Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(551,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.551");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.4 | ||
Root | \(-1.62589 + 0.597052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.551 |
Dual form | 690.2.e.a.551.12 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −0.597052 | − | 1.62589i | −0.344708 | − | 0.938710i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.62589 | + | 0.597052i | −0.663768 | + | 0.243746i | ||||
\(7\) | − | 3.80421i | − | 1.43786i | −0.695085 | − | 0.718928i | \(-0.744633\pi\) | ||
0.695085 | − | 0.718928i | \(-0.255367\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.28706 | + | 1.94149i | −0.762352 | + | 0.647162i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | −3.48413 | −1.05050 | −0.525252 | − | 0.850947i | \(-0.676029\pi\) | ||||
−0.525252 | + | 0.850947i | \(0.676029\pi\) | |||||||
\(12\) | 0.597052 | + | 1.62589i | 0.172354 | + | 0.469355i | ||||
\(13\) | 3.19916 | 0.887287 | 0.443644 | − | 0.896203i | \(-0.353686\pi\) | ||||
0.443644 | + | 0.896203i | \(0.353686\pi\) | |||||||
\(14\) | −3.80421 | −1.01672 | ||||||||
\(15\) | 0.597052 | + | 1.62589i | 0.154158 | + | 0.419804i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.76053 | −1.15460 | −0.577299 | − | 0.816533i | \(-0.695893\pi\) | ||||
−0.577299 | + | 0.816533i | \(0.695893\pi\) | |||||||
\(18\) | 1.94149 | + | 2.28706i | 0.457613 | + | 0.539064i | ||||
\(19\) | 1.88297i | 0.431984i | 0.976395 | + | 0.215992i | \(0.0692985\pi\) | ||||
−0.976395 | + | 0.215992i | \(0.930702\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −6.18523 | + | 2.27131i | −1.34973 | + | 0.495641i | ||||
\(22\) | 3.48413i | 0.742818i | ||||||||
\(23\) | 0.785398 | − | 4.73108i | 0.163767 | − | 0.986499i | ||||
\(24\) | 1.62589 | − | 0.597052i | 0.331884 | − | 0.121873i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | − | 3.19916i | − | 0.627407i | ||||||
\(27\) | 4.52214 | + | 2.55934i | 0.870287 | + | 0.492545i | ||||
\(28\) | 3.80421i | 0.718928i | ||||||||
\(29\) | 7.50582i | 1.39380i | 0.717170 | + | 0.696898i | \(0.245437\pi\) | ||||
−0.717170 | + | 0.696898i | \(0.754563\pi\) | |||||||
\(30\) | 1.62589 | − | 0.597052i | 0.296846 | − | 0.109006i | ||||
\(31\) | −3.72122 | −0.668351 | −0.334176 | − | 0.942511i | \(-0.608458\pi\) | ||||
−0.334176 | + | 0.942511i | \(0.608458\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 2.08021 | + | 5.66482i | 0.362117 | + | 0.986118i | ||||
\(34\) | 4.76053i | 0.816424i | ||||||||
\(35\) | 3.80421i | 0.643028i | ||||||||
\(36\) | 2.28706 | − | 1.94149i | 0.381176 | − | 0.323581i | ||||
\(37\) | 4.88527i | 0.803133i | 0.915830 | + | 0.401567i | \(0.131534\pi\) | ||||
−0.915830 | + | 0.401567i | \(0.868466\pi\) | |||||||
\(38\) | 1.88297 | 0.305459 | ||||||||
\(39\) | −1.91007 | − | 5.20149i | −0.305855 | − | 0.832905i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | − | 3.99062i | − | 0.623231i | −0.950208 | − | 0.311615i | \(-0.899130\pi\) | ||
0.950208 | − | 0.311615i | \(-0.100870\pi\) | |||||||
\(42\) | 2.27131 | + | 6.18523i | 0.350471 | + | 0.954402i | ||||
\(43\) | − | 6.96125i | − | 1.06158i | −0.847503 | − | 0.530791i | \(-0.821895\pi\) | ||
0.847503 | − | 0.530791i | \(-0.178105\pi\) | |||||||
\(44\) | 3.48413 | 0.525252 | ||||||||
\(45\) | 2.28706 | − | 1.94149i | 0.340934 | − | 0.289420i | ||||
\(46\) | −4.73108 | − | 0.785398i | −0.697560 | − | 0.115801i | ||||
\(47\) | 10.8399i | 1.58116i | 0.612357 | + | 0.790581i | \(0.290221\pi\) | ||||
−0.612357 | + | 0.790581i | \(0.709779\pi\) | |||||||
\(48\) | −0.597052 | − | 1.62589i | −0.0861771 | − | 0.234677i | ||||
\(49\) | −7.47199 | −1.06743 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 2.84229 | + | 7.74011i | 0.398000 | + | 1.08383i | ||||
\(52\) | −3.19916 | −0.443644 | ||||||||
\(53\) | −7.07396 | −0.971683 | −0.485841 | − | 0.874047i | \(-0.661487\pi\) | ||||
−0.485841 | + | 0.874047i | \(0.661487\pi\) | |||||||
\(54\) | 2.55934 | − | 4.52214i | 0.348282 | − | 0.615386i | ||||
\(55\) | 3.48413 | 0.469800 | ||||||||
\(56\) | 3.80421 | 0.508359 | ||||||||
\(57\) | 3.06151 | − | 1.12423i | 0.405507 | − | 0.148908i | ||||
\(58\) | 7.50582 | 0.985562 | ||||||||
\(59\) | − | 7.35646i | − | 0.957730i | −0.877889 | − | 0.478865i | \(-0.841048\pi\) | ||
0.877889 | − | 0.478865i | \(-0.158952\pi\) | |||||||
\(60\) | −0.597052 | − | 1.62589i | −0.0770791 | − | 0.209902i | ||||
\(61\) | 3.31936i | 0.425000i | 0.977161 | + | 0.212500i | \(0.0681606\pi\) | ||||
−0.977161 | + | 0.212500i | \(0.931839\pi\) | |||||||
\(62\) | 3.72122i | 0.472596i | ||||||||
\(63\) | 7.38582 | + | 8.70044i | 0.930526 | + | 1.09615i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.19916 | −0.396807 | ||||||||
\(66\) | 5.66482 | − | 2.08021i | 0.697291 | − | 0.256056i | ||||
\(67\) | − | 3.70440i | − | 0.452564i | −0.974062 | − | 0.226282i | \(-0.927343\pi\) | ||
0.974062 | − | 0.226282i | \(-0.0726571\pi\) | |||||||
\(68\) | 4.76053 | 0.577299 | ||||||||
\(69\) | −8.16116 | + | 1.54773i | −0.982488 | + | 0.186325i | ||||
\(70\) | 3.80421 | 0.454690 | ||||||||
\(71\) | − | 9.92565i | − | 1.17796i | −0.808148 | − | 0.588979i | \(-0.799530\pi\) | ||
0.808148 | − | 0.588979i | \(-0.200470\pi\) | |||||||
\(72\) | −1.94149 | − | 2.28706i | −0.228806 | − | 0.269532i | ||||
\(73\) | 3.18473 | 0.372744 | 0.186372 | − | 0.982479i | \(-0.440327\pi\) | ||||
0.186372 | + | 0.982479i | \(0.440327\pi\) | |||||||
\(74\) | 4.88527 | 0.567901 | ||||||||
\(75\) | −0.597052 | − | 1.62589i | −0.0689417 | − | 0.187742i | ||||
\(76\) | − | 1.88297i | − | 0.215992i | ||||||
\(77\) | 13.2543i | 1.51047i | ||||||||
\(78\) | −5.20149 | + | 1.91007i | −0.588953 | + | 0.216272i | ||||
\(79\) | 10.1264i | 1.13931i | 0.821885 | + | 0.569653i | \(0.192922\pi\) | ||||
−0.821885 | + | 0.569653i | \(0.807078\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.46126 | − | 8.88058i | 0.162362 | − | 0.986731i | ||||
\(82\) | −3.99062 | −0.440691 | ||||||||
\(83\) | −12.8088 | −1.40595 | −0.702974 | − | 0.711215i | \(-0.748145\pi\) | ||||
−0.702974 | + | 0.711215i | \(0.748145\pi\) | |||||||
\(84\) | 6.18523 | − | 2.27131i | 0.674864 | − | 0.247820i | ||||
\(85\) | 4.76053 | 0.516352 | ||||||||
\(86\) | −6.96125 | −0.750651 | ||||||||
\(87\) | 12.2037 | − | 4.48137i | 1.30837 | − | 0.480453i | ||||
\(88\) | − | 3.48413i | − | 0.371409i | ||||||
\(89\) | −11.0510 | −1.17140 | −0.585700 | − | 0.810528i | \(-0.699180\pi\) | ||||
−0.585700 | + | 0.810528i | \(0.699180\pi\) | |||||||
\(90\) | −1.94149 | − | 2.28706i | −0.204651 | − | 0.241077i | ||||
\(91\) | − | 12.1703i | − | 1.27579i | ||||||
\(92\) | −0.785398 | + | 4.73108i | −0.0818834 | + | 0.493250i | ||||
\(93\) | 2.22176 | + | 6.05031i | 0.230386 | + | 0.627388i | ||||
\(94\) | 10.8399 | 1.11805 | ||||||||
\(95\) | − | 1.88297i | − | 0.193189i | ||||||
\(96\) | −1.62589 | + | 0.597052i | −0.165942 | + | 0.0609364i | ||||
\(97\) | 2.98155i | 0.302730i | 0.988478 | + | 0.151365i | \(0.0483669\pi\) | ||||
−0.988478 | + | 0.151365i | \(0.951633\pi\) | |||||||
\(98\) | 7.47199i | 0.754785i | ||||||||
\(99\) | 7.96840 | − | 6.76439i | 0.800854 | − | 0.679846i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | − | 9.15523i | − | 0.910979i | −0.890241 | − | 0.455490i | \(-0.849464\pi\) | ||
0.890241 | − | 0.455490i | \(-0.150536\pi\) | |||||||
\(102\) | 7.74011 | − | 2.84229i | 0.766385 | − | 0.281428i | ||||
\(103\) | − | 16.0594i | − | 1.58238i | −0.611570 | − | 0.791190i | \(-0.709462\pi\) | ||
0.611570 | − | 0.791190i | \(-0.290538\pi\) | |||||||
\(104\) | 3.19916i | 0.313703i | ||||||||
\(105\) | 6.18523 | − | 2.27131i | 0.603617 | − | 0.221657i | ||||
\(106\) | 7.07396i | 0.687083i | ||||||||
\(107\) | 17.6195 | 1.70334 | 0.851669 | − | 0.524080i | \(-0.175591\pi\) | ||||
0.851669 | + | 0.524080i | \(0.175591\pi\) | |||||||
\(108\) | −4.52214 | − | 2.55934i | −0.435143 | − | 0.246273i | ||||
\(109\) | − | 12.7316i | − | 1.21947i | −0.792607 | − | 0.609733i | \(-0.791277\pi\) | ||
0.792607 | − | 0.609733i | \(-0.208723\pi\) | |||||||
\(110\) | − | 3.48413i | − | 0.332198i | ||||||
\(111\) | 7.94293 | − | 2.91676i | 0.753909 | − | 0.276847i | ||||
\(112\) | − | 3.80421i | − | 0.359464i | ||||||
\(113\) | −9.34208 | −0.878829 | −0.439414 | − | 0.898284i | \(-0.644814\pi\) | ||||
−0.439414 | + | 0.898284i | \(0.644814\pi\) | |||||||
\(114\) | −1.12423 | − | 3.06151i | −0.105294 | − | 0.286737i | ||||
\(115\) | −0.785398 | + | 4.73108i | −0.0732387 | + | 0.441176i | ||||
