.0129590i | ||||||
\(359\) | 1.18009 | 0.0622826 | 0.0311413 | − | 0.999515i | \(-0.490086\pi\) | ||||
0.0311413 | + | 0.999515i | \(0.490086\pi\) | |||||||
\(360\) | 2.85127 | − | 0.479262i | 0.150275 | − | 0.0252593i | ||||
\(361\) | −6.35282 | −0.334359 | ||||||||
\(362\) | − | 5.38356i | − | 0.282954i | ||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −10.4054 | −0.545393 | ||||||||
\(365\) | 2.27523 | − | 0.382438i | 0.119091 | − | 0.0200177i | ||||
\(366\) | 3.72563 | 0.194742 | ||||||||
\(367\) | − | 9.34246i | − | 0.487673i | −0.969816 | − | 0.243836i | \(-0.921594\pi\) | ||
0.969816 | − | 0.243836i | \(-0.0784059\pi\) | |||||||
\(368\) | − | 28.0723i | − | 1.46337i | ||||||
\(369\) | −6.19751 | −0.322629 | ||||||||
\(370\) | 1.20856 | + | 7.19009i | 0.0628302 | + | 0.373795i | ||||
\(371\) | 14.0460 | 0.729233 | ||||||||
\(372\) | 1.09968i | 0.0570158i | ||||||||
\(373\) | − | 14.1464i | − | 0.732473i | −0.930522 | − | 0.366236i | \(-0.880646\pi\) | ||
0.930522 | − | 0.366236i | \(-0.119354\pi\) | |||||||
\(374\) | −2.27910 | −0.117849 | ||||||||
\(375\) | −9.81386 | + | 5.35614i | −0.506785 | + | 0.276590i | ||||
\(376\) | −8.71258 | −0.449317 | ||||||||
\(377\) | 45.3786i | 2.33711i | ||||||||
\(378\) | 0.332438i | 0.0170988i | ||||||||
\(379\) | 6.99655 | 0.359389 | 0.179694 | − | 0.983723i | \(-0.442489\pi\) | ||||
0.179694 | + | 0.983723i | \(0.442489\pi\) | |||||||
\(380\) | −2.49064 | − | 14.8175i | −0.127767 | − | 0.760122i | ||||
\(381\) | −21.8825 | −1.12108 | ||||||||
\(382\) | 4.67617i | 0.239254i | ||||||||
\(383\) | 0.0280405i | 0.00143280i | 1.00000 | 0.000716402i | \(0.000228038\pi\) | |||||
−1.00000 | 0.000716402i | \(0.999772\pi\) | ||||||||
\(384\) | 9.21672 | 0.470339 | ||||||||
\(385\) | 2.20513 | − | 0.370655i | 0.112384 | − | 0.0188903i | ||||
\(386\) | 0.468534 | 0.0238478 | ||||||||
\(387\) | 3.22504i | 0.163938i | ||||||||
\(388\) | − | 21.2560i | − | 1.07911i | ||||||
\(389\) | 29.0572 | 1.47326 | 0.736630 | − | 0.676296i | \(-0.236416\pi\) | ||||
0.736630 | + | 0.676296i | \(0.236416\pi\) | |||||||
\(390\) | −4.03704 | + | 0.678575i | −0.204423 | + | 0.0343610i | ||||
\(391\) | 57.4644 | 2.90610 | ||||||||
\(392\) | 1.29301i | 0.0653071i | ||||||||
\(393\) | − | 2.60035i | − | 0.131170i | ||||||
\(394\) | −0.786492 | −0.0396229 | ||||||||
\(395\) | −0.657891 | − | 3.91398i | −0.0331021 | − | 0.196934i | ||||
\(396\) | 1.88948 | 0.0949502 | ||||||||
\(397\) | − | 34.6718i | − | 1.74013i | −0.492941 | − | 0.870063i | \(-0.664078\pi\) | ||
0.492941 | − | 0.870063i | \(-0.335922\pi\) | |||||||
\(398\) | 2.55636i | 0.128139i | ||||||||
\(399\) | 3.55629 | 0.178037 | ||||||||
\(400\) | −15.8254 | + | 5.47477i | −0.791269 | + | 0.273738i | ||||
\(401\) | 35.3446 | 1.76502 | 0.882512 | − | 0.470291i | \(-0.155851\pi\) | ||||
0.882512 | + | 0.470291i | \(0.155851\pi\) | |||||||
\(402\) | 0.508234i | 0.0253484i | ||||||||
\(403\) | − | 3.20509i | − | 0.159657i | ||||||
\(404\) | 29.6899 | 1.47713 | ||||||||
\(405\) | −0.370655 | − | 2.20513i | −0.0184180 | − | 0.109574i | ||||
\(406\) | 2.73933 | 0.135951 | ||||||||
\(407\) | 9.80818i | 0.486174i | ||||||||
\(408\) | 8.86452i | 0.438859i | ||||||||
\(409\) | 13.5552 | 0.670261 | 0.335131 | − | 0.942172i | \(-0.391220\pi\) | ||||
0.335131 | + | 0.942172i | \(0.391220\pi\) | |||||||
\(410\) | −4.54321 | + | 0.763656i | −0.224373 | + | 0.0377143i | ||||
\(411\) | 16.2047 | 0.799317 | ||||||||
\(412\) | 17.0129i | 0.838168i | ||||||||
\(413\) | 2.05642i | 0.101190i | ||||||||
\(414\) | 2.78649 | 0.136949 | ||||||||
\(415\) | 9.78426 | − | 1.64461i | 0.480290 | − | 0.0807307i | ||||
\(416\) | −20.3727 | −0.998853 | ||||||||
\(417\) | 6.94911i | 0.340299i | ||||||||
\(418\) | 1.18225i | 0.0578255i | ||||||||
\(419\) | −17.6316 | −0.861361 | −0.430680 | − | 0.902505i | \(-0.641726\pi\) | ||||
−0.430680 | + | 0.902505i | \(0.641726\pi\) | |||||||
\(420\) | −0.700347 | − | 4.16657i | −0.0341734 | − | 0.203308i | ||||
\(421\) | 10.1093 | 0.492697 | 0.246349 | − | 0.969181i | \(-0.420769\pi\) | ||||
0.246349 | + | 0.969181i | \(0.420769\pi\) | |||||||
\(422\) | 8.28417i | 0.403267i | ||||||||
\(423\) | 6.73820i | 0.327622i | ||||||||
\(424\) | 18.1617 | 0.882010 | ||||||||
\(425\) | −11.2069 | − | 32.3948i | −0.543616 | − | 1.57138i | ||||
\(426\) | −0.705968 | −0.0342042 | ||||||||
\(427\) | − | 11.2070i | − | 0.542345i | ||||||
\(428\) | 13.4444i | 0.649861i | ||||||||
\(429\) | −5.50702 | −0.265881 | ||||||||
\(430\) | 0.397390 | + | 2.36419i | 0.0191638 | + | 0.114011i | ||||
\(431\) | 27.4527 | 1.32235 | 0.661175 | − | 0.750232i | \(-0.270058\pi\) | ||||
0.661175 | + | 0.750232i | \(0.270058\pi\) | |||||||
\(432\) | − | 3.34912i | − | 0.161135i | ||||||
\(433\) | − | 35.3493i | − | 1.69878i | −0.527767 | − | 0.849389i | \(-0.676971\pi\) | ||
0.527767 | − | 0.849389i | \(-0.323029\pi\) | |||||||
\(434\) | −0.193479 | −0.00928729 | ||||||||
\(435\) | −18.1706 | + | 3.05424i | −0.871213 | + | 0.146440i | ||||
\(436\) | 3.47925 | 0.166626 | ||||||||
\(437\) | − | 29.8087i | − | 1.42595i | ||||||
\(438\) | 0.343006i | 0.0163895i | ||||||||
