Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,4,Mod(3,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.e (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: | \(1.18003820011\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.5 | ||
Root | \(1.83244 + 0.801352i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.7 |
Dual form | 20.4.e.b.3.5 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.03109 | − | 2.63379i | 0.364544 | − | 0.931186i | ||||
\(3\) | 5.55970 | + | 5.55970i | 1.06996 | + | 1.06996i | 0.997361 | + | 0.0726035i | \(0.0231308\pi\) |
0.0726035 | + | 0.997361i | \(0.476869\pi\) | |||||||
\(4\) | −5.87372 | − | 5.43134i | −0.734215 | − | 0.678917i | ||||
\(5\) | −10.4994 | − | 3.84216i | −0.939097 | − | 0.343653i | ||||
\(6\) | 20.3756 | − | 8.91056i | 1.38639 | − | 0.606286i | ||||
\(7\) | −1.14202 | + | 1.14202i | −0.0616631 | + | 0.0616631i | −0.737266 | − | 0.675603i | \(-0.763883\pi\) |
0.675603 | + | 0.737266i | \(0.263883\pi\) | |||||||
\(8\) | −20.3613 | + | 9.86997i | −0.899852 | + | 0.436195i | ||||
\(9\) | 34.8205i | 1.28965i | ||||||||
\(10\) | −20.9453 | + | 23.6917i | −0.662347 | + | 0.749197i | ||||
\(11\) | 27.0350i | 0.741033i | 0.928826 | + | 0.370516i | \(0.120819\pi\) | ||||
−0.928826 | + | 0.370516i | \(0.879181\pi\) | |||||||
\(12\) | −2.45951 | − | 62.8527i | −0.0591667 | − | 1.51200i | ||||
\(13\) | 40.4777 | − | 40.4777i | 0.863577 | − | 0.863577i | −0.128174 | − | 0.991752i | \(-0.540912\pi\) |
0.991752 | + | 0.128174i | \(0.0409117\pi\) | |||||||
\(14\) | 1.83032 | + | 4.18535i | 0.0349409 | + | 0.0798988i | ||||
\(15\) | −37.0124 | − | 79.7348i | −0.637104 | − | 1.37250i | ||||
\(16\) | 5.00116 | + | 63.8043i | 0.0781431 | + | 0.996942i | ||||
\(17\) | −36.2735 | − | 36.2735i | −0.517507 | − | 0.517507i | 0.399309 | − | 0.916816i | \(-0.369250\pi\) |
−0.916816 | + | 0.399309i | \(0.869250\pi\) | |||||||
\(18\) | 91.7099 | + | 35.9029i | 1.20090 | + | 0.470134i | ||||
\(19\) | 56.8829 | 0.686834 | 0.343417 | − | 0.939183i | \(-0.388416\pi\) | ||||
0.343417 | + | 0.939183i | \(0.388416\pi\) | |||||||
\(20\) | 40.8026 | + | 79.5936i | 0.456187 | + | 0.889884i | ||||
\(21\) | −12.6985 | −0.131955 | ||||||||
\(22\) | 71.2046 | + | 27.8754i | 0.690039 | + | 0.270139i | ||||
\(23\) | −54.9839 | − | 54.9839i | −0.498475 | − | 0.498475i | 0.412488 | − | 0.910963i | \(-0.364660\pi\) |
−0.910963 | + | 0.412488i | \(0.864660\pi\) | |||||||
\(24\) | −168.077 | − | 58.3288i | −1.42952 | − | 0.496096i | ||||
\(25\) | 95.4757 | + | 80.6808i | 0.763805 | + | 0.645447i | ||||
\(26\) | −64.8739 | − | 148.346i | −0.489339 | − | 1.11896i | ||||
\(27\) | −43.4795 | + | 43.4795i | −0.309912 | + | 0.309912i | ||||
\(28\) | 12.9106 | − | 0.505208i | 0.0871381 | − | 0.00340983i | ||||
\(29\) | − | 57.1173i | − | 0.365739i | −0.983137 | − | 0.182869i | \(-0.941461\pi\) | ||
0.983137 | − | 0.182869i | \(-0.0585385\pi\) | |||||||
\(30\) | −248.168 | + | 15.2693i | −1.51030 | + | 0.0929263i | ||||
\(31\) | 190.845i | 1.10570i | 0.833281 | + | 0.552850i | \(0.186460\pi\) | ||||
−0.833281 | + | 0.552850i | \(0.813540\pi\) | |||||||
\(32\) | 173.204 | + | 52.6158i | 0.956825 | + | 0.290664i | ||||
\(33\) | −150.306 | + | 150.306i | −0.792878 | + | 0.792878i | ||||
\(34\) | −132.938 | + | 58.1357i | −0.670549 | + | 0.293241i | ||||
\(35\) | 16.3783 | − | 7.60271i | 0.0790983 | − | 0.0367169i | ||||
\(36\) | 189.122 | − | 204.526i | 0.875564 | − | 0.946878i | ||||
\(37\) | −50.4605 | − | 50.4605i | −0.224207 | − | 0.224207i | 0.586060 | − | 0.810267i | \(-0.300678\pi\) |
−0.810267 | + | 0.586060i | \(0.800678\pi\) | |||||||
\(38\) | 58.6513 | − | 149.818i | 0.250381 | − | 0.639570i | ||||
\(39\) | 450.088 | 1.84799 | ||||||||
\(40\) | 251.704 | − | 25.3976i | 0.994948 | − | 0.100393i | ||||
\(41\) | −71.5197 | −0.272427 | −0.136213 | − | 0.990680i | \(-0.543493\pi\) | ||||
−0.136213 | + | 0.990680i | \(0.543493\pi\) | |||||||
\(42\) | −13.0933 | + | 33.4453i | −0.0481033 | + | 0.122874i | ||||
\(43\) | −66.9381 | − | 66.9381i | −0.237394 | − | 0.237394i | 0.578376 | − | 0.815770i | \(-0.303687\pi\) |
−0.815770 | + | 0.578376i | \(0.803687\pi\) | |||||||
\(44\) | 146.836 | − | 158.796i | 0.503100 | − | 0.544077i | ||||
\(45\) | 133.786 | − | 365.595i | 0.443191 | − | 1.21110i | ||||
\(46\) | −201.509 | + | 88.1229i | −0.645889 | + | 0.282457i | ||||
\(47\) | −343.017 | + | 343.017i | −1.06456 | + | 1.06456i | −0.0667913 | + | 0.997767i | \(0.521276\pi\) |
−0.997767 | + | 0.0667913i | \(0.978724\pi\) | |||||||
\(48\) | −326.928 | + | 382.538i | −0.983082 | + | 1.15030i | ||||
\(49\) | 340.392i | 0.992395i | ||||||||
\(50\) | 310.940 | − | 168.274i | 0.879472 | − | 0.475951i | ||||
\(51\) | − | 403.339i | − | 1.10743i | ||||||
\(52\) | −457.603 | + | 17.9066i | −1.22035 | + | 0.0477539i | ||||
\(53\) | 240.148 | − | 240.148i | 0.622394 | − | 0.622394i | −0.323749 | − | 0.946143i | \(-0.604943\pi\) |
0.946143 | + | 0.323749i | \(0.104943\pi\) | |||||||
\(54\) | 69.6848 | + | 159.347i | 0.175609 | + | 0.401563i | ||||
\(55\) | 103.873 | − | 283.852i | 0.254658 | − | 0.695901i | ||||
\(56\) | 11.9813 | − | 34.5247i | 0.0285905 | − | 0.0823848i | ||||
\(57\) | 316.252 | + | 316.252i | 0.734888 | + | 0.734888i | ||||
\(58\) | −150.435 | − | 58.8929i | −0.340571 | − | 0.133328i | ||||
\(59\) | −738.207 | −1.62892 | −0.814461 | − | 0.580218i | \(-0.802967\pi\) | ||||
−0.814461 | + | 0.580218i | \(0.802967\pi\) | |||||||
\(60\) | −215.666 | + | 669.367i | −0.464040 | + | 1.44025i | ||||
\(61\) | −187.952 | −0.394506 | −0.197253 | − | 0.980353i | \(-0.563202\pi\) | ||||
−0.197253 | + | 0.980353i | \(0.563202\pi\) | |||||||
\(62\) | 502.645 | + | 196.777i | 1.02961 | + | 0.403077i | ||||
\(63\) | −39.7656 | − | 39.7656i | −0.0795237 | − | 0.0795237i | ||||
\(64\) | 317.167 | − | 401.932i | 0.619467 | − | 0.785022i | ||||
\(65\) | −580.515 | + | 269.471i | −1.10775 | + | 0.514212i | ||||
\(66\) | 240.897 | + | 550.855i | 0.449278 | + | 1.02736i | ||||
\(67\) | 576.434 | − | 576.434i | 1.05108 | − | 1.05108i | 0.0524612 | − | 0.998623i | \(-0.483293\pi\) |
0.998623 | − | 0.0524612i | \(-0.0167066\pi\) | |||||||
\(68\) | 16.0468 | + | 410.074i | 0.0286170 | + | 0.731305i | ||||
\(69\) | − | 611.387i | − | 1.06670i | ||||||
\(70\) | −3.13647 | − | 50.9761i | −0.00535543 | − | 0.0870402i | ||||
\(71\) | 157.380i | 0.263064i | 0.991312 | + | 0.131532i | \(0.0419896\pi\) | ||||
−0.991312 | + | 0.131532i | \(0.958010\pi\) | |||||||
\(72\) | −343.677 | − | 708.991i | −0.562538 | − | 1.16049i | ||||
\(73\) | 180.613 | − | 180.613i | 0.289577 | − | 0.289577i | −0.547336 | − | 0.836913i | \(-0.684358\pi\) |
0.836913 | + | 0.547336i | \(0.184358\pi\) | |||||||
\(74\) | −184.932 | + | 80.8733i | −0.290512 | + | 0.127045i | ||||
\(75\) | 82.2548 | + | 979.377i | 0.126640 | + | 1.50785i | ||||
\(76\) | −334.114 | − | 308.950i | −0.504284 | − | 0.466303i | ||||
\(77\) | −30.8744 | − | 30.8744i | −0.0456944 | − | 0.0456944i | ||||
\(78\) | 464.080 | − | 1185.44i | 0.673676 | − | 1.72083i | ||||
\(79\) | −55.6778 | −0.0792942 | −0.0396471 | − | 0.999214i | \(-0.512623\pi\) | ||||
−0.0396471 | + | 0.999214i | \(0.512623\pi\) | |||||||
\(80\) | 192.637 | − | 689.123i | 0.269218 | − | 0.963079i | ||||
\(81\) | 456.687 | 0.626457 | ||||||||
\(82\) | −73.7430 | + | 188.368i | −0.0993116 | + | 0.253680i | ||||
\(83\) | 858.601 | + | 858.601i | 1.13547 | + | 1.13547i | 0.989253 | + | 0.146213i | \(0.0467085\pi\) |
0.146213 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(84\) | 74.5876 | + | 68.9700i | 0.0968831 | + | 0.0895863i | ||||
\(85\) | 241.482 | + | 520.219i | 0.308146 | + | 0.663832i | ||||
\(86\) | −245.320 | + | 107.282i | −0.307599 | + | 0.134518i | ||||
\(87\) | 317.555 | − | 317.555i | 0.391327 | − | 0.391327i | ||||
\(88\) | −266.835 | − | 550.468i | −0.323235 | − | 0.666820i | ||||
\(89\) | 158.689i | 0.189000i | 0.995525 | + | 0.0944998i | \(0.0301252\pi\) | ||||
−0.995525 | + | 0.0944998i | \(0.969875\pi\) | |||||||
\(90\) | −824.956 | − | 729.324i | −0.966200 | − | 0.854194i | ||||
\(91\) | 92.4525i | 0.106502i | ||||||||
\(92\) | 24.3239 | + | 621.596i | 0.0275646 | + | 0.704411i | ||||
\(93\) | −1061.04 | + | 1061.04i | −1.18306 | + | 1.18306i | ||||
\(94\) | 549.756 | + | 1257.12i | 0.603223 | + | 1.37938i | ||||
\(95\) | −597.238 | − | 218.553i | −0.645003 | − | 0.236032i | ||||
\(96\) | 670.433 | + | 1255.49i | 0.712769 | + | 1.33477i | ||||
\(97\) | −1117.12 | − | 1117.12i | −1.16935 | − | 1.16935i | −0.982363 | − | 0.186986i | \(-0.940128\pi\) |
−0.186986 | − | 0.982363i | \(-0.559872\pi\) | |||||||
\(98\) | 896.521 | + | 350.973i | 0.924105 | + | 0.361772i | ||||
\(99\) | −941.372 | −0.955671 | ||||||||
\(100\) | −122.592 | − | 992.457i | −0.122592 | − | 0.992457i | ||||
\(101\) | 787.780 | 0.776109 | 0.388055 | − | 0.921636i | \(-0.373147\pi\) | ||||
0.388055 | + | 0.921636i | \(0.373147\pi\) | |||||||
\(102\) | −1062.31 | − | 415.878i | −1.03122 | − | 0.403706i | ||||
\(103\) | −522.455 | − | 522.455i | −0.499796 | − | 0.499796i | 0.411578 | − | 0.911374i | \(-0.364978\pi\) |
−0.911374 | + | 0.411578i | \(0.864978\pi\) | |||||||
\(104\) | −424.666 | + | 1223.69i | −0.400403 | + | 1.15378i | ||||
\(105\) | 133.327 | + | 48.7898i | 0.123918 | + | 0.0453466i | ||||
\(106\) | −384.887 | − | 880.114i | −0.352674 | − | 0.806455i | ||||
\(107\) | 615.276 | − | 615.276i | 0.555897 | − | 0.555897i | −0.372240 | − | 0.928137i | \(-0.621410\pi\) |
0.928137 | + | 0.372240i | \(0.121410\pi\) | |||||||
\(108\) | 491.538 | − | 19.2346i | 0.437947 | − | 0.0171375i | ||||
\(109\) | − | 398.877i | − | 0.350509i | −0.984523 | − | 0.175254i | \(-0.943925\pi\) | ||
0.984523 | − | 0.175254i | \(-0.0560748\pi\) | |||||||
\(110\) | −640.505 | − | 566.255i | −0.555179 | − | 0.490821i | ||||
\(111\) | − | 561.091i | − | 0.479787i | ||||||
\(112\) | −78.5770 | − | 67.1542i | −0.0662931 | − | 0.0566560i | ||||
\(113\) | 692.888 | − | 692.888i | 0.576826 | − | 0.576826i | −0.357201 | − | 0.934028i | \(-0.616269\pi\) |
0.934028 | + | 0.357201i | \(0.116269\pi\) | |||||||
