Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(27,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.27");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.f (of order \(6\), 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: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.3 | ||
Character | \(\chi\) | \(=\) | 76.27 |
Dual form | 76.4.f.a.31.3 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68912 | + | 0.876719i | −0.950747 | + | 0.309967i | ||||
\(3\) | 4.88508 | − | 8.46120i | 0.940134 | − | 1.62836i | 0.174920 | − | 0.984583i | \(-0.444033\pi\) |
0.765213 | − | 0.643777i | \(-0.222634\pi\) | |||||||
\(4\) | 6.46273 | − | 4.71521i | 0.807841 | − | 0.589401i | ||||
\(5\) | 6.65041 | − | 11.5188i | 0.594831 | − | 1.03028i | −0.398740 | − | 0.917064i | \(-0.630552\pi\) |
0.993571 | − | 0.113213i | \(-0.0361142\pi\) | |||||||
\(6\) | −5.71846 | + | 27.0360i | −0.389092 | + | 1.83957i | ||||
\(7\) | 4.05088i | 0.218727i | 0.994002 | + | 0.109364i | \(0.0348813\pi\) | ||||
−0.994002 | + | 0.109364i | \(0.965119\pi\) | |||||||
\(8\) | −13.2451 | + | 18.3457i | −0.585358 | + | 0.810775i | ||||
\(9\) | −34.2280 | − | 59.2846i | −1.26770 | − | 2.19573i | ||||
\(10\) | −7.78495 | + | 36.8061i | −0.246182 | + | 1.16391i | ||||
\(11\) | 56.7832i | 1.55643i | 0.627996 | + | 0.778217i | \(0.283875\pi\) | ||||
−0.627996 | + | 0.778217i | \(0.716125\pi\) | |||||||
\(12\) | −8.32539 | − | 77.7166i | −0.200278 | − | 1.86957i | ||||
\(13\) | −0.249360 | + | 0.143968i | −0.00532001 | + | 0.00307151i | −0.502658 | − | 0.864486i | \(-0.667644\pi\) |
0.497338 | + | 0.867557i | \(0.334311\pi\) | |||||||
\(14\) | −3.55149 | − | 10.8933i | −0.0677982 | − | 0.207954i | ||||
\(15\) | −64.9755 | − | 112.541i | −1.11844 | − | 1.93720i | ||||
\(16\) | 19.5337 | − | 60.9462i | 0.305214 | − | 0.952284i | ||||
\(17\) | 26.3870 | − | 45.7035i | 0.376457 | − | 0.652043i | −0.614087 | − | 0.789239i | \(-0.710475\pi\) |
0.990544 | + | 0.137195i | \(0.0438088\pi\) | |||||||
\(18\) | 144.019 | + | 129.415i | 1.88587 | + | 1.69463i | ||||
\(19\) | 82.3338 | − | 8.95232i | 0.994141 | − | 0.108095i | ||||
\(20\) | −11.3340 | − | 105.801i | −0.126717 | − | 1.18289i | ||||
\(21\) | 34.2753 | + | 19.7889i | 0.356166 | + | 0.205633i | ||||
\(22\) | −49.7829 | − | 152.697i | −0.482443 | − | 1.47977i | ||||
\(23\) | −96.2060 | + | 55.5446i | −0.872189 | + | 0.503558i | −0.868075 | − | 0.496433i | \(-0.834643\pi\) |
−0.00411382 | + | 0.999992i | \(0.501309\pi\) | |||||||
\(24\) | 90.5236 | + | 201.690i | 0.769919 | + | 1.71541i | ||||
\(25\) | −25.9559 | − | 44.9569i | −0.207647 | − | 0.359655i | ||||
\(26\) | 0.544340 | − | 0.605767i | 0.00410592 | − | 0.00456926i | ||||
\(27\) | −405.031 | −2.88697 | ||||||||
\(28\) | 19.1007 | + | 26.1797i | 0.128918 | + | 0.176697i | ||||
\(29\) | −85.4732 | + | 49.3480i | −0.547309 | + | 0.315989i | −0.748036 | − | 0.663658i | \(-0.769003\pi\) |
0.200727 | + | 0.979647i | \(0.435670\pi\) | |||||||
\(30\) | 273.394 | + | 245.671i | 1.66382 | + | 1.49510i | ||||
\(31\) | 136.866 | 0.792961 | 0.396481 | − | 0.918043i | \(-0.370231\pi\) | ||||
0.396481 | + | 0.918043i | \(0.370231\pi\) | |||||||
\(32\) | 0.904330 | + | 181.017i | 0.00499576 | + | 0.999988i | ||||
\(33\) | 480.454 | + | 277.390i | 2.53443 | + | 1.46326i | ||||
\(34\) | −30.8885 | + | 146.036i | −0.155804 | + | 0.736618i | ||||
\(35\) | 46.6615 | + | 26.9400i | 0.225349 | + | 0.130106i | ||||
\(36\) | −500.745 | − | 221.748i | −2.31826 | − | 1.02661i | ||||
\(37\) | − | 259.739i | − | 1.15408i | −0.816717 | − | 0.577039i | \(-0.804208\pi\) | ||
0.816717 | − | 0.577039i | \(-0.195792\pi\) | |||||||
\(38\) | −213.557 | + | 96.2575i | −0.911671 | + | 0.410922i | ||||
\(39\) | 2.81319i | 0.0115505i | ||||||||
\(40\) | 123.236 | + | 274.575i | 0.487134 | + | 1.08535i | ||||
\(41\) | −38.5859 | − | 22.2776i | −0.146978 | − | 0.0848579i | 0.424707 | − | 0.905331i | \(-0.360377\pi\) |
−0.571686 | + | 0.820473i | \(0.693710\pi\) | |||||||
\(42\) | −109.520 | − | 23.1648i | −0.402364 | − | 0.0851049i | ||||
\(43\) | 299.816 | + | 173.099i | 1.06329 | + | 0.613892i | 0.926341 | − | 0.376686i | \(-0.122936\pi\) |
0.136951 | + | 0.990578i | \(0.456270\pi\) | |||||||
\(44\) | 267.744 | + | 366.974i | 0.917363 | + | 1.25735i | ||||
\(45\) | −910.520 | −3.01627 | ||||||||
\(46\) | 210.012 | − | 233.712i | 0.673145 | − | 0.749107i | ||||
\(47\) | 159.549 | − | 92.1155i | 0.495161 | − | 0.285881i | −0.231552 | − | 0.972823i | \(-0.574380\pi\) |
0.726713 | + | 0.686941i | \(0.241047\pi\) | |||||||
\(48\) | −420.255 | − | 463.005i | −1.26372 | − | 1.39227i | ||||
\(49\) | 326.590 | 0.952158 | ||||||||
\(50\) | 109.213 | + | 98.1384i | 0.308901 | + | 0.277577i | ||||
\(51\) | −257.805 | − | 446.531i | −0.707841 | − | 1.22602i | ||||
\(52\) | −0.932708 | + | 2.10621i | −0.00248737 | + | 0.00561691i | ||||
\(53\) | −277.723 | + | 160.344i | −0.719778 | + | 0.415564i | −0.814671 | − | 0.579923i | \(-0.803083\pi\) |
0.0948928 | + | 0.995488i | \(0.469749\pi\) | |||||||
\(54\) | 1089.18 | − | 355.099i | 2.74478 | − | 0.894867i | ||||
\(55\) | 654.076 | + | 377.631i | 1.60356 | + | 0.925814i | ||||
\(56\) | −74.3165 | − | 53.6545i | −0.177339 | − | 0.128034i | ||||
\(57\) | 326.460 | − | 740.376i | 0.758608 | − | 1.72044i | ||||
\(58\) | 186.583 | − | 207.639i | 0.422407 | − | 0.470074i | ||||
\(59\) | 158.257 | − | 274.110i | 0.349209 | − | 0.604848i | −0.636900 | − | 0.770946i | \(-0.719784\pi\) |
0.986109 | + | 0.166099i | \(0.0531170\pi\) | |||||||
\(60\) | −950.573 | − | 420.948i | −2.04531 | − | 0.905736i | ||||
\(61\) | 277.980 | + | 481.476i | 0.583471 | + | 1.01060i | 0.995064 | + | 0.0992331i | \(0.0316390\pi\) |
−0.411594 | + | 0.911367i | \(0.635028\pi\) | |||||||
\(62\) | −368.048 | + | 119.993i | −0.753906 | + | 0.245792i | ||||
\(63\) | 240.155 | − | 138.654i | 0.480265 | − | 0.277281i | ||||
\(64\) | −161.133 | − | 485.984i | −0.314713 | − | 0.949187i | ||||
\(65\) | 3.82979i | 0.00730811i | ||||||||
\(66\) | −1535.19 | − | 324.712i | −2.86317 | − | 0.605595i | ||||
\(67\) | −169.518 | − | 293.613i | −0.309103 | − | 0.535382i | 0.669063 | − | 0.743205i | \(-0.266695\pi\) |
−0.978166 | + | 0.207823i | \(0.933362\pi\) | |||||||
\(68\) | −44.9700 | − | 419.789i | −0.0801972 | − | 0.748632i | ||||
\(69\) | 1085.36i | 1.89365i | ||||||||
\(70\) | −149.097 | − | 31.5359i | −0.254579 | − | 0.0538466i | ||||
\(71\) | −397.258 | + | 688.071i | −0.664026 | + | 1.15013i | 0.315522 | + | 0.948918i | \(0.397820\pi\) |
−0.979548 | + | 0.201209i | \(0.935513\pi\) | |||||||
\(72\) | 1540.97 | + | 157.294i | 2.52230 | + | 0.257463i | ||||
\(73\) | 385.864 | − | 668.337i | 0.618658 | − | 1.07155i | −0.371073 | − | 0.928604i | \(-0.621010\pi\) |
0.989731 | − | 0.142943i | \(-0.0456565\pi\) | |||||||
\(74\) | 227.718 | + | 698.470i | 0.357726 | + | 1.09724i | ||||
\(75\) | −507.186 | −0.780863 | ||||||||
\(76\) | 489.889 | − | 446.077i | 0.739396 | − | 0.673271i | ||||
\(77\) | −230.022 | −0.340434 | ||||||||
\(78\) | −2.46637 | − | 7.56499i | −0.00358028 | − | 0.0109816i | ||||
\(79\) | −455.916 | + | 789.670i | −0.649298 | + | 1.12462i | 0.333993 | + | 0.942576i | \(0.391604\pi\) |
−0.983291 | + | 0.182042i | \(0.941729\pi\) | |||||||
\(80\) | −572.123 | − | 630.322i | −0.799566 | − | 0.880902i | ||||
\(81\) | −1054.45 | + | 1826.37i | −1.44644 | + | 2.50531i | ||||
\(82\) | 123.293 | + | 26.0781i | 0.166042 | + | 0.0351200i | ||||
\(83\) | 235.455i | 0.311379i | 0.987806 | + | 0.155690i | \(0.0497600\pi\) | ||||
−0.987806 | + | 0.155690i | \(0.950240\pi\) | |||||||
\(84\) | 314.821 | − | 33.7252i | 0.408926 | − | 0.0438062i | ||||
\(85\) | −350.968 | − | 607.894i | −0.447857 | − | 0.775711i | ||||
\(86\) | −958.001 | − | 202.629i | −1.20121 | − | 0.254071i | ||||
\(87\) | 964.274i | 1.18829i | ||||||||
\(88\) | −1041.73 | − | 752.100i | −1.26192 | − | 0.911070i | ||||
\(89\) | 117.025 | − | 67.5646i | 0.139378 | − | 0.0804700i | −0.428689 | − | 0.903452i | \(-0.641025\pi\) |
0.568068 | + | 0.822982i | \(0.307691\pi\) | |||||||
\(90\) | 2448.50 | − | 798.271i | 2.86771 | − | 0.934946i | ||||
\(91\) | −0.583199 | − | 1.01013i | −0.000671822 | − | 0.00116363i | ||||
\(92\) | −359.849 | + | 812.601i | −0.407792 | + | 0.920864i | ||||
\(93\) | 668.600 | − | 1158.05i | 0.745490 | − | 1.29123i | ||||
\(94\) | −348.286 | + | 387.589i | −0.382159 | + | 0.425285i | ||||
\(95\) | 444.433 | − | 1007.93i | 0.479978 | − | 1.08854i | ||||
\(96\) | 1536.04 | + | 876.631i | 1.63304 | + | 0.931987i | ||||
\(97\) | 383.862 | + | 221.623i | 0.401807 | + | 0.231983i | 0.687263 | − | 0.726408i | \(-0.258812\pi\) |
−0.285456 | + | 0.958392i | \(0.592145\pi\) | |||||||
\(98\) | −878.240 | + | 286.328i | −0.905262 | + | 0.295138i | ||||
\(99\) | 3366.37 | − | 1943.57i | 3.41750 | − | 1.97310i | ||||
\(100\) | −379.726 | − | 168.157i | −0.379726 | − | 0.168157i | ||||
\(101\) | 828.405 | + | 1434.84i | 0.816132 | + | 1.41358i | 0.908512 | + | 0.417859i | \(0.137219\pi\) |
−0.0923795 | + | 0.995724i | \(0.529447\pi\) | |||||||
\(102\) | 1084.75 | + | 974.752i | 1.05300 | + | 0.946224i | ||||
\(103\) | −162.275 | −0.155237 | −0.0776186 | − | 0.996983i | \(-0.524732\pi\) | ||||
−0.0776186 | + | 0.996983i | \(0.524732\pi\) | |||||||
\(104\) | 0.661605 | − | 6.48158i | 0.000623805 | − | 0.00611127i | ||||
\(105\) | 455.890 | − | 263.208i | 0.423717 | − | 0.244633i | ||||
\(106\) | 606.255 | − | 674.669i | 0.555516 | − | 0.618204i | ||||
\(107\) | 142.586 | 0.128825 | 0.0644127 | − | 0.997923i | \(-0.479483\pi\) | ||||
0.0644127 | + | 0.997923i | \(0.479483\pi\) | |||||||
\(108\) | −2617.61 | + | 1909.81i | −2.33222 | + | 1.70158i | ||||
\(109\) | −1686.55 | − | 973.733i | −1.48204 | − | 0.855658i | −0.482250 | − | 0.876034i | \(-0.660180\pi\) |
−0.999792 | + | 0.0203760i | \(0.993514\pi\) | |||||||
\(110\) | −2089.97 | − | 442.054i | −1.81155 | − | 0.383165i | ||||
\(111\) | −2197.71 | − | 1268.85i | −1.87925 | − | 1.08499i | ||||
\(112\) | 246.886 | + | 79.1286i | 0.208290 | + | 0.0667585i | ||||
\(113\) | − | 1077.25i | − | 0.896810i | −0.893831 | − | 0.448405i | \(-0.851992\pi\) | ||