\(439\) | −17.0486 | −0.813687 | −0.406844 | − | 0.913498i | \(-0.633371\pi\) | ||||
−0.406844 | + | 0.913498i | \(0.633371\pi\) | |||||||
\(440\) | 2.85127 | − | 0.479262i | 0.135929 | − | 0.0228479i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − | 12.5510i | − | 0.596992i | ||||||
\(443\) | 29.6424i | 1.40835i | 0.710026 | + | 0.704176i | \(0.248683\pi\) | ||||
−0.710026 | + | 0.704176i | \(0.751317\pi\) | |||||||
\(444\) | 18.5324 | 0.879510 | ||||||||
\(445\) | 0.828527 | + | 4.92915i | 0.0392759 | + | 0.233664i | ||||
\(446\) | 4.23483 | 0.200525 | ||||||||
\(447\) | 1.33816i | 0.0632926i | ||||||||
\(448\) | − | 5.46842i | − | 0.258359i | ||||||
\(449\) | −5.74336 | −0.271046 | −0.135523 | − | 0.990774i | \(-0.543271\pi\) | ||||
−0.135523 | + | 0.990774i | \(0.543271\pi\) | |||||||
\(450\) | −0.543433 | − | 1.57085i | −0.0256177 | − | 0.0740504i | ||||
\(451\) | −6.19751 | −0.291829 | ||||||||
\(452\) | − | 32.5549i | − | 1.53125i | ||||||
\(453\) | 7.67483i | 0.360595i | ||||||||
\(454\) | 6.63258 | 0.311282 | ||||||||
\(455\) | 2.04120 | + | 12.1437i | 0.0956932 | + | 0.569306i | ||||
\(456\) | 4.59833 | 0.215336 | ||||||||
\(457\) | 36.8697i | 1.72469i | 0.506320 | + | 0.862346i | \(0.331005\pi\) | ||||
−0.506320 | + | 0.862346i | \(0.668995\pi\) | |||||||
\(458\) | − | 1.05998i | − | 0.0495296i | ||||||
\(459\) | 6.85571 | 0.319997 | ||||||||
\(460\) | −34.9241 | + | 5.87030i | −1.62834 | + | 0.273704i | ||||
\(461\) | 19.6725 | 0.916238 | 0.458119 | − | 0.888891i | \(-0.348523\pi\) | ||||
0.458119 | + | 0.888891i | \(0.348523\pi\) | |||||||
\(462\) | 0.332438i | 0.0154664i | ||||||||
\(463\) | − | 35.9987i | − | 1.67300i | −0.547967 | − | 0.836500i | \(-0.684598\pi\) | ||
0.547967 | − | 0.836500i | \(-0.315402\pi\) | |||||||
\(464\) | −27.5972 | −1.28117 | ||||||||
\(465\) | 1.28339 | − | 0.215721i | 0.0595157 | − | 0.0100038i | ||||
\(466\) | −2.55462 | −0.118341 | ||||||||
\(467\) | − | 11.9968i | − | 0.555144i | −0.960705 | − | 0.277572i | \(-0.910470\pi\) | ||
0.960705 | − | 0.277572i | \(-0.0895297\pi\) | |||||||
\(468\) | 10.4054i | 0.480991i | ||||||||
\(469\) | 1.52881 | 0.0705938 | ||||||||
\(470\) | 0.830281 | + | 4.93958i | 0.0382980 | + | 0.227846i | ||||
\(471\) | −14.3690 | −0.662086 | ||||||||
\(472\) | 2.65898i | 0.122389i | ||||||||
\(473\) | 3.22504i | 0.148288i | ||||||||
\(474\) | 0.590059 | 0.0271023 | ||||||||
\(475\) | −16.8043 | + | 5.81342i | −0.771033 | + | 0.266738i | ||||
\(476\) | 12.9538 | 0.593734 | ||||||||
\(477\) | − | 14.0460i | − | 0.643123i | ||||||
\(478\) | 3.83853i | 0.175570i | ||||||||
\(479\) | 7.45562 | 0.340656 | 0.170328 | − | 0.985387i | \(-0.445517\pi\) | ||||
0.170328 | + | 0.985387i | \(0.445517\pi\) | |||||||
\(480\) | −1.37120 | − | 8.15768i | −0.0625866 | − | 0.372345i | ||||
\(481\) | −54.0139 | −2.46282 | ||||||||
\(482\) | − | 0.978462i | − | 0.0445677i | ||||||
\(483\) | − | 8.38198i | − | 0.381393i | ||||||
\(484\) | 1.88948 | 0.0858857 | ||||||||
\(485\) | −24.8070 | + | 4.16974i | −1.12643 | + | 0.189338i | ||||
\(486\) | 0.332438 | 0.0150797 | ||||||||
\(487\) | − | 25.2921i | − | 1.14609i | −0.819523 | − | 0.573046i | \(-0.805761\pi\) | ||
0.819523 | − | 0.573046i | \(-0.194239\pi\) | |||||||
\(488\) | − | 14.4908i | − | 0.655968i | ||||||
\(489\) | −12.5382 | −0.566998 | ||||||||
\(490\) | 0.733071 | − | 0.123220i | 0.0331168 | − | 0.00556651i | ||||
\(491\) | −22.2420 | −1.00377 | −0.501883 | − | 0.864936i | \(-0.667359\pi\) | ||||
−0.501883 | + | 0.864936i | \(0.667359\pi\) | |||||||
\(492\) | 11.7101i | 0.527932i | ||||||||
\(493\) | − | 56.4919i | − | 2.54427i | ||||||
\(494\) | −6.51065 | −0.292928 | ||||||||
\(495\) | −0.370655 | − | 2.20513i | −0.0166597 | − | 0.0991134i | ||||
\(496\) | 1.94919 | 0.0875212 | ||||||||
\(497\) | 2.12361i | 0.0952567i | ||||||||
\(498\) | 1.47504i | 0.0660981i | ||||||||
\(499\) | 11.9546 | 0.535163 | 0.267582 | − | 0.963535i | \(-0.413776\pi\) | ||||
0.267582 | + | 0.963535i | \(0.413776\pi\) | |||||||
\(500\) | 10.1203 | + | 18.5431i | 0.452595 | + | 0.829274i | ||||
\(501\) | −4.04140 | −0.180556 | ||||||||
\(502\) | − | 6.43477i | − | 0.287198i | ||||||
\(503\) | 1.86300i | 0.0830672i | 0.999137 | + | 0.0415336i | \(0.0132244\pi\) | ||||
−0.999137 | + | 0.0415336i | \(0.986776\pi\) | |||||||
\(504\) | 1.29301 | 0.0575954 | ||||||||
\(505\) | −5.82419 | − | 34.6498i | −0.259173 | − | 1.54189i | ||||
\(506\) | 2.78649 | 0.123875 | ||||||||
\(507\) | − | 17.3273i | − | 0.769531i | ||||||
\(508\) | 41.3467i | 1.83447i | ||||||||
\(509\) | −3.50365 | −0.155297 | −0.0776483 | − | 0.996981i | \(-0.524741\pi\) | ||||
−0.0776483 | + | 0.996981i | \(0.524741\pi\) | |||||||
\(510\) | 5.02572 | − | 0.844760i | 0.222543 | − | 0.0374066i | ||||
\(511\) | 1.03179 | 0.0456436 | ||||||||
\(512\) | − | 21.0507i | − | 0.930317i | ||||||
\(513\) | − | 3.55629i | − | 0.157014i | ||||||
\(514\) | 3.76658 | 0.166137 | ||||||||
\(515\) | 19.8551 | − | 3.33738i | 0.874918 | − | 0.147063i | ||||
\(516\) | 6.09367 | 0.268259 | ||||||||
\(517\) | 6.73820i | 0.296346i | ||||||||
\(518\) | 3.26062i | 0.143263i | ||||||||
