Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), 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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(-1.65831 + 2.87228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.4.e.k.116.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15831 | + | 3.73831i | −0.763079 | + | 1.32169i | 0.178178 | + | 0.983998i | \(0.442980\pi\) |
−0.941256 | + | 0.337693i | \(0.890354\pi\) | |||||||
\(3\) | 2.50000 | + | 4.33013i | 0.481125 | + | 0.833333i | 0.999765 | − | 0.0216593i | \(-0.00689490\pi\) |
−0.518640 | + | 0.854993i | \(0.673562\pi\) | |||||||
\(4\) | −5.31662 | − | 9.20866i | −0.664578 | − | 1.15108i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | −21.5831 | −1.46855 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 11.3668 | 0.502344 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.0370370 | − | 0.0641500i | ||||
\(10\) | 10.7916 | + | 18.6915i | 0.341259 | + | 0.591078i | ||||
\(11\) | −9.86675 | − | 17.0897i | −0.270449 | − | 0.468431i | 0.698528 | − | 0.715583i | \(-0.253839\pi\) |
−0.968977 | + | 0.247152i | \(0.920505\pi\) | |||||||
\(12\) | 26.5831 | − | 46.0433i | 0.639491 | − | 1.10763i | ||||
\(13\) | −71.3325 | −1.52185 | −0.760926 | − | 0.648839i | \(-0.775255\pi\) | ||||
−0.760926 | + | 0.648839i | \(0.775255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.0000 | 0.430331 | ||||||||
\(16\) | 18.0000 | − | 31.1769i | 0.281250 | − | 0.487139i | ||||
\(17\) | −15.6662 | − | 27.1347i | −0.223507 | − | 0.387126i | 0.732363 | − | 0.680914i | \(-0.238417\pi\) |
−0.955871 | + | 0.293788i | \(0.905084\pi\) | |||||||
\(18\) | 4.31662 | + | 7.47661i | 0.0565243 | + | 0.0979030i | ||||
\(19\) | 68.1662 | − | 118.067i | 0.823074 | − | 1.42561i | −0.0803080 | − | 0.996770i | \(-0.525590\pi\) |
0.903382 | − | 0.428836i | \(-0.141076\pi\) | |||||||
\(20\) | −53.1662 | −0.594417 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 85.1821 | 0.825495 | ||||||||
\(23\) | 50.4327 | − | 87.3521i | 0.457215 | − | 0.791920i | −0.541597 | − | 0.840638i | \(-0.682180\pi\) |
0.998813 | + | 0.0487178i | \(0.0155135\pi\) | |||||||
\(24\) | 28.4169 | + | 49.2195i | 0.241690 | + | 0.418620i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 153.958 | − | 266.663i | 1.16129 | − | 2.01142i | ||||
\(27\) | 145.000 | 1.03353 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −288.198 | −1.84541 | −0.922707 | − | 0.385501i | \(-0.874029\pi\) | ||||
−0.922707 | + | 0.385501i | \(0.874029\pi\) | |||||||
\(30\) | −53.9578 | + | 93.4577i | −0.328377 | + | 0.568765i | ||||
\(31\) | −104.499 | − | 180.997i | −0.605436 | − | 1.04865i | −0.991982 | − | 0.126376i | \(-0.959665\pi\) |
0.386546 | − | 0.922270i | \(-0.373668\pi\) | |||||||
\(32\) | 123.166 | + | 213.330i | 0.680404 | + | 1.17849i | ||||
\(33\) | 49.3338 | − | 85.4486i | 0.260240 | − | 0.450748i | ||||
\(34\) | 135.251 | 0.682214 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −21.2665 | −0.0984560 | ||||||||
\(37\) | −154.966 | + | 268.409i | −0.688546 | + | 1.19260i | 0.283762 | + | 0.958895i | \(0.408417\pi\) |
−0.972308 | + | 0.233702i | \(0.924916\pi\) | |||||||
\(38\) | 294.248 | + | 509.653i | 1.25614 | + | 2.17570i | ||||
\(39\) | −178.331 | − | 308.879i | −0.732201 | − | 1.26821i | ||||
\(40\) | 28.4169 | − | 49.2195i | 0.112328 | − | 0.194557i | ||||
\(41\) | 181.662 | 0.691973 | 0.345987 | − | 0.938239i | \(-0.387544\pi\) | ||||
0.345987 | + | 0.938239i | \(0.387544\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18.2005 | −0.0645477 | −0.0322738 | − | 0.999479i | \(-0.510275\pi\) | ||||
−0.0322738 | + | 0.999479i | \(0.510275\pi\) | |||||||
\(44\) | −104.916 | + | 181.719i | −0.359469 | + | 0.622618i | ||||
\(45\) | −5.00000 | − | 8.66025i | −0.0165635 | − | 0.0286888i | ||||
\(46\) | 217.699 | + | 377.066i | 0.697783 | + | 1.20860i | ||||
\(47\) | −73.8325 | + | 127.882i | −0.229140 | + | 0.396882i | −0.957553 | − | 0.288256i | \(-0.906925\pi\) |
0.728414 | + | 0.685138i | \(0.240258\pi\) | |||||||
\(48\) | 180.000 | 0.541266 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 107.916 | 0.305231 | ||||||||
\(51\) | 78.3312 | − | 135.674i | 0.215070 | − | 0.372512i | ||||
\(52\) | 379.248 | + | 656.877i | 1.01139 | + | 1.75178i | ||||
\(53\) | 63.9975 | + | 110.847i | 0.165863 | + | 0.287283i | 0.936961 | − | 0.349433i | \(-0.113626\pi\) |
−0.771099 | + | 0.636716i | \(0.780292\pi\) | |||||||
\(54\) | −312.955 | + | 542.054i | −0.788663 | + | 1.36601i | ||||
\(55\) | −98.6675 | −0.241897 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 681.662 | 1.58401 | ||||||||
\(58\) | 622.021 | − | 1077.37i | 1.40820 | − | 2.43907i | ||||
\(59\) | 161.332 | + | 279.436i | 0.355995 | + | 0.616601i | 0.987288 | − | 0.158943i | \(-0.0508087\pi\) |
−0.631293 | + | 0.775545i | \(0.717475\pi\) | |||||||
\(60\) | −132.916 | − | 230.217i | −0.285989 | − | 0.495347i | ||||
\(61\) | 170.501 | − | 295.317i | 0.357876 | − | 0.619860i | −0.629730 | − | 0.776814i | \(-0.716834\pi\) |
0.987606 | + | 0.156955i | \(0.0501676\pi\) | |||||||
\(62\) | 902.164 | 1.84798 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −775.325 | −1.51431 | ||||||||
\(65\) | −178.331 | + | 308.879i | −0.340296 | + | 0.589411i | ||||
\(66\) | 212.955 | + | 368.849i | 0.397166 | + | 0.687912i | ||||
\(67\) | 42.1980 | + | 73.0891i | 0.0769449 | + | 0.133272i | 0.901930 | − | 0.431881i | \(-0.142150\pi\) |
−0.824986 | + | 0.565154i | \(0.808817\pi\) | |||||||
\(68\) | −166.583 | + | 288.530i | −0.297076 | + | 0.514551i | ||||
\(69\) | 504.327 | 0.879911 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −315.736 | −0.527760 | −0.263880 | − | 0.964555i | \(-0.585002\pi\) | ||||
−0.263880 | + | 0.964555i | \(0.585002\pi\) | |||||||
\(72\) | 11.3668 | − | 19.6878i | 0.0186053 | − | 0.0322254i | ||||
\(73\) | −546.662 | − | 946.847i | −0.876466 | − | 1.51808i | −0.855193 | − | 0.518310i | \(-0.826561\pi\) |
−0.0212727 | − | 0.999774i | \(-0.506772\pi\) | |||||||
\(74\) | −668.929 | − | 1158.62i | −1.05083 | − | 1.82009i | ||||
\(75\) | 62.5000 | − | 108.253i | 0.0962250 | − | 0.166667i | ||||
\(76\) | −1449.66 | −2.18799 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1539.58 | 2.23491 | ||||||||
\(79\) | −616.593 | + | 1067.97i | −0.878128 | + | 1.52096i | −0.0247348 | + | 0.999694i | \(0.507874\pi\) |
−0.853393 | + | 0.521268i | \(0.825459\pi\) | |||||||
\(80\) | −90.0000 | − | 155.885i | −0.125779 | − | 0.217855i | ||||
\(81\) | 335.500 | + | 581.103i | 0.460219 | + | 0.797124i | ||||
\(82\) | −392.084 | + | 679.110i | −0.528030 | + | 0.914575i | ||||
\(83\) | 643.325 | 0.850772 | 0.425386 | − | 0.905012i | \(-0.360138\pi\) | ||||
0.425386 | + | 0.905012i | \(0.360138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −156.662 | −0.199911 | ||||||||
\(86\) | 39.2824 | − | 68.0391i | 0.0492550 | − | 0.0853121i | ||||
\(87\) | −720.495 | − | 1247.93i | −0.887876 | − | 1.53785i | ||||
\(88\) | −112.153 | − | 194.255i | −0.135858 | − | 0.235314i | ||||
\(89\) | 570.159 | − | 987.544i | 0.679064 | − | 1.17617i | −0.296199 | − | 0.955126i | \(-0.595719\pi\) |
0.975263 | − | 0.221047i | \(-0.0709475\pi\) | |||||||
\(90\) | 43.1662 | 0.0505569 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1072.53 | −1.21542 | ||||||||
\(93\) | 522.494 | − | 904.986i | 0.582581 | − | 1.00906i | ||||
\(94\) | −318.707 | − | 552.017i | −0.349704 | − | 0.605704i | ||||
\(95\) | −340.831 | − | 590.337i | −0.368090 | − | 0.637551i | ||||
\(96\) | −615.831 | + | 1066.65i | −0.654719 | + | 1.13401i | ||||
\(97\) | −1411.99 | −1.47800 | −0.739001 | − | 0.673705i | \(-0.764702\pi\) | ||||
−0.739001 | + | 0.673705i | \(0.764702\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −39.4670 | −0.0400665 | ||||||||
\(100\) | −132.916 | + | 230.217i | −0.132916 | + | 0.230217i | ||||
\(101\) | −272.836 | − | 472.566i | −0.268794 | − | 0.465565i | 0.699756 | − | 0.714381i | \(-0.253292\pi\) |
−0.968551 | + | 0.248816i | \(0.919959\pi\) | |||||||
\(102\) | 338.127 | + | 585.652i | 0.328231 | + | 0.568512i | ||||
\(103\) | 390.495 | − | 676.357i | 0.373559 | − | 0.647024i | −0.616551 | − | 0.787315i | \(-0.711471\pi\) |
0.990110 | + | 0.140291i | \(0.0448039\pi\) | |||||||
\(104\) | −810.819 | −0.764493 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −552.506 | −0.506266 | ||||||||
\(107\) | 310.330 | − | 537.507i | 0.280381 | − | 0.485634i | −0.691098 | − | 0.722761i | \(-0.742873\pi\) |
0.971478 | + | 0.237128i | \(0.0762060\pi\) | |||||||
\(108\) | −770.911 | − | 1335.26i | −0.686860 | − | 1.18968i | ||||
\(109\) | −2.09397 | − | 3.62686i | −0.00184005 | − | 0.00318707i | 0.865104 | − | 0.501593i | \(-0.167252\pi\) |
−0.866944 | + | 0.498406i | \(0.833919\pi\) | |||||||
\(110\) | 212.955 | − | 368.849i | 0.184586 | − | 0.319713i | ||||
\(111\) | −1549.66 | −1.32511 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1413.53 | 1.17676 | 0.588379 | − | 0.808585i | \(-0.299766\pi\) | ||||
0.588379 | + | 0.808585i | \(0.299766\pi\) | |||||||
