Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(165,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.e (of order \(3\), 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: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Root | \(0.809017 + 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.165 |
Dual form | 287.2.e.a.247.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 1.40126i | −0.572061 | − | 0.990839i | −0.996354 | − | 0.0853143i | \(-0.972811\pi\) |
0.424293 | − | 0.905525i | \(-0.360523\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) |
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | −0.309017 | + | 0.535233i | −0.154508 | + | 0.267617i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0.809017 | − | 1.40126i | 0.255834 | − | 0.443117i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | −0.309017 | − | 0.535233i | −0.0892055 | − | 0.154508i | ||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 4.04508 | + | 1.40126i | 1.08109 | + | 0.374502i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 2.42705 | + | 4.20378i | 0.606763 | + | 1.05094i | ||||
\(17\) | −2.11803 | + | 3.66854i | −0.513699 | + | 0.889752i | 0.486175 | + | 0.873861i | \(0.338392\pi\) |
−0.999874 | + | 0.0158908i | \(0.994942\pi\) | |||||||
\(18\) | 1.61803 | − | 2.80252i | 0.381374 | − | 0.660560i | ||||
\(19\) | −0.736068 | − | 1.27491i | −0.168866 | − | 0.292484i | 0.769156 | − | 0.639061i | \(-0.220677\pi\) |
−0.938021 | + | 0.346578i | \(0.887344\pi\) | |||||||
\(20\) | −0.618034 | −0.138197 | ||||||||
\(21\) | −0.500000 | − | 2.59808i | −0.109109 | − | 0.566947i | ||||
\(22\) | 1.61803 | 0.344966 | ||||||||
\(23\) | 4.35410 | + | 7.54153i | 0.907893 | + | 1.57252i | 0.816986 | + | 0.576657i | \(0.195643\pi\) |
0.0909070 | + | 0.995859i | \(0.471023\pi\) | |||||||
\(24\) | 1.11803 | − | 1.93649i | 0.228218 | − | 0.395285i | ||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 3.61803 | + | 6.26662i | 0.709555 | + | 1.22899i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −0.309017 | − | 1.60570i | −0.0583987 | − | 0.303449i | ||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0.809017 | + | 1.40126i | 0.147706 | + | 0.255834i | ||||
\(31\) | 0.118034 | − | 0.204441i | 0.0211995 | − | 0.0367187i | −0.855231 | − | 0.518247i | \(-0.826585\pi\) |
0.876431 | + | 0.481528i | \(0.159918\pi\) | |||||||
\(32\) | 1.69098 | − | 2.92887i | 0.298926 | − | 0.517756i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 6.85410 | 1.17547 | ||||||||
\(35\) | −2.50000 | − | 0.866025i | −0.422577 | − | 0.146385i | ||||
\(36\) | −1.23607 | −0.206011 | ||||||||
\(37\) | 1.73607 | + | 3.00696i | 0.285408 | + | 0.494341i | 0.972708 | − | 0.232033i | \(-0.0745376\pi\) |
−0.687300 | + | 0.726374i | \(0.741204\pi\) | |||||||
\(38\) | −1.19098 | + | 2.06284i | −0.193203 | + | 0.334637i | ||||
\(39\) | 2.23607 | − | 3.87298i | 0.358057 | − | 0.620174i | ||||
\(40\) | −1.11803 | − | 1.93649i | −0.176777 | − | 0.306186i | ||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | −3.23607 | + | 2.80252i | −0.499336 | + | 0.432438i | ||||
\(43\) | −6.47214 | −0.986991 | −0.493496 | − | 0.869748i | \(-0.664281\pi\) | ||||
−0.493496 | + | 0.869748i | \(0.664281\pi\) | |||||||
\(44\) | −0.309017 | − | 0.535233i | −0.0465861 | − | 0.0806894i | ||||
\(45\) | −1.00000 | + | 1.73205i | −0.149071 | + | 0.258199i | ||||
\(46\) | 7.04508 | − | 12.2024i | 1.03874 | − | 1.79915i | ||||
\(47\) | 1.73607 | + | 3.00696i | 0.253232 | + | 0.438610i | 0.964414 | − | 0.264398i | \(-0.0851732\pi\) |
−0.711182 | + | 0.703008i | \(0.751840\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | −6.47214 | −0.915298 | ||||||||
\(51\) | −2.11803 | − | 3.66854i | −0.296584 | − | 0.513699i | ||||
\(52\) | 1.38197 | − | 2.39364i | 0.191644 | − | 0.331937i | ||||
\(53\) | 5.11803 | − | 8.86469i | 0.703016 | − | 1.21766i | −0.264387 | − | 0.964417i | \(-0.585170\pi\) |
0.967403 | − | 0.253243i | \(-0.0814971\pi\) | |||||||
\(54\) | 4.04508 | + | 7.00629i | 0.550466 | + | 0.953436i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 4.47214 | − | 3.87298i | 0.597614 | − | 0.517549i | ||||
\(57\) | 1.47214 | 0.194989 | ||||||||
\(58\) | −3.61803 | − | 6.26662i | −0.475071 | − | 0.822847i | ||||
\(59\) | −4.35410 | + | 7.54153i | −0.566856 | + | 0.981823i | 0.430019 | + | 0.902820i | \(0.358507\pi\) |
−0.996874 | + | 0.0790030i | \(0.974826\pi\) | |||||||
\(60\) | 0.309017 | − | 0.535233i | 0.0398939 | − | 0.0690983i | ||||
\(61\) | −4.73607 | − | 8.20311i | −0.606391 | − | 1.05030i | −0.991830 | − | 0.127567i | \(-0.959283\pi\) |
0.385439 | − | 0.922733i | \(-0.374050\pi\) | |||||||
\(62\) | −0.381966 | −0.0485097 | ||||||||
\(63\) | −5.00000 | − | 1.73205i | −0.629941 | − | 0.218218i | ||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −2.23607 | − | 3.87298i | −0.277350 | − | 0.480384i | ||||
\(66\) | −0.809017 | + | 1.40126i | −0.0995831 | + | 0.172483i | ||||
\(67\) | −2.97214 | + | 5.14789i | −0.363104 | + | 0.628915i | −0.988470 | − | 0.151417i | \(-0.951616\pi\) |
0.625366 | + | 0.780332i | \(0.284950\pi\) | |||||||
\(68\) | −1.30902 | − | 2.26728i | −0.158742 | − | 0.274949i | ||||
\(69\) | −8.70820 | −1.04834 | ||||||||
\(70\) | 0.809017 | + | 4.20378i | 0.0966960 | + | 0.502447i | ||||
\(71\) | −14.4721 | −1.71753 | −0.858763 | − | 0.512373i | \(-0.828767\pi\) | ||||
−0.858763 | + | 0.512373i | \(0.828767\pi\) | |||||||
\(72\) | −2.23607 | − | 3.87298i | −0.263523 | − | 0.456435i | ||||
\(73\) | 1.26393 | − | 2.18919i | 0.147932 | − | 0.256226i | −0.782531 | − | 0.622612i | \(-0.786072\pi\) |
0.930463 | + | 0.366386i | \(0.119405\pi\) | |||||||
\(74\) | 2.80902 | − | 4.86536i | 0.326542 | − | 0.565587i | ||||
\(75\) | 2.00000 | + | 3.46410i | 0.230940 | + | 0.400000i | ||||
\(76\) | 0.909830 | 0.104365 | ||||||||
\(77\) | −0.500000 | − | 2.59808i | −0.0569803 | − | 0.296078i | ||||
\(78\) | −7.23607 | −0.819323 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | −2.42705 | + | 4.20378i | −0.271353 | + | 0.469996i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.809017 | + | 1.40126i | 0.0893410 | + | 0.154743i | ||||
\(83\) | −1.52786 | −0.167705 | −0.0838524 | − | 0.996478i | \(-0.526722\pi\) | ||||
−0.0838524 | + | 0.996478i | \(0.526722\pi\) | |||||||
\(84\) | 1.54508 | + | 0.535233i | 0.168583 | + | 0.0583987i | ||||
\(85\) | −4.23607 | −0.459466 | ||||||||
\(86\) | 5.23607 | + | 9.06914i | 0.564620 | + | 0.977950i | ||||
\(87\) | −2.23607 | + | 3.87298i | −0.239732 | + | 0.415227i | ||||
\(88\) | 1.11803 | − | 1.93649i | 0.119183 | − | 0.206431i | ||||
\(89\) | 7.11803 | + | 12.3288i | 0.754510 | + | 1.30685i | 0.945618 | + | 0.325281i | \(0.105459\pi\) |
−0.191107 | + | 0.981569i | \(0.561208\pi\) | |||||||
\(90\) | 3.23607 | 0.341112 | ||||||||
\(91\) | 8.94427 | − | 7.74597i | 0.937614 | − | 0.811998i | ||||
\(92\) | −5.38197 | −0.561109 | ||||||||
\(93\) | 0.118034 | + | 0.204441i | 0.0122396 | + | 0.0211995i | ||||
\(94\) | 2.80902 | − | 4.86536i | 0.289728 | − | 0.501824i | ||||
\(95\) | 0.736068 | − | 1.27491i | 0.0755190 | − | 0.130803i | ||||
\(96\) | 1.69098 | + | 2.92887i | 0.172585 | + | 0.298926i | ||||
\(97\) | 8.47214 | 0.860215 | 0.430108 | − | 0.902778i | \(-0.358476\pi\) | ||||
0.430108 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(98\) | −10.5172 | + | 4.20378i | −1.06240 | + | 0.424645i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 1.23607 | + | 2.14093i | 0.123607 | + | 0.214093i | ||||
\(101\) | −1.64590 | + | 2.85078i | −0.163773 | + | 0.283663i | −0.936219 | − | 0.351417i | \(-0.885700\pi\) |
0.772446 | + | 0.635081i | \(0.219033\pi\) | |||||||
\(102\) | −3.42705 | + | 5.93583i | −0.339329 | + | 0.587734i | ||||
\(103\) | −8.59017 | − | 14.8786i | −0.846415 | − | 1.46603i | −0.884387 | − | 0.466754i | \(-0.845423\pi\) |
0.0379724 | − | 0.999279i | \(-0.487910\pi\) | |||||||
\(104\) | 10.0000 | 0.980581 | ||||||||
\(105\) | 2.00000 | − | 1.73205i | 0.195180 | − | 0.169031i | ||||
\(106\) | −16.5623 | −1.60867 | ||||||||
\(107\) | 0.645898 | + | 1.11873i | 0.0624413 | + | 0.108152i | 0.895556 | − | 0.444949i | \(-0.146778\pi\) |
−0.833115 | + | 0.553100i | \(0.813445\pi\) | |||||||
\(108\) | 1.54508 | − | 2.67617i | 0.148676 | − | 0.257514i | ||||
\(109\) | 7.11803 | − | 12.3288i | 0.681784 | − | 1.18088i | −0.292652 | − | 0.956219i | \(-0.594538\pi\) |
0.974436 | − | 0.224666i | \(-0.0721289\pi\) | |||||||
\(110\) | 0.809017 | + | 1.40126i | 0.0771367 | + | 0.133605i | ||||
\(111\) | −3.47214 | −0.329561 | ||||||||
\(112\) | −12.1353 | − | 4.20378i | −1.14667 | − | 0.397219i | ||||
\(113\) | 19.8885 | 1.87096 | 0.935478 | − | 0.353384i | \(-0.114969\pi\) | ||||
0.935478 | + | 0.353384i | \(0.114969\pi\) | |||||||
\(114\) | −1.19098 | − | 2.06284i | −0.111546 | − | 0.193203i | ||||
\(115\) | −4.35410 | + | 7.54153i | −0.406022 | + | 0.703251i | ||||
\(116\) | −1.38197 | + | 2.39364i | −0.128312 | + | 0.222243i | ||||
\(117\) | −4.47214 | − | 7.74597i | −0.413449 | − | 0.716115i | ||||
\(118\) | 14.0902 | 1.29711 | ||||||||
\(119\) | −2.11803 | − | 11.0056i | −0.194160 | − | 1.00888i | ||||
\(120\) | 2.23607 | 0.204124 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | −7.66312 | + | 13.2729i | −0.693786 | + | 1.20167i | ||||
\(123\) | 0.500000 | − | 0.866025i | 0.0450835 | − | 0.0780869i | ||||
\(124\) | 0.0729490 | + | 0.126351i | 0.00655102 | + | 0.0113467i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 1.61803 | + | 8.40755i | 0.144146 | + | 0.749004i | ||||
