Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,4,Mod(5,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(0.944030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.4 | ||
Root | \(0.932438 + 1.76934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.5 |
Dual form | 16.4.e.a.13.4 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.836901 | + | 2.70178i | 0.295889 | + | 0.955222i | ||||
\(3\) | 1.98356 | − | 1.98356i | 0.381737 | − | 0.381737i | −0.489991 | − | 0.871728i | \(-0.663000\pi\) |
0.871728 | + | 0.489991i | \(0.163000\pi\) | |||||||
\(4\) | −6.59919 | + | 4.52224i | −0.824899 | + | 0.565280i | ||||
\(5\) | −0.596848 | − | 0.596848i | −0.0533837 | − | 0.0533837i | 0.679911 | − | 0.733295i | \(-0.262018\pi\) |
−0.733295 | + | 0.679911i | \(0.762018\pi\) | |||||||
\(6\) | 7.01918 | + | 3.69910i | 0.477595 | + | 0.251692i | ||||
\(7\) | − | 29.0828i | − | 1.57033i | −0.619289 | − | 0.785163i | \(-0.712579\pi\) | ||
0.619289 | − | 0.785163i | \(-0.287421\pi\) | |||||||
\(8\) | −17.7410 | − | 14.0449i | −0.784047 | − | 0.620702i | ||||
\(9\) | 19.1310i | 0.708554i | ||||||||
\(10\) | 1.11305 | − | 2.11205i | 0.0351976 | − | 0.0667890i | ||||
\(11\) | 12.1291 | + | 12.1291i | 0.332461 | + | 0.332461i | 0.853520 | − | 0.521059i | \(-0.174463\pi\) |
−0.521059 | + | 0.853520i | \(0.674463\pi\) | |||||||
\(12\) | −4.11977 | + | 22.0600i | −0.0991062 | + | 0.530682i | ||||
\(13\) | −48.5658 | + | 48.5658i | −1.03613 | + | 1.03613i | −0.0368113 | + | 0.999322i | \(0.511720\pi\) |
−0.999322 | + | 0.0368113i | \(0.988280\pi\) | |||||||
\(14\) | 78.5754 | − | 24.3395i | 1.50001 | − | 0.464643i | ||||
\(15\) | −2.36777 | −0.0407570 | ||||||||
\(16\) | 23.0987 | − | 59.6863i | 0.360917 | − | 0.932598i | ||||
\(17\) | 86.7193 | 1.23721 | 0.618604 | − | 0.785703i | \(-0.287699\pi\) | ||||
0.618604 | + | 0.785703i | \(0.287699\pi\) | |||||||
\(18\) | −51.6876 | + | 16.0107i | −0.676827 | + | 0.209654i | ||||
\(19\) | −54.8442 | + | 54.8442i | −0.662217 | + | 0.662217i | −0.955902 | − | 0.293685i | \(-0.905118\pi\) |
0.293685 | + | 0.955902i | \(0.405118\pi\) | |||||||
\(20\) | 6.63780 | + | 1.23963i | 0.0742129 | + | 0.0138594i | ||||
\(21\) | −57.6876 | − | 57.6876i | −0.599451 | − | 0.599451i | ||||
\(22\) | −22.6193 | + | 42.9211i | −0.219203 | + | 0.415946i | ||||
\(23\) | − | 70.2145i | − | 0.636554i | −0.947998 | − | 0.318277i | \(-0.896896\pi\) | ||
0.947998 | − | 0.318277i | \(-0.103104\pi\) | |||||||
\(24\) | −63.0492 | + | 7.33139i | −0.536244 | + | 0.0623547i | ||||
\(25\) | − | 124.288i | − | 0.994300i | ||||||
\(26\) | −171.859 | − | 90.5692i | −1.29632 | − | 0.683157i | ||||
\(27\) | 91.5036 | + | 91.5036i | 0.652218 | + | 0.652218i | ||||
\(28\) | 131.520 | + | 191.923i | 0.887674 | + | 1.29536i | ||||
\(29\) | 63.4021 | − | 63.4021i | 0.405982 | − | 0.405982i | −0.474353 | − | 0.880335i | \(-0.657318\pi\) |
0.880335 | + | 0.474353i | \(0.157318\pi\) | |||||||
\(30\) | −1.98159 | − | 6.39718i | −0.0120596 | − | 0.0389320i | ||||
\(31\) | −8.86868 | −0.0513826 | −0.0256913 | − | 0.999670i | \(-0.508179\pi\) | ||||
−0.0256913 | + | 0.999670i | \(0.508179\pi\) | |||||||
\(32\) | 180.590 | + | 12.4560i | 0.997630 | + | 0.0688106i | ||||
\(33\) | 48.1178 | 0.253825 | ||||||||
\(34\) | 72.5755 | + | 234.296i | 0.366076 | + | 1.18181i | ||||
\(35\) | −17.3580 | + | 17.3580i | −0.0838298 | + | 0.0838298i | ||||
\(36\) | −86.5148 | − | 126.249i | −0.400532 | − | 0.584486i | ||||
\(37\) | −21.7145 | − | 21.7145i | −0.0964820 | − | 0.0964820i | 0.657218 | − | 0.753700i | \(-0.271733\pi\) |
−0.753700 | + | 0.657218i | \(0.771733\pi\) | |||||||
\(38\) | −194.076 | − | 102.278i | −0.828508 | − | 0.436622i | ||||
\(39\) | 192.667i | 0.791060i | ||||||||
\(40\) | 2.20599 | + | 18.9713i | 0.00871995 | + | 0.0749907i | ||||
\(41\) | 153.274i | 0.583840i | 0.956443 | + | 0.291920i | \(0.0942941\pi\) | ||||
−0.956443 | + | 0.291920i | \(0.905706\pi\) | |||||||
\(42\) | 107.580 | − | 204.138i | 0.395238 | − | 0.749980i | ||||
\(43\) | −120.951 | − | 120.951i | −0.428949 | − | 0.428949i | 0.459322 | − | 0.888270i | \(-0.348093\pi\) |
−0.888270 | + | 0.459322i | \(0.848093\pi\) | |||||||
\(44\) | −134.893 | − | 25.1917i | −0.462181 | − | 0.0863133i | ||||
\(45\) | 11.4183 | − | 11.4183i | 0.0378253 | − | 0.0378253i | ||||
\(46\) | 189.704 | − | 58.7626i | 0.608051 | − | 0.188349i | ||||
\(47\) | −99.9792 | −0.310286 | −0.155143 | − | 0.987892i | \(-0.549584\pi\) | ||||
−0.155143 | + | 0.987892i | \(0.549584\pi\) | |||||||
\(48\) | −72.5737 | − | 164.209i | −0.218231 | − | 0.493782i | ||||
\(49\) | −502.812 | −1.46592 | ||||||||
\(50\) | 335.797 | − | 104.016i | 0.949778 | − | 0.294203i | ||||
\(51\) | 172.013 | − | 172.013i | 0.472287 | − | 0.472287i | ||||
\(52\) | 100.869 | − | 540.122i | 0.269000 | − | 1.44041i | ||||
\(53\) | 389.132 | + | 389.132i | 1.00852 | + | 1.00852i | 0.999963 | + | 0.00855213i | \(0.00272226\pi\) |
0.00855213 | + | 0.999963i | \(0.497278\pi\) | |||||||
\(54\) | −170.643 | + | 323.802i | −0.430029 | + | 0.815997i | ||||
\(55\) | − | 14.4785i | − | 0.0354960i | ||||||
\(56\) | −408.465 | + | 515.957i | −0.974704 | + | 1.23121i | ||||
\(57\) | 217.574i | 0.505585i | ||||||||
\(58\) | 224.359 | + | 118.237i | 0.507928 | + | 0.267677i | ||||
\(59\) | −324.819 | − | 324.819i | −0.716744 | − | 0.716744i | 0.251193 | − | 0.967937i | \(-0.419177\pi\) |
−0.967937 | + | 0.251193i | \(0.919177\pi\) | |||||||
\(60\) | 15.6254 | − | 10.7076i | 0.0336204 | − | 0.0230391i | ||||
\(61\) | −0.339194 | + | 0.339194i | −0.000711957 | + | 0.000711957i | −0.707463 | − | 0.706751i | \(-0.750160\pi\) |
0.706751 | + | 0.707463i | \(0.250160\pi\) | |||||||
\(62\) | −7.42220 | − | 23.9612i | −0.0152036 | − | 0.0490818i | ||||
\(63\) | 556.383 | 1.11266 | ||||||||
\(64\) | 117.483 | + | 498.339i | 0.229458 | + | 0.973318i | ||||
\(65\) | 57.9728 | 0.110625 | ||||||||
\(66\) | 40.2698 | + | 130.004i | 0.0751041 | + | 0.242459i | ||||
\(67\) | 565.288 | − | 565.288i | 1.03076 | − | 1.03076i | 0.0312478 | − | 0.999512i | \(-0.490052\pi\) |
0.999512 | − | 0.0312478i | \(-0.00994810\pi\) | |||||||
\(68\) | −572.278 | + | 392.166i | −1.02057 | + | 0.699368i | ||||
\(69\) | −139.275 | − | 139.275i | −0.242996 | − | 0.242996i | ||||
\(70\) | −61.4245 | − | 32.3706i | −0.104880 | − | 0.0552718i | ||||
\(71\) | 419.500i | 0.701205i | 0.936524 | + | 0.350602i | \(0.114023\pi\) | ||||
−0.936524 | + | 0.350602i | \(0.885977\pi\) | |||||||
\(72\) | 268.692 | − | 339.402i | 0.439801 | − | 0.555540i | ||||
\(73\) | − | 374.833i | − | 0.600971i | −0.953786 | − | 0.300485i | \(-0.902851\pi\) | ||
0.953786 | − | 0.300485i | \(-0.0971487\pi\) | |||||||
\(74\) | 40.4947 | − | 76.8404i | 0.0636138 | − | 0.120710i | ||||
\(75\) | −246.532 | − | 246.532i | −0.379561 | − | 0.379561i | ||||
\(76\) | 113.909 | − | 609.946i | 0.171924 | − | 0.920600i | ||||
\(77\) | 352.750 | − | 352.750i | 0.522072 | − | 0.522072i | ||||
\(78\) | −520.542 | + | 161.243i | −0.755638 | + | 0.234066i | ||||
\(79\) | −705.750 | −1.00510 | −0.502551 | − | 0.864547i | \(-0.667605\pi\) | ||||
−0.502551 | + | 0.864547i | \(0.667605\pi\) | |||||||
\(80\) | −49.4100 | + | 21.8372i | −0.0690526 | + | 0.0305184i | ||||
\(81\) | −153.530 | −0.210604 | ||||||||
\(82\) | −414.113 | + | 128.275i | −0.557697 | + | 0.172752i | ||||
\(83\) | −947.092 | + | 947.092i | −1.25249 | + | 1.25249i | −0.297893 | + | 0.954599i | \(0.596284\pi\) |
−0.954599 | + | 0.297893i | \(0.903716\pi\) | |||||||
\(84\) | 641.569 | + | 119.815i | 0.833344 | + | 0.155629i | ||||
\(85\) | −51.7582 | − | 51.7582i | −0.0660467 | − | 0.0660467i | ||||
\(86\) | 225.558 | − | 428.005i | 0.282820 | − | 0.536662i | ||||
\(87\) | − | 251.524i | − | 0.309956i | ||||||
\(88\) | −44.8302 | − | 385.535i | −0.0543058 | − | 0.467024i | ||||
\(89\) | 4.72918i | 0.00563249i | 0.999996 | + | 0.00281625i | \(0.000896440\pi\) | ||||
−0.999996 | + | 0.00281625i | \(0.999104\pi\) | |||||||
\(90\) | 40.4056 | + | 21.2937i | 0.0473236 | + | 0.0249394i | ||||
\(91\) | 1412.43 | + | 1412.43i | 1.62707 | + | 1.62707i | ||||
\(92\) | 317.527 | + | 463.359i | 0.359831 | + | 0.525093i | ||||
\(93\) | −17.5916 | + | 17.5916i | −0.0196146 | + | 0.0196146i | ||||
\(94\) | −83.6727 | − | 270.121i | −0.0918104 | − | 0.296392i | ||||
\(95\) | 65.4673 | 0.0707032 | ||||||||
\(96\) | 382.919 | − | 333.505i | 0.407099 | − | 0.354564i | ||||
\(97\) | 379.542 | 0.397285 | 0.198643 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198643 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(98\) | −420.804 | − | 1358.49i | −0.433751 | − | 1.40028i | ||||
\(99\) | −232.042 | + | 232.042i | −0.235567 | + | 0.235567i | ||||
\(100\) | 562.058 | + | 820.198i | 0.562058 | + | 0.820198i | ||||
\(101\) | −391.005 | − | 391.005i | −0.385212 | − | 0.385212i | 0.487764 | − | 0.872976i | \(-0.337813\pi\) |
−0.872976 | + | 0.487764i | \(0.837813\pi\) | |||||||
\(102\) | 608.699 | + | 320.783i | 0.590884 | + | 0.311395i | ||||
\(103\) | 307.935i | 0.294580i | 0.989093 | + | 0.147290i | \(0.0470551\pi\) | ||||
−0.989093 | + | 0.147290i | \(0.952945\pi\) | |||||||
\(104\) | 1543.71 | − | 179.503i | 1.45551 | − | 0.169247i | ||||
\(105\) | 68.8615i | 0.0640018i | ||||||||
\(106\) | −725.682 | + | 1377.01i | −0.664948 | + | 1.26177i | ||||
\(107\) | −601.607 | − | 601.607i | −0.543548 | − | 0.543548i | 0.381019 | − | 0.924567i | \(-0.375573\pi\) |
−0.924567 | + | 0.381019i | \(0.875573\pi\) | |||||||
\(108\) | −1017.65 | − | 190.049i | −0.906699 | − | 0.169328i | ||||
\(109\) | −948.890 | + | 948.890i | −0.833827 | + | 0.833827i | −0.988038 | − | 0.154211i | \(-0.950717\pi\) |
0.154211 | + | 0.988038i | \(0.450717\pi\) | |||||||
\(110\) | 39.1177 | − | 12.1171i | 0.0339066 | − | 0.0105029i | ||||
\(111\) | −86.1439 | −0.0736614 | ||||||||
\(112\) | −1735.85 | − | 671.776i | −1.46448 | − | 0.566758i | ||||
\(113\) | 1824.02 | 1.51849 | 0.759244 | − | 0.650807i | \(-0.225569\pi\) | ||||
0.759244 | + | 0.650807i | \(0.225569\pi\) | |||||||