\(114\) | −1471.24 | + | 2548.26i | −1.20872 | + | 2.09357i | ||||
\(115\) | −252.164 | − | 436.760i | −0.204473 | − | 0.354158i | ||||
\(116\) | 1532.24 | + | 2653.92i | 1.22642 | + | 2.12423i | ||||
\(117\) | −71.3325 | + | 123.552i | −0.0563649 | + | 0.0976268i | ||||
\(118\) | −1392.82 | −1.08661 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 284.169 | 0.216175 | ||||||||
\(121\) | 470.794 | − | 815.440i | 0.353715 | − | 0.612652i | ||||
\(122\) | 735.990 | + | 1274.77i | 0.546175 | + | 0.946004i | ||||
\(123\) | 454.156 | + | 786.622i | 0.332926 | + | 0.576645i | ||||
\(124\) | −1111.16 | + | 1924.59i | −0.804720 | + | 1.39382i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2046.26 | −1.42974 | −0.714868 | − | 0.699259i | \(-0.753513\pi\) | ||||
−0.714868 | + | 0.699259i | \(0.753513\pi\) | |||||||
\(128\) | 688.063 | − | 1191.76i | 0.475131 | − | 0.822951i | ||||
\(129\) | −45.5013 | − | 78.8105i | −0.0310555 | − | 0.0537897i | ||||
\(130\) | −769.789 | − | 1333.31i | −0.519346 | − | 0.899533i | ||||
\(131\) | 570.159 | − | 987.544i | 0.380267 | − | 0.658642i | −0.610833 | − | 0.791759i | \(-0.709165\pi\) |
0.991100 | + | 0.133117i | \(0.0424987\pi\) | |||||||
\(132\) | −1049.16 | −0.691798 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −364.306 | −0.234860 | ||||||||
\(135\) | 362.500 | − | 627.868i | 0.231104 | − | 0.400284i | ||||
\(136\) | −178.074 | − | 308.434i | −0.112278 | − | 0.194470i | ||||
\(137\) | 245.171 | + | 424.649i | 0.152893 | + | 0.264819i | 0.932290 | − | 0.361712i | \(-0.117808\pi\) |
−0.779397 | + | 0.626531i | \(0.784474\pi\) | |||||||
\(138\) | −1088.50 | + | 1885.33i | −0.671442 | + | 1.16297i | ||||
\(139\) | −2800.00 | −1.70858 | −0.854291 | − | 0.519795i | \(-0.826008\pi\) | ||||
−0.854291 | + | 0.519795i | \(0.826008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −738.325 | −0.440980 | ||||||||
\(142\) | 681.457 | − | 1180.32i | 0.402723 | − | 0.697536i | ||||
\(143\) | 703.820 | + | 1219.05i | 0.411583 | + | 0.712883i | ||||
\(144\) | −36.0000 | − | 62.3538i | −0.0208333 | − | 0.0360844i | ||||
\(145\) | −720.495 | + | 1247.93i | −0.412647 | + | 0.714726i | ||||
\(146\) | 4719.47 | 2.67525 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3295.58 | 1.83037 | ||||||||
\(149\) | −583.058 | + | 1009.89i | −0.320577 | + | 0.555256i | −0.980607 | − | 0.195983i | \(-0.937210\pi\) |
0.660030 | + | 0.751239i | \(0.270544\pi\) | |||||||
\(150\) | 269.789 | + | 467.288i | 0.146855 | + | 0.254360i | ||||
\(151\) | −479.791 | − | 831.022i | −0.258575 | − | 0.447865i | 0.707285 | − | 0.706928i | \(-0.249920\pi\) |
−0.965860 | + | 0.259063i | \(0.916586\pi\) | |||||||
\(152\) | 774.829 | − | 1342.04i | 0.413467 | − | 0.716145i | ||||
\(153\) | −62.6650 | −0.0331122 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1044.99 | −0.541519 | ||||||||
\(156\) | −1896.24 | + | 3284.39i | −0.973210 | + | 1.68565i | ||||
\(157\) | −510.330 | − | 883.917i | −0.259419 | − | 0.449327i | 0.706667 | − | 0.707546i | \(-0.250198\pi\) |
−0.966086 | + | 0.258219i | \(0.916864\pi\) | |||||||
\(158\) | −2661.60 | − | 4610.03i | −1.34016 | − | 2.32123i | ||||
\(159\) | −319.987 | + | 554.234i | −0.159602 | + | 0.276438i | ||||
\(160\) | 1231.66 | 0.608572 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2896.46 | −1.40473 | ||||||||
\(163\) | 783.008 | − | 1356.21i | 0.376257 | − | 0.651696i | −0.614257 | − | 0.789106i | \(-0.710544\pi\) |
0.990514 | + | 0.137410i | \(0.0438777\pi\) | |||||||
\(164\) | −965.831 | − | 1672.87i | −0.459870 | − | 0.796519i | ||||
\(165\) | −246.669 | − | 427.243i | −0.116383 | − | 0.201581i | ||||
\(166\) | −1388.50 | + | 2404.95i | −0.649206 | + | 1.12446i | ||||
\(167\) | 1130.30 | 0.523746 | 0.261873 | − | 0.965102i | \(-0.415660\pi\) | ||||
0.261873 | + | 0.965102i | \(0.415660\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2891.32 | 1.31603 | ||||||||
\(170\) | 338.127 | − | 585.652i | 0.152548 | − | 0.264221i | ||||
\(171\) | −136.332 | − | 236.135i | −0.0609685 | − | 0.105600i | ||||
\(172\) | 96.7652 | + | 167.602i | 0.0428970 | + | 0.0742997i | ||||
\(173\) | 1271.67 | − | 2202.59i | 0.558862 | − | 0.967978i | −0.438729 | − | 0.898619i | \(-0.644571\pi\) |
0.997592 | − | 0.0693588i | \(-0.0220953\pi\) | |||||||
\(174\) | 6220.21 | 2.71008 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −710.406 | −0.304255 | ||||||||
\(177\) | −806.662 | + | 1397.18i | −0.342556 | + | 0.593325i | ||||
\(178\) | 2461.16 | + | 4262.86i | 1.03636 | + | 1.79503i | ||||
\(179\) | 605.325 | + | 1048.45i | 0.252760 | + | 0.437794i | 0.964285 | − | 0.264868i | \(-0.0853282\pi\) |
−0.711524 | + | 0.702661i | \(0.751995\pi\) | |||||||
\(180\) | −53.1662 | + | 92.0866i | −0.0220154 | + | 0.0381319i | ||||
\(181\) | 3031.32 | 1.24484 | 0.622421 | − | 0.782683i | \(-0.286149\pi\) | ||||
0.622421 | + | 0.782683i | \(0.286149\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1705.01 | 0.688733 | ||||||||
\(184\) | 573.256 | − | 992.909i | 0.229679 | − | 0.397817i | ||||
\(185\) | 774.829 | + | 1342.04i | 0.307927 | + | 0.533346i | ||||
\(186\) | 2255.41 | + | 3906.48i | 0.889111 | + | 1.53999i | ||||
\(187\) | −309.150 | + | 535.463i | −0.120895 | + | 0.209396i | ||||
\(188\) | 1570.16 | 0.609125 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2942.48 | 1.12353 | ||||||||
\(191\) | 1084.32 | − | 1878.10i | 0.410778 | − | 0.711488i | −0.584197 | − | 0.811612i | \(-0.698591\pi\) |
0.994975 | + | 0.100124i | \(0.0319239\pi\) | |||||||
\(192\) | −1938.31 | − | 3357.26i | −0.728571 | − | 1.26192i | ||||
\(193\) | −745.240 | − | 1290.79i | −0.277946 | − | 0.481416i | 0.692928 | − | 0.721006i | \(-0.256320\pi\) |
−0.970874 | + | 0.239590i | \(0.922987\pi\) | |||||||
\(194\) | 3047.52 | − | 5278.46i | 1.12783 | − | 1.95346i | ||||
\(195\) | −1783.31 | −0.654901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3380.57 | 1.22262 | 0.611308 | − | 0.791393i | \(-0.290644\pi\) | ||||
0.611308 | + | 0.791393i | \(0.290644\pi\) | |||||||
\(198\) | 85.1821 | − | 147.540i | 0.0305739 | − | 0.0529555i | ||||
\(199\) | 2297.66 | + | 3979.67i | 0.818478 | + | 1.41765i | 0.906803 | + | 0.421554i | \(0.138515\pi\) |
−0.0883251 | + | 0.996092i | \(0.528151\pi\) | |||||||
\(200\) | −142.084 | − | 246.097i | −0.0502344 | − | 0.0870086i | ||||
\(201\) | −210.990 | + | 365.445i | −0.0740402 | + | 0.128241i | ||||
\(202\) | 2355.46 | 0.820445 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1665.83 | −0.571723 | ||||||||
\(205\) | 454.156 | − | 786.622i | 0.154730 | − | 0.268000i | ||||
\(206\) | 1685.62 | + | 2919.58i | 0.570110 | + | 0.987460i | ||||
\(207\) | −100.865 | − | 174.704i | −0.0338678 | − | 0.0586608i | ||||
\(208\) | −1283.98 | + | 2223.93i | −0.428021 | + | 0.741354i | ||||
\(209\) | −2690.32 | −0.890398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4988.66 | −1.62765 | −0.813824 | − | 0.581112i | \(-0.802618\pi\) | ||||
−0.813824 | + | 0.581112i | \(0.802618\pi\) | |||||||
\(212\) | 680.501 | − | 1178.66i | 0.220458 | − | 0.381844i | ||||
\(213\) | −789.340 | − | 1367.18i | −0.253919 | − | 0.439800i | ||||
\(214\) | 1339.58 | + | 2320.22i | 0.427905 | + | 0.741153i | ||||
\(215\) | −45.5013 | + | 78.8105i | −0.0144333 | + | 0.0249992i | ||||
\(216\) | 1648.18 | 0.519187 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.0778 | 0.00561643 | ||||||||
\(219\) | 2733.31 | − | 4734.24i | 0.843380 | − | 1.46078i | ||||
\(220\) | 524.578 | + | 908.596i | 0.160759 | + | 0.278443i | ||||
\(221\) | 1117.51 | + | 1935.59i | 0.340145 | + | 0.589148i | ||||
\(222\) | 3344.64 | − | 5793.09i | 1.01116 | − | 1.75138i | ||||
\(223\) | −3792.97 | −1.13900 | −0.569498 | − | 0.821993i | \(-0.692862\pi\) | ||||
−0.569498 | + | 0.821993i | \(0.692862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −50.0000 | −0.0148148 | ||||||||
\(226\) | −3050.84 | + | 5284.21i | −0.897960 | + | 1.55531i | ||||
\(227\) | 1955.48 | + | 3386.99i | 0.571762 | + | 0.990320i | 0.996385 | + | 0.0849504i | \(0.0270732\pi\) |
−0.424623 | + | 0.905370i | \(0.639593\pi\) | |||||||
\(228\) | −3624.14 | − | 6277.20i | −1.05270 | − | 1.82332i | ||||
\(229\) | 177.164 | − | 306.857i | 0.0511236 | − | 0.0885487i | −0.839331 | − | 0.543621i | \(-0.817053\pi\) |
0.890455 | + | 0.455072i | \(0.150386\pi\) | |||||||
\(230\) | 2176.99 | 0.624116 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3275.87 | −0.927033 | ||||||||
\(233\) | −3246.24 | + | 5622.65i | −0.912739 | + | 1.58091i | −0.102561 | + | 0.994727i | \(0.532704\pi\) |
−0.810178 | + | 0.586184i | \(0.800630\pi\) | |||||||
\(234\) | −307.916 | − | 533.325i | −0.0860217 | − | 0.148994i | ||||
\(235\) | 369.162 | + | 639.408i | 0.102474 | + | 0.177491i | ||||
\(236\) | 1715.49 | − | 2971.31i | 0.473173 | − | 0.819559i | ||||
\(237\) | −6165.93 | −1.68996 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −342.688 | −0.0927474 | −0.0463737 | − | 0.998924i | \(-0.514766\pi\) | ||||
−0.0463737 | + | 0.998924i | \(0.514766\pi\) | |||||||
