Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(62,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.62");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 433x^{8} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 62.8 | ||
Root | \(0.817327 + 1.97320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.62 |
Dual form | 105.3.k.c.83.8 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.353553 | − | 0.353553i | −0.507877 | − | 0.861430i | \(-0.669569\pi\) |
0.861430 | + | 0.507877i | \(0.169569\pi\) | |||||||
\(3\) | 2.99611 | + | 0.152778i | 0.998702 | + | 0.0509259i | ||||
\(4\) | 3.00000i | 0.750000i | ||||||||
\(5\) | −4.24762 | + | 2.63775i | −0.849524 | + | 0.527550i | ||||
\(6\) | 2.22660 | − | 2.01054i | 0.371100 | − | 0.335090i | ||||
\(7\) | 5.49694 | + | 4.33402i | 0.785277 | + | 0.619145i | ||||
\(8\) | 4.94975 | + | 4.94975i | 0.618718 | + | 0.618718i | ||||
\(9\) | 8.95332 | + | 0.915476i | 0.994813 | + | 0.101720i | ||||
\(10\) | −1.13835 | + | 4.86869i | −0.113835 | + | 0.486869i | ||||
\(11\) | − | 13.9031i | − | 1.26392i | −0.775003 | − | 0.631958i | \(-0.782252\pi\) | ||
0.775003 | − | 0.631958i | \(-0.217748\pi\) | |||||||
\(12\) | −0.458333 | + | 8.98832i | −0.0381944 | + | 0.749027i | ||||
\(13\) | −14.6307 | − | 14.6307i | −1.12543 | − | 1.12543i | −0.990910 | − | 0.134524i | \(-0.957049\pi\) |
−0.134524 | − | 0.990910i | \(-0.542951\pi\) | |||||||
\(14\) | 6.95153 | − | 0.822309i | 0.496538 | − | 0.0587364i | ||||
\(15\) | −13.1293 | + | 7.25405i | −0.875287 | + | 0.483603i | ||||
\(16\) | −5.00000 | −0.312500 | ||||||||
\(17\) | −4.86435 | − | 4.86435i | −0.286138 | − | 0.286138i | 0.549413 | − | 0.835551i | \(-0.314851\pi\) |
−0.835551 | + | 0.549413i | \(0.814851\pi\) | |||||||
\(18\) | 6.97829 | − | 5.68361i | 0.387683 | − | 0.315756i | ||||
\(19\) | 21.7515 | 1.14481 | 0.572407 | − | 0.819970i | \(-0.306010\pi\) | ||||
0.572407 | + | 0.819970i | \(0.306010\pi\) | |||||||
\(20\) | −7.91326 | − | 12.7429i | −0.395663 | − | 0.637143i | ||||
\(21\) | 15.8073 | + | 13.8250i | 0.752727 | + | 0.658333i | ||||
\(22\) | −9.83095 | − | 9.83095i | −0.446861 | − | 0.446861i | ||||
\(23\) | 1.77282 | + | 1.77282i | 0.0770791 | + | 0.0770791i | 0.744595 | − | 0.667516i | \(-0.232643\pi\) |
−0.667516 | + | 0.744595i | \(0.732643\pi\) | |||||||
\(24\) | 14.0738 | + | 15.5862i | 0.586407 | + | 0.649424i | ||||
\(25\) | 11.0845 | − | 22.4083i | 0.443381 | − | 0.896333i | ||||
\(26\) | −20.6909 | −0.795802 | ||||||||
\(27\) | 26.6852 | + | 4.11073i | 0.988342 | + | 0.152249i | ||||
\(28\) | −13.0020 | + | 16.4908i | −0.464359 | + | 0.588957i | ||||
\(29\) | −28.0452 | −0.967076 | −0.483538 | − | 0.875323i | \(-0.660648\pi\) | ||||
−0.483538 | + | 0.875323i | \(0.660648\pi\) | |||||||
\(30\) | −4.15444 | + | 14.4132i | −0.138481 | + | 0.480440i | ||||
\(31\) | 17.2472i | 0.556362i | 0.960529 | + | 0.278181i | \(0.0897315\pi\) | ||||
−0.960529 | + | 0.278181i | \(0.910268\pi\) | |||||||
\(32\) | −23.3345 | + | 23.3345i | −0.729204 | + | 0.729204i | ||||
\(33\) | 2.12408 | − | 41.6551i | 0.0643660 | − | 1.26228i | ||||
\(34\) | −6.87923 | −0.202330 | ||||||||
\(35\) | −34.7809 | − | 3.90969i | −0.993741 | − | 0.111705i | ||||
\(36\) | −2.74643 | + | 26.8600i | −0.0762897 | + | 0.746110i | ||||
\(37\) | −6.50714 | − | 6.50714i | −0.175869 | − | 0.175869i | 0.613683 | − | 0.789552i | \(-0.289687\pi\) |
−0.789552 | + | 0.613683i | \(0.789687\pi\) | |||||||
\(38\) | 15.3806 | − | 15.3806i | 0.404753 | − | 0.404753i | ||||
\(39\) | −41.5998 | − | 46.0702i | −1.06666 | − | 1.18129i | ||||
\(40\) | −34.0808 | − | 7.96843i | −0.852021 | − | 0.199211i | ||||
\(41\) | −26.7192 | −0.651687 | −0.325844 | − | 0.945424i | \(-0.605648\pi\) | ||||
−0.325844 | + | 0.945424i | \(0.605648\pi\) | |||||||
\(42\) | 20.9532 | − | 1.40169i | 0.498885 | − | 0.0333735i | ||||
\(43\) | 33.1548 | − | 33.1548i | 0.771041 | − | 0.771041i | −0.207248 | − | 0.978289i | \(-0.566451\pi\) |
0.978289 | + | 0.207248i | \(0.0664506\pi\) | |||||||
\(44\) | 41.7092 | 0.947936 | ||||||||
\(45\) | −40.4451 | + | 19.7280i | −0.898779 | + | 0.438401i | ||||
\(46\) | 2.50714 | 0.0545031 | ||||||||
\(47\) | 18.5656 | + | 18.5656i | 0.395012 | + | 0.395012i | 0.876470 | − | 0.481457i | \(-0.159892\pi\) |
−0.481457 | + | 0.876470i | \(0.659892\pi\) | |||||||
\(48\) | −14.9805 | − | 0.763888i | −0.312095 | − | 0.0159143i | ||||
\(49\) | 11.4326 | + | 47.6476i | 0.233319 | + | 0.972400i | ||||
\(50\) | −8.00714 | − | 23.6830i | −0.160143 | − | 0.473661i | ||||
\(51\) | −13.8310 | − | 15.3173i | −0.271195 | − | 0.300339i | ||||
\(52\) | 43.8920 | − | 43.8920i | 0.844076 | − | 0.844076i | ||||
\(53\) | −48.3021 | − | 48.3021i | −0.911361 | − | 0.911361i | 0.0850185 | − | 0.996379i | \(-0.472905\pi\) |
−0.996379 | + | 0.0850185i | \(0.972905\pi\) | |||||||
\(54\) | 21.7760 | − | 15.9626i | 0.403260 | − | 0.295603i | ||||
\(55\) | 36.6728 | + | 59.0549i | 0.666779 | + | 1.07373i | ||||
\(56\) | 5.75616 | + | 48.6607i | 0.102789 | + | 0.868942i | ||||
\(57\) | 65.1697 | + | 3.32314i | 1.14333 | + | 0.0583006i | ||||
\(58\) | −19.8310 | + | 19.8310i | −0.341913 | + | 0.341913i | ||||
\(59\) | 29.6668i | 0.502826i | 0.967880 | + | 0.251413i | \(0.0808953\pi\) | ||||
−0.967880 | + | 0.251413i | \(0.919105\pi\) | |||||||
\(60\) | −21.7621 | − | 39.3879i | −0.362702 | − | 0.656465i | ||||
\(61\) | 21.0717i | 0.345438i | 0.984971 | + | 0.172719i | \(0.0552552\pi\) | ||||
−0.984971 | + | 0.172719i | \(0.944745\pi\) | |||||||
\(62\) | 12.1956 | + | 12.1956i | 0.196704 | + | 0.196704i | ||||
\(63\) | 45.2481 | + | 43.8361i | 0.718224 | + | 0.695812i | ||||
\(64\) | 13.0000i | 0.203125i | ||||||||
\(65\) | 100.737 | + | 23.5534i | 1.54981 | + | 0.362360i | ||||
\(66\) | −27.9526 | − | 30.9565i | −0.423525 | − | 0.469038i | ||||
\(67\) | −32.4786 | − | 32.4786i | −0.484755 | − | 0.484755i | 0.421892 | − | 0.906646i | \(-0.361366\pi\) |
−0.906646 | + | 0.421892i | \(0.861366\pi\) | |||||||
\(68\) | 14.5931 | − | 14.5931i | 0.214604 | − | 0.214604i | ||||
\(69\) | 5.04071 | + | 5.58240i | 0.0730537 | + | 0.0809044i | ||||
\(70\) | −27.3584 | + | 21.8293i | −0.390834 | + | 0.311847i | ||||
\(71\) | − | 16.0345i | − | 0.225838i | −0.993604 | − | 0.112919i | \(-0.963980\pi\) | ||
0.993604 | − | 0.112919i | \(-0.0360200\pi\) | |||||||
\(72\) | 39.7853 | + | 48.8480i | 0.552573 | + | 0.678445i | ||||
\(73\) | −57.3597 | − | 57.3597i | −0.785749 | − | 0.785749i | 0.195045 | − | 0.980794i | \(-0.437515\pi\) |
−0.980794 | + | 0.195045i | \(0.937515\pi\) | |||||||
\(74\) | −9.20249 | −0.124358 | ||||||||
\(75\) | 36.6339 | − | 65.4443i | 0.488452 | − | 0.872591i | ||||
\(76\) | 65.2544i | 0.858610i | ||||||||
\(77\) | 60.2561 | − | 76.4243i | 0.782547 | − | 0.992523i | ||||
\(78\) | −61.9921 | − | 3.16110i | −0.794770 | − | 0.0405269i | ||||
\(79\) | 75.8024i | 0.959524i | 0.877399 | + | 0.479762i | \(0.159277\pi\) | ||||
−0.877399 | + | 0.479762i | \(0.840723\pi\) | |||||||
\(80\) | 21.2381 | − | 13.1888i | 0.265476 | − | 0.164860i | ||||
\(81\) | 79.3238 | + | 16.3931i | 0.979306 | + | 0.202384i | ||||
\(82\) | −18.8933 | + | 18.8933i | −0.230406 | + | 0.230406i | ||||
\(83\) | 51.9675 | − | 51.9675i | 0.626114 | − | 0.626114i | −0.320974 | − | 0.947088i | \(-0.604010\pi\) |
0.947088 | + | 0.320974i | \(0.104010\pi\) | |||||||
\(84\) | −41.4750 | + | 47.4218i | −0.493749 | + | 0.564545i | ||||
\(85\) | 33.4929 | + | 7.83095i | 0.394034 | + | 0.0921288i | ||||
\(86\) | − | 46.8879i | − | 0.545208i | ||||||
\(87\) | −84.0264 | − | 4.28468i | −0.965821 | − | 0.0492492i | ||||
\(88\) | 68.8167 | − | 68.8167i | 0.782008 | − | 0.782008i | ||||
\(89\) | 174.294i | 1.95836i | 0.202987 | + | 0.979181i | \(0.434935\pi\) | ||||
−0.202987 | + | 0.979181i | \(0.565065\pi\) | |||||||
\(90\) | −14.6492 | + | 42.5488i | −0.162768 | + | 0.472765i | ||||
\(91\) | −17.0143 | − | 143.833i | −0.186970 | − | 1.58058i | ||||
\(92\) | −5.31846 | + | 5.31846i | −0.0578093 | + | 0.0578093i | ||||
\(93\) | −2.63499 | + | 51.6745i | −0.0283332 | + | 0.555640i | ||||
\(94\) | 26.2557 | 0.279316 | ||||||||
\(95\) | −92.3919 | + | 57.3750i | −0.972547 | + | 0.603947i | ||||
\(96\) | −73.4777 | + | 66.3477i | −0.765393 | + | 0.691122i | ||||
\(97\) | 16.6658 | − | 16.6658i | 0.171812 | − | 0.171812i | −0.615963 | − | 0.787775i | \(-0.711233\pi\) |
0.787775 | + | 0.615963i | \(0.211233\pi\) | |||||||
\(98\) | 41.7760 | + | 25.6079i | 0.426286 | + | 0.261305i | ||||
\(99\) | 12.7279 | − | 124.479i | 0.128565 | − | 1.25736i | ||||
\(100\) | 67.2250 | + | 33.2536i | 0.672250 | + | 0.332536i | ||||
\(101\) | 113.114 | 1.11994 | 0.559968 | − | 0.828514i | \(-0.310813\pi\) | ||||
0.559968 | + | 0.828514i | \(0.310813\pi\) | |||||||
\(102\) | −20.6109 | − | 1.05099i | −0.202068 | − | 0.0103038i | ||||
\(103\) | 16.1826 | + | 16.1826i | 0.157113 | + | 0.157113i | 0.781286 | − | 0.624173i | \(-0.214564\pi\) |
−0.624173 | + | 0.781286i | \(0.714564\pi\) | |||||||
\(104\) | − | 144.836i | − | 1.39265i | ||||||
\(105\) | −103.610 | − | 17.0276i | −0.986763 | − | 0.162168i | ||||
\(106\) | −68.3095 | −0.644429 | ||||||||
\(107\) | −139.010 | + | 139.010i | −1.29916 | + | 1.29916i | −0.370218 | + | 0.928945i | \(0.620717\pi\) |
−0.928945 | + | 0.370218i | \(0.879283\pi\) | |||||||
\(108\) | −12.3322 | + | 80.0557i | −0.114187 | + | 0.741257i | ||||
\(109\) | 3.01429i | 0.0276540i | 0.999904 | + | 0.0138270i | \(0.00440141\pi\) | ||||
−0.999904 | + | 0.0138270i | \(0.995599\pi\) | |||||||
\(110\) | 67.6897 | + | 15.8265i | 0.615361 | + | 0.143877i | ||||
\(111\) | −18.5020 | − | 20.4902i | −0.166684 | − | 0.184597i | ||||
\(112\) | −27.4847 | − | 21.6701i | −0.245399 | − | 0.193483i | ||||
\(113\) | 80.1118 | + | 80.1118i | 0.708954 | + | 0.708954i | 0.966315 | − | 0.257361i | \(-0.0828530\pi\) |
−0.257361 | + | 0.966315i | \(0.582853\pi\) | |||||||
\(114\) | 48.4318 | − | 43.7321i | 0.424840 | − | 0.383615i | ||||