\(127\) | 15.4164 | 1.36798 | 0.683992 | − | 0.729489i | \(-0.260242\pi\) | ||||
0.683992 | + | 0.729489i | \(0.260242\pi\) | |||||||
\(128\) | −6.80902 | − | 11.7936i | −0.601838 | − | 1.04241i | ||||
\(129\) | 3.23607 | − | 5.60503i | 0.284920 | − | 0.493496i | ||||
\(130\) | −3.61803 | + | 6.26662i | −0.317323 | + | 0.549619i | ||||
\(131\) | 6.82624 | + | 11.8234i | 0.596411 | + | 1.03301i | 0.993346 | + | 0.115168i | \(0.0367405\pi\) |
−0.396935 | + | 0.917847i | \(0.629926\pi\) | |||||||
\(132\) | 0.618034 | 0.0537930 | ||||||||
\(133\) | 3.68034 | + | 1.27491i | 0.319126 | + | 0.110548i | ||||
\(134\) | 9.61803 | 0.830872 | ||||||||
\(135\) | −2.50000 | − | 4.33013i | −0.215166 | − | 0.372678i | ||||
\(136\) | 4.73607 | − | 8.20311i | 0.406114 | − | 0.703411i | ||||
\(137\) | −7.82624 | + | 13.5554i | −0.668641 | + | 1.15812i | 0.309644 | + | 0.950853i | \(0.399790\pi\) |
−0.978284 | + | 0.207267i | \(0.933543\pi\) | |||||||
\(138\) | 7.04508 | + | 12.2024i | 0.599717 | + | 1.03874i | ||||
\(139\) | 16.9443 | 1.43719 | 0.718597 | − | 0.695427i | \(-0.244785\pi\) | ||||
0.718597 | + | 0.695427i | \(0.244785\pi\) | |||||||
\(140\) | 1.23607 | − | 1.07047i | 0.104467 | − | 0.0904709i | ||||
\(141\) | −3.47214 | −0.292407 | ||||||||
\(142\) | 11.7082 | + | 20.2792i | 0.982531 | + | 1.70179i | ||||
\(143\) | 2.23607 | − | 3.87298i | 0.186989 | − | 0.323875i | ||||
\(144\) | −4.85410 | + | 8.40755i | −0.404508 | + | 0.700629i | ||||
\(145\) | 2.23607 | + | 3.87298i | 0.185695 | + | 0.321634i | ||||
\(146\) | −4.09017 | −0.338505 | ||||||||
\(147\) | 5.50000 | + | 4.33013i | 0.453632 | + | 0.357143i | ||||
\(148\) | −2.14590 | −0.176392 | ||||||||
\(149\) | −0.590170 | − | 1.02220i | −0.0483486 | − | 0.0837422i | 0.840838 | − | 0.541286i | \(-0.182063\pi\) |
−0.889187 | + | 0.457544i | \(0.848729\pi\) | |||||||
\(150\) | 3.23607 | − | 5.60503i | 0.264224 | − | 0.457649i | ||||
\(151\) | −2.97214 | + | 5.14789i | −0.241869 | + | 0.418929i | −0.961247 | − | 0.275690i | \(-0.911094\pi\) |
0.719378 | + | 0.694619i | \(0.244427\pi\) | |||||||
\(152\) | 1.64590 | + | 2.85078i | 0.133500 | + | 0.231229i | ||||
\(153\) | −8.47214 | −0.684932 | ||||||||
\(154\) | −3.23607 | + | 2.80252i | −0.260770 | + | 0.225833i | ||||
\(155\) | 0.236068 | 0.0189614 | ||||||||
\(156\) | 1.38197 | + | 2.39364i | 0.110646 | + | 0.191644i | ||||
\(157\) | 1.11803 | − | 1.93649i | 0.0892288 | − | 0.154549i | −0.817957 | − | 0.575280i | \(-0.804893\pi\) |
0.907185 | + | 0.420731i | \(0.138226\pi\) | |||||||
\(158\) | 0.809017 | − | 1.40126i | 0.0643619 | − | 0.111478i | ||||
\(159\) | 5.11803 | + | 8.86469i | 0.405886 | + | 0.703016i | ||||
\(160\) | 3.38197 | 0.267368 | ||||||||
\(161\) | −21.7705 | − | 7.54153i | −1.71576 | − | 0.594355i | ||||
\(162\) | 1.61803 | 0.127125 | ||||||||
\(163\) | 2.64590 | + | 4.58283i | 0.207243 | + | 0.358955i | 0.950845 | − | 0.309667i | \(-0.100218\pi\) |
−0.743602 | + | 0.668622i | \(0.766884\pi\) | |||||||
\(164\) | 0.309017 | − | 0.535233i | 0.0241302 | − | 0.0417947i | ||||
\(165\) | 0.500000 | − | 0.866025i | 0.0389249 | − | 0.0674200i | ||||
\(166\) | 1.23607 | + | 2.14093i | 0.0959375 | + | 0.166169i | ||||
\(167\) | −2.47214 | −0.191300 | −0.0956498 | − | 0.995415i | \(-0.530493\pi\) | ||||
−0.0956498 | + | 0.995415i | \(0.530493\pi\) | |||||||
\(168\) | 1.11803 | + | 5.80948i | 0.0862582 | + | 0.448211i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 3.42705 | + | 5.93583i | 0.262843 | + | 0.455257i | ||||
\(171\) | 1.47214 | − | 2.54981i | 0.112577 | − | 0.194989i | ||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | 9.44427 | + | 16.3580i | 0.718035 | + | 1.24367i | 0.961777 | + | 0.273833i | \(0.0882914\pi\) |
−0.243743 | + | 0.969840i | \(0.578375\pi\) | |||||||
\(174\) | 7.23607 | 0.548565 | ||||||||
\(175\) | 2.00000 | + | 10.3923i | 0.151186 | + | 0.785584i | ||||
\(176\) | −4.85410 | −0.365892 | ||||||||
\(177\) | −4.35410 | − | 7.54153i | −0.327274 | − | 0.566856i | ||||
\(178\) | 11.5172 | − | 19.9484i | 0.863252 | − | 1.49520i | ||||
\(179\) | 5.20820 | − | 9.02087i | 0.389279 | − | 0.674252i | −0.603073 | − | 0.797686i | \(-0.706057\pi\) |
0.992353 | + | 0.123434i | \(0.0393907\pi\) | |||||||
\(180\) | −0.618034 | − | 1.07047i | −0.0460655 | − | 0.0797878i | ||||
\(181\) | −21.4164 | −1.59187 | −0.795935 | − | 0.605383i | \(-0.793020\pi\) | ||||
−0.795935 | + | 0.605383i | \(0.793020\pi\) | |||||||
\(182\) | −18.0902 | − | 6.26662i | −1.34093 | − | 0.464513i | ||||
\(183\) | 9.47214 | 0.700200 | ||||||||
\(184\) | −9.73607 | − | 16.8634i | −0.717752 | − | 1.24318i | ||||
\(185\) | −1.73607 | + | 3.00696i | −0.127638 | + | 0.221076i | ||||
\(186\) | 0.190983 | − | 0.330792i | 0.0140036 | − | 0.0242549i | ||||
\(187\) | −2.11803 | − | 3.66854i | −0.154886 | − | 0.268270i | ||||
\(188\) | −2.14590 | −0.156506 | ||||||||
\(189\) | 10.0000 | − | 8.66025i | 0.727393 | − | 0.629941i | ||||
\(190\) | −2.38197 | −0.172806 | ||||||||
\(191\) | −2.73607 | − | 4.73901i | −0.197975 | − | 0.342903i | 0.749897 | − | 0.661555i | \(-0.230103\pi\) |
−0.947872 | + | 0.318652i | \(0.896770\pi\) | |||||||
\(192\) | −2.11803 | + | 3.66854i | −0.152856 | + | 0.264754i | ||||
\(193\) | −0.409830 | + | 0.709846i | −0.0295002 | + | 0.0510959i | −0.880399 | − | 0.474234i | \(-0.842725\pi\) |
0.850898 | + | 0.525330i | \(0.176058\pi\) | |||||||
\(194\) | −6.85410 | − | 11.8717i | −0.492096 | − | 0.852335i | ||||
\(195\) | 4.47214 | 0.320256 | ||||||||
\(196\) | 3.39919 | + | 2.67617i | 0.242799 | + | 0.191155i | ||||
\(197\) | −2.94427 | −0.209771 | −0.104885 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104885 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(198\) | 1.61803 | + | 2.80252i | 0.114989 | + | 0.199166i | ||||
\(199\) | −8.97214 | + | 15.5402i | −0.636018 | + | 1.10162i | 0.350281 | + | 0.936645i | \(0.386086\pi\) |
−0.986299 | + | 0.164970i | \(0.947247\pi\) | |||||||
\(200\) | −4.47214 | + | 7.74597i | −0.316228 | + | 0.547723i | ||||
\(201\) | −2.97214 | − | 5.14789i | −0.209638 | − | 0.363104i | ||||
\(202\) | 5.32624 | 0.374753 | ||||||||
\(203\) | −8.94427 | + | 7.74597i | −0.627765 | + | 0.543660i | ||||
\(204\) | 2.61803 | 0.183299 | ||||||||
\(205\) | −0.500000 | − | 0.866025i | −0.0349215 | − | 0.0604858i | ||||
\(206\) | −13.8992 | + | 24.0741i | −0.968402 | + | 1.67732i | ||||
\(207\) | −8.70820 | + | 15.0831i | −0.605262 | + | 1.04834i | ||||
\(208\) | −10.8541 | − | 18.7999i | −0.752597 | − | 1.30354i | ||||
\(209\) | 1.47214 | 0.101830 | ||||||||
\(210\) | −4.04508 | − | 1.40126i | −0.279137 | − | 0.0966960i | ||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 3.16312 | + | 5.47868i | 0.217244 | + | 0.376277i | ||||
\(213\) | 7.23607 | − | 12.5332i | 0.495807 | − | 0.858763i | ||||
\(214\) | 1.04508 | − | 1.81014i | 0.0714405 | − | 0.123739i | ||||
\(215\) | −3.23607 | − | 5.60503i | −0.220698 | − | 0.382260i | ||||
\(216\) | 11.1803 | 0.760726 | ||||||||
\(217\) | 0.118034 | + | 0.613323i | 0.00801267 | + | 0.0416351i | ||||
\(218\) | −23.0344 | −1.56009 | ||||||||
\(219\) | 1.26393 | + | 2.18919i | 0.0854086 | + | 0.147932i | ||||
\(220\) | 0.309017 | − | 0.535233i | 0.0208339 | − | 0.0360854i | ||||
\(221\) | 9.47214 | − | 16.4062i | 0.637165 | − | 1.10360i | ||||
\(222\) | 2.80902 | + | 4.86536i | 0.188529 | + | 0.326542i | ||||
\(223\) | −16.9443 | −1.13467 | −0.567336 | − | 0.823486i | \(-0.692026\pi\) | ||||
−0.567336 | + | 0.823486i | \(0.692026\pi\) | |||||||
\(224\) | 1.69098 | + | 8.78661i | 0.112984 | + | 0.587080i | ||||
\(225\) | 8.00000 | 0.533333 | ||||||||
\(226\) | −16.0902 | − | 27.8690i | −1.07030 | − | 1.85382i | ||||
\(227\) | 2.73607 | − | 4.73901i | 0.181599 | − | 0.314539i | −0.760826 | − | 0.648956i | \(-0.775206\pi\) |
0.942425 | + | 0.334417i | \(0.108539\pi\) | |||||||
\(228\) | −0.454915 | + | 0.787936i | −0.0301275 | + | 0.0521823i | ||||
\(229\) | 10.0623 | + | 17.4284i | 0.664936 | + | 1.15170i | 0.979303 | + | 0.202401i | \(0.0648745\pi\) |
−0.314367 | + | 0.949302i | \(0.601792\pi\) | |||||||
\(230\) | 14.0902 | 0.929078 | ||||||||
\(231\) | 2.50000 | + | 0.866025i | 0.164488 | + | 0.0569803i | ||||
\(232\) | −10.0000 | −0.656532 | ||||||||
\(233\) | −1.64590 | − | 2.85078i | −0.107826 | − | 0.186761i | 0.807063 | − | 0.590465i | \(-0.201056\pi\) |
−0.914889 | + | 0.403704i | \(0.867722\pi\) | |||||||
\(234\) | −7.23607 | + | 12.5332i | −0.473037 | + | 0.819323i | ||||
\(235\) | −1.73607 | + | 3.00696i | −0.113249 | + | 0.196152i | ||||
\(236\) | −2.69098 | − | 4.66092i | −0.175168 | − | 0.303400i | ||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −13.7082 | + | 11.8717i | −0.888571 | + | 0.769525i | ||||
\(239\) | −2.47214 | −0.159909 | −0.0799546 | − | 0.996799i | \(-0.525478\pi\) | ||||
−0.0799546 | + | 0.996799i | \(0.525478\pi\) | |||||||
\(240\) | −2.42705 | − | 4.20378i | −0.156665 | − | 0.271353i | ||||
\(241\) | −0.736068 | + | 1.27491i | −0.0474143 | + | 0.0821240i | −0.888759 | − | 0.458376i | \(-0.848431\pi\) |
0.841344 | + | 0.540500i | \(0.181765\pi\) | |||||||
\(242\) | 8.09017 | − | 14.0126i | 0.520056 | − | 0.900763i | ||||
\(243\) | −8.00000 | − | 13.8564i | −0.513200 | − | 0.888889i | ||||
\(244\) | 5.85410 | 0.374770 | ||||||||
\(245\) | 6.50000 | − | 2.59808i | 0.415270 | − | 0.165985i | ||||
\(246\) | −1.61803 | −0.103162 | ||||||||
\(247\) | 3.29180 | + | 5.70156i | 0.209452 | + | 0.362781i | ||||
