Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 557.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.557 |
Dual form | 784.2.x.h.373.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.707107 | − | 0.707107i | ||||
\(3\) | −0.500000 | + | 0.133975i | −0.288675 | + | 0.0773503i | −0.400251 | − | 0.916406i | \(-0.631077\pi\) |
0.111576 | + | 0.993756i | \(0.464410\pi\) | |||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 0.866025 | + | 0.232051i | 0.387298 | + | 0.103776i | 0.447214 | − | 0.894427i | \(-0.352416\pi\) |
−0.0599153 | + | 0.998203i | \(0.519083\pi\) | |||||||
\(6\) | −0.366025 | + | 0.633975i | −0.149429 | + | 0.258819i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | −2.36603 | + | 1.36603i | −0.788675 | + | 0.455342i | ||||
\(10\) | 1.09808 | − | 0.633975i | 0.347242 | − | 0.200480i | ||||
\(11\) | −0.767949 | − | 2.86603i | −0.231545 | − | 0.864139i | −0.979676 | − | 0.200587i | \(-0.935715\pi\) |
0.748130 | − | 0.663552i | \(-0.230952\pi\) | |||||||
\(12\) | 0.267949 | + | 1.00000i | 0.0773503 | + | 0.288675i | ||||
\(13\) | −3.73205 | − | 3.73205i | −1.03508 | − | 1.03508i | −0.999362 | − | 0.0357229i | \(-0.988627\pi\) |
−0.0357229 | − | 0.999362i | \(-0.511373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.464102 | −0.119831 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 3.23205 | − | 5.59808i | 0.783887 | − | 1.35773i | −0.145774 | − | 0.989318i | \(-0.546567\pi\) |
0.929661 | − | 0.368415i | \(-0.120099\pi\) | |||||||
\(18\) | −1.00000 | + | 3.73205i | −0.235702 | + | 0.879653i | ||||
\(19\) | −0.767949 | + | 2.86603i | −0.176180 | + | 0.657511i | 0.820168 | + | 0.572123i | \(0.193880\pi\) |
−0.996348 | + | 0.0853887i | \(0.972787\pi\) | |||||||
\(20\) | 0.464102 | − | 1.73205i | 0.103776 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.63397 | − | 2.09808i | −0.774766 | − | 0.447311i | ||||
\(23\) | 3.86603 | − | 2.23205i | 0.806122 | − | 0.465415i | −0.0394853 | − | 0.999220i | \(-0.512572\pi\) |
0.845607 | + | 0.533805i | \(0.179239\pi\) | |||||||
\(24\) | 1.26795 | + | 0.732051i | 0.258819 | + | 0.149429i | ||||
\(25\) | −3.63397 | − | 2.09808i | −0.726795 | − | 0.419615i | ||||
\(26\) | −7.46410 | −1.46383 | ||||||||
\(27\) | 2.09808 | − | 2.09808i | 0.403775 | − | 0.403775i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.267949 | − | 0.267949i | −0.0497569 | − | 0.0497569i | 0.681791 | − | 0.731547i | \(-0.261202\pi\) |
−0.731547 | + | 0.681791i | \(0.761202\pi\) | |||||||
\(30\) | −0.464102 | + | 0.464102i | −0.0847330 | + | 0.0847330i | ||||
\(31\) | 1.86603 | − | 3.23205i | 0.335148 | − | 0.580493i | −0.648365 | − | 0.761329i | \(-0.724547\pi\) |
0.983513 | + | 0.180836i | \(0.0578803\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.707107 | + | 0.707107i | ||||
\(33\) | 0.767949 | + | 1.33013i | 0.133683 | + | 0.231545i | ||||
\(34\) | −2.36603 | − | 8.83013i | −0.405770 | − | 1.51435i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.73205 | + | 4.73205i | 0.455342 | + | 0.788675i | ||||
\(37\) | −1.13397 | − | 0.303848i | −0.186424 | − | 0.0499522i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
−0.350823 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(38\) | 2.09808 | + | 3.63397i | 0.340353 | + | 0.589509i | ||||
\(39\) | 2.36603 | + | 1.36603i | 0.378867 | + | 0.218739i | ||||
\(40\) | −1.26795 | − | 2.19615i | −0.200480 | − | 0.347242i | ||||
\(41\) | 4.92820i | 0.769656i | 0.922988 | + | 0.384828i | \(0.125739\pi\) | ||||
−0.922988 | + | 0.384828i | \(0.874261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.46410 | − | 6.46410i | 0.985766 | − | 0.985766i | −0.0141339 | − | 0.999900i | \(-0.504499\pi\) |
0.999900 | + | 0.0141339i | \(0.00449910\pi\) | |||||||
\(44\) | −5.73205 | + | 1.53590i | −0.864139 | + | 0.231545i | ||||
\(45\) | −2.36603 | + | 0.633975i | −0.352706 | + | 0.0945074i | ||||
\(46\) | 1.63397 | − | 6.09808i | 0.240916 | − | 0.899112i | ||||
\(47\) | 2.13397 | + | 3.69615i | 0.311272 | + | 0.539139i | 0.978638 | − | 0.205591i | \(-0.0659116\pi\) |
−0.667366 | + | 0.744730i | \(0.732578\pi\) | |||||||
\(48\) | 2.00000 | − | 0.535898i | 0.288675 | − | 0.0773503i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.73205 | + | 1.53590i | −0.810634 | + | 0.217209i | ||||
\(51\) | −0.866025 | + | 3.23205i | −0.121268 | + | 0.452578i | ||||
\(52\) | −7.46410 | + | 7.46410i | −1.03508 | + | 1.03508i | ||||
\(53\) | −1.06218 | − | 3.96410i | −0.145901 | − | 0.544511i | −0.999714 | − | 0.0239302i | \(-0.992382\pi\) |
0.853812 | − | 0.520581i | \(-0.174285\pi\) | |||||||
\(54\) | − | 4.19615i | − | 0.571024i | ||||||
\(55\) | − | 2.66025i | − | 0.358709i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.53590i | − | 0.203435i | ||||||
\(58\) | −0.535898 | −0.0703669 | ||||||||
\(59\) | 3.03590 | + | 11.3301i | 0.395240 | + | 1.47506i | 0.821370 | + | 0.570395i | \(0.193210\pi\) |
−0.426130 | + | 0.904662i | \(0.640123\pi\) | |||||||
\(60\) | 0.928203i | 0.119831i | ||||||||
\(61\) | −1.86603 | + | 6.96410i | −0.238920 | + | 0.891662i | 0.737422 | + | 0.675432i | \(0.236043\pi\) |
−0.976342 | + | 0.216230i | \(0.930624\pi\) | |||||||
\(62\) | −1.36603 | − | 5.09808i | −0.173485 | − | 0.647456i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −2.36603 | − | 4.09808i | −0.293469 | − | 0.508304i | ||||
\(66\) | 2.09808 | + | 0.562178i | 0.258255 | + | 0.0691993i | ||||
\(67\) | −4.96410 | + | 1.33013i | −0.606462 | + | 0.162501i | −0.548966 | − | 0.835845i | \(-0.684978\pi\) |
−0.0574958 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(68\) | −11.1962 | − | 6.46410i | −1.35773 | − | 0.783887i | ||||
\(69\) | −1.63397 | + | 1.63397i | −0.196707 | + | 0.196707i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.535898i | 0.0635994i | 0.999494 | + | 0.0317997i | \(0.0101239\pi\) | ||||
−0.999494 | + | 0.0317997i | \(0.989876\pi\) | |||||||
\(72\) | 7.46410 | + | 2.00000i | 0.879653 | + | 0.235702i | ||||
\(73\) | −6.23205 | − | 3.59808i | −0.729406 | − | 0.421123i | 0.0887986 | − | 0.996050i | \(-0.471697\pi\) |
−0.818205 | + | 0.574927i | \(0.805031\pi\) | |||||||
\(74\) | −1.43782 | + | 0.830127i | −0.167143 | + | 0.0965003i | ||||
\(75\) | 2.09808 | + | 0.562178i | 0.242265 | + | 0.0649147i | ||||
\(76\) | 5.73205 | + | 1.53590i | 0.657511 | + | 0.176180i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.73205 | − | 1.00000i | 0.422572 | − | 0.113228i | ||||
\(79\) | 8.33013 | + | 14.4282i | 0.937213 | + | 1.62330i | 0.770640 | + | 0.637270i | \(0.219937\pi\) |
0.166572 | + | 0.986029i | \(0.446730\pi\) | |||||||
\(80\) | −3.46410 | − | 0.928203i | −0.387298 | − | 0.103776i | ||||
\(81\) | 3.33013 | − | 5.76795i | 0.370014 | − | 0.640883i | ||||
\(82\) | 4.92820 | + | 4.92820i | 0.544229 | + | 0.544229i | ||||
\(83\) | −1.53590 | − | 1.53590i | −0.168587 | − | 0.168587i | 0.617771 | − | 0.786358i | \(-0.288036\pi\) |
−0.786358 | + | 0.617771i | \(0.788036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.09808 | − | 4.09808i | 0.444499 | − | 0.444499i | ||||
\(86\) | − | 12.9282i | − | 1.39408i | ||||||
\(87\) | 0.169873 | + | 0.0980762i | 0.0182123 | + | 0.0105149i | ||||
\(88\) | −4.19615 | + | 7.26795i | −0.447311 | + | 0.774766i | ||||
\(89\) | 4.50000 | − | 2.59808i | 0.476999 | − | 0.275396i | −0.242166 | − | 0.970235i | \(-0.577858\pi\) |
0.719165 | + | 0.694839i | \(0.244525\pi\) | |||||||
\(90\) | −1.73205 | + | 3.00000i | −0.182574 | + | 0.316228i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.46410 | − | 7.73205i | −0.465415 | − | 0.806122i | ||||
\(93\) | −0.500000 | + | 1.86603i | −0.0518476 | + | 0.193498i | ||||
\(94\) | 5.83013 | + | 1.56218i | 0.601332 | + | 0.161126i | ||||
\(95\) | −1.33013 | + | 2.30385i | −0.136468 | + | 0.236370i | ||||
\(96\) | 1.46410 | − | 2.53590i | 0.149429 | − | 0.258819i | ||||
\(97\) | 2.92820 | 0.297314 | 0.148657 | − | 0.988889i | \(-0.452505\pi\) | ||||
0.148657 | + | 0.988889i | \(0.452505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.73205 | + | 5.73205i | 0.576093 | + | 0.576093i | ||||
\(100\) | −4.19615 | + | 7.26795i | −0.419615 | + | 0.726795i | ||||
\(101\) | −5.06218 | − | 18.8923i | −0.503706 | − | 1.87985i | −0.474450 | − | 0.880283i | \(-0.657353\pi\) |
−0.0292559 | − | 0.999572i | \(-0.509314\pi\) | |||||||
\(102\) | 2.36603 | + | 4.09808i | 0.234271 | + | 0.405770i | ||||
\(103\) | 5.59808 | − | 3.23205i | 0.551595 | − | 0.318463i | −0.198170 | − | 0.980168i | \(-0.563500\pi\) |
0.749765 | + | 0.661704i | \(0.230167\pi\) | |||||||
\(104\) | 14.9282i | 1.46383i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.02628 | − | 2.90192i | −0.488195 | − | 0.281860i | ||||
\(107\) | 3.23205 | + | 0.866025i | 0.312454 | + | 0.0837218i | 0.411638 | − | 0.911347i | \(-0.364957\pi\) |
−0.0991843 | + | 0.995069i | \(0.531623\pi\) | |||||||
\(108\) | −4.19615 | − | 4.19615i | −0.403775 | − | 0.403775i | ||||
\(109\) | −2.13397 | + | 0.571797i | −0.204398 | + | 0.0547682i | −0.359565 | − | 0.933120i | \(-0.617075\pi\) |
0.155167 | + | 0.987888i | \(0.450408\pi\) | |||||||
\(110\) | −2.66025 | − | 2.66025i | −0.253645 | − | 0.253645i | ||||
\(111\) | 0.607695 | 0.0576799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.46410 | −0.137731 | −0.0688655 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688655 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(114\) | −1.53590 | − | 1.53590i | −0.143850 | − | 0.143850i | ||||
\(115\) | 3.86603 | − | 1.03590i | 0.360509 | − | 0.0965980i | ||||
\(116\) | −0.535898 | + | 0.535898i | −0.0497569 | + | 0.0497569i | ||||
\(117\) | 13.9282 | + | 3.73205i | 1.28766 | + | 0.345028i | ||||