\(115\) | −12.2065 | − | 2.85400i | −0.106144 | − | 0.0248174i | ||||
\(116\) | − | 84.1356i | − | 0.725307i | ||||||
\(117\) | −117.599 | − | 144.387i | −1.00512 | − | 1.23408i | ||||
\(118\) | 20.9776 | + | 20.9776i | 0.177776 | + | 0.177776i | ||||
\(119\) | −5.65685 | − | 47.8212i | −0.0475366 | − | 0.401859i | ||||
\(120\) | −100.892 | − | 29.0811i | −0.840771 | − | 0.242342i | ||||
\(121\) | −72.2952 | −0.597481 | ||||||||
\(122\) | 14.8999 | + | 14.8999i | 0.122131 | + | 0.122131i | ||||
\(123\) | −80.0535 | − | 4.08209i | −0.650842 | − | 0.0331877i | ||||
\(124\) | −51.7417 | −0.417272 | ||||||||
\(125\) | 12.0248 | + | 124.420i | 0.0961984 | + | 0.995362i | ||||
\(126\) | 62.9921 | − | 0.998435i | 0.499937 | − | 0.00792409i | ||||
\(127\) | −71.6476 | − | 71.6476i | −0.564154 | − | 0.564154i | 0.366330 | − | 0.930485i | \(-0.380614\pi\) |
−0.930485 | + | 0.366330i | \(0.880614\pi\) | |||||||
\(128\) | −84.1457 | − | 84.1457i | −0.657388 | − | 0.657388i | ||||
\(129\) | 104.401 | − | 94.2699i | 0.809306 | − | 0.730775i | ||||
\(130\) | 87.8869 | − | 54.5774i | 0.676053 | − | 0.419826i | ||||
\(131\) | 79.4683 | 0.606629 | 0.303314 | − | 0.952891i | \(-0.401907\pi\) | ||||
0.303314 | + | 0.952891i | \(0.401907\pi\) | |||||||
\(132\) | 124.965 | + | 6.37223i | 0.946706 | + | 0.0482745i | ||||
\(133\) | 119.566 | + | 94.2712i | 0.898996 | + | 0.708806i | ||||
\(134\) | −45.9316 | −0.342773 | ||||||||
\(135\) | −124.192 | + | 52.9282i | −0.919939 | + | 0.392061i | ||||
\(136\) | − | 48.1546i | − | 0.354078i | ||||||
\(137\) | 7.42967 | − | 7.42967i | 0.0542312 | − | 0.0542312i | −0.679471 | − | 0.733702i | \(-0.737791\pi\) |
0.733702 | + | 0.679471i | \(0.237791\pi\) | |||||||
\(138\) | 7.51167 | + | 0.383035i | 0.0544324 | + | 0.00277562i | ||||
\(139\) | −179.589 | −1.29201 | −0.646003 | − | 0.763335i | \(-0.723561\pi\) | ||||
−0.646003 | + | 0.763335i | \(0.723561\pi\) | |||||||
\(140\) | 11.7291 | − | 104.343i | 0.0837790 | − | 0.745306i | ||||
\(141\) | 52.7881 | + | 58.4609i | 0.374384 | + | 0.414616i | ||||
\(142\) | −11.3381 | − | 11.3381i | −0.0798457 | − | 0.0798457i | ||||
\(143\) | −203.411 | + | 203.411i | −1.42245 | + | 1.42245i | ||||
\(144\) | −44.7666 | − | 4.57738i | −0.310879 | − | 0.0317874i | ||||
\(145\) | 119.125 | − | 73.9763i | 0.821554 | − | 0.510181i | ||||
\(146\) | −81.1188 | −0.555609 | ||||||||
\(147\) | 26.9739 | + | 144.504i | 0.183496 | + | 0.983021i | ||||
\(148\) | 19.5214 | − | 19.5214i | 0.131902 | − | 0.131902i | ||||
\(149\) | 24.7386 | 0.166031 | 0.0830155 | − | 0.996548i | \(-0.473545\pi\) | ||||
0.0830155 | + | 0.996548i | \(0.473545\pi\) | |||||||
\(150\) | −20.3720 | − | 72.1802i | −0.135813 | − | 0.481201i | ||||
\(151\) | −163.324 | −1.08161 | −0.540807 | − | 0.841147i | \(-0.681881\pi\) | ||||
−0.540807 | + | 0.841147i | \(0.681881\pi\) | |||||||
\(152\) | 107.664 | + | 107.664i | 0.708317 | + | 0.708317i | ||||
\(153\) | −39.0989 | − | 48.0053i | −0.255548 | − | 0.313760i | ||||
\(154\) | −11.4326 | − | 96.6476i | −0.0742378 | − | 0.627582i | ||||
\(155\) | −45.4939 | − | 73.2596i | −0.293509 | − | 0.472643i | ||||
\(156\) | 138.211 | − | 124.799i | 0.885966 | − | 0.799995i | ||||
\(157\) | −108.368 | + | 108.368i | −0.690244 | + | 0.690244i | −0.962285 | − | 0.272042i | \(-0.912301\pi\) |
0.272042 | + | 0.962285i | \(0.412301\pi\) | |||||||
\(158\) | 53.6004 | + | 53.6004i | 0.339243 | + | 0.339243i | ||||
\(159\) | −137.339 | − | 152.098i | −0.863766 | − | 0.956590i | ||||
\(160\) | 37.5655 | − | 160.667i | 0.234784 | − | 1.00417i | ||||
\(161\) | 2.06165 | + | 17.4285i | 0.0128053 | + | 0.108252i | ||||
\(162\) | 67.6821 | − | 44.4987i | 0.417791 | − | 0.274684i | ||||
\(163\) | 38.8452 | − | 38.8452i | 0.238314 | − | 0.238314i | −0.577837 | − | 0.816152i | \(-0.696103\pi\) |
0.816152 | + | 0.577837i | \(0.196103\pi\) | |||||||
\(164\) | − | 80.1575i | − | 0.488765i | ||||||
\(165\) | 100.854 | + | 182.538i | 0.611233 | + | 1.10629i | ||||
\(166\) | − | 73.4931i | − | 0.442730i | ||||||
\(167\) | −138.252 | − | 138.252i | −0.827855 | − | 0.827855i | 0.159365 | − | 0.987220i | \(-0.449055\pi\) |
−0.987220 | + | 0.159365i | \(0.949055\pi\) | |||||||
\(168\) | 9.81182 | + | 146.672i | 0.0584037 | + | 0.873049i | ||||
\(169\) | 259.112i | 1.53321i | ||||||||
\(170\) | 29.2203 | − | 18.1457i | 0.171884 | − | 0.106739i | ||||
\(171\) | 194.748 | + | 19.9129i | 1.13888 | + | 0.116450i | ||||
\(172\) | 99.4643 | + | 99.4643i | 0.578281 | + | 0.578281i | ||||
\(173\) | 26.9566 | − | 26.9566i | 0.155818 | − | 0.155818i | −0.624893 | − | 0.780711i | \(-0.714857\pi\) |
0.780711 | + | 0.624893i | \(0.214857\pi\) | |||||||
\(174\) | −62.4454 | + | 56.3859i | −0.358882 | + | 0.324057i | ||||
\(175\) | 158.049 | − | 75.1367i | 0.903137 | − | 0.429352i | ||||
\(176\) | 69.5153i | 0.394973i | ||||||||
\(177\) | −4.53242 | + | 88.8848i | −0.0256069 | + | 0.502174i | ||||
\(178\) | 123.245 | + | 123.245i | 0.692386 | + | 0.692386i | ||||
\(179\) | 187.393 | 1.04689 | 0.523445 | − | 0.852059i | \(-0.324646\pi\) | ||||
0.523445 | + | 0.852059i | \(0.324646\pi\) | |||||||
\(180\) | −59.1841 | − | 121.335i | −0.328801 | − | 0.674085i | ||||
\(181\) | 179.581i | 0.992158i | 0.868277 | + | 0.496079i | \(0.165227\pi\) | ||||
−0.868277 | + | 0.496079i | \(0.834773\pi\) | |||||||
\(182\) | −113.736 | − | 89.6745i | −0.624925 | − | 0.492717i | ||||
\(183\) | −3.21928 | + | 63.1331i | −0.0175917 | + | 0.344990i | ||||
\(184\) | 17.5500i | 0.0953805i | ||||||||
\(185\) | 44.8041 | + | 10.4756i | 0.242184 | + | 0.0566250i | ||||
\(186\) | 34.6762 | + | 38.4026i | 0.186431 | + | 0.206466i | ||||
\(187\) | −67.6294 | + | 67.6294i | −0.361654 | + | 0.361654i | ||||
\(188\) | −55.6968 | + | 55.6968i | −0.296259 | + | 0.296259i | ||||
\(189\) | 128.871 | + | 138.251i | 0.681858 | + | 0.731485i | ||||
\(190\) | −24.7607 | + | 105.901i | −0.130320 | + | 0.557375i | ||||
\(191\) | 107.063i | 0.560538i | 0.959922 | + | 0.280269i | \(0.0904236\pi\) | ||||
−0.959922 | + | 0.280269i | \(0.909576\pi\) | |||||||
\(192\) | −1.98611 | + | 38.9494i | −0.0103443 | + | 0.202861i | ||||
\(193\) | −81.6333 | + | 81.6333i | −0.422971 | + | 0.422971i | −0.886225 | − | 0.463255i | \(-0.846682\pi\) |
0.463255 | + | 0.886225i | \(0.346682\pi\) | |||||||
\(194\) | − | 23.5689i | − | 0.121489i | ||||||
\(195\) | 298.222 | + | 85.9589i | 1.52934 | + | 0.440815i | ||||
\(196\) | −142.943 | + | 34.2979i | −0.729300 | + | 0.174989i | ||||
\(197\) | 165.702 | − | 165.702i | 0.841127 | − | 0.841127i | −0.147878 | − | 0.989006i | \(-0.547244\pi\) |
0.989006 | + | 0.147878i | \(0.0472444\pi\) | |||||||
\(198\) | −79.0196 | − | 97.0196i | −0.399089 | − | 0.489998i | ||||
\(199\) | 220.037 | 1.10571 | 0.552857 | − | 0.833276i | \(-0.313538\pi\) | ||||
0.552857 | + | 0.833276i | \(0.313538\pi\) | |||||||
\(200\) | 165.781 | − | 56.0500i | 0.828906 | − | 0.280250i | ||||
\(201\) | −92.3473 | − | 102.271i | −0.459439 | − | 0.508812i | ||||
\(202\) | 79.9833 | − | 79.9833i | 0.395957 | − | 0.395957i | ||||
\(203\) | −154.163 | − | 121.548i | −0.759422 | − | 0.598760i | ||||
\(204\) | 45.9518 | − | 41.4929i | 0.225254 | − | 0.203396i | ||||
\(205\) | 113.493 | − | 70.4786i | 0.553624 | − | 0.343798i | ||||
\(206\) | 22.8856 | 0.111095 | ||||||||
\(207\) | 14.2496 | + | 17.4956i | 0.0688388 | + | 0.0845197i | ||||
\(208\) | 73.1533 | + | 73.1533i | 0.351698 | + | 0.351698i | ||||
\(209\) | − | 302.412i | − | 1.44695i | ||||||
\(210\) | −85.3038 | + | 61.2231i | −0.406208 | + | 0.291539i | ||||
\(211\) | 276.590 | 1.31086 | 0.655428 | − | 0.755258i | \(-0.272488\pi\) | ||||
0.655428 | + | 0.755258i | \(0.272488\pi\) | |||||||
\(212\) | 144.906 | − | 144.906i | 0.683521 | − | 0.683521i | ||||
\(213\) | 2.44971 | − | 48.0411i | 0.0115010 | − | 0.225545i | ||||
\(214\) | 196.590i | 0.918647i | ||||||||
\(215\) | −53.3747 | + | 228.283i | −0.248255 | + | 1.06178i | ||||
\(216\) | 111.738 | + | 152.432i | 0.517306 | + | 0.705705i | ||||
\(217\) | −74.7497 | + | 94.8069i | −0.344469 | + | 0.436898i | ||||
\(218\) | 2.13142 | + | 2.13142i | 0.00977717 | + | 0.00977717i | ||||
\(219\) | −163.092 | − | 180.619i | −0.744715 | − | 0.824744i | ||||
\(220\) | −177.165 | + | 110.019i | −0.805294 | + | 0.500084i | ||||
\(221\) | 142.337i | 0.644060i | ||||||||
\(222\) | −27.5717 | − | 1.40593i | −0.124197 | − | 0.00633304i | ||||
\(223\) | −173.529 | − | 173.529i | −0.778155 | − | 0.778155i | 0.201362 | − | 0.979517i | \(-0.435463\pi\) |
−0.979517 | + | 0.201362i | \(0.935463\pi\) | |||||||
\(224\) | −229.401 | + | 27.1362i | −1.02411 | + | 0.121144i | ||||
\(225\) | 119.758 | − | 190.481i | 0.532256 | − | 0.846584i | ||||
\(226\) | 113.295 | 0.501306 | ||||||||
\(227\) | −191.389 | − | 191.389i | −0.843123 | − | 0.843123i | 0.146140 | − | 0.989264i | \(-0.453315\pi\) |
−0.989264 | + | 0.146140i | \(0.953315\pi\) | |||||||
\(228\) | −9.96941 | + | 195.509i | −0.0437255 | + | 0.857496i | ||||
\(229\) | −123.490 | −0.539259 | −0.269630 | − | 0.962964i | \(-0.586901\pi\) | ||||
−0.269630 | + | 0.962964i | \(0.586901\pi\) | |||||||
\(230\) | −10.6494 | + | 6.61323i | −0.0463017 | + | 0.0287532i | ||||
\(231\) | 192.210 | − | 219.770i | 0.832076 | − | 0.951383i | ||||
\(232\) | −138.817 | − | 138.817i | −0.598348 | − | 0.598348i | ||||
\(233\) | −89.8918 | − | 89.8918i | −0.385802 | − | 0.385802i | 0.487385 | − | 0.873187i | \(-0.337951\pi\) |
−0.873187 | + | 0.487385i | \(0.837951\pi\) | |||||||
\(234\) | −185.252 | − | 18.9420i | −0.791675 | − | 0.0809487i | ||||
\(235\) | −127.831 | − | 29.8881i | −0.543961 | − | 0.127183i | ||||
\(236\) | −89.0003 | −0.377120 | ||||||||
\(237\) | −11.5809 | + | 227.112i | −0.0488646 | + | 0.958279i | ||||
\(238\) | −37.8147 | − | 29.8147i | −0.158885 | − | 0.125272i | ||||
\(239\) | −49.2786 | −0.206187 | −0.103093 | − | 0.994672i | \(-0.532874\pi\) | ||||
−0.103093 | + | 0.994672i | \(0.532874\pi\) | |||||||
