Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(361,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.i (of order \(3\), degree \(2\), not 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.361 |
Dual form | 1470.2.i.x.961.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −1.12132 | + | 1.94218i | −0.338091 | + | 0.585590i | −0.984074 | − | 0.177762i | \(-0.943114\pi\) |
0.645983 | + | 0.763352i | \(0.276448\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.29289 | + | 2.23936i | −0.313573 | + | 0.543124i | −0.979133 | − | 0.203220i | \(-0.934859\pi\) |
0.665560 | + | 0.746344i | \(0.268193\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 3.41421 | + | 5.91359i | 0.783274 | + | 1.35667i | 0.930025 | + | 0.367497i | \(0.119785\pi\) |
−0.146750 | + | 0.989174i | \(0.546881\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.24264 | −0.478133 | ||||||||
\(23\) | −1.58579 | − | 2.74666i | −0.330659 | − | 0.572719i | 0.651982 | − | 0.758234i | \(-0.273938\pi\) |
−0.982641 | + | 0.185516i | \(0.940604\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.82843 | + | 4.89898i | 0.554700 | + | 0.960769i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58579 | 0.480168 | 0.240084 | − | 0.970752i | \(-0.422825\pi\) | ||||
0.240084 | + | 0.970752i | \(0.422825\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | 5.12132 | − | 8.87039i | 0.919816 | − | 1.59317i | 0.120124 | − | 0.992759i | \(-0.461671\pi\) |
0.799693 | − | 0.600410i | \(-0.204996\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.12132 | + | 1.94218i | 0.195197 | + | 0.338091i | ||||
\(34\) | −2.58579 | −0.443459 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.121320 | + | 0.210133i | 0.0199449 | + | 0.0345457i | 0.875826 | − | 0.482628i | \(-0.160318\pi\) |
−0.855881 | + | 0.517173i | \(0.826984\pi\) | |||||||
\(38\) | −3.41421 | + | 5.91359i | −0.553859 | + | 0.959311i | ||||
\(39\) | 2.82843 | − | 4.89898i | 0.452911 | − | 0.784465i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 10.4853 | 1.63753 | 0.818763 | − | 0.574132i | \(-0.194660\pi\) | ||||
0.818763 | + | 0.574132i | \(0.194660\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.07107 | 1.38332 | 0.691662 | − | 0.722221i | \(-0.256879\pi\) | ||||
0.691662 | + | 0.722221i | \(0.256879\pi\) | |||||||
\(44\) | −1.12132 | − | 1.94218i | −0.169045 | − | 0.292795i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 1.58579 | − | 2.74666i | 0.233811 | − | 0.404973i | ||||
\(47\) | 1.12132 | + | 1.94218i | 0.163561 | + | 0.283297i | 0.936143 | − | 0.351618i | \(-0.114368\pi\) |
−0.772582 | + | 0.634915i | \(0.781035\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.29289 | + | 2.23936i | 0.181041 | + | 0.313573i | ||||
\(52\) | −2.82843 | + | 4.89898i | −0.392232 | + | 0.679366i | ||||
\(53\) | −0.171573 | + | 0.297173i | −0.0235673 | + | 0.0408198i | −0.877569 | − | 0.479451i | \(-0.840836\pi\) |
0.854001 | + | 0.520271i | \(0.174169\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 2.24264 | 0.302398 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.82843 | 0.904447 | ||||||||
\(58\) | 1.29289 | + | 2.23936i | 0.169765 | + | 0.294042i | ||||
\(59\) | 1.58579 | − | 2.74666i | 0.206452 | − | 0.357585i | −0.744143 | − | 0.668021i | \(-0.767142\pi\) |
0.950594 | + | 0.310436i | \(0.100475\pi\) | |||||||
\(60\) | 0.500000 | − | 0.866025i | 0.0645497 | − | 0.111803i | ||||
\(61\) | 5.82843 | + | 10.0951i | 0.746254 | + | 1.29255i | 0.949607 | + | 0.313444i | \(0.101483\pi\) |
−0.203353 | + | 0.979105i | \(0.565184\pi\) | |||||||
\(62\) | 10.2426 | 1.30082 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.82843 | − | 4.89898i | −0.350823 | − | 0.607644i | ||||
\(66\) | −1.12132 | + | 1.94218i | −0.138025 | + | 0.239066i | ||||
\(67\) | −4.53553 | + | 7.85578i | −0.554104 | + | 0.959736i | 0.443869 | + | 0.896092i | \(0.353606\pi\) |
−0.997973 | + | 0.0636440i | \(0.979728\pi\) | |||||||
\(68\) | −1.29289 | − | 2.23936i | −0.156786 | − | 0.271562i | ||||
\(69\) | −3.17157 | −0.381813 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48528 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | −0.121320 | + | 0.210133i | −0.0141032 | + | 0.0244275i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | −6.82843 | −0.783274 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.65685 | 0.640513 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.24264 | + | 9.08052i | 0.578953 | + | 1.00278i | ||||
\(83\) | 5.17157 | 0.567654 | 0.283827 | − | 0.958876i | \(-0.408396\pi\) | ||||
0.283827 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58579 | 0.280468 | ||||||||
\(86\) | 4.53553 | + | 7.85578i | 0.489079 | + | 0.847110i | ||||
\(87\) | 1.29289 | − | 2.23936i | 0.138613 | − | 0.240084i | ||||
\(88\) | 1.12132 | − | 1.94218i | 0.119533 | − | 0.207037i | ||||
\(89\) | 0.414214 | + | 0.717439i | 0.0439065 | + | 0.0760484i | 0.887144 | − | 0.461494i | \(-0.152686\pi\) |
−0.843237 | + | 0.537542i | \(0.819353\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.17157 | 0.330659 | ||||||||
\(93\) | −5.12132 | − | 8.87039i | −0.531056 | − | 0.919816i | ||||
\(94\) | −1.12132 | + | 1.94218i | −0.115655 | + | 0.200321i | ||||
\(95\) | 3.41421 | − | 5.91359i | 0.350291 | − | 0.606722i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −6.48528 | −0.658481 | −0.329240 | − | 0.944246i | \(-0.606793\pi\) | ||||
−0.329240 | + | 0.944246i | \(0.606793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.24264 | 0.225394 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −8.82843 | + | 15.2913i | −0.878461 | + | 1.52154i | −0.0254321 | + | 0.999677i | \(0.508096\pi\) |
−0.853029 | + | 0.521863i | \(0.825237\pi\) | |||||||
\(102\) | −1.29289 | + | 2.23936i | −0.128016 | + | 0.221729i | ||||
\(103\) | −7.41421 | − | 12.8418i | −0.730544 | − | 1.26534i | −0.956651 | − | 0.291237i | \(-0.905933\pi\) |
0.226107 | − | 0.974103i | \(-0.427400\pi\) | |||||||
\(104\) | −5.65685 | −0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.343146 | −0.0333293 | ||||||||
\(107\) | −4.82843 | − | 8.36308i | −0.466782 | − | 0.808490i | 0.532498 | − | 0.846431i | \(-0.321253\pi\) |
−0.999280 | + | 0.0379415i | \(0.987920\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 1.82843 | − | 3.16693i | 0.175132 | − | 0.303337i | −0.765075 | − | 0.643941i | \(-0.777298\pi\) |
0.940207 | + | 0.340604i | \(0.110632\pi\) | |||||||
\(110\) | 1.12132 | + | 1.94218i | 0.106914 | + | 0.185180i | ||||
\(111\) | 0.242641 | 0.0230304 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 3.41421 | + | 5.91359i | 0.319770 | + | 0.553859i | ||||
\(115\) | −1.58579 | + | 2.74666i | −0.147875 | + | 0.256128i | ||||
\(116\) | −1.29289 | + | 2.23936i | −0.120042 | + | 0.207919i | ||||
\(117\) | −2.82843 | − | 4.89898i | −0.261488 | − | 0.452911i | ||||
\(118\) | 3.17157 | 0.291967 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 2.98528 | + | 5.17066i | 0.271389 | + | 0.470060i | ||||
\(122\) | −5.82843 | + | 10.0951i | −0.527681 | + | 0.913970i | ||||
\(123\) | 5.24264 | − | 9.08052i | 0.472713 | − | 0.818763i | ||||
\(124\) | 5.12132 | + | 8.87039i | 0.459908 | + | 0.796584i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843 | 0.250982 | 0.125491 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125491 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.53553 | − | 7.85578i | 0.399331 | − | 0.691662i | ||||
\(130\) | 2.82843 | − | 4.89898i | 0.248069 | − | 0.429669i | ||||
\(131\) | 1.58579 | + | 2.74666i | 0.138551 | + | 0.239977i | 0.926948 | − | 0.375189i | \(-0.122422\pi\) |
−0.788397 | + | 0.615166i | \(0.789089\pi\) | |||||||
\(132\) | −2.24264 | −0.195197 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.07107 | −0.783621 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 1.29289 | − | 2.23936i | 0.110865 | − | 0.192023i | ||||
\(137\) | −6.82843 | + | 11.8272i | −0.583392 | + | 1.01046i | 0.411682 | + | 0.911328i | \(0.364941\pi\) |
−0.995074 | + | 0.0991368i | \(0.968392\pi\) | |||||||
\(138\) | −1.58579 | − | 2.74666i | −0.134991 | − | 0.233811i | ||||
\(139\) | −2.34315 | −0.198743 | −0.0993715 | − | 0.995050i | \(-0.531683\pi\) | ||||
−0.0993715 | + | 0.995050i | \(0.531683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.24264 | 0.188864 | ||||||||
\(142\) | −2.24264 | − | 3.88437i | −0.188198 | − | 0.325969i | ||||
