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 | 62.5 | ||
Root | \(-0.817327 - 1.97320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.62 |
Dual form | 105.3.k.c.83.5 |
$q$-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 | ||||
\(7\) | 4.33402 | + | 5.49694i | 0.619145 | + | 0.785277i | ||||
\(8\) | 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 | \(0.0429507\pi\) |
0.134524 | + | 0.990910i | \(0.457049\pi\) | |||||||
\(14\) | 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 | 0.835551 | − | 0.549413i | \(-0.185149\pi\) |
−0.549413 | + | 0.835551i | \(0.685149\pi\) | |||||||
\(18\) | 6.97829 | − | 5.68361i | 0.387683 | − | 0.315756i | ||||
\(19\) | −21.7515 | −1.14481 | −0.572407 | − | 0.819970i | \(-0.693990\pi\) | ||||
−0.572407 | + | 0.819970i | \(0.693990\pi\) | |||||||
\(20\) | 7.91326 | + | 12.7429i | 0.395663 | + | 0.637143i | ||||
\(21\) | −12.1454 | − | 17.1316i | −0.578351 | − | 0.815788i | ||||
\(22\) | −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 | ||||
\(28\) | −16.4908 | + | 13.0020i | −0.588957 | + | 0.464359i | ||||
\(29\) | −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 | \(-0.910268\pi\) | ||
0.960529 | − | 0.278181i | \(-0.0897315\pi\) | |||||||
\(32\) | −23.3345 | + | 23.3345i | −0.729204 | + | 0.729204i | ||||
\(33\) | −2.12408 | + | 41.6551i | −0.0643660 | + | 1.26228i | ||||
\(34\) | 6.87923 | 0.202330 | ||||||||
\(35\) | 32.9088 | + | 11.9168i | 0.940251 | + | 0.340481i | ||||
\(36\) | −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 | \(-0.394352\pi\) | ||||
0.325844 | + | 0.945424i | \(0.394352\pi\) | |||||||
\(42\) | −20.7019 | − | 3.52576i | −0.492903 | − | 0.0839468i | ||||
\(43\) | 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 | 0.481457 | − | 0.876470i | \(-0.340108\pi\) |
−0.876470 | + | 0.481457i | \(0.840108\pi\) | |||||||
\(48\) | 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 | \(-0.919105\pi\) | ||
0.967880 | − | 0.251413i | \(-0.0808953\pi\) | |||||||
\(60\) | −21.7621 | − | 39.3879i | −0.362702 | − | 0.656465i | ||||
\(61\) | − | 21.0717i | − | 0.345438i | −0.984971 | − | 0.172719i | \(-0.944745\pi\) | ||
0.984971 | − | 0.172719i | \(-0.0552552\pi\) | |||||||
\(62\) | −12.1956 | − | 12.1956i | −0.196704 | − | 0.196704i | ||||
\(63\) | 33.7715 | + | 53.1835i | 0.536056 | + | 0.844183i | ||||
\(64\) | 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 | ||||
\(70\) | 31.6965 | − | 14.8436i | 0.452807 | − | 0.212051i | ||||
\(71\) | − | 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 | 0.980794 | − | 0.195045i | \(-0.0624853\pi\) |
−0.195045 | + | 0.980794i | \(0.562485\pi\) | |||||||
\(74\) | −9.20249 | −0.124358 | ||||||||
\(75\) | −36.6339 | + | 65.4443i | −0.488452 | + | 0.872591i | ||||
\(76\) | − | 65.2544i | − | 0.858610i | ||||||
\(77\) | 76.4243 | − | 60.2561i | 0.992523 | − | 0.782547i | ||||
\(78\) | −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 | −0.947088 | − | 0.320974i | \(-0.895990\pi\) |
0.320974 | + | 0.947088i | \(0.395990\pi\) | |||||||
\(84\) | 51.3947 | − | 36.4361i | 0.611841 | − | 0.433763i | ||||
\(85\) | 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 | \(-0.565065\pi\) | ||
0.202987 | − | 0.979181i | \(-0.434935\pi\) | |||||||
\(90\) | 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 | −0.787775 | − | 0.615963i | \(-0.788767\pi\) |
0.615963 | + | 0.787775i | \(0.288767\pi\) | |||||||
\(98\) | 25.6079 | + | 41.7760i | 0.261305 | + | 0.426286i | ||||
\(99\) | 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 | \(-0.689187\pi\) | ||||
−0.559968 | + | 0.828514i | \(0.689187\pi\) | |||||||
\(102\) | −20.6109 | − | 1.05099i | −0.202068 | − | 0.0103038i | ||||
\(103\) | −16.1826 | − | 16.1826i | −0.157113 | − | 0.157113i | 0.624173 | − | 0.781286i | \(-0.285436\pi\) |