\(240\) | 450.000 | − | 779.423i | 0.121031 | − | 0.209631i | ||||
\(241\) | 1156.83 | + | 2003.69i | 0.309204 | + | 0.535557i | 0.978189 | − | 0.207719i | \(-0.0666040\pi\) |
−0.668984 | + | 0.743277i | \(0.733271\pi\) | |||||||
\(242\) | 2032.24 | + | 3519.95i | 0.539825 | + | 0.935003i | ||||
\(243\) | 280.000 | − | 484.974i | 0.0739177 | − | 0.128029i | ||||
\(244\) | −3625.96 | −0.951347 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3920.84 | −1.01619 | ||||||||
\(247\) | −4862.47 | + | 8422.04i | −1.25260 | + | 2.16956i | ||||
\(248\) | −1187.81 | − | 2057.35i | −0.304137 | − | 0.526781i | ||||
\(249\) | 1608.31 | + | 2785.68i | 0.409328 | + | 0.708977i | ||||
\(250\) | 269.789 | − | 467.288i | 0.0682518 | − | 0.118216i | ||||
\(251\) | −3989.29 | −1.00319 | −0.501597 | − | 0.865101i | \(-0.667254\pi\) | ||||
−0.501597 | + | 0.865101i | \(0.667254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1990.43 | −0.494614 | ||||||||
\(254\) | 4416.48 | − | 7649.56i | 1.09100 | − | 1.88967i | ||||
\(255\) | −391.656 | − | 678.368i | −0.0961822 | − | 0.166592i | ||||
\(256\) | −131.188 | − | 227.224i | −0.0320283 | − | 0.0554747i | ||||
\(257\) | 1145.66 | − | 1984.34i | 0.278071 | − | 0.481633i | −0.692834 | − | 0.721097i | \(-0.743638\pi\) |
0.970905 | + | 0.239463i | \(0.0769715\pi\) | |||||||
\(258\) | 392.824 | 0.0947912 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3792.48 | 0.904614 | ||||||||
\(261\) | −288.198 | + | 499.174i | −0.0683487 | + | 0.118383i | ||||
\(262\) | 2461.16 | + | 4262.86i | 0.580348 | + | 1.00519i | ||||
\(263\) | −3180.24 | − | 5508.33i | −0.745634 | − | 1.29148i | −0.949898 | − | 0.312560i | \(-0.898813\pi\) |
0.204264 | − | 0.978916i | \(-0.434520\pi\) | |||||||
\(264\) | 560.764 | − | 971.273i | 0.130730 | − | 0.226431i | ||||
\(265\) | 639.975 | 0.148352 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5701.59 | 1.30686 | ||||||||
\(268\) | 448.702 | − | 777.174i | 0.102272 | − | 0.177140i | ||||
\(269\) | −495.673 | − | 858.530i | −0.112348 | − | 0.194593i | 0.804368 | − | 0.594131i | \(-0.202504\pi\) |
−0.916717 | + | 0.399538i | \(0.869171\pi\) | |||||||
\(270\) | 1564.78 | + | 2710.27i | 0.352701 | + | 0.610896i | ||||
\(271\) | 365.489 | − | 633.045i | 0.0819257 | − | 0.141899i | −0.822151 | − | 0.569269i | \(-0.807226\pi\) |
0.904077 | + | 0.427370i | \(0.140560\pi\) | |||||||
\(272\) | −1127.97 | −0.251446 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2116.62 | −0.466679 | ||||||||
\(275\) | −246.669 | + | 427.243i | −0.0540898 | + | 0.0936862i | ||||
\(276\) | −2681.32 | − | 4644.18i | −0.584770 | − | 1.01285i | ||||
\(277\) | 1769.31 | + | 3064.54i | 0.383783 | + | 0.664731i | 0.991600 | − | 0.129346i | \(-0.0412878\pi\) |
−0.607817 | + | 0.794077i | \(0.707954\pi\) | |||||||
\(278\) | 6043.27 | − | 10467.3i | 1.30378 | − | 2.25822i | ||||
\(279\) | −417.995 | −0.0896943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4663.20 | −0.989975 | −0.494988 | − | 0.868900i | \(-0.664827\pi\) | ||||
−0.494988 | + | 0.868900i | \(0.664827\pi\) | |||||||
\(282\) | 1593.54 | − | 2760.09i | 0.336502 | − | 0.582839i | ||||
\(283\) | −1052.47 | − | 1822.94i | −0.221071 | − | 0.382906i | 0.734062 | − | 0.679082i | \(-0.237622\pi\) |
−0.955134 | + | 0.296176i | \(0.904289\pi\) | |||||||
\(284\) | 1678.65 | + | 2907.51i | 0.350738 | + | 0.607496i | ||||
\(285\) | 1704.16 | − | 2951.69i | 0.354195 | − | 0.613483i | ||||
\(286\) | −6076.25 | −1.25628 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 492.665 | 0.100801 | ||||||||
\(289\) | 1965.64 | − | 3404.58i | 0.400089 | − | 0.692975i | ||||
\(290\) | −3110.11 | − | 5386.86i | −0.629765 | − | 1.09078i | ||||
\(291\) | −3529.98 | − | 6114.11i | −0.711104 | − | 1.23167i | ||||
\(292\) | −5812.80 | + | 10068.1i | −1.16496 | + | 2.01777i | ||||
\(293\) | 6594.66 | 1.31489 | 0.657447 | − | 0.753501i | \(-0.271636\pi\) | ||||
0.657447 | + | 0.753501i | \(0.271636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1613.32 | 0.318412 | ||||||||
\(296\) | −1761.46 | + | 3050.93i | −0.345887 | + | 0.599094i | ||||
\(297\) | −1430.68 | − | 2478.01i | −0.279517 | − | 0.484137i | ||||
\(298\) | −2516.84 | − | 4359.30i | −0.489251 | − | 0.847408i | ||||
\(299\) | −3597.49 | + | 6231.04i | −0.695814 | + | 1.20519i | ||||
\(300\) | −1329.16 | −0.255796 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4142.15 | 0.789252 | ||||||||
\(303\) | 1364.18 | − | 2362.83i | 0.258647 | − | 0.447990i | ||||
\(304\) | −2453.98 | − | 4250.43i | −0.462979 | − | 0.801904i | ||||
\(305\) | −852.506 | − | 1476.58i | −0.160047 | − | 0.277210i | ||||
\(306\) | 135.251 | − | 234.261i | 0.0252672 | − | 0.0437641i | ||||
\(307\) | 2672.97 | 0.496920 | 0.248460 | − | 0.968642i | \(-0.420076\pi\) | ||||
0.248460 | + | 0.968642i | \(0.420076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3904.95 | 0.718915 | ||||||||
\(310\) | 2255.41 | − | 3906.48i | 0.413221 | − | 0.715721i | ||||
\(311\) | −427.849 | − | 741.056i | −0.0780099 | − | 0.135117i | 0.824381 | − | 0.566035i | \(-0.191523\pi\) |
−0.902391 | + | 0.430918i | \(0.858190\pi\) | |||||||
\(312\) | −2027.05 | − | 3510.95i | −0.367817 | − | 0.637078i | ||||
\(313\) | −1674.99 | + | 2901.17i | −0.302480 | + | 0.523911i | −0.976697 | − | 0.214622i | \(-0.931148\pi\) |
0.674217 | + | 0.738533i | \(0.264481\pi\) | |||||||
\(314\) | 4405.81 | 0.791828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13112.8 | 2.33434 | ||||||||
\(317\) | −3816.53 | + | 6610.42i | −0.676206 | + | 1.17122i | 0.299908 | + | 0.953968i | \(0.403044\pi\) |
−0.976115 | + | 0.217256i | \(0.930289\pi\) | |||||||
\(318\) | −1381.27 | − | 2392.42i | −0.243577 | − | 0.421888i | ||||
\(319\) | 2843.58 | + | 4925.22i | 0.499090 | + | 0.864450i | ||||
\(320\) | −1938.31 | + | 3357.26i | −0.338609 | + | 0.586488i | ||||
\(321\) | 3103.30 | 0.539593 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4271.64 | −0.735852 | ||||||||
\(324\) | 3567.46 | − | 6179.01i | 0.611704 | − | 1.05950i | ||||
\(325\) | 891.656 | + | 1544.39i | 0.152185 | + | 0.263592i | ||||
\(326\) | 3379.95 | + | 5854.24i | 0.574227 | + | 0.994591i | ||||
\(327\) | 10.4698 | − | 18.1343i | 0.00177059 | − | 0.00306676i | ||||
\(328\) | 2064.91 | 0.347609 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2129.55 | 0.355236 | ||||||||
\(331\) | 1660.85 | − | 2876.68i | 0.275796 | − | 0.477693i | −0.694539 | − | 0.719455i | \(-0.744392\pi\) |
0.970336 | + | 0.241761i | \(0.0777251\pi\) | |||||||
\(332\) | −3420.32 | − | 5924.16i | −0.565405 | − | 0.979309i | ||||
\(333\) | 309.931 | + | 536.817i | 0.0510034 | + | 0.0883405i | ||||
\(334\) | −2439.55 | + | 4225.43i | −0.399660 | + | 0.692231i | ||||
\(335\) | 421.980 | 0.0688216 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2233.98 | −0.361107 | −0.180553 | − | 0.983565i | \(-0.557789\pi\) | ||||
−0.180553 | + | 0.983565i | \(0.557789\pi\) | |||||||
\(338\) | −6240.38 | + | 10808.7i | −1.00424 | + | 1.73939i | ||||
\(339\) | 3533.83 | + | 6120.77i | 0.566168 | + | 0.980632i | ||||
\(340\) | 832.916 | + | 1442.65i | 0.132856 | + | 0.230114i | ||||
\(341\) | −2062.13 | + | 3571.71i | −0.327479 | + | 0.567211i | ||||
\(342\) | 1176.99 | 0.186095 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −206.881 | −0.0324252 | ||||||||
\(345\) | 1260.82 | − | 2183.80i | 0.196754 | − | 0.340788i | ||||
\(346\) | 5489.32 | + | 9507.78i | 0.852912 | + | 1.47729i | ||||
\(347\) | −1264.31 | − | 2189.84i | −0.195595 | − | 0.338781i | 0.751500 | − | 0.659733i | \(-0.229330\pi\) |
−0.947095 | + | 0.320952i | \(0.895997\pi\) | |||||||
\(348\) | −7661.20 | + | 13269.6i | −1.18013 | + | 2.04404i | ||||
\(349\) | −1291.00 | −0.198011 | −0.0990054 | − | 0.995087i | \(-0.531566\pi\) | ||||
−0.0990054 | + | 0.995087i | \(0.531566\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10343.2 | −1.57288 | ||||||||
\(352\) | 2430.50 | − | 4209.75i | 0.368029 | − | 0.637445i | ||||
\(353\) | −3884.32 | − | 6727.84i | −0.585670 | − | 1.01441i | −0.994792 | − | 0.101930i | \(-0.967498\pi\) |
0.409121 | − | 0.912480i | \(-0.365835\pi\) | |||||||
\(354\) | −3482.06 | − | 6031.10i | −0.522795 | − | 0.905507i | ||||
\(355\) | −789.340 | + | 1367.18i | −0.118011 | + | 0.204401i | ||||
\(356\) | −12125.3 | −1.80516 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5225.92 | −0.771504 | ||||||||
\(359\) | 1142.07 | − | 1978.12i | 0.167900 | − | 0.290811i | −0.769781 | − | 0.638308i | \(-0.779635\pi\) |
0.937681 | + | 0.347496i | \(0.112968\pi\) | |||||||
\(360\) | −56.8338 | − | 98.4389i | −0.00832056 | − | 0.0144116i | ||||
\(361\) | −5863.77 | − | 10156.4i | −0.854902 | − | 1.48073i | ||||
\(362\) | −6542.54 | + | 11332.0i | −0.949912 | + | 1.64530i | ||||
\(363\) | 4707.94 | 0.680725 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5466.62 | −0.783935 | ||||||||
\(366\) | −3679.95 | + | 6373.86i | −0.525558 | + | 0.910292i | ||||