\(248\) | −0.263932 | + | 0.457144i | −0.0167597 | + | 0.0290287i | ||||
\(249\) | 0.763932 | − | 1.32317i | 0.0484122 | − | 0.0838524i | ||||
\(250\) | −7.28115 | − | 12.6113i | −0.460501 | − | 0.797610i | ||||
\(251\) | 26.8328 | 1.69367 | 0.846836 | − | 0.531854i | \(-0.178504\pi\) | ||||
0.846836 | + | 0.531854i | \(0.178504\pi\) | |||||||
\(252\) | 2.47214 | − | 2.14093i | 0.155730 | − | 0.134866i | ||||
\(253\) | −8.70820 | −0.547480 | ||||||||
\(254\) | −12.4721 | − | 21.6024i | −0.782571 | − | 1.35545i | ||||
\(255\) | 2.11803 | − | 3.66854i | 0.132636 | − | 0.229733i | ||||
\(256\) | −6.78115 | + | 11.7453i | −0.423822 | + | 0.734081i | ||||
\(257\) | 0.645898 | + | 1.11873i | 0.0402900 | + | 0.0697843i | 0.885467 | − | 0.464702i | \(-0.153838\pi\) |
−0.845177 | + | 0.534486i | \(0.820505\pi\) | |||||||
\(258\) | −10.4721 | −0.651967 | ||||||||
\(259\) | −8.68034 | − | 3.00696i | −0.539370 | − | 0.186843i | ||||
\(260\) | 2.76393 | 0.171412 | ||||||||
\(261\) | 4.47214 | + | 7.74597i | 0.276818 | + | 0.479463i | ||||
\(262\) | 11.0451 | − | 19.1306i | 0.682368 | − | 1.18190i | ||||
\(263\) | −3.73607 | + | 6.47106i | −0.230376 | + | 0.399023i | −0.957919 | − | 0.287040i | \(-0.907329\pi\) |
0.727543 | + | 0.686062i | \(0.240662\pi\) | |||||||
\(264\) | 1.11803 | + | 1.93649i | 0.0688102 | + | 0.119183i | ||||
\(265\) | 10.2361 | 0.628797 | ||||||||
\(266\) | −1.19098 | − | 6.18853i | −0.0730239 | − | 0.379443i | ||||
\(267\) | −14.2361 | −0.871233 | ||||||||
\(268\) | −1.83688 | − | 3.18157i | −0.112205 | − | 0.194345i | ||||
\(269\) | 9.73607 | − | 16.8634i | 0.593619 | − | 1.02818i | −0.400122 | − | 0.916462i | \(-0.631032\pi\) |
0.993740 | − | 0.111715i | \(-0.0356345\pi\) | |||||||
\(270\) | −4.04508 | + | 7.00629i | −0.246176 | + | 0.426389i | ||||
\(271\) | 10.8262 | + | 18.7516i | 0.657647 | + | 1.13908i | 0.981223 | + | 0.192876i | \(0.0617815\pi\) |
−0.323576 | + | 0.946202i | \(0.604885\pi\) | |||||||
\(272\) | −20.5623 | −1.24677 | ||||||||
\(273\) | 2.23607 | + | 11.6190i | 0.135333 | + | 0.703211i | ||||
\(274\) | 25.3262 | 1.53001 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | 2.69098 | − | 4.66092i | 0.161978 | − | 0.280554i | ||||
\(277\) | 2.02786 | − | 3.51236i | 0.121843 | − | 0.211037i | −0.798652 | − | 0.601793i | \(-0.794453\pi\) |
0.920494 | + | 0.390756i | \(0.127786\pi\) | |||||||
\(278\) | −13.7082 | − | 23.7433i | −0.822163 | − | 1.42403i | ||||
\(279\) | 0.472136 | 0.0282660 | ||||||||
\(280\) | 5.59017 | + | 1.93649i | 0.334077 | + | 0.115728i | ||||
\(281\) | −4.47214 | −0.266785 | −0.133393 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133393 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(282\) | 2.80902 | + | 4.86536i | 0.167275 | + | 0.289728i | ||||
\(283\) | −5.59017 | + | 9.68246i | −0.332301 | + | 0.575562i | −0.982963 | − | 0.183805i | \(-0.941158\pi\) |
0.650662 | + | 0.759368i | \(0.274492\pi\) | |||||||
\(284\) | 4.47214 | − | 7.74597i | 0.265372 | − | 0.459639i | ||||
\(285\) | 0.736068 | + | 1.27491i | 0.0436009 | + | 0.0755190i | ||||
\(286\) | −7.23607 | −0.427878 | ||||||||
\(287\) | 2.00000 | − | 1.73205i | 0.118056 | − | 0.102240i | ||||
\(288\) | 6.76393 | 0.398569 | ||||||||
\(289\) | −0.472136 | − | 0.817763i | −0.0277727 | − | 0.0481037i | ||||
\(290\) | 3.61803 | − | 6.26662i | 0.212458 | − | 0.367989i | ||||
\(291\) | −4.23607 | + | 7.33708i | −0.248323 | + | 0.430108i | ||||
\(292\) | 0.781153 | + | 1.35300i | 0.0457135 | + | 0.0791781i | ||||
\(293\) | 28.8328 | 1.68443 | 0.842216 | − | 0.539141i | \(-0.181251\pi\) | ||||
0.842216 | + | 0.539141i | \(0.181251\pi\) | |||||||
\(294\) | 1.61803 | − | 11.2101i | 0.0943657 | − | 0.653784i | ||||
\(295\) | −8.70820 | −0.507011 | ||||||||
\(296\) | −3.88197 | − | 6.72376i | −0.225635 | − | 0.390811i | ||||
\(297\) | 2.50000 | − | 4.33013i | 0.145065 | − | 0.251259i | ||||
\(298\) | −0.954915 | + | 1.65396i | −0.0553167 | + | 0.0958114i | ||||
\(299\) | −19.4721 | − | 33.7267i | −1.12610 | − | 1.95047i | ||||
\(300\) | −2.47214 | −0.142729 | ||||||||
\(301\) | 12.9443 | − | 11.2101i | 0.746095 | − | 0.646138i | ||||
\(302\) | 9.61803 | 0.553456 | ||||||||
\(303\) | −1.64590 | − | 2.85078i | −0.0945544 | − | 0.163773i | ||||
\(304\) | 3.57295 | − | 6.18853i | 0.204923 | − | 0.354936i | ||||
\(305\) | 4.73607 | − | 8.20311i | 0.271186 | − | 0.469709i | ||||
\(306\) | 6.85410 | + | 11.8717i | 0.391823 | + | 0.678657i | ||||
\(307\) | −9.88854 | −0.564369 | −0.282185 | − | 0.959360i | \(-0.591059\pi\) | ||||
−0.282185 | + | 0.959360i | \(0.591059\pi\) | |||||||
\(308\) | 1.54508 | + | 0.535233i | 0.0880394 | + | 0.0304977i | ||||
\(309\) | 17.1803 | 0.977355 | ||||||||
\(310\) | −0.190983 | − | 0.330792i | −0.0108471 | − | 0.0187877i | ||||
\(311\) | 10.9164 | − | 18.9078i | 0.619013 | − | 1.07216i | −0.370654 | − | 0.928771i | \(-0.620866\pi\) |
0.989666 | − | 0.143390i | \(-0.0458004\pi\) | |||||||
\(312\) | −5.00000 | + | 8.66025i | −0.283069 | + | 0.490290i | ||||
\(313\) | 8.64590 | + | 14.9751i | 0.488695 | + | 0.846445i | 0.999915 | − | 0.0130050i | \(-0.00413974\pi\) |
−0.511220 | + | 0.859450i | \(0.670806\pi\) | |||||||
\(314\) | −3.61803 | −0.204177 | ||||||||
\(315\) | −1.00000 | − | 5.19615i | −0.0563436 | − | 0.292770i | ||||
\(316\) | −0.618034 | −0.0347671 | ||||||||
\(317\) | −12.8820 | − | 22.3122i | −0.723523 | − | 1.25318i | −0.959579 | − | 0.281440i | \(-0.909188\pi\) |
0.236056 | − | 0.971740i | \(-0.424145\pi\) | |||||||
\(318\) | 8.28115 | − | 14.3434i | 0.464384 | − | 0.804337i | ||||
\(319\) | −2.23607 | + | 3.87298i | −0.125196 | + | 0.216845i | ||||
\(320\) | 2.11803 | + | 3.66854i | 0.118402 | + | 0.205078i | ||||
\(321\) | −1.29180 | −0.0721010 | ||||||||
\(322\) | 7.04508 | + | 36.6073i | 0.392607 | + | 2.04005i | ||||
\(323\) | 6.23607 | 0.346984 | ||||||||
\(324\) | −0.309017 | − | 0.535233i | −0.0171676 | − | 0.0297352i | ||||
\(325\) | −8.94427 | + | 15.4919i | −0.496139 | + | 0.859338i | ||||
\(326\) | 4.28115 | − | 7.41517i | 0.237111 | − | 0.410689i | ||||
\(327\) | 7.11803 | + | 12.3288i | 0.393628 | + | 0.681784i | ||||
\(328\) | 2.23607 | 0.123466 | ||||||||
\(329\) | −8.68034 | − | 3.00696i | −0.478563 | − | 0.165779i | ||||
\(330\) | −1.61803 | −0.0890698 | ||||||||
\(331\) | 15.9164 | + | 27.5680i | 0.874845 | + | 1.51528i | 0.856928 | + | 0.515436i | \(0.172370\pi\) |
0.0179170 | + | 0.999839i | \(0.494297\pi\) | |||||||
\(332\) | 0.472136 | − | 0.817763i | 0.0259118 | − | 0.0448806i | ||||
\(333\) | −3.47214 | + | 6.01392i | −0.190272 | + | 0.329561i | ||||
\(334\) | 2.00000 | + | 3.46410i | 0.109435 | + | 0.189547i | ||||
\(335\) | −5.94427 | −0.324770 | ||||||||
\(336\) | 9.70820 | − | 8.40755i | 0.529626 | − | 0.458670i | ||||
\(337\) | −8.47214 | −0.461507 | −0.230753 | − | 0.973012i | \(-0.574119\pi\) | ||||
−0.230753 | + | 0.973012i | \(0.574119\pi\) | |||||||
\(338\) | −5.66312 | − | 9.80881i | −0.308033 | − | 0.533529i | ||||
\(339\) | −9.94427 | + | 17.2240i | −0.540099 | + | 0.935478i | ||||
\(340\) | 1.30902 | − | 2.26728i | 0.0709914 | − | 0.122961i | ||||
\(341\) | 0.118034 | + | 0.204441i | 0.00639190 | + | 0.0110711i | ||||
\(342\) | −4.76393 | −0.257604 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 14.4721 | 0.780285 | ||||||||
\(345\) | −4.35410 | − | 7.54153i | −0.234417 | − | 0.406022i | ||||
\(346\) | 15.2812 | − | 26.4677i | 0.821520 | − | 1.42291i | ||||
\(347\) | 1.50000 | − | 2.59808i | 0.0805242 | − | 0.139472i | −0.822951 | − | 0.568112i | \(-0.807674\pi\) |
0.903475 | + | 0.428640i | \(0.141007\pi\) | |||||||
\(348\) | −1.38197 | − | 2.39364i | −0.0740812 | − | 0.128312i | ||||
\(349\) | −20.4721 | −1.09585 | −0.547924 | − | 0.836528i | \(-0.684582\pi\) | ||||
−0.547924 | + | 0.836528i | \(0.684582\pi\) | |||||||
\(350\) | 12.9443 | − | 11.2101i | 0.691900 | − | 0.599203i | ||||
\(351\) | 22.3607 | 1.19352 | ||||||||
\(352\) | 1.69098 | + | 2.92887i | 0.0901297 | + | 0.156109i | ||||
\(353\) | −12.7361 | + | 22.0595i | −0.677872 | + | 1.17411i | 0.297748 | + | 0.954645i | \(0.403765\pi\) |
−0.975620 | + | 0.219465i | \(0.929569\pi\) | |||||||
\(354\) | −7.04508 | + | 12.2024i | −0.374442 | + | 0.648553i | ||||
\(355\) | −7.23607 | − | 12.5332i | −0.384051 | − | 0.665195i | ||||
\(356\) | −8.79837 | −0.466313 | ||||||||
\(357\) | 10.5902 | + | 3.66854i | 0.560491 | + | 0.194160i | ||||
\(358\) | −16.8541 | −0.890767 | ||||||||
\(359\) | 6.82624 | + | 11.8234i | 0.360275 | + | 0.624015i | 0.988006 | − | 0.154416i | \(-0.0493495\pi\) |
−0.627731 | + | 0.778430i | \(0.716016\pi\) | |||||||
\(360\) | 2.23607 | − | 3.87298i | 0.117851 | − | 0.204124i | ||||
\(361\) | 8.41641 | − | 14.5776i | 0.442969 | − | 0.767245i | ||||
\(362\) | 17.3262 | + | 30.0099i | 0.910647 | + | 1.57729i | ||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 1.38197 | + | 7.18091i | 0.0724347 | + | 0.376382i | ||||
\(365\) | 2.52786 | 0.132314 | ||||||||
\(366\) | −7.66312 | − | 13.2729i | −0.400558 | − | 0.693786i | ||||
\(367\) | 2.59017 | − | 4.48631i | 0.135206 | − | 0.234183i | −0.790470 | − | 0.612500i | \(-0.790164\pi\) |
0.925676 | + | 0.378317i | \(0.123497\pi\) | |||||||
\(368\) | −21.1353 | + | 36.6073i | −1.10175 | + | 1.90829i | ||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | 5.61803 | 0.292068 | ||||||||
\(371\) | 5.11803 | + | 26.5941i | 0.265715 | + | 1.38070i | ||||
\(372\) | −0.145898 | −0.00756446 | ||||||||
