Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,4,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.149");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.6506685020\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 66 x^{14} + 3127 x^{12} - 69136 x^{10} + 1110267 x^{8} - 6713681 x^{6} + 29846021 x^{4} + \cdots + 24010000 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.7 | ||
Root | \(-5.28099 - 3.04898i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.4.j.j.149.7 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.00000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 2.69618 | + | 1.55664i | 0.518880 | + | 0.299576i | 0.736476 | − | 0.676463i | \(-0.236488\pi\) |
−0.217596 | + | 0.976039i | \(0.569822\pi\) | |||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.22657 | 0.423664 | ||||||||
\(7\) | −3.64704 | − | 18.1576i | −0.196922 | − | 0.980419i | ||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −8.65373 | − | 14.9887i | −0.320509 | − | 0.555137i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50388 | − | 4.33685i | 0.0686317 | − | 0.118874i | −0.829668 | − | 0.558258i | \(-0.811470\pi\) |
0.898299 | + | 0.439384i | \(0.144803\pi\) | |||||||
\(12\) | 10.7847 | − | 6.22657i | 0.259440 | − | 0.149788i | ||||
\(13\) | − | 2.87313i | − | 0.0612972i | −0.999530 | − | 0.0306486i | \(-0.990243\pi\) | ||
0.999530 | − | 0.0306486i | \(-0.00975727\pi\) | |||||||
\(14\) | −24.4745 | − | 27.8029i | −0.467220 | − | 0.530759i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −40.9643 | − | 23.6508i | −0.584430 | − | 0.337421i | 0.178462 | − | 0.983947i | \(-0.442888\pi\) |
−0.762892 | + | 0.646526i | \(0.776221\pi\) | |||||||
\(18\) | −29.9774 | − | 17.3075i | −0.392541 | − | 0.226634i | ||||
\(19\) | −11.8450 | − | 20.5162i | −0.143023 | − | 0.247723i | 0.785611 | − | 0.618721i | \(-0.212349\pi\) |
−0.928634 | + | 0.370998i | \(0.879016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.4318 | − | 54.6334i | 0.191531 | − | 0.567713i | ||||
\(22\) | − | 10.0155i | − | 0.0970599i | ||||||
\(23\) | −56.9621 | + | 32.8871i | −0.516410 | + | 0.298149i | −0.735464 | − | 0.677563i | \(-0.763036\pi\) |
0.219055 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(24\) | 12.4531 | − | 21.5695i | 0.105916 | − | 0.183452i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.87313 | − | 4.97641i | −0.0216718 | − | 0.0375367i | ||||
\(27\) | − | 137.942i | − | 0.983218i | ||||||
\(28\) | −70.1939 | − | 23.6815i | −0.473764 | − | 0.159835i | ||||
\(29\) | −91.7175 | −0.587293 | −0.293647 | − | 0.955914i | \(-0.594869\pi\) | ||||
−0.293647 | + | 0.955914i | \(0.594869\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 64.7258 | − | 112.108i | 0.375003 | − | 0.649524i | −0.615325 | − | 0.788274i | \(-0.710975\pi\) |
0.990327 | + | 0.138750i | \(0.0443084\pi\) | |||||||
\(32\) | −27.7128 | − | 16.0000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 13.5018 | − | 7.79530i | 0.0712233 | − | 0.0411208i | ||||
\(34\) | −94.6030 | −0.477185 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −69.2299 | −0.320509 | ||||||||
\(37\) | 321.313 | − | 185.510i | 1.42766 | − | 0.824261i | 0.430726 | − | 0.902483i | \(-0.358257\pi\) |
0.996936 | + | 0.0782216i | \(0.0249242\pi\) | |||||||
\(38\) | −41.0323 | − | 23.6900i | −0.175166 | − | 0.101132i | ||||
\(39\) | 4.47243 | − | 7.74648i | 0.0183631 | − | 0.0318059i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −19.0608 | −0.0726048 | −0.0363024 | − | 0.999341i | \(-0.511558\pi\) | ||||
−0.0363024 | + | 0.999341i | \(0.511558\pi\) | |||||||
\(42\) | −22.7086 | − | 113.060i | −0.0834287 | − | 0.415368i | ||||
\(43\) | 117.314i | 0.416053i | 0.978123 | + | 0.208026i | \(0.0667040\pi\) | ||||
−0.978123 | + | 0.208026i | \(0.933296\pi\) | |||||||
\(44\) | −10.0155 | − | 17.3474i | −0.0343159 | − | 0.0594368i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −65.7742 | + | 113.924i | −0.210823 | + | 0.365157i | ||||
\(47\) | 519.754 | − | 300.080i | 1.61306 | − | 0.931301i | 0.624405 | − | 0.781100i | \(-0.285341\pi\) |
0.988656 | − | 0.150201i | \(-0.0479920\pi\) | |||||||
\(48\) | − | 49.8125i | − | 0.149788i | ||||||
\(49\) | −316.398 | + | 132.443i | −0.922444 | + | 0.386132i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −73.6315 | − | 127.533i | −0.202166 | − | 0.350162i | ||||
\(52\) | −9.95282 | − | 5.74626i | −0.0265425 | − | 0.0153243i | ||||
\(53\) | 151.403 | + | 87.4128i | 0.392394 | + | 0.226549i | 0.683197 | − | 0.730234i | \(-0.260589\pi\) |
−0.290803 | + | 0.956783i | \(0.593922\pi\) | |||||||
\(54\) | −137.942 | − | 238.922i | −0.347620 | − | 0.602096i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −145.261 | + | 29.1764i | −0.346631 | + | 0.0696224i | ||||
\(57\) | − | 73.7537i | − | 0.171385i | ||||||
\(58\) | −158.859 | + | 91.7175i | −0.359642 | + | 0.207640i | ||||
\(59\) | −24.4427 | + | 42.3359i | −0.0539350 | + | 0.0934181i | −0.891732 | − | 0.452563i | \(-0.850510\pi\) |
0.837797 | + | 0.545981i | \(0.183843\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −349.341 | − | 605.076i | −0.733254 | − | 1.27003i | −0.955485 | − | 0.295040i | \(-0.904667\pi\) |
0.222231 | − | 0.974994i | \(-0.428666\pi\) | |||||||
\(62\) | − | 258.903i | − | 0.530334i | ||||||
\(63\) | −240.599 | + | 211.796i | −0.481152 | + | 0.423552i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.5906 | − | 27.0037i | 0.0290768 | − | 0.0503625i | ||||
\(67\) | 507.083 | + | 292.764i | 0.924627 | + | 0.533834i | 0.885108 | − | 0.465385i | \(-0.154084\pi\) |
0.0395189 | + | 0.999219i | \(0.487417\pi\) | |||||||
\(68\) | −163.857 | + | 94.6030i | −0.292215 | + | 0.168710i | ||||
\(69\) | −204.774 | −0.357273 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −756.468 | −1.26445 | −0.632227 | − | 0.774783i | \(-0.717859\pi\) | ||||
−0.632227 | + | 0.774783i | \(0.717859\pi\) | |||||||
\(72\) | −119.910 | + | 69.2299i | −0.196271 | + | 0.113317i | ||||
\(73\) | 709.970 | + | 409.901i | 1.13830 | + | 0.657196i | 0.946008 | − | 0.324142i | \(-0.105076\pi\) |
0.192289 | + | 0.981338i | \(0.438409\pi\) | |||||||
\(74\) | 371.020 | − | 642.626i | 0.582841 | − | 1.00951i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −94.7601 | −0.143023 | ||||||||
\(77\) | −87.8787 | − | 29.6479i | −0.130061 | − | 0.0438790i | ||||
\(78\) | − | 17.8897i | − | 0.0259694i | ||||||
\(79\) | 240.970 | + | 417.372i | 0.343180 | + | 0.594405i | 0.985021 | − | 0.172433i | \(-0.0551627\pi\) |
−0.641842 | + | 0.766837i | \(0.721829\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −18.9251 | + | 32.7792i | −0.0259603 | + | 0.0449646i | ||||
\(82\) | −33.0143 | + | 19.0608i | −0.0444612 | + | 0.0256697i | ||||
\(83\) | 269.803i | 0.356804i | 0.983958 | + | 0.178402i | \(0.0570927\pi\) | ||||
−0.983958 | + | 0.178402i | \(0.942907\pi\) | |||||||
\(84\) | −152.392 | − | 173.116i | −0.197944 | − | 0.224864i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 117.314 | + | 203.194i | 0.147097 | + | 0.254779i | ||||
\(87\) | −247.287 | − | 142.771i | −0.304735 | − | 0.175939i | ||||
\(88\) | −34.6948 | − | 20.0311i | −0.0420282 | − | 0.0242650i | ||||
\(89\) | 73.2952 | + | 126.951i | 0.0872952 | + | 0.151200i | 0.906367 | − | 0.422491i | \(-0.138844\pi\) |
−0.819072 | + | 0.573691i | \(0.805511\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −52.1692 | + | 10.4784i | −0.0600969 | + | 0.0120708i | ||||
\(92\) | 263.097i | 0.298149i | ||||||||
\(93\) | 349.025 | − | 201.510i | 0.389163 | − | 0.224684i | ||||
\(94\) | 600.160 | − | 1039.51i | 0.658529 | − | 1.14061i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −49.8125 | − | 86.2778i | −0.0529580 | − | 0.0917260i | ||||
\(97\) | 241.036i | 0.252304i | 0.992011 | + | 0.126152i | \(0.0402627\pi\) | ||||
−0.992011 | + | 0.126152i | \(0.959737\pi\) | |||||||
\(98\) | −415.574 | + | 545.797i | −0.428361 | + | 0.562590i | ||||
\(99\) | −86.6717 | −0.0879883 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −474.936 | + | 822.613i | −0.467900 | + | 0.810426i | −0.999327 | − | 0.0366778i | \(-0.988322\pi\) |
0.531428 | + | 0.847104i | \(0.321656\pi\) | |||||||
\(102\) | −255.067 | − | 147.263i | −0.247602 | − | 0.142953i | ||||
\(103\) | 42.9711 | − | 24.8094i | 0.0411074 | − | 0.0237334i | −0.479305 | − | 0.877648i | \(-0.659111\pi\) |
0.520413 | + | 0.853915i | \(0.325778\pi\) | |||||||
\(104\) | −22.9850 | −0.0216718 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 349.651 | 0.320388 | ||||||||
\(107\) | 650.048 | − | 375.306i | 0.587314 | − | 0.339086i | −0.176721 | − | 0.984261i | \(-0.556549\pi\) |
0.764035 | + | 0.645175i | \(0.223216\pi\) | |||||||
\(108\) | −477.844 | − | 275.883i | −0.425746 | − | 0.245805i | ||||
\(109\) | −205.055 | + | 355.166i | −0.180190 | + | 0.312098i | −0.941945 | − | 0.335767i | \(-0.891005\pi\) |
0.761755 | + | 0.647865i | \(0.224338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1155.09 | 0.987715 | ||||||||
\(112\) | −222.423 | + | 195.796i | −0.187652 | + | 0.165187i | ||||
\(113\) | − | 1885.39i | − | 1.56958i | −0.619763 | − | 0.784789i | \(-0.712771\pi\) | ||