\(116\) | − | 7.50582i | − | 0.696898i | ||||||
\(117\) | −7.31666 | + | 6.21113i | −0.676426 | + | 0.574219i | ||||
\(118\) | −7.35646 | −0.677217 | ||||||||
\(119\) | 18.1100i | 1.66014i | ||||||||
\(120\) | −1.62589 | + | 0.597052i | −0.148423 | + | 0.0545032i | ||||
\(121\) | 1.13914 | 0.103558 | ||||||||
\(122\) | 3.31936 | 0.300520 | ||||||||
\(123\) | −6.48833 | + | 2.38261i | −0.585033 | + | 0.214833i | ||||
\(124\) | 3.72122 | 0.334176 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 8.70044 | − | 7.38582i | 0.775097 | − | 0.657981i | ||||
\(127\) | −15.6846 | −1.39178 | −0.695892 | − | 0.718146i | \(-0.744991\pi\) | ||||
−0.695892 | + | 0.718146i | \(0.744991\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −11.3183 | + | 4.15623i | −0.996517 | + | 0.365936i | ||||
\(130\) | 3.19916i | 0.280585i | ||||||||
\(131\) | − | 10.5503i | − | 0.921787i | −0.887455 | − | 0.460894i | \(-0.847529\pi\) | ||
0.887455 | − | 0.460894i | \(-0.152471\pi\) | |||||||
\(132\) | −2.08021 | − | 5.66482i | −0.181059 | − | 0.493059i | ||||
\(133\) | 7.16322 | 0.621130 | ||||||||
\(134\) | −3.70440 | −0.320011 | ||||||||
\(135\) | −4.52214 | − | 2.55934i | −0.389204 | − | 0.220273i | ||||
\(136\) | − | 4.76053i | − | 0.408212i | ||||||
\(137\) | −16.2614 | −1.38930 | −0.694652 | − | 0.719346i | \(-0.744442\pi\) | ||||
−0.694652 | + | 0.719346i | \(0.744442\pi\) | |||||||
\(138\) | 1.54773 | + | 8.16116i | 0.131752 | + | 0.694724i | ||||
\(139\) | −23.3435 | −1.97997 | −0.989984 | − | 0.141180i | \(-0.954910\pi\) | ||||
−0.989984 | + | 0.141180i | \(0.954910\pi\) | |||||||
\(140\) | − | 3.80421i | − | 0.321514i | ||||||
\(141\) | 17.6245 | − | 6.47199i | 1.48425 | − | 0.545040i | ||||
\(142\) | −9.92565 | −0.832942 | ||||||||
\(143\) | −11.1463 | −0.932099 | ||||||||
\(144\) | −2.28706 | + | 1.94149i | −0.190588 | + | 0.161791i | ||||
\(145\) | − | 7.50582i | − | 0.623324i | ||||||
\(146\) | − | 3.18473i | − | 0.263570i | ||||||
\(147\) | 4.46117 | + | 12.1487i | 0.367951 | + | 1.00200i | ||||
\(148\) | − | 4.88527i | − | 0.401567i | ||||||
\(149\) | 7.01303 | 0.574530 | 0.287265 | − | 0.957851i | \(-0.407254\pi\) | ||||
0.287265 | + | 0.957851i | \(0.407254\pi\) | |||||||
\(150\) | −1.62589 | + | 0.597052i | −0.132754 | + | 0.0487491i | ||||
\(151\) | −14.3153 | −1.16496 | −0.582481 | − | 0.812844i | \(-0.697918\pi\) | ||||
−0.582481 | + | 0.812844i | \(0.697918\pi\) | |||||||
\(152\) | −1.88297 | −0.152729 | ||||||||
\(153\) | 10.8876 | − | 9.24251i | 0.880210 | − | 0.747212i | ||||
\(154\) | 13.2543 | 1.06807 | ||||||||
\(155\) | 3.72122 | 0.298896 | ||||||||
\(156\) | 1.91007 | + | 5.20149i | 0.152928 | + | 0.416453i | ||||
\(157\) | − | 16.3884i | − | 1.30794i | −0.756521 | − | 0.653970i | \(-0.773102\pi\) | ||
0.756521 | − | 0.653970i | \(-0.226898\pi\) | |||||||
\(158\) | 10.1264 | 0.805611 | ||||||||
\(159\) | 4.22352 | + | 11.5015i | 0.334947 | + | 0.912128i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | −17.9980 | − | 2.98781i | −1.41844 | − | 0.235473i | ||||
\(162\) | −8.88058 | − | 1.46126i | −0.697724 | − | 0.114807i | ||||
\(163\) | 5.26525 | 0.412407 | 0.206203 | − | 0.978509i | \(-0.433889\pi\) | ||||
0.206203 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(164\) | 3.99062i | 0.311615i | ||||||||
\(165\) | −2.08021 | − | 5.66482i | −0.161944 | − | 0.441006i | ||||
\(166\) | 12.8088i | 0.994156i | ||||||||
\(167\) | − | 7.87574i | − | 0.609443i | −0.952441 | − | 0.304722i | \(-0.901437\pi\) | ||
0.952441 | − | 0.304722i | \(-0.0985634\pi\) | |||||||
\(168\) | −2.27131 | − | 6.18523i | −0.175235 | − | 0.477201i | ||||
\(169\) | −2.76537 | −0.212721 | ||||||||
\(170\) | − | 4.76053i | − | 0.365116i | ||||||
\(171\) | −3.65577 | − | 4.30647i | −0.279564 | − | 0.329324i | ||||
\(172\) | 6.96125i | 0.530791i | ||||||||
\(173\) | 2.12595i | 0.161633i | 0.996729 | + | 0.0808165i | \(0.0257528\pi\) | ||||
−0.996729 | + | 0.0808165i | \(0.974247\pi\) | |||||||
\(174\) | −4.48137 | − | 12.2037i | −0.339732 | − | 0.925157i | ||||
\(175\) | − | 3.80421i | − | 0.287571i | ||||||
\(176\) | −3.48413 | −0.262626 | ||||||||
\(177\) | −11.9608 | + | 4.39219i | −0.899031 | + | 0.330138i | ||||
\(178\) | 11.0510i | 0.828305i | ||||||||
\(179\) | 12.4614i | 0.931409i | 0.884940 | + | 0.465704i | \(0.154199\pi\) | ||||
−0.884940 | + | 0.465704i | \(0.845801\pi\) | |||||||
\(180\) | −2.28706 | + | 1.94149i | −0.170467 | + | 0.144710i | ||||
\(181\) | − | 10.2922i | − | 0.765012i | −0.923953 | − | 0.382506i | \(-0.875061\pi\) | ||
0.923953 | − | 0.382506i | \(-0.124939\pi\) | |||||||
\(182\) | −12.1703 | −0.902120 | ||||||||
\(183\) | 5.39692 | − | 1.98183i | 0.398952 | − | 0.146501i | ||||
\(184\) | 4.73108 | + | 0.785398i | 0.348780 | + | 0.0579003i | ||||
\(185\) | − | 4.88527i | − | 0.359172i | ||||||
\(186\) | 6.05031 | − | 2.22176i | 0.443630 | − | 0.162908i | ||||
\(187\) | 16.5863 | 1.21291 | ||||||||
\(188\) | − | 10.8399i | − | 0.790581i | ||||||
\(189\) | 9.73626 | − | 17.2032i | 0.708209 | − | 1.25135i | ||||
\(190\) | −1.88297 | −0.136605 | ||||||||
\(191\) | 22.5181 | 1.62935 | 0.814676 | − | 0.579916i | \(-0.196915\pi\) | ||||
0.814676 | + | 0.579916i | \(0.196915\pi\) | |||||||
\(192\) | 0.597052 | + | 1.62589i | 0.0430885 | + | 0.117339i | ||||
\(193\) | 12.3106 | 0.886134 | 0.443067 | − | 0.896489i | \(-0.353890\pi\) | ||||
0.443067 | + | 0.896489i | \(0.353890\pi\) | |||||||
\(194\) | 2.98155 | 0.214063 | ||||||||
\(195\) | 1.91007 | + | 5.20149i | 0.136783 | + | 0.372487i | ||||
\(196\) | 7.47199 | 0.533714 | ||||||||
\(197\) | − | 0.321151i | − | 0.0228811i | −0.999935 | − | 0.0114405i | \(-0.996358\pi\) | ||
0.999935 | − | 0.0114405i | \(-0.00364171\pi\) | |||||||
\(198\) | −6.76439 | − | 7.96840i | −0.480724 | − | 0.566289i | ||||
\(199\) | 14.6664i | 1.03968i | 0.854265 | + | 0.519838i | \(0.174008\pi\) | ||||
−0.854265 | + | 0.519838i | \(0.825992\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −6.02295 | + | 2.21172i | −0.424826 | + | 0.156003i | ||||
\(202\) | −9.15523 | −0.644160 | ||||||||
\(203\) | 28.5537 | 2.00408 | ||||||||
\(204\) | −2.84229 | − | 7.74011i | −0.199000 | − | 0.541916i | ||||
\(205\) | 3.99062i | 0.278717i | ||||||||
\(206\) | −16.0594 | −1.11891 | ||||||||
\(207\) | 7.38909 | + | 12.3451i | 0.513577 | + | 0.858043i | ||||
\(208\) | 3.19916 | 0.221822 | ||||||||
\(209\) | − | 6.56052i | − | 0.453801i | ||||||
\(210\) | −2.27131 | − | 6.18523i | −0.156735 | − | 0.426822i | ||||
\(211\) | 12.3848 | 0.852604 | 0.426302 | − | 0.904581i | \(-0.359816\pi\) | ||||
0.426302 | + | 0.904581i | \(0.359816\pi\) | |||||||
\(212\) | 7.07396 | 0.485841 | ||||||||
\(213\) | −16.1380 | + | 5.92613i | −1.10576 | + | 0.406052i | ||||
\(214\) | − | 17.6195i | − | 1.20444i | ||||||
\(215\) | 6.96125i | 0.474753i | ||||||||
\(216\) | −2.55934 | + | 4.52214i | −0.174141 | + | 0.307693i | ||||
\(217\) | 14.1563i | 0.960992i | ||||||||
\(218\) | −12.7316 | −0.862292 | ||||||||
\(219\) | −1.90145 | − | 5.17803i | −0.128488 | − | 0.349899i | ||||
\(220\) | −3.48413 | −0.234900 | ||||||||
\(221\) | −15.2297 | −1.02446 | ||||||||
\(222\) | −2.91676 | − | 7.94293i | −0.195760 | − | 0.533094i | ||||
\(223\) | 5.19193 | 0.347677 | 0.173839 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173839 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(224\) | −3.80421 | −0.254179 | ||||||||
\(225\) | −2.28706 | + | 1.94149i | −0.152470 | + | 0.129432i | ||||
\(226\) | 9.34208i | 0.621426i | ||||||||
\(227\) | 16.7298 | 1.11040 | 0.555199 | − | 0.831718i | \(-0.312642\pi\) | ||||
0.555199 | + | 0.831718i | \(0.312642\pi\) | |||||||
\(228\) | −3.06151 | + | 1.12423i | −0.202754 | + | 0.0744542i | ||||
\(229\) | − | 18.2985i | − | 1.20920i | −0.796530 | − | 0.604599i | \(-0.793334\pi\) | ||
0.796530 | − | 0.604599i | \(-0.206666\pi\) | |||||||
\(230\) | 4.73108 | + | 0.785398i | 0.311958 | + | 0.0517876i | ||||
\(231\) | 21.5501 | − | 7.91354i | 1.41790 | − | 0.520672i | ||||
\(232\) | −7.50582 | −0.492781 | ||||||||
\(233\) | − | 6.92267i | − | 0.453519i | −0.973951 | − | 0.226759i | \(-0.927187\pi\) | ||
0.973951 | − | 0.226759i | \(-0.0728131\pi\) | |||||||
\(234\) | 6.21113 | + | 7.31666i | 0.406034 | + | 0.478305i | ||||
\(235\) | − | 10.8399i | − | 0.707117i | ||||||
\(236\) | 7.35646i | 0.478865i | ||||||||
\(237\) | 16.4644 | − | 6.04597i | 1.06948 | − | 0.392728i | ||||
\(238\) | 18.1100 | 1.17390 | ||||||||
\(239\) | − | 2.10045i | − | 0.135867i | −0.997690 | − | 0.0679335i | \(-0.978359\pi\) | ||
0.997690 | − | 0.0679335i | \(-0.0216406\pi\) | |||||||