0.893831 | − | 0.448405i | \(-0.148008\pi\) | |||||||
\(114\) | −228.787 | + | 2277.17i | −0.187964 | + | 1.87085i | ||||
\(115\) | 1477.58i | 1.19813i | ||||||||
\(116\) | −319.704 | + | 721.946i | −0.255895 | + | 0.577853i | ||||
\(117\) | 17.0702 | + | 9.85549i | 0.0134884 | + | 0.00778752i | ||||
\(118\) | −185.255 | + | 875.860i | −0.144527 | + | 0.683301i | ||||
\(119\) | 185.140 | + | 106.890i | 0.142620 | + | 0.0823414i | ||||
\(120\) | 2925.26 | + | 298.594i | 2.22532 | + | 0.227148i | ||||
\(121\) | −1893.33 | −1.42249 | ||||||||
\(122\) | −1169.64 | − | 1051.03i | −0.867986 | − | 0.779969i | ||||
\(123\) | −376.990 | + | 217.655i | −0.276358 | + | 0.159555i | ||||
\(124\) | 884.525 | − | 645.350i | 0.640587 | − | 0.467372i | ||||
\(125\) | 972.134 | 0.695602 | ||||||||
\(126\) | −524.245 | + | 583.404i | −0.370662 | + | 0.412490i | ||||
\(127\) | −741.945 | − | 1285.09i | −0.518401 | − | 0.897897i | −0.999771 | − | 0.0213799i | \(-0.993194\pi\) |
0.481370 | − | 0.876517i | \(-0.340139\pi\) | |||||||
\(128\) | 859.377 | + | 1165.60i | 0.593429 | + | 0.804886i | ||||
\(129\) | 2929.25 | − | 1691.20i | 1.99927 | − | 1.15428i | ||||
\(130\) | −3.35765 | − | 10.2988i | −0.00226527 | − | 0.00694817i | ||||
\(131\) | −1442.57 | − | 832.867i | −0.962120 | − | 0.555480i | −0.0652953 | − | 0.997866i | \(-0.520799\pi\) |
−0.896825 | + | 0.442386i | \(0.854132\pi\) | |||||||
\(132\) | 4412.99 | − | 472.742i | 2.90986 | − | 0.311719i | ||||
\(133\) | 36.2648 | + | 333.525i | 0.0236433 | + | 0.217445i | ||||
\(134\) | 713.270 | + | 640.942i | 0.459830 | + | 0.413201i | ||||
\(135\) | −2693.62 | + | 4665.49i | −1.71726 | + | 2.97438i | ||||
\(136\) | 488.967 | + | 1089.44i | 0.308298 | + | 0.686901i | ||||
\(137\) | 601.173 | + | 1041.26i | 0.374903 | + | 0.649351i | 0.990312 | − | 0.138857i | \(-0.0443428\pi\) |
−0.615410 | + | 0.788207i | \(0.711009\pi\) | |||||||
\(138\) | −951.555 | − | 2918.66i | −0.586969 | − | 1.80038i | ||||
\(139\) | −530.911 | + | 306.522i | −0.323966 | + | 0.187042i | −0.653159 | − | 0.757221i | \(-0.726557\pi\) |
0.329193 | + | 0.944263i | \(0.393223\pi\) | |||||||
\(140\) | 428.588 | − | 45.9125i | 0.258731 | − | 0.0277166i | ||||
\(141\) | − | 1799.97i | − | 1.07507i | ||||||
\(142\) | 465.029 | − | 2198.59i | 0.274820 | − | 1.29931i | ||||
\(143\) | −8.17498 | − | 14.1595i | −0.00478060 | − | 0.00828024i | ||||
\(144\) | −4281.77 | + | 928.019i | −2.47787 | + | 0.537048i | ||||
\(145\) | 1312.74i | 0.751840i | ||||||||
\(146\) | −451.692 | + | 2135.53i | −0.256043 | + | 1.21053i | ||||
\(147\) | 1595.42 | − | 2763.35i | 0.895156 | − | 1.55046i | ||||
\(148\) | −1224.72 | − | 1678.62i | −0.680214 | − | 0.932311i | ||||
\(149\) | −738.302 | + | 1278.78i | −0.405933 | + | 0.703097i | −0.994430 | − | 0.105403i | \(-0.966387\pi\) |
0.588496 | + | 0.808500i | \(0.299720\pi\) | |||||||
\(150\) | 1363.88 | − | 444.659i | 0.742404 | − | 0.242042i | ||||
\(151\) | −113.984 | −0.0614297 | −0.0307149 | − | 0.999528i | \(-0.509778\pi\) | ||||
−0.0307149 | + | 0.999528i | \(0.509778\pi\) | |||||||
\(152\) | −926.285 | + | 1629.05i | −0.494287 | + | 0.869299i | ||||
\(153\) | −3612.69 | −1.90894 | ||||||||
\(154\) | 618.556 | − | 201.665i | 0.323667 | − | 0.105523i | ||||
\(155\) | 910.213 | − | 1576.53i | 0.471678 | − | 0.816970i | ||||
\(156\) | 13.2648 | + | 18.1809i | 0.00680789 | + | 0.00933098i | ||||
\(157\) | −175.650 | + | 304.234i | −0.0892889 | + | 0.154653i | −0.907211 | − | 0.420676i | \(-0.861793\pi\) |
0.817922 | + | 0.575329i | \(0.195126\pi\) | |||||||
\(158\) | 533.694 | − | 2523.23i | 0.268724 | − | 1.27049i | ||||
\(159\) | 3133.17i | 1.56274i | ||||||||
\(160\) | 2091.12 | + | 1193.42i | 1.03324 | + | 0.589676i | ||||
\(161\) | −225.005 | − | 389.719i | −0.110142 | − | 0.190771i | ||||
\(162\) | 1234.34 | − | 5835.78i | 0.598635 | − | 2.83026i | ||||
\(163\) | 1784.70i | 0.857599i | 0.903400 | + | 0.428800i | \(0.141063\pi\) | ||||
−0.903400 | + | 0.428800i | \(0.858937\pi\) | |||||||
\(164\) | −354.413 | + | 37.9666i | −0.168750 | + | 0.0180774i | ||||
\(165\) | 6390.43 | − | 3689.52i | 3.01512 | − | 1.74078i | ||||
\(166\) | −206.428 | − | 633.165i | −0.0965174 | − | 0.296043i | ||||
\(167\) | −401.466 | − | 695.359i | −0.186026 | − | 0.322207i | 0.757896 | − | 0.652376i | \(-0.226228\pi\) |
−0.943922 | + | 0.330169i | \(0.892894\pi\) | |||||||
\(168\) | −817.023 | + | 366.701i | −0.375207 | + | 0.168402i | ||||
\(169\) | −1098.46 | + | 1902.59i | −0.499981 | + | 0.865993i | ||||
\(170\) | 1476.75 | + | 1327.00i | 0.666243 | + | 0.598684i | ||||
\(171\) | −3348.85 | − | 4574.71i | −1.49762 | − | 2.04583i | ||||
\(172\) | 2753.83 | − | 295.004i | 1.22080 | − | 0.130778i | ||||
\(173\) | −906.485 | − | 523.359i | −0.398374 | − | 0.230002i | 0.287408 | − | 0.957808i | \(-0.407206\pi\) |
−0.685782 | + | 0.727807i | \(0.740540\pi\) | |||||||
\(174\) | −845.398 | − | 2593.05i | −0.368330 | − | 1.12976i | ||||
\(175\) | 182.115 | − | 105.144i | 0.0786663 | − | 0.0454180i | ||||
\(176\) | 3460.72 | + | 1109.18i | 1.48217 | + | 0.475045i | ||||
\(177\) | −1546.20 | − | 2678.09i | −0.656606 | − | 1.13728i | ||||
\(178\) | −255.460 | + | 284.288i | −0.107570 | + | 0.119709i | ||||
\(179\) | −1108.77 | −0.462979 | −0.231489 | − | 0.972837i | \(-0.574360\pi\) | ||||
−0.231489 | + | 0.972837i | \(0.574360\pi\) | |||||||
\(180\) | −5884.44 | + | 4293.29i | −2.43667 | + | 1.77779i | ||||
\(181\) | −552.714 | + | 319.110i | −0.226977 | + | 0.131045i | −0.609177 | − | 0.793034i | \(-0.708500\pi\) |
0.382199 | + | 0.924080i | \(0.375167\pi\) | |||||||
\(182\) | 2.45389 | + | 2.20506i | 0.000999421 | + | 0.000898076i | ||||
\(183\) | 5431.82 | 2.19416 | ||||||||
\(184\) | 255.255 | − | 2500.67i | 0.102270 | − | 1.00191i | ||||
\(185\) | −2991.90 | − | 1727.37i | −1.18902 | − | 0.686480i | ||||
\(186\) | −782.661 | + | 3700.30i | −0.308535 | + | 1.45871i | ||||
\(187\) | 2595.19 | + | 1498.33i | 1.01486 | + | 0.585931i | ||||
\(188\) | 596.776 | − | 1347.62i | 0.231513 | − | 0.522795i | ||||
\(189\) | − | 1640.73i | − | 0.631459i | ||||||
\(190\) | −311.464 | + | 3100.08i | −0.118926 | + | 1.18370i | ||||
\(191\) | 531.544i | 0.201367i | 0.994918 | + | 0.100684i | \(0.0321030\pi\) | ||||
−0.994918 | + | 0.100684i | \(0.967897\pi\) | |||||||
\(192\) | −4899.15 | − | 1010.69i | −1.84149 | − | 0.379897i | ||||
\(193\) | 3093.64 | + | 1786.11i | 1.15381 | + | 0.666152i | 0.949813 | − | 0.312820i | \(-0.101274\pi\) |
0.203996 | + | 0.978972i | \(0.434607\pi\) | |||||||
\(194\) | −1226.55 | − | 259.431i | −0.453924 | − | 0.0960106i | ||||
\(195\) | 32.4047 | + | 18.7088i | 0.0119002 | + | 0.00687060i | ||||
\(196\) | 2110.66 | − | 1539.94i | 0.769192 | − | 0.561203i | ||||
\(197\) | 931.892 | 0.337028 | 0.168514 | − | 0.985699i | \(-0.446103\pi\) | ||||
0.168514 | + | 0.985699i | \(0.446103\pi\) | |||||||
\(198\) | −7348.60 | + | 8177.86i | −2.63759 | + | 2.93523i | ||||
\(199\) | 163.543 | − | 94.4218i | 0.0582577 | − | 0.0336351i | −0.470588 | − | 0.882353i | \(-0.655958\pi\) |
0.528846 | + | 0.848718i | \(0.322625\pi\) | |||||||
\(200\) | 1168.56 | + | 119.280i | 0.413147 | + | 0.0421718i | ||||
\(201\) | −3312.43 | −1.16239 | ||||||||
\(202\) | −3485.63 | − | 3132.18i | −1.21410 | − | 1.09099i | ||||
\(203\) | −199.903 | − | 346.242i | −0.0691154 | − | 0.119711i | ||||
\(204\) | −3771.61 | − | 1670.20i | −1.29444 | − | 0.573224i | ||||
\(205\) | −513.224 | + | 296.310i | −0.174854 | + | 0.100952i | ||||
\(206\) | 436.377 | − | 142.270i | 0.147591 | − | 0.0481184i | ||||
\(207\) | 6585.88 | + | 3802.36i | 2.21135 | + | 1.27673i | ||||
\(208\) | 3.90339 | + | 18.0098i | 0.00130121 | + | 0.00600363i | ||||
\(209\) | 508.341 | + | 4675.17i | 0.168243 | + | 1.54731i | ||||
\(210\) | −995.183 | + | 1107.49i | −0.327020 | + | 0.363923i | ||||
\(211\) | 728.851 | − | 1262.41i | 0.237802 | − | 0.411885i | −0.722281 | − | 0.691599i | \(-0.756906\pi\) |
0.960083 | + | 0.279714i | \(0.0902398\pi\) | |||||||
\(212\) | −1038.80 | + | 2345.78i | −0.336532 | + | 0.759948i | ||||
\(213\) | 3881.28 | + | 6722.57i | 1.24855 | + | 2.16255i | ||||
\(214\) | −383.431 | + | 125.008i | −0.122480 | + | 0.0399316i | ||||
\(215\) | 3987.80 | − | 2302.36i | 1.26496 | − | 0.730323i | ||||
\(216\) | 5364.69 | − | 7430.60i | 1.68991 | − | 2.34069i | ||||
\(217\) | 554.427i | 0.173442i | ||||||||
\(218\) | 5389.04 | + | 1139.85i | 1.67427 | + | 0.354130i | ||||
\(219\) | −3769.96 | − | 6529.75i | −1.16324 | − | 2.01479i | ||||
\(220\) | 6007.73 | − | 643.578i | 1.84109 | − | 0.197227i | ||||
\(221\) | 15.1955i | 0.00462517i | ||||||||
\(222\) | 7022.32 | + | 1485.31i | 2.12300 | + | 0.449042i | ||||
\(223\) | −2640.14 | + | 4572.86i | −0.792811 | + | 1.37319i | 0.131409 | + | 0.991328i | \(0.458050\pi\) |
−0.924220 | + | 0.381861i | \(0.875283\pi\) | |||||||
\(224\) | −733.279 | + | 3.66333i | −0.218724 | + | 0.00109271i | ||||
\(225\) | −1776.83 | + | 3077.57i | −0.526469 | + | 0.911871i | ||||
\(226\) | 944.449 | + | 2896.86i | 0.277981 | + | 0.852639i | ||||
\(227\) | −2572.67 | −0.752221 | −0.376110 | − | 0.926575i | \(-0.622739\pi\) | ||||
−0.376110 | + | 0.926575i | \(0.622739\pi\) | |||||||
\(228\) | −1381.21 | − | 6324.17i | −0.401195 | − | 1.83697i | ||||
\(229\) | −4095.87 | −1.18193 | −0.590967 | − | 0.806696i | \(-0.701254\pi\) | ||||
−0.590967 | + | 0.806696i | \(0.701254\pi\) | |||||||
\(230\) | −1295.42 | − | 3973.38i | −0.371380 | − | 1.13912i | ||||
\(231\) | −1123.68 | + | 1946.26i | −0.320054 | + | 0.554349i | ||||
\(232\) | 226.778 | − | 2221.69i | 0.0641755 | − | 0.628711i | ||||
\(233\) | 1701.86 | − | 2947.71i | 0.478508 | − | 0.828801i | −0.521188 | − | 0.853442i | \(-0.674511\pi\) |
0.999696 | + | 0.0246411i | \(0.00784429\pi\) | |||||||
\(234\) | −54.5443 | − | 11.5368i | −0.0152379 | − | 0.00322301i | ||||
\(235\) | − | 2450.42i | − | 0.680204i | ||||||
\(236\) | −269.710 | − | 2517.71i | −0.0743924 | − | 0.694445i | ||||
\(237\) | 4454.37 | + | 7715.19i | 1.22085 | + | 2.11458i | ||||
\(238\) | −591.576 | − | 125.126i | −0.161118 | − | 0.0340785i | ||||