\(114\) | −587.836 | + | 182.088i | −0.482946 | + | 0.149597i | ||||
\(115\) | −41.9074 | + | 41.9074i | −0.0339816 | + | 0.0339816i | ||||
\(116\) | −131.683 | + | 705.122i | −0.105401 | + | 0.564387i | ||||
\(117\) | −929.111 | − | 929.111i | −0.734157 | − | 0.734157i | ||||
\(118\) | 605.748 | − | 1149.43i | 0.472573 | − | 0.896727i | ||||
\(119\) | − | 2522.04i | − | 1.94282i | ||||||
\(120\) | 42.0065 | + | 33.2550i | 0.0319554 | + | 0.0252980i | ||||
\(121\) | − | 1036.77i | − | 0.778939i | ||||||
\(122\) | −1.20030 | − | 0.632555i | −0.000890738 | − | 0.000469417i | ||||
\(123\) | 304.029 | + | 304.029i | 0.222873 | + | 0.222873i | ||||
\(124\) | 58.5261 | − | 40.1063i | 0.0423855 | − | 0.0290456i | ||||
\(125\) | −148.787 | + | 148.787i | −0.106463 | + | 0.106463i | ||||
\(126\) | 465.638 | + | 1503.22i | 0.329224 | + | 1.06284i | ||||
\(127\) | 988.748 | 0.690844 | 0.345422 | − | 0.938447i | \(-0.387736\pi\) | ||||
0.345422 | + | 0.938447i | \(0.387736\pi\) | |||||||
\(128\) | −1248.08 | + | 734.473i | −0.861841 | + | 0.507178i | ||||
\(129\) | −479.826 | −0.327491 | ||||||||
\(130\) | 48.5175 | + | 156.630i | 0.0327328 | + | 0.105672i | ||||
\(131\) | 793.572 | − | 793.572i | 0.529273 | − | 0.529273i | −0.391083 | − | 0.920356i | \(-0.627899\pi\) |
0.920356 | + | 0.391083i | \(0.127899\pi\) | |||||||
\(132\) | −317.539 | + | 217.600i | −0.209380 | + | 0.143482i | ||||
\(133\) | 1595.03 | + | 1595.03i | 1.03990 | + | 1.03990i | ||||
\(134\) | 2000.37 | + | 1054.19i | 1.28959 | + | 0.679614i | ||||
\(135\) | − | 109.227i | − | 0.0696356i | ||||||
\(136\) | −1538.48 | − | 1217.96i | −0.970028 | − | 0.767937i | ||||
\(137\) | 1595.30i | 0.994856i | 0.867505 | + | 0.497428i | \(0.165722\pi\) | ||||
−0.867505 | + | 0.497428i | \(0.834278\pi\) | |||||||
\(138\) | 259.730 | − | 492.849i | 0.160215 | − | 0.304015i | ||||
\(139\) | −277.696 | − | 277.696i | −0.169452 | − | 0.169452i | 0.617286 | − | 0.786738i | \(-0.288232\pi\) |
−0.786738 | + | 0.617286i | \(0.788232\pi\) | |||||||
\(140\) | 36.0518 | − | 193.046i | 0.0217638 | − | 0.116538i | ||||
\(141\) | −198.315 | + | 198.315i | −0.118448 | + | 0.118448i | ||||
\(142\) | −1133.40 | + | 351.080i | −0.669806 | + | 0.207479i | ||||
\(143\) | −1178.12 | −0.688948 | ||||||||
\(144\) | 1141.86 | + | 441.901i | 0.660796 | + | 0.255729i | ||||
\(145\) | −75.6828 | −0.0433456 | ||||||||
\(146\) | 1012.71 | − | 313.698i | 0.574061 | − | 0.177821i | ||||
\(147\) | −997.359 | + | 997.359i | −0.559597 | + | 0.559597i | ||||
\(148\) | 241.496 | + | 45.0999i | 0.134127 | + | 0.0250486i | ||||
\(149\) | −593.272 | − | 593.272i | −0.326193 | − | 0.326193i | 0.524944 | − | 0.851137i | \(-0.324086\pi\) |
−0.851137 | + | 0.524944i | \(0.824086\pi\) | |||||||
\(150\) | 459.751 | − | 872.397i | 0.250257 | − | 0.474873i | ||||
\(151\) | 160.655i | 0.0865821i | 0.999063 | + | 0.0432911i | \(0.0137843\pi\) | ||||
−0.999063 | + | 0.0432911i | \(0.986216\pi\) | |||||||
\(152\) | 1743.27 | − | 202.708i | 0.930249 | − | 0.108170i | ||||
\(153\) | 1659.02i | 0.876629i | ||||||||
\(154\) | 1248.27 | + | 657.835i | 0.653171 | + | 0.344220i | ||||
\(155\) | 5.29325 | + | 5.29325i | 0.00274299 | + | 0.00274299i | ||||
\(156\) | −871.284 | − | 1271.44i | −0.447170 | − | 0.652545i | ||||
\(157\) | −705.762 | + | 705.762i | −0.358764 | + | 0.358764i | −0.863357 | − | 0.504593i | \(-0.831642\pi\) |
0.504593 | + | 0.863357i | \(0.331642\pi\) | |||||||
\(158\) | −590.643 | − | 1906.78i | −0.297399 | − | 0.960096i | ||||
\(159\) | 1543.73 | 0.769975 | ||||||||
\(160\) | −100.351 | − | 115.219i | −0.0495838 | − | 0.0569305i | ||||
\(161\) | −2042.04 | −0.999598 | ||||||||
\(162\) | −128.489 | − | 414.804i | −0.0623153 | − | 0.201173i | ||||
\(163\) | 1872.64 | − | 1872.64i | 0.899855 | − | 0.899855i | −0.0955676 | − | 0.995423i | \(-0.530467\pi\) |
0.995423 | + | 0.0955676i | \(0.0304666\pi\) | |||||||
\(164\) | −693.143 | − | 1011.49i | −0.330033 | − | 0.481609i | ||||
\(165\) | −28.7190 | − | 28.7190i | −0.0135501 | − | 0.0135501i | ||||
\(166\) | −3351.45 | − | 1766.21i | −1.56701 | − | 0.825810i | ||||
\(167\) | 3852.19i | 1.78498i | 0.451066 | + | 0.892490i | \(0.351044\pi\) | ||||
−0.451066 | + | 0.892490i | \(0.648956\pi\) | |||||||
\(168\) | 213.218 | + | 1833.65i | 0.0979172 | + | 0.842078i | ||||
\(169\) | − | 2520.28i | − | 1.14715i | ||||||
\(170\) | 96.5227 | − | 183.156i | 0.0435468 | − | 0.0826318i | ||||
\(171\) | −1049.22 | − | 1049.22i | −0.469217 | − | 0.469217i | ||||
\(172\) | 1345.14 | + | 251.209i | 0.596315 | + | 0.111363i | ||||
\(173\) | 2625.61 | − | 2625.61i | 1.15388 | − | 1.15388i | 0.168112 | − | 0.985768i | \(-0.446233\pi\) |
0.985768 | − | 0.168112i | \(-0.0537671\pi\) | |||||||
\(174\) | 679.561 | − | 210.501i | 0.296077 | − | 0.0917127i | ||||
\(175\) | −3614.64 | −1.56138 | ||||||||
\(176\) | 1004.11 | − | 443.776i | 0.430044 | − | 0.190062i | ||||
\(177\) | −1288.60 | −0.547215 | ||||||||
\(178\) | −12.7772 | + | 3.95785i | −0.00538028 | + | 0.00166659i | ||||
\(179\) | −1236.73 | + | 1236.73i | −0.516413 | + | 0.516413i | −0.916484 | − | 0.400071i | \(-0.868985\pi\) |
0.400071 | + | 0.916484i | \(0.368985\pi\) | |||||||
\(180\) | −23.7152 | + | 126.988i | −0.00982016 | + | 0.0525839i | ||||
\(181\) | 1574.90 | + | 1574.90i | 0.646748 | + | 0.646748i | 0.952206 | − | 0.305458i | \(-0.0988094\pi\) |
−0.305458 | + | 0.952206i | \(0.598809\pi\) | |||||||
\(182\) | −2634.01 | + | 4998.14i | −1.07278 | + | 2.03564i | ||||
\(183\) | 1.34563i | 0.000543560i | ||||||||
\(184\) | −986.155 | + | 1245.67i | −0.395110 | + | 0.499088i | ||||
\(185\) | 25.9204i | 0.0103011i | ||||||||
\(186\) | −62.2509 | − | 32.8061i | −0.0245401 | − | 0.0129326i | ||||
\(187\) | 1051.83 | + | 1051.83i | 0.411323 | + | 0.411323i | ||||
\(188\) | 659.782 | − | 452.130i | 0.255955 | − | 0.175399i | ||||
\(189\) | 2661.19 | − | 2661.19i | 1.02419 | − | 1.02419i | ||||
\(190\) | 54.7897 | + | 176.878i | 0.0209203 | + | 0.0675373i | ||||
\(191\) | 3585.92 | 1.35847 | 0.679236 | − | 0.733920i | \(-0.262311\pi\) | ||||
0.679236 | + | 0.733920i | \(0.262311\pi\) | |||||||
\(192\) | 1221.52 | + | 755.452i | 0.459144 | + | 0.283959i | ||||
\(193\) | 523.601 | 0.195283 | 0.0976415 | − | 0.995222i | \(-0.468870\pi\) | ||||
0.0976415 | + | 0.995222i | \(0.468870\pi\) | |||||||
\(194\) | 317.639 | + | 1025.44i | 0.117552 | + | 0.379496i | ||||
\(195\) | 114.993 | − | 114.993i | 0.0422297 | − | 0.0422297i | ||||
\(196\) | 3318.15 | − | 2273.84i | 1.20924 | − | 0.828658i | ||||
\(197\) | −1125.64 | − | 1125.64i | −0.407098 | − | 0.407098i | 0.473627 | − | 0.880725i | \(-0.342944\pi\) |
−0.880725 | + | 0.473627i | \(0.842944\pi\) | |||||||
\(198\) | −821.122 | − | 432.730i | −0.294720 | − | 0.155317i | ||||
\(199\) | 2312.48i | 0.823757i | 0.911239 | + | 0.411878i | \(0.135127\pi\) | ||||
−0.911239 | + | 0.411878i | \(0.864873\pi\) | |||||||
\(200\) | −1745.60 | + | 2204.98i | −0.617164 | + | 0.779578i | ||||
\(201\) | − | 2242.57i | − | 0.786957i | ||||||
\(202\) | 729.175 | − | 1383.64i | 0.253983 | − | 0.481943i | ||||
\(203\) | −1843.91 | − | 1843.91i | −0.637524 | − | 0.637524i | ||||
\(204\) | −357.263 | + | 1913.03i | −0.122615 | + | 0.656564i | ||||
\(205\) | 91.4815 | − | 91.4815i | 0.0311675 | − | 0.0311675i | ||||
\(206\) | −831.973 | + | 257.711i | −0.281390 | + | 0.0871631i | ||||
\(207\) | 1343.27 | 0.451033 | ||||||||
\(208\) | 1776.90 | + | 4020.52i | 0.592337 | + | 1.34025i | ||||
\(209\) | −1330.43 | −0.440323 | ||||||||
\(210\) | −186.048 | + | 57.6302i | −0.0611360 | + | 0.0189374i | ||||
\(211\) | 1418.59 | − | 1418.59i | 0.462842 | − | 0.462842i | −0.436744 | − | 0.899586i | \(-0.643868\pi\) |
0.899586 | + | 0.436744i | \(0.143868\pi\) | |||||||
\(212\) | −4327.70 | − | 808.208i | −1.40202 | − | 0.261830i | ||||
\(213\) | 832.105 | + | 832.105i | 0.267675 | + | 0.267675i | ||||
\(214\) | 1121.92 | − | 2128.89i | 0.358379 | − | 0.680039i | ||||
\(215\) | 144.378i | 0.0457977i | ||||||||
\(216\) | −338.204 | − | 2908.52i | −0.106536 | − | 0.916202i | ||||
\(217\) | 257.926i | 0.0806875i | ||||||||
\(218\) | −3357.82 | − | 1769.56i | −1.04321 | − | 0.549770i | ||||
\(219\) | −743.504 | − | 743.504i | −0.229413 | − | 0.229413i | ||||
\(220\) | 65.4752 | + | 95.5464i | 0.0200652 | + | 0.0292806i | ||||
\(221\) | −4211.60 | + | 4211.60i | −1.28191 | + | 1.28191i | ||||
\(222\) | −72.0939 | − | 232.742i | −0.0217956 | − | 0.0703630i | ||||
\(223\) | −4315.08 | −1.29578 | −0.647890 | − | 0.761734i | \(-0.724349\pi\) | ||||
−0.647890 | + | 0.761734i | \(0.724349\pi\) | |||||||
\(224\) | 362.257 | − | 5252.08i | 0.108055 | − | 1.56660i | ||||
\(225\) | 2377.74 | 0.704516 | ||||||||
\(226\) | 1526.52 | + | 4928.09i | 0.449304 | + | 1.45049i | ||||
\(227\) | 701.203 | − | 701.203i | 0.205024 | − | 0.205024i | −0.597124 | − | 0.802149i | \(-0.703690\pi\) |
0.802149 | + | 0.597124i | \(0.203690\pi\) | |||||||
\(228\) | −983.921 | − | 1435.81i | −0.285797 | − | 0.417057i | ||||
\(229\) | −663.351 | − | 663.351i | −0.191421 | − | 0.191421i | 0.604889 | − | 0.796310i | \(-0.293218\pi\) |
−0.796310 | + | 0.604889i | \(0.793218\pi\) | |||||||
\(230\) | −148.297 | − | 78.1521i | −0.0425148 | − | 0.0224052i | ||||
\(231\) | − | 1399.40i | − | 0.398588i | ||||||
\(232\) | −2015.29 | + | 234.339i | −0.570302 | + | 0.0663150i | ||||
\(233\) | 3490.15i | 0.981318i | 0.871352 | + | 0.490659i | \(0.163244\pi\) | ||||
−0.871352 | + | 0.490659i | \(0.836756\pi\) | |||||||
\(234\) | 1732.68 | − | 3287.82i | 0.484054 | − | 0.918512i | ||||
\(235\) | 59.6724 | + | 59.6724i | 0.0165642 | + | 0.0165642i | ||||
\(236\) | 3612.46 | + | 674.635i | 0.996402 | + | 0.186081i | ||||
\(237\) | −1399.90 | + | 1399.90i | −0.383684 | + | 0.383684i | ||||
\(238\) | 6814.00 | − | 2110.70i | 1.85582 | − | 0.574859i | ||||
\(239\) | 2950.43 | 0.798525 | 0.399263 | − | 0.916837i | \(-0.369266\pi\) | ||||
0.399263 | + | 0.916837i | \(0.369266\pi\) | |||||||
\(240\) | −54.6924 | + | 141.323i | −0.0147099 | + | 0.0380099i | ||||