\(240\) | 0.597052 | + | 1.62589i | 0.0385396 | + | 0.104951i | ||||
\(241\) | 0.0258170i | 0.00166302i | 1.00000 | 0.000831511i | \(0.000264678\pi\) | |||||
−1.00000 | 0.000831511i | \(0.999735\pi\) | ||||||||
\(242\) | − | 1.13914i | − | 0.0732268i | ||||||
\(243\) | −15.3113 | + | 2.92632i | −0.982222 | + | 0.187724i | ||||
\(244\) | − | 3.31936i | − | 0.212500i | ||||||
\(245\) | 7.47199 | 0.477368 | ||||||||
\(246\) | 2.38261 | + | 6.48833i | 0.151910 | + | 0.413681i | ||||
\(247\) | 6.02393i | 0.383294i | ||||||||
\(248\) | − | 3.72122i | − | 0.236298i | ||||||
\(249\) | 7.64752 | + | 20.8257i | 0.484642 | + | 1.31978i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | 7.11730 | 0.449240 | 0.224620 | − | 0.974446i | \(-0.427886\pi\) | ||||
0.224620 | + | 0.974446i | \(0.427886\pi\) | |||||||
\(252\) | −7.38582 | − | 8.70044i | −0.465263 | − | 0.548076i | ||||
\(253\) | −2.73642 | + | 16.4837i | −0.172038 | + | 1.03632i | ||||
\(254\) | 15.6846i | 0.984141i | ||||||||
\(255\) | −2.84229 | − | 7.74011i | −0.177991 | − | 0.484705i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 5.27667i | − | 0.329150i | −0.986365 | − | 0.164575i | \(-0.947375\pi\) | ||
0.986365 | − | 0.164575i | \(-0.0526252\pi\) | |||||||
\(258\) | 4.15623 | + | 11.3183i | 0.258756 | + | 0.704644i | ||||
\(259\) | 18.5846 | 1.15479 | ||||||||
\(260\) | 3.19916 | 0.198404 | ||||||||
\(261\) | −14.5725 | − | 17.1662i | −0.902012 | − | 1.06256i | ||||
\(262\) | −10.5503 | −0.651802 | ||||||||
\(263\) | 13.6544 | 0.841967 | 0.420984 | − | 0.907068i | \(-0.361685\pi\) | ||||
0.420984 | + | 0.907068i | \(0.361685\pi\) | |||||||
\(264\) | −5.66482 | + | 2.08021i | −0.348645 | + | 0.128028i | ||||
\(265\) | 7.07396 | 0.434550 | ||||||||
\(266\) | − | 7.16322i | − | 0.439205i | ||||||
\(267\) | 6.59801 | + | 17.9677i | 0.403792 | + | 1.09961i | ||||
\(268\) | 3.70440i | 0.226282i | ||||||||
\(269\) | 14.9128i | 0.909249i | 0.890683 | + | 0.454624i | \(0.150226\pi\) | ||||
−0.890683 | + | 0.454624i | \(0.849774\pi\) | |||||||
\(270\) | −2.55934 | + | 4.52214i | −0.155757 | + | 0.275209i | ||||
\(271\) | −22.4734 | −1.36516 | −0.682580 | − | 0.730811i | \(-0.739142\pi\) | ||||
−0.682580 | + | 0.730811i | \(0.739142\pi\) | |||||||
\(272\) | −4.76053 | −0.288650 | ||||||||
\(273\) | −19.7876 | + | 7.26629i | −1.19760 | + | 0.439776i | ||||
\(274\) | 16.2614i | 0.982387i | ||||||||
\(275\) | −3.48413 | −0.210101 | ||||||||
\(276\) | 8.16116 | − | 1.54773i | 0.491244 | − | 0.0931625i | ||||
\(277\) | −25.7920 | −1.54969 | −0.774846 | − | 0.632150i | \(-0.782173\pi\) | ||||
−0.774846 | + | 0.632150i | \(0.782173\pi\) | |||||||
\(278\) | 23.3435i | 1.40005i | ||||||||
\(279\) | 8.51065 | − | 7.22470i | 0.509519 | − | 0.432532i | ||||
\(280\) | −3.80421 | −0.227345 | ||||||||
\(281\) | 5.19176 | 0.309714 | 0.154857 | − | 0.987937i | \(-0.450508\pi\) | ||||
0.154857 | + | 0.987937i | \(0.450508\pi\) | |||||||
\(282\) | −6.47199 | − | 17.6245i | −0.385401 | − | 1.04953i | ||||
\(283\) | 6.60335i | 0.392528i | 0.980551 | + | 0.196264i | \(0.0628810\pi\) | ||||
−0.980551 | + | 0.196264i | \(0.937119\pi\) | |||||||
\(284\) | 9.92565i | 0.588979i | ||||||||
\(285\) | −3.06151 | + | 1.12423i | −0.181348 | + | 0.0665939i | ||||
\(286\) | 11.1463i | 0.659093i | ||||||||
\(287\) | −15.1812 | −0.896115 | ||||||||
\(288\) | 1.94149 | + | 2.28706i | 0.114403 | + | 0.134766i | ||||
\(289\) | 5.66264 | 0.333097 | ||||||||
\(290\) | −7.50582 | −0.440757 | ||||||||
\(291\) | 4.84768 | − | 1.78014i | 0.284176 | − | 0.104354i | ||||
\(292\) | −3.18473 | −0.186372 | ||||||||
\(293\) | 30.6756 | 1.79209 | 0.896044 | − | 0.443964i | \(-0.146428\pi\) | ||||
0.896044 | + | 0.443964i | \(0.146428\pi\) | |||||||
\(294\) | 12.1487 | − | 4.46117i | 0.708524 | − | 0.260181i | ||||
\(295\) | 7.35646i | 0.428310i | ||||||||
\(296\) | −4.88527 | −0.283951 | ||||||||
\(297\) | −15.7557 | − | 8.91707i | −0.914240 | − | 0.517421i | ||||
\(298\) | − | 7.01303i | − | 0.406254i | ||||||
\(299\) | 2.51261 | − | 15.1355i | 0.145308 | − | 0.875308i | ||||
\(300\) | 0.597052 | + | 1.62589i | 0.0344708 | + | 0.0938710i | ||||
\(301\) | −26.4820 | −1.52640 | ||||||||
\(302\) | 14.3153i | 0.823753i | ||||||||
\(303\) | −14.8854 | + | 5.46615i | −0.855145 | + | 0.314022i | ||||
\(304\) | 1.88297i | 0.107996i | ||||||||
\(305\) | − | 3.31936i | − | 0.190066i | ||||||
\(306\) | −9.24251 | − | 10.8876i | −0.528359 | − | 0.622403i | ||||
\(307\) | 19.3975 | 1.10707 | 0.553537 | − | 0.832825i | \(-0.313278\pi\) | ||||
0.553537 | + | 0.832825i | \(0.313278\pi\) | |||||||
\(308\) | − | 13.2543i | − | 0.755236i | ||||||
\(309\) | −26.1109 | + | 9.58831i | −1.48540 | + | 0.545460i | ||||
\(310\) | − | 3.72122i | − | 0.211351i | ||||||
\(311\) | 16.8790i | 0.957118i | 0.878055 | + | 0.478559i | \(0.158841\pi\) | ||||
−0.878055 | + | 0.478559i | \(0.841159\pi\) | |||||||
\(312\) | 5.20149 | − | 1.91007i | 0.294477 | − | 0.108136i | ||||
\(313\) | 26.7256i | 1.51062i | 0.655367 | + | 0.755310i | \(0.272514\pi\) | ||||
−0.655367 | + | 0.755310i | \(0.727486\pi\) | |||||||
\(314\) | −16.3884 | −0.924853 | ||||||||
\(315\) | −7.38582 | − | 8.70044i | −0.416144 | − | 0.490214i | ||||
\(316\) | − | 10.1264i | − | 0.569653i | ||||||
\(317\) | − | 7.55156i | − | 0.424138i | −0.977255 | − | 0.212069i | \(-0.931980\pi\) | ||
0.977255 | − | 0.212069i | \(-0.0680201\pi\) | |||||||
\(318\) | 11.5015 | − | 4.22352i | 0.644972 | − | 0.236843i | ||||
\(319\) | − | 26.1512i | − | 1.46419i | ||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −10.5197 | − | 28.6474i | −0.587155 | − | 1.59894i | ||||
\(322\) | −2.98781 | + | 17.9980i | −0.166504 | + | 1.00299i | ||||
\(323\) | − | 8.96395i | − | 0.498768i | ||||||
\(324\) | −1.46126 | + | 8.88058i | −0.0811810 | + | 0.493366i | ||||
\(325\) | 3.19916 | 0.177457 | ||||||||
\(326\) | − | 5.26525i | − | 0.291615i | ||||||
\(327\) | −20.7002 | + | 7.60143i | −1.14472 | + | 0.420360i | ||||
\(328\) | 3.99062 | 0.220345 | ||||||||
\(329\) | 41.2372 | 2.27348 | ||||||||
\(330\) | −5.66482 | + | 2.08021i | −0.311838 | + | 0.114512i | ||||
\(331\) | 25.3475 | 1.39323 | 0.696613 | − | 0.717447i | \(-0.254690\pi\) | ||||
0.696613 | + | 0.717447i | \(0.254690\pi\) | |||||||
\(332\) | 12.8088 | 0.702974 | ||||||||
\(333\) | −9.48469 | − | 11.1729i | −0.519758 | − | 0.612271i | ||||
\(334\) | −7.87574 | −0.430941 | ||||||||
\(335\) | 3.70440i | 0.202393i | ||||||||
\(336\) | −6.18523 | + | 2.27131i | −0.337432 | + | 0.123910i | ||||
\(337\) | 21.0505i | 1.14669i | 0.819313 | + | 0.573346i | \(0.194355\pi\) | ||||
−0.819313 | + | 0.573346i | \(0.805645\pi\) | |||||||
\(338\) | 2.76537i | 0.150416i | ||||||||
\(339\) | 5.57771 | + | 15.1892i | 0.302940 | + | 0.824965i | ||||
\(340\) | −4.76053 | −0.258176 | ||||||||
\(341\) | 12.9652 | 0.702106 | ||||||||
\(342\) | −4.30647 | + | 3.65577i | −0.232867 | + | 0.197681i | ||||
\(343\) | 1.79555i | 0.0969506i | ||||||||
\(344\) | 6.96125 | 0.375326 | ||||||||
\(345\) | 8.16116 | − | 1.54773i | 0.439382 | − | 0.0833271i | ||||
\(346\) | 2.12595 | 0.114292 | ||||||||
\(347\) | − | 6.08253i | − | 0.326528i | −0.986582 | − | 0.163264i | \(-0.947798\pi\) | ||
0.986582 | − | 0.163264i | \(-0.0522022\pi\) | |||||||
\(348\) | −12.2037 | + | 4.48137i | −0.654185 | + | 0.240227i | ||||
\(349\) | 1.98670 | 0.106345 | 0.0531727 | − | 0.998585i | \(-0.483067\pi\) | ||||
0.0531727 | + | 0.998585i | \(0.483067\pi\) | |||||||
\(350\) | −3.80421 | −0.203343 | ||||||||
\(351\) | 14.4671 | + | 8.18774i | 0.772195 | + | 0.437029i | ||||
\(352\) | 3.48413i | 0.185705i | ||||||||
\(353\) | − | 8.53950i | − | 0.454512i | −0.973835 | − | 0.227256i | \(-0.927025\pi\) | ||
0.973835 | − | 0.227256i | \(-0.0729754\pi\) | |||||||
\(354\) | 4.39219 | + | 11.9608i | 0.233442 | + | 0.635711i | ||||
\(355\) | 9.92565i | 0.526799i | ||||||||
\(356\) | 11.0510 | 0.585700 | ||||||||
\(357\) | 29.4450 | − | 10.8126i | 1.55839 | − | 0.572266i | ||||
\(358\) | 12.4614 | 0.658606 | ||||||||
\(359\) | −27.5129 | −1.45207 | −0.726037 | − | 0.687656i | \(-0.758640\pi\) | ||||
−0.726037 | + | 0.687656i | \(0.758640\pi\) | |||||||
\(360\) | 1.94149 | + | 2.28706i | 0.102325 | + | 0.120538i | ||||
\(361\) | 15.4544 | 0.813390 | ||||||||
\(362\) | −10.2922 | −0.540945 | ||||||||
\(363\) | −0.680127 | − | 1.85212i | −0.0356974 | − | 0.0972112i | ||||
\(364\) | 12.1703i | 0.637895i | ||||||||
\(365\) | −3.18473 | −0.166696 | ||||||||
\(366\) | −1.98183 | − | 5.39692i | −0.103592 | − | 0.282101i | ||||