\(239\) | 2007.39i | 0.543294i | 0.962397 | + | 0.271647i | \(0.0875683\pi\) | ||||
−0.962397 | + | 0.271647i | \(0.912432\pi\) | |||||||
\(240\) | −8128.15 | + | 1761.67i | −2.18612 | + | 0.473815i | ||||
\(241\) | −4846.05 | + | 2797.87i | −1.29528 | + | 0.747828i | −0.979584 | − | 0.201034i | \(-0.935570\pi\) |
−0.315691 | + | 0.948862i | \(0.602236\pi\) | |||||||
\(242\) | 5091.38 | − | 1659.92i | 1.35242 | − | 0.440924i | ||||
\(243\) | 4834.26 | + | 8373.18i | 1.27620 | + | 2.21045i | ||||
\(244\) | 4066.77 | + | 1800.91i | 1.06700 | + | 0.472506i | ||||
\(245\) | 2171.96 | − | 3761.94i | 0.566373 | − | 0.980987i | ||||
\(246\) | 822.949 | − | 915.816i | 0.213290 | − | 0.237359i | ||||
\(247\) | −19.2419 | + | 14.0858i | −0.00495682 | + | 0.00362858i | ||||
\(248\) | −1812.80 | + | 2510.90i | −0.464166 | + | 0.642913i | ||||
\(249\) | 1992.23 | + | 1150.21i | 0.507038 | + | 0.292738i | ||||
\(250\) | −2614.18 | + | 852.289i | −0.661342 | + | 0.215614i | ||||
\(251\) | −2109.36 | + | 1217.84i | −0.530445 | + | 0.306253i | −0.741198 | − | 0.671287i | \(-0.765742\pi\) |
0.210753 | + | 0.977539i | \(0.432409\pi\) | |||||||
\(252\) | 898.276 | − | 2028.46i | 0.224548 | − | 0.507067i | ||||
\(253\) | −3154.00 | − | 5462.88i | −0.783755 | − | 1.35750i | ||||
\(254\) | 3121.84 | + | 2805.27i | 0.771187 | + | 0.692986i | ||||
\(255\) | −6858.03 | −1.68418 | ||||||||
\(256\) | −3332.87 | − | 2381.00i | −0.813689 | − | 0.581300i | ||||
\(257\) | 3262.98 | − | 1883.88i | 0.791982 | − | 0.457251i | −0.0486778 | − | 0.998815i | \(-0.515501\pi\) |
0.840660 | + | 0.541563i | \(0.182167\pi\) | |||||||
\(258\) | −6394.40 | + | 7115.98i | −1.54301 | + | 1.71714i | ||||
\(259\) | 1052.17 | 0.252428 | ||||||||
\(260\) | 18.0583 | + | 24.7509i | 0.00430741 | + | 0.00590379i | ||||
\(261\) | 5851.15 | + | 3378.16i | 1.38765 | + | 0.801161i | ||||
\(262\) | 4609.43 | + | 974.952i | 1.08691 | + | 0.229896i | ||||
\(263\) | −3408.14 | − | 1967.69i | −0.799069 | − | 0.461343i | 0.0440767 | − | 0.999028i | \(-0.485965\pi\) |
−0.843145 | + | 0.537686i | \(0.819299\pi\) | |||||||
\(264\) | −11452.6 | + | 5140.22i | −2.66992 | + | 1.19833i | ||||
\(265\) | 4265.40i | 0.988761i | ||||||||
\(266\) | −389.928 | − | 865.093i | −0.0898797 | − | 0.199407i | ||||
\(267\) | − | 1320.23i | − | 0.302610i | ||||||
\(268\) | −2480.00 | − | 1098.23i | −0.565260 | − | 0.250318i | ||||
\(269\) | −849.160 | − | 490.263i | −0.192469 | − | 0.111122i | 0.400669 | − | 0.916223i | \(-0.368778\pi\) |
−0.593138 | + | 0.805101i | \(0.702111\pi\) | |||||||
\(270\) | 3153.15 | − | 14907.6i | 0.710720 | − | 3.36018i | ||||
\(271\) | −887.611 | − | 512.463i | −0.198961 | − | 0.114870i | 0.397210 | − | 0.917728i | \(-0.369979\pi\) |
−0.596171 | + | 0.802858i | \(0.703312\pi\) | |||||||
\(272\) | −2270.02 | − | 2500.94i | −0.506031 | − | 0.557507i | ||||
\(273\) | −11.3959 | −0.00252641 | ||||||||
\(274\) | −2529.52 | − | 2273.02i | −0.557715 | − | 0.501161i | ||||
\(275\) | 2552.79 | − | 1473.86i | 0.559779 | − | 0.323189i | ||||
\(276\) | 5117.69 | + | 7014.37i | 1.11612 | + | 1.52977i | ||||
\(277\) | −3535.60 | −0.766908 | −0.383454 | − | 0.923560i | \(-0.625265\pi\) | ||||
−0.383454 | + | 0.923560i | \(0.625265\pi\) | |||||||
\(278\) | 1158.95 | − | 1289.73i | 0.250033 | − | 0.278249i | ||||
\(279\) | −4684.64 | − | 8114.03i | −1.00524 | − | 1.74113i | ||||
\(280\) | −1112.27 | + | 499.216i | −0.237396 | + | 0.106549i | ||||
\(281\) | −2176.96 | + | 1256.87i | −0.462158 | + | 0.266827i | −0.712951 | − | 0.701214i | \(-0.752642\pi\) |
0.250793 | + | 0.968041i | \(0.419309\pi\) | |||||||
\(282\) | 1578.06 | + | 4840.32i | 0.333235 | + | 1.02212i | ||||
\(283\) | 4003.89 | + | 2311.65i | 0.841013 | + | 0.485559i | 0.857609 | − | 0.514303i | \(-0.171949\pi\) |
−0.0165953 | + | 0.999862i | \(0.505283\pi\) | |||||||
\(284\) | 677.027 | + | 6319.97i | 0.141458 | + | 1.32050i | ||||
\(285\) | −6357.19 | − | 8684.24i | −1.32129 | − | 1.80495i | ||||
\(286\) | 34.3974 | + | 30.9094i | 0.00711175 | + | 0.00639059i | ||||
\(287\) | 90.2438 | − | 156.307i | 0.0185607 | − | 0.0321481i | ||||
\(288\) | 10700.6 | − | 6249.46i | 2.18937 | − | 1.27866i | ||||
\(289\) | 1063.96 | + | 1842.83i | 0.216560 | + | 0.375092i | ||||
\(290\) | −1150.90 | − | 3530.10i | −0.233046 | − | 0.714810i | ||||
\(291\) | 3750.39 | − | 2165.29i | 0.755505 | − | 0.436191i | ||||
\(292\) | −657.609 | − | 6138.71i | −0.131793 | − | 1.23028i | ||||
\(293\) | − | 6471.88i | − | 1.29041i | −0.764008 | − | 0.645207i | \(-0.776771\pi\) | ||
0.764008 | − | 0.645207i | \(-0.223229\pi\) | |||||||
\(294\) | −1867.59 | + | 8829.71i | −0.370477 | + | 1.75156i | ||||
\(295\) | −2104.95 | − | 3645.88i | −0.415440 | − | 0.719564i | ||||
\(296\) | 4765.11 | + | 3440.28i | 0.935697 | + | 0.675548i | ||||
\(297\) | − | 22999.0i | − | 4.49338i | ||||||
\(298\) | 864.254 | − | 4086.07i | 0.168003 | − | 0.794294i | ||||
\(299\) | 15.9933 | − | 27.7012i | 0.00309337 | − | 0.00535787i | ||||
\(300\) | −3277.80 | + | 2391.48i | −0.630813 | + | 0.460241i | ||||
\(301\) | −701.204 | + | 1214.52i | −0.134275 | + | 0.232571i | ||||
\(302\) | 306.517 | − | 99.9320i | 0.0584041 | − | 0.0190412i | ||||
\(303\) | 16187.3 | 3.06909 | ||||||||
\(304\) | 1062.67 | − | 5192.80i | 0.200488 | − | 0.979696i | ||||
\(305\) | 7394.72 | 1.38826 | ||||||||
\(306\) | 9714.95 | − | 3167.31i | 1.81492 | − | 0.591710i | ||||
\(307\) | −2327.72 | + | 4031.73i | −0.432737 | + | 0.749522i | −0.997108 | − | 0.0759993i | \(-0.975785\pi\) |
0.564371 | + | 0.825521i | \(0.309119\pi\) | |||||||
\(308\) | −1486.57 | + | 1084.60i | −0.275017 | + | 0.200652i | ||||
\(309\) | −792.726 | + | 1373.04i | −0.145944 | + | 0.252782i | ||||
\(310\) | −1065.49 | + | 5037.49i | −0.195213 | + | 0.922936i | ||||
\(311\) | 7840.95i | 1.42964i | 0.699306 | + | 0.714822i | \(0.253492\pi\) | ||||
−0.699306 | + | 0.714822i | \(0.746508\pi\) | |||||||
\(312\) | −51.6100 | − | 37.2610i | −0.00936488 | − | 0.00676119i | ||||
\(313\) | −3754.37 | − | 6502.76i | −0.677985 | − | 1.17431i | −0.975587 | − | 0.219615i | \(-0.929520\pi\) |
0.297601 | − | 0.954690i | \(-0.403813\pi\) | |||||||
\(314\) | 205.615 | − | 972.117i | 0.0369539 | − | 0.174713i | ||||
\(315\) | − | 3688.41i | − | 0.659741i | ||||||
\(316\) | 776.995 | + | 7253.16i | 0.138321 | + | 1.29121i | ||||
\(317\) | −549.251 | + | 317.110i | −0.0973155 | + | 0.0561852i | −0.547868 | − | 0.836565i | \(-0.684560\pi\) |
0.450552 | + | 0.892750i | \(0.351227\pi\) | |||||||
\(318\) | −2746.91 | − | 8425.46i | −0.484399 | − | 1.48577i | ||||
\(319\) | −2802.13 | − | 4853.44i | −0.491816 | − | 0.851850i | ||||
\(320\) | −6669.57 | − | 1375.92i | −1.16513 | − | 0.240364i | ||||
\(321\) | 696.544 | − | 1206.45i | 0.121113 | − | 0.209774i | ||||
\(322\) | 946.739 | + | 850.736i | 0.163850 | + | 0.147235i | ||||
\(323\) | 1763.39 | − | 3999.17i | 0.303769 | − | 0.688916i | ||||
\(324\) | 1797.05 | + | 16775.3i | 0.308137 | + | 2.87642i | ||||
\(325\) | 12.9447 | + | 7.47364i | 0.00220937 | + | 0.00127558i | ||||
\(326\) | −1564.68 | − | 4799.28i | −0.265828 | − | 0.815360i | ||||
\(327\) | −16477.9 | + | 9513.52i | −2.78664 | + | 1.60887i | ||||
\(328\) | 919.774 | − | 412.818i | 0.154835 | − | 0.0694940i | ||||
\(329\) | 373.149 | + | 646.313i | 0.0625300 | + | 0.108305i | ||||
\(330\) | −13950.0 | + | 15524.2i | −2.32703 | + | 2.58963i | ||||
\(331\) | 11305.5 | 1.87737 | 0.938684 | − | 0.344778i | \(-0.112046\pi\) | ||||
0.938684 | + | 0.344778i | \(0.112046\pi\) | |||||||
\(332\) | 1110.22 | + | 1521.68i | 0.183527 | + | 0.251545i | ||||
\(333\) | −15398.5 | + | 8890.35i | −2.53404 | + | 1.46303i | ||||
\(334\) | 1689.22 | + | 1517.93i | 0.276737 | + | 0.248675i | ||||
\(335\) | −4509.45 | −0.735456 | ||||||||
\(336\) | 1875.58 | − | 1702.40i | 0.304528 | − | 0.276410i | ||||
\(337\) | 16.3493 | + | 9.43926i | 0.00264274 | + | 0.00152578i | 0.501321 | − | 0.865262i | \(-0.332848\pi\) |
−0.498678 | + | 0.866787i | \(0.666181\pi\) | |||||||
\(338\) | 1285.85 | − | 6079.32i | 0.206926 | − | 0.978318i | ||||
\(339\) | −9114.86 | − | 5262.47i | −1.46033 | − | 0.843121i | ||||
\(340\) | −5134.56 | − | 2273.77i | −0.819001 | − | 0.362684i | ||||
\(341\) | 7771.67i | 1.23419i | ||||||||
\(342\) | 13016.2 | + | 9365.93i | 2.05800 | + | 1.48085i | ||||
\(343\) | 2712.43i | 0.426990i | ||||||||
\(344\) | −7146.74 | + | 3207.64i | −1.12013 | + | 0.502745i | ||||
\(345\) | 12502.1 | + | 7218.08i | 1.95098 | + | 1.12640i | ||||
\(346\) | 2896.49 | + | 612.643i | 0.450046 | + | 0.0951904i | ||||
\(347\) | −9010.47 | − | 5202.20i | −1.39397 | − | 0.804808i | −0.400217 | − | 0.916420i | \(-0.631065\pi\) |
−0.993752 | + | 0.111612i | \(0.964399\pi\) | |||||||
\(348\) | 4546.75 | + | 6231.84i | 0.700378 | + | 0.959948i | ||||
\(349\) | 8605.64 | 1.31991 | 0.659956 | − | 0.751304i | \(-0.270575\pi\) | ||||
0.659956 | + | 0.751304i | \(0.270575\pi\) | |||||||
\(350\) | −397.547 | + | 442.409i | −0.0607137 | + | 0.0675650i | ||||
\(351\) | 100.999 | − | 58.3117i | 0.0153587 | − | 0.00886737i | ||||
\(352\) | −10278.7 | + | 51.3507i | −1.55641 | + | 0.00777557i | ||||
\(353\) | 10867.8 | 1.63862 | 0.819311 | − | 0.573349i | \(-0.194356\pi\) | ||||
0.819311 | + | 0.573349i | \(0.194356\pi\) | |||||||
\(354\) | 6505.85 | + | 5846.13i | 0.976785 | + | 0.877735i | ||||
\(355\) | 5283.86 | + | 9151.91i | 0.789967 | + | 1.36826i | ||||
\(356\) | 437.722 | − | 988.450i | 0.0651663 | − | 0.147157i | ||||
\(357\) | 1808.84 | − | 1044.34i | 0.268163 | − | 0.154824i | ||||
\(358\) | 2981.61 | − | 972.078i | 0.440176 | − | 0.143508i | ||||
\(359\) | −1789.50 | − | 1033.17i | −0.263081 | − | 0.151890i | 0.362658 | − | 0.931922i | \(-0.381869\pi\) |
−0.625739 | + | 0.780032i | \(0.715203\pi\) | |||||||
\(360\) | 12060.0 | − | 16704.2i | 1.76560 | − | 2.44552i | ||||
\(361\) | 6698.71 | − | 1474.16i | 0.976631 | − | 0.214923i | ||||
\(362\) | 1206.54 | − | 1342.70i | 0.175178 | − | 0.194947i | ||||
\(363\) | −9249.05 | + | 16019.8i | −1.33733 | + | 2.31632i | ||||
\(364\) | −8.53202 | − | 3.77829i | −0.00122857 | − | 0.000544056i | ||||