\(143\) | −6.34315 | + | 10.9867i | −0.530440 | + | 0.918750i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.29289 | − | 2.23936i | −0.107369 | − | 0.185968i | ||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.242641 | −0.0199449 | ||||||||
\(149\) | −11.1924 | − | 19.3858i | −0.916916 | − | 1.58815i | −0.804071 | − | 0.594533i | \(-0.797337\pi\) |
−0.112845 | − | 0.993613i | \(-0.535996\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −10.0711 | + | 17.4436i | −0.819572 | + | 1.41954i | 0.0864262 | + | 0.996258i | \(0.472455\pi\) |
−0.905998 | + | 0.423282i | \(0.860878\pi\) | |||||||
\(152\) | −3.41421 | − | 5.91359i | −0.276929 | − | 0.479656i | ||||
\(153\) | 2.58579 | 0.209048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2426 | −0.822709 | ||||||||
\(156\) | 2.82843 | + | 4.89898i | 0.226455 | + | 0.392232i | ||||
\(157\) | 4.17157 | − | 7.22538i | 0.332928 | − | 0.576648i | −0.650157 | − | 0.759800i | \(-0.725297\pi\) |
0.983085 | + | 0.183152i | \(0.0586301\pi\) | |||||||
\(158\) | 4.00000 | − | 6.92820i | 0.318223 | − | 0.551178i | ||||
\(159\) | 0.171573 | + | 0.297173i | 0.0136066 | + | 0.0235673i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 8.53553 | + | 14.7840i | 0.668555 | + | 1.15797i | 0.978308 | + | 0.207154i | \(0.0664200\pi\) |
−0.309754 | + | 0.950817i | \(0.600247\pi\) | |||||||
\(164\) | −5.24264 | + | 9.08052i | −0.409381 | + | 0.709069i | ||||
\(165\) | 1.12132 | − | 1.94218i | 0.0872947 | − | 0.151199i | ||||
\(166\) | 2.58579 | + | 4.47871i | 0.200696 | + | 0.347616i | ||||
\(167\) | 2.24264 | 0.173541 | 0.0867704 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867704 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 1.29289 | + | 2.23936i | 0.0991604 | + | 0.171751i | ||||
\(171\) | 3.41421 | − | 5.91359i | 0.261091 | − | 0.452224i | ||||
\(172\) | −4.53553 | + | 7.85578i | −0.345831 | + | 0.598997i | ||||
\(173\) | −10.4142 | − | 18.0379i | −0.791778 | − | 1.37140i | −0.924865 | − | 0.380295i | \(-0.875822\pi\) |
0.133087 | − | 0.991104i | \(-0.457511\pi\) | |||||||
\(174\) | 2.58579 | 0.196028 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.24264 | 0.169045 | ||||||||
\(177\) | −1.58579 | − | 2.74666i | −0.119195 | − | 0.206452i | ||||
\(178\) | −0.414214 | + | 0.717439i | −0.0310466 | + | 0.0537743i | ||||
\(179\) | −13.1213 | + | 22.7268i | −0.980734 | + | 1.69868i | −0.321188 | + | 0.947015i | \(0.604082\pi\) |
−0.659545 | + | 0.751665i | \(0.729251\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 18.4853 | 1.37400 | 0.687000 | − | 0.726657i | \(-0.258927\pi\) | ||||
0.687000 | + | 0.726657i | \(0.258927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.6569 | 0.861699 | ||||||||
\(184\) | 1.58579 | + | 2.74666i | 0.116906 | + | 0.202487i | ||||
\(185\) | 0.121320 | − | 0.210133i | 0.00891965 | − | 0.0154493i | ||||
\(186\) | 5.12132 | − | 8.87039i | 0.375513 | − | 0.650408i | ||||
\(187\) | −2.89949 | − | 5.02207i | −0.212032 | − | 0.367250i | ||||
\(188\) | −2.24264 | −0.163561 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.82843 | 0.495386 | ||||||||
\(191\) | −2.00000 | − | 3.46410i | −0.144715 | − | 0.250654i | 0.784552 | − | 0.620063i | \(-0.212893\pi\) |
−0.929267 | + | 0.369410i | \(0.879560\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.41421 | − | 4.18154i | 0.173779 | − | 0.300994i | −0.765959 | − | 0.642889i | \(-0.777736\pi\) |
0.939738 | + | 0.341895i | \(0.111069\pi\) | |||||||
\(194\) | −3.24264 | − | 5.61642i | −0.232808 | − | 0.403235i | ||||
\(195\) | −5.65685 | −0.405096 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.7990 | −1.83810 | −0.919051 | − | 0.394139i | \(-0.871043\pi\) | ||||
−0.919051 | + | 0.394139i | \(0.871043\pi\) | |||||||
\(198\) | 1.12132 | + | 1.94218i | 0.0796888 | + | 0.138025i | ||||
\(199\) | 2.87868 | − | 4.98602i | 0.204064 | − | 0.353450i | −0.745770 | − | 0.666204i | \(-0.767918\pi\) |
0.949834 | + | 0.312754i | \(0.101252\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 4.53553 | + | 7.85578i | 0.319912 | + | 0.554104i | ||||
\(202\) | −17.6569 | −1.24233 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.58579 | −0.181041 | ||||||||
\(205\) | −5.24264 | − | 9.08052i | −0.366162 | − | 0.634211i | ||||
\(206\) | 7.41421 | − | 12.8418i | 0.516573 | − | 0.894730i | ||||
\(207\) | −1.58579 | + | 2.74666i | −0.110220 | + | 0.190906i | ||||
\(208\) | −2.82843 | − | 4.89898i | −0.196116 | − | 0.339683i | ||||
\(209\) | −15.3137 | −1.05927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3137 | −1.60498 | −0.802491 | − | 0.596664i | \(-0.796492\pi\) | ||||
−0.802491 | + | 0.596664i | \(0.796492\pi\) | |||||||
\(212\) | −0.171573 | − | 0.297173i | −0.0117837 | − | 0.0204099i | ||||
\(213\) | −2.24264 | + | 3.88437i | −0.153663 | + | 0.266152i | ||||
\(214\) | 4.82843 | − | 8.36308i | 0.330064 | − | 0.571688i | ||||
\(215\) | −4.53553 | − | 7.85578i | −0.309321 | − | 0.535759i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.65685 | 0.247673 | ||||||||
\(219\) | −1.00000 | − | 1.73205i | −0.0675737 | − | 0.117041i | ||||
\(220\) | −1.12132 | + | 1.94218i | −0.0755994 | + | 0.130942i | ||||
\(221\) | −7.31371 | + | 12.6677i | −0.491973 | + | 0.852123i | ||||
\(222\) | 0.121320 | + | 0.210133i | 0.00814249 | + | 0.0141032i | ||||
\(223\) | −7.31371 | −0.489762 | −0.244881 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244881 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 5.00000 | + | 8.66025i | 0.332595 | + | 0.576072i | ||||
\(227\) | 12.4853 | − | 21.6251i | 0.828677 | − | 1.43531i | −0.0703990 | − | 0.997519i | \(-0.522427\pi\) |
0.899076 | − | 0.437792i | \(-0.144239\pi\) | |||||||
\(228\) | −3.41421 | + | 5.91359i | −0.226112 | + | 0.391637i | ||||
\(229\) | 8.07107 | + | 13.9795i | 0.533351 | + | 0.923791i | 0.999241 | + | 0.0389487i | \(0.0124009\pi\) |
−0.465890 | + | 0.884843i | \(0.654266\pi\) | |||||||
\(230\) | −3.17157 | −0.209127 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.58579 | −0.169765 | ||||||||
\(233\) | −9.48528 | − | 16.4290i | −0.621401 | − | 1.07630i | −0.989225 | − | 0.146403i | \(-0.953230\pi\) |
0.367824 | − | 0.929896i | \(-0.380103\pi\) | |||||||
\(234\) | 2.82843 | − | 4.89898i | 0.184900 | − | 0.320256i | ||||
\(235\) | 1.12132 | − | 1.94218i | 0.0731469 | − | 0.126694i | ||||
\(236\) | 1.58579 | + | 2.74666i | 0.103226 | + | 0.178793i | ||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3137 | −1.24930 | −0.624650 | − | 0.780905i | \(-0.714758\pi\) | ||||
−0.624650 | + | 0.780905i | \(0.714758\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | 9.77817 | − | 16.9363i | 0.629868 | − | 1.09096i | −0.357710 | − | 0.933833i | \(-0.616442\pi\) |
0.987578 | − | 0.157130i | \(-0.0502242\pi\) | |||||||
\(242\) | −2.98528 | + | 5.17066i | −0.191901 | + | 0.332383i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −11.6569 | −0.746254 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4853 | 0.668517 | ||||||||
\(247\) | 19.3137 | + | 33.4523i | 1.22890 | + | 2.12852i | ||||
\(248\) | −5.12132 | + | 8.87039i | −0.325204 | + | 0.563270i | ||||
\(249\) | 2.58579 | − | 4.47871i | 0.163868 | − | 0.283827i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −12.9706 | −0.818695 | −0.409347 | − | 0.912379i | \(-0.634244\pi\) | ||||
−0.409347 | + | 0.912379i | \(0.634244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.11270 | 0.447172 | ||||||||
\(254\) | 1.41421 | + | 2.44949i | 0.0887357 | + | 0.153695i | ||||
\(255\) | 1.29289 | − | 2.23936i | 0.0809641 | − | 0.140234i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.29289 | + | 16.0958i | 0.579675 | + | 1.00403i | 0.995516 | + | 0.0945891i | \(0.0301537\pi\) |
−0.415842 | + | 0.909437i | \(0.636513\pi\) | |||||||
\(258\) | 9.07107 | 0.564740 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.65685 | 0.350823 | ||||||||
\(261\) | −1.29289 | − | 2.23936i | −0.0800281 | − | 0.138613i | ||||
\(262\) | −1.58579 | + | 2.74666i | −0.0979702 | + | 0.169689i | ||||
\(263\) | 6.07107 | − | 10.5154i | 0.374358 | − | 0.648407i | −0.615873 | − | 0.787846i | \(-0.711196\pi\) |
0.990231 | + | 0.139439i | \(0.0445298\pi\) | |||||||
\(264\) | −1.12132 | − | 1.94218i | −0.0690125 | − | 0.119533i | ||||
\(265\) | 0.343146 | 0.0210793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.828427 | 0.0506989 | ||||||||
\(268\) | −4.53553 | − | 7.85578i | −0.277052 | − | 0.479868i | ||||