\(241\) | −1128.96 | −0.301755 | −0.150877 | − | 0.988552i | \(-0.548210\pi\) | ||||
−0.150877 | + | 0.988552i | \(0.548210\pi\) | |||||||
\(242\) | 2801.12 | − | 867.672i | 0.744060 | − | 0.230480i | ||||
\(243\) | −2775.13 | + | 2775.13i | −0.732613 | + | 0.732613i | ||||
\(244\) | 0.704491 | − | 3.77233i | 0.000184838 | − | 0.000989748i | ||||
\(245\) | 300.102 | + | 300.102i | 0.0782565 | + | 0.0782565i | ||||
\(246\) | −566.977 | + | 1075.86i | −0.146948 | + | 0.278839i | ||||
\(247\) | − | 5327.11i | − | 1.37229i | ||||||
\(248\) | 157.339 | + | 124.559i | 0.0402864 | + | 0.0318933i | ||||
\(249\) | 3757.23i | 0.956244i | ||||||||
\(250\) | −526.508 | − | 277.469i | −0.133197 | − | 0.0701947i | ||||
\(251\) | 4621.86 | + | 4621.86i | 1.16227 | + | 1.16227i | 0.983978 | + | 0.178291i | \(0.0570569\pi\) |
0.178291 | + | 0.983978i | \(0.442943\pi\) | |||||||
\(252\) | −3671.68 | + | 2516.10i | −0.917833 | + | 0.628965i | ||||
\(253\) | 851.642 | − | 851.642i | 0.211630 | − | 0.211630i | ||||
\(254\) | 827.485 | + | 2671.38i | 0.204413 | + | 0.659910i | ||||
\(255\) | −205.331 | −0.0504249 | ||||||||
\(256\) | −3028.90 | − | 2757.35i | −0.739477 | − | 0.673181i | ||||
\(257\) | 610.977 | 0.148295 | 0.0741473 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741473 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(258\) | −401.567 | − | 1296.38i | −0.0969010 | − | 0.312826i | ||||
\(259\) | −631.518 | + | 631.518i | −0.151508 | + | 0.151508i | ||||
\(260\) | −382.574 | + | 262.167i | −0.0912547 | + | 0.0625342i | ||||
\(261\) | 1212.94 | + | 1212.94i | 0.287660 | + | 0.287660i | ||||
\(262\) | 2808.20 | + | 1479.91i | 0.662179 | + | 0.348967i | ||||
\(263\) | − | 4973.57i | − | 1.16610i | −0.812438 | − | 0.583048i | \(-0.801860\pi\) | ||
0.812438 | − | 0.583048i | \(-0.198140\pi\) | |||||||
\(264\) | −853.655 | − | 675.809i | −0.199011 | − | 0.157550i | ||||
\(265\) | − | 464.505i | − | 0.107677i | ||||||
\(266\) | −2974.53 | + | 5644.28i | −0.685638 | + | 1.30103i | ||||
\(267\) | 9.38061 | + | 9.38061i | 0.00215013 | + | 0.00215013i | ||||
\(268\) | −1174.08 | + | 6286.81i | −0.267605 | + | 1.43294i | ||||
\(269\) | −938.415 | + | 938.415i | −0.212700 | + | 0.212700i | −0.805413 | − | 0.592714i | \(-0.798057\pi\) |
0.592714 | + | 0.805413i | \(0.298057\pi\) | |||||||
\(270\) | 295.108 | − | 91.4126i | 0.0665175 | − | 0.0206044i | ||||
\(271\) | −4010.64 | −0.898999 | −0.449500 | − | 0.893280i | \(-0.648398\pi\) | ||||
−0.449500 | + | 0.893280i | \(0.648398\pi\) | |||||||
\(272\) | 2003.10 | − | 5175.95i | 0.446530 | − | 1.15382i | ||||
\(273\) | 5603.29 | 1.24222 | ||||||||
\(274\) | −4310.13 | + | 1335.10i | −0.950309 | + | 0.294367i | ||||
\(275\) | 1507.50 | − | 1507.50i | 0.330566 | − | 0.330566i | ||||
\(276\) | 1548.94 | + | 289.268i | 0.337808 | + | 0.0630864i | ||||
\(277\) | −3534.99 | − | 3534.99i | −0.766776 | − | 0.766776i | 0.210762 | − | 0.977538i | \(-0.432406\pi\) |
−0.977538 | + | 0.210762i | \(0.932406\pi\) | |||||||
\(278\) | 517.868 | − | 982.675i | 0.111725 | − | 0.212003i | ||||
\(279\) | − | 169.666i | − | 0.0364074i | ||||||
\(280\) | 551.740 | − | 64.1566i | 0.117760 | − | 0.0136932i | ||||
\(281\) | − | 7468.35i | − | 1.58550i | −0.609550 | − | 0.792748i | \(-0.708650\pi\) | ||
0.609550 | − | 0.792748i | \(-0.291350\pi\) | |||||||
\(282\) | −701.772 | − | 369.833i | −0.148191 | − | 0.0780965i | ||||
\(283\) | −2249.22 | − | 2249.22i | −0.472447 | − | 0.472447i | 0.430259 | − | 0.902705i | \(-0.358422\pi\) |
−0.902705 | + | 0.430259i | \(0.858422\pi\) | |||||||
\(284\) | −1897.08 | − | 2768.36i | −0.396377 | − | 0.578423i | ||||
\(285\) | 129.858 | − | 129.858i | 0.0269900 | − | 0.0269900i | ||||
\(286\) | −985.973 | − | 3183.03i | −0.203852 | − | 0.658099i | ||||
\(287\) | 4457.66 | 0.916819 | ||||||||
\(288\) | −238.296 | + | 3454.87i | −0.0487560 | + | 0.706875i | ||||
\(289\) | 2607.24 | 0.530682 | ||||||||
\(290\) | −63.3390 | − | 204.478i | −0.0128255 | − | 0.0414047i | ||||
\(291\) | 752.845 | − | 752.845i | 0.151658 | − | 0.151658i | ||||
\(292\) | 1695.08 | + | 2473.60i | 0.339717 | + | 0.495740i | ||||
\(293\) | −3952.79 | − | 3952.79i | −0.788139 | − | 0.788139i | 0.193050 | − | 0.981189i | \(-0.438162\pi\) |
−0.981189 | + | 0.193050i | \(0.938162\pi\) | |||||||
\(294\) | −3529.33 | − | 1859.95i | −0.700118 | − | 0.368961i | ||||
\(295\) | 387.736i | 0.0765249i | ||||||||
\(296\) | 80.2582 | + | 690.212i | 0.0157598 | + | 0.135533i | ||||
\(297\) | 2219.72i | 0.433674i | ||||||||
\(298\) | 1106.38 | − | 2099.40i | 0.215070 | − | 0.408104i | ||||
\(299\) | 3410.03 | + | 3410.03i | 0.659555 | + | 0.659555i | ||||
\(300\) | 2741.79 | + | 512.036i | 0.527658 | + | 0.0985413i | ||||
\(301\) | −3517.59 | + | 3517.59i | −0.673589 | + | 0.673589i | ||||
\(302\) | −434.053 | + | 134.452i | −0.0827052 | + | 0.0256187i | ||||
\(303\) | −1551.16 | −0.294099 | ||||||||
\(304\) | 2006.62 | + | 4540.28i | 0.378577 | + | 0.856588i | ||||
\(305\) | 0.404895 | 7.60138e−5 | ||||||||
\(306\) | −4482.31 | + | 1388.44i | −0.837375 | + | 0.259385i | ||||
\(307\) | −3855.24 | + | 3855.24i | −0.716711 | + | 0.716711i | −0.967930 | − | 0.251219i | \(-0.919168\pi\) |
0.251219 | + | 0.967930i | \(0.419168\pi\) | |||||||
\(308\) | −732.645 | + | 3923.08i | −0.135540 | + | 0.725774i | ||||
\(309\) | 610.809 | + | 610.809i | 0.112452 | + | 0.112452i | ||||
\(310\) | −9.87125 | + | 18.7311i | −0.00180855 | + | 0.00343179i | ||||
\(311\) | 5194.39i | 0.947096i | 0.880768 | + | 0.473548i | \(0.157027\pi\) | ||||
−0.880768 | + | 0.473548i | \(0.842973\pi\) | |||||||
\(312\) | 2705.98 | − | 3418.09i | 0.491013 | − | 0.620228i | ||||
\(313\) | − | 4710.01i | − | 0.850561i | −0.905062 | − | 0.425281i | \(-0.860175\pi\) | ||
0.905062 | − | 0.425281i | \(-0.139825\pi\) | |||||||
\(314\) | −2497.46 | − | 1316.16i | −0.448854 | − | 0.236545i | ||||
\(315\) | −332.076 | − | 332.076i | −0.0593980 | − | 0.0593980i | ||||
\(316\) | 4657.38 | − | 3191.57i | 0.829108 | − | 0.568164i | ||||
\(317\) | 5680.21 | − | 5680.21i | 1.00641 | − | 1.00641i | 0.00643263 | − | 0.999979i | \(-0.497952\pi\) |
0.999979 | − | 0.00643263i | \(-0.00204758\pi\) | |||||||
\(318\) | 1291.95 | + | 4170.82i | 0.227827 | + | 0.735497i | ||||
\(319\) | 1538.03 | 0.269946 | ||||||||
\(320\) | 227.313 | − | 367.552i | 0.0397100 | − | 0.0642087i | ||||
\(321\) | −2386.65 | −0.414984 | ||||||||
\(322\) | −1708.98 | − | 5517.13i | −0.295770 | − | 0.954838i | ||||
\(323\) | −4756.05 | + | 4756.05i | −0.819300 | + | 0.819300i | ||||
\(324\) | 1013.17 | − | 694.299i | 0.173727 | − | 0.119050i | ||||
\(325\) | 6036.13 | + | 6036.13i | 1.03023 | + | 1.03023i | ||||
\(326\) | 6626.67 | + | 3492.24i | 1.12582 | + | 0.593304i | ||||
\(327\) | 3764.36i | 0.636605i | ||||||||
\(328\) | 2152.72 | − | 2719.23i | 0.362390 | − | 0.457758i | ||||
\(329\) | 2907.68i | 0.487251i | ||||||||
\(330\) | 53.5574 | − | 101.627i | 0.00893405 | − | 0.0169527i | ||||
\(331\) | 1815.80 | + | 1815.80i | 0.301526 | + | 0.301526i | 0.841611 | − | 0.540084i | \(-0.181608\pi\) |
−0.540084 | + | 0.841611i | \(0.681608\pi\) | |||||||
\(332\) | 1967.07 | − | 10533.0i | 0.325171 | − | 1.74119i | ||||
\(333\) | 415.418 | − | 415.418i | 0.0683627 | − | 0.0683627i | ||||
\(334\) | −10407.8 | + | 3223.91i | −1.70505 | + | 0.528157i | ||||
\(335\) | −674.782 | −0.110052 | ||||||||
\(336\) | −4775.67 | + | 2110.65i | −0.775399 | + | 0.342694i | ||||
\(337\) | −2683.29 | −0.433733 | −0.216867 | − | 0.976201i | \(-0.569584\pi\) | ||||
−0.216867 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(338\) | 6809.23 | − | 2109.22i | 1.09578 | − | 0.339428i | ||||
\(339\) | 3618.05 | − | 3618.05i | 0.579662 | − | 0.579662i | ||||
\(340\) | 575.626 | + | 107.500i | 0.0918167 | + | 0.0171470i | ||||
\(341\) | −107.569 | − | 107.569i | −0.0170827 | − | 0.0170827i | ||||
\(342\) | 1956.67 | − | 3712.86i | 0.309370 | − | 0.587043i | ||||
\(343\) | 4647.79i | 0.731653i | ||||||||
\(344\) | 447.042 | + | 3844.51i | 0.0700665 | + | 0.602565i | ||||
\(345\) | 166.252i | 0.0259440i | ||||||||
\(346\) | 9291.18 | + | 4896.43i | 1.44363 | + | 0.760791i | ||||
\(347\) | −5291.81 | − | 5291.81i | −0.818671 | − | 0.818671i | 0.167244 | − | 0.985916i | \(-0.446513\pi\) |
−0.985916 | + | 0.167244i | \(0.946513\pi\) | |||||||
\(348\) | 1137.45 | + | 1659.85i | 0.175212 | + | 0.255683i | ||||
\(349\) | 73.7084 | − | 73.7084i | 0.0113052 | − | 0.0113052i | −0.701432 | − | 0.712737i | \(-0.747455\pi\) |
0.712737 | + | 0.701432i | \(0.247455\pi\) | |||||||
\(350\) | −3025.09 | − | 9765.94i | −0.461994 | − | 1.49146i | ||||
\(351\) | −8887.90 | −1.35157 | ||||||||
\(352\) | 2039.32 | + | 2341.49i | 0.308796 | + | 0.354550i | ||||
\(353\) | −5067.25 | −0.764030 | −0.382015 | − | 0.924156i | \(-0.624770\pi\) | ||||
−0.382015 | + | 0.924156i | \(0.624770\pi\) | |||||||
\(354\) | −1078.43 | − | 3481.51i | −0.161915 | − | 0.522712i | ||||
\(355\) | 250.378 | − | 250.378i | 0.0374329 | − | 0.0374329i | ||||
\(356\) | −21.3865 | − | 31.2088i | −0.00318393 | − | 0.00464624i | ||||
\(357\) | −5002.63 | − | 5002.63i | −0.741645 | − | 0.741645i | ||||
\(358\) | −4376.41 | − | 2306.36i | −0.646090 | − | 0.340488i | ||||
\(359\) | − | 970.230i | − | 0.142637i | −0.997454 | − | 0.0713186i | \(-0.977279\pi\) | ||
0.997454 | − | 0.0713186i | \(-0.0227207\pi\) | |||||||
\(360\) | −362.939 | + | 42.2028i | −0.0531350 | + | 0.00617856i | ||||
\(361\) | 843.224i | 0.122937i | ||||||||
\(362\) | −2936.99 | + | 5573.06i | −0.426422 | + | 0.809154i | ||||
\(363\) | −2056.49 | − | 2056.49i | −0.297350 | − | 0.297350i | ||||
\(364\) | −15708.3 | − | 2933.56i | −2.26192 | − | 0.422418i | ||||
\(365\) | −223.718 | + | 223.718i | −0.0320821 | + | 0.0320821i | ||||
\(366\) | −3.63558 | + | 1.12616i | −0.000519221 | + | 0.000160834i | ||||
\(367\) | 13451.4 | 1.91323 | 0.956617 | − | 0.291347i | \(-0.0941035\pi\) | ||||
0.956617 | + | 0.291347i | \(0.0941035\pi\) | |||||||
\(368\) | −4190.84 | − | 1621.86i | −0.593649 | − | 0.229743i | ||||
