Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,3,Mod(5,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.30790526893\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(-1.38255 + 0.297594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.5 |
Dual form | 48.3.i.a.29.1 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.68014 | − | 1.08495i | −0.840071 | − | 0.542477i | ||||
\(3\) | 2.90783 | − | 0.737922i | 0.969276 | − | 0.245974i | ||||
\(4\) | 1.64575 | + | 3.64575i | 0.411438 | + | 0.911438i | ||||
\(5\) | 1.57472 | − | 1.57472i | 0.314944 | − | 0.314944i | −0.531877 | − | 0.846821i | \(-0.678513\pi\) |
0.846821 | + | 0.531877i | \(0.178513\pi\) | |||||||
\(6\) | −5.68618 | − | 1.91505i | −0.947696 | − | 0.319174i | ||||
\(7\) | − | 3.64575i | − | 0.520822i | −0.965498 | − | 0.260411i | \(-0.916142\pi\) | ||
0.965498 | − | 0.260411i | \(-0.0838580\pi\) | |||||||
\(8\) | 1.19038 | − | 7.91094i | 0.148797 | − | 0.988868i | ||||
\(9\) | 7.91094 | − | 4.29150i | 0.878994 | − | 0.476834i | ||||
\(10\) | −4.35425 | + | 0.937254i | −0.435425 | + | 0.0937254i | ||||
\(11\) | 1.19038 | − | 1.19038i | 0.108216 | − | 0.108216i | −0.650926 | − | 0.759142i | \(-0.725619\pi\) |
0.759142 | + | 0.650926i | \(0.225619\pi\) | |||||||
\(12\) | 7.47584 | + | 9.38679i | 0.622987 | + | 0.782232i | ||||
\(13\) | −14.6458 | + | 14.6458i | −1.12660 | + | 1.12660i | −0.135870 | + | 0.990727i | \(0.543383\pi\) |
−0.990727 | + | 0.135870i | \(0.956617\pi\) | |||||||
\(14\) | −3.95547 | + | 6.12538i | −0.282534 | + | 0.437527i | ||||
\(15\) | 3.41699 | − | 5.74103i | 0.227800 | − | 0.382736i | ||||
\(16\) | −10.5830 | + | 12.0000i | −0.661438 | + | 0.750000i | ||||
\(17\) | 28.0726i | 1.65133i | 0.564159 | + | 0.825666i | \(0.309200\pi\) | ||||
−0.564159 | + | 0.825666i | \(0.690800\pi\) | |||||||
\(18\) | −17.9476 | − | 1.37267i | −0.997088 | − | 0.0762596i | ||||
\(19\) | 12.5830 | − | 12.5830i | 0.662263 | − | 0.662263i | −0.293650 | − | 0.955913i | \(-0.594870\pi\) |
0.955913 | + | 0.293650i | \(0.0948699\pi\) | |||||||
\(20\) | 8.33263 | + | 3.14944i | 0.416632 | + | 0.157472i | ||||
\(21\) | −2.69028 | − | 10.6012i | −0.128109 | − | 0.504820i | ||||
\(22\) | −3.29150 | + | 0.708497i | −0.149614 | + | 0.0322044i | ||||
\(23\) | −29.2630 | −1.27231 | −0.636153 | − | 0.771563i | \(-0.719475\pi\) | ||||
−0.636153 | + | 0.771563i | \(0.719475\pi\) | |||||||
\(24\) | −2.37625 | − | 23.8821i | −0.0990104 | − | 0.995086i | ||||
\(25\) | 20.0405i | 0.801621i | ||||||||
\(26\) | 40.4969 | − | 8.71697i | 1.55757 | − | 0.335268i | ||||
\(27\) | 19.8369 | − | 18.3166i | 0.734699 | − | 0.678393i | ||||
\(28\) | 13.2915 | − | 6.00000i | 0.474697 | − | 0.214286i | ||||
\(29\) | −19.3557 | − | 19.3557i | −0.667437 | − | 0.667437i | 0.289685 | − | 0.957122i | \(-0.406449\pi\) |
−0.957122 | + | 0.289685i | \(0.906449\pi\) | |||||||
\(30\) | −11.9698 | + | 5.93847i | −0.398993 | + | 0.197949i | ||||
\(31\) | 11.6458 | 0.375669 | 0.187835 | − | 0.982201i | \(-0.439853\pi\) | ||||
0.187835 | + | 0.982201i | \(0.439853\pi\) | |||||||
\(32\) | 30.8004 | − | 8.67963i | 0.962512 | − | 0.271238i | ||||
\(33\) | 2.58301 | − | 4.33981i | 0.0782729 | − | 0.131510i | ||||
\(34\) | 30.4575 | − | 47.1660i | 0.895809 | − | 1.38724i | ||||
\(35\) | −5.74103 | − | 5.74103i | −0.164030 | − | 0.164030i | ||||
\(36\) | 28.6652 | + | 21.7786i | 0.796255 | + | 0.604961i | ||||
\(37\) | 0.771243 | + | 0.771243i | 0.0208444 | + | 0.0208444i | 0.717452 | − | 0.696608i | \(-0.245308\pi\) |
−0.696608 | + | 0.717452i | \(0.745308\pi\) | |||||||
\(38\) | −34.7932 | + | 7.48925i | −0.915611 | + | 0.197086i | ||||
\(39\) | −31.7799 | + | 53.3948i | −0.814870 | + | 1.36910i | ||||
\(40\) | −10.5830 | − | 14.3320i | −0.264575 | − | 0.358301i | ||||
\(41\) | −25.6919 | −0.626631 | −0.313316 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313316 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(42\) | −6.98178 | + | 20.7304i | −0.166233 | + | 0.493581i | ||||
\(43\) | −40.5830 | − | 40.5830i | −0.943791 | − | 0.943791i | 0.0547114 | − | 0.998502i | \(-0.482576\pi\) |
−0.998502 | + | 0.0547114i | \(0.982576\pi\) | |||||||
\(44\) | 6.29888 | + | 2.38075i | 0.143156 | + | 0.0541080i | ||||
\(45\) | 5.69960 | − | 19.2154i | 0.126658 | − | 0.427009i | ||||
\(46\) | 49.1660 | + | 31.7490i | 1.06883 | + | 0.690196i | ||||
\(47\) | 50.2681i | 1.06953i | 0.845000 | + | 0.534767i | \(0.179601\pi\) | ||||
−0.845000 | + | 0.534767i | \(0.820399\pi\) | |||||||
\(48\) | −21.9185 | + | 42.7034i | −0.456636 | + | 0.889654i | ||||
\(49\) | 35.7085 | 0.728745 | ||||||||
\(50\) | 21.7430 | − | 33.6709i | 0.434861 | − | 0.673418i | ||||
\(51\) | 20.7154 | + | 81.6304i | 0.406185 | + | 1.60060i | ||||
\(52\) | −77.4980 | − | 29.2915i | −1.49035 | − | 0.563298i | ||||
\(53\) | 46.2379 | − | 46.2379i | 0.872414 | − | 0.872414i | −0.120321 | − | 0.992735i | \(-0.538392\pi\) |
0.992735 | + | 0.120321i | \(0.0383925\pi\) | |||||||
\(54\) | −53.2014 | + | 9.25242i | −0.985212 | + | 0.171341i | ||||
\(55\) | − | 3.74902i | − | 0.0681639i | ||||||
\(56\) | −28.8413 | − | 4.33981i | −0.515024 | − | 0.0774967i | ||||
\(57\) | 27.3040 | − | 45.8745i | 0.479017 | − | 0.804816i | ||||
\(58\) | 11.5203 | + | 53.5203i | 0.198625 | + | 0.922763i | ||||
\(59\) | 22.7533 | − | 22.7533i | 0.385649 | − | 0.385649i | −0.487483 | − | 0.873132i | \(-0.662085\pi\) |
0.873132 | + | 0.487483i | \(0.162085\pi\) | |||||||
\(60\) | 26.5539 | + | 3.00920i | 0.442565 | + | 0.0501533i | ||||
\(61\) | 12.7712 | − | 12.7712i | 0.209365 | − | 0.209365i | −0.594633 | − | 0.803997i | \(-0.702703\pi\) |
0.803997 | + | 0.594633i | \(0.202703\pi\) | |||||||
\(62\) | −19.5665 | − | 12.6351i | −0.315589 | − | 0.203792i | ||||
\(63\) | −15.6458 | − | 28.8413i | −0.248345 | − | 0.457799i | ||||
\(64\) | −61.1660 | − | 18.8340i | −0.955719 | − | 0.294281i | ||||
\(65\) | 46.1259i | 0.709629i | ||||||||
\(66\) | −9.04831 | + | 4.48906i | −0.137096 | + | 0.0680161i | ||||
\(67\) | 10.6863 | − | 10.6863i | 0.159497 | − | 0.159497i | −0.622847 | − | 0.782344i | \(-0.714024\pi\) |
0.782344 | + | 0.622847i | \(0.214024\pi\) | |||||||
\(68\) | −102.346 | + | 46.2006i | −1.50509 | + | 0.679420i | ||||
\(69\) | −85.0919 | + | 21.5938i | −1.23322 | + | 0.312954i | ||||
\(70\) | 3.41699 | + | 15.8745i | 0.0488142 | + | 0.226779i | ||||
\(71\) | 122.086 | 1.71952 | 0.859760 | − | 0.510699i | \(-0.170613\pi\) | ||||
0.859760 | + | 0.510699i | \(0.170613\pi\) | |||||||
\(72\) | −24.5328 | − | 67.6915i | −0.340734 | − | 0.940160i | ||||
\(73\) | − | 15.0405i | − | 0.206034i | −0.994680 | − | 0.103017i | \(-0.967150\pi\) | ||
0.994680 | − | 0.103017i | \(-0.0328497\pi\) | |||||||
\(74\) | −0.459035 | − | 2.13256i | −0.00620317 | − | 0.0288184i | ||||
\(75\) | 14.7883 | + | 58.2744i | 0.197178 | + | 0.776992i | ||||
\(76\) | 66.5830 | + | 25.1660i | 0.876092 | + | 0.331132i | ||||
\(77\) | −4.33981 | − | 4.33981i | −0.0563612 | − | 0.0563612i | ||||
\(78\) | 111.326 | − | 55.2310i | 1.42725 | − | 0.708090i | ||||
\(79\) | −51.3948 | −0.650567 | −0.325283 | − | 0.945617i | \(-0.605460\pi\) | ||||
−0.325283 | + | 0.945617i | \(0.605460\pi\) | |||||||
\(80\) | 2.23137 | + | 35.5619i | 0.0278921 | + | 0.444524i | ||||
\(81\) | 44.1660 | − | 67.8997i | 0.545259 | − | 0.838267i | ||||
\(82\) | 43.1660 | + | 27.8745i | 0.526415 | + | 0.339933i | ||||
\(83\) | −37.8680 | − | 37.8680i | −0.456240 | − | 0.456240i | 0.441179 | − | 0.897419i | \(-0.354560\pi\) |
−0.897419 | + | 0.441179i | \(0.854560\pi\) | |||||||
\(84\) | 34.2219 | − | 27.2551i | 0.407403 | − | 0.324465i | ||||
\(85\) | 44.2065 | + | 44.2065i | 0.520077 | + | 0.520077i | ||||
\(86\) | 24.1545 | + | 112.216i | 0.280866 | + | 1.30484i | ||||
\(87\) | −70.5659 | − | 42.0000i | −0.811103 | − | 0.482759i | ||||
\(88\) | −8.00000 | − | 10.8340i | −0.0909091 | − | 0.123114i | ||||
\(89\) | 5.45550 | 0.0612977 | 0.0306489 | − | 0.999530i | \(-0.490243\pi\) | ||||
0.0306489 | + | 0.999530i | \(0.490243\pi\) | |||||||
\(90\) | −30.4240 | + | 26.1008i | −0.338044 | + | 0.290009i | ||||
\(91\) | 53.3948 | + | 53.3948i | 0.586756 | + | 0.586756i | ||||
\(92\) | −48.1596 | − | 106.686i | −0.523474 | − | 1.15963i | ||||
\(93\) | 33.8639 | − | 8.59366i | 0.364127 | − | 0.0924049i | ||||
\(94\) | 54.5385 | − | 84.4575i | 0.580197 | − | 0.898484i | ||||
\(95\) | − | 39.6294i | − | 0.417152i | ||||||
\(96\) | 83.1574 | − | 47.9672i | 0.866223 | − | 0.499658i | ||||
\(97\) | −81.1660 | −0.836763 | −0.418381 | − | 0.908271i | \(-0.637402\pi\) | ||||
−0.418381 | + | 0.908271i | \(0.637402\pi\) | |||||||
\(98\) | −59.9953 | − | 38.7421i | −0.612197 | − | 0.395327i | ||||
\(99\) | 4.30849 | − | 14.5255i | 0.0435201 | − | 0.146722i | ||||
\(100\) | −73.0627 | + | 32.9817i | −0.730627 | + | 0.329817i | ||||
\(101\) | 32.4498 | − | 32.4498i | 0.321285 | − | 0.321285i | −0.527975 | − | 0.849260i | \(-0.677048\pi\) |
0.849260 | + | 0.527975i | \(0.177048\pi\) | |||||||
\(102\) | 53.7604 | − | 159.626i | 0.527063 | − | 1.56496i | ||||
\(103\) | − | 51.1882i | − | 0.496973i | −0.968635 | − | 0.248487i | \(-0.920067\pi\) | ||
0.968635 | − | 0.248487i | \(-0.0799332\pi\) | |||||||
\(104\) | 98.4277 | + | 133.296i | 0.946421 | + | 1.28169i | ||||
\(105\) | −20.9304 | − | 12.4575i | −0.199337 | − | 0.118643i | ||||
\(106\) | −127.852 | + | 27.5203i | −1.20615 | + | 0.259625i | ||||
\(107\) | −85.4698 | + | 85.4698i | −0.798783 | + | 0.798783i | −0.982904 | − | 0.184121i | \(-0.941056\pi\) |
0.184121 | + | 0.982904i | \(0.441056\pi\) | |||||||
\(108\) | 99.4244 | + | 42.1757i | 0.920596 | + | 0.390516i | ||||
\(109\) | −52.8523 | + | 52.8523i | −0.484883 | + | 0.484883i | −0.906687 | − | 0.421804i | \(-0.861397\pi\) |
0.421804 | + | 0.906687i | \(0.361397\pi\) | |||||||
\(110\) | −4.06751 | + | 6.29888i | −0.0369773 | + | 0.0572625i | ||||
\(111\) | 2.81176 | + | 1.67353i | 0.0253312 | + | 0.0150768i | ||||
\(112\) | 43.7490 | + | 38.5830i | 0.390616 | + | 0.344491i | ||||
\(113\) | − | 73.5045i | − | 0.650483i | −0.945631 | − | 0.325241i | \(-0.894554\pi\) | ||
0.945631 | − | 0.325241i | \(-0.105446\pi\) | |||||||
\(114\) | −95.6462 | + | 47.4521i | −0.839002 | + | 0.416247i | ||||