\(118\) | 14.3660 | + | 8.29423i | 1.32250 | + | 0.763546i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.928203 | + | 0.928203i | 0.0847330 | + | 0.0847330i | ||||
\(121\) | 1.90192 | − | 1.09808i | 0.172902 | − | 0.0998251i | ||||
\(122\) | 5.09808 | + | 8.83013i | 0.461558 | + | 0.799442i | ||||
\(123\) | −0.660254 | − | 2.46410i | −0.0595331 | − | 0.222181i | ||||
\(124\) | −6.46410 | − | 3.73205i | −0.580493 | − | 0.335148i | ||||
\(125\) | −5.83013 | − | 5.83013i | −0.521462 | − | 0.521462i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.46410 | 0.839803 | 0.419902 | − | 0.907570i | \(-0.362065\pi\) | ||||
0.419902 | + | 0.907570i | \(0.362065\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.707107 | + | 0.707107i | ||||
\(129\) | −2.36603 | + | 4.09808i | −0.208317 | + | 0.360815i | ||||
\(130\) | −6.46410 | − | 1.73205i | −0.566939 | − | 0.151911i | ||||
\(131\) | 2.03590 | − | 7.59808i | 0.177877 | − | 0.663847i | −0.818166 | − | 0.574982i | \(-0.805009\pi\) |
0.996044 | − | 0.0888654i | \(-0.0283241\pi\) | |||||||
\(132\) | 2.66025 | − | 1.53590i | 0.231545 | − | 0.133683i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.63397 | + | 6.29423i | −0.313928 | + | 0.543739i | ||||
\(135\) | 2.30385 | − | 1.33013i | 0.198284 | − | 0.114479i | ||||
\(136\) | −17.6603 | + | 4.73205i | −1.51435 | + | 0.405770i | ||||
\(137\) | 15.2321 | + | 8.79423i | 1.30136 | + | 0.751342i | 0.980638 | − | 0.195831i | \(-0.0627404\pi\) |
0.320724 | + | 0.947173i | \(0.396074\pi\) | |||||||
\(138\) | 3.26795i | 0.278186i | ||||||||
\(139\) | 11.9282 | − | 11.9282i | 1.01174 | − | 1.01174i | 0.0118067 | − | 0.999930i | \(-0.496242\pi\) |
0.999930 | − | 0.0118067i | \(-0.00375827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.56218 | − | 1.56218i | −0.131559 | − | 0.131559i | ||||
\(142\) | 0.535898 | + | 0.535898i | 0.0449716 | + | 0.0449716i | ||||
\(143\) | −7.83013 | + | 13.5622i | −0.654788 | + | 1.13413i | ||||
\(144\) | 9.46410 | − | 5.46410i | 0.788675 | − | 0.455342i | ||||
\(145\) | −0.169873 | − | 0.294229i | −0.0141072 | − | 0.0244344i | ||||
\(146\) | −9.83013 | + | 2.63397i | −0.813547 | + | 0.217989i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.607695 | + | 2.26795i | −0.0499522 | + | 0.186424i | ||||
\(149\) | −7.59808 | − | 2.03590i | −0.622459 | − | 0.166787i | −0.0662134 | − | 0.997805i | \(-0.521092\pi\) |
−0.556245 | + | 0.831018i | \(0.687758\pi\) | |||||||
\(150\) | 2.66025 | − | 1.53590i | 0.217209 | − | 0.125406i | ||||
\(151\) | 9.86603 | + | 5.69615i | 0.802886 | + | 0.463546i | 0.844479 | − | 0.535588i | \(-0.179910\pi\) |
−0.0415935 | + | 0.999135i | \(0.513243\pi\) | |||||||
\(152\) | 7.26795 | − | 4.19615i | 0.589509 | − | 0.340353i | ||||
\(153\) | 17.6603i | 1.42775i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.36603 | − | 2.36603i | 0.190044 | − | 0.190044i | ||||
\(156\) | 2.73205 | − | 4.73205i | 0.218739 | − | 0.378867i | ||||
\(157\) | 18.2583 | − | 4.89230i | 1.45717 | − | 0.390448i | 0.558661 | − | 0.829396i | \(-0.311315\pi\) |
0.898513 | + | 0.438948i | \(0.144649\pi\) | |||||||
\(158\) | 22.7583 | + | 6.09808i | 1.81056 | + | 0.485137i | ||||
\(159\) | 1.06218 | + | 1.83975i | 0.0842362 | + | 0.145901i | ||||
\(160\) | −4.39230 | + | 2.53590i | −0.347242 | + | 0.200480i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.43782 | − | 9.09808i | −0.191533 | − | 0.714812i | ||||
\(163\) | 3.23205 | − | 12.0622i | 0.253154 | − | 0.944783i | −0.715954 | − | 0.698147i | \(-0.754008\pi\) |
0.969108 | − | 0.246636i | \(-0.0793251\pi\) | |||||||
\(164\) | 9.85641 | 0.769656 | ||||||||
\(165\) | 0.356406 | + | 1.33013i | 0.0277462 | + | 0.103550i | ||||
\(166\) | −3.07180 | −0.238418 | ||||||||
\(167\) | 21.8564i | 1.69130i | 0.533738 | + | 0.845650i | \(0.320787\pi\) | ||||
−0.533738 | + | 0.845650i | \(0.679213\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.8564i | 1.14280i | ||||||||
\(170\) | − | 8.19615i | − | 0.628616i | ||||||
\(171\) | −2.09808 | − | 7.83013i | −0.160444 | − | 0.598785i | ||||
\(172\) | −12.9282 | − | 12.9282i | −0.985766 | − | 0.985766i | ||||
\(173\) | −0.598076 | + | 2.23205i | −0.0454709 | + | 0.169700i | −0.984927 | − | 0.172969i | \(-0.944664\pi\) |
0.939456 | + | 0.342668i | \(0.111331\pi\) | |||||||
\(174\) | 0.267949 | − | 0.0717968i | 0.0203132 | − | 0.00544290i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.07180 | + | 11.4641i | 0.231545 | + | 0.864139i | ||||
\(177\) | −3.03590 | − | 5.25833i | −0.228192 | − | 0.395240i | ||||
\(178\) | 1.90192 | − | 7.09808i | 0.142555 | − | 0.532023i | ||||
\(179\) | 8.96410 | − | 2.40192i | 0.670008 | − | 0.179528i | 0.0922498 | − | 0.995736i | \(-0.470594\pi\) |
0.577759 | + | 0.816208i | \(0.303928\pi\) | |||||||
\(180\) | 1.26795 | + | 4.73205i | 0.0945074 | + | 0.352706i | ||||
\(181\) | −13.3923 | + | 13.3923i | −0.995442 | + | 0.995442i | −0.999990 | − | 0.00454748i | \(-0.998552\pi\) |
0.00454748 | + | 0.999990i | \(0.498552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.73205i | − | 0.275881i | ||||||
\(184\) | −12.1962 | − | 3.26795i | −0.899112 | − | 0.240916i | ||||
\(185\) | −0.911543 | − | 0.526279i | −0.0670180 | − | 0.0386928i | ||||
\(186\) | 1.36603 | + | 2.36603i | 0.100162 | + | 0.173485i | ||||
\(187\) | −18.5263 | − | 4.96410i | −1.35478 | − | 0.363011i | ||||
\(188\) | 7.39230 | − | 4.26795i | 0.539139 | − | 0.311272i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.973721 | + | 3.63397i | 0.0706411 | + | 0.263636i | ||||
\(191\) | −4.33013 | − | 7.50000i | −0.313317 | − | 0.542681i | 0.665761 | − | 0.746165i | \(-0.268107\pi\) |
−0.979078 | + | 0.203484i | \(0.934774\pi\) | |||||||
\(192\) | −1.07180 | − | 4.00000i | −0.0773503 | − | 0.288675i | ||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | 2.92820 | − | 2.92820i | 0.210233 | − | 0.210233i | ||||
\(195\) | 1.73205 | + | 1.73205i | 0.124035 | + | 0.124035i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.6603 | + | 16.6603i | −1.18699 | + | 1.18699i | −0.209100 | + | 0.977894i | \(0.567053\pi\) |
−0.977894 | + | 0.209100i | \(0.932947\pi\) | |||||||
\(198\) | 11.4641 | 0.814718 | ||||||||
\(199\) | 10.3301 | + | 5.96410i | 0.732283 | + | 0.422784i | 0.819257 | − | 0.573427i | \(-0.194386\pi\) |
−0.0869736 | + | 0.996211i | \(0.527720\pi\) | |||||||
\(200\) | 3.07180 | + | 11.4641i | 0.217209 | + | 0.810634i | ||||
\(201\) | 2.30385 | − | 1.33013i | 0.162501 | − | 0.0938199i | ||||
\(202\) | −23.9545 | − | 13.8301i | −1.68543 | − | 0.973084i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.46410 | + | 1.73205i | 0.452578 | + | 0.121268i | ||||
\(205\) | −1.14359 | + | 4.26795i | −0.0798720 | + | 0.298087i | ||||
\(206\) | 2.36603 | − | 8.83013i | 0.164849 | − | 0.615224i | ||||
\(207\) | −6.09808 | + | 10.5622i | −0.423846 | + | 0.734122i | ||||
\(208\) | 14.9282 | + | 14.9282i | 1.03508 | + | 1.03508i | ||||
\(209\) | 8.80385 | 0.608975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9282 | − | 15.9282i | −1.09654 | − | 1.09654i | −0.994812 | − | 0.101731i | \(-0.967562\pi\) |
−0.101731 | − | 0.994812i | \(-0.532438\pi\) | |||||||
\(212\) | −7.92820 | + | 2.12436i | −0.544511 | + | 0.145901i | ||||
\(213\) | −0.0717968 | − | 0.267949i | −0.00491943 | − | 0.0183596i | ||||
\(214\) | 4.09808 | − | 2.36603i | 0.280139 | − | 0.161738i | ||||
\(215\) | 7.09808 | − | 4.09808i | 0.484085 | − | 0.279486i | ||||
\(216\) | −8.39230 | −0.571024 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.56218 | + | 2.70577i | −0.105804 | + | 0.183258i | ||||
\(219\) | 3.59808 | + | 0.964102i | 0.243135 | + | 0.0651479i | ||||
\(220\) | −5.32051 | −0.358709 | ||||||||
\(221\) | −32.9545 | + | 8.83013i | −2.21676 | + | 0.593979i | ||||
\(222\) | 0.607695 | − | 0.607695i | 0.0407858 | − | 0.0407858i | ||||
\(223\) | −9.85641 | −0.660034 | −0.330017 | − | 0.943975i | \(-0.607054\pi\) | ||||
−0.330017 | + | 0.943975i | \(0.607054\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.4641 | 0.764273 | ||||||||
\(226\) | −1.46410 | + | 1.46410i | −0.0973906 | + | 0.0973906i | ||||
\(227\) | −11.1603 | + | 2.99038i | −0.740732 | + | 0.198479i | −0.609403 | − | 0.792860i | \(-0.708591\pi\) |
−0.131329 | + | 0.991339i | \(0.541924\pi\) | |||||||
\(228\) | −3.07180 | −0.203435 | ||||||||
\(229\) | −13.3301 | − | 3.57180i | −0.880880 | − | 0.236031i | −0.210093 | − | 0.977681i | \(-0.567377\pi\) |
−0.670787 | + | 0.741650i | \(0.734043\pi\) | |||||||
\(230\) | 2.83013 | − | 4.90192i | 0.186613 | − | 0.323223i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.07180i | 0.0703669i | ||||||||
\(233\) | 0.696152 | − | 0.401924i | 0.0456065 | − | 0.0263309i | −0.477023 | − | 0.878891i | \(-0.658284\pi\) |
0.522630 | + | 0.852560i | \(0.324951\pi\) | |||||||
\(234\) | 17.6603 | − | 10.1962i | 1.15449 | − | 0.666543i | ||||
\(235\) | 0.990381 | + | 3.69615i | 0.0646053 | + | 0.241110i | ||||
\(236\) | 22.6603 | − | 6.07180i | 1.47506 | − | 0.395240i | ||||
\(237\) | −6.09808 | − | 6.09808i | −0.396113 | − | 0.396113i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.53590 | −0.552141 | −0.276071 | − | 0.961137i | \(-0.589032\pi\) | ||||
−0.276071 | + | 0.961137i | \(0.589032\pi\) | |||||||
\(240\) | 1.85641 | 0.119831 | ||||||||
\(241\) | 6.96410 | − | 12.0622i | 0.448597 | − | 0.776993i | −0.549698 | − | 0.835364i | \(-0.685257\pi\) |
0.998295 | + | 0.0583704i | \(0.0185905\pi\) | |||||||
\(242\) | 0.803848 | − | 3.00000i | 0.0516733 | − | 0.192847i | ||||
\(243\) | −3.19615 | + | 11.9282i | −0.205033 | + | 0.765195i | ||||
\(244\) | 13.9282 | + | 3.73205i | 0.891662 | + | 0.238920i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.12436 | − | 1.80385i | −0.199202 | − | 0.115009i | ||||