\(114\) | 1159.03 | − | 506.859i | 0.952216 | − | 0.416418i | ||||
\(115\) | 366.042 | + | 788.555i | 0.296814 | + | 0.639419i | ||||
\(116\) | −310.223 | + | 335.491i | −0.248306 | + | 0.268531i | ||||
\(117\) | 1409.45 | + | 1409.45i | 1.11371 | + | 1.11371i | ||||
\(118\) | −761.156 | + | 1944.28i | −0.593814 | + | 1.51683i | ||||
\(119\) | 82.8499 | 0.0638221 | ||||||||
\(120\) | 1540.60 | + | 1258.20i | 1.17198 | + | 0.957142i | ||||
\(121\) | 600.109 | 0.450871 | ||||||||
\(122\) | −193.795 | + | 495.028i | −0.143815 | + | 0.367358i | ||||
\(123\) | −397.628 | − | 397.628i | −0.291487 | − | 0.291487i | ||||
\(124\) | 1036.54 | − | 1120.97i | 0.750679 | − | 0.811821i | ||||
\(125\) | −692.451 | − | 1213.93i | −0.495477 | − | 0.868621i | ||||
\(126\) | −145.736 | + | 63.7325i | −0.103041 | + | 0.0450614i | ||||
\(127\) | −498.629 | + | 498.629i | −0.348395 | + | 0.348395i | −0.859512 | − | 0.511116i | \(-0.829232\pi\) |
0.511116 | + | 0.859512i | \(0.329232\pi\) | |||||||
\(128\) | −731.577 | − | 1249.78i | −0.505179 | − | 0.863015i | ||||
\(129\) | − | 744.311i | − | 0.508007i | ||||||
\(130\) | 111.169 | + | 1806.80i | 0.0750016 | + | 1.21898i | ||||
\(131\) | − | 1747.61i | − | 1.16557i | −0.812626 | − | 0.582785i | \(-0.801963\pi\) | ||
0.812626 | − | 0.582785i | \(-0.198037\pi\) | |||||||
\(132\) | 1699.22 | − | 66.4929i | 1.12044 | − | 0.0438444i | ||||
\(133\) | −64.9613 | + | 64.9613i | −0.0423523 | + | 0.0423523i | ||||
\(134\) | −923.854 | − | 2112.56i | −0.595588 | − | 1.36192i | ||||
\(135\) | 623.565 | − | 289.455i | 0.397540 | − | 0.184535i | ||||
\(136\) | 1096.59 | + | 380.558i | 0.691413 | + | 0.239945i | ||||
\(137\) | 124.289 | + | 124.289i | 0.0775092 | + | 0.0775092i | 0.744799 | − | 0.667289i | \(-0.232546\pi\) |
−0.667289 | + | 0.744799i | \(0.732546\pi\) | |||||||
\(138\) | −1610.27 | − | 630.394i | −0.993297 | − | 0.388860i | ||||
\(139\) | −9.83873 | −0.00600367 | −0.00300184 | − | 0.999995i | \(-0.500956\pi\) | ||||
−0.00300184 | + | 0.999995i | \(0.500956\pi\) | |||||||
\(140\) | −137.495 | − | 44.3000i | −0.0830029 | − | 0.0267431i | ||||
\(141\) | −3814.15 | −2.27808 | ||||||||
\(142\) | 414.506 | + | 162.272i | 0.244962 | + | 0.0958985i | ||||
\(143\) | 1094.32 | + | 1094.32i | 0.639939 | + | 0.639939i | ||||
\(144\) | −2221.70 | + | 174.143i | −1.28570 | + | 0.100777i | ||||
\(145\) | −219.454 | + | 599.699i | −0.125687 | + | 0.343464i | ||||
\(146\) | −289.469 | − | 661.925i | −0.164087 | − | 0.375214i | ||||
\(147\) | −1892.47 | + | 1892.47i | −1.06183 | + | 1.06183i | ||||
\(148\) | 22.3229 | + | 570.459i | 0.0123982 | + | 0.316834i | ||||
\(149\) | 2840.41i | 1.56171i | 0.624711 | + | 0.780856i | \(0.285217\pi\) | ||||
−0.624711 | + | 0.780856i | \(0.714783\pi\) | |||||||
\(150\) | 2664.29 | + | 793.181i | 1.45025 | + | 0.431753i | ||||
\(151\) | 2913.54i | 1.57020i | 0.619368 | + | 0.785101i | \(0.287389\pi\) | ||||
−0.619368 | + | 0.785101i | \(0.712611\pi\) | |||||||
\(152\) | −1158.21 | + | 561.433i | −0.618049 | + | 0.299594i | ||||
\(153\) | 1263.06 | − | 1263.06i | 0.667401 | − | 0.667401i | ||||
\(154\) | −113.151 | + | 49.4826i | −0.0592076 | + | 0.0258923i | ||||
\(155\) | 733.255 | − | 2003.76i | 0.379977 | − | 1.03836i | ||||
\(156\) | −2643.69 | − | 2444.58i | −1.35682 | − | 1.25463i | ||||
\(157\) | 1572.29 | + | 1572.29i | 0.799251 | + | 0.799251i | 0.982977 | − | 0.183727i | \(-0.0588161\pi\) |
−0.183727 | + | 0.982977i | \(0.558816\pi\) | |||||||
\(158\) | −57.4087 | + | 146.644i | −0.0289063 | + | 0.0738377i | ||||
\(159\) | 2670.30 | 1.33188 | ||||||||
\(160\) | −1616.38 | − | 1217.91i | −0.798664 | − | 0.601777i | ||||
\(161\) | 125.585 | 0.0614751 | ||||||||
\(162\) | 470.884 | − | 1202.82i | 0.228371 | − | 0.583348i | ||||
\(163\) | −1457.19 | − | 1457.19i | −0.700222 | − | 0.700222i | 0.264236 | − | 0.964458i | \(-0.414880\pi\) |
−0.964458 | + | 0.264236i | \(0.914880\pi\) | |||||||
\(164\) | 420.087 | + | 388.448i | 0.200020 | + | 0.184955i | ||||
\(165\) | 2155.63 | − | 1000.63i | 1.01706 | − | 0.472115i | ||||
\(166\) | 3146.67 | − | 1376.08i | 1.47126 | − | 0.643402i | ||||
\(167\) | −801.239 | + | 801.239i | −0.371268 | + | 0.371268i | −0.867939 | − | 0.496671i | \(-0.834556\pi\) |
0.496671 | + | 0.867939i | \(0.334556\pi\) | |||||||
\(168\) | 258.559 | − | 125.334i | 0.118740 | − | 0.0575580i | ||||
\(169\) | − | 1079.90i | − | 0.491532i | ||||||
\(170\) | 1619.14 | − | 99.6228i | 0.730484 | − | 0.0449454i | ||||
\(171\) | 1980.69i | 0.885773i | ||||||||
\(172\) | 29.6122 | + | 756.739i | 0.0131274 | + | 0.335470i | ||||
\(173\) | −1180.59 | + | 1180.59i | −0.518837 | + | 0.518837i | −0.917220 | − | 0.398382i | \(-0.869572\pi\) |
0.398382 | + | 0.917220i | \(0.369572\pi\) | |||||||
\(174\) | −508.947 | − | 1163.80i | −0.221742 | − | 0.507055i | ||||
\(175\) | −201.174 | + | 16.8959i | −0.0868989 | + | 0.00729836i | ||||
\(176\) | −1724.95 | + | 135.206i | −0.738767 | + | 0.0579066i | ||||
\(177\) | −4104.21 | − | 4104.21i | −1.74289 | − | 1.74289i | ||||
\(178\) | 417.953 | + | 163.622i | 0.175994 | + | 0.0688987i | ||||
\(179\) | 3724.41 | 1.55517 | 0.777585 | − | 0.628778i | \(-0.216445\pi\) | ||||
0.777585 | + | 0.628778i | \(0.216445\pi\) | |||||||
\(180\) | −2771.49 | + | 1420.77i | −1.14764 | + | 0.588320i | ||||
\(181\) | 545.856 | 0.224161 | 0.112081 | − | 0.993699i | \(-0.464249\pi\) | ||||
0.112081 | + | 0.993699i | \(0.464249\pi\) | |||||||
\(182\) | 243.501 | + | 95.3266i | 0.0991729 | + | 0.0388246i | ||||
\(183\) | −1044.96 | − | 1044.96i | −0.422107 | − | 0.422107i | ||||
\(184\) | 1662.23 | + | 576.855i | 0.665986 | + | 0.231121i | ||||
\(185\) | 335.929 | + | 723.683i | 0.133503 | + | 0.287601i | ||||
\(186\) | 1700.53 | + | 3888.58i | 0.670371 | + | 1.53293i | ||||
\(187\) | 980.654 | − | 980.654i | 0.383489 | − | 0.383489i | ||||
\(188\) | 3877.83 | − | 151.745i | 1.50436 | − | 0.0588677i | ||||
\(189\) | − | 99.3087i | − | 0.0382203i | ||||||
\(190\) | −1191.43 | + | 1347.65i | −0.454922 | + | 0.514574i | ||||
\(191\) | − | 3668.60i | − | 1.38980i | −0.719109 | − | 0.694898i | \(-0.755450\pi\) | ||
0.719109 | − | 0.694898i | \(-0.244550\pi\) | |||||||
\(192\) | 3997.97 | − | 471.264i | 1.50275 | − | 0.177138i | ||||
\(193\) | −715.028 | + | 715.028i | −0.266678 | + | 0.266678i | −0.827760 | − | 0.561082i | \(-0.810385\pi\) |
0.561082 | + | 0.827760i | \(0.310385\pi\) | |||||||
\(194\) | −4094.13 | + | 1790.42i | −1.51516 | + | 0.662602i | ||||
\(195\) | −4725.66 | − | 1729.31i | −1.73545 | − | 0.635069i | ||||
\(196\) | 1848.78 | − | 1999.36i | 0.673754 | − | 0.728631i | ||||
\(197\) | 272.976 | + | 272.976i | 0.0987246 | + | 0.0987246i | 0.754744 | − | 0.656019i | \(-0.227761\pi\) |
−0.656019 | + | 0.754744i | \(0.727761\pi\) | |||||||
\(198\) | −970.636 | + | 2479.38i | −0.348384 | + | 0.889907i | ||||
\(199\) | −4554.16 | −1.62229 | −0.811146 | − | 0.584844i | \(-0.801156\pi\) | ||||
−0.811146 | + | 0.584844i | \(0.801156\pi\) | |||||||
\(200\) | −2740.33 | − | 700.427i | −0.968853 | − | 0.247638i | ||||
\(201\) | 6409.60 | 2.24925 | ||||||||
\(202\) | 812.269 | − | 2074.85i | 0.282926 | − | 0.722702i | ||||
\(203\) | 65.2289 | + | 65.2289i | 0.0225526 | + | 0.0225526i | ||||
\(204\) | −2190.67 | + | 2369.10i | −0.751851 | + | 0.813090i | ||||
\(205\) | 750.915 | + | 274.790i | 0.255835 | + | 0.0936203i | ||||
\(206\) | −1914.73 | + | 837.341i | −0.647601 | + | 0.283205i | ||||
\(207\) | 1914.56 | − | 1914.56i | 0.642857 | − | 0.642857i | ||||
\(208\) | 2785.09 | + | 2380.22i | 0.928419 | + | 0.793454i | ||||
\(209\) | 1537.83i | 0.508966i | ||||||||
\(210\) | 265.974 | − | 300.850i | 0.0873998 | − | 0.0988600i | ||||
\(211\) | 4250.89i | 1.38694i | 0.720487 | + | 0.693468i | \(0.243918\pi\) | ||||
−0.720487 | + | 0.693468i | \(0.756082\pi\) | |||||||
\(212\) | −2714.89 | + | 106.237i | −0.879525 | + | 0.0344170i | ||||
\(213\) | −874.984 | + | 874.984i | −0.281469 | + | 0.281469i | ||||
\(214\) | −986.105 | − | 2254.91i | −0.314994 | − | 0.720292i | ||||
\(215\) | 445.624 | + | 959.998i | 0.141355 | + | 0.304518i | ||||
\(216\) | 456.159 | − | 1314.44i | 0.143693 | − | 0.414058i | ||||
\(217\) | −217.948 | − | 217.948i | −0.0681809 | − | 0.0681809i | ||||
\(218\) | −1050.56 | − | 411.276i | −0.326389 | − | 0.127776i | ||||
\(219\) | 2008.31 | 0.619675 | ||||||||
\(220\) | −2151.81 | + | 1103.10i | −0.659433 | + | 0.338049i | ||||
\(221\) | −2936.54 | −0.893814 | ||||||||
\(222\) | −1477.80 | − | 578.533i | −0.446771 | − | 0.174904i | ||||
\(223\) | 258.746 | + | 258.746i | 0.0776991 | + | 0.0776991i | 0.744888 | − | 0.667189i | \(-0.232503\pi\) |
−0.667189 | + | 0.744888i | \(0.732503\pi\) | |||||||
\(224\) | −257.890 | + | 137.714i | −0.0769241 | + | 0.0410776i | ||||
\(225\) | −2809.35 | + | 3324.51i | −0.832399 | + | 0.985040i | ||||
\(226\) | −1110.49 | − | 2539.35i | −0.326854 | − | 0.747412i | ||||
\(227\) | −2127.58 | + | 2127.58i | −0.622080 | + | 0.622080i | −0.946063 | − | 0.323983i | \(-0.894978\pi\) |
0.323983 | + | 0.946063i | \(0.394978\pi\) | |||||||
\(228\) | −139.904 | − | 3575.25i | −0.0406377 | − | 1.03849i | ||||
\(229\) | − | 4654.98i | − | 1.34328i | −0.740880 | − | 0.671638i | \(-0.765591\pi\) | ||
0.740880 | − | 0.671638i | \(-0.234409\pi\) | |||||||
\(230\) | 2454.31 | − | 151.010i | 0.703620 | − | 0.0432925i | ||||
\(231\) | − | 343.305i | − | 0.0977827i | ||||||
\(232\) | 563.746 | + | 1162.98i | 0.159533 | + | 0.329111i | ||||
\(233\) | 3392.53 | − | 3392.53i | 0.953871 | − | 0.953871i | −0.0451108 | − | 0.998982i | \(-0.514364\pi\) |
0.998982 | + | 0.0451108i | \(0.0143641\pi\) | |||||||
\(234\) | 5165.48 | − | 2258.94i | 1.44307 | − | 0.631075i | ||||
\(235\) | 4919.41 | − | 2283.56i | 1.36556 | − | 0.633885i | ||||
\(236\) | 4336.02 | + | 4009.45i | 1.19598 | + | 1.10590i | ||||
\(237\) | −309.552 | − | 309.552i | −0.0848420 | − | 0.0848420i | ||||
\(238\) | 85.4254 | − | 218.209i | 0.0232660 | − | 0.0594303i | ||||
\(239\) | −1434.32 | −0.388195 | −0.194098 | − | 0.980982i | \(-0.562178\pi\) | ||||
−0.194098 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(240\) | 4902.32 | − | 2760.32i | 1.31851 | − | 0.742407i | ||||