\(115\) | −46.0810 | + | 46.0810i | −0.400705 | + | 0.400705i | ||||
\(116\) | 38.7113 | − | 102.421i | 0.333718 | − | 0.882936i | ||||
\(117\) | −53.0094 | + | 178.714i | −0.453072 | + | 1.52747i | ||||
\(118\) | −62.9150 | + | 13.5425i | −0.533178 | + | 0.114767i | ||||
\(119\) | 102.346 | 0.860049 | ||||||||
\(120\) | −41.3495 | − | 33.8656i | −0.344579 | − | 0.282214i | ||||
\(121\) | 118.166i | 0.976579i | ||||||||
\(122\) | −35.3137 | + | 7.60129i | −0.289457 | + | 0.0623057i | ||||
\(123\) | −74.7076 | + | 18.9586i | −0.607379 | + | 0.154135i | ||||
\(124\) | 19.1660 | + | 42.4575i | 0.154565 | + | 0.342399i | ||||
\(125\) | 70.9262 | + | 70.9262i | 0.567409 | + | 0.567409i | ||||
\(126\) | −5.00443 | + | 65.4324i | −0.0397177 | + | 0.519305i | ||||
\(127\) | 73.9333 | 0.582152 | 0.291076 | − | 0.956700i | \(-0.405987\pi\) | ||||
0.291076 | + | 0.956700i | \(0.405987\pi\) | |||||||
\(128\) | 82.3336 | + | 98.0061i | 0.643231 | + | 0.765672i | ||||
\(129\) | −147.956 | − | 88.0614i | −1.14694 | − | 0.682646i | ||||
\(130\) | 50.0445 | − | 77.4980i | 0.384957 | − | 0.596139i | ||||
\(131\) | −158.430 | − | 158.430i | −1.20939 | − | 1.20939i | −0.971226 | − | 0.238161i | \(-0.923455\pi\) |
−0.238161 | − | 0.971226i | \(-0.576545\pi\) | |||||||
\(132\) | 20.0729 | + | 2.27474i | 0.152067 | + | 0.0172329i | ||||
\(133\) | −45.8745 | − | 45.8745i | −0.344921 | − | 0.344921i | ||||
\(134\) | −29.5486 | + | 6.36034i | −0.220512 | + | 0.0474652i | ||||
\(135\) | 2.39398 | − | 60.0810i | 0.0177332 | − | 0.445045i | ||||
\(136\) | 222.081 | + | 33.4170i | 1.63295 | + | 0.245713i | ||||
\(137\) | −100.734 | −0.735283 | −0.367642 | − | 0.929968i | \(-0.619835\pi\) | ||||
−0.367642 | + | 0.929968i | \(0.619835\pi\) | |||||||
\(138\) | 166.395 | + | 56.0400i | 1.20576 | + | 0.406087i | ||||
\(139\) | 18.2732 | + | 18.2732i | 0.131462 | + | 0.131462i | 0.769776 | − | 0.638314i | \(-0.220368\pi\) |
−0.638314 | + | 0.769776i | \(0.720368\pi\) | |||||||
\(140\) | 11.4821 | − | 30.3787i | 0.0820148 | − | 0.216991i | ||||
\(141\) | 37.0939 | + | 146.171i | 0.263078 | + | 1.03667i | ||||
\(142\) | −205.122 | − | 132.458i | −1.44452 | − | 0.932799i | ||||
\(143\) | 34.8679i | 0.243831i | ||||||||
\(144\) | −32.2235 | + | 140.348i | −0.223774 | + | 0.974641i | ||||
\(145\) | −60.9595 | −0.420410 | ||||||||
\(146\) | −16.3183 | + | 25.2702i | −0.111769 | + | 0.173084i | ||||
\(147\) | 103.834 | − | 26.3501i | 0.706355 | − | 0.179252i | ||||
\(148\) | −1.54249 | + | 4.08104i | −0.0104222 | + | 0.0275746i | ||||
\(149\) | 44.9729 | − | 44.9729i | 0.301831 | − | 0.301831i | −0.539899 | − | 0.841730i | \(-0.681537\pi\) |
0.841730 | + | 0.539899i | \(0.181537\pi\) | |||||||
\(150\) | 38.3785 | − | 113.954i | 0.255857 | − | 0.759693i | ||||
\(151\) | − | 28.1033i | − | 0.186114i | −0.995661 | − | 0.0930572i | \(-0.970336\pi\) | ||
0.995661 | − | 0.0930572i | \(-0.0296639\pi\) | |||||||
\(152\) | −84.5649 | − | 114.522i | −0.556348 | − | 0.753434i | ||||
\(153\) | 120.474 | + | 222.081i | 0.787411 | + | 1.45151i | ||||
\(154\) | 2.58301 | + | 12.0000i | 0.0167728 | + | 0.0779221i | ||||
\(155\) | 18.3388 | − | 18.3388i | 0.118315 | − | 0.118315i | ||||
\(156\) | −246.966 | − | 27.9872i | −1.58311 | − | 0.179405i | ||||
\(157\) | 173.265 | − | 173.265i | 1.10360 | − | 1.10360i | 0.109628 | − | 0.993973i | \(-0.465034\pi\) |
0.993973 | − | 0.109628i | \(-0.0349660\pi\) | |||||||
\(158\) | 86.3505 | + | 55.7609i | 0.546522 | + | 0.352917i | ||||
\(159\) | 100.332 | − | 168.572i | 0.631019 | − | 1.06020i | ||||
\(160\) | 34.8340 | − | 62.1699i | 0.217712 | − | 0.388562i | ||||
\(161\) | 106.686i | 0.662644i | ||||||||
\(162\) | −147.873 | + | 66.1630i | −0.912797 | + | 0.408413i | ||||
\(163\) | 51.9190 | − | 51.9190i | 0.318521 | − | 0.318521i | −0.529678 | − | 0.848199i | \(-0.677687\pi\) |
0.848199 | + | 0.529678i | \(0.177687\pi\) | |||||||
\(164\) | −42.2825 | − | 93.6662i | −0.257820 | − | 0.571136i | ||||
\(165\) | −2.76648 | − | 10.9015i | −0.0167666 | − | 0.0660697i | ||||
\(166\) | 22.5385 | + | 104.708i | 0.135774 | + | 0.630774i | ||||
\(167\) | 57.5333 | 0.344511 | 0.172255 | − | 0.985052i | \(-0.444895\pi\) | ||||
0.172255 | + | 0.985052i | \(0.444895\pi\) | |||||||
\(168\) | −87.0681 | + | 8.66321i | −0.518263 | + | 0.0515667i | ||||
\(169\) | − | 259.996i | − | 1.53844i | ||||||
\(170\) | −26.3112 | − | 122.235i | −0.154772 | − | 0.719031i | ||||
\(171\) | 45.5434 | − | 153.543i | 0.266336 | − | 0.897915i | ||||
\(172\) | 81.1660 | − | 214.745i | 0.471895 | − | 1.24852i | ||||
\(173\) | 112.600 | + | 112.600i | 0.650868 | + | 0.650868i | 0.953202 | − | 0.302334i | \(-0.0977657\pi\) |
−0.302334 | + | 0.953202i | \(0.597766\pi\) | |||||||
\(174\) | 72.9927 | + | 147.127i | 0.419498 | + | 0.845556i | ||||
\(175\) | 73.0627 | 0.417501 | ||||||||
\(176\) | 1.68676 | + | 26.8823i | 0.00958384 | + | 0.152740i | ||||
\(177\) | 49.3725 | − | 82.9529i | 0.278941 | − | 0.468660i | ||||
\(178\) | −9.16601 | − | 5.91896i | −0.0514944 | − | 0.0332526i | ||||
\(179\) | 22.4810 | + | 22.4810i | 0.125592 | + | 0.125592i | 0.767109 | − | 0.641517i | \(-0.221695\pi\) |
−0.641517 | + | 0.767109i | \(0.721695\pi\) | |||||||
\(180\) | 79.4348 | − | 10.8445i | 0.441304 | − | 0.0602471i | ||||
\(181\) | −18.6013 | − | 18.6013i | −0.102770 | − | 0.102770i | 0.653852 | − | 0.756622i | \(-0.273152\pi\) |
−0.756622 | + | 0.653852i | \(0.773152\pi\) | |||||||
\(182\) | −31.7799 | − | 147.642i | −0.174615 | − | 0.811218i | ||||
\(183\) | 27.7124 | − | 46.5608i | 0.151434 | − | 0.254430i | ||||
\(184\) | −34.8340 | + | 231.498i | −0.189315 | + | 1.25814i | ||||
\(185\) | 2.42898 | 0.0131296 | ||||||||
\(186\) | −66.2198 | − | 22.3022i | −0.356020 | − | 0.119904i | ||||
\(187\) | 33.4170 | + | 33.4170i | 0.178701 | + | 0.178701i | ||||
\(188\) | −183.265 | + | 82.7288i | −0.974814 | + | 0.440047i | ||||
\(189\) | −66.7778 | − | 72.3203i | −0.353322 | − | 0.382647i | ||||
\(190\) | −42.9961 | + | 66.5830i | −0.226295 | + | 0.350437i | ||||
\(191\) | 191.672i | 1.00352i | 0.865007 | + | 0.501760i | \(0.167314\pi\) | ||||
−0.865007 | + | 0.501760i | \(0.832686\pi\) | |||||||
\(192\) | −191.758 | − | 9.63028i | −0.998741 | − | 0.0501577i | ||||
\(193\) | 48.6275 | 0.251956 | 0.125978 | − | 0.992033i | \(-0.459793\pi\) | ||||
0.125978 | + | 0.992033i | \(0.459793\pi\) | |||||||
\(194\) | 136.370 | + | 88.0614i | 0.702940 | + | 0.453925i | ||||
\(195\) | 34.0373 | + | 134.126i | 0.174550 | + | 0.687827i | ||||
\(196\) | 58.7673 | + | 130.184i | 0.299833 | + | 0.664206i | ||||
\(197\) | −136.258 | + | 136.258i | −0.691667 | + | 0.691667i | −0.962599 | − | 0.270932i | \(-0.912668\pi\) |
0.270932 | + | 0.962599i | \(0.412668\pi\) | |||||||
\(198\) | −22.9984 | + | 19.7304i | −0.116153 | + | 0.0996484i | ||||
\(199\) | 144.767i | 0.727474i | 0.931502 | + | 0.363737i | \(0.118499\pi\) | ||||
−0.931502 | + | 0.363737i | \(0.881501\pi\) | |||||||
\(200\) | 158.539 | + | 23.8557i | 0.792697 | + | 0.119279i | ||||
\(201\) | 23.1882 | − | 38.9595i | 0.115364 | − | 0.193828i | ||||
\(202\) | −89.7268 | + | 19.3137i | −0.444192 | + | 0.0956125i | ||||
\(203\) | −70.5659 | + | 70.5659i | −0.347615 | + | 0.347615i | ||||
\(204\) | −263.512 | + | 209.867i | −1.29172 | + | 1.02876i | ||||
\(205\) | −40.4575 | + | 40.4575i | −0.197354 | + | 0.197354i | ||||
\(206\) | −55.5369 | + | 86.0035i | −0.269596 | + | 0.417493i | ||||
\(207\) | −231.498 | + | 125.582i | −1.11835 | + | 0.606678i | ||||
\(208\) | −20.7530 | − | 330.745i | −0.0997738 | − | 1.59012i | ||||
\(209\) | − | 29.9570i | − | 0.143335i | ||||||
\(210\) | 21.6502 | + | 43.6389i | 0.103096 | + | 0.207804i | ||||
\(211\) | −196.354 | + | 196.354i | −0.930589 | + | 0.930589i | −0.997743 | − | 0.0671538i | \(-0.978608\pi\) |
0.0671538 | + | 0.997743i | \(0.478608\pi\) | |||||||
\(212\) | 244.668 | + | 92.4759i | 1.15409 | + | 0.436207i | ||||
\(213\) | 355.005 | − | 90.0899i | 1.66669 | − | 0.422957i | ||||
\(214\) | 236.332 | − | 50.8706i | 1.10436 | − | 0.237713i | ||||
\(215\) | −127.814 | −0.594482 | ||||||||
\(216\) | −121.288 | − | 178.732i | −0.561520 | − | 0.827463i | ||||
\(217\) | − | 42.4575i | − | 0.195657i | ||||||
\(218\) | 146.142 | − | 31.4570i | 0.670374 | − | 0.144298i | ||||
\(219\) | −11.0987 | − | 43.7353i | −0.0506791 | − | 0.199704i | ||||
\(220\) | 13.6680 | − | 6.16995i | 0.0621272 | − | 0.0280452i | ||||
\(221\) | −411.145 | − | 411.145i | −1.86038 | − | 1.86038i | ||||
\(222\) | −2.90846 | − | 5.86239i | −0.0131012 | − | 0.0264072i | ||||
\(223\) | −375.261 | −1.68279 | −0.841393 | − | 0.540423i | \(-0.818264\pi\) | ||||
−0.841393 | + | 0.540423i | \(0.818264\pi\) | |||||||
\(224\) | −31.6438 | − | 112.291i | −0.141267 | − | 0.501297i | ||||
\(225\) | 86.0039 | + | 158.539i | 0.382240 | + | 0.704619i | ||||
\(226\) | −79.7490 | + | 123.498i | −0.352872 | + | 0.546451i | ||||
\(227\) | 181.108 | + | 181.108i | 0.797834 | + | 0.797834i | 0.982754 | − | 0.184920i | \(-0.0592025\pi\) |
−0.184920 | + | 0.982754i | \(0.559203\pi\) | |||||||
\(228\) | 212.183 | + | 24.0454i | 0.930625 | + | 0.105462i | ||||
\(229\) | −153.937 | − | 153.937i | −0.672215 | − | 0.672215i | 0.286011 | − | 0.958226i | \(-0.407671\pi\) |
−0.958226 | + | 0.286011i | \(0.907671\pi\) | |||||||
\(230\) | 127.418 | − | 27.4269i | 0.553993 | − | 0.119247i | ||||
\(231\) | −15.8219 | − | 9.41699i | −0.0684930 | − | 0.0407662i | ||||
\(232\) | −176.162 | + | 130.081i | −0.759319 | + | 0.560694i | ||||
\(233\) | −51.7790 | −0.222228 | −0.111114 | − | 0.993808i | \(-0.535442\pi\) | ||||
−0.111114 | + | 0.993808i | \(0.535442\pi\) | |||||||
\(234\) | 282.960 | − | 242.752i | 1.20923 | − | 1.03740i | ||||
\(235\) | 79.1581 | + | 79.1581i | 0.336843 | + | 0.336843i | ||||
\(236\) | 120.399 | + | 45.5066i | 0.510166 | + | 0.192825i | ||||
\(237\) | −149.447 | + | 37.9253i | −0.630579 | + | 0.160022i | ||||
\(238\) | −171.956 | − | 111.041i | −0.722502 | − | 0.466557i | ||||
\(239\) | − | 249.900i | − | 1.04560i | −0.852454 | − | 0.522802i | \(-0.824887\pi\) | ||
0.852454 | − | 0.522802i | \(-0.175113\pi\) | |||||||
\(240\) | 32.7303 | + | 101.761i | 0.136376 | + | 0.424006i | ||||
\(241\) | 442.531 | 1.83623 | 0.918113 | − | 0.396318i | \(-0.129712\pi\) | ||||