\(240\) | 65.6465 | − | 36.2702i | 0.273527 | − | 0.151126i | ||||
\(241\) | − | 421.664i | − | 1.74964i | −0.484445 | − | 0.874822i | \(-0.660979\pi\) | ||
0.484445 | − | 0.874822i | \(-0.339021\pi\) | |||||||
\(242\) | −51.1204 | + | 51.1204i | −0.211242 | + | 0.211242i | ||||
\(243\) | 235.158 | + | 61.2344i | 0.967729 | + | 0.251993i | ||||
\(244\) | −63.2151 | −0.259078 | ||||||||
\(245\) | −174.244 | − | 172.232i | −0.711200 | − | 0.702990i | ||||
\(246\) | −59.4929 | + | 53.7199i | −0.241841 | + | 0.218374i | ||||
\(247\) | −318.238 | − | 318.238i | −1.28841 | − | 1.28841i | ||||
\(248\) | −85.3694 | + | 85.3694i | −0.344231 | + | 0.344231i | ||||
\(249\) | 163.640 | − | 147.761i | 0.657187 | − | 0.593417i | ||||
\(250\) | 96.4812 | + | 79.4756i | 0.385925 | + | 0.317902i | ||||
\(251\) | −345.514 | −1.37655 | −0.688274 | − | 0.725450i | \(-0.741631\pi\) | ||||
−0.688274 | + | 0.725450i | \(0.741631\pi\) | |||||||
\(252\) | −131.508 | + | 135.744i | −0.521859 | + | 0.538668i | ||||
\(253\) | 24.6476 | − | 24.6476i | 0.0974214 | − | 0.0974214i | ||||
\(254\) | −101.325 | −0.398917 | ||||||||
\(255\) | 99.1518 | + | 28.5793i | 0.388831 | + | 0.112076i | ||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | 216.568 | + | 216.568i | 0.842676 | + | 0.842676i | 0.989206 | − | 0.146530i | \(-0.0468104\pi\) |
−0.146530 | + | 0.989206i | \(0.546810\pi\) | |||||||
\(258\) | 7.16342 | − | 140.481i | 0.0277652 | − | 0.544501i | ||||
\(259\) | −7.56729 | − | 63.9714i | −0.0292173 | − | 0.246994i | ||||
\(260\) | −70.6602 | + | 302.212i | −0.271770 | + | 1.16236i | ||||
\(261\) | −251.098 | − | 25.6747i | −0.962060 | − | 0.0983705i | ||||
\(262\) | 56.1926 | − | 56.1926i | 0.214476 | − | 0.214476i | ||||
\(263\) | 196.555 | + | 196.555i | 0.747359 | + | 0.747359i | 0.973982 | − | 0.226623i | \(-0.0727686\pi\) |
−0.226623 | + | 0.973982i | \(0.572769\pi\) | |||||||
\(264\) | 216.696 | − | 195.668i | 0.820817 | − | 0.741168i | ||||
\(265\) | 332.578 | + | 77.7599i | 1.25501 | + | 0.293434i | ||||
\(266\) | 151.206 | − | 17.8864i | 0.568444 | − | 0.0672422i | ||||
\(267\) | −26.6283 | + | 522.204i | −0.0997313 | + | 1.95582i | ||||
\(268\) | 97.4357 | − | 97.4357i | 0.363566 | − | 0.363566i | ||||
\(269\) | 349.961i | 1.30097i | 0.759519 | + | 0.650485i | \(0.225434\pi\) | ||||
−0.759519 | + | 0.650485i | \(0.774566\pi\) | |||||||
\(270\) | −50.3909 | + | 125.243i | −0.186633 | + | 0.463862i | ||||
\(271\) | 137.978i | 0.509143i | 0.967054 | + | 0.254572i | \(0.0819344\pi\) | ||||
−0.967054 | + | 0.254572i | \(0.918066\pi\) | |||||||
\(272\) | 24.3218 | + | 24.3218i | 0.0894182 | + | 0.0894182i | ||||
\(273\) | −29.0021 | − | 433.539i | −0.106235 | − | 1.58806i | ||||
\(274\) | − | 10.5071i | − | 0.0383472i | ||||||
\(275\) | −311.545 | − | 154.109i | −1.13289 | − | 0.560396i | ||||
\(276\) | −16.7472 | + | 15.1221i | −0.0606783 | + | 0.0547903i | ||||
\(277\) | 132.817 | + | 132.817i | 0.479483 | + | 0.479483i | 0.904966 | − | 0.425484i | \(-0.139896\pi\) |
−0.425484 | + | 0.904966i | \(0.639896\pi\) | |||||||
\(278\) | −126.989 | + | 126.989i | −0.456793 | + | 0.456793i | ||||
\(279\) | −15.7894 | + | 154.420i | −0.0565929 | + | 0.553476i | ||||
\(280\) | −152.805 | − | 191.509i | −0.545732 | − | 0.683960i | ||||
\(281\) | − | 142.098i | − | 0.505687i | −0.967507 | − | 0.252844i | \(-0.918634\pi\) | ||
0.967507 | − | 0.252844i | \(-0.0813658\pi\) | |||||||
\(282\) | 78.6649 | + | 4.01128i | 0.278954 | + | 0.0142244i | ||||
\(283\) | 120.235 | + | 120.235i | 0.424858 | + | 0.424858i | 0.886873 | − | 0.462014i | \(-0.152873\pi\) |
−0.462014 | + | 0.886873i | \(0.652873\pi\) | |||||||
\(284\) | 48.1035 | 0.169378 | ||||||||
\(285\) | −285.582 | + | 157.786i | −1.00204 | + | 0.553636i | ||||
\(286\) | 287.666i | 1.00583i | ||||||||
\(287\) | −146.874 | − | 115.801i | −0.511755 | − | 0.403489i | ||||
\(288\) | −230.284 | + | 187.559i | −0.799596 | + | 0.651247i | ||||
\(289\) | − | 241.676i | − | 0.836250i | ||||||
\(290\) | 31.9252 | − | 136.543i | 0.110087 | − | 0.470840i | ||||
\(291\) | 52.4786 | − | 47.3863i | 0.180339 | − | 0.162839i | ||||
\(292\) | 172.079 | − | 172.079i | 0.589312 | − | 0.589312i | ||||
\(293\) | 377.885 | − | 377.885i | 1.28971 | − | 1.28971i | 0.354747 | − | 0.934962i | \(-0.384567\pi\) |
0.934962 | − | 0.354747i | \(-0.115433\pi\) | |||||||
\(294\) | 121.253 | + | 83.1064i | 0.412426 | + | 0.282675i | ||||
\(295\) | −78.2536 | − | 126.013i | −0.265266 | − | 0.427163i | ||||
\(296\) | − | 64.4174i | − | 0.217626i | ||||||
\(297\) | 57.1518 | − | 371.007i | 0.192430 | − | 1.24918i | ||||
\(298\) | 17.4929 | − | 17.4929i | 0.0587009 | − | 0.0587009i | ||||
\(299\) | − | 51.8750i | − | 0.173495i | ||||||
\(300\) | 196.333 | + | 109.902i | 0.654443 | + | 0.366339i | ||||
\(301\) | 325.943 | − | 38.5564i | 1.08287 | − | 0.128094i | ||||
\(302\) | −115.487 | + | 115.487i | −0.382409 | + | 0.382409i | ||||
\(303\) | 338.900 | + | 17.2812i | 1.11848 | + | 0.0570337i | ||||
\(304\) | −108.757 | −0.357754 | ||||||||
\(305\) | −55.5820 | − | 89.5046i | −0.182236 | − | 0.293458i | ||||
\(306\) | −61.5919 | − | 6.29777i | −0.201281 | − | 0.0205809i | ||||
\(307\) | 94.6590 | − | 94.6590i | 0.308335 | − | 0.308335i | −0.535928 | − | 0.844264i | \(-0.680038\pi\) |
0.844264 | + | 0.535928i | \(0.180038\pi\) | |||||||
\(308\) | 229.273 | + | 180.768i | 0.744392 | + | 0.586910i | ||||
\(309\) | 46.0125 | + | 50.9571i | 0.148908 | + | 0.164910i | ||||
\(310\) | −83.9714 | − | 19.6333i | −0.270876 | − | 0.0633333i | ||||
\(311\) | 221.432 | 0.712001 | 0.356000 | − | 0.934486i | \(-0.384140\pi\) | ||||
0.356000 | + | 0.934486i | \(0.384140\pi\) | |||||||
\(312\) | 22.1277 | − | 433.944i | 0.0709221 | − | 1.39085i | ||||
\(313\) | −225.950 | − | 225.950i | −0.721885 | − | 0.721885i | 0.247104 | − | 0.968989i | \(-0.420521\pi\) |
−0.968989 | + | 0.247104i | \(0.920521\pi\) | |||||||
\(314\) | 153.256i | 0.488076i | ||||||||
\(315\) | −307.826 | − | 66.8458i | −0.977224 | − | 0.212209i | ||||
\(316\) | −227.407 | −0.719643 | ||||||||
\(317\) | −96.2271 | + | 96.2271i | −0.303556 | + | 0.303556i | −0.842403 | − | 0.538848i | \(-0.818860\pi\) |
0.538848 | + | 0.842403i | \(0.318860\pi\) | |||||||
\(318\) | −204.663 | − | 10.4362i | −0.643593 | − | 0.0328181i | ||||
\(319\) | 389.914i | 1.22230i | ||||||||
\(320\) | −34.2908 | − | 55.2190i | −0.107159 | − | 0.172559i | ||||
\(321\) | −437.728 | + | 395.253i | −1.36364 | + | 1.23132i | ||||
\(322\) | 13.7816 | + | 10.8660i | 0.0428000 | + | 0.0337453i | ||||
\(323\) | −105.807 | − | 105.807i | −0.327575 | − | 0.327575i | ||||
\(324\) | −49.1793 | + | 237.971i | −0.151788 | + | 0.734480i | ||||
\(325\) | −490.022 | + | 165.675i | −1.50776 | + | 0.509768i | ||||
\(326\) | − | 54.9355i | − | 0.168514i | ||||||
\(327\) | −0.460516 | + | 9.03113i | −0.00140830 | + | 0.0276181i | ||||
\(328\) | −132.253 | − | 132.253i | −0.403211 | − | 0.403211i | ||||
\(329\) | 21.5903 | + | 182.517i | 0.0656240 | + | 0.554764i | ||||
\(330\) | 200.388 | + | 57.7594i | 0.607236 | + | 0.175029i | ||||
\(331\) | 175.014 | 0.528744 | 0.264372 | − | 0.964421i | \(-0.414835\pi\) | ||||
0.264372 | + | 0.964421i | \(0.414835\pi\) | |||||||
\(332\) | 155.902 | + | 155.902i | 0.469586 | + | 0.469586i | ||||
\(333\) | −52.3034 | − | 64.2177i | −0.157067 | − | 0.192846i | ||||
\(334\) | −195.517 | −0.585382 | ||||||||
\(335\) | 223.627 | + | 52.2861i | 0.667543 | + | 0.156078i | ||||
\(336\) | −79.0364 | − | 69.1249i | −0.235227 | − | 0.205729i | ||||
\(337\) | 109.576 | + | 109.576i | 0.325152 | + | 0.325152i | 0.850739 | − | 0.525588i | \(-0.176155\pi\) |
−0.525588 | + | 0.850739i | \(0.676155\pi\) | |||||||
\(338\) | 183.220 | + | 183.220i | 0.542070 | + | 0.542070i | ||||
\(339\) | 227.784 | + | 252.263i | 0.671930 | + | 0.744138i | ||||
\(340\) | −23.4929 | + | 100.479i | −0.0690966 | + | 0.295525i | ||||
\(341\) | 239.789 | 0.703194 | ||||||||
\(342\) | 151.788 | − | 123.627i | 0.443825 | − | 0.361482i | ||||
\(343\) | −143.661 | + | 311.465i | −0.418837 | + | 0.908061i | ||||
\(344\) | 328.215 | 0.954114 | ||||||||
\(345\) | −36.1360 | − | 10.4158i | −0.104742 | − | 0.0301906i | ||||
\(346\) | − | 38.1223i | − | 0.110180i | ||||||
\(347\) | 268.600 | − | 268.600i | 0.774062 | − | 0.774062i | −0.204752 | − | 0.978814i | \(-0.565639\pi\) |
0.978814 | + | 0.204752i | \(0.0656387\pi\) | |||||||
\(348\) | 12.8540 | − | 252.079i | 0.0369369 | − | 0.724366i | ||||
\(349\) | 304.193 | 0.871613 | 0.435807 | − | 0.900040i | \(-0.356463\pi\) | ||||
0.435807 | + | 0.900040i | \(0.356463\pi\) | |||||||
\(350\) | 58.6279 | − | 164.887i | 0.167508 | − | 0.471106i | ||||
\(351\) | −330.280 | − | 450.565i | −0.940968 | − | 1.28366i | ||||
\(352\) | 324.421 | + | 324.421i | 0.921652 | + | 0.921652i | ||||
\(353\) | 240.264 | − | 240.264i | 0.680635 | − | 0.680635i | −0.279509 | − | 0.960143i | \(-0.590172\pi\) |
0.960143 | + | 0.279509i | \(0.0901715\pi\) | |||||||
\(354\) | 59.6461 | + | 66.0559i | 0.168492 | + | 0.186599i | ||||
\(355\) | 42.2950 | + | 68.1084i | 0.119141 | + | 0.191855i | ||||
\(356\) | −522.883 | −1.46877 | ||||||||
\(357\) | −9.64254 | − | 144.142i | −0.0270099 | − | 0.403758i | ||||
\(358\) | 132.507 | − | 132.507i | 0.370132 | − | 0.370132i | ||||
\(359\) | 161.739 | 0.450526 | 0.225263 | − | 0.974298i | \(-0.427676\pi\) | ||||
0.225263 | + | 0.974298i | \(0.427676\pi\) | |||||||
\(360\) | −297.842 | − | 102.544i | −0.827338 | − | 0.284845i | ||||
\(361\) | 112.126 | 0.310599 | ||||||||
\(362\) | 126.983 | + | 126.983i | 0.350781 | + | 0.350781i | ||||
\(363\) | −216.604 | − | 11.0451i | −0.596706 | − | 0.0304272i | ||||
\(364\) | 431.500 | − | 51.0429i | 1.18544 | − | 0.140228i | ||||
\(365\) | 394.943 | + | 92.3414i | 1.08203 | + | 0.252990i | ||||
\(366\) | 42.3655 | + | 46.9182i | 0.115753 | + | 0.128192i | ||||
\(367\) | −101.051 | + | 101.051i | −0.275343 | + | 0.275343i | −0.831247 | − | 0.555904i | \(-0.812372\pi\) |