\(369\) | −2932.29 | −0.413682 | ||||||||
\(370\) | −70.0313 | + | 21.6928i | −0.00983987 | + | 0.00304799i | ||||
\(371\) | 11317.1 | − | 11317.1i | 1.58370 | − | 1.58370i | ||||
\(372\) | 36.5369 | − | 195.643i | 0.00509234 | − | 0.0272678i | ||||
\(373\) | 5898.22 | + | 5898.22i | 0.818762 | + | 0.818762i | 0.985929 | − | 0.167167i | \(-0.0534619\pi\) |
−0.167167 | + | 0.985929i | \(0.553462\pi\) | |||||||
\(374\) | −1961.53 | + | 3722.09i | −0.271199 | + | 0.514611i | ||||
\(375\) | 590.255i | 0.0812817i | ||||||||
\(376\) | 1773.73 | + | 1404.20i | 0.243279 | + | 0.192595i | ||||
\(377\) | 6158.35i | 0.841302i | ||||||||
\(378\) | 9417.08 | + | 4962.78i | 1.28138 | + | 0.675285i | ||||
\(379\) | −4446.72 | − | 4446.72i | −0.602673 | − | 0.602673i | 0.338348 | − | 0.941021i | \(-0.390132\pi\) |
−0.941021 | + | 0.338348i | \(0.890132\pi\) | |||||||
\(380\) | −432.031 | + | 296.059i | −0.0583230 | + | 0.0399671i | ||||
\(381\) | 1961.24 | − | 1961.24i | 0.263721 | − | 0.263721i | ||||
\(382\) | 3001.06 | + | 9688.35i | 0.401957 | + | 1.29764i | ||||
\(383\) | −6417.68 | −0.856209 | −0.428105 | − | 0.903729i | \(-0.640819\pi\) | ||||
−0.428105 | + | 0.903729i | \(0.640819\pi\) | |||||||
\(384\) | −1018.77 | + | 3932.51i | −0.135388 | + | 0.522605i | ||||
\(385\) | −421.076 | −0.0557403 | ||||||||
\(386\) | 438.202 | + | 1414.65i | 0.0577821 | + | 0.186539i | ||||
\(387\) | 2313.90 | − | 2313.90i | 0.303933 | − | 0.303933i | ||||
\(388\) | −2504.67 | + | 1716.38i | −0.327720 | + | 0.224577i | ||||
\(389\) | 6555.61 | + | 6555.61i | 0.854455 | + | 0.854455i | 0.990678 | − | 0.136223i | \(-0.0434965\pi\) |
−0.136223 | + | 0.990678i | \(0.543497\pi\) | |||||||
\(390\) | 406.922 | + | 214.447i | 0.0528341 | + | 0.0278434i | ||||
\(391\) | − | 6088.96i | − | 0.787549i | ||||||
\(392\) | 8920.36 | + | 7061.93i | 1.14935 | + | 0.909902i | ||||
\(393\) | − | 3148.20i | − | 0.404086i | ||||||
\(394\) | 2099.17 | − | 3983.27i | 0.268413 | − | 0.509325i | ||||
\(395\) | 421.226 | + | 421.226i | 0.0536561 | + | 0.0536561i | ||||
\(396\) | 481.941 | − | 2580.64i | 0.0611577 | − | 0.327480i | ||||
\(397\) | 8902.51 | − | 8902.51i | 1.12545 | − | 1.12545i | 0.134543 | − | 0.990908i | \(-0.457043\pi\) |
0.990908 | − | 0.134543i | \(-0.0429566\pi\) | |||||||
\(398\) | −6247.81 | + | 1935.32i | −0.786871 | + | 0.243741i | ||||
\(399\) | 6327.66 | 0.793933 | ||||||||
\(400\) | −7418.26 | − | 2870.88i | −0.927282 | − | 0.358860i | ||||
\(401\) | −6425.77 | −0.800218 | −0.400109 | − | 0.916468i | \(-0.631028\pi\) | ||||
−0.400109 | + | 0.916468i | \(0.631028\pi\) | |||||||
\(402\) | 6058.91 | − | 1876.81i | 0.751719 | − | 0.232852i | ||||
\(403\) | 430.715 | − | 430.715i | 0.0532393 | − | 0.0532393i | ||||
\(404\) | 4348.53 | + | 812.098i | 0.535514 | + | 0.100008i | ||||
\(405\) | 91.6341 | + | 91.6341i | 0.0112428 | + | 0.0112428i | ||||
\(406\) | 3438.67 | − | 6525.01i | 0.420340 | − | 0.797613i | ||||
\(407\) | − | 526.755i | − | 0.0641530i | ||||||
\(408\) | −5467.58 | + | 635.773i | −0.663445 | + | 0.0771457i | ||||
\(409\) | 12796.0i | 1.54699i | 0.633801 | + | 0.773496i | \(0.281494\pi\) | ||||
−0.633801 | + | 0.773496i | \(0.718506\pi\) | |||||||
\(410\) | 323.723 | + | 170.602i | 0.0389941 | + | 0.0205498i | ||||
\(411\) | 3164.37 | + | 3164.37i | 0.379773 | + | 0.379773i | ||||
\(412\) | −1392.56 | − | 2032.13i | −0.166520 | − | 0.242999i | ||||
\(413\) | −9446.67 | + | 9446.67i | −1.12552 | + | 1.12552i | ||||
\(414\) | 1124.19 | + | 3629.22i | 0.133456 | + | 0.430837i | ||||
\(415\) | 1130.54 | 0.133725 | ||||||||
\(416\) | −9375.45 | + | 8165.58i | −1.10497 | + | 0.962381i | ||||
\(417\) | −1101.65 | −0.129372 | ||||||||
\(418\) | −1113.44 | − | 3594.51i | −0.130287 | − | 0.420606i | ||||
\(419\) | −6545.21 | + | 6545.21i | −0.763137 | + | 0.763137i | −0.976888 | − | 0.213751i | \(-0.931432\pi\) |
0.213751 | + | 0.976888i | \(0.431432\pi\) | |||||||
\(420\) | −311.408 | − | 454.430i | −0.0361789 | − | 0.0527950i | ||||
\(421\) | −6390.00 | − | 6390.00i | −0.739738 | − | 0.739738i | 0.232789 | − | 0.972527i | \(-0.425215\pi\) |
−0.972527 | + | 0.232789i | \(0.925215\pi\) | |||||||
\(422\) | 5019.93 | + | 2645.49i | 0.579067 | + | 0.305167i | ||||
\(423\) | − | 1912.70i | − | 0.219855i | ||||||
\(424\) | −1438.26 | − | 12368.9i | −0.164736 | − | 1.41671i | ||||
\(425\) | − | 10778.1i | − | 1.23016i | ||||||
\(426\) | −1551.77 | + | 2944.55i | −0.176487 | + | 0.334892i | ||||
\(427\) | 9.86474 | + | 9.86474i | 0.00111801 | + | 0.00111801i | ||||
\(428\) | 6690.74 | + | 1249.51i | 0.755628 | + | 0.141115i | ||||
\(429\) | −2336.88 | + | 2336.88i | −0.262997 | + | 0.262997i | ||||
\(430\) | −390.078 | + | 120.830i | −0.0437470 | + | 0.0135510i | ||||
\(431\) | −10639.3 | −1.18904 | −0.594519 | − | 0.804081i | \(-0.702658\pi\) | ||||
−0.594519 | + | 0.804081i | \(0.702658\pi\) | |||||||
\(432\) | 7575.12 | − | 3347.89i | 0.843653 | − | 0.372860i | ||||
\(433\) | 3806.14 | 0.422428 | 0.211214 | − | 0.977440i | \(-0.432258\pi\) | ||||
0.211214 | + | 0.977440i | \(0.432258\pi\) | |||||||
\(434\) | −696.859 | + | 215.859i | −0.0770745 | + | 0.0238746i | ||||
\(435\) | −150.121 | + | 150.121i | −0.0165466 | + | 0.0165466i | ||||
\(436\) | 1970.80 | − | 10553.0i | 0.216478 | − | 1.15917i | ||||
\(437\) | 3850.86 | + | 3850.86i | 0.421537 | + | 0.421537i | ||||
\(438\) | 1386.54 | − | 2631.02i | 0.151259 | − | 0.287021i | ||||
\(439\) | 14102.8i | 1.53323i | 0.642106 | + | 0.766616i | \(0.278061\pi\) | ||||
−0.642106 | + | 0.766616i | \(0.721939\pi\) | |||||||
\(440\) | −203.349 | + | 256.862i | −0.0220324 | + | 0.0278305i | ||||
\(441\) | − | 9619.28i | − | 1.03869i | ||||||
\(442\) | −14903.5 | − | 7854.10i | −1.60381 | − | 0.845207i | ||||
\(443\) | −7662.45 | − | 7662.45i | −0.821792 | − | 0.821792i | 0.164573 | − | 0.986365i | \(-0.447375\pi\) |
−0.986365 | + | 0.164573i | \(0.947375\pi\) | |||||||
\(444\) | 568.480 | − | 389.563i | 0.0607632 | − | 0.0416393i | ||||
\(445\) | 2.82260 | − | 2.82260i | 0.000300683 | − | 0.000300683i | ||||
\(446\) | −3611.29 | − | 11658.4i | −0.383408 | − | 1.23776i | ||||
\(447\) | −2353.58 | −0.249040 | ||||||||
\(448\) | 14493.1 | − | 3416.73i | 1.52843 | − | 0.360325i | ||||
\(449\) | 13679.4 | 1.43779 | 0.718897 | − | 0.695117i | \(-0.244647\pi\) | ||||
0.718897 | + | 0.695117i | \(0.244647\pi\) | |||||||
\(450\) | 1989.93 | + | 6424.12i | 0.208459 | + | 0.672969i | ||||
\(451\) | −1859.09 | + | 1859.09i | −0.194104 | + | 0.194104i | ||||
\(452\) | −12037.0 | + | 8248.64i | −1.25260 | + | 0.858370i | ||||
\(453\) | 318.669 | + | 318.669i | 0.0330516 | + | 0.0330516i | ||||
\(454\) | 2481.33 | + | 1307.66i | 0.256508 | + | 0.135179i | ||||
\(455\) | − | 1686.01i | − | 0.173718i | ||||||
\(456\) | 3055.80 | − | 3859.97i | 0.313818 | − | 0.396402i | ||||
\(457\) | 7913.48i | 0.810016i | 0.914313 | + | 0.405008i | \(0.132731\pi\) | ||||
−0.914313 | + | 0.405008i | \(0.867269\pi\) | |||||||
\(458\) | 1237.07 | − | 2347.39i | 0.126210 | − | 0.239489i | ||||
\(459\) | 7935.13 | + | 7935.13i | 0.806929 | + | 0.806929i | ||||
\(460\) | 87.0397 | − | 466.070i | 0.00882228 | − | 0.0472405i | ||||
\(461\) | −580.215 | + | 580.215i | −0.0586189 | + | 0.0586189i | −0.735809 | − | 0.677190i | \(-0.763198\pi\) |
0.677190 | + | 0.735809i | \(0.263198\pi\) | |||||||
\(462\) | 3780.87 | − | 1171.16i | 0.380740 | − | 0.117938i | ||||
\(463\) | 14236.5 | 1.42899 | 0.714497 | − | 0.699638i | \(-0.246656\pi\) | ||||
0.714497 | + | 0.699638i | \(0.246656\pi\) | |||||||
\(464\) | −2319.73 | − | 5248.74i | −0.232092 | − | 0.525143i | ||||
\(465\) | 20.9990 | 0.00209420 | ||||||||
\(466\) | −9429.60 | + | 2920.91i | −0.937377 | + | 0.290361i | ||||
\(467\) | −8344.57 | + | 8344.57i | −0.826853 | + | 0.826853i | −0.987080 | − | 0.160227i | \(-0.948777\pi\) |
0.160227 | + | 0.987080i | \(0.448777\pi\) | |||||||
\(468\) | 10333.0 | + | 1929.72i | 1.02061 | + | 0.190601i | ||||
\(469\) | −16440.2 | − | 16440.2i | −1.61863 | − | 1.61863i | ||||
\(470\) | −111.282 | + | 211.161i | −0.0109213 | + | 0.0207237i | ||||
\(471\) | 2799.85i | 0.273907i | ||||||||
\(472\) | 1200.56 | + | 10324.7i | 0.117076 | + | 1.00684i | ||||
\(473\) | − | 2934.05i | − | 0.285217i | ||||||
\(474\) | −4953.79 | − | 2610.64i | −0.480032 | − | 0.252976i | ||||
\(475\) | 6816.45 | + | 6816.45i | 0.658443 | + | 0.658443i | ||||
\(476\) | 11405.3 | + | 16643.5i | 1.09824 | + | 1.60263i | ||||
\(477\) | −7444.46 | + | 7444.46i | −0.714588 | + | 0.714588i | ||||
\(478\) | 2469.22 | + | 7971.41i | 0.236275 | + | 0.762769i | ||||
\(479\) | −5563.77 | −0.530720 | −0.265360 | − | 0.964149i | \(-0.585491\pi\) | ||||
−0.265360 | + | 0.964149i | \(0.585491\pi\) | |||||||
\(480\) | −427.596 | − | 29.4930i | −0.0406604 | − | 0.00280452i | ||||
\(481\) | 2109.16 | 0.199936 | ||||||||
\(482\) | −944.830 | − | 3050.20i | −0.0892859 | − | 0.288243i | ||||
\(483\) | −4050.51 | + | 4050.51i | −0.381583 | + | 0.381583i | ||||
\(484\) | 4688.51 | + | 6841.83i | 0.440319 | + | 0.642546i | ||||
\(485\) | −226.529 | − | 226.529i | −0.0212085 | − | 0.0212085i | ||||
\(486\) | −9820.30 | − | 5175.28i | −0.916580 | − | 0.483036i | ||||
\(487\) | − | 18150.5i | − | 1.68886i | −0.535662 | − | 0.844432i | \(-0.679938\pi\) | ||
0.535662 | − | 0.844432i | \(-0.320062\pi\) | |||||||
\(488\) | 10.7816 | − | 1.25369i | 0.00100012 | − | 0.000116295i | ||||
\(489\) | − | 7428.99i | − | 0.687015i | ||||||
\(490\) | −559.653 | + | 1061.97i | −0.0515971 | + | 0.0979076i | ||||
\(491\) | 11593.0 | + | 11593.0i | 1.06555 | + | 1.06555i | 0.997695 | + | 0.0678570i | \(0.0216162\pi\) |
0.0678570 | + | 0.997695i | \(0.478384\pi\) | |||||||
\(492\) | −3381.24 | − | 631.455i | −0.309833 | − | 0.0578621i | ||||
\(493\) | 5498.18 | − | 5498.18i | 0.502284 | − | 0.502284i | ||||
\(494\) | 14392.7 | − | 4458.26i | 1.31084 | − | 0.406046i | ||||
\(495\) | 276.988 | 0.0251509 | ||||||||
\(496\) | −204.855 | + | 529.338i | −0.0185449 | + | 0.0479193i | ||||
\(497\) | 12200.3 | 1.10112 | ||||||||