−0.781286 | + | 0.624173i | \(0.785436\pi\) | |||||||
\(104\) | 144.836i | 1.39265i | ||||||||
\(105\) | −96.7777 | − | 40.7318i | −0.921692 | − | 0.387922i | ||||
\(106\) | −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 | ||||
\(112\) | −21.6701 | − | 27.4847i | −0.193483 | − | 0.245399i | ||||
\(113\) | 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 | ||||
\(126\) | 61.4865 | + | 13.7264i | 0.487988 | + | 0.108939i | ||||
\(127\) | −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 | \(-0.598093\pi\) | ||||
−0.303314 | + | 0.952891i | \(0.598093\pi\) | |||||||
\(132\) | −124.965 | − | 6.37223i | −0.946706 | − | 0.0482745i | ||||
\(133\) | −94.2712 | − | 119.566i | −0.708806 | − | 0.898996i | ||||
\(134\) | −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 | \(-0.276439\pi\) | ||||
0.646003 | + | 0.763335i | \(0.276439\pi\) | |||||||
\(140\) | −35.7505 | + | 98.7264i | −0.255361 | + | 0.705189i | ||||
\(141\) | 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 | ||||||||
\(147\) | 41.5328 | − | 141.011i | 0.282536 | − | 0.959257i | ||||
\(148\) | 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 | −0.272042 | − | 0.962285i | \(-0.587699\pi\) |
0.962285 | + | 0.272042i | \(0.0876988\pi\) | |||||||
\(158\) | 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 | 0.987220 | − | 0.159365i | \(-0.0509447\pi\) |
−0.159365 | + | 0.987220i | \(0.550945\pi\) | |||||||
\(168\) | 24.6804 | − | 144.913i | 0.146907 | − | 0.862579i | ||||
\(169\) | 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 | −0.780711 | − | 0.624893i | \(-0.785143\pi\) |
0.624893 | + | 0.780711i | \(0.285143\pi\) | |||||||
\(174\) | 62.4454 | − | 56.3859i | 0.358882 | − | 0.324057i | ||||
\(175\) | 171.218 | − | 36.1871i | 0.978387 | − | 0.206784i | ||||
\(176\) | 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 | \(-0.834773\pi\) | ||
0.868277 | − | 0.496079i | \(-0.165227\pi\) | |||||||
\(182\) | 89.6745 | + | 113.736i | 0.492717 | + | 0.624925i | ||||
\(183\) | −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 | ||||
\(189\) | −93.0578 | − | 164.503i | −0.492369 | − | 0.870386i | ||||
\(190\) | −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 | \(-0.686462\pi\) | ||||
−0.552857 | + | 0.833276i | \(0.686462\pi\) | |||||||
\(200\) | 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 | ||||
\(203\) | −121.548 | − | 154.163i | −0.598760 | − | 0.759422i | ||||
\(204\) | 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 | ||||||||
\(210\) | −97.2339 | + | 39.6304i | −0.463019 | + | 0.188716i | ||||
\(211\) | 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 | ||||
\(217\) | 94.8069 | − | 74.7497i | 0.436898 | − | 0.344469i | ||||
\(218\) | 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 | 0.979517 | − | 0.201362i | \(-0.0645368\pi\) |
−0.201362 | + | 0.979517i | \(0.564537\pi\) | |||||||
\(224\) | −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 | 0.989264 | − | 0.146140i | \(-0.0466851\pi\) |
−0.146140 | + | 0.989264i | \(0.546685\pi\) | |||||||
\(228\) | −9.96941 | + | 195.509i | −0.0437255 | + | 0.857496i | ||||
\(229\) | 123.490 | 0.539259 | 0.269630 | − | 0.962964i | \(-0.413099\pi\) | ||||
0.269630 | + | 0.962964i | \(0.413099\pi\) | |||||||
\(230\) | 10.6494 | − | 6.61323i | 0.0463017 | − | 0.0287532i | ||||
\(231\) | −238.181 | + | 168.858i | −1.03109 | + | 0.730986i | ||||
\(232\) | −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 | ||||
\(238\) | 29.8147 | + | 37.8147i | 0.125272 | + | 0.158885i | ||||
\(239\) | −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 | \(0.339021\pi\) | ||||
−0.484445 | + | 0.874822i | \(0.660979\pi\) | |||||||
\(242\) | −51.1204 | + | 51.1204i | −0.211242 | + | 0.211242i | ||||