0.555904 | + | 0.831247i | \(0.312372\pi\) | |||||||
\(368\) | −8.86409 | − | 8.86409i | −0.0240872 | − | 0.0240872i | ||||
\(369\) | −239.225 | − | 24.4608i | −0.648307 | − | 0.0662893i | ||||
\(370\) | 39.0887 | − | 24.2739i | 0.105645 | − | 0.0656051i | ||||
\(371\) | −56.1715 | − | 474.856i | −0.151406 | − | 1.27993i | ||||
\(372\) | −155.024 | − | 7.90497i | −0.416730 | − | 0.0212499i | ||||
\(373\) | −369.464 | + | 369.464i | −0.990521 | + | 0.990521i | −0.999955 | − | 0.00943464i | \(-0.996997\pi\) |
0.00943464 | + | 0.999955i | \(0.496997\pi\) | |||||||
\(374\) | 95.6424i | 0.255728i | ||||||||
\(375\) | 17.0190 | + | 374.614i | 0.0453839 | + | 0.998970i | ||||
\(376\) | 183.790i | 0.488803i | ||||||||
\(377\) | 410.320 | + | 410.320i | 1.08838 | + | 1.08838i | ||||
\(378\) | 188.884 | + | 6.63236i | 0.499692 | + | 0.0175459i | ||||
\(379\) | − | 261.209i | − | 0.689207i | −0.938748 | − | 0.344604i | \(-0.888013\pi\) | ||
0.938748 | − | 0.344604i | \(-0.111987\pi\) | |||||||
\(380\) | −172.125 | − | 277.176i | −0.452960 | − | 0.729410i | ||||
\(381\) | −203.718 | − | 225.610i | −0.534692 | − | 0.592152i | ||||
\(382\) | 75.7048 | + | 75.7048i | 0.198180 | + | 0.198180i | ||||
\(383\) | 163.813 | − | 163.813i | 0.427710 | − | 0.427710i | −0.460138 | − | 0.887847i | \(-0.652200\pi\) |
0.887847 | + | 0.460138i | \(0.152200\pi\) | |||||||
\(384\) | −239.254 | − | 264.965i | −0.623057 | − | 0.690013i | ||||
\(385\) | −54.3566 | + | 483.562i | −0.141186 | + | 1.25600i | ||||
\(386\) | 115.447i | 0.299085i | ||||||||
\(387\) | 327.197 | − | 266.493i | 0.845472 | − | 0.688612i | ||||
\(388\) | 49.9973 | + | 49.9973i | 0.128859 | + | 0.128859i | ||||
\(389\) | −401.000 | −1.03085 | −0.515425 | − | 0.856935i | \(-0.672366\pi\) | ||||
−0.515425 | + | 0.856935i | \(0.672366\pi\) | |||||||
\(390\) | 271.657 | − | 150.093i | 0.696556 | − | 0.384853i | ||||
\(391\) | − | 17.2472i | − | 0.0441105i | ||||||
\(392\) | −179.255 | + | 292.432i | −0.457283 | + | 0.746001i | ||||
\(393\) | 238.096 | + | 12.1410i | 0.605841 | + | 0.0308931i | ||||
\(394\) | − | 234.338i | − | 0.594767i | ||||||
\(395\) | −199.948 | − | 321.980i | −0.506197 | − | 0.815138i | ||||
\(396\) | 373.436 | + | 38.1838i | 0.943019 | + | 0.0964237i | ||||
\(397\) | 304.082 | − | 304.082i | 0.765950 | − | 0.765950i | −0.211440 | − | 0.977391i | \(-0.567815\pi\) |
0.977391 | + | 0.211440i | \(0.0678154\pi\) | |||||||
\(398\) | 155.590 | − | 155.590i | 0.390929 | − | 0.390929i | ||||
\(399\) | 343.831 | + | 300.714i | 0.861733 | + | 0.753668i | ||||
\(400\) | −55.4226 | + | 112.042i | −0.138557 | + | 0.280104i | ||||
\(401\) | 582.912i | 1.45365i | 0.686825 | + | 0.726823i | \(0.259004\pi\) | ||||
−0.686825 | + | 0.726823i | \(0.740996\pi\) | |||||||
\(402\) | −137.616 | − | 7.01732i | −0.342329 | − | 0.0174560i | ||||
\(403\) | 252.338 | − | 252.338i | 0.626149 | − | 0.626149i | ||||
\(404\) | 339.341i | 0.839952i | ||||||||
\(405\) | −380.178 | + | 139.605i | −0.938712 | + | 0.344704i | ||||
\(406\) | −194.957 | + | 23.0618i | −0.480190 | + | 0.0568025i | ||||
\(407\) | −90.4693 | + | 90.4693i | −0.222283 | + | 0.222283i | ||||
\(408\) | 7.35694 | − | 144.276i | 0.0180317 | − | 0.353619i | ||||
\(409\) | 344.830 | 0.843104 | 0.421552 | − | 0.906804i | \(-0.361485\pi\) | ||||
0.421552 | + | 0.906804i | \(0.361485\pi\) | |||||||
\(410\) | 30.4157 | − | 130.087i | 0.0741846 | − | 0.317286i | ||||
\(411\) | 23.3952 | − | 21.1250i | 0.0569226 | − | 0.0513991i | ||||
\(412\) | −48.5478 | + | 48.5478i | −0.117834 | + | 0.117834i | ||||
\(413\) | −128.576 | + | 163.076i | −0.311323 | + | 0.394858i | ||||
\(414\) | 22.4473 | + | 2.29523i | 0.0542204 | + | 0.00554403i | ||||
\(415\) | −83.6607 | + | 357.815i | −0.201592 | + | 0.862206i | ||||
\(416\) | 682.799 | 1.64134 | ||||||||
\(417\) | −538.068 | − | 27.4372i | −1.29033 | − | 0.0657965i | ||||
\(418\) | −213.838 | − | 213.838i | −0.511573 | − | 0.511573i | ||||
\(419\) | − | 343.927i | − | 0.820828i | −0.911899 | − | 0.410414i | \(-0.865384\pi\) | ||
0.911899 | − | 0.410414i | \(-0.134616\pi\) | |||||||
\(420\) | 51.0828 | − | 310.830i | 0.121626 | − | 0.740072i | ||||
\(421\) | 14.6762 | 0.0348603 | 0.0174302 | − | 0.999848i | \(-0.494452\pi\) | ||||
0.0174302 | + | 0.999848i | \(0.494452\pi\) | |||||||
\(422\) | 195.579 | − | 195.579i | 0.463457 | − | 0.463457i | ||||
\(423\) | 149.227 | + | 183.220i | 0.352783 | + | 0.433144i | ||||
\(424\) | − | 478.167i | − | 1.12775i | ||||||
\(425\) | −162.921 | + | 55.0830i | −0.383343 | + | 0.129607i | ||||
\(426\) | −32.2379 | − | 35.7024i | −0.0756759 | − | 0.0838084i | ||||
\(427\) | −91.3251 | + | 115.830i | −0.213876 | + | 0.271264i | ||||
\(428\) | −417.031 | − | 417.031i | −0.974372 | − | 0.974372i | ||||
\(429\) | −640.518 | + | 578.364i | −1.49305 | + | 1.34817i | ||||
\(430\) | 123.679 | + | 199.162i | 0.287625 | + | 0.463167i | ||||
\(431\) | 443.066i | 1.02800i | 0.857791 | + | 0.513998i | \(0.171836\pi\) | ||||
−0.857791 | + | 0.513998i | \(0.828164\pi\) | |||||||
\(432\) | −133.426 | − | 20.5537i | −0.308857 | − | 0.0475779i | ||||
\(433\) | −487.352 | − | 487.352i | −1.12553 | − | 1.12553i | −0.990896 | − | 0.134629i | \(-0.957016\pi\) |
−0.134629 | − | 0.990896i | \(-0.542984\pi\) | |||||||
\(434\) | 14.1825 | + | 119.895i | 0.0326787 | + | 0.276255i | ||||
\(435\) | 368.214 | − | 203.441i | 0.846469 | − | 0.467681i | ||||
\(436\) | −9.04287 | −0.0207405 | ||||||||
\(437\) | 38.5614 | + | 38.5614i | 0.0882412 | + | 0.0882412i | ||||
\(438\) | −243.041 | − | 12.3931i | −0.554888 | − | 0.0282948i | ||||
\(439\) | 151.065 | 0.344111 | 0.172056 | − | 0.985087i | \(-0.444959\pi\) | ||||
0.172056 | + | 0.985087i | \(0.444959\pi\) | |||||||
\(440\) | −110.786 | + | 473.828i | −0.251785 | + | 1.07688i | ||||
\(441\) | 58.7396 | + | 437.071i | 0.133196 | + | 0.991090i | ||||
\(442\) | 100.648 | + | 100.648i | 0.227710 | + | 0.227710i | ||||
\(443\) | 188.010 | + | 188.010i | 0.424401 | + | 0.424401i | 0.886716 | − | 0.462315i | \(-0.152981\pi\) |
−0.462315 | + | 0.886716i | \(0.652981\pi\) | |||||||
\(444\) | 61.4707 | − | 55.5059i | 0.138448 | − | 0.125013i | ||||
\(445\) | −459.745 | − | 740.336i | −1.03314 | − | 1.66368i | ||||
\(446\) | −245.406 | −0.550239 | ||||||||
\(447\) | 74.1196 | + | 3.77951i | 0.165816 | + | 0.00845528i | ||||
\(448\) | −56.3422 | + | 71.4602i | −0.125764 | + | 0.159509i | ||||
\(449\) | −397.613 | −0.885552 | −0.442776 | − | 0.896632i | \(-0.646006\pi\) | ||||
−0.442776 | + | 0.896632i | \(0.646006\pi\) | |||||||
\(450\) | −50.0092 | − | 219.372i | −0.111132 | − | 0.487493i | ||||
\(451\) | 371.478i | 0.823677i | ||||||||
\(452\) | −240.335 | + | 240.335i | −0.531716 | + | 0.531716i | ||||
\(453\) | −489.336 | − | 24.9522i | −1.08021 | − | 0.0550821i | ||||
\(454\) | −270.665 | −0.596178 | ||||||||
\(455\) | 451.667 | + | 566.069i | 0.992674 | + | 1.24411i | ||||
\(456\) | 306.125 | + | 339.022i | 0.671327 | + | 0.743470i | ||||
\(457\) | −66.2262 | − | 66.2262i | −0.144915 | − | 0.144915i | 0.630927 | − | 0.775842i | \(-0.282675\pi\) |
−0.775842 | + | 0.630927i | \(0.782675\pi\) | |||||||
\(458\) | −87.3209 | + | 87.3209i | −0.190657 | + | 0.190657i | ||||
\(459\) | −109.810 | − | 149.802i | −0.239238 | − | 0.326367i | ||||
\(460\) | 8.56200 | − | 36.6195i | 0.0186130 | − | 0.0796077i | ||||
\(461\) | 191.545 | 0.415499 | 0.207750 | − | 0.978182i | \(-0.433386\pi\) | ||||
0.207750 | + | 0.978182i | \(0.433386\pi\) | |||||||
\(462\) | −19.4878 | − | 291.313i | −0.0421813 | − | 0.630548i | ||||
\(463\) | 42.9857 | − | 42.9857i | 0.0928417 | − | 0.0928417i | −0.659161 | − | 0.752002i | \(-0.729088\pi\) |
0.752002 | + | 0.659161i | \(0.229088\pi\) | |||||||
\(464\) | 140.226 | 0.302211 | ||||||||
\(465\) | −125.112 | − | 226.444i | −0.269058 | − | 0.486977i | ||||
\(466\) | −127.126 | −0.272803 | ||||||||
\(467\) | −252.836 | − | 252.836i | −0.541405 | − | 0.541405i | 0.382536 | − | 0.923941i | \(-0.375051\pi\) |
−0.923941 | + | 0.382536i | \(0.875051\pi\) | |||||||
\(468\) | 433.161 | − | 352.797i | 0.925557 | − | 0.753839i | ||||
\(469\) | −37.7700 | − | 319.295i | −0.0805331 | − | 0.680800i | ||||
\(470\) | −111.524 | + | 69.2561i | −0.237286 | + | 0.147353i | ||||
\(471\) | −341.239 | + | 308.127i | −0.724500 | + | 0.654197i | ||||
\(472\) | −146.843 | + | 146.843i | −0.311108 | + | 0.311108i | ||||
\(473\) | −460.953 | − | 460.953i | −0.974530 | − | 0.974530i | ||||
\(474\) | 152.404 | + | 168.781i | 0.321526 | + | 0.356079i | ||||
\(475\) | 241.105 | − | 487.414i | 0.507589 | − | 1.02613i | ||||
\(476\) | 143.464 | − | 16.9706i | 0.301394 | − | 0.0356524i | ||||
\(477\) | −388.245 | − | 476.684i | −0.813930 | − | 0.999337i | ||||
\(478\) | −34.8452 | + | 34.8452i | −0.0728980 | + | 0.0728980i | ||||
\(479\) | − | 91.5191i | − | 0.191063i | −0.995426 | − | 0.0955314i | \(-0.969545\pi\) | ||
0.995426 | − | 0.0955314i | \(-0.0304550\pi\) | |||||||
\(480\) | 137.096 | − | 475.636i | 0.285618 | − | 0.990908i | ||||
\(481\) | 190.408i | 0.395858i | ||||||||
\(482\) | −298.161 | − | 298.161i | −0.618592 | − | 0.618592i | ||||
\(483\) | 3.51424 | + | 52.5326i | 0.00727585 | + | 0.108763i | ||||
\(484\) | − | 216.886i | − | 0.448111i | ||||||
\(485\) | −26.8296 | + | 114.750i | −0.0553189 | + | 0.236598i | ||||
\(486\) | 209.581 | − | 122.983i | 0.431237 | − | 0.253051i | ||||
\(487\) | 252.690 | + | 252.690i | 0.518872 | + | 0.518872i | 0.917230 | − | 0.398358i | \(-0.130420\pi\) |
−0.398358 | + | 0.917230i | \(0.630420\pi\) | |||||||
\(488\) | −104.300 | + | 104.300i | −0.213729 | + | 0.213729i | ||||
\(489\) | 122.319 | − | 110.450i | 0.250141 | − | 0.225869i | ||||
\(490\) | −244.996 | + | 1.42238i | −0.499992 | + | 0.00290281i | ||||
\(491\) | − | 518.117i | − | 1.05523i | −0.849484 | − | 0.527614i | \(-0.823087\pi\) | ||
0.849484 | − | 0.527614i | \(-0.176913\pi\) | |||||||
\(492\) | 12.2463 | − | 240.161i | 0.0248908 | − | 0.488131i | ||||