\(367\) | − | 31.2664i | − | 1.63209i | −0.577986 | − | 0.816046i | \(-0.696161\pi\) | ||
0.577986 | − | 0.816046i | \(-0.303839\pi\) | |||||||
\(368\) | 0.785398 | − | 4.73108i | 0.0409417 | − | 0.246625i | ||||
\(369\) | 7.74774 | + | 9.12678i | 0.403331 | + | 0.475121i | ||||
\(370\) | −4.88527 | −0.253973 | ||||||||
\(371\) | 26.9108i | 1.39714i | ||||||||
\(372\) | −2.22176 | − | 6.05031i | −0.115193 | − | 0.313694i | ||||
\(373\) | 13.5799i | 0.703138i | 0.936162 | + | 0.351569i | \(0.114352\pi\) | ||||
−0.936162 | + | 0.351569i | \(0.885648\pi\) | |||||||
\(374\) | − | 16.5863i | − | 0.857657i | ||||||
\(375\) | 0.597052 | + | 1.62589i | 0.0308317 | + | 0.0839608i | ||||
\(376\) | −10.8399 | −0.559025 | ||||||||
\(377\) | 24.0123i | 1.23670i | ||||||||
\(378\) | −17.2032 | − | 9.73626i | −0.884835 | − | 0.500779i | ||||
\(379\) | 31.3374i | 1.60970i | 0.593482 | + | 0.804848i | \(0.297753\pi\) | ||||
−0.593482 | + | 0.804848i | \(0.702247\pi\) | |||||||
\(380\) | 1.88297i | 0.0965945i | ||||||||
\(381\) | 9.36454 | + | 25.5015i | 0.479760 | + | 1.30648i | ||||
\(382\) | − | 22.5181i | − | 1.15213i | ||||||
\(383\) | −11.1675 | −0.570632 | −0.285316 | − | 0.958433i | \(-0.592099\pi\) | ||||
−0.285316 | + | 0.958433i | \(0.592099\pi\) | |||||||
\(384\) | 1.62589 | − | 0.597052i | 0.0829710 | − | 0.0304682i | ||||
\(385\) | − | 13.2543i | − | 0.675504i | ||||||
\(386\) | − | 12.3106i | − | 0.626591i | ||||||
\(387\) | 13.5152 | + | 15.9208i | 0.687015 | + | 0.809299i | ||||
\(388\) | − | 2.98155i | − | 0.151365i | ||||||
\(389\) | −12.5852 | −0.638093 | −0.319046 | − | 0.947739i | \(-0.603363\pi\) | ||||
−0.319046 | + | 0.947739i | \(0.603363\pi\) | |||||||
\(390\) | 5.20149 | − | 1.91007i | 0.263388 | − | 0.0967200i | ||||
\(391\) | −3.73891 | + | 22.5225i | −0.189085 | + | 1.13901i | ||||
\(392\) | − | 7.47199i | − | 0.377393i | ||||||
\(393\) | −17.1537 | + | 6.29910i | −0.865291 | + | 0.317748i | ||||
\(394\) | −0.321151 | −0.0161793 | ||||||||
\(395\) | − | 10.1264i | − | 0.509513i | ||||||
\(396\) | −7.96840 | + | 6.76439i | −0.400427 | + | 0.339923i | ||||
\(397\) | 12.3539 | 0.620024 | 0.310012 | − | 0.950733i | \(-0.399667\pi\) | ||||
0.310012 | + | 0.950733i | \(0.399667\pi\) | |||||||
\(398\) | 14.6664 | 0.735162 | ||||||||
\(399\) | −4.27682 | − | 11.6466i | −0.214109 | − | 0.583061i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 27.2453 | 1.36057 | 0.680283 | − | 0.732950i | \(-0.261857\pi\) | ||||
0.680283 | + | 0.732950i | \(0.261857\pi\) | |||||||
\(402\) | 2.21172 | + | 6.02295i | 0.110311 | + | 0.300398i | ||||
\(403\) | −11.9048 | −0.593020 | ||||||||
\(404\) | 9.15523i | 0.455490i | ||||||||
\(405\) | −1.46126 | + | 8.88058i | −0.0726105 | + | 0.441280i | ||||
\(406\) | − | 28.5537i | − | 1.41710i | ||||||
\(407\) | − | 17.0209i | − | 0.843695i | ||||||
\(408\) | −7.74011 | + | 2.84229i | −0.383193 | + | 0.140714i | ||||
\(409\) | −27.3294 | −1.35135 | −0.675675 | − | 0.737200i | \(-0.736148\pi\) | ||||
−0.675675 | + | 0.737200i | \(0.736148\pi\) | |||||||
\(410\) | 3.99062 | 0.197083 | ||||||||
\(411\) | 9.70890 | + | 26.4393i | 0.478905 | + | 1.30415i | ||||
\(412\) | 16.0594i | 0.791190i | ||||||||
\(413\) | −27.9855 | −1.37708 | ||||||||
\(414\) | 12.3451 | − | 7.38909i | 0.606728 | − | 0.363154i | ||||
\(415\) | 12.8088 | 0.628759 | ||||||||
\(416\) | − | 3.19916i | − | 0.156852i | ||||||
\(417\) | 13.9373 | + | 37.9540i | 0.682511 | + | 1.85862i | ||||
\(418\) | −6.56052 | −0.320885 | ||||||||
\(419\) | 15.1668 | 0.740949 | 0.370474 | − | 0.928843i | \(-0.379195\pi\) | ||||
0.370474 | + | 0.928843i | \(0.379195\pi\) | |||||||
\(420\) | −6.18523 | + | 2.27131i | −0.301809 | + | 0.110829i | ||||
\(421\) | 34.7728i | 1.69472i | 0.531018 | + | 0.847361i | \(0.321810\pi\) | ||||
−0.531018 | + | 0.847361i | \(0.678190\pi\) | |||||||
\(422\) | − | 12.3848i | − | 0.602882i | ||||||
\(423\) | −21.0455 | − | 24.7915i | −1.02327 | − | 1.20540i | ||||
\(424\) | − | 7.07396i | − | 0.343542i | ||||||
\(425\) | −4.76053 | −0.230920 | ||||||||
\(426\) | 5.92613 | + | 16.1380i | 0.287122 | + | 0.781891i | ||||
\(427\) | 12.6275 | 0.611088 | ||||||||
\(428\) | −17.6195 | −0.851669 | ||||||||
\(429\) | 6.65491 | + | 18.1227i | 0.321302 | + | 0.874970i | ||||
\(430\) | 6.96125 | 0.335701 | ||||||||
\(431\) | −5.86936 | −0.282717 | −0.141358 | − | 0.989958i | \(-0.545147\pi\) | ||||
−0.141358 | + | 0.989958i | \(0.545147\pi\) | |||||||
\(432\) | 4.52214 | + | 2.55934i | 0.217572 | + | 0.123136i | ||||
\(433\) | − | 30.4782i | − | 1.46469i | −0.680935 | − | 0.732344i | \(-0.738426\pi\) | ||
0.680935 | − | 0.732344i | \(-0.261574\pi\) | |||||||
\(434\) | 14.1563 | 0.679524 | ||||||||
\(435\) | −12.2037 | + | 4.48137i | −0.585121 | + | 0.214865i | ||||
\(436\) | 12.7316i | 0.609733i | ||||||||
\(437\) | 8.90850 | + | 1.47888i | 0.426152 | + | 0.0707446i | ||||
\(438\) | −5.17803 | + | 1.90145i | −0.247416 | + | 0.0908548i | ||||
\(439\) | 20.8965 | 0.997334 | 0.498667 | − | 0.866794i | \(-0.333823\pi\) | ||||
0.498667 | + | 0.866794i | \(0.333823\pi\) | |||||||
\(440\) | 3.48413i | 0.166099i | ||||||||
\(441\) | 17.0889 | − | 14.5068i | 0.813756 | − | 0.690799i | ||||
\(442\) | 15.2297i | 0.724403i | ||||||||
\(443\) | − | 38.9828i | − | 1.85213i | −0.377365 | − | 0.926065i | \(-0.623170\pi\) | ||
0.377365 | − | 0.926065i | \(-0.376830\pi\) | |||||||
\(444\) | −7.94293 | + | 2.91676i | −0.376955 | + | 0.138423i | ||||
\(445\) | 11.0510 | 0.523866 | ||||||||
\(446\) | − | 5.19193i | − | 0.245845i | ||||||
\(447\) | −4.18714 | − | 11.4024i | −0.198045 | − | 0.539317i | ||||
\(448\) | 3.80421i | 0.179732i | ||||||||
\(449\) | 8.98085i | 0.423832i | 0.977288 | + | 0.211916i | \(0.0679704\pi\) | ||||
−0.977288 | + | 0.211916i | \(0.932030\pi\) | |||||||
\(450\) | 1.94149 | + | 2.28706i | 0.0915226 | + | 0.107813i | ||||
\(451\) | 13.9038i | 0.654706i | ||||||||
\(452\) | 9.34208 | 0.439414 | ||||||||
\(453\) | 8.54699 | + | 23.2752i | 0.401572 | + | 1.09356i | ||||
\(454\) | − | 16.7298i | − | 0.785170i | ||||||
\(455\) | 12.1703i | 0.570551i | ||||||||
\(456\) | 1.12423 | + | 3.06151i | 0.0526471 | + | 0.143369i | ||||
\(457\) | 5.68472i | 0.265920i | 0.991121 | + | 0.132960i | \(0.0424482\pi\) | ||||
−0.991121 | + | 0.132960i | \(0.957552\pi\) | |||||||
\(458\) | −18.2985 | −0.855031 | ||||||||
\(459\) | −21.5278 | − | 12.1838i | −1.00483 | − | 0.568692i | ||||
\(460\) | 0.785398 | − | 4.73108i | 0.0366194 | − | 0.220588i | ||||
\(461\) | − | 23.4737i | − | 1.09328i | −0.837368 | − | 0.546640i | \(-0.815907\pi\) | ||
0.837368 | − | 0.546640i | \(-0.184093\pi\) | |||||||
\(462\) | −7.91354 | − | 21.5501i | −0.368171 | − | 1.00260i | ||||
\(463\) | −41.4142 | −1.92468 | −0.962339 | − | 0.271851i | \(-0.912364\pi\) | ||||
−0.962339 | + | 0.271851i | \(0.912364\pi\) | |||||||
\(464\) | 7.50582i | 0.348449i | ||||||||
\(465\) | −2.22176 | − | 6.05031i | −0.103032 | − | 0.280576i | ||||
\(466\) | −6.92267 | −0.320686 | ||||||||
\(467\) | 28.5266 | 1.32006 | 0.660028 | − | 0.751241i | \(-0.270545\pi\) | ||||
0.660028 | + | 0.751241i | \(0.270545\pi\) | |||||||
\(468\) | 7.31666 | − | 6.21113i | 0.338213 | − | 0.287109i | ||||
\(469\) | −14.0923 | −0.650722 | ||||||||
\(470\) | −10.8399 | −0.500007 | ||||||||
\(471\) | −26.6458 | + | 9.78475i | −1.22778 | + | 0.450858i | ||||
\(472\) | 7.35646 | 0.338609 | ||||||||
\(473\) | 24.2539i | 1.11519i | ||||||||
\(474\) | −6.04597 | − | 16.4644i | −0.277701 | − | 0.756235i | ||||
\(475\) | 1.88297i | 0.0863967i | ||||||||
\(476\) | − | 18.1100i | − | 0.830072i | ||||||
\(477\) | 16.1785 | − | 13.7340i | 0.740765 | − | 0.628836i | ||||
\(478\) | −2.10045 | −0.0960724 | ||||||||
\(479\) | 3.94290 | 0.180155 | 0.0900777 | − | 0.995935i | \(-0.471288\pi\) | ||||
0.0900777 | + | 0.995935i | \(0.471288\pi\) | |||||||
\(480\) | 1.62589 | − | 0.597052i | 0.0742115 | − | 0.0272516i | ||||
\(481\) | 15.6288i | 0.712610i | ||||||||
\(482\) | 0.0258170 | 0.00117593 | ||||||||
\(483\) | 5.88789 | + | 31.0467i | 0.267908 | + | 1.41268i | ||||
\(484\) | −1.13914 | −0.0517792 | ||||||||
\(485\) | − | 2.98155i | − | 0.135385i | ||||||
\(486\) | 2.92632 | + | 15.3113i | 0.132741 | + | 0.694536i | ||||
\(487\) | 1.02454 | 0.0464262 | 0.0232131 | − | 0.999731i | \(-0.492610\pi\) | ||||
0.0232131 | + | 0.999731i | \(0.492610\pi\) | |||||||
\(488\) | −3.31936 | −0.150260 | ||||||||
\(489\) | −3.14363 | − | 8.56074i | −0.142160 | − | 0.387130i | ||||
\(490\) | − | 7.47199i | − | 0.337550i | ||||||
\(491\) | 12.3413i | 0.556954i | 0.960443 | + | 0.278477i | \(0.0898296\pi\) | ||||