\(519\) | −15.8667 | −0.696470 | ||||||||
\(520\) | 2.63931 | + | 15.7020i | 0.115741 | + | 0.688578i | ||||
\(521\) | −30.0815 | −1.31789 | −0.658947 | − | 0.752190i | \(-0.728998\pi\) | ||||
−0.658947 | + | 0.752190i | \(0.728998\pi\) | |||||||
\(522\) | − | 2.73933i | − | 0.119897i | ||||||
\(523\) | − | 15.9803i | − | 0.698771i | −0.936979 | − | 0.349386i | \(-0.886390\pi\) | ||
0.936979 | − | 0.349386i | \(-0.113610\pi\) | |||||||
\(524\) | −4.91331 | −0.214639 | ||||||||
\(525\) | −4.72523 | + | 1.63469i | −0.206226 | + | 0.0713436i | ||||
\(526\) | 1.11763 | 0.0487312 | ||||||||
\(527\) | 3.99002i | 0.173808i | ||||||||
\(528\) | − | 3.34912i | − | 0.145752i | ||||||
\(529\) | −47.2576 | −2.05468 | ||||||||
\(530\) | −1.73075 | − | 10.2967i | −0.0751790 | − | 0.447261i | ||||
\(531\) | 2.05642 | 0.0892409 | ||||||||
\(532\) | − | 6.71955i | − | 0.291329i | ||||||
\(533\) | − | 34.1298i | − | 1.47833i | ||||||
\(534\) | −0.743101 | −0.0321571 | ||||||||
\(535\) | 15.6904 | − | 2.63735i | 0.678355 | − | 0.114023i | ||||
\(536\) | 1.97677 | 0.0853834 | ||||||||
\(537\) | 0.737568i | 0.0318284i | ||||||||
\(538\) | − | 2.11114i | − | 0.0910177i | ||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −4.16657 | + | 0.700347i | −0.179300 | + | 0.0301381i | ||||
\(541\) | 11.8502 | 0.509479 | 0.254740 | − | 0.967010i | \(-0.418010\pi\) | ||||
0.254740 | + | 0.967010i | \(0.418010\pi\) | |||||||
\(542\) | − | 4.74195i | − | 0.203684i | ||||||
\(543\) | 16.1942i | 0.694958i | ||||||||
\(544\) | 25.3620 | 1.08739 | ||||||||
\(545\) | −0.682514 | − | 4.06047i | −0.0292357 | − | 0.173932i | ||||
\(546\) | −1.83074 | −0.0783486 | ||||||||
\(547\) | 6.76118i | 0.289087i | 0.989498 | + | 0.144544i | \(0.0461714\pi\) | ||||
−0.989498 | + | 0.144544i | \(0.953829\pi\) | |||||||
\(548\) | − | 30.6185i | − | 1.30796i | ||||||
\(549\) | −11.2070 | −0.478303 | ||||||||
\(550\) | −0.543433 | − | 1.57085i | −0.0231721 | − | 0.0669812i | ||||
\(551\) | −29.3043 | −1.24840 | ||||||||
\(552\) | − | 10.8380i | − | 0.461297i | ||||||
\(553\) | − | 1.77494i | − | 0.0754782i | ||||||
\(554\) | 7.98809 | 0.339381 | ||||||||
\(555\) | −3.63545 | − | 21.6284i | −0.154316 | − | 0.918073i | ||||
\(556\) | 13.1302 | 0.556846 | ||||||||
\(557\) | − | 3.53109i | − | 0.149617i | −0.997198 | − | 0.0748086i | \(-0.976165\pi\) | ||
0.997198 | − | 0.0748086i | \(-0.0238346\pi\) | |||||||
\(558\) | 0.193479i | 0.00819062i | ||||||||
\(559\) | −17.7604 | −0.751184 | ||||||||
\(560\) | −7.38526 | + | 1.24137i | −0.312084 | + | 0.0524574i | ||||
\(561\) | 6.85571 | 0.289448 | ||||||||
\(562\) | − | 3.86621i | − | 0.163086i | ||||||
\(563\) | 41.0193i | 1.72876i | 0.502842 | + | 0.864379i | \(0.332288\pi\) | ||||
−0.502842 | + | 0.864379i | \(0.667712\pi\) | |||||||
\(564\) | 12.7317 | 0.536102 | ||||||||
\(565\) | −37.9934 | + | 6.38620i | −1.59839 | + | 0.268670i | ||||
\(566\) | 2.33398 | 0.0981045 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 2.74585i | 0.115213i | ||||||||
\(569\) | −27.9208 | −1.17050 | −0.585250 | − | 0.810853i | \(-0.699004\pi\) | ||||
−0.585250 | + | 0.810853i | \(0.699004\pi\) | |||||||
\(570\) | −0.438205 | − | 2.60701i | −0.0183544 | − | 0.109196i | ||||
\(571\) | 25.8993 | 1.08385 | 0.541927 | − | 0.840426i | \(-0.317695\pi\) | ||||
0.541927 | + | 0.840426i | \(0.317695\pi\) | |||||||
\(572\) | 10.4054i | 0.435073i | ||||||||
\(573\) | − | 14.0663i | − | 0.587628i | ||||||
\(574\) | −2.06029 | −0.0859948 | ||||||||
\(575\) | 13.7019 | + | 39.6068i | 0.571410 | + | 1.65172i | ||||
\(576\) | −5.46842 | −0.227851 | ||||||||
\(577\) | 15.3525i | 0.639132i | 0.947564 | + | 0.319566i | \(0.103537\pi\) | ||||
−0.947564 | + | 0.319566i | \(0.896463\pi\) | |||||||
\(578\) | 9.97338i | 0.414838i | ||||||||
\(579\) | −1.40939 | −0.0585721 | ||||||||
\(580\) | 5.77095 | + | 34.3330i | 0.239626 | + | 1.42560i | ||||
\(581\) | 4.43704 | 0.184079 | ||||||||
\(582\) | − | 3.73981i | − | 0.155020i | ||||||
\(583\) | − | 14.0460i | − | 0.581727i | ||||||
\(584\) | 1.33412 | 0.0552061 | ||||||||
\(585\) | 12.1437 | − | 2.04120i | 0.502081 | − | 0.0843934i | ||||
\(586\) | 4.11792 | 0.170110 | ||||||||
\(587\) | 13.4591i | 0.555518i | 0.960651 | + | 0.277759i | \(0.0895916\pi\) | ||||
−0.960651 | + | 0.277759i | \(0.910408\pi\) | |||||||
\(588\) | − | 1.88948i | − | 0.0779210i | ||||||
\(589\) | 2.06976 | 0.0852829 | ||||||||
\(590\) | 1.50750 | − | 0.253392i | 0.0620628 | − | 0.0104320i | ||||
\(591\) | 2.36583 | 0.0973172 | ||||||||
\(592\) | − | 32.8488i | − | 1.35008i | ||||||
\(593\) | − | 15.3775i | − | 0.631479i | −0.948846 | − | 0.315740i | \(-0.897747\pi\) | ||
0.948846 | − | 0.315740i | \(-0.102253\pi\) | |||||||
\(594\) | 0.332438 | 0.0136401 | ||||||||
\(595\) | −2.54110 | − | 15.1177i | −0.104175 | − | 0.619767i | ||||
\(596\) | 2.52843 | 0.103568 | ||||||||
\(597\) | − | 7.68972i | − | 0.314719i | ||||||
\(598\) | 15.3453i | 0.627515i | ||||||||
\(599\) | 0.728071 | 0.0297482 | 0.0148741 | − | 0.999889i | \(-0.495265\pi\) | ||||
0.0148741 | + | 0.999889i | \(0.495265\pi\) | |||||||
\(600\) | −6.10979 | + | 2.11367i | −0.249431 | + | 0.0862904i | ||||