\(241\) | −6438.62 | −1.72094 | −0.860472 | − | 0.509497i | \(-0.829831\pi\) | ||||
−0.860472 | + | 0.509497i | \(0.829831\pi\) | |||||||
\(242\) | 618.764 | − | 1580.56i | 0.164362 | − | 0.419845i | ||||
\(243\) | 3712.99 | + | 3712.99i | 0.980199 | + | 0.980199i | ||||
\(244\) | 1103.98 | + | 1020.83i | 0.289652 | + | 0.267837i | ||||
\(245\) | 1307.84 | − | 3573.91i | 0.341040 | − | 0.931955i | ||||
\(246\) | −1457.26 | + | 637.280i | −0.377689 | + | 0.165169i | ||||
\(247\) | 2302.49 | − | 2302.49i | 0.593134 | − | 0.593134i | ||||
\(248\) | −1883.63 | − | 3885.85i | −0.482301 | − | 0.994966i | ||||
\(249\) | 9547.12i | 2.42982i | ||||||||
\(250\) | −3911.23 | + | 572.099i | −0.989471 | + | 0.144731i | ||||
\(251\) | 1877.58i | 0.472159i | 0.971734 | + | 0.236079i | \(0.0758626\pi\) | ||||
−0.971734 | + | 0.236079i | \(0.924137\pi\) | |||||||
\(252\) | 17.5916 | + | 449.552i | 0.00439748 | + | 0.112377i | ||||
\(253\) | 1486.49 | − | 1486.49i | 0.369386 | − | 0.369386i | ||||
\(254\) | 799.156 | + | 1827.42i | 0.197415 | + | 0.451426i | ||||
\(255\) | −1549.69 | + | 4234.83i | −0.380571 | + | 1.03998i | ||||
\(256\) | −4045.98 | + | 638.191i | −0.987787 | + | 0.155808i | ||||
\(257\) | 1940.33 | + | 1940.33i | 0.470952 | + | 0.470952i | 0.902223 | − | 0.431270i | \(-0.141934\pi\) |
−0.431270 | + | 0.902223i | \(0.641934\pi\) | |||||||
\(258\) | −1960.36 | − | 767.449i | −0.473049 | − | 0.185191i | ||||
\(259\) | 115.254 | 0.0276506 | ||||||||
\(260\) | 4873.37 | + | 1570.17i | 1.16244 | + | 0.374531i | ||||
\(261\) | 1988.85 | 0.471674 | ||||||||
\(262\) | −4602.85 | − | 1801.94i | −1.08536 | − | 0.424902i | ||||
\(263\) | 1004.94 | + | 1004.94i | 0.235616 | + | 0.235616i | 0.815032 | − | 0.579416i | \(-0.196719\pi\) |
−0.579416 | + | 0.815032i | \(0.696719\pi\) | |||||||
\(264\) | 1576.92 | − | 4543.96i | 0.367623 | − | 1.05932i | ||||
\(265\) | −3444.10 | + | 1598.73i | −0.798376 | + | 0.370601i | ||||
\(266\) | 104.114 | + | 238.075i | 0.0239986 | + | 0.0548772i | ||||
\(267\) | −882.261 | + | 882.261i | −0.202223 | + | 0.202223i | ||||
\(268\) | −6516.62 | + | 255.004i | −1.48532 | + | 0.0581227i | ||||
\(269\) | − | 6594.94i | − | 1.49480i | −0.664376 | − | 0.747398i | \(-0.731303\pi\) | ||
0.664376 | − | 0.747398i | \(-0.268697\pi\) | |||||||
\(270\) | −119.414 | − | 1940.79i | −0.0269159 | − | 0.437455i | ||||
\(271\) | − | 4781.49i | − | 1.07179i | −0.844285 | − | 0.535895i | \(-0.819974\pi\) | ||
0.844285 | − | 0.535895i | \(-0.180026\pi\) | |||||||
\(272\) | 2133.00 | − | 2495.81i | 0.475485 | − | 0.556364i | ||||
\(273\) | −514.008 | + | 514.008i | −0.113953 | + | 0.113953i | ||||
\(274\) | 455.506 | − | 199.199i | 0.100431 | − | 0.0439200i | ||||
\(275\) | −2181.21 | + | 2581.18i | −0.478297 | + | 0.566005i | ||||
\(276\) | −3320.65 | + | 3591.12i | −0.724202 | + | 0.783188i | ||||
\(277\) | 5490.27 | + | 5490.27i | 1.19090 | + | 1.19090i | 0.976816 | + | 0.214082i | \(0.0686760\pi\) |
0.214082 | + | 0.976816i | \(0.431324\pi\) | |||||||
\(278\) | −10.1446 | + | 25.9132i | −0.00218860 | + | 0.00559053i | ||||
\(279\) | −6645.30 | −1.42596 | ||||||||
\(280\) | −258.446 | + | 316.455i | −0.0551610 | + | 0.0675421i | ||||
\(281\) | 3046.29 | 0.646714 | 0.323357 | − | 0.946277i | \(-0.395189\pi\) | ||||
0.323357 | + | 0.946277i | \(0.395189\pi\) | |||||||
\(282\) | −3932.72 | + | 10045.7i | −0.830461 | + | 2.12132i | ||||
\(283\) | −5858.21 | − | 5858.21i | −1.23051 | − | 1.23051i | −0.963768 | − | 0.266743i | \(-0.914053\pi\) |
−0.266743 | − | 0.963768i | \(-0.585947\pi\) | |||||||
\(284\) | 854.783 | − | 924.405i | 0.178599 | − | 0.193146i | ||||
\(285\) | −2105.37 | − | 4535.55i | −0.437584 | − | 0.942677i | ||||
\(286\) | 4010.53 | − | 1753.87i | 0.829188 | − | 0.362616i | ||||
\(287\) | 81.6767 | − | 81.6767i | 0.0167987 | − | 0.0167987i | ||||
\(288\) | −1832.11 | + | 6031.04i | −0.374854 | + | 1.23397i | ||||
\(289\) | − | 2281.47i | − | 0.464374i | ||||||
\(290\) | 1353.21 | + | 1196.34i | 0.274010 | + | 0.242246i | ||||
\(291\) | − | 12421.8i | − | 2.50232i | ||||||
\(292\) | −2041.84 | + | 79.9000i | −0.409211 | + | 0.0160130i | ||||
\(293\) | −5371.12 | + | 5371.12i | −1.07094 | + | 1.07094i | −0.0736515 | + | 0.997284i | \(0.523465\pi\) |
−0.997284 | + | 0.0736515i | \(0.976535\pi\) | |||||||
\(294\) | 3033.08 | + | 6935.69i | 0.601676 | + | 1.37584i | ||||
\(295\) | 7750.75 | + | 2836.31i | 1.52972 | + | 0.559784i | ||||
\(296\) | 1525.49 | + | 529.399i | 0.299551 | + | 0.103955i | ||||
\(297\) | −1175.47 | − | 1175.47i | −0.229655 | − | 0.229655i | ||||
\(298\) | 7481.04 | + | 2928.71i | 1.45425 | + | 0.569314i | ||||
\(299\) | −4451.25 | −0.860944 | ||||||||
\(300\) | 4836.18 | − | 6199.34i | 0.930724 | − | 1.19306i | ||||
\(301\) | 152.889 | 0.0292770 | ||||||||
\(302\) | 7673.66 | + | 3004.11i | 1.46215 | + | 0.572408i | ||||
\(303\) | 4379.82 | + | 4379.82i | 0.830409 | + | 0.830409i | ||||
\(304\) | 284.481 | + | 3629.38i | 0.0536713 | + | 0.684734i | ||||
\(305\) | 1973.39 | + | 722.143i | 0.370479 | + | 0.135573i | ||||
\(306\) | −2024.31 | − | 4628.96i | −0.378177 | − | 0.864772i | ||||
\(307\) | 1464.75 | − | 1464.75i | 0.272306 | − | 0.272306i | −0.557722 | − | 0.830028i | \(-0.688324\pi\) |
0.830028 | + | 0.557722i | \(0.188324\pi\) | |||||||
\(308\) | 13.6583 | + | 349.037i | 0.00252680 | + | 0.0645722i | ||||
\(309\) | − | 5809.38i | − | 1.06953i | ||||||
\(310\) | −4521.43 | − | 3997.29i | −0.828387 | − | 0.732357i | ||||
\(311\) | 1381.23i | 0.251840i | 0.992040 | + | 0.125920i | \(0.0401882\pi\) | ||||
−0.992040 | + | 0.125920i | \(0.959812\pi\) | |||||||
\(312\) | −9164.39 | + | 4442.36i | −1.66292 | + | 0.806086i | ||||
\(313\) | −1989.95 | + | 1989.95i | −0.359356 | + | 0.359356i | −0.863575 | − | 0.504220i | \(-0.831780\pi\) |
0.504220 | + | 0.863575i | \(0.331780\pi\) | |||||||
\(314\) | 5762.25 | − | 2519.92i | 1.03561 | − | 0.452889i | ||||
\(315\) | 264.730 | + | 570.301i | 0.0473519 | + | 0.102009i | ||||
\(316\) | 327.036 | + | 302.405i | 0.0582190 | + | 0.0538342i | ||||
\(317\) | −2078.83 | − | 2078.83i | −0.368325 | − | 0.368325i | 0.498541 | − | 0.866866i | \(-0.333869\pi\) |
−0.866866 | + | 0.498541i | \(0.833869\pi\) | |||||||
\(318\) | 2753.31 | − | 7033.02i | 0.485529 | − | 1.24023i | ||||
\(319\) | 1544.17 | 0.271024 | ||||||||
\(320\) | −4874.36 | + | 3001.44i | −0.851515 | + | 0.524330i | ||||
\(321\) | 6841.49 | 1.18958 | ||||||||
\(322\) | 129.489 | − | 330.765i | 0.0224104 | − | 0.0572447i | ||||
\(323\) | −2063.34 | − | 2063.34i | −0.355441 | − | 0.355441i | ||||
\(324\) | −2682.45 | − | 2480.42i | −0.459954 | − | 0.425312i | ||||
\(325\) | 7130.42 | − | 598.861i | 1.21700 | − | 0.102212i | ||||
\(326\) | −5340.43 | + | 2335.45i | −0.907298 | + | 0.396775i | ||||
\(327\) | 2217.63 | − | 2217.63i | 0.375032 | − | 0.375032i | ||||
\(328\) | 1456.24 | − | 705.898i | 0.245144 | − | 0.118831i | ||||
\(329\) | − | 783.463i | − | 0.131288i | ||||||
\(330\) | −412.807 | − | 6709.22i | −0.0688614 | − | 1.11918i | ||||
\(331\) | 8633.95i | 1.43373i | 0.697211 | + | 0.716866i | \(0.254424\pi\) | ||||
−0.697211 | + | 0.716866i | \(0.745576\pi\) | |||||||
\(332\) | −379.830 | − | 9706.53i | −0.0627888 | − | 1.60456i | ||||
\(333\) | 1757.06 | − | 1757.06i | 0.289148 | − | 0.289148i | ||||
\(334\) | 1284.15 | + | 2936.44i | 0.210376 | + | 0.481063i | ||||
\(335\) | −8266.97 | + | 3837.47i | −1.34828 | + | 0.625862i | ||||
\(336\) | −63.5074 | − | 810.221i | −0.0103113 | − | 0.131551i | ||||
\(337\) | −3115.08 | − | 3115.08i | −0.503528 | − | 0.503528i | 0.409004 | − | 0.912532i | \(-0.365876\pi\) |
−0.912532 | + | 0.409004i | \(0.865876\pi\) | |||||||
\(338\) | −2844.22 | − | 1113.47i | −0.457708 | − | 0.179185i | ||||
\(339\) | 7704.49 | 1.23437 | ||||||||
\(340\) | 1407.09 | − | 4367.19i | 0.224441 | − | 0.696601i | ||||
\(341\) | −5159.48 | −0.819360 | ||||||||
\(342\) | 5216.73 | + | 2042.26i | 0.824820 | + | 0.322904i | ||||
\(343\) | −780.445 | − | 780.445i | −0.122857 | − | 0.122857i | ||||
\(344\) | 2023.62 | + | 702.271i | 0.317170 | + | 0.110070i | ||||
\(345\) | −2349.05 | + | 6419.21i | −0.366575 | + | 1.00174i | ||||
\(346\) | 1892.14 | + | 4326.73i | 0.293995 | + | 0.672273i | ||||
\(347\) | −646.980 | + | 646.980i | −0.100091 | + | 0.100091i | −0.755379 | − | 0.655288i | \(-0.772547\pi\) |
0.655288 | + | 0.755379i | \(0.272547\pi\) | |||||||
\(348\) | −3589.98 | + | 140.481i | −0.552997 | + | 0.0216395i | ||||
\(349\) | 9611.76i | 1.47423i | 0.675768 | + | 0.737114i | \(0.263812\pi\) | ||||
−0.675768 | + | 0.737114i | \(0.736188\pi\) | |||||||
\(350\) | −162.927 | + | 547.271i | −0.0248824 | + | 0.0835796i | ||||
\(351\) | 3519.90i | 0.535267i | ||||||||
\(352\) | −1422.47 | + | 4682.57i | −0.215391 | + | 0.709039i | ||||
\(353\) | −5085.16 | + | 5085.16i | −0.766730 | + | 0.766730i | −0.977529 | − | 0.210799i | \(-0.932393\pi\) |
0.210799 | + | 0.977529i | \(0.432393\pi\) | |||||||
\(354\) | −15041.4 | + | 6577.84i | −2.25831 | + | 0.987593i | ||||
\(355\) | 604.678 | − | 1652.40i | 0.0904027 | − | 0.247043i | ||||
\(356\) | 861.892 | − | 932.093i | 0.128315 | − | 0.138766i | ||||
\(357\) | 460.620 | + | 460.620i | 0.0682874 | + | 0.0682874i | ||||
\(358\) | 3840.19 | − | 9809.32i | 0.566928 | − | 1.44815i | ||||
\(359\) | 5598.06 | 0.822992 | 0.411496 | − | 0.911411i | \(-0.365006\pi\) | ||||
0.411496 | + | 0.911411i | \(0.365006\pi\) | |||||||
\(360\) | 884.357 | + | 8764.46i | 0.129471 | + | 1.28313i | ||||
\(361\) | −3623.33 | −0.528259 | ||||||||
\(362\) | 562.825 | − | 1437.67i | 0.0817167 | − | 0.208736i | ||||
\(363\) | 3336.42 | + | 3336.42i | 0.482416 | + | 0.482416i | ||||
\(364\) | 502.141 | − | 543.040i | 0.0723059 | − | 0.0781952i | ||||
\(365\) | −2590.28 | + | 1202.39i | −0.371455 | + | 0.172427i | ||||
\(366\) | −3829.65 | + | 1674.76i | −0.546937 | + | 0.239183i | ||||
\(367\) | −3676.76 | + | 3676.76i | −0.522957 | + | 0.522957i | −0.918463 | − | 0.395506i | \(-0.870569\pi\) |
0.395506 | + | 0.918463i | \(0.370569\pi\) | |||||||
\(368\) | 3233.22 | − | 3783.19i | 0.457999 | − | 0.535903i | ||||