\(498\) | −10151.2 | + | 3144.43i | −0.913426 | + | 0.282942i | ||||
\(499\) | 3109.58 | − | 3109.58i | 0.278966 | − | 0.278966i | −0.553730 | − | 0.832696i | \(-0.686796\pi\) |
0.832696 | + | 0.553730i | \(0.186796\pi\) | |||||||
\(500\) | 309.023 | − | 1654.72i | 0.0276399 | − | 0.148003i | ||||
\(501\) | 7641.07 | + | 7641.07i | 0.681393 | + | 0.681393i | ||||
\(502\) | −8619.20 | + | 16355.3i | −0.766322 | + | 1.45413i | ||||
\(503\) | − | 6221.21i | − | 0.551471i | −0.961233 | − | 0.275736i | \(-0.911079\pi\) | ||
0.961233 | − | 0.275736i | \(-0.0889215\pi\) | |||||||
\(504\) | −9870.76 | − | 7814.33i | −0.872379 | − | 0.690631i | ||||
\(505\) | 466.740i | 0.0411281i | ||||||||
\(506\) | 3013.69 | + | 1588.21i | 0.264772 | + | 0.139534i | ||||
\(507\) | −4999.13 | − | 4999.13i | −0.437907 | − | 0.437907i | ||||
\(508\) | −6524.94 | + | 4471.36i | −0.569877 | + | 0.390520i | ||||
\(509\) | 13800.4 | − | 13800.4i | 1.20176 | − | 1.20176i | 0.228124 | − | 0.973632i | \(-0.426741\pi\) |
0.973632 | − | 0.228124i | \(-0.0732591\pi\) | |||||||
\(510\) | −171.842 | − | 554.759i | −0.0149202 | − | 0.0481670i | ||||
\(511\) | −10901.2 | −0.943720 | ||||||||
\(512\) | 4914.86 | − | 10491.0i | 0.424234 | − | 0.905552i | ||||
\(513\) | −10036.9 | −0.863820 | ||||||||
\(514\) | 511.327 | + | 1650.72i | 0.0438787 | + | 0.141654i | ||||
\(515\) | 183.791 | − | 183.791i | 0.0157258 | − | 0.0157258i | ||||
\(516\) | 3166.46 | − | 2169.89i | 0.270147 | − | 0.185124i | ||||
\(517\) | −1212.66 | − | 1212.66i | −0.103158 | − | 0.103158i | ||||
\(518\) | −2234.74 | − | 1177.70i | −0.189554 | − | 0.0998944i | ||||
\(519\) | − | 10416.1i | − | 0.880957i | ||||||
\(520\) | −1028.49 | − | 814.221i | −0.0867354 | − | 0.0686653i | ||||
\(521\) | − | 6874.63i | − | 0.578086i | −0.957316 | − | 0.289043i | \(-0.906663\pi\) | ||
0.957316 | − | 0.289043i | \(-0.0933371\pi\) | |||||||
\(522\) | −2261.99 | + | 4292.21i | −0.189664 | + | 0.359895i | ||||
\(523\) | 2306.52 | + | 2306.52i | 0.192843 | + | 0.192843i | 0.796924 | − | 0.604080i | \(-0.206459\pi\) |
−0.604080 | + | 0.796924i | \(0.706459\pi\) | |||||||
\(524\) | −1648.21 | + | 8825.66i | −0.137409 | + | 0.735784i | ||||
\(525\) | −7169.85 | + | 7169.85i | −0.596034 | + | 0.596034i | ||||
\(526\) | 13437.5 | − | 4162.38i | 1.11388 | − | 0.345035i | ||||
\(527\) | −769.086 | −0.0635710 | ||||||||
\(528\) | 1111.46 | − | 2871.97i | 0.0916099 | − | 0.236717i | ||||
\(529\) | 7236.92 | 0.594799 | ||||||||
\(530\) | 1254.99 | − | 388.744i | 0.102855 | − | 0.0318603i | ||||
\(531\) | 6214.11 | − | 6214.11i | 0.507852 | − | 0.507852i | ||||
\(532\) | −17739.0 | − | 3312.80i | −1.44564 | − | 0.269977i | ||||
\(533\) | −7443.90 | − | 7443.90i | −0.604936 | − | 0.604936i | ||||
\(534\) | −17.4937 | + | 33.1950i | −0.00141765 | + | 0.00269005i | ||||
\(535\) | 718.136i | 0.0580332i | ||||||||
\(536\) | −17968.1 | + | 2089.34i | −1.44796 | + | 0.168369i | ||||
\(537\) | 4906.28i | 0.394267i | ||||||||
\(538\) | −3320.75 | − | 1750.03i | −0.266111 | − | 0.140240i | ||||
\(539\) | −6098.68 | − | 6098.68i | −0.487363 | − | 0.487363i | ||||
\(540\) | 493.953 | + | 720.813i | 0.0393636 | + | 0.0574423i | ||||
\(541\) | −13240.0 | + | 13240.0i | −1.05218 | + | 1.05218i | −0.0536210 | + | 0.998561i | \(0.517076\pi\) |
−0.998561 | + | 0.0536210i | \(0.982924\pi\) | |||||||
\(542\) | −3356.51 | − | 10835.8i | −0.266004 | − | 0.858744i | ||||
\(543\) | 6247.82 | 0.493775 | ||||||||
\(544\) | 15660.7 | + | 1080.18i | 1.23427 | + | 0.0851330i | ||||
\(545\) | 1132.69 | 0.0890256 | ||||||||
\(546\) | 4689.40 | + | 15138.8i | 0.367560 | + | 1.18660i | ||||
\(547\) | −13271.3 | + | 13271.3i | −1.03737 | + | 1.03737i | −0.0380940 | + | 0.999274i | \(0.512129\pi\) |
−0.999274 | + | 0.0380940i | \(0.987871\pi\) | |||||||
\(548\) | −7214.31 | − | 10527.7i | −0.562372 | − | 0.820656i | ||||
\(549\) | −6.48912 | − | 6.48912i | −0.000504460 | − | 0.000504460i | ||||
\(550\) | 5334.56 | + | 2811.30i | 0.413575 | + | 0.217953i | ||||
\(551\) | 6954.47i | 0.537696i | ||||||||
\(552\) | 514.770 | + | 4426.97i | 0.0396921 | + | 0.341348i | ||||
\(553\) | 20525.2i | 1.57834i | ||||||||
\(554\) | 6592.32 | − | 12509.2i | 0.505561 | − | 0.959322i | ||||
\(555\) | 51.4148 | + | 51.4148i | 0.00393232 | + | 0.00393232i | ||||
\(556\) | 3088.37 | + | 576.761i | 0.235569 | + | 0.0439930i | ||||
\(557\) | −8500.61 | + | 8500.61i | −0.646647 | + | 0.646647i | −0.952181 | − | 0.305534i | \(-0.901165\pi\) |
0.305534 | + | 0.952181i | \(0.401165\pi\) | |||||||
\(558\) | 458.401 | − | 141.994i | 0.0347771 | − | 0.0107725i | ||||
\(559\) | 11748.1 | 0.888896 | ||||||||
\(560\) | 635.088 | + | 1436.98i | 0.0479239 | + | 0.108435i | ||||
\(561\) | 4172.74 | 0.314034 | ||||||||
\(562\) | 20177.8 | − | 6250.27i | 1.51450 | − | 0.469131i | ||||
\(563\) | 17327.2 | − | 17327.2i | 1.29708 | − | 1.29708i | 0.366763 | − | 0.930314i | \(-0.380466\pi\) |
0.930314 | − | 0.366763i | \(-0.119534\pi\) | |||||||
\(564\) | 411.891 | − | 2205.55i | 0.0307513 | − | 0.164663i | ||||
\(565\) | −1088.66 | − | 1088.66i | −0.0810625 | − | 0.0810625i | ||||
\(566\) | 4194.52 | − | 7959.27i | 0.311500 | − | 0.591083i | ||||
\(567\) | 4465.09i | 0.330716i | ||||||||
\(568\) | 5891.83 | − | 7442.33i | 0.435239 | − | 0.549777i | ||||
\(569\) | 8998.54i | 0.662985i | 0.943458 | + | 0.331492i | \(0.107552\pi\) | ||||
−0.943458 | + | 0.331492i | \(0.892448\pi\) | |||||||
\(570\) | 459.527 | + | 242.170i | 0.0337675 | + | 0.0177954i | ||||
\(571\) | −9849.25 | − | 9849.25i | −0.721853 | − | 0.721853i | 0.247129 | − | 0.968983i | \(-0.420513\pi\) |
−0.968983 | + | 0.247129i | \(0.920513\pi\) | |||||||
\(572\) | 7774.66 | − | 5327.75i | 0.568313 | − | 0.389449i | ||||
\(573\) | 7112.89 | − | 7112.89i | 0.518578 | − | 0.518578i | ||||
\(574\) | 3730.62 | + | 12043.6i | 0.271277 | + | 0.875766i | ||||
\(575\) | −8726.79 | −0.632926 | ||||||||
\(576\) | −9533.71 | + | 2247.56i | −0.689649 | + | 0.162584i | ||||
\(577\) | −20584.4 | −1.48516 | −0.742580 | − | 0.669757i | \(-0.766398\pi\) | ||||
−0.742580 | + | 0.669757i | \(0.766398\pi\) | |||||||
\(578\) | 2182.00 | + | 7044.18i | 0.157023 | + | 0.506919i | ||||
\(579\) | 1038.59 | − | 1038.59i | 0.0745467 | − | 0.0745467i | ||||
\(580\) | 499.445 | − | 342.256i | 0.0357558 | − | 0.0245024i | ||||
\(581\) | 27544.1 | + | 27544.1i | 1.96682 | + | 1.96682i | ||||
\(582\) | 2664.08 | + | 1403.96i | 0.189741 | + | 0.0999933i | ||||
\(583\) | 9439.66i | 0.670585i | ||||||||
\(584\) | −5264.48 | + | 6649.89i | −0.373024 | + | 0.471189i | ||||
\(585\) | 1109.08i | 0.0783840i | ||||||||
\(586\) | 7371.47 | − | 13987.7i | 0.519646 | − | 0.986049i | ||||
\(587\) | −2586.77 | − | 2586.77i | −0.181887 | − | 0.181887i | 0.610291 | − | 0.792177i | \(-0.291053\pi\) |
−0.792177 | + | 0.610291i | \(0.791053\pi\) | |||||||
\(588\) | 2071.47 | − | 11092.1i | 0.145282 | − | 0.777940i | ||||
\(589\) | 486.396 | − | 486.396i | 0.0340265 | − | 0.0340265i | ||||
\(590\) | −1047.57 | + | 324.496i | −0.0730983 | + | 0.0226429i | ||||
\(591\) | −4465.54 | −0.310809 | ||||||||
\(592\) | −1797.63 | + | 794.479i | −0.124801 | + | 0.0551569i | ||||
\(593\) | −6035.89 | −0.417984 | −0.208992 | − | 0.977917i | \(-0.567018\pi\) | ||||
−0.208992 | + | 0.977917i | \(0.567018\pi\) | |||||||
\(594\) | −5997.19 | + | 1857.69i | −0.414255 | + | 0.128319i | ||||
\(595\) | −1505.28 | + | 1505.28i | −0.103715 | + | 0.103715i | ||||
\(596\) | 6598.04 | + | 1232.20i | 0.453467 | + | 0.0846860i | ||||
\(597\) | 4586.95 | + | 4586.95i | 0.314458 | + | 0.314458i | ||||
\(598\) | −6359.28 | + | 12067.0i | −0.434866 | + | 0.825177i | ||||
\(599\) | − | 5427.20i | − | 0.370199i | −0.982720 | − | 0.185100i | \(-0.940739\pi\) | ||
0.982720 | − | 0.185100i | \(-0.0592608\pi\) | |||||||
\(600\) | 911.200 | + | 7836.22i | 0.0619993 | + | 0.533188i | ||||
\(601\) | − | 17725.7i | − | 1.20307i | −0.798847 | − | 0.601535i | \(-0.794556\pi\) | ||
0.798847 | − | 0.601535i | \(-0.205444\pi\) | |||||||
\(602\) | −12447.6 | − | 6559.86i | −0.842735 | − | 0.444120i | ||||
\(603\) | 10814.5 | + | 10814.5i | 0.730349 | + | 0.730349i | ||||
\(604\) | −726.520 | − | 1060.19i | −0.0489431 | − | 0.0714215i | ||||
\(605\) | −618.793 | + | 618.793i | −0.0415827 | + | 0.0415827i | ||||
\(606\) | −1298.17 | − | 4190.90i | −0.0870207 | − | 0.280930i | ||||
\(607\) | 13487.6 | 0.901884 | 0.450942 | − | 0.892553i | \(-0.351088\pi\) | ||||
0.450942 | + | 0.892553i | \(0.351088\pi\) | |||||||
\(608\) | −10587.5 | + | 9221.19i | −0.706215 | + | 0.615080i | ||||
\(609\) | −7315.03 | −0.486732 | ||||||||
\(610\) | 0.338857 | + | 1.09394i | 2.24917e−5 | + | 7.26101e-5i | ||||
\(611\) | 4855.57 | − | 4855.57i | 0.321498 | − | 0.321498i | ||||
\(612\) | −7502.51 | − | 10948.2i | −0.495541 | − | 0.723130i | ||||
\(613\) | −16850.4 | − | 16850.4i | −1.11025 | − | 1.11025i | −0.993117 | − | 0.117129i | \(-0.962631\pi\) |
−0.117129 | − | 0.993117i | \(-0.537369\pi\) | |||||||
\(614\) | −13642.5 | − | 7189.54i | −0.896685 | − | 0.472551i | ||||
\(615\) | − | 362.918i | − | 0.0237956i | ||||||
\(616\) | −11212.4 | + | 1303.79i | −0.733381 | + | 0.0852779i | ||||
\(617\) | 535.243i | 0.0349239i | 0.999848 | + | 0.0174620i | \(0.00555860\pi\) | ||||
−0.999848 | + | 0.0174620i | \(0.994441\pi\) | |||||||
\(618\) | −1139.08 | + | 2161.46i | −0.0741434 | + | 0.140690i | ||||
\(619\) | −19691.0 | − | 19691.0i | −1.27859 | − | 1.27859i | −0.941458 | − | 0.337130i | \(-0.890544\pi\) |
−0.337130 | − | 0.941458i | \(-0.609456\pi\) | |||||||
\(620\) | −58.8685 | − | 10.9938i | −0.00381325 | − | 0.000712134i | ||||
\(621\) | 6424.88 | − | 6424.88i | 0.415172 | − | 0.415172i | ||||
\(622\) | −14034.1 | + | 4347.19i | −0.904688 | + | 0.280236i | ||||
\(623\) | 137.538 | 0.00884485 | ||||||||
\(624\) | 11499.5 | + | 4450.35i | 0.737741 | + | 0.285507i | ||||
\(625\) | −15358.3 | −0.982934 | ||||||||
\(626\) | 12725.4 | − | 3941.81i | 0.812475 | − | 0.251672i | ||||
\(627\) | −2638.98 | + | 2638.98i | −0.168087 | + | 0.168087i | ||||