\(247\) | 13.5622 | − | 7.83013i | 0.862941 | − | 0.498219i | ||||
\(248\) | −10.1962 | + | 2.73205i | −0.647456 | + | 0.173485i | ||||
\(249\) | 0.973721 | + | 0.562178i | 0.0617070 | + | 0.0356266i | ||||
\(250\) | −11.6603 | −0.737459 | ||||||||
\(251\) | 17.5885 | − | 17.5885i | 1.11017 | − | 1.11017i | 0.117047 | − | 0.993126i | \(-0.462657\pi\) |
0.993126 | − | 0.117047i | \(-0.0373429\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.36603 | − | 9.36603i | −0.588837 | − | 0.588837i | ||||
\(254\) | 9.46410 | − | 9.46410i | 0.593831 | − | 0.593831i | ||||
\(255\) | −1.50000 | + | 2.59808i | −0.0939336 | + | 0.162698i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −9.69615 | − | 16.7942i | −0.604829 | − | 1.04760i | −0.992078 | − | 0.125620i | \(-0.959908\pi\) |
0.387249 | − | 0.921975i | \(-0.373425\pi\) | |||||||
\(258\) | 1.73205 | + | 6.46410i | 0.107833 | + | 0.402437i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.19615 | + | 4.73205i | −0.508304 | + | 0.293469i | ||||
\(261\) | 1.00000 | + | 0.267949i | 0.0618984 | + | 0.0165856i | ||||
\(262\) | −5.56218 | − | 9.63397i | −0.343632 | − | 0.595189i | ||||
\(263\) | 3.99038 | + | 2.30385i | 0.246057 | + | 0.142061i | 0.617958 | − | 0.786211i | \(-0.287960\pi\) |
−0.371900 | + | 0.928273i | \(0.621294\pi\) | |||||||
\(264\) | 1.12436 | − | 4.19615i | 0.0691993 | − | 0.258255i | ||||
\(265\) | − | 3.67949i | − | 0.226029i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.90192 | + | 1.90192i | −0.116396 | + | 0.116396i | ||||
\(268\) | 2.66025 | + | 9.92820i | 0.162501 | + | 0.606462i | ||||
\(269\) | −9.79423 | + | 2.62436i | −0.597165 | + | 0.160010i | −0.544726 | − | 0.838614i | \(-0.683366\pi\) |
−0.0524390 | + | 0.998624i | \(0.516700\pi\) | |||||||
\(270\) | 0.973721 | − | 3.63397i | 0.0592587 | − | 0.221157i | ||||
\(271\) | 6.06218 | + | 10.5000i | 0.368251 | + | 0.637830i | 0.989292 | − | 0.145948i | \(-0.0466233\pi\) |
−0.621041 | + | 0.783778i | \(0.713290\pi\) | |||||||
\(272\) | −12.9282 | + | 22.3923i | −0.783887 | + | 1.35773i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.0263 | − | 6.43782i | 1.45148 | − | 0.388923i | ||||
\(275\) | −3.22243 | + | 12.0263i | −0.194320 | + | 0.725212i | ||||
\(276\) | 3.26795 | + | 3.26795i | 0.196707 | + | 0.196707i | ||||
\(277\) | −1.20577 | − | 4.50000i | −0.0724478 | − | 0.270379i | 0.920195 | − | 0.391461i | \(-0.128030\pi\) |
−0.992642 | + | 0.121082i | \(0.961364\pi\) | |||||||
\(278\) | − | 23.8564i | − | 1.43081i | ||||||
\(279\) | 10.1962i | 0.610428i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.928203i | − | 0.0553720i | −0.999617 | − | 0.0276860i | \(-0.991186\pi\) | ||
0.999617 | − | 0.0276860i | \(-0.00881385\pi\) | |||||||
\(282\) | −3.12436 | −0.186053 | ||||||||
\(283\) | 3.89230 | + | 14.5263i | 0.231374 | + | 0.863498i | 0.979750 | + | 0.200224i | \(0.0641669\pi\) |
−0.748377 | + | 0.663274i | \(0.769166\pi\) | |||||||
\(284\) | 1.07180 | 0.0635994 | ||||||||
\(285\) | 0.356406 | − | 1.33013i | 0.0211117 | − | 0.0787899i | ||||
\(286\) | 5.73205 | + | 21.3923i | 0.338943 | + | 1.26495i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.00000 | − | 14.9282i | 0.235702 | − | 0.879653i | ||||
\(289\) | −12.3923 | − | 21.4641i | −0.728959 | − | 1.26259i | ||||
\(290\) | −0.464102 | − | 0.124356i | −0.0272530 | − | 0.00730242i | ||||
\(291\) | −1.46410 | + | 0.392305i | −0.0858272 | + | 0.0229973i | ||||
\(292\) | −7.19615 | + | 12.4641i | −0.421123 | + | 0.729406i | ||||
\(293\) | 7.92820 | − | 7.92820i | 0.463171 | − | 0.463171i | −0.436523 | − | 0.899693i | \(-0.643790\pi\) |
0.899693 | + | 0.436523i | \(0.143790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5167i | 0.612304i | ||||||||
\(296\) | 1.66025 | + | 2.87564i | 0.0965003 | + | 0.167143i | ||||
\(297\) | −7.62436 | − | 4.40192i | −0.442410 | − | 0.255426i | ||||
\(298\) | −9.63397 | + | 5.56218i | −0.558081 | + | 0.322208i | ||||
\(299\) | −22.7583 | − | 6.09808i | −1.31615 | − | 0.352661i | ||||
\(300\) | 1.12436 | − | 4.19615i | 0.0649147 | − | 0.242265i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.5622 | − | 4.16987i | 0.895503 | − | 0.239949i | ||||
\(303\) | 5.06218 | + | 8.76795i | 0.290815 | + | 0.503706i | ||||
\(304\) | 3.07180 | − | 11.4641i | 0.176180 | − | 0.657511i | ||||
\(305\) | −3.23205 | + | 5.59808i | −0.185067 | + | 0.320545i | ||||
\(306\) | 17.6603 | + | 17.6603i | 1.00957 | + | 1.00957i | ||||
\(307\) | −9.00000 | − | 9.00000i | −0.513657 | − | 0.513657i | 0.401988 | − | 0.915645i | \(-0.368319\pi\) |
−0.915645 | + | 0.401988i | \(0.868319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.36603 | + | 2.36603i | −0.134598 | + | 0.134598i | ||||
\(310\) | − | 4.73205i | − | 0.268762i | ||||||
\(311\) | −5.59808 | − | 3.23205i | −0.317438 | − | 0.183273i | 0.332812 | − | 0.942993i | \(-0.392002\pi\) |
−0.650250 | + | 0.759720i | \(0.725336\pi\) | |||||||
\(312\) | −2.00000 | − | 7.46410i | −0.113228 | − | 0.422572i | ||||
\(313\) | 18.6962 | − | 10.7942i | 1.05677 | − | 0.610126i | 0.132232 | − | 0.991219i | \(-0.457786\pi\) |
0.924537 | + | 0.381093i | \(0.124452\pi\) | |||||||
\(314\) | 13.3660 | − | 23.1506i | 0.754288 | − | 1.30647i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.8564 | − | 16.6603i | 1.62330 | − | 0.937213i | ||||
\(317\) | −3.79423 | + | 14.1603i | −0.213105 | + | 0.795319i | 0.773720 | + | 0.633528i | \(0.218394\pi\) |
−0.986825 | + | 0.161791i | \(0.948273\pi\) | |||||||
\(318\) | 2.90192 | + | 0.777568i | 0.162732 | + | 0.0436039i | ||||
\(319\) | −0.562178 | + | 0.973721i | −0.0314759 | + | 0.0545179i | ||||
\(320\) | −1.85641 | + | 6.92820i | −0.103776 | + | 0.387298i | ||||
\(321\) | −1.73205 | −0.0966736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.5622 | + | 13.5622i | 0.754620 | + | 0.754620i | ||||
\(324\) | −11.5359 | − | 6.66025i | −0.640883 | − | 0.370014i | ||||
\(325\) | 5.73205 | + | 21.3923i | 0.317957 | + | 1.18663i | ||||
\(326\) | −8.83013 | − | 15.2942i | −0.489056 | − | 0.847069i | ||||
\(327\) | 0.990381 | − | 0.571797i | 0.0547682 | − | 0.0316204i | ||||
\(328\) | 9.85641 | − | 9.85641i | 0.544229 | − | 0.544229i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.68653 | + | 0.973721i | 0.0928406 | + | 0.0536016i | ||||
\(331\) | −19.6244 | − | 5.25833i | −1.07865 | − | 0.289024i | −0.324609 | − | 0.945848i | \(-0.605233\pi\) |
−0.754044 | + | 0.656824i | \(0.771899\pi\) | |||||||
\(332\) | −3.07180 | + | 3.07180i | −0.168587 | + | 0.168587i | ||||
\(333\) | 3.09808 | − | 0.830127i | 0.169774 | − | 0.0454907i | ||||
\(334\) | 21.8564 | + | 21.8564i | 1.19593 | + | 1.19593i | ||||
\(335\) | −4.60770 | −0.251745 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.14359 | −0.334663 | −0.167331 | − | 0.985901i | \(-0.553515\pi\) | ||||
−0.167331 | + | 0.985901i | \(0.553515\pi\) | |||||||
\(338\) | 14.8564 | + | 14.8564i | 0.808082 | + | 0.808082i | ||||
\(339\) | 0.732051 | − | 0.196152i | 0.0397595 | − | 0.0106535i | ||||
\(340\) | −8.19615 | − | 8.19615i | −0.444499 | − | 0.444499i | ||||
\(341\) | −10.6962 | − | 2.86603i | −0.579229 | − | 0.155204i | ||||
\(342\) | −9.92820 | − | 5.73205i | −0.536856 | − | 0.309954i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −25.8564 | −1.39408 | ||||||||
\(345\) | −1.79423 | + | 1.03590i | −0.0965980 | + | 0.0557709i | ||||
\(346\) | 1.63397 | + | 2.83013i | 0.0878430 | + | 0.152149i | ||||
\(347\) | −6.30385 | − | 23.5263i | −0.338408 | − | 1.26296i | −0.900127 | − | 0.435628i | \(-0.856526\pi\) |
0.561718 | − | 0.827329i | \(-0.310140\pi\) | |||||||
\(348\) | 0.196152 | − | 0.339746i | 0.0105149 | − | 0.0182123i | ||||
\(349\) | −6.12436 | − | 6.12436i | −0.327829 | − | 0.327829i | 0.523931 | − | 0.851761i | \(-0.324465\pi\) |
−0.851761 | + | 0.523931i | \(0.824465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.6603 | −0.835883 | ||||||||
\(352\) | 14.5359 | + | 8.39230i | 0.774766 | + | 0.447311i | ||||
\(353\) | −13.8923 | + | 24.0622i | −0.739413 | + | 1.28070i | 0.213347 | + | 0.976976i | \(0.431563\pi\) |
−0.952760 | + | 0.303724i | \(0.901770\pi\) | |||||||
\(354\) | −8.29423 | − | 2.22243i | −0.440833 | − | 0.118121i | ||||
\(355\) | −0.124356 | + | 0.464102i | −0.00660011 | + | 0.0246320i | ||||
\(356\) | −5.19615 | − | 9.00000i | −0.275396 | − | 0.476999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.56218 | − | 11.3660i | 0.346822 | − | 0.600713i | ||||
\(359\) | −3.86603 | + | 2.23205i | −0.204041 | + | 0.117803i | −0.598539 | − | 0.801094i | \(-0.704252\pi\) |
0.394498 | + | 0.918897i | \(0.370919\pi\) | |||||||
\(360\) | 6.00000 | + | 3.46410i | 0.316228 | + | 0.182574i | ||||
\(361\) | 8.83013 | + | 5.09808i | 0.464744 | + | 0.268320i | ||||
\(362\) | 26.7846i | 1.40777i | ||||||||
\(363\) | −0.803848 | + | 0.803848i | −0.0421911 | + | 0.0421911i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.56218 | − | 4.56218i | −0.238795 | − | 0.238795i | ||||
\(366\) | −3.73205 | − | 3.73205i | −0.195077 | − | 0.195077i | ||||
\(367\) | 3.06218 | − | 5.30385i | 0.159844 | − | 0.276859i | −0.774968 | − | 0.632000i | \(-0.782234\pi\) |
0.934812 | + | 0.355142i | \(0.115567\pi\) | |||||||
\(368\) | −15.4641 | + | 8.92820i | −0.806122 | + | 0.465415i | ||||
\(369\) | −6.73205 | − | 11.6603i | −0.350457 | − | 0.607009i | ||||
\(370\) | −1.43782 | + | 0.385263i | −0.0747488 | + | 0.0200289i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.73205 | + | 1.00000i | 0.193498 | + | 0.0518476i | ||||
\(373\) | 0.866025 | + | 0.232051i | 0.0448411 | + | 0.0120151i | 0.281170 | − | 0.959658i | \(-0.409278\pi\) |
−0.236329 | + | 0.971673i | \(0.575944\pi\) | |||||||