\(369\) | − | 2490.35i | − | 0.351335i | ||||||
\(370\) | 2252.40 | − | 138.587i | 0.316478 | − | 0.0194724i | ||||
\(371\) | 548.506i | 0.0767575i | ||||||||
\(372\) | 11995.1 | − | 469.385i | 1.67182 | − | 0.0654206i | ||||
\(373\) | 6801.10 | − | 6801.10i | 0.944096 | − | 0.944096i | −0.0544219 | − | 0.998518i | \(-0.517332\pi\) |
0.998518 | + | 0.0544219i | \(0.0173316\pi\) | |||||||
\(374\) | −1571.70 | − | 3593.98i | −0.217301 | − | 0.496899i | ||||
\(375\) | 2899.29 | − | 10598.9i | 0.399250 | − | 1.45954i | ||||
\(376\) | 3598.72 | − | 10369.9i | 0.493590 | − | 1.42230i | ||||
\(377\) | −2311.98 | − | 2311.98i | −0.315844 | − | 0.315844i | ||||
\(378\) | −261.558 | − | 102.396i | −0.0355902 | − | 0.0139330i | ||||
\(379\) | −9992.48 | −1.35430 | −0.677150 | − | 0.735845i | \(-0.736785\pi\) | ||||
−0.677150 | + | 0.735845i | \(0.736785\pi\) | |||||||
\(380\) | 2320.97 | + | 4527.52i | 0.313325 | + | 0.611202i | ||||
\(381\) | −5544.46 | −0.745541 | ||||||||
\(382\) | −9662.34 | − | 3782.65i | −1.29416 | − | 0.506642i | ||||
\(383\) | −1910.84 | − | 1910.84i | −0.254932 | − | 0.254932i | 0.568057 | − | 0.822989i | \(-0.307695\pi\) |
−0.822989 | + | 0.568057i | \(0.807695\pi\) | |||||||
\(384\) | 2881.05 | − | 11015.7i | 0.382872 | − | 1.46392i | ||||
\(385\) | 205.539 | + | 442.788i | 0.0272084 | + | 0.0586144i | ||||
\(386\) | 1145.98 | + | 2620.49i | 0.151111 | + | 0.345543i | ||||
\(387\) | 2330.82 | − | 2330.82i | 0.306155 | − | 0.306155i | ||||
\(388\) | 494.196 | + | 12629.2i | 0.0646624 | + | 1.65244i | ||||
\(389\) | 152.974i | 0.0199385i | 0.999950 | + | 0.00996927i | \(0.00317337\pi\) | ||||
−0.999950 | + | 0.00996927i | \(0.996827\pi\) | |||||||
\(390\) | −9427.21 | + | 10663.3i | −1.22401 | + | 1.38451i | ||||
\(391\) | 3988.91i | 0.515929i | ||||||||
\(392\) | −3359.66 | − | 6930.82i | −0.432878 | − | 0.893009i | ||||
\(393\) | 9716.21 | − | 9716.21i | 1.24712 | − | 1.24712i | ||||
\(394\) | 1000.42 | − | 437.500i | 0.127920 | − | 0.0559415i | ||||
\(395\) | 584.585 | + | 213.923i | 0.0744649 | + | 0.0272497i | ||||
\(396\) | 5529.35 | + | 5112.91i | 0.701668 | + | 0.648821i | ||||
\(397\) | 3823.37 | + | 3823.37i | 0.483349 | + | 0.483349i | 0.906199 | − | 0.422850i | \(-0.138970\pi\) |
−0.422850 | + | 0.906199i | \(0.638970\pi\) | |||||||
\(398\) | −4695.74 | + | 11994.7i | −0.591397 | + | 1.51065i | ||||
\(399\) | −722.330 | −0.0906309 | ||||||||
\(400\) | −4670.30 | + | 6495.26i | −0.583787 | + | 0.811907i | ||||
\(401\) | 10939.9 | 1.36238 | 0.681190 | − | 0.732106i | \(-0.261463\pi\) | ||||
0.681190 | + | 0.732106i | \(0.261463\pi\) | |||||||
\(402\) | 6608.85 | − | 16881.6i | 0.819949 | − | 2.09447i | ||||
\(403\) | 7724.96 | + | 7724.96i | 0.954858 | + | 0.954858i | ||||
\(404\) | −4627.20 | − | 4278.70i | −0.569831 | − | 0.526914i | ||||
\(405\) | −4794.95 | − | 1754.66i | −0.588304 | − | 0.215284i | ||||
\(406\) | 239.056 | − | 104.543i | 0.0292221 | − | 0.0127792i | ||||
\(407\) | 1364.20 | − | 1364.20i | 0.166145 | − | 0.166145i | ||||
\(408\) | 3980.95 | + | 8212.52i | 0.483055 | + | 0.996521i | ||||
\(409\) | 2982.65i | 0.360593i | 0.983612 | + | 0.180296i | \(0.0577057\pi\) | ||||
−0.983612 | + | 0.180296i | \(0.942294\pi\) | |||||||
\(410\) | 1498.00 | − | 1694.42i | 0.180441 | − | 0.204101i | ||||
\(411\) | 1382.02i | 0.165864i | ||||||||
\(412\) | 231.125 | + | 5906.38i | 0.0276376 | + | 0.706278i | ||||
\(413\) | 843.045 | − | 843.045i | 0.100444 | − | 0.100444i | ||||
\(414\) | −3068.48 | − | 7016.65i | −0.364270 | − | 0.832970i | ||||
\(415\) | −5715.93 | − | 12313.7i | −0.676106 | − | 1.45652i | ||||
\(416\) | 9140.67 | − | 4881.13i | 1.07730 | − | 0.575282i | ||||
\(417\) | −54.7004 | − | 54.7004i | −0.00642371 | − | 0.00642371i | ||||
\(418\) | 4050.32 | + | 1585.64i | 0.473942 | + | 0.185541i | ||||
\(419\) | 2828.22 | 0.329755 | 0.164878 | − | 0.986314i | \(-0.447277\pi\) | ||||
0.164878 | + | 0.986314i | \(0.447277\pi\) | |||||||
\(420\) | −518.133 | − | 1010.72i | −0.0601960 | − | 0.117424i | ||||
\(421\) | 739.946 | 0.0856597 | 0.0428299 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428299 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(422\) | 11196.0 | + | 4383.04i | 1.29150 | + | 0.505600i | ||||
\(423\) | −11944.0 | − | 11944.0i | −1.37290 | − | 1.37290i | ||||
\(424\) | −2519.48 | + | 7259.99i | −0.288577 | + | 0.831548i | ||||
\(425\) | −536.660 | − | 6389.81i | −0.0612514 | − | 0.729297i | ||||
\(426\) | 1402.34 | + | 3206.71i | 0.159492 | + | 0.364708i | ||||
\(427\) | 214.645 | − | 214.645i | 0.0243265 | − | 0.0243265i | ||||
\(428\) | −6955.73 | + | 272.187i | −0.785555 | + | 0.0307399i | ||||
\(429\) | 12168.1i | 1.36942i | ||||||||
\(430\) | 2987.91 | − | 183.841i | 0.335093 | − | 0.0206177i | ||||
\(431\) | − | 7074.45i | − | 0.790636i | −0.918544 | − | 0.395318i | \(-0.870634\pi\) | ||
0.918544 | − | 0.395318i | \(-0.129366\pi\) | |||||||
\(432\) | −2991.63 | − | 2556.73i | −0.333182 | − | 0.284747i | ||||
\(433\) | 2645.06 | − | 2645.06i | 0.293564 | − | 0.293564i | −0.544922 | − | 0.838487i | \(-0.683441\pi\) |
0.838487 | + | 0.544922i | \(0.183441\pi\) | |||||||
\(434\) | −798.752 | + | 349.306i | −0.0883441 | + | 0.0386341i | ||||
\(435\) | −4554.24 | + | 2114.05i | −0.501975 | + | 0.233013i | ||||
\(436\) | −2166.43 | + | 2342.89i | −0.237966 | + | 0.257349i | ||||
\(437\) | −3127.64 | − | 3127.64i | −0.342370 | − | 0.342370i | ||||
\(438\) | 2070.74 | − | 5289.46i | 0.225899 | − | 0.577033i | ||||
\(439\) | 12903.4 | 1.40284 | 0.701419 | − | 0.712750i | \(-0.252550\pi\) | ||||
0.701419 | + | 0.712750i | \(0.252550\pi\) | |||||||
\(440\) | 686.624 | + | 6804.82i | 0.0743944 | + | 0.737289i | ||||
\(441\) | −11852.6 | −1.27984 | ||||||||
\(442\) | −3027.83 | + | 7734.23i | −0.325835 | + | 0.832307i | ||||
\(443\) | −2108.72 | − | 2108.72i | −0.226159 | − | 0.226159i | 0.584927 | − | 0.811086i | \(-0.301123\pi\) |
−0.811086 | + | 0.584927i | \(0.801123\pi\) | |||||||
\(444\) | −3047.47 | + | 3295.69i | −0.325736 | + | 0.352267i | ||||
\(445\) | 609.707 | − | 1666.14i | 0.0649503 | − | 0.177489i | ||||
\(446\) | 948.272 | − | 414.693i | 0.100677 | − | 0.0440275i | ||||
\(447\) | −15791.8 | + | 15791.8i | −1.67098 | + | 1.67098i | ||||
\(448\) | 96.8022 | + | 821.223i | 0.0102087 | + | 0.0866052i | ||||
\(449\) | 136.127i | 0.0143079i | 0.999974 | + | 0.00715394i | \(0.00227719\pi\) | ||||
−0.999974 | + | 0.00715394i | \(0.997723\pi\) | |||||||
\(450\) | 5859.38 | + | 10827.1i | 0.613809 | + | 1.13421i | ||||
\(451\) | − | 1933.53i | − | 0.201877i | ||||||
\(452\) | −7833.13 | + | 306.521i | −0.815132 | + | 0.0318972i | ||||
\(453\) | −16198.4 | + | 16198.4i | −1.68006 | + | 1.68006i | ||||
\(454\) | 3409.88 | + | 7797.31i | 0.352497 | + | 0.806048i | ||||
\(455\) | 355.217 | − | 970.698i | 0.0365996 | − | 0.100015i | ||||
\(456\) | −9560.71 | − | 3317.91i | −0.981845 | − | 0.340736i | ||||
\(457\) | −6660.47 | − | 6660.47i | −0.681759 | − | 0.681759i | 0.278638 | − | 0.960396i | \(-0.410117\pi\) |
−0.960396 | + | 0.278638i | \(0.910117\pi\) | |||||||
\(458\) | −12260.3 | − | 4799.69i | −1.25084 | − | 0.489683i | ||||
\(459\) | 3154.31 | 0.320764 | ||||||||
\(460\) | 2132.88 | − | 6619.85i | 0.216187 | − | 0.670983i | ||||
\(461\) | 9556.54 | 0.965493 | 0.482747 | − | 0.875760i | \(-0.339639\pi\) | ||||
0.482747 | + | 0.875760i | \(0.339639\pi\) | |||||||
\(462\) | −904.194 | − | 353.977i | −0.0910539 | − | 0.0356461i | ||||
\(463\) | 914.613 | + | 914.613i | 0.0918049 | + | 0.0918049i | 0.751518 | − | 0.659713i | \(-0.229322\pi\) |
−0.659713 | + | 0.751518i | \(0.729322\pi\) | |||||||
\(464\) | 3644.33 | − | 285.653i | 0.364620 | − | 0.0285799i | ||||
\(465\) | 15217.0 | − | 7063.61i | 1.51757 | − | 0.704446i | ||||
\(466\) | −5437.22 | − | 12433.2i | −0.540503 | − | 1.23596i | ||||
\(467\) | 541.819 | − | 541.819i | 0.0536882 | − | 0.0536882i | −0.679753 | − | 0.733441i | \(-0.737913\pi\) |
0.733441 | + | 0.679753i | \(0.237913\pi\) | |||||||
\(468\) | −623.518 | − | 15934.0i | −0.0615857 | − | 1.57382i | ||||
\(469\) | 1316.59i | 0.129626i | ||||||||
\(470\) | −942.075 | − | 15311.3i | −0.0924568 | − | 1.50267i | ||||
\(471\) | 17482.9i | 1.71034i | ||||||||
\(472\) | 15030.9 | − | 7286.09i | 1.46579 | − | 0.710528i | ||||
\(473\) | 1809.67 | − | 1809.67i | 0.175917 | − | 0.175917i | ||||
\(474\) | −1134.47 | + | 496.120i | −0.109932 | + | 0.0480750i | ||||
\(475\) | 5430.94 | + | 4589.36i | 0.524607 | + | 0.443315i | ||||
\(476\) | −486.637 | − | 449.986i | −0.0468592 | − | 0.0433299i | ||||
\(477\) | 8362.07 | + | 8362.07i | 0.802669 | + | 0.802669i | ||||
\(478\) | −1478.91 | + | 3777.71i | −0.141514 | + | 0.361482i | ||||
\(479\) | 19357.9 | 1.84652 | 0.923260 | − | 0.384176i | \(-0.125514\pi\) | ||||
0.923260 | + | 0.384176i | \(0.125514\pi\) | |||||||
\(480\) | −2215.38 | − | 15757.8i | −0.210662 | − | 1.49842i | ||||
\(481\) | −4085.06 | −0.387240 | ||||||||
\(482\) | −6638.77 | + | 16958.0i | −0.627361 | + | 1.60252i | ||||
\(483\) | 698.215 | + | 698.215i | 0.0657761 | + | 0.0657761i | ||||
\(484\) | −3524.87 | − | 3259.39i | −0.331036 | − | 0.306104i | ||||
\(485\) | 7436.99 | + | 16021.3i | 0.696281 | + | 1.49998i | ||||
\(486\) | 13607.7 | − | 5950.83i | 1.27007 | − | 0.555422i | ||||
\(487\) | 141.166 | − | 141.166i | 0.0131352 | − | 0.0131352i | −0.700509 | − | 0.713644i | \(-0.747044\pi\) |
0.713644 | + | 0.700509i | \(0.247044\pi\) | |||||||
\(488\) | 3826.96 | − | 1855.09i | 0.354997 | − | 0.172082i | ||||
\(489\) | − | 16203.1i | − | 1.49842i | ||||||
\(490\) | −8064.45 | − | 7129.59i | −0.743500 | − | 0.657310i | ||||
\(491\) | − | 929.849i | − | 0.0854654i | −0.999087 | − | 0.0427327i | \(-0.986394\pi\) | ||
0.999087 | − | 0.0427327i | \(-0.0136064\pi\) | |||||||
\(492\) | 175.904 | + | 4495.21i | 0.0161186 | + | 0.411910i | ||||
\(493\) | −2071.84 | + | 2071.84i | −0.189272 | + | 0.189272i | ||||
\(494\) | −3690.22 | − | 8438.36i | −0.336095 | − | 0.768542i | ||||
\(495\) | 9883.86 | + | 3616.90i | 0.897467 | + | 0.328419i | ||||
\(496\) | −12176.7 | + | 954.444i | −1.10232 | + | 0.0864028i | ||||