\(269\) | −6.17157 | + | 10.6895i | −0.376287 | + | 0.651749i | −0.990519 | − | 0.137377i | \(-0.956133\pi\) |
0.614231 | + | 0.789126i | \(0.289466\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | −15.8492 | − | 27.4517i | −0.962773 | − | 1.66757i | −0.715483 | − | 0.698630i | \(-0.753793\pi\) |
−0.247290 | − | 0.968942i | \(-0.579540\pi\) | |||||||
\(272\) | 2.58579 | 0.156786 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6569 | −0.825041 | ||||||||
\(275\) | −1.12132 | − | 1.94218i | −0.0676182 | − | 0.117118i | ||||
\(276\) | 1.58579 | − | 2.74666i | 0.0954531 | − | 0.165330i | ||||
\(277\) | 7.77817 | − | 13.4722i | 0.467345 | − | 0.809466i | −0.531959 | − | 0.846770i | \(-0.678544\pi\) |
0.999304 | + | 0.0373046i | \(0.0118772\pi\) | |||||||
\(278\) | −1.17157 | − | 2.02922i | −0.0702663 | − | 0.121705i | ||||
\(279\) | −10.2426 | −0.613211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.4558 | −1.39926 | −0.699629 | − | 0.714506i | \(-0.746651\pi\) | ||||
−0.699629 | + | 0.714506i | \(0.746651\pi\) | |||||||
\(282\) | 1.12132 | + | 1.94218i | 0.0667737 | + | 0.115655i | ||||
\(283\) | −4.75736 | + | 8.23999i | −0.282796 | + | 0.489816i | −0.972072 | − | 0.234682i | \(-0.924595\pi\) |
0.689277 | + | 0.724498i | \(0.257928\pi\) | |||||||
\(284\) | 2.24264 | − | 3.88437i | 0.133076 | − | 0.230495i | ||||
\(285\) | −3.41421 | − | 5.91359i | −0.202241 | − | 0.350291i | ||||
\(286\) | −12.6863 | −0.750156 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 5.15685 | + | 8.93193i | 0.303344 | + | 0.525408i | ||||
\(290\) | 1.29289 | − | 2.23936i | 0.0759213 | − | 0.131500i | ||||
\(291\) | −3.24264 | + | 5.61642i | −0.190087 | + | 0.329240i | ||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | 21.3137 | 1.24516 | 0.622580 | − | 0.782556i | \(-0.286084\pi\) | ||||
0.622580 | + | 0.782556i | \(0.286084\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.17157 | −0.184656 | ||||||||
\(296\) | −0.121320 | − | 0.210133i | −0.00705160 | − | 0.0122137i | ||||
\(297\) | 1.12132 | − | 1.94218i | 0.0650656 | − | 0.112697i | ||||
\(298\) | 11.1924 | − | 19.3858i | 0.648358 | − | 1.12299i | ||||
\(299\) | −8.97056 | − | 15.5375i | −0.518781 | − | 0.898555i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.1421 | −1.15905 | ||||||||
\(303\) | 8.82843 | + | 15.2913i | 0.507180 | + | 0.878461i | ||||
\(304\) | 3.41421 | − | 5.91359i | 0.195819 | − | 0.339168i | ||||
\(305\) | 5.82843 | − | 10.0951i | 0.333735 | − | 0.578046i | ||||
\(306\) | 1.29289 | + | 2.23936i | 0.0739098 | + | 0.128016i | ||||
\(307\) | −7.31371 | −0.417415 | −0.208708 | − | 0.977978i | \(-0.566926\pi\) | ||||
−0.208708 | + | 0.977978i | \(0.566926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.8284 | −0.843560 | ||||||||
\(310\) | −5.12132 | − | 8.87039i | −0.290871 | − | 0.503804i | ||||
\(311\) | 5.41421 | − | 9.37769i | 0.307012 | − | 0.531760i | −0.670695 | − | 0.741733i | \(-0.734004\pi\) |
0.977707 | + | 0.209973i | \(0.0673375\pi\) | |||||||
\(312\) | −2.82843 | + | 4.89898i | −0.160128 | + | 0.277350i | ||||
\(313\) | −15.2426 | − | 26.4010i | −0.861565 | − | 1.49227i | −0.870418 | − | 0.492314i | \(-0.836151\pi\) |
0.00885295 | − | 0.999961i | \(-0.497182\pi\) | |||||||
\(314\) | 8.34315 | 0.470831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 12.6569 | + | 21.9223i | 0.710880 | + | 1.23128i | 0.964527 | + | 0.263983i | \(0.0850363\pi\) |
−0.253648 | + | 0.967297i | \(0.581630\pi\) | |||||||
\(318\) | −0.171573 | + | 0.297173i | −0.00962133 | + | 0.0166646i | ||||
\(319\) | −2.89949 | + | 5.02207i | −0.162341 | + | 0.281182i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −9.65685 | −0.538993 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.6569 | −0.982454 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −2.82843 | + | 4.89898i | −0.156893 | + | 0.271746i | ||||
\(326\) | −8.53553 | + | 14.7840i | −0.472740 | + | 0.818809i | ||||
\(327\) | −1.82843 | − | 3.16693i | −0.101112 | − | 0.175132i | ||||
\(328\) | −10.4853 | −0.578953 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.24264 | 0.123453 | ||||||||
\(331\) | 3.17157 | + | 5.49333i | 0.174325 | + | 0.301940i | 0.939928 | − | 0.341374i | \(-0.110892\pi\) |
−0.765602 | + | 0.643314i | \(0.777559\pi\) | |||||||
\(332\) | −2.58579 | + | 4.47871i | −0.141913 | + | 0.245801i | ||||
\(333\) | 0.121320 | − | 0.210133i | 0.00664831 | − | 0.0115152i | ||||
\(334\) | 1.12132 | + | 1.94218i | 0.0613559 | + | 0.106272i | ||||
\(335\) | 9.07107 | 0.495605 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.1127 | 1.80376 | 0.901882 | − | 0.431983i | \(-0.142186\pi\) | ||||
0.901882 | + | 0.431983i | \(0.142186\pi\) | |||||||
\(338\) | 9.50000 | + | 16.4545i | 0.516732 | + | 0.895006i | ||||
\(339\) | 5.00000 | − | 8.66025i | 0.271563 | − | 0.470360i | ||||
\(340\) | −1.29289 | + | 2.23936i | −0.0701170 | + | 0.121446i | ||||
\(341\) | 11.4853 | + | 19.8931i | 0.621963 | + | 1.07727i | ||||
\(342\) | 6.82843 | 0.369239 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.07107 | −0.489079 | ||||||||
\(345\) | 1.58579 | + | 2.74666i | 0.0853759 | + | 0.147875i | ||||
\(346\) | 10.4142 | − | 18.0379i | 0.559872 | − | 0.969726i | ||||
\(347\) | 11.1716 | − | 19.3497i | 0.599721 | − | 1.03875i | −0.393140 | − | 0.919478i | \(-0.628611\pi\) |
0.992862 | − | 0.119270i | \(-0.0380553\pi\) | |||||||
\(348\) | 1.29289 | + | 2.23936i | 0.0693064 | + | 0.120042i | ||||
\(349\) | 23.4558 | 1.25556 | 0.627781 | − | 0.778390i | \(-0.283963\pi\) | ||||
0.627781 | + | 0.778390i | \(0.283963\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | 1.12132 | + | 1.94218i | 0.0597666 | + | 0.103519i | ||||
\(353\) | −8.02082 | + | 13.8925i | −0.426905 | + | 0.739421i | −0.996596 | − | 0.0824378i | \(-0.973729\pi\) |
0.569691 | + | 0.821859i | \(0.307063\pi\) | |||||||
\(354\) | 1.58579 | − | 2.74666i | 0.0842836 | − | 0.145983i | ||||
\(355\) | 2.24264 | + | 3.88437i | 0.119027 | + | 0.206161i | ||||
\(356\) | −0.828427 | −0.0439065 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.2426 | −1.38697 | ||||||||
\(359\) | 14.2426 | + | 24.6690i | 0.751698 | + | 1.30198i | 0.946999 | + | 0.321236i | \(0.104098\pi\) |
−0.195301 | + | 0.980743i | \(0.562569\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | −13.8137 | + | 23.9260i | −0.727037 | + | 1.25927i | ||||
\(362\) | 9.24264 | + | 16.0087i | 0.485782 | + | 0.841400i | ||||
\(363\) | 5.97056 | 0.313373 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 5.82843 | + | 10.0951i | 0.304657 | + | 0.527681i | ||||
\(367\) | 5.41421 | − | 9.37769i | 0.282620 | − | 0.489512i | −0.689410 | − | 0.724372i | \(-0.742130\pi\) |
0.972029 | + | 0.234860i | \(0.0754632\pi\) | |||||||
\(368\) | −1.58579 | + | 2.74666i | −0.0826648 | + | 0.143180i | ||||
\(369\) | −5.24264 | − | 9.08052i | −0.272921 | − | 0.472713i | ||||
\(370\) | 0.242641 | 0.0126143 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.2426 | 0.531056 | ||||||||
\(373\) | −3.29289 | − | 5.70346i | −0.170500 | − | 0.295314i | 0.768095 | − | 0.640336i | \(-0.221205\pi\) |
−0.938595 | + | 0.345022i | \(0.887871\pi\) | |||||||
\(374\) | 2.89949 | − | 5.02207i | 0.149929 | − | 0.259685i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | −1.12132 | − | 1.94218i | −0.0578277 | − | 0.100160i | ||||
\(377\) | 14.6274 | 0.753350 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.485281 | 0.0249272 | 0.0124636 | − | 0.999922i | \(-0.496033\pi\) | ||||
0.0124636 | + | 0.999922i | \(0.496033\pi\) | |||||||
\(380\) | 3.41421 | + | 5.91359i | 0.175145 | + | 0.303361i | ||||
\(381\) | 1.41421 | − | 2.44949i | 0.0724524 | − | 0.125491i | ||||
\(382\) | 2.00000 | − | 3.46410i | 0.102329 | − | 0.177239i | ||||
\(383\) | −9.70711 | − | 16.8132i | −0.496010 | − | 0.859114i | 0.503979 | − | 0.863716i | \(-0.331869\pi\) |
−0.999989 | + | 0.00460116i | \(0.998535\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.82843 | 0.245760 | ||||||||
\(387\) | −4.53553 | − | 7.85578i | −0.230554 | − | 0.399331i | ||||
\(388\) | 3.24264 | − | 5.61642i | 0.164620 | − | 0.285130i | ||||
\(389\) | 14.9497 | − | 25.8937i | 0.757982 | − | 1.31286i | −0.185896 | − | 0.982569i | \(-0.559519\pi\) |
0.943878 | − | 0.330294i | \(-0.107148\pi\) | |||||||
\(390\) | −2.82843 | − | 4.89898i | −0.143223 | − | 0.248069i | ||||
\(391\) | 8.20101 | 0.414743 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.17157 | 0.159985 | ||||||||