\(367\) | 5353.50 | + | 9272.54i | 0.761446 | + | 1.31886i | 0.942105 | + | 0.335317i | \(0.108843\pi\) |
−0.180660 | + | 0.983546i | \(0.557823\pi\) | |||||||
\(368\) | −1815.58 | − | 3144.67i | −0.257184 | − | 0.445455i | ||||
\(369\) | 181.662 | − | 314.649i | 0.0256286 | − | 0.0443901i | ||||
\(370\) | −6689.29 | −0.939891 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11111.6 | −1.54868 | ||||||||
\(373\) | 415.215 | − | 719.173i | 0.0576381 | − | 0.0998321i | −0.835767 | − | 0.549085i | \(-0.814976\pi\) |
0.893405 | + | 0.449253i | \(0.148310\pi\) | |||||||
\(374\) | −1334.48 | − | 2311.39i | −0.184504 | − | 0.319570i | ||||
\(375\) | −312.500 | − | 541.266i | −0.0430331 | − | 0.0745356i | ||||
\(376\) | −839.236 | + | 1453.60i | −0.115107 | + | 0.199371i | ||||
\(377\) | 20557.9 | 2.80845 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5253.17 | 0.711972 | 0.355986 | − | 0.934491i | \(-0.384145\pi\) | ||||
0.355986 | + | 0.934491i | \(0.384145\pi\) | |||||||
\(380\) | −3624.14 | + | 6277.20i | −0.489249 | + | 0.847404i | ||||
\(381\) | −5115.66 | − | 8860.58i | −0.687882 | − | 1.19145i | ||||
\(382\) | 4680.60 | + | 8107.03i | 0.626911 | + | 1.08584i | ||||
\(383\) | −5621.95 | + | 9737.51i | −0.750048 | + | 1.29912i | 0.197750 | + | 0.980252i | \(0.436636\pi\) |
−0.947799 | + | 0.318869i | \(0.896697\pi\) | |||||||
\(384\) | 6880.63 | 0.914390 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6433.84 | 0.848378 | ||||||||
\(387\) | −18.2005 | + | 31.5242i | −0.00239066 | + | 0.00414074i | ||||
\(388\) | 7507.03 | + | 13002.6i | 0.982247 | + | 1.70130i | ||||
\(389\) | 4253.43 | + | 7367.15i | 0.554389 | + | 0.960230i | 0.997951 | + | 0.0639860i | \(0.0203813\pi\) |
−0.443562 | + | 0.896244i | \(0.646285\pi\) | |||||||
\(390\) | 3848.95 | − | 6666.57i | 0.499741 | − | 0.865576i | ||||
\(391\) | −3160.37 | −0.408764 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5701.59 | 0.731824 | ||||||||
\(394\) | −7296.32 | + | 12637.6i | −0.932952 | + | 1.61592i | ||||
\(395\) | 3082.96 | + | 5339.85i | 0.392711 | + | 0.680195i | ||||
\(396\) | 209.831 | + | 363.438i | 0.0266273 | + | 0.0461199i | ||||
\(397\) | 1561.62 | − | 2704.80i | 0.197419 | − | 0.341940i | −0.750272 | − | 0.661130i | \(-0.770077\pi\) |
0.947691 | + | 0.319190i | \(0.103411\pi\) | |||||||
\(398\) | −19836.3 | −2.49825 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −900.000 | −0.112500 | ||||||||
\(401\) | 5627.67 | − | 9747.40i | 0.700828 | − | 1.21387i | −0.267348 | − | 0.963600i | \(-0.586147\pi\) |
0.968176 | − | 0.250270i | \(-0.0805195\pi\) | |||||||
\(402\) | −910.764 | − | 1577.49i | −0.112997 | − | 0.195717i | ||||
\(403\) | 7454.16 | + | 12911.0i | 0.921385 | + | 1.59588i | ||||
\(404\) | −2901.14 | + | 5024.92i | −0.357270 | + | 0.618809i | ||||
\(405\) | 3355.00 | 0.411633 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6116.03 | 0.744866 | ||||||||
\(408\) | 890.372 | − | 1542.17i | 0.108039 | − | 0.187129i | ||||
\(409\) | −3959.96 | − | 6858.86i | −0.478747 | − | 0.829214i | 0.520956 | − | 0.853584i | \(-0.325576\pi\) |
−0.999703 | + | 0.0243694i | \(0.992242\pi\) | |||||||
\(410\) | 1960.42 | + | 3395.55i | 0.236142 | + | 0.409010i | ||||
\(411\) | −1225.86 | + | 2123.25i | −0.147122 | + | 0.254822i | ||||
\(412\) | −8304.46 | −0.993037 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 870.797 | 0.103375 | ||||||||
\(415\) | 1608.31 | − | 2785.68i | 0.190238 | − | 0.329503i | ||||
\(416\) | −8785.76 | − | 15217.4i | −1.03547 | − | 1.79349i | ||||
\(417\) | −7000.00 | − | 12124.4i | −0.822042 | − | 1.42382i | ||||
\(418\) | 5806.55 | − | 10057.2i | 0.679444 | − | 1.17683i | ||||
\(419\) | 5257.28 | 0.612972 | 0.306486 | − | 0.951875i | \(-0.400847\pi\) | ||||
0.306486 | + | 0.951875i | \(0.400847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1457.36 | 0.168711 | 0.0843556 | − | 0.996436i | \(-0.473117\pi\) | ||||
0.0843556 | + | 0.996436i | \(0.473117\pi\) | |||||||
\(422\) | 10767.1 | − | 18649.2i | 1.24202 | − | 2.15125i | ||||
\(423\) | 147.665 | + | 255.763i | 0.0169733 | + | 0.0293987i | ||||
\(424\) | 727.443 | + | 1259.97i | 0.0833202 | + | 0.144315i | ||||
\(425\) | −391.656 | + | 678.368i | −0.0447014 | + | 0.0774252i | ||||
\(426\) | 6814.57 | 0.775040 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6599.63 | −0.745339 | ||||||||
\(429\) | −3519.10 | + | 6095.26i | −0.396046 | + | 0.685972i | ||||
\(430\) | −196.412 | − | 340.195i | −0.0220275 | − | 0.0381527i | ||||
\(431\) | 7645.59 | + | 13242.6i | 0.854467 | + | 1.47998i | 0.877139 | + | 0.480237i | \(0.159449\pi\) |
−0.0226716 | + | 0.999743i | \(0.507217\pi\) | |||||||
\(432\) | 2610.00 | − | 4520.65i | 0.290680 | − | 0.503472i | ||||
\(433\) | −187.260 | −0.0207832 | −0.0103916 | − | 0.999946i | \(-0.503308\pi\) | ||||
−0.0103916 | + | 0.999946i | \(0.503308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7204.95 | −0.794140 | ||||||||
\(436\) | −22.2657 | + | 38.5653i | −0.00244572 | + | 0.00423611i | ||||
\(437\) | −6875.62 | − | 11908.9i | −0.752644 | − | 1.30362i | ||||
\(438\) | 11798.7 | + | 20435.9i | 1.28713 | + | 2.22937i | ||||
\(439\) | 1793.96 | − | 3107.23i | 0.195037 | − | 0.337813i | −0.751876 | − | 0.659305i | \(-0.770851\pi\) |
0.946912 | + | 0.321491i | \(0.104184\pi\) | |||||||
\(440\) | −1121.53 | −0.121515 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9647.76 | −1.03823 | ||||||||
\(443\) | −2457.82 | + | 4257.08i | −0.263600 | + | 0.456568i | −0.967196 | − | 0.254032i | \(-0.918243\pi\) |
0.703596 | + | 0.710600i | \(0.251577\pi\) | |||||||
\(444\) | 8238.95 | + | 14270.3i | 0.880638 | + | 1.52531i | ||||
\(445\) | −2850.79 | − | 4937.72i | −0.303687 | − | 0.526001i | ||||
\(446\) | 8186.41 | − | 14179.3i | 0.869143 | − | 1.50540i | ||||
\(447\) | −5830.58 | −0.616951 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7091.12 | 0.745324 | 0.372662 | − | 0.927967i | \(-0.378445\pi\) | ||||
0.372662 | + | 0.927967i | \(0.378445\pi\) | |||||||
\(450\) | 107.916 | − | 186.915i | 0.0113049 | − | 0.0195806i | ||||
\(451\) | −1792.42 | − | 3104.56i | −0.187143 | − | 0.324142i | ||||
\(452\) | −7515.21 | − | 13016.7i | −0.782048 | − | 1.35455i | ||||
\(453\) | 2398.95 | − | 4155.11i | 0.248814 | − | 0.430958i | ||||
\(454\) | −16882.2 | −1.74520 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7748.29 | 0.795717 | ||||||||
\(457\) | −2525.91 | + | 4375.00i | −0.258549 | + | 0.447820i | −0.965853 | − | 0.259089i | \(-0.916578\pi\) |
0.707304 | + | 0.706909i | \(0.249911\pi\) | |||||||
\(458\) | 764.749 | + | 1324.58i | 0.0780227 | + | 0.135139i | ||||
\(459\) | −2271.61 | − | 3934.54i | −0.231001 | − | 0.400106i | ||||
\(460\) | −2681.32 | + | 4644.18i | −0.271776 | + | 0.470731i | ||||
\(461\) | 16681.3 | 1.68531 | 0.842653 | − | 0.538456i | \(-0.180992\pi\) | ||||
0.842653 | + | 0.538456i | \(0.180992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15569.6 | 1.56280 | 0.781402 | − | 0.624027i | \(-0.214505\pi\) | ||||
0.781402 | + | 0.624027i | \(0.214505\pi\) | |||||||
\(464\) | −5187.56 | + | 8985.12i | −0.519023 | + | 0.898974i | ||||
\(465\) | −2612.47 | − | 4524.93i | −0.260538 | − | 0.451266i | ||||
\(466\) | −14012.8 | − | 24270.9i | −1.39298 | − | 2.41272i | ||||
\(467\) | 1664.18 | − | 2882.44i | 0.164901 | − | 0.285617i | −0.771719 | − | 0.635964i | \(-0.780603\pi\) |
0.936620 | + | 0.350346i | \(0.113936\pi\) | |||||||
\(468\) | 1516.99 | 0.149835 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3187.07 | −0.312784 | ||||||||
\(471\) | 2551.65 | − | 4419.59i | 0.249626 | − | 0.432365i | ||||
\(472\) | 1833.83 | + | 3176.28i | 0.178832 | + | 0.309746i | ||||
\(473\) | 179.580 | + | 311.041i | 0.0174568 | + | 0.0302361i | ||||
\(474\) | 13308.0 | − | 23050.1i | 1.28957 | − | 2.23360i | ||||
\(475\) | −3408.31 | −0.329230 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 255.990 | 0.0245723 | ||||||||
\(478\) | 739.627 | − | 1281.07i | 0.0707735 | − | 0.122583i | ||||
\(479\) | −7303.75 | − | 12650.5i | −0.696695 | − | 1.20671i | −0.969606 | − | 0.244672i | \(-0.921320\pi\) |
0.272911 | − | 0.962039i | \(-0.412014\pi\) | |||||||
\(480\) | 3079.16 | + | 5333.25i | 0.292799 | + | 0.507143i | ||||
\(481\) | 11054.1 | − | 19146.3i | 1.04787 | − | 1.81496i | ||||
\(482\) | −9987.23 | −0.943789 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10012.2 | −0.940285 | ||||||||
\(485\) | −3529.98 | + | 6114.11i | −0.330491 | + | 0.572427i | ||||
\(486\) | 1208.65 | + | 2093.45i | 0.112810 | + | 0.195393i | ||||
\(487\) | 939.744 | + | 1627.68i | 0.0874412 | + | 0.151453i | 0.906429 | − | 0.422359i | \(-0.138798\pi\) |
−0.818988 | + | 0.573811i | \(0.805464\pi\) | |||||||
\(488\) | 1938.05 | − | 3356.79i | 0.179777 | − | 0.311383i | ||||
\(489\) | 7830.08 | 0.724107 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3221.13 | 0.296064 | 0.148032 | − | 0.988983i | \(-0.452706\pi\) | ||||
0.148032 | + | 0.988983i | \(0.452706\pi\) | |||||||
\(492\) | 4829.16 | − | 8364.34i | 0.442511 | − | 0.766451i | ||||