0.918113 | + | 0.396318i | \(0.129712\pi\) | |||||||
\(242\) | 128.205 | − | 198.536i | 0.529771 | − | 0.820395i | ||||
\(243\) | 78.3226 | − | 230.032i | 0.322315 | − | 0.946632i | ||||
\(244\) | 67.5791 | + | 25.5425i | 0.276963 | + | 0.104682i | ||||
\(245\) | 56.2309 | − | 56.2309i | 0.229514 | − | 0.229514i | ||||
\(246\) | 146.089 | + | 49.2012i | 0.593856 | + | 0.200005i | ||||
\(247\) | 368.575i | 1.49221i | ||||||||
\(248\) | 13.8628 | − | 92.1289i | 0.0558985 | − | 0.371487i | ||||
\(249\) | −138.057 | − | 82.1699i | −0.554446 | − | 0.330000i | ||||
\(250\) | −42.2144 | − | 196.118i | −0.168858 | − | 0.784470i | ||||
\(251\) | 43.3235 | − | 43.3235i | 0.172603 | − | 0.172603i | −0.615519 | − | 0.788122i | \(-0.711053\pi\) |
0.788122 | + | 0.615519i | \(0.211053\pi\) | |||||||
\(252\) | 79.3993 | − | 104.506i | 0.315077 | − | 0.414707i | ||||
\(253\) | −34.8340 | + | 34.8340i | −0.137684 | + | 0.137684i | ||||
\(254\) | −124.218 | − | 80.2142i | −0.489049 | − | 0.315804i | ||||
\(255\) | 161.166 | + | 95.9241i | 0.632024 | + | 0.376173i | ||||
\(256\) | −32.0000 | − | 253.992i | −0.125000 | − | 0.992157i | ||||
\(257\) | 179.197i | 0.697266i | 0.937259 | + | 0.348633i | \(0.113354\pi\) | ||||
−0.937259 | + | 0.348633i | \(0.886646\pi\) | |||||||
\(258\) | 153.044 | + | 308.480i | 0.593193 | + | 1.19566i | ||||
\(259\) | 2.81176 | − | 2.81176i | 0.0108562 | − | 0.0108562i | ||||
\(260\) | −168.164 | + | 75.9118i | −0.646783 | + | 0.291968i | ||||
\(261\) | −236.186 | − | 70.0567i | −0.904929 | − | 0.268416i | ||||
\(262\) | 94.2954 | + | 438.073i | 0.359906 | + | 1.67203i | ||||
\(263\) | −419.478 | −1.59497 | −0.797486 | − | 0.603338i | \(-0.793837\pi\) | ||||
−0.797486 | + | 0.603338i | \(0.793837\pi\) | |||||||
\(264\) | −31.2573 | − | 25.6000i | −0.118399 | − | 0.0969698i | ||||
\(265\) | − | 145.624i | − | 0.549523i | ||||||
\(266\) | 27.3040 | + | 126.847i | 0.102646 | + | 0.476870i | ||||
\(267\) | 15.8637 | − | 4.02573i | 0.0594145 | − | 0.0150777i | ||||
\(268\) | 56.5464 | + | 21.3725i | 0.210994 | + | 0.0797483i | ||||
\(269\) | 33.7631 | + | 33.7631i | 0.125513 | + | 0.125513i | 0.767073 | − | 0.641560i | \(-0.221712\pi\) |
−0.641560 | + | 0.767073i | \(0.721712\pi\) | |||||||
\(270\) | −69.2074 | + | 98.3473i | −0.256324 | + | 0.364249i | ||||
\(271\) | 329.269 | 1.21502 | 0.607508 | − | 0.794314i | \(-0.292169\pi\) | ||||
0.607508 | + | 0.794314i | \(0.292169\pi\) | |||||||
\(272\) | −336.872 | − | 297.093i | −1.23850 | − | 1.09225i | ||||
\(273\) | 194.664 | + | 115.862i | 0.713055 | + | 0.424402i | ||||
\(274\) | 169.247 | + | 109.292i | 0.617690 | + | 0.398874i | ||||
\(275\) | 23.8557 | + | 23.8557i | 0.0867482 | + | 0.0867482i | ||||
\(276\) | −218.766 | − | 274.686i | −0.792630 | − | 0.995238i | ||||
\(277\) | 251.265 | + | 251.265i | 0.907095 | + | 0.907095i | 0.996037 | − | 0.0889417i | \(-0.0283485\pi\) |
−0.0889417 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(278\) | −10.8760 | − | 50.5272i | −0.0391223 | − | 0.181752i | ||||
\(279\) | 92.1289 | − | 49.9778i | 0.330211 | − | 0.179132i | ||||
\(280\) | −52.2510 | + | 38.5830i | −0.186611 | + | 0.137796i | ||||
\(281\) | 171.809 | 0.611421 | 0.305711 | − | 0.952124i | \(-0.401106\pi\) | ||||
0.305711 | + | 0.952124i | \(0.401106\pi\) | |||||||
\(282\) | 96.2657 | − | 285.833i | 0.341368 | − | 1.01359i | ||||
\(283\) | −193.476 | − | 193.476i | −0.683660 | − | 0.683660i | 0.277163 | − | 0.960823i | \(-0.410606\pi\) |
−0.960823 | + | 0.277163i | \(0.910606\pi\) | |||||||
\(284\) | 200.923 | + | 445.095i | 0.707475 | + | 1.56724i | ||||
\(285\) | −29.2434 | − | 115.236i | −0.102608 | − | 0.404335i | ||||
\(286\) | 37.8301 | − | 58.5830i | 0.132273 | − | 0.204836i | ||||
\(287\) | 93.6662i | 0.326363i | ||||||||
\(288\) | 206.411 | − | 200.844i | 0.716706 | − | 0.697375i | ||||
\(289\) | −499.073 | −1.72690 | ||||||||
\(290\) | 102.421 | + | 66.1382i | 0.353174 | + | 0.228063i | ||||
\(291\) | −236.017 | + | 59.8942i | −0.811055 | + | 0.205822i | ||||
\(292\) | 54.8340 | − | 24.7530i | 0.187788 | − | 0.0847704i | ||||
\(293\) | 73.4937 | − | 73.4937i | 0.250832 | − | 0.250832i | −0.570480 | − | 0.821312i | \(-0.693243\pi\) |
0.821312 | + | 0.570480i | \(0.193243\pi\) | |||||||
\(294\) | −203.045 | − | 68.3834i | −0.690629 | − | 0.232597i | ||||
\(295\) | − | 71.6601i | − | 0.242916i | ||||||
\(296\) | 7.01933 | − | 5.18319i | 0.0237140 | − | 0.0175108i | ||||
\(297\) | 1.80968 | − | 45.4170i | 0.00609320 | − | 0.152919i | ||||
\(298\) | −124.354 | + | 26.7673i | −0.417296 | + | 0.0898232i | ||||
\(299\) | 428.579 | − | 428.579i | 1.43337 | − | 1.43337i | ||||
\(300\) | −188.116 | + | 149.820i | −0.627054 | + | 0.499399i | ||||
\(301\) | −147.956 | + | 147.956i | −0.491547 | + | 0.491547i | ||||
\(302\) | −30.4907 | + | 47.2175i | −0.100963 | + | 0.156349i | ||||
\(303\) | 70.4131 | − | 118.304i | 0.232386 | − | 0.390442i | ||||
\(304\) | 17.8301 | + | 284.162i | 0.0586515 | + | 0.934744i | ||||
\(305\) | − | 40.2222i | − | 0.131876i | ||||||
\(306\) | 38.5346 | − | 503.836i | 0.125930 | − | 1.64652i | ||||
\(307\) | 283.055 | − | 283.055i | 0.922003 | − | 0.922003i | −0.0751680 | − | 0.997171i | \(-0.523949\pi\) |
0.997171 | + | 0.0751680i | \(0.0239493\pi\) | |||||||
\(308\) | 8.67963 | − | 22.9641i | 0.0281806 | − | 0.0745589i | ||||
\(309\) | −37.7729 | − | 148.847i | −0.122242 | − | 0.481704i | ||||
\(310\) | −50.7085 | + | 10.9150i | −0.163576 | + | 0.0352098i | ||||
\(311\) | −54.0368 | −0.173752 | −0.0868759 | − | 0.996219i | \(-0.527688\pi\) | ||||
−0.0868759 | + | 0.996219i | \(0.527688\pi\) | |||||||
\(312\) | 384.573 | + | 314.969i | 1.23261 | + | 1.00952i | ||||
\(313\) | 490.280i | 1.56639i | 0.621777 | + | 0.783194i | \(0.286411\pi\) | ||||
−0.621777 | + | 0.783194i | \(0.713589\pi\) | |||||||
\(314\) | −479.095 | + | 103.125i | −1.52578 | + | 0.328425i | ||||
\(315\) | −70.0547 | − | 20.7793i | −0.222396 | − | 0.0659661i | ||||
\(316\) | −84.5830 | − | 187.373i | −0.267668 | − | 0.592951i | ||||
\(317\) | 319.550 | + | 319.550i | 1.00804 | + | 1.00804i | 0.999967 | + | 0.00807607i | \(0.00257072\pi\) |
0.00807607 | + | 0.999967i | \(0.497429\pi\) | |||||||
\(318\) | −351.465 | + | 174.369i | −1.10524 | + | 0.548331i | ||||
\(319\) | −46.0810 | −0.144455 | ||||||||
\(320\) | −125.978 | + | 66.6610i | −0.393680 | + | 0.208316i | ||||
\(321\) | −185.461 | + | 311.601i | −0.577762 | + | 0.970721i | ||||
\(322\) | 115.749 | − | 179.247i | 0.359469 | − | 0.556668i | ||||
\(323\) | 353.238 | + | 353.238i | 1.09362 | + | 1.09362i | ||||
\(324\) | 320.232 | + | 49.2723i | 0.988369 | + | 0.152075i | ||||
\(325\) | −293.508 | − | 293.508i | −0.903103 | − | 0.903103i | ||||
\(326\) | −143.561 | + | 30.9015i | −0.440371 | + | 0.0947900i | ||||
\(327\) | −114.685 | + | 192.686i | −0.350717 | + | 0.589255i | ||||
\(328\) | −30.5830 | + | 203.247i | −0.0932409 | + | 0.619656i | ||||
\(329\) | 183.265 | 0.557036 | ||||||||
\(330\) | −7.17954 | + | 21.3176i | −0.0217562 | + | 0.0645987i | ||||
\(331\) | −269.431 | − | 269.431i | −0.813992 | − | 0.813992i | 0.171238 | − | 0.985230i | \(-0.445223\pi\) |
−0.985230 | + | 0.171238i | \(0.945223\pi\) | |||||||
\(332\) | 75.7359 | − | 200.378i | 0.228120 | − | 0.603549i | ||||
\(333\) | 9.41106 | + | 2.79147i | 0.0282614 | + | 0.00838279i | ||||
\(334\) | −96.6640 | − | 62.4209i | −0.289413 | − | 0.186889i | ||||
\(335\) | − | 33.6557i | − | 0.100465i | ||||||
\(336\) | 155.686 | + | 79.9094i | 0.463351 | + | 0.237826i | ||||
\(337\) | 143.041 | 0.424453 | 0.212226 | − | 0.977221i | \(-0.431929\pi\) | ||||
0.212226 | + | 0.977221i | \(0.431929\pi\) | |||||||
\(338\) | −282.084 | + | 436.830i | −0.834567 | + | 1.29240i | ||||
\(339\) | −54.2406 | − | 213.739i | −0.160002 | − | 0.630497i | ||||
\(340\) | −88.4131 | + | 233.919i | −0.260038 | + | 0.687997i | ||||
\(341\) | 13.8628 | − | 13.8628i | 0.0406534 | − | 0.0406534i | ||||
\(342\) | −243.107 | + | 208.562i | −0.710839 | + | 0.609831i | ||||
\(343\) | − | 308.826i | − | 0.900368i | ||||||
\(344\) | −369.359 | + | 272.741i | −1.07372 | + | 0.792851i | ||||
\(345\) | −99.9916 | + | 168.000i | −0.289831 | + | 0.486957i | ||||
\(346\) | −67.0183 | − | 311.350i | −0.193694 | − | 0.899856i | ||||
\(347\) | −126.922 | + | 126.922i | −0.365770 | + | 0.365770i | −0.865932 | − | 0.500162i | \(-0.833274\pi\) |
0.500162 | + | 0.865932i | \(0.333274\pi\) | |||||||
\(348\) | 36.9876 | − | 326.387i | 0.106286 | − | 0.937895i | ||||
\(349\) | 195.893 | − | 195.893i | 0.561297 | − | 0.561297i | −0.368378 | − | 0.929676i | \(-0.620087\pi\) |
0.929676 | + | 0.368378i | \(0.120087\pi\) | |||||||
\(350\) | −122.756 | − | 79.2697i | −0.350731 | − | 0.226485i | ||||
\(351\) | −22.2653 | + | 558.787i | −0.0634340 | + | 1.59198i | ||||
\(352\) | 26.3320 | − | 46.9961i | 0.0748069 | − | 0.133512i | ||||
\(353\) | − | 291.488i | − | 0.825745i | −0.910789 | − | 0.412873i | \(-0.864525\pi\) | ||
0.910789 | − | 0.412873i | \(-0.135475\pi\) | |||||||
\(354\) | −172.953 | + | 85.8056i | −0.488567 | + | 0.242389i | ||||
\(355\) | 192.251 | − | 192.251i | 0.541552 | − | 0.541552i | ||||
\(356\) | 8.97839 | + | 19.8894i | 0.0252202 | + | 0.0558691i | ||||
\(357\) | 297.604 | − | 75.5233i | 0.833626 | − | 0.211550i | ||||
\(358\) | −13.3804 | − | 62.1621i | −0.0373755 | − | 0.173637i | ||||
\(359\) | 40.3499 | 0.112395 | 0.0561976 | − | 0.998420i | \(-0.482102\pi\) | ||||
0.0561976 | + | 0.998420i | \(0.482102\pi\) | |||||||
\(360\) | −145.227 | − | 67.9628i | −0.403410 | − | 0.188786i | ||||
\(361\) | 44.3360i | 0.122814i | ||||||||
\(362\) | 11.0713 | + | 51.4344i | 0.0305836 | + | 0.142084i | ||||
\(363\) | 87.1973 | + | 343.607i | 0.240213 | + | 0.946575i | ||||
\(364\) | −106.790 | + | 282.539i | −0.293378 | + | 0.776205i | ||||
\(365\) | −23.6846 | − | 23.6846i | −0.0648893 | − | 0.0648893i | ||||
\(366\) | −97.0771 | + | 48.1620i | −0.265238 | + | 0.131590i | ||||
\(367\) | 340.678 | 0.928279 | 0.464140 | − | 0.885762i | \(-0.346364\pi\) | ||||
0.464140 | + | 0.885762i | \(0.346364\pi\) | |||||||
\(368\) | 309.691 | − | 351.156i | 0.841551 | − | 0.954229i | ||||
\(369\) | −203.247 | + | 110.257i | −0.550805 | + | 0.298799i | ||||