\(394\) | −12.8995 | − | 22.3426i | −0.649867 | − | 1.12560i | ||||
\(395\) | −4.00000 | + | 6.92820i | −0.201262 | + | 0.348596i | ||||
\(396\) | −1.12132 | + | 1.94218i | −0.0563485 | + | 0.0975984i | ||||
\(397\) | −3.34315 | − | 5.79050i | −0.167788 | − | 0.290617i | 0.769854 | − | 0.638220i | \(-0.220329\pi\) |
−0.937642 | + | 0.347603i | \(0.886996\pi\) | |||||||
\(398\) | 5.75736 | 0.288590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 3.00000 | + | 5.19615i | 0.149813 | + | 0.259483i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | −4.53553 | + | 7.85578i | −0.226212 | + | 0.391810i | ||||
\(403\) | 28.9706 | − | 50.1785i | 1.44313 | − | 2.49957i | ||||
\(404\) | −8.82843 | − | 15.2913i | −0.439231 | − | 0.760770i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.544156 | −0.0269728 | ||||||||
\(408\) | −1.29289 | − | 2.23936i | −0.0640078 | − | 0.110865i | ||||
\(409\) | −2.12132 | + | 3.67423i | −0.104893 | + | 0.181679i | −0.913694 | − | 0.406402i | \(-0.866783\pi\) |
0.808802 | + | 0.588081i | \(0.200117\pi\) | |||||||
\(410\) | 5.24264 | − | 9.08052i | 0.258916 | − | 0.448455i | ||||
\(411\) | 6.82843 | + | 11.8272i | 0.336821 | + | 0.583392i | ||||
\(412\) | 14.8284 | 0.730544 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.17157 | −0.155874 | ||||||||
\(415\) | −2.58579 | − | 4.47871i | −0.126931 | − | 0.219851i | ||||
\(416\) | 2.82843 | − | 4.89898i | 0.138675 | − | 0.240192i | ||||
\(417\) | −1.17157 | + | 2.02922i | −0.0573722 | + | 0.0993715i | ||||
\(418\) | −7.65685 | − | 13.2621i | −0.374509 | − | 0.648669i | ||||
\(419\) | −36.9706 | −1.80613 | −0.903065 | − | 0.429504i | \(-0.858689\pi\) | ||||
−0.903065 | + | 0.429504i | \(0.858689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.65685 | −0.178224 | −0.0891121 | − | 0.996022i | \(-0.528403\pi\) | ||||
−0.0891121 | + | 0.996022i | \(0.528403\pi\) | |||||||
\(422\) | −11.6569 | − | 20.1903i | −0.567447 | − | 0.982847i | ||||
\(423\) | 1.12132 | − | 1.94218i | 0.0545205 | − | 0.0944322i | ||||
\(424\) | 0.171573 | − | 0.297173i | 0.00833232 | − | 0.0144320i | ||||
\(425\) | −1.29289 | − | 2.23936i | −0.0627145 | − | 0.108625i | ||||
\(426\) | −4.48528 | −0.217313 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.65685 | 0.466782 | ||||||||
\(429\) | 6.34315 | + | 10.9867i | 0.306250 | + | 0.530440i | ||||
\(430\) | 4.53553 | − | 7.85578i | 0.218723 | − | 0.378839i | ||||
\(431\) | −6.72792 | + | 11.6531i | −0.324073 | + | 0.561310i | −0.981324 | − | 0.192361i | \(-0.938386\pi\) |
0.657252 | + | 0.753671i | \(0.271719\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −17.7990 | −0.855365 | −0.427682 | − | 0.903929i | \(-0.640670\pi\) | ||||
−0.427682 | + | 0.903929i | \(0.640670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.58579 | −0.123979 | ||||||||
\(436\) | 1.82843 | + | 3.16693i | 0.0875658 | + | 0.151668i | ||||
\(437\) | 10.8284 | − | 18.7554i | 0.517994 | − | 0.897192i | ||||
\(438\) | 1.00000 | − | 1.73205i | 0.0477818 | − | 0.0827606i | ||||
\(439\) | 11.8492 | + | 20.5235i | 0.565533 | + | 0.979533i | 0.997000 | + | 0.0774037i | \(0.0246630\pi\) |
−0.431466 | + | 0.902129i | \(0.642004\pi\) | |||||||
\(440\) | −2.24264 | −0.106914 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.6274 | −0.695755 | ||||||||
\(443\) | −18.1421 | − | 31.4231i | −0.861959 | − | 1.49296i | −0.870035 | − | 0.492989i | \(-0.835904\pi\) |
0.00807656 | − | 0.999967i | \(-0.497429\pi\) | |||||||
\(444\) | −0.121320 | + | 0.210133i | −0.00575761 | + | 0.00997247i | ||||
\(445\) | 0.414214 | − | 0.717439i | 0.0196356 | − | 0.0340099i | ||||
\(446\) | −3.65685 | − | 6.33386i | −0.173157 | − | 0.299917i | ||||
\(447\) | −22.3848 | −1.05876 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4853 | −0.494831 | −0.247416 | − | 0.968909i | \(-0.579581\pi\) | ||||
−0.247416 | + | 0.968909i | \(0.579581\pi\) | |||||||
\(450\) | 0.500000 | + | 0.866025i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | −11.7574 | + | 20.3643i | −0.553632 | + | 0.958919i | ||||
\(452\) | −5.00000 | + | 8.66025i | −0.235180 | + | 0.407344i | ||||
\(453\) | 10.0711 | + | 17.4436i | 0.473180 | + | 0.819572i | ||||
\(454\) | 24.9706 | 1.17193 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.82843 | −0.319770 | ||||||||
\(457\) | −1.24264 | − | 2.15232i | −0.0581283 | − | 0.100681i | 0.835497 | − | 0.549495i | \(-0.185180\pi\) |
−0.893625 | + | 0.448814i | \(0.851847\pi\) | |||||||
\(458\) | −8.07107 | + | 13.9795i | −0.377136 | + | 0.653219i | ||||
\(459\) | 1.29289 | − | 2.23936i | 0.0603471 | − | 0.104524i | ||||
\(460\) | −1.58579 | − | 2.74666i | −0.0739377 | − | 0.128064i | ||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.6569 | −1.19238 | −0.596188 | − | 0.802845i | \(-0.703319\pi\) | ||||
−0.596188 | + | 0.802845i | \(0.703319\pi\) | |||||||
\(464\) | −1.29289 | − | 2.23936i | −0.0600211 | − | 0.103960i | ||||
\(465\) | −5.12132 | + | 8.87039i | −0.237496 | + | 0.411354i | ||||
\(466\) | 9.48528 | − | 16.4290i | 0.439397 | − | 0.761058i | ||||
\(467\) | −6.24264 | − | 10.8126i | −0.288875 | − | 0.500346i | 0.684667 | − | 0.728856i | \(-0.259948\pi\) |
−0.973541 | + | 0.228510i | \(0.926615\pi\) | |||||||
\(468\) | 5.65685 | 0.261488 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.24264 | 0.103445 | ||||||||
\(471\) | −4.17157 | − | 7.22538i | −0.192216 | − | 0.332928i | ||||
\(472\) | −1.58579 | + | 2.74666i | −0.0729917 | + | 0.126425i | ||||
\(473\) | −10.1716 | + | 17.6177i | −0.467689 | + | 0.810062i | ||||
\(474\) | −4.00000 | − | 6.92820i | −0.183726 | − | 0.318223i | ||||
\(475\) | −6.82843 | −0.313310 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.343146 | 0.0157116 | ||||||||
\(478\) | −9.65685 | − | 16.7262i | −0.441694 | − | 0.765037i | ||||
\(479\) | 4.24264 | − | 7.34847i | 0.193851 | − | 0.335760i | −0.752672 | − | 0.658396i | \(-0.771235\pi\) |
0.946523 | + | 0.322635i | \(0.104569\pi\) | |||||||
\(480\) | −0.500000 | + | 0.866025i | −0.0228218 | + | 0.0395285i | ||||
\(481\) | 0.686292 | + | 1.18869i | 0.0312922 | + | 0.0541997i | ||||
\(482\) | 19.5563 | 0.890767 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.97056 | −0.271389 | ||||||||
\(485\) | 3.24264 | + | 5.61642i | 0.147241 | + | 0.255028i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −5.41421 | + | 9.37769i | −0.245341 | + | 0.424944i | −0.962228 | − | 0.272246i | \(-0.912233\pi\) |
0.716886 | + | 0.697190i | \(0.245567\pi\) | |||||||
\(488\) | −5.82843 | − | 10.0951i | −0.263840 | − | 0.456985i | ||||
\(489\) | 17.0711 | 0.771980 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.0711 | −0.770407 | −0.385203 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385203 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(492\) | 5.24264 | + | 9.08052i | 0.236356 | + | 0.409381i | ||||
\(493\) | −3.34315 | + | 5.79050i | −0.150568 | + | 0.260791i | ||||
\(494\) | −19.3137 | + | 33.4523i | −0.868965 | + | 1.50509i | ||||
\(495\) | −1.12132 | − | 1.94218i | −0.0503996 | − | 0.0872947i | ||||
\(496\) | −10.2426 | −0.459908 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.17157 | 0.231744 | ||||||||
\(499\) | −3.41421 | − | 5.91359i | −0.152841 | − | 0.264729i | 0.779430 | − | 0.626490i | \(-0.215509\pi\) |
−0.932271 | + | 0.361761i | \(0.882176\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 1.12132 | − | 1.94218i | 0.0500969 | − | 0.0867704i | ||||
\(502\) | −6.48528 | − | 11.2328i | −0.289452 | − | 0.501346i | ||||
\(503\) | −4.58579 | −0.204470 | −0.102235 | − | 0.994760i | \(-0.532599\pi\) | ||||
−0.102235 | + | 0.994760i | \(0.532599\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.6569 | 0.785720 | ||||||||
\(506\) | 3.55635 | + | 6.15978i | 0.158099 | + | 0.273836i | ||||
\(507\) | 9.50000 | − | 16.4545i | 0.421910 | − | 0.730769i | ||||
\(508\) | −1.41421 | + | 2.44949i | −0.0627456 | + | 0.108679i | ||||
\(509\) | 8.48528 | + | 14.6969i | 0.376103 | + | 0.651430i | 0.990492 | − | 0.137574i | \(-0.0439304\pi\) |
−0.614388 | + | 0.789004i | \(0.710597\pi\) | |||||||
\(510\) | 2.58579 | 0.114501 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.41421 | − | 5.91359i | −0.150741 | − | 0.261091i | ||||
\(514\) | −9.29289 | + | 16.0958i | −0.409892 | + | 0.709954i | ||||
\(515\) | −7.41421 | + | 12.8418i | −0.326709 | + | 0.565877i | ||||
\(516\) | 4.53553 | + | 7.85578i | 0.199666 | + | 0.345831i | ||||