\(628\) | 1465.84 | − | 7849.09i | 0.0931420 | − | 0.498746i | ||||
\(629\) | −1883.06 | − | 1883.06i | −0.119368 | − | 0.119368i | ||||
\(630\) | 619.280 | − | 1175.11i | 0.0391631 | − | 0.0743135i | ||||
\(631\) | 11880.2i | 0.749511i | 0.927124 | + | 0.374755i | \(0.122273\pi\) | ||||
−0.927124 | + | 0.374755i | \(0.877727\pi\) | |||||||
\(632\) | 12520.7 | + | 9912.18i | 0.788047 | + | 0.623869i | ||||
\(633\) | − | 5627.72i | − | 0.353368i | ||||||
\(634\) | 20100.4 | + | 10592.9i | 1.25913 | + | 0.663561i | ||||
\(635\) | −590.132 | − | 590.132i | −0.0368798 | − | 0.0368798i | ||||
\(636\) | −10187.4 | + | 6981.13i | −0.635151 | + | 0.435251i | ||||
\(637\) | 24419.5 | − | 24419.5i | 1.51889 | − | 1.51889i | ||||
\(638\) | 1287.17 | + | 4155.40i | 0.0798742 | + | 0.257859i | ||||
\(639\) | −8025.45 | −0.496842 | ||||||||
\(640\) | 1183.28 | + | 306.545i | 0.0730833 | + | 0.0189332i | ||||
\(641\) | 18341.0 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(642\) | −1997.39 | − | 6448.20i | −0.122789 | − | 0.396402i | ||||
\(643\) | 7026.21 | − | 7026.21i | 0.430928 | − | 0.430928i | −0.458016 | − | 0.888944i | \(-0.651440\pi\) |
0.888944 | + | 0.458016i | \(0.151440\pi\) | |||||||
\(644\) | 13475.8 | − | 9234.59i | 0.824567 | − | 0.565052i | ||||
\(645\) | 286.383 | + | 286.383i | 0.0174827 | + | 0.0174827i | ||||
\(646\) | −16830.1 | − | 8869.45i | −1.02504 | − | 0.540192i | ||||
\(647\) | 21429.7i | 1.30215i | 0.759015 | + | 0.651073i | \(0.225681\pi\) | ||||
−0.759015 | + | 0.651073i | \(0.774319\pi\) | |||||||
\(648\) | 2723.77 | + | 2156.31i | 0.165123 | + | 0.130722i | ||||
\(649\) | − | 7879.56i | − | 0.476579i | ||||||
\(650\) | −11256.6 | + | 21359.9i | −0.679263 | + | 1.28893i | ||||
\(651\) | 511.613 | + | 511.613i | 0.0308014 | + | 0.0308014i | ||||
\(652\) | −3889.39 | + | 20826.4i | −0.233620 | + | 1.25096i | ||||
\(653\) | 8681.22 | − | 8681.22i | 0.520248 | − | 0.520248i | −0.397398 | − | 0.917646i | \(-0.630087\pi\) |
0.917646 | + | 0.397398i | \(0.130087\pi\) | |||||||
\(654\) | −10170.5 | + | 3150.40i | −0.608099 | + | 0.188364i | ||||
\(655\) | −947.284 | −0.0565091 | ||||||||
\(656\) | 9148.37 | + | 3540.44i | 0.544488 | + | 0.210718i | ||||
\(657\) | 7170.92 | 0.425821 | ||||||||
\(658\) | −7855.90 | + | 2433.44i | −0.465433 | + | 0.144172i | ||||
\(659\) | −4151.60 | + | 4151.60i | −0.245407 | + | 0.245407i | −0.819083 | − | 0.573675i | \(-0.805517\pi\) |
0.573675 | + | 0.819083i | \(0.305517\pi\) | |||||||
\(660\) | 319.396 | + | 59.6480i | 0.0188371 | + | 0.00351787i | ||||
\(661\) | 12239.0 | + | 12239.0i | 0.720182 | + | 0.720182i | 0.968642 | − | 0.248460i | \(-0.0799244\pi\) |
−0.248460 | + | 0.968642i | \(0.579924\pi\) | |||||||
\(662\) | −3386.23 | + | 6425.52i | −0.198806 | + | 0.377243i | ||||
\(663\) | 16707.9i | 0.978706i | ||||||||
\(664\) | 30104.1 | − | 3500.52i | 1.75944 | − | 0.204588i | ||||
\(665\) | − | 1903.98i | − | 0.111027i | ||||||
\(666\) | 1470.03 | + | 774.704i | 0.0855294 | + | 0.0450738i | ||||
\(667\) | −4451.75 | − | 4451.75i | −0.258429 | − | 0.258429i | ||||
\(668\) | −17420.5 | − | 25421.4i | −1.00901 | − | 1.47243i | ||||
\(669\) | −8559.23 | + | 8559.23i | −0.494647 | + | 0.494647i | ||||
\(670\) | −564.725 | − | 1823.11i | −0.0325631 | − | 0.105124i | ||||
\(671\) | −8.22827 | −0.000473396 | ||||||||
\(672\) | −9699.26 | − | 11136.4i | −0.556782 | − | 0.639279i | ||||
\(673\) | 6528.62 | 0.373937 | 0.186969 | − | 0.982366i | \(-0.440134\pi\) | ||||
0.186969 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(674\) | −2245.65 | − | 7249.65i | −0.128337 | − | 0.414312i | ||||
\(675\) | 11372.8 | − | 11372.8i | 0.648500 | − | 0.648500i | ||||
\(676\) | 11397.3 | + | 16631.8i | 0.648458 | + | 0.946279i | ||||
\(677\) | −14220.6 | − | 14220.6i | −0.807299 | − | 0.807299i | 0.176925 | − | 0.984224i | \(-0.443385\pi\) |
−0.984224 | + | 0.176925i | \(0.943385\pi\) | |||||||
\(678\) | 12803.1 | + | 6747.21i | 0.725222 | + | 0.382190i | ||||
\(679\) | − | 11038.2i | − | 0.623867i | ||||||
\(680\) | 191.302 | + | 1645.18i | 0.0107884 | + | 0.0927790i | ||||
\(681\) | − | 2781.76i | − | 0.156530i | ||||||
\(682\) | 200.604 | − | 380.653i | 0.0112632 | − | 0.0213724i | ||||
\(683\) | 21419.5 | + | 21419.5i | 1.19999 | + | 1.19999i | 0.974167 | + | 0.225827i | \(0.0725084\pi\) |
0.225827 | + | 0.974167i | \(0.427492\pi\) | |||||||
\(684\) | 11668.9 | + | 2179.19i | 0.652295 | + | 0.121818i | ||||
\(685\) | 952.149 | − | 952.149i | 0.0531091 | − | 0.0531091i | ||||
\(686\) | −12557.3 | + | 3889.74i | −0.698891 | + | 0.216488i | ||||
\(687\) | −2631.60 | −0.146145 | ||||||||
\(688\) | −10012.9 | + | 4425.28i | −0.554851 | + | 0.245222i | ||||
\(689\) | −37797.0 | −2.08991 | ||||||||
\(690\) | −449.175 | + | 139.136i | −0.0247823 | + | 0.00767656i | ||||
\(691\) | −16537.1 | + | 16537.1i | −0.910423 | + | 0.910423i | −0.996305 | − | 0.0858818i | \(-0.972629\pi\) |
0.0858818 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(692\) | −5453.27 | + | 29200.5i | −0.299570 | + | 1.60410i | ||||
\(693\) | 6748.45 | + | 6748.45i | 0.369917 | + | 0.369917i | ||||
\(694\) | 9868.56 | − | 18726.0i | 0.539777 | − | 1.02425i | ||||
\(695\) | 331.484i | 0.0180920i | ||||||||
\(696\) | −3532.62 | + | 4462.27i | −0.192390 | + | 0.243020i | ||||
\(697\) | 13291.8i | 0.722331i | ||||||||
\(698\) | 260.830 | + | 137.457i | 0.0141441 | + | 0.00745390i | ||||
\(699\) | 6922.92 | + | 6922.92i | 0.374605 | + | 0.374605i | ||||
\(700\) | 23853.7 | − | 16346.2i | 1.28798 | − | 0.882614i | ||||
\(701\) | −3026.52 | + | 3026.52i | −0.163067 | + | 0.163067i | −0.783924 | − | 0.620857i | \(-0.786785\pi\) |
0.620857 | + | 0.783924i | \(0.286785\pi\) | |||||||
\(702\) | −7438.29 | − | 24013.1i | −0.399915 | − | 1.29105i | ||||
\(703\) | 2381.82 | 0.127784 | ||||||||
\(704\) | −4619.46 | + | 7469.39i | −0.247305 | + | 0.399877i | ||||
\(705\) | 236.728 | 0.0126464 | ||||||||
\(706\) | −4240.79 | − | 13690.6i | −0.226068 | − | 0.729819i | ||||
\(707\) | −11371.5 | + | 11371.5i | −0.604908 | + | 0.604908i | ||||
\(708\) | 8503.71 | − | 5827.35i | 0.451397 | − | 0.309330i | ||||
\(709\) | 3981.14 | + | 3981.14i | 0.210881 | + | 0.210881i | 0.804642 | − | 0.593761i | \(-0.202357\pi\) |
−0.593761 | + | 0.804642i | \(0.702357\pi\) | |||||||
\(710\) | 886.007 | + | 466.924i | 0.0468327 | + | 0.0246807i | ||||
\(711\) | − | 13501.7i | − | 0.712170i | ||||||
\(712\) | 66.4207 | − | 83.9001i | 0.00349610 | − | 0.00441614i | ||||
\(713\) | 622.710i | 0.0327078i | ||||||||
\(714\) | 9329.29 | − | 17702.7i | 0.488991 | − | 0.927881i | ||||
\(715\) | 703.160 | + | 703.160i | 0.0367786 | + | 0.0367786i | ||||
\(716\) | 2568.64 | − | 13754.3i | 0.134071 | − | 0.717906i | ||||
\(717\) | 5852.36 | − | 5852.36i | 0.304826 | − | 0.304826i | ||||
\(718\) | 2621.34 | − | 811.986i | 0.136250 | − | 0.0422048i | ||||
\(719\) | −5682.25 | −0.294732 | −0.147366 | − | 0.989082i | \(-0.547079\pi\) | ||||
−0.147366 | + | 0.989082i | \(0.547079\pi\) | |||||||
\(720\) | −417.767 | − | 945.262i | −0.0216240 | − | 0.0489275i | ||||
\(721\) | 8955.64 | 0.462587 | ||||||||
\(722\) | −2278.20 | + | 705.695i | −0.117432 | + | 0.0363757i | ||||
\(723\) | −2239.37 | + | 2239.37i | −0.115191 | + | 0.115191i | ||||
\(724\) | −17515.1 | − | 3271.00i | −0.899096 | − | 0.167908i | ||||
\(725\) | −7880.09 | − | 7880.09i | −0.403668 | − | 0.403668i | ||||
\(726\) | 3835.10 | − | 7277.27i | 0.196052 | − | 0.372017i | ||||
\(727\) | − | 18883.0i | − | 0.963317i | −0.876359 | − | 0.481658i | \(-0.840035\pi\) | ||
0.876359 | − | 0.481658i | \(-0.159965\pi\) | |||||||
\(728\) | −5220.45 | − | 44895.3i | −0.265773 | − | 2.28562i | ||||
\(729\) | 6863.99i | 0.348727i | ||||||||
\(730\) | −791.667 | − | 417.207i | −0.0401382 | − | 0.0211528i | ||||
\(731\) | −10488.8 | − | 10488.8i | −0.530698 | − | 0.530698i | ||||
\(732\) | −6.08524 | − | 8.88005i | −0.000307264 | − | 0.000448382i | ||||
\(733\) | −24962.5 | + | 24962.5i | −1.25786 | + | 1.25786i | −0.305748 | + | 0.952113i | \(0.598906\pi\) |
−0.952113 | + | 0.305748i | \(0.901094\pi\) | |||||||
\(734\) | 11257.5 | + | 36342.7i | 0.566105 | + | 1.82756i | ||||
\(735\) | 1190.54 | 0.0597467 | ||||||||
\(736\) | 874.596 | − | 12680.1i | 0.0438017 | − | 0.635045i | ||||
\(737\) | 13712.9 | 0.685375 | ||||||||
\(738\) | −2454.03 | − | 7922.38i | −0.122404 | − | 0.395159i | ||||
\(739\) | 6202.38 | − | 6202.38i | 0.308739 | − | 0.308739i | −0.535681 | − | 0.844420i | \(-0.679945\pi\) |
0.844420 | + | 0.535681i | \(0.179945\pi\) | |||||||
\(740\) | −117.218 | − | 171.054i | −0.00582302 | − | 0.00849739i | ||||
\(741\) | −10566.6 | − | 10566.6i | −0.523854 | − | 0.523854i | ||||
\(742\) | 40047.4 | + | 21104.9i | 1.98138 | + | 1.04418i | ||||
\(743\) | 30.9140i | 0.00152641i | 1.00000 | 0.000763205i | \(0.000242936\pi\) | |||||
−1.00000 | 0.000763205i | \(0.999757\pi\) | ||||||||
\(744\) | 559.163 | − | 65.0197i | 0.0275536 | − | 0.00320395i | ||||
\(745\) | 708.187i | 0.0348268i | ||||||||
\(746\) | −10999.4 | + | 20871.9i | −0.539837 | + | 1.02436i | ||||
\(747\) | −18118.8 | − | 18118.8i | −0.887459 | − | 0.887459i | ||||
\(748\) | −11697.9 | − | 2184.60i | −0.571813 | − | 0.106787i | ||||
\(749\) | −17496.5 | + | 17496.5i | −0.853547 | + | 0.853547i | ||||
\(750\) | −1594.74 | + | 493.985i | −0.0776421 | + | 0.0240504i | ||||
\(751\) | −16318.5 | −0.792905 | −0.396453 | − | 0.918055i | \(-0.629759\pi\) | ||||
−0.396453 | + | 0.918055i | \(0.629759\pi\) | |||||||
\(752\) | −2309.39 | + | 5967.38i | −0.111988 | + | 0.289372i | ||||
\(753\) | 18335.5 | 0.887361 | ||||||||
\(754\) | −16638.5 | + | 5153.93i | −0.803631 | + | 0.248932i | ||||
\(755\) | 95.8865 | − | 95.8865i | 0.00462208 | − | 0.00462208i | ||||
\(756\) | −5527.16 | + | 29596.2i | −0.265901 | + | 1.42381i | ||||
\(757\) | 9854.59 | + | 9854.59i | 0.473146 | + | 0.473146i | 0.902931 | − | 0.429786i | \(-0.141411\pi\) |
−0.429786 | + | 0.902931i | \(0.641411\pi\) | |||||||
\(758\) | 8292.59 | − | 15735.5i | 0.397362 | − | 0.754011i | ||||