0.619763 | − | 0.784789i | \(-0.287229\pi\) | |||||||
\(114\) | −73.7537 | − | 127.745i | −0.0605936 | − | 0.104951i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −183.435 | + | 317.719i | −0.146823 | + | 0.254305i | ||||
\(117\) | −43.0645 | + | 24.8633i | −0.0340283 | + | 0.0196463i | ||||
\(118\) | 97.7706i | 0.0762755i | ||||||||
\(119\) | −280.043 | + | 830.070i | −0.215727 | + | 0.639432i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 652.961 | + | 1130.96i | 0.490579 | + | 0.849708i | ||||
\(122\) | −1210.15 | − | 698.682i | −0.898050 | − | 0.518489i | ||||
\(123\) | −51.3914 | − | 29.6708i | −0.0376732 | − | 0.0217506i | ||||
\(124\) | −258.903 | − | 448.433i | −0.187501 | − | 0.324762i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −204.933 | + | 607.440i | −0.144896 | + | 0.429484i | ||||
\(127\) | 2336.23i | 1.63234i | 0.577814 | + | 0.816169i | \(0.303906\pi\) | ||||
−0.577814 | + | 0.816169i | \(0.696094\pi\) | |||||||
\(128\) | −110.851 | + | 64.0000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −182.616 | + | 316.301i | −0.124639 | + | 0.215882i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −939.864 | − | 1627.89i | −0.626842 | − | 1.08572i | −0.988182 | − | 0.153288i | \(-0.951014\pi\) |
0.361339 | − | 0.932434i | \(-0.382320\pi\) | |||||||
\(132\) | − | 62.3624i | − | 0.0411208i | ||||||
\(133\) | −329.325 | + | 289.901i | −0.214708 | + | 0.189004i | ||||
\(134\) | 1171.06 | 0.754955 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −189.206 | + | 327.714i | −0.119296 | + | 0.206627i | ||||
\(137\) | 705.830 | + | 407.511i | 0.440169 | + | 0.254132i | 0.703669 | − | 0.710528i | \(-0.251544\pi\) |
−0.263500 | + | 0.964659i | \(0.584877\pi\) | |||||||
\(138\) | −354.678 | + | 204.774i | −0.218784 | + | 0.126315i | ||||
\(139\) | −10.2265 | −0.00624028 | −0.00312014 | − | 0.999995i | \(-0.500993\pi\) | ||||
−0.00312014 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1868.47 | 1.11598 | ||||||||
\(142\) | −1310.24 | + | 756.468i | −0.774316 | + | 0.447052i | ||||
\(143\) | −12.4603 | − | 7.19398i | −0.00728662 | − | 0.00420693i | ||||
\(144\) | −138.460 | + | 239.819i | −0.0801272 | + | 0.138784i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1639.61 | 0.929416 | ||||||||
\(147\) | −1059.23 | − | 135.427i | −0.594314 | − | 0.0759854i | ||||
\(148\) | − | 1484.08i | − | 0.824261i | ||||||
\(149\) | 1768.00 | + | 3062.27i | 0.972084 | + | 1.68370i | 0.689240 | + | 0.724533i | \(0.257944\pi\) |
0.282844 | + | 0.959166i | \(0.408722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1079.99 | − | 1870.60i | 0.582043 | − | 1.00813i | −0.413194 | − | 0.910643i | \(-0.635587\pi\) |
0.995237 | − | 0.0974851i | \(-0.0310798\pi\) | |||||||
\(152\) | −164.129 | + | 94.7601i | −0.0875832 | + | 0.0505662i | ||||
\(153\) | 818.669i | 0.432585i | ||||||||
\(154\) | −181.858 | + | 36.5271i | −0.0951594 | + | 0.0191132i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −17.8897 | − | 30.9859i | −0.00918157 | − | 0.0159030i | ||||
\(157\) | −1872.78 | − | 1081.25i | −0.952003 | − | 0.549639i | −0.0583005 | − | 0.998299i | \(-0.518568\pi\) |
−0.893703 | + | 0.448660i | \(0.851901\pi\) | |||||||
\(158\) | 834.743 | + | 481.939i | 0.420308 | + | 0.242665i | ||||
\(159\) | 272.141 | + | 471.362i | 0.135737 | + | 0.235103i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 804.895 | + | 914.356i | 0.394004 | + | 0.447586i | ||||
\(162\) | 75.7003i | 0.0367135i | ||||||||
\(163\) | 2080.13 | − | 1200.96i | 0.999560 | − | 0.577096i | 0.0914420 | − | 0.995810i | \(-0.470852\pi\) |
0.908118 | + | 0.418714i | \(0.137519\pi\) | |||||||
\(164\) | −38.1216 | + | 66.0285i | −0.0181512 | + | 0.0314388i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 269.803 | + | 467.312i | 0.126149 | + | 0.218497i | ||||
\(167\) | 2844.04i | 1.31784i | 0.752214 | + | 0.658919i | \(0.228986\pi\) | ||||
−0.752214 | + | 0.658919i | \(0.771014\pi\) | |||||||
\(168\) | −437.067 | − | 147.454i | −0.200717 | − | 0.0677164i | ||||
\(169\) | 2188.75 | 0.996243 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −205.007 | + | 355.083i | −0.0916801 | + | 0.158795i | ||||
\(172\) | 406.389 | + | 234.629i | 0.180156 | + | 0.104013i | ||||
\(173\) | 1518.15 | − | 876.505i | 0.667185 | − | 0.385199i | −0.127824 | − | 0.991797i | \(-0.540799\pi\) |
0.795009 | + | 0.606598i | \(0.207466\pi\) | |||||||
\(174\) | −571.085 | −0.248815 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −80.1242 | −0.0343159 | ||||||||
\(177\) | −131.804 | + | 76.0969i | −0.0559716 | + | 0.0323152i | ||||
\(178\) | 253.902 | + | 146.590i | 0.106914 | + | 0.0617270i | ||||
\(179\) | −1074.66 | + | 1861.36i | −0.448735 | + | 0.777232i | −0.998304 | − | 0.0582164i | \(-0.981459\pi\) |
0.549569 | + | 0.835448i | \(0.314792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2403.89 | 0.987180 | 0.493590 | − | 0.869695i | \(-0.335684\pi\) | ||||
0.493590 | + | 0.869695i | \(0.335684\pi\) | |||||||
\(182\) | −79.8813 | + | 70.3184i | −0.0325340 | + | 0.0286393i | ||||
\(183\) | − | 2175.19i | − | 0.878661i | ||||||
\(184\) | 263.097 | + | 455.697i | 0.105412 | + | 0.182578i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 403.019 | − | 698.050i | 0.158875 | − | 0.275180i | ||||
\(187\) | −205.140 | + | 118.437i | −0.0802208 | + | 0.0463155i | ||||
\(188\) | − | 2400.64i | − | 0.931301i | ||||||
\(189\) | −2504.69 | + | 503.079i | −0.963966 | + | 0.193617i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 254.284 | + | 440.432i | 0.0963315 | + | 0.166851i | 0.910164 | − | 0.414249i | \(-0.135956\pi\) |
−0.813832 | + | 0.581100i | \(0.802622\pi\) | |||||||
\(192\) | −172.556 | − | 99.6251i | −0.0648601 | − | 0.0374470i | ||||
\(193\) | 1314.17 | + | 758.738i | 0.490136 | + | 0.282980i | 0.724631 | − | 0.689137i | \(-0.242010\pi\) |
−0.234495 | + | 0.972117i | \(0.575344\pi\) | |||||||
\(194\) | 241.036 | + | 417.487i | 0.0892030 | + | 0.154504i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −173.999 | + | 1360.92i | −0.0634108 | + | 0.495963i | ||||
\(197\) | − | 25.9685i | − | 0.00939176i | −0.999989 | − | 0.00469588i | \(-0.998505\pi\) | ||
0.999989 | − | 0.00469588i | \(-0.00149475\pi\) | |||||||
\(198\) | −150.120 | + | 86.6717i | −0.0538816 | + | 0.0311085i | ||||
\(199\) | 2416.64 | − | 4185.74i | 0.860858 | − | 1.49105i | −0.0102436 | − | 0.999948i | \(-0.503261\pi\) |
0.871102 | − | 0.491103i | \(-0.163406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 911.458 | + | 1578.69i | 0.319847 | + | 0.553992i | ||||
\(202\) | 1899.74i | 0.661710i | ||||||||
\(203\) | 334.498 | + | 1665.37i | 0.115651 | + | 0.575794i | ||||
\(204\) | −589.052 | −0.202166 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 49.6187 | − | 85.9421i | 0.0167820 | − | 0.0290673i | ||||
\(207\) | 985.870 | + | 569.192i | 0.331028 | + | 0.191119i | ||||
\(208\) | −39.8113 | + | 22.9850i | −0.0132712 | + | 0.00766215i | ||||
\(209\) | −118.634 | −0.0392636 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1880.24 | −0.613464 | −0.306732 | − | 0.951796i | \(-0.599235\pi\) | ||||
−0.306732 | + | 0.951796i | \(0.599235\pi\) | |||||||
\(212\) | 605.614 | − | 349.651i | 0.196197 | − | 0.113274i | ||||
\(213\) | −2039.57 | − | 1177.55i | −0.656100 | − | 0.378800i | ||||
\(214\) | 750.611 | − | 1300.10i | 0.239770 | − | 0.415293i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1103.53 | −0.347620 | ||||||||
\(217\) | −2271.68 | − | 766.402i | −0.710652 | − | 0.239755i | ||||
\(218\) | 820.221i | 0.254827i | ||||||||
\(219\) | 1276.14 | + | 2210.34i | 0.393760 | + | 0.682013i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −67.9517 | + | 117.696i | −0.0206829 | + | 0.0358239i | ||||
\(222\) | 2000.68 | − | 1155.09i | 0.604849 | − | 0.349210i | ||||
\(223\) | 5199.43i | 1.56134i | 0.624942 | + | 0.780671i | \(0.285123\pi\) | ||||
−0.624942 | + | 0.780671i | \(0.714877\pi\) | |||||||
\(224\) | −189.452 | + | 561.551i | −0.0565102 | + | 0.167501i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1885.39 | − | 3265.59i | −0.554930 | − | 0.961167i | ||||
\(227\) | −3358.21 | − | 1938.86i | −0.981903 | − | 0.566902i | −0.0790590 | − | 0.996870i | \(-0.525192\pi\) |
−0.902844 | + | 0.429968i | \(0.858525\pi\) | |||||||
\(228\) | −255.490 | − | 147.507i | −0.0742117 | − | 0.0428461i | ||||
\(229\) | −2380.36 | − | 4122.90i | −0.686893 | − | 1.18973i | −0.972838 | − | 0.231487i | \(-0.925641\pi\) |
0.285945 | − | 0.958246i | \(-0.407692\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −190.786 | − | 216.732i | −0.0543411 | − | 0.0617311i | ||||
\(232\) | 733.740i | 0.207640i | ||||||||
\(233\) | 495.185 | − | 285.895i | 0.139230 | − | 0.0803846i | −0.428767 | − | 0.903415i | \(-0.641052\pi\) |
0.567997 | + | 0.823031i | \(0.307718\pi\) | |||||||
\(234\) | −49.7266 | + | 86.1290i | −0.0138920 | + | 0.0240617i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 97.7706 | + | 169.344i | 0.0269675 | + | 0.0467090i | ||||
\(237\) | 1500.41i | 0.411233i | ||||||||
\(238\) | 345.021 | + | 1717.77i | 0.0939681 | + | 0.467841i | ||||