\(517\) | −5.02944 | −0.221194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8284 | −0.914266 | ||||||||
\(520\) | 2.82843 | + | 4.89898i | 0.124035 | + | 0.214834i | ||||
\(521\) | −19.3848 | + | 33.5754i | −0.849262 | + | 1.47097i | 0.0326050 | + | 0.999468i | \(0.489620\pi\) |
−0.881867 | + | 0.471497i | \(0.843714\pi\) | |||||||
\(522\) | 1.29289 | − | 2.23936i | 0.0565884 | − | 0.0980140i | ||||
\(523\) | −20.8995 | − | 36.1990i | −0.913871 | − | 1.58287i | −0.808546 | − | 0.588433i | \(-0.799745\pi\) |
−0.105325 | − | 0.994438i | \(-0.533588\pi\) | |||||||
\(524\) | −3.17157 | −0.138551 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.1421 | 0.529422 | ||||||||
\(527\) | 13.2426 | + | 22.9369i | 0.576858 | + | 0.999148i | ||||
\(528\) | 1.12132 | − | 1.94218i | 0.0487992 | − | 0.0845227i | ||||
\(529\) | 6.47056 | − | 11.2073i | 0.281329 | − | 0.487276i | ||||
\(530\) | 0.171573 | + | 0.297173i | 0.00745265 | + | 0.0129084i | ||||
\(531\) | −3.17157 | −0.137635 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 59.3137 | 2.56916 | ||||||||
\(534\) | 0.414214 | + | 0.717439i | 0.0179248 | + | 0.0310466i | ||||
\(535\) | −4.82843 | + | 8.36308i | −0.208751 | + | 0.361568i | ||||
\(536\) | 4.53553 | − | 7.85578i | 0.195905 | − | 0.339318i | ||||
\(537\) | 13.1213 | + | 22.7268i | 0.566227 | + | 0.980734i | ||||
\(538\) | −12.3431 | −0.532151 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 14.8995 | + | 25.8067i | 0.640579 | + | 1.10952i | 0.985304 | + | 0.170812i | \(0.0546391\pi\) |
−0.344724 | + | 0.938704i | \(0.612028\pi\) | |||||||
\(542\) | 15.8492 | − | 27.4517i | 0.680783 | − | 1.17915i | ||||
\(543\) | 9.24264 | − | 16.0087i | 0.396640 | − | 0.687000i | ||||
\(544\) | 1.29289 | + | 2.23936i | 0.0554323 | + | 0.0960116i | ||||
\(545\) | −3.65685 | −0.156642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.3848 | −1.21365 | −0.606823 | − | 0.794837i | \(-0.707556\pi\) | ||||
−0.606823 | + | 0.794837i | \(0.707556\pi\) | |||||||
\(548\) | −6.82843 | − | 11.8272i | −0.291696 | − | 0.505232i | ||||
\(549\) | 5.82843 | − | 10.0951i | 0.248751 | − | 0.430850i | ||||
\(550\) | 1.12132 | − | 1.94218i | 0.0478133 | − | 0.0828150i | ||||
\(551\) | 8.82843 | + | 15.2913i | 0.376104 | + | 0.651431i | ||||
\(552\) | 3.17157 | 0.134991 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.5563 | 0.660926 | ||||||||
\(555\) | −0.121320 | − | 0.210133i | −0.00514976 | − | 0.00891965i | ||||
\(556\) | 1.17157 | − | 2.02922i | 0.0496858 | − | 0.0860583i | ||||
\(557\) | 19.0000 | − | 32.9090i | 0.805056 | − | 1.39440i | −0.111198 | − | 0.993798i | \(-0.535469\pi\) |
0.916253 | − | 0.400599i | \(-0.131198\pi\) | |||||||
\(558\) | −5.12132 | − | 8.87039i | −0.216803 | − | 0.375513i | ||||
\(559\) | 51.3137 | 2.17034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.79899 | −0.244834 | ||||||||
\(562\) | −11.7279 | − | 20.3134i | −0.494713 | − | 0.856867i | ||||
\(563\) | 10.2426 | − | 17.7408i | 0.431676 | − | 0.747684i | −0.565342 | − | 0.824857i | \(-0.691256\pi\) |
0.997018 | + | 0.0771722i | \(0.0245891\pi\) | |||||||
\(564\) | −1.12132 | + | 1.94218i | −0.0472161 | + | 0.0817807i | ||||
\(565\) | −5.00000 | − | 8.66025i | −0.210352 | − | 0.364340i | ||||
\(566\) | −9.51472 | −0.399933 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.48528 | 0.188198 | ||||||||
\(569\) | −4.51472 | − | 7.81972i | −0.189267 | − | 0.327820i | 0.755739 | − | 0.654873i | \(-0.227278\pi\) |
−0.945006 | + | 0.327053i | \(0.893944\pi\) | |||||||
\(570\) | 3.41421 | − | 5.91359i | 0.143006 | − | 0.247693i | ||||
\(571\) | −2.34315 | + | 4.05845i | −0.0980576 | + | 0.169841i | −0.910881 | − | 0.412670i | \(-0.864596\pi\) |
0.812823 | + | 0.582511i | \(0.197930\pi\) | |||||||
\(572\) | −6.34315 | − | 10.9867i | −0.265220 | − | 0.459375i | ||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.17157 | 0.132264 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 1.92893 | − | 3.34101i | 0.0803025 | − | 0.139088i | −0.823077 | − | 0.567929i | \(-0.807745\pi\) |
0.903380 | + | 0.428841i | \(0.141078\pi\) | |||||||
\(578\) | −5.15685 | + | 8.93193i | −0.214497 | + | 0.371519i | ||||
\(579\) | −2.41421 | − | 4.18154i | −0.100331 | − | 0.173779i | ||||
\(580\) | 2.58579 | 0.107369 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.48528 | −0.268824 | ||||||||
\(583\) | −0.384776 | − | 0.666452i | −0.0159358 | − | 0.0276016i | ||||
\(584\) | −1.00000 | + | 1.73205i | −0.0413803 | + | 0.0716728i | ||||
\(585\) | −2.82843 | + | 4.89898i | −0.116941 | + | 0.202548i | ||||
\(586\) | 10.6569 | + | 18.4582i | 0.440231 | + | 0.762502i | ||||
\(587\) | −5.17157 | −0.213454 | −0.106727 | − | 0.994288i | \(-0.534037\pi\) | ||||
−0.106727 | + | 0.994288i | \(0.534037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 69.9411 | 2.88187 | ||||||||
\(590\) | −1.58579 | − | 2.74666i | −0.0652858 | − | 0.113078i | ||||
\(591\) | −12.8995 | + | 22.3426i | −0.530614 | + | 0.919051i | ||||
\(592\) | 0.121320 | − | 0.210133i | 0.00498624 | − | 0.00863641i | ||||
\(593\) | 20.6066 | + | 35.6917i | 0.846212 | + | 1.46568i | 0.884565 | + | 0.466417i | \(0.154456\pi\) |
−0.0383530 | + | 0.999264i | \(0.512211\pi\) | |||||||
\(594\) | 2.24264 | 0.0920167 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.3848 | 0.916916 | ||||||||
\(597\) | −2.87868 | − | 4.98602i | −0.117817 | − | 0.204064i | ||||
\(598\) | 8.97056 | − | 15.5375i | 0.366834 | − | 0.635374i | ||||
\(599\) | −2.00000 | + | 3.46410i | −0.0817178 | + | 0.141539i | −0.903988 | − | 0.427558i | \(-0.859374\pi\) |
0.822270 | + | 0.569097i | \(0.192707\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | −31.7574 | −1.29541 | −0.647705 | − | 0.761891i | \(-0.724271\pi\) | ||||
−0.647705 | + | 0.761891i | \(0.724271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.07107 | 0.369402 | ||||||||
\(604\) | −10.0711 | − | 17.4436i | −0.409786 | − | 0.709770i | ||||
\(605\) | 2.98528 | − | 5.17066i | 0.121369 | − | 0.210217i | ||||
\(606\) | −8.82843 | + | 15.2913i | −0.358630 | + | 0.621166i | ||||
\(607\) | −2.00000 | − | 3.46410i | −0.0811775 | − | 0.140604i | 0.822578 | − | 0.568652i | \(-0.192535\pi\) |
−0.903756 | + | 0.428048i | \(0.859201\pi\) | |||||||
\(608\) | 6.82843 | 0.276929 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.6569 | 0.471972 | ||||||||
\(611\) | 6.34315 | + | 10.9867i | 0.256616 | + | 0.444472i | ||||
\(612\) | −1.29289 | + | 2.23936i | −0.0522621 | + | 0.0905206i | ||||
\(613\) | 5.53553 | − | 9.58783i | 0.223578 | − | 0.387249i | −0.732314 | − | 0.680967i | \(-0.761560\pi\) |
0.955892 | + | 0.293719i | \(0.0948929\pi\) | |||||||
\(614\) | −3.65685 | − | 6.33386i | −0.147579 | − | 0.255614i | ||||
\(615\) | −10.4853 | −0.422807 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9411 | 1.36642 | 0.683209 | − | 0.730223i | \(-0.260584\pi\) | ||||
0.683209 | + | 0.730223i | \(0.260584\pi\) | |||||||
\(618\) | −7.41421 | − | 12.8418i | −0.298243 | − | 0.516573i | ||||
\(619\) | −9.55635 | + | 16.5521i | −0.384102 | + | 0.665284i | −0.991644 | − | 0.129003i | \(-0.958822\pi\) |
0.607542 | + | 0.794287i | \(0.292156\pi\) | |||||||
\(620\) | 5.12132 | − | 8.87039i | 0.205677 | − | 0.356243i | ||||
\(621\) | 1.58579 | + | 2.74666i | 0.0636354 | + | 0.110220i | ||||
\(622\) | 10.8284 | 0.434180 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.65685 | −0.226455 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 15.2426 | − | 26.4010i | 0.609218 | − | 1.05520i | ||||
\(627\) | −7.65685 | + | 13.2621i | −0.305785 | + | 0.529636i | ||||
\(628\) | 4.17157 | + | 7.22538i | 0.166464 | + | 0.288324i | ||||
\(629\) | −0.627417 | −0.0250168 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.14214 | −0.324133 | −0.162067 | − | 0.986780i | \(-0.551816\pi\) | ||||
−0.162067 | + | 0.986780i | \(0.551816\pi\) | |||||||
\(632\) | 4.00000 | + | 6.92820i | 0.159111 | + | 0.275589i | ||||
\(633\) | −11.6569 | + | 20.1903i | −0.463318 | + | 0.802491i | ||||
\(634\) | −12.6569 | + | 21.9223i | −0.502668 | + | 0.870646i | ||||
\(635\) | −1.41421 | − | 2.44949i | −0.0561214 | − | 0.0972050i | ||||
\(636\) | −0.343146 | −0.0136066 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.79899 | −0.229584 | ||||||||
\(639\) | 2.24264 | + | 3.88437i | 0.0887175 | + | 0.153663i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −13.0000 | + | 22.5167i | −0.513469 | + | 0.889355i | 0.486409 | + | 0.873731i | \(0.338307\pi\) |