\(493\) | 136.422 | + | 136.422i | 0.276717 | + | 0.276717i | ||||
\(494\) | −450.057 | −0.911046 | ||||||||
\(495\) | 274.280 | + | 562.311i | 0.554102 | + | 1.13598i | ||||
\(496\) | − | 86.2361i | − | 0.173863i | ||||||
\(497\) | 69.4937 | − | 88.1406i | 0.139826 | − | 0.177345i | ||||
\(498\) | 11.2281 | − | 220.193i | 0.0225464 | − | 0.442155i | ||||
\(499\) | 217.267i | 0.435404i | 0.976015 | + | 0.217702i | \(0.0698561\pi\) | ||||
−0.976015 | + | 0.217702i | \(0.930144\pi\) | |||||||
\(500\) | −373.261 | + | 36.0744i | −0.746522 | + | 0.0721488i | ||||
\(501\) | −393.095 | − | 435.339i | −0.784621 | − | 0.868940i | ||||
\(502\) | −244.315 | + | 244.315i | −0.486684 | + | 0.486684i | ||||
\(503\) | 12.7399 | − | 12.7399i | 0.0253279 | − | 0.0253279i | −0.694329 | − | 0.719657i | \(-0.744299\pi\) |
0.719657 | + | 0.694329i | \(0.244299\pi\) | |||||||
\(504\) | 6.98904 | + | 440.945i | 0.0138671 | + | 0.874890i | ||||
\(505\) | −480.463 | + | 298.365i | −0.951412 | + | 0.590823i | ||||
\(506\) | − | 34.8570i | − | 0.0688873i | ||||||
\(507\) | −39.5865 | + | 776.327i | −0.0780798 | + | 1.53122i | ||||
\(508\) | 214.943 | − | 214.943i | 0.423116 | − | 0.423116i | ||||
\(509\) | − | 611.593i | − | 1.20156i | −0.799415 | − | 0.600779i | \(-0.794857\pi\) | ||
0.799415 | − | 0.600779i | \(-0.205143\pi\) | |||||||
\(510\) | 90.3195 | − | 49.9023i | 0.177097 | − | 0.0978476i | ||||
\(511\) | −66.7048 | − | 563.900i | −0.130538 | − | 1.10352i | ||||
\(512\) | 215.668 | − | 215.668i | 0.421226 | − | 0.421226i | ||||
\(513\) | 580.443 | + | 89.4144i | 1.13147 | + | 0.174297i | ||||
\(514\) | 306.273 | 0.595862 | ||||||||
\(515\) | −111.423 | − | 26.0518i | −0.216356 | − | 0.0505860i | ||||
\(516\) | 282.810 | + | 313.202i | 0.548081 | + | 0.606980i | ||||
\(517\) | 258.119 | − | 258.119i | 0.499262 | − | 0.499262i | ||||
\(518\) | −50.5855 | − | 39.8837i | −0.0976554 | − | 0.0769956i | ||||
\(519\) | 84.8831 | − | 76.6464i | 0.163551 | − | 0.147681i | ||||
\(520\) | 382.042 | + | 615.208i | 0.734695 | + | 1.18309i | ||||
\(521\) | −692.510 | −1.32919 | −0.664597 | − | 0.747202i | \(-0.731397\pi\) | ||||
−0.664597 | + | 0.747202i | \(0.731397\pi\) | |||||||
\(522\) | −195.708 | + | 159.398i | −0.374919 | + | 0.305360i | ||||
\(523\) | 583.903 | + | 583.903i | 1.11645 | + | 1.11645i | 0.992258 | + | 0.124191i | \(0.0396337\pi\) |
0.124191 | + | 0.992258i | \(0.460366\pi\) | |||||||
\(524\) | 238.405i | 0.454971i | ||||||||
\(525\) | 485.011 | − | 200.971i | 0.923830 | − | 0.382802i | ||||
\(526\) | 277.971 | 0.528463 | ||||||||
\(527\) | 83.8965 | − | 83.8965i | 0.159196 | − | 0.159196i | ||||
\(528\) | −10.6204 | + | 208.275i | −0.0201144 | + | 0.394461i | ||||
\(529\) | − | 522.714i | − | 0.988118i | ||||||
\(530\) | 290.153 | − | 180.184i | 0.547458 | − | 0.339969i | ||||
\(531\) | −27.1592 | + | 265.616i | −0.0511473 | + | 0.500218i | ||||
\(532\) | −282.814 | + | 358.699i | −0.531604 | + | 0.674247i | ||||
\(533\) | 390.919 | + | 390.919i | 0.733431 | + | 0.733431i | ||||
\(534\) | 350.425 | + | 388.083i | 0.656227 | + | 0.726748i | ||||
\(535\) | 223.788 | − | 957.138i | 0.418296 | − | 1.78904i | ||||
\(536\) | − | 321.521i | − | 0.599853i | ||||||
\(537\) | 561.451 | + | 28.6295i | 1.04553 | + | 0.0533138i | ||||
\(538\) | 247.460 | + | 247.460i | 0.459963 | + | 0.459963i | ||||
\(539\) | 662.448 | − | 158.948i | 1.22903 | − | 0.294895i | ||||
\(540\) | −158.785 | − | 372.575i | −0.294046 | − | 0.689954i | ||||
\(541\) | 314.562 | 0.581445 | 0.290723 | − | 0.956807i | \(-0.406104\pi\) | ||||
0.290723 | + | 0.956807i | \(0.406104\pi\) | |||||||
\(542\) | 97.5650 | + | 97.5650i | 0.180009 | + | 0.180009i | ||||
\(543\) | −27.4359 | + | 538.043i | −0.0505265 | + | 0.990871i | ||||
\(544\) | 227.015 | 0.417306 | ||||||||
\(545\) | −7.95095 | − | 12.8035i | −0.0145889 | − | 0.0234927i | ||||
\(546\) | −327.066 | − | 286.051i | −0.599022 | − | 0.523903i | ||||
\(547\) | 223.888 | + | 223.888i | 0.409302 | + | 0.409302i | 0.881495 | − | 0.472193i | \(-0.156538\pi\) |
−0.472193 | + | 0.881495i | \(0.656538\pi\) | |||||||
\(548\) | 22.2890 | + | 22.2890i | 0.0406734 | + | 0.0406734i | ||||
\(549\) | −19.2906 | + | 188.662i | −0.0351378 | + | 0.343646i | ||||
\(550\) | −329.267 | + | 111.324i | −0.598667 | + | 0.202407i | ||||
\(551\) | −610.024 | −1.10712 | ||||||||
\(552\) | −2.68125 | + | 52.5817i | −0.00485733 | + | 0.0952567i | ||||
\(553\) | −328.529 | + | 416.681i | −0.594084 | + | 0.753492i | ||||
\(554\) | 187.831 | 0.339045 | ||||||||
\(555\) | 132.637 | + | 38.2312i | 0.238986 | + | 0.0688850i | ||||
\(556\) | − | 538.767i | − | 0.969005i | ||||||
\(557\) | −245.854 | + | 245.854i | −0.441390 | + | 0.441390i | −0.892479 | − | 0.451089i | \(-0.851036\pi\) |
0.451089 | + | 0.892479i | \(0.351036\pi\) | |||||||
\(558\) | 98.0265 | + | 120.356i | 0.175675 | + | 0.215692i | ||||
\(559\) | −970.151 | −1.73551 | ||||||||
\(560\) | 173.905 | + | 19.5484i | 0.310544 | + | 0.0349079i | ||||
\(561\) | −212.957 | + | 192.293i | −0.379603 | + | 0.342768i | ||||
\(562\) | −100.479 | − | 100.479i | −0.178787 | − | 0.178787i | ||||
\(563\) | −406.434 | + | 406.434i | −0.721907 | + | 0.721907i | −0.968993 | − | 0.247086i | \(-0.920527\pi\) |
0.247086 | + | 0.968993i | \(0.420527\pi\) | |||||||
\(564\) | −175.383 | + | 158.364i | −0.310962 | + | 0.280788i | ||||
\(565\) | −551.600 | − | 128.969i | −0.976283 | − | 0.228264i | ||||
\(566\) | 170.038 | 0.300420 | ||||||||
\(567\) | 364.990 | + | 433.902i | 0.643721 | + | 0.765260i | ||||
\(568\) | 79.3667 | − | 79.3667i | 0.139730 | − | 0.139730i | ||||
\(569\) | 690.156 | 1.21293 | 0.606464 | − | 0.795111i | \(-0.292587\pi\) | ||||
0.606464 | + | 0.795111i | \(0.292587\pi\) | |||||||
\(570\) | −90.3651 | + | 313.508i | −0.158535 | + | 0.550015i | ||||
\(571\) | 612.476 | 1.07264 | 0.536319 | − | 0.844015i | \(-0.319814\pi\) | ||||
0.536319 | + | 0.844015i | \(0.319814\pi\) | |||||||
\(572\) | −610.233 | − | 610.233i | −1.06684 | − | 1.06684i | ||||
\(573\) | −16.3568 | + | 320.771i | −0.0285459 | + | 0.559810i | ||||
\(574\) | −185.739 | + | 21.9714i | −0.323587 | + | 0.0382777i | ||||
\(575\) | 59.3768 | − | 20.0751i | 0.103264 | − | 0.0349131i | ||||
\(576\) | −11.9012 | + | 116.393i | −0.0206618 | + | 0.202071i | ||||
\(577\) | −254.442 | + | 254.442i | −0.440973 | + | 0.440973i | −0.892339 | − | 0.451366i | \(-0.850937\pi\) |
0.451366 | + | 0.892339i | \(0.350937\pi\) | |||||||
\(578\) | −170.891 | − | 170.891i | −0.295659 | − | 0.295659i | ||||
\(579\) | −257.054 | + | 232.110i | −0.443962 | + | 0.400882i | ||||
\(580\) | 221.929 | + | 357.376i | 0.382636 | + | 0.616165i | ||||
\(581\) | 510.890 | − | 60.4341i | 0.879329 | − | 0.104017i | ||||
\(582\) | 3.60081 | − | 70.6151i | 0.00618695 | − | 0.121332i | ||||
\(583\) | −671.548 | + | 671.548i | −1.15188 | + | 1.15188i | ||||
\(584\) | − | 567.832i | − | 0.972315i | ||||||
\(585\) | 880.372 | + | 303.104i | 1.50491 | + | 0.518126i | ||||
\(586\) | − | 534.410i | − | 0.911962i | ||||||
\(587\) | 195.495 | + | 195.495i | 0.333040 | + | 0.333040i | 0.853740 | − | 0.520700i | \(-0.174329\pi\) |
−0.520700 | + | 0.853740i | \(0.674329\pi\) | |||||||
\(588\) | −433.512 | + | 80.9216i | −0.737265 | + | 0.137622i | ||||
\(589\) | 375.152i | 0.636931i | ||||||||
\(590\) | −144.438 | − | 33.7711i | −0.244811 | − | 0.0572391i | ||||
\(591\) | 521.777 | − | 471.146i | 0.882871 | − | 0.797201i | ||||
\(592\) | 32.5357 | + | 32.5357i | 0.0549590 | + | 0.0549590i | ||||
\(593\) | 181.904 | − | 181.904i | 0.306751 | − | 0.306751i | −0.536897 | − | 0.843648i | \(-0.680403\pi\) |
0.843648 | + | 0.536897i | \(0.180403\pi\) | |||||||
\(594\) | −221.929 | − | 302.754i | −0.373618 | − | 0.509686i | ||||
\(595\) | 150.169 | + | 188.205i | 0.252384 | + | 0.316311i | ||||
\(596\) | 74.2159i | 0.124523i | ||||||||
\(597\) | 659.255 | + | 33.6167i | 1.10428 | + | 0.0563094i | ||||
\(598\) | −36.6812 | − | 36.6812i | −0.0613397 | − | 0.0613397i | ||||
\(599\) | 376.201 | 0.628048 | 0.314024 | − | 0.949415i | \(-0.398323\pi\) | ||||
0.314024 | + | 0.949415i | \(0.398323\pi\) | |||||||
\(600\) | 505.261 | − | 142.604i | 0.842102 | − | 0.237674i | ||||
\(601\) | 1122.87i | 1.86834i | 0.356832 | + | 0.934169i | \(0.383857\pi\) | ||||
−0.356832 | + | 0.934169i | \(0.616143\pi\) | |||||||
\(602\) | 203.213 | − | 257.740i | 0.337563 | − | 0.428139i | ||||
\(603\) | −261.058 | − | 320.524i | −0.432931 | − | 0.531549i | ||||
\(604\) | − | 489.971i | − | 0.811211i | ||||||
\(605\) | 307.083 | − | 190.697i | 0.507574 | − | 0.315202i | ||||
\(606\) | 251.858 | − | 227.419i | 0.415608 | − | 0.375279i | ||||
\(607\) | −127.880 | + | 127.880i | −0.210675 | + | 0.210675i | −0.804554 | − | 0.593879i | \(-0.797596\pi\) |
0.593879 | + | 0.804554i | \(0.297596\pi\) | |||||||
\(608\) | −507.560 | + | 507.560i | −0.834803 | + | 0.834803i | ||||
\(609\) | −443.318 | − | 387.724i | −0.727944 | − | 0.636658i | ||||
\(610\) | −102.592 | − | 23.9869i | −0.168183 | − | 0.0393228i | ||||
\(611\) | − | 543.253i | − | 0.889122i | ||||||
\(612\) | 144.016 | − | 117.297i | 0.235320 | − | 0.191661i | ||||
\(613\) | 668.817 | − | 668.817i | 1.09105 | − | 1.09105i | 0.0956388 | − | 0.995416i | \(-0.469511\pi\) |
0.995416 | − | 0.0956388i | \(-0.0304894\pi\) | |||||||
\(614\) | − | 133.868i | − | 0.218026i | ||||||
\(615\) | 350.804 | − | 193.822i | 0.570414 | − | 0.315158i | ||||
\(616\) | 676.533 | − | 80.0283i | 1.09827 | − | 0.129916i | ||||
\(617\) | −416.614 | + | 416.614i | −0.675225 | + | 0.675225i | −0.958916 | − | 0.283691i | \(-0.908441\pi\) |
0.283691 | + | 0.958916i | \(0.408441\pi\) | |||||||
\(618\) | 68.5679 | + | 3.49641i | 0.110951 | + | 0.00565763i | ||||
\(619\) | −1140.08 | −1.84180 | −0.920902 | − | 0.389794i | \(-0.872546\pi\) | ||||
−0.920902 | + | 0.389794i | \(0.872546\pi\) | |||||||
\(620\) | 219.779 | − | 136.482i | 0.354482 | − | 0.220132i | ||||
\(621\) | 40.0205 | + | 54.5957i | 0.0644453 | + | 0.0879157i | ||||