\(239\) | 4842.24 | 1.31054 | 0.655269 | − | 0.755396i | \(-0.272555\pi\) | ||||
0.655269 | + | 0.755396i | \(0.272555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1587.99 | + | 2750.48i | −0.424445 | + | 0.735161i | −0.996368 | − | 0.0851464i | \(-0.972864\pi\) |
0.571923 | + | 0.820307i | \(0.306198\pi\) | |||||||
\(242\) | 2261.92 | + | 1305.92i | 0.600835 | + | 0.346892i | ||||
\(243\) | −3327.50 | + | 1921.13i | −0.878433 | + | 0.507163i | ||||
\(244\) | −2794.73 | −0.733254 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −118.683 | −0.0307600 | ||||||||
\(247\) | −58.9456 | + | 34.0323i | −0.0151847 | + | 0.00876689i | ||||
\(248\) | −896.866 | − | 517.806i | −0.229641 | − | 0.132584i | ||||
\(249\) | −419.986 | + | 727.438i | −0.106890 | + | 0.185138i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6433.53 | −1.61785 | −0.808926 | − | 0.587910i | \(-0.799951\pi\) | ||||
−0.808926 | + | 0.587910i | \(0.799951\pi\) | |||||||
\(252\) | 252.484 | + | 1257.05i | 0.0631152 | + | 0.314233i | ||||
\(253\) | 329.382i | 0.0818500i | ||||||||
\(254\) | 2336.23 | + | 4046.47i | 0.577118 | + | 0.999598i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6115.84 | − | 3530.98i | 1.48442 | − | 0.857030i | 0.484576 | − | 0.874749i | \(-0.338974\pi\) |
0.999843 | + | 0.0177196i | \(0.00564063\pi\) | |||||||
\(258\) | 730.466i | 0.176267i | ||||||||
\(259\) | −4540.26 | − | 5157.71i | −1.08926 | − | 1.23739i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 793.699 | + | 1374.73i | 0.188233 | + | 0.326028i | ||||
\(262\) | −3255.79 | − | 1879.73i | −0.767722 | − | 0.443244i | ||||
\(263\) | −4031.21 | − | 2327.42i | −0.945152 | − | 0.545684i | −0.0535805 | − | 0.998564i | \(-0.517063\pi\) |
−0.891572 | + | 0.452880i | \(0.850397\pi\) | |||||||
\(264\) | −62.3624 | − | 108.015i | −0.0145384 | − | 0.0251813i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −280.508 | + | 831.448i | −0.0646580 | + | 0.191652i | ||||
\(267\) | 456.377i | 0.104606i | ||||||||
\(268\) | 2028.33 | − | 1171.06i | 0.462314 | − | 0.266917i | ||||
\(269\) | 2577.99 | − | 4465.21i | 0.584322 | − | 1.01208i | −0.410637 | − | 0.911799i | \(-0.634694\pi\) |
0.994960 | − | 0.100277i | \(-0.0319729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2514.12 | − | 4354.58i | −0.563549 | − | 0.976095i | −0.997183 | − | 0.0750058i | \(-0.976102\pi\) |
0.433635 | − | 0.901089i | \(-0.357231\pi\) | |||||||
\(272\) | 756.824i | 0.168710i | ||||||||
\(273\) | −156.969 | − | 52.9570i | −0.0347992 | − | 0.0117403i | ||||
\(274\) | 1630.05 | 0.359397 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −409.547 | + | 709.357i | −0.0893183 | + | 0.154704i | ||||
\(277\) | 99.8881 | + | 57.6704i | 0.0216668 | + | 0.0125093i | 0.510794 | − | 0.859703i | \(-0.329351\pi\) |
−0.489127 | + | 0.872212i | \(0.662685\pi\) | |||||||
\(278\) | −17.7128 | + | 10.2265i | −0.00382137 | + | 0.00220627i | ||||
\(279\) | −2240.48 | −0.480767 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −977.317 | −0.207480 | −0.103740 | − | 0.994604i | \(-0.533081\pi\) | ||||
−0.103740 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(282\) | 3236.28 | − | 1868.47i | 0.683396 | − | 0.394559i | ||||
\(283\) | −3652.15 | − | 2108.57i | −0.767131 | − | 0.442903i | 0.0647192 | − | 0.997904i | \(-0.479385\pi\) |
−0.831850 | + | 0.555000i | \(0.812718\pi\) | |||||||
\(284\) | −1512.94 | + | 2620.48i | −0.316113 | + | 0.547524i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.7759 | −0.00594950 | ||||||||
\(287\) | 69.5156 | + | 346.099i | 0.0142975 | + | 0.0711831i | ||||
\(288\) | 553.839i | 0.113317i | ||||||||
\(289\) | −1337.78 | − | 2317.11i | −0.272295 | − | 0.471628i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −375.207 | + | 649.877i | −0.0755842 | + | 0.130916i | ||||
\(292\) | 2839.88 | − | 1639.61i | 0.569149 | − | 0.328598i | ||||
\(293\) | 4064.73i | 0.810458i | 0.914215 | + | 0.405229i | \(0.132808\pi\) | ||||
−0.914215 | + | 0.405229i | \(0.867192\pi\) | |||||||
\(294\) | −1970.07 | + | 824.667i | −0.390806 | + | 0.163590i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1484.08 | − | 2570.50i | −0.291420 | − | 0.504755i | ||||
\(297\) | −598.233 | − | 345.390i | −0.116879 | − | 0.0674800i | ||||
\(298\) | 6124.54 | + | 3536.01i | 1.19055 | + | 0.687367i | ||||
\(299\) | 94.4889 | + | 163.660i | 0.0182757 | + | 0.0316544i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2130.15 | − | 427.851i | 0.407906 | − | 0.0819299i | ||||
\(302\) | − | 4319.97i | − | 0.823133i | ||||||
\(303\) | −2561.03 | + | 1478.61i | −0.485568 | + | 0.280343i | ||||
\(304\) | −189.520 | + | 328.259i | −0.0357557 | + | 0.0619307i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 818.669 | + | 1417.98i | 0.152942 | + | 0.264903i | ||||
\(307\) | − | 1650.69i | − | 0.306872i | −0.988159 | − | 0.153436i | \(-0.950966\pi\) | ||
0.988159 | − | 0.153436i | \(-0.0490339\pi\) | |||||||
\(308\) | −278.461 | + | 245.125i | −0.0515155 | + | 0.0453483i | ||||
\(309\) | 154.477 | 0.0284398 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2143.20 | + | 3712.13i | −0.390771 | + | 0.676835i | −0.992551 | − | 0.121827i | \(-0.961125\pi\) |
0.601781 | + | 0.798661i | \(0.294458\pi\) | |||||||
\(312\) | −61.9719 | − | 35.7795i | −0.0112451 | − | 0.00649235i | ||||
\(313\) | 6159.68 | − | 3556.29i | 1.11235 | − | 0.642216i | 0.172913 | − | 0.984937i | \(-0.444682\pi\) |
0.939437 | + | 0.342721i | \(0.111349\pi\) | |||||||
\(314\) | −4325.01 | −0.777307 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1927.76 | 0.343180 | ||||||||
\(317\) | 7904.73 | − | 4563.80i | 1.40055 | − | 0.808607i | 0.406100 | − | 0.913829i | \(-0.366889\pi\) |
0.994449 | + | 0.105222i | \(0.0335552\pi\) | |||||||
\(318\) | 942.723 | + | 544.282i | 0.166243 | + | 0.0959805i | ||||
\(319\) | −229.650 | + | 397.765i | −0.0403070 | + | 0.0698137i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2336.86 | 0.406327 | ||||||||
\(322\) | 2308.47 | + | 778.816i | 0.399522 | + | 0.134788i | ||||
\(323\) | 1120.57i | 0.193035i | ||||||||
\(324\) | 75.7003 | + | 131.117i | 0.0129802 | + | 0.0224823i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2401.93 | − | 4160.26i | 0.408069 | − | 0.706796i | ||||
\(327\) | −1105.73 | + | 638.395i | −0.186994 | + | 0.107961i | ||||
\(328\) | 152.486i | 0.0256697i | ||||||||
\(329\) | −7344.30 | − | 8343.08i | −1.23071 | − | 1.39808i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4458.65 | − | 7722.61i | −0.740392 | − | 1.28240i | −0.952317 | − | 0.305110i | \(-0.901307\pi\) |
0.211925 | − | 0.977286i | \(-0.432027\pi\) | |||||||
\(332\) | 934.624 | + | 539.606i | 0.154501 | + | 0.0892009i | ||||
\(333\) | −5561.11 | − | 3210.71i | −0.915156 | − | 0.528366i | ||||
\(334\) | 2844.04 | + | 4926.03i | 0.465926 | + | 0.807007i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −904.477 | + | 181.668i | −0.146855 | + | 0.0294965i | ||||
\(337\) | − | 9427.08i | − | 1.52382i | −0.647685 | − | 0.761908i | \(-0.724263\pi\) | ||
0.647685 | − | 0.761908i | \(-0.275737\pi\) | |||||||
\(338\) | 3791.02 | − | 2188.75i | 0.610072 | − | 0.352225i | ||||
\(339\) | 2934.87 | − | 5083.35i | 0.470208 | − | 0.814424i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −324.131 | − | 561.412i | −0.0514742 | − | 0.0891559i | ||||
\(342\) | 820.029i | 0.129655i | ||||||||
\(343\) | 3558.77 | + | 5262.01i | 0.560221 | + | 0.828344i | ||||
\(344\) | 938.515 | 0.147097 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1753.01 | − | 3036.30i | 0.272377 | − | 0.471771i | ||||
\(347\) | −385.004 | − | 222.282i | −0.0595623 | − | 0.0343883i | 0.469923 | − | 0.882707i | \(-0.344282\pi\) |
−0.529485 | + | 0.848319i | \(0.677615\pi\) | |||||||
\(348\) | −989.148 | + | 571.085i | −0.152368 | + | 0.0879694i | ||||
\(349\) | −8417.98 | −1.29113 | −0.645565 | − | 0.763706i | \(-0.723378\pi\) | ||||
−0.645565 | + | 0.763706i | \(0.723378\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −396.325 | −0.0602685 | ||||||||
\(352\) | −138.779 | + | 80.1242i | −0.0210141 | + | 0.0121325i | ||||
\(353\) | −9652.68 | − | 5572.98i | −1.45541 | − | 0.840282i | −0.456631 | − | 0.889656i | \(-0.650944\pi\) |
−0.998780 | + | 0.0493743i | \(0.984277\pi\) | |||||||
\(354\) | −152.194 | + | 263.607i | −0.0228503 | + | 0.0395779i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 586.361 | 0.0872952 | ||||||||
\(357\) | −2047.17 | + | 1802.09i | −0.303495 | + | 0.267162i | ||||
\(358\) | 4298.63i | 0.634607i | ||||||||
\(359\) | 4939.32 | + | 8555.15i | 0.726148 | + | 1.25773i | 0.958500 | + | 0.285094i | \(0.0920247\pi\) |
−0.232351 | + | 0.972632i | \(0.574642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3148.89 | − | 5454.04i | 0.459089 | − | 0.795165i | ||||
\(362\) | 4163.66 | − | 2403.89i | 0.604522 | − | 0.349021i | ||||
\(363\) | 4065.71i | 0.587863i | ||||||||
\(364\) | −68.0401 | + | 201.676i | −0.00979744 | + | 0.0290404i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2175.19 | − | 3767.55i | −0.310654 | − | 0.538068i | ||||
\(367\) | −6950.29 | − | 4012.75i | −0.988561 | − | 0.570746i | −0.0837174 | − | 0.996490i | \(-0.526679\pi\) |