\(243\) | −235.158 | − | 61.2344i | −0.967729 | − | 0.251993i | ||||
\(244\) | 63.2151 | 0.259078 | ||||||||
\(245\) | 77.1212 | + | 232.545i | 0.314780 | + | 0.949165i | ||||
\(246\) | −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 | \(-0.258369\pi\) | ||||
0.688274 | + | 0.725450i | \(0.258369\pi\) | |||||||
\(252\) | −159.551 | + | 101.315i | −0.633137 | + | 0.402042i | ||||
\(253\) | 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 | 0.146530 | − | 0.989206i | \(-0.453190\pi\) |
−0.989206 | + | 0.146530i | \(0.953190\pi\) | |||||||
\(258\) | −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 | \(-0.774566\pi\) | ||
0.759519 | − | 0.650485i | \(-0.225434\pi\) | |||||||
\(270\) | −50.3909 | + | 125.243i | −0.186633 | + | 0.463862i | ||||
\(271\) | − | 137.978i | − | 0.509143i | −0.967054 | − | 0.254572i | \(-0.918066\pi\) | ||
0.967054 | − | 0.254572i | \(-0.0819344\pi\) | |||||||
\(272\) | −24.3218 | − | 24.3218i | −0.0894182 | − | 0.0894182i | ||||
\(273\) | 72.9511 | − | 428.340i | 0.267220 | − | 1.56901i | ||||
\(274\) | − | 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 | ||||
\(280\) | 103.905 | + | 221.876i | 0.371089 | + | 0.792413i | ||||
\(281\) | − | 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 | 0.462014 | − | 0.886873i | \(-0.347127\pi\) |
−0.886873 | + | 0.462014i | \(0.847127\pi\) | |||||||
\(284\) | 48.1035 | 0.169378 | ||||||||
\(285\) | 285.582 | − | 157.786i | 1.00204 | − | 0.553636i | ||||
\(286\) | − | 287.666i | − | 1.00583i | ||||||
\(287\) | 115.801 | + | 146.874i | 0.403489 | + | 0.511755i | ||||
\(288\) | −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 | \(0.615433\pi\) |
−0.934962 | + | 0.354747i | \(0.884567\pi\) | |||||||
\(294\) | −70.3415 | − | 129.078i | −0.239257 | − | 0.439040i | ||||
\(295\) | −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 | −0.844264 | − | 0.535928i | \(-0.819962\pi\) |
0.535928 | + | 0.844264i | \(0.319962\pi\) | |||||||
\(308\) | 180.768 | + | 229.273i | 0.586910 | + | 0.744392i | ||||
\(309\) | 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 | \(-0.615860\pi\) | ||||
−0.356000 | + | 0.934486i | \(0.615860\pi\) | |||||||
\(312\) | 22.1277 | − | 433.944i | 0.0709221 | − | 1.39085i | ||||
\(313\) | 225.950 | + | 225.950i | 0.721885 | + | 0.721885i | 0.968989 | − | 0.247104i | \(-0.0794790\pi\) |
−0.247104 | + | 0.968989i | \(0.579479\pi\) | |||||||
\(314\) | − | 153.256i | − | 0.488076i | ||||||
\(315\) | 283.733 | + | 136.822i | 0.900741 | + | 0.434357i | ||||
\(316\) | −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 | ||||
\(322\) | 10.8660 | + | 13.7816i | 0.0337453 | + | 0.0428000i | ||||
\(323\) | −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 | ||||
\(336\) | 60.7268 | + | 85.6578i | 0.180735 | + | 0.254934i | ||||
\(337\) | 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 | ||||
\(343\) | −311.465 | + | 143.661i | −0.908061 | + | 0.418837i | ||||
\(344\) | 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 | \(-0.643537\pi\) | ||||
−0.435807 | + | 0.900040i | \(0.643537\pi\) | |||||||
\(350\) | 95.4810 | − | 146.657i | 0.272803 | − | 0.419021i | ||||
\(351\) | −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 | −0.960143 | − | 0.279509i | \(-0.909828\pi\) |
0.279509 | + | 0.960143i | \(0.409828\pi\) | |||||||
\(354\) | 59.6461 | + | 66.0559i | 0.168492 | + | 0.186599i | ||||
\(355\) | −42.2950 | − | 68.1084i | −0.119141 | − | 0.191855i | ||||
\(356\) | 522.883 | 1.46877 | ||||||||
\(357\) | 24.2545 | − | 142.413i | 0.0679399 | − | 0.398916i | ||||
\(358\) | 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 | −0.555904 | − | 0.831247i | \(-0.687628\pi\) |
0.831247 | + | 0.555904i | \(0.187628\pi\) | |||||||