\(622\) | 156.576 | − | 156.576i | 0.251730 | − | 0.251730i | ||||
\(623\) | −755.394 | + | 958.085i | −1.21251 | + | 1.53786i | ||||
\(624\) | 207.999 | + | 230.351i | 0.333331 | + | 0.369153i | ||||
\(625\) | −379.267 | − | 496.771i | −0.606827 | − | 0.794834i | ||||
\(626\) | −319.542 | −0.510450 | ||||||||
\(627\) | 46.2018 | − | 906.059i | 0.0736870 | − | 1.44507i | ||||
\(628\) | −325.105 | − | 325.105i | −0.517683 | − | 0.517683i | ||||
\(629\) | 63.3061i | 0.100646i | ||||||||
\(630\) | −264.933 | + | 170.399i | −0.420528 | + | 0.270474i | ||||
\(631\) | −76.8167 | −0.121738 | −0.0608690 | − | 0.998146i | \(-0.519387\pi\) | ||||
−0.0608690 | + | 0.998146i | \(0.519387\pi\) | |||||||
\(632\) | −375.203 | + | 375.203i | −0.593675 | + | 0.593675i | ||||
\(633\) | 828.695 | + | 42.2568i | 1.30915 | + | 0.0667564i | ||||
\(634\) | 136.086i | 0.214646i | ||||||||
\(635\) | 493.320 | + | 115.343i | 0.776883 | + | 0.181643i | ||||
\(636\) | 456.293 | − | 412.017i | 0.717443 | − | 0.647825i | ||||
\(637\) | 529.849 | − | 864.382i | 0.831788 | − | 1.35696i | ||||
\(638\) | 275.711 | + | 275.711i | 0.432149 | + | 0.432149i | ||||
\(639\) | 14.6792 | − | 143.562i | 0.0229721 | − | 0.224666i | ||||
\(640\) | 579.374 | + | 135.463i | 0.905272 | + | 0.211661i | ||||
\(641\) | − | 187.134i | − | 0.291941i | −0.989289 | − | 0.145970i | \(-0.953370\pi\) | ||
0.989289 | − | 0.145970i | \(-0.0466304\pi\) | |||||||
\(642\) | −30.0346 | + | 589.006i | −0.0467829 | + | 0.917455i | ||||
\(643\) | 767.988 | + | 767.988i | 1.19438 | + | 1.19438i | 0.975824 | + | 0.218559i | \(0.0701356\pi\) |
0.218559 | + | 0.975824i | \(0.429864\pi\) | |||||||
\(644\) | −52.2855 | + | 6.18494i | −0.0811886 | + | 0.00960395i | ||||
\(645\) | −194.793 | + | 675.805i | −0.302004 | + | 1.04776i | ||||
\(646\) | −149.633 | −0.231631 | ||||||||
\(647\) | −573.588 | − | 573.588i | −0.886535 | − | 0.886535i | 0.107654 | − | 0.994188i | \(-0.465666\pi\) |
−0.994188 | + | 0.107654i | \(0.965666\pi\) | |||||||
\(648\) | 311.491 | + | 473.774i | 0.480696 | + | 0.731133i | ||||
\(649\) | 412.459 | 0.635530 | ||||||||
\(650\) | −229.348 | + | 463.648i | −0.352844 | + | 0.713304i | ||||
\(651\) | −238.443 | + | 272.632i | −0.366271 | + | 0.418789i | ||||
\(652\) | 116.536 | + | 116.536i | 0.178736 | + | 0.178736i | ||||
\(653\) | −142.398 | − | 142.398i | −0.218067 | − | 0.218067i | 0.589616 | − | 0.807683i | \(-0.299279\pi\) |
−0.807683 | + | 0.589616i | \(0.799279\pi\) | |||||||
\(654\) | 6.06034 | + | 6.71161i | 0.00926658 | + | 0.0102624i | ||||
\(655\) | −337.551 | + | 209.618i | −0.515345 | + | 0.320027i | ||||
\(656\) | 133.596 | 0.203652 | ||||||||
\(657\) | −461.048 | − | 566.071i | −0.701747 | − | 0.861600i | ||||
\(658\) | 144.326 | + | 113.793i | 0.219340 | + | 0.172937i | ||||
\(659\) | −960.106 | −1.45691 | −0.728457 | − | 0.685092i | \(-0.759762\pi\) | ||||
−0.728457 | + | 0.685092i | \(0.759762\pi\) | |||||||
\(660\) | −547.613 | + | 302.561i | −0.829717 | + | 0.458425i | ||||
\(661\) | 94.8355i | 0.143473i | 0.997424 | + | 0.0717364i | \(0.0228540\pi\) | ||||
−0.997424 | + | 0.0717364i | \(0.977146\pi\) | |||||||
\(662\) | 123.754 | − | 123.754i | 0.186939 | − | 0.186939i | ||||
\(663\) | −21.7459 | + | 426.458i | −0.0327993 | + | 0.643224i | ||||
\(664\) | 514.452 | 0.774777 | ||||||||
\(665\) | −756.537 | − | 85.0414i | −1.13765 | − | 0.127882i | ||||
\(666\) | −82.3928 | − | 8.42466i | −0.123713 | − | 0.0126496i | ||||
\(667\) | −49.7191 | − | 49.7191i | −0.0745413 | − | 0.0745413i | ||||
\(668\) | 414.755 | − | 414.755i | 0.620891 | − | 0.620891i | ||||
\(669\) | −493.399 | − | 546.421i | −0.737517 | − | 0.816773i | ||||
\(670\) | 195.100 | − | 121.156i | 0.291194 | − | 0.180830i | ||||
\(671\) | 292.961 | 0.436604 | ||||||||
\(672\) | −691.455 | + | 46.2557i | −1.02895 | + | 0.0688329i | ||||
\(673\) | −442.857 | + | 442.857i | −0.658034 | + | 0.658034i | −0.954915 | − | 0.296880i | \(-0.904054\pi\) |
0.296880 | + | 0.954915i | \(0.404054\pi\) | |||||||
\(674\) | 154.964 | 0.229917 | ||||||||
\(675\) | 387.908 | − | 552.406i | 0.574678 | − | 0.818379i | ||||
\(676\) | −777.336 | −1.14990 | ||||||||
\(677\) | −447.410 | − | 447.410i | −0.660872 | − | 0.660872i | 0.294714 | − | 0.955586i | \(-0.404776\pi\) |
−0.955586 | + | 0.294714i | \(0.904776\pi\) | |||||||
\(678\) | 339.445 | + | 17.3090i | 0.500656 | + | 0.0255295i | ||||
\(679\) | 163.840 | − | 19.3810i | 0.241296 | − | 0.0285434i | ||||
\(680\) | 127.020 | + | 204.542i | 0.186794 | + | 0.300798i | ||||
\(681\) | −544.182 | − | 602.662i | −0.799093 | − | 0.884966i | ||||
\(682\) | 169.557 | − | 169.557i | 0.248617 | − | 0.248617i | ||||
\(683\) | −199.643 | − | 199.643i | −0.292303 | − | 0.292303i | 0.545686 | − | 0.837990i | \(-0.316269\pi\) |
−0.837990 | + | 0.545686i | \(0.816269\pi\) | |||||||
\(684\) | −59.7388 | + | 584.243i | −0.0873375 | + | 0.854157i | ||||
\(685\) | −11.9608 | + | 51.1561i | −0.0174610 | + | 0.0746804i | ||||
\(686\) | 118.655 | + | 321.823i | 0.172967 | + | 0.469129i | ||||
\(687\) | −369.991 | − | 18.8666i | −0.538560 | − | 0.0274622i | ||||
\(688\) | −165.774 | + | 165.774i | −0.240950 | + | 0.240950i | ||||
\(689\) | 1413.38i | 2.05135i | ||||||||
\(690\) | −32.9171 | + | 18.1869i | −0.0477059 | + | 0.0263579i | ||||
\(691\) | − | 207.196i | − | 0.299849i | −0.988697 | − | 0.149925i | \(-0.952097\pi\) | ||
0.988697 | − | 0.149925i | \(-0.0479031\pi\) | |||||||
\(692\) | 80.8697 | + | 80.8697i | 0.116864 | + | 0.116864i | ||||
\(693\) | 609.457 | − | 629.088i | 0.879447 | − | 0.907775i | ||||
\(694\) | − | 379.857i | − | 0.547345i | ||||||
\(695\) | 762.825 | − | 473.711i | 1.09759 | − | 0.681599i | ||||
\(696\) | −394.702 | − | 437.118i | −0.567100 | − | 0.628043i | ||||
\(697\) | 129.971 | + | 129.971i | 0.186473 | + | 0.186473i | ||||
\(698\) | 215.097 | − | 215.097i | 0.308162 | − | 0.308162i | ||||
\(699\) | −255.592 | − | 283.059i | −0.365654 | − | 0.404948i | ||||
\(700\) | 225.410 | + | 474.147i | 0.322014 | + | 0.677353i | ||||
\(701\) | 8.12497i | 0.0115905i | 0.999983 | + | 0.00579527i | \(0.00184470\pi\) | ||||
−0.999983 | + | 0.00579527i | \(0.998155\pi\) | |||||||
\(702\) | −552.141 | − | 85.0546i | −0.786525 | − | 0.121160i | ||||
\(703\) | −141.540 | − | 141.540i | −0.201337 | − | 0.201337i | ||||
\(704\) | 180.740 | 0.256733 | ||||||||
\(705\) | −378.429 | − | 109.078i | −0.536779 | − | 0.154720i | ||||
\(706\) | − | 339.785i | − | 0.481281i | ||||||
\(707\) | 621.778 | + | 490.236i | 0.879459 | + | 0.693403i | ||||
\(708\) | −266.654 | − | 13.5972i | −0.376631 | − | 0.0192052i | ||||
\(709\) | − | 854.167i | − | 1.20475i | −0.798214 | − | 0.602374i | \(-0.794222\pi\) | ||
0.798214 | − | 0.602374i | \(-0.205778\pi\) | |||||||
\(710\) | 78.0670 | + | 18.2528i | 0.109954 | + | 0.0257082i | ||||
\(711\) | −69.3953 | + | 678.683i | −0.0976023 | + | 0.954547i | ||||
\(712\) | −862.713 | + | 862.713i | −1.21168 | + | 1.21168i | ||||
\(713\) | −30.5762 | + | 30.5762i | −0.0428839 | + | 0.0428839i | ||||
\(714\) | −108.742 | − | 95.1052i | −0.152300 | − | 0.133201i | ||||
\(715\) | 327.464 | − | 1400.56i | 0.457992 | − | 1.95882i | ||||
\(716\) | 562.180i | 0.785168i | ||||||||
\(717\) | −147.644 | − | 7.52867i | −0.205919 | − | 0.0105002i | ||||
\(718\) | 114.367 | − | 114.367i | 0.159285 | − | 0.159285i | ||||
\(719\) | − | 1236.22i | − | 1.71936i | −0.510837 | − | 0.859678i | \(-0.670664\pi\) | ||
0.510837 | − | 0.859678i | \(-0.329336\pi\) | |||||||
\(720\) | 202.225 | − | 98.6402i | 0.280869 | − | 0.137000i | ||||
\(721\) | 18.8191 | + | 159.090i | 0.0261014 | + | 0.220652i | ||||
\(722\) | 79.2852 | − | 79.2852i | 0.109813 | − | 0.109813i | ||||
\(723\) | 64.4208 | − | 1263.35i | 0.0891021 | − | 1.74737i | ||||
\(724\) | −538.742 | −0.744118 | ||||||||
\(725\) | −310.868 | + | 628.446i | −0.428783 | + | 0.866822i | ||||
\(726\) | −160.972 | + | 145.352i | −0.221725 | + | 0.200210i | ||||
\(727\) | −635.035 | + | 635.035i | −0.873501 | + | 0.873501i | −0.992852 | − | 0.119351i | \(-0.961919\pi\) |
0.119351 | + | 0.992852i | \(0.461919\pi\) | |||||||
\(728\) | 627.722 | − | 796.155i | 0.862255 | − | 1.09362i | ||||
\(729\) | 695.204 | + | 219.392i | 0.953640 | + | 0.300949i | ||||
\(730\) | 344.562 | − | 213.971i | 0.472003 | − | 0.293112i | ||||
\(731\) | −322.553 | −0.441249 | ||||||||
\(732\) | −189.399 | − | 9.65785i | −0.258742 | − | 0.0131938i | ||||
\(733\) | −174.851 | − | 174.851i | −0.238542 | − | 0.238542i | 0.577704 | − | 0.816246i | \(-0.303949\pi\) |
−0.816246 | + | 0.577704i | \(0.803949\pi\) | |||||||
\(734\) | 142.908i | 0.194697i | ||||||||
\(735\) | −495.741 | − | 542.648i | −0.674477 | − | 0.738296i | ||||
\(736\) | −82.7358 | −0.112413 | ||||||||
\(737\) | −451.552 | + | 451.552i | −0.612689 | + | 0.612689i | ||||
\(738\) | −186.454 | + | 151.861i | −0.252648 | + | 0.205774i | ||||
\(739\) | 1448.98i | 1.96073i | 0.197187 | + | 0.980366i | \(0.436819\pi\) | ||||
−0.197187 | + | 0.980366i | \(0.563181\pi\) | |||||||
\(740\) | −31.4269 | + | 134.412i | −0.0424688 | + | 0.181638i | ||||
\(741\) | −904.856 | − | 1002.10i | −1.22113 | − | 1.35236i | ||||
\(742\) | −375.493 | − | 296.055i | −0.506055 | − | 0.398995i | ||||
\(743\) | −30.8955 | − | 30.8955i | −0.0415822 | − | 0.0415822i | 0.686010 | − | 0.727592i | \(-0.259361\pi\) |
−0.727592 | + | 0.686010i | \(0.759361\pi\) | |||||||
\(744\) | −268.818 | + | 242.733i | −0.361315 | + | 0.326254i | ||||
\(745\) | −105.080 | + | 65.2544i | −0.141047 | + | 0.0875898i | ||||
\(746\) | 522.501i | 0.700404i | ||||||||
\(747\) | 512.856 | − | 417.706i | 0.686555 | − | 0.559179i | ||||
\(748\) | −202.888 | − | 202.888i | −0.271241 | − | 0.271241i | ||||
\(749\) | −1366.61 | + | 161.658i | −1.82457 | + | 0.215832i | ||||
\(750\) | 276.926 | + | 252.858i | 0.369235 | + | 0.337143i | ||||
\(751\) | 1095.21 | 1.45833 | 0.729167 | − | 0.684335i | \(-0.239908\pi\) | ||||