\(497\) | −179.730 | − | 179.730i | −0.0162213 | − | 0.0162213i | ||||
\(498\) | 25145.1 | + | 9843.91i | 2.26261 | + | 0.885776i | ||||
\(499\) | −13526.6 | −1.21349 | −0.606747 | − | 0.794895i | \(-0.707526\pi\) | ||||
−0.606747 | + | 0.794895i | \(0.707526\pi\) | |||||||
\(500\) | −2526.03 | + | 10891.2i | −0.225935 | + | 0.974142i | ||||
\(501\) | −8909.29 | −0.794487 | ||||||||
\(502\) | 4945.16 | + | 1935.95i | 0.439668 | + | 0.172123i | ||||
\(503\) | 4770.81 | + | 4770.81i | 0.422902 | + | 0.422902i | 0.886202 | − | 0.463300i | \(-0.153335\pi\) |
−0.463300 | + | 0.886202i | \(0.653335\pi\) | |||||||
\(504\) | 1202.16 | + | 417.195i | 0.106247 | + | 0.0368717i | ||||
\(505\) | −8271.23 | − | 3026.77i | −0.728842 | − | 0.266712i | ||||
\(506\) | −2382.40 | − | 5447.80i | −0.209310 | − | 0.478625i | ||||
\(507\) | 6003.89 | − | 6003.89i | 0.525922 | − | 0.525922i | ||||
\(508\) | 5637.03 | − | 220.585i | 0.492328 | − | 0.0192655i | ||||
\(509\) | − | 8188.23i | − | 0.713039i | −0.934288 | − | 0.356520i | \(-0.883963\pi\) | ||
0.934288 | − | 0.356520i | \(-0.116037\pi\) | |||||||
\(510\) | 9555.79 | + | 8448.05i | 0.829681 | + | 0.733501i | ||||
\(511\) | 412.526i | 0.0357125i | ||||||||
\(512\) | −2490.89 | + | 11314.3i | −0.215006 | + | 0.976613i | ||||
\(513\) | −2473.24 | + | 2473.24i | −0.212858 | + | 0.212858i | ||||
\(514\) | 7111.09 | − | 3109.78i | 0.610227 | − | 0.266861i | ||||
\(515\) | 3478.12 | + | 7492.83i | 0.297600 | + | 0.641113i | ||||
\(516\) | −4042.60 | + | 4371.87i | −0.344895 | + | 0.372986i | ||||
\(517\) | −9273.48 | − | 9273.48i | −0.788872 | − | 0.788872i | ||||
\(518\) | 118.836 | − | 303.554i | 0.0100799 | − | 0.0257479i | ||||
\(519\) | −13127.5 | −1.11028 | ||||||||
\(520\) | 9160.38 | − | 11216.5i | 0.772518 | − | 0.945912i | ||||
\(521\) | −5465.70 | −0.459610 | −0.229805 | − | 0.973237i | \(-0.573809\pi\) | ||||
−0.229805 | + | 0.973237i | \(0.573809\pi\) | |||||||
\(522\) | 2050.68 | − | 5238.22i | 0.171946 | − | 0.439216i | ||||
\(523\) | −9877.72 | − | 9877.72i | −0.825856 | − | 0.825856i | 0.161085 | − | 0.986941i | \(-0.448501\pi\) |
−0.986941 | + | 0.161085i | \(0.948501\pi\) | |||||||
\(524\) | −9491.88 | + | 10265.0i | −0.791326 | + | 0.855780i | ||||
\(525\) | −1212.40 | − | 1024.53i | −0.100788 | − | 0.0851697i | ||||
\(526\) | 3682.97 | − | 1610.62i | 0.305295 | − | 0.133510i | ||||
\(527\) | 6922.60 | − | 6922.60i | 0.572207 | − | 0.572207i | ||||
\(528\) | −10341.9 | − | 8838.49i | −0.852412 | − | 0.728496i | ||||
\(529\) | − | 6120.55i | − | 0.503045i | ||||||
\(530\) | 659.551 | + | 10719.5i | 0.0540549 | + | 0.878537i | ||||
\(531\) | − | 25704.7i | − | 2.10073i | ||||||
\(532\) | 734.391 | − | 28.7377i | 0.0598494 | − | 0.00234199i | ||||
\(533\) | −2894.96 | + | 2894.96i | −0.235262 | + | 0.235262i | ||||
\(534\) | 1414.00 | + | 3233.38i | 0.114588 | + | 0.262026i | ||||
\(535\) | −8824.02 | + | 4096.05i | −0.713076 | + | 0.331005i | ||||
\(536\) | −6047.57 | + | 17426.4i | −0.487342 | + | 1.40430i | ||||
\(537\) | 20706.6 | + | 20706.6i | 1.66398 | + | 1.66398i | ||||
\(538\) | −17369.7 | − | 6799.95i | −1.39193 | − | 0.544920i | ||||
\(539\) | −9202.49 | −0.735397 | ||||||||
\(540\) | −5234.77 | − | 1686.62i | −0.417164 | − | 0.134408i | ||||
\(541\) | 15069.4 | 1.19757 | 0.598784 | − | 0.800910i | \(-0.295651\pi\) | ||||
0.598784 | + | 0.800910i | \(0.295651\pi\) | |||||||
\(542\) | −12593.5 | − | 4930.13i | −0.998035 | − | 0.390715i | ||||
\(543\) | 3034.80 | + | 3034.80i | 0.239845 | + | 0.239845i | ||||
\(544\) | −4374.15 | − | 8191.27i | −0.344743 | − | 0.645584i | ||||
\(545\) | −1532.55 | + | 4187.97i | −0.120453 | + | 0.329162i | ||||
\(546\) | 823.803 | + | 1883.78i | 0.0645706 | + | 0.147652i | ||||
\(547\) | −4573.04 | + | 4573.04i | −0.357457 | + | 0.357457i | −0.862875 | − | 0.505418i | \(-0.831338\pi\) |
0.505418 | + | 0.862875i | \(0.331338\pi\) | |||||||
\(548\) | −54.9835 | − | 1405.10i | −0.00428609 | − | 0.109531i | ||||
\(549\) | − | 6544.60i | − | 0.508773i | ||||||
\(550\) | 4549.29 | + | 8406.27i | 0.352695 | + | 0.651717i | ||||
\(551\) | − | 3249.00i | − | 0.251202i | ||||||
\(552\) | 6034.38 | + | 12448.7i | 0.465290 | + | 0.959873i | ||||
\(553\) | 63.5850 | − | 63.5850i | 0.00488953 | − | 0.00488953i | ||||
\(554\) | 20121.2 | − | 8799.29i | 1.54308 | − | 0.674812i | ||||
\(555\) | −2155.80 | + | 5891.13i | −0.164880 | + | 0.450566i | ||||
\(556\) | 57.7899 | + | 53.4375i | 0.00440798 | + | 0.00407599i | ||||
\(557\) | 1915.65 | + | 1915.65i | 0.145725 | + | 0.145725i | 0.776205 | − | 0.630480i | \(-0.217142\pi\) |
−0.630480 | + | 0.776205i | \(0.717142\pi\) | |||||||
\(558\) | −6851.88 | + | 17502.3i | −0.519827 | + | 1.32784i | ||||
\(559\) | −5419.00 | −0.410017 | ||||||||
\(560\) | 566.996 | + | 1006.98i | 0.0427856 | + | 0.0759873i | ||||
\(561\) | 10904.3 | 0.820640 | ||||||||
\(562\) | 3140.99 | − | 8023.30i | 0.235756 | − | 0.602211i | ||||
\(563\) | −1561.15 | − | 1561.15i | −0.116864 | − | 0.116864i | 0.646256 | − | 0.763120i | \(-0.276334\pi\) |
−0.763120 | + | 0.646256i | \(0.776334\pi\) | |||||||
\(564\) | 22403.2 | + | 20715.9i | 1.67260 | + | 1.54663i | ||||
\(565\) | −9937.10 | + | 4612.74i | −0.739924 | + | 0.343468i | ||||
\(566\) | −21469.6 | + | 9388.98i | −1.59441 | + | 0.697259i | ||||
\(567\) | −521.544 | + | 521.544i | −0.0386293 | + | 0.0386293i | ||||
\(568\) | −1553.33 | − | 3204.46i | −0.114747 | − | 0.236719i | ||||
\(569\) | 21457.5i | 1.58093i | 0.612510 | + | 0.790463i | \(0.290160\pi\) | ||||
−0.612510 | + | 0.790463i | \(0.709840\pi\) | |||||||
\(570\) | −14116.5 | + | 868.565i | −1.03733 | + | 0.0638249i | ||||
\(571\) | − | 5553.22i | − | 0.406997i | −0.979075 | − | 0.203498i | \(-0.934769\pi\) | ||
0.979075 | − | 0.203498i | \(-0.0652312\pi\) | |||||||
\(572\) | −484.106 | − | 12371.3i | −0.0353872 | − | 0.904318i | ||||
\(573\) | 20396.3 | − | 20396.3i | 1.48703 | − | 1.48703i | ||||
\(574\) | −130.904 | − | 299.335i | −0.00951884 | − | 0.0217666i | ||||
\(575\) | −813.477 | − | 9685.77i | −0.0589988 | − | 0.702477i | ||||
\(576\) | 13995.4 | + | 11043.9i | 1.01240 | + | 0.798894i | ||||
\(577\) | 762.522 | + | 762.522i | 0.0550160 | + | 0.0550160i | 0.734079 | − | 0.679064i | \(-0.237614\pi\) |
−0.679064 | + | 0.734079i | \(0.737614\pi\) | |||||||
\(578\) | −6008.91 | − | 2352.39i | −0.432418 | − | 0.169285i | ||||
\(579\) | −7950.68 | −0.570672 | ||||||||
\(580\) | 4546.17 | − | 2330.53i | 0.325465 | − | 0.166845i | ||||
\(581\) | −1961.07 | −0.140033 | ||||||||
\(582\) | −32716.3 | − | 12807.9i | −2.33013 | − | 0.912208i | ||||
\(583\) | 6492.40 | + | 6492.40i | 0.461214 | + | 0.461214i | ||||
\(584\) | −1894.87 | + | 5460.17i | −0.134265 | + | 0.386889i | ||||
\(585\) | −9383.11 | − | 20213.8i | −0.663152 | − | 1.42861i | ||||
\(586\) | 8608.32 | + | 19684.5i | 0.606837 | + | 1.38764i | ||||
\(587\) | 15138.4 | − | 15138.4i | 1.06445 | − | 1.06445i | 0.0666722 | − | 0.997775i | \(-0.478762\pi\) |
0.997775 | − | 0.0666722i | \(-0.0212382\pi\) | |||||||
\(588\) | 21394.5 | − | 837.198i | 1.50050 | − | 0.0587167i | ||||
\(589\) | 10855.8i | 0.759432i | ||||||||
\(590\) | 15461.9 | − | 17489.4i | 1.07891 | − | 1.22038i | ||||
\(591\) | 3035.33i | 0.211264i | ||||||||
\(592\) | 2967.24 | − | 3471.96i | 0.206001 | − | 0.241042i | ||||
\(593\) | 1637.51 | − | 1637.51i | 0.113397 | − | 0.113397i | −0.648131 | − | 0.761529i | \(-0.724449\pi\) |
0.761529 | + | 0.648131i | \(0.224449\pi\) | |||||||
\(594\) | −4307.95 | + | 1883.93i | −0.297571 | + | 0.130132i | ||||
\(595\) | −869.876 | − | 318.322i | −0.0599352 | − | 0.0219327i | ||||
\(596\) | 15427.2 | − | 16683.8i | 1.06027 | − | 1.14663i | ||||
\(597\) | −25319.8 | − | 25319.8i | −1.73579 | − | 1.73579i | ||||
\(598\) | −4589.62 | + | 11723.7i | −0.313852 | + | 0.801699i | ||||
\(599\) | −10193.4 | −0.695312 | −0.347656 | − | 0.937622i | \(-0.613022\pi\) | ||||
−0.347656 | + | 0.937622i | \(0.613022\pi\) | |||||||
\(600\) | −11341.2 | − | 19129.6i | −0.771674 | − | 1.30160i | ||||
\(601\) | −10688.6 | −0.725454 | −0.362727 | − | 0.931895i | \(-0.618154\pi\) | ||||
−0.362727 | + | 0.931895i | \(0.618154\pi\) | |||||||
\(602\) | 157.642 | − | 402.677i | 0.0106727 | − | 0.0272623i | ||||
\(603\) | 20071.7 | + | 20071.7i | 1.35553 | + | 1.35553i | ||||
\(604\) | 15824.4 | − | 17113.3i | 1.06604 | − | 1.15287i | ||||
\(605\) | −6300.80 | − | 2305.71i | −0.423411 | − | 0.154943i | ||||
\(606\) | 16051.5 | − | 7019.56i | 1.07599 | − | 0.470544i | ||||
\(607\) | 12050.0 | − | 12050.0i | 0.805759 | − | 0.805759i | −0.178230 | − | 0.983989i | \(-0.557037\pi\) |
0.983989 | + | 0.178230i | \(0.0570372\pi\) | |||||||
\(608\) | 9852.35 | + | 2992.94i | 0.657180 | + | 0.199638i | ||||
\(609\) | 725.306i | 0.0482609i | ||||||||
\(610\) | 3936.71 | − | 4452.91i | 0.261300 | − | 0.295563i | ||||
\(611\) | 27769.1i | 1.83866i | ||||||||
\(612\) | −14279.0 | + | 558.756i | −0.943126 | + | 0.0369058i | ||||
\(613\) | 3893.39 | − | 3893.39i | 0.256529 | − | 0.256529i | −0.567112 | − | 0.823641i | \(-0.691939\pi\) |
0.823641 | + | 0.567112i | \(0.191939\pi\) | |||||||
\(614\) | −2347.57 | − | 5368.15i | −0.154300 | − | 0.352835i | ||||
\(615\) | 2647.11 | + | 5702.61i | 0.173564 | + | 0.373905i | ||||
\(616\) | 933.374 | + | 323.914i | 0.0610498 | + | 0.0211865i | ||||
\(617\) | 4210.58 | + | 4210.58i | 0.274735 | + | 0.274735i | 0.831003 | − | 0.556268i | \(-0.187767\pi\) |
−0.556268 | + | 0.831003i | \(0.687767\pi\) | |||||||
\(618\) | −15300.7 | − | 5989.98i | −0.995930 | − | 0.389890i | ||||
\(619\) | 6990.42 | 0.453907 | 0.226954 | − | 0.973906i | \(-0.427123\pi\) | ||||
0.226954 | + | 0.973906i | \(0.427123\pi\) | |||||||
\(620\) | −15190.0 | + | 7786.96i | −0.983945 | + | 0.504406i | ||||
\(621\) | 4781.34 | 0.308967 | ||||||||
\(622\) | 3637.86 | + | 1424.16i | 0.234510 | + | 0.0918068i | ||||
\(623\) | −181.225 | − | 181.225i | −0.0116543 | − | 0.0116543i | ||||
\(624\) | 2250.96 | + | 28717.6i | 0.144408 | + | 1.84234i | ||||
\(625\) | 2606.21 | + | 15406.1i | 0.166797 | + | 0.985991i | ||||
\(626\) | 3189.30 | + | 7292.91i | 0.203626 | + | 0.465628i | ||||