\(368\) | −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 | ||||
\(378\) | −182.123 | − | 50.5194i | −0.481807 | − | 0.133649i | ||||
\(379\) | − | 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 | −0.887847 | − | 0.460138i | \(-0.847800\pi\) |
0.460138 | + | 0.887847i | \(0.347800\pi\) | |||||||
\(384\) | 239.254 | + | 264.965i | 0.623057 | + | 0.690013i | ||||
\(385\) | 165.680 | − | 457.533i | 0.430339 | − | 1.18840i | ||||
\(386\) | 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 | ||||||||
\(392\) | −292.432 | + | 179.255i | −0.746001 | + | 0.457283i | ||||
\(393\) | 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 | −0.977391 | − | 0.211440i | \(-0.932185\pi\) |
0.211440 | + | 0.977391i | \(0.432185\pi\) | |||||||
\(398\) | −155.590 | + | 155.590i | −0.390929 | + | 0.390929i | ||||
\(399\) | 264.180 | + | 372.636i | 0.662104 | + | 0.933926i | ||||
\(400\) | −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 | \(-0.638515\pi\) | ||||
−0.421552 | + | 0.906804i | \(0.638515\pi\) | |||||||
\(410\) | 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 | ||||
\(413\) | 163.076 | − | 128.576i | 0.394858 | − | 0.311323i | ||||
\(414\) | 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 | \(0.134616\pi\) | ||||
−0.911899 | + | 0.410414i | \(0.865384\pi\) | |||||||
\(420\) | 122.195 | − | 290.333i | 0.290942 | − | 0.691269i | ||||
\(421\) | 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 | ||||
\(427\) | 115.830 | − | 91.3251i | 0.271264 | − | 0.213876i | ||||
\(428\) | −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 | \(0.0429843\pi\) |
0.134629 | + | 0.990896i | \(0.457016\pi\) | |||||||
\(434\) | 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 | \(-0.555041\pi\) | ||||
−0.172056 | + | 0.985087i | \(0.555041\pi\) | |||||||
\(440\) | 110.786 | − | 473.828i | 0.251785 | − | 1.07688i | ||||
\(441\) | −145.980 | + | 416.138i | −0.331021 | + | 0.943624i | ||||
\(442\) | 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 | ||||
\(448\) | −71.4602 | + | 56.3422i | −0.159509 | + | 0.125764i | ||||
\(449\) | −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 | ||||||||
\(455\) | 307.126 | + | 655.828i | 0.675003 | + | 1.44138i | ||||
\(456\) | 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 | \(-0.566614\pi\) | ||||
−0.207750 | + | 0.978182i | \(0.566614\pi\) | |||||||
\(462\) | −49.0189 | + | 287.820i | −0.106102 | + | 0.622987i | ||||
\(463\) | 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 | 0.923941 | − | 0.382536i | \(-0.124949\pi\) |
−0.382536 | + | 0.923941i | \(0.624949\pi\) | |||||||
\(468\) | −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 | \(0.0304550\pi\) | ||||
−0.995426 | + | 0.0955314i | \(0.969545\pi\) | |||||||
\(480\) | 137.096 | − | 475.636i | 0.285618 | − | 0.990908i | ||||
\(481\) | − | 190.408i | − | 0.395858i | ||||||
\(482\) | 298.161 | + | 298.161i | 0.618592 | + | 0.618592i | ||||
\(483\) | 8.83960 | − | 51.9027i | 0.0183015 | − | 0.107459i | ||||
\(484\) | − | 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 | ||||
\(490\) | 218.967 | + | 109.901i | 0.446872 | + | 0.224289i | ||||
\(491\) | − | 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 | ||||||||
\(497\) | 88.1406 | − | 69.4937i | 0.177345 | − | 0.139826i | ||||
\(498\) | 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 | −0.719657 | − | 0.694329i | \(-0.755701\pi\) |
0.694329 | + | 0.719657i | \(0.255701\pi\) | |||||||
\(504\) | −96.0845 | + | 430.405i | −0.190644 | + | 0.853979i | ||||
\(505\) | −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 | \(0.205143\pi\) | ||||
−0.799415 | + | 0.600779i | \(0.794857\pi\) | |||||||
\(510\) | −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 | ||||
\(518\) | −39.8837 | − | 50.5855i | −0.0769956 | − | 0.0976554i | ||||