−0.999878 | + | 0.0156233i | \(0.995027\pi\) | |||||||
\(642\) | −4.82843 | − | 8.36308i | −0.190563 | − | 0.330064i | ||||
\(643\) | 28.8284 | 1.13688 | 0.568441 | − | 0.822724i | \(-0.307547\pi\) | ||||
0.568441 | + | 0.822724i | \(0.307547\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.07107 | −0.357173 | ||||||||
\(646\) | −8.82843 | − | 15.2913i | −0.347350 | − | 0.601628i | ||||
\(647\) | −4.43503 | + | 7.68170i | −0.174359 | + | 0.301999i | −0.939939 | − | 0.341342i | \(-0.889119\pi\) |
0.765580 | + | 0.643340i | \(0.222452\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 3.55635 | + | 6.15978i | 0.139599 | + | 0.241792i | ||||
\(650\) | −5.65685 | −0.221880 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.0711 | −0.668555 | ||||||||
\(653\) | 0.899495 | + | 1.55797i | 0.0352000 | + | 0.0609681i | 0.883089 | − | 0.469206i | \(-0.155460\pi\) |
−0.847889 | + | 0.530174i | \(0.822127\pi\) | |||||||
\(654\) | 1.82843 | − | 3.16693i | 0.0714972 | − | 0.123837i | ||||
\(655\) | 1.58579 | − | 2.74666i | 0.0619618 | − | 0.107321i | ||||
\(656\) | −5.24264 | − | 9.08052i | −0.204691 | − | 0.354535i | ||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3848 | 0.794078 | 0.397039 | − | 0.917802i | \(-0.370038\pi\) | ||||
0.397039 | + | 0.917802i | \(0.370038\pi\) | |||||||
\(660\) | 1.12132 | + | 1.94218i | 0.0436473 | + | 0.0755994i | ||||
\(661\) | 2.51472 | − | 4.35562i | 0.0978112 | − | 0.169414i | −0.812967 | − | 0.582309i | \(-0.802149\pi\) |
0.910778 | + | 0.412895i | \(0.135483\pi\) | |||||||
\(662\) | −3.17157 | + | 5.49333i | −0.123267 | + | 0.213504i | ||||
\(663\) | 7.31371 | + | 12.6677i | 0.284041 | + | 0.491973i | ||||
\(664\) | −5.17157 | −0.200696 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.242641 | 0.00940214 | ||||||||
\(667\) | −4.10051 | − | 7.10228i | −0.158772 | − | 0.275002i | ||||
\(668\) | −1.12132 | + | 1.94218i | −0.0433852 | + | 0.0751453i | ||||
\(669\) | −3.65685 | + | 6.33386i | −0.141382 | + | 0.244881i | ||||
\(670\) | 4.53553 | + | 7.85578i | 0.175223 | + | 0.303495i | ||||
\(671\) | −26.1421 | −1.00921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.2843 | −1.01318 | −0.506592 | − | 0.862186i | \(-0.669095\pi\) | ||||
−0.506592 | + | 0.862186i | \(0.669095\pi\) | |||||||
\(674\) | 16.5563 | + | 28.6764i | 0.637727 | + | 1.10458i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | −9.50000 | + | 16.4545i | −0.365385 | + | 0.632865i | ||||
\(677\) | 22.2132 | + | 38.4744i | 0.853723 | + | 1.47869i | 0.877825 | + | 0.478982i | \(0.158994\pi\) |
−0.0241021 | + | 0.999710i | \(0.507673\pi\) | |||||||
\(678\) | 10.0000 | 0.384048 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.58579 | −0.0991604 | ||||||||
\(681\) | −12.4853 | − | 21.6251i | −0.478437 | − | 0.828677i | ||||
\(682\) | −11.4853 | + | 19.8931i | −0.439794 | + | 0.761746i | ||||
\(683\) | 15.8995 | − | 27.5387i | 0.608377 | − | 1.05374i | −0.383131 | − | 0.923694i | \(-0.625154\pi\) |
0.991508 | − | 0.130046i | \(-0.0415126\pi\) | |||||||
\(684\) | 3.41421 | + | 5.91359i | 0.130546 | + | 0.226112i | ||||
\(685\) | 13.6569 | 0.521802 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.1421 | 0.615861 | ||||||||
\(688\) | −4.53553 | − | 7.85578i | −0.172916 | − | 0.299499i | ||||
\(689\) | −0.970563 | + | 1.68106i | −0.0369755 | + | 0.0640434i | ||||
\(690\) | −1.58579 | + | 2.74666i | −0.0603699 | + | 0.104564i | ||||
\(691\) | −1.51472 | − | 2.62357i | −0.0576226 | − | 0.0998053i | 0.835775 | − | 0.549072i | \(-0.185019\pi\) |
−0.893398 | + | 0.449267i | \(0.851685\pi\) | |||||||
\(692\) | 20.8284 | 0.791778 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.3431 | 0.848134 | ||||||||
\(695\) | 1.17157 | + | 2.02922i | 0.0444403 | + | 0.0769728i | ||||
\(696\) | −1.29289 | + | 2.23936i | −0.0490070 | + | 0.0848826i | ||||
\(697\) | −13.5563 | + | 23.4803i | −0.513483 | + | 0.889379i | ||||
\(698\) | 11.7279 | + | 20.3134i | 0.443908 | + | 0.768872i | ||||
\(699\) | −18.9706 | −0.717533 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2132 | −0.650134 | −0.325067 | − | 0.945691i | \(-0.605387\pi\) | ||||
−0.325067 | + | 0.945691i | \(0.605387\pi\) | |||||||
\(702\) | −2.82843 | − | 4.89898i | −0.106752 | − | 0.184900i | ||||
\(703\) | −0.828427 | + | 1.43488i | −0.0312447 | + | 0.0541174i | ||||
\(704\) | −1.12132 | + | 1.94218i | −0.0422614 | + | 0.0731988i | ||||
\(705\) | −1.12132 | − | 1.94218i | −0.0422314 | − | 0.0731469i | ||||
\(706\) | −16.0416 | −0.603735 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.17157 | 0.119195 | ||||||||
\(709\) | −5.92893 | − | 10.2692i | −0.222666 | − | 0.385668i | 0.732951 | − | 0.680282i | \(-0.238143\pi\) |
−0.955617 | + | 0.294613i | \(0.904809\pi\) | |||||||
\(710\) | −2.24264 | + | 3.88437i | −0.0841648 | + | 0.145778i | ||||
\(711\) | −4.00000 | + | 6.92820i | −0.150012 | + | 0.259828i | ||||
\(712\) | −0.414214 | − | 0.717439i | −0.0155233 | − | 0.0268872i | ||||
\(713\) | −32.4853 | −1.21658 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.6863 | 0.474440 | ||||||||
\(716\) | −13.1213 | − | 22.7268i | −0.490367 | − | 0.849340i | ||||
\(717\) | −9.65685 | + | 16.7262i | −0.360642 | + | 0.624650i | ||||
\(718\) | −14.2426 | + | 24.6690i | −0.531531 | + | 0.920638i | ||||
\(719\) | −8.97056 | − | 15.5375i | −0.334546 | − | 0.579450i | 0.648852 | − | 0.760915i | \(-0.275249\pi\) |
−0.983397 | + | 0.181465i | \(0.941916\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −27.6274 | −1.02819 | ||||||||
\(723\) | −9.77817 | − | 16.9363i | −0.363654 | − | 0.629868i | ||||
\(724\) | −9.24264 | + | 16.0087i | −0.343500 | + | 0.594960i | ||||
\(725\) | −1.29289 | + | 2.23936i | −0.0480168 | + | 0.0831676i | ||||
\(726\) | 2.98528 | + | 5.17066i | 0.110794 | + | 0.191901i | ||||
\(727\) | −30.6274 | −1.13591 | −0.567954 | − | 0.823060i | \(-0.692265\pi\) | ||||
−0.567954 | + | 0.823060i | \(0.692265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | − | 1.73205i | −0.0370117 | − | 0.0641061i | ||||
\(731\) | −11.7279 | + | 20.3134i | −0.433773 | + | 0.751317i | ||||
\(732\) | −5.82843 | + | 10.0951i | −0.215425 | + | 0.373127i | ||||
\(733\) | 17.0000 | + | 29.4449i | 0.627909 | + | 1.08757i | 0.987971 | + | 0.154642i | \(0.0494225\pi\) |
−0.360061 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(734\) | 10.8284 | 0.399685 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.17157 | −0.116906 | ||||||||
\(737\) | −10.1716 | − | 17.6177i | −0.374675 | − | 0.648956i | ||||
\(738\) | 5.24264 | − | 9.08052i | 0.192984 | − | 0.334259i | ||||
\(739\) | −5.55635 | + | 9.62388i | −0.204394 | + | 0.354020i | −0.949939 | − | 0.312434i | \(-0.898856\pi\) |
0.745546 | + | 0.666454i | \(0.232189\pi\) | |||||||
\(740\) | 0.121320 | + | 0.210133i | 0.00445982 | + | 0.00772464i | ||||
\(741\) | 38.6274 | 1.41901 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2843 | 1.03765 | 0.518825 | − | 0.854881i | \(-0.326370\pi\) | ||||
0.518825 | + | 0.854881i | \(0.326370\pi\) | |||||||
\(744\) | 5.12132 | + | 8.87039i | 0.187757 | + | 0.325204i | ||||
\(745\) | −11.1924 | + | 19.3858i | −0.410057 | + | 0.710240i | ||||
\(746\) | 3.29289 | − | 5.70346i | 0.120561 | − | 0.208818i | ||||
\(747\) | −2.58579 | − | 4.47871i | −0.0946090 | − | 0.163868i | ||||
\(748\) | 5.79899 | 0.212032 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −10.8995 | − | 18.8785i | −0.397728 | − | 0.688885i | 0.595717 | − | 0.803194i | \(-0.296868\pi\) |
−0.993445 | + | 0.114309i | \(0.963535\pi\) | |||||||
\(752\) | 1.12132 | − | 1.94218i | 0.0408903 | − | 0.0708242i | ||||
\(753\) | −6.48528 | + | 11.2328i | −0.236337 | + | 0.409347i | ||||
\(754\) | 7.31371 | + | 12.6677i | 0.266350 | + | 0.461331i | ||||
\(755\) | 20.1421 | 0.733047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.8995 | 0.941333 | 0.470667 | − | 0.882311i | \(-0.344013\pi\) | ||||
0.470667 | + | 0.882311i | \(0.344013\pi\) | |||||||
\(758\) | 0.242641 | + | 0.420266i | 0.00881311 | + | 0.0152647i | ||||
\(759\) | 3.55635 | − | 6.15978i | 0.129087 | − | 0.223586i | ||||
\(760\) | −3.41421 | + | 5.91359i | −0.123847 | + | 0.214509i | ||||
\(761\) | 13.4853 | + | 23.3572i | 0.488841 | + | 0.846698i | 0.999918 | − | 0.0128376i | \(-0.00408646\pi\) |
−0.511077 | + | 0.859535i | \(0.670753\pi\) | |||||||
\(762\) | 2.82843 | 0.102463 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.00000 | 0.144715 | ||||||||