−0.904844 | + | 0.425743i | \(0.860013\pi\) | |||||||
\(368\) | 911.394 | + | 526.193i | 0.129102 | + | 0.0745373i | ||||
\(369\) | 164.947 | + | 285.697i | 0.0232705 | + | 0.0403056i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1035.03 | − | 3067.92i | 0.144842 | − | 0.429323i | ||||
\(372\) | − | 1612.08i | − | 0.224684i | ||||||
\(373\) | 10465.0 | − | 6041.97i | 1.45270 | − | 0.838717i | 0.454066 | − | 0.890968i | \(-0.349973\pi\) |
0.998634 | + | 0.0522510i | \(0.0166396\pi\) | |||||||
\(374\) | −236.875 | + | 410.279i | −0.0327500 | + | 0.0567247i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2400.64 | − | 4158.03i | −0.329265 | − | 0.570303i | ||||
\(377\) | 263.516i | 0.0359994i | ||||||||
\(378\) | −3835.18 | + | 3376.05i | −0.521852 | + | 0.459379i | ||||
\(379\) | −3034.22 | −0.411234 | −0.205617 | − | 0.978633i | \(-0.565920\pi\) | ||||
−0.205617 | + | 0.978633i | \(0.565920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3636.67 | + | 6298.90i | −0.489009 | + | 0.846988i | ||||
\(382\) | 880.864 | + | 508.567i | 0.117981 | + | 0.0681166i | ||||
\(383\) | −6887.54 | + | 3976.52i | −0.918895 | + | 0.530524i | −0.883282 | − | 0.468842i | \(-0.844671\pi\) |
−0.0356123 | + | 0.999366i | \(0.511338\pi\) | |||||||
\(384\) | −398.500 | −0.0529580 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3034.95 | 0.400194 | ||||||||
\(387\) | 1758.39 | − | 1015.21i | 0.230967 | − | 0.133349i | ||||
\(388\) | 834.973 | + | 482.072i | 0.109251 | + | 0.0630760i | ||||
\(389\) | −1789.65 | + | 3099.77i | −0.233262 | + | 0.404022i | −0.958766 | − | 0.284196i | \(-0.908273\pi\) |
0.725504 | + | 0.688218i | \(0.241607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3111.22 | 0.402407 | ||||||||
\(392\) | 1059.55 | + | 2531.19i | 0.136518 | + | 0.326133i | ||||
\(393\) | − | 5852.13i | − | 0.751147i | ||||||
\(394\) | −25.9685 | − | 44.9787i | −0.00332049 | − | 0.00575126i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −173.343 | + | 300.240i | −0.0219971 | + | 0.0381000i | ||||
\(397\) | −1604.06 | + | 926.104i | −0.202785 | + | 0.117078i | −0.597954 | − | 0.801531i | \(-0.704019\pi\) |
0.395169 | + | 0.918608i | \(0.370686\pi\) | |||||||
\(398\) | − | 9666.54i | − | 1.21744i | ||||||
\(399\) | −1339.19 | + | 268.983i | −0.168029 | + | 0.0337494i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2992.38 | + | 5182.96i | 0.372649 | + | 0.645448i | 0.989972 | − | 0.141262i | \(-0.0451161\pi\) |
−0.617323 | + | 0.786710i | \(0.711783\pi\) | |||||||
\(402\) | 3157.38 | + | 1822.92i | 0.391731 | + | 0.226166i | ||||
\(403\) | −322.102 | − | 185.966i | −0.0398140 | − | 0.0229866i | ||||
\(404\) | 1899.74 | + | 3290.45i | 0.233950 | + | 0.405213i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2244.74 | + | 2550.01i | 0.274395 | + | 0.311711i | ||||
\(407\) | − | 1857.98i | − | 0.226282i | ||||||
\(408\) | −1020.27 | + | 589.052i | −0.123801 | + | 0.0714765i | ||||
\(409\) | 4805.85 | − | 8323.98i | 0.581013 | − | 1.00634i | −0.414347 | − | 0.910119i | \(-0.635990\pi\) |
0.995360 | − | 0.0962245i | \(-0.0306767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1268.70 | + | 2197.45i | 0.152263 | + | 0.263728i | ||||
\(412\) | − | 198.475i | − | 0.0237334i | ||||||
\(413\) | 857.863 | + | 289.419i | 0.102210 | + | 0.0344828i | ||||
\(414\) | 2276.77 | 0.270283 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −45.9701 | + | 79.6225i | −0.00541796 | + | 0.00938417i | ||||
\(417\) | −27.5724 | − | 15.9190i | −0.00323796 | − | 0.00186944i | ||||
\(418\) | −205.480 | + | 118.634i | −0.0240439 | + | 0.0138818i | ||||
\(419\) | 2060.89 | 0.240289 | 0.120145 | − | 0.992756i | \(-0.461664\pi\) | ||||
0.120145 | + | 0.992756i | \(0.461664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4670.81 | 0.540716 | 0.270358 | − | 0.962760i | \(-0.412858\pi\) | ||||
0.270358 | + | 0.962760i | \(0.412858\pi\) | |||||||
\(422\) | −3256.67 | + | 1880.24i | −0.375668 | + | 0.216892i | ||||
\(423\) | −8995.62 | − | 5193.62i | −1.03400 | − | 0.596980i | ||||
\(424\) | 699.302 | − | 1211.23i | 0.0800970 | − | 0.138732i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4710.20 | −0.535704 | ||||||||
\(427\) | −9712.68 | + | 8549.94i | −1.10077 | + | 0.968994i | ||||
\(428\) | − | 3002.44i | − | 0.339086i | ||||||
\(429\) | −22.3969 | − | 38.7926i | −0.00252059 | − | 0.00436579i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5866.94 | + | 10161.8i | −0.655686 | + | 1.13568i | 0.326035 | + | 0.945358i | \(0.394287\pi\) |
−0.981721 | + | 0.190324i | \(0.939046\pi\) | |||||||
\(432\) | −1911.38 | + | 1103.53i | −0.212873 | + | 0.122902i | ||||
\(433\) | 3982.03i | 0.441949i | 0.975280 | + | 0.220975i | \(0.0709238\pi\) | ||||
−0.975280 | + | 0.220975i | \(0.929076\pi\) | |||||||
\(434\) | −4701.06 | + | 944.231i | −0.519950 | + | 0.104434i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 820.221 | + | 1420.66i | 0.0900950 | + | 0.156049i | ||||
\(437\) | 1349.43 | + | 779.096i | 0.147717 | + | 0.0852842i | ||||
\(438\) | 4420.67 | + | 2552.28i | 0.482256 | + | 0.278430i | ||||
\(439\) | 3077.50 | + | 5330.38i | 0.334581 | + | 0.579511i | 0.983404 | − | 0.181428i | \(-0.0580719\pi\) |
−0.648823 | + | 0.760939i | \(0.724739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4723.18 | + | 3596.27i | 0.510007 | + | 0.388324i | ||||
\(442\) | 271.807i | 0.0292501i | ||||||||
\(443\) | 2681.24 | − | 1548.02i | 0.287561 | − | 0.166024i | −0.349280 | − | 0.937018i | \(-0.613574\pi\) |
0.636842 | + | 0.770995i | \(0.280241\pi\) | |||||||
\(444\) | 2310.18 | − | 4001.35i | 0.246929 | − | 0.427693i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5199.43 | + | 9005.67i | 0.552018 | + | 0.956123i | ||||
\(447\) | 11008.6i | 1.16485i | ||||||||
\(448\) | 233.411 | + | 1162.09i | 0.0246152 | + | 0.122552i | ||||
\(449\) | 7810.84 | 0.820972 | 0.410486 | − | 0.911867i | \(-0.365359\pi\) | ||||
0.410486 | + | 0.911867i | \(0.365359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −47.7260 | + | 82.6638i | −0.00498299 | + | 0.00863079i | ||||
\(452\) | −6531.18 | − | 3770.78i | −0.679647 | − | 0.392395i | ||||
\(453\) | 5823.71 | − | 3362.32i | 0.604022 | − | 0.348732i | ||||
\(454\) | −7755.45 | −0.801721 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −590.030 | −0.0605936 | ||||||||
\(457\) | 5833.50 | − | 3367.97i | 0.597111 | − | 0.344742i | −0.170793 | − | 0.985307i | \(-0.554633\pi\) |
0.767904 | + | 0.640565i | \(0.221300\pi\) | |||||||
\(458\) | −8245.80 | − | 4760.71i | −0.841268 | − | 0.485706i | ||||
\(459\) | −3262.43 | + | 5650.69i | −0.331758 | + | 0.574622i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17562.3 | 1.77431 | 0.887157 | − | 0.461468i | \(-0.152677\pi\) | ||||
0.887157 | + | 0.461468i | \(0.152677\pi\) | |||||||
\(462\) | −547.182 | − | 184.604i | −0.0551022 | − | 0.0185900i | ||||
\(463\) | 3575.44i | 0.358887i | 0.983768 | + | 0.179444i | \(0.0574297\pi\) | ||||
−0.983768 | + | 0.179444i | \(0.942570\pi\) | |||||||
\(464\) | 733.740 | + | 1270.87i | 0.0734117 | + | 0.127153i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 571.790 | − | 990.370i | 0.0568405 | − | 0.0984506i | ||||
\(467\) | −15006.8 | + | 8664.19i | −1.48701 | + | 0.858524i | −0.999890 | − | 0.0148125i | \(-0.995285\pi\) |
−0.487117 | + | 0.873337i | \(0.661952\pi\) | |||||||
\(468\) | 198.906i | 0.0196463i | ||||||||
\(469\) | 3466.55 | − | 10275.1i | 0.341302 | − | 1.01165i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3366.25 | − | 5830.51i | −0.329317 | − | 0.570394i | ||||
\(472\) | 338.687 | + | 195.541i | 0.0330283 | + | 0.0190689i | ||||
\(473\) | 508.775 | + | 293.741i | 0.0494577 | + | 0.0285544i | ||||
\(474\) | 1500.41 | + | 2598.79i | 0.145393 | + | 0.251828i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2315.36 | + | 2630.24i | 0.222950 | + | 0.253270i | ||||
\(477\) | − | 3025.79i | − | 0.290443i | ||||||
\(478\) | 8387.01 | − | 4842.24i | 0.802537 | − | 0.463345i | ||||
\(479\) | 2625.98 | − | 4548.33i | 0.250488 | − | 0.433859i | −0.713172 | − | 0.700989i | \(-0.752742\pi\) |
0.963660 | + | 0.267130i | \(0.0860755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −532.995 | − | 923.174i | −0.0505249 | − | 0.0875116i | ||||
\(482\) | 6351.95i | 0.600256i | ||||||||
\(483\) | 746.819 | + | 3718.20i | 0.0703549 | + | 0.350278i | ||||
\(484\) | 5223.69 | 0.490579 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3842.26 | + | 6655.00i | −0.358619 | + | 0.621146i | ||||
\(487\) | 757.266 | + | 437.208i | 0.0704620 | + | 0.0406813i | 0.534817 | − | 0.844968i | \(-0.320381\pi\) |
−0.464355 | + | 0.885649i | \(0.653714\pi\) | |||||||
\(488\) | −4840.61 | + | 2794.73i | −0.449025 | + | 0.259245i | ||||
\(489\) | 7477.88 | 0.691536 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15821.1 | −1.45417 | −0.727085 | − | 0.686547i | \(-0.759126\pi\) | ||||
−0.727085 | + | 0.686547i | \(0.759126\pi\) | |||||||
\(492\) | −205.565 | + | 118.683i | −0.0188366 | + | 0.0108753i | ||||
\(493\) | 3757.14 | + | 2169.19i | 0.343232 | + | 0.198165i | ||||