\(370\) | −4.08104 | − | 2.63533i | −0.0110298 | − | 0.00712253i | ||||
\(371\) | −168.572 | − | 168.572i | −0.454372 | − | 0.454372i | ||||
\(372\) | 87.0618 | + | 109.316i | 0.234037 | + | 0.293861i | ||||
\(373\) | 237.678 | + | 237.678i | 0.637207 | + | 0.637207i | 0.949866 | − | 0.312658i | \(-0.101219\pi\) |
−0.312658 | + | 0.949866i | \(0.601219\pi\) | |||||||
\(374\) | −19.8894 | − | 92.4012i | −0.0531802 | − | 0.247062i | ||||
\(375\) | 258.579 | + | 153.903i | 0.689544 | + | 0.410409i | ||||
\(376\) | 397.668 | + | 59.8379i | 1.05763 | + | 0.159143i | ||||
\(377\) | 566.957 | 1.50386 | ||||||||
\(378\) | 33.7320 | + | 193.959i | 0.0892381 | + | 0.513120i | ||||
\(379\) | 320.332 | + | 320.332i | 0.845203 | + | 0.845203i | 0.989530 | − | 0.144327i | \(-0.0461017\pi\) |
−0.144327 | + | 0.989530i | \(0.546102\pi\) | |||||||
\(380\) | 144.479 | − | 65.2201i | 0.380208 | − | 0.171632i | ||||
\(381\) | 214.985 | − | 54.5570i | 0.564266 | − | 0.143194i | ||||
\(382\) | 207.956 | − | 322.037i | 0.544386 | − | 0.843028i | ||||
\(383\) | − | 632.700i | − | 1.65196i | −0.563702 | − | 0.825978i | \(-0.690623\pi\) | ||
0.563702 | − | 0.825978i | \(-0.309377\pi\) | |||||||
\(384\) | 311.733 | + | 224.229i | 0.811804 | + | 0.583930i | ||||
\(385\) | −13.6680 | −0.0355012 | ||||||||
\(386\) | −81.7010 | − | 52.7585i | −0.211661 | − | 0.136680i | ||||
\(387\) | −495.212 | − | 146.888i | −1.27962 | − | 0.379555i | ||||
\(388\) | −133.579 | − | 295.911i | −0.344276 | − | 0.762657i | ||||
\(389\) | −424.351 | + | 424.351i | −1.09088 | + | 1.09088i | −0.0954418 | + | 0.995435i | \(0.530426\pi\) |
−0.995435 | + | 0.0954418i | \(0.969574\pi\) | |||||||
\(390\) | 88.3332 | − | 262.280i | 0.226495 | − | 0.672513i | ||||
\(391\) | − | 821.490i | − | 2.10100i | ||||||
\(392\) | 42.5065 | − | 282.488i | 0.108435 | − | 0.720632i | ||||
\(393\) | −577.595 | − | 343.778i | −1.46971 | − | 0.874752i | ||||
\(394\) | 376.767 | − | 81.0993i | 0.956262 | − | 0.205836i | ||||
\(395\) | −80.9323 | + | 80.9323i | −0.204892 | + | 0.204892i | ||||
\(396\) | 60.0471 | − | 8.19766i | 0.151634 | − | 0.0207012i | ||||
\(397\) | −445.678 | + | 445.678i | −1.12262 | + | 1.12262i | −0.131269 | + | 0.991347i | \(0.541905\pi\) |
−0.991347 | + | 0.131269i | \(0.958095\pi\) | |||||||
\(398\) | 157.066 | − | 243.230i | 0.394638 | − | 0.611130i | ||||
\(399\) | −167.247 | − | 99.5434i | −0.419166 | − | 0.249482i | ||||
\(400\) | −240.486 | − | 212.089i | −0.601216 | − | 0.530222i | ||||
\(401\) | − | 555.896i | − | 1.38627i | −0.720806 | − | 0.693137i | \(-0.756228\pi\) | ||
0.720806 | − | 0.693137i | \(-0.243772\pi\) | |||||||
\(402\) | −81.2287 | + | 40.2993i | −0.202061 | + | 0.100247i | ||||
\(403\) | −170.561 | + | 170.561i | −0.423228 | + | 0.423228i | ||||
\(404\) | 171.708 | + | 64.8996i | 0.425020 | + | 0.160643i | ||||
\(405\) | −37.3738 | − | 176.472i | −0.0922811 | − | 0.435733i | ||||
\(406\) | 195.122 | − | 42.0000i | 0.480595 | − | 0.103448i | ||||
\(407\) | 1.83614 | 0.00451140 | ||||||||
\(408\) | 670.433 | − | 66.7076i | 1.64322 | − | 0.163499i | ||||
\(409\) | 44.8261i | 0.109599i | 0.998497 | + | 0.0547997i | \(0.0174520\pi\) | ||||
−0.998497 | + | 0.0547997i | \(0.982548\pi\) | |||||||
\(410\) | 111.869 | − | 24.0798i | 0.272851 | − | 0.0587313i | ||||
\(411\) | −292.917 | + | 74.3337i | −0.712693 | + | 0.180861i | ||||
\(412\) | 186.620 | − | 84.2431i | 0.452960 | − | 0.204474i | ||||
\(413\) | −82.9529 | − | 82.9529i | −0.200854 | − | 0.200854i | ||||
\(414\) | 525.200 | + | 40.1686i | 1.26860 | + | 0.0970255i | ||||
\(415\) | −119.263 | −0.287380 | ||||||||
\(416\) | −323.975 | + | 578.215i | −0.778786 | + | 1.38994i | ||||
\(417\) | 66.6196 | + | 39.6512i | 0.159759 | + | 0.0950868i | ||||
\(418\) | −32.5020 | + | 50.3320i | −0.0777559 | + | 0.120412i | ||||
\(419\) | 15.2026 | + | 15.2026i | 0.0362830 | + | 0.0362830i | 0.725016 | − | 0.688733i | \(-0.241833\pi\) |
−0.688733 | + | 0.725016i | \(0.741833\pi\) | |||||||
\(420\) | 10.9708 | − | 96.8089i | 0.0261209 | − | 0.230497i | ||||
\(421\) | 262.889 | + | 262.889i | 0.624439 | + | 0.624439i | 0.946663 | − | 0.322224i | \(-0.104431\pi\) |
−0.322224 | + | 0.946663i | \(0.604431\pi\) | |||||||
\(422\) | 542.938 | − | 116.868i | 1.28658 | − | 0.276938i | ||||
\(423\) | 215.726 | + | 397.668i | 0.509990 | + | 0.940113i | ||||
\(424\) | −310.745 | − | 420.826i | −0.732889 | − | 0.992514i | ||||
\(425\) | −562.590 | −1.32374 | ||||||||
\(426\) | −694.202 | − | 233.800i | −1.62958 | − | 0.548827i | ||||
\(427\) | −46.5608 | − | 46.5608i | −0.109042 | − | 0.109042i | ||||
\(428\) | −452.263 | − | 170.940i | −1.05669 | − | 0.399391i | ||||
\(429\) | 25.7298 | + | 101.390i | 0.0599762 | + | 0.236340i | ||||
\(430\) | 214.745 | + | 138.672i | 0.499407 | + | 0.322493i | ||||
\(431\) | − | 163.103i | − | 0.378430i | −0.981936 | − | 0.189215i | \(-0.939406\pi\) | ||
0.981936 | − | 0.189215i | \(-0.0605943\pi\) | |||||||
\(432\) | 9.86564 | + | 431.887i | 0.0228371 | + | 0.999739i | ||||
\(433\) | −140.737 | −0.325028 | −0.162514 | − | 0.986706i | \(-0.551960\pi\) | ||||
−0.162514 | + | 0.986706i | \(0.551960\pi\) | |||||||
\(434\) | −46.0644 | + | 71.3346i | −0.106139 | + | 0.164366i | ||||
\(435\) | −177.260 | + | 44.9833i | −0.407494 | + | 0.103410i | ||||
\(436\) | −279.668 | − | 105.705i | −0.641440 | − | 0.242442i | ||||
\(437\) | −368.217 | + | 368.217i | −0.842601 | + | 0.842601i | ||||
\(438\) | −28.8033 | + | 85.5230i | −0.0657609 | + | 0.195258i | ||||
\(439\) | 434.893i | 0.990644i | 0.868709 | + | 0.495322i | \(0.164950\pi\) | ||||
−0.868709 | + | 0.495322i | \(0.835050\pi\) | |||||||
\(440\) | −29.6582 | − | 4.46274i | −0.0674051 | − | 0.0101426i | ||||
\(441\) | 282.488 | − | 153.243i | 0.640562 | − | 0.347490i | ||||
\(442\) | 244.708 | + | 1136.85i | 0.553639 | + | 2.57207i | ||||
\(443\) | −260.367 | + | 260.367i | −0.587736 | + | 0.587736i | −0.937018 | − | 0.349282i | \(-0.886426\pi\) |
0.349282 | + | 0.937018i | \(0.386426\pi\) | |||||||
\(444\) | −1.47380 | + | 13.0052i | −0.00331937 | + | 0.0292910i | ||||
\(445\) | 8.59088 | − | 8.59088i | 0.0193053 | − | 0.0193053i | ||||
\(446\) | 630.492 | + | 407.141i | 1.41366 | + | 0.912873i | ||||
\(447\) | 97.5869 | − | 163.960i | 0.218315 | − | 0.366801i | ||||
\(448\) | −68.6640 | + | 222.996i | −0.153268 | + | 0.497759i | ||||
\(449\) | − | 98.9506i | − | 0.220380i | −0.993911 | − | 0.110190i | \(-0.964854\pi\) | ||
0.993911 | − | 0.110190i | \(-0.0351459\pi\) | |||||||
\(450\) | 27.5091 | − | 359.679i | 0.0611313 | − | 0.799286i | ||||
\(451\) | −30.5830 | + | 30.5830i | −0.0678115 | + | 0.0678115i | ||||
\(452\) | 267.979 | − | 120.970i | 0.592874 | − | 0.267633i | ||||
\(453\) | −20.7380 | − | 81.7195i | −0.0457793 | − | 0.180396i | ||||
\(454\) | −107.793 | − | 500.782i | −0.237431 | − | 1.10304i | ||||
\(455\) | 168.164 | 0.369590 | ||||||||
\(456\) | −330.409 | − | 270.608i | −0.724580 | − | 0.593438i | ||||
\(457\) | 14.4209i | 0.0315556i | 0.999876 | + | 0.0157778i | \(0.00502245\pi\) | ||||
−0.999876 | + | 0.0157778i | \(0.994978\pi\) | |||||||
\(458\) | 91.6216 | + | 425.651i | 0.200047 | + | 0.929369i | ||||
\(459\) | 514.196 | + | 556.873i | 1.12025 | + | 1.21323i | ||||
\(460\) | −243.838 | − | 92.1621i | −0.530082 | − | 0.200352i | ||||
\(461\) | 328.278 | + | 328.278i | 0.712099 | + | 0.712099i | 0.966974 | − | 0.254875i | \(-0.0820343\pi\) |
−0.254875 | + | 0.966974i | \(0.582034\pi\) | |||||||
\(462\) | 16.3660 | + | 32.9879i | 0.0354242 | + | 0.0714024i | ||||
\(463\) | −848.427 | −1.83246 | −0.916228 | − | 0.400657i | \(-0.868782\pi\) | ||||
−0.916228 | + | 0.400657i | \(0.868782\pi\) | |||||||
\(464\) | 437.109 | − | 27.4269i | 0.942045 | − | 0.0591096i | ||||
\(465\) | 39.7935 | − | 66.8587i | 0.0855774 | − | 0.143782i | ||||
\(466\) | 86.9961 | + | 56.1778i | 0.186687 | + | 0.120553i | ||||
\(467\) | 56.0706 | + | 56.0706i | 0.120066 | + | 0.120066i | 0.764587 | − | 0.644521i | \(-0.222943\pi\) |
−0.644521 | + | 0.764587i | \(0.722943\pi\) | |||||||
\(468\) | −738.787 | + | 100.860i | −1.57860 | + | 0.215512i | ||||
\(469\) | −38.9595 | − | 38.9595i | −0.0830693 | − | 0.0830693i | ||||
\(470\) | −47.1140 | − | 218.880i | −0.100242 | − | 0.465702i | ||||
\(471\) | 375.970 | − | 631.682i | 0.798237 | − | 1.34115i | ||||
\(472\) | −152.915 | − | 207.085i | −0.323973 | − | 0.438739i | ||||
\(473\) | −96.6181 | −0.204267 | ||||||||
\(474\) | 292.240 | + | 98.4234i | 0.616539 | + | 0.207644i | ||||
\(475\) | 252.170 | + | 252.170i | 0.530884 | + | 0.530884i | ||||
\(476\) | 168.436 | + | 373.128i | 0.353857 | + | 0.783881i | ||||
\(477\) | 167.355 | − | 564.216i | 0.350850 | − | 1.18284i | ||||
\(478\) | −271.129 | + | 419.867i | −0.567216 | + | 0.878382i | ||||
\(479\) | 648.794i | 1.35448i | 0.735764 | + | 0.677238i | \(0.236823\pi\) | ||||
−0.735764 | + | 0.677238i | \(0.763177\pi\) | |||||||
\(480\) | 55.4147 | − | 206.484i | 0.115447 | − | 0.430176i | ||||
\(481\) | −22.5909 | −0.0469665 | ||||||||
\(482\) | −743.514 | − | 480.125i | −1.54256 | − | 0.996110i | ||||
\(483\) | 78.7257 | + | 310.224i | 0.162993 | + | 0.642285i | ||||
\(484\) | −430.804 | + | 194.472i | −0.890091 | + | 0.401801i | ||||
\(485\) | −127.814 | + | 127.814i | −0.263533 | + | 0.263533i | ||||
\(486\) | −381.167 | + | 301.509i | −0.784294 | + | 0.620390i | ||||
\(487\) | − | 176.783i | − | 0.363004i | −0.983391 | − | 0.181502i | \(-0.941904\pi\) | ||
0.983391 | − | 0.181502i | \(-0.0580959\pi\) | |||||||
\(488\) | −85.8300 | − | 116.235i | −0.175881 | − | 0.238187i | ||||
\(489\) | 112.659 | − | 189.284i | 0.230387 | − | 0.387083i | ||||
\(490\) | −155.484 | + | 33.4679i | −0.317314 | + | 0.0683019i | ||||
\(491\) | −317.369 | + | 317.369i | −0.646373 | + | 0.646373i | −0.952114 | − | 0.305742i | \(-0.901096\pi\) |
0.305742 | + | 0.952114i | \(0.401096\pi\) | |||||||
\(492\) | −192.069 | − | 241.164i | −0.390383 | − | 0.490171i | ||||
\(493\) | 543.365 | − | 543.365i | 1.10216 | − | 1.10216i | ||||
\(494\) | 399.887 | − | 619.258i | 0.809488 | − | 1.25356i | ||||
\(495\) | −16.0889 | − | 29.6582i | −0.0325029 | − | 0.0599156i | ||||
\(496\) | −123.247 | + | 139.749i | −0.248482 | + | 0.281752i | ||||
\(497\) | − | 445.095i | − | 0.895563i | ||||||