\(765\) | −1.29289 | − | 2.23936i | −0.0467447 | − | 0.0809641i | ||||
\(766\) | 9.70711 | − | 16.8132i | 0.350732 | − | 0.607486i | ||||
\(767\) | 8.97056 | − | 15.5375i | 0.323908 | − | 0.561026i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 4.72792 | 0.170493 | 0.0852466 | − | 0.996360i | \(-0.472832\pi\) | ||||
0.0852466 | + | 0.996360i | \(0.472832\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.5858 | 0.669351 | ||||||||
\(772\) | 2.41421 | + | 4.18154i | 0.0868894 | + | 0.150497i | ||||
\(773\) | 11.4853 | − | 19.8931i | 0.413097 | − | 0.715505i | −0.582130 | − | 0.813096i | \(-0.697780\pi\) |
0.995227 | + | 0.0975912i | \(0.0311138\pi\) | |||||||
\(774\) | 4.53553 | − | 7.85578i | 0.163026 | − | 0.282370i | ||||
\(775\) | 5.12132 | + | 8.87039i | 0.183963 | + | 0.318634i | ||||
\(776\) | 6.48528 | 0.232808 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.8995 | 1.07195 | ||||||||
\(779\) | 35.7990 | + | 62.0057i | 1.28263 | + | 2.22158i | ||||
\(780\) | 2.82843 | − | 4.89898i | 0.101274 | − | 0.175412i | ||||
\(781\) | 5.02944 | − | 8.71124i | 0.179967 | − | 0.311713i | ||||
\(782\) | 4.10051 | + | 7.10228i | 0.146634 | + | 0.253977i | ||||
\(783\) | −2.58579 | −0.0924085 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.34315 | −0.297780 | ||||||||
\(786\) | 1.58579 | + | 2.74666i | 0.0565631 | + | 0.0979702i | ||||
\(787\) | −19.1716 | + | 33.2061i | −0.683393 | + | 1.18367i | 0.290546 | + | 0.956861i | \(0.406163\pi\) |
−0.973939 | + | 0.226810i | \(0.927170\pi\) | |||||||
\(788\) | 12.8995 | − | 22.3426i | 0.459525 | − | 0.795921i | ||||
\(789\) | −6.07107 | − | 10.5154i | −0.216136 | − | 0.374358i | ||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.24264 | −0.0796888 | ||||||||
\(793\) | 32.9706 | + | 57.1067i | 1.17082 | + | 2.02792i | ||||
\(794\) | 3.34315 | − | 5.79050i | 0.118644 | − | 0.205497i | ||||
\(795\) | 0.171573 | − | 0.297173i | 0.00608506 | − | 0.0105396i | ||||
\(796\) | 2.87868 | + | 4.98602i | 0.102032 | + | 0.176725i | ||||
\(797\) | 0.142136 | 0.00503470 | 0.00251735 | − | 0.999997i | \(-0.499199\pi\) | ||||
0.00251735 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.79899 | −0.205154 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 0.414214 | − | 0.717439i | 0.0146355 | − | 0.0253495i | ||||
\(802\) | −3.00000 | + | 5.19615i | −0.105934 | + | 0.183483i | ||||
\(803\) | 2.24264 | + | 3.88437i | 0.0791411 | + | 0.137076i | ||||
\(804\) | −9.07107 | −0.319912 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 57.9411 | 2.04089 | ||||||||
\(807\) | 6.17157 | + | 10.6895i | 0.217250 | + | 0.376287i | ||||
\(808\) | 8.82843 | − | 15.2913i | 0.310583 | − | 0.537946i | ||||
\(809\) | −17.2426 | + | 29.8651i | −0.606219 | + | 1.05000i | 0.385639 | + | 0.922650i | \(0.373981\pi\) |
−0.991858 | + | 0.127352i | \(0.959352\pi\) | |||||||
\(810\) | 0.500000 | + | 0.866025i | 0.0175682 | + | 0.0304290i | ||||
\(811\) | 10.3431 | 0.363197 | 0.181598 | − | 0.983373i | \(-0.441873\pi\) | ||||
0.181598 | + | 0.983373i | \(0.441873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.6985 | −1.11171 | ||||||||
\(814\) | −0.272078 | − | 0.471253i | −0.00953633 | − | 0.0165174i | ||||
\(815\) | 8.53553 | − | 14.7840i | 0.298987 | − | 0.517860i | ||||
\(816\) | 1.29289 | − | 2.23936i | 0.0452603 | − | 0.0783932i | ||||
\(817\) | 30.9706 | + | 53.6426i | 1.08352 | + | 1.87672i | ||||
\(818\) | −4.24264 | −0.148340 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4853 | 0.366162 | ||||||||
\(821\) | −0.606602 | − | 1.05066i | −0.0211705 | − | 0.0366685i | 0.855246 | − | 0.518222i | \(-0.173406\pi\) |
−0.876417 | + | 0.481554i | \(0.840073\pi\) | |||||||
\(822\) | −6.82843 | + | 11.8272i | −0.238169 | + | 0.412520i | ||||
\(823\) | −14.4853 | + | 25.0892i | −0.504925 | + | 0.874556i | 0.495059 | + | 0.868860i | \(0.335147\pi\) |
−0.999984 | + | 0.00569646i | \(0.998187\pi\) | |||||||
\(824\) | 7.41421 | + | 12.8418i | 0.258286 | + | 0.447365i | ||||
\(825\) | −2.24264 | −0.0780787 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.5147 | 1.23497 | 0.617484 | − | 0.786584i | \(-0.288152\pi\) | ||||
0.617484 | + | 0.786584i | \(0.288152\pi\) | |||||||
\(828\) | −1.58579 | − | 2.74666i | −0.0551099 | − | 0.0954531i | ||||
\(829\) | −16.6569 | + | 28.8505i | −0.578516 | + | 1.00202i | 0.417133 | + | 0.908845i | \(0.363035\pi\) |
−0.995650 | + | 0.0931746i | \(0.970299\pi\) | |||||||
\(830\) | 2.58579 | − | 4.47871i | 0.0897540 | − | 0.155458i | ||||
\(831\) | −7.77817 | − | 13.4722i | −0.269822 | − | 0.467345i | ||||
\(832\) | 5.65685 | 0.196116 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.34315 | −0.0811365 | ||||||||
\(835\) | −1.12132 | − | 1.94218i | −0.0388049 | − | 0.0672120i | ||||
\(836\) | 7.65685 | − | 13.2621i | 0.264818 | − | 0.458678i | ||||
\(837\) | −5.12132 | + | 8.87039i | −0.177019 | + | 0.306605i | ||||
\(838\) | −18.4853 | − | 32.0174i | −0.638563 | − | 1.10602i | ||||
\(839\) | 8.48528 | 0.292944 | 0.146472 | − | 0.989215i | \(-0.453208\pi\) | ||||
0.146472 | + | 0.989215i | \(0.453208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3137 | −0.769438 | ||||||||
\(842\) | −1.82843 | − | 3.16693i | −0.0630118 | − | 0.109140i | ||||
\(843\) | −11.7279 | + | 20.3134i | −0.403931 | + | 0.699629i | ||||
\(844\) | 11.6569 | − | 20.1903i | 0.401245 | − | 0.694978i | ||||
\(845\) | −9.50000 | − | 16.4545i | −0.326810 | − | 0.566051i | ||||
\(846\) | 2.24264 | 0.0771036 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.343146 | 0.0117837 | ||||||||
\(849\) | 4.75736 | + | 8.23999i | 0.163272 | + | 0.282796i | ||||
\(850\) | 1.29289 | − | 2.23936i | 0.0443459 | − | 0.0768093i | ||||
\(851\) | 0.384776 | − | 0.666452i | 0.0131900 | − | 0.0228457i | ||||
\(852\) | −2.24264 | − | 3.88437i | −0.0768316 | − | 0.133076i | ||||
\(853\) | −40.6274 | −1.39106 | −0.695528 | − | 0.718499i | \(-0.744830\pi\) | ||||
−0.695528 | + | 0.718499i | \(0.744830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.82843 | −0.233527 | ||||||||
\(856\) | 4.82843 | + | 8.36308i | 0.165032 | + | 0.285844i | ||||
\(857\) | −12.3640 | + | 21.4150i | −0.422345 | + | 0.731523i | −0.996168 | − | 0.0874562i | \(-0.972126\pi\) |
0.573823 | + | 0.818979i | \(0.305460\pi\) | |||||||
\(858\) | −6.34315 | + | 10.9867i | −0.216551 | + | 0.375078i | ||||
\(859\) | 17.7990 | + | 30.8288i | 0.607294 | + | 1.05186i | 0.991684 | + | 0.128693i | \(0.0410782\pi\) |
−0.384391 | + | 0.923170i | \(0.625588\pi\) | |||||||
\(860\) | 9.07107 | 0.309321 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.4558 | −0.458308 | ||||||||
\(863\) | −22.8284 | − | 39.5400i | −0.777089 | − | 1.34596i | −0.933613 | − | 0.358283i | \(-0.883362\pi\) |
0.156524 | − | 0.987674i | \(-0.449971\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −10.4142 | + | 18.0379i | −0.354094 | + | 0.613309i | ||||
\(866\) | −8.89949 | − | 15.4144i | −0.302417 | − | 0.523802i | ||||
\(867\) | 10.3137 | 0.350272 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.9411 | 0.608611 | ||||||||
\(870\) | −1.29289 | − | 2.23936i | −0.0438332 | − | 0.0759213i | ||||
\(871\) | −25.6569 | + | 44.4390i | −0.869349 | + | 1.50576i | ||||
\(872\) | −1.82843 | + | 3.16693i | −0.0619184 | + | 0.107246i | ||||
\(873\) | 3.24264 | + | 5.61642i | 0.109747 | + | 0.190087i | ||||
\(874\) | 21.6569 | 0.732554 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −2.12132 | − | 3.67423i | −0.0716319 | − | 0.124070i | 0.827985 | − | 0.560751i | \(-0.189487\pi\) |
−0.899617 | + | 0.436681i | \(0.856154\pi\) | |||||||
\(878\) | −11.8492 | + | 20.5235i | −0.399893 | + | 0.692634i | ||||
\(879\) | 10.6569 | − | 18.4582i | 0.359447 | − | 0.622580i | ||||
\(880\) | −1.12132 | − | 1.94218i | −0.0377997 | − | 0.0654710i | ||||
\(881\) | 26.0000 | 0.875962 | 0.437981 | − | 0.898984i | \(-0.355694\pi\) | ||||
0.437981 | + | 0.898984i | \(0.355694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.2426 | −1.15236 | −0.576178 | − | 0.817324i | \(-0.695457\pi\) | ||||
−0.576178 | + | 0.817324i | \(0.695457\pi\) | |||||||
\(884\) | −7.31371 | − | 12.6677i | −0.245987 | − | 0.426061i | ||||
\(885\) | −1.58579 | + | 2.74666i | −0.0533056 | + | 0.0923281i | ||||
\(886\) | 18.1421 | − | 31.4231i | 0.609497 | − | 1.05568i | ||||
\(887\) | 16.4350 | + | 28.4663i | 0.551834 | + | 0.955805i | 0.998142 | + | 0.0609256i | \(0.0194052\pi\) |