\(494\) | −68.0645 | + | 117.891i | −0.00619913 | + | 0.0107372i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2071.22 | −0.187501 | ||||||||
\(497\) | 2758.87 | + | 13735.6i | 0.248999 | + | 1.23969i | ||||
\(498\) | 1679.95i | 0.151165i | ||||||||
\(499\) | 5881.17 | + | 10186.5i | 0.527610 | + | 0.913847i | 0.999482 | + | 0.0321800i | \(0.0102450\pi\) |
−0.471872 | + | 0.881667i | \(0.656422\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4427.16 | + | 7668.06i | −0.394792 | + | 0.683800i | ||||
\(502\) | −11143.2 | + | 6433.53i | −0.990728 | + | 0.571997i | ||||
\(503\) | 14178.9i | 1.25687i | 0.777863 | + | 0.628434i | \(0.216304\pi\) | ||||
−0.777863 | + | 0.628434i | \(0.783696\pi\) | |||||||
\(504\) | 1694.37 | + | 1924.79i | 0.149748 | + | 0.170113i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 329.382 | + | 570.506i | 0.0289383 | + | 0.0501227i | ||||
\(507\) | 5901.26 | + | 3407.09i | 0.516931 | + | 0.298450i | ||||
\(508\) | 8092.94 | + | 4672.46i | 0.706823 | + | 0.408084i | ||||
\(509\) | 3701.46 | + | 6411.11i | 0.322327 | + | 0.558286i | 0.980968 | − | 0.194171i | \(-0.0622017\pi\) |
−0.658641 | + | 0.752457i | \(0.728868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4853.54 | − | 14386.3i | 0.420172 | − | 1.24542i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | −2830.03 | + | 1633.92i | −0.243565 | + | 0.140623i | ||||
\(514\) | 7061.96 | − | 12231.7i | 0.606011 | − | 1.04964i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 730.466 | + | 1265.20i | 0.0623197 | + | 0.107941i | ||||
\(517\) | − | 3005.46i | − | 0.255667i | ||||||
\(518\) | −13021.7 | − | 4393.16i | −1.10452 | − | 0.372634i | ||||
\(519\) | 5457.62 | 0.461585 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −712.532 | + | 1234.14i | −0.0599167 | + | 0.103779i | −0.894428 | − | 0.447212i | \(-0.852417\pi\) |
0.834511 | + | 0.550991i | \(0.185750\pi\) | |||||||
\(522\) | 2749.45 | + | 1587.40i | 0.230537 | + | 0.133101i | ||||
\(523\) | 19274.1 | − | 11127.9i | 1.61147 | − | 0.930380i | 0.622435 | − | 0.782672i | \(-0.286144\pi\) |
0.989031 | − | 0.147708i | \(-0.0471896\pi\) | |||||||
\(524\) | −7518.91 | −0.626842 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9309.68 | −0.771714 | ||||||||
\(527\) | −5302.89 | + | 3061.63i | −0.438326 | + | 0.253067i | ||||
\(528\) | −216.030 | − | 124.725i | −0.0178058 | − | 0.0102802i | ||||
\(529\) | −3920.38 | + | 6790.29i | −0.322214 | + | 0.558091i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 846.081 | 0.0691465 | ||||||||
\(532\) | 345.594 | + | 1720.62i | 0.0281643 | + | 0.140222i | ||||
\(533\) | 54.7642i | 0.00445047i | ||||||||
\(534\) | 456.377 | + | 790.468i | 0.0369838 | + | 0.0640579i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2342.12 | − | 4056.66i | 0.188739 | − | 0.326905i | ||||
\(537\) | −5794.94 | + | 3345.71i | −0.465680 | + | 0.268860i | ||||
\(538\) | − | 10311.9i | − | 0.826356i | ||||||
\(539\) | −217.837 | + | 1703.79i | −0.0174080 | + | 0.136155i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2661.08 | + | 4609.13i | 0.211477 | + | 0.366288i | 0.952177 | − | 0.305547i | \(-0.0988394\pi\) |
−0.740700 | + | 0.671836i | \(0.765506\pi\) | |||||||
\(542\) | −8709.15 | − | 5028.23i | −0.690203 | − | 0.398489i | ||||
\(543\) | 6481.32 | + | 3741.99i | 0.512228 | + | 0.295735i | ||||
\(544\) | 756.824 | + | 1310.86i | 0.0596481 | + | 0.103314i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −324.835 | + | 65.2447i | −0.0254609 | + | 0.00511395i | ||||
\(547\) | 10627.6i | 0.830718i | 0.909658 | + | 0.415359i | \(0.136344\pi\) | ||||
−0.909658 | + | 0.415359i | \(0.863656\pi\) | |||||||
\(548\) | 2823.32 | − | 1630.05i | 0.220085 | − | 0.127066i | ||||
\(549\) | −6046.21 | + | 10472.3i | −0.470029 | + | 0.814114i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1086.39 | + | 1881.69i | 0.0839963 | + | 0.145486i | ||||
\(552\) | 1638.19i | 0.126315i | ||||||||
\(553\) | 6699.65 | − | 5897.61i | 0.515186 | − | 0.453511i | ||||
\(554\) | 230.682 | 0.0176908 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4529 | + | 35.4255i | −0.00156007 | + | 0.00270212i | ||||
\(557\) | 17369.4 | + | 10028.2i | 1.32130 | + | 0.762853i | 0.983936 | − | 0.178521i | \(-0.0571311\pi\) |
0.337365 | + | 0.941374i | \(0.390464\pi\) | |||||||
\(558\) | −3880.62 | + | 2240.48i | −0.294408 | + | 0.169977i | ||||
\(559\) | 337.060 | 0.0255029 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −737.458 | −0.0555000 | ||||||||
\(562\) | −1692.76 | + | 977.317i | −0.127055 | + | 0.0733552i | ||||
\(563\) | 1049.30 | + | 605.816i | 0.0785487 | + | 0.0453501i | 0.538760 | − | 0.842459i | \(-0.318893\pi\) |
−0.460211 | + | 0.887809i | \(0.652226\pi\) | |||||||
\(564\) | 3736.93 | − | 6472.56i | 0.278995 | − | 0.483234i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8434.29 | −0.626360 | ||||||||
\(567\) | 664.213 | + | 224.087i | 0.0491963 | + | 0.0165975i | ||||
\(568\) | 6051.74i | 0.447052i | ||||||||
\(569\) | 5391.08 | + | 9337.63i | 0.397199 | + | 0.687968i | 0.993379 | − | 0.114882i | \(-0.0366491\pi\) |
−0.596181 | + | 0.802850i | \(0.703316\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2071.37 | − | 3587.72i | 0.151811 | − | 0.262944i | −0.780082 | − | 0.625677i | \(-0.784823\pi\) |
0.931893 | + | 0.362733i | \(0.118156\pi\) | |||||||
\(572\) | −49.8414 | + | 28.7759i | −0.00364331 | + | 0.00210347i | ||||
\(573\) | 1583.31i | 0.115434i | ||||||||
\(574\) | 466.503 | + | 529.945i | 0.0339224 | + | 0.0385357i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 553.839 | + | 959.277i | 0.0400636 | + | 0.0693922i | ||||
\(577\) | −9881.54 | − | 5705.11i | −0.712953 | − | 0.411624i | 0.0992005 | − | 0.995067i | \(-0.468371\pi\) |
−0.812153 | + | 0.583444i | \(0.801705\pi\) | |||||||
\(578\) | −4634.22 | − | 2675.57i | −0.333491 | − | 0.192541i | ||||
\(579\) | 2362.17 | + | 4091.39i | 0.169548 | + | 0.293666i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4898.98 | − | 983.983i | 0.349817 | − | 0.0702625i | ||||
\(582\) | 1500.83i | 0.106892i | ||||||||
\(583\) | 758.193 | − | 437.743i | 0.0538613 | − | 0.0310968i | ||||
\(584\) | 3279.21 | − | 5679.76i | 0.232354 | − | 0.402449i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4064.73 | + | 7040.32i | 0.286540 | + | 0.496302i | ||||
\(587\) | − | 3848.96i | − | 0.270637i | −0.990802 | − | 0.135318i | \(-0.956794\pi\) | ||
0.990802 | − | 0.135318i | \(-0.0432057\pi\) | |||||||
\(588\) | −2587.60 | + | 3398.44i | −0.181481 | + | 0.238349i | ||||
\(589\) | −3066.71 | −0.214536 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.4236 | − | 70.0157i | 0.00281354 | − | 0.00487320i | ||||
\(592\) | −5141.00 | − | 2968.16i | −0.356916 | − | 0.206065i | ||||
\(593\) | 7212.04 | − | 4163.88i | 0.499432 | − | 0.288347i | −0.229047 | − | 0.973415i | \(-0.573561\pi\) |
0.728479 | + | 0.685068i | \(0.240228\pi\) | |||||||
\(594\) | −1381.56 | −0.0954311 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14144.0 | 0.972084 | ||||||||
\(597\) | 13031.4 | − | 7523.67i | 0.893365 | − | 0.515785i | ||||
\(598\) | 327.319 | + | 188.978i | 0.0223831 | + | 0.0129229i | ||||
\(599\) | −9899.97 | + | 17147.3i | −0.675295 | + | 1.16965i | 0.301087 | + | 0.953597i | \(0.402650\pi\) |
−0.976382 | + | 0.216049i | \(0.930683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19424.3 | 1.31836 | 0.659180 | − | 0.751985i | \(-0.270904\pi\) | ||||
0.659180 | + | 0.751985i | \(0.270904\pi\) | |||||||
\(602\) | 3261.68 | − | 2871.21i | 0.220824 | − | 0.194388i | ||||
\(603\) | − | 10134.0i | − | 0.684393i | ||||||
\(604\) | −4319.97 | − | 7482.40i | −0.291022 | − | 0.504064i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2957.22 | + | 5122.05i | −0.198232 | + | 0.343348i | ||||
\(607\) | −348.327 | + | 201.106i | −0.0232918 | + | 0.0134475i | −0.511601 | − | 0.859223i | \(-0.670947\pi\) |
0.488309 | + | 0.872671i | \(0.337614\pi\) | |||||||
\(608\) | 758.081i | 0.0505662i | ||||||||
\(609\) | −1690.52 | + | 5010.84i | −0.112485 | + | 0.333414i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −862.169 | − | 1493.32i | −0.0570861 | − | 0.0988761i | ||||
\(612\) | 2835.95 | + | 1637.34i | 0.187315 | + | 0.108146i | ||||
\(613\) | 10750.4 | + | 6206.75i | 0.708327 | + | 0.408953i | 0.810441 | − | 0.585820i | \(-0.199227\pi\) |
−0.102114 | + | 0.994773i | \(0.532561\pi\) | |||||||
\(614\) | −1650.69 | − | 2859.08i | −0.108496 | − | 0.187920i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −237.183 | + | 703.029i | −0.0155136 | + | 0.0459835i | ||||
\(617\) | − | 12205.8i | − | 0.796412i | −0.917296 | − | 0.398206i | \(-0.869633\pi\) | ||
0.917296 | − | 0.398206i | \(-0.130367\pi\) | |||||||
\(618\) | 267.562 | − | 154.477i | 0.0174157 | − | 0.0100550i | ||||
\(619\) | 8500.05 | − | 14722.5i | 0.551932 | − | 0.955974i | −0.446204 | − | 0.894931i | \(-0.647224\pi\) |
0.998135 | − | 0.0610421i | \(-0.0194424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4536.50 | + | 7857.45i | 0.293146 | + | 0.507743i | ||||
\(622\) | 8572.80i | 0.552633i | ||||||||
\(623\) | 2037.82 | − | 1793.86i | 0.131049 | − | 0.115360i | ||||