\(627\) | −8549.87 | + | 8549.87i | −0.544576 | + | 0.544576i | ||||
\(628\) | −695.553 | − | 17774.8i | −0.0441968 | − | 1.12945i | ||||
\(629\) | 3660.76i | 0.232057i | ||||||||
\(630\) | 1775.01 | − | 109.214i | 0.112251 | − | 0.00690662i | ||||
\(631\) | − | 16801.3i | − | 1.05998i | −0.848003 | − | 0.529991i | \(-0.822195\pi\) | ||
0.848003 | − | 0.529991i | \(-0.177805\pi\) | |||||||
\(632\) | 1133.67 | − | 549.539i | 0.0713531 | − | 0.0345878i | ||||
\(633\) | −23633.7 | + | 23633.7i | −1.48397 | + | 1.48397i | ||||
\(634\) | −7618.67 | + | 3331.76i | −0.477249 | + | 0.208708i | ||||
\(635\) | 7151.13 | − | 3319.51i | 0.446904 | − | 0.207450i | ||||
\(636\) | −15684.6 | − | 14503.3i | −0.977885 | − | 0.904235i | ||||
\(637\) | 13778.3 | + | 13778.3i | 0.857010 | + | 0.857010i | ||||
\(638\) | 1592.17 | − | 4067.01i | 0.0988003 | − | 0.252374i | ||||
\(639\) | −5480.04 | −0.339260 | ||||||||
\(640\) | 2879.29 | + | 15932.8i | 0.177834 | + | 0.984060i | ||||
\(641\) | 7637.22 | 0.470596 | 0.235298 | − | 0.971923i | \(-0.424393\pi\) | ||||
0.235298 | + | 0.971923i | \(0.424393\pi\) | |||||||
\(642\) | 7054.17 | − | 18019.1i | 0.433654 | − | 1.10772i | ||||
\(643\) | 13378.3 | + | 13378.3i | 0.820509 | + | 0.820509i | 0.986181 | − | 0.165672i | \(-0.0529793\pi\) |
−0.165672 | + | 0.986181i | \(0.552979\pi\) | |||||||
\(644\) | −737.651 | − | 682.094i | −0.0451359 | − | 0.0417365i | ||||
\(645\) | −2859.76 | + | 7814.83i | −0.174578 | + | 0.477068i | ||||
\(646\) | −7561.90 | + | 3306.93i | −0.460556 | + | 0.201408i | ||||
\(647\) | −9497.02 | + | 9497.02i | −0.577073 | + | 0.577073i | −0.934096 | − | 0.357023i | \(-0.883792\pi\) |
0.357023 | + | 0.934096i | \(0.383792\pi\) | |||||||
\(648\) | −9298.76 | + | 4507.49i | −0.563719 | + | 0.273258i | ||||
\(649\) | − | 19957.4i | − | 1.20708i | ||||||
\(650\) | 5774.80 | − | 19397.5i | 0.348472 | − | 1.17051i | ||||
\(651\) | − | 2423.45i | − | 0.145902i | ||||||
\(652\) | 644.636 | + | 16473.6i | 0.0387207 | + | 0.989506i | ||||
\(653\) | 12420.7 | − | 12420.7i | 0.744346 | − | 0.744346i | −0.229065 | − | 0.973411i | \(-0.573567\pi\) |
0.973411 | + | 0.229065i | \(0.0735667\pi\) | |||||||
\(654\) | −3554.21 | − | 8127.36i | −0.212509 | − | 0.485940i | ||||
\(655\) | −6714.61 | + | 18348.9i | −0.400552 | + | 1.09458i | ||||
\(656\) | −357.681 | − | 4563.26i | −0.0212883 | − | 0.271594i | ||||
\(657\) | 6289.03 | + | 6289.03i | 0.373453 | + | 0.373453i | ||||
\(658\) | −2063.48 | − | 807.819i | −0.122254 | − | 0.0478603i | ||||
\(659\) | −5899.85 | −0.348749 | −0.174374 | − | 0.984679i | \(-0.555790\pi\) | ||||
−0.174374 | + | 0.984679i | \(0.555790\pi\) | |||||||
\(660\) | −18096.3 | − | 5830.54i | −1.06727 | − | 0.343869i | ||||
\(661\) | 25892.6 | 1.52361 | 0.761804 | − | 0.647808i | \(-0.224314\pi\) | ||||
0.761804 | + | 0.647808i | \(0.224314\pi\) | |||||||
\(662\) | 22740.0 | + | 8902.36i | 1.33507 | + | 0.522658i | ||||
\(663\) | −16326.3 | − | 16326.3i | −0.956349 | − | 0.956349i | ||||
\(664\) | −25956.6 | − | 9007.88i | −1.51704 | − | 0.526466i | ||||
\(665\) | 931.647 | − | 432.464i | 0.0543274 | − | 0.0252184i | ||||
\(666\) | −2816.05 | − | 6439.41i | −0.163843 | − | 0.374658i | ||||
\(667\) | −3140.53 | + | 3140.53i | −0.182312 | + | 0.182312i | ||||
\(668\) | 9058.05 | − | 354.454i | 0.524650 | − | 0.0205303i | ||||
\(669\) | 2877.10i | 0.166270i | ||||||||
\(670\) | 1583.14 | + | 25730.3i | 0.0912865 | + | 1.48365i | ||||
\(671\) | − | 5081.29i | − | 0.292342i | ||||||
\(672\) | −2199.44 | − | 668.143i | −0.126258 | − | 0.0383544i | ||||
\(673\) | −19481.3 | + | 19481.3i | −1.11582 | + | 1.11582i | −0.123475 | + | 0.992348i | \(0.539404\pi\) |
−0.992348 | + | 0.123475i | \(0.960596\pi\) | |||||||
\(674\) | −11416.4 | + | 4992.55i | −0.652437 | + | 0.285320i | ||||
\(675\) | −7659.20 | + | 643.272i | −0.436745 | + | 0.0366808i | ||||
\(676\) | −5865.28 | + | 6343.00i | −0.333709 | + | 0.360890i | ||||
\(677\) | −17811.4 | − | 17811.4i | −1.01115 | − | 1.01115i | −0.999937 | − | 0.0112114i | \(-0.996431\pi\) |
−0.0112114 | − | 0.999937i | \(-0.503569\pi\) | |||||||
\(678\) | 7944.00 | − | 20292.0i | 0.449982 | − | 1.14943i | ||||
\(679\) | 2551.55 | 0.144211 | ||||||||
\(680\) | −10051.4 | − | 8208.93i | −0.566846 | − | 0.462938i | ||||
\(681\) | −23657.4 | −1.33121 | ||||||||
\(682\) | −5319.88 | + | 13589.0i | −0.298693 | + | 0.762976i | ||||
\(683\) | −13579.6 | − | 13579.6i | −0.760775 | − | 0.760775i | 0.215687 | − | 0.976463i | \(-0.430801\pi\) |
−0.976463 | + | 0.215687i | \(0.930801\pi\) | |||||||
\(684\) | 10757.8 | − | 11634.0i | 0.601367 | − | 0.650348i | ||||
\(685\) | −827.428 | − | 1782.51i | −0.0461524 | − | 0.0994249i | ||||
\(686\) | −2860.24 | + | 1250.82i | −0.159190 | + | 0.0696161i | ||||
\(687\) | 25880.3 | − | 25880.3i | 1.43726 | − | 1.43726i | ||||
\(688\) | 3936.17 | − | 4605.70i | 0.218118 | − | 0.255219i | ||||
\(689\) | − | 19441.3i | − | 1.07497i | ||||||
\(690\) | 14484.8 | + | 12805.7i | 0.799170 | + | 0.706527i | ||||
\(691\) | 12840.8i | 0.706928i | 0.935448 | + | 0.353464i | \(0.114996\pi\) | ||||
−0.935448 | + | 0.353464i | \(0.885004\pi\) | |||||||
\(692\) | 13346.7 | − | 522.274i | 0.733186 | − | 0.0286906i | ||||
\(693\) | 1075.06 | − | 1075.06i | 0.0589296 | − | 0.0589296i | ||||
\(694\) | 1036.92 | + | 2371.10i | 0.0567159 | + | 0.129691i | ||||
\(695\) | 103.301 | + | 37.8019i | 0.00563803 | + | 0.00206318i | ||||
\(696\) | −3331.58 | + | 9600.10i | −0.181441 | + | 0.522832i | ||||
\(697\) | 2594.27 | + | 2594.27i | 0.140983 | + | 0.140983i | ||||
\(698\) | 25315.4 | + | 9910.56i | 1.37278 | + | 0.537422i | ||||
\(699\) | 37722.9 | 2.04122 | ||||||||
\(700\) | 1273.41 | + | 993.400i | 0.0687574 | + | 0.0536386i | ||||
\(701\) | −23786.6 | −1.28161 | −0.640805 | − | 0.767704i | \(-0.721399\pi\) | ||||
−0.640805 | + | 0.767704i | \(0.721399\pi\) | |||||||
\(702\) | 9270.70 | + | 3629.33i | 0.498433 | + | 0.195128i | ||||
\(703\) | −2870.34 | − | 2870.34i | −0.153993 | − | 0.153993i | ||||
\(704\) | 10866.2 | + | 8574.62i | 0.581727 | + | 0.459045i | ||||
\(705\) | 40046.3 | + | 14654.5i | 2.13934 | + | 0.782868i | ||||
\(706\) | 8150.01 | + | 18636.5i | 0.434461 | + | 0.993476i | ||||
\(707\) | −899.658 | + | 899.658i | −0.0478573 | + | 0.0478573i | ||||
\(708\) | 1815.63 | + | 46398.3i | 0.0963779 | + | 2.46293i | ||||
\(709\) | − | 21270.0i | − | 1.12667i | −0.826227 | − | 0.563337i | \(-0.809517\pi\) | ||
0.826227 | − | 0.563337i | \(-0.190483\pi\) | |||||||
\(710\) | −3728.59 | − | 3296.36i | −0.197087 | − | 0.174240i | ||||
\(711\) | − | 1938.73i | − | 0.102262i | ||||||
\(712\) | −1566.25 | − | 3231.11i | −0.0824408 | − | 0.170072i | ||||
\(713\) | 10493.4 | − | 10493.4i | 0.551164 | − | 0.551164i | ||||
\(714\) | 1688.12 | − | 738.238i | 0.0884821 | − | 0.0386945i | ||||
\(715\) | −7285.15 | − | 15694.2i | −0.381048 | − | 0.820882i | ||||
\(716\) | −21876.1 | − | 20228.5i | −1.14183 | − | 1.05583i | ||||
\(717\) | −7974.40 | − | 7974.40i | −0.415355 | − | 0.415355i | ||||
\(718\) | 5772.09 | − | 14744.1i | 0.300017 | − | 0.766359i | ||||
\(719\) | −22553.8 | −1.16984 | −0.584921 | − | 0.811090i | \(-0.698874\pi\) | ||||
−0.584921 | + | 0.811090i | \(0.698874\pi\) | |||||||
\(720\) | 23995.6 | + | 6707.71i | 1.24203 | + | 0.347197i | ||||
\(721\) | 1193.30 | 0.0616380 | ||||||||
\(722\) | −3735.97 | + | 9543.10i | −0.192574 | + | 0.491908i | ||||
\(723\) | −35796.8 | − | 35796.8i | −1.84135 | − | 1.84135i | ||||
\(724\) | −3206.21 | − | 2964.73i | −0.164583 | − | 0.152187i | ||||
\(725\) | 4608.27 | − | 5453.31i | 0.236065 | − | 0.279353i | ||||
\(726\) | 12227.6 | − | 5347.30i | 0.625081 | − | 0.273357i | ||||
\(727\) | −19795.0 | + | 19795.0i | −1.00984 | + | 1.00984i | −0.00989382 | + | 0.999951i | \(0.503149\pi\) |
−0.999951 | + | 0.00989382i | \(0.996851\pi\) | |||||||
\(728\) | −912.504 | − | 1882.46i | −0.0464556 | − | 0.0958358i | ||||
\(729\) | 28955.6i | 1.47110i | ||||||||
\(730\) | 496.042 | + | 8062.01i | 0.0251498 | + | 0.408751i | ||||
\(731\) | 4856.16i | 0.245706i | ||||||||
\(732\) | 462.272 | + | 11813.3i | 0.0233416 | + | 0.596493i | ||||
\(733\) | 10191.1 | − | 10191.1i | 0.513528 | − | 0.513528i | −0.402078 | − | 0.915606i | \(-0.631712\pi\) |
0.915606 | + | 0.402078i | \(0.131712\pi\) | |||||||
\(734\) | 5892.76 | + | 13474.9i | 0.296329 | + | 0.677612i | ||||
\(735\) | 27141.1 | − | 12598.7i | 1.36206 | − | 0.632259i | ||||
\(736\) | −6630.40 | − | 12416.4i | −0.332065 | − | 0.621842i | ||||
\(737\) | 15583.9 | + | 15583.9i | 0.778888 | + | 0.778888i | ||||
\(738\) | −6559.06 | − | 2567.77i | −0.327158 | − | 0.128077i | ||||
\(739\) | 28579.3 | 1.42261 | 0.711304 | − | 0.702885i | \(-0.248105\pi\) | ||||
0.711304 | + | 0.702885i | \(0.248105\pi\) | |||||||
\(740\) | 1957.42 | − | 6075.26i | 0.0972379 | − | 0.301799i | ||||
\(741\) | 25602.3 | 1.26926 | ||||||||
\(742\) | 1444.65 | + | 565.558i | 0.0714755 | + | 0.0279815i | ||||
\(743\) | 20848.1 | + | 20848.1i | 1.02940 | + | 1.02940i | 0.999555 | + | 0.0298445i | \(0.00950122\pi\) |
0.0298445 | + | 0.999555i | \(0.490499\pi\) | |||||||
\(744\) | 11131.7 | − | 32076.6i | 0.548533 | − | 1.58062i | ||||
\(745\) | 10913.3 | − | 29822.6i | 0.536687 | − | 1.46660i | ||||
\(746\) | −10900.2 | − | 24925.2i | −0.534964 | − | 1.22329i | ||||
\(747\) | −29896.9 | + | 29896.9i | −1.46435 | + | 1.46435i | ||||
\(748\) | −11086.3 | + | 433.824i | −0.541921 | + | 0.0212061i | ||||
\(749\) | 1405.31i | 0.0685566i | ||||||||
\(750\) | −24925.9 | − | 18564.5i | −1.21356 | − | 0.903842i | ||||
\(751\) | − | 13588.4i | − | 0.660252i | −0.943937 | − | 0.330126i | \(-0.892909\pi\) | ||
0.943937 | − | 0.330126i | \(-0.107091\pi\) | |||||||
\(752\) | −23601.5 | − | 20170.5i | −1.14449 | − | 0.978115i | ||||
\(753\) | −10438.8 | + | 10438.8i | −0.505193 | + | 0.505193i | ||||
\(754\) | −8473.13 | + | 3705.42i | −0.409248 | + | 0.178970i | ||||
\(755\) | 11194.3 | − | 30590.5i | 0.539605 | − | 1.47457i | ||||
\(756\) | −539.379 | + | 583.311i | −0.0259484 | + | 0.0280619i | ||||