\(759\) | − | 3378.57i | − | 0.161573i | ||||||
\(760\) | −1161.45 | − | 919.480i | −0.0554346 | − | 0.0438856i | ||||
\(761\) | − | 3823.42i | − | 0.182127i | −0.995845 | − | 0.0910637i | \(-0.970973\pi\) | ||
0.995845 | − | 0.0910637i | \(-0.0290267\pi\) | |||||||
\(762\) | 6940.21 | + | 3657.47i | 0.329944 | + | 0.173880i | ||||
\(763\) | 27596.4 | + | 27596.4i | 1.30938 | + | 1.30938i | ||||
\(764\) | −23664.2 | + | 16216.4i | −1.12060 | + | 0.767917i | ||||
\(765\) | 990.185 | − | 990.185i | 0.0467977 | − | 0.0467977i | ||||
\(766\) | −5370.96 | − | 17339.1i | −0.253343 | − | 0.817870i | ||||
\(767\) | 31550.2 | 1.48528 | ||||||||
\(768\) | −11477.4 | + | 538.634i | −0.539264 | + | 0.0253076i | ||||
\(769\) | 31689.1 | 1.48601 | 0.743003 | − | 0.669288i | \(-0.233401\pi\) | ||||
0.743003 | + | 0.669288i | \(0.233401\pi\) | |||||||
\(770\) | −352.399 | − | 1137.65i | −0.0164930 | − | 0.0532444i | ||||
\(771\) | 1211.91 | − | 1211.91i | 0.0566094 | − | 0.0566094i | ||||
\(772\) | −3455.34 | + | 2367.85i | −0.161089 | + | 0.110390i | ||||
\(773\) | −1305.84 | − | 1305.84i | −0.0607604 | − | 0.0607604i | 0.676074 | − | 0.736834i | \(-0.263680\pi\) |
−0.736834 | + | 0.676074i | \(0.763680\pi\) | |||||||
\(774\) | 8188.15 | + | 4315.14i | 0.380254 | + | 0.200393i | ||||
\(775\) | 1102.27i | 0.0510898i | ||||||||
\(776\) | −6733.44 | − | 5330.62i | −0.311490 | − | 0.246596i | ||||
\(777\) | 2505.31i | 0.115672i | ||||||||
\(778\) | −12225.4 | + | 23198.2i | −0.563370 | + | 1.06902i | ||||
\(779\) | −8406.21 | − | 8406.21i | −0.386629 | − | 0.386629i | ||||
\(780\) | −238.834 | + | 1278.88i | −0.0109636 | + | 0.0587069i | ||||
\(781\) | −5088.18 | + | 5088.18i | −0.233123 | + | 0.233123i | ||||
\(782\) | 16451.0 | − | 5095.85i | 0.752285 | − | 0.233027i | ||||
\(783\) | 11603.0 | 0.529577 | ||||||||
\(784\) | −11614.3 | + | 30011.0i | −0.529077 | + | 1.36712i | ||||
\(785\) | 842.465 | 0.0383043 | ||||||||
\(786\) | 8505.73 | − | 2634.73i | 0.385992 | − | 0.119565i | ||||
\(787\) | 14399.5 | − | 14399.5i | 0.652209 | − | 0.652209i | −0.301316 | − | 0.953524i | \(-0.597426\pi\) |
0.953524 | + | 0.301316i | \(0.0974258\pi\) | |||||||
\(788\) | 12518.7 | + | 2337.90i | 0.565939 | + | 0.105691i | ||||
\(789\) | −9865.37 | − | 9865.37i | −0.445141 | − | 0.445141i | ||||
\(790\) | −785.533 | + | 1490.58i | −0.0353772 | + | 0.0671297i | ||||
\(791\) | − | 53047.6i | − | 2.38452i | ||||||
\(792\) | 7375.65 | − | 857.645i | 0.330912 | − | 0.0384786i | ||||
\(793\) | − | 32.9465i | − | 0.00147537i | ||||||
\(794\) | 31503.1 | + | 16602.1i | 1.40806 | + | 0.742047i | ||||
\(795\) | −921.374 | − | 921.374i | −0.0411041 | − | 0.0411041i | ||||
\(796\) | −10457.6 | − | 15260.5i | −0.465653 | − | 0.679516i | ||||
\(797\) | −5572.19 | + | 5572.19i | −0.247650 | + | 0.247650i | −0.820006 | − | 0.572356i | \(-0.806030\pi\) |
0.572356 | + | 0.820006i | \(0.306030\pi\) | |||||||
\(798\) | 5295.63 | + | 17095.9i | 0.234916 | + | 0.758383i | ||||
\(799\) | −8670.13 | −0.383889 | ||||||||
\(800\) | 1548.13 | − | 22445.1i | 0.0684184 | − | 0.991944i | ||||
\(801\) | −90.4737 | −0.00399093 | ||||||||
\(802\) | −5377.73 | − | 17361.0i | −0.236776 | − | 0.764386i | ||||
\(803\) | 4546.40 | − | 4546.40i | 0.199800 | − | 0.199800i | ||||
\(804\) | 10141.4 | + | 14799.1i | 0.444851 | + | 0.649160i | ||||
\(805\) | 1218.79 | + | 1218.79i | 0.0533622 | + | 0.0533622i | ||||
\(806\) | 1524.16 | + | 803.229i | 0.0666082 | + | 0.0351024i | ||||
\(807\) | 3722.81i | 0.162390i | ||||||||
\(808\) | 1445.18 | + | 12428.4i | 0.0629224 | + | 0.541126i | ||||
\(809\) | − | 5081.28i | − | 0.220826i | −0.993886 | − | 0.110413i | \(-0.964783\pi\) | ||
0.993886 | − | 0.110413i | \(-0.0352174\pi\) | |||||||
\(810\) | −170.886 | + | 324.263i | −0.00741275 | + | 0.0140660i | ||||
\(811\) | 4493.19 | + | 4493.19i | 0.194546 | + | 0.194546i | 0.797657 | − | 0.603111i | \(-0.206072\pi\) |
−0.603111 | + | 0.797657i | \(0.706072\pi\) | |||||||
\(812\) | 20507.0 | + | 3829.72i | 0.886272 | + | 0.165513i | ||||
\(813\) | −7955.35 | + | 7955.35i | −0.343181 | + | 0.343181i | ||||
\(814\) | 1423.17 | − | 440.842i | 0.0612804 | − | 0.0189822i | ||||
\(815\) | −2235.36 | −0.0960752 | ||||||||
\(816\) | −6293.54 | − | 14240.1i | −0.269997 | − | 0.610911i | ||||
\(817\) | 13266.9 | 0.568114 | ||||||||
\(818\) | −34571.8 | + | 10709.0i | −1.47772 | + | 0.457738i | ||||
\(819\) | −27021.2 | + | 27021.2i | −1.15287 | + | 1.15287i | ||||
\(820\) | −190.003 | + | 1017.41i | −0.00809169 | + | 0.0433284i | ||||
\(821\) | 2115.54 | + | 2115.54i | 0.0899304 | + | 0.0899304i | 0.750641 | − | 0.660710i | \(-0.229745\pi\) |
−0.660710 | + | 0.750641i | \(0.729745\pi\) | |||||||
\(822\) | −5901.15 | + | 11197.7i | −0.250397 | + | 0.475138i | ||||
\(823\) | − | 24432.6i | − | 1.03483i | −0.855734 | − | 0.517416i | \(-0.826894\pi\) | ||
0.855734 | − | 0.517416i | \(-0.173106\pi\) | |||||||
\(824\) | 4324.92 | − | 5463.07i | 0.182847 | − | 0.230965i | ||||
\(825\) | − | 5980.44i | − | 0.252378i | ||||||
\(826\) | −33428.7 | − | 17616.9i | −1.40815 | − | 0.742094i | ||||
\(827\) | 21051.4 | + | 21051.4i | 0.885162 | + | 0.885162i | 0.994054 | − | 0.108892i | \(-0.0347302\pi\) |
−0.108892 | + | 0.994054i | \(0.534730\pi\) | |||||||
\(828\) | −8864.51 | + | 6074.60i | −0.372057 | + | 0.254960i | ||||
\(829\) | 25442.0 | − | 25442.0i | 1.06591 | − | 1.06591i | 0.0682392 | − | 0.997669i | \(-0.478262\pi\) |
0.997669 | − | 0.0682392i | \(-0.0217381\pi\) | |||||||
\(830\) | 946.150 | + | 3054.47i | 0.0395679 | + | 0.127737i | ||||
\(831\) | −14023.7 | −0.585413 | ||||||||
\(832\) | −29907.9 | − | 18496.6i | −1.24624 | − | 0.770738i | ||||
\(833\) | −43603.5 | −1.81365 | ||||||||
\(834\) | −921.974 | − | 2976.42i | −0.0382798 | − | 0.123579i | ||||
\(835\) | 2299.17 | − | 2299.17i | 0.0952889 | − | 0.0952889i | ||||
\(836\) | 8779.74 | − | 6016.51i | 0.363222 | − | 0.248906i | ||||
\(837\) | −811.516 | − | 811.516i | −0.0335127 | − | 0.0335127i | ||||
\(838\) | −23161.4 | − | 12206.0i | −0.954770 | − | 0.503162i | ||||
\(839\) | 18757.2i | 0.771837i | 0.922533 | + | 0.385919i | \(0.126115\pi\) | ||||
−0.922533 | + | 0.385919i | \(0.873885\pi\) | |||||||
\(840\) | 967.151 | − | 1221.67i | 0.0397260 | − | 0.0501804i | ||||
\(841\) | 16349.4i | 0.670358i | ||||||||
\(842\) | 11916.6 | − | 22612.2i | 0.487734 | − | 0.925495i | ||||
\(843\) | −14813.9 | − | 14813.9i | −0.605242 | − | 0.605242i | ||||
\(844\) | −2946.35 | + | 15776.8i | −0.120163 | + | 0.643434i | ||||
\(845\) | −1504.22 | + | 1504.22i | −0.0612389 | + | 0.0612389i | ||||
\(846\) | 5167.68 | − | 1600.74i | 0.210010 | − | 0.0650527i | ||||
\(847\) | −30152.2 | −1.22319 | ||||||||
\(848\) | 32214.2 | − | 14237.4i | 1.30453 | − | 0.576549i | ||||
\(849\) | −8922.94 | −0.360700 | ||||||||
\(850\) | 29120.1 | − | 9020.23i | 1.17507 | − | 0.363990i | ||||
\(851\) | −1524.67 | + | 1524.67i | −0.0614160 | + | 0.0614160i | ||||
\(852\) | −9254.20 | − | 1728.24i | −0.372117 | − | 0.0694937i | ||||
\(853\) | −6100.17 | − | 6100.17i | −0.244860 | − | 0.244860i | 0.573997 | − | 0.818857i | \(-0.305392\pi\) |
−0.818857 | + | 0.573997i | \(0.805392\pi\) | |||||||
\(854\) | −18.3965 | + | 34.9081i | −0.000737138 | + | 0.00139875i | ||||
\(855\) | 1252.45i | 0.0500971i | ||||||||
\(856\) | 2223.58 | + | 19122.6i | 0.0887857 | + | 0.763548i | ||||
\(857\) | − | 2079.04i | − | 0.0828687i | −0.999141 | − | 0.0414344i | \(-0.986807\pi\) | ||
0.999141 | − | 0.0414344i | \(-0.0131927\pi\) | |||||||
\(858\) | −8269.46 | − | 4357.99i | −0.329038 | − | 0.173402i | ||||
\(859\) | 8301.95 | + | 8301.95i | 0.329754 | + | 0.329754i | 0.852493 | − | 0.522739i | \(-0.175090\pi\) |
−0.522739 | + | 0.852493i | \(0.675090\pi\) | |||||||
\(860\) | −652.913 | − | 952.779i | −0.0258885 | − | 0.0377785i | ||||
\(861\) | 8842.03 | − | 8842.03i | 0.349983 | − | 0.349983i | ||||
\(862\) | −8904.02 | − | 28744.9i | −0.351824 | − | 1.13580i | ||||
\(863\) | 43830.8 | 1.72887 | 0.864436 | − | 0.502743i | \(-0.167676\pi\) | ||||
0.864436 | + | 0.502743i | \(0.167676\pi\) | |||||||
\(864\) | 15384.9 | + | 17664.4i | 0.605792 | + | 0.695551i | ||||
\(865\) | −3134.18 | −0.123197 | ||||||||
\(866\) | 3185.36 | + | 10283.3i | 0.124992 | + | 0.403512i | ||||
\(867\) | 5171.62 | − | 5171.62i | 0.202581 | − | 0.202581i | ||||
\(868\) | −1166.40 | − | 1702.11i | −0.0456110 | − | 0.0665590i | ||||
\(869\) | −8560.14 | − | 8560.14i | −0.334158 | − | 0.334158i | ||||
\(870\) | −531.231 | − | 279.958i | −0.0207016 | − | 0.0109097i | ||||
\(871\) | 54907.3i | 2.13601i | ||||||||
\(872\) | 30161.3 | − | 3507.17i | 1.17132 | − | 0.136201i | ||||
\(873\) | 7261.01i | 0.281498i | ||||||||
\(874\) | −7181.38 | + | 13627.0i | −0.277933 | + | 0.527390i | ||||
\(875\) | 4327.14 | + | 4327.14i | 0.167182 | + | 0.167182i | ||||
\(876\) | 8268.83 | + | 1544.22i | 0.318925 | + | 0.0595599i | ||||
\(877\) | −2565.89 | + | 2565.89i | −0.0987958 | + | 0.0987958i | −0.754777 | − | 0.655981i | \(-0.772255\pi\) |
0.655981 | + | 0.754777i | \(0.272255\pi\) | |||||||
\(878\) | −38102.6 | + | 11802.6i | −1.46458 | + | 0.453667i | ||||
\(879\) | −15681.2 | −0.601723 | ||||||||
\(880\) | −864.168 | − | 334.435i | −0.0331035 | − | 0.0128111i | ||||
\(881\) | 26429.8 | 1.01072 | 0.505360 | − | 0.862909i | \(-0.331360\pi\) | ||||
0.505360 | + | 0.862909i | \(0.331360\pi\) | |||||||
\(882\) | 25989.1 | − | 8050.39i | 0.992177 | − | 0.307336i | ||||
\(883\) | −20708.4 | + | 20708.4i | −0.789232 | + | 0.789232i | −0.981368 | − | 0.192136i | \(-0.938458\pi\) |
0.192136 | + | 0.981368i | \(0.438458\pi\) | |||||||
\(884\) | 8747.29 | − | 46839.0i | 0.332809 | − | 1.78209i | ||||
\(885\) | 769.097 | + | 769.097i | 0.0292123 | + | 0.0292123i | ||||
\(886\) | 14289.5 | − | 27114.9i | 0.541835 | − | 1.02815i | ||||
\(887\) | 22350.0i | 0.846042i | 0.906120 | + | 0.423021i | \(0.139030\pi\) | ||||
−0.906120 | + | 0.423021i | \(0.860970\pi\) | |||||||
\(888\) | 1528.27 | + | 1209.88i | 0.0577540 | + | 0.0457218i | ||||