\(601\) | 11.3171 | 0.461636 | 0.230818 | − | 0.972997i | \(-0.425860\pi\) | ||||
0.230818 | + | 0.972997i | \(0.425860\pi\) | |||||||
\(602\) | 1.07213i | 0.0436967i | ||||||||
\(603\) | − | 1.52881i | − | 0.0622579i | ||||||
\(604\) | 14.5015 | 0.590056 | ||||||||
\(605\) | −0.370655 | − | 2.20513i | −0.0150693 | − | 0.0896514i | ||||
\(606\) | 5.22368 | 0.212197 | ||||||||
\(607\) | 25.4779i | 1.03411i | 0.855951 | + | 0.517057i | \(0.172973\pi\) | ||||
−0.855951 | + | 0.517057i | \(0.827027\pi\) | |||||||
\(608\) | − | 13.1561i | − | 0.533552i | ||||||
\(609\) | −8.24013 | −0.333907 | ||||||||
\(610\) | −8.21552 | + | 1.38093i | −0.332637 | + | 0.0559120i | ||||
\(611\) | −37.1074 | −1.50120 | ||||||||
\(612\) | − | 12.9538i | − | 0.523624i | ||||||
\(613\) | − | 2.51148i | − | 0.101438i | −0.998713 | − | 0.0507189i | \(-0.983849\pi\) | ||
0.998713 | − | 0.0507189i | \(-0.0161513\pi\) | |||||||
\(614\) | 2.91422 | 0.117608 | ||||||||
\(615\) | 13.6663 | − | 2.29714i | 0.551080 | − | 0.0926295i | ||||
\(616\) | 1.29301 | 0.0520970 | ||||||||
\(617\) | − | 16.4368i | − | 0.661722i | −0.943680 | − | 0.330861i | \(-0.892661\pi\) | ||
0.943680 | − | 0.330861i | \(-0.107339\pi\) | |||||||
\(618\) | 2.99328i | 0.120407i | ||||||||
\(619\) | −46.1846 | −1.85632 | −0.928158 | − | 0.372187i | \(-0.878608\pi\) | ||||
−0.928158 | + | 0.372187i | \(0.878608\pi\) | |||||||
\(620\) | −0.407602 | − | 2.42494i | −0.0163697 | − | 0.0973880i | ||||
\(621\) | −8.38198 | −0.336357 | ||||||||
\(622\) | 4.53958i | 0.182021i | ||||||||
\(623\) | 2.23530i | 0.0895556i | ||||||||
\(624\) | 18.4437 | 0.738338 | ||||||||
\(625\) | 19.6556 | − | 15.4486i | 0.786224 | − | 0.617942i | ||||
\(626\) | 6.90827 | 0.276110 | ||||||||
\(627\) | − | 3.55629i | − | 0.142024i | ||||||
\(628\) | 27.1499i | 1.08340i | ||||||||
\(629\) | 67.2420 | 2.68112 | ||||||||
\(630\) | −0.123220 | − | 0.733071i | −0.00490920 | − | 0.0292062i | ||||
\(631\) | −28.4586 | −1.13292 | −0.566459 | − | 0.824090i | \(-0.691687\pi\) | ||||
−0.566459 | + | 0.824090i | \(0.691687\pi\) | |||||||
\(632\) | − | 2.29502i | − | 0.0912912i | ||||||
\(633\) | − | 24.9194i | − | 0.990458i | ||||||
\(634\) | −3.46935 | −0.137785 | ||||||||
\(635\) | 48.2539 | − | 8.11088i | 1.91490 | − | 0.321870i | ||||
\(636\) | −26.5397 | −1.05237 | ||||||||
\(637\) | 5.50702i | 0.218196i | ||||||||
\(638\) | − | 2.73933i | − | 0.108451i | ||||||
\(639\) | 2.12361 | 0.0840085 | ||||||||
\(640\) | −20.3241 | + | 3.41622i | −0.803381 | + | 0.135038i | ||||
\(641\) | 37.0419 | 1.46307 | 0.731533 | − | 0.681806i | \(-0.238805\pi\) | ||||
0.731533 | + | 0.681806i | \(0.238805\pi\) | |||||||
\(642\) | 2.36543i | 0.0933560i | ||||||||
\(643\) | − | 36.6680i | − | 1.44604i | −0.690825 | − | 0.723022i | \(-0.742752\pi\) | ||
0.690825 | − | 0.723022i | \(-0.257248\pi\) | |||||||
\(644\) | −15.8376 | −0.624090 | ||||||||
\(645\) | −1.19538 | − | 7.11166i | −0.0470680 | − | 0.280021i | ||||
\(646\) | 8.10513 | 0.318892 | ||||||||
\(647\) | − | 12.8196i | − | 0.503992i | −0.967728 | − | 0.251996i | \(-0.918913\pi\) | ||
0.967728 | − | 0.251996i | \(-0.0810869\pi\) | |||||||
\(648\) | − | 1.29301i | − | 0.0507944i | ||||||
\(649\) | 2.05642 | 0.0807214 | ||||||||
\(650\) | 8.65069 | − | 2.99270i | 0.339308 | − | 0.117383i | ||||
\(651\) | 0.582000 | 0.0228104 | ||||||||
\(652\) | 23.6908i | 0.927803i | ||||||||
\(653\) | − | 14.5397i | − | 0.568981i | −0.958679 | − | 0.284490i | \(-0.908176\pi\) | ||
0.958679 | − | 0.284490i | \(-0.0918243\pi\) | |||||||
\(654\) | 0.612143 | 0.0239367 | ||||||||
\(655\) | 0.963832 | + | 5.73411i | 0.0376600 | + | 0.224050i | ||||
\(656\) | 20.7562 | 0.810394 | ||||||||
\(657\) | − | 1.03179i | − | 0.0402539i | ||||||
\(658\) | 2.24004i | 0.0873257i | ||||||||
\(659\) | 15.8977 | 0.619285 | 0.309642 | − | 0.950853i | \(-0.399791\pi\) | ||||
0.309642 | + | 0.950853i | \(0.399791\pi\) | |||||||
\(660\) | −4.16657 | + | 0.700347i | −0.162183 | + | 0.0272610i | ||||
\(661\) | −3.04949 | −0.118611 | −0.0593057 | − | 0.998240i | \(-0.518889\pi\) | ||||
−0.0593057 | + | 0.998240i | \(0.518889\pi\) | |||||||
\(662\) | 2.20697i | 0.0857762i | ||||||||
\(663\) | 37.7545i | 1.46626i | ||||||||
\(664\) | 5.73715 | 0.222644 | ||||||||
\(665\) | −7.84209 | + | 1.31816i | −0.304103 | + | 0.0511159i | ||||
\(666\) | 3.26062 | 0.126346 | ||||||||
\(667\) | 69.0686i | 2.67435i | ||||||||
\(668\) | 7.63616i | 0.295452i | ||||||||
\(669\) | −12.7387 | −0.492507 | ||||||||
\(670\) | −0.188380 | − | 1.12072i | −0.00727774 | − | 0.0432974i | ||||
\(671\) | −11.2070 | −0.432641 | ||||||||
\(672\) | − | 3.69940i | − | 0.142708i | ||||||
\(673\) | − | 21.2732i | − | 0.820023i | −0.912080 | − | 0.410012i | \(-0.865525\pi\) | ||
0.912080 | − | 0.410012i | \(-0.134475\pi\) | |||||||
\(674\) | 5.39266 | 0.207718 | ||||||||
\(675\) | 1.63469 | + | 4.72523i | 0.0629192 | + | 0.181874i | ||||
\(676\) | −32.7396 | −1.25922 | ||||||||
\(677\) | − | 8.51680i | − | 0.327327i | −0.986516 | − | 0.163664i | \(-0.947669\pi\) | ||
0.986516 | − | 0.163664i | \(-0.0523312\pi\) | |||||||