−0.960443 | + | 0.278477i | \(0.910170\pi\) | |||||||
\(492\) | 6.48833 | − | 2.38261i | 0.292516 | − | 0.107416i | ||||
\(493\) | − | 35.7317i | − | 1.60927i | ||||||
\(494\) | 6.02393 | 0.271030 | ||||||||
\(495\) | −7.96840 | + | 6.76439i | −0.358153 | + | 0.304037i | ||||
\(496\) | −3.72122 | −0.167088 | ||||||||
\(497\) | −37.7592 | −1.69373 | ||||||||
\(498\) | 20.8257 | − | 7.64752i | 0.933224 | − | 0.342694i | ||||
\(499\) | −29.3987 | −1.31607 | −0.658033 | − | 0.752989i | \(-0.728611\pi\) | ||||
−0.658033 | + | 0.752989i | \(0.728611\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −12.8051 | + | 4.70223i | −0.572090 | + | 0.210080i | ||||
\(502\) | − | 7.11730i | − | 0.317661i | ||||||
\(503\) | −27.8709 | −1.24270 | −0.621350 | − | 0.783533i | \(-0.713416\pi\) | ||||
−0.621350 | + | 0.783533i | \(0.713416\pi\) | |||||||
\(504\) | −8.70044 | + | 7.38582i | −0.387548 | + | 0.328990i | ||||
\(505\) | 9.15523i | 0.407402i | ||||||||
\(506\) | 16.4837 | + | 2.73642i | 0.732790 | + | 0.121649i | ||||
\(507\) | 1.65107 | + | 4.49620i | 0.0733267 | + | 0.199683i | ||||
\(508\) | 15.6846 | 0.695892 | ||||||||
\(509\) | − | 33.5429i | − | 1.48676i | −0.668868 | − | 0.743381i | \(-0.733221\pi\) | ||
0.668868 | − | 0.743381i | \(-0.266779\pi\) | |||||||
\(510\) | −7.74011 | + | 2.84229i | −0.342738 | + | 0.125859i | ||||
\(511\) | − | 12.1154i | − | 0.535952i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −4.81917 | + | 8.51507i | −0.212772 | + | 0.375950i | ||||
\(514\) | −5.27667 | −0.232744 | ||||||||
\(515\) | 16.0594i | 0.707662i | ||||||||
\(516\) | 11.3183 | − | 4.15623i | 0.498258 | − | 0.182968i | ||||
\(517\) | − | 37.7676i | − | 1.66102i | ||||||
\(518\) | − | 18.5846i | − | 0.816559i | ||||||
\(519\) | 3.45657 | − | 1.26930i | 0.151727 | − | 0.0557163i | ||||
\(520\) | − | 3.19916i | − | 0.140292i | ||||||
\(521\) | 4.78488 | 0.209629 | 0.104815 | − | 0.994492i | \(-0.466575\pi\) | ||||
0.104815 | + | 0.994492i | \(0.466575\pi\) | |||||||
\(522\) | −17.1662 | + | 14.5725i | −0.751346 | + | 0.637819i | ||||
\(523\) | 16.7160i | 0.730939i | 0.930823 | + | 0.365470i | \(0.119092\pi\) | ||||
−0.930823 | + | 0.365470i | \(0.880908\pi\) | |||||||
\(524\) | 10.5503i | 0.460894i | ||||||||
\(525\) | −6.18523 | + | 2.27131i | −0.269946 | + | 0.0991281i | ||||
\(526\) | − | 13.6544i | − | 0.595361i | ||||||
\(527\) | 17.7150 | 0.771677 | ||||||||
\(528\) | 2.08021 | + | 5.66482i | 0.0905294 | + | 0.246530i | ||||
\(529\) | −21.7663 | − | 7.43156i | −0.946361 | − | 0.323111i | ||||
\(530\) | − | 7.07396i | − | 0.307273i | ||||||
\(531\) | 14.2825 | + | 16.8247i | 0.619807 | + | 0.730128i | ||||
\(532\) | −7.16322 | −0.310565 | ||||||||
\(533\) | − | 12.7666i | − | 0.552985i | ||||||
\(534\) | 17.9677 | − | 6.59801i | 0.777538 | − | 0.285524i | ||||
\(535\) | −17.6195 | −0.761756 | ||||||||
\(536\) | 3.70440 | 0.160006 | ||||||||
\(537\) | 20.2609 | − | 7.44011i | 0.874323 | − | 0.321064i | ||||
\(538\) | 14.9128 | 0.642936 | ||||||||
\(539\) | 26.0334 | 1.12134 | ||||||||
\(540\) | 4.52214 | + | 2.55934i | 0.194602 | + | 0.110136i | ||||
\(541\) | −16.8464 | −0.724284 | −0.362142 | − | 0.932123i | \(-0.617954\pi\) | ||||
−0.362142 | + | 0.932123i | \(0.617954\pi\) | |||||||
\(542\) | 22.4734i | 0.965314i | ||||||||
\(543\) | −16.7340 | + | 6.14497i | −0.718124 | + | 0.263706i | ||||
\(544\) | 4.76053i | 0.204106i | ||||||||
\(545\) | 12.7316i | 0.545361i | ||||||||
\(546\) | 7.26629 | + | 19.7876i | 0.310968 | + | 0.846829i | ||||
\(547\) | 17.5645 | 0.751005 | 0.375503 | − | 0.926821i | \(-0.377470\pi\) | ||||
0.375503 | + | 0.926821i | \(0.377470\pi\) | |||||||
\(548\) | 16.2614 | 0.694652 | ||||||||
\(549\) | −6.44449 | − | 7.59156i | −0.275044 | − | 0.324000i | ||||
\(550\) | 3.48413i | 0.148564i | ||||||||
\(551\) | −14.1333 | −0.602097 | ||||||||
\(552\) | −1.54773 | − | 8.16116i | −0.0658759 | − | 0.347362i | ||||
\(553\) | 38.5228 | 1.63816 | ||||||||
\(554\) | 25.7920i | 1.09580i | ||||||||
\(555\) | −7.94293 | + | 2.91676i | −0.337158 | + | 0.123810i | ||||
\(556\) | 23.3435 | 0.989984 | ||||||||
\(557\) | 6.58788 | 0.279137 | 0.139569 | − | 0.990212i | \(-0.455428\pi\) | ||||
0.139569 | + | 0.990212i | \(0.455428\pi\) | |||||||
\(558\) | −7.22470 | − | 8.51065i | −0.305846 | − | 0.360284i | ||||
\(559\) | − | 22.2702i | − | 0.941928i | ||||||
\(560\) | 3.80421i | 0.160757i | ||||||||
\(561\) | −9.90288 | − | 26.9675i | −0.418100 | − | 1.13857i | ||||
\(562\) | − | 5.19176i | − | 0.219001i | ||||||
\(563\) | 32.6960 | 1.37797 | 0.688987 | − | 0.724774i | \(-0.258056\pi\) | ||||
0.688987 | + | 0.724774i | \(0.258056\pi\) | |||||||
\(564\) | −17.6245 | + | 6.47199i | −0.742126 | + | 0.272520i | ||||
\(565\) | 9.34208 | 0.393024 | ||||||||
\(566\) | 6.60335 | 0.277560 | ||||||||
\(567\) | −33.7836 | − | 5.55893i | −1.41878 | − | 0.233453i | ||||
\(568\) | 9.92565 | 0.416471 | ||||||||
\(569\) | 0.358940 | 0.0150476 | 0.00752378 | − | 0.999972i | \(-0.497605\pi\) | ||||
0.00752378 | + | 0.999972i | \(0.497605\pi\) | |||||||
\(570\) | 1.12423 | + | 3.06151i | 0.0470890 | + | 0.128233i | ||||
\(571\) | − | 32.0526i | − | 1.34136i | −0.741747 | − | 0.670680i | \(-0.766002\pi\) | ||
0.741747 | − | 0.670680i | \(-0.233998\pi\) | |||||||
\(572\) | 11.1463 | 0.466049 | ||||||||
\(573\) | −13.4445 | − | 36.6120i | −0.561651 | − | 1.52949i | ||||
\(574\) | 15.1812i | 0.633649i | ||||||||
\(575\) | 0.785398 | − | 4.73108i | 0.0327533 | − | 0.197300i | ||||
\(576\) | 2.28706 | − | 1.94149i | 0.0952940 | − | 0.0808953i | ||||
\(577\) | 4.12555 | 0.171749 | 0.0858745 | − | 0.996306i | \(-0.472632\pi\) | ||||
0.0858745 | + | 0.996306i | \(0.472632\pi\) | |||||||
\(578\) | − | 5.66264i | − | 0.235535i | ||||||
\(579\) | −7.35005 | − | 20.0157i | −0.305458 | − | 0.831822i | ||||
\(580\) | 7.50582i | 0.311662i | ||||||||
\(581\) | 48.7273i | 2.02155i | ||||||||
\(582\) | −1.78014 | − | 4.84768i | −0.0737892 | − | 0.200943i | ||||
\(583\) | 24.6466 | 1.02076 | ||||||||
\(584\) | 3.18473i | 0.131785i | ||||||||
\(585\) | 7.31666 | − | 6.21113i | 0.302507 | − | 0.256799i | ||||
\(586\) | − | 30.6756i | − | 1.26720i | ||||||
\(587\) | − | 41.6293i | − | 1.71822i | −0.511787 | − | 0.859112i | \(-0.671016\pi\) | ||
0.511787 | − | 0.859112i | \(-0.328984\pi\) | |||||||
\(588\) | −4.46117 | − | 12.1487i | −0.183976 | − | 0.501002i | ||||
\(589\) | − | 7.00696i | − | 0.288717i | ||||||
\(590\) | 7.35646 | 0.302861 | ||||||||
\(591\) | −0.522157 | + | 0.191744i | −0.0214787 | + | 0.00788729i | ||||
\(592\) | 4.88527i | 0.200783i | ||||||||
\(593\) | 7.96907i | 0.327250i | 0.986523 | + | 0.163625i | \(0.0523188\pi\) | ||||
−0.986523 | + | 0.163625i | \(0.947681\pi\) | |||||||
\(594\) | −8.91707 | + | 15.7557i | −0.365872 | + | 0.646465i | ||||
\(595\) | − | 18.1100i | − | 0.742439i | ||||||
\(596\) | −7.01303 | −0.287265 | ||||||||
\(597\) | 23.8461 | − | 8.75663i | 0.975955 | − | 0.358385i | ||||
\(598\) | −15.1355 | − | 2.51261i | −0.618936 | − | 0.102748i | ||||
\(599\) | − | 18.0460i | − | 0.737338i | −0.929561 | − | 0.368669i | \(-0.879814\pi\) | ||
0.929561 | − | 0.368669i | \(-0.120186\pi\) | |||||||
\(600\) | 1.62589 | − | 0.597052i | 0.0663768 | − | 0.0243746i | ||||
\(601\) | −14.6307 | −0.596800 | −0.298400 | − | 0.954441i | \(-0.596453\pi\) | ||||
−0.298400 | + | 0.954441i | \(0.596453\pi\) | |||||||
\(602\) | 26.4820i | 1.07933i | ||||||||
\(603\) | 7.19204 | + | 8.47217i | 0.292882 | + | 0.345013i | ||||
\(604\) | 14.3153 | 0.582481 | ||||||||
\(605\) | −1.13914 | −0.0463127 | ||||||||
\(606\) | 5.46615 | + | 14.8854i | 0.222047 | + | 0.604679i | ||||
\(607\) | −6.64798 | −0.269833 | −0.134917 | − | 0.990857i | \(-0.543077\pi\) | ||||
−0.134917 | + | 0.990857i | \(0.543077\pi\) | |||||||
\(608\) | 1.88297 | 0.0763647 | ||||||||
\(609\) | −17.0481 | − | 46.4253i | −0.690822 | − | 1.88125i | ||||
\(610\) | −3.31936 | −0.134397 | ||||||||
\(611\) | 34.6786i | 1.40295i | ||||||||
\(612\) | −10.8876 | + | 9.24251i | −0.440105 | + | 0.373606i | ||||
\(613\) | − | 3.79751i | − | 0.153380i | −0.997055 | − | 0.0766899i | \(-0.975565\pi\) | ||
0.997055 | − | 0.0766899i | \(-0.0244351\pi\) | |||||||
\(614\) | − | 19.3975i | − | 0.782819i | ||||||
\(615\) | 6.48833 | − | 2.38261i | 0.261635 | − | 0.0960761i | ||||
\(616\) | −13.2543 | −0.534033 | ||||||||
\(617\) | 10.0968 | 0.406483 | 0.203242 | − | 0.979129i | \(-0.434852\pi\) | ||||
0.203242 | + | 0.979129i | \(0.434852\pi\) | |||||||
\(618\) | 9.58831 | + | 26.1109i | 0.385698 | + | 1.05033i | ||||