\(365\) | −5132.31 | − | 8889.42i | −0.735993 | − | 1.27478i | ||||
\(366\) | −14606.8 | + | 4762.18i | −2.08609 | + | 0.680118i | ||||
\(367\) | 370.035 | − | 213.640i | 0.0526312 | − | 0.0303866i | −0.473454 | − | 0.880819i | \(-0.656993\pi\) |
0.526085 | + | 0.850432i | \(0.323659\pi\) | |||||||
\(368\) | 1505.97 | + | 6948.38i | 0.213327 | + | 0.984264i | ||||
\(369\) | 3050.07i | 0.430298i | ||||||||
\(370\) | 9559.98 | + | 2022.06i | 1.34324 | + | 0.284113i | ||||
\(371\) | −649.534 | − | 1125.03i | −0.0908952 | − | 0.157435i | ||||
\(372\) | −1139.46 | − | 10636.7i | −0.158813 | − | 1.48250i | ||||
\(373\) | 8581.85i | 1.19129i | 0.803248 | + | 0.595645i | \(0.203103\pi\) | ||||
−0.803248 | + | 0.595645i | \(0.796897\pi\) | |||||||
\(374\) | −8292.40 | − | 1753.95i | −1.14650 | − | 0.242498i | ||||
\(375\) | 4748.95 | − | 8225.42i | 0.653959 | − | 1.13269i | ||||
\(376\) | −423.316 | + | 4147.12i | −0.0580608 | + | 0.568807i | ||||
\(377\) | 14.2091 | − | 24.6109i | 0.00194113 | − | 0.00336213i | ||||
\(378\) | 1438.46 | + | 4412.13i | 0.195732 | + | 0.600358i | ||||
\(379\) | −9558.59 | −1.29549 | −0.647746 | − | 0.761856i | \(-0.724288\pi\) | ||||
−0.647746 | + | 0.761856i | \(0.724288\pi\) | |||||||
\(380\) | −1880.33 | − | 8609.55i | −0.253840 | − | 1.16226i | ||||
\(381\) | −14497.8 | −1.94947 | ||||||||
\(382\) | −466.015 | − | 1429.39i | −0.0624173 | − | 0.191450i | ||||
\(383\) | 2716.77 | − | 4705.59i | 0.362456 | − | 0.627792i | −0.625909 | − | 0.779896i | \(-0.715272\pi\) |
0.988364 | + | 0.152104i | \(0.0486050\pi\) | |||||||
\(384\) | 14060.5 | − | 1577.32i | 1.86855 | − | 0.209615i | ||||
\(385\) | −1529.74 | + | 2649.59i | −0.202501 | + | 0.350741i | ||||
\(386\) | −9885.09 | − | 2090.82i | −1.30347 | − | 0.275699i | ||||
\(387\) | − | 23699.3i | − | 3.11293i | ||||||
\(388\) | 3525.79 | − | 377.701i | 0.461327 | − | 0.0494197i | ||||
\(389\) | −4690.10 | − | 8123.49i | −0.611305 | − | 1.05881i | −0.991021 | − | 0.133708i | \(-0.957312\pi\) |
0.379716 | − | 0.925103i | \(-0.376022\pi\) | |||||||
\(390\) | −103.542 | − | 21.9005i | −0.0134438 | − | 0.00284353i | ||||
\(391\) | 5862.61i | 0.758273i | ||||||||
\(392\) | −4325.73 | + | 5991.54i | −0.557353 | + | 0.771986i | ||||
\(393\) | −14094.1 | + | 8137.24i | −1.80904 | + | 1.04445i | ||||
\(394\) | −2505.97 | + | 817.008i | −0.320429 | + | 0.104468i | ||||
\(395\) | 6064.05 | + | 10503.2i | 0.772445 | + | 1.33791i | ||||
\(396\) | 12591.6 | − | 28433.9i | 1.59785 | − | 3.60822i | ||||
\(397\) | 5135.51 | − | 8894.97i | 0.649229 | − | 1.12450i | −0.334078 | − | 0.942545i | \(-0.608425\pi\) |
0.983307 | − | 0.181953i | \(-0.0582418\pi\) | |||||||
\(398\) | −357.006 | + | 397.293i | −0.0449626 | + | 0.0500365i | ||||
\(399\) | 2999.18 | + | 1322.45i | 0.376307 | + | 0.165928i | ||||
\(400\) | −3246.96 | + | 703.738i | −0.405870 | + | 0.0879672i | ||||
\(401\) | 12168.0 | + | 7025.20i | 1.51531 | + | 0.874867i | 0.999839 | + | 0.0179623i | \(0.00571789\pi\) |
0.515475 | + | 0.856905i | \(0.327615\pi\) | |||||||
\(402\) | 8907.52 | − | 2904.07i | 1.10514 | − | 0.360303i | ||||
\(403\) | −34.1289 | + | 19.7043i | −0.00421856 | + | 0.00243559i | ||||
\(404\) | 12119.3 | + | 5366.88i | 1.49247 | + | 0.660921i | ||||
\(405\) | 14025.1 | + | 24292.2i | 1.72077 | + | 2.98046i | ||||
\(406\) | 841.119 | + | 755.827i | 0.102818 | + | 0.0923918i | ||||
\(407\) | 14748.8 | 1.79624 | ||||||||
\(408\) | 11606.6 | + | 1184.74i | 1.40836 | + | 0.143758i | ||||
\(409\) | 674.864 | − | 389.633i | 0.0815889 | − | 0.0471054i | −0.458650 | − | 0.888617i | \(-0.651667\pi\) |
0.540239 | + | 0.841511i | \(0.318334\pi\) | |||||||
\(410\) | 1120.34 | − | 1246.77i | 0.134950 | − | 0.150179i | ||||
\(411\) | 11747.1 | 1.40983 | ||||||||
\(412\) | −1048.74 | + | 765.160i | −0.125407 | + | 0.0914969i | ||||
\(413\) | 1110.39 | + | 641.081i | 0.132297 | + | 0.0763815i | ||||
\(414\) | −21043.8 | − | 4451.03i | −2.49818 | − | 0.528396i | ||||
\(415\) | 2712.16 | + | 1565.87i | 0.320807 | + | 0.185218i | ||||
\(416\) | −26.2862 | − | 45.0083i | −0.00309805 | − | 0.00530460i | ||||
\(417\) | 5989.53i | 0.703378i | ||||||||
\(418\) | −5465.81 | − | 12126.4i | −0.639572 | − | 1.41895i | ||||
\(419\) | − | 8913.38i | − | 1.03925i | −0.854394 | − | 0.519626i | \(-0.826071\pi\) | ||
0.854394 | − | 0.519626i | \(-0.173929\pi\) | |||||||
\(420\) | 1705.21 | − | 3850.66i | 0.198109 | − | 0.447364i | ||||
\(421\) | −12775.1 | − | 7375.68i | −1.47890 | − | 0.853845i | −0.479187 | − | 0.877713i | \(-0.659069\pi\) |
−0.999715 | + | 0.0238679i | \(0.992402\pi\) | |||||||
\(422\) | −853.191 | + | 4033.76i | −0.0984187 | + | 0.465309i | ||||
\(423\) | −10922.1 | − | 6305.85i | −1.25543 | − | 0.724825i | ||||
\(424\) | 736.858 | − | 7218.82i | 0.0843986 | − | 0.826832i | ||||
\(425\) | −2739.58 | −0.312681 | ||||||||
\(426\) | −16331.0 | − | 14675.0i | −1.85737 | − | 1.66903i | ||||
\(427\) | −1950.40 | + | 1126.06i | −0.221046 | + | 0.127621i | ||||
\(428\) | 921.495 | − | 672.323i | 0.104070 | − | 0.0759298i | ||||
\(429\) | −159.742 | −0.0179776 | ||||||||
\(430\) | −8705.15 | + | 9687.50i | −0.976279 | + | 1.08645i | ||||
\(431\) | 6789.52 | + | 11759.8i | 0.758793 | + | 1.31427i | 0.943466 | + | 0.331468i | \(0.107544\pi\) |
−0.184673 | + | 0.982800i | \(0.559123\pi\) | |||||||
\(432\) | −7911.74 | + | 24685.1i | −0.881143 | + | 2.74922i | ||||
\(433\) | 3828.82 | − | 2210.57i | 0.424945 | − | 0.245342i | −0.272246 | − | 0.962228i | \(-0.587766\pi\) |
0.697191 | + | 0.716886i | \(0.254433\pi\) | |||||||
\(434\) | −486.077 | − | 1490.92i | −0.0537614 | − | 0.164900i | ||||
\(435\) | 11107.3 | + | 6412.82i | 1.22427 | + | 0.706830i | ||||
\(436\) | −15491.1 | + | 1659.48i | −1.70158 | + | 0.182282i | ||||
\(437\) | −7423.76 | + | 5434.46i | −0.812646 | + | 0.594887i | ||||
\(438\) | 15862.6 | + | 14254.1i | 1.73047 | + | 1.55499i | ||||
\(439\) | 1605.89 | − | 2781.49i | 0.174590 | − | 0.302399i | −0.765429 | − | 0.643520i | \(-0.777473\pi\) |
0.940019 | + | 0.341121i | \(0.110807\pi\) | |||||||
\(440\) | −15591.3 | + | 6997.75i | −1.68928 | + | 0.758192i | ||||
\(441\) | −11178.5 | − | 19361.8i | −1.20705 | − | 2.09068i | ||||
\(442\) | −13.3222 | − | 40.8626i | −0.00143365 | − | 0.00439737i | ||||
\(443\) | −4315.10 | + | 2491.33i | −0.462792 | + | 0.267193i | −0.713217 | − | 0.700943i | \(-0.752763\pi\) |
0.250426 | + | 0.968136i | \(0.419429\pi\) | |||||||
\(444\) | −20186.0 | + | 2162.43i | −2.15763 | + | 0.231136i | ||||
\(445\) | − | 1797.33i | − | 0.191464i | ||||||
\(446\) | 3090.54 | − | 14611.6i | 0.328120 | − | 1.55130i | ||||
\(447\) | 7213.33 | + | 12493.8i | 0.763263 | + | 1.32201i | ||||
\(448\) | 1968.66 | − | 652.731i | 0.207613 | − | 0.0688362i | ||||
\(449\) | − | 9598.58i | − | 1.00888i | −0.863448 | − | 0.504438i | \(-0.831700\pi\) | ||
0.863448 | − | 0.504438i | \(-0.168300\pi\) | |||||||
\(450\) | 2079.96 | − | 9833.72i | 0.217889 | − | 1.03015i | ||||
\(451\) | 1264.99 | − | 2191.03i | 0.132076 | − | 0.228762i | ||||
\(452\) | −5079.47 | − | 6961.99i | −0.528580 | − | 0.724479i | ||||
\(453\) | −556.821 | + | 964.442i | −0.0577522 | + | 0.100030i | ||||
\(454\) | 6918.21 | − | 2255.51i | 0.715172 | − | 0.233164i | ||||
\(455\) | −15.5140 | −0.00159848 | ||||||||
\(456\) | 9258.75 | + | 15795.5i | 0.950835 | + | 1.62213i | ||||
\(457\) | −3080.49 | −0.315315 | −0.157658 | − | 0.987494i | \(-0.550394\pi\) | ||||
−0.157658 | + | 0.987494i | \(0.550394\pi\) | |||||||
\(458\) | 11014.3 | − | 3590.93i | 1.12372 | − | 0.366361i | ||||
\(459\) | −10687.5 | + | 18511.4i | −1.08682 | + | 1.88243i | ||||
\(460\) | 6967.08 | + | 9549.17i | 0.706177 | + | 0.967897i | ||||
\(461\) | 6520.48 | − | 11293.8i | 0.658762 | − | 1.14101i | −0.322175 | − | 0.946680i | \(-0.604414\pi\) |
0.980936 | − | 0.194329i | \(-0.0622528\pi\) | |||||||
\(462\) | 1315.37 | − | 6218.88i | 0.132460 | − | 0.626252i | ||||
\(463\) | − | 17814.9i | − | 1.78818i | −0.447883 | − | 0.894092i | \(-0.647822\pi\) | ||
0.447883 | − | 0.894092i | \(-0.352178\pi\) | |||||||
\(464\) | 1337.96 | + | 6173.21i | 0.133865 | + | 0.617638i | ||||
\(465\) | −8892.92 | − | 15403.0i | −0.886880 | − | 1.53612i | ||||
\(466\) | −1992.19 | + | 9418.78i | −0.198040 | + | 0.936302i | ||||
\(467\) | 7272.18i | 0.720592i | 0.932838 | + | 0.360296i | \(0.117324\pi\) | ||||
−0.932838 | + | 0.360296i | \(0.882676\pi\) | |||||||
\(468\) | 156.791 | − | 16.7962i | 0.0154864 | − | 0.00165899i | ||||
\(469\) | 1189.39 | − | 686.697i | 0.117103 | − | 0.0676092i | ||||
\(470\) | 2148.33 | + | 6589.48i | 0.210841 | + | 0.646702i | ||||
\(471\) | 1716.12 | + | 2972.41i | 0.167887 | + | 0.290789i | ||||
\(472\) | 2932.61 | + | 6533.96i | 0.285983 | + | 0.637182i | ||||
\(473\) | −9829.11 | + | 17024.5i | −0.955482 | + | 1.65494i | ||||
\(474\) | −18742.4 | − | 16841.8i | −1.81617 | − | 1.63201i | ||||
\(475\) | −2539.51 | − | 3469.10i | −0.245307 | − | 0.335102i | ||||
\(476\) | 1700.52 | − | 182.168i | 0.163746 | − | 0.0175413i | ||||
\(477\) | 19011.8 | + | 10976.5i | 1.82493 | + | 1.05362i | ||||
\(478\) | −1759.92 | − | 5398.11i | −0.168403 | − | 0.516535i | ||||
\(479\) | 16914.9 | − | 9765.82i | 1.61349 | − | 0.931548i | 0.624935 | − | 0.780676i | \(-0.285125\pi\) |
0.988553 | − | 0.150872i | \(-0.0482080\pi\) | |||||||
\(480\) | 20313.1 | − | 11863.5i | 1.93158 | − | 1.12810i | ||||
\(481\) | 37.3942 | + | 64.7687i | 0.00354476 | + | 0.00613970i | ||||
\(482\) | 10578.7 | − | 11772.4i | 0.999678 | − | 1.11249i | ||||
\(483\) | −4396.66 | −0.414192 | ||||||||
\(484\) | −12236.1 | + | 8927.43i | −1.14914 | + | 0.838414i | ||||
\(485\) | 5105.68 | − | 2947.76i | 0.478014 | − | 0.275982i | ||||
\(486\) | −20340.8 | − | 18278.2i | −1.89852 | − | 1.70600i | ||||
\(487\) | −14833.4 | −1.38022 | −0.690111 | − | 0.723704i | \(-0.742438\pi\) | ||||
−0.690111 | + | 0.723704i | \(0.742438\pi\) | |||||||
\(488\) | −12514.9 | − | 1277.45i | −1.16091 | − | 0.118499i | ||||
\(489\) | 15100.7 | + | 8718.41i | 1.39648 | + | 0.806258i | ||||
\(490\) | −2542.49 | + | 12020.5i | −0.234404 | + | 1.10823i | ||||