\(757\) | −1630.23 | − | 1630.23i | −0.0782719 | − | 0.0782719i | 0.666887 | − | 0.745159i | \(-0.267626\pi\) |
−0.745159 | + | 0.666887i | \(0.767626\pi\) | |||||||
\(758\) | −10303.1 | + | 26318.1i | −0.493702 | + | 1.26110i | ||||
\(759\) | 16528.9 | 0.790461 | ||||||||
\(760\) | 14317.7 | − | 1444.69i | 0.683364 | − | 0.0689532i | ||||
\(761\) | −33489.9 | −1.59528 | −0.797640 | − | 0.603134i | \(-0.793919\pi\) | ||||
−0.797640 | + | 0.603134i | \(0.793919\pi\) | |||||||
\(762\) | −5716.82 | + | 14602.9i | −0.271783 | + | 0.694237i | ||||
\(763\) | 455.524 | + | 455.524i | 0.0216135 | + | 0.0216135i | ||||
\(764\) | −19925.4 | + | 21548.4i | −0.943556 | + | 1.02041i | ||||
\(765\) | −18114.3 | + | 8408.53i | −0.856109 | + | 0.397400i | ||||
\(766\) | −7002.98 | + | 3062.51i | −0.330324 | + | 0.144455i | ||||
\(767\) | −29881.0 | + | 29881.0i | −1.40670 | + | 1.40670i | ||||
\(768\) | −26042.6 | − | 18946.3i | −1.22361 | − | 0.890188i | ||||
\(769\) | 26755.6i | 1.25466i | 0.778755 | + | 0.627328i | \(0.215851\pi\) | ||||
−0.778755 | + | 0.627328i | \(0.784149\pi\) | |||||||
\(770\) | 1378.14 | − | 84.7946i | 0.0644996 | − | 0.00396855i | ||||
\(771\) | 21575.4i | 1.00780i | ||||||||
\(772\) | 8083.43 | − | 316.316i | 0.376851 | − | 0.0147467i | ||||
\(773\) | −6155.27 | + | 6155.27i | −0.286403 | + | 0.286403i | −0.835656 | − | 0.549253i | \(-0.814912\pi\) |
0.549253 | + | 0.835656i | \(0.314912\pi\) | |||||||
\(774\) | −3735.61 | − | 8542.16i | −0.173480 | − | 0.396694i | ||||
\(775\) | −15397.5 | + | 18221.0i | −0.713670 | + | 0.844540i | ||||
\(776\) | 33772.1 | + | 11720.1i | 1.56231 | + | 0.542176i | ||||
\(777\) | 640.775 | + | 640.775i | 0.0295852 | + | 0.0295852i | ||||
\(778\) | 402.902 | + | 157.729i | 0.0185665 | + | 0.00726848i | ||||
\(779\) | −4068.25 | −0.187112 | ||||||||
\(780\) | 18364.8 | + | 35824.1i | 0.843031 | + | 1.64450i | ||||
\(781\) | −4254.76 | −0.194939 | ||||||||
\(782\) | 10506.0 | + | 4112.92i | 0.480425 | + | 0.188079i | ||||
\(783\) | 2483.43 | + | 2483.43i | 0.113347 | + | 0.113347i | ||||
\(784\) | −21718.4 | + | 1702.35i | −0.989361 | + | 0.0775489i | ||||
\(785\) | −10467.1 | − | 22549.1i | −0.475909 | − | 1.02524i | ||||
\(786\) | −15572.2 | − | 35608.7i | −0.706670 | − | 1.61593i | ||||
\(787\) | 11524.6 | − | 11524.6i | 0.521993 | − | 0.521993i | −0.396180 | − | 0.918173i | \(-0.629664\pi\) |
0.918173 | + | 0.396180i | \(0.129664\pi\) | |||||||
\(788\) | −120.760 | − | 3086.01i | −0.00545925 | − | 0.139511i | ||||
\(789\) | 11174.3i | 0.504202i | ||||||||
\(790\) | 1166.19 | − | 1319.10i | 0.0525203 | − | 0.0594070i | ||||
\(791\) | 1582.58i | 0.0711378i | ||||||||
\(792\) | 19167.6 | − | 9291.31i | 0.859962 | − | 0.416859i | ||||
\(793\) | −7607.89 | + | 7607.89i | −0.340686 | + | 0.340686i | ||||
\(794\) | 14012.2 | − | 6127.74i | 0.626290 | − | 0.273886i | ||||
\(795\) | −28036.6 | − | 10259.7i | −1.25076 | − | 0.457704i | ||||
\(796\) | 26749.9 | + | 24735.2i | 1.19111 | + | 1.10140i | ||||
\(797\) | 656.794 | + | 656.794i | 0.0291905 | + | 0.0291905i | 0.721551 | − | 0.692361i | \(-0.243429\pi\) |
−0.692361 | + | 0.721551i | \(0.743429\pi\) | |||||||
\(798\) | −744.785 | + | 1902.47i | −0.0330390 | + | 0.0843942i | ||||
\(799\) | 24884.9 | 1.10183 | ||||||||
\(800\) | 12291.7 | + | 18997.8i | 0.543220 | + | 0.839590i | ||||
\(801\) | −5525.62 | −0.243743 | ||||||||
\(802\) | 11280.0 | − | 28813.5i | 0.496648 | − | 1.26863i | ||||
\(803\) | 4882.87 | + | 4882.87i | 0.214586 | + | 0.214586i | ||||
\(804\) | −37648.2 | − | 34812.7i | −1.65143 | − | 1.52705i | ||||
\(805\) | −1318.57 | − | 482.517i | −0.0577310 | − | 0.0211261i | ||||
\(806\) | 28311.0 | − | 12380.8i | 1.23724 | − | 0.541062i | ||||
\(807\) | 36665.9 | − | 36665.9i | 1.59938 | − | 1.59938i | ||||
\(808\) | −16040.2 | + | 7775.37i | −0.698383 | + | 0.338535i | ||||
\(809\) | 14179.8i | 0.616238i | 0.951348 | + | 0.308119i | \(0.0996994\pi\) | ||||
−0.951348 | + | 0.308119i | \(0.900301\pi\) | |||||||
\(810\) | −9565.43 | + | 10819.7i | −0.414932 | + | 0.469340i | ||||
\(811\) | − | 29366.2i | − | 1.27150i | −0.771896 | − | 0.635749i | \(-0.780691\pi\) | ||
0.771896 | − | 0.635749i | \(-0.219309\pi\) | |||||||
\(812\) | −28.8561 | − | 737.417i | −0.00124711 | − | 0.0318698i | ||||
\(813\) | 26583.7 | − | 26583.7i | 1.14678 | − | 1.14678i | ||||
\(814\) | −2186.41 | − | 4999.63i | −0.0941445 | − | 0.215279i | ||||
\(815\) | 9700.92 | + | 20898.4i | 0.416943 | + | 0.898209i | ||||
\(816\) | 25734.8 | − | 2017.16i | 1.10404 | − | 0.0865378i | ||||
\(817\) | −3807.63 | − | 3807.63i | −0.163050 | − | 0.163050i | ||||
\(818\) | 7855.67 | + | 3075.37i | 0.335779 | + | 0.131452i | ||||
\(819\) | −3219.24 | −0.137350 | ||||||||
\(820\) | −2918.19 | − | 5692.51i | −0.124278 | − | 0.242428i | ||||
\(821\) | 8845.67 | 0.376025 | 0.188012 | − | 0.982167i | \(-0.439796\pi\) | ||||
0.188012 | + | 0.982167i | \(0.439796\pi\) | |||||||
\(822\) | 3639.96 | + | 1424.99i | 0.154450 | + | 0.0604649i | ||||
\(823\) | 16257.0 | + | 16257.0i | 0.688559 | + | 0.688559i | 0.961913 | − | 0.273355i | \(-0.0881332\pi\) |
−0.273355 | + | 0.961913i | \(0.588133\pi\) | |||||||
\(824\) | 15794.5 | + | 5481.26i | 0.667751 | + | 0.231734i | ||||
\(825\) | −26477.5 | + | 2223.76i | −1.11737 | + | 0.0938440i | ||||
\(826\) | −1351.15 | − | 3089.66i | −0.0569160 | − | 0.130149i | ||||
\(827\) | −19183.3 | + | 19183.3i | −0.806612 | + | 0.806612i | −0.984119 | − | 0.177507i | \(-0.943197\pi\) |
0.177507 | + | 0.984119i | \(0.443197\pi\) | |||||||
\(828\) | −21644.3 | + | 846.970i | −0.908442 | + | 0.0355486i | ||||
\(829\) | 27097.5i | 1.13527i | 0.823282 | + | 0.567633i | \(0.192141\pi\) | ||||
−0.823282 | + | 0.567633i | \(0.807859\pi\) | |||||||
\(830\) | −38325.3 | + | 2358.09i | −1.60276 | + | 0.0986151i | ||||
\(831\) | 61048.5i | 2.54844i | ||||||||
\(832\) | −3431.07 | − | 29107.5i | −0.142970 | − | 1.21289i | ||||
\(833\) | 12347.2 | − | 12347.2i | 0.513571 | − | 0.513571i | ||||
\(834\) | −200.470 | + | 87.6685i | −0.00832340 | + | 0.00363994i | ||||
\(835\) | 11491.0 | − | 5334.06i | 0.476244 | − | 0.221069i | ||||
\(836\) | 8352.47 | − | 9032.78i | 0.345546 | − | 0.373691i | ||||
\(837\) | −8297.83 | − | 8297.83i | −0.342670 | − | 0.342670i | ||||
\(838\) | 2916.14 | − | 7448.93i | 0.120210 | − | 0.307063i | ||||
\(839\) | −13726.1 | −0.564814 | −0.282407 | − | 0.959295i | \(-0.591133\pi\) | ||||
−0.282407 | + | 0.959295i | \(0.591133\pi\) | |||||||
\(840\) | −3196.27 | + | 322.512i | −0.131288 | + | 0.0132473i | ||||
\(841\) | 21126.6 | 0.866235 | ||||||||
\(842\) | 762.948 | − | 1948.86i | 0.0312268 | − | 0.0797651i | ||||
\(843\) | 16936.5 | + | 16936.5i | 0.691961 | + | 0.691961i | ||||
\(844\) | 23088.0 | − | 24968.6i | 0.941615 | − | 1.01831i | ||||
\(845\) | −4149.13 | + | 11338.3i | −0.168916 | + | 0.461596i | ||||
\(846\) | −43773.4 | + | 19142.8i | −1.77891 | + | 0.777945i | ||||
\(847\) | −685.334 | + | 685.334i | −0.0278021 | + | 0.0278021i | ||||
\(848\) | 16523.5 | + | 14121.5i | 0.669127 | + | 0.571855i | ||||
\(849\) | − | 65139.8i | − | 2.63320i | ||||||
\(850\) | −17382.8 | − | 5175.00i | −0.701440 | − | 0.208825i | ||||
\(851\) | 5549.03i | 0.223523i | ||||||||
\(852\) | 9891.74 | − | 387.078i | 0.397753 | − | 0.0155646i | ||||
\(853\) | −20720.5 | + | 20720.5i | −0.831720 | + | 0.831720i | −0.987752 | − | 0.156032i | \(-0.950130\pi\) |
0.156032 | + | 0.987752i | \(0.450130\pi\) | |||||||
\(854\) | −344.012 | − | 786.648i | −0.0137844 | − | 0.0315205i | ||||
\(855\) | 7610.13 | − | 20796.1i | 0.304399 | − | 0.831827i | ||||
\(856\) | −6455.07 | + | 18600.6i | −0.257745 | + | 0.742704i | ||||
\(857\) | 26011.0 | + | 26011.0i | 1.03678 | + | 1.03678i | 0.999297 | + | 0.0374797i | \(0.0119329\pi\) |
0.0374797 | + | 0.999297i | \(0.488067\pi\) | |||||||
\(858\) | 32048.3 | + | 12546.4i | 1.27519 | + | 0.499216i | ||||
\(859\) | 4857.84 | 0.192954 | 0.0964769 | − | 0.995335i | \(-0.469243\pi\) | ||||
0.0964769 | + | 0.995335i | \(0.469243\pi\) | |||||||
\(860\) | 2596.60 | − | 8059.09i | 0.102957 | − | 0.319550i | ||||
\(861\) | 908.196 | 0.0359480 | ||||||||
\(862\) | −18632.6 | − | 7294.37i | −0.736229 | − | 0.288222i | ||||
\(863\) | −23423.0 | − | 23423.0i | −0.923904 | − | 0.923904i | 0.0733988 | − | 0.997303i | \(-0.476615\pi\) |
−0.997303 | + | 0.0733988i | \(0.976615\pi\) | |||||||
\(864\) | −9818.53 | + | 5243.11i | −0.386612 | + | 0.206452i | ||||
\(865\) | 16931.6 | − | 7859.52i | 0.665539 | − | 0.308939i | ||||
\(866\) | −4239.25 | − | 9693.81i | −0.166346 | − | 0.380380i | ||||
\(867\) | 12684.3 | − | 12684.3i | 0.496863 | − | 0.496863i | ||||
\(868\) | 96.4163 | + | 2463.91i | 0.00377025 | + | 0.0963486i | ||||
\(869\) | − | 1505.25i | − | 0.0587596i | ||||||
\(870\) | 872.144 | + | 14174.7i | 0.0339867 | + | 0.552376i | ||||
\(871\) | − | 46665.5i | − | 1.81539i | ||||||
\(872\) | 3936.90 | + | 8121.66i | 0.152890 | + | 0.315406i | ||||
\(873\) | 38898.8 | − | 38898.8i | 1.50805 | − | 1.50805i | ||||
\(874\) | −11462.4 | + | 5012.69i | −0.443619 | + | 0.194001i | ||||
\(875\) | 2177.12 | + | 595.543i | 0.0841145 | + | 0.0230092i | ||||
\(876\) | −11796.2 | − | 10907.8i | −0.454975 | − | 0.420708i | ||||
\(877\) | −19062.6 | − | 19062.6i | −0.733976 | − | 0.733976i | 0.237429 | − | 0.971405i | \(-0.423695\pi\) |
−0.971405 | + | 0.237429i | \(0.923695\pi\) | |||||||
\(878\) | 13304.5 | − | 33984.9i | 0.511396 | − | 1.30630i | ||||
\(879\) | −59723.6 | −2.29173 | ||||||||
\(880\) | 18630.4 | + | 5207.94i | 0.713673 | + | 0.199499i | ||||
\(881\) | −6538.78 | −0.250053 | −0.125027 | − | 0.992153i | \(-0.539902\pi\) | ||||
−0.125027 | + | 0.992153i | \(0.539902\pi\) | |||||||
\(882\) | −12221.1 | + | 31217.3i | −0.466558 | + | 1.19177i | ||||
\(883\) | −23546.4 | − | 23546.4i | −0.897395 | − | 0.897395i | 0.0978097 | − | 0.995205i | \(-0.468816\pi\) |
−0.995205 | + | 0.0978097i | \(0.968816\pi\) | |||||||
\(884\) | 17248.4 | + | 15949.3i | 0.656252 | + | 0.606826i | ||||
\(885\) | 27322.8 | + | 58860.8i | 1.03779 | + | 2.23569i | ||||
\(886\) | −7728.22 | + | 3379.66i | −0.293041 | + | 0.128151i | ||||