\(374\) | −23.4904 | + | 13.5622i | −1.21466 | + | 0.701284i | ||||
\(375\) | 3.69615 | + | 2.13397i | 0.190868 | + | 0.110198i | ||||
\(376\) | 3.12436 | − | 11.6603i | 0.161126 | − | 0.601332i | ||||
\(377\) | 2.00000i | 0.103005i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.124356 | − | 0.124356i | 0.00638772 | − | 0.00638772i | −0.703906 | − | 0.710293i | \(-0.748562\pi\) |
0.710293 | + | 0.703906i | \(0.248562\pi\) | |||||||
\(380\) | 4.60770 | + | 2.66025i | 0.236370 | + | 0.136468i | ||||
\(381\) | −4.73205 | + | 1.26795i | −0.242430 | + | 0.0649590i | ||||
\(382\) | −11.8301 | − | 3.16987i | −0.605282 | − | 0.162185i | ||||
\(383\) | −12.5981 | − | 21.8205i | −0.643732 | − | 1.11498i | −0.984593 | − | 0.174862i | \(-0.944052\pi\) |
0.340861 | − | 0.940114i | \(-0.389281\pi\) | |||||||
\(384\) | −5.07180 | − | 2.92820i | −0.258819 | − | 0.149429i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.41858 | − | 31.4186i | −0.428495 | − | 1.59916i | ||||
\(387\) | −6.46410 | + | 24.1244i | −0.328589 | + | 1.22631i | ||||
\(388\) | − | 5.85641i | − | 0.297314i | ||||||
\(389\) | 5.99038 | + | 22.3564i | 0.303724 | + | 1.13351i | 0.934038 | + | 0.357174i | \(0.116260\pi\) |
−0.630313 | + | 0.776341i | \(0.717074\pi\) | |||||||
\(390\) | 3.46410 | 0.175412 | ||||||||
\(391\) | − | 28.8564i | − | 1.45933i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.07180i | 0.205395i | ||||||||
\(394\) | 33.3205i | 1.67866i | ||||||||
\(395\) | 3.86603 | + | 14.4282i | 0.194521 | + | 0.725962i | ||||
\(396\) | 11.4641 | − | 11.4641i | 0.576093 | − | 0.576093i | ||||
\(397\) | −6.86603 | + | 25.6244i | −0.344596 | + | 1.28605i | 0.548488 | + | 0.836159i | \(0.315204\pi\) |
−0.893084 | + | 0.449891i | \(0.851463\pi\) | |||||||
\(398\) | 16.2942 | − | 4.36603i | 0.816756 | − | 0.218849i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.5359 | + | 8.39230i | 0.726795 | + | 0.419615i | ||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | 0.973721 | − | 3.63397i | 0.0485648 | − | 0.181246i | ||||
\(403\) | −19.0263 | + | 5.09808i | −0.947766 | + | 0.253953i | ||||
\(404\) | −37.7846 | + | 10.1244i | −1.87985 | + | 0.503706i | ||||
\(405\) | 4.22243 | − | 4.22243i | 0.209814 | − | 0.209814i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.48334i | 0.172663i | ||||||||
\(408\) | 8.19615 | − | 4.73205i | 0.405770 | − | 0.234271i | ||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | 3.12436 | + | 5.41154i | 0.154301 | + | 0.267257i | ||||
\(411\) | −8.79423 | − | 2.35641i | −0.433787 | − | 0.116233i | ||||
\(412\) | −6.46410 | − | 11.1962i | −0.318463 | − | 0.551595i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.46410 | + | 16.6603i | 0.219399 | + | 0.818807i | ||||
\(415\) | −0.973721 | − | 1.68653i | −0.0477981 | − | 0.0827887i | ||||
\(416\) | 29.8564 | 1.46383 | ||||||||
\(417\) | −4.36603 | + | 7.56218i | −0.213805 | + | 0.370321i | ||||
\(418\) | 8.80385 | − | 8.80385i | 0.430610 | − | 0.430610i | ||||
\(419\) | 19.0000 | + | 19.0000i | 0.928211 | + | 0.928211i | 0.997590 | − | 0.0693796i | \(-0.0221020\pi\) |
−0.0693796 | + | 0.997590i | \(0.522102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.66025 | − | 8.66025i | 0.422075 | − | 0.422075i | −0.463843 | − | 0.885918i | \(-0.653530\pi\) |
0.885918 | + | 0.463843i | \(0.153530\pi\) | |||||||
\(422\) | −31.8564 | −1.55075 | ||||||||
\(423\) | −10.0981 | − | 5.83013i | −0.490985 | − | 0.283470i | ||||
\(424\) | −5.80385 | + | 10.0526i | −0.281860 | + | 0.488195i | ||||
\(425\) | −23.4904 | + | 13.5622i | −1.13945 | + | 0.657862i | ||||
\(426\) | −0.339746 | − | 0.196152i | −0.0164607 | − | 0.00950362i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.73205 | − | 6.46410i | 0.0837218 | − | 0.312454i | ||||
\(429\) | 2.09808 | − | 7.83013i | 0.101296 | − | 0.378042i | ||||
\(430\) | 3.00000 | − | 11.1962i | 0.144673 | − | 0.539926i | ||||
\(431\) | −15.3301 | + | 26.5526i | −0.738426 | + | 1.27899i | 0.214777 | + | 0.976663i | \(0.431097\pi\) |
−0.953204 | + | 0.302329i | \(0.902236\pi\) | |||||||
\(432\) | −8.39230 | + | 8.39230i | −0.403775 | + | 0.403775i | ||||
\(433\) | 33.1769 | 1.59438 | 0.797190 | − | 0.603728i | \(-0.206319\pi\) | ||||
0.797190 | + | 0.603728i | \(0.206319\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.124356 | + | 0.124356i | 0.00596240 | + | 0.00596240i | ||||
\(436\) | 1.14359 | + | 4.26795i | 0.0547682 | + | 0.204398i | ||||
\(437\) | 3.42820 | + | 12.7942i | 0.163993 | + | 0.612031i | ||||
\(438\) | 4.56218 | − | 2.63397i | 0.217989 | − | 0.125856i | ||||
\(439\) | −6.52628 | + | 3.76795i | −0.311482 | + | 0.179834i | −0.647590 | − | 0.761989i | \(-0.724223\pi\) |
0.336107 | + | 0.941824i | \(0.390890\pi\) | |||||||
\(440\) | −5.32051 | + | 5.32051i | −0.253645 | + | 0.253645i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.1244 | + | 41.7846i | −1.14748 | + | 1.98749i | ||||
\(443\) | −10.4282 | − | 2.79423i | −0.495459 | − | 0.132758i | 0.00243278 | − | 0.999997i | \(-0.499226\pi\) |
−0.497892 | + | 0.867239i | \(0.665892\pi\) | |||||||
\(444\) | − | 1.21539i | − | 0.0576799i | ||||||
\(445\) | 4.50000 | − | 1.20577i | 0.213320 | − | 0.0571590i | ||||
\(446\) | −9.85641 | + | 9.85641i | −0.466714 | + | 0.466714i | ||||
\(447\) | 4.07180 | 0.192589 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.3205 | −1.10056 | −0.550281 | − | 0.834979i | \(-0.685480\pi\) | ||||
−0.550281 | + | 0.834979i | \(0.685480\pi\) | |||||||
\(450\) | 11.4641 | − | 11.4641i | 0.540423 | − | 0.540423i | ||||
\(451\) | 14.1244 | − | 3.78461i | 0.665090 | − | 0.178210i | ||||
\(452\) | 2.92820i | 0.137731i | ||||||||
\(453\) | −5.69615 | − | 1.52628i | −0.267629 | − | 0.0717109i | ||||
\(454\) | −8.16987 | + | 14.1506i | −0.383431 | + | 0.664122i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.07180 | + | 3.07180i | −0.143850 | + | 0.143850i | ||||
\(457\) | 16.2846 | − | 9.40192i | 0.761762 | − | 0.439803i | −0.0681661 | − | 0.997674i | \(-0.521715\pi\) |
0.829928 | + | 0.557871i | \(0.188381\pi\) | |||||||
\(458\) | −16.9019 | + | 9.75833i | −0.789775 | + | 0.455977i | ||||
\(459\) | −4.96410 | − | 18.5263i | −0.231704 | − | 0.864733i | ||||
\(460\) | −2.07180 | − | 7.73205i | −0.0965980 | − | 0.360509i | ||||
\(461\) | −18.6603 | − | 18.6603i | −0.869095 | − | 0.869095i | 0.123278 | − | 0.992372i | \(-0.460659\pi\) |
−0.992372 | + | 0.123278i | \(0.960659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.14359 | 0.0996212 | 0.0498106 | − | 0.998759i | \(-0.484138\pi\) | ||||
0.0498106 | + | 0.998759i | \(0.484138\pi\) | |||||||
\(464\) | 1.07180 | + | 1.07180i | 0.0497569 | + | 0.0497569i | ||||
\(465\) | −0.866025 | + | 1.50000i | −0.0401610 | + | 0.0695608i | ||||
\(466\) | 0.294229 | − | 1.09808i | 0.0136299 | − | 0.0508674i | ||||
\(467\) | 6.96410 | − | 25.9904i | 0.322260 | − | 1.20269i | −0.594777 | − | 0.803890i | \(-0.702760\pi\) |
0.917038 | − | 0.398801i | \(-0.130574\pi\) | |||||||
\(468\) | 7.46410 | − | 27.8564i | 0.345028 | − | 1.28766i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.68653 | + | 2.70577i | 0.216174 | + | 0.124808i | ||||
\(471\) | −8.47372 | + | 4.89230i | −0.390448 | + | 0.225426i | ||||
\(472\) | 16.5885 | − | 28.7321i | 0.763546 | − | 1.32250i | ||||
\(473\) | −23.4904 | − | 13.5622i | −1.08009 | − | 0.623590i | ||||
\(474\) | −12.1962 | −0.560188 | ||||||||
\(475\) | 8.80385 | − | 8.80385i | 0.403948 | − | 0.403948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.92820 | + | 7.92820i | 0.363007 | + | 0.363007i | ||||
\(478\) | −8.53590 | + | 8.53590i | −0.390423 | + | 0.390423i | ||||
\(479\) | 7.79423 | − | 13.5000i | 0.356127 | − | 0.616831i | −0.631183 | − | 0.775634i | \(-0.717430\pi\) |
0.987310 | + | 0.158803i | \(0.0507636\pi\) | |||||||
\(480\) | 1.85641 | − | 1.85641i | 0.0847330 | − | 0.0847330i | ||||
\(481\) | 3.09808 | + | 5.36603i | 0.141260 | + | 0.244670i | ||||
\(482\) | −5.09808 | − | 19.0263i | −0.232211 | − | 0.866623i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.19615 | − | 3.80385i | −0.0998251 | − | 0.172902i | ||||
\(485\) | 2.53590 | + | 0.679492i | 0.115149 | + | 0.0308541i | ||||
\(486\) | 8.73205 | + | 15.1244i | 0.396094 | + | 0.686055i | ||||
\(487\) | 10.6699 | + | 6.16025i | 0.483498 | + | 0.279148i | 0.721873 | − | 0.692025i | \(-0.243281\pi\) |
−0.238375 | + | 0.971173i | \(0.576615\pi\) | |||||||
\(488\) | 17.6603 | − | 10.1962i | 0.799442 | − | 0.461558i | ||||
\(489\) | 6.46410i | 0.292317i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.58846 | + | 3.58846i | −0.161945 | + | 0.161945i | −0.783428 | − | 0.621483i | \(-0.786531\pi\) |
0.621483 | + | 0.783428i | \(0.286531\pi\) | |||||||
\(492\) | −4.92820 | + | 1.32051i | −0.222181 | + | 0.0595331i | ||||
\(493\) | −2.36603 | + | 0.633975i | −0.106560 | + | 0.0285528i | ||||
\(494\) | 5.73205 | − | 21.3923i | 0.257897 | − | 0.962485i | ||||
\(495\) | 3.63397 | + | 6.29423i | 0.163335 | + | 0.282905i | ||||
\(496\) | −7.46410 | + | 12.9282i | −0.335148 | + | 0.580493i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.53590 | − | 0.411543i | 0.0688253 | − | 0.0184417i | ||||
\(499\) | 6.69615 | − | 24.9904i | 0.299761 | − | 1.11872i | −0.637601 | − | 0.770367i | \(-0.720073\pi\) |
0.937362 | − | 0.348356i | \(-0.113260\pi\) | |||||||
\(500\) | −11.6603 | + | 11.6603i | −0.521462 | + | 0.521462i | ||||
\(501\) | −2.92820 | − | 10.9282i | −0.130822 | − | 0.488236i | ||||
\(502\) | − | 35.1769i | − | 1.57002i | ||||||
\(503\) | 31.8564i | 1.42041i | 0.703996 | + | 0.710203i | \(0.251397\pi\) | ||||
−0.703996 | + | 0.710203i | \(0.748603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 17.5359i | − | 0.780337i | ||||||