\(491\) | 6313.74 | + | 3645.24i | 0.580316 | + | 0.335046i | 0.761259 | − | 0.648448i | \(-0.224582\pi\) |
−0.180943 | + | 0.983494i | \(0.557915\pi\) | |||||||
\(492\) | −1410.09 | + | 3184.23i | −0.129211 | + | 0.291781i | ||||
\(493\) | 5208.57i | 0.475826i | ||||||||
\(494\) | 39.3946 | − | 54.7482i | 0.00358795 | − | 0.00498631i | ||||
\(495\) | − | 51702.2i | − | 4.69463i | ||||||
\(496\) | 2673.49 | − | 8341.44i | 0.242023 | − | 0.755124i | ||||
\(497\) | −2787.30 | − | 1609.25i | −0.251564 | − | 0.145241i | ||||
\(498\) | −6365.76 | − | 1346.44i | −0.572804 | − | 0.121155i | ||||
\(499\) | 7653.24 | + | 4418.60i | 0.686585 | + | 0.396400i | 0.802331 | − | 0.596879i | \(-0.203593\pi\) |
−0.115746 | + | 0.993279i | \(0.536926\pi\) | |||||||
\(500\) | 6282.64 | − | 4583.81i | 0.561936 | − | 0.409989i | ||||
\(501\) | −7844.76 | −0.699557 | ||||||||
\(502\) | 4604.62 | − | 5124.24i | 0.409391 | − | 0.455589i | ||||
\(503\) | −5544.70 | + | 3201.24i | −0.491503 | + | 0.283769i | −0.725198 | − | 0.688541i | \(-0.758252\pi\) |
0.233695 | + | 0.972310i | \(0.424918\pi\) | |||||||
\(504\) | −637.181 | + | 6242.31i | −0.0563141 | + | 0.551695i | ||||
\(505\) | 22036.9 | 1.94184 | ||||||||
\(506\) | 13270.9 | + | 11925.2i | 1.16593 | + | 1.04770i | ||||
\(507\) | 10732.1 | + | 18588.6i | 0.940098 | + | 1.62830i | ||||
\(508\) | −10854.4 | − | 4806.74i | −0.948007 | − | 0.419812i | ||||
\(509\) | 1793.83 | − | 1035.67i | 0.156209 | − | 0.0901871i | −0.419858 | − | 0.907590i | \(-0.637920\pi\) |
0.576067 | + | 0.817403i | \(0.304587\pi\) | |||||||
\(510\) | 18442.0 | − | 6012.56i | 1.60123 | − | 0.522041i | ||||
\(511\) | 2707.35 | + | 1563.09i | 0.234376 | + | 0.135317i | ||||
\(512\) | 11050.0 | + | 3480.81i | 0.953797 | + | 0.300452i | ||||
\(513\) | −33347.8 | + | 3625.97i | −2.87006 | + | 0.312067i | ||||
\(514\) | −7122.92 | + | 7926.71i | −0.611242 | + | 0.680219i | ||||
\(515\) | −1079.20 | + | 1869.22i | −0.0923398 | + | 0.159937i | ||||
\(516\) | 10956.6 | − | 24741.8i | 0.934761 | − | 2.11085i | ||||
\(517\) | 5230.61 | + | 9059.68i | 0.444955 | + | 0.770685i | ||||
\(518\) | −2829.42 | + | 922.460i | −0.239995 | + | 0.0782444i | ||||
\(519\) | −8856.50 | + | 5113.30i | −0.749051 | + | 0.432465i | ||||
\(520\) | −70.2604 | − | 50.7261i | −0.00592524 | − | 0.00427786i | ||||
\(521\) | 2713.14i | 0.228147i | 0.993472 | + | 0.114074i | \(0.0363900\pi\) | ||||
−0.993472 | + | 0.114074i | \(0.963610\pi\) | |||||||
\(522\) | −18696.1 | − | 3954.47i | −1.56764 | − | 0.331575i | ||||
\(523\) | −2006.27 | − | 3474.96i | −0.167740 | − | 0.290534i | 0.769885 | − | 0.638183i | \(-0.220314\pi\) |
−0.937625 | + | 0.347648i | \(0.886980\pi\) | |||||||
\(524\) | −13250.1 | + | 1419.41i | −1.10464 | + | 0.118335i | ||||
\(525\) | − | 2054.55i | − | 0.170796i | ||||||
\(526\) | 10890.0 | + | 2303.37i | 0.902713 | + | 0.190935i | ||||
\(527\) | 3611.47 | − | 6255.25i | 0.298516 | − | 0.517045i | ||||
\(528\) | 26290.9 | − | 23863.4i | 2.16698 | − | 1.96689i | ||||
\(529\) | 86.8993 | − | 150.514i | 0.00714221 | − | 0.0123707i | ||||
\(530\) | −3739.56 | − | 11470.2i | −0.306483 | − | 0.940062i | ||||
\(531\) | −21667.3 | −1.77077 | ||||||||
\(532\) | 1807.01 | + | 1984.48i | 0.147263 | + | 0.161726i | ||||
\(533\) | 12.8291 | 0.00104257 | ||||||||
\(534\) | 1157.47 | + | 3550.27i | 0.0937993 | + | 0.287706i | ||||
\(535\) | 948.256 | − | 1642.43i | 0.0766293 | − | 0.132726i | ||||
\(536\) | 7631.84 | + | 779.017i | 0.615010 | + | 0.0627769i | ||||
\(537\) | −5416.42 | + | 9381.51i | −0.435262 | + | 0.753896i | ||||
\(538\) | 2713.32 | + | 573.900i | 0.217434 | + | 0.0459900i | ||||
\(539\) | 18544.8i | 1.48197i | ||||||||
\(540\) | 4590.61 | + | 42852.8i | 0.365830 | + | 3.41498i | ||||
\(541\) | 4951.03 | + | 8575.44i | 0.393459 | + | 0.681491i | 0.992903 | − | 0.118925i | \(-0.0379449\pi\) |
−0.599444 | + | 0.800417i | \(0.704612\pi\) | |||||||
\(542\) | 2836.18 | + | 599.887i | 0.224768 | + | 0.0475413i | ||||
\(543\) | 6235.50i | 0.492801i | ||||||||
\(544\) | 8296.98 | + | 4735.16i | 0.653916 | + | 0.373195i | ||||
\(545\) | −22432.6 | + | 12951.4i | −1.76313 | + | 1.01794i | ||||
\(546\) | 30.6449 | − | 9.99099i | 0.00240198 | − | 0.000783105i | ||||
\(547\) | −442.697 | − | 766.774i | −0.0346039 | − | 0.0599358i | 0.848205 | − | 0.529668i | \(-0.177684\pi\) |
−0.882809 | + | 0.469733i | \(0.844350\pi\) | |||||||
\(548\) | 8794.98 | + | 3894.74i | 0.685589 | + | 0.303604i | ||||
\(549\) | 19029.4 | − | 32959.9i | 1.47933 | − | 2.56228i | ||||
\(550\) | −5572.61 | + | 6201.46i | −0.432031 | + | 0.480784i | ||||
\(551\) | −6595.55 | + | 4828.19i | −0.509946 | + | 0.373299i | ||||
\(552\) | −19911.7 | − | 14375.7i | −1.53532 | − | 1.10846i | ||||
\(553\) | −3198.86 | − | 1846.86i | −0.245984 | − | 0.142019i | ||||
\(554\) | 9507.64 | − | 3099.73i | 0.729135 | − | 0.237716i | ||||
\(555\) | −29231.3 | + | 16876.7i | −2.23567 | + | 1.29077i | ||||
\(556\) | −1985.82 | + | 4484.32i | −0.151470 | + | 0.342046i | ||||
\(557\) | −3225.57 | − | 5586.85i | −0.245371 | − | 0.424995i | 0.716865 | − | 0.697212i | \(-0.245576\pi\) |
−0.962236 | + | 0.272217i | \(0.912243\pi\) | |||||||
\(558\) | 19711.3 | + | 17712.5i | 1.49542 | + | 1.34378i | ||||
\(559\) | −99.6831 | −0.00754230 | ||||||||
\(560\) | 2553.36 | − | 2317.60i | 0.192677 | − | 0.174887i | ||||
\(561\) | 25355.4 | − | 14639.0i | 1.90821 | − | 1.10171i | ||||
\(562\) | 4752.18 | − | 5288.44i | 0.356688 | − | 0.396939i | ||||
\(563\) | −4949.63 | −0.370519 | −0.185259 | − | 0.982690i | \(-0.559313\pi\) | ||||
−0.185259 | + | 0.982690i | \(0.559313\pi\) | |||||||
\(564\) | −8487.21 | − | 11632.7i | −0.633645 | − | 0.868483i | ||||
\(565\) | −12408.7 | − | 7164.17i | −0.923962 | − | 0.533450i | ||||
\(566\) | −12793.6 | − | 2706.01i | −0.950098 | − | 0.200958i | ||||
\(567\) | −7398.40 | − | 4271.47i | −0.547978 | − | 0.316375i | ||||
\(568\) | −7361.45 | − | 16401.6i | −0.543802 | − | 1.21161i | ||||
\(569\) | 18553.2i | 1.36694i | 0.729979 | + | 0.683470i | \(0.239530\pi\) | ||||
−0.729979 | + | 0.683470i | \(0.760470\pi\) | |||||||
\(570\) | 24708.9 | + | 17779.5i | 1.81569 | + | 1.30649i | ||||
\(571\) | 2466.39i | 0.180762i | 0.995907 | + | 0.0903811i | \(0.0288085\pi\) | ||||
−0.995907 | + | 0.0903811i | \(0.971191\pi\) | |||||||
\(572\) | −119.597 | − | 52.9621i | −0.00874235 | − | 0.00387143i | ||||
\(573\) | 4497.50 | + | 2596.63i | 0.327899 | + | 0.189312i | ||||
\(574\) | −105.639 | + | 499.446i | −0.00768170 | + | 0.0363179i | ||||
\(575\) | 4994.22 | + | 2883.41i | 0.362215 | + | 0.209125i | ||||
\(576\) | −23296.1 | + | 26186.9i | −1.68519 | + | 1.89431i | ||||
\(577\) | 6937.93 | 0.500572 | 0.250286 | − | 0.968172i | \(-0.419475\pi\) | ||||
0.250286 | + | 0.968172i | \(0.419475\pi\) | |||||||
\(578\) | −4476.75 | − | 4022.79i | −0.322160 | − | 0.289492i | ||||
\(579\) | 30225.4 | − | 17450.6i | 2.16947 | − | 1.25254i | ||||
\(580\) | 6189.82 | + | 8483.85i | 0.443135 | + | 0.607367i | ||||
\(581\) | −953.799 | −0.0681071 | ||||||||
\(582\) | −8186.90 | + | 9110.76i | −0.583089 | + | 0.648889i | ||||
\(583\) | −9104.82 | − | 15770.0i | −0.646798 | − | 1.12029i | ||||
\(584\) | 7150.31 | + | 15931.2i | 0.506647 | + | 1.12883i | ||||
\(585\) | 227.048 | − | 131.086i | 0.0160466 | − | 0.00926452i | ||||
\(586\) | 5674.02 | + | 17403.7i | 0.399986 | + | 1.22686i | ||||
\(587\) | −13706.4 | − | 7913.39i | −0.963754 | − | 0.556423i | −0.0664273 | − | 0.997791i | \(-0.521160\pi\) |
−0.897326 | + | 0.441368i | \(0.854493\pi\) | |||||||
\(588\) | −2718.99 | − | 25381.5i | −0.190696 | − | 1.78013i | ||||
\(589\) | 11268.7 | − | 1225.27i | 0.788315 | − | 0.0857151i | ||||
\(590\) | 8856.88 | + | 7958.76i | 0.618020 | + | 0.555351i | ||||
\(591\) | 4552.37 | − | 7884.93i | 0.316852 | − | 0.548803i | ||||
\(592\) | −15830.1 | − | 5073.66i | −1.09901 | − | 0.352240i | ||||
\(593\) | −826.677 | − | 1431.85i | −0.0572472 | − | 0.0991550i | 0.835982 | − | 0.548758i | \(-0.184899\pi\) |
−0.893229 | + | 0.449603i | \(0.851566\pi\) | |||||||
\(594\) | 20163.6 | + | 61846.9i | 1.39280 | + | 4.27207i | ||||
\(595\) | 2462.51 | − | 1421.73i | 0.169669 | − | 0.0979584i | ||||
\(596\) | 1258.25 | + | 11745.6i | 0.0864765 | + | 0.807248i | ||||
\(597\) | − | 1845.03i | − | 0.126486i | ||||||
\(598\) | −18.7217 | + | 88.5136i | −0.00128025 | + | 0.00605283i | ||||
\(599\) | −4014.41 | − | 6953.16i | −0.273830 | − | 0.474288i | 0.696009 | − | 0.718033i | \(-0.254957\pi\) |
−0.969839 | + | 0.243745i | \(0.921624\pi\) | |||||||
\(600\) | 6717.74 | − | 9304.70i | 0.457084 | − | 0.633105i | ||||
\(601\) | − | 8354.32i | − | 0.567021i | −0.958969 | − | 0.283511i | \(-0.908501\pi\) | ||
0.958969 | − | 0.283511i | \(-0.0914992\pi\) | |||||||
\(602\) | 820.827 | − | 3880.75i | 0.0555721 | − | 0.262737i | ||||
\(603\) | −11604.5 | + | 20099.6i | −0.783701 | + | 1.35741i | ||||
\(604\) | −736.647 | + | 537.458i | −0.0496254 | + | 0.0362067i | ||||
\(605\) | −12591.4 | + | 21808.9i | −0.846138 | + | 1.46555i | ||||
\(606\) | −43529.6 | + | 14191.7i | −2.91793 | + | 0.951318i | ||||
\(607\) | 14668.9 | 0.980874 | 0.490437 | − | 0.871477i | \(-0.336837\pi\) | ||||
0.490437 | + | 0.871477i | \(0.336837\pi\) | |||||||
\(608\) | 1694.98 | + | 14895.7i | 0.113060 | + | 0.993588i | ||||
\(609\) | −3906.16 | −0.259911 | ||||||||
\(610\) | −19885.3 | + | 6483.10i | −1.31989 | + | 0.430316i | ||||
\(611\) | −26.5234 | + | 45.9399i | −0.00175617 | + | 0.00304178i | ||||
\(612\) | −23347.8 | + | 17034.6i | −1.54212 | + | 1.12513i | ||||
\(613\) | 1160.52 | − | 2010.07i | 0.0764646 | − | 0.132441i | −0.825258 | − | 0.564756i | \(-0.808970\pi\) |
0.901722 | + | 0.432316i | \(0.142303\pi\) | |||||||
\(614\) | 2724.82 | − | 12882.6i | 0.179096 | − | 0.846740i | ||||
\(615\) | 5789.99i | 0.379634i | ||||||||
\(616\) | 3046.67 | − | 4219.92i | 0.199276 | − | 0.276016i | ||||
\(617\) | −3927.18 | − | 6802.07i | −0.256244 | − | 0.443827i | 0.708989 | − | 0.705220i | \(-0.249152\pi\) |
−0.965233 | + | 0.261393i | \(0.915818\pi\) | |||||||