\(619\) | − | 19.8519i | − | 0.797917i | −0.916969 | − | 0.398959i | \(-0.869372\pi\) | ||
0.916969 | − | 0.398959i | \(-0.130628\pi\) | |||||||
\(620\) | −3.72122 | −0.149448 | ||||||||
\(621\) | 15.6601 | − | 19.3845i | 0.628420 | − | 0.777875i | ||||
\(622\) | 16.8790 | 0.676785 | ||||||||
\(623\) | 42.0402i | 1.68430i | ||||||||
\(624\) | −1.91007 | − | 5.20149i | −0.0764638 | − | 0.208226i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.7256 | 1.06817 | ||||||||
\(627\) | −10.6667 | + | 3.91697i | −0.425987 | + | 0.156429i | ||||
\(628\) | 16.3884i | 0.653970i | ||||||||
\(629\) | − | 23.2565i | − | 0.927296i | ||||||
\(630\) | −8.70044 | + | 7.38582i | −0.346634 | + | 0.294258i | ||||
\(631\) | − | 32.8990i | − | 1.30969i | −0.755764 | − | 0.654845i | \(-0.772734\pi\) | ||
0.755764 | − | 0.654845i | \(-0.227266\pi\) | |||||||
\(632\) | −10.1264 | −0.402805 | ||||||||
\(633\) | −7.39437 | − | 20.1363i | −0.293900 | − | 0.800348i | ||||
\(634\) | −7.55156 | −0.299911 | ||||||||
\(635\) | 15.6846 | 0.622425 | ||||||||
\(636\) | −4.22352 | − | 11.5015i | −0.167474 | − | 0.456064i | ||||
\(637\) | −23.9041 | −0.947115 | ||||||||
\(638\) | −26.1512 | −1.03534 | ||||||||
\(639\) | 19.2705 | + | 22.7005i | 0.762330 | + | 0.898019i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | −3.24280 | −0.128083 | −0.0640415 | − | 0.997947i | \(-0.520399\pi\) | ||||
−0.0640415 | + | 0.997947i | \(0.520399\pi\) | |||||||
\(642\) | −28.6474 | + | 10.5197i | −1.13062 | + | 0.415181i | ||||
\(643\) | − | 29.2876i | − | 1.15499i | −0.816395 | − | 0.577494i | \(-0.804031\pi\) | ||
0.816395 | − | 0.577494i | \(-0.195969\pi\) | |||||||
\(644\) | 17.9980 | + | 2.98781i | 0.709221 | + | 0.117736i | ||||
\(645\) | 11.3183 | − | 4.15623i | 0.445656 | − | 0.163651i | ||||
\(646\) | −8.96395 | −0.352682 | ||||||||
\(647\) | 1.01376i | 0.0398551i | 0.999801 | + | 0.0199276i | \(0.00634356\pi\) | ||||
−0.999801 | + | 0.0199276i | \(0.993656\pi\) | |||||||
\(648\) | 8.88058 | + | 1.46126i | 0.348862 | + | 0.0574037i | ||||
\(649\) | 25.6309i | 1.00610i | ||||||||
\(650\) | − | 3.19916i | − | 0.125481i | ||||||
\(651\) | 23.0166 | − | 8.45205i | 0.902093 | − | 0.331262i | ||||
\(652\) | −5.26525 | −0.206203 | ||||||||
\(653\) | − | 1.94489i | − | 0.0761093i | −0.999276 | − | 0.0380546i | \(-0.987884\pi\) | ||
0.999276 | − | 0.0380546i | \(-0.0121161\pi\) | |||||||
\(654\) | 7.60143 | + | 20.7002i | 0.297239 | + | 0.809442i | ||||
\(655\) | 10.5503i | 0.412236i | ||||||||
\(656\) | − | 3.99062i | − | 0.155808i | ||||||
\(657\) | −7.28365 | + | 6.18311i | −0.284162 | + | 0.241226i | ||||
\(658\) | − | 41.2372i | − | 1.60759i | ||||||
\(659\) | −40.4721 | −1.57657 | −0.788285 | − | 0.615310i | \(-0.789031\pi\) | ||||
−0.788285 | + | 0.615310i | \(0.789031\pi\) | |||||||
\(660\) | 2.08021 | + | 5.66482i | 0.0809719 | + | 0.220503i | ||||
\(661\) | − | 18.3138i | − | 0.712324i | −0.934424 | − | 0.356162i | \(-0.884085\pi\) | ||
0.934424 | − | 0.356162i | \(-0.115915\pi\) | |||||||
\(662\) | − | 25.3475i | − | 0.985159i | ||||||
\(663\) | 9.09293 | + | 24.7619i | 0.353140 | + | 0.961671i | ||||
\(664\) | − | 12.8088i | − | 0.497078i | ||||||
\(665\) | −7.16322 | −0.277778 | ||||||||
\(666\) | −11.1729 | + | 9.48469i | −0.432941 | + | 0.367524i | ||||
\(667\) | 35.5107 | + | 5.89505i | 1.37498 | + | 0.228257i | ||||
\(668\) | 7.87574i | 0.304722i | ||||||||
\(669\) | −3.09985 | − | 8.44152i | −0.119847 | − | 0.326368i | ||||
\(670\) | 3.70440 | 0.143113 | ||||||||
\(671\) | − | 11.5651i | − | 0.446464i | ||||||
\(672\) | 2.27131 | + | 6.18523i | 0.0876177 | + | 0.238601i | ||||
\(673\) | 31.8250 | 1.22676 | 0.613381 | − | 0.789787i | \(-0.289809\pi\) | ||||
0.613381 | + | 0.789787i | \(0.289809\pi\) | |||||||
\(674\) | 21.0505 | 0.810834 | ||||||||
\(675\) | 4.52214 | + | 2.55934i | 0.174057 | + | 0.0985091i | ||||
\(676\) | 2.76537 | 0.106360 | ||||||||
\(677\) | 18.5947 | 0.714654 | 0.357327 | − | 0.933979i | \(-0.383688\pi\) | ||||
0.357327 | + | 0.933979i | \(0.383688\pi\) | |||||||
\(678\) | 15.1892 | − | 5.57771i | 0.583339 | − | 0.214211i | ||||
\(679\) | 11.3424 | 0.435282 | ||||||||
\(680\) | 4.76053i | 0.182558i | ||||||||
\(681\) | −9.98859 | − | 27.2009i | −0.382763 | − | 1.04234i | ||||
\(682\) | − | 12.9652i | − | 0.496464i | ||||||
\(683\) | − | 12.1437i | − | 0.464667i | −0.972636 | − | 0.232334i | \(-0.925364\pi\) | ||
0.972636 | − | 0.232334i | \(-0.0746361\pi\) | |||||||
\(684\) | 3.65577 | + | 4.30647i | 0.139782 | + | 0.164662i | ||||
\(685\) | 16.2614 | 0.621316 | ||||||||
\(686\) | 1.79555 | 0.0685544 | ||||||||
\(687\) | −29.7514 | + | 10.9251i | −1.13509 | + | 0.416820i | ||||
\(688\) | − | 6.96125i | − | 0.265395i | ||||||
\(689\) | −22.6307 | −0.862162 | ||||||||
\(690\) | −1.54773 | − | 8.16116i | −0.0589212 | − | 0.310690i | ||||
\(691\) | −33.6060 | −1.27843 | −0.639217 | − | 0.769027i | \(-0.720741\pi\) | ||||
−0.639217 | + | 0.769027i | \(0.720741\pi\) | |||||||
\(692\) | − | 2.12595i | − | 0.0808165i | ||||||
\(693\) | −25.7331 | − | 30.3134i | −0.977521 | − | 1.15151i | ||||
\(694\) | −6.08253 | −0.230890 | ||||||||
\(695\) | 23.3435 | 0.885469 | ||||||||
\(696\) | 4.48137 | + | 12.2037i | 0.169866 | + | 0.462579i | ||||
\(697\) | 18.9975i | 0.719581i | ||||||||
\(698\) | − | 1.98670i | − | 0.0751975i | ||||||
\(699\) | −11.2555 | + | 4.13319i | −0.425723 | + | 0.156332i | ||||
\(700\) | 3.80421i | 0.143786i | ||||||||
\(701\) | −36.0032 | −1.35982 | −0.679911 | − | 0.733295i | \(-0.737982\pi\) | ||||
−0.679911 | + | 0.733295i | \(0.737982\pi\) | |||||||
\(702\) | 8.18774 | − | 14.4671i | 0.309026 | − | 0.546024i | ||||
\(703\) | −9.19883 | −0.346941 | ||||||||
\(704\) | 3.48413 | 0.131313 | ||||||||
\(705\) | −17.6245 | + | 6.47199i | −0.663778 | + | 0.243749i | ||||
\(706\) | −8.53950 | −0.321388 | ||||||||
\(707\) | −34.8284 | −1.30986 | ||||||||
\(708\) | 11.9608 | − | 4.39219i | 0.449515 | − | 0.165069i | ||||
\(709\) | 37.0502i | 1.39145i | 0.718308 | + | 0.695725i | \(0.244917\pi\) | ||||
−0.718308 | + | 0.695725i | \(0.755083\pi\) | |||||||
\(710\) | 9.92565 | 0.372503 | ||||||||
\(711\) | −19.6602 | − | 23.1596i | −0.737316 | − | 0.868552i | ||||
\(712\) | − | 11.0510i | − | 0.414153i | ||||||
\(713\) | −2.92264 | + | 17.6054i | −0.109454 | + | 0.659328i | ||||
\(714\) | −10.8126 | − | 29.4450i | −0.404653 | − | 1.10195i | ||||
\(715\) | 11.1463 | 0.416847 | ||||||||
\(716\) | − | 12.4614i | − | 0.465704i | ||||||
\(717\) | −3.41511 | + | 1.25408i | −0.127540 | + | 0.0468345i | ||||
\(718\) | 27.5129i | 1.02677i | ||||||||
\(719\) | − | 22.1798i | − | 0.827167i | −0.910466 | − | 0.413583i | \(-0.864277\pi\) | ||
0.910466 | − | 0.413583i | \(-0.135723\pi\) | |||||||
\(720\) | 2.28706 | − | 1.94149i | 0.0852336 | − | 0.0723549i | ||||
\(721\) | −61.0933 | −2.27523 | ||||||||
\(722\) | − | 15.4544i | − | 0.575154i | ||||||
\(723\) | 0.0419757 | − | 0.0154141i | 0.00156109 | − | 0.000573257i | ||||
\(724\) | 10.2922i | 0.382506i | ||||||||
\(725\) | 7.50582i | 0.278759i | ||||||||
\(726\) | −1.85212 | + | 0.680127i | −0.0687387 | + | 0.0252419i | ||||
\(727\) | − | 25.7337i | − | 0.954410i | −0.878792 | − | 0.477205i | \(-0.841650\pi\) | ||
0.878792 | − | 0.477205i | \(-0.158350\pi\) | |||||||
\(728\) | 12.1703 | 0.451060 | ||||||||
\(729\) | 13.8995 | + | 23.1474i | 0.514798 | + | 0.857311i | ||||
\(730\) | 3.18473i | 0.117872i | ||||||||
\(731\) | 33.1392i | 1.22570i | ||||||||
\(732\) | −5.39692 | + | 1.98183i | −0.199476 | + | 0.0732505i | ||||
\(733\) | − | 29.9581i | − | 1.10653i | −0.833006 | − | 0.553264i | \(-0.813382\pi\) | ||
0.833006 | − | 0.553264i | \(-0.186618\pi\) | |||||||
\(734\) | −31.2664 | −1.15406 | ||||||||
\(735\) | −4.46117 | − | 12.1487i | −0.164553 | − | 0.448110i | ||||
\(736\) | −4.73108 | − | 0.785398i | −0.174390 | − | 0.0289501i | ||||
\(737\) | 12.9066i | 0.475420i | ||||||||
\(738\) | 9.12678 | − | 7.74774i | 0.335961 | − | 0.285198i | ||||
\(739\) | −5.95900 | −0.219206 | −0.109603 | − | 0.993975i | \(-0.534958\pi\) | ||||
−0.109603 | + | 0.993975i | \(0.534958\pi\) | |||||||
\(740\) | 4.88527i | 0.179586i | ||||||||
\(741\) | 9.79427 | − | 3.59660i | 0.359802 | − | 0.132125i | ||||
\(742\) | 26.9108 | 0.987926 | ||||||||
\(743\) | 20.9476 | 0.768494 | 0.384247 | − | 0.923230i | \(-0.374461\pi\) | ||||
0.384247 | + | 0.923230i | \(0.374461\pi\) | |||||||
\(744\) | −6.05031 | + | 2.22176i | −0.221815 | + | 0.0814539i | ||||
\(745\) | −7.01303 | −0.256937 | ||||||||
\(746\) | 13.5799 | 0.497194 | ||||||||