\(506\) | −18.7321 | −0.832741 | ||||||||
\(507\) | −1.99038 | − | 7.42820i | −0.0883959 | − | 0.329898i | ||||
\(508\) | − | 18.9282i | − | 0.839803i | ||||||
\(509\) | −2.52628 | + | 9.42820i | −0.111975 | + | 0.417898i | −0.999043 | − | 0.0437420i | \(-0.986072\pi\) |
0.887067 | + | 0.461640i | \(0.152739\pi\) | |||||||
\(510\) | 1.09808 | + | 4.09808i | 0.0486236 | + | 0.181466i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 4.40192 | + | 7.62436i | 0.194350 | + | 0.336624i | ||||
\(514\) | −26.4904 | − | 7.09808i | −1.16844 | − | 0.313083i | ||||
\(515\) | 5.59808 | − | 1.50000i | 0.246681 | − | 0.0660979i | ||||
\(516\) | 8.19615 | + | 4.73205i | 0.360815 | + | 0.208317i | ||||
\(517\) | 8.95448 | − | 8.95448i | 0.393818 | − | 0.393818i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.19615i | − | 0.0525053i | ||||||
\(520\) | −3.46410 | + | 12.9282i | −0.151911 | + | 0.566939i | ||||
\(521\) | 13.3756 | + | 7.72243i | 0.585998 | + | 0.338326i | 0.763513 | − | 0.645792i | \(-0.223473\pi\) |
−0.177516 | + | 0.984118i | \(0.556806\pi\) | |||||||
\(522\) | 1.26795 | − | 0.732051i | 0.0554966 | − | 0.0320410i | ||||
\(523\) | 32.2846 | + | 8.65064i | 1.41171 | + | 0.378266i | 0.882534 | − | 0.470248i | \(-0.155836\pi\) |
0.529173 | + | 0.848514i | \(0.322502\pi\) | |||||||
\(524\) | −15.1962 | − | 4.07180i | −0.663847 | − | 0.177877i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.29423 | − | 1.68653i | 0.274441 | − | 0.0735364i | ||||
\(527\) | −12.0622 | − | 20.8923i | −0.525437 | − | 0.910083i | ||||
\(528\) | −3.07180 | − | 5.32051i | −0.133683 | − | 0.231545i | ||||
\(529\) | −1.53590 | + | 2.66025i | −0.0667782 | + | 0.115663i | ||||
\(530\) | −3.67949 | − | 3.67949i | −0.159827 | − | 0.159827i | ||||
\(531\) | −22.6603 | − | 22.6603i | −0.983371 | − | 0.983371i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.3923 | − | 18.3923i | 0.796659 | − | 0.796659i | ||||
\(534\) | 3.80385i | 0.164609i | ||||||||
\(535\) | 2.59808 | + | 1.50000i | 0.112325 | + | 0.0648507i | ||||
\(536\) | 12.5885 | + | 7.26795i | 0.543739 | + | 0.313928i | ||||
\(537\) | −4.16025 | + | 2.40192i | −0.179528 | + | 0.103651i | ||||
\(538\) | −7.16987 | + | 12.4186i | −0.309115 | + | 0.535403i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.66025 | − | 4.60770i | −0.114479 | − | 0.198284i | ||||
\(541\) | 2.47372 | − | 9.23205i | 0.106354 | − | 0.396917i | −0.892142 | − | 0.451756i | \(-0.850798\pi\) |
0.998495 | + | 0.0548389i | \(0.0174645\pi\) | |||||||
\(542\) | 16.5622 | + | 4.43782i | 0.711406 | + | 0.190621i | ||||
\(543\) | 4.90192 | − | 8.49038i | 0.210362 | − | 0.364357i | ||||
\(544\) | 9.46410 | + | 35.3205i | 0.405770 | + | 1.51435i | ||||
\(545\) | −1.98076 | −0.0848465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.0526 | − | 23.0526i | −0.985656 | − | 0.985656i | 0.0142423 | − | 0.999899i | \(-0.495466\pi\) |
−0.999899 | + | 0.0142423i | \(0.995466\pi\) | |||||||
\(548\) | 17.5885 | − | 30.4641i | 0.751342 | − | 1.30136i | ||||
\(549\) | −5.09808 | − | 19.0263i | −0.217581 | − | 0.812022i | ||||
\(550\) | 8.80385 | + | 15.2487i | 0.375397 | + | 0.650207i | ||||
\(551\) | 0.973721 | − | 0.562178i | 0.0414819 | − | 0.0239496i | ||||
\(552\) | 6.53590 | 0.278186 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.70577 | − | 3.29423i | −0.242415 | − | 0.139958i | ||||
\(555\) | 0.526279 | + | 0.141016i | 0.0223393 | + | 0.00598580i | ||||
\(556\) | −23.8564 | − | 23.8564i | −1.01174 | − | 1.01174i | ||||
\(557\) | 6.59808 | − | 1.76795i | 0.279569 | − | 0.0749104i | −0.116310 | − | 0.993213i | \(-0.537107\pi\) |
0.395879 | + | 0.918303i | \(0.370440\pi\) | |||||||
\(558\) | 10.1962 | + | 10.1962i | 0.431638 | + | 0.431638i | ||||
\(559\) | −48.2487 | −2.04070 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.92820 | 0.419169 | ||||||||
\(562\) | −0.928203 | − | 0.928203i | −0.0391539 | − | 0.0391539i | ||||
\(563\) | 2.42820 | − | 0.650635i | 0.102337 | − | 0.0274210i | −0.207287 | − | 0.978280i | \(-0.566464\pi\) |
0.309624 | + | 0.950859i | \(0.399797\pi\) | |||||||
\(564\) | −3.12436 | + | 3.12436i | −0.131559 | + | 0.131559i | ||||
\(565\) | −1.26795 | − | 0.339746i | −0.0533430 | − | 0.0142932i | ||||
\(566\) | 18.4186 | + | 10.6340i | 0.774191 | + | 0.446979i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.07180 | − | 1.07180i | 0.0449716 | − | 0.0449716i | ||||
\(569\) | −5.08846 | + | 2.93782i | −0.213319 | + | 0.123160i | −0.602853 | − | 0.797852i | \(-0.705969\pi\) |
0.389534 | + | 0.921012i | \(0.372636\pi\) | |||||||
\(570\) | −0.973721 | − | 1.68653i | −0.0407847 | − | 0.0706411i | ||||
\(571\) | −7.16025 | − | 26.7224i | −0.299647 | − | 1.11830i | −0.937456 | − | 0.348104i | \(-0.886826\pi\) |
0.637809 | − | 0.770195i | \(-0.279841\pi\) | |||||||
\(572\) | 27.1244 | + | 15.6603i | 1.13413 | + | 0.654788i | ||||
\(573\) | 3.16987 | + | 3.16987i | 0.132423 | + | 0.132423i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.7321 | −0.781181 | ||||||||
\(576\) | −10.9282 | − | 18.9282i | −0.455342 | − | 0.788675i | ||||
\(577\) | 6.62436 | − | 11.4737i | 0.275776 | − | 0.477657i | −0.694555 | − | 0.719440i | \(-0.744399\pi\) |
0.970330 | + | 0.241782i | \(0.0777320\pi\) | |||||||
\(578\) | −33.8564 | − | 9.07180i | −1.40824 | − | 0.377337i | ||||
\(579\) | −3.08142 | + | 11.5000i | −0.128059 | + | 0.477924i | ||||
\(580\) | −0.588457 | + | 0.339746i | −0.0244344 | + | 0.0141072i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.07180 | + | 1.85641i | −0.0444274 | + | 0.0769505i | ||||
\(583\) | −10.5455 | + | 6.08846i | −0.436751 | + | 0.252158i | ||||
\(584\) | 5.26795 | + | 19.6603i | 0.217989 | + | 0.813547i | ||||
\(585\) | 11.1962 | + | 6.46410i | 0.462904 | + | 0.267258i | ||||
\(586\) | − | 15.8564i | − | 0.655022i | ||||||
\(587\) | −21.9282 | + | 21.9282i | −0.905074 | + | 0.905074i | −0.995870 | − | 0.0907957i | \(-0.971059\pi\) |
0.0907957 | + | 0.995870i | \(0.471059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.83013 | + | 7.83013i | 0.322635 | + | 0.322635i | ||||
\(590\) | 10.5167 | + | 10.5167i | 0.432964 | + | 0.432964i | ||||
\(591\) | 6.09808 | − | 10.5622i | 0.250841 | − | 0.434470i | ||||
\(592\) | 4.53590 | + | 1.21539i | 0.186424 | + | 0.0499522i | ||||
\(593\) | −5.69615 | − | 9.86603i | −0.233913 | − | 0.405149i | 0.725043 | − | 0.688703i | \(-0.241820\pi\) |
−0.958956 | + | 0.283554i | \(0.908486\pi\) | |||||||
\(594\) | −12.0263 | + | 3.22243i | −0.493444 | + | 0.132218i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.07180 | + | 15.1962i | −0.166787 | + | 0.622459i | ||||
\(597\) | −5.96410 | − | 1.59808i | −0.244094 | − | 0.0654049i | ||||
\(598\) | −28.8564 | + | 16.6603i | −1.18003 | + | 0.681288i | ||||
\(599\) | 16.6699 | + | 9.62436i | 0.681113 | + | 0.393241i | 0.800274 | − | 0.599634i | \(-0.204687\pi\) |
−0.119162 | + | 0.992875i | \(0.538021\pi\) | |||||||
\(600\) | −3.07180 | − | 5.32051i | −0.125406 | − | 0.217209i | ||||
\(601\) | − | 10.0000i | − | 0.407909i | −0.978980 | − | 0.203954i | \(-0.934621\pi\) | ||
0.978980 | − | 0.203954i | \(-0.0653794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.92820 | − | 9.92820i | 0.404308 | − | 0.404308i | ||||
\(604\) | 11.3923 | − | 19.7321i | 0.463546 | − | 0.802886i | ||||
\(605\) | 1.90192 | − | 0.509619i | 0.0773242 | − | 0.0207190i | ||||
\(606\) | 13.8301 | + | 3.70577i | 0.561811 | + | 0.150537i | ||||
\(607\) | 8.52628 | + | 14.7679i | 0.346071 | + | 0.599413i | 0.985548 | − | 0.169398i | \(-0.0541823\pi\) |
−0.639477 | + | 0.768810i | \(0.720849\pi\) | |||||||
\(608\) | −8.39230 | − | 14.5359i | −0.340353 | − | 0.589509i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.36603 | + | 8.83013i | 0.0957976 | + | 0.357521i | ||||
\(611\) | 5.83013 | − | 21.7583i | 0.235862 | − | 0.880248i | ||||
\(612\) | 35.3205 | 1.42775 | ||||||||
\(613\) | 2.47372 | + | 9.23205i | 0.0999126 | + | 0.372879i | 0.997718 | − | 0.0675126i | \(-0.0215063\pi\) |
−0.897806 | + | 0.440392i | \(0.854840\pi\) | |||||||
\(614\) | −18.0000 | −0.726421 | ||||||||
\(615\) | − | 2.28719i | − | 0.0922283i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.535898i | 0.0215745i | 0.999942 | + | 0.0107872i | \(0.00343375\pi\) | ||||
−0.999942 | + | 0.0107872i | \(0.996566\pi\) | |||||||
\(618\) | 4.73205i | 0.190351i | ||||||||
\(619\) | −5.10770 | − | 19.0622i | −0.205296 | − | 0.766174i | −0.989359 | − | 0.145493i | \(-0.953523\pi\) |
0.784064 | − | 0.620680i | \(-0.213144\pi\) | |||||||
\(620\) | −4.73205 | − | 4.73205i | −0.190044 | − | 0.190044i | ||||
\(621\) | 3.42820 | − | 12.7942i | 0.137569 | − | 0.513415i | ||||
\(622\) | −8.83013 | + | 2.36603i | −0.354056 | + | 0.0948690i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.46410 | − | 5.46410i | −0.378867 | − | 0.218739i | ||||
\(625\) | 6.79423 | + | 11.7679i | 0.271769 | + | 0.470718i | ||||
\(626\) | 7.90192 | − | 29.4904i | 0.315824 | − | 1.17867i | ||||
\(627\) | −4.40192 | + | 1.17949i | −0.175796 | + | 0.0471044i | ||||
\(628\) | −9.78461 | − | 36.5167i | −0.390448 | − | 1.45717i | ||||
\(629\) | −5.36603 | + | 5.36603i | −0.213957 | + | 0.213957i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2487i | 1.28380i | 0.766788 | + | 0.641900i | \(0.221854\pi\) | ||||
−0.766788 | + | 0.641900i | \(0.778146\pi\) | |||||||
\(632\) | 12.1962 | − | 45.5167i | 0.485137 | − | 1.81056i | ||||
\(633\) | 10.0981 | + | 5.83013i | 0.401362 | + | 0.231727i | ||||
\(634\) | 10.3660 | + | 17.9545i | 0.411687 | + | 0.713064i | ||||
\(635\) | 8.19615 | + | 2.19615i | 0.325254 | + | 0.0871517i | ||||