\(678\) | − | 5.72775i | − | 0.219973i | ||||||
\(679\) | −11.2496 | −0.431722 | ||||||||
\(680\) | −3.28568 | − | 19.5475i | −0.126000 | − | 0.749611i | ||||
\(681\) | −19.9513 | −0.764536 | ||||||||
\(682\) | 0.193479i | 0.00740870i | ||||||||
\(683\) | 17.2169i | 0.658785i | 0.944193 | + | 0.329393i | \(0.106844\pi\) | ||||
−0.944193 | + | 0.329393i | \(0.893156\pi\) | |||||||
\(684\) | −6.71955 | −0.256928 | ||||||||
\(685\) | −35.7334 | + | 6.00634i | −1.36530 | + | 0.229490i | ||||
\(686\) | 0.332438 | 0.0126926 | ||||||||
\(687\) | 3.18850i | 0.121649i | ||||||||
\(688\) | − | 10.8011i | − | 0.411787i | ||||||
\(689\) | 77.3517 | 2.94687 | ||||||||
\(690\) | −6.14459 | + | 1.03283i | −0.233920 | + | 0.0393191i | ||||
\(691\) | 41.7563 | 1.58848 | 0.794242 | − | 0.607602i | \(-0.207868\pi\) | ||||
0.794242 | + | 0.607602i | \(0.207868\pi\) | |||||||
\(692\) | 29.9799i | 1.13966i | ||||||||
\(693\) | − | 1.00000i | − | 0.0379869i | ||||||
\(694\) | −8.81853 | −0.334747 | ||||||||
\(695\) | −2.57572 | − | 15.3237i | −0.0977028 | − | 0.581262i | ||||
\(696\) | −10.6546 | −0.403861 | ||||||||
\(697\) | 42.4883i | 1.60936i | ||||||||
\(698\) | 9.77495i | 0.369987i | ||||||||
\(699\) | 7.68450 | 0.290655 | ||||||||
\(700\) | 3.08872 | + | 8.92825i | 0.116743 | + | 0.337456i | ||||
\(701\) | −8.05791 | −0.304343 | −0.152172 | − | 0.988354i | \(-0.548627\pi\) | ||||
−0.152172 | + | 0.988354i | \(0.548627\pi\) | |||||||
\(702\) | 1.83074i | 0.0690970i | ||||||||
\(703\) | − | 34.8807i | − | 1.31555i | ||||||
\(704\) | −5.46842 | −0.206099 | ||||||||
\(705\) | −2.49755 | − | 14.8586i | −0.0940631 | − | 0.559608i | ||||
\(706\) | −0.869313 | −0.0327170 | ||||||||
\(707\) | − | 15.7132i | − | 0.590957i | ||||||
\(708\) | − | 3.88557i | − | 0.146029i | ||||||
\(709\) | 13.4079 | 0.503543 | 0.251771 | − | 0.967787i | \(-0.418987\pi\) | ||||
0.251771 | + | 0.967787i | \(0.418987\pi\) | |||||||
\(710\) | 1.55675 | − | 0.261670i | 0.0584239 | − | 0.00982032i | ||||
\(711\) | −1.77494 | −0.0665655 | ||||||||
\(712\) | 2.89028i | 0.108318i | ||||||||
\(713\) | − | 4.87831i | − | 0.182694i | ||||||
\(714\) | 2.27910 | 0.0852931 | ||||||||
\(715\) | 12.1437 | − | 2.04120i | 0.454149 | − | 0.0763367i | ||||
\(716\) | 1.39362 | 0.0520822 | ||||||||
\(717\) | − | 11.5466i | − | 0.431215i | ||||||
\(718\) | − | 0.392306i | − | 0.0146407i | ||||||
\(719\) | 27.1797 | 1.01363 | 0.506815 | − | 0.862055i | \(-0.330823\pi\) | ||||
0.506815 | + | 0.862055i | \(0.330823\pi\) | |||||||
\(720\) | 1.24137 | + | 7.38526i | 0.0462631 | + | 0.275232i | ||||
\(721\) | 9.00401 | 0.335327 | ||||||||
\(722\) | 2.11192i | 0.0785975i | ||||||||
\(723\) | 2.94329i | 0.109462i | ||||||||
\(724\) | 30.5986 | 1.13719 | ||||||||
\(725\) | 38.9365 | − | 13.4700i | 1.44607 | − | 0.500265i | ||||
\(726\) | 0.332438 | 0.0123379 | ||||||||
\(727\) | − | 18.7437i | − | 0.695165i | −0.937649 | − | 0.347582i | \(-0.887003\pi\) | ||
0.937649 | − | 0.347582i | \(-0.112997\pi\) | |||||||
\(728\) | 7.12065i | 0.263909i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −0.127137 | − | 0.756374i | −0.00470555 | − | 0.0279947i | ||||
\(731\) | 22.1100 | 0.817766 | ||||||||
\(732\) | 21.1754i | 0.782667i | ||||||||
\(733\) | − | 15.1358i | − | 0.559053i | −0.960138 | − | 0.279526i | \(-0.909823\pi\) | ||
0.960138 | − | 0.279526i | \(-0.0901774\pi\) | |||||||
\(734\) | −3.10579 | −0.114637 | ||||||||
\(735\) | −2.20513 | + | 0.370655i | −0.0813376 | + | 0.0136718i | ||||
\(736\) | −31.0083 | −1.14298 | ||||||||
\(737\) | − | 1.52881i | − | 0.0563144i | ||||||
\(738\) | 2.06029i | 0.0758403i | ||||||||
\(739\) | −48.3650 | −1.77914 | −0.889568 | − | 0.456804i | \(-0.848994\pi\) | ||||
−0.889568 | + | 0.456804i | \(0.848994\pi\) | |||||||
\(740\) | −40.8665 | + | 6.86913i | −1.50228 | + | 0.252514i | ||||
\(741\) | 19.5845 | 0.719456 | ||||||||
\(742\) | − | 4.66944i | − | 0.171420i | ||||||
\(743\) | − | 4.53993i | − | 0.166554i | −0.996526 | − | 0.0832770i | \(-0.973461\pi\) | ||
0.996526 | − | 0.0832770i | \(-0.0265386\pi\) | |||||||
\(744\) | 0.752534 | 0.0275892 | ||||||||
\(745\) | −0.495994 | − | 2.95081i | −0.0181718 | − | 0.108109i | ||||
\(746\) | −4.70280 | −0.172182 | ||||||||
\(747\) | − | 4.43704i | − | 0.162343i | ||||||
\(748\) | − | 12.9538i | − | 0.473636i | ||||||
\(749\) | 7.11539 | 0.259991 | ||||||||
\(750\) | 1.78058 | + | 3.26250i | 0.0650178 | + | 0.119130i | ||||
\(751\) | −25.3018 | −0.923277 | −0.461639 | − | 0.887068i | \(-0.652738\pi\) | ||||
−0.461639 | + | 0.887068i | \(0.652738\pi\) | |||||||
\(752\) | − | 22.5671i | − | 0.822936i | ||||||
\(753\) | 19.3563i | 0.705382i | ||||||||
\(754\) | 15.0856 | 0.549384 | ||||||||
\(755\) | −2.84471 | − | 16.9240i | −0.103530 | − | 0.615928i | ||||
\(756\) | −1.88948 | −0.0687199 | ||||||||
\(757\) | 5.94684i | 0.216142i | 0.994143 | + | 0.108071i | \(0.0344673\pi\) | ||||
−0.994143 | + | 0.108071i | \(0.965533\pi\) | |||||||
\(758\) | − | 2.32592i | − | 0.0844812i | ||||||
\(759\) | −8.38198 | −0.304247 | ||||||||
\(760\) | −10.1399 | + | 1.70439i | −0.367814 | + | 0.0618249i | ||||