\(373\) | 0.0278640 | + | 0.0482619i | 0.00144275 | + | 0.00249891i | 0.866746 | − | 0.498750i | \(-0.166207\pi\) |
−0.865303 | + | 0.501249i | \(0.832874\pi\) | |||||||
\(374\) | −3.42705 | + | 5.93583i | −0.177209 | + | 0.306934i | ||||
\(375\) | −4.50000 | + | 7.79423i | −0.232379 | + | 0.402492i | ||||
\(376\) | −3.88197 | − | 6.72376i | −0.200197 | − | 0.346752i | ||||
\(377\) | −20.0000 | −1.03005 | ||||||||
\(378\) | −20.2254 | − | 7.00629i | −1.04028 | − | 0.360365i | ||||
\(379\) | 31.4164 | 1.61375 | 0.806876 | − | 0.590721i | \(-0.201156\pi\) | ||||
0.806876 | + | 0.590721i | \(0.201156\pi\) | |||||||
\(380\) | 0.454915 | + | 0.787936i | 0.0233366 | + | 0.0404203i | ||||
\(381\) | −7.70820 | + | 13.3510i | −0.394903 | + | 0.683992i | ||||
\(382\) | −4.42705 | + | 7.66788i | −0.226508 | + | 0.392323i | ||||
\(383\) | −10.4443 | − | 18.0900i | −0.533677 | − | 0.924356i | −0.999226 | − | 0.0393341i | \(-0.987476\pi\) |
0.465549 | − | 0.885022i | \(-0.345857\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | 2.00000 | − | 1.73205i | 0.101929 | − | 0.0882735i | ||||
\(386\) | 1.32624 | 0.0675037 | ||||||||
\(387\) | −6.47214 | − | 11.2101i | −0.328997 | − | 0.569840i | ||||
\(388\) | −2.61803 | + | 4.53457i | −0.132911 | + | 0.230208i | ||||
\(389\) | 0.500000 | − | 0.866025i | 0.0253510 | − | 0.0439092i | −0.853072 | − | 0.521794i | \(-0.825263\pi\) |
0.878423 | + | 0.477885i | \(0.158596\pi\) | |||||||
\(390\) | −3.61803 | − | 6.26662i | −0.183206 | − | 0.317323i | ||||
\(391\) | −36.8885 | −1.86553 | ||||||||
\(392\) | −2.23607 | + | 15.4919i | −0.112938 | + | 0.782461i | ||||
\(393\) | −13.6525 | −0.688676 | ||||||||
\(394\) | 2.38197 | + | 4.12569i | 0.120002 | + | 0.207849i | ||||
\(395\) | −0.500000 | + | 0.866025i | −0.0251577 | + | 0.0435745i | ||||
\(396\) | 0.618034 | − | 1.07047i | 0.0310574 | − | 0.0537930i | ||||
\(397\) | −13.8262 | − | 23.9477i | −0.693919 | − | 1.20190i | −0.970544 | − | 0.240925i | \(-0.922549\pi\) |
0.276625 | − | 0.960978i | \(-0.410784\pi\) | |||||||
\(398\) | 29.0344 | 1.45537 | ||||||||
\(399\) | −2.94427 | + | 2.54981i | −0.147398 | + | 0.127650i | ||||
\(400\) | 19.4164 | 0.970820 | ||||||||
\(401\) | −3.97214 | − | 6.87994i | −0.198359 | − | 0.343568i | 0.749637 | − | 0.661849i | \(-0.230228\pi\) |
−0.947996 | + | 0.318281i | \(0.896895\pi\) | |||||||
\(402\) | −4.80902 | + | 8.32946i | −0.239852 | + | 0.415436i | ||||
\(403\) | −0.527864 | + | 0.914287i | −0.0262948 | + | 0.0455439i | ||||
\(404\) | −1.01722 | − | 1.76188i | −0.0506086 | − | 0.0876567i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 18.0902 | + | 6.26662i | 0.897800 | + | 0.311007i | ||||
\(407\) | −3.47214 | −0.172107 | ||||||||
\(408\) | 4.73607 | + | 8.20311i | 0.234470 | + | 0.406114i | ||||
\(409\) | 11.4443 | − | 19.8221i | 0.565883 | − | 0.980138i | −0.431084 | − | 0.902312i | \(-0.641869\pi\) |
0.996967 | − | 0.0778261i | \(-0.0247979\pi\) | |||||||
\(410\) | −0.809017 | + | 1.40126i | −0.0399545 | + | 0.0692032i | ||||
\(411\) | −7.82624 | − | 13.5554i | −0.386040 | − | 0.668641i | ||||
\(412\) | 10.6180 | 0.523113 | ||||||||
\(413\) | −4.35410 | − | 22.6246i | −0.214251 | − | 1.11328i | ||||
\(414\) | 28.1803 | 1.38499 | ||||||||
\(415\) | −0.763932 | − | 1.32317i | −0.0374999 | − | 0.0649518i | ||||
\(416\) | −7.56231 | + | 13.0983i | −0.370773 | + | 0.642197i | ||||
\(417\) | −8.47214 | + | 14.6742i | −0.414882 | + | 0.718597i | ||||
\(418\) | −1.19098 | − | 2.06284i | −0.0582529 | − | 0.100897i | ||||
\(419\) | −17.8885 | −0.873913 | −0.436956 | − | 0.899483i | \(-0.643944\pi\) | ||||
−0.436956 | + | 0.899483i | \(0.643944\pi\) | |||||||
\(420\) | 0.309017 | + | 1.60570i | 0.0150785 | + | 0.0783501i | ||||
\(421\) | −16.4721 | −0.802803 | −0.401401 | − | 0.915902i | \(-0.631477\pi\) | ||||
−0.401401 | + | 0.915902i | \(0.631477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.47214 | + | 6.01392i | −0.168821 | + | 0.292407i | ||||
\(424\) | −11.4443 | + | 19.8221i | −0.555783 | + | 0.962644i | ||||
\(425\) | 8.47214 | + | 14.6742i | 0.410959 | + | 0.711802i | ||||
\(426\) | −23.4164 | −1.13453 | ||||||||
\(427\) | 23.6803 | + | 8.20311i | 1.14597 | + | 0.396976i | ||||
\(428\) | −0.798374 | −0.0385909 | ||||||||
\(429\) | 2.23607 | + | 3.87298i | 0.107958 | + | 0.186989i | ||||
\(430\) | −5.23607 | + | 9.06914i | −0.252506 | + | 0.437353i | ||||
\(431\) | 1.17376 | − | 2.03302i | 0.0565381 | − | 0.0979269i | −0.836371 | − | 0.548164i | \(-0.815327\pi\) |
0.892909 | + | 0.450237i | \(0.148660\pi\) | |||||||
\(432\) | −12.1353 | − | 21.0189i | −0.583858 | − | 1.01127i | ||||
\(433\) | 6.94427 | 0.333720 | 0.166860 | − | 0.985981i | \(-0.446637\pi\) | ||||
0.166860 | + | 0.985981i | \(0.446637\pi\) | |||||||
\(434\) | 0.763932 | − | 0.661585i | 0.0366699 | − | 0.0317571i | ||||
\(435\) | −4.47214 | −0.214423 | ||||||||
\(436\) | 4.39919 | + | 7.61962i | 0.210683 | + | 0.364913i | ||||
\(437\) | 6.40983 | − | 11.1022i | 0.306624 | − | 0.531088i | ||||
\(438\) | 2.04508 | − | 3.54219i | 0.0977179 | − | 0.169252i | ||||
\(439\) | 18.2082 | + | 31.5375i | 0.869030 | + | 1.50520i | 0.862989 | + | 0.505223i | \(0.168590\pi\) |
0.00604112 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(440\) | 2.23607 | 0.106600 | ||||||||
\(441\) | 13.0000 | − | 5.19615i | 0.619048 | − | 0.247436i | ||||
\(442\) | −30.6525 | −1.45799 | ||||||||
\(443\) | 3.88197 | + | 6.72376i | 0.184438 | + | 0.319456i | 0.943387 | − | 0.331694i | \(-0.107620\pi\) |
−0.758949 | + | 0.651150i | \(0.774287\pi\) | |||||||
\(444\) | 1.07295 | − | 1.85840i | 0.0509199 | − | 0.0881959i | ||||
\(445\) | −7.11803 | + | 12.3288i | −0.337427 | + | 0.584441i | ||||
\(446\) | 13.7082 | + | 23.7433i | 0.649102 | + | 1.12428i | ||||
\(447\) | 1.18034 | 0.0558282 | ||||||||
\(448\) | −8.47214 | + | 7.33708i | −0.400271 | + | 0.346645i | ||||
\(449\) | 21.0557 | 0.993681 | 0.496841 | − | 0.867842i | \(-0.334493\pi\) | ||||
0.496841 | + | 0.867842i | \(0.334493\pi\) | |||||||
\(450\) | −6.47214 | − | 11.2101i | −0.305099 | − | 0.528448i | ||||
\(451\) | 0.500000 | − | 0.866025i | 0.0235441 | − | 0.0407795i | ||||
\(452\) | −6.14590 | + | 10.6450i | −0.289079 | + | 0.500699i | ||||
\(453\) | −2.97214 | − | 5.14789i | −0.139643 | − | 0.241869i | ||||
\(454\) | −8.85410 | −0.415544 | ||||||||
\(455\) | 11.1803 | + | 3.87298i | 0.524142 | + | 0.181568i | ||||
\(456\) | −3.29180 | −0.154152 | ||||||||
\(457\) | 13.1180 | + | 22.7211i | 0.613636 | + | 1.06285i | 0.990622 | + | 0.136630i | \(0.0436270\pi\) |
−0.376986 | + | 0.926219i | \(0.623040\pi\) | |||||||
\(458\) | 16.2812 | − | 28.1998i | 0.760768 | − | 1.31769i | ||||
\(459\) | 10.5902 | − | 18.3427i | 0.494307 | − | 0.856164i | ||||
\(460\) | −2.69098 | − | 4.66092i | −0.125468 | − | 0.217316i | ||||
\(461\) | −38.9443 | −1.81382 | −0.906908 | − | 0.421329i | \(-0.861564\pi\) | ||||
−0.906908 | + | 0.421329i | \(0.861564\pi\) | |||||||
\(462\) | −0.809017 | − | 4.20378i | −0.0376389 | − | 0.195577i | ||||
\(463\) | −2.11146 | −0.0981277 | −0.0490638 | − | 0.998796i | \(-0.515624\pi\) | ||||
−0.0490638 | + | 0.998796i | \(0.515624\pi\) | |||||||
\(464\) | 10.8541 | + | 18.7999i | 0.503889 | + | 0.872761i | ||||
\(465\) | −0.118034 | + | 0.204441i | −0.00547370 | + | 0.00948072i | ||||
\(466\) | −2.66312 | + | 4.61266i | −0.123367 | + | 0.213677i | ||||
\(467\) | −4.40983 | − | 7.63805i | −0.204063 | − | 0.353447i | 0.745771 | − | 0.666202i | \(-0.232081\pi\) |
−0.949834 | + | 0.312756i | \(0.898748\pi\) | |||||||
\(468\) | 5.52786 | 0.255526 | ||||||||
\(469\) | −2.97214 | − | 15.4437i | −0.137240 | − | 0.713122i | ||||
\(470\) | 5.61803 | 0.259141 | ||||||||
\(471\) | 1.11803 | + | 1.93649i | 0.0515163 | + | 0.0892288i | ||||
\(472\) | 9.73607 | − | 16.8634i | 0.448139 | − | 0.776199i | ||||
\(473\) | 3.23607 | − | 5.60503i | 0.148795 | − | 0.257720i | ||||
\(474\) | 0.809017 | + | 1.40126i | 0.0371594 | + | 0.0643619i | ||||
\(475\) | −5.88854 | −0.270185 | ||||||||
\(476\) | 6.54508 | + | 2.26728i | 0.299993 | + | 0.103921i | ||||
\(477\) | 20.4721 | 0.937355 | ||||||||
\(478\) | 2.00000 | + | 3.46410i | 0.0914779 | + | 0.158444i | ||||
\(479\) | −10.5000 | + | 18.1865i | −0.479757 | + | 0.830964i | −0.999730 | − | 0.0232187i | \(-0.992609\pi\) |
0.519973 | + | 0.854183i | \(0.325942\pi\) | |||||||
\(480\) | −1.69098 | + | 2.92887i | −0.0771825 | + | 0.133684i | ||||
\(481\) | −7.76393 | − | 13.4475i | −0.354005 | − | 0.613154i | ||||
\(482\) | 2.38197 | 0.108496 | ||||||||
\(483\) | 17.4164 | − | 15.0831i | 0.792474 | − | 0.686303i | ||||
\(484\) | −6.18034 | −0.280925 | ||||||||
\(485\) | 4.23607 | + | 7.33708i | 0.192350 | + | 0.333160i | ||||
\(486\) | −12.9443 | + | 22.4201i | −0.587164 | + | 1.01700i | ||||
\(487\) | 12.7705 | − | 22.1192i | 0.578687 | − | 1.00232i | −0.416943 | − | 0.908933i | \(-0.636899\pi\) |
0.995630 | − | 0.0933828i | \(-0.0297680\pi\) | |||||||
\(488\) | 10.5902 | + | 18.3427i | 0.479394 | + | 0.830336i | ||||
\(489\) | −5.29180 | −0.239303 | ||||||||
\(490\) | −8.89919 | − | 7.00629i | −0.402024 | − | 0.316512i | ||||
\(491\) | −12.3607 | −0.557830 | −0.278915 | − | 0.960316i | \(-0.589975\pi\) | ||||
−0.278915 | + | 0.960316i | \(0.589975\pi\) | |||||||
\(492\) | 0.309017 | + | 0.535233i | 0.0139316 | + | 0.0241302i | ||||
\(493\) | −9.47214 | + | 16.4062i | −0.426604 | + | 0.738899i | ||||
\(494\) | 5.32624 | − | 9.22531i | 0.239639 | − | 0.415067i | ||||
\(495\) | −1.00000 | − | 1.73205i | −0.0449467 | − | 0.0778499i | ||||