\(624\) | −143.118 | −0.00918157 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7112.59 | − | 12319.4i | 0.454115 | − | 0.786551i | ||||
\(627\) | −319.859 | − | 184.671i | −0.0203731 | − | 0.0117624i | ||||
\(628\) | −7491.14 | + | 4325.01i | −0.476002 | + | 0.274820i | ||||
\(629\) | −17549.8 | −1.11249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9451.75 | −0.596305 | −0.298152 | − | 0.954518i | \(-0.596370\pi\) | ||||
−0.298152 | + | 0.954518i | \(0.596370\pi\) | |||||||
\(632\) | 3338.97 | − | 1927.76i | 0.210154 | − | 0.121332i | ||||
\(633\) | −5069.46 | − | 2926.85i | −0.318314 | − | 0.183779i | ||||
\(634\) | 9127.60 | − | 15809.5i | 0.571772 | − | 0.990337i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2177.13 | 0.135737 | ||||||||
\(637\) | 380.527 | + | 909.053i | 0.0236688 | + | 0.0565432i | ||||
\(638\) | 918.599i | 0.0570026i | ||||||||
\(639\) | 6546.27 | + | 11338.5i | 0.405268 | + | 0.701945i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8356.38 | + | 14473.7i | −0.514910 | + | 0.891850i | 0.484941 | + | 0.874547i | \(0.338841\pi\) |
−0.999850 | + | 0.0173025i | \(0.994492\pi\) | |||||||
\(642\) | 4047.57 | − | 2336.86i | 0.248824 | − | 0.143658i | ||||
\(643\) | 4835.69i | 0.296580i | 0.988944 | + | 0.148290i | \(0.0473769\pi\) | ||||
−0.988944 | + | 0.148290i | \(0.952623\pi\) | |||||||
\(644\) | 4777.21 | − | 959.525i | 0.292311 | − | 0.0587121i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1120.57 | + | 1940.89i | 0.0682483 | + | 0.118209i | ||||
\(647\) | 5994.48 | + | 3460.92i | 0.364246 | + | 0.210298i | 0.670942 | − | 0.741510i | \(-0.265890\pi\) |
−0.306696 | + | 0.951808i | \(0.599223\pi\) | |||||||
\(648\) | 262.234 | + | 151.401i | 0.0158974 | + | 0.00917836i | ||||
\(649\) | 122.403 | + | 212.008i | 0.00740330 | + | 0.0128229i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4931.84 | − | 5602.55i | −0.296919 | − | 0.337298i | ||||
\(652\) | − | 9607.71i | − | 0.577096i | ||||||
\(653\) | −21626.6 | + | 12486.1i | −1.29604 | + | 0.748270i | −0.979718 | − | 0.200382i | \(-0.935782\pi\) |
−0.316323 | + | 0.948651i | \(0.602448\pi\) | |||||||
\(654\) | −1276.79 | + | 2211.46i | −0.0763401 | + | 0.132225i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 152.486 | + | 264.114i | 0.00907560 | + | 0.0157194i | ||||
\(657\) | − | 14188.7i | − | 0.842548i | ||||||
\(658\) | −21063.8 | − | 7106.34i | −1.24795 | − | 0.421025i | ||||
\(659\) | −22380.5 | −1.32294 | −0.661471 | − | 0.749971i | \(-0.730068\pi\) | ||||
−0.661471 | + | 0.749971i | \(0.730068\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11571.4 | − | 20042.3i | 0.680903 | − | 1.17936i | −0.293802 | − | 0.955866i | \(-0.594921\pi\) |
0.974705 | − | 0.223493i | \(-0.0717460\pi\) | |||||||
\(662\) | −15445.2 | − | 8917.30i | −0.906791 | − | 0.523536i | ||||
\(663\) | −366.420 | + | 211.553i | −0.0214639 | + | 0.0123922i | ||||
\(664\) | 2158.42 | 0.126149 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12842.8 | −0.747222 | ||||||||
\(667\) | 5224.42 | − | 3016.32i | 0.303284 | − | 0.175101i | ||||
\(668\) | 9852.06 | + | 5688.09i | 0.570640 | + | 0.329459i | ||||
\(669\) | −8093.65 | + | 14018.6i | −0.467741 | + | 0.810150i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3498.83 | −0.201298 | ||||||||
\(672\) | −1384.93 | + | 1219.14i | −0.0795013 | + | 0.0699839i | ||||
\(673\) | − | 17263.9i | − | 0.988820i | −0.869229 | − | 0.494410i | \(-0.835384\pi\) | ||
0.869229 | − | 0.494410i | \(-0.164616\pi\) | |||||||
\(674\) | −9427.08 | − | 16328.2i | −0.538750 | − | 0.933143i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4377.49 | − | 7582.04i | 0.249061 | − | 0.431386i | ||||
\(677\) | 2390.54 | − | 1380.18i | 0.135711 | − | 0.0783525i | −0.430608 | − | 0.902539i | \(-0.641701\pi\) |
0.566318 | + | 0.824187i | \(0.308367\pi\) | |||||||
\(678\) | − | 11739.5i | − | 0.664974i | ||||||
\(679\) | 4376.64 | − | 879.069i | 0.247364 | − | 0.0496842i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6036.22 | − | 10455.0i | −0.339660 | − | 0.588309i | ||||
\(682\) | −1122.82 | − | 648.263i | −0.0630428 | − | 0.0363978i | ||||
\(683\) | −19169.9 | − | 11067.8i | −1.07396 | − | 0.620053i | −0.144701 | − | 0.989475i | \(-0.546222\pi\) |
−0.929261 | + | 0.369423i | \(0.879555\pi\) | |||||||
\(684\) | 820.029 | + | 1420.33i | 0.0458400 | + | 0.0793973i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11426.0 | + | 5555.30i | 0.635927 | + | 0.309187i | ||||
\(687\) | − | 14821.4i | − | 0.823106i | ||||||
\(688\) | 1625.56 | − | 938.515i | 0.0900781 | − | 0.0520066i | ||||
\(689\) | 251.148 | − | 435.002i | 0.0138868 | − | 0.0240526i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13507.9 | − | 23396.3i | −0.743653 | − | 1.28804i | −0.950822 | − | 0.309739i | \(-0.899758\pi\) |
0.207169 | − | 0.978305i | \(-0.433575\pi\) | |||||||
\(692\) | − | 7012.04i | − | 0.385199i | ||||||
\(693\) | 316.096 | + | 1573.75i | 0.0173268 | + | 0.0862654i | ||||
\(694\) | −889.129 | −0.0486324 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1142.17 | + | 1978.30i | −0.0622038 | + | 0.107740i | ||||
\(697\) | 780.812 | + | 450.802i | 0.0424324 | + | 0.0244983i | ||||
\(698\) | −14580.4 | + | 8417.98i | −0.790652 | + | 0.456483i | ||||
\(699\) | 1780.14 | 0.0963251 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19107.2 | −1.02949 | −0.514743 | − | 0.857345i | \(-0.672112\pi\) | ||||
−0.514743 | + | 0.857345i | \(0.672112\pi\) | |||||||
\(702\) | −686.454 | + | 396.325i | −0.0369068 | + | 0.0213081i | ||||
\(703\) | −7611.91 | − | 4394.74i | −0.408376 | − | 0.235776i | ||||
\(704\) | −160.248 | + | 277.559i | −0.00857897 | + | 0.0148592i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22291.9 | −1.18834 | ||||||||
\(707\) | 16668.8 | + | 5623.59i | 0.886697 | + | 0.299147i | ||||
\(708\) | 608.775i | 0.0323152i | ||||||||
\(709\) | −6276.78 | − | 10871.7i | −0.332481 | − | 0.575875i | 0.650516 | − | 0.759492i | \(-0.274553\pi\) |
−0.982998 | + | 0.183618i | \(0.941219\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4170.57 | − | 7223.65i | 0.219984 | − | 0.381024i | ||||
\(712\) | 1015.61 | − | 586.361i | 0.0534572 | − | 0.0308635i | ||||
\(713\) | 8514.57i | 0.447227i | ||||||||
\(714\) | −1743.70 | + | 5168.48i | −0.0913957 | + | 0.270904i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4298.63 | + | 7445.44i | 0.224368 | + | 0.388616i | ||||
\(717\) | 13055.6 | + | 7537.63i | 0.680012 | + | 0.392605i | ||||
\(718\) | 17110.3 | + | 9878.64i | 0.889346 | + | 0.513464i | ||||
\(719\) | −11122.9 | − | 19265.4i | −0.576933 | − | 0.999276i | −0.995829 | − | 0.0912423i | \(-0.970916\pi\) |
0.418896 | − | 0.908034i | \(-0.362417\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −607.196 | − | 689.771i | −0.0313636 | − | 0.0356289i | ||||
\(722\) | − | 12595.6i | − | 0.649250i | ||||||
\(723\) | −8563.01 | + | 4943.86i | −0.440473 | + | 0.254307i | ||||
\(724\) | 4807.78 | − | 8327.31i | 0.246795 | − | 0.427461i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4065.71 | + | 7042.01i | 0.207841 | + | 0.359991i | ||||
\(727\) | − | 34604.1i | − | 1.76533i | −0.470004 | − | 0.882665i | \(-0.655747\pi\) | ||
0.470004 | − | 0.882665i | \(-0.344253\pi\) | |||||||
\(728\) | 83.8275 | + | 417.354i | 0.00426766 | + | 0.0212475i | ||||
\(729\) | −10940.1 | −0.555815 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2774.57 | − | 4805.70i | 0.140385 | − | 0.243154i | ||||
\(732\) | −7535.09 | − | 4350.39i | −0.380471 | − | 0.219665i | ||||
\(733\) | 11728.4 | − | 6771.39i | 0.590993 | − | 0.341210i | −0.174497 | − | 0.984658i | \(-0.555830\pi\) |
0.765490 | + | 0.643448i | \(0.222497\pi\) | |||||||
\(734\) | −16051.0 | −0.807157 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2104.77 | 0.105412 | ||||||||
\(737\) | 2539.35 | − | 1466.10i | 0.126918 | − | 0.0732759i | ||||
\(738\) | 571.393 | + | 329.894i | 0.0285004 | + | 0.0164547i | ||||
\(739\) | 8669.99 | − | 15016.9i | 0.431571 | − | 0.747503i | −0.565438 | − | 0.824791i | \(-0.691293\pi\) |
0.997009 | + | 0.0772883i | \(0.0246262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −211.904 | −0.0105054 | ||||||||
\(742\) | −1275.19 | − | 6348.83i | −0.0630914 | − | 0.314115i | ||||
\(743\) | 14341.8i | 0.708142i | 0.935219 | + | 0.354071i | \(0.115203\pi\) | ||||
−0.935219 | + | 0.354071i | \(0.884797\pi\) | |||||||
\(744\) | −1612.08 | − | 2792.20i | −0.0794376 | − | 0.137590i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12083.9 | − | 20930.0i | 0.593062 | − | 1.02721i | ||||
\(747\) | 4044.00 | − | 2334.80i | 0.198075 | − | 0.114359i | ||||
\(748\) | 947.499i | 0.0463155i | ||||||||
\(749\) | −9185.41 | − | 10434.6i | −0.448101 | − | 0.509040i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3005.17 | + | 5205.12i | 0.146019 | + | 0.252913i | 0.929753 | − | 0.368185i | \(-0.120021\pi\) |
−0.783734 | + | 0.621097i | \(0.786687\pi\) | |||||||
\(752\) | −8316.06 | − | 4801.28i | −0.403265 | − | 0.232825i | ||||
\(753\) | −17346.0 | − | 10014.7i | −0.839472 | − | 0.484669i | ||||