\(493\) | 4514.98 | + | 7820.18i | 0.412464 | + | 0.714408i | ||||
\(494\) | −20989.5 | − | 36354.8i | −1.91166 | − | 3.31109i | ||||
\(495\) | −98.6675 | + | 170.897i | −0.00895914 | + | 0.0155177i | ||||
\(496\) | −7523.91 | −0.681116 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13885.0 | −1.24940 | ||||||||
\(499\) | −4856.91 | + | 8412.41i | −0.435721 | + | 0.754692i | −0.997354 | − | 0.0726950i | \(-0.976840\pi\) |
0.561633 | + | 0.827387i | \(0.310173\pi\) | |||||||
\(500\) | 664.578 | + | 1151.08i | 0.0594417 | + | 0.102956i | ||||
\(501\) | 2825.76 | + | 4894.36i | 0.251988 | + | 0.436455i | ||||
\(502\) | 8610.13 | − | 14913.2i | 0.765516 | − | 1.32591i | ||||
\(503\) | −2078.32 | −0.184230 | −0.0921152 | − | 0.995748i | \(-0.529363\pi\) | ||||
−0.0921152 | + | 0.995748i | \(0.529363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2728.36 | −0.240417 | ||||||||
\(506\) | 4295.97 | − | 7440.84i | 0.377429 | − | 0.653726i | ||||
\(507\) | 7228.31 | + | 12519.8i | 0.633177 | + | 1.09669i | ||||
\(508\) | 10879.2 | + | 18843.4i | 0.950172 | + | 1.64575i | ||||
\(509\) | −9487.23 | + | 16432.4i | −0.826158 | + | 1.43095i | 0.0748736 | + | 0.997193i | \(0.476145\pi\) |
−0.901031 | + | 0.433754i | \(0.857189\pi\) | |||||||
\(510\) | 3381.27 | 0.293578 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 12141.6 | 1.04802 | ||||||||
\(513\) | 9884.11 | − | 17119.8i | 0.850670 | − | 1.47340i | ||||
\(514\) | 4945.38 | + | 8565.66i | 0.424380 | + | 0.735048i | ||||
\(515\) | −1952.47 | − | 3381.79i | −0.167061 | − | 0.289358i | ||||
\(516\) | −483.826 | + | 838.012i | −0.0412776 | + | 0.0714950i | ||||
\(517\) | 2913.95 | 0.247883 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12716.7 | 1.07553 | ||||||||
\(520\) | −2027.05 | + | 3510.95i | −0.170946 | + | 0.296087i | ||||
\(521\) | 8761.78 | + | 15175.9i | 0.736777 | + | 1.27613i | 0.953939 | + | 0.299999i | \(0.0969865\pi\) |
−0.217163 | + | 0.976135i | \(0.569680\pi\) | |||||||
\(522\) | −1244.04 | − | 2154.74i | −0.104311 | − | 0.180672i | ||||
\(523\) | 7609.29 | − | 13179.7i | 0.636197 | − | 1.10193i | −0.350063 | − | 0.936726i | \(-0.613840\pi\) |
0.986260 | − | 0.165199i | \(-0.0528268\pi\) | |||||||
\(524\) | −12125.3 | −1.01087 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27455.8 | 2.27591 | ||||||||
\(527\) | −3274.21 | + | 5671.09i | −0.270639 | + | 0.468760i | ||||
\(528\) | −1776.02 | − | 3076.15i | −0.146385 | − | 0.253546i | ||||
\(529\) | 996.576 | + | 1726.12i | 0.0819081 | + | 0.141869i | ||||
\(530\) | −1381.27 | + | 2392.42i | −0.113204 | + | 0.196076i | ||||
\(531\) | 645.330 | 0.0527400 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12958.4 | −1.05308 | ||||||||
\(534\) | −12305.8 | + | 21314.3i | −0.997237 | + | 1.72726i | ||||
\(535\) | −1551.65 | − | 2687.54i | −0.125390 | − | 0.217182i | ||||
\(536\) | 479.654 | + | 830.785i | 0.0386528 | + | 0.0669486i | ||||
\(537\) | −3026.62 | + | 5242.27i | −0.243219 | + | 0.421267i | ||||
\(538\) | 4279.26 | 0.342922 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7709.11 | −0.614346 | ||||||||
\(541\) | 7779.63 | − | 13474.7i | 0.618249 | − | 1.07084i | −0.371557 | − | 0.928410i | \(-0.621176\pi\) |
0.989805 | − | 0.142428i | \(-0.0454909\pi\) | |||||||
\(542\) | 1577.68 | + | 2732.62i | 0.125031 | + | 0.216561i | ||||
\(543\) | 7578.30 | + | 13126.0i | 0.598924 | + | 1.03737i | ||||
\(544\) | 3859.11 | − | 6684.17i | 0.304150 | − | 0.526804i | ||||
\(545\) | −20.9397 | −0.00164579 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8690.70 | −0.679319 | −0.339660 | − | 0.940548i | \(-0.610312\pi\) | ||||
−0.339660 | + | 0.940548i | \(0.610312\pi\) | |||||||
\(548\) | 2606.97 | − | 4515.40i | 0.203219 | − | 0.351986i | ||||
\(549\) | −341.003 | − | 590.634i | −0.0265093 | − | 0.0459155i | ||||
\(550\) | −1064.78 | − | 1844.25i | −0.0825495 | − | 0.142980i | ||||
\(551\) | −19645.4 | + | 34026.8i | −1.51891 | + | 2.63083i | ||||
\(552\) | 5732.56 | 0.442018 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15274.9 | −1.17143 | ||||||||
\(555\) | −3874.14 | + | 6710.21i | −0.296303 | + | 0.513212i | ||||
\(556\) | 14886.5 | + | 25784.3i | 1.13549 | + | 1.96672i | ||||
\(557\) | 3688.13 | + | 6388.03i | 0.280559 | + | 0.485942i | 0.971522 | − | 0.236948i | \(-0.0761469\pi\) |
−0.690964 | + | 0.722889i | \(0.742814\pi\) | |||||||
\(558\) | 902.164 | − | 1562.59i | 0.0684438 | − | 0.118548i | ||||
\(559\) | 1298.29 | 0.0982320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3091.50 | −0.232662 | ||||||||
\(562\) | 10064.6 | − | 17432.5i | 0.755429 | − | 1.30844i | ||||
\(563\) | 6437.70 | + | 11150.4i | 0.481913 | + | 0.834697i | 0.999784 | − | 0.0207610i | \(-0.00660892\pi\) |
−0.517872 | + | 0.855458i | \(0.673276\pi\) | |||||||
\(564\) | 3925.40 | + | 6798.99i | 0.293066 | + | 0.507605i | ||||
\(565\) | 3533.83 | − | 6120.77i | 0.263131 | − | 0.455757i | ||||
\(566\) | 9086.28 | 0.674779 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3588.89 | −0.265117 | ||||||||
\(569\) | 6032.30 | − | 10448.2i | 0.444441 | − | 0.769795i | −0.553572 | − | 0.832801i | \(-0.686736\pi\) |
0.998013 | + | 0.0630067i | \(0.0200689\pi\) | |||||||
\(570\) | 7356.20 | + | 12741.3i | 0.540557 | + | 0.936272i | ||||
\(571\) | −11872.8 | − | 20564.3i | −0.870158 | − | 1.50716i | −0.861832 | − | 0.507193i | \(-0.830683\pi\) |
−0.00832580 | − | 0.999965i | \(-0.502650\pi\) | |||||||
\(572\) | 7483.89 | − | 12962.5i | 0.547058 | − | 0.947533i | ||||
\(573\) | 10843.2 | 0.790542 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2521.64 | −0.182886 | ||||||||
\(576\) | −775.325 | + | 1342.90i | −0.0560854 | + | 0.0971428i | ||||
\(577\) | −4923.04 | − | 8526.95i | −0.355197 | − | 0.615220i | 0.631954 | − | 0.775006i | \(-0.282253\pi\) |
−0.987152 | + | 0.159786i | \(0.948920\pi\) | |||||||
\(578\) | 8484.92 | + | 14696.3i | 0.610599 | + | 1.05759i | ||||
\(579\) | 3726.20 | − | 6453.97i | 0.267453 | − | 0.463243i | ||||
\(580\) | 15322.4 | 1.09695 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 30475.2 | 2.17051 | ||||||||
\(583\) | 1262.89 | − | 2187.40i | 0.0897148 | − | 0.155391i | ||||
\(584\) | −6213.78 | − | 10762.6i | −0.440287 | − | 0.762600i | ||||
\(585\) | 356.662 | + | 617.758i | 0.0252071 | + | 0.0436601i | ||||
\(586\) | −14233.3 | + | 24652.9i | −1.00337 | + | 1.73788i | ||||
\(587\) | −10074.7 | −0.708392 | −0.354196 | − | 0.935171i | \(-0.615245\pi\) | ||||
−0.354196 | + | 0.935171i | \(0.615245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28493.1 | −1.99328 | ||||||||
\(590\) | −3482.06 | + | 6031.10i | −0.242973 | + | 0.420842i | ||||
\(591\) | 8451.42 | + | 14638.3i | 0.588231 | + | 1.01885i | ||||
\(592\) | 5578.77 | + | 9662.71i | 0.387307 | + | 0.670836i | ||||
\(593\) | −3693.62 | + | 6397.54i | −0.255782 | + | 0.443028i | −0.965108 | − | 0.261853i | \(-0.915666\pi\) |
0.709325 | + | 0.704881i | \(0.249000\pi\) | |||||||
\(594\) | 12351.4 | 0.853172 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12399.6 | 0.852194 | ||||||||
\(597\) | −11488.3 | + | 19898.4i | −0.787581 | + | 1.36413i | ||||
\(598\) | −15529.0 | − | 26897.1i | −1.06192 | − | 1.83930i | ||||
\(599\) | −626.365 | − | 1084.90i | −0.0427255 | − | 0.0740027i | 0.843872 | − | 0.536545i | \(-0.180271\pi\) |
−0.886597 | + | 0.462542i | \(0.846937\pi\) | |||||||
\(600\) | 710.422 | − | 1230.49i | 0.0483381 | − | 0.0837240i | ||||
\(601\) | 1800.81 | 0.122224 | 0.0611120 | − | 0.998131i | \(-0.480535\pi\) | ||||
0.0611120 | + | 0.998131i | \(0.480535\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 168.792 | 0.0113992 | ||||||||
\(604\) | −5101.73 | + | 8836.46i | −0.343686 | + | 0.595282i | ||||
\(605\) | −2353.97 | − | 4077.20i | −0.158186 | − | 0.273986i | ||||
\(606\) | 5888.66 | + | 10199.5i | 0.394737 | + | 0.683704i | ||||
\(607\) | 1248.53 | − | 2162.51i | 0.0834863 | − | 0.144602i | −0.821259 | − | 0.570556i | \(-0.806728\pi\) |
0.904745 | + | 0.425953i | \(0.140061\pi\) | |||||||
\(608\) | 33583.1 | 2.24009 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7359.90 | 0.488514 | ||||||||
\(611\) | 5266.66 | − | 9122.12i | 0.348717 | − | 0.603996i | ||||
\(612\) | 333.166 | + | 577.061i | 0.0220056 | + | 0.0381149i | ||||
\(613\) | 9875.39 | + | 17104.7i | 0.650674 | + | 1.12700i | 0.982960 | + | 0.183821i | \(0.0588468\pi\) |
−0.332286 | + | 0.943179i | \(0.607820\pi\) | |||||||
\(614\) | −5769.10 | + | 9992.38i | −0.379189 | + | 0.656775i | ||||
\(615\) | 4541.56 | 0.297778 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16797.4 | 1.09601 | 0.548004 | − | 0.836476i | \(-0.315388\pi\) | ||||
0.548004 | + | 0.836476i | \(0.315388\pi\) | |||||||
\(618\) | −8428.10 | + | 14597.9i | −0.548589 | + | 0.950184i | ||||
\(619\) | 13273.7 | + | 22990.7i | 0.861897 | + | 1.49285i | 0.870096 | + | 0.492883i | \(0.164057\pi\) |
−0.00819917 | + | 0.999966i | \(0.502610\pi\) | |||||||
\(620\) | 5555.81 | + | 9622.94i | 0.359882 | + | 0.623333i | ||||