\(761\) | 23.3343 | 0.845867 | 0.422934 | − | 0.906161i | \(-0.361000\pi\) | ||||
0.422934 | + | 0.906161i | \(0.361000\pi\) | |||||||
\(762\) | 7.27460i | 0.263531i | ||||||||
\(763\) | − | 1.84137i | − | 0.0666622i | ||||||
\(764\) | −26.5780 | −0.961560 | ||||||||
\(765\) | −15.1177 | + | 2.54110i | −0.546583 | + | 0.0918737i | ||||
\(766\) | 0.00932174 | 0.000336808 | ||||||||
\(767\) | 11.3247i | 0.408912i | ||||||||
\(768\) | 7.87285i | 0.284087i | ||||||||
\(769\) | 36.2453 | 1.30704 | 0.653520 | − | 0.756909i | \(-0.273292\pi\) | ||||
0.653520 | + | 0.756909i | \(0.273292\pi\) | |||||||
\(770\) | −0.123220 | − | 0.733071i | −0.00444054 | − | 0.0264180i | ||||
\(771\) | −11.3301 | −0.408045 | ||||||||
\(772\) | 2.66301i | 0.0958440i | ||||||||
\(773\) | 36.7722i | 1.32261i | 0.750119 | + | 0.661303i | \(0.229996\pi\) | ||||
−0.750119 | + | 0.661303i | \(0.770004\pi\) | |||||||
\(774\) | 1.07213 | 0.0385369 | ||||||||
\(775\) | −2.75008 | + | 0.951388i | −0.0987859 | + | 0.0341749i | ||||
\(776\) | −14.5459 | −0.522169 | ||||||||
\(777\) | − | 9.80818i | − | 0.351867i | ||||||
\(778\) | − | 9.65974i | − | 0.346318i | ||||||
\(779\) | 22.0401 | 0.789669 | ||||||||
\(780\) | −3.85683 | − | 22.9454i | −0.138097 | − | 0.821576i | ||||
\(781\) | 2.12361 | 0.0759886 | ||||||||
\(782\) | − | 19.1034i | − | 0.683135i | ||||||
\(783\) | 8.24013i | 0.294478i | ||||||||
\(784\) | −3.34912 | −0.119612 | ||||||||
\(785\) | 31.6855 | − | 5.32592i | 1.13090 | − | 0.190090i | ||||
\(786\) | −0.864455 | −0.0308341 | ||||||||
\(787\) | − | 53.8452i | − | 1.91937i | −0.281071 | − | 0.959687i | \(-0.590690\pi\) | ||
0.281071 | − | 0.959687i | \(-0.409310\pi\) | |||||||
\(788\) | − | 4.47020i | − | 0.159244i | ||||||
\(789\) | −3.36193 | −0.119688 | ||||||||
\(790\) | −1.30116 | + | 0.218708i | −0.0462931 | + | 0.00778129i | ||||
\(791\) | −17.2295 | −0.612611 | ||||||||
\(792\) | − | 1.29301i | − | 0.0459452i | ||||||
\(793\) | − | 61.7172i | − | 2.19164i | ||||||
\(794\) | −11.5262 | −0.409050 | ||||||||
\(795\) | 5.20623 | + | 30.9734i | 0.184646 | + | 1.09851i | ||||
\(796\) | −14.5296 | −0.514988 | ||||||||
\(797\) | − | 16.1632i | − | 0.572529i | −0.958151 | − | 0.286264i | \(-0.907586\pi\) | ||
0.958151 | − | 0.286264i | \(-0.0924136\pi\) | |||||||
\(798\) | − | 1.18225i | − | 0.0418511i | ||||||
\(799\) | 46.1951 | 1.63427 | ||||||||
\(800\) | 6.04737 | + | 17.4805i | 0.213807 | + | 0.618030i | ||||
\(801\) | 2.23530 | 0.0789806 | ||||||||
\(802\) | − | 11.7499i | − | 0.414903i | ||||||
\(803\) | − | 1.03179i | − | 0.0364110i | ||||||
\(804\) | −2.88866 | −0.101875 | ||||||||
\(805\) | 3.10682 | + | 18.4834i | 0.109501 | + | 0.651454i | ||||
\(806\) | −1.06549 | −0.0375304 | ||||||||
\(807\) | 6.35047i | 0.223547i | ||||||||
\(808\) | − | 20.3174i | − | 0.714764i | ||||||
\(809\) | 42.7944 | 1.50457 | 0.752286 | − | 0.658837i | \(-0.228951\pi\) | ||||
0.752286 | + | 0.658837i | \(0.228951\pi\) | |||||||
\(810\) | −0.733071 | + | 0.123220i | −0.0257575 | + | 0.00432951i | ||||
\(811\) | −41.4027 | −1.45384 | −0.726922 | − | 0.686720i | \(-0.759050\pi\) | ||||
−0.726922 | + | 0.686720i | \(0.759050\pi\) | |||||||
\(812\) | 15.5696i | 0.546386i | ||||||||
\(813\) | 14.2641i | 0.500265i | ||||||||
\(814\) | 3.26062 | 0.114285 | ||||||||
\(815\) | 27.6485 | − | 4.64736i | 0.968483 | − | 0.162790i | ||||
\(816\) | −22.9606 | −0.803782 | ||||||||
\(817\) | − | 11.4692i | − | 0.401256i | ||||||
\(818\) | − | 4.50626i | − | 0.157558i | ||||||
\(819\) | 5.50702 | 0.192431 | ||||||||
\(820\) | −4.34041 | − | 25.8223i | −0.151574 | − | 0.901755i | ||||
\(821\) | 42.0113 | 1.46620 | 0.733102 | − | 0.680119i | \(-0.238072\pi\) | ||||
0.733102 | + | 0.680119i | \(0.238072\pi\) | |||||||
\(822\) | − | 5.38705i | − | 0.187895i | ||||||
\(823\) | − | 4.54879i | − | 0.158561i | −0.996852 | − | 0.0792804i | \(-0.974738\pi\) | ||
0.996852 | − | 0.0792804i | \(-0.0252622\pi\) | |||||||
\(824\) | 11.6423 | 0.405579 | ||||||||
\(825\) | 1.63469 | + | 4.72523i | 0.0569125 | + | 0.164511i | ||||
\(826\) | 0.683632 | 0.0237866 | ||||||||
\(827\) | 51.8270i | 1.80220i | 0.433609 | + | 0.901101i | \(0.357240\pi\) | ||||
−0.433609 | + | 0.901101i | \(0.642760\pi\) | |||||||
\(828\) | 15.8376i | 0.550396i | ||||||||
\(829\) | −0.130463 | −0.00453116 | −0.00226558 | − | 0.999997i | \(-0.500721\pi\) | ||||
−0.00226558 | + | 0.999997i | \(0.500721\pi\) | |||||||
\(830\) | −0.546731 | − | 3.25266i | −0.0189773 | − | 0.112902i | ||||
\(831\) | −24.0288 | −0.833549 | ||||||||
\(832\) | − | 30.1147i | − | 1.04404i | ||||||
\(833\) | − | 6.85571i | − | 0.237536i | ||||||
\(834\) | 2.31015 | 0.0799940 | ||||||||
\(835\) | 8.91182 | − | 1.49796i | 0.308406 | − | 0.0518392i | ||||
\(836\) | −6.71955 | −0.232401 | ||||||||
\(837\) | − | 0.582000i | − | 0.0201169i | ||||||
\(838\) | 5.86142i | 0.202480i | ||||||||
\(839\) | 46.9683 | 1.62153 | 0.810763 | − | 0.585375i | \(-0.199053\pi\) | ||||
0.810763 | + | 0.585375i | \(0.199053\pi\) | |||||||
\(840\) | −2.85127 | + | 0.479262i | −0.0983781 | + | 0.0165361i | ||||
\(841\) | 38.8997 | 1.34137 | ||||||||