\(496\) | 1.14590 | 0.0514523 | ||||||||
\(497\) | 28.9443 | − | 25.0665i | 1.29833 | − | 1.12439i | ||||
\(498\) | −2.47214 | −0.110779 | ||||||||
\(499\) | 8.02786 | + | 13.9047i | 0.359377 | + | 0.622458i | 0.987857 | − | 0.155367i | \(-0.0496560\pi\) |
−0.628480 | + | 0.777826i | \(0.716323\pi\) | |||||||
\(500\) | −2.78115 | + | 4.81710i | −0.124377 | + | 0.215427i | ||||
\(501\) | 1.23607 | − | 2.14093i | 0.0552234 | − | 0.0956498i | ||||
\(502\) | −21.7082 | − | 37.5997i | −0.968885 | − | 1.67816i | ||||
\(503\) | 4.00000 | 0.178351 | 0.0891756 | − | 0.996016i | \(-0.471577\pi\) | ||||
0.0891756 | + | 0.996016i | \(0.471577\pi\) | |||||||
\(504\) | 11.1803 | + | 3.87298i | 0.498012 | + | 0.172516i | ||||
\(505\) | −3.29180 | −0.146483 | ||||||||
\(506\) | 7.04508 | + | 12.2024i | 0.313192 | + | 0.542465i | ||||
\(507\) | −3.50000 | + | 6.06218i | −0.155440 | + | 0.269231i | ||||
\(508\) | −4.76393 | + | 8.25137i | −0.211365 | + | 0.366095i | ||||
\(509\) | −2.40983 | − | 4.17395i | −0.106814 | − | 0.185007i | 0.807664 | − | 0.589643i | \(-0.200732\pi\) |
−0.914478 | + | 0.404636i | \(0.867398\pi\) | |||||||
\(510\) | −6.85410 | −0.303505 | ||||||||
\(511\) | 1.26393 | + | 6.56758i | 0.0559131 | + | 0.290533i | ||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 3.68034 | + | 6.37454i | 0.162491 | + | 0.281443i | ||||
\(514\) | 1.04508 | − | 1.81014i | 0.0460967 | − | 0.0798419i | ||||
\(515\) | 8.59017 | − | 14.8786i | 0.378528 | − | 0.655630i | ||||
\(516\) | 2.00000 | + | 3.46410i | 0.0880451 | + | 0.152499i | ||||
\(517\) | −3.47214 | −0.152704 | ||||||||
\(518\) | 2.80902 | + | 14.5961i | 0.123421 | + | 0.641315i | ||||
\(519\) | −18.8885 | −0.829115 | ||||||||
\(520\) | 5.00000 | + | 8.66025i | 0.219265 | + | 0.379777i | ||||
\(521\) | −19.8262 | + | 34.3401i | −0.868603 | + | 1.50446i | −0.00517893 | + | 0.999987i | \(0.501649\pi\) |
−0.863424 | + | 0.504478i | \(0.831685\pi\) | |||||||
\(522\) | 7.23607 | − | 12.5332i | 0.316714 | − | 0.548565i | ||||
\(523\) | −8.11803 | − | 14.0608i | −0.354977 | − | 0.614838i | 0.632137 | − | 0.774857i | \(-0.282178\pi\) |
−0.987114 | + | 0.160019i | \(0.948845\pi\) | |||||||
\(524\) | −8.43769 | −0.368602 | ||||||||
\(525\) | −10.0000 | − | 3.46410i | −0.436436 | − | 0.151186i | ||||
\(526\) | 12.0902 | 0.527156 | ||||||||
\(527\) | 0.500000 | + | 0.866025i | 0.0217803 | + | 0.0377247i | ||||
\(528\) | 2.42705 | − | 4.20378i | 0.105624 | − | 0.182946i | ||||
\(529\) | −26.4164 | + | 45.7546i | −1.14854 | + | 1.98933i | ||||
\(530\) | −8.28115 | − | 14.3434i | −0.359710 | − | 0.623037i | ||||
\(531\) | −17.4164 | −0.755808 | ||||||||
\(532\) | −1.81966 | + | 1.57587i | −0.0788923 | + | 0.0683227i | ||||
\(533\) | 4.47214 | 0.193710 | ||||||||
\(534\) | 11.5172 | + | 19.9484i | 0.498399 | + | 0.863252i | ||||
\(535\) | −0.645898 | + | 1.11873i | −0.0279246 | + | 0.0483668i | ||||
\(536\) | 6.64590 | − | 11.5110i | 0.287059 | − | 0.497201i | ||||
\(537\) | 5.20820 | + | 9.02087i | 0.224751 | + | 0.389279i | ||||
\(538\) | −31.5066 | −1.35835 | ||||||||
\(539\) | 5.50000 | + | 4.33013i | 0.236902 | + | 0.186512i | ||||
\(540\) | 3.09017 | 0.132980 | ||||||||
\(541\) | −10.2639 | − | 17.7777i | −0.441281 | − | 0.764321i | 0.556504 | − | 0.830845i | \(-0.312142\pi\) |
−0.997785 | + | 0.0665240i | \(0.978809\pi\) | |||||||
\(542\) | 17.5172 | − | 30.3407i | 0.752429 | − | 1.30325i | ||||
\(543\) | 10.7082 | − | 18.5472i | 0.459533 | − | 0.795935i | ||||
\(544\) | 7.16312 | + | 12.4069i | 0.307116 | + | 0.531941i | ||||
\(545\) | 14.2361 | 0.609806 | ||||||||
\(546\) | 14.4721 | − | 12.5332i | 0.619350 | − | 0.536373i | ||||
\(547\) | −9.52786 | −0.407382 | −0.203691 | − | 0.979035i | \(-0.565294\pi\) | ||||
−0.203691 | + | 0.979035i | \(0.565294\pi\) | |||||||
\(548\) | −4.83688 | − | 8.37772i | −0.206621 | − | 0.357879i | ||||
\(549\) | 9.47214 | − | 16.4062i | 0.404261 | − | 0.700200i | ||||
\(550\) | 3.23607 | − | 5.60503i | 0.137986 | − | 0.238999i | ||||
\(551\) | −3.29180 | − | 5.70156i | −0.140235 | − | 0.242895i | ||||
\(552\) | 19.4721 | 0.828789 | ||||||||
\(553\) | −2.50000 | − | 0.866025i | −0.106311 | − | 0.0368271i | ||||
\(554\) | −6.56231 | −0.278806 | ||||||||
\(555\) | −1.73607 | − | 3.00696i | −0.0736920 | − | 0.127638i | ||||
\(556\) | −5.23607 | + | 9.06914i | −0.222059 | + | 0.384617i | ||||
\(557\) | 7.59017 | − | 13.1466i | 0.321606 | − | 0.557038i | −0.659214 | − | 0.751956i | \(-0.729111\pi\) |
0.980820 | + | 0.194918i | \(0.0624441\pi\) | |||||||
\(558\) | −0.381966 | − | 0.661585i | −0.0161699 | − | 0.0280071i | ||||
\(559\) | 28.9443 | 1.22421 | ||||||||
\(560\) | −2.42705 | − | 12.6113i | −0.102562 | − | 0.532926i | ||||
\(561\) | 4.23607 | 0.178847 | ||||||||
\(562\) | 3.61803 | + | 6.26662i | 0.152618 | + | 0.264341i | ||||
\(563\) | 5.50000 | − | 9.52628i | 0.231797 | − | 0.401485i | −0.726540 | − | 0.687124i | \(-0.758873\pi\) |
0.958337 | + | 0.285640i | \(0.0922060\pi\) | |||||||
\(564\) | 1.07295 | − | 1.85840i | 0.0451793 | − | 0.0782528i | ||||
\(565\) | 9.94427 | + | 17.2240i | 0.418359 | + | 0.724618i | ||||
\(566\) | 18.0902 | 0.760387 | ||||||||
\(567\) | −0.500000 | − | 2.59808i | −0.0209980 | − | 0.109109i | ||||
\(568\) | 32.3607 | 1.35782 | ||||||||
\(569\) | 14.9721 | + | 25.9325i | 0.627665 | + | 1.08715i | 0.988019 | + | 0.154332i | \(0.0493224\pi\) |
−0.360355 | + | 0.932815i | \(0.617344\pi\) | |||||||
\(570\) | 1.19098 | − | 2.06284i | 0.0498848 | − | 0.0864030i | ||||
\(571\) | 14.2639 | − | 24.7059i | 0.596927 | − | 1.03391i | −0.396345 | − | 0.918102i | \(-0.629722\pi\) |
0.993272 | − | 0.115806i | \(-0.0369451\pi\) | |||||||
\(572\) | 1.38197 | + | 2.39364i | 0.0577829 | + | 0.100083i | ||||
\(573\) | 5.47214 | 0.228602 | ||||||||
\(574\) | −4.04508 | − | 1.40126i | −0.168839 | − | 0.0584874i | ||||
\(575\) | 34.8328 | 1.45263 | ||||||||
\(576\) | 4.23607 | + | 7.33708i | 0.176503 | + | 0.305712i | ||||
\(577\) | 15.7705 | − | 27.3153i | 0.656535 | − | 1.13715i | −0.324972 | − | 0.945724i | \(-0.605355\pi\) |
0.981507 | − | 0.191428i | \(-0.0613119\pi\) | |||||||
\(578\) | −0.763932 | + | 1.32317i | −0.0317754 | + | 0.0550366i | ||||
\(579\) | −0.409830 | − | 0.709846i | −0.0170320 | − | 0.0295002i | ||||
\(580\) | −2.76393 | −0.114766 | ||||||||
\(581\) | 3.05573 | − | 2.64634i | 0.126773 | − | 0.109789i | ||||
\(582\) | 13.7082 | 0.568223 | ||||||||
\(583\) | 5.11803 | + | 8.86469i | 0.211967 | + | 0.367138i | ||||
\(584\) | −2.82624 | + | 4.89519i | −0.116951 | + | 0.202564i | ||||
\(585\) | 4.47214 | − | 7.74597i | 0.184900 | − | 0.320256i | ||||
\(586\) | −23.3262 | − | 40.4022i | −0.963598 | − | 1.66900i | ||||
\(587\) | −16.0000 | −0.660391 | −0.330195 | − | 0.943913i | \(-0.607115\pi\) | ||||
−0.330195 | + | 0.943913i | \(0.607115\pi\) | |||||||
\(588\) | −4.01722 | + | 1.60570i | −0.165667 | + | 0.0662179i | ||||
\(589\) | −0.347524 | −0.0143195 | ||||||||
\(590\) | 7.04508 | + | 12.2024i | 0.290042 | + | 0.502367i | ||||
\(591\) | 1.47214 | − | 2.54981i | 0.0605556 | − | 0.104885i | ||||
\(592\) | −8.42705 | + | 14.5961i | −0.346350 | + | 0.599895i | ||||
\(593\) | 3.88197 | + | 6.72376i | 0.159413 | + | 0.276112i | 0.934657 | − | 0.355550i | \(-0.115706\pi\) |
−0.775244 | + | 0.631662i | \(0.782373\pi\) | |||||||
\(594\) | −8.09017 | −0.331944 | ||||||||
\(595\) | 8.47214 | − | 7.33708i | 0.347324 | − | 0.300791i | ||||
\(596\) | 0.729490 | 0.0298811 | ||||||||
\(597\) | −8.97214 | − | 15.5402i | −0.367205 | − | 0.636018i | ||||
\(598\) | −31.5066 | + | 54.5710i | −1.28840 | + | 2.23157i | ||||
\(599\) | 9.06231 | − | 15.6964i | 0.370276 | − | 0.641336i | −0.619332 | − | 0.785129i | \(-0.712597\pi\) |
0.989608 | + | 0.143793i | \(0.0459299\pi\) | |||||||
\(600\) | −4.47214 | − | 7.74597i | −0.182574 | − | 0.316228i | ||||
\(601\) | 0.472136 | 0.0192588 | 0.00962941 | − | 0.999954i | \(-0.496935\pi\) | ||||
0.00962941 | + | 0.999954i | \(0.496935\pi\) | |||||||
\(602\) | −26.1803 | − | 9.06914i | −1.06703 | − | 0.369630i | ||||
\(603\) | −11.8885 | −0.484139 | ||||||||
\(604\) | −1.83688 | − | 3.18157i | −0.0747416 | − | 0.129456i | ||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | −2.66312 | + | 4.61266i | −0.108182 | + | 0.187376i | ||||
\(607\) | −14.5902 | − | 25.2709i | −0.592197 | − | 1.02571i | −0.993936 | − | 0.109961i | \(-0.964927\pi\) |
0.401739 | − | 0.915754i | \(-0.368406\pi\) | |||||||
\(608\) | −4.97871 | −0.201914 | ||||||||
\(609\) | −2.23607 | − | 11.6190i | −0.0906100 | − | 0.470824i | ||||
\(610\) | −15.3262 | −0.620541 | ||||||||
\(611\) | −7.76393 | − | 13.4475i | −0.314095 | − | 0.544029i | ||||
\(612\) | 2.61803 | − | 4.53457i | 0.105828 | − | 0.183299i | ||||
\(613\) | −22.4443 | + | 38.8746i | −0.906516 | + | 1.57013i | −0.0876459 | + | 0.996152i | \(0.527934\pi\) |
−0.818870 | + | 0.573979i | \(0.805399\pi\) | |||||||
\(614\) | 8.00000 | + | 13.8564i | 0.322854 | + | 0.559199i | ||||
\(615\) | 1.00000 | 0.0403239 | ||||||||
\(616\) | 1.11803 | + | 5.80948i | 0.0450469 | + | 0.234070i | ||||
\(617\) | 25.4164 | 1.02323 | 0.511613 | − | 0.859216i | \(-0.329048\pi\) | ||||
0.511613 | + | 0.859216i | \(0.329048\pi\) | |||||||
\(618\) | −13.8992 | − | 24.0741i | −0.559107 | − | 0.968402i | ||||
\(619\) | 10.8820 | − | 18.8481i | 0.437383 | − | 0.757570i | −0.560104 | − | 0.828423i | \(-0.689239\pi\) |
0.997487 | + | 0.0708527i | \(0.0225720\pi\) | |||||||
\(620\) | −0.0729490 | + | 0.126351i | −0.00292970 | + | 0.00507439i | ||||