−0.446308 | + | 0.894879i | \(0.647261\pi\) | |||||||
\(888\) | −0.242641 | −0.00814249 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.828427 | 0.0277689 | ||||||||
\(891\) | −1.12132 | − | 1.94218i | −0.0375656 | − | 0.0650656i | ||||
\(892\) | 3.65685 | − | 6.33386i | 0.122441 | − | 0.212073i | ||||
\(893\) | −7.65685 | + | 13.2621i | −0.256227 | + | 0.443798i | ||||
\(894\) | −11.1924 | − | 19.3858i | −0.374329 | − | 0.648358i | ||||
\(895\) | 26.2426 | 0.877195 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.9411 | −0.599037 | ||||||||
\(898\) | −5.24264 | − | 9.08052i | −0.174949 | − | 0.303021i | ||||
\(899\) | 13.2426 | − | 22.9369i | 0.441667 | − | 0.764989i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −0.443651 | − | 0.768426i | −0.0147802 | − | 0.0256000i | ||||
\(902\) | −23.5147 | −0.782954 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | −9.24264 | − | 16.0087i | −0.307236 | − | 0.532148i | ||||
\(906\) | −10.0711 | + | 17.4436i | −0.334589 | + | 0.579525i | ||||
\(907\) | 8.43503 | − | 14.6099i | 0.280081 | − | 0.485114i | −0.691324 | − | 0.722545i | \(-0.742972\pi\) |
0.971404 | + | 0.237431i | \(0.0763055\pi\) | |||||||
\(908\) | 12.4853 | + | 21.6251i | 0.414339 | + | 0.717656i | ||||
\(909\) | 17.6569 | 0.585641 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.9706 | 1.48994 | 0.744971 | − | 0.667097i | \(-0.232463\pi\) | ||||
0.744971 | + | 0.667097i | \(0.232463\pi\) | |||||||
\(912\) | −3.41421 | − | 5.91359i | −0.113056 | − | 0.195819i | ||||
\(913\) | −5.79899 | + | 10.0441i | −0.191919 | + | 0.332413i | ||||
\(914\) | 1.24264 | − | 2.15232i | 0.0411029 | − | 0.0711923i | ||||
\(915\) | −5.82843 | − | 10.0951i | −0.192682 | − | 0.333735i | ||||
\(916\) | −16.1421 | −0.533351 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.58579 | 0.0853437 | ||||||||
\(919\) | 15.3848 | + | 26.6472i | 0.507497 | + | 0.879010i | 0.999962 | + | 0.00867847i | \(0.00276248\pi\) |
−0.492465 | + | 0.870332i | \(0.663904\pi\) | |||||||
\(920\) | 1.58579 | − | 2.74666i | 0.0522818 | − | 0.0905548i | ||||
\(921\) | −3.65685 | + | 6.33386i | −0.120497 | + | 0.208708i | ||||
\(922\) | 1.00000 | + | 1.73205i | 0.0329332 | + | 0.0570421i | ||||
\(923\) | −25.3726 | −0.835149 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.242641 | −0.00797798 | ||||||||
\(926\) | −12.8284 | − | 22.2195i | −0.421568 | − | 0.730178i | ||||
\(927\) | −7.41421 | + | 12.8418i | −0.243515 | + | 0.421780i | ||||
\(928\) | 1.29289 | − | 2.23936i | 0.0424413 | − | 0.0735105i | ||||
\(929\) | −27.8284 | − | 48.2002i | −0.913021 | − | 1.58140i | −0.809773 | − | 0.586743i | \(-0.800410\pi\) |
−0.103248 | − | 0.994656i | \(-0.532924\pi\) | |||||||
\(930\) | −10.2426 | −0.335869 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.9706 | 0.621401 | ||||||||
\(933\) | −5.41421 | − | 9.37769i | −0.177253 | − | 0.307012i | ||||
\(934\) | 6.24264 | − | 10.8126i | 0.204265 | − | 0.353798i | ||||
\(935\) | −2.89949 | + | 5.02207i | −0.0948236 | + | 0.164239i | ||||
\(936\) | 2.82843 | + | 4.89898i | 0.0924500 | + | 0.160128i | ||||
\(937\) | 36.3431 | 1.18728 | 0.593639 | − | 0.804731i | \(-0.297691\pi\) | ||||
0.593639 | + | 0.804731i | \(0.297691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.4853 | −0.994850 | ||||||||
\(940\) | 1.12132 | + | 1.94218i | 0.0365734 | + | 0.0633471i | ||||
\(941\) | 14.1421 | − | 24.4949i | 0.461020 | − | 0.798511i | −0.537992 | − | 0.842950i | \(-0.680817\pi\) |
0.999012 | + | 0.0444393i | \(0.0141501\pi\) | |||||||
\(942\) | 4.17157 | − | 7.22538i | 0.135917 | − | 0.235415i | ||||
\(943\) | −16.6274 | − | 28.7995i | −0.541463 | − | 0.937842i | ||||
\(944\) | −3.17157 | −0.103226 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.3431 | −0.661413 | ||||||||
\(947\) | 4.58579 | + | 7.94282i | 0.149018 | + | 0.258107i | 0.930865 | − | 0.365364i | \(-0.119055\pi\) |
−0.781847 | + | 0.623471i | \(0.785722\pi\) | |||||||
\(948\) | 4.00000 | − | 6.92820i | 0.129914 | − | 0.225018i | ||||
\(949\) | 5.65685 | − | 9.79796i | 0.183629 | − | 0.318055i | ||||
\(950\) | −3.41421 | − | 5.91359i | −0.110772 | − | 0.191862i | ||||
\(951\) | 25.3137 | 0.820853 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.68629 | 0.151804 | 0.0759019 | − | 0.997115i | \(-0.475816\pi\) | ||||
0.0759019 | + | 0.997115i | \(0.475816\pi\) | |||||||
\(954\) | 0.171573 | + | 0.297173i | 0.00555488 | + | 0.00962133i | ||||
\(955\) | −2.00000 | + | 3.46410i | −0.0647185 | + | 0.112096i | ||||
\(956\) | 9.65685 | − | 16.7262i | 0.312325 | − | 0.540963i | ||||
\(957\) | 2.89949 | + | 5.02207i | 0.0937274 | + | 0.162341i | ||||
\(958\) | 8.48528 | 0.274147 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −36.9558 | − | 64.0094i | −1.19212 | − | 2.06482i | ||||
\(962\) | −0.686292 | + | 1.18869i | −0.0221269 | + | 0.0383250i | ||||
\(963\) | −4.82843 | + | 8.36308i | −0.155594 | + | 0.269497i | ||||
\(964\) | 9.77817 | + | 16.9363i | 0.314934 | + | 0.545481i | ||||
\(965\) | −4.82843 | −0.155433 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.3431 | −0.332613 | −0.166307 | − | 0.986074i | \(-0.553184\pi\) | ||||
−0.166307 | + | 0.986074i | \(0.553184\pi\) | |||||||
\(968\) | −2.98528 | − | 5.17066i | −0.0959506 | − | 0.166191i | ||||
\(969\) | −8.82843 | + | 15.2913i | −0.283610 | + | 0.491227i | ||||
\(970\) | −3.24264 | + | 5.61642i | −0.104115 | + | 0.180332i | ||||
\(971\) | 2.48528 | + | 4.30463i | 0.0797565 | + | 0.138142i | 0.903145 | − | 0.429336i | \(-0.141252\pi\) |
−0.823388 | + | 0.567478i | \(0.807919\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.8284 | −0.346965 | ||||||||
\(975\) | 2.82843 | + | 4.89898i | 0.0905822 | + | 0.156893i | ||||
\(976\) | 5.82843 | − | 10.0951i | 0.186563 | − | 0.323137i | ||||
\(977\) | 14.6569 | − | 25.3864i | 0.468914 | − | 0.812183i | −0.530454 | − | 0.847714i | \(-0.677979\pi\) |
0.999369 | + | 0.0355301i | \(0.0113120\pi\) | |||||||
\(978\) | 8.53553 | + | 14.7840i | 0.272936 | + | 0.472740i | ||||
\(979\) | −1.85786 | −0.0593776 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.65685 | −0.116754 | ||||||||
\(982\) | −8.53553 | − | 14.7840i | −0.272380 | − | 0.471776i | ||||
\(983\) | 8.53553 | − | 14.7840i | 0.272241 | − | 0.471536i | −0.697194 | − | 0.716882i | \(-0.745568\pi\) |
0.969435 | + | 0.245347i | \(0.0789018\pi\) | |||||||
\(984\) | −5.24264 | + | 9.08052i | −0.167129 | + | 0.289476i | ||||
\(985\) | 12.8995 | + | 22.3426i | 0.411012 | + | 0.711894i | ||||
\(986\) | −6.68629 | −0.212935 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.6274 | −1.22890 | ||||||||
\(989\) | −14.3848 | − | 24.9152i | −0.457409 | − | 0.792256i | ||||
\(990\) | 1.12132 | − | 1.94218i | 0.0356379 | − | 0.0617267i | ||||
\(991\) | 5.10051 | − | 8.83433i | 0.162023 | − | 0.280632i | −0.773571 | − | 0.633709i | \(-0.781531\pi\) |
0.935594 | + | 0.353078i | \(0.114865\pi\) | |||||||
\(992\) | −5.12132 | − | 8.87039i | −0.162602 | − | 0.281635i | ||||
\(993\) | 6.34315 | 0.201294 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.75736 | −0.182521 | ||||||||
\(996\) | 2.58579 | + | 4.47871i | 0.0819338 | + | 0.141913i | ||||
\(997\) | 28.3137 | − | 49.0408i | 0.896704 | − | 1.55314i | 0.0650229 | − | 0.997884i | \(-0.479288\pi\) |
0.831681 | − | 0.555253i | \(-0.187379\pi\) | |||||||
\(998\) | 3.41421 | − | 5.91359i | 0.108075 | − | 0.187191i | ||||
\(999\) | −0.121320 | − | 0.210133i | −0.00383841 | − | 0.00664831i |
(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 | 1470.2.i.x.361.1 | 4 | ||
7.2 | even | 3 | inner | 1470.2.i.x.961.1 | 4 | ||
7.3 | odd | 6 | 1470.2.a.t.1.2 | yes | 2 | ||
7.4 | even | 3 | 1470.2.a.s.1.2 | ✓ | 2 | ||
7.5 | odd | 6 | 1470.2.i.w.961.1 | 4 | |||
7.6 | odd | 2 | 1470.2.i.w.361.1 | 4 | |||
21.11 | odd | 6 | 4410.2.a.bw.1.1 | 2 | |||
21.17 | even | 6 | 4410.2.a.bz.1.1 | 2 | |||
35.4 | even | 6 | 7350.2.a.dl.1.2 | 2 | |||
35.24 | odd | 6 | 7350.2.a.dh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.a.s.1.2 | ✓ | 2 | 7.4 | even | 3 | ||
1470.2.a.t.1.2 | yes | 2 | 7.3 | odd | 6 | ||
1470.2.i.w.361.1 | 4 | 7.6 | odd | 2 | |||
1470.2.i.w.961.1 | 4 | 7.5 | odd | 6 | |||
1470.2.i.x.361.1 | 4 | 1.1 | even | 1 | trivial | ||
1470.2.i.x.961.1 | 4 | 7.2 | even | 3 | inner | ||
4410.2.a.bw.1.1 | 2 | 21.11 | odd | 6 | |||
4410.2.a.bz.1.1 | 2 | 21.17 | even | 6 | |||
7350.2.a.dh.1.2 | 2 | 35.24 | odd | 6 | |||
7350.2.a.dl.1.2 | 2 | 35.4 | even | 6 |