0.729167 | + | 0.684335i | \(0.239908\pi\) | |||||||
\(752\) | −92.8279 | − | 92.8279i | −0.123441 | − | 0.123441i | ||||
\(753\) | −1035.20 | − | 52.7867i | −1.37476 | − | 0.0701019i | ||||
\(754\) | 580.279 | 0.769601 | ||||||||
\(755\) | 693.737 | − | 430.808i | 0.918857 | − | 0.570606i | ||||
\(756\) | −414.752 | + | 386.613i | −0.548614 | + | 0.511393i | ||||
\(757\) | 209.069 | + | 209.069i | 0.276181 | + | 0.276181i | 0.831582 | − | 0.555401i | \(-0.187435\pi\) |
−0.555401 | + | 0.831582i | \(0.687435\pi\) | |||||||
\(758\) | −184.703 | − | 184.703i | −0.243672 | − | 0.243672i | ||||
\(759\) | 77.6125 | − | 70.0813i | 0.102256 | − | 0.0923337i | ||||
\(760\) | −741.308 | − | 173.325i | −0.975406 | − | 0.228059i | ||||
\(761\) | 710.902 | 0.934168 | 0.467084 | − | 0.884213i | \(-0.345305\pi\) | ||||
0.467084 | + | 0.884213i | \(0.345305\pi\) | |||||||
\(762\) | −303.581 | − | 15.4802i | −0.398400 | − | 0.0203152i | ||||
\(763\) | −13.0640 | + | 16.5694i | −0.0171219 | + | 0.0217161i | ||||
\(764\) | −321.188 | −0.420403 | ||||||||
\(765\) | 292.703 | + | 100.775i | 0.382618 | + | 0.131732i | ||||
\(766\) | − | 231.666i | − | 0.302436i | ||||||
\(767\) | 434.044 | − | 434.044i | 0.565898 | − | 0.565898i | ||||
\(768\) | −512.334 | − | 26.1250i | −0.667102 | − | 0.0340169i | ||||
\(769\) | −248.259 | −0.322833 | −0.161417 | − | 0.986886i | \(-0.551606\pi\) | ||||
−0.161417 | + | 0.986886i | \(0.551606\pi\) | |||||||
\(770\) | 303.494 | + | 380.366i | 0.394148 | + | 0.493982i | ||||
\(771\) | 615.774 | + | 681.947i | 0.798669 | + | 0.884497i | ||||
\(772\) | −244.900 | − | 244.900i | −0.317228 | − | 0.317228i | ||||
\(773\) | 307.323 | − | 307.323i | 0.397572 | − | 0.397572i | −0.479804 | − | 0.877376i | \(-0.659292\pi\) |
0.877376 | + | 0.479804i | \(0.159292\pi\) | |||||||
\(774\) | 42.9248 | − | 419.802i | 0.0554583 | − | 0.542380i | ||||
\(775\) | 386.481 | + | 191.177i | 0.498686 | + | 0.246680i | ||||
\(776\) | 164.983 | 0.212606 | ||||||||
\(777\) | −12.8990 | − | 192.821i | −0.0166011 | − | 0.248161i | ||||
\(778\) | −283.550 | + | 283.550i | −0.364460 | + | 0.364460i | ||||
\(779\) | −581.181 | −0.746061 | ||||||||
\(780\) | −257.877 | + | 894.665i | −0.330611 | + | 1.14701i | ||||
\(781\) | −222.929 | −0.285440 | ||||||||
\(782\) | −12.1956 | − | 12.1956i | −0.0155954 | − | 0.0155954i | ||||
\(783\) | −748.393 | − | 115.286i | −0.955802 | − | 0.147237i | ||||
\(784\) | −57.1631 | − | 238.238i | −0.0729121 | − | 0.303875i | ||||
\(785\) | 174.458 | − | 746.156i | 0.222240 | − | 0.950517i | ||||
\(786\) | 176.944 | − | 159.774i | 0.225120 | − | 0.203275i | ||||
\(787\) | 196.357 | − | 196.357i | 0.249501 | − | 0.249501i | −0.571265 | − | 0.820766i | \(-0.693547\pi\) |
0.820766 | + | 0.571265i | \(0.193547\pi\) | |||||||
\(788\) | 497.106 | + | 497.106i | 0.630845 | + | 0.630845i | ||||
\(789\) | 558.872 | + | 618.931i | 0.708330 | + | 0.784449i | ||||
\(790\) | −369.058 | − | 86.2894i | −0.467163 | − | 0.109227i | ||||
\(791\) | 93.1637 | + | 787.576i | 0.117780 | + | 0.995671i | ||||
\(792\) | 679.137 | − | 553.137i | 0.857497 | − | 0.698406i | ||||
\(793\) | 308.293 | − | 308.293i | 0.388768 | − | 0.388768i | ||||
\(794\) | − | 430.037i | − | 0.541609i | ||||||
\(795\) | 984.560 | + | 283.788i | 1.23844 | + | 0.356966i | ||||
\(796\) | 660.111i | 0.829285i | ||||||||
\(797\) | 941.657 | + | 941.657i | 1.18150 | + | 1.18150i | 0.979355 | + | 0.202147i | \(0.0647918\pi\) |
0.202147 | + | 0.979355i | \(0.435208\pi\) | |||||||
\(798\) | 455.762 | − | 30.4888i | 0.571130 | − | 0.0382065i | ||||
\(799\) | − | 180.619i | − | 0.226056i | ||||||
\(800\) | 264.236 | + | 781.540i | 0.330295 | + | 0.976925i | ||||
\(801\) | −159.562 | + | 1560.51i | −0.199204 | + | 1.94821i | ||||
\(802\) | 412.181 | + | 412.181i | 0.513941 | + | 0.513941i | ||||
\(803\) | −797.475 | + | 797.475i | −0.993120 | + | 0.993120i | ||||
\(804\) | 306.814 | − | 277.042i | 0.381609 | − | 0.344579i | ||||
\(805\) | −54.7292 | − | 68.5915i | −0.0679865 | − | 0.0852068i | ||||
\(806\) | − | 356.860i | − | 0.442754i | ||||||
\(807\) | −53.4662 | + | 1048.52i | −0.0662530 | + | 1.29928i | ||||
\(808\) | 559.883 | + | 559.883i | 0.692925 | + | 0.692925i | ||||
\(809\) | 1461.04 | 1.80598 | 0.902990 | − | 0.429662i | \(-0.141367\pi\) | ||||
0.902990 | + | 0.429662i | \(0.141367\pi\) | |||||||
\(810\) | −170.111 | + | 367.542i | −0.210014 | + | 0.453756i | ||||
\(811\) | − | 1284.35i | − | 1.58367i | −0.610738 | − | 0.791833i | \(-0.709127\pi\) | ||
0.610738 | − | 0.791833i | \(-0.290873\pi\) | |||||||
\(812\) | 364.645 | − | 462.488i | 0.449070 | − | 0.569567i | ||||
\(813\) | −21.0799 | + | 413.396i | −0.0259285 | + | 0.508482i | ||||
\(814\) | 127.943i | 0.157178i | ||||||||
\(815\) | −62.5356 | + | 267.464i | −0.0767308 | + | 0.328177i | ||||
\(816\) | 69.1548 | + | 76.5864i | 0.0847485 | + | 0.0938559i | ||||
\(817\) | 721.165 | − | 721.165i | 0.882698 | − | 0.882698i | ||||
\(818\) | 243.831 | − | 243.831i | 0.298082 | − | 0.298082i | ||||
\(819\) | −20.6585 | − | 1303.36i | −0.0252240 | − | 1.59141i | ||||
\(820\) | 211.436 | + | 340.479i | 0.257848 | + | 0.415218i | ||||
\(821\) | − | 782.279i | − | 0.952837i | −0.879219 | − | 0.476418i | \(-0.841935\pi\) | ||
0.879219 | − | 0.476418i | \(-0.158065\pi\) | |||||||
\(822\) | 1.60526 | − | 31.4805i | 0.00195287 | − | 0.0382975i | ||||
\(823\) | −361.067 | + | 361.067i | −0.438720 | + | 0.438720i | −0.891581 | − | 0.452861i | \(-0.850403\pi\) |
0.452861 | + | 0.891581i | \(0.350403\pi\) | |||||||
\(824\) | 160.200i | 0.194417i | ||||||||
\(825\) | −909.876 | − | 509.324i | −1.10288 | − | 0.617362i | ||||
\(826\) | 24.3953 | + | 206.229i | 0.0295342 | + | 0.249672i | ||||
\(827\) | 711.346 | − | 711.346i | 0.860152 | − | 0.860152i | −0.131203 | − | 0.991356i | \(-0.541884\pi\) |
0.991356 | + | 0.131203i | \(0.0418840\pi\) | |||||||
\(828\) | −52.4867 | + | 42.7489i | −0.0633898 | + | 0.0516291i | ||||
\(829\) | 1369.60 | 1.65211 | 0.826054 | − | 0.563591i | \(-0.190581\pi\) | ||||
0.826054 | + | 0.563591i | \(0.190581\pi\) | |||||||
\(830\) | 193.857 | + | 312.171i | 0.233562 | + | 0.376109i | ||||
\(831\) | 377.642 | + | 418.224i | 0.454442 | + | 0.503278i | ||||
\(832\) | 190.198 | − | 190.198i | 0.228604 | − | 0.228604i | ||||
\(833\) | 176.162 | − | 287.387i | 0.211480 | − | 0.345002i | ||||
\(834\) | −399.872 | + | 361.070i | −0.479463 | + | 0.432938i | ||||
\(835\) | 951.914 | + | 222.567i | 1.14002 | + | 0.266547i | ||||
\(836\) | 907.236 | 1.08521 | ||||||||
\(837\) | −70.8987 | + | 460.246i | −0.0847057 | + | 0.549876i | ||||
\(838\) | −243.193 | − | 243.193i | −0.290206 | − | 0.290206i | ||||
\(839\) | 915.483i | 1.09116i | 0.838059 | + | 0.545580i | \(0.183690\pi\) | ||||
−0.838059 | + | 0.545580i | \(0.816310\pi\) | |||||||
\(840\) | −428.562 | − | 597.126i | −0.510193 | − | 0.710865i | ||||
\(841\) | −54.4667 | −0.0647642 | ||||||||
\(842\) | 10.3776 | − | 10.3776i | 0.0123250 | − | 0.0123250i | ||||
\(843\) | 21.7094 | − | 425.741i | 0.0257526 | − | 0.505031i | ||||
\(844\) | 829.771i | 0.983141i | ||||||||
\(845\) | −683.473 | − | 1100.61i | −0.808844 | − | 1.30250i | ||||
\(846\) | 235.076 | + | 24.0365i | 0.277867 | + | 0.0284119i | ||||
\(847\) | −397.402 | − | 313.329i | −0.469188 | − | 0.369928i | ||||
\(848\) | 241.511 | + | 241.511i | 0.284800 | + | 0.284800i | ||||
\(849\) | 341.868 | + | 378.606i | 0.402671 | + | 0.445943i | ||||
\(850\) | −76.2530 | + | 154.152i | −0.0897094 | + | 0.181355i | ||||
\(851\) | − | 23.0720i | − | 0.0271116i | ||||||
\(852\) | 144.123 | + | 7.34913i | 0.169159 | + | 0.00862574i | ||||
\(853\) | −286.958 | − | 286.958i | −0.336411 | − | 0.336411i | 0.518604 | − | 0.855015i | \(-0.326452\pi\) |
−0.855015 | + | 0.518604i | \(0.826452\pi\) | |||||||
\(854\) | 17.3275 | + | 146.481i | 0.0202898 | + | 0.171523i | ||||
\(855\) | −879.740 | + | 429.114i | −1.02894 | + | 0.501888i | ||||
\(856\) | −1376.13 | −1.60763 | ||||||||
\(857\) | 605.241 | + | 605.241i | 0.706232 | + | 0.706232i | 0.965741 | − | 0.259509i | \(-0.0835606\pi\) |
−0.259509 | + | 0.965741i | \(0.583561\pi\) | |||||||
\(858\) | −43.9490 | + | 861.880i | −0.0512226 | + | 1.00452i | ||||
\(859\) | −1440.15 | −1.67654 | −0.838272 | − | 0.545253i | \(-0.816434\pi\) | ||||
−0.838272 | + | 0.545253i | \(0.816434\pi\) | |||||||
\(860\) | −684.848 | − | 160.124i | −0.796335 | − | 0.186191i | ||||
\(861\) | −422.357 | − | 369.392i | −0.490543 | − | 0.429027i | ||||
\(862\) | 313.295 | + | 313.295i | 0.363452 | + | 0.363452i | ||||
\(863\) | −761.642 | − | 761.642i | −0.882551 | − | 0.882551i | 0.111242 | − | 0.993793i | \(-0.464517\pi\) |
−0.993793 | + | 0.111242i | \(0.964517\pi\) | |||||||
\(864\) | −718.609 | + | 526.765i | −0.831724 | + | 0.609682i | ||||
\(865\) | −43.3965 | + | 185.606i | −0.0501693 | + | 0.214573i | ||||
\(866\) | −689.220 | −0.795866 | ||||||||
\(867\) | 36.9227 | − | 724.088i | 0.0425867 | − | 0.835165i | ||||
\(868\) | −284.421 | − | 224.249i | −0.327674 | − | 0.258352i | ||||
\(869\) | 1053.89 | 1.21276 | ||||||||
\(870\) | 116.512 | − | 404.221i | 0.133922 | − | 0.464622i | ||||
\(871\) | 950.365i | 1.09112i | ||||||||
\(872\) | −14.9200 | + | 14.9200i | −0.0171101 | + | 0.0171101i | ||||
\(873\) | 164.471 | − | 133.957i | 0.188397 | − | 0.153444i | ||||
\(874\) | 54.5341 | 0.0623959 | ||||||||
\(875\) | −473.140 | + | 736.046i | −0.540731 | + | 0.841195i | ||||
\(876\) | 541.857 | − | 489.277i | 0.618558 | − | 0.558536i | ||||
\(877\) | −21.5786 | − | 21.5786i | −0.0246050 | − | 0.0246050i | 0.694697 | − | 0.719302i | \(-0.255538\pi\) |
−0.719302 | + | 0.694697i | \(0.755538\pi\) | |||||||
\(878\) | 106.819 | − | 106.819i | 0.121662 | − | 0.121662i | ||||
\(879\) | 1189.92 | − | 1074.45i | 1.35372 | − | 1.22236i | ||||
\(880\) | −183.364 | − | 295.275i | −0.208368 | − | 0.335539i | ||||