\(621\) | −21.7705 | − | 37.7076i | −0.873620 | − | 1.51316i | ||||
\(622\) | −35.3262 | −1.41645 | ||||||||
\(623\) | −35.5902 | − | 12.3288i | −1.42589 | − | 0.493943i | ||||
\(624\) | 21.7082 | 0.869024 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 13.9894 | − | 24.2303i | 0.559127 | − | 0.968437i | ||||
\(627\) | −0.736068 | + | 1.27491i | −0.0293957 | + | 0.0509149i | ||||
\(628\) | 0.690983 | + | 1.19682i | 0.0275732 | + | 0.0477582i | ||||
\(629\) | −14.7082 | −0.586454 | ||||||||
\(630\) | −6.47214 | + | 5.60503i | −0.257856 | + | 0.223310i | ||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | −1.11803 | − | 1.93649i | −0.0444730 | − | 0.0770295i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.8435 | + | 36.1019i | −0.827800 | + | 1.43379i | ||||
\(635\) | 7.70820 | + | 13.3510i | 0.305891 | + | 0.529818i | ||||
\(636\) | −6.32624 | −0.250852 | ||||||||
\(637\) | −4.47214 | + | 30.9839i | −0.177192 | + | 1.22763i | ||||
\(638\) | 7.23607 | 0.286479 | ||||||||
\(639\) | −14.4721 | − | 25.0665i | −0.572509 | − | 0.991614i | ||||
\(640\) | 6.80902 | − | 11.7936i | 0.269150 | − | 0.466182i | ||||
\(641\) | −22.1180 | + | 38.3096i | −0.873610 | + | 1.51314i | −0.0153735 | + | 0.999882i | \(0.504894\pi\) |
−0.858236 | + | 0.513255i | \(0.828440\pi\) | |||||||
\(642\) | 1.04508 | + | 1.81014i | 0.0412462 | + | 0.0714405i | ||||
\(643\) | 27.7771 | 1.09542 | 0.547711 | − | 0.836668i | \(-0.315499\pi\) | ||||
0.547711 | + | 0.836668i | \(0.315499\pi\) | |||||||
\(644\) | 10.7639 | − | 9.32184i | 0.424158 | − | 0.367332i | ||||
\(645\) | 6.47214 | 0.254840 | ||||||||
\(646\) | −5.04508 | − | 8.73834i | −0.198496 | − | 0.343806i | ||||
\(647\) | 8.88197 | − | 15.3840i | 0.349186 | − | 0.604808i | −0.636919 | − | 0.770931i | \(-0.719791\pi\) |
0.986105 | + | 0.166123i | \(0.0531248\pi\) | |||||||
\(648\) | 1.11803 | − | 1.93649i | 0.0439205 | − | 0.0760726i | ||||
\(649\) | −4.35410 | − | 7.54153i | −0.170913 | − | 0.296031i | ||||
\(650\) | 28.9443 | 1.13529 | ||||||||
\(651\) | −0.590170 | − | 0.204441i | −0.0231306 | − | 0.00801267i | ||||
\(652\) | −3.27051 | −0.128083 | ||||||||
\(653\) | 6.53444 | + | 11.3180i | 0.255712 | + | 0.442907i | 0.965089 | − | 0.261923i | \(-0.0843566\pi\) |
−0.709376 | + | 0.704830i | \(0.751023\pi\) | |||||||
\(654\) | 11.5172 | − | 19.9484i | 0.450359 | − | 0.780045i | ||||
\(655\) | −6.82624 | + | 11.8234i | −0.266723 | + | 0.461978i | ||||
\(656\) | −2.42705 | − | 4.20378i | −0.0947604 | − | 0.164130i | ||||
\(657\) | 5.05573 | 0.197243 | ||||||||
\(658\) | 2.80902 | + | 14.5961i | 0.109507 | + | 0.569014i | ||||
\(659\) | −24.9443 | −0.971691 | −0.485845 | − | 0.874045i | \(-0.661488\pi\) | ||||
−0.485845 | + | 0.874045i | \(0.661488\pi\) | |||||||
\(660\) | 0.309017 | + | 0.535233i | 0.0120285 | + | 0.0208339i | ||||
\(661\) | −1.31966 | + | 2.28572i | −0.0513288 | + | 0.0889041i | −0.890548 | − | 0.454889i | \(-0.849679\pi\) |
0.839219 | + | 0.543793i | \(0.183012\pi\) | |||||||
\(662\) | 25.7533 | − | 44.6060i | 1.00093 | − | 1.73366i | ||||
\(663\) | 9.47214 | + | 16.4062i | 0.367867 | + | 0.637165i | ||||
\(664\) | 3.41641 | 0.132582 | ||||||||
\(665\) | 0.736068 | + | 3.82472i | 0.0285435 | + | 0.148316i | ||||
\(666\) | 11.2361 | 0.435389 | ||||||||
\(667\) | 19.4721 | + | 33.7267i | 0.753964 | + | 1.30590i | ||||
\(668\) | 0.763932 | − | 1.32317i | 0.0295574 | − | 0.0511949i | ||||
\(669\) | 8.47214 | − | 14.6742i | 0.327552 | − | 0.567336i | ||||
\(670\) | 4.80902 | + | 8.32946i | 0.185789 | + | 0.321795i | ||||
\(671\) | 9.47214 | 0.365668 | ||||||||
\(672\) | −8.45492 | − | 2.92887i | −0.326155 | − | 0.112984i | ||||
\(673\) | −45.4164 | −1.75067 | −0.875337 | − | 0.483513i | \(-0.839360\pi\) | ||||
−0.875337 | + | 0.483513i | \(0.839360\pi\) | |||||||
\(674\) | 6.85410 | + | 11.8717i | 0.264010 | + | 0.457279i | ||||
\(675\) | −10.0000 | + | 17.3205i | −0.384900 | + | 0.666667i | ||||
\(676\) | −2.16312 | + | 3.74663i | −0.0831969 | + | 0.144101i | ||||
\(677\) | −7.97214 | − | 13.8081i | −0.306394 | − | 0.530690i | 0.671177 | − | 0.741297i | \(-0.265789\pi\) |
−0.977571 | + | 0.210607i | \(0.932456\pi\) | |||||||
\(678\) | 32.1803 | 1.23588 | ||||||||
\(679\) | −16.9443 | + | 14.6742i | −0.650261 | + | 0.563143i | ||||
\(680\) | 9.47214 | 0.363240 | ||||||||
\(681\) | 2.73607 | + | 4.73901i | 0.104846 | + | 0.181599i | ||||
\(682\) | 0.190983 | − | 0.330792i | 0.00731312 | − | 0.0126667i | ||||
\(683\) | −7.73607 | + | 13.3993i | −0.296012 | + | 0.512709i | −0.975220 | − | 0.221238i | \(-0.928990\pi\) |
0.679207 | + | 0.733946i | \(0.262324\pi\) | |||||||
\(684\) | 0.909830 | + | 1.57587i | 0.0347882 | + | 0.0602550i | ||||
\(685\) | −15.6525 | −0.598050 | ||||||||
\(686\) | 13.7533 | − | 26.6239i | 0.525103 | − | 1.01651i | ||||
\(687\) | −20.1246 | −0.767802 | ||||||||
\(688\) | −15.7082 | − | 27.2074i | −0.598870 | − | 1.03727i | ||||
\(689\) | −22.8885 | + | 39.6441i | −0.871984 | + | 1.51032i | ||||
\(690\) | −7.04508 | + | 12.2024i | −0.268202 | + | 0.464539i | ||||
\(691\) | −23.6803 | − | 41.0156i | −0.900843 | − | 1.56031i | −0.826403 | − | 0.563080i | \(-0.809616\pi\) |
−0.0744399 | − | 0.997225i | \(-0.523717\pi\) | |||||||
\(692\) | −11.6738 | −0.443770 | ||||||||
\(693\) | 4.00000 | − | 3.46410i | 0.151947 | − | 0.131590i | ||||
\(694\) | −4.85410 | −0.184259 | ||||||||
\(695\) | 8.47214 | + | 14.6742i | 0.321366 | + | 0.556623i | ||||
\(696\) | 5.00000 | − | 8.66025i | 0.189525 | − | 0.328266i | ||||
\(697\) | 2.11803 | − | 3.66854i | 0.0802263 | − | 0.138956i | ||||
\(698\) | 16.5623 | + | 28.6868i | 0.626893 | + | 1.08581i | ||||
\(699\) | 3.29180 | 0.124507 | ||||||||
\(700\) | −6.18034 | − | 2.14093i | −0.233595 | − | 0.0809196i | ||||
\(701\) | −42.3607 | −1.59994 | −0.799970 | − | 0.600039i | \(-0.795152\pi\) | ||||
−0.799970 | + | 0.600039i | \(0.795152\pi\) | |||||||
\(702\) | −18.0902 | − | 31.3331i | −0.682769 | − | 1.18259i | ||||
\(703\) | 2.55573 | − | 4.42665i | 0.0963911 | − | 0.166954i | ||||
\(704\) | −2.11803 | + | 3.66854i | −0.0798264 | + | 0.138263i | ||||
\(705\) | −1.73607 | − | 3.00696i | −0.0653841 | − | 0.113249i | ||||
\(706\) | 41.2148 | 1.55114 | ||||||||
\(707\) | −1.64590 | − | 8.55234i | −0.0619004 | − | 0.321644i | ||||
\(708\) | 5.38197 | 0.202267 | ||||||||
\(709\) | −19.0623 | − | 33.0169i | −0.715900 | − | 1.23998i | −0.962611 | − | 0.270886i | \(-0.912683\pi\) |
0.246711 | − | 0.969089i | \(-0.420650\pi\) | |||||||
\(710\) | −11.7082 | + | 20.2792i | −0.439401 | + | 0.761065i | ||||
\(711\) | −1.00000 | + | 1.73205i | −0.0375029 | + | 0.0649570i | ||||
\(712\) | −15.9164 | − | 27.5680i | −0.596493 | − | 1.03316i | ||||
\(713\) | 2.05573 | 0.0769876 | ||||||||
\(714\) | −3.42705 | − | 17.8075i | −0.128254 | − | 0.666428i | ||||
\(715\) | 4.47214 | 0.167248 | ||||||||
\(716\) | 3.21885 | + | 5.57521i | 0.120294 | + | 0.208355i | ||||
\(717\) | 1.23607 | − | 2.14093i | 0.0461618 | − | 0.0799546i | ||||
\(718\) | 11.0451 | − | 19.1306i | 0.412199 | − | 0.713949i | ||||
\(719\) | 0.680340 | + | 1.17838i | 0.0253724 | + | 0.0439463i | 0.878433 | − | 0.477866i | \(-0.158590\pi\) |
−0.853060 | + | 0.521812i | \(0.825256\pi\) | |||||||
\(720\) | −9.70820 | −0.361803 | ||||||||
\(721\) | 42.9508 | + | 14.8786i | 1.59957 | + | 0.554108i | ||||
\(722\) | −27.2361 | −1.01362 | ||||||||
\(723\) | −0.736068 | − | 1.27491i | −0.0273747 | − | 0.0474143i | ||||
\(724\) | 6.61803 | − | 11.4628i | 0.245957 | − | 0.426011i | ||||
\(725\) | 8.94427 | − | 15.4919i | 0.332182 | − | 0.575356i | ||||
\(726\) | 8.09017 | + | 14.0126i | 0.300254 | + | 0.520056i | ||||
\(727\) | 7.05573 | 0.261682 | 0.130841 | − | 0.991403i | \(-0.458232\pi\) | ||||
0.130841 | + | 0.991403i | \(0.458232\pi\) | |||||||
\(728\) | −20.0000 | + | 17.3205i | −0.741249 | + | 0.641941i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −2.04508 | − | 3.54219i | −0.0756920 | − | 0.131102i | ||||
\(731\) | 13.7082 | − | 23.7433i | 0.507016 | − | 0.878178i | ||||
\(732\) | −2.92705 | + | 5.06980i | −0.108187 | + | 0.187385i | ||||
\(733\) | −8.91641 | − | 15.4437i | −0.329335 | − | 0.570425i | 0.653045 | − | 0.757319i | \(-0.273491\pi\) |
−0.982380 | + | 0.186894i | \(0.940158\pi\) | |||||||
\(734\) | −8.38197 | −0.309384 | ||||||||
\(735\) | −1.00000 | + | 6.92820i | −0.0368856 | + | 0.255551i | ||||
\(736\) | 29.4508 | 1.08557 | ||||||||
\(737\) | −2.97214 | − | 5.14789i | −0.109480 | − | 0.189625i | ||||
\(738\) | −1.61803 | + | 2.80252i | −0.0595607 | + | 0.103162i | ||||
\(739\) | 21.8262 | − | 37.8042i | 0.802891 | − | 1.39065i | −0.114814 | − | 0.993387i | \(-0.536627\pi\) |
0.917706 | − | 0.397261i | \(-0.130039\pi\) | |||||||
\(740\) | −1.07295 | − | 1.85840i | −0.0394424 | − | 0.0683162i | ||||
\(741\) | −6.58359 | −0.241854 | ||||||||
\(742\) | 33.1246 | − | 28.6868i | 1.21604 | − | 1.05312i | ||||
\(743\) | −44.7214 | −1.64067 | −0.820334 | − | 0.571885i | \(-0.806212\pi\) | ||||
−0.820334 | + | 0.571885i | \(0.806212\pi\) | |||||||
\(744\) | −0.263932 | − | 0.457144i | −0.00967622 | − | 0.0167597i | ||||
\(745\) | 0.590170 | − | 1.02220i | 0.0216222 | − | 0.0374507i | ||||
\(746\) | 0.0450850 | − | 0.0780895i | 0.00165068 | − | 0.00285906i | ||||
\(747\) | −1.52786 | − | 2.64634i | −0.0559016 | − | 0.0968244i | ||||
\(748\) | 2.61803 | 0.0957248 | ||||||||
\(749\) | −3.22949 | − | 1.11873i | −0.118003 | − | 0.0408774i | ||||
\(750\) | 14.5623 | 0.531740 | ||||||||