\(618\) | 927.963 | − | 4387.27i | 0.0604015 | − | 0.285570i | ||||
\(619\) | − | 28000.8i | − | 1.81817i | −0.416610 | − | 0.909085i | \(-0.636782\pi\) | ||
0.416610 | − | 0.909085i | \(-0.363218\pi\) | |||||||
\(620\) | −1551.23 | − | 14480.6i | −0.100482 | − | 0.937989i | ||||
\(621\) | 38966.4 | − | 22497.3i | 2.51799 | − | 1.45376i | ||||
\(622\) | −6874.31 | − | 21085.3i | −0.443143 | − | 1.35923i | ||||
\(623\) | 273.696 | + | 474.056i | 0.0176010 | + | 0.0304858i | ||||
\(624\) | 171.453 | + | 54.9518i | 0.0109994 | + | 0.00352538i | ||||
\(625\) | 9709.57 | − | 16817.5i | 0.621412 | − | 1.07632i | ||||
\(626\) | 15797.0 | + | 14195.2i | 1.00859 | + | 0.906314i | ||||
\(627\) | 42040.9 | + | 18537.4i | 2.67775 | + | 1.18072i | ||||
\(628\) | 299.351 | + | 2794.41i | 0.0190213 | + | 0.177562i | ||||
\(629\) | −11871.0 | − | 6853.73i | −0.752508 | − | 0.434461i | ||||
\(630\) | 3233.70 | + | 9918.58i | 0.204498 | + | 0.627247i | ||||
\(631\) | −11552.6 | + | 6669.90i | −0.728847 | + | 0.420800i | −0.818000 | − | 0.575218i | \(-0.804917\pi\) |
0.0891535 | + | 0.996018i | \(0.471584\pi\) | |||||||
\(632\) | −8448.41 | − | 18823.4i | −0.531740 | − | 1.18474i | ||||
\(633\) | −7120.99 | − | 12333.9i | −0.447131 | − | 0.774454i | ||||
\(634\) | 1198.99 | − | 1334.29i | 0.0751069 | − | 0.0835825i | ||||
\(635\) | −19736.9 | −1.23344 | ||||||||
\(636\) | 14773.5 | + | 20248.8i | 0.921082 | + | 1.26245i | ||||
\(637\) | −81.4387 | + | 47.0187i | −0.00506549 | + | 0.00292456i | ||||
\(638\) | 11790.4 | + | 10594.8i | 0.731638 | + | 0.657448i | ||||
\(639\) | 54389.4 | 3.36715 | ||||||||
\(640\) | 19141.6 | − | 2147.32i | 1.18225 | − | 0.132625i | ||||
\(641\) | −7809.28 | − | 4508.69i | −0.481198 | − | 0.277820i | 0.239718 | − | 0.970843i | \(-0.422945\pi\) |
−0.720916 | + | 0.693023i | \(0.756278\pi\) | |||||||
\(642\) | −815.373 | + | 3854.96i | −0.0501249 | + | 0.236983i | ||||
\(643\) | −22442.4 | − | 12957.1i | −1.37643 | − | 0.794680i | −0.384698 | − | 0.923042i | \(-0.625694\pi\) |
−0.991727 | + | 0.128363i | \(0.959028\pi\) | |||||||
\(644\) | −3291.75 | − | 1457.71i | −0.201418 | − | 0.0891952i | ||||
\(645\) | − | 44988.8i | − | 2.74641i | ||||||
\(646\) | −1235.80 | + | 12300.2i | −0.0752663 | + | 0.749143i | ||||
\(647\) | − | 24631.3i | − | 1.49669i | −0.663312 | − | 0.748343i | \(-0.730850\pi\) | ||
0.663312 | − | 0.748343i | \(-0.269150\pi\) | |||||||
\(648\) | −19539.7 | − | 43535.2i | −1.18456 | − | 2.63924i | ||||
\(649\) | 15564.8 | + | 8986.34i | 0.941405 | + | 0.543521i | ||||
\(650\) | −41.3622 | − | 8.74862i | −0.00249594 | − | 0.000527922i | ||||
\(651\) | 4691.12 | + | 2708.42i | 0.282426 | + | 0.163059i | ||||
\(652\) | 8415.24 | + | 11534.0i | 0.505470 | + | 0.692804i | ||||
\(653\) | −26232.7 | −1.57208 | −0.786039 | − | 0.618177i | \(-0.787871\pi\) | ||||
−0.786039 | + | 0.618177i | \(0.787871\pi\) | |||||||
\(654\) | 35970.4 | − | 40029.5i | 2.15069 | − | 2.39339i | ||||
\(655\) | −19187.3 | + | 11077.8i | −1.14460 | + | 0.660833i | ||||
\(656\) | −2111.46 | + | 1916.50i | −0.125668 | + | 0.114065i | ||||
\(657\) | −52829.4 | −3.13710 | ||||||||
\(658\) | −1570.08 | − | 1410.87i | −0.0930213 | − | 0.0835886i | ||||
\(659\) | −921.364 | − | 1595.85i | −0.0544632 | − | 0.0943330i | 0.837508 | − | 0.546424i | \(-0.184011\pi\) |
−0.891972 | + | 0.452091i | \(0.850678\pi\) | |||||||
\(660\) | 23902.8 | − | 53976.5i | 1.40972 | − | 3.18338i | ||||
\(661\) | 3081.85 | − | 1779.31i | 0.181347 | − | 0.104701i | −0.406579 | − | 0.913616i | \(-0.633278\pi\) |
0.587925 | + | 0.808915i | \(0.299945\pi\) | |||||||
\(662\) | −30402.0 | + | 9911.79i | −1.78490 | + | 0.581923i | ||||
\(663\) | 128.573 | + | 74.2314i | 0.00753144 | + | 0.00434828i | ||||
\(664\) | −4319.59 | − | 3118.63i | −0.252459 | − | 0.182268i | ||||
\(665\) | 4082.99 | + | 1800.35i | 0.238093 | + | 0.104984i | ||||
\(666\) | 33614.2 | − | 37407.4i | 1.95574 | − | 2.17644i | ||||
\(667\) | 5482.02 | − | 9495.14i | 0.318238 | − | 0.551204i | ||||
\(668\) | −5873.32 | − | 2600.92i | −0.340188 | − | 0.150648i | ||||
\(669\) | 25794.6 | + | 44677.5i | 1.49070 | + | 2.58196i | ||||
\(670\) | 12126.5 | − | 3953.52i | 0.699232 | − | 0.227967i | ||||
\(671\) | −27339.7 | + | 15784.6i | −1.57293 | + | 0.908133i | ||||
\(672\) | −3551.13 | + | 6222.32i | −0.203851 | + | 0.357189i | ||||
\(673\) | 6765.24i | 0.387490i | 0.981052 | + | 0.193745i | \(0.0620634\pi\) | ||||
−0.981052 | + | 0.193745i | \(0.937937\pi\) | |||||||
\(674\) | −52.2407 | − | 11.0496i | −0.00298552 | − | 0.000631474i | ||||
\(675\) | 10512.9 | + | 18208.9i | 0.599471 | + | 1.03831i | ||||
\(676\) | 1872.05 | + | 17475.4i | 0.106512 | + | 0.994274i | ||||
\(677\) | − | 3782.89i | − | 0.214754i | −0.994218 | − | 0.107377i | \(-0.965755\pi\) | ||
0.994218 | − | 0.107377i | \(-0.0342452\pi\) | |||||||
\(678\) | 29124.7 | + | 6160.23i | 1.64974 | + | 0.348941i | ||||
\(679\) | −897.768 | + | 1554.98i | −0.0507411 | + | 0.0878861i | ||||
\(680\) | 15800.9 | + | 1612.87i | 0.891083 | + | 0.0909570i | ||||
\(681\) | −12567.7 | + | 21767.9i | −0.707188 | + | 1.22489i | ||||
\(682\) | −6813.57 | − | 20898.9i | −0.382559 | − | 1.17340i | ||||
\(683\) | −6443.78 | −0.361002 | −0.180501 | − | 0.983575i | \(-0.557772\pi\) | ||||
−0.180501 | + | 0.983575i | \(0.557772\pi\) | |||||||
\(684\) | −43213.4 | − | 13774.5i | −2.41565 | − | 0.770004i | ||||
\(685\) | 15992.2 | 0.892014 | ||||||||
\(686\) | −2378.04 | − | 7294.05i | −0.132353 | − | 0.405960i | ||||
\(687\) | −20008.7 | + | 34656.0i | −1.11118 | + | 1.92461i | ||||
\(688\) | 16406.2 | − | 14891.4i | 0.909131 | − | 0.825188i | ||||
\(689\) | 46.1688 | − | 79.9668i | 0.00255282 | − | 0.00442161i | ||||
\(690\) | −39947.8 | − | 8449.46i | −2.20404 | − | 0.466182i | ||||
\(691\) | − | 4407.36i | − | 0.242639i | −0.992613 | − | 0.121320i | \(-0.961287\pi\) | ||
0.992613 | − | 0.121320i | \(-0.0387126\pi\) | |||||||
\(692\) | −8326.11 | + | 891.935i | −0.457386 | + | 0.0489975i | ||||
\(693\) | 7873.19 | + | 13636.8i | 0.431569 | + | 0.747500i | ||||
\(694\) | 28791.1 | + | 6089.68i | 1.57478 | + | 0.333085i | ||||
\(695\) | 8153.98i | 0.445033i | ||||||||
\(696\) | −17690.3 | − | 12771.9i | −0.963435 | − | 0.695574i | ||||
\(697\) | −2036.33 | + | 1175.67i | −0.110662 | + | 0.0638907i | ||||
\(698\) | −23141.6 | + | 7544.73i | −1.25490 | + | 0.409129i | ||||
\(699\) | −16627.4 | − | 28799.5i | −0.899724 | − | 1.55837i | ||||
\(700\) | 681.183 | − | 1538.23i | 0.0367804 | − | 0.0830565i | ||||
\(701\) | −18486.8 | + | 32020.1i | −0.996059 | + | 1.72522i | −0.421217 | + | 0.906960i | \(0.638397\pi\) |
−0.574842 | + | 0.818264i | \(0.694936\pi\) | |||||||
\(702\) | −220.475 | + | 245.355i | −0.0118537 | + | 0.0131913i | ||||
\(703\) | −2325.27 | − | 21385.3i | −0.124750 | − | 1.14731i | ||||
\(704\) | 27595.7 | − | 9149.64i | 1.47735 | − | 0.489830i | ||||
\(705\) | −20733.5 | − | 11970.5i | −1.10762 | − | 0.639483i | ||||
\(706\) | −29224.8 | + | 9527.99i | −1.55792 | + | 0.507919i | ||||
\(707\) | −5812.37 | + | 3355.77i | −0.309189 | + | 0.178510i | ||||
\(708\) | −22620.4 | − | 10017.1i | −1.20074 | − | 0.531733i | ||||
\(709\) | −15601.8 | − | 27023.1i | −0.826430 | − | 1.43142i | −0.900822 | − | 0.434189i | \(-0.857035\pi\) |
0.0743922 | − | 0.997229i | \(-0.476298\pi\) | |||||||
\(710\) | −22232.6 | − | 19978.1i | −1.17517 | − | 1.05601i | ||||
\(711\) | 62420.3 | 3.29247 | ||||||||
\(712\) | −310.492 | + | 3041.82i | −0.0163430 | + | 0.160108i | ||||
\(713\) | −13167.3 | + | 7602.15i | −0.691612 | + | 0.399302i | ||||
\(714\) | −3948.61 | + | 4394.19i | −0.206965 | + | 0.230320i | ||||
\(715\) | −217.468 | −0.0113746 | ||||||||
\(716\) | −7165.66 | + | 5228.07i | −0.374013 | + | 0.272880i | ||||
\(717\) | 16984.9 | + | 9806.26i | 0.884678 | + | 0.510769i | ||||
\(718\) | 5717.97 | + | 1209.42i | 0.297204 | + | 0.0628624i | ||||
\(719\) | −4769.10 | − | 2753.44i | −0.247368 | − | 0.142818i | 0.371191 | − | 0.928557i | \(-0.378950\pi\) |
−0.618558 | + | 0.785739i | \(0.712283\pi\) | |||||||
\(720\) | −17785.8 | + | 55492.7i | −0.920608 | + | 2.87235i | ||||
\(721\) | − | 657.357i | − | 0.0339546i | ||||||
\(722\) | −16721.2 | + | 9837.07i | −0.861910 | + | 0.507061i | ||||
\(723\) | 54671.2i | 2.81223i | ||||||||
\(724\) | −2067.37 | + | 4668.48i | −0.106123 | + | 0.239645i | ||||
\(725\) | 4437.06 | + | 2561.74i | 0.227294 | + | 0.131228i | ||||
\(726\) | 10826.9 | − | 51188.1i | 0.553477 | − | 2.61676i | ||||
\(727\) | 12494.2 | + | 7213.56i | 0.637395 | + | 0.368000i | 0.783610 | − | 0.621253i | \(-0.213376\pi\) |
−0.146216 | + | 0.989253i | \(0.546709\pi\) | |||||||
\(728\) | 26.2561 | + | 2.68008i | 0.00133670 | + | 0.000136443i | ||||
\(729\) | 37522.4 | 1.90633 | ||||||||
\(730\) | 21594.9 | + | 19405.1i | 1.09488 | + | 0.983857i | ||||
\(731\) | 15822.5 | − | 9135.11i | 0.800568 | − | 0.462208i | ||||
\(732\) | 35104.4 | − | 25612.1i | 1.77253 | − | 1.29324i | ||||
\(733\) | 21303.6 | 1.07349 | 0.536743 | − | 0.843746i | \(-0.319655\pi\) | ||||
0.536743 | + | 0.843746i | \(0.319655\pi\) | |||||||
\(734\) | −807.765 | + | 898.919i | −0.0406201 | + | 0.0452040i | ||||
\(735\) | −21220.4 | − | 36754.8i | −1.06493 | − | 1.84452i | ||||
\(736\) | −10141.5 | − | 17364.7i | −0.507909 | − | 0.869662i | ||||
\(737\) | 16672.3 | − | 9625.76i | 0.833286 | − | 0.481098i | ||||
\(738\) | −2674.05 | − | 8201.99i | −0.133378 | − | 0.409105i | ||||
\(739\) | 17191.3 | + | 9925.41i | 0.855741 | + | 0.494062i | 0.862584 | − | 0.505914i | \(-0.168845\pi\) |
−0.00684290 | + | 0.999977i | \(0.502178\pi\) | |||||||
\(740\) | −27480.7 | + | 2943.87i | −1.36515 | + | 0.146242i | ||||
\(741\) | 25.1845 | + | 231.620i | 0.00124855 | + | 0.0114828i | ||||
\(742\) | 2733.00 | + | 2455.87i | 0.135218 | + | 0.121506i | ||||
\(743\) | −1271.77 | + | 2202.78i | −0.0627952 | + | 0.108765i | −0.895714 | − | 0.444631i | \(-0.853335\pi\) |
0.832919 | + | 0.553395i | \(0.186668\pi\) | |||||||
\(744\) | 12389.6 | + | 27604.5i | 0.610516 | + | 1.36025i | ||||
\(745\) | 9820.02 | + | 17008.8i | 0.482923 | + | 0.836447i | ||||