\(842\) | − | 3.36072i | − | 0.115818i | ||||||
\(843\) | 11.6299i | 0.400554i | ||||||||
\(844\) | −47.0849 | −1.62073 | ||||||||
\(845\) | 6.42244 | + | 38.2090i | 0.220939 | + | 1.31443i | ||||
\(846\) | 2.24004 | 0.0770140 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 47.0418i | 1.61542i | ||||||||
\(849\) | −7.02079 | −0.240953 | ||||||||
\(850\) | −10.7693 | + | 3.72562i | −0.369383 | + | 0.127788i | ||||
\(851\) | −82.2120 | −2.81819 | ||||||||
\(852\) | − | 4.01252i | − | 0.137467i | ||||||
\(853\) | 35.5217i | 1.21624i | 0.793845 | + | 0.608120i | \(0.208076\pi\) | ||||
−0.793845 | + | 0.608120i | \(0.791924\pi\) | |||||||
\(854\) | −3.72563 | −0.127489 | ||||||||
\(855\) | 1.31816 | + | 7.84209i | 0.0450800 | + | 0.268194i | ||||
\(856\) | 9.20030 | 0.314460 | ||||||||
\(857\) | − | 37.8906i | − | 1.29432i | −0.762355 | − | 0.647160i | \(-0.775957\pi\) | ||
0.762355 | − | 0.647160i | \(-0.224043\pi\) | |||||||
\(858\) | 1.83074i | 0.0625006i | ||||||||
\(859\) | 47.6594 | 1.62612 | 0.813059 | − | 0.582182i | \(-0.197801\pi\) | ||||
0.813059 | + | 0.582182i | \(0.197801\pi\) | |||||||
\(860\) | −13.4374 | + | 2.25865i | −0.458210 | + | 0.0770194i | ||||
\(861\) | 6.19751 | 0.211210 | ||||||||
\(862\) | − | 9.12633i | − | 0.310844i | ||||||
\(863\) | − | 12.3002i | − | 0.418703i | −0.977840 | − | 0.209352i | \(-0.932865\pi\) | ||
0.977840 | − | 0.209352i | \(-0.0671353\pi\) | |||||||
\(864\) | −3.69940 | −0.125856 | ||||||||
\(865\) | 34.9882 | − | 5.88107i | 1.18963 | − | 0.199962i | ||||
\(866\) | −11.7515 | −0.399331 | ||||||||
\(867\) | − | 30.0007i | − | 1.01888i | ||||||
\(868\) | − | 1.09968i | − | 0.0373256i | ||||||
\(869\) | −1.77494 | −0.0602108 | ||||||||
\(870\) | 1.01535 | + | 6.04060i | 0.0344235 | + | 0.204795i | ||||
\(871\) | 8.41918 | 0.285273 | ||||||||
\(872\) | − | 2.38092i | − | 0.0806281i | ||||||
\(873\) | 11.2496i | 0.380743i | ||||||||
\(874\) | −9.90957 | −0.335196 | ||||||||
\(875\) | 9.81386 | − | 5.35614i | 0.331769 | − | 0.181070i | ||||
\(876\) | −1.94955 | −0.0658692 | ||||||||
\(877\) | 26.0524i | 0.879727i | 0.898065 | + | 0.439864i | \(0.144973\pi\) | ||||
−0.898065 | + | 0.439864i | \(0.855027\pi\) | |||||||
\(878\) | 5.66762i | 0.191273i | ||||||||
\(879\) | −12.3870 | −0.417804 | ||||||||
\(880\) | 1.24137 | + | 7.38526i | 0.0418465 | + | 0.248957i | ||||
\(881\) | 19.1202 | 0.644176 | 0.322088 | − | 0.946710i | \(-0.395615\pi\) | ||||
0.322088 | + | 0.946710i | \(0.395615\pi\) | |||||||
\(882\) | − | 0.332438i | − | 0.0111938i | ||||||
\(883\) | 46.6003i | 1.56823i | 0.620618 | + | 0.784113i | \(0.286882\pi\) | ||||
−0.620618 | + | 0.784113i | \(0.713118\pi\) | |||||||
\(884\) | 71.3366 | 2.39931 | ||||||||
\(885\) | −4.53467 | + | 0.762221i | −0.152431 | + | 0.0256218i | ||||
\(886\) | 9.85426 | 0.331060 | ||||||||
\(887\) | − | 43.9801i | − | 1.47671i | −0.674413 | − | 0.738354i | \(-0.735603\pi\) | ||
0.674413 | − | 0.738354i | \(-0.264397\pi\) | |||||||
\(888\) | − | 12.6821i | − | 0.425584i | ||||||
\(889\) | 21.8825 | 0.733917 | ||||||||
\(890\) | 1.63864 | − | 0.275434i | 0.0549272 | − | 0.00923257i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 24.0696i | 0.805909i | ||||||||
\(893\) | − | 23.9630i | − | 0.801890i | ||||||
\(894\) | 0.444854 | 0.0148782 | ||||||||
\(895\) | −0.273383 | − | 1.62644i | −0.00913820 | − | 0.0543658i | ||||
\(896\) | −9.21672 | −0.307909 | ||||||||
\(897\) | − | 46.1597i | − | 1.54123i | ||||||
\(898\) | 1.90931i | 0.0637146i | ||||||||
\(899\) | −4.79575 | −0.159947 | ||||||||
\(900\) | 8.92825 | − | 3.08872i | 0.297608 | − | 0.102957i | ||||
\(901\) | −96.2954 | −3.20806 | ||||||||
\(902\) | 2.06029i | 0.0686001i | ||||||||
\(903\) | − | 3.22504i | − | 0.107323i | ||||||
\(904\) | −22.2780 | −0.740955 | ||||||||
\(905\) | −6.00245 | − | 35.7103i | −0.199528 | − | 1.18705i | ||||
\(906\) | 2.55141 | 0.0847648 | ||||||||
\(907\) | 52.4317i | 1.74097i | 0.492199 | + | 0.870483i | \(0.336193\pi\) | ||||
−0.492199 | + | 0.870483i | \(0.663807\pi\) | |||||||
\(908\) | 37.6977i | 1.25104i | ||||||||
\(909\) | −15.7132 | −0.521175 | ||||||||
\(910\) | 4.03704 | − | 0.678575i | 0.133826 | − | 0.0224945i | ||||
\(911\) | 6.08013 | 0.201444 | 0.100722 | − | 0.994915i | \(-0.467885\pi\) | ||||
0.100722 | + | 0.994915i | \(0.467885\pi\) | |||||||
\(912\) | 11.9104i | 0.394394i | ||||||||
\(913\) | − | 4.43704i | − | 0.146844i | ||||||
\(914\) | 12.2569 | 0.405422 | ||||||||
\(915\) | 24.7129 | − | 4.15393i | 0.816984 | − | 0.137325i | ||||
\(916\) | 6.02462 | 0.199059 | ||||||||
\(917\) | 2.60035i | 0.0858710i | ||||||||
\(918\) | − | 2.27910i | − | 0.0752215i | ||||||
\(919\) | −44.3509 | −1.46300 | −0.731500 | − | 0.681841i | \(-0.761180\pi\) | ||||
−0.731500 | + | 0.681841i | \(0.761180\pi\) | |||||||
\(920\) | 4.01717 | + | 23.8993i | 0.132442 | + | 0.787936i | ||||
\(921\) | −8.76620 | −0.288856 | ||||||||
\(922\) | − | 6.53988i | − | 0.215379i | ||||||
\(923\) | 11.6947i | 0.384937i | ||||||||
\(924\) | −1.88948 | −0.0621595 | ||||||||
\(925\) | 16.0333 | + | 46.3459i | 0.527172 | + | 1.52384i | ||||
\(926\) | −11.9673 | −0.393271 | ||||||||