\(889\) | − | 28755.6i | − | 1.08485i | ||||||
\(890\) | 9.98827 | + | 5.26380i | 0.000376188 | + | 0.000198250i | ||||
\(891\) | −1862.19 | − | 1862.19i | −0.0700175 | − | 0.0700175i | ||||
\(892\) | 28476.0 | − | 19513.8i | 1.06889 | − | 0.732479i | ||||
\(893\) | 5483.28 | − | 5483.28i | 0.205477 | − | 0.205477i | ||||
\(894\) | −1969.72 | − | 6358.86i | −0.0736882 | − | 0.237888i | ||||
\(895\) | 1476.28 | 0.0551360 | ||||||||
\(896\) | 21360.6 | + | 36297.7i | 0.796435 | + | 1.35337i | ||||
\(897\) | 13528.0 | 0.503553 | ||||||||
\(898\) | 11448.3 | + | 36958.6i | 0.425428 | + | 1.37341i | ||||
\(899\) | −562.292 | + | 562.292i | −0.0208604 | + | 0.0208604i | ||||
\(900\) | −15691.2 | + | 10752.7i | −0.581155 | + | 0.398249i | ||||
\(901\) | 33745.2 | + | 33745.2i | 1.24774 | + | 1.24774i | ||||
\(902\) | −6578.71 | − | 3466.96i | −0.242846 | − | 0.127979i | ||||
\(903\) | 13954.7i | 0.514267i | ||||||||
\(904\) | −32359.8 | − | 25618.1i | −1.19056 | − | 0.942528i | ||||
\(905\) | − | 1879.95i | − | 0.0690516i | ||||||
\(906\) | −594.278 | + | 1127.67i | −0.0217920 | + | 0.0413512i | ||||
\(907\) | −4086.93 | − | 4086.93i | −0.149619 | − | 0.149619i | 0.628329 | − | 0.777948i | \(-0.283739\pi\) |
−0.777948 | + | 0.628329i | \(0.783739\pi\) | |||||||
\(908\) | −1456.37 | + | 7798.38i | −0.0532282 | + | 0.285020i | ||||
\(909\) | 7480.29 | − | 7480.29i | 0.272944 | − | 0.272944i | ||||
\(910\) | 4555.23 | − | 1411.03i | 0.165939 | − | 0.0514012i | ||||
\(911\) | −20024.6 | −0.728259 | −0.364130 | − | 0.931348i | \(-0.618633\pi\) | ||||
−0.364130 | + | 0.931348i | \(0.618633\pi\) | |||||||
\(912\) | 12986.2 | + | 5025.67i | 0.471508 | + | 0.182474i | ||||
\(913\) | −22974.8 | −0.832810 | ||||||||
\(914\) | −21380.5 | + | 6622.80i | −0.773745 | + | 0.239675i | ||||
\(915\) | 0.803134 | − | 0.803134i | 2.90173e−5 | − | 2.90173e-5i | ||||
\(916\) | 7377.42 | + | 1377.75i | 0.266110 | + | 0.0496967i | ||||
\(917\) | −23079.3 | − | 23079.3i | −0.831131 | − | 0.831131i | ||||
\(918\) | −14798.0 | + | 28079.9i | −0.532035 | + | 1.00956i | ||||
\(919\) | 26977.7i | 0.968349i | 0.874971 | + | 0.484175i | \(0.160880\pi\) | ||||
−0.874971 | + | 0.484175i | \(0.839120\pi\) | |||||||
\(920\) | 1332.06 | − | 154.893i | 0.0477356 | − | 0.00555072i | ||||
\(921\) | 15294.2i | 0.547189i | ||||||||
\(922\) | −2053.19 | − | 1082.03i | −0.0733388 | − | 0.0386494i | ||||
\(923\) | −20373.4 | − | 20373.4i | −0.726542 | − | 0.726542i | ||||
\(924\) | 6328.43 | + | 9234.93i | 0.225314 | + | 0.328795i | ||||
\(925\) | −2698.84 | + | 2698.84i | −0.0959321 | + | 0.0959321i | ||||
\(926\) | 11914.5 | + | 38463.7i | 0.422824 | + | 1.36501i | ||||
\(927\) | −5891.10 | −0.208726 | ||||||||
\(928\) | 12239.5 | − | 10660.1i | 0.432955 | − | 0.377084i | ||||
\(929\) | −34371.4 | −1.21387 | −0.606937 | − | 0.794750i | \(-0.707602\pi\) | ||||
−0.606937 | + | 0.794750i | \(0.707602\pi\) | |||||||
\(930\) | 17.5741 | + | 56.7345i | 0.000619652 | + | 0.00200043i | ||||
\(931\) | 27576.3 | − | 27576.3i | 0.970760 | − | 0.970760i | ||||
\(932\) | −15783.3 | − | 23032.2i | −0.554719 | − | 0.809489i | ||||
\(933\) | 10303.4 | + | 10303.4i | 0.361541 | + | 0.361541i | ||||
\(934\) | −29528.7 | − | 15561.6i | −1.03449 | − | 0.545172i | ||||
\(935\) | − | 1255.57i | − | 0.0439159i | ||||||
\(936\) | 3434.06 | + | 29532.6i | 0.119921 | + | 1.03131i | ||||
\(937\) | − | 32901.8i | − | 1.14712i | −0.819163 | − | 0.573561i | \(-0.805561\pi\) | ||
0.819163 | − | 0.573561i | \(-0.194439\pi\) | |||||||
\(938\) | 30658.9 | − | 58176.5i | 1.06722 | − | 2.02508i | ||||
\(939\) | −9342.60 | − | 9342.60i | −0.324690 | − | 0.324690i | ||||
\(940\) | −663.642 | − | 123.937i | −0.0230273 | − | 0.00430039i | ||||
\(941\) | 33381.6 | − | 33381.6i | 1.15644 | − | 1.15644i | 0.171204 | − | 0.985236i | \(-0.445234\pi\) |
0.985236 | − | 0.171204i | \(-0.0547656\pi\) | |||||||
\(942\) | −7564.56 | + | 2343.19i | −0.261642 | + | 0.0810460i | ||||
\(943\) | 10762.1 | 0.371646 | ||||||||
\(944\) | −26890.2 | + | 11884.3i | −0.927119 | + | 0.409749i | ||||
\(945\) | −3176.65 | −0.109351 | ||||||||
\(946\) | 7927.15 | − | 2455.51i | 0.272446 | − | 0.0843928i | ||||
\(947\) | 13611.9 | − | 13611.9i | 0.467084 | − | 0.467084i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(948\) | 2907.53 | − | 15568.9i | 0.0996119 | − | 0.533390i | ||||
\(949\) | 18204.1 | + | 18204.1i | 0.622686 | + | 0.622686i | ||||
\(950\) | −12711.8 | + | 24121.2i | −0.434133 | + | 0.823785i | ||||
\(951\) | − | 22534.1i | − | 0.768369i | ||||||
\(952\) | −35421.8 | + | 44743.5i | −1.20591 | + | 1.52326i | ||||
\(953\) | − | 4572.49i | − | 0.155422i | −0.996976 | − | 0.0777112i | \(-0.975239\pi\) | ||
0.996976 | − | 0.0777112i | \(-0.0247612\pi\) | |||||||
\(954\) | −26343.6 | − | 13883.0i | −0.894029 | − | 0.471152i | ||||
\(955\) | −2140.25 | − | 2140.25i | −0.0725202 | − | 0.0725202i | ||||
\(956\) | −19470.5 | + | 13342.6i | −0.658703 | + | 0.451390i | ||||
\(957\) | 3050.77 | − | 3050.77i | 0.103048 | − | 0.103048i | ||||
\(958\) | −4656.32 | − | 15032.1i | −0.157034 | − | 0.506956i | ||||
\(959\) | 46395.7 | 1.56225 | ||||||||
\(960\) | −278.172 | − | 1179.95i | −0.00935204 | − | 0.0396696i | ||||
\(961\) | −29712.3 | −0.997360 | ||||||||
\(962\) | 1765.16 | + | 5698.48i | 0.0591590 | + | 0.190984i | ||||
\(963\) | 11509.3 | − | 11509.3i | 0.385133 | − | 0.385133i | ||||
\(964\) | 7450.24 | − | 5105.44i | 0.248917 | − | 0.170576i | ||||
\(965\) | −312.510 | − | 312.510i | −0.0104249 | − | 0.0104249i | ||||
\(966\) | −14333.4 | − | 7553.70i | −0.477403 | − | 0.251590i | ||||
\(967\) | − | 33060.9i | − | 1.09945i | −0.835346 | − | 0.549725i | \(-0.814732\pi\) | ||
0.835346 | − | 0.549725i | \(-0.185268\pi\) | |||||||
\(968\) | −14561.3 | + | 18393.3i | −0.483489 | + | 0.610725i | ||||
\(969\) | 18867.9i | 0.625514i | ||||||||
\(970\) | 422.448 | − | 801.613i | 0.0139835 | − | 0.0265343i | ||||
\(971\) | −15553.4 | − | 15553.4i | −0.514041 | − | 0.514041i | 0.401721 | − | 0.915762i | \(-0.368412\pi\) |
−0.915762 | + | 0.401721i | \(0.868412\pi\) | |||||||
\(972\) | 5763.83 | − | 30863.5i | 0.190200 | − | 1.01846i | ||||
\(973\) | −8076.18 | + | 8076.18i | −0.266095 | + | 0.266095i | ||||
\(974\) | 49038.6 | − | 15190.2i | 1.61324 | − | 0.499717i | ||||
\(975\) | 23946.1 | 0.786551 | ||||||||
\(976\) | 12.4103 | + | 28.0802i | 0.000407012 | + | 0.000920928i | ||||
\(977\) | 1241.54 | 0.0406555 | 0.0203277 | − | 0.999793i | \(-0.493529\pi\) | ||||
0.0203277 | + | 0.999793i | \(0.493529\pi\) | |||||||
\(978\) | 20071.5 | − | 6217.33i | 0.656252 | − | 0.203280i | ||||
\(979\) | −57.3608 | + | 57.3608i | −0.00187258 | + | 0.00187258i | ||||
\(980\) | −3337.57 | − | 623.299i | −0.108790 | − | 0.0203169i | ||||
\(981\) | −18153.2 | − | 18153.2i | −0.590812 | − | 0.590812i | ||||
\(982\) | −21619.6 | + | 41024.0i | −0.702554 | + | 1.33312i | ||||
\(983\) | 10797.7i | 0.350349i | 0.984537 | + | 0.175175i | \(0.0560490\pi\) | ||||
−0.984537 | + | 0.175175i | \(0.943951\pi\) | |||||||
\(984\) | −1123.71 | − | 9663.82i | −0.0364052 | − | 0.313081i | ||||
\(985\) | 1343.67i | 0.0434648i | ||||||||
\(986\) | 19456.3 | + | 10253.4i | 0.628413 | + | 0.331172i | ||||
\(987\) | 5767.56 | + | 5767.56i | 0.186001 | + | 0.186001i | ||||
\(988\) | 24090.5 | + | 35154.6i | 0.775728 | + | 1.13200i | ||||
\(989\) | −8492.49 | + | 8492.49i | −0.273049 | + | 0.273049i | ||||
\(990\) | 231.811 | + | 748.359i | 0.00744187 | + | 0.0240247i | ||||
\(991\) | −10204.8 | −0.327112 | −0.163556 | − | 0.986534i | \(-0.552296\pi\) | ||||
−0.163556 | + | 0.986534i | \(0.552296\pi\) | |||||||
\(992\) | −1601.60 | − | 110.469i | −0.0512608 | − | 0.00353567i | ||||
\(993\) | 7203.49 | 0.230207 | ||||||||
\(994\) | 10210.4 | + | 32962.4i | 0.325809 | + | 1.05181i | ||||
\(995\) | 1380.20 | − | 1380.20i | 0.0439752 | − | 0.0439752i | ||||
\(996\) | −16991.1 | − | 24794.7i | −0.540546 | − | 0.788805i | ||||
\(997\) | 15046.7 | + | 15046.7i | 0.477967 | + | 0.477967i | 0.904481 | − | 0.426514i | \(-0.140259\pi\) |
−0.426514 | + | 0.904481i | \(0.640259\pi\) | |||||||
\(998\) | 11003.8 | + | 5798.98i | 0.349017 | + | 0.183931i | ||||
\(999\) | − | 3973.90i | − | 0.125855i |
(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 | 16.4.e.a.5.4 | ✓ | 10 | |
3.2 | odd | 2 | 144.4.k.a.37.2 | 10 | |||
4.3 | odd | 2 | 64.4.e.a.49.2 | 10 | |||
8.3 | odd | 2 | 128.4.e.a.97.4 | 10 | |||
8.5 | even | 2 | 128.4.e.b.97.2 | 10 | |||
12.11 | even | 2 | 576.4.k.a.433.3 | 10 | |||
16.3 | odd | 4 | 64.4.e.a.17.2 | 10 | |||
16.5 | even | 4 | 128.4.e.b.33.2 | 10 | |||
16.11 | odd | 4 | 128.4.e.a.33.4 | 10 | |||
16.13 | even | 4 | inner | 16.4.e.a.13.4 | yes | 10 | |
32.3 | odd | 8 | 1024.4.a.m.1.4 | 10 | |||
32.5 | even | 8 | 1024.4.b.j.513.7 | 10 | |||
32.11 | odd | 8 | 1024.4.b.k.513.7 | 10 | |||
32.13 | even | 8 | 1024.4.a.n.1.4 | 10 | |||
32.19 | odd | 8 | 1024.4.a.m.1.7 | 10 | |||
32.21 | even | 8 | 1024.4.b.j.513.4 | 10 | |||
32.27 | odd | 8 | 1024.4.b.k.513.4 | 10 | |||
32.29 | even | 8 | 1024.4.a.n.1.7 | 10 | |||
48.29 | odd | 4 | 144.4.k.a.109.2 | 10 | |||
48.35 | even | 4 | 576.4.k.a.145.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
16.4.e.a.13.4 | yes | 10 | 16.13 | even | 4 | inner | |
64.4.e.a.17.2 | 10 | 16.3 | odd | 4 | |||
64.4.e.a.49.2 | 10 | 4.3 | odd | 2 | |||
128.4.e.a.33.4 | 10 | 16.11 | odd | 4 | |||
128.4.e.a.97.4 | 10 | 8.3 | odd | 2 | |||
128.4.e.b.33.2 | 10 | 16.5 | even | 4 | |||
128.4.e.b.97.2 | 10 | 8.5 | even | 2 | |||
144.4.k.a.37.2 | 10 | 3.2 | odd | 2 | |||
144.4.k.a.109.2 | 10 | 48.29 | odd | 4 | |||
576.4.k.a.145.3 | 10 | 48.35 | even | 4 | |||
576.4.k.a.433.3 | 10 | 12.11 | even | 2 | |||
1024.4.a.m.1.4 | 10 | 32.3 | odd | 8 | |||
1024.4.a.m.1.7 | 10 | 32.19 | odd | 8 | |||
1024.4.a.n.1.4 | 10 | 32.13 | even | 8 | |||
1024.4.a.n.1.7 | 10 | 32.29 | even | 8 | |||
1024.4.b.j.513.4 | 10 | 32.21 | even | 8 | |||
1024.4.b.j.513.7 | 10 | 32.5 | even | 8 | |||
1024.4.b.k.513.4 | 10 | 32.27 | odd | 8 | |||
1024.4.b.k.513.7 | 10 | 32.11 | odd | 8 |