\(754\) | 263.516 | + | 456.424i | 0.0127277 | + | 0.0220451i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3266.67 | + | 9682.67i | −0.157153 | + | 0.465814i | ||||
\(757\) | − | 1057.57i | − | 0.0507767i | −0.999678 | − | 0.0253884i | \(-0.991918\pi\) | ||
0.999678 | − | 0.0253884i | \(-0.00808224\pi\) | |||||||
\(758\) | −5255.43 | + | 3034.22i | −0.251828 | + | 0.145393i | ||||
\(759\) | −512.729 | + | 888.073i | −0.0245203 | + | 0.0424704i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2947.79 | − | 5105.72i | −0.140417 | − | 0.243209i | 0.787237 | − | 0.616651i | \(-0.211511\pi\) |
−0.927654 | + | 0.373442i | \(0.878178\pi\) | |||||||
\(762\) | 14546.7i | 0.691563i | ||||||||
\(763\) | 7196.81 | + | 2428.01i | 0.341471 | + | 0.115203i | ||||
\(764\) | 2034.27 | 0.0963315 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7953.04 | + | 13775.1i | −0.375137 | + | 0.649757i | ||||
\(767\) | 121.637 | + | 70.2269i | 0.00572626 | + | 0.00330606i | ||||
\(768\) | −690.223 | + | 398.500i | −0.0324300 | + | 0.0187235i | ||||
\(769\) | 25098.6 | 1.17696 | 0.588478 | − | 0.808513i | \(-0.299727\pi\) | ||||
0.588478 | + | 0.808513i | \(0.299727\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21985.9 | 1.02698 | ||||||||
\(772\) | 5256.69 | − | 3034.95i | 0.245068 | − | 0.141490i | ||||
\(773\) | 32283.7 | + | 18639.0i | 1.50215 | + | 0.867268i | 0.999997 | + | 0.00249151i | \(0.000793072\pi\) |
0.502156 | + | 0.864777i | \(0.332540\pi\) | |||||||
\(774\) | 2030.42 | − | 3516.78i | 0.0942917 | − | 0.163318i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1928.29 | 0.0892030 | ||||||||
\(777\) | −4212.67 | − | 20973.7i | −0.194503 | − | 0.968374i | ||||
\(778\) | 7158.61i | 0.329883i | ||||||||
\(779\) | 225.775 | + | 391.054i | 0.0103841 | + | 0.0179858i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1894.11 | + | 3280.69i | −0.0867816 | + | 0.150310i | ||||
\(782\) | 5388.79 | − | 3111.22i | 0.246423 | − | 0.142272i | ||||
\(783\) | 12651.7i | 0.577437i | ||||||||
\(784\) | 4366.37 | + | 3324.60i | 0.198905 | + | 0.151448i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5852.13 | − | 10136.2i | −0.265571 | − | 0.459982i | ||||
\(787\) | 11670.4 | + | 6737.93i | 0.528597 | + | 0.305186i | 0.740445 | − | 0.672117i | \(-0.234615\pi\) |
−0.211848 | + | 0.977303i | \(0.567948\pi\) | |||||||
\(788\) | −89.9574 | − | 51.9369i | −0.00406675 | − | 0.00234794i | ||||
\(789\) | −7245.92 | − | 12550.3i | −0.326947 | − | 0.566289i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34234.2 | + | 6876.09i | −1.53884 | + | 0.309084i | ||||
\(792\) | 693.374i | 0.0311085i | ||||||||
\(793\) | −1738.46 | + | 1003.70i | −0.0778495 | + | 0.0449464i | ||||
\(794\) | −1852.21 | + | 3208.12i | −0.0827864 | + | 0.143390i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9666.54 | − | 16742.9i | −0.430429 | − | 0.745525i | ||||
\(797\) | 10414.0i | 0.462839i | 0.972854 | + | 0.231420i | \(0.0743371\pi\) | ||||
−0.972854 | + | 0.231420i | \(0.925663\pi\) | |||||||
\(798\) | −2050.57 | + | 1805.08i | −0.0909640 | + | 0.0800743i | ||||
\(799\) | −28388.5 | −1.25696 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1268.55 | − | 2197.20i | 0.0559577 | − | 0.0969216i | ||||
\(802\) | 10365.9 | + | 5984.76i | 0.456400 | + | 0.263503i | ||||
\(803\) | 3555.36 | − | 2052.69i | 0.156247 | − | 0.0902090i | ||||
\(804\) | 7291.67 | 0.319847 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −743.862 | −0.0325080 | ||||||||
\(807\) | 13901.4 | − | 8026.00i | 0.606387 | − | 0.350098i | ||||
\(808\) | 6580.90 | + | 3799.49i | 0.286529 | + | 0.165428i | ||||
\(809\) | 10167.0 | − | 17609.7i | 0.441843 | − | 0.765295i | −0.555983 | − | 0.831194i | \(-0.687658\pi\) |
0.997826 | + | 0.0658988i | \(0.0209914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16769.3 | 0.726081 | 0.363040 | − | 0.931773i | \(-0.381739\pi\) | ||||
0.363040 | + | 0.931773i | \(0.381739\pi\) | |||||||
\(812\) | 6438.01 | + | 2172.01i | 0.278239 | + | 0.0938701i | ||||
\(813\) | − | 15654.3i | − | 0.675302i | ||||||
\(814\) | −1857.98 | − | 3218.12i | −0.0800027 | − | 0.138569i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1178.10 | + | 2040.54i | −0.0505415 | + | 0.0875405i | ||||
\(817\) | 2406.84 | − | 1389.59i | 0.103066 | − | 0.0595050i | ||||
\(818\) | − | 19223.4i | − | 0.821676i | ||||||
\(819\) | 608.517 | + | 691.271i | 0.0259625 | + | 0.0294933i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3510.97 | + | 6081.17i | 0.149249 | + | 0.258507i | 0.930950 | − | 0.365146i | \(-0.118981\pi\) |
−0.781701 | + | 0.623653i | \(0.785648\pi\) | |||||||
\(822\) | 4394.90 | + | 2537.40i | 0.186484 | + | 0.107667i | ||||
\(823\) | −727.886 | − | 420.245i | −0.0308293 | − | 0.0177993i | 0.484506 | − | 0.874788i | \(-0.338999\pi\) |
−0.515335 | + | 0.856989i | \(0.672333\pi\) | |||||||
\(824\) | −198.475 | − | 343.769i | −0.00839102 | − | 0.0145337i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1775.28 | − | 356.574i | 0.0747820 | − | 0.0150203i | ||||
\(827\) | 30133.0i | 1.26702i | 0.773735 | + | 0.633510i | \(0.218386\pi\) | ||||
−0.773735 | + | 0.633510i | \(0.781614\pi\) | |||||||
\(828\) | 3943.48 | − | 2276.77i | 0.165514 | − | 0.0955594i | ||||
\(829\) | −23055.0 | + | 39932.5i | −0.965903 | + | 1.67299i | −0.258735 | + | 0.965948i | \(0.583306\pi\) |
−0.707168 | + | 0.707045i | \(0.750028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 179.544 | + | 310.980i | 0.00749497 | + | 0.0129817i | ||||
\(832\) | 183.880i | 0.00766215i | ||||||||
\(833\) | 16093.4 | + | 2057.61i | 0.669392 | + | 0.0855845i | ||||
\(834\) | −63.6758 | −0.00264378 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −237.268 | + | 410.960i | −0.00981590 | + | 0.0170016i | ||||
\(837\) | −15464.4 | − | 8928.38i | −0.638624 | − | 0.368710i | ||||
\(838\) | 3569.57 | − | 2060.89i | 0.147147 | − | 0.0849551i | ||||
\(839\) | 34470.7 | 1.41843 | 0.709214 | − | 0.704993i | \(-0.249050\pi\) | ||||
0.709214 | + | 0.704993i | \(0.249050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15976.9 | −0.655087 | ||||||||
\(842\) | 8090.09 | − | 4670.81i | 0.331120 | − | 0.191172i | ||||
\(843\) | −2635.03 | − | 1521.33i | −0.107657 | − | 0.0621560i | ||||
\(844\) | −3760.47 | + | 6513.33i | −0.153366 | + | 0.265638i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −20774.5 | −0.844258 | ||||||||
\(847\) | 18154.2 | − | 15980.9i | 0.736465 | − | 0.648300i | ||||
\(848\) | − | 2797.21i | − | 0.113274i | ||||||
\(849\) | −6564.58 | − | 11370.2i | −0.265366 | − | 0.459628i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12201.8 | + | 21134.1i | −0.491506 | + | 0.851313i | ||||
\(852\) | −8158.30 | + | 4710.20i | −0.328050 | + | 0.189400i | ||||
\(853\) | 28159.1i | 1.13031i | 0.824986 | + | 0.565153i | \(0.191183\pi\) | ||||
−0.824986 | + | 0.565153i | \(0.808817\pi\) | |||||||
\(854\) | −8272.92 | + | 24521.6i | −0.331491 | + | 0.982567i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3002.44 | − | 5200.39i | −0.119885 | − | 0.207647i | ||||
\(857\) | −1141.95 | − | 659.305i | −0.0455172 | − | 0.0262794i | 0.477069 | − | 0.878866i | \(-0.341699\pi\) |
−0.522586 | + | 0.852587i | \(0.675033\pi\) | |||||||
\(858\) | −77.5851 | − | 44.7938i | −0.00308708 | − | 0.00178233i | ||||
\(859\) | 2269.32 | + | 3930.57i | 0.0901374 | + | 0.156123i | 0.907569 | − | 0.419903i | \(-0.137936\pi\) |
−0.817431 | + | 0.576026i | \(0.804603\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −351.325 | + | 1041.36i | −0.0139061 | + | 0.0412187i | ||||
\(862\) | 23467.8i | 0.927280i | ||||||||
\(863\) | −24902.0 | + | 14377.2i | −0.982240 | + | 0.567096i | −0.902946 | − | 0.429755i | \(-0.858600\pi\) |
−0.0792943 | + | 0.996851i | \(0.525267\pi\) | |||||||
\(864\) | −2207.07 | + | 3822.75i | −0.0869050 | + | 0.150524i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3982.03 | + | 6897.08i | 0.156253 | + | 0.270638i | ||||
\(867\) | − | 8329.80i | − | 0.326292i | ||||||
\(868\) | −7198.25 | + | 6336.52i | −0.281480 | + | 0.247783i | ||||
\(869\) | 2413.44 | 0.0942121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 841.150 | − | 1456.92i | 0.0327225 | − | 0.0566770i | ||||
\(872\) | 2841.33 | + | 1640.44i | 0.110343 | + | 0.0637068i | ||||
\(873\) | 3612.82 | − | 2085.86i | 0.140063 | − | 0.0808657i | ||||
\(874\) | 3116.38 | 0.120610 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10209.1 | 0.393760 | ||||||||
\(877\) | −37453.6 | + | 21623.9i | −1.44210 | + | 0.832595i | −0.997990 | − | 0.0633789i | \(-0.979812\pi\) |
−0.444107 | + | 0.895974i | \(0.646479\pi\) | |||||||
\(878\) | 10660.8 | + | 6155.00i | 0.409776 | + | 0.236584i | ||||
\(879\) | −6327.33 | + | 10959.3i | −0.242794 | + | 0.420531i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43971.7 | −1.68155 | −0.840775 | − | 0.541385i | \(-0.817900\pi\) | ||||
−0.840775 | + | 0.541385i | \(0.817900\pi\) | |||||||
\(882\) | 11777.1 | + | 1505.74i | 0.449608 | + | 0.0574842i | ||||
\(883\) | − | 2936.92i | − | 0.111931i | −0.998433 | − | 0.0559656i | \(-0.982176\pi\) | ||
0.998433 | − | 0.0559656i | \(-0.0178237\pi\) | |||||||