\(927\) | − | 9.00401i | − | 0.295731i | ||||||
\(928\) | 30.4836i | 1.00067i | ||||||||
\(929\) | 14.1527 | 0.464336 | 0.232168 | − | 0.972676i | \(-0.425418\pi\) | ||||
0.232168 | + | 0.972676i | \(0.425418\pi\) | |||||||
\(930\) | −0.0717140 | − | 0.426647i | −0.00235159 | − | 0.0139903i | ||||
\(931\) | −3.55629 | −0.116553 | ||||||||
\(932\) | − | 14.5198i | − | 0.475610i | ||||||
\(933\) | − | 13.6554i | − | 0.447058i | ||||||
\(934\) | −3.98818 | −0.130497 | ||||||||
\(935\) | −15.1177 | + | 2.54110i | −0.494403 | + | 0.0831029i | ||||
\(936\) | 7.12065 | 0.232746 | ||||||||
\(937\) | 4.00932i | 0.130979i | 0.997853 | + | 0.0654894i | \(0.0208609\pi\) | ||||
−0.997853 | + | 0.0654894i | \(0.979139\pi\) | |||||||
\(938\) | − | 0.508234i | − | 0.0165944i | ||||||
\(939\) | −20.7806 | −0.678150 | ||||||||
\(940\) | −28.0752 | + | 4.71908i | −0.915711 | + | 0.153919i | ||||
\(941\) | −11.6092 | −0.378449 | −0.189224 | − | 0.981934i | \(-0.560597\pi\) | ||||
−0.189224 | + | 0.981934i | \(0.560597\pi\) | |||||||
\(942\) | 4.77679i | 0.155636i | ||||||||
\(943\) | − | 51.9474i | − | 1.69164i | ||||||
\(944\) | −6.88719 | −0.224159 | ||||||||
\(945\) | 0.370655 | + | 2.20513i | 0.0120574 | + | 0.0717330i | ||||
\(946\) | 1.07213 | 0.0348579 | ||||||||
\(947\) | − | 4.89950i | − | 0.159212i | −0.996826 | − | 0.0796062i | \(-0.974634\pi\) | ||
0.996826 | − | 0.0796062i | \(-0.0253663\pi\) | |||||||
\(948\) | 3.35373i | 0.108924i | ||||||||
\(949\) | 5.68208 | 0.184448 | ||||||||
\(950\) | 1.93260 | + | 5.58638i | 0.0627019 | + | 0.181246i | ||||
\(951\) | 10.4361 | 0.338413 | ||||||||
\(952\) | − | 8.86452i | − | 0.287301i | ||||||
\(953\) | − | 13.1770i | − | 0.426844i | −0.976960 | − | 0.213422i | \(-0.931539\pi\) | ||
0.976960 | − | 0.213422i | \(-0.0684609\pi\) | |||||||
\(954\) | −4.66944 | −0.151179 | ||||||||
\(955\) | 5.21374 | + | 31.0181i | 0.168713 | + | 1.00372i | ||||
\(956\) | −21.8171 | −0.705616 | ||||||||
\(957\) | 8.24013i | 0.266365i | ||||||||
\(958\) | − | 2.47853i | − | 0.0800778i | ||||||
\(959\) | −16.2047 | −0.523276 | ||||||||
\(960\) | 12.0586 | − | 2.02690i | 0.389190 | − | 0.0654178i | ||||
\(961\) | −30.6613 | −0.989073 | ||||||||
\(962\) | 17.9563i | 0.578934i | ||||||||
\(963\) | − | 7.11539i | − | 0.229290i | ||||||
\(964\) | 5.56130 | 0.179117 | ||||||||
\(965\) | 3.10789 | − | 0.522396i | 0.100046 | − | 0.0168165i | ||||
\(966\) | −2.78649 | −0.0896539 | ||||||||
\(967\) | − | 1.72537i | − | 0.0554841i | −0.999615 | − | 0.0277420i | \(-0.991168\pi\) | ||
0.999615 | − | 0.0277420i | \(-0.00883170\pi\) | |||||||
\(968\) | − | 1.29301i | − | 0.0415590i | ||||||
\(969\) | −24.3809 | −0.783226 | ||||||||
\(970\) | 1.38618 | + | 8.24679i | 0.0445076 | + | 0.264788i | ||||
\(971\) | 41.2450 | 1.32362 | 0.661808 | − | 0.749674i | \(-0.269790\pi\) | ||||
0.661808 | + | 0.749674i | \(0.269790\pi\) | |||||||
\(972\) | 1.88948i | 0.0606053i | ||||||||
\(973\) | − | 6.94911i | − | 0.222778i | ||||||
\(974\) | −8.40805 | −0.269411 | ||||||||
\(975\) | −26.0219 | + | 9.00226i | −0.833369 | + | 0.288303i | ||||
\(976\) | 37.5336 | 1.20142 | ||||||||
\(977\) | − | 59.1538i | − | 1.89250i | −0.323438 | − | 0.946249i | \(-0.604839\pi\) | ||
0.323438 | − | 0.946249i | \(-0.395161\pi\) | |||||||
\(978\) | 4.16819i | 0.133284i | ||||||||
\(979\) | 2.23530 | 0.0714406 | ||||||||
\(980\) | 0.700347 | + | 4.16657i | 0.0223718 | + | 0.133096i | ||||
\(981\) | −1.84137 | −0.0587905 | ||||||||
\(982\) | 7.39408i | 0.235955i | ||||||||
\(983\) | 22.6606i | 0.722761i | 0.932418 | + | 0.361381i | \(0.117695\pi\) | ||||
−0.932418 | + | 0.361381i | \(0.882305\pi\) | |||||||
\(984\) | 8.01346 | 0.255460 | ||||||||
\(985\) | −5.21697 | + | 0.876906i | −0.166226 | + | 0.0279406i | ||||
\(986\) | −18.7801 | −0.598079 | ||||||||
\(987\) | − | 6.73820i | − | 0.214479i | ||||||
\(988\) | − | 37.0047i | − | 1.17728i | ||||||
\(989\) | −27.0323 | −0.859576 | ||||||||
\(990\) | −0.733071 | + | 0.123220i | −0.0232985 | + | 0.00391619i | ||||
\(991\) | 57.8514 | 1.83771 | 0.918855 | − | 0.394595i | \(-0.129115\pi\) | ||||
0.918855 | + | 0.394595i | \(0.129115\pi\) | |||||||
\(992\) | − | 2.15305i | − | 0.0683595i | ||||||
\(993\) | − | 6.63873i | − | 0.210674i | ||||||
\(994\) | 0.705968 | 0.0223919 | ||||||||
\(995\) | 2.85023 | + | 16.9569i | 0.0903584 | + | 0.537568i | ||||
\(996\) | −8.38371 | −0.265648 | ||||||||
\(997\) | − | 13.9388i | − | 0.441446i | −0.975337 | − | 0.220723i | \(-0.929158\pi\) | ||
0.975337 | − | 0.220723i | \(-0.0708417\pi\) | |||||||
\(998\) | − | 3.97418i | − | 0.125800i | ||||||
\(999\) | −9.80818 | −0.310317 |
(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.e.694.10 | ✓ | 20 | |
5.2 | odd | 4 | 5775.2.a.cp.1.5 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cm.1.6 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.e.694.11 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.e.694.10 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1155.2.c.e.694.11 | yes | 20 | 5.4 | even | 2 | inner | |
5775.2.a.cm.1.6 | 10 | 5.3 | odd | 4 | |||
5775.2.a.cp.1.5 | 10 | 5.2 | odd | 4 |