\(751\) | 11.2639 | + | 19.5097i | 0.411027 | + | 0.711919i | 0.995002 | − | 0.0998521i | \(-0.0318370\pi\) |
−0.583976 | + | 0.811771i | \(0.698504\pi\) | |||||||
\(752\) | −8.42705 | + | 14.5961i | −0.307303 | + | 0.532264i | ||||
\(753\) | −13.4164 | + | 23.2379i | −0.488921 | + | 0.846836i | ||||
\(754\) | 16.1803 | + | 28.0252i | 0.589253 | + | 1.02062i | ||||
\(755\) | −5.94427 | −0.216334 | ||||||||
\(756\) | 1.54508 | + | 8.02850i | 0.0561942 | + | 0.291994i | ||||
\(757\) | −2.94427 | −0.107011 | −0.0535057 | − | 0.998568i | \(-0.517040\pi\) | ||||
−0.0535057 | + | 0.998568i | \(0.517040\pi\) | |||||||
\(758\) | −25.4164 | − | 44.0225i | −0.923166 | − | 1.59897i | ||||
\(759\) | 4.35410 | − | 7.54153i | 0.158044 | − | 0.273740i | ||||
\(760\) | −1.64590 | + | 2.85078i | −0.0597030 | + | 0.103409i | ||||
\(761\) | −8.15248 | − | 14.1205i | −0.295527 | − | 0.511868i | 0.679580 | − | 0.733601i | \(-0.262162\pi\) |
−0.975107 | + | 0.221733i | \(0.928829\pi\) | |||||||
\(762\) | 24.9443 | 0.903636 | ||||||||
\(763\) | 7.11803 | + | 36.9864i | 0.257690 | + | 1.33900i | ||||
\(764\) | 3.38197 | 0.122355 | ||||||||
\(765\) | −4.23607 | − | 7.33708i | −0.153155 | − | 0.265273i | ||||
\(766\) | −16.8992 | + | 29.2703i | −0.610592 | + | 1.05758i | ||||
\(767\) | 19.4721 | − | 33.7267i | 0.703098 | − | 1.21780i | ||||
\(768\) | −6.78115 | − | 11.7453i | −0.244694 | − | 0.423822i | ||||
\(769\) | −16.8328 | −0.607007 | −0.303503 | − | 0.952830i | \(-0.598156\pi\) | ||||
−0.303503 | + | 0.952830i | \(0.598156\pi\) | |||||||
\(770\) | −4.04508 | − | 1.40126i | −0.145775 | − | 0.0504979i | ||||
\(771\) | −1.29180 | −0.0465229 | ||||||||
\(772\) | −0.253289 | − | 0.438709i | −0.00911607 | − | 0.0157895i | ||||
\(773\) | 4.82624 | − | 8.35929i | 0.173588 | − | 0.300663i | −0.766084 | − | 0.642741i | \(-0.777797\pi\) |
0.939672 | + | 0.342078i | \(0.111131\pi\) | |||||||
\(774\) | −10.4721 | + | 18.1383i | −0.376413 | + | 0.651967i | ||||
\(775\) | −0.472136 | − | 0.817763i | −0.0169596 | − | 0.0293749i | ||||
\(776\) | −18.9443 | −0.680060 | ||||||||
\(777\) | 6.94427 | − | 6.01392i | 0.249124 | − | 0.215748i | ||||
\(778\) | −1.61803 | −0.0580093 | ||||||||
\(779\) | 0.736068 | + | 1.27491i | 0.0263724 | + | 0.0456783i | ||||
\(780\) | −1.38197 | + | 2.39364i | −0.0494823 | + | 0.0857059i | ||||
\(781\) | 7.23607 | − | 12.5332i | 0.258927 | − | 0.448474i | ||||
\(782\) | 29.8435 | + | 51.6904i | 1.06720 | + | 1.84844i | ||||
\(783\) | −22.3607 | −0.799106 | ||||||||
\(784\) | 31.5517 | − | 12.6113i | 1.12685 | − | 0.450405i | ||||
\(785\) | 2.23607 | 0.0798087 | ||||||||
\(786\) | 11.0451 | + | 19.1306i | 0.393965 | + | 0.682368i | ||||
\(787\) | −4.82624 | + | 8.35929i | −0.172037 | + | 0.297976i | −0.939132 | − | 0.343557i | \(-0.888368\pi\) |
0.767095 | + | 0.641534i | \(0.221701\pi\) | |||||||
\(788\) | 0.909830 | − | 1.57587i | 0.0324114 | − | 0.0561381i | ||||
\(789\) | −3.73607 | − | 6.47106i | −0.133008 | − | 0.230376i | ||||
\(790\) | 1.61803 | 0.0575671 | ||||||||
\(791\) | −39.7771 | + | 34.4480i | −1.41431 | + | 1.22483i | ||||
\(792\) | 4.47214 | 0.158910 | ||||||||
\(793\) | 21.1803 | + | 36.6854i | 0.752136 | + | 1.30274i | ||||
\(794\) | −22.3713 | + | 38.7483i | −0.793929 | + | 1.37512i | ||||
\(795\) | −5.11803 | + | 8.86469i | −0.181518 | + | 0.314398i | ||||
\(796\) | −5.54508 | − | 9.60437i | −0.196540 | − | 0.340418i | ||||
\(797\) | 24.8328 | 0.879623 | 0.439812 | − | 0.898090i | \(-0.355045\pi\) | ||||
0.439812 | + | 0.898090i | \(0.355045\pi\) | |||||||
\(798\) | 5.95492 | + | 2.06284i | 0.210802 | + | 0.0730239i | ||||
\(799\) | −14.7082 | −0.520339 | ||||||||
\(800\) | −6.76393 | − | 11.7155i | −0.239141 | − | 0.414205i | ||||
\(801\) | −14.2361 | + | 24.6576i | −0.503007 | + | 0.871233i | ||||
\(802\) | −6.42705 | + | 11.1320i | −0.226947 | + | 0.393084i | ||||
\(803\) | 1.26393 | + | 2.18919i | 0.0446032 | + | 0.0772550i | ||||
\(804\) | 3.67376 | 0.129564 | ||||||||
\(805\) | −4.35410 | − | 22.6246i | −0.153462 | − | 0.797412i | ||||
\(806\) | 1.70820 | 0.0601689 | ||||||||
\(807\) | 9.73607 | + | 16.8634i | 0.342726 | + | 0.593619i | ||||
\(808\) | 3.68034 | − | 6.37454i | 0.129474 | − | 0.224255i | ||||
\(809\) | 2.82624 | − | 4.89519i | 0.0993652 | − | 0.172106i | −0.812057 | − | 0.583578i | \(-0.801652\pi\) |
0.911422 | + | 0.411473i | \(0.134985\pi\) | |||||||
\(810\) | 0.809017 | + | 1.40126i | 0.0284260 | + | 0.0492352i | ||||
\(811\) | 52.7214 | 1.85130 | 0.925649 | − | 0.378384i | \(-0.123520\pi\) | ||||
0.925649 | + | 0.378384i | \(0.123520\pi\) | |||||||
\(812\) | −1.38197 | − | 7.18091i | −0.0484975 | − | 0.252000i | ||||
\(813\) | −21.6525 | −0.759385 | ||||||||
\(814\) | 2.80902 | + | 4.86536i | 0.0984560 | + | 0.170531i | ||||
\(815\) | −2.64590 | + | 4.58283i | −0.0926818 | + | 0.160530i | ||||
\(816\) | 10.2812 | − | 17.8075i | 0.359912 | − | 0.623386i | ||||
\(817\) | 4.76393 | + | 8.25137i | 0.166669 | + | 0.288679i | ||||
\(818\) | −37.0344 | −1.29488 | ||||||||
\(819\) | 22.3607 | + | 7.74597i | 0.781345 | + | 0.270666i | ||||
\(820\) | 0.618034 | 0.0215827 | ||||||||
\(821\) | 10.5000 | + | 18.1865i | 0.366453 | + | 0.634714i | 0.989008 | − | 0.147861i | \(-0.0472389\pi\) |
−0.622556 | + | 0.782576i | \(0.713906\pi\) | |||||||
\(822\) | −12.6631 | + | 21.9332i | −0.441677 | + | 0.765007i | ||||
\(823\) | 6.73607 | − | 11.6672i | 0.234805 | − | 0.406693i | −0.724411 | − | 0.689368i | \(-0.757888\pi\) |
0.959216 | + | 0.282675i | \(0.0912216\pi\) | |||||||
\(824\) | 19.2082 | + | 33.2696i | 0.669149 | + | 1.15900i | ||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | −28.1803 | + | 24.4049i | −0.980519 | + | 0.849155i | ||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | −5.38197 | − | 9.32184i | −0.187036 | − | 0.323956i | ||||
\(829\) | −1.97214 | + | 3.41584i | −0.0684951 | + | 0.118637i | −0.898239 | − | 0.439507i | \(-0.855153\pi\) |
0.829744 | + | 0.558144i | \(0.188486\pi\) | |||||||
\(830\) | −1.23607 | + | 2.14093i | −0.0429045 | + | 0.0743129i | ||||
\(831\) | 2.02786 | + | 3.51236i | 0.0703458 | + | 0.121843i | ||||
\(832\) | −18.9443 | −0.656774 | ||||||||
\(833\) | 23.2984 | + | 18.3427i | 0.807241 | + | 0.635537i | ||||
\(834\) | 27.4164 | 0.949353 | ||||||||
\(835\) | −1.23607 | − | 2.14093i | −0.0427759 | − | 0.0740900i | ||||
\(836\) | −0.454915 | + | 0.787936i | −0.0157336 | + | 0.0272513i | ||||
\(837\) | −0.590170 | + | 1.02220i | −0.0203993 | + | 0.0353326i | ||||
\(838\) | 14.4721 | + | 25.0665i | 0.499932 | + | 0.865907i | ||||
\(839\) | 20.9443 | 0.723077 | 0.361538 | − | 0.932357i | \(-0.382252\pi\) | ||||
0.361538 | + | 0.932357i | \(0.382252\pi\) | |||||||
\(840\) | −4.47214 | + | 3.87298i | −0.154303 | + | 0.133631i | ||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 13.3262 | + | 23.0817i | 0.459252 | + | 0.795449i | ||||
\(843\) | 2.23607 | − | 3.87298i | 0.0770143 | − | 0.133393i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.50000 | + | 6.06218i | 0.120404 | + | 0.208545i | ||||
\(846\) | 11.2361 | 0.386304 | ||||||||
\(847\) | −25.0000 | − | 8.66025i | −0.859010 | − | 0.297570i | ||||
\(848\) | 49.6869 | 1.70626 | ||||||||
\(849\) | −5.59017 | − | 9.68246i | −0.191854 | − | 0.332301i | ||||
\(850\) | 13.7082 | − | 23.7433i | 0.470188 | − | 0.814389i | ||||
\(851\) | −15.1180 | + | 26.1852i | −0.518240 | + | 0.897617i | ||||
\(852\) | 4.47214 | + | 7.74597i | 0.153213 | + | 0.265372i | ||||
\(853\) | 18.9443 | 0.648640 | 0.324320 | − | 0.945948i | \(-0.394865\pi\) | ||||
0.324320 | + | 0.945948i | \(0.394865\pi\) | |||||||
\(854\) | −7.66312 | − | 39.8187i | −0.262227 | − | 1.36257i | ||||
\(855\) | 2.94427 | 0.100692 | ||||||||
\(856\) | −1.44427 | − | 2.50155i | −0.0493642 | − | 0.0855013i | ||||
\(857\) | 5.15248 | − | 8.92435i | 0.176005 | − | 0.304850i | −0.764503 | − | 0.644620i | \(-0.777016\pi\) |
0.940509 | + | 0.339770i | \(0.110349\pi\) | |||||||
\(858\) | 3.61803 | − | 6.26662i | 0.123518 | − | 0.213939i | ||||
\(859\) | 14.6459 | + | 25.3674i | 0.499712 | + | 0.865526i | 1.00000 | 0.000332993i | \(-0.000105995\pi\) | |
−0.500288 | + | 0.865859i | \(0.666773\pi\) | |||||||
\(860\) | 4.00000 | 0.136399 | ||||||||
\(861\) | 0.500000 | + | 2.59808i | 0.0170400 | + | 0.0885422i | ||||
\(862\) | −3.79837 | −0.129373 | ||||||||
\(863\) | −0.409830 | − | 0.709846i | −0.0139508 | − | 0.0241635i | 0.858966 | − | 0.512033i | \(-0.171107\pi\) |
−0.872917 | + | 0.487870i | \(0.837774\pi\) | |||||||
\(864\) | −8.45492 | + | 14.6443i | −0.287642 | + | 0.498211i | ||||
\(865\) | −9.44427 | + | 16.3580i | −0.321115 | + | 0.556187i | ||||
\(866\) | −5.61803 | − | 9.73072i | −0.190909 | − | 0.330663i | ||||
\(867\) | 0.944272 | 0.0320692 | ||||||||
\(868\) | −0.364745 | − | 0.126351i | −0.0123803 | − | 0.00428865i | ||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 3.61803 | + | 6.26662i | 0.122663 | + | 0.212458i | ||||
\(871\) | 13.2918 | − | 23.0221i | 0.450375 | − | 0.780073i | ||||
\(872\) | −15.9164 | + | 27.5680i | −0.538998 | + | 0.933571i | ||||
\(873\) | 8.47214 | + | 14.6742i | 0.286738 | + | 0.496645i | ||||
\(874\) | −20.7426 | −0.701630 | ||||||||
\(875\) | −18.0000 | + | 15.5885i | −0.608511 | + | 0.526986i | ||||
\(876\) | −1.56231 | −0.0527854 | ||||||||
\(877\) | −0.736068 | − | 1.27491i | −0.0248552 | − | 0.0430506i | 0.853330 | − | 0.521371i | \(-0.174579\pi\) |
−0.878185 | + | 0.478320i | \(0.841246\pi\) | |||||||
\(878\) | 29.4615 | − | 51.0288i | 0.994277 | − | 1.72214i | ||||