\(746\) | −7523.87 | − | 23077.6i | −0.369261 | − | 1.13262i | ||||
\(747\) | 13958.8 | − | 8059.13i | 0.683704 | − | 0.394737i | ||||
\(748\) | 23837.0 | − | 2553.54i | 1.16520 | − | 0.124822i | ||||
\(749\) | 577.599i | 0.0281776i | ||||||||
\(750\) | −5559.11 | + | 26282.6i | −0.270653 | + | 1.27961i | ||||
\(751\) | 14412.8 | + | 24963.6i | 0.700305 | + | 1.21296i | 0.968359 | + | 0.249560i | \(0.0802859\pi\) |
−0.268055 | + | 0.963404i | \(0.586381\pi\) | |||||||
\(752\) | −2497.52 | − | 11523.2i | −0.121110 | − | 0.558789i | ||||
\(753\) | 23797.0i | 1.15167i | ||||||||
\(754\) | −16.6331 | + | 78.6389i | −0.000803372 | + | 0.00379822i | ||||
\(755\) | −758.040 | + | 1312.96i | −0.0365403 | + | 0.0632896i | ||||
\(756\) | −7736.40 | − | 10603.6i | −0.372183 | − | 0.510119i | ||||
\(757\) | −5755.55 | + | 9968.90i | −0.276339 | + | 0.478634i | −0.970472 | − | 0.241213i | \(-0.922455\pi\) |
0.694133 | + | 0.719847i | \(0.255788\pi\) | |||||||
\(758\) | 25704.2 | − | 8380.20i | 1.23169 | − | 0.401560i | ||||
\(759\) | −61630.1 | −2.94734 | ||||||||
\(760\) | 12604.6 | + | 21503.6i | 0.601601 | + | 1.02634i | ||||
\(761\) | 18062.6 | 0.860404 | 0.430202 | − | 0.902733i | \(-0.358442\pi\) | ||||
0.430202 | + | 0.902733i | \(0.358442\pi\) | |||||||
\(762\) | 38986.4 | − | 12710.5i | 1.85345 | − | 0.604270i | ||||
\(763\) | 3944.48 | − | 6832.03i | 0.187156 | − | 0.324163i | ||||
\(764\) | 2506.34 | + | 3435.22i | 0.118686 | + | 0.162673i | ||||
\(765\) | −24025.9 | + | 41614.0i | −1.13550 | + | 1.96674i | ||||
\(766\) | −3180.25 | + | 15035.7i | −0.150009 | + | 0.709221i | ||||
\(767\) | 91.1361i | 0.00429040i | ||||||||
\(768\) | −36427.5 | + | 16568.7i | −1.71154 | + | 0.778479i | ||||
\(769\) | −4277.98 | − | 7409.68i | −0.200609 | − | 0.347464i | 0.748116 | − | 0.663568i | \(-0.230959\pi\) |
−0.948725 | + | 0.316104i | \(0.897625\pi\) | |||||||
\(770\) | 1790.71 | − | 8466.21i | 0.0838087 | − | 0.396235i | ||||
\(771\) | − | 36811.7i | − | 1.71951i | ||||||
\(772\) | 28415.2 | − | 3043.99i | 1.32472 | − | 0.141911i | ||||
\(773\) | 8786.94 | − | 5073.14i | 0.408854 | − | 0.236052i | −0.281443 | − | 0.959578i | \(-0.590813\pi\) |
0.690297 | + | 0.723526i | \(0.257480\pi\) | |||||||
\(774\) | 20777.7 | + | 63730.3i | 0.964906 | + | 2.95961i | ||||
\(775\) | −3552.47 | − | 6153.05i | −0.164656 | − | 0.285192i | ||||
\(776\) | −9150.14 | + | 4106.81i | −0.423287 | + | 0.189982i | ||||
\(777\) | 5139.95 | − | 8902.65i | 0.237316 | − | 0.411043i | ||||
\(778\) | 19734.3 | + | 17733.1i | 0.909393 | + | 0.817177i | ||||
\(779\) | −3376.36 | − | 1488.76i | −0.155290 | − | 0.0684731i | ||||
\(780\) | 297.638 | − | 31.8845i | 0.0136630 | − | 0.00146365i | ||||
\(781\) | −39070.9 | − | 22557.6i | −1.79010 | − | 1.03351i | ||||
\(782\) | −5139.86 | − | 15765.3i | −0.235040 | − | 0.720926i | ||||
\(783\) | 34619.3 | − | 19987.5i | 1.58007 | − | 0.912252i | ||||
\(784\) | 6379.51 | − | 19904.4i | 0.290612 | − | 0.906725i | ||||
\(785\) | 2336.28 | + | 4046.56i | 0.106224 | + | 0.183985i | ||||
\(786\) | 30766.7 | − | 34238.6i | 1.39620 | − | 1.55375i | ||||
\(787\) | −3785.48 | −0.171458 | −0.0857292 | − | 0.996318i | \(-0.527322\pi\) | ||||
−0.0857292 | + | 0.996318i | \(0.527322\pi\) | |||||||
\(788\) | 6022.56 | − | 4394.06i | 0.272265 | − | 0.198645i | ||||
\(789\) | −33298.1 | + | 19224.7i | −1.50246 | + | 0.867447i | ||||
\(790\) | −25515.4 | − | 22928.0i | −1.14911 | − | 1.03259i | ||||
\(791\) | 4363.83 | 0.196157 | ||||||||
\(792\) | −8931.67 | + | 87501.4i | −0.400724 | + | 3.92579i | ||||
\(793\) | −138.634 | − | 80.0407i | −0.00620814 | − | 0.00358427i | ||||
\(794\) | −6011.62 | + | 28422.0i | −0.268696 | + | 1.27035i | ||||
\(795\) | 36090.5 | + | 20836.8i | 1.61006 | + | 0.929568i | ||||
\(796\) | 611.718 | − | 1381.36i | 0.0272384 | − | 0.0615090i | ||||
\(797\) | 9371.27i | 0.416496i | 0.978076 | + | 0.208248i | \(0.0667762\pi\) | ||||
−0.978076 | + | 0.208248i | \(0.933224\pi\) | |||||||
\(798\) | −9224.56 | − | 926.790i | −0.409205 | − | 0.0411128i | ||||
\(799\) | − | 9722.59i | − | 0.430489i | ||||||
\(800\) | 8114.49 | − | 4739.11i | 0.358613 | − | 0.209441i | ||||
\(801\) | −8011.08 | − | 4625.20i | −0.353380 | − | 0.204024i | ||||
\(802\) | −38880.3 | − | 8223.67i | −1.71186 | − | 0.362080i | ||||
\(803\) | 37950.3 | + | 21910.6i | 1.66779 | + | 0.962899i | ||||
\(804\) | −21407.3 | + | 15618.8i | −0.939028 | + | 0.685115i | ||||
\(805\) | −5985.49 | −0.262063 | ||||||||
\(806\) | 74.5015 | − | 82.9087i | 0.00325584 | − | 0.00362325i | ||||
\(807\) | −8296.43 | + | 4789.95i | −0.361894 | + | 0.208939i | ||||
\(808\) | −37295.5 | − | 3806.93i | −1.62383 | − | 0.165752i | ||||
\(809\) | 40309.1 | 1.75178 | 0.875892 | − | 0.482507i | \(-0.160274\pi\) | ||||
0.875892 | + | 0.482507i | \(0.160274\pi\) | |||||||
\(810\) | −59012.6 | − | 53028.5i | −2.55986 | − | 2.30029i | ||||
\(811\) | 1440.58 | + | 2495.16i | 0.0623745 | + | 0.108036i | 0.895526 | − | 0.445009i | \(-0.146799\pi\) |
−0.833152 | + | 0.553044i | \(0.813466\pi\) | |||||||
\(812\) | −2924.52 | − | 1295.08i | −0.126392 | − | 0.0559711i | ||||
\(813\) | −8672.10 | + | 5006.84i | −0.374101 | + | 0.215987i | ||||
\(814\) | −39661.3 | + | 12930.6i | −1.70777 | + | 0.556777i | ||||
\(815\) | 20557.7 | + | 11869.0i | 0.883565 | + | 0.510126i | ||||
\(816\) | −32250.2 | + | 6989.83i | −1.38356 | + | 0.299869i | ||||
\(817\) | 26234.7 | + | 11567.9i | 1.12342 | + | 0.495358i | ||||
\(818\) | −1473.19 | + | 1639.44i | −0.0629693 | + | 0.0700752i | ||||
\(819\) | −39.9234 | + | 69.1494i | −0.00170334 | + | 0.00295028i | ||||
\(820\) | −1919.66 | + | 4334.93i | −0.0817531 | + | 0.184612i | ||||
\(821\) | −1058.77 | − | 1833.85i | −0.0450078 | − | 0.0779558i | 0.842644 | − | 0.538471i | \(-0.180998\pi\) |
−0.887652 | + | 0.460515i | \(0.847665\pi\) | |||||||
\(822\) | −31589.4 | + | 10298.9i | −1.34040 | + | 0.437002i | ||||
\(823\) | −1651.13 | + | 953.280i | −0.0699329 | + | 0.0403758i | −0.534559 | − | 0.845131i | \(-0.679522\pi\) |
0.464626 | + | 0.885507i | \(0.346189\pi\) | |||||||
\(824\) | 2149.35 | − | 2977.06i | 0.0908693 | − | 0.125862i | ||||
\(825\) | − | 28799.6i | − | 1.21536i | ||||||
\(826\) | −3548.01 | − | 750.448i | −0.149456 | − | 0.0316119i | ||||
\(827\) | −14773.2 | − | 25588.0i | −0.621179 | − | 1.07591i | −0.989267 | − | 0.146122i | \(-0.953321\pi\) |
0.368088 | − | 0.929791i | \(-0.380013\pi\) | |||||||
\(828\) | 60491.6 | − | 6480.17i | 2.53892 | − | 0.271982i | ||||
\(829\) | − | 39343.8i | − | 1.64833i | −0.566350 | − | 0.824165i | \(-0.691645\pi\) | ||
0.566350 | − | 0.824165i | \(-0.308355\pi\) | |||||||
\(830\) | −8666.16 | − | 1833.00i | −0.362418 | − | 0.0766559i | ||||
\(831\) | −17271.7 | + | 29915.4i | −0.720996 | + | 1.24880i | ||||
\(832\) | 110.146 | + | 97.9871i | 0.00458971 | + | 0.00408304i | ||||
\(833\) | 8617.72 | − | 14926.3i | 0.358447 | − | 0.620849i | ||||
\(834\) | −5251.14 | − | 16106.6i | −0.218024 | − | 0.668735i | ||||
\(835\) | −10679.6 | −0.442616 | ||||||||
\(836\) | 25329.7 | + | 27817.4i | 1.04790 | + | 1.15082i | ||||
\(837\) | −55434.9 | −2.28926 | ||||||||
\(838\) | 7814.53 | + | 23969.1i | 0.322134 | + | 0.988067i | ||||
\(839\) | 21355.2 | − | 36988.4i | 0.878742 | − | 1.52203i | 0.0260200 | − | 0.999661i | \(-0.491717\pi\) |
0.852722 | − | 0.522365i | \(-0.174950\pi\) | |||||||
\(840\) | −1209.57 | + | 11849.9i | −0.0496835 | + | 0.486737i | ||||
\(841\) | −7324.06 | + | 12685.6i | −0.300302 | + | 0.520138i | ||||
\(842\) | 40820.0 | + | 8633.95i | 1.67073 | + | 0.353379i | ||||
\(843\) | 24559.6i | 1.00341i | ||||||||
\(844\) | −1242.14 | − | 11595.3i | −0.0506592 | − | 0.472898i | ||||
\(845\) | 14610.4 | + | 25305.9i | 0.594808 | + | 1.03024i | ||||
\(846\) | 34899.2 | + | 7381.61i | 1.41827 | + | 0.299982i | ||||
\(847\) | − | 7669.65i | − | 0.311136i | ||||||
\(848\) | 4347.38 | + | 20058.3i | 0.176049 | + | 0.812269i | ||||
\(849\) | 39118.7 | − | 22585.2i | 1.58133 | − | 0.912981i | ||||
\(850\) | 7367.07 | − | 2401.85i | 0.297280 | − | 0.0969208i | ||||
\(851\) | 14427.1 | + | 24988.5i | 0.581145 | + | 1.00657i | ||||
\(852\) | 56781.9 | + | 25145.1i | 2.28323 | + | 1.01110i | ||||
\(853\) | −5028.70 | + | 8709.96i | −0.201852 | + | 0.349617i | −0.949125 | − | 0.314899i | \(-0.898029\pi\) |
0.747273 | + | 0.664517i | \(0.231363\pi\) | |||||||
\(854\) | 4257.62 | − | 4738.08i | 0.170600 | − | 0.189852i | ||||
\(855\) | −74966.6 | + | 8151.27i | −2.99860 | + | 0.326044i | ||||
\(856\) | −1888.57 | + | 2615.85i | −0.0754089 | + | 0.104448i | ||||
\(857\) | 27628.2 | + | 15951.1i | 1.10124 | + | 0.635800i | 0.936546 | − | 0.350545i | \(-0.114004\pi\) |
0.164692 | + | 0.986345i | \(0.447337\pi\) | |||||||
\(858\) | 429.564 | − | 140.049i | 0.0170922 | − | 0.00557247i | ||||
\(859\) | −1562.95 | + | 902.369i | −0.0620805 | + | 0.0358422i | −0.530719 | − | 0.847548i | \(-0.678078\pi\) |
0.468639 | + | 0.883390i | \(0.344745\pi\) | |||||||
\(860\) | 14916.0 | − | 33682.8i | 0.591431 | − | 1.33555i | ||||
\(861\) | −881.696 | − | 1527.14i | −0.0348991 | − | 0.0604470i | ||||
\(862\) | −28567.9 | − | 25671.0i | −1.12880 | − | 1.01434i | ||||
\(863\) | 28060.5 | 1.10683 | 0.553413 | − | 0.832907i | \(-0.313325\pi\) | ||||
0.553413 | + | 0.832907i | \(0.313325\pi\) | |||||||
\(864\) | −366.282 | − | 73317.6i | −0.0144226 | − | 2.88694i | ||||
\(865\) | −12057.0 | + | 6961.11i | −0.473931 | + | 0.273624i | ||||
\(866\) | −8358.10 | + | 9301.28i | −0.327967 | + | 0.364977i | ||||
\(867\) | 20790.1 | 0.814380 | ||||||||
\(868\) | 2614.24 | + | 3583.11i | 0.102227 | + | 0.140114i | ||||
\(869\) | −44839.9 | − | 25888.3i | −1.75039 | − | 1.01059i | ||||
\(870\) | −35491.2 | − | 7506.83i | −1.38306 | − | 0.292535i | ||||
\(871\) | 84.5421 | + | 48.8104i | 0.00328886 | + | 0.00189883i | ||||
\(872\) | 40202.5 | − | 18043.9i | 1.56127 | − | 0.700738i | ||||
\(873\) | − | 30342.8i | − | 1.17634i | ||||||
\(874\) | 15198.9 | − | 21122.5i | 0.588226 | − | 0.817481i | ||||
\(875\) | 3938.00i | 0.152147i | ||||||||
\(876\) | −55153.3 | − | 24423.9i | −2.12724 | − | 0.942017i | ||||