\(498\) | 142.805 | + | 287.843i | 0.286757 | + | 0.577997i | ||||
\(499\) | −374.391 | + | 374.391i | −0.750282 | + | 0.750282i | −0.974532 | − | 0.224250i | \(-0.928007\pi\) |
0.224250 | + | 0.974532i | \(0.428007\pi\) | |||||||
\(500\) | −141.852 | + | 375.306i | −0.283705 | + | 0.750612i | ||||
\(501\) | 167.297 | − | 42.4551i | 0.333926 | − | 0.0847407i | ||||
\(502\) | −119.793 | + | 25.7856i | −0.238632 | + | 0.0513657i | ||||
\(503\) | 386.094 | 0.767583 | 0.383791 | − | 0.923420i | \(-0.374618\pi\) | ||||
0.383791 | + | 0.923420i | \(0.374618\pi\) | |||||||
\(504\) | −246.786 | + | 89.4406i | −0.489656 | + | 0.177462i | ||||
\(505\) | − | 102.199i | − | 0.202374i | ||||||
\(506\) | 96.3193 | − | 20.7328i | 0.190354 | − | 0.0409739i | ||||
\(507\) | −191.857 | − | 756.024i | −0.378416 | − | 1.49117i | ||||
\(508\) | 121.676 | + | 269.542i | 0.239519 | + | 0.530595i | ||||
\(509\) | 41.6258 | + | 41.6258i | 0.0817796 | + | 0.0817796i | 0.746813 | − | 0.665034i | \(-0.231583\pi\) |
−0.665034 | + | 0.746813i | \(0.731583\pi\) | |||||||
\(510\) | −166.709 | − | 336.024i | −0.326880 | − | 0.658870i | ||||
\(511\) | −54.8340 | −0.107307 | ||||||||
\(512\) | −221.805 | + | 461.461i | −0.433213 | + | 0.901291i | ||||
\(513\) | 19.1294 | − | 480.086i | 0.0372893 | − | 0.935839i | ||||
\(514\) | 194.421 | − | 301.077i | 0.378251 | − | 0.585753i | ||||
\(515\) | −80.6071 | − | 80.6071i | −0.156519 | − | 0.156519i | ||||
\(516\) | 77.5518 | − | 684.336i | 0.150294 | − | 1.32623i | ||||
\(517\) | 59.8379 | + | 59.8379i | 0.115741 | + | 0.115741i | ||||
\(518\) | −7.77479 | + | 1.67353i | −0.0150092 | + | 0.00323075i | ||||
\(519\) | 410.512 | + | 244.332i | 0.790968 | + | 0.470775i | ||||
\(520\) | 364.899 | + | 54.9072i | 0.701729 | + | 0.105591i | ||||
\(521\) | 233.704 | 0.448569 | 0.224284 | − | 0.974524i | \(-0.427996\pi\) | ||||
0.224284 | + | 0.974524i | \(0.427996\pi\) | |||||||
\(522\) | 320.818 | + | 373.956i | 0.614595 | + | 0.716392i | ||||
\(523\) | −219.506 | − | 219.506i | −0.419705 | − | 0.419705i | 0.465397 | − | 0.885102i | \(-0.345912\pi\) |
−0.885102 | + | 0.465397i | \(0.845912\pi\) | |||||||
\(524\) | 316.859 | − | 838.331i | 0.604693 | − | 1.59987i | ||||
\(525\) | 212.454 | − | 53.9146i | 0.404674 | − | 0.102694i | ||||
\(526\) | 704.782 | + | 455.114i | 1.33989 | + | 0.865235i | ||||
\(527\) | 326.927i | 0.620355i | ||||||||
\(528\) | 24.7418 | + | 76.9243i | 0.0468595 | + | 0.145690i | ||||
\(529\) | 327.324 | 0.618760 | ||||||||
\(530\) | −157.995 | + | 244.668i | −0.298103 | + | 0.461638i | ||||
\(531\) | 82.3542 | − | 277.646i | 0.155093 | − | 0.522873i | ||||
\(532\) | 91.7490 | − | 242.745i | 0.172461 | − | 0.456288i | ||||
\(533\) | 376.277 | − | 376.277i | 0.705961 | − | 0.705961i | ||||
\(534\) | −31.0209 | − | 10.4475i | −0.0580916 | − | 0.0195647i | ||||
\(535\) | 269.182i | 0.503143i | ||||||||
\(536\) | −71.8178 | − | 97.2591i | −0.133988 | − | 0.181454i | ||||
\(537\) | 81.9601 | + | 48.7817i | 0.152626 | + | 0.0908411i | ||||
\(538\) | −20.0954 | − | 93.3582i | −0.0373520 | − | 0.173528i | ||||
\(539\) | 42.5065 | − | 42.5065i | 0.0788618 | − | 0.0788618i | ||||
\(540\) | 222.980 | − | 90.1506i | 0.412927 | − | 0.166946i | ||||
\(541\) | 80.5203 | − | 80.5203i | 0.148836 | − | 0.148836i | −0.628762 | − | 0.777598i | \(-0.716438\pi\) |
0.777598 | + | 0.628762i | \(0.216438\pi\) | |||||||
\(542\) | −553.219 | − | 357.242i | −1.02070 | − | 0.659118i | ||||
\(543\) | −67.8157 | − | 40.3631i | −0.124891 | − | 0.0743335i | ||||
\(544\) | 243.660 | + | 864.648i | 0.447905 | + | 1.58943i | ||||
\(545\) | 166.455i | 0.305422i | ||||||||
\(546\) | −201.359 | − | 405.865i | −0.368789 | − | 0.743343i | ||||
\(547\) | 1.49803 | − | 1.49803i | 0.00273863 | − | 0.00273863i | −0.705736 | − | 0.708475i | \(-0.749384\pi\) |
0.708475 | + | 0.705736i | \(0.249384\pi\) | |||||||
\(548\) | −165.783 | − | 367.250i | −0.302523 | − | 0.670165i | ||||
\(549\) | 46.2247 | − | 155.840i | 0.0841981 | − | 0.283862i | ||||
\(550\) | −14.1987 | − | 65.9634i | −0.0258157 | − | 0.119933i | ||||
\(551\) | −487.105 | −0.884038 | ||||||||
\(552\) | 69.5362 | + | 698.862i | 0.125971 | + | 1.26605i | ||||
\(553\) | 187.373i | 0.338829i | ||||||||
\(554\) | −149.550 | − | 694.773i | −0.269946 | − | 1.25410i | ||||
\(555\) | 7.06307 | − | 1.79240i | 0.0127263 | − | 0.00322955i | ||||
\(556\) | −36.5464 | + | 96.6927i | −0.0657310 | + | 0.173908i | ||||
\(557\) | −322.326 | − | 322.326i | −0.578682 | − | 0.578682i | 0.355858 | − | 0.934540i | \(-0.384189\pi\) |
−0.934540 | + | 0.355858i | \(0.884189\pi\) | |||||||
\(558\) | −209.013 | − | 15.9858i | −0.374575 | − | 0.0286484i | ||||
\(559\) | 1188.74 | 2.12654 | ||||||||
\(560\) | 129.650 | − | 8.13502i | 0.231518 | − | 0.0145268i | ||||
\(561\) | 121.830 | + | 72.5118i | 0.217166 | + | 0.129255i | ||||
\(562\) | −288.664 | − | 186.405i | −0.513637 | − | 0.331682i | ||||
\(563\) | 523.954 | + | 523.954i | 0.930646 | + | 0.930646i | 0.997746 | − | 0.0671003i | \(-0.0213748\pi\) |
−0.0671003 | + | 0.997746i | \(0.521375\pi\) | |||||||
\(564\) | −471.856 | + | 375.796i | −0.836624 | + | 0.666306i | ||||
\(565\) | −115.749 | − | 115.749i | −0.204866 | − | 0.204866i | ||||
\(566\) | 115.154 | + | 534.979i | 0.203453 | + | 0.945193i | ||||
\(567\) | −247.545 | − | 161.018i | −0.436588 | − | 0.283983i | ||||
\(568\) | 145.328 | − | 965.814i | 0.255859 | − | 1.70038i | ||||
\(569\) | −767.880 | −1.34952 | −0.674762 | − | 0.738035i | \(-0.735754\pi\) | ||||
−0.674762 | + | 0.738035i | \(0.735754\pi\) | |||||||
\(570\) | −75.8921 | + | 225.340i | −0.133144 | + | 0.395333i | ||||
\(571\) | −3.43922 | − | 3.43922i | −0.00602316 | − | 0.00602316i | 0.704089 | − | 0.710112i | \(-0.251356\pi\) |
−0.710112 | + | 0.704089i | \(0.751356\pi\) | |||||||
\(572\) | −127.120 | + | 57.3839i | −0.222237 | + | 0.100321i | ||||
\(573\) | 141.439 | + | 557.350i | 0.246840 | + | 0.972688i | ||||
\(574\) | 101.624 | − | 157.373i | 0.177044 | − | 0.274168i | ||||
\(575\) | − | 586.446i | − | 1.01991i | ||||||
\(576\) | −564.707 | + | 113.499i | −0.980394 | + | 0.197048i | ||||
\(577\) | −572.442 | −0.992100 | −0.496050 | − | 0.868294i | \(-0.665217\pi\) | ||||
−0.496050 | + | 0.868294i | \(0.665217\pi\) | |||||||
\(578\) | 838.514 | + | 541.471i | 1.45072 | + | 0.936801i | ||||
\(579\) | 141.400 | − | 35.8833i | 0.244215 | − | 0.0619746i | ||||
\(580\) | −100.324 | − | 222.243i | −0.172973 | − | 0.383178i | ||||
\(581\) | −138.057 | + | 138.057i | −0.237620 | + | 0.237620i | ||||
\(582\) | 461.524 | + | 155.437i | 0.792997 | + | 0.267073i | ||||
\(583\) | − | 110.081i | − | 0.188818i | ||||||
\(584\) | −118.985 | − | 17.9039i | −0.203741 | − | 0.0306573i | ||||
\(585\) | 197.949 | + | 364.899i | 0.338375 | + | 0.623759i | ||||
\(586\) | −203.217 | + | 43.7425i | −0.346787 | + | 0.0746460i | ||||
\(587\) | 446.694 | − | 446.694i | 0.760977 | − | 0.760977i | −0.215522 | − | 0.976499i | \(-0.569145\pi\) |
0.976499 | + | 0.215522i | \(0.0691453\pi\) | |||||||
\(588\) | 266.951 | + | 335.188i | 0.453999 | + | 0.570048i | ||||
\(589\) | 146.539 | − | 146.539i | 0.248792 | − | 0.248792i | ||||
\(590\) | −77.7479 | + | 120.399i | −0.131776 | + | 0.204066i | ||||
\(591\) | −295.668 | + | 496.764i | −0.500284 | + | 0.840548i | ||||
\(592\) | −17.4170 | + | 1.09285i | −0.0294206 | + | 0.00184603i | ||||
\(593\) | 838.112i | 1.41334i | 0.707542 | + | 0.706671i | \(0.249804\pi\) | ||||
−0.707542 | + | 0.706671i | \(0.750196\pi\) | |||||||
\(594\) | −52.3159 | + | 74.3436i | −0.0880738 | + | 0.125158i | ||||
\(595\) | 161.166 | − | 161.166i | 0.270867 | − | 0.270867i | ||||
\(596\) | 237.974 | + | 89.9457i | 0.399285 | + | 0.150916i | ||||
\(597\) | 106.827 | + | 420.959i | 0.178940 | + | 0.705123i | ||||
\(598\) | −1185.06 | + | 255.085i | −1.98171 | + | 0.426564i | ||||
\(599\) | −414.241 | −0.691555 | −0.345777 | − | 0.938317i | \(-0.612385\pi\) | ||||
−0.345777 | + | 0.938317i | \(0.612385\pi\) | |||||||
\(600\) | 478.609 | − | 47.6213i | 0.797682 | − | 0.0793688i | ||||
\(601\) | − | 305.786i | − | 0.508795i | −0.967100 | − | 0.254397i | \(-0.918123\pi\) | ||
0.967100 | − | 0.254397i | \(-0.0818771\pi\) | |||||||
\(602\) | 409.111 | − | 88.0614i | 0.679587 | − | 0.146281i | ||||
\(603\) | 38.6783 | − | 130.399i | 0.0641431 | − | 0.216250i | ||||
\(604\) | 102.458 | − | 46.2510i | 0.169632 | − | 0.0765745i | ||||
\(605\) | 186.078 | + | 186.078i | 0.307567 | + | 0.307567i | ||||
\(606\) | −246.658 | + | 122.372i | −0.407027 | + | 0.201935i | ||||
\(607\) | −103.217 | −0.170044 | −0.0850222 | − | 0.996379i | \(-0.527096\pi\) | ||||
−0.0850222 | + | 0.996379i | \(0.527096\pi\) | |||||||
\(608\) | 278.346 | − | 496.777i | 0.457805 | − | 0.817068i | ||||
\(609\) | −153.122 | + | 257.266i | −0.251431 | + | 0.422440i | ||||
\(610\) | −43.6393 | + | 67.5791i | −0.0715398 | + | 0.110785i | ||||
\(611\) | −736.214 | − | 736.214i | −1.20493 | − | 1.20493i | ||||
\(612\) | −611.382 | + | 804.708i | −0.998991 | + | 1.31488i | ||||
\(613\) | −391.273 | − | 391.273i | −0.638292 | − | 0.638292i | 0.311842 | − | 0.950134i | \(-0.399054\pi\) |
−0.950134 | + | 0.311842i | \(0.899054\pi\) | |||||||
\(614\) | −782.674 | + | 168.471i | −1.27471 | + | 0.274382i | ||||
\(615\) | −87.7891 | + | 147.498i | −0.142746 | + | 0.239834i | ||||
\(616\) | −39.4980 | + | 29.1660i | −0.0641202 | + | 0.0473474i | ||||
\(617\) | 713.373 | 1.15620 | 0.578098 | − | 0.815967i | \(-0.303795\pi\) | ||||
0.578098 | + | 0.815967i | \(0.303795\pi\) | |||||||
\(618\) | −98.0279 | + | 291.065i | −0.158621 | + | 0.470979i | ||||
\(619\) | −399.763 | − | 399.763i | −0.645821 | − | 0.645821i | 0.306159 | − | 0.951980i | \(-0.400956\pi\) |
−0.951980 | + | 0.306159i | \(0.900956\pi\) | |||||||
\(620\) | 97.0398 | + | 36.6776i | 0.156516 | + | 0.0591574i | ||||
\(621\) | −580.487 | + | 535.999i | −0.934761 | + | 0.863123i | ||||
\(622\) | 90.7895 | + | 58.6275i | 0.145964 | + | 0.0942564i | ||||
\(623\) | − | 19.8894i | − | 0.0319252i | ||||||
\(624\) | −304.410 | − | 946.436i | −0.487837 | − | 1.51672i | ||||
\(625\) | −277.635 | −0.444217 | ||||||||
\(626\) | 531.931 | − | 823.739i | 0.849730 | − | 1.31588i | ||||