\(747\) | 29.2944 | − | 24.8681i | 1.07183 | − | 0.909877i | ||||
\(748\) | −16.5863 | −0.606455 | ||||||||
\(749\) | − | 67.0281i | − | 2.44915i | ||||||
\(750\) | 1.62589 | − | 0.597052i | 0.0593692 | − | 0.0218013i | ||||
\(751\) | 30.8923i | 1.12727i | 0.826022 | + | 0.563637i | \(0.190598\pi\) | ||||
−0.826022 | + | 0.563637i | \(0.809402\pi\) | |||||||
\(752\) | 10.8399i | 0.395291i | ||||||||
\(753\) | −4.24940 | − | 11.5720i | −0.154857 | − | 0.421706i | ||||
\(754\) | 24.0123 | 0.874477 | ||||||||
\(755\) | 14.3153 | 0.520987 | ||||||||
\(756\) | −9.73626 | + | 17.2032i | −0.354104 | + | 0.625673i | ||||
\(757\) | 15.9263i | 0.578851i | 0.957200 | + | 0.289426i | \(0.0934643\pi\) | ||||
−0.957200 | + | 0.289426i | \(0.906536\pi\) | |||||||
\(758\) | 31.3374 | 1.13823 | ||||||||
\(759\) | 28.4345 | − | 5.39250i | 1.03211 | − | 0.195735i | ||||
\(760\) | 1.88297 | 0.0683026 | ||||||||
\(761\) | 23.2817i | 0.843960i | 0.906605 | + | 0.421980i | \(0.138665\pi\) | ||||
−0.906605 | + | 0.421980i | \(0.861335\pi\) | |||||||
\(762\) | 25.5015 | − | 9.36454i | 0.923822 | − | 0.339241i | ||||
\(763\) | −48.4336 | −1.75341 | ||||||||
\(764\) | −22.5181 | −0.814676 | ||||||||
\(765\) | −10.8876 | + | 9.24251i | −0.393642 | + | 0.334163i | ||||
\(766\) | 11.1675i | 0.403498i | ||||||||
\(767\) | − | 23.5345i | − | 0.849782i | ||||||
\(768\) | −0.597052 | − | 1.62589i | −0.0215443 | − | 0.0586694i | ||||
\(769\) | 33.0800i | 1.19289i | 0.802653 | + | 0.596447i | \(0.203421\pi\) | ||||
−0.802653 | + | 0.596447i | \(0.796579\pi\) | |||||||
\(770\) | −13.2543 | −0.477653 | ||||||||
\(771\) | −8.57931 | + | 3.15045i | −0.308976 | + | 0.113461i | ||||
\(772\) | −12.3106 | −0.443067 | ||||||||
\(773\) | 37.7407 | 1.35744 | 0.678720 | − | 0.734397i | \(-0.262535\pi\) | ||||
0.678720 | + | 0.734397i | \(0.262535\pi\) | |||||||
\(774\) | 15.9208 | − | 13.5152i | 0.572261 | − | 0.485793i | ||||
\(775\) | −3.72122 | −0.133670 | ||||||||
\(776\) | −2.98155 | −0.107031 | ||||||||
\(777\) | −11.0960 | − | 30.2165i | −0.398066 | − | 1.08401i | ||||
\(778\) | 12.5852i | 0.451200i | ||||||||
\(779\) | 7.51424 | 0.269225 | ||||||||
\(780\) | −1.91007 | − | 5.20149i | −0.0683913 | − | 0.186243i | ||||
\(781\) | 34.5822i | 1.23745i | ||||||||
\(782\) | 22.5225 | + | 3.73891i | 0.805402 | + | 0.133703i | ||||
\(783\) | −19.2100 | + | 33.9424i | −0.686508 | + | 1.21300i | ||||
\(784\) | −7.47199 | −0.266857 | ||||||||
\(785\) | 16.3884i | 0.584928i | ||||||||
\(786\) | 6.29910 | + | 17.1537i | 0.224682 | + | 0.611853i | ||||
\(787\) | − | 10.3941i | − | 0.370508i | −0.982691 | − | 0.185254i | \(-0.940689\pi\) | ||
0.982691 | − | 0.185254i | \(-0.0593108\pi\) | |||||||
\(788\) | 0.321151i | 0.0114405i | ||||||||
\(789\) | −8.15240 | − | 22.2006i | −0.290233 | − | 0.790363i | ||||
\(790\) | −10.1264 | −0.360280 | ||||||||
\(791\) | 35.5392i | 1.26363i | ||||||||
\(792\) | 6.76439 | + | 7.96840i | 0.240362 | + | 0.283145i | ||||
\(793\) | 10.6192i | 0.377097i | ||||||||
\(794\) | − | 12.3539i | − | 0.438423i | ||||||
\(795\) | −4.22352 | − | 11.5015i | −0.149793 | − | 0.407916i | ||||
\(796\) | − | 14.6664i | − | 0.519838i | ||||||
\(797\) | 18.4049 | 0.651934 | 0.325967 | − | 0.945381i | \(-0.394310\pi\) | ||||
0.325967 | + | 0.945381i | \(0.394310\pi\) | |||||||
\(798\) | −11.6466 | + | 4.27682i | −0.412286 | + | 0.151398i | ||||
\(799\) | − | 51.6037i | − | 1.82561i | ||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 25.2742 | − | 21.4553i | 0.893020 | − | 0.758086i | ||||
\(802\) | − | 27.2453i | − | 0.962065i | ||||||
\(803\) | −11.0960 | −0.391569 | ||||||||
\(804\) | 6.02295 | − | 2.21172i | 0.212413 | − | 0.0780013i | ||||
\(805\) | 17.9980 | + | 2.98781i | 0.634347 | + | 0.105307i | ||||
\(806\) | 11.9048i | 0.419328i | ||||||||
\(807\) | 24.2466 | − | 8.90372i | 0.853521 | − | 0.313426i | ||||
\(808\) | 9.15523 | 0.322080 | ||||||||
\(809\) | 38.2278i | 1.34402i | 0.740543 | + | 0.672009i | \(0.234569\pi\) | ||||
−0.740543 | + | 0.672009i | \(0.765431\pi\) | |||||||
\(810\) | 8.88058 | + | 1.46126i | 0.312032 | + | 0.0513434i | ||||
\(811\) | −34.0643 | −1.19616 | −0.598080 | − | 0.801436i | \(-0.704070\pi\) | ||||
−0.598080 | + | 0.801436i | \(0.704070\pi\) | |||||||
\(812\) | −28.5537 | −1.00204 | ||||||||
\(813\) | 13.4178 | + | 36.5393i | 0.470582 | + | 1.28149i | ||||
\(814\) | −17.0209 | −0.596582 | ||||||||
\(815\) | −5.26525 | −0.184434 | ||||||||
\(816\) | 2.84229 | + | 7.74011i | 0.0994999 | + | 0.270958i | ||||
\(817\) | 13.1079 | 0.458586 | ||||||||
\(818\) | 27.3294i | 0.955549i | ||||||||
\(819\) | 23.6284 | + | 27.8341i | 0.825644 | + | 0.972602i | ||||
\(820\) | − | 3.99062i | − | 0.139359i | ||||||
\(821\) | − | 10.8083i | − | 0.377212i | −0.982053 | − | 0.188606i | \(-0.939603\pi\) | ||
0.982053 | − | 0.188606i | \(-0.0603969\pi\) | |||||||
\(822\) | 26.4393 | − | 9.70890i | 0.922176 | − | 0.338637i | ||||
\(823\) | 52.1001 | 1.81610 | 0.908048 | − | 0.418865i | \(-0.137572\pi\) | ||||
0.908048 | + | 0.418865i | \(0.137572\pi\) | |||||||
\(824\) | 16.0594 | 0.559456 | ||||||||
\(825\) | 2.08021 | + | 5.66482i | 0.0724235 | + | 0.197224i | ||||
\(826\) | 27.9855i | 0.973740i | ||||||||
\(827\) | −56.5967 | −1.96806 | −0.984030 | − | 0.178005i | \(-0.943036\pi\) | ||||
−0.984030 | + | 0.178005i | \(0.943036\pi\) | |||||||
\(828\) | −7.38909 | − | 12.3451i | −0.256789 | − | 0.429022i | ||||
\(829\) | 32.2985 | 1.12177 | 0.560887 | − | 0.827892i | \(-0.310460\pi\) | ||||
0.560887 | + | 0.827892i | \(0.310460\pi\) | |||||||
\(830\) | − | 12.8088i | − | 0.444600i | ||||||
\(831\) | 15.3992 | + | 41.9351i | 0.534192 | + | 1.45471i | ||||
\(832\) | −3.19916 | −0.110911 | ||||||||
\(833\) | 35.5706 | 1.23245 | ||||||||
\(834\) | 37.9540 | − | 13.9373i | 1.31424 | − | 0.482608i | ||||
\(835\) | 7.87574i | 0.272551i | ||||||||
\(836\) | 6.56052i | 0.226900i | ||||||||
\(837\) | −16.8279 | − | 9.52388i | −0.581657 | − | 0.329193i | ||||
\(838\) | − | 15.1668i | − | 0.523930i | ||||||
\(839\) | −28.9576 | −0.999728 | −0.499864 | − | 0.866104i | \(-0.666617\pi\) | ||||
−0.499864 | + | 0.866104i | \(0.666617\pi\) | |||||||
\(840\) | 2.27131 | + | 6.18523i | 0.0783677 | + | 0.213411i | ||||
\(841\) | −27.3373 | −0.942667 | ||||||||
\(842\) | 34.7728 | 1.19835 | ||||||||
\(843\) | −3.09975 | − | 8.44124i | −0.106761 | − | 0.290732i | ||||
\(844\) | −12.3848 | −0.426302 | ||||||||
\(845\) | 2.76537 | 0.0951317 | ||||||||
\(846\) | −24.7915 | + | 21.0455i | −0.852349 | + | 0.723560i | ||||
\(847\) | − | 4.33353i | − | 0.148902i | ||||||
\(848\) | −7.07396 | −0.242921 | ||||||||
\(849\) | 10.7363 | − | 3.94255i | 0.368470 | − | 0.135308i | ||||
\(850\) | 4.76053i | 0.163285i | ||||||||
\(851\) | 23.1126 | + | 3.83688i | 0.792290 | + | 0.131527i | ||||
\(852\) | 16.1380 | − | 5.92613i | 0.552880 | − | 0.203026i | ||||
\(853\) | 7.15727 | 0.245060 | 0.122530 | − | 0.992465i | \(-0.460899\pi\) | ||||
0.122530 | + | 0.992465i | \(0.460899\pi\) | |||||||
\(854\) | − | 12.6275i | − | 0.432105i | ||||||
\(855\) | 3.65577 | + | 4.30647i | 0.125025 | + | 0.147278i | ||||
\(856\) | 17.6195i | 0.602221i | ||||||||
\(857\) | − | 48.9333i | − | 1.67153i | −0.549089 | − | 0.835764i | \(-0.685025\pi\) | ||
0.549089 | − | 0.835764i | \(-0.314975\pi\) | |||||||
\(858\) | 18.1227 | − | 6.65491i | 0.618697 | − | 0.227195i | ||||
\(859\) | 25.7121 | 0.877286 | 0.438643 | − | 0.898661i | \(-0.355459\pi\) | ||||
0.438643 | + | 0.898661i | \(0.355459\pi\) | |||||||
\(860\) | − | 6.96125i | − | 0.237377i | ||||||
\(861\) | 9.06394 | + | 24.6829i | 0.308898 | + | 0.841192i | ||||
\(862\) | 5.86936i | 0.199911i | ||||||||
\(863\) | − | 11.0725i | − | 0.376912i | −0.982082 | − | 0.188456i | \(-0.939652\pi\) | ||
0.982082 | − | 0.188456i | \(-0.0603483\pi\) | |||||||
\(864\) | 2.55934 | − | 4.52214i | 0.0870705 | − | 0.153846i | ||||
\(865\) | − | 2.12595i | − | 0.0722845i | ||||||
\(866\) | −30.4782 | −1.03569 | ||||||||
\(867\) | −3.38089 | − | 9.20685i | −0.114821 | − | 0.312681i | ||||
\(868\) | − | 14.1563i | − | 0.480496i | ||||||
\(869\) | − | 35.2816i | − | 1.19685i | ||||||
\(870\) | 4.48137 | + | 12.2037i | 0.151933 | + | 0.413743i | ||||
\(871\) | − | 11.8510i | − | 0.401554i | ||||||
\(872\) | 12.7316 | 0.431146 | ||||||||
\(873\) | −5.78864 | − | 6.81897i | −0.195916 | − | 0.230787i | ||||
\(874\) | 1.47888 | − | 8.90850i | 0.0500240 | − | 0.301335i | ||||
\(875\) | 3.80421i | 0.128606i | ||||||||
\(876\) | 1.90145 | + | 5.17803i | 0.0642440 | + | 0.174949i | ||||
\(877\) | 34.2809 | 1.15758 | 0.578791 | − | 0.815476i | \(-0.303525\pi\) | ||||