\(636\) | 3.67949 | − | 2.12436i | 0.145901 | − | 0.0842362i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.411543 | + | 1.53590i | 0.0162931 | + | 0.0608068i | ||||
\(639\) | −0.732051 | − | 1.26795i | −0.0289595 | − | 0.0501593i | ||||
\(640\) | 5.07180 | + | 8.78461i | 0.200480 | + | 0.347242i | ||||
\(641\) | 5.57180 | − | 9.65064i | 0.220073 | − | 0.381177i | −0.734757 | − | 0.678330i | \(-0.762704\pi\) |
0.954830 | + | 0.297153i | \(0.0960372\pi\) | |||||||
\(642\) | −1.73205 | + | 1.73205i | −0.0683586 | + | 0.0683586i | ||||
\(643\) | 5.39230 | + | 5.39230i | 0.212652 | + | 0.212652i | 0.805393 | − | 0.592741i | \(-0.201954\pi\) |
−0.592741 | + | 0.805393i | \(0.701954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.00000 | + | 3.00000i | −0.118125 | + | 0.118125i | ||||
\(646\) | 27.1244 | 1.06719 | ||||||||
\(647\) | −30.8660 | − | 17.8205i | −1.21347 | − | 0.700596i | −0.249955 | − | 0.968257i | \(-0.580416\pi\) |
−0.963513 | + | 0.267661i | \(0.913749\pi\) | |||||||
\(648\) | −18.1962 | + | 4.87564i | −0.714812 | + | 0.191533i | ||||
\(649\) | 30.1410 | − | 17.4019i | 1.18314 | − | 0.683085i | ||||
\(650\) | 27.1244 | + | 15.6603i | 1.06390 | + | 0.614246i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.1244 | − | 6.46410i | −0.944783 | − | 0.253154i | ||||
\(653\) | −8.72243 | + | 32.5526i | −0.341335 | + | 1.27388i | 0.555501 | + | 0.831516i | \(0.312527\pi\) |
−0.896836 | + | 0.442364i | \(0.854140\pi\) | |||||||
\(654\) | 0.418584 | − | 1.56218i | 0.0163679 | − | 0.0610860i | ||||
\(655\) | 3.52628 | − | 6.10770i | 0.137783 | − | 0.238647i | ||||
\(656\) | − | 19.7128i | − | 0.769656i | ||||||
\(657\) | 19.6603 | 0.767020 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8564 | + | 18.8564i | 0.734541 | + | 0.734541i | 0.971516 | − | 0.236975i | \(-0.0761558\pi\) |
−0.236975 | + | 0.971516i | \(0.576156\pi\) | |||||||
\(660\) | 2.66025 | − | 0.712813i | 0.103550 | − | 0.0277462i | ||||
\(661\) | 5.93782 | + | 22.1603i | 0.230955 | + | 0.861934i | 0.979931 | + | 0.199337i | \(0.0638789\pi\) |
−0.748976 | + | 0.662597i | \(0.769454\pi\) | |||||||
\(662\) | −24.8827 | + | 14.3660i | −0.967093 | + | 0.558351i | ||||
\(663\) | 15.2942 | − | 8.83013i | 0.593979 | − | 0.342934i | ||||
\(664\) | 6.14359i | 0.238418i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.26795 | − | 3.92820i | 0.0878812 | − | 0.152215i | ||||
\(667\) | −1.63397 | − | 0.437822i | −0.0632677 | − | 0.0169525i | ||||
\(668\) | 43.7128 | 1.69130 | ||||||||
\(669\) | 4.92820 | − | 1.32051i | 0.190535 | − | 0.0510538i | ||||
\(670\) | −4.60770 | + | 4.60770i | −0.178011 | + | 0.178011i | ||||
\(671\) | 21.3923 | 0.825841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.7846 | 1.57213 | 0.786066 | − | 0.618143i | \(-0.212115\pi\) | ||||
0.786066 | + | 0.618143i | \(0.212115\pi\) | |||||||
\(674\) | −6.14359 | + | 6.14359i | −0.236642 | + | 0.236642i | ||||
\(675\) | −12.0263 | + | 3.22243i | −0.462892 | + | 0.124031i | ||||
\(676\) | 29.7128 | 1.14280 | ||||||||
\(677\) | 42.7224 | + | 11.4474i | 1.64196 | + | 0.439961i | 0.957345 | − | 0.288947i | \(-0.0933052\pi\) |
0.684611 | + | 0.728908i | \(0.259972\pi\) | |||||||
\(678\) | 0.535898 | − | 0.928203i | 0.0205811 | − | 0.0356474i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.3923 | −0.628616 | ||||||||
\(681\) | 5.17949 | − | 2.99038i | 0.198479 | − | 0.114592i | ||||
\(682\) | −13.5622 | + | 7.83013i | −0.519323 | + | 0.299831i | ||||
\(683\) | 12.2128 | + | 45.5788i | 0.467310 | + | 1.74403i | 0.649114 | + | 0.760691i | \(0.275140\pi\) |
−0.181804 | + | 0.983335i | \(0.558194\pi\) | |||||||
\(684\) | −15.6603 | + | 4.19615i | −0.598785 | + | 0.160444i | ||||
\(685\) | 11.1506 | + | 11.1506i | 0.426044 | + | 0.426044i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.14359 | 0.272545 | ||||||||
\(688\) | −25.8564 | + | 25.8564i | −0.985766 | + | 0.985766i | ||||
\(689\) | −10.8301 | + | 18.7583i | −0.412595 | + | 0.714635i | ||||
\(690\) | −0.758330 | + | 2.83013i | −0.0288691 | + | 0.107741i | ||||
\(691\) | −6.16025 | + | 22.9904i | −0.234347 | + | 0.874595i | 0.744095 | + | 0.668074i | \(0.232881\pi\) |
−0.978442 | + | 0.206521i | \(0.933786\pi\) | |||||||
\(692\) | 4.46410 | + | 1.19615i | 0.169700 | + | 0.0454709i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.8301 | − | 17.2224i | −1.13234 | − | 0.653755i | ||||
\(695\) | 13.0981 | − | 7.56218i | 0.496838 | − | 0.286850i | ||||
\(696\) | −0.143594 | − | 0.535898i | −0.00544290 | − | 0.0203132i | ||||
\(697\) | 27.5885 | + | 15.9282i | 1.04499 | + | 0.603324i | ||||
\(698\) | −12.2487 | −0.463621 | ||||||||
\(699\) | −0.294229 | + | 0.294229i | −0.0111287 | + | 0.0111287i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.3923 | − | 13.3923i | −0.505820 | − | 0.505820i | 0.407420 | − | 0.913241i | \(-0.366428\pi\) |
−0.913241 | + | 0.407420i | \(0.866428\pi\) | |||||||
\(702\) | −15.6603 | + | 15.6603i | −0.591058 | + | 0.591058i | ||||
\(703\) | 1.74167 | − | 3.01666i | 0.0656883 | − | 0.113776i | ||||
\(704\) | 22.9282 | − | 6.14359i | 0.864139 | − | 0.231545i | ||||
\(705\) | −0.990381 | − | 1.71539i | −0.0372999 | − | 0.0646053i | ||||
\(706\) | 10.1699 | + | 37.9545i | 0.382748 | + | 1.42844i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −10.5167 | + | 6.07180i | −0.395240 | + | 0.228192i | ||||
\(709\) | 45.6506 | + | 12.2321i | 1.71445 | + | 0.459384i | 0.976507 | − | 0.215484i | \(-0.0691329\pi\) |
0.737938 | + | 0.674868i | \(0.235800\pi\) | |||||||
\(710\) | 0.339746 | + | 0.588457i | 0.0127504 | + | 0.0220844i | ||||
\(711\) | −39.4186 | − | 22.7583i | −1.47831 | − | 0.853504i | ||||
\(712\) | −14.1962 | − | 3.80385i | −0.532023 | − | 0.142555i | ||||
\(713\) | − | 16.6603i | − | 0.623931i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.92820 | + | 9.92820i | −0.371294 | + | 0.371294i | ||||
\(716\) | −4.80385 | − | 17.9282i | −0.179528 | − | 0.670008i | ||||
\(717\) | 4.26795 | − | 1.14359i | 0.159389 | − | 0.0427083i | ||||
\(718\) | −1.63397 | + | 6.09808i | −0.0609794 | + | 0.227578i | ||||
\(719\) | 0.205771 | + | 0.356406i | 0.00767398 | + | 0.0132917i | 0.869837 | − | 0.493339i | \(-0.164224\pi\) |
−0.862163 | + | 0.506631i | \(0.830891\pi\) | |||||||
\(720\) | 9.46410 | − | 2.53590i | 0.352706 | − | 0.0945074i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.9282 | − | 3.73205i | 0.518354 | − | 0.138893i | ||||
\(723\) | −1.86603 | + | 6.96410i | −0.0693982 | + | 0.258998i | ||||
\(724\) | 26.7846 | + | 26.7846i | 0.995442 | + | 0.995442i | ||||
\(725\) | 0.411543 | + | 1.53590i | 0.0152843 | + | 0.0570418i | ||||
\(726\) | 1.60770i | 0.0596672i | ||||||||
\(727\) | 41.3205i | 1.53249i | 0.642547 | + | 0.766246i | \(0.277878\pi\) | ||||
−0.642547 | + | 0.766246i | \(0.722122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5885i | 0.503276i | ||||||||
\(730\) | −9.12436 | −0.337708 | ||||||||
\(731\) | −15.2942 | − | 57.0788i | −0.565677 | − | 2.11114i | ||||
\(732\) | −7.46410 | −0.275881 | ||||||||
\(733\) | 8.81347 | − | 32.8923i | 0.325533 | − | 1.21490i | −0.588242 | − | 0.808685i | \(-0.700180\pi\) |
0.913775 | − | 0.406220i | \(-0.133153\pi\) | |||||||
\(734\) | −2.24167 | − | 8.36603i | −0.0827415 | − | 0.308796i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.53590 | + | 24.3923i | −0.240916 | + | 0.899112i | ||||
\(737\) | 7.62436 | + | 13.2058i | 0.280847 | + | 0.486441i | ||||
\(738\) | −18.3923 | − | 4.92820i | −0.677030 | − | 0.181410i | ||||
\(739\) | 38.4808 | − | 10.3109i | 1.41554 | − | 0.379292i | 0.531639 | − | 0.846971i | \(-0.321576\pi\) |
0.883899 | + | 0.467679i | \(0.154910\pi\) | |||||||
\(740\) | −1.05256 | + | 1.82309i | −0.0386928 | + | 0.0670180i | ||||
\(741\) | −5.73205 | + | 5.73205i | −0.210572 | + | 0.210572i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.0718i | − | 0.406185i | −0.979160 | − | 0.203092i | \(-0.934901\pi\) | ||
0.979160 | − | 0.203092i | \(-0.0650992\pi\) | |||||||
\(744\) | 4.73205 | − | 2.73205i | 0.173485 | − | 0.100162i | ||||
\(745\) | −6.10770 | − | 3.52628i | −0.223769 | − | 0.129193i | ||||
\(746\) | 1.09808 | − | 0.633975i | 0.0402034 | − | 0.0232115i | ||||
\(747\) | 5.73205 | + | 1.53590i | 0.209725 | + | 0.0561956i | ||||
\(748\) | −9.92820 | + | 37.0526i | −0.363011 | + | 1.35478i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.83013 | − | 1.56218i | 0.212886 | − | 0.0570427i | ||||
\(751\) | −6.52628 | − | 11.3038i | −0.238147 | − | 0.412483i | 0.722035 | − | 0.691856i | \(-0.243207\pi\) |
−0.960183 | + | 0.279373i | \(0.909873\pi\) | |||||||
\(752\) | −8.53590 | − | 14.7846i | −0.311272 | − | 0.539139i | ||||
\(753\) | −6.43782 | + | 11.1506i | −0.234607 | + | 0.406352i | ||||
\(754\) | 2.00000 | + | 2.00000i | 0.0728357 | + | 0.0728357i | ||||
\(755\) | 7.22243 | + | 7.22243i | 0.262851 | + | 0.262851i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.6603 | + | 18.6603i | −0.678218 | + | 0.678218i | −0.959597 | − | 0.281378i | \(-0.909208\pi\) |
0.281378 | + | 0.959597i | \(0.409208\pi\) | |||||||
\(758\) | − | 0.248711i | − | 0.00903360i | ||||||
\(759\) | 5.93782 | + | 3.42820i | 0.215529 | + | 0.124436i | ||||
\(760\) | 7.26795 | − | 1.94744i | 0.263636 | − | 0.0706411i | ||||
\(761\) | −11.7679 | + | 6.79423i | −0.426588 | + | 0.246291i | −0.697892 | − | 0.716203i | \(-0.745878\pi\) |
0.271304 | + | 0.962494i | \(0.412545\pi\) | |||||||
\(762\) | −3.46410 | + | 6.00000i | −0.125491 | + | 0.217357i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.0000 | + | 8.66025i | −0.542681 | + | 0.313317i | ||||
\(765\) | −4.09808 | + | 15.2942i | −0.148166 | + | 0.552964i | ||||
\(766\) | −34.4186 | − | 9.22243i | −1.24359 | − | 0.333220i | ||||