\(887\) | 13448.5 | − | 13448.5i | 0.509082 | − | 0.509082i | −0.405162 | − | 0.914245i | \(-0.632785\pi\) |
0.914245 | + | 0.405162i | \(0.132785\pi\) | |||||||
\(888\) | 5537.95 | + | 11424.5i | 0.209281 | + | 0.431737i | ||||
\(889\) | − | 1138.89i | − | 0.0429663i | ||||||
\(890\) | −3759.60 | − | 3323.78i | −0.141598 | − | 0.125183i | ||||
\(891\) | 12346.5i | 0.464225i | ||||||||
\(892\) | −114.465 | − | 2925.13i | −0.00429659 | − | 0.109799i | ||||
\(893\) | −19511.8 | + | 19511.8i | −0.731175 | + | 0.731175i | ||||
\(894\) | 25309.6 | + | 57875.1i | 0.946845 | + | 2.16514i | ||||
\(895\) | −39104.1 | − | 14309.8i | −1.46045 | − | 0.534439i | ||||
\(896\) | 2262.74 | + | 591.795i | 0.0843671 | + | 0.0220653i | ||||
\(897\) | −24747.6 | − | 24747.6i | −0.921179 | − | 0.921179i | ||||
\(898\) | 358.531 | + | 140.359i | 0.0133233 | + | 0.00521585i | ||||
\(899\) | 10900.5 | 0.404397 | ||||||||
\(900\) | 34557.8 | − | 4268.73i | 1.27992 | − | 0.158101i | ||||
\(901\) | −17422.0 | −0.644186 | ||||||||
\(902\) | −5092.53 | − | 1993.64i | −0.187985 | − | 0.0735932i | ||||
\(903\) | 850.016 | + | 850.016i | 0.0313253 | + | 0.0313253i | ||||
\(904\) | −7269.33 | + | 20946.9i | −0.267449 | + | 0.770667i | ||||
\(905\) | −5731.17 | − | 2097.27i | −0.210509 | − | 0.0770337i | ||||
\(906\) | 25961.3 | + | 59365.2i | 0.951992 | + | 2.17690i | ||||
\(907\) | −200.288 | + | 200.288i | −0.00733237 | + | 0.00733237i | −0.710763 | − | 0.703431i | \(-0.751650\pi\) |
0.703431 | + | 0.710763i | \(0.251650\pi\) | |||||||
\(908\) | 24052.4 | − | 941.202i | 0.879081 | − | 0.0343997i | ||||
\(909\) | 27430.9i | 1.00091i | ||||||||
\(910\) | −2190.36 | − | 1936.44i | −0.0797908 | − | 0.0705411i | ||||
\(911\) | − | 7662.84i | − | 0.278684i | −0.990244 | − | 0.139342i | \(-0.955501\pi\) | ||
0.990244 | − | 0.139342i | \(-0.0444987\pi\) | |||||||
\(912\) | −18596.6 | + | 21759.9i | −0.675214 | + | 0.790067i | ||||
\(913\) | −23212.3 | + | 23212.3i | −0.841417 | + | 0.841417i | ||||
\(914\) | −24409.8 | + | 10674.8i | −0.883375 | + | 0.386313i | ||||
\(915\) | 6956.57 | + | 14986.4i | 0.251341 | + | 0.541458i | ||||
\(916\) | −25282.8 | + | 27342.1i | −0.911973 | + | 0.986253i | ||||
\(917\) | 1995.81 | + | 1995.81i | 0.0718727 | + | 0.0718727i | ||||
\(918\) | 3252.37 | − | 8307.79i | 0.116933 | − | 0.298691i | ||||
\(919\) | 17176.1 | 0.616527 | 0.308263 | − | 0.951301i | \(-0.400252\pi\) | ||||
0.308263 | + | 0.951301i | \(0.400252\pi\) | |||||||
\(920\) | −15236.1 | − | 12443.2i | −0.546000 | − | 0.445914i | ||||
\(921\) | 16287.2 | 0.582715 | ||||||||
\(922\) | 9853.62 | − | 25169.9i | 0.351965 | − | 0.899054i | ||||
\(923\) | 6370.38 | + | 6370.38i | 0.227176 | + | 0.227176i | ||||
\(924\) | −1864.60 | + | 2016.48i | −0.0663863 | + | 0.0717935i | ||||
\(925\) | −746.555 | − | 8888.95i | −0.0265368 | − | 0.315964i | ||||
\(926\) | 3351.95 | − | 1465.85i | 0.118954 | − | 0.0520205i | ||||
\(927\) | 18192.1 | − | 18192.1i | 0.644561 | − | 0.644561i | ||||
\(928\) | 3005.27 | − | 9892.94i | 0.106307 | − | 0.349948i | ||||
\(929\) | − | 27097.0i | − | 0.956968i | −0.878096 | − | 0.478484i | \(-0.841186\pi\) | ||
0.878096 | − | 0.478484i | \(-0.158814\pi\) | |||||||
\(930\) | −2914.07 | − | 47361.5i | −0.102749 | − | 1.66994i | ||||
\(931\) | 19362.5i | 0.681611i | ||||||||
\(932\) | −38352.7 | + | 1500.80i | −1.34795 | + | 0.0527470i | ||||
\(933\) | −7679.20 | + | 7679.20i | −0.269460 | + | 0.269460i | ||||
\(934\) | −868.376 | − | 1985.70i | −0.0304220 | − | 0.0695654i | ||||
\(935\) | −14064.1 | + | 6528.47i | −0.491921 | + | 0.228346i | ||||
\(936\) | −42609.6 | − | 14787.1i | −1.48797 | − | 0.516379i | ||||
\(937\) | −4000.15 | − | 4000.15i | −0.139465 | − | 0.139465i | 0.633927 | − | 0.773393i | \(-0.281442\pi\) |
−0.773393 | + | 0.633927i | \(0.781442\pi\) | |||||||
\(938\) | 3467.64 | + | 1357.52i | 0.120706 | + | 0.0472545i | ||||
\(939\) | −22127.0 | −0.768996 | ||||||||
\(940\) | −41298.0 | − | 13306.0i | −1.43297 | − | 0.461696i | ||||
\(941\) | 37957.6 | 1.31496 | 0.657482 | − | 0.753470i | \(-0.271621\pi\) | ||||
0.657482 | + | 0.753470i | \(0.271621\pi\) | |||||||
\(942\) | 46046.3 | + | 18026.4i | 1.59264 | + | 0.623495i | ||||
\(943\) | 3932.43 | + | 3932.43i | 0.135798 | + | 0.135798i | ||||
\(944\) | −3691.89 | − | 47100.8i | −0.127289 | − | 1.62394i | ||||
\(945\) | −381.559 | + | 1042.68i | −0.0131345 | + | 0.0358926i | ||||
\(946\) | −2900.37 | − | 6632.22i | −0.0996819 | − | 0.227941i | ||||
\(947\) | 13560.7 | − | 13560.7i | 0.465327 | − | 0.465327i | −0.435070 | − | 0.900397i | \(-0.643276\pi\) |
0.900397 | + | 0.435070i | \(0.143276\pi\) | |||||||
\(948\) | 136.940 | + | 3499.50i | 0.00469158 | + | 0.119893i | ||||
\(949\) | − | 14621.6i | − | 0.500145i | ||||||
\(950\) | 17687.2 | − | 9571.92i | 0.604051 | − | 0.326899i | ||||
\(951\) | − | 23115.4i | − | 0.788189i | ||||||
\(952\) | −1686.93 | + | 817.726i | −0.0574305 | + | 0.0278389i | ||||
\(953\) | 15366.0 | − | 15366.0i | 0.522302 | − | 0.522302i | −0.395964 | − | 0.918266i | \(-0.629589\pi\) |
0.918266 | + | 0.395964i | \(0.129589\pi\) | |||||||
\(954\) | 30646.0 | − | 13401.9i | 1.04004 | − | 0.454826i | ||||
\(955\) | −14095.4 | + | 38518.2i | −0.477607 | + | 1.30515i | ||||
\(956\) | 8424.81 | + | 7790.29i | 0.285019 | + | 0.263552i | ||||
\(957\) | 8585.10 | + | 8585.10i | 0.289986 | + | 0.289986i | ||||
\(958\) | 19959.6 | − | 50984.6i | 0.673138 | − | 1.71945i | ||||
\(959\) | −283.881 | −0.00955892 | ||||||||
\(960\) | −43787.1 | − | 10412.8i | −1.47211 | − | 0.350076i | ||||
\(961\) | −6630.66 | −0.222573 | ||||||||
\(962\) | −4212.05 | + | 10759.2i | −0.141166 | + | 0.360593i | ||||
\(963\) | 21424.2 | + | 21424.2i | 0.716911 | + | 0.716911i | ||||
\(964\) | 37818.6 | + | 34970.3i | 1.26354 | + | 1.16838i | ||||
\(965\) | 10254.6 | − | 4760.13i | 0.342081 | − | 0.158792i | ||||
\(966\) | 2558.87 | − | 1119.03i | 0.0852281 | − | 0.0372715i | ||||
\(967\) | −14792.8 | + | 14792.8i | −0.491939 | + | 0.491939i | −0.908917 | − | 0.416978i | \(-0.863089\pi\) |
0.416978 | + | 0.908917i | \(0.363089\pi\) | |||||||
\(968\) | −12219.0 | + | 5923.06i | −0.405717 | + | 0.196668i | ||||
\(969\) | − | 22943.1i | − | 0.760619i | ||||||
\(970\) | 49865.0 | − | 3068.11i | 1.65059 | − | 0.101558i | ||||
\(971\) | − | 14139.9i | − | 0.467322i | −0.972318 | − | 0.233661i | \(-0.924929\pi\) | ||
0.972318 | − | 0.233661i | \(-0.0750706\pi\) | |||||||
\(972\) | −1642.56 | − | 41975.6i | −0.0542029 | − | 1.38515i | ||||
\(973\) | 11.2360 | − | 11.2360i | 0.000370205 | − | 0.000370205i | ||||
\(974\) | −226.247 | − | 517.355i | −0.00744294 | − | 0.0170196i | ||||
\(975\) | 42972.5 | + | 36313.5i | 1.41151 | + | 1.19278i | ||||
\(976\) | −939.980 | − | 11992.2i | −0.0308279 | − | 0.393299i | ||||
\(977\) | 2288.77 | + | 2288.77i | 0.0749481 | + | 0.0749481i | 0.743587 | − | 0.668639i | \(-0.233123\pi\) |
−0.668639 | + | 0.743587i | \(0.733123\pi\) | |||||||
\(978\) | −42675.6 | − | 16706.8i | −1.39531 | − | 0.546242i | ||||
\(979\) | −4290.15 | −0.140055 | ||||||||
\(980\) | −27093.0 | + | 13888.9i | −0.883117 | + | 0.452718i | ||||
\(981\) | 13889.1 | 0.452033 | ||||||||
\(982\) | −2449.03 | − | 958.755i | −0.0795842 | − | 0.0311559i | ||||
\(983\) | 6757.28 | + | 6757.28i | 0.219251 | + | 0.219251i | 0.808183 | − | 0.588932i | \(-0.200451\pi\) |
−0.588932 | + | 0.808183i | \(0.700451\pi\) | |||||||
\(984\) | 12020.8 | + | 4171.65i | 0.389440 | + | 0.135150i | ||||
\(985\) | −1817.27 | − | 3914.91i | −0.0587849 | − | 0.126639i | ||||
\(986\) | 3320.56 | + | 7593.06i | 0.107250 | + | 0.245246i | ||||
\(987\) | 4355.82 | − | 4355.82i | 0.140473 | − | 0.140473i | ||||
\(988\) | −26029.8 | + | 1018.58i | −0.838177 | + | 0.0327990i | ||||
\(989\) | 7361.03i | 0.236670i | ||||||||
\(990\) | 19717.3 | − | 22302.7i | 0.632986 | − | 0.715986i | ||||
\(991\) | 18118.1i | 0.580767i | 0.956910 | + | 0.290384i | \(0.0937829\pi\) | ||||
−0.956910 | + | 0.290384i | \(0.906217\pi\) | |||||||
\(992\) | −10041.4 | + | 33055.0i | −0.321387 | + | 1.05796i | ||||
\(993\) | −48002.2 | + | 48002.2i | −1.53404 | + | 1.53404i | ||||
\(994\) | −658.690 | + | 288.055i | −0.0210185 | + | 0.00919169i | ||||
\(995\) | 47816.1 | + | 17497.8i | 1.52349 | + | 0.557505i | ||||
\(996\) | 51853.6 | − | 56077.1i | 1.64964 | − | 1.78401i | ||||
\(997\) | 18211.2 | + | 18211.2i | 0.578491 | + | 0.578491i | 0.934487 | − | 0.355996i | \(-0.115858\pi\) |
−0.355996 | + | 0.934487i | \(0.615858\pi\) | |||||||
\(998\) | −13947.1 | + | 35626.2i | −0.442372 | + | 1.12999i | ||||
\(999\) | 4388.00 | 0.138969 |
(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 | 20.4.e.b.7.5 | yes | 12 | |
3.2 | odd | 2 | 180.4.k.e.127.2 | 12 | |||
4.3 | odd | 2 | inner | 20.4.e.b.7.2 | yes | 12 | |
5.2 | odd | 4 | 100.4.e.e.43.5 | 12 | |||
5.3 | odd | 4 | inner | 20.4.e.b.3.2 | ✓ | 12 | |
5.4 | even | 2 | 100.4.e.e.7.2 | 12 | |||
8.3 | odd | 2 | 320.4.n.k.127.6 | 12 | |||
8.5 | even | 2 | 320.4.n.k.127.1 | 12 | |||
12.11 | even | 2 | 180.4.k.e.127.5 | 12 | |||
15.8 | even | 4 | 180.4.k.e.163.5 | 12 | |||
20.3 | even | 4 | inner | 20.4.e.b.3.5 | yes | 12 | |
20.7 | even | 4 | 100.4.e.e.43.2 | 12 | |||
20.19 | odd | 2 | 100.4.e.e.7.5 | 12 | |||
40.3 | even | 4 | 320.4.n.k.63.1 | 12 | |||
40.13 | odd | 4 | 320.4.n.k.63.6 | 12 | |||
60.23 | odd | 4 | 180.4.k.e.163.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.4.e.b.3.2 | ✓ | 12 | 5.3 | odd | 4 | inner | |
20.4.e.b.3.5 | yes | 12 | 20.3 | even | 4 | inner | |
20.4.e.b.7.2 | yes | 12 | 4.3 | odd | 2 | inner | |
20.4.e.b.7.5 | yes | 12 | 1.1 | even | 1 | trivial | |
100.4.e.e.7.2 | 12 | 5.4 | even | 2 | |||
100.4.e.e.7.5 | 12 | 20.19 | odd | 2 | |||
100.4.e.e.43.2 | 12 | 20.7 | even | 4 | |||
100.4.e.e.43.5 | 12 | 5.2 | odd | 4 | |||
180.4.k.e.127.2 | 12 | 3.2 | odd | 2 | |||
180.4.k.e.127.5 | 12 | 12.11 | even | 2 | |||
180.4.k.e.163.2 | 12 | 60.23 | odd | 4 | |||
180.4.k.e.163.5 | 12 | 15.8 | even | 4 | |||
320.4.n.k.63.1 | 12 | 40.3 | even | 4 | |||
320.4.n.k.63.6 | 12 | 40.13 | odd | 4 | |||
320.4.n.k.127.1 | 12 | 8.5 | even | 2 | |||
320.4.n.k.127.6 | 12 | 8.3 | odd | 2 |