\(519\) | 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 | \(-0.268603\pi\) | ||||
0.664597 | + | 0.747202i | \(0.268603\pi\) | |||||||
\(522\) | −195.708 | + | 159.398i | −0.374919 | + | 0.305360i | ||||
\(523\) | −583.903 | − | 583.903i | −1.11645 | − | 1.11645i | −0.992258 | − | 0.124191i | \(-0.960366\pi\) |
−0.124191 | − | 0.992258i | \(-0.539634\pi\) | |||||||
\(524\) | − | 238.405i | − | 0.454971i | ||||||
\(525\) | −518.515 | + | 82.2623i | −0.987648 | + | 0.156690i | ||||
\(526\) | 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 | ||||
\(532\) | 358.699 | − | 282.814i | 0.674247 | − | 0.531604i | ||||
\(533\) | 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 | ||||
\(546\) | −251.298 | − | 354.467i | −0.460253 | − | 0.649206i | ||||
\(547\) | 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 | ||||
\(553\) | −416.681 | + | 328.529i | −0.753492 | + | 0.594084i | ||||
\(554\) | 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 | ||||||||
\(560\) | −164.544 | − | 59.5841i | −0.293829 | − | 0.106400i | ||||
\(561\) | −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 | −0.247086 | − | 0.968993i | \(-0.579473\pi\) |
0.968993 | + | 0.247086i | \(0.0794732\pi\) | |||||||
\(564\) | −175.383 | + | 158.364i | −0.310962 | + | 0.280788i | ||||
\(565\) | 551.600 | + | 128.969i | 0.976283 | + | 0.228264i | ||||
\(566\) | −170.038 | −0.300420 | ||||||||
\(567\) | 253.679 | + | 507.086i | 0.447405 | + | 0.894331i | ||||
\(568\) | 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 | −0.451366 | − | 0.892339i | \(-0.649063\pi\) |
0.892339 | + | 0.451366i | \(0.149063\pi\) | |||||||
\(578\) | −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 | 0.520700 | − | 0.853740i | \(-0.325671\pi\) |
−0.853740 | + | 0.520700i | \(0.825671\pi\) | |||||||
\(588\) | 423.032 | + | 124.599i | 0.719442 | + | 0.211902i | ||||
\(589\) | 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 | −0.843648 | − | 0.536897i | \(-0.819597\pi\) |
0.536897 | + | 0.843648i | \(0.319597\pi\) | |||||||
\(594\) | 221.929 | + | 302.754i | 0.373618 | + | 0.509686i | ||||
\(595\) | 102.112 | + | 218.048i | 0.171617 | + | 0.366466i | ||||
\(596\) | 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 | \(-0.616143\pi\) | ||
0.356832 | − | 0.934169i | \(-0.383857\pi\) | |||||||
\(602\) | 257.740 | − | 203.213i | 0.428139 | − | 0.337563i | ||||
\(603\) | −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 | −0.593879 | − | 0.804554i | \(-0.702404\pi\) |
0.804554 | + | 0.593879i | \(0.202404\pi\) | |||||||
\(608\) | 507.560 | − | 507.560i | 0.834803 | − | 0.834803i | ||||
\(609\) | 340.619 | + | 480.458i | 0.559309 | + | 0.788929i | ||||
\(610\) | −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 | \(-0.127454\pi\) | ||||
0.920902 | + | 0.389794i | \(0.127454\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 958.085 | − | 755.394i | 1.53786 | − | 1.21251i | ||||
\(624\) | 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 | ||||||
\(630\) | 297.378 | − | 103.882i | 0.472028 | − | 0.164892i | ||||
\(631\) | −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 | ||||
\(637\) | −864.382 | + | 529.849i | −1.35696 | + | 0.831788i | ||||
\(638\) | 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 | \(-0.929864\pi\) |
−0.218559 | − | 0.975824i | \(-0.570136\pi\) | |||||||
\(644\) | −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 | 0.994188 | − | 0.107654i | \(-0.0343337\pi\) |
−0.107654 | + | 0.994188i | \(0.534334\pi\) | |||||||
\(648\) | 311.491 | + | 473.774i | 0.480696 | + | 0.731133i | ||||
\(649\) | −412.459 | −0.635530 | ||||||||
\(650\) | 229.348 | − | 463.648i | 0.352844 | − | 0.713304i | ||||
\(651\) | −295.472 | + | 209.474i | −0.453874 | + | 0.321772i | ||||