\(627\) | −22.1059 | − | 87.1099i | −0.0352567 | − | 0.138931i | ||||
\(628\) | 916.834 | + | 346.531i | 1.45993 | + | 0.551800i | ||||
\(629\) | −21.6508 | + | 21.6508i | −0.0344210 | + | 0.0344210i | ||||
\(630\) | 95.1571 | + | 110.918i | 0.151043 | + | 0.176061i | ||||
\(631\) | 934.242i | 1.48057i | 0.672291 | + | 0.740287i | \(0.265310\pi\) | ||||
−0.672291 | + | 0.740287i | \(0.734690\pi\) | |||||||
\(632\) | −61.1791 | + | 406.581i | −0.0968024 | + | 0.643324i | ||||
\(633\) | −426.071 | + | 715.859i | −0.673097 | + | 1.13090i | ||||
\(634\) | −190.192 | − | 883.586i | −0.299988 | − | 1.39367i | ||||
\(635\) | 116.424 | − | 116.424i | 0.183345 | − | 0.183345i | ||||
\(636\) | 779.693 | + | 88.3580i | 1.22593 | + | 0.138928i | ||||
\(637\) | −522.978 | + | 522.978i | −0.821001 | + | 0.821001i | ||||
\(638\) | 77.4227 | + | 49.9958i | 0.121352 | + | 0.0783633i | ||||
\(639\) | 965.814 | − | 523.932i | 1.51145 | − | 0.819925i | ||||
\(640\) | 283.984 | + | 24.6798i | 0.443725 | + | 0.0385622i | ||||
\(641\) | 26.1836i | 0.0408480i | 0.999791 | + | 0.0204240i | \(0.00650162\pi\) | ||||
−0.999791 | + | 0.0204240i | \(0.993498\pi\) | |||||||
\(642\) | 649.675 | − | 322.318i | 1.01195 | − | 0.502052i | ||||
\(643\) | 625.336 | − | 625.336i | 0.972529 | − | 0.972529i | −0.0271039 | − | 0.999633i | \(-0.508629\pi\) |
0.999633 | + | 0.0271039i | \(0.00862850\pi\) | |||||||
\(644\) | −388.949 | + | 175.578i | −0.603959 | + | 0.272637i | ||||
\(645\) | −371.660 | + | 94.3165i | −0.576218 | + | 0.146227i | ||||
\(646\) | −210.243 | − | 976.737i | −0.325454 | − | 1.51198i | ||||
\(647\) | −97.2591 | −0.150323 | −0.0751616 | − | 0.997171i | \(-0.523947\pi\) | ||||
−0.0751616 | + | 0.997171i | \(0.523947\pi\) | |||||||
\(648\) | −484.576 | − | 430.221i | −0.747803 | − | 0.663921i | ||||
\(649\) | − | 54.1699i | − | 0.0834668i | ||||||
\(650\) | 174.693 | + | 811.579i | 0.268758 | + | 1.24858i | ||||
\(651\) | −31.3303 | − | 123.459i | −0.0481265 | − | 0.189645i | ||||
\(652\) | 274.729 | + | 103.838i | 0.421364 | + | 0.159261i | ||||
\(653\) | −129.213 | − | 129.213i | −0.197875 | − | 0.197875i | 0.601213 | − | 0.799089i | \(-0.294684\pi\) |
−0.799089 | + | 0.601213i | \(0.794684\pi\) | |||||||
\(654\) | 401.742 | − | 199.313i | 0.614284 | − | 0.304760i | ||||
\(655\) | −498.965 | −0.761778 | ||||||||
\(656\) | 271.897 | − | 308.303i | 0.414478 | − | 0.469974i | ||||
\(657\) | −64.5464 | − | 118.985i | −0.0982442 | − | 0.181103i | ||||
\(658\) | −307.911 | − | 198.834i | −0.467950 | − | 0.302179i | ||||
\(659\) | −3.10975 | − | 3.10975i | −0.00471889 | − | 0.00471889i | 0.704743 | − | 0.709462i | \(-0.251062\pi\) |
−0.709462 | + | 0.704743i | \(0.751062\pi\) | |||||||
\(660\) | 35.1912 | − | 28.0271i | 0.0533200 | − | 0.0424652i | ||||
\(661\) | −22.3424 | − | 22.3424i | −0.0338010 | − | 0.0338010i | 0.690004 | − | 0.723805i | \(-0.257609\pi\) |
−0.723805 | + | 0.690004i | \(0.757609\pi\) | |||||||
\(662\) | 160.362 | + | 745.003i | 0.242239 | + | 1.12538i | ||||
\(663\) | −1498.93 | − | 892.146i | −2.26083 | − | 1.34562i | ||||
\(664\) | −344.648 | + | 254.494i | −0.519049 | + | 0.383274i | ||||
\(665\) | −144.479 | −0.217262 | ||||||||
\(666\) | −12.7833 | − | 14.9006i | −0.0191941 | − | 0.0223733i | ||||
\(667\) | 566.405 | + | 566.405i | 0.849183 | + | 0.849183i | ||||
\(668\) | 94.6855 | + | 209.752i | 0.141745 | + | 0.314000i | ||||
\(669\) | −1091.20 | + | 276.914i | −1.63109 | + | 0.413922i | ||||
\(670\) | −36.5149 | + | 56.5464i | −0.0544999 | + | 0.0843976i | ||||
\(671\) | − | 30.4052i | − | 0.0453132i | ||||||
\(672\) | −174.876 | − | 303.171i | −0.260233 | − | 0.451148i | ||||
\(673\) | 1085.74 | 1.61329 | 0.806643 | − | 0.591039i | \(-0.201282\pi\) | ||||
0.806643 | + | 0.591039i | \(0.201282\pi\) | |||||||
\(674\) | −240.328 | − | 155.192i | −0.356570 | − | 0.230256i | ||||
\(675\) | 367.074 | + | 397.541i | 0.543814 | + | 0.588950i | ||||
\(676\) | 947.881 | − | 427.889i | 1.40219 | − | 0.632972i | ||||
\(677\) | 813.520 | − | 813.520i | 1.20165 | − | 1.20165i | 0.227991 | − | 0.973663i | \(-0.426784\pi\) |
0.973663 | − | 0.227991i | \(-0.0732157\pi\) | |||||||
\(678\) | −140.765 | + | 417.960i | −0.207617 | + | 0.616460i | ||||
\(679\) | 295.911i | 0.435804i | ||||||||
\(680\) | 402.338 | − | 297.093i | 0.591673 | − | 0.436901i | ||||
\(681\) | 660.276 | + | 392.988i | 0.969568 | + | 0.577075i | ||||
\(682\) | −38.3320 | + | 8.25098i | −0.0562053 | + | 0.0120982i | ||||
\(683\) | −427.362 | + | 427.362i | −0.625713 | + | 0.625713i | −0.946986 | − | 0.321273i | \(-0.895889\pi\) |
0.321273 | + | 0.946986i | \(0.395889\pi\) | |||||||
\(684\) | 634.734 | − | 86.6543i | 0.927974 | − | 0.126688i | ||||
\(685\) | −158.627 | + | 158.627i | −0.231573 | + | 0.231573i | ||||
\(686\) | −335.062 | + | 518.872i | −0.488429 | + | 0.756373i | ||||
\(687\) | −561.217 | − | 334.030i | −0.816910 | − | 0.486215i | ||||
\(688\) | 916.486 | − | 57.5059i | 1.33210 | − | 0.0835842i | ||||
\(689\) | 1354.38i | 1.96572i | ||||||||
\(690\) | 350.272 | − | 173.778i | 0.507641 | − | 0.251852i | ||||
\(691\) | −420.170 | + | 420.170i | −0.608061 | + | 0.608061i | −0.942439 | − | 0.334378i | \(-0.891474\pi\) |
0.334378 | + | 0.942439i | \(0.391474\pi\) | |||||||
\(692\) | −225.200 | + | 595.824i | −0.325434 | + | 0.861018i | ||||
\(693\) | −52.9563 | − | 15.7077i | −0.0764161 | − | 0.0226662i | ||||
\(694\) | 350.952 | − | 75.5425i | 0.505694 | − | 0.108851i | ||||
\(695\) | 57.5504 | 0.0828063 | ||||||||
\(696\) | −416.260 | + | 508.247i | −0.598074 | + | 0.730240i | ||||
\(697\) | − | 721.239i | − | 1.03478i | ||||||
\(698\) | −541.662 | + | 116.593i | −0.776020 | + | 0.167039i | ||||
\(699\) | −150.565 | + | 38.2089i | −0.215400 | + | 0.0546622i | ||||
\(700\) | 120.243 | + | 266.369i | 0.171776 | + | 0.380527i | ||||
\(701\) | −774.018 | − | 774.018i | −1.10416 | − | 1.10416i | −0.993903 | − | 0.110260i | \(-0.964832\pi\) |
−0.110260 | − | 0.993903i | \(-0.535168\pi\) | |||||||
\(702\) | 643.666 | − | 914.684i | 0.916904 | − | 1.30297i | ||||
\(703\) | 19.4091 | 0.0276090 | ||||||||
\(704\) | −95.2301 | + | 50.3910i | −0.135270 | + | 0.0715781i | ||||
\(705\) | 288.591 | + | 171.766i | 0.409349 | + | 0.243639i | ||||
\(706\) | −316.251 | + | 489.741i | −0.447948 | + | 0.693684i | ||||
\(707\) | −118.304 | − | 118.304i | −0.167332 | − | 0.167332i | ||||
\(708\) | 383.680 | + | 43.4802i | 0.541921 | + | 0.0614128i | ||||
\(709\) | 198.261 | + | 198.261i | 0.279635 | + | 0.279635i | 0.832963 | − | 0.553328i | \(-0.186642\pi\) |
−0.553328 | + | 0.832963i | \(0.686642\pi\) | |||||||
\(710\) | −531.592 | + | 114.425i | −0.748722 | + | 0.161163i | ||||
\(711\) | −406.581 | + | 220.561i | −0.571844 | + | 0.310212i | ||||
\(712\) | 6.49409 | − | 43.1581i | 0.00912092 | − | 0.0606154i | ||||
\(713\) | −340.790 | −0.477966 | ||||||||
\(714\) | −581.957 | − | 195.997i | −0.815065 | − | 0.274506i | ||||
\(715\) | 54.9072 | + | 54.9072i | 0.0767932 | + | 0.0767932i | ||||
\(716\) | −44.9620 | + | 118.958i | −0.0627961 | + | 0.166143i | ||||
\(717\) | −184.406 | − | 726.665i | −0.257192 | − | 1.01348i | ||||
\(718\) | −67.7935 | − | 43.7777i | −0.0944199 | − | 0.0609718i | ||||
\(719\) | 639.218i | 0.889037i | 0.895770 | + | 0.444519i | \(0.146625\pi\) | ||||
−0.895770 | + | 0.444519i | \(0.853375\pi\) | |||||||
\(720\) | 170.266 | + | 271.752i | 0.236481 | + | 0.377434i | ||||
\(721\) | −186.620 | −0.258834 | ||||||||
\(722\) | 48.1025 | − | 74.4907i | 0.0666239 | − | 0.103173i | ||||
\(723\) | 1286.80 | − | 326.553i | 1.77981 | − | 0.451664i | ||||
\(724\) | 37.2026 | − | 98.4288i | 0.0513848 | − | 0.135951i | ||||
\(725\) | 387.898 | − | 387.898i | 0.535031 | − | 0.535031i | ||||
\(726\) | 226.293 | − | 671.913i | 0.311699 | − | 0.925500i | ||||
\(727\) | − | 789.136i | − | 1.08547i | −0.839904 | − | 0.542734i | \(-0.817389\pi\) | ||
0.839904 | − | 0.542734i | \(-0.182611\pi\) | |||||||
\(728\) | 485.963 | − | 358.843i | 0.667531 | − | 0.492916i | ||||
\(729\) | 58.0032 | − | 726.689i | 0.0795654 | − | 0.996830i | ||||
\(730\) | 14.0968 | + | 65.4902i | 0.0193107 | + | 0.0897125i | ||||
\(731\) | 1139.27 | − | 1139.27i | 1.55851 | − | 1.55851i | ||||
\(732\) | 215.357 | + | 24.4051i | 0.294203 | + | 0.0333403i | ||||
\(733\) | −49.8641 | + | 49.8641i | −0.0680274 | + | 0.0680274i | −0.740302 | − | 0.672275i | \(-0.765317\pi\) |
0.672275 | + | 0.740302i | \(0.265317\pi\) | |||||||
\(734\) | −572.388 | − | 369.620i | −0.779820 | − | 0.503570i | ||||
\(735\) | 122.016 | − | 205.004i | 0.166008 | − | 0.278917i | ||||
\(736\) | −901.312 | + | 253.992i | −1.22461 | + | 0.345098i | ||||
\(737\) | − | 25.4414i | − | 0.0345202i | ||||||
\(738\) | 461.107 | + | 35.2666i | 0.624807 | + | 0.0477867i | ||||
\(739\) | 157.593 | − | 157.593i | 0.213252 | − | 0.213252i | −0.592395 | − | 0.805647i | \(-0.701818\pi\) |
0.805647 | + | 0.592395i | \(0.201818\pi\) | |||||||
\(740\) | 3.99750 | + | 8.85547i | 0.00540203 | + | 0.0119669i | ||||
\(741\) | 271.980 | + | 1071.75i | 0.367044 | + | 1.44636i | ||||
\(742\) | 100.332 | + | 466.118i | 0.135218 | + | 0.628191i | ||||
\(743\) | 1305.03 | 1.75643 | 0.878216 | − | 0.478265i | \(-0.158734\pi\) | ||||
0.878216 | + | 0.478265i | \(0.158734\pi\) | |||||||
\(744\) | −27.6732 | − | 278.125i | −0.0371952 | − | 0.373824i | ||||
\(745\) | − | 141.639i | − | 0.190120i | ||||||
\(746\) | −141.463 | − | 657.203i | −0.189629 | − | 0.880970i | ||||
\(747\) | −462.082 | − | 137.061i | −0.618583 | − | 0.183482i | ||||
\(748\) | −66.8340 | + | 176.826i | −0.0893503 | + | 0.236399i | ||||
\(749\) | 311.601 | + | 311.601i | 0.416023 | + | 0.416023i | ||||
\(750\) | −267.472 | − | 539.126i | −0.356629 | − | 0.718834i | ||||
\(751\) | 793.800 | 1.05699 | 0.528495 | − | 0.848936i | \(-0.322756\pi\) | ||||
0.528495 | + | 0.848936i | \(0.322756\pi\) | |||||||
\(752\) | −603.217 | − | 531.987i | −0.802150 | − | 0.707430i | ||||
\(753\) | 94.0079 | − | 157.947i | 0.124844 | − | 0.209756i | ||||
\(754\) | −952.567 | − | 615.122i | −1.26335 | − | 0.815811i | ||||
\(755\) | −44.2548 | − | 44.2548i | −0.0586156 | − | 0.0586156i | ||||
\(756\) | 153.762 | − | 362.477i | 0.203389 | − | 0.479466i | ||||
\(757\) | −750.497 | − | 750.497i | −0.991409 | − | 0.991409i | 0.00855438 | − | 0.999963i | \(-0.497277\pi\) |