\(767\) | 30.9545 | − | 53.6147i | 1.11770 | − | 1.93592i | ||||
\(768\) | −8.00000 | + | 2.14359i | −0.288675 | + | 0.0773503i | ||||
\(769\) | −9.85641 | −0.355431 | −0.177716 | − | 0.984082i | \(-0.556871\pi\) | ||||
−0.177716 | + | 0.984082i | \(0.556871\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.09808 | + | 7.09808i | 0.255631 | + | 0.255631i | ||||
\(772\) | −39.8372 | − | 23.0000i | −1.43377 | − | 0.827788i | ||||
\(773\) | 2.93782 | + | 10.9641i | 0.105666 | + | 0.394351i | 0.998420 | − | 0.0561936i | \(-0.0178964\pi\) |
−0.892754 | + | 0.450545i | \(0.851230\pi\) | |||||||
\(774\) | 17.6603 | + | 30.5885i | 0.634785 | + | 1.09948i | ||||
\(775\) | −13.5622 | + | 7.83013i | −0.487168 | + | 0.281266i | ||||
\(776\) | −5.85641 | − | 5.85641i | −0.210233 | − | 0.210233i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.3468 | + | 16.3660i | 1.01628 | + | 0.586750i | ||||
\(779\) | −14.1244 | − | 3.78461i | −0.506058 | − | 0.135598i | ||||
\(780\) | 3.46410 | − | 3.46410i | 0.124035 | − | 0.124035i | ||||
\(781\) | 1.53590 | − | 0.411543i | 0.0549588 | − | 0.0147262i | ||||
\(782\) | −28.8564 | − | 28.8564i | −1.03190 | − | 1.03190i | ||||
\(783\) | −1.12436 | −0.0401812 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.9474 | 0.604880 | ||||||||
\(786\) | 4.07180 | + | 4.07180i | 0.145236 | + | 0.145236i | ||||
\(787\) | 13.1603 | − | 3.52628i | 0.469112 | − | 0.125698i | −0.0165161 | − | 0.999864i | \(-0.505257\pi\) |
0.485628 | + | 0.874165i | \(0.338591\pi\) | |||||||
\(788\) | 33.3205 | + | 33.3205i | 1.18699 | + | 1.18699i | ||||
\(789\) | −2.30385 | − | 0.617314i | −0.0820191 | − | 0.0219770i | ||||
\(790\) | 18.2942 | + | 10.5622i | 0.650879 | + | 0.375785i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 22.9282i | − | 0.814718i | ||||||
\(793\) | 32.9545 | − | 19.0263i | 1.17025 | − | 0.675643i | ||||
\(794\) | 18.7583 | + | 32.4904i | 0.665708 | + | 1.15304i | ||||
\(795\) | 0.492958 | + | 1.83975i | 0.0174834 | + | 0.0652491i | ||||
\(796\) | 11.9282 | − | 20.6603i | 0.422784 | − | 0.732283i | ||||
\(797\) | 13.3397 | + | 13.3397i | 0.472518 | + | 0.472518i | 0.902729 | − | 0.430211i | \(-0.141561\pi\) |
−0.430211 | + | 0.902729i | \(0.641561\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.5885 | 0.976009 | ||||||||
\(800\) | 22.9282 | − | 6.14359i | 0.810634 | − | 0.217209i | ||||
\(801\) | −7.09808 | + | 12.2942i | −0.250798 | + | 0.434395i | ||||
\(802\) | 20.4904 | + | 5.49038i | 0.723541 | + | 0.193872i | ||||
\(803\) | −5.52628 | + | 20.6244i | −0.195018 | + | 0.727818i | ||||
\(804\) | −2.66025 | − | 4.60770i | −0.0938199 | − | 0.162501i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.9282 | + | 24.1244i | −0.490600 | + | 0.849744i | ||||
\(807\) | 4.54552 | − | 2.62436i | 0.160010 | − | 0.0923817i | ||||
\(808\) | −27.6603 | + | 47.9090i | −0.973084 | + | 1.68543i | ||||
\(809\) | −29.4282 | − | 16.9904i | −1.03464 | − | 0.597350i | −0.116330 | − | 0.993211i | \(-0.537113\pi\) |
−0.918311 | + | 0.395861i | \(0.870446\pi\) | |||||||
\(810\) | − | 8.44486i | − | 0.296722i | ||||||
\(811\) | −24.3205 | + | 24.3205i | −0.854009 | + | 0.854009i | −0.990624 | − | 0.136616i | \(-0.956377\pi\) |
0.136616 | + | 0.990624i | \(0.456377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.43782 | − | 4.43782i | −0.155641 | − | 0.155641i | ||||
\(814\) | 3.48334 | + | 3.48334i | 0.122091 | + | 0.122091i | ||||
\(815\) | 5.59808 | − | 9.69615i | 0.196092 | − | 0.339641i | ||||
\(816\) | 3.46410 | − | 12.9282i | 0.121268 | − | 0.452578i | ||||
\(817\) | 13.5622 | + | 23.4904i | 0.474481 | + | 0.821824i | ||||
\(818\) | 11.8301 | − | 3.16987i | 0.413631 | − | 0.110832i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.53590 | + | 2.28719i | 0.298087 | + | 0.0798720i | ||||
\(821\) | 0.598076 | + | 0.160254i | 0.0208730 | + | 0.00559290i | 0.269240 | − | 0.963073i | \(-0.413227\pi\) |
−0.248367 | + | 0.968666i | \(0.579894\pi\) | |||||||
\(822\) | −11.1506 | + | 6.43782i | −0.388923 | + | 0.224545i | ||||
\(823\) | −14.9378 | − | 8.62436i | −0.520700 | − | 0.300626i | 0.216521 | − | 0.976278i | \(-0.430529\pi\) |
−0.737221 | + | 0.675652i | \(0.763862\pi\) | |||||||
\(824\) | −17.6603 | − | 4.73205i | −0.615224 | − | 0.164849i | ||||
\(825\) | − | 6.44486i | − | 0.224381i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.78461 | + | 3.78461i | −0.131604 | + | 0.131604i | −0.769840 | − | 0.638237i | \(-0.779664\pi\) |
0.638237 | + | 0.769840i | \(0.279664\pi\) | |||||||
\(828\) | 21.1244 | + | 12.1962i | 0.734122 | + | 0.423846i | ||||
\(829\) | 3.06218 | − | 0.820508i | 0.106354 | − | 0.0284974i | −0.205250 | − | 0.978710i | \(-0.565801\pi\) |
0.311603 | + | 0.950212i | \(0.399134\pi\) | |||||||
\(830\) | −2.66025 | − | 0.712813i | −0.0923388 | − | 0.0247421i | ||||
\(831\) | 1.20577 | + | 2.08846i | 0.0418277 | + | 0.0724478i | ||||
\(832\) | 29.8564 | − | 29.8564i | 1.03508 | − | 1.03508i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.19615 | + | 11.9282i | 0.110674 | + | 0.413040i | ||||
\(835\) | −5.07180 | + | 18.9282i | −0.175517 | + | 0.655037i | ||||
\(836\) | − | 17.6077i | − | 0.608975i | ||||||
\(837\) | −2.86603 | − | 10.6962i | −0.0990643 | − | 0.369713i | ||||
\(838\) | 38.0000 | 1.31269 | ||||||||
\(839\) | − | 17.7128i | − | 0.611514i | −0.952110 | − | 0.305757i | \(-0.901090\pi\) | ||
0.952110 | − | 0.305757i | \(-0.0989096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.8564i | − | 0.995048i | ||||||
\(842\) | − | 17.3205i | − | 0.596904i | ||||||
\(843\) | 0.124356 | + | 0.464102i | 0.00428304 | + | 0.0159845i | ||||
\(844\) | −31.8564 | + | 31.8564i | −1.09654 | + | 1.09654i | ||||
\(845\) | −3.44744 | + | 12.8660i | −0.118596 | + | 0.442605i | ||||
\(846\) | −15.9282 | + | 4.26795i | −0.547623 | + | 0.146735i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.24871 | + | 15.8564i | 0.145901 | + | 0.544511i | ||||
\(849\) | −3.89230 | − | 6.74167i | −0.133584 | − | 0.231374i | ||||
\(850\) | −9.92820 | + | 37.0526i | −0.340535 | + | 1.27089i | ||||
\(851\) | −5.06218 | + | 1.35641i | −0.173529 | + | 0.0464970i | ||||
\(852\) | −0.535898 | + | 0.143594i | −0.0183596 | + | 0.00491943i | ||||
\(853\) | 11.8756 | − | 11.8756i | 0.406614 | − | 0.406614i | −0.473942 | − | 0.880556i | \(-0.657169\pi\) |
0.880556 | + | 0.473942i | \(0.157169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 7.26795i | − | 0.248559i | ||||||
\(856\) | −4.73205 | − | 8.19615i | −0.161738 | − | 0.280139i | ||||
\(857\) | −11.8923 | − | 6.86603i | −0.406233 | − | 0.234539i | 0.282937 | − | 0.959139i | \(-0.408691\pi\) |
−0.689170 | + | 0.724600i | \(0.742025\pi\) | |||||||
\(858\) | −5.73205 | − | 9.92820i | −0.195689 | − | 0.338943i | ||||
\(859\) | −13.6244 | − | 3.65064i | −0.464857 | − | 0.124558i | 0.0187858 | − | 0.999824i | \(-0.494020\pi\) |
−0.483643 | + | 0.875265i | \(0.660687\pi\) | |||||||
\(860\) | −8.19615 | − | 14.1962i | −0.279486 | − | 0.484085i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.2224 | + | 41.8827i | 0.382238 | + | 1.42653i | ||||
\(863\) | 16.3301 | + | 28.2846i | 0.555884 | + | 0.962819i | 0.997834 | + | 0.0657797i | \(0.0209535\pi\) |
−0.441950 | + | 0.897040i | \(0.645713\pi\) | |||||||
\(864\) | 16.7846i | 0.571024i | ||||||||
\(865\) | −1.03590 | + | 1.79423i | −0.0352216 | + | 0.0610056i | ||||
\(866\) | 33.1769 | − | 33.1769i | 1.12740 | − | 1.12740i | ||||
\(867\) | 9.07180 | + | 9.07180i | 0.308094 | + | 0.308094i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.9545 | − | 34.9545i | 1.18575 | − | 1.18575i | ||||
\(870\) | 0.248711 | 0.00843210 | ||||||||
\(871\) | 23.4904 | + | 13.5622i | 0.795941 | + | 0.459537i | ||||
\(872\) | 5.41154 | + | 3.12436i | 0.183258 | + | 0.105804i | ||||
\(873\) | −6.92820 | + | 4.00000i | −0.234484 | + | 0.135379i | ||||
\(874\) | 16.2224 | + | 9.36603i | 0.548732 | + | 0.316811i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.92820 | − | 7.19615i | 0.0651479 | − | 0.243135i | ||||
\(877\) | 8.18653 | − | 30.5526i | 0.276440 | − | 1.03169i | −0.678431 | − | 0.734664i | \(-0.737340\pi\) |
0.954871 | − | 0.297022i | \(-0.0959936\pi\) | |||||||
\(878\) | −2.75833 | + | 10.2942i | −0.0930891 | + | 0.347413i | ||||
\(879\) | −2.90192 | + | 5.02628i | −0.0978795 | + | 0.169532i | ||||
\(880\) | 10.6410i | 0.358709i | ||||||||
\(881\) | −50.0000 | −1.68454 | −0.842271 | − | 0.539054i | \(-0.818782\pi\) | ||||
−0.842271 | + | 0.539054i | \(0.818782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.00000 | − | 5.00000i | −0.168263 | − | 0.168263i | 0.617952 | − | 0.786216i | \(-0.287963\pi\) |
−0.786216 | + | 0.617952i | \(0.787963\pi\) | |||||||
\(884\) | 17.6603 | + | 65.9090i | 0.593979 | + | 2.21676i | ||||
\(885\) | −1.40897 | − | 5.25833i | −0.0473619 | − | 0.176757i | ||||
\(886\) | −13.2224 | + | 7.63397i | −0.444216 | + | 0.256468i | ||||
\(887\) | 39.7750 | − | 22.9641i | 1.33551 | − | 0.771059i | 0.349375 | − | 0.936983i | \(-0.386394\pi\) |
0.986139 | + | 0.165924i | \(0.0530606\pi\) | |||||||
\(888\) | −1.21539 | − | 1.21539i | −0.0407858 | − | 0.0407858i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.29423 | − | 5.70577i | 0.110423 | − | 0.191258i | ||||
\(891\) | −19.0885 | − | 5.11474i | −0.639487 | − | 0.171350i | ||||
\(892\) | 19.7128i | 0.660034i | ||||||||
\(893\) | −12.2321 | + | 3.27757i | −0.409330 | + | 0.109680i | ||||
\(894\) | 4.07180 | − | 4.07180i | 0.136181 | − | 0.136181i | ||||
\(895\) | 8.32051 | 0.278124 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.1962 | 0.407218 | ||||||||
\(898\) | −23.3205 | + | 23.3205i | −0.778215 | + | 0.778215i | ||||