\(621\) | 7312.75 | − | 12666.1i | 0.472545 | − | 0.818472i | ||||
\(622\) | 3693.73 | 0.238111 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12839.8 | −0.823727 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −7230.32 | − | 12523.3i | −0.461632 | − | 0.799570i | ||||
\(627\) | −6725.79 | − | 11649.4i | −0.428393 | − | 0.741998i | ||||
\(628\) | −5426.47 | + | 9398.91i | −0.344808 | + | 0.597225i | ||||
\(629\) | 9710.93 | 0.615580 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5394.86 | 0.340358 | 0.170179 | − | 0.985413i | \(-0.445565\pi\) | ||||
0.170179 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(632\) | −7008.66 | + | 12139.3i | −0.441122 | + | 0.764046i | ||||
\(633\) | −12471.7 | − | 21601.5i | −0.783102 | − | 1.35637i | ||||
\(634\) | −16474.5 | − | 28534.7i | −1.03200 | − | 1.78747i | ||||
\(635\) | −5115.66 | + | 8860.58i | −0.319699 | + | 0.553735i | ||||
\(636\) | 6805.01 | 0.424271 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24549.3 | −1.52338 | ||||||||
\(639\) | −315.736 | + | 546.871i | −0.0195467 | + | 0.0338558i | ||||
\(640\) | −3440.32 | − | 5958.80i | −0.212485 | − | 0.368035i | ||||
\(641\) | −1226.20 | − | 2123.85i | −0.0755572 | − | 0.130869i | 0.825771 | − | 0.564005i | \(-0.190740\pi\) |
−0.901328 | + | 0.433136i | \(0.857407\pi\) | |||||||
\(642\) | −6697.89 | + | 11601.1i | −0.411752 | + | 0.713175i | ||||
\(643\) | −7074.97 | −0.433919 | −0.216959 | − | 0.976181i | \(-0.569614\pi\) | ||||
−0.216959 | + | 0.976181i | \(0.569614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −455.013 | −0.0277769 | ||||||||
\(646\) | 9219.53 | − | 15968.7i | 0.561513 | − | 0.972569i | ||||
\(647\) | 1670.69 | + | 2893.71i | 0.101517 | + | 0.175832i | 0.912310 | − | 0.409501i | \(-0.134297\pi\) |
−0.810793 | + | 0.585333i | \(0.800964\pi\) | |||||||
\(648\) | 3813.54 | + | 6605.25i | 0.231189 | + | 0.400430i | ||||
\(649\) | 3183.65 | − | 5514.25i | 0.192557 | − | 0.333518i | ||||
\(650\) | −7697.89 | −0.464517 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16651.8 | −1.00021 | ||||||||
\(653\) | 11530.8 | − | 19971.9i | 0.691019 | − | 1.19688i | −0.280486 | − | 0.959858i | \(-0.590495\pi\) |
0.971504 | − | 0.237022i | \(-0.0761712\pi\) | |||||||
\(654\) | 45.1944 | + | 78.2790i | 0.00270220 | + | 0.00468035i | ||||
\(655\) | −2850.79 | − | 4937.72i | −0.170061 | − | 0.294554i | ||||
\(656\) | 3269.92 | − | 5663.68i | 0.194618 | − | 0.337087i | ||||
\(657\) | −2186.65 | −0.129847 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1742.64 | 0.103010 | 0.0515049 | − | 0.998673i | \(-0.483598\pi\) | ||||
0.0515049 | + | 0.998673i | \(0.483598\pi\) | |||||||
\(660\) | −2622.89 | + | 4542.98i | −0.154691 | + | 0.267932i | ||||
\(661\) | −6288.26 | − | 10891.6i | −0.370023 | − | 0.640898i | 0.619546 | − | 0.784960i | \(-0.287317\pi\) |
−0.989569 | + | 0.144062i | \(0.953983\pi\) | |||||||
\(662\) | 7169.27 | + | 12417.5i | 0.420909 | + | 0.729035i | ||||
\(663\) | −5587.56 | + | 9677.94i | −0.327305 | + | 0.566908i | ||||
\(664\) | 7312.51 | 0.427380 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2675.72 | −0.155679 | ||||||||
\(667\) | −14534.6 | + | 25174.7i | −0.843752 | + | 1.46142i | ||||
\(668\) | −6009.41 | − | 10408.6i | −0.348070 | − | 0.602875i | ||||
\(669\) | −9482.42 | − | 16424.0i | −0.548000 | − | 0.949163i | ||||
\(670\) | −910.764 | + | 1577.49i | −0.0525163 | + | 0.0909608i | ||||
\(671\) | −6729.17 | −0.387149 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10680.8 | −0.611760 | −0.305880 | − | 0.952070i | \(-0.598951\pi\) | ||||
−0.305880 | + | 0.952070i | \(0.598951\pi\) | |||||||
\(674\) | 4821.64 | − | 8351.32i | 0.275553 | − | 0.477271i | ||||
\(675\) | −1812.50 | − | 3139.34i | −0.103353 | − | 0.179012i | ||||
\(676\) | −15372.1 | − | 26625.2i | −0.874607 | − | 1.51486i | ||||
\(677\) | −14779.6 | + | 25599.0i | −0.839032 | + | 1.45325i | 0.0516726 | + | 0.998664i | \(0.483545\pi\) |
−0.890705 | + | 0.454582i | \(0.849789\pi\) | |||||||
\(678\) | −30508.4 | −1.72812 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1780.74 | −0.100424 | ||||||||
\(681\) | −9777.41 | + | 16935.0i | −0.550178 | + | 0.952936i | ||||
\(682\) | −8901.42 | − | 15417.7i | −0.499785 | − | 0.865652i | ||||
\(683\) | −5125.21 | − | 8877.13i | −0.287132 | − | 0.497327i | 0.685992 | − | 0.727609i | \(-0.259368\pi\) |
−0.973124 | + | 0.230282i | \(0.926035\pi\) | |||||||
\(684\) | −1449.66 | + | 2510.88i | −0.0810366 | + | 0.140360i | ||||
\(685\) | 2451.71 | 0.136752 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1771.64 | 0.0983875 | ||||||||
\(688\) | −327.609 | + | 567.436i | −0.0181540 | + | 0.0314437i | ||||
\(689\) | −4565.10 | − | 7906.99i | −0.252419 | − | 0.437202i | ||||
\(690\) | 5442.48 | + | 9426.65i | 0.300278 | + | 0.520096i | ||||
\(691\) | −4437.02 | + | 7685.14i | −0.244272 | + | 0.423092i | −0.961927 | − | 0.273307i | \(-0.911882\pi\) |
0.717655 | + | 0.696399i | \(0.245216\pi\) | |||||||
\(692\) | −27043.9 | −1.48563 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10915.1 | 0.597018 | ||||||||
\(695\) | −7000.00 | + | 12124.4i | −0.382051 | + | 0.661731i | ||||
\(696\) | −8189.69 | − | 14185.0i | −0.446019 | − | 0.772528i | ||||
\(697\) | −2845.97 | − | 4929.36i | −0.154661 | − | 0.267881i | ||||
\(698\) | 2786.39 | − | 4826.16i | 0.151098 | − | 0.261709i | ||||
\(699\) | −32462.4 | −1.75657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22086.2 | −1.18999 | −0.594996 | − | 0.803729i | \(-0.702846\pi\) | ||||
−0.594996 | + | 0.803729i | \(0.702846\pi\) | |||||||
\(702\) | 22323.9 | − | 38666.1i | 1.20023 | − | 2.07886i | ||||
\(703\) | 21126.9 | + | 36592.8i | 1.13345 | + | 1.96319i | ||||
\(704\) | 7649.94 | + | 13250.1i | 0.409542 | + | 0.709348i | ||||
\(705\) | −1845.81 | + | 3197.04i | −0.0986061 | + | 0.170791i | ||||
\(706\) | 33534.3 | 1.78765 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17154.9 | 0.910622 | ||||||||
\(709\) | 13939.4 | − | 24143.8i | 0.738373 | − | 1.27890i | −0.214854 | − | 0.976646i | \(-0.568928\pi\) |
0.953228 | − | 0.302254i | \(-0.0977390\pi\) | |||||||
\(710\) | −3407.28 | − | 5901.59i | −0.180103 | − | 0.311948i | ||||
\(711\) | 1233.19 | + | 2135.94i | 0.0650465 | + | 0.112664i | ||||
\(712\) | 6480.85 | − | 11225.2i | 0.341124 | − | 0.590844i | ||||
\(713\) | −21080.6 | −1.10726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7038.20 | 0.368131 | ||||||||
\(716\) | 6436.57 | − | 11148.5i | 0.335958 | − | 0.581896i | ||||
\(717\) | −856.719 | − | 1483.88i | −0.0446231 | − | 0.0772895i | ||||
\(718\) | 4929.88 | + | 8538.80i | 0.256242 | + | 0.443824i | ||||
\(719\) | 12931.6 | − | 22398.3i | 0.670750 | − | 1.16177i | −0.306942 | − | 0.951728i | \(-0.599306\pi\) |
0.977692 | − | 0.210044i | \(-0.0673608\pi\) | |||||||
\(720\) | −360.000 | −0.0186339 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 50623.4 | 2.60943 | ||||||||
\(723\) | −5784.17 | + | 10018.5i | −0.297532 | + | 0.515340i | ||||
\(724\) | −16116.4 | − | 27914.4i | −0.827294 | − | 1.43292i | ||||
\(725\) | 3602.47 | + | 6239.67i | 0.184541 | + | 0.319635i | ||||
\(726\) | −10161.2 | + | 17599.7i | −0.519446 | + | 0.899708i | ||||
\(727\) | −29157.0 | −1.48744 | −0.743722 | − | 0.668489i | \(-0.766941\pi\) | ||||
−0.743722 | + | 0.668489i | \(0.766941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 11798.7 | − | 20435.9i | 0.598204 | − | 1.03612i | ||||
\(731\) | 285.134 | + | 493.866i | 0.0144269 | + | 0.0249881i | ||||
\(732\) | −9064.91 | − | 15700.9i | −0.457717 | − | 0.792789i | ||||
\(733\) | 5503.03 | − | 9531.52i | 0.277297 | − | 0.480293i | −0.693415 | − | 0.720539i | \(-0.743895\pi\) |
0.970712 | + | 0.240246i | \(0.0772280\pi\) | |||||||
\(734\) | −46218.1 | −2.32417 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24846.4 | 1.24436 | ||||||||
\(737\) | 832.714 | − | 1442.30i | 0.0416193 | − | 0.0720867i | ||||
\(738\) | 784.169 | + | 1358.22i | 0.0391133 | + | 0.0677463i | ||||
\(739\) | 18607.2 | + | 32228.6i | 0.926221 | + | 1.60426i | 0.789586 | + | 0.613640i | \(0.210295\pi\) |
0.136634 | + | 0.990622i | \(0.456371\pi\) | |||||||
\(740\) | 8238.95 | − | 14270.3i | 0.409283 | − | 0.708900i | ||||
\(741\) | −48624.7 | −2.41062 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11214.5 | 0.553730 | 0.276865 | − | 0.960909i | \(-0.410704\pi\) | ||||
0.276865 | + | 0.960909i | \(0.410704\pi\) | |||||||
\(744\) | 5939.06 | − | 10286.7i | 0.292656 | − | 0.506896i | ||||
\(745\) | 2915.29 | + | 5049.43i | 0.143367 | + | 0.248318i | ||||
\(746\) | 1792.33 | + | 3104.40i | 0.0879648 | + | 0.152359i | ||||
\(747\) | 643.325 | − | 1114.27i | 0.0315101 | − | 0.0545771i | ||||
\(748\) | 6574.54 | 0.321375 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2697.89 | 0.131351 | ||||||||
\(751\) | −3482.63 | + | 6032.09i | −0.169218 | + | 0.293095i | −0.938145 | − | 0.346242i | \(-0.887458\pi\) |
0.768927 | + | 0.639337i | \(0.220791\pi\) | |||||||
\(752\) | 2657.97 | + | 4603.74i | 0.128891 | + | 0.223246i | ||||