−0.999963 | + | 0.00855438i | \(0.997277\pi\) | |||||||
\(758\) | −190.658 | − | 885.749i | −0.251527 | − | 1.16853i | ||||
\(759\) | −75.5865 | + | 126.996i | −0.0995870 | + | 0.167320i | ||||
\(760\) | −313.506 | − | 47.1739i | −0.412508 | − | 0.0620709i | ||||
\(761\) | 1055.45 | 1.38692 | 0.693462 | − | 0.720493i | \(-0.256084\pi\) | ||||
0.693462 | + | 0.720493i | \(0.256084\pi\) | |||||||
\(762\) | −420.398 | − | 141.586i | −0.551703 | − | 0.185808i | ||||
\(763\) | 192.686 | + | 192.686i | 0.252538 | + | 0.252538i | ||||
\(764\) | −698.790 | + | 315.445i | −0.914646 | + | 0.412886i | ||||
\(765\) | 539.428 | + | 160.003i | 0.705134 | + | 0.209154i | ||||
\(766\) | −686.450 | + | 1063.02i | −0.896148 | + | 1.38776i | ||||
\(767\) | 666.478i | 0.868942i | ||||||||
\(768\) | −280.477 | − | 714.952i | −0.365204 | − | 0.930927i | ||||
\(769\) | 883.681 | 1.14913 | 0.574565 | − | 0.818459i | \(-0.305171\pi\) | ||||
0.574565 | + | 0.818459i | \(0.305171\pi\) | |||||||
\(770\) | 22.9641 | + | 14.8291i | 0.0298236 | + | 0.0192586i | ||||
\(771\) | 132.234 | + | 521.076i | 0.171509 | + | 0.675844i | ||||
\(772\) | 80.0287 | + | 177.284i | 0.103664 | + | 0.229642i | ||||
\(773\) | 894.518 | − | 894.518i | 1.15720 | − | 1.15720i | 0.172129 | − | 0.985074i | \(-0.444935\pi\) |
0.985074 | − | 0.172129i | \(-0.0550647\pi\) | |||||||
\(774\) | 672.660 | + | 784.074i | 0.869069 | + | 1.01302i | ||||
\(775\) | 233.387i | 0.301144i | ||||||||
\(776\) | −96.6181 | + | 642.100i | −0.124508 | + | 0.827448i | ||||
\(777\) | 6.10126 | − | 10.2510i | 0.00785233 | − | 0.0131930i | ||||
\(778\) | 1173.37 | − | 252.569i | 1.50819 | − | 0.324638i | ||||
\(779\) | −323.281 | + | 323.281i | −0.414995 | + | 0.414995i | ||||
\(780\) | −432.974 | + | 344.830i | −0.555095 | + | 0.442090i | ||||
\(781\) | 145.328 | − | 145.328i | 0.186079 | − | 0.186079i | ||||
\(782\) | −891.279 | + | 1380.22i | −1.13974 | + | 1.76499i | ||||
\(783\) | −738.486 | − | 29.4256i | −0.943150 | − | 0.0375806i | ||||
\(784\) | −377.903 | + | 428.502i | −0.482019 | + | 0.546559i | ||||
\(785\) | − | 545.689i | − | 0.695145i | ||||||
\(786\) | 597.459 | + | 1204.26i | 0.760126 | + | 1.53214i | ||||
\(787\) | −779.150 | + | 779.150i | −0.990026 | + | 0.990026i | −0.999951 | − | 0.00992500i | \(-0.996841\pi\) |
0.00992500 | + | 0.999951i | \(0.496841\pi\) | |||||||
\(788\) | −721.011 | − | 272.517i | −0.914989 | − | 0.345833i | ||||
\(789\) | −1219.77 | + | 309.542i | −1.54597 | + | 0.392322i | ||||
\(790\) | 223.786 | − | 48.1699i | 0.283273 | − | 0.0609746i | ||||
\(791\) | −267.979 | −0.338785 | ||||||||
\(792\) | −109.782 | − | 51.3750i | −0.138613 | − | 0.0648675i | ||||
\(793\) | 374.089i | 0.471739i | ||||||||
\(794\) | 1232.34 | − | 265.262i | 1.55207 | − | 0.334084i | ||||
\(795\) | −107.459 | − | 423.448i | −0.135168 | − | 0.532639i | ||||
\(796\) | −527.786 | + | 238.251i | −0.663047 | + | 0.299310i | ||||
\(797\) | 149.801 | + | 149.801i | 0.187956 | + | 0.187956i | 0.794812 | − | 0.606856i | \(-0.207570\pi\) |
−0.606856 | + | 0.794812i | \(0.707570\pi\) | |||||||
\(798\) | 172.999 | + | 348.702i | 0.216790 | + | 0.436970i | ||||
\(799\) | −1411.16 | −1.76616 | ||||||||
\(800\) | 173.944 | + | 617.256i | 0.217430 | + | 0.771570i | ||||
\(801\) | 43.1581 | − | 23.4123i | 0.0538803 | − | 0.0292288i | ||||
\(802\) | −603.122 | + | 933.984i | −0.752022 | + | 1.16457i | ||||
\(803\) | −17.9039 | − | 17.9039i | −0.0222962 | − | 0.0222962i | ||||
\(804\) | 180.199 | + | 20.4208i | 0.224128 | + | 0.0253991i | ||||
\(805\) | 168.000 | + | 168.000i | 0.208696 | + | 0.208696i | ||||
\(806\) | 471.617 | − | 101.516i | 0.585132 | − | 0.125950i | ||||
\(807\) | 123.092 | + | 73.2628i | 0.152530 | + | 0.0907841i | ||||
\(808\) | −218.081 | − | 295.336i | −0.269902 | − | 0.365515i | ||||
\(809\) | −373.773 | −0.462019 | −0.231009 | − | 0.972951i | \(-0.574203\pi\) | ||||
−0.231009 | + | 0.972951i | \(0.574203\pi\) | |||||||
\(810\) | −128.671 | + | 337.047i | −0.158853 | + | 0.416107i | ||||
\(811\) | −239.150 | − | 239.150i | −0.294883 | − | 0.294883i | 0.544123 | − | 0.839006i | \(-0.316863\pi\) |
−0.839006 | + | 0.544123i | \(0.816863\pi\) | |||||||
\(812\) | −373.400 | − | 141.132i | −0.459852 | − | 0.173808i | ||||
\(813\) | 957.459 | − | 242.975i | 1.17769 | − | 0.298862i | ||||
\(814\) | −3.08497 | − | 1.99213i | −0.00378989 | − | 0.00244733i | ||||
\(815\) | − | 163.516i | − | 0.200633i | ||||||
\(816\) | −1198.80 | − | 615.310i | −1.46911 | − | 0.754057i | ||||
\(817\) | −1021.31 | −1.25008 | ||||||||
\(818\) | 48.6343 | − | 75.3142i | 0.0594551 | − | 0.0920712i | ||||
\(819\) | 651.547 | + | 193.259i | 0.795539 | + | 0.235970i | ||||
\(820\) | −214.081 | − | 80.9150i | −0.261074 | − | 0.0986769i | ||||
\(821\) | −385.069 | + | 385.069i | −0.469024 | + | 0.469024i | −0.901598 | − | 0.432574i | \(-0.857605\pi\) |
0.432574 | + | 0.901598i | \(0.357605\pi\) | |||||||
\(822\) | 572.790 | + | 192.910i | 0.696825 | + | 0.234684i | ||||
\(823\) | 1270.78i | 1.54408i | 0.635576 | + | 0.772038i | \(0.280763\pi\) | ||||
−0.635576 | + | 0.772038i | \(0.719237\pi\) | |||||||
\(824\) | −404.947 | − | 60.9332i | −0.491441 | − | 0.0739481i | ||||
\(825\) | 86.9721 | + | 51.7648i | 0.105421 | + | 0.0627452i | ||||
\(826\) | 49.3725 | + | 229.373i | 0.0597731 | + | 0.277691i | ||||
\(827\) | −113.766 | + | 113.766i | −0.137565 | + | 0.137565i | −0.772536 | − | 0.634971i | \(-0.781012\pi\) |
0.634971 | + | 0.772536i | \(0.281012\pi\) | |||||||
\(828\) | −838.830 | − | 637.307i | −1.01308 | − | 0.769694i | ||||
\(829\) | 238.593 | − | 238.593i | 0.287809 | − | 0.287809i | −0.548404 | − | 0.836213i | \(-0.684765\pi\) |
0.836213 | + | 0.548404i | \(0.184765\pi\) | |||||||
\(830\) | 200.378 | + | 129.395i | 0.241420 | + | 0.155897i | ||||
\(831\) | 916.051 | + | 545.222i | 1.10235 | + | 0.656104i | ||||
\(832\) | 1171.66 | − | 619.984i | 1.40825 | − | 0.745173i | ||||
\(833\) | 1002.43i | 1.20340i | ||||||||
\(834\) | −68.9107 | − | 138.899i | −0.0826267 | − | 0.166545i | ||||
\(835\) | 90.5988 | − | 90.5988i | 0.108502 | − | 0.108502i | ||||
\(836\) | 109.216 | − | 49.3018i | 0.130641 | − | 0.0589734i | ||||
\(837\) | 231.015 | − | 213.311i | 0.276004 | − | 0.254852i | ||||
\(838\) | −9.04839 | − | 42.0366i | −0.0107976 | − | 0.0501630i | ||||
\(839\) | −65.2466 | −0.0777671 | −0.0388836 | − | 0.999244i | \(-0.512380\pi\) | ||||
−0.0388836 | + | 0.999244i | \(0.512380\pi\) | |||||||
\(840\) | −123.466 | + | 150.750i | −0.146983 | + | 0.179464i | ||||
\(841\) | − | 91.7164i | − | 0.109056i | ||||||
\(842\) | −156.468 | − | 726.913i | −0.185829 | − | 0.863317i | ||||
\(843\) | 499.592 | − | 126.782i | 0.592636 | − | 0.150394i | ||||
\(844\) | −1039.01 | − | 392.708i | −1.23105 | − | 0.465294i | ||||
\(845\) | −409.421 | − | 409.421i | −0.484522 | − | 0.484522i | ||||
\(846\) | 69.0017 | − | 902.191i | 0.0815623 | − | 1.06642i | ||||
\(847\) | 430.804 | 0.508623 | ||||||||
\(848\) | 65.5189 | + | 1044.19i | 0.0772629 | + | 1.23136i | ||||
\(849\) | −705.365 | − | 419.825i | −0.830818 | − | 0.494493i | ||||
\(850\) | 945.231 | + | 610.384i | 1.11204 | + | 0.718099i | ||||
\(851\) | −22.5689 | − | 22.5689i | −0.0265205 | − | 0.0265205i | ||||
\(852\) | 912.695 | + | 1145.99i | 1.07124 | + | 1.34506i | ||||
\(853\) | −245.067 | − | 245.067i | −0.287300 | − | 0.287300i | 0.548712 | − | 0.836012i | \(-0.315118\pi\) |
−0.836012 | + | 0.548712i | \(0.815118\pi\) | |||||||
\(854\) | 27.7124 | + | 128.745i | 0.0324501 | + | 0.150755i | ||||
\(855\) | −170.070 | − | 313.506i | −0.198912 | − | 0.366674i | ||||
\(856\) | 574.405 | + | 777.887i | 0.671034 | + | 0.908747i | ||||
\(857\) | −1408.63 | −1.64368 | −0.821841 | − | 0.569718i | \(-0.807053\pi\) | ||||
−0.821841 | + | 0.569718i | \(0.807053\pi\) | |||||||
\(858\) | 66.7736 | − | 198.265i | 0.0778248 | − | 0.231078i | ||||
\(859\) | −50.1621 | − | 50.1621i | −0.0583959 | − | 0.0583959i | 0.677306 | − | 0.735702i | \(-0.263147\pi\) |
−0.735702 | + | 0.677306i | \(0.763147\pi\) | |||||||
\(860\) | −210.350 | − | 465.977i | −0.244592 | − | 0.541834i | ||||
\(861\) | 69.1184 | + | 272.365i | 0.0802769 | + | 0.316336i | ||||
\(862\) | −176.959 | + | 274.037i | −0.205289 | + | 0.317908i | ||||
\(863\) | − | 1027.80i | − | 1.19096i | −0.803370 | − | 0.595480i | \(-0.796962\pi\) | ||
0.803370 | − | 0.595480i | \(-0.203038\pi\) | |||||||
\(864\) | 452.002 | − | 736.336i | 0.523151 | − | 0.852240i | ||||
\(865\) | 354.627 | 0.409974 | ||||||||
\(866\) | 236.458 | + | 152.693i | 0.273047 | + | 0.176320i | ||||
\(867\) | −1451.22 | + | 368.277i | −1.67384 | + | 0.424772i | ||||
\(868\) | 154.790 | − | 69.8745i | 0.178329 | − | 0.0805006i | ||||
\(869\) | −61.1791 | + | 61.1791i | −0.0704017 | + | 0.0704017i | ||||
\(870\) | 346.626 | + | 116.740i | 0.398421 | + | 0.134184i | ||||
\(871\) | 313.017i | 0.359376i | ||||||||
\(872\) | 355.197 | + | 481.025i | 0.407336 | + | 0.551635i | ||||
\(873\) | −642.100 | + | 348.324i | −0.735509 | + | 0.398997i | ||||
\(874\) | 1018.15 | − | 219.158i | 1.16494 | − | 0.250753i | ||||
\(875\) | 258.579 | − | 258.579i | 0.295519 | − | 0.295519i | ||||
\(876\) | 141.182 | − | 112.441i | 0.161167 | − | 0.128357i | ||||
\(877\) | 600.071 | − | 600.071i | 0.684231 | − | 0.684231i | −0.276720 | − | 0.960951i | \(-0.589247\pi\) |
0.960951 | + | 0.276720i | \(0.0892473\pi\) | |||||||
\(878\) | 471.839 | − | 730.681i | 0.537401 | − | 0.832211i | ||||
\(879\) | 159.474 | − | 267.940i | 0.181427 | − | 0.304823i | ||||
\(880\) | 44.9882 | + | 39.6759i | 0.0511229 | + | 0.0450862i | ||||
\(881\) | − | 786.482i | − | 0.892715i | −0.894855 | − | 0.446358i | \(-0.852721\pi\) | ||
0.894855 | − | 0.446358i | \(-0.147279\pi\) | |||||||
\(882\) | −640.881 | − | 49.0161i | −0.726623 | − | 0.0555738i | ||||
\(883\) | −390.413 | + | 390.413i | −0.442144 | + | 0.442144i | −0.892732 | − | 0.450588i | \(-0.851214\pi\) |
0.450588 | + | 0.892732i | \(0.351214\pi\) | |||||||
\(884\) | 822.290 | − | 2175.57i | 0.930192 | − | 2.46106i | ||||
\(885\) | −52.8796 | − | 208.375i | −0.0597509 | − | 0.235452i | ||||
\(886\) | 719.940 | − | 154.967i | 0.812573 | − | 0.174907i | ||||