0.578791 | + | 0.815476i | \(0.303525\pi\) | |||||||
\(878\) | − | 20.8965i | − | 0.705222i | ||||||
\(879\) | −18.3150 | − | 49.8753i | −0.617748 | − | 1.68225i | ||||
\(880\) | 3.48413 | 0.117450 | ||||||||
\(881\) | 21.4410 | 0.722367 | 0.361183 | − | 0.932495i | \(-0.382373\pi\) | ||||
0.361183 | + | 0.932495i | \(0.382373\pi\) | |||||||
\(882\) | −14.5068 | − | 17.0889i | −0.488468 | − | 0.575412i | ||||
\(883\) | 14.2372 | 0.479119 | 0.239560 | − | 0.970882i | \(-0.422997\pi\) | ||||
0.239560 | + | 0.970882i | \(0.422997\pi\) | |||||||
\(884\) | 15.2297 | 0.512230 | ||||||||
\(885\) | 11.9608 | − | 4.39219i | 0.402059 | − | 0.147642i | ||||
\(886\) | −38.9828 | −1.30965 | ||||||||
\(887\) | − | 54.3381i | − | 1.82449i | −0.409640 | − | 0.912247i | \(-0.634346\pi\) | ||
0.409640 | − | 0.912247i | \(-0.365654\pi\) | |||||||
\(888\) | 2.91676 | + | 7.94293i | 0.0978801 | + | 0.266547i | ||||
\(889\) | 59.6675i | 2.00118i | ||||||||
\(890\) | − | 11.0510i | − | 0.370429i | ||||||
\(891\) | −5.09121 | + | 30.9411i | −0.170562 | + | 1.03656i | ||||
\(892\) | −5.19193 | −0.173839 | ||||||||
\(893\) | −20.4113 | −0.683037 | ||||||||
\(894\) | −11.4024 | + | 4.18714i | −0.381354 | + | 0.140039i | ||||
\(895\) | − | 12.4614i | − | 0.416539i | ||||||
\(896\) | 3.80421 | 0.127090 | ||||||||
\(897\) | −26.1089 | + | 4.95144i | −0.871749 | + | 0.165324i | ||||
\(898\) | 8.98085 | 0.299695 | ||||||||
\(899\) | − | 27.9308i | − | 0.931545i | ||||||
\(900\) | 2.28706 | − | 1.94149i | 0.0762352 | − | 0.0647162i | ||||
\(901\) | 33.6758 | 1.12190 | ||||||||
\(902\) | 13.9038 | 0.462947 | ||||||||
\(903\) | 15.8112 | + | 43.0570i | 0.526163 | + | 1.43285i | ||||
\(904\) | − | 9.34208i | − | 0.310713i | ||||||
\(905\) | 10.2922i | 0.342124i | ||||||||
\(906\) | 23.2752 | − | 8.54699i | 0.773265 | − | 0.283955i | ||||
\(907\) | 23.3635i | 0.775772i | 0.921707 | + | 0.387886i | \(0.126794\pi\) | ||||
−0.921707 | + | 0.387886i | \(0.873206\pi\) | |||||||
\(908\) | −16.7298 | −0.555199 | ||||||||
\(909\) | 17.7748 | + | 20.9385i | 0.589551 | + | 0.694487i | ||||
\(910\) | 12.1703 | 0.403440 | ||||||||
\(911\) | −54.0556 | −1.79094 | −0.895471 | − | 0.445119i | \(-0.853161\pi\) | ||||
−0.895471 | + | 0.445119i | \(0.853161\pi\) | |||||||
\(912\) | 3.06151 | − | 1.12423i | 0.101377 | − | 0.0372271i | ||||
\(913\) | 44.6275 | 1.47695 | ||||||||
\(914\) | 5.68472 | 0.188034 | ||||||||
\(915\) | −5.39692 | + | 1.98183i | −0.178417 | + | 0.0655173i | ||||
\(916\) | 18.2985i | 0.604599i | ||||||||
\(917\) | −40.1357 | −1.32540 | ||||||||
\(918\) | −12.1838 | + | 21.5278i | −0.402126 | + | 0.710523i | ||||
\(919\) | 26.4439i | 0.872303i | 0.899873 | + | 0.436152i | \(0.143659\pi\) | ||||
−0.899873 | + | 0.436152i | \(0.856341\pi\) | |||||||
\(920\) | −4.73108 | − | 0.785398i | −0.155979 | − | 0.0258938i | ||||
\(921\) | −11.5813 | − | 31.5382i | −0.381617 | − | 1.03922i | ||||
\(922\) | −23.4737 | −0.773066 | ||||||||
\(923\) | − | 31.7537i | − | 1.04519i | ||||||
\(924\) | −21.5501 | + | 7.91354i | −0.708948 | + | 0.260336i | ||||
\(925\) | 4.88527i | 0.160627i | ||||||||
\(926\) | 41.4142i | 1.36095i | ||||||||
\(927\) | 31.1791 | + | 36.7288i | 1.02406 | + | 1.20633i | ||||
\(928\) | 7.50582 | 0.246391 | ||||||||
\(929\) | 0.525207i | 0.0172315i | 0.999963 | + | 0.00861575i | \(0.00274251\pi\) | ||||
−0.999963 | + | 0.00861575i | \(0.997257\pi\) | |||||||
\(930\) | −6.05031 | + | 2.22176i | −0.198397 | + | 0.0728545i | ||||
\(931\) | − | 14.0696i | − | 0.461111i | ||||||
\(932\) | 6.92267i | 0.226759i | ||||||||
\(933\) | 27.4434 | − | 10.0776i | 0.898456 | − | 0.329927i | ||||
\(934\) | − | 28.5266i | − | 0.933420i | ||||||
\(935\) | −16.5863 | −0.542430 | ||||||||
\(936\) | −6.21113 | − | 7.31666i | −0.203017 | − | 0.239153i | ||||
\(937\) | 22.6417i | 0.739673i | 0.929097 | + | 0.369836i | \(0.120586\pi\) | ||||
−0.929097 | + | 0.369836i | \(0.879414\pi\) | |||||||
\(938\) | 14.0923i | 0.460130i | ||||||||
\(939\) | 43.4530 | − | 15.9566i | 1.41803 | − | 0.520724i | ||||
\(940\) | 10.8399i | 0.353559i | ||||||||
\(941\) | 22.1089 | 0.720731 | 0.360366 | − | 0.932811i | \(-0.382652\pi\) | ||||
0.360366 | + | 0.932811i | \(0.382652\pi\) | |||||||
\(942\) | 9.78475 | + | 26.6458i | 0.318804 | + | 0.868168i | ||||
\(943\) | −18.8800 | − | 3.13423i | −0.614816 | − | 0.102064i | ||||
\(944\) | − | 7.35646i | − | 0.239432i | ||||||
\(945\) | −9.73626 | + | 17.2032i | −0.316721 | + | 0.559619i | ||||
\(946\) | 24.2539 | 0.788562 | ||||||||
\(947\) | 37.4498i | 1.21696i | 0.793571 | + | 0.608478i | \(0.208220\pi\) | ||||
−0.793571 | + | 0.608478i | \(0.791780\pi\) | |||||||
\(948\) | −16.4644 | + | 6.04597i | −0.534739 | + | 0.196364i | ||||
\(949\) | 10.1885 | 0.330731 | ||||||||
\(950\) | 1.88297 | 0.0610917 | ||||||||
\(951\) | −12.2780 | + | 4.50868i | −0.398142 | + | 0.146204i | ||||
\(952\) | −18.1100 | −0.586950 | ||||||||
\(953\) | 39.1208 | 1.26725 | 0.633624 | − | 0.773641i | \(-0.281567\pi\) | ||||
0.633624 | + | 0.773641i | \(0.281567\pi\) | |||||||
\(954\) | −13.7340 | − | 16.1785i | −0.444654 | − | 0.523800i | ||||
\(955\) | −22.5181 | −0.728668 | ||||||||
\(956\) | 2.10045i | 0.0679335i | ||||||||
\(957\) | −42.5191 | + | 15.6137i | −1.37445 | + | 0.504718i | ||||
\(958\) | − | 3.94290i | − | 0.127389i | ||||||
\(959\) | 61.8617i | 1.99762i | ||||||||
\(960\) | −0.597052 | − | 1.62589i | −0.0192698 | − | 0.0524755i | ||||
\(961\) | −17.1525 | −0.553307 | ||||||||
\(962\) | 15.6288 | 0.503892 | ||||||||
\(963\) | −40.2967 | + | 34.2080i | −1.29854 | + | 1.10234i | ||||
\(964\) | − | 0.0258170i | − | 0.000831511i | ||||||
\(965\) | −12.3106 | −0.396291 | ||||||||
\(966\) | 31.0467 | − | 5.88789i | 0.998912 | − | 0.189440i | ||||
\(967\) | −37.1788 | −1.19559 | −0.597795 | − | 0.801649i | \(-0.703956\pi\) | ||||
−0.597795 | + | 0.801649i | \(0.703956\pi\) | |||||||
\(968\) | 1.13914i | 0.0366134i | ||||||||
\(969\) | −14.5744 | + | 5.35195i | −0.468198 | + | 0.171929i | ||||
\(970\) | −2.98155 | −0.0957317 | ||||||||
\(971\) | −27.4914 | −0.882240 | −0.441120 | − | 0.897448i | \(-0.645419\pi\) | ||||
−0.441120 | + | 0.897448i | \(0.645419\pi\) | |||||||
\(972\) | 15.3113 | − | 2.92632i | 0.491111 | − | 0.0938618i | ||||
\(973\) | 88.8034i | 2.84691i | ||||||||
\(974\) | − | 1.02454i | − | 0.0328283i | ||||||
\(975\) | −1.91007 | − | 5.20149i | −0.0611711 | − | 0.166581i | ||||
\(976\) | 3.31936i | 0.106250i | ||||||||
\(977\) | −41.7887 | −1.33694 | −0.668469 | − | 0.743740i | \(-0.733050\pi\) | ||||
−0.668469 | + | 0.743740i | \(0.733050\pi\) | |||||||
\(978\) | −8.56074 | + | 3.14363i | −0.273742 | + | 0.100522i | ||||
\(979\) | 38.5030 | 1.23056 | ||||||||
\(980\) | −7.47199 | −0.238684 | ||||||||
\(981\) | 24.7182 | + | 29.1179i | 0.789192 | + | 0.929662i | ||||
\(982\) | 12.3413 | 0.393826 | ||||||||
\(983\) | −58.4135 | −1.86310 | −0.931550 | − | 0.363612i | \(-0.881543\pi\) | ||||
−0.931550 | + | 0.363612i | \(0.881543\pi\) | |||||||
\(984\) | −2.38261 | − | 6.48833i | −0.0759549 | − | 0.206840i | ||||
\(985\) | 0.321151i | 0.0102327i | ||||||||
\(986\) | −35.7317 | −1.13793 | ||||||||
\(987\) | −24.6208 | − | 67.0473i | −0.783688 | − | 2.13414i | ||||
\(988\) | − | 6.02393i | − | 0.191647i | ||||||
\(989\) | −32.9343 | − | 5.46735i | −1.04725 | − | 0.173852i | ||||
\(990\) | 6.76439 | + | 7.96840i | 0.214986 | + | 0.253252i | ||||
\(991\) | 55.2646 | 1.75554 | 0.877768 | − | 0.479085i | \(-0.159031\pi\) | ||||
0.877768 | + | 0.479085i | \(0.159031\pi\) | |||||||
\(992\) | 3.72122i | 0.118149i | ||||||||
\(993\) | −15.1338 | − | 41.2124i | −0.480257 | − | 1.30783i | ||||
\(994\) | 37.7592i | 1.19765i | ||||||||
\(995\) | − | 14.6664i | − | 0.464958i | ||||||
\(996\) | −7.64752 | − | 20.8257i | −0.242321 | − | 0.659889i | ||||
\(997\) | −45.4910 | −1.44071 | −0.720357 | − | 0.693604i | \(-0.756022\pi\) | ||||
−0.720357 | + | 0.693604i | \(0.756022\pi\) | |||||||
\(998\) | 29.3987i | 0.930599i | ||||||||
\(999\) | −12.5031 | + | 22.0919i | −0.395580 | + | 0.698956i |
(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 | 690.2.e.a.551.4 | ✓ | 16 | |
3.2 | odd | 2 | 690.2.e.b.551.12 | yes | 16 | ||
23.22 | odd | 2 | 690.2.e.b.551.4 | yes | 16 | ||
69.68 | even | 2 | inner | 690.2.e.a.551.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.e.a.551.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
690.2.e.a.551.12 | yes | 16 | 69.68 | even | 2 | inner | |
690.2.e.b.551.4 | yes | 16 | 23.22 | odd | 2 | ||
690.2.e.b.551.12 | yes | 16 | 3.2 | odd | 2 |