\(753\) | −9973.22 | − | 17274.1i | −0.482662 | − | 0.835995i | ||||
\(754\) | −44370.3 | + | 76851.7i | −2.14307 | + | 3.71190i | ||||
\(755\) | −4797.91 | −0.231276 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19352.8 | −0.929180 | −0.464590 | − | 0.885526i | \(-0.653798\pi\) | ||||
−0.464590 | + | 0.885526i | \(0.653798\pi\) | |||||||
\(758\) | −11338.0 | + | 19638.0i | −0.543291 | + | 0.941007i | ||||
\(759\) | −4976.07 | − | 8618.81i | −0.237971 | − | 0.412178i | ||||
\(760\) | −3874.14 | − | 6710.21i | −0.184908 | − | 0.320270i | ||||
\(761\) | 16191.8 | − | 28045.0i | 0.771291 | − | 1.33591i | −0.165565 | − | 0.986199i | \(-0.552945\pi\) |
0.936856 | − | 0.349716i | \(-0.113722\pi\) | |||||||
\(762\) | 44164.8 | 2.09963 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −23059.7 | −1.09198 | ||||||||
\(765\) | −156.662 | + | 271.347i | −0.00740411 | + | 0.0128243i | ||||
\(766\) | −24267.9 | − | 42033.2i | −1.14469 | − | 1.98266i | ||||
\(767\) | −11508.2 | − | 19932.9i | −0.541772 | − | 0.938376i | ||||
\(768\) | 655.940 | − | 1136.12i | 0.0308193 | − | 0.0533805i | ||||
\(769\) | 25353.9 | 1.18893 | 0.594463 | − | 0.804123i | \(-0.297365\pi\) | ||||
0.594463 | + | 0.804123i | \(0.297365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11456.6 | 0.535148 | ||||||||
\(772\) | −7924.32 | + | 13725.3i | −0.369433 | + | 0.639877i | ||||
\(773\) | 13058.5 | + | 22618.0i | 0.607610 | + | 1.05241i | 0.991633 | + | 0.129088i | \(0.0412049\pi\) |
−0.384023 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(774\) | −78.5647 | − | 136.078i | −0.00364852 | − | 0.00631941i | ||||
\(775\) | −2612.47 | + | 4524.93i | −0.121087 | + | 0.209729i | ||||
\(776\) | −16049.8 | −0.742465 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36720.9 | −1.69217 | ||||||||
\(779\) | 12383.2 | − | 21448.4i | 0.569546 | − | 0.986482i | ||||
\(780\) | 9481.20 | + | 16421.9i | 0.435233 | + | 0.753845i | ||||
\(781\) | 3115.29 | + | 5395.84i | 0.142732 | + | 0.247219i | ||||
\(782\) | 6821.06 | − | 11814.4i | 0.311919 | − | 0.540260i | ||||
\(783\) | −41788.7 | −1.90729 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5103.30 | −0.232031 | ||||||||
\(786\) | −12305.8 | + | 21314.3i | −0.558440 | + | 0.967246i | ||||
\(787\) | −1136.69 | − | 1968.80i | −0.0514849 | − | 0.0891744i | 0.839134 | − | 0.543924i | \(-0.183062\pi\) |
−0.890619 | + | 0.454750i | \(0.849729\pi\) | |||||||
\(788\) | −17973.2 | − | 31130.5i | −0.812524 | − | 1.40733i | ||||
\(789\) | 15901.2 | − | 27541.7i | 0.717487 | − | 1.24272i | ||||
\(790\) | −26616.0 | −1.19868 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −448.612 | −0.0201272 | ||||||||
\(793\) | −12162.3 | + | 21065.7i | −0.544635 | + | 0.943335i | ||||
\(794\) | 6740.92 | + | 11675.6i | 0.301293 | + | 0.521854i | ||||
\(795\) | 1599.94 | + | 2771.17i | 0.0713760 | + | 0.123627i | ||||
\(796\) | 24431.6 | − | 42316.9i | 1.08789 | − | 1.88427i | ||||
\(797\) | −2937.42 | −0.130551 | −0.0652753 | − | 0.997867i | \(-0.520793\pi\) | ||||
−0.0652753 | + | 0.997867i | \(0.520793\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4626.71 | 0.204858 | ||||||||
\(800\) | 3079.16 | − | 5333.25i | 0.136081 | − | 0.235699i | ||||
\(801\) | −1140.32 | − | 1975.09i | −0.0503010 | − | 0.0871240i | ||||
\(802\) | 24292.5 | + | 42075.9i | 1.06957 | + | 1.85256i | ||||
\(803\) | −10787.6 | + | 18684.6i | −0.474078 | + | 0.821128i | ||||
\(804\) | 4487.02 | 0.196822 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −64353.6 | −2.81236 | ||||||||
\(807\) | 2478.36 | − | 4292.65i | 0.108107 | − | 0.187247i | ||||
\(808\) | −3101.26 | − | 5371.54i | −0.135027 | − | 0.233874i | ||||
\(809\) | 2158.76 | + | 3739.08i | 0.0938169 | + | 0.162496i | 0.909114 | − | 0.416547i | \(-0.136760\pi\) |
−0.815297 | + | 0.579043i | \(0.803427\pi\) | |||||||
\(810\) | −7241.14 | + | 12542.0i | −0.314108 | + | 0.544051i | ||||
\(811\) | −1286.12 | −0.0556863 | −0.0278432 | − | 0.999612i | \(-0.508864\pi\) | ||||
−0.0278432 | + | 0.999612i | \(0.508864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3654.89 | 0.157666 | ||||||||
\(814\) | −13200.3 | + | 22863.6i | −0.568391 | + | 0.984483i | ||||
\(815\) | −3915.04 | − | 6781.04i | −0.168267 | − | 0.291447i | ||||
\(816\) | −2819.92 | − | 4884.25i | −0.120977 | − | 0.209538i | ||||
\(817\) | −1240.66 | + | 2148.89i | −0.0531275 | + | 0.0920196i | ||||
\(818\) | 34187.3 | 1.46129 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9658.31 | −0.411321 | ||||||||
\(821\) | −13175.1 | + | 22819.9i | −0.560066 | + | 0.970063i | 0.437424 | + | 0.899255i | \(0.355891\pi\) |
−0.997490 | + | 0.0708073i | \(0.977442\pi\) | |||||||
\(822\) | −5291.56 | − | 9165.25i | −0.224531 | − | 0.388899i | ||||
\(823\) | −4910.03 | − | 8504.42i | −0.207962 | − | 0.360201i | 0.743110 | − | 0.669169i | \(-0.233350\pi\) |
−0.951072 | + | 0.308968i | \(0.900016\pi\) | |||||||
\(824\) | 4438.66 | − | 7687.98i | 0.187655 | − | 0.325029i | ||||
\(825\) | −2466.69 | −0.104096 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30370.7 | −1.27702 | −0.638509 | − | 0.769615i | \(-0.720448\pi\) | ||||
−0.638509 | + | 0.769615i | \(0.720448\pi\) | |||||||
\(828\) | −1072.53 | + | 1857.67i | −0.0450156 | + | 0.0779693i | ||||
\(829\) | −15408.8 | − | 26688.9i | −0.645562 | − | 1.11815i | −0.984171 | − | 0.177219i | \(-0.943290\pi\) |
0.338610 | − | 0.940927i | \(-0.390043\pi\) | |||||||
\(830\) | 6942.48 | + | 12024.7i | 0.290334 | + | 0.502873i | ||||
\(831\) | −8846.57 | + | 15322.7i | −0.369295 | + | 0.639638i | ||||
\(832\) | 55305.9 | 2.30455 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 60432.7 | 2.50913 | ||||||||
\(835\) | 2825.76 | − | 4894.36i | 0.117113 | − | 0.202846i | ||||
\(836\) | 14303.4 | + | 24774.2i | 0.591739 | + | 1.02492i | ||||
\(837\) | −15152.3 | − | 26244.6i | −0.625736 | − | 1.08381i | ||||
\(838\) | −11346.9 | + | 19653.3i | −0.467746 | + | 0.810159i | ||||
\(839\) | 24746.0 | 1.01827 | 0.509134 | − | 0.860688i | \(-0.329966\pi\) | ||||
0.509134 | + | 0.860688i | \(0.329966\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58669.1 | 2.40556 | ||||||||
\(842\) | −3145.44 | + | 5448.06i | −0.128740 | + | 0.222984i | ||||
\(843\) | −11658.0 | − | 20192.2i | −0.476302 | − | 0.824980i | ||||
\(844\) | 26522.8 | + | 45938.9i | 1.08170 | + | 1.87356i | ||||
\(845\) | 7228.31 | − | 12519.8i | 0.294274 | − | 0.509697i | ||||
\(846\) | −1274.83 | −0.0518079 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4607.82 | 0.186596 | ||||||||
\(849\) | 5262.37 | − | 9114.70i | 0.212726 | − | 0.368452i | ||||
\(850\) | −1690.63 | − | 2928.26i | −0.0682214 | − | 0.118163i | ||||
\(851\) | 15630.7 | + | 27073.2i | 0.629628 | + | 1.09055i | ||||
\(852\) | −8393.25 | + | 14537.5i | −0.337498 | + | 0.584563i | ||||
\(853\) | 11812.1 | 0.474135 | 0.237067 | − | 0.971493i | \(-0.423814\pi\) | ||||
0.237067 | + | 0.971493i | \(0.423814\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1363.32 | −0.0545318 | ||||||||
\(856\) | 3527.44 | − | 6109.71i | 0.140848 | − | 0.243955i | ||||
\(857\) | −11720.3 | − | 20300.1i | −0.467161 | − | 0.809147i | 0.532135 | − | 0.846660i | \(-0.321390\pi\) |
−0.999296 | + | 0.0375126i | \(0.988057\pi\) | |||||||
\(858\) | −15190.6 | − | 26310.9i | −0.604429 | − | 1.04690i | ||||
\(859\) | 4472.79 | − | 7747.10i | 0.177660 | − | 0.307716i | −0.763419 | − | 0.645904i | \(-0.776481\pi\) |
0.941078 | + | 0.338188i | \(0.109814\pi\) | |||||||
\(860\) | 967.652 | 0.0383682 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −66006.3 | −2.60810 | ||||||||
\(863\) | −9656.74 | + | 16726.0i | −0.380903 | + | 0.659743i | −0.991192 | − | 0.132436i | \(-0.957720\pi\) |
0.610289 | + | 0.792179i | \(0.291053\pi\) | |||||||
\(864\) | 17859.1 | + | 30932.9i | 0.703217 | + | 1.21801i | ||||
\(865\) | −6358.34 | − | 11013.0i | −0.249931 | − | 0.432893i | ||||
\(866\) | 404.165 | − | 700.034i | 0.0158592 | − | 0.0274690i | ||||
\(867\) | 19656.4 | 0.769972 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24335.1 | 0.949955 | ||||||||
\(870\) | 15550.5 | − | 26934.3i | 0.605991 | − | 1.04961i | ||||
\(871\) | −3010.09 | − | 5213.63i | −0.117099 | − | 0.202821i | ||||
\(872\) | −23.8016 | − | 41.2256i | −0.000924341 | − | 0.00160100i | ||||
\(873\) | −1411.99 | + | 2445.64i | −0.0547408 | + | 0.0948138i | ||||
\(874\) | 59359.0 | 2.29731 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −58128.0 | −2.24197 | ||||||||
\(877\) | 6077.38 | − | 10526.3i | 0.234001 | − | 0.405301i | −0.724981 | − | 0.688769i | \(-0.758152\pi\) |
0.958982 | + | 0.283468i | \(0.0914849\pi\) | |||||||
\(878\) | 7743.85 | + | 13412.7i | 0.297656 | + | 0.515556i | ||||
\(879\) | 16486.6 | + | 28555.7i | 0.632629 | + | 1.09575i | ||||
\(880\) | −1776.02 | + | 3076.15i | −0.0680335 | + | 0.117837i | ||||
\(881\) | 29390.4 | 1.12394 | 0.561968 | − | 0.827159i | \(-0.310044\pi\) | ||||