\(877\) | 9617.77 | + | 5552.82i | 0.370318 | + | 0.213803i | 0.673597 | − | 0.739098i | \(-0.264748\pi\) |
−0.303279 | + | 0.952902i | \(0.598082\pi\) | |||||||
\(878\) | −1879.86 | + | 8887.68i | −0.0722574 | + | 0.341623i | ||||
\(879\) | −54759.9 | − | 31615.6i | −2.10126 | − | 1.21316i | ||||
\(880\) | 35791.7 | − | 32486.9i | 1.37107 | − | 1.24447i | ||||
\(881\) | −11683.0 | −0.446779 | −0.223389 | − | 0.974729i | \(-0.571712\pi\) | ||||
−0.223389 | + | 0.974729i | \(0.571712\pi\) | |||||||
\(882\) | 47035.2 | + | 42265.7i | 1.79565 | + | 1.61356i | ||||
\(883\) | 196.074 | − | 113.203i | 0.00747271 | − | 0.00431437i | −0.496259 | − | 0.868175i | \(-0.665293\pi\) |
0.503732 | + | 0.863860i | \(0.331960\pi\) | |||||||
\(884\) | 71.6501 | + | 98.2046i | 0.00272608 | + | 0.00373640i | ||||
\(885\) | −41131.4 | −1.56228 | ||||||||
\(886\) | 9419.64 | − | 10482.6i | 0.357177 | − | 0.397483i | ||||
\(887\) | 6497.99 | + | 11254.9i | 0.245977 | + | 0.426044i | 0.962406 | − | 0.271616i | \(-0.0875580\pi\) |
−0.716429 | + | 0.697660i | \(0.754225\pi\) | |||||||
\(888\) | 52386.8 | − | 23512.5i | 1.97972 | − | 0.888546i | ||||
\(889\) | 5205.73 | − | 3005.53i | 0.196394 | − | 0.113388i | ||||
\(890\) | 1575.75 | + | 4833.23i | 0.0593476 | + | 0.182034i | ||||
\(891\) | −103707. | − | 59875.2i | −3.89934 | − | 2.25129i | ||||
\(892\) | 4499.46 | + | 42001.9i | 0.168894 | + | 1.57660i | ||||
\(893\) | 12311.6 | − | 9012.55i | 0.461357 | − | 0.337731i | ||||
\(894\) | −30351.1 | − | 27273.4i | −1.13545 | − | 1.02031i | ||||
\(895\) | −7373.76 | + | 12771.7i | −0.275394 | + | 0.476996i | ||||
\(896\) | −4721.71 | + | 3481.24i | −0.176050 | + | 0.129799i | ||||
\(897\) | −156.257 | − | 270.645i | −0.00581636 | − | 0.0100742i | ||||
\(898\) | 8415.26 | + | 25811.7i | 0.312718 | + | 0.959186i | ||||
\(899\) | −11698.3 | + | 6754.04i | −0.433995 | + | 0.250567i | ||||
\(900\) | 3028.17 | + | 28267.6i | 0.112154 | + | 1.04695i | ||||
\(901\) | 16923.9i | 0.625769i | ||||||||
\(902\) | −1480.79 | + | 7000.98i | −0.0546619 | + | 0.258434i | ||||
\(903\) | 6850.87 | + | 11866.1i | 0.252473 | + | 0.437295i | ||||
\(904\) | 19763.0 | + | 14268.4i | 0.727111 | + | 0.524954i | ||||
\(905\) | 8488.84i | 0.311799i | ||||||||
\(906\) | 651.813 | − | 3081.68i | 0.0239018 | − | 0.113004i | ||||
\(907\) | −6153.08 | + | 10657.4i | −0.225259 | + | 0.390159i | −0.956397 | − | 0.292070i | \(-0.905656\pi\) |
0.731138 | + | 0.682229i | \(0.238989\pi\) | |||||||
\(908\) | −16626.5 | + | 12130.7i | −0.607674 | + | 0.443359i | ||||
\(909\) | 56709.3 | − | 98223.3i | 2.06923 | − | 3.58401i | ||||
\(910\) | 41.7191 | − | 13.6015i | 0.00151975 | − | 0.000495477i | ||||
\(911\) | 19098.9 | 0.694595 | 0.347297 | − | 0.937755i | \(-0.387099\pi\) | ||||
0.347297 | + | 0.937755i | \(0.387099\pi\) | |||||||
\(912\) | −38746.1 | − | 34358.7i | −1.40681 | − | 1.24751i | ||||
\(913\) | −13369.9 | −0.484641 | ||||||||
\(914\) | 8283.79 | − | 2700.72i | 0.299785 | − | 0.0977373i | ||||
\(915\) | 36123.8 | − | 62568.3i | 1.30515 | − | 2.26059i | ||||
\(916\) | −26470.5 | + | 19312.9i | −0.954815 | + | 0.696633i | ||||
\(917\) | 3373.85 | − | 5843.67i | 0.121499 | − | 0.210442i | ||||
\(918\) | 12510.8 | − | 59149.2i | 0.449802 | − | 2.12660i | ||||
\(919\) | 50194.6i | 1.80170i | 0.434125 | + | 0.900852i | \(0.357057\pi\) | ||||
−0.434125 | + | 0.900852i | \(0.642943\pi\) | |||||||
\(920\) | −27107.2 | − | 19570.7i | −0.971412 | − | 0.701333i | ||||
\(921\) | 22742.2 | + | 39390.7i | 0.813661 | + | 1.40930i | ||||
\(922\) | −7632.86 | + | 36087.0i | −0.272641 | + | 1.28901i | ||||
\(923\) | − | 228.770i | − | 0.00815826i | ||||||
\(924\) | 1915.02 | + | 17876.5i | 0.0681814 | + | 0.636466i | ||||
\(925\) | −11677.1 | + | 6741.75i | −0.415070 | + | 0.239641i | ||||
\(926\) | 15618.7 | + | 47906.4i | 0.554278 | + | 1.70011i | ||||
\(927\) | 5554.35 | + | 9620.41i | 0.196795 | + | 0.340858i | ||||
\(928\) | −9010.12 | − | 15427.5i | −0.318719 | − | 0.545724i | ||||
\(929\) | 204.746 | − | 354.631i | 0.00723090 | − | 0.0125243i | −0.862387 | − | 0.506249i | \(-0.831032\pi\) |
0.869618 | + | 0.493725i | \(0.164365\pi\) | |||||||
\(930\) | 37418.2 | + | 33623.9i | 1.31935 | + | 1.18556i | ||||
\(931\) | 26889.4 | − | 2923.74i | 0.946579 | − | 0.102923i | ||||
\(932\) | −2900.39 | − | 27074.8i | −0.101937 | − | 0.951572i | ||||
\(933\) | 66343.9 | + | 38303.7i | 2.32798 | + | 1.34406i | ||||
\(934\) | −6375.66 | − | 19555.8i | −0.223360 | − | 0.685101i | ||||
\(935\) | 34518.2 | − | 19929.1i | 1.20734 | − | 0.697059i | ||||
\(936\) | −406.903 | + | 182.629i | −0.0142095 | + | 0.00637756i | ||||
\(937\) | 12487.2 | + | 21628.4i | 0.435366 | + | 0.754076i | 0.997325 | − | 0.0730889i | \(-0.0232857\pi\) |
−0.561960 | + | 0.827165i | \(0.689952\pi\) | |||||||
\(938\) | −2596.38 | + | 2889.37i | −0.0903783 | + | 0.100577i | ||||
\(939\) | −73361.5 | −2.54959 | ||||||||
\(940\) | −11554.2 | − | 15836.4i | −0.400913 | − | 0.549496i | ||||
\(941\) | 45335.1 | − | 26174.2i | 1.57055 | − | 0.906755i | 0.574443 | − | 0.818544i | \(-0.305219\pi\) |
0.996102 | − | 0.0882101i | \(-0.0281147\pi\) | |||||||
\(942\) | −7220.84 | − | 6488.62i | −0.249753 | − | 0.224427i | ||||
\(943\) | 4949.59 | 0.170924 | ||||||||
\(944\) | −13614.6 | − | 14999.5i | −0.469404 | − | 0.517154i | ||||
\(945\) | −18899.4 | − | 10911.6i | −0.650578 | − | 0.375611i | ||||
\(946\) | 11505.9 | − | 54398.3i | 0.395444 | − | 1.86960i | ||||
\(947\) | −44702.3 | − | 25808.9i | −1.53393 | − | 0.885614i | −0.999175 | − | 0.0406056i | \(-0.987071\pi\) |
−0.534753 | − | 0.845008i | \(-0.679595\pi\) | |||||||
\(948\) | 65166.1 | + | 28857.9i | 2.23259 | + | 0.988673i | ||||
\(949\) | 222.209i | 0.00760085i | ||||||||
\(950\) | 9870.48 | + | 7102.40i | 0.337096 | + | 0.242560i | ||||
\(951\) | 6196.44i | 0.211286i | ||||||||
\(952\) | −4413.18 | + | 1980.75i | −0.150244 | + | 0.0674332i | ||||
\(953\) | −41075.5 | − | 23714.9i | −1.39619 | − | 0.806088i | −0.402195 | − | 0.915554i | \(-0.631753\pi\) |
−0.993991 | + | 0.109466i | \(0.965086\pi\) | |||||||
\(954\) | −60748.4 | − | 12849.0i | −2.06164 | − | 0.436062i | ||||
\(955\) | 6122.77 | + | 3534.98i | 0.207464 | + | 0.119779i | ||||
\(956\) | 9465.26 | + | 12973.2i | 0.320218 | + | 0.438895i | ||||
\(957\) | −54754.6 | −1.84949 | ||||||||
\(958\) | −36924.3 | + | 41091.1i | −1.24527 | + | 1.38580i | ||||
\(959\) | −4218.03 | + | 2435.28i | −0.142031 | + | 0.0820014i | ||||
\(960\) | −44223.3 | + | 49711.1i | −1.48677 | + | 1.67127i | ||||
\(961\) | −11058.8 | −0.371212 | ||||||||
\(962\) | −157.341 | − | 141.386i | −0.00527328 | − | 0.00473855i | ||||
\(963\) | −4880.43 | − | 8453.16i | −0.163312 | − | 0.282865i | ||||
\(964\) | −18126.2 | + | 40932.0i | −0.605606 | + | 1.36756i | ||||
\(965\) | 41147.9 | − | 23756.8i | 1.37264 | − | 0.792495i | ||||
\(966\) | 11823.1 | − | 3854.64i | 0.393792 | − | 0.128386i | ||||
\(967\) | 14113.4 | + | 8148.37i | 0.469344 | + | 0.270976i | 0.715965 | − | 0.698136i | \(-0.245987\pi\) |
−0.246621 | + | 0.969112i | \(0.579320\pi\) | |||||||
\(968\) | 25077.4 | − | 34734.5i | 0.832662 | − | 1.15332i | ||||
\(969\) | −25223.5 | − | 34456.6i | −0.836219 | − | 1.14232i | ||||
\(970\) | −11145.4 | + | 12403.1i | −0.368926 | + | 0.410558i | ||||
\(971\) | −16135.6 | + | 27947.7i | −0.533282 | + | 0.923671i | 0.465963 | + | 0.884804i | \(0.345708\pi\) |
−0.999244 | + | 0.0388666i | \(0.987625\pi\) | |||||||
\(972\) | 70723.7 | + | 31319.0i | 2.33381 | + | 1.03350i | ||||
\(973\) | −1241.68 | − | 2150.66i | −0.0409111 | − | 0.0708602i | ||||
\(974\) | 39888.9 | − | 13004.8i | 1.31224 | − | 0.427823i | ||||
\(975\) | 126.472 | − | 73.0187i | 0.00415420 | − | 0.00239843i | ||||
\(976\) | 34774.1 | − | 7536.84i | 1.14046 | − | 0.247181i | ||||
\(977\) | − | 50638.1i | − | 1.65819i | −0.559105 | − | 0.829097i | \(-0.688855\pi\) | ||
0.559105 | − | 0.829097i | \(-0.311145\pi\) | |||||||
\(978\) | −48251.3 | − | 10205.7i | −1.57761 | − | 0.333685i | ||||
\(979\) | 3836.53 | + | 6645.07i | 0.125246 | + | 0.216933i | ||||
\(980\) | −3701.56 | − | 34553.6i | −0.120655 | − | 1.12630i | ||||
\(981\) | 133316.i | 4.33888i | ||||||||
\(982\) | −20174.3 | − | 4267.11i | −0.655587 | − | 0.138665i | ||||
\(983\) | −2627.13 | + | 4550.32i | −0.0852415 | + | 0.147643i | −0.905494 | − | 0.424359i | \(-0.860500\pi\) |
0.820253 | + | 0.572001i | \(0.193833\pi\) | |||||||
\(984\) | 1000.23 | − | 9799.04i | 0.0324047 | − | 0.317461i | ||||
\(985\) | 6197.46 | − | 10734.3i | 0.200475 | − | 0.347232i | ||||
\(986\) | −4566.45 | − | 14006.5i | −0.147490 | − | 0.452390i | ||||
\(987\) | 7291.45 | 0.235146 | ||||||||
\(988\) | −57.9379 | + | 181.763i | −0.00186564 | + | 0.00585287i | ||||
\(989\) | −38458.8 | −1.23652 | ||||||||
\(990\) | 45328.3 | + | 139033.i | 1.45518 | + | 4.46341i | ||||
\(991\) | 15120.7 | − | 26189.9i | 0.484689 | − | 0.839505i | −0.515157 | − | 0.857096i | \(-0.672266\pi\) |
0.999845 | + | 0.0175908i | \(0.00559962\pi\) | |||||||
\(992\) | 123.772 | + | 24775.0i | 0.00396145 | + | 0.792951i | ||||
\(993\) | 55228.5 | − | 95658.5i | 1.76498 | − | 3.05703i | ||||
\(994\) | 8906.23 | + | 1883.78i | 0.284194 | + | 0.0601105i | ||||
\(995\) | − | 2511.78i | − | 0.0800288i | ||||||
\(996\) | 18298.7 | − | 1960.25i | 0.582146 | − | 0.0623624i | ||||
\(997\) | −18426.2 | − | 31915.2i | −0.585321 | − | 1.01381i | −0.994835 | − | 0.101502i | \(-0.967635\pi\) |
0.409514 | − | 0.912304i | \(-0.365698\pi\) | |||||||
\(998\) | −24454.3 | − | 5172.40i | −0.775640 | − | 0.164058i | ||||
\(999\) | 105202.i | 3.33179i |
(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 | 76.4.f.a.27.3 | ✓ | 56 | |
4.3 | odd | 2 | inner | 76.4.f.a.27.13 | yes | 56 | |
19.12 | odd | 6 | inner | 76.4.f.a.31.13 | yes | 56 | |
76.31 | even | 6 | inner | 76.4.f.a.31.3 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.f.a.27.3 | ✓ | 56 | 1.1 | even | 1 | trivial | |
76.4.f.a.27.13 | yes | 56 | 4.3 | odd | 2 | inner | |
76.4.f.a.31.3 | yes | 56 | 76.31 | even | 6 | inner | |
76.4.f.a.31.13 | yes | 56 | 19.12 | odd | 6 | inner |