\(899\) | −1.36603 | + | 0.366025i | −0.0455595 | + | 0.0122076i | ||||
\(900\) | − | 22.9282i | − | 0.764273i | ||||||
\(901\) | −25.6244 | − | 6.86603i | −0.853671 | − | 0.228740i | ||||
\(902\) | 10.3397 | − | 17.9090i | 0.344276 | − | 0.596303i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.92820 | + | 2.92820i | 0.0973906 | + | 0.0973906i | ||||
\(905\) | −14.7058 | + | 8.49038i | −0.488836 | + | 0.282230i | ||||
\(906\) | −7.22243 | + | 4.16987i | −0.239949 | + | 0.138535i | ||||
\(907\) | 7.16025 | + | 26.7224i | 0.237752 | + | 0.887304i | 0.976889 | + | 0.213748i | \(0.0685672\pi\) |
−0.739136 | + | 0.673556i | \(0.764766\pi\) | |||||||
\(908\) | 5.98076 | + | 22.3205i | 0.198479 | + | 0.740732i | ||||
\(909\) | 37.7846 | + | 37.7846i | 1.25324 | + | 1.25324i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.32051 | 0.242539 | 0.121270 | − | 0.992620i | \(-0.461303\pi\) | ||||
0.121270 | + | 0.992620i | \(0.461303\pi\) | |||||||
\(912\) | 6.14359i | 0.203435i | ||||||||
\(913\) | −3.22243 | + | 5.58142i | −0.106647 | + | 0.184718i | ||||
\(914\) | 6.88269 | − | 25.6865i | 0.227659 | − | 0.849635i | ||||
\(915\) | 0.866025 | − | 3.23205i | 0.0286299 | − | 0.106848i | ||||
\(916\) | −7.14359 | + | 26.6603i | −0.236031 | + | 0.880880i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −23.4904 | − | 13.5622i | −0.775298 | − | 0.447619i | ||||
\(919\) | −15.8660 | + | 9.16025i | −0.523372 | + | 0.302169i | −0.738313 | − | 0.674458i | \(-0.764377\pi\) |
0.214941 | + | 0.976627i | \(0.431044\pi\) | |||||||
\(920\) | −9.80385 | − | 5.66025i | −0.323223 | − | 0.186613i | ||||
\(921\) | 5.70577 | + | 3.29423i | 0.188012 | + | 0.108549i | ||||
\(922\) | −37.3205 | −1.22909 | ||||||||
\(923\) | 2.00000 | − | 2.00000i | 0.0658308 | − | 0.0658308i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.48334 | + | 3.48334i | 0.114531 | + | 0.114531i | ||||
\(926\) | 2.14359 | − | 2.14359i | 0.0704429 | − | 0.0704429i | ||||
\(927\) | −8.83013 | + | 15.2942i | −0.290019 | + | 0.502328i | ||||
\(928\) | 2.14359 | 0.0703669 | ||||||||
\(929\) | 25.0167 | + | 43.3301i | 0.820770 | + | 1.42162i | 0.905110 | + | 0.425178i | \(0.139789\pi\) |
−0.0843396 | + | 0.996437i | \(0.526878\pi\) | |||||||
\(930\) | 0.633975 | + | 2.36603i | 0.0207888 | + | 0.0775850i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.803848 | − | 1.39230i | −0.0263309 | − | 0.0456065i | ||||
\(933\) | 3.23205 | + | 0.866025i | 0.105813 | + | 0.0283524i | ||||
\(934\) | −19.0263 | − | 32.9545i | −0.622559 | − | 1.07830i | ||||
\(935\) | −14.8923 | − | 8.59808i | −0.487030 | − | 0.281187i | ||||
\(936\) | −20.3923 | − | 35.3205i | −0.666543 | − | 1.15449i | ||||
\(937\) | 29.0718i | 0.949734i | 0.880058 | + | 0.474867i | \(0.157504\pi\) | ||||
−0.880058 | + | 0.474867i | \(0.842496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.90192 | + | 7.90192i | −0.257870 | + | 0.257870i | ||||
\(940\) | 7.39230 | − | 1.98076i | 0.241110 | − | 0.0646053i | ||||
\(941\) | 23.5263 | − | 6.30385i | 0.766935 | − | 0.205500i | 0.145918 | − | 0.989297i | \(-0.453386\pi\) |
0.621017 | + | 0.783797i | \(0.286720\pi\) | |||||||
\(942\) | −3.58142 | + | 13.3660i | −0.116689 | + | 0.435489i | ||||
\(943\) | 11.0000 | + | 19.0526i | 0.358209 | + | 0.620437i | ||||
\(944\) | −12.1436 | − | 45.3205i | −0.395240 | − | 1.47506i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37.0526 | + | 9.92820i | −1.20468 | + | 0.322794i | ||||
\(947\) | −1.44744 | + | 5.40192i | −0.0470355 | + | 0.175539i | −0.985448 | − | 0.169979i | \(-0.945630\pi\) |
0.938412 | + | 0.345518i | \(0.112297\pi\) | |||||||
\(948\) | −12.1962 | + | 12.1962i | −0.396113 | + | 0.396113i | ||||
\(949\) | 9.83013 | + | 36.6865i | 0.319099 | + | 1.19090i | ||||
\(950\) | − | 17.6077i | − | 0.571269i | ||||||
\(951\) | − | 7.58846i | − | 0.246073i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.5359i | 0.535650i | 0.963468 | + | 0.267825i | \(0.0863050\pi\) | ||||
−0.963468 | + | 0.267825i | \(0.913695\pi\) | |||||||
\(954\) | 15.8564 | 0.513370 | ||||||||
\(955\) | −2.00962 | − | 7.50000i | −0.0650297 | − | 0.242694i | ||||
\(956\) | 17.0718i | 0.552141i | ||||||||
\(957\) | 0.150635 | − | 0.562178i | 0.00486934 | − | 0.0181726i | ||||
\(958\) | −5.70577 | − | 21.2942i | −0.184345 | − | 0.687985i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 3.71281i | − | 0.119831i | ||||||
\(961\) | 8.53590 | + | 14.7846i | 0.275352 | + | 0.476923i | ||||
\(962\) | 8.46410 | + | 2.26795i | 0.272894 | + | 0.0731216i | ||||
\(963\) | −8.83013 | + | 2.36603i | −0.284547 | + | 0.0762441i | ||||
\(964\) | −24.1244 | − | 13.9282i | −0.776993 | − | 0.448597i | ||||
\(965\) | 14.5814 | − | 14.5814i | 0.469392 | − | 0.469392i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 60.2487i | − | 1.93747i | −0.248102 | − | 0.968734i | \(-0.579807\pi\) | ||
0.248102 | − | 0.968734i | \(-0.420193\pi\) | |||||||
\(968\) | −6.00000 | − | 1.60770i | −0.192847 | − | 0.0516733i | ||||
\(969\) | −8.59808 | − | 4.96410i | −0.276210 | − | 0.159470i | ||||
\(970\) | 3.21539 | − | 1.85641i | 0.103240 | − | 0.0596056i | ||||
\(971\) | 52.4090 | + | 14.0429i | 1.68188 | + | 0.450659i | 0.968275 | − | 0.249885i | \(-0.0803930\pi\) |
0.713608 | + | 0.700545i | \(0.247060\pi\) | |||||||
\(972\) | 23.8564 | + | 6.39230i | 0.765195 | + | 0.205033i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.8301 | − | 4.50962i | 0.539272 | − | 0.144498i | ||||
\(975\) | −5.73205 | − | 9.92820i | −0.183573 | − | 0.317957i | ||||
\(976\) | 7.46410 | − | 27.8564i | 0.238920 | − | 0.891662i | ||||
\(977\) | 8.57180 | − | 14.8468i | 0.274236 | − | 0.474991i | −0.695706 | − | 0.718327i | \(-0.744908\pi\) |
0.969942 | + | 0.243336i | \(0.0782417\pi\) | |||||||
\(978\) | 6.46410 | + | 6.46410i | 0.206699 | + | 0.206699i | ||||
\(979\) | −10.9019 | − | 10.9019i | −0.348427 | − | 0.348427i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.26795 | − | 4.26795i | 0.136265 | − | 0.136265i | ||||
\(982\) | 7.17691i | 0.229025i | ||||||||
\(983\) | −17.1340 | − | 9.89230i | −0.546489 | − | 0.315516i | 0.201216 | − | 0.979547i | \(-0.435511\pi\) |
−0.747705 | + | 0.664031i | \(0.768844\pi\) | |||||||
\(984\) | −3.60770 | + | 6.24871i | −0.115009 | + | 0.199202i | ||||
\(985\) | −18.2942 | + | 10.5622i | −0.582903 | + | 0.336539i | ||||
\(986\) | −1.73205 | + | 3.00000i | −0.0551597 | + | 0.0955395i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.6603 | − | 27.1244i | −0.498219 | − | 0.862941i | ||||
\(989\) | 10.5622 | − | 39.4186i | 0.335858 | − | 1.25344i | ||||
\(990\) | 9.92820 | + | 2.66025i | 0.315539 | + | 0.0845484i | ||||
\(991\) | 4.20577 | − | 7.28461i | 0.133601 | − | 0.231403i | −0.791461 | − | 0.611219i | \(-0.790679\pi\) |
0.925062 | + | 0.379816i | \(0.124013\pi\) | |||||||
\(992\) | 5.46410 | + | 20.3923i | 0.173485 | + | 0.647456i | ||||
\(993\) | 10.5167 | 0.333736 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.56218 | + | 7.56218i | 0.239737 | + | 0.239737i | ||||
\(996\) | 1.12436 | − | 1.94744i | 0.0356266 | − | 0.0617070i | ||||
\(997\) | −0.401924 | − | 1.50000i | −0.0127291 | − | 0.0475055i | 0.959269 | − | 0.282494i | \(-0.0911616\pi\) |
−0.971998 | + | 0.234988i | \(0.924495\pi\) | |||||||
\(998\) | −18.2942 | − | 31.6865i | −0.579094 | − | 1.00302i | ||||
\(999\) | −3.01666 | + | 1.74167i | −0.0954429 | + | 0.0551040i |
(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 | 784.2.x.h.557.1 | 4 | ||
7.2 | even | 3 | 784.2.x.a.765.1 | 4 | |||
7.3 | odd | 6 | 784.2.m.e.589.2 | 4 | |||
7.4 | even | 3 | 784.2.m.d.589.2 | 4 | |||
7.5 | odd | 6 | 112.2.w.a.93.1 | yes | 4 | ||
7.6 | odd | 2 | 112.2.w.b.109.1 | yes | 4 | ||
16.5 | even | 4 | 784.2.x.a.165.1 | 4 | |||
28.19 | even | 6 | 448.2.ba.b.401.1 | 4 | |||
28.27 | even | 2 | 448.2.ba.a.81.1 | 4 | |||
56.5 | odd | 6 | 896.2.ba.d.289.1 | 4 | |||
56.13 | odd | 2 | 896.2.ba.b.417.1 | 4 | |||
56.19 | even | 6 | 896.2.ba.a.289.1 | 4 | |||
56.27 | even | 2 | 896.2.ba.c.417.1 | 4 | |||
112.5 | odd | 12 | 112.2.w.b.37.1 | yes | 4 | ||
112.13 | odd | 4 | 896.2.ba.d.865.1 | 4 | |||
112.19 | even | 12 | 896.2.ba.c.737.1 | 4 | |||
112.27 | even | 4 | 448.2.ba.b.305.1 | 4 | |||
112.37 | even | 12 | inner | 784.2.x.h.373.1 | 4 | ||
112.53 | even | 12 | 784.2.m.d.197.2 | 4 | |||
112.61 | odd | 12 | 896.2.ba.b.737.1 | 4 | |||
112.69 | odd | 4 | 112.2.w.a.53.1 | ✓ | 4 | ||
112.75 | even | 12 | 448.2.ba.a.177.1 | 4 | |||
112.83 | even | 4 | 896.2.ba.a.865.1 | 4 | |||
112.101 | odd | 12 | 784.2.m.e.197.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.a.53.1 | ✓ | 4 | 112.69 | odd | 4 | ||
112.2.w.a.93.1 | yes | 4 | 7.5 | odd | 6 | ||
112.2.w.b.37.1 | yes | 4 | 112.5 | odd | 12 | ||
112.2.w.b.109.1 | yes | 4 | 7.6 | odd | 2 | ||
448.2.ba.a.81.1 | 4 | 28.27 | even | 2 | |||
448.2.ba.a.177.1 | 4 | 112.75 | even | 12 | |||
448.2.ba.b.305.1 | 4 | 112.27 | even | 4 | |||
448.2.ba.b.401.1 | 4 | 28.19 | even | 6 | |||
784.2.m.d.197.2 | 4 | 112.53 | even | 12 | |||
784.2.m.d.589.2 | 4 | 7.4 | even | 3 | |||
784.2.m.e.197.2 | 4 | 112.101 | odd | 12 | |||
784.2.m.e.589.2 | 4 | 7.3 | odd | 6 | |||
784.2.x.a.165.1 | 4 | 16.5 | even | 4 | |||
784.2.x.a.765.1 | 4 | 7.2 | even | 3 | |||
784.2.x.h.373.1 | 4 | 112.37 | even | 12 | inner | ||
784.2.x.h.557.1 | 4 | 1.1 | even | 1 | trivial | ||
896.2.ba.a.289.1 | 4 | 56.19 | even | 6 | |||
896.2.ba.a.865.1 | 4 | 112.83 | even | 4 | |||
896.2.ba.b.417.1 | 4 | 56.13 | odd | 2 | |||
896.2.ba.b.737.1 | 4 | 112.61 | odd | 12 | |||
896.2.ba.c.417.1 | 4 | 56.27 | even | 2 | |||
896.2.ba.c.737.1 | 4 | 112.19 | even | 12 | |||
896.2.ba.d.289.1 | 4 | 56.5 | odd | 6 | |||
896.2.ba.d.865.1 | 4 | 112.13 | odd | 4 |