\(881\) | 269.114 | 0.305465 | 0.152732 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152732 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(882\) | 350.591 | + | 267.520i | 0.397495 | + | 0.303311i | ||||
\(883\) | 659.321 | − | 659.321i | 0.746683 | − | 0.746683i | −0.227171 | − | 0.973855i | \(-0.572948\pi\) |
0.973855 | + | 0.227171i | \(0.0729478\pi\) | |||||||
\(884\) | −427.012 | −0.483045 | ||||||||
\(885\) | −215.204 | − | 389.504i | −0.243169 | − | 0.440118i | ||||
\(886\) | 265.886 | 0.300097 | ||||||||
\(887\) | 366.008 | + | 366.008i | 0.412636 | + | 0.412636i | 0.882656 | − | 0.470020i | \(-0.155753\pi\) |
−0.470020 | + | 0.882656i | \(0.655753\pi\) | |||||||
\(888\) | 9.84154 | − | 193.002i | 0.0110828 | − | 0.217344i | ||||
\(889\) | −83.3205 | − | 704.364i | −0.0937239 | − | 0.792311i | ||||
\(890\) | −848.585 | − | 198.407i | −0.953467 | − | 0.222930i | ||||
\(891\) | 227.914 | − | 1102.84i | 0.255796 | − | 1.23776i | ||||
\(892\) | 520.586 | − | 520.586i | 0.583616 | − | 0.583616i | ||||
\(893\) | 403.829 | + | 403.829i | 0.452216 | + | 0.452216i | ||||
\(894\) | 55.0830 | − | 49.7380i | 0.0616141 | − | 0.0556353i | ||||
\(895\) | −795.976 | + | 494.297i | −0.889358 | + | 0.552288i | ||||
\(896\) | −97.8548 | − | 827.232i | −0.109213 | − | 0.923250i | ||||
\(897\) | 7.92533 | − | 155.423i | 0.00883538 | − | 0.173270i | ||||
\(898\) | −281.155 | + | 281.155i | −0.313090 | + | 0.313090i | ||||
\(899\) | − | 483.702i | − | 0.538044i | ||||||
\(900\) | 571.444 | + | 359.273i | 0.634938 | + | 0.399192i | ||||
\(901\) | 469.917i | 0.521550i | ||||||||
\(902\) | 262.675 | + | 262.675i | 0.291214 | + | 0.291214i | ||||
\(903\) | 982.450 | − | 65.7222i | 1.08798 | − | 0.0727821i | ||||
\(904\) | 793.067i | 0.877286i | ||||||||
\(905\) | −473.689 | − | 762.790i | −0.523413 | − | 0.842862i | ||||
\(906\) | −363.656 | + | 328.369i | −0.401387 | + | 0.362438i | ||||
\(907\) | 65.0405 | + | 65.0405i | 0.0717094 | + | 0.0717094i | 0.742052 | − | 0.670342i | \(-0.233853\pi\) |
−0.670342 | + | 0.742052i | \(0.733853\pi\) | |||||||
\(908\) | 574.167 | − | 574.167i | 0.632343 | − | 0.632343i | ||||
\(909\) | 1012.74 | + | 103.553i | 1.11413 | + | 0.113919i | ||||
\(910\) | 719.648 | + | 80.8948i | 0.790822 | + | 0.0888954i | ||||
\(911\) | 1604.19i | 1.76091i | 0.474126 | + | 0.880457i | \(0.342764\pi\) | ||||
−0.474126 | + | 0.880457i | \(0.657236\pi\) | |||||||
\(912\) | −325.849 | − | 16.6157i | −0.357290 | − | 0.0182189i | ||||
\(913\) | −722.507 | − | 722.507i | −0.791355 | − | 0.791355i | ||||
\(914\) | −93.6580 | −0.102470 | ||||||||
\(915\) | −152.855 | − | 276.657i | −0.167055 | − | 0.302357i | ||||
\(916\) | − | 370.471i | − | 0.404445i | ||||||
\(917\) | 436.832 | + | 344.417i | 0.476371 | + | 0.375591i | ||||
\(918\) | −183.574 | − | 28.2787i | −0.199972 | − | 0.0308046i | ||||
\(919\) | 18.0596i | 0.0196513i | 0.999952 | + | 0.00982566i | \(0.00312766\pi\) | ||||
−0.999952 | + | 0.00982566i | \(0.996872\pi\) | |||||||
\(920\) | −46.2926 | − | 74.5457i | −0.0503180 | − | 0.0810280i | ||||
\(921\) | 298.070 | − | 269.147i | 0.323638 | − | 0.292233i | ||||
\(922\) | 135.443 | − | 135.443i | 0.146901 | − | 0.146901i | ||||
\(923\) | −234.595 | + | 234.595i | −0.254166 | + | 0.254166i | ||||
\(924\) | 659.309 | + | 576.629i | 0.713537 | + | 0.624057i | ||||
\(925\) | −217.943 | + | 73.6857i | −0.235614 | + | 0.0796602i | ||||
\(926\) | − | 60.7910i | − | 0.0656490i | ||||||
\(927\) | 130.073 | + | 159.703i | 0.140316 | + | 0.172279i | ||||
\(928\) | 654.421 | − | 654.421i | 0.705195 | − | 0.705195i | ||||
\(929\) | 891.704i | 0.959854i | 0.877308 | + | 0.479927i | \(0.159337\pi\) | ||||
−0.877308 | + | 0.479927i | \(0.840663\pi\) | |||||||
\(930\) | −248.588 | − | 71.6525i | −0.267299 | − | 0.0770457i | ||||
\(931\) | 248.676 | + | 1036.41i | 0.267107 | + | 1.11322i | ||||
\(932\) | 269.675 | − | 269.675i | 0.289351 | − | 0.289351i | ||||
\(933\) | 663.435 | + | 33.8299i | 0.711077 | + | 0.0362592i | ||||
\(934\) | −357.564 | −0.382831 | ||||||||
\(935\) | 108.874 | − | 465.653i | 0.116443 | − | 0.498025i | ||||
\(936\) | 132.594 | − | 1296.76i | 0.141660 | − | 1.38543i | ||||
\(937\) | −485.788 | + | 485.788i | −0.518450 | + | 0.518450i | −0.917102 | − | 0.398652i | \(-0.869478\pi\) |
0.398652 | + | 0.917102i | \(0.369478\pi\) | |||||||
\(938\) | −252.483 | − | 199.068i | −0.269172 | − | 0.212226i | ||||
\(939\) | −642.450 | − | 711.490i | −0.684186 | − | 0.757711i | ||||
\(940\) | 89.6643 | − | 383.493i | 0.0953876 | − | 0.407971i | ||||
\(941\) | −1356.29 | −1.44133 | −0.720665 | − | 0.693284i | \(-0.756163\pi\) | ||||
−0.720665 | + | 0.693284i | \(0.756163\pi\) | |||||||
\(942\) | −23.4141 | + | 459.171i | −0.0248557 | + | 0.487443i | ||||
\(943\) | −47.3683 | − | 47.3683i | −0.0502314 | − | 0.0502314i | ||||
\(944\) | − | 148.334i | − | 0.157133i | ||||||
\(945\) | −912.066 | − | 247.306i | −0.965149 | − | 0.261699i | ||||
\(946\) | −651.886 | −0.689097 | ||||||||
\(947\) | −757.557 | + | 757.557i | −0.799955 | + | 0.799955i | −0.983088 | − | 0.183133i | \(-0.941376\pi\) |
0.183133 | + | 0.983088i | \(0.441376\pi\) | |||||||
\(948\) | −681.336 | − | 34.7427i | −0.718709 | − | 0.0366484i | ||||
\(949\) | 1678.42i | 1.76862i | ||||||||
\(950\) | −174.167 | − | 515.140i | −0.183334 | − | 0.542253i | ||||
\(951\) | −303.008 | + | 273.606i | −0.318621 | + | 0.287703i | ||||
\(952\) | 208.703 | − | 264.703i | 0.219226 | − | 0.278049i | ||||
\(953\) | 1083.39 | + | 1083.39i | 1.13682 | + | 1.13682i | 0.989017 | + | 0.147800i | \(0.0472192\pi\) |
0.147800 | + | 0.989017i | \(0.452781\pi\) | |||||||
\(954\) | −611.597 | − | 62.5357i | −0.641087 | − | 0.0655511i | ||||
\(955\) | −282.405 | − | 454.762i | −0.295712 | − | 0.476190i | ||||
\(956\) | − | 147.836i | − | 0.154640i | ||||||
\(957\) | −59.5702 | + | 1168.22i | −0.0622468 | + | 1.22072i | ||||
\(958\) | −64.7138 | − | 64.7138i | −0.0675509 | − | 0.0675509i | ||||
\(959\) | 73.0408 | − | 8.64012i | 0.0761635 | − | 0.00900951i | ||||
\(960\) | −94.3026 | − | 170.681i | −0.0982319 | − | 0.177793i | ||||
\(961\) | 663.533 | 0.690461 | ||||||||
\(962\) | 134.638 | + | 134.638i | 0.139957 | + | 0.139957i | ||||
\(963\) | −1371.87 | + | 1117.34i | −1.42457 | + | 1.16027i | ||||
\(964\) | 1264.99 | 1.31223 | ||||||||
\(965\) | 131.419 | − | 562.076i | 0.136185 | − | 0.582462i | ||||
\(966\) | 39.6311 | + | 34.6612i | 0.0410260 | + | 0.0358812i | ||||
\(967\) | −981.586 | − | 981.586i | −1.01508 | − | 1.01508i | −0.999884 | − | 0.0151989i | \(-0.995162\pi\) |
−0.0151989 | − | 0.999884i | \(-0.504838\pi\) | |||||||
\(968\) | −357.843 | − | 357.843i | −0.369673 | − | 0.369673i | ||||
\(969\) | −300.843 | − | 333.173i | −0.310468 | − | 0.343832i | ||||
\(970\) | 62.1690 | + | 100.112i | 0.0640918 | + | 0.103208i | ||||
\(971\) | 366.616 | 0.377565 | 0.188783 | − | 0.982019i | \(-0.439546\pi\) | ||||
0.188783 | + | 0.982019i | \(0.439546\pi\) | |||||||
\(972\) | −183.703 | + | 705.474i | −0.188995 | + | 0.725797i | ||||
\(973\) | −987.189 | − | 778.341i | −1.01458 | − | 0.799939i | ||||
\(974\) | 357.358 | 0.366898 | ||||||||
\(975\) | −1493.47 | + | 421.515i | −1.53176 | + | 0.432323i | ||||
\(976\) | − | 105.359i | − | 0.107949i | ||||||
\(977\) | −576.937 | + | 576.937i | −0.590519 | + | 0.590519i | −0.937772 | − | 0.347253i | \(-0.887115\pi\) |
0.347253 | + | 0.937772i | \(0.387115\pi\) | |||||||
\(978\) | 8.39291 | − | 164.593i | 0.00858170 | − | 0.168295i | ||||
\(979\) | 2423.23 | 2.47520 | ||||||||
\(980\) | 516.697 | − | 522.732i | 0.527242 | − | 0.533400i | ||||
\(981\) | −2.75951 | + | 26.9879i | −0.00281295 | + | 0.0275106i | ||||
\(982\) | −366.364 | − | 366.364i | −0.373080 | − | 0.373080i | ||||
\(983\) | 618.375 | − | 618.375i | 0.629069 | − | 0.629069i | −0.318765 | − | 0.947834i | \(-0.603268\pi\) |
0.947834 | + | 0.318765i | \(0.103268\pi\) | |||||||
\(984\) | −376.039 | − | 416.450i | −0.382154 | − | 0.423222i | ||||
\(985\) | −266.758 | + | 1140.92i | −0.270820 | + | 1.15829i | ||||
\(986\) | 192.929 | 0.195669 | ||||||||
\(987\) | 36.8023 | + | 550.140i | 0.0372870 | + | 0.557386i | ||||
\(988\) | 954.714 | − | 954.714i | 0.966310 | − | 0.966310i | ||||
\(989\) | 117.555 | 0.118862 | ||||||||
\(990\) | 591.559 | + | 203.668i | 0.597534 | + | 0.205725i | ||||
\(991\) | −1797.04 | −1.81336 | −0.906680 | − | 0.421818i | \(-0.861392\pi\) | ||||
−0.906680 | + | 0.421818i | \(0.861392\pi\) | |||||||
\(992\) | −402.456 | − | 402.456i | −0.405701 | − | 0.405701i | ||||
\(993\) | 524.362 | + | 26.7383i | 0.528058 | + | 0.0269267i | ||||
\(994\) | −13.1853 | − | 111.464i | −0.0132649 | − | 0.112137i | ||||
\(995\) | −934.634 | + | 580.403i | −0.939330 | + | 0.583320i | ||||
\(996\) | 443.282 | + | 490.919i | 0.445062 | + | 0.492891i | ||||
\(997\) | 86.1420 | − | 86.1420i | 0.0864012 | − | 0.0864012i | −0.662585 | − | 0.748986i | \(-0.730541\pi\) |
0.748986 | + | 0.662585i | \(0.230541\pi\) | |||||||
\(998\) | 153.631 | + | 153.631i | 0.153939 | + | 0.153939i | ||||
\(999\) | −146.896 | − | 200.394i | −0.147043 | − | 0.200594i |
(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 | 105.3.k.c.62.8 | yes | 16 | |
3.2 | odd | 2 | inner | 105.3.k.c.62.3 | yes | 16 | |
5.3 | odd | 4 | inner | 105.3.k.c.83.2 | yes | 16 | |
7.6 | odd | 2 | inner | 105.3.k.c.62.5 | yes | 16 | |
15.8 | even | 4 | inner | 105.3.k.c.83.5 | yes | 16 | |
21.20 | even | 2 | inner | 105.3.k.c.62.2 | ✓ | 16 | |
35.13 | even | 4 | inner | 105.3.k.c.83.3 | yes | 16 | |
105.83 | odd | 4 | inner | 105.3.k.c.83.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.c.62.2 | ✓ | 16 | 21.20 | even | 2 | inner | |
105.3.k.c.62.3 | yes | 16 | 3.2 | odd | 2 | inner | |
105.3.k.c.62.5 | yes | 16 | 7.6 | odd | 2 | inner | |
105.3.k.c.62.8 | yes | 16 | 1.1 | even | 1 | trivial | |
105.3.k.c.83.2 | yes | 16 | 5.3 | odd | 4 | inner | |
105.3.k.c.83.3 | yes | 16 | 35.13 | even | 4 | inner | |
105.3.k.c.83.5 | yes | 16 | 15.8 | even | 4 | inner | |
105.3.k.c.83.8 | yes | 16 | 105.83 | odd | 4 | inner |