\(887\) | 1446.61 | 1.63090 | 0.815450 | − | 0.578827i | \(-0.196489\pi\) | ||||
0.815450 | + | 0.578827i | \(0.196489\pi\) | |||||||
\(888\) | 16.5862 | − | 20.2516i | 0.0186782 | − | 0.0228058i | ||||
\(889\) | − | 269.542i | − | 0.303197i | ||||||
\(890\) | −23.7546 | + | 5.11319i | −0.0266906 | + | 0.00574515i | ||||
\(891\) | −28.2520 | − | 133.400i | −0.0317081 | − | 0.149720i | ||||
\(892\) | −617.587 | − | 1368.11i | −0.692362 | − | 1.53376i | ||||
\(893\) | 632.524 | + | 632.524i | 0.708313 | + | 0.708313i | ||||
\(894\) | −341.849 | + | 169.598i | −0.382381 | + | 0.189707i | ||||
\(895\) | 70.8025 | 0.0791089 | ||||||||
\(896\) | 357.306 | − | 300.168i | 0.398779 | − | 0.335009i | ||||
\(897\) | 929.976 | − | 1562.49i | 1.03676 | − | 1.74191i | ||||
\(898\) | −107.357 | + | 166.251i | −0.119551 | + | 0.185135i | ||||
\(899\) | −225.411 | − | 225.411i | −0.250736 | − | 0.250736i | ||||
\(900\) | −436.454 | + | 574.465i | −0.484949 | + | 0.638295i | ||||
\(901\) | 1298.02 | + | 1298.02i | 1.44064 | + | 1.44064i | ||||
\(902\) | 84.5649 | − | 18.2026i | 0.0937527 | − | 0.0201803i | ||||
\(903\) | −321.050 | + | 539.409i | −0.355537 | + | 0.597352i | ||||
\(904\) | −581.490 | − | 87.4980i | −0.643241 | − | 0.0967899i | ||||
\(905\) | −58.5836 | −0.0647333 | ||||||||
\(906\) | −53.8191 | + | 159.800i | −0.0594029 | + | 0.176380i | ||||
\(907\) | −535.919 | − | 535.919i | −0.590870 | − | 0.590870i | 0.346997 | − | 0.937866i | \(-0.387202\pi\) |
−0.937866 | + | 0.346997i | \(0.887202\pi\) | |||||||
\(908\) | −362.217 | + | 958.335i | −0.398917 | + | 1.05544i | ||||
\(909\) | 117.450 | − | 395.967i | 0.129208 | − | 0.435607i | ||||
\(910\) | −282.539 | − | 182.450i | −0.310482 | − | 0.200494i | ||||
\(911\) | 1580.22i | 1.73460i | 0.497786 | + | 0.867300i | \(0.334146\pi\) | ||||
−0.497786 | + | 0.867300i | \(0.665854\pi\) | |||||||
\(912\) | 261.536 | + | 813.138i | 0.286772 | + | 0.891598i | ||||
\(913\) | −90.1542 | −0.0987450 | ||||||||
\(914\) | 15.6460 | − | 24.2292i | 0.0171182 | − | 0.0265090i | ||||
\(915\) | −29.6809 | − | 116.959i | −0.0324381 | − | 0.127825i | ||||
\(916\) | 307.875 | − | 814.559i | 0.336108 | − | 0.889257i | ||||
\(917\) | −577.595 | + | 577.595i | −0.629875 | + | 0.629875i | ||||
\(918\) | −259.740 | − | 1493.50i | −0.282941 | − | 1.62691i | ||||
\(919\) | − | 1486.86i | − | 1.61791i | −0.587869 | − | 0.808956i | \(-0.700033\pi\) | ||
0.587869 | − | 0.808956i | \(-0.299967\pi\) | |||||||
\(920\) | 309.691 | + | 419.398i | 0.336620 | + | 0.455868i | ||||
\(921\) | 614.203 | − | 1031.95i | 0.666887 | − | 1.12046i | ||||
\(922\) | −195.387 | − | 907.719i | −0.211916 | − | 0.984511i | ||||
\(923\) | −1788.04 | + | 1788.04i | −1.93720 | + | 1.93720i | ||||
\(924\) | 8.29313 | − | 73.1807i | 0.00897525 | − | 0.0791999i | ||||
\(925\) | −15.4561 | + | 15.4561i | −0.0167093 | + | 0.0167093i | ||||
\(926\) | 1425.48 | + | 920.504i | 1.53939 | + | 0.994065i | ||||
\(927\) | −219.674 | − | 404.947i | −0.236974 | − | 0.436836i | ||||
\(928\) | −764.162 | − | 428.162i | −0.823451 | − | 0.461382i | ||||
\(929\) | − | 1091.41i | − | 1.17482i | −0.809290 | − | 0.587409i | \(-0.800148\pi\) | ||
0.809290 | − | 0.587409i | \(-0.199852\pi\) | |||||||
\(930\) | −139.397 | + | 69.1580i | −0.149889 | + | 0.0743634i | ||||
\(931\) | 449.320 | − | 449.320i | 0.482621 | − | 0.482621i | ||||
\(932\) | −85.2154 | − | 188.773i | −0.0914328 | − | 0.202547i | ||||
\(933\) | −157.130 | + | 39.8750i | −0.168414 | + | 0.0427384i | ||||
\(934\) | −33.3725 | − | 155.041i | −0.0357308 | − | 0.165996i | ||||
\(935\) | 105.245 | 0.112561 | ||||||||
\(936\) | 1350.69 | + | 632.091i | 1.44305 | + | 0.675311i | ||||
\(937\) | 887.919i | 0.947619i | 0.880627 | + | 0.473809i | \(0.157121\pi\) | ||||
−0.880627 | + | 0.473809i | \(0.842879\pi\) | |||||||
\(938\) | 23.1882 | + | 107.727i | 0.0247209 | + | 0.114847i | ||||
\(939\) | 361.788 | + | 1425.65i | 0.385291 | + | 1.51826i | ||||
\(940\) | −158.316 | + | 418.865i | −0.168422 | + | 0.445602i | ||||
\(941\) | −790.753 | − | 790.753i | −0.840333 | − | 0.840333i | 0.148569 | − | 0.988902i | \(-0.452533\pi\) |
−0.988902 | + | 0.148569i | \(0.952533\pi\) | |||||||
\(942\) | −1317.03 | + | 653.406i | −1.39812 | + | 0.693637i | ||||
\(943\) | 751.822 | 0.797266 | ||||||||
\(944\) | 32.2413 | + | 513.838i | 0.0341539 | + | 0.544320i | ||||
\(945\) | −219.041 | − | 8.72786i | −0.231789 | − | 0.00923583i | ||||
\(946\) | 162.332 | + | 104.826i | 0.171598 | + | 0.110810i | ||||
\(947\) | −1170.78 | − | 1170.78i | −1.23630 | − | 1.23630i | −0.961502 | − | 0.274796i | \(-0.911390\pi\) |
−0.274796 | − | 0.961502i | \(-0.588610\pi\) | |||||||
\(948\) | −384.219 | − | 482.432i | −0.405295 | − | 0.508894i | ||||
\(949\) | 220.280 | + | 220.280i | 0.232118 | + | 0.232118i | ||||
\(950\) | −150.089 | − | 697.274i | −0.157988 | − | 0.733973i | ||||
\(951\) | 1165.00 | + | 693.393i | 1.22503 | + | 0.729120i | ||||
\(952\) | 121.830 | − | 809.652i | 0.127973 | − | 0.850475i | ||||
\(953\) | −1148.50 | −1.20514 | −0.602571 | − | 0.798065i | \(-0.705857\pi\) | ||||
−0.602571 | + | 0.798065i | \(0.705857\pi\) | |||||||
\(954\) | −893.329 | + | 766.390i | −0.936403 | + | 0.803343i | ||||
\(955\) | 301.830 | + | 301.830i | 0.316052 | + | 0.316052i | ||||
\(956\) | 911.072 | − | 411.273i | 0.953004 | − | 0.430201i | ||||
\(957\) | −133.996 | + | 34.0042i | −0.140016 | + | 0.0355321i | ||||
\(958\) | 703.911 | − | 1090.07i | 0.734771 | − | 1.13786i | ||||
\(959\) | 367.250i | 0.382951i | ||||||||
\(960\) | −317.131 | + | 286.801i | −0.330344 | + | 0.298751i | ||||
\(961\) | −825.376 | −0.858873 | ||||||||
\(962\) | 37.9559 | + | 24.5101i | 0.0394552 | + | 0.0254782i | ||||
\(963\) | −309.353 | + | 1042.94i | −0.321238 | + | 1.08301i | ||||
\(964\) | 728.295 | + | 1613.36i | 0.755493 | + | 1.67361i | ||||
\(965\) | 76.5746 | − | 76.5746i | 0.0793519 | − | 0.0793519i | ||||
\(966\) | 204.308 | − | 606.634i | 0.211499 | − | 0.627985i | ||||
\(967\) | − | 1696.75i | − | 1.75466i | −0.479892 | − | 0.877328i | \(-0.659324\pi\) | ||
0.479892 | − | 0.877328i | \(-0.340676\pi\) | |||||||
\(968\) | 934.804 | + | 140.662i | 0.965707 | + | 0.145312i | ||||
\(969\) | 1287.82 | + | 766.494i | 1.32902 | + | 0.791016i | ||||
\(970\) | 353.417 | − | 76.0732i | 0.364347 | − | 0.0784259i | ||||
\(971\) | −119.876 | + | 119.876i | −0.123457 | + | 0.123457i | −0.766136 | − | 0.642679i | \(-0.777823\pi\) |
0.642679 | + | 0.766136i | \(0.277823\pi\) | |||||||
\(972\) | 967.538 | − | 93.0304i | 0.995409 | − | 0.0957102i | ||||
\(973\) | 66.6196 | − | 66.6196i | 0.0684682 | − | 0.0684682i | ||||
\(974\) | −191.801 | + | 297.021i | −0.196921 | + | 0.304949i | ||||
\(975\) | −1070.06 | − | 636.886i | −1.09750 | − | 0.653217i | ||||
\(976\) | 18.0968 | + | 288.413i | 0.0185418 | + | 0.295505i | ||||
\(977\) | 1408.74i | 1.44190i | 0.692985 | + | 0.720952i | \(0.256295\pi\) | ||||
−0.692985 | + | 0.720952i | \(0.743705\pi\) | |||||||
\(978\) | −394.648 | + | 195.793i | −0.403525 | + | 0.200197i | ||||
\(979\) | 6.49409 | − | 6.49409i | 0.00663340 | − | 0.00663340i | ||||
\(980\) | 297.546 | + | 112.462i | 0.303618 | + | 0.114757i | ||||
\(981\) | −191.296 | + | 644.927i | −0.195001 | + | 0.657418i | ||||
\(982\) | 877.555 | − | 188.894i | 0.893641 | − | 0.192357i | ||||
\(983\) | −1288.34 | −1.31062 | −0.655309 | − | 0.755361i | \(-0.727461\pi\) | ||||
−0.655309 | + | 0.755361i | \(0.727461\pi\) | |||||||
\(984\) | 61.0503 | + | 613.576i | 0.0620430 | + | 0.623552i | ||||
\(985\) | 429.137i | 0.435672i | ||||||||
\(986\) | −1502.46 | + | 323.404i | −1.52379 | + | 0.327996i | ||||
\(987\) | 532.903 | − | 135.235i | 0.539922 | − | 0.137016i | ||||
\(988\) | −1343.73 | + | 606.583i | −1.36005 | + | 0.613950i | ||||
\(989\) | 1187.58 | + | 1187.58i | 1.20079 | + | 1.20079i | ||||
\(990\) | −5.14617 | + | 67.2858i | −0.00519816 | + | 0.0679654i | ||||
\(991\) | −1013.28 | −1.02248 | −0.511242 | − | 0.859437i | \(-0.670815\pi\) | ||||
−0.511242 | + | 0.859437i | \(0.670815\pi\) | |||||||
\(992\) | 358.694 | − | 101.081i | 0.361586 | − | 0.101896i | ||||
\(993\) | −982.280 | − | 584.641i | −0.989204 | − | 0.588762i | ||||
\(994\) | −482.907 | + | 747.822i | −0.485822 | + | 0.752336i | ||||
\(995\) | 227.968 | + | 227.968i | 0.229113 | + | 0.229113i | ||||
\(996\) | 72.3635 | − | 638.553i | 0.0726541 | − | 0.641118i | ||||
\(997\) | −537.885 | − | 537.885i | −0.539503 | − | 0.539503i | 0.383880 | − | 0.923383i | \(-0.374588\pi\) |
−0.923383 | + | 0.383880i | \(0.874588\pi\) | |||||||
\(998\) | 1035.23 | − | 222.833i | 1.03730 | − | 0.223279i | ||||
\(999\) | 29.4256 | + | 1.17249i | 0.0294551 | + | 0.00117366i |
(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 | 48.3.i.a.5.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 48.3.i.a.5.4 | yes | 8 | |
4.3 | odd | 2 | 192.3.i.a.113.1 | 8 | |||
8.3 | odd | 2 | 384.3.i.b.353.4 | 8 | |||
8.5 | even | 2 | 384.3.i.a.353.1 | 8 | |||
12.11 | even | 2 | 192.3.i.a.113.3 | 8 | |||
16.3 | odd | 4 | 192.3.i.a.17.3 | 8 | |||
16.5 | even | 4 | 384.3.i.a.161.3 | 8 | |||
16.11 | odd | 4 | 384.3.i.b.161.2 | 8 | |||
16.13 | even | 4 | inner | 48.3.i.a.29.4 | yes | 8 | |
24.5 | odd | 2 | 384.3.i.a.353.3 | 8 | |||
24.11 | even | 2 | 384.3.i.b.353.2 | 8 | |||
48.5 | odd | 4 | 384.3.i.a.161.1 | 8 | |||
48.11 | even | 4 | 384.3.i.b.161.4 | 8 | |||
48.29 | odd | 4 | inner | 48.3.i.a.29.1 | yes | 8 | |
48.35 | even | 4 | 192.3.i.a.17.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.a.5.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
48.3.i.a.5.4 | yes | 8 | 3.2 | odd | 2 | inner | |
48.3.i.a.29.1 | yes | 8 | 48.29 | odd | 4 | inner | |
48.3.i.a.29.4 | yes | 8 | 16.13 | even | 4 | inner | |
192.3.i.a.17.1 | 8 | 48.35 | even | 4 | |||
192.3.i.a.17.3 | 8 | 16.3 | odd | 4 | |||
192.3.i.a.113.1 | 8 | 4.3 | odd | 2 | |||
192.3.i.a.113.3 | 8 | 12.11 | even | 2 | |||
384.3.i.a.161.1 | 8 | 48.5 | odd | 4 | |||
384.3.i.a.161.3 | 8 | 16.5 | even | 4 | |||
384.3.i.a.353.1 | 8 | 8.5 | even | 2 | |||
384.3.i.a.353.3 | 8 | 24.5 | odd | 2 | |||
384.3.i.b.161.2 | 8 | 16.11 | odd | 4 | |||
384.3.i.b.161.4 | 8 | 48.11 | even | 4 | |||
384.3.i.b.353.2 | 8 | 24.11 | even | 2 | |||
384.3.i.b.353.4 | 8 | 8.3 | odd | 2 |