0.561968 | + | 0.827159i | \(0.310044\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4180.02 | 0.159308 | 0.0796540 | − | 0.996823i | \(-0.474618\pi\) | ||||
0.0796540 | + | 0.996823i | \(0.474618\pi\) | |||||||
\(884\) | 11882.8 | − | 20581.6i | 0.452106 | − | 0.783070i | ||||
\(885\) | 4033.31 | + | 6985.90i | 0.153196 | + | 0.265343i | ||||
\(886\) | −10609.5 | − | 18376.2i | −0.402295 | − | 0.696795i | ||||
\(887\) | 10912.9 | − | 18901.7i | 0.413099 | − | 0.715508i | −0.582128 | − | 0.813097i | \(-0.697780\pi\) |
0.995227 | + | 0.0975890i | \(0.0311130\pi\) | |||||||
\(888\) | −17614.6 | −0.665660 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24611.6 | 0.926947 | ||||||||
\(891\) | 6620.59 | − | 11467.2i | 0.248932 | − | 0.431162i | ||||
\(892\) | 20165.8 | + | 34928.2i | 0.756952 | + | 1.31108i | ||||
\(893\) | 10065.8 | + | 17434.4i | 0.377198 | + | 0.653327i | ||||
\(894\) | 12584.2 | − | 21796.5i | 0.470782 | − | 0.815419i | ||||
\(895\) | 6053.25 | 0.226076 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35974.9 | −1.33909 | ||||||||
\(898\) | −15304.8 | + | 26508.8i | −0.568741 | + | 0.985088i | ||||
\(899\) | 30116.3 | + | 52163.0i | 1.11728 | + | 1.93519i | ||||
\(900\) | 265.831 | + | 460.433i | 0.00984560 | + | 0.0170531i | ||||
\(901\) | 2005.20 | − | 3473.11i | 0.0741431 | − | 0.128420i | ||||
\(902\) | 15474.4 | 0.571221 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16067.2 | 0.591138 | ||||||||
\(905\) | 7578.30 | − | 13126.0i | 0.278355 | − | 0.482125i | ||||
\(906\) | 10355.4 | + | 17936.0i | 0.379729 | + | 0.657710i | ||||
\(907\) | 4178.05 | + | 7236.60i | 0.152955 | + | 0.264925i | 0.932312 | − | 0.361654i | \(-0.117788\pi\) |
−0.779358 | + | 0.626579i | \(0.784454\pi\) | |||||||
\(908\) | 20793.1 | − | 36014.8i | 0.759961 | − | 1.31629i | ||||
\(909\) | −1091.35 | −0.0398214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4419.80 | −0.160740 | −0.0803701 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803701 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(912\) | 12269.9 | − | 21252.1i | 0.445502 | − | 0.771632i | ||||
\(913\) | −6347.53 | − | 10994.2i | −0.230090 | − | 0.398528i | ||||
\(914\) | −10903.4 | − | 18885.2i | −0.394586 | − | 0.683444i | ||||
\(915\) | 4262.53 | − | 7382.92i | 0.154005 | − | 0.266745i | ||||
\(916\) | −3767.65 | −0.135903 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 19611.3 | 0.705088 | ||||||||
\(919\) | 19628.8 | − | 33998.0i | 0.704563 | − | 1.22034i | −0.262286 | − | 0.964990i | \(-0.584476\pi\) |
0.966849 | − | 0.255349i | \(-0.0821904\pi\) | |||||||
\(920\) | −2866.28 | − | 4964.55i | −0.102716 | − | 0.177909i | ||||
\(921\) | 6682.42 | + | 11574.3i | 0.239081 | + | 0.414100i | ||||
\(922\) | −36003.5 | + | 62359.9i | −1.28602 | + | 2.22746i | ||||
\(923\) | 22522.2 | 0.803173 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7748.29 | 0.275419 | ||||||||
\(926\) | −33604.0 | + | 58203.8i | −1.19254 | + | 2.06555i | ||||
\(927\) | −780.990 | − | 1352.71i | −0.0276711 | − | 0.0479277i | ||||
\(928\) | −35496.3 | − | 61481.3i | −1.25563 | − | 2.17481i | ||||
\(929\) | −6699.94 | + | 11604.6i | −0.236618 | + | 0.409834i | −0.959742 | − | 0.280885i | \(-0.909372\pi\) |
0.723124 | + | 0.690718i | \(0.242706\pi\) | |||||||
\(930\) | 22554.1 | 0.795245 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 69036.1 | 2.42635 | ||||||||
\(933\) | 2139.24 | − | 3705.28i | 0.0750651 | − | 0.130017i | ||||
\(934\) | 7183.62 | + | 12442.4i | 0.251665 | + | 0.435897i | ||||
\(935\) | 1545.75 | + | 2677.32i | 0.0540657 | + | 0.0936445i | ||||
\(936\) | −810.819 | + | 1404.38i | −0.0283146 | + | 0.0490423i | ||||
\(937\) | −27539.8 | −0.960176 | −0.480088 | − | 0.877220i | \(-0.659395\pi\) | ||||
−0.480088 | + | 0.877220i | \(0.659395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16749.9 | −0.582123 | ||||||||
\(940\) | 3925.40 | − | 6798.99i | 0.136205 | − | 0.235913i | ||||
\(941\) | 7181.90 | + | 12439.4i | 0.248802 | + | 0.430939i | 0.963194 | − | 0.268808i | \(-0.0866297\pi\) |
−0.714391 | + | 0.699746i | \(0.753296\pi\) | |||||||
\(942\) | 11014.5 | + | 19077.7i | 0.380968 | + | 0.659857i | ||||
\(943\) | 9161.74 | − | 15868.6i | 0.316381 | − | 0.547988i | ||||
\(944\) | 11615.9 | 0.400494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1550.36 | −0.0532838 | ||||||||
\(947\) | 3186.06 | − | 5518.42i | 0.109327 | − | 0.189361i | −0.806171 | − | 0.591683i | \(-0.798464\pi\) |
0.915498 | + | 0.402323i | \(0.131797\pi\) | |||||||
\(948\) | 32781.9 | + | 56780.0i | 1.12311 | + | 1.94528i | ||||
\(949\) | 38994.8 | + | 67541.0i | 1.33385 | + | 2.31030i | ||||
\(950\) | 7356.20 | − | 12741.3i | 0.251228 | − | 0.435140i | ||||
\(951\) | −38165.3 | −1.30136 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 958.776 | 0.0325895 | 0.0162948 | − | 0.999867i | \(-0.494813\pi\) | ||||
0.0162948 | + | 0.999867i | \(0.494813\pi\) | |||||||
\(954\) | −552.506 | + | 956.969i | −0.0187506 | + | 0.0324770i | ||||
\(955\) | −5421.59 | − | 9390.48i | −0.183705 | − | 0.318187i | ||||
\(956\) | 1821.94 | + | 3155.70i | 0.0616379 | + | 0.106760i | ||||
\(957\) | −14217.9 | + | 24626.1i | −0.480250 | + | 0.831817i | ||||
\(958\) | 63055.1 | 2.12653 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −19383.1 | −0.651654 | ||||||||
\(961\) | −6944.47 | + | 12028.2i | −0.233106 | + | 0.403752i | ||||
\(962\) | 47716.4 | + | 82647.2i | 1.59921 | + | 2.76991i | ||||
\(963\) | −620.660 | − | 1075.01i | −0.0207689 | − | 0.0359729i | ||||
\(964\) | 12300.9 | − | 21305.8i | 0.410981 | − | 0.711839i | ||||
\(965\) | −7452.40 | −0.248602 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40104.5 | −1.33369 | −0.666843 | − | 0.745198i | \(-0.732355\pi\) | ||||
−0.666843 | + | 0.745198i | \(0.732355\pi\) | |||||||
\(968\) | 5351.40 | − | 9268.90i | 0.177687 | − | 0.307762i | ||||
\(969\) | −10679.1 | − | 18496.7i | −0.354037 | − | 0.613210i | ||||
\(970\) | −15237.6 | − | 26392.3i | −0.504381 | − | 0.873614i | ||||
\(971\) | 6198.68 | − | 10736.4i | 0.204866 | − | 0.354838i | −0.745224 | − | 0.666814i | \(-0.767657\pi\) |
0.950090 | + | 0.311976i | \(0.100991\pi\) | |||||||
\(972\) | −5954.62 | −0.196496 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8113.05 | −0.266898 | ||||||||
\(975\) | −4458.28 | + | 7721.97i | −0.146440 | + | 0.253642i | ||||
\(976\) | −6138.05 | − | 10631.4i | −0.201305 | − | 0.348671i | ||||
\(977\) | −22491.5 | − | 38956.4i | −0.736506 | − | 1.27566i | −0.954060 | − | 0.299617i | \(-0.903141\pi\) |
0.217554 | − | 0.976048i | \(-0.430192\pi\) | |||||||
\(978\) | −16899.7 | + | 29271.2i | −0.552550 | + | 0.957046i | ||||
\(979\) | −22502.5 | −0.734608 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.37588 | −0.000272601 | ||||||||
\(982\) | −6952.20 | + | 12041.6i | −0.225920 | + | 0.391305i | ||||
\(983\) | −3947.88 | − | 6837.93i | −0.128095 | − | 0.221868i | 0.794843 | − | 0.606815i | \(-0.207553\pi\) |
−0.922939 | + | 0.384947i | \(0.874220\pi\) | |||||||
\(984\) | 5162.28 | + | 8941.33i | 0.167243 | + | 0.289674i | ||||
\(985\) | 8451.42 | − | 14638.3i | 0.273385 | − | 0.473517i | ||||
\(986\) | −38979.0 | −1.25897 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 103408. | 3.32979 | ||||||||
\(989\) | −917.901 | + | 1589.85i | −0.0295122 | + | 0.0511166i | ||||
\(990\) | −425.911 | − | 737.699i | −0.0136731 | − | 0.0236824i | ||||
\(991\) | −27267.5 | − | 47228.6i | −0.874046 | − | 1.51389i | −0.857776 | − | 0.514024i | \(-0.828154\pi\) |
−0.0162696 | − | 0.999868i | \(-0.505179\pi\) | |||||||
\(992\) | 25741.4 | − | 44585.5i | 0.823882 | − | 1.42701i | ||||
\(993\) | 16608.5 | 0.530770 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22976.6 | 0.732069 | ||||||||
\(996\) | 17101.6 | − | 29620.8i | 0.544061 | − | 0.942341i | ||||
\(997\) | −3014.03 | − | 5220.45i | −0.0957425 | − | 0.165831i | 0.814176 | − | 0.580618i | \(-0.197189\pi\) |
−0.909918 | + | 0.414788i | \(0.863856\pi\) | |||||||
\(998\) | −20965.4 | − | 36313.2i | −0.664979 | − | 1.15178i | ||||
\(999\) | −22470.0 | + | 38919.2i | −0.711632 | + | 1.23258i |
(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 | 245.4.e.k.226.1 | 4 | ||
7.2 | even | 3 | 245.4.a.i.1.2 | ✓ | 2 | ||
7.3 | odd | 6 | 245.4.e.j.116.1 | 4 | |||
7.4 | even | 3 | inner | 245.4.e.k.116.1 | 4 | ||
7.5 | odd | 6 | 245.4.a.j.1.2 | yes | 2 | ||
7.6 | odd | 2 | 245.4.e.j.226.1 | 4 | |||
21.2 | odd | 6 | 2205.4.a.x.1.1 | 2 | |||
21.5 | even | 6 | 2205.4.a.w.1.1 | 2 | |||
35.9 | even | 6 | 1225.4.a.q.1.1 | 2 | |||
35.19 | odd | 6 | 1225.4.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.i.1.2 | ✓ | 2 | 7.2 | even | 3 | ||
245.4.a.j.1.2 | yes | 2 | 7.5 | odd | 6 | ||
245.4.e.j.116.1 | 4 | 7.3 | odd | 6 | |||
245.4.e.j.226.1 | 4 | 7.6 | odd | 2 | |||
245.4.e.k.116.1 | 4 | 7.4 | even | 3 | inner | ||
245.4.e.k.226.1 | 4 | 1.1 | even | 1 | trivial | ||
1225.4.a.p.1.1 | 2 | 35.19 | odd | 6 | |||
1225.4.a.q.1.1 | 2 | 35.9 | even | 6 | |||
2205.4.a.w.1.1 | 2 | 21.5 | even | 6 | |||
2205.4.a.x.1.1 | 2 | 21.2 | odd | 6 |