\(884\) | 271.807 | + | 470.783i | 0.0103415 | + | 0.0179119i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3096.03 | − | 5362.48i | 0.117396 | − | 0.203337i | ||||
\(887\) | −3721.73 | + | 2148.74i | −0.140883 | + | 0.0813390i | −0.568785 | − | 0.822486i | \(-0.692586\pi\) |
0.427902 | + | 0.903825i | \(0.359253\pi\) | |||||||
\(888\) | − | 9240.72i | − | 0.349210i | ||||||
\(889\) | 42420.4 | − | 8520.33i | 1.60037 | − | 0.321443i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 94.7724 | + | 164.151i | 0.00356341 | + | 0.00617200i | ||||
\(892\) | 18011.3 | + | 10398.9i | 0.676081 | + | 0.390336i | ||||
\(893\) | −12313.0 | − | 7108.90i | −0.461409 | − | 0.266394i | ||||
\(894\) | 11008.6 | + | 19067.4i | 0.411837 | + | 0.713323i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1566.37 | + | 1779.38i | 0.0584025 | + | 0.0663449i | ||||
\(897\) | 588.342i | 0.0218998i | ||||||||
\(898\) | 13528.8 | − | 7810.84i | 0.502741 | − | 0.290257i | ||||
\(899\) | −5936.48 | + | 10282.3i | −0.220237 | + | 0.381461i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4134.76 | − | 7161.61i | −0.152884 | − | 0.264803i | ||||
\(902\) | 190.904i | 0.00704701i | ||||||||
\(903\) | 6409.28 | + | 2162.32i | 0.236199 | + | 0.0796870i | ||||
\(904\) | −15083.1 | −0.554930 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6724.64 | − | 11647.4i | 0.246591 | − | 0.427108i | ||||
\(907\) | 6705.54 | + | 3871.45i | 0.245484 | + | 0.141730i | 0.617695 | − | 0.786418i | \(-0.288067\pi\) |
−0.372211 | + | 0.928148i | \(0.621400\pi\) | |||||||
\(908\) | −13432.8 | + | 7755.45i | −0.490952 | + | 0.283451i | ||||
\(909\) | 16439.9 | 0.599864 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27691.3 | 1.00709 | 0.503543 | − | 0.863970i | \(-0.332030\pi\) | ||||
0.503543 | + | 0.863970i | \(0.332030\pi\) | |||||||
\(912\) | −1021.96 | + | 590.030i | −0.0371059 | + | 0.0214231i | ||||
\(913\) | 1170.09 | + | 675.555i | 0.0424146 | + | 0.0244881i | ||||
\(914\) | 6735.95 | − | 11667.0i | 0.243770 | − | 0.422221i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19042.9 | −0.686893 | ||||||||
\(917\) | −26130.9 | + | 23002.7i | −0.941024 | + | 0.828371i | ||||
\(918\) | 13049.7i | 0.469177i | ||||||||
\(919\) | −2233.76 | − | 3868.99i | −0.0801796 | − | 0.138875i | 0.823147 | − | 0.567828i | \(-0.192216\pi\) |
−0.903327 | + | 0.428953i | \(0.858883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2569.53 | − | 4450.56i | 0.0919315 | − | 0.159230i | ||||
\(922\) | 30418.8 | − | 17562.3i | 1.08654 | − | 0.627315i | ||||
\(923\) | 2173.43i | 0.0775074i | ||||||||
\(924\) | −1132.35 | + | 227.438i | −0.0403156 | + | 0.00809759i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3575.44 | + | 6192.84i | 0.126886 | + | 0.219773i | ||||
\(927\) | −743.721 | − | 429.387i | −0.0263506 | − | 0.0152135i | ||||
\(928\) | 2541.75 | + | 1467.48i | 0.0899106 | + | 0.0519099i | ||||
\(929\) | −4526.82 | − | 7840.67i | −0.159871 | − | 0.276904i | 0.774951 | − | 0.632021i | \(-0.217774\pi\) |
−0.934822 | + | 0.355117i | \(0.884441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6464.97 | + | 4922.48i | 0.227584 | + | 0.173284i | ||||
\(932\) | − | 2287.16i | − | 0.0803846i | ||||||
\(933\) | −11556.9 | + | 6672.38i | −0.405526 | + | 0.234131i | ||||
\(934\) | −17328.4 | + | 30013.6i | −0.607068 | + | 1.05147i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 198.906 | + | 344.516i | 0.00694601 | + | 0.0120308i | ||||
\(937\) | − | 4004.41i | − | 0.139614i | −0.997561 | − | 0.0698071i | \(-0.977762\pi\) | ||
0.997561 | − | 0.0698071i | \(-0.0222384\pi\) | |||||||
\(938\) | −4270.90 | − | 21263.6i | −0.148667 | − | 0.740172i | ||||
\(939\) | 22143.5 | 0.769569 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8569.25 | + | 14842.4i | −0.296865 | + | 0.514185i | −0.975417 | − | 0.220367i | \(-0.929274\pi\) |
0.678552 | + | 0.734552i | \(0.262608\pi\) | |||||||
\(942\) | −11661.0 | − | 6732.49i | −0.403330 | − | 0.232862i | ||||
\(943\) | 1085.74 | − | 626.854i | 0.0374938 | − | 0.0216471i | ||||
\(944\) | 782.165 | 0.0269675 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1174.97 | 0.0403821 | ||||||||
\(947\) | −34381.9 | + | 19850.4i | −1.17979 | + | 0.681153i | −0.955966 | − | 0.293477i | \(-0.905188\pi\) |
−0.223825 | + | 0.974629i | \(0.571854\pi\) | |||||||
\(948\) | 5197.58 | + | 3000.83i | 0.178069 | + | 0.102808i | ||||
\(949\) | 1177.70 | − | 2039.84i | 0.0402843 | − | 0.0697744i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28416.8 | 0.968956 | ||||||||
\(952\) | 6640.56 | + | 2240.34i | 0.226073 | + | 0.0762709i | ||||
\(953\) | − | 4918.22i | − | 0.167174i | −0.996500 | − | 0.0835870i | \(-0.973362\pi\) | ||
0.996500 | − | 0.0835870i | \(-0.0266376\pi\) | |||||||
\(954\) | −3025.79 | − | 5240.82i | −0.102687 | − | 0.177859i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9684.48 | − | 16774.0i | 0.327634 | − | 0.567479i | ||||
\(957\) | −1238.36 | + | 714.965i | −0.0418290 | + | 0.0241500i | ||||
\(958\) | − | 10503.9i | − | 0.354244i | ||||||
\(959\) | 4825.24 | − | 14302.4i | 0.162477 | − | 0.481594i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6516.65 | + | 11287.2i | 0.218746 | + | 0.378879i | ||||
\(962\) | −1846.35 | − | 1065.99i | −0.0618801 | − | 0.0357265i | ||||
\(963\) | −11250.7 | − | 6495.59i | −0.376478 | − | 0.217360i | ||||
\(964\) | 6351.95 | + | 11001.9i | 0.212223 | + | 0.367580i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5011.73 | + | 5693.30i | 0.166925 | + | 0.189626i | ||||
\(967\) | 39789.7i | 1.32322i | 0.749850 | + | 0.661608i | \(0.230126\pi\) | ||||
−0.749850 | + | 0.661608i | \(0.769874\pi\) | |||||||
\(968\) | 9047.69 | − | 5223.69i | 0.300417 | − | 0.173446i | ||||
\(969\) | −1744.33 | + | 3021.27i | −0.0578287 | + | 0.100162i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15427.5 | + | 26721.2i | 0.509879 | + | 0.883136i | 0.999935 | + | 0.0114448i | \(0.00364307\pi\) |
−0.490056 | + | 0.871691i | \(0.663024\pi\) | |||||||
\(972\) | 15369.1i | 0.507163i | ||||||||
\(973\) | 37.2964 | + | 185.688i | 0.00122885 | + | 0.00611809i | ||||
\(974\) | 1748.83 | 0.0575320 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5589.45 | + | 9681.22i | −0.183314 | + | 0.317508i | ||||
\(977\) | −2911.01 | − | 1680.67i | −0.0953239 | − | 0.0550353i | 0.451580 | − | 0.892230i | \(-0.350860\pi\) |
−0.546904 | + | 0.837195i | \(0.684194\pi\) | |||||||
\(978\) | 12952.1 | − | 7477.88i | 0.423478 | − | 0.244495i | ||||
\(979\) | 734.090 | 0.0239649 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7097.97 | 0.231010 | ||||||||
\(982\) | −27403.0 | + | 15821.1i | −0.890494 | + | 0.514127i | ||||
\(983\) | 7497.42 | + | 4328.64i | 0.243266 | + | 0.140450i | 0.616677 | − | 0.787216i | \(-0.288478\pi\) |
−0.373411 | + | 0.927666i | \(0.621812\pi\) | |||||||
\(984\) | −237.367 | + | 411.131i | −0.00769001 | + | 0.0133195i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8676.75 | 0.280247 | ||||||||
\(987\) | −6814.38 | − | 33926.9i | −0.219761 | − | 1.09413i | ||||
\(988\) | 272.258i | 0.00876689i | ||||||||
\(989\) | −3858.13 | − | 6682.48i | −0.124046 | − | 0.214854i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13322.8 | + | 23075.7i | −0.427055 | + | 0.739680i | −0.996610 | − | 0.0822726i | \(-0.973782\pi\) |
0.569555 | + | 0.821953i | \(0.307116\pi\) | |||||||
\(992\) | −3587.47 | + | 2071.22i | −0.114821 | + | 0.0662918i | ||||
\(993\) | − | 27762.1i | − | 0.887214i | ||||||
\(994\) | 18514.2 | + | 21032.0i | 0.590778 | + | 0.671120i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1679.95 | + | 2909.75i | 0.0534449 | + | 0.0925692i | ||||
\(997\) | −11359.3 | − | 6558.28i | −0.360834 | − | 0.208328i | 0.308612 | − | 0.951188i | \(-0.400135\pi\) |
−0.669447 | + | 0.742860i | \(0.733469\pi\) | |||||||
\(998\) | 20373.0 | + | 11762.3i | 0.646187 | + | 0.373076i | ||||
\(999\) | −25589.6 | − | 44322.4i | −0.810428 | − | 1.40370i |
(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 | 350.4.j.j.249.7 | 16 | ||
5.2 | odd | 4 | 350.4.e.m.151.3 | yes | 8 | ||
5.3 | odd | 4 | 350.4.e.l.151.2 | yes | 8 | ||
5.4 | even | 2 | inner | 350.4.j.j.249.2 | 16 | ||
7.2 | even | 3 | inner | 350.4.j.j.149.2 | 16 | ||
35.2 | odd | 12 | 350.4.e.m.51.3 | yes | 8 | ||
35.3 | even | 12 | 2450.4.a.cu.1.2 | 4 | |||
35.9 | even | 6 | inner | 350.4.j.j.149.7 | 16 | ||
35.17 | even | 12 | 2450.4.a.ck.1.3 | 4 | |||
35.18 | odd | 12 | 2450.4.a.cq.1.3 | 4 | |||
35.23 | odd | 12 | 350.4.e.l.51.2 | ✓ | 8 | ||
35.32 | odd | 12 | 2450.4.a.co.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.4.e.l.51.2 | ✓ | 8 | 35.23 | odd | 12 | ||
350.4.e.l.151.2 | yes | 8 | 5.3 | odd | 4 | ||
350.4.e.m.51.3 | yes | 8 | 35.2 | odd | 12 | ||
350.4.e.m.151.3 | yes | 8 | 5.2 | odd | 4 | ||
350.4.j.j.149.2 | 16 | 7.2 | even | 3 | inner | ||
350.4.j.j.149.7 | 16 | 35.9 | even | 6 | inner | ||
350.4.j.j.249.2 | 16 | 5.4 | even | 2 | inner | ||
350.4.j.j.249.7 | 16 | 1.1 | even | 1 | trivial | ||
2450.4.a.ck.1.3 | 4 | 35.17 | even | 12 | |||
2450.4.a.co.1.2 | 4 | 35.32 | odd | 12 | |||
2450.4.a.cq.1.3 | 4 | 35.18 | odd | 12 | |||
2450.4.a.cu.1.2 | 4 | 35.3 | even | 12 |