\(879\) | −14.4164 | + | 24.9700i | −0.486253 | + | 0.842216i | ||||
\(880\) | −2.42705 | − | 4.20378i | −0.0818159 | − | 0.141709i | ||||
\(881\) | 24.4721 | 0.824487 | 0.412244 | − | 0.911074i | \(-0.364745\pi\) | ||||
0.412244 | + | 0.911074i | \(0.364745\pi\) | |||||||
\(882\) | −17.7984 | − | 14.0126i | −0.599302 | − | 0.471828i | ||||
\(883\) | −16.5836 | −0.558082 | −0.279041 | − | 0.960279i | \(-0.590017\pi\) | ||||
−0.279041 | + | 0.960279i | \(0.590017\pi\) | |||||||
\(884\) | 5.85410 | + | 10.1396i | 0.196895 | + | 0.341032i | ||||
\(885\) | 4.35410 | − | 7.54153i | 0.146362 | − | 0.253506i | ||||
\(886\) | 6.28115 | − | 10.8793i | 0.211019 | − | 0.365496i | ||||
\(887\) | 23.4443 | + | 40.6067i | 0.787182 | + | 1.36344i | 0.927687 | + | 0.373359i | \(0.121794\pi\) |
−0.140505 | + | 0.990080i | \(0.544873\pi\) | |||||||
\(888\) | 7.76393 | 0.260540 | ||||||||
\(889\) | −30.8328 | + | 26.7020i | −1.03410 | + | 0.895556i | ||||
\(890\) | 23.0344 | 0.772116 | ||||||||
\(891\) | −0.500000 | − | 0.866025i | −0.0167506 | − | 0.0290129i | ||||
\(892\) | 5.23607 | − | 9.06914i | 0.175317 | − | 0.303657i | ||||
\(893\) | 2.55573 | − | 4.42665i | 0.0855242 | − | 0.148132i | ||||
\(894\) | −0.954915 | − | 1.65396i | −0.0319371 | − | 0.0553167i | ||||
\(895\) | 10.4164 | 0.348182 | ||||||||
\(896\) | 34.0451 | + | 11.7936i | 1.13737 | + | 0.393995i | ||||
\(897\) | 38.9443 | 1.30031 | ||||||||
\(898\) | −17.0344 | − | 29.5045i | −0.568447 | − | 0.984579i | ||||
\(899\) | 0.527864 | − | 0.914287i | 0.0176053 | − | 0.0304932i | ||||
\(900\) | −2.47214 | + | 4.28187i | −0.0824045 | + | 0.142729i | ||||
\(901\) | 21.6803 | + | 37.5515i | 0.722277 | + | 1.25102i | ||||
\(902\) | −1.61803 | −0.0538746 | ||||||||
\(903\) | 3.23607 | + | 16.8151i | 0.107690 | + | 0.559572i | ||||
\(904\) | −44.4721 | −1.47912 | ||||||||
\(905\) | −10.7082 | − | 18.5472i | −0.355953 | − | 0.616528i | ||||
\(906\) | −4.80902 | + | 8.32946i | −0.159769 | + | 0.276728i | ||||
\(907\) | 7.17376 | − | 12.4253i | 0.238201 | − | 0.412576i | −0.721997 | − | 0.691896i | \(-0.756776\pi\) |
0.960198 | + | 0.279320i | \(0.0901090\pi\) | |||||||
\(908\) | 1.69098 | + | 2.92887i | 0.0561172 | + | 0.0971979i | ||||
\(909\) | −6.58359 | −0.218364 | ||||||||
\(910\) | −3.61803 | − | 18.7999i | −0.119937 | − | 0.623209i | ||||
\(911\) | −47.4164 | −1.57098 | −0.785488 | − | 0.618877i | \(-0.787588\pi\) | ||||
−0.785488 | + | 0.618877i | \(0.787588\pi\) | |||||||
\(912\) | 3.57295 | + | 6.18853i | 0.118312 | + | 0.204923i | ||||
\(913\) | 0.763932 | − | 1.32317i | 0.0252825 | − | 0.0437905i | ||||
\(914\) | 21.2254 | − | 36.7635i | 0.702075 | − | 1.21603i | ||||
\(915\) | 4.73607 | + | 8.20311i | 0.156570 | + | 0.271186i | ||||
\(916\) | −12.4377 | −0.410953 | ||||||||
\(917\) | −34.1312 | − | 11.8234i | −1.12711 | − | 0.390443i | ||||
\(918\) | −34.2705 | −1.13110 | ||||||||
\(919\) | 2.02786 | + | 3.51236i | 0.0668931 | + | 0.115862i | 0.897532 | − | 0.440949i | \(-0.145358\pi\) |
−0.830639 | + | 0.556811i | \(0.812025\pi\) | |||||||
\(920\) | 9.73607 | − | 16.8634i | 0.320989 | − | 0.555969i | ||||
\(921\) | 4.94427 | − | 8.56373i | 0.162919 | − | 0.282185i | ||||
\(922\) | 31.5066 | + | 54.5710i | 1.03761 | + | 1.79720i | ||||
\(923\) | 64.7214 | 2.13033 | ||||||||
\(924\) | −1.23607 | + | 1.07047i | −0.0406637 | + | 0.0352158i | ||||
\(925\) | 13.8885 | 0.456653 | ||||||||
\(926\) | 1.70820 | + | 2.95870i | 0.0561351 | + | 0.0972288i | ||||
\(927\) | 17.1803 | − | 29.7572i | 0.564276 | − | 0.977355i | ||||
\(928\) | 7.56231 | − | 13.0983i | 0.248245 | − | 0.429973i | ||||
\(929\) | 19.7705 | + | 34.2435i | 0.648649 | + | 1.12349i | 0.983446 | + | 0.181203i | \(0.0579992\pi\) |
−0.334796 | + | 0.942291i | \(0.608668\pi\) | |||||||
\(930\) | 0.381966 | 0.0125252 | ||||||||
\(931\) | −9.56888 | + | 3.82472i | −0.313607 | + | 0.125350i | ||||
\(932\) | 2.03444 | 0.0666404 | ||||||||
\(933\) | 10.9164 | + | 18.9078i | 0.357387 | + | 0.619013i | ||||
\(934\) | −7.13525 | + | 12.3586i | −0.233473 | + | 0.404387i | ||||
\(935\) | 2.11803 | − | 3.66854i | 0.0692671 | − | 0.119974i | ||||
\(936\) | 10.0000 | + | 17.3205i | 0.326860 | + | 0.566139i | ||||
\(937\) | 29.4164 | 0.960992 | 0.480496 | − | 0.876997i | \(-0.340457\pi\) | ||||
0.480496 | + | 0.876997i | \(0.340457\pi\) | |||||||
\(938\) | −19.2361 | + | 16.6589i | −0.628080 | + | 0.543933i | ||||
\(939\) | −17.2918 | −0.564296 | ||||||||
\(940\) | −1.07295 | − | 1.85840i | −0.0349957 | − | 0.0606144i | ||||
\(941\) | −17.2082 | + | 29.8055i | −0.560971 | + | 0.971631i | 0.436441 | + | 0.899733i | \(0.356239\pi\) |
−0.997412 | + | 0.0718979i | \(0.977094\pi\) | |||||||
\(942\) | 1.80902 | − | 3.13331i | 0.0589410 | − | 0.102089i | ||||
\(943\) | −4.35410 | − | 7.54153i | −0.141789 | − | 0.245586i | ||||
\(944\) | −42.2705 | −1.37579 | ||||||||
\(945\) | 12.5000 | + | 4.33013i | 0.406625 | + | 0.140859i | ||||
\(946\) | −10.4721 | −0.340479 | ||||||||
\(947\) | −15.3541 | − | 26.5941i | −0.498941 | − | 0.864192i | 0.501058 | − | 0.865414i | \(-0.332944\pi\) |
−0.999999 | + | 0.00122208i | \(0.999611\pi\) | |||||||
\(948\) | 0.309017 | − | 0.535233i | 0.0100364 | − | 0.0173836i | ||||
\(949\) | −5.65248 | + | 9.79038i | −0.183487 | + | 0.317809i | ||||
\(950\) | 4.76393 | + | 8.25137i | 0.154562 | + | 0.267710i | ||||
\(951\) | 25.7639 | 0.835453 | ||||||||
\(952\) | 4.73607 | + | 24.6093i | 0.153497 | + | 0.797593i | ||||
\(953\) | 43.8885 | 1.42169 | 0.710845 | − | 0.703349i | \(-0.248313\pi\) | ||||
0.710845 | + | 0.703349i | \(0.248313\pi\) | |||||||
\(954\) | −16.5623 | − | 28.6868i | −0.536224 | − | 0.928768i | ||||
\(955\) | 2.73607 | − | 4.73901i | 0.0885371 | − | 0.153351i | ||||
\(956\) | 0.763932 | − | 1.32317i | 0.0247073 | − | 0.0427943i | ||||
\(957\) | −2.23607 | − | 3.87298i | −0.0722818 | − | 0.125196i | ||||
\(958\) | 33.9787 | 1.09780 | ||||||||
\(959\) | −7.82624 | − | 40.6663i | −0.252722 | − | 1.31318i | ||||
\(960\) | −4.23607 | −0.136719 | ||||||||
\(961\) | 15.4721 | + | 26.7985i | 0.499101 | + | 0.864469i | ||||
\(962\) | −12.5623 | + | 21.7586i | −0.405025 | + | 0.701524i | ||||
\(963\) | −1.29180 | + | 2.23746i | −0.0416275 | + | 0.0721010i | ||||
\(964\) | −0.454915 | − | 0.787936i | −0.0146518 | − | 0.0253777i | ||||
\(965\) | −0.819660 | −0.0263858 | ||||||||
\(966\) | −35.2254 | − | 12.2024i | −1.13336 | − | 0.392607i | ||||
\(967\) | 21.3050 | 0.685121 | 0.342561 | − | 0.939496i | \(-0.388706\pi\) | ||||
0.342561 | + | 0.939496i | \(0.388706\pi\) | |||||||
\(968\) | −11.1803 | − | 19.3649i | −0.359350 | − | 0.622412i | ||||
\(969\) | −3.11803 | + | 5.40059i | −0.100166 | + | 0.173492i | ||||
\(970\) | 6.85410 | − | 11.8717i | 0.220072 | − | 0.381176i | ||||
\(971\) | −23.3885 | − | 40.5101i | −0.750574 | − | 1.30003i | −0.947545 | − | 0.319623i | \(-0.896444\pi\) |
0.196971 | − | 0.980409i | \(-0.436890\pi\) | |||||||
\(972\) | 9.88854 | 0.317175 | ||||||||
\(973\) | −33.8885 | + | 29.3483i | −1.08642 | + | 0.940865i | ||||
\(974\) | −41.3262 | −1.32418 | ||||||||
\(975\) | −8.94427 | − | 15.4919i | −0.286446 | − | 0.496139i | ||||
\(976\) | 22.9894 | − | 39.8187i | 0.735871 | − | 1.27457i | ||||
\(977\) | −11.8262 | + | 20.4836i | −0.378355 | + | 0.655330i | −0.990823 | − | 0.135165i | \(-0.956843\pi\) |
0.612468 | + | 0.790495i | \(0.290177\pi\) | |||||||
\(978\) | 4.28115 | + | 7.41517i | 0.136896 | + | 0.237111i | ||||
\(979\) | −14.2361 | −0.454987 | ||||||||
\(980\) | −0.618034 | + | 4.28187i | −0.0197424 | + | 0.136779i | ||||
\(981\) | 28.4721 | 0.909045 | ||||||||
\(982\) | 10.0000 | + | 17.3205i | 0.319113 | + | 0.552720i | ||||
\(983\) | 25.0623 | − | 43.4092i | 0.799363 | − | 1.38454i | −0.120668 | − | 0.992693i | \(-0.538504\pi\) |
0.920031 | − | 0.391845i | \(-0.128163\pi\) | |||||||
\(984\) | −1.11803 | + | 1.93649i | −0.0356416 | + | 0.0617331i | ||||
\(985\) | −1.47214 | − | 2.54981i | −0.0469062 | − | 0.0812438i | ||||
\(986\) | 30.6525 | 0.976174 | ||||||||
\(987\) | 6.94427 | − | 6.01392i | 0.221039 | − | 0.191425i | ||||
\(988\) | −4.06888 | −0.129448 | ||||||||
\(989\) | −28.1803 | − | 48.8098i | −0.896083 | − | 1.55206i | ||||
\(990\) | −1.61803 | + | 2.80252i | −0.0514245 | + | 0.0890698i | ||||
\(991\) | 23.2082 | − | 40.1978i | 0.737233 | − | 1.27692i | −0.216504 | − | 0.976282i | \(-0.569465\pi\) |
0.953737 | − | 0.300643i | \(-0.0972013\pi\) | |||||||
\(992\) | −0.399187 | − | 0.691412i | −0.0126742 | − | 0.0219524i | ||||
\(993\) | −31.8328 | −1.01018 | ||||||||
\(994\) | −58.5410 | − | 20.2792i | −1.85681 | − | 0.643217i | ||||
\(995\) | −17.9443 | −0.568872 | ||||||||
\(996\) | 0.472136 | + | 0.817763i | 0.0149602 | + | 0.0259118i | ||||
\(997\) | 20.5344 | − | 35.5667i | 0.650332 | − | 1.12641i | −0.332710 | − | 0.943029i | \(-0.607963\pi\) |
0.983042 | − | 0.183379i | \(-0.0587037\pi\) | |||||||
\(998\) | 12.9894 | − | 22.4982i | 0.411171 | − | 0.712169i | ||||
\(999\) | −8.68034 | − | 15.0348i | −0.274634 | − | 0.475680i |
(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 | 287.2.e.a.165.1 | ✓ | 4 | |
7.2 | even | 3 | inner | 287.2.e.a.247.1 | yes | 4 | |
7.3 | odd | 6 | 2009.2.a.e.1.2 | 2 | |||
7.4 | even | 3 | 2009.2.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.a.165.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
287.2.e.a.247.1 | yes | 4 | 7.2 | even | 3 | inner | |
2009.2.a.e.1.2 | 2 | 7.3 | odd | 6 | |||
2009.2.a.f.1.2 | 2 | 7.4 | even | 3 |