\(652\) | 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 | ||||
\(658\) | −113.793 | − | 144.326i | −0.172937 | − | 0.219340i | ||||
\(659\) | −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 | \(-0.977146\pi\) | ||
0.997424 | − | 0.0717364i | \(-0.0228540\pi\) | |||||||
\(662\) | 123.754 | − | 123.754i | 0.186939 | − | 0.186939i | ||||
\(663\) | 21.7459 | − | 426.458i | 0.0327993 | − | 0.643224i | ||||
\(664\) | −514.452 | −0.774777 | ||||||||
\(665\) | −715.815 | − | 259.208i | −1.07641 | − | 0.389787i | ||||
\(666\) | −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 | ||||||||
\(672\) | 683.163 | + | 116.350i | 1.01661 | + | 0.173140i | ||||
\(673\) | −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 | 0.955586 | − | 0.294714i | \(-0.0952243\pi\) |
−0.294714 | + | 0.955586i | \(0.595224\pi\) | |||||||
\(678\) | −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 | \(0.0479031\pi\) | ||||
−0.988697 | + | 0.149925i | \(0.952097\pi\) | |||||||
\(692\) | −80.8697 | − | 80.8697i | −0.116864 | − | 0.116864i | ||||
\(693\) | 739.414 | − | 469.527i | 1.06698 | − | 0.677529i | ||||
\(694\) | − | 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 | ||||
\(700\) | 108.561 | + | 513.653i | 0.155088 | + | 0.733790i | ||||
\(701\) | 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 | ||||||||
\(707\) | −490.236 | − | 621.778i | −0.693403 | − | 0.879459i | ||||
\(708\) | −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 | ||||
\(714\) | −83.5508 | − | 117.852i | −0.117018 | − | 0.165059i | ||||
\(715\) | 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 | \(0.329336\pi\) | ||||
−0.510837 | + | 0.859678i | \(0.670664\pi\) | |||||||
\(720\) | −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 | −0.119351 | − | 0.992852i | \(-0.538081\pi\) |
0.992852 | + | 0.119351i | \(0.0380815\pi\) | |||||||
\(728\) | −796.155 | + | 627.722i | −1.09362 | + | 0.862255i | ||||
\(729\) | 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 | 0.816246 | − | 0.577704i | \(-0.196051\pi\) |
−0.577704 | + | 0.816246i | \(0.696051\pi\) | |||||||
\(734\) | − | 142.908i | − | 0.194697i | ||||||
\(735\) | −195.536 | − | 708.513i | −0.266035 | − | 0.963963i | ||||
\(736\) | −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 | ||||
\(742\) | −296.055 | − | 375.493i | −0.398995 | − | 0.506055i | ||||
\(743\) | −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 | ||||
\(756\) | 493.509 | − | 279.173i | 0.652790 | − | 0.369277i | ||||
\(757\) | 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 | \(-0.654695\pi\) | ||||
−0.467084 | + | 0.884213i | \(0.654695\pi\) | |||||||
\(762\) | 303.581 | + | 15.4802i | 0.398400 | + | 0.0203152i | ||||
\(763\) | −16.5694 | + | 13.0640i | −0.0217161 | + | 0.0171219i | ||||
\(764\) | −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 | \(-0.448394\pi\) | ||||
0.161417 | + | 0.986886i | \(0.448394\pi\) | |||||||
\(770\) | −206.371 | − | 440.679i | −0.268014 | − | 0.572310i | ||||
\(771\) | 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 | −0.877376 | − | 0.479804i | \(-0.840708\pi\) |
0.479804 | + | 0.877376i | \(0.340708\pi\) | |||||||
\(774\) | 42.9248 | − | 419.802i | 0.0554583 | − | 0.542380i | ||||
\(775\) | −386.481 | − | 191.177i | −0.498686 | − | 0.246680i | ||||
\(776\) | −164.983 | −0.212606 | ||||||||
\(777\) | −32.4458 | + | 190.509i | −0.0417578 | + | 0.245186i | ||||
\(778\) | −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 | −0.820766 | − | 0.571265i | \(-0.806453\pi\) |
0.571265 | + | 0.820766i | \(0.306453\pi\) | |||||||
\(788\) | 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 | \(-0.935208\pi\) |
−0.202147 | − | 0.979355i | \(-0.564792\pi\) | |||||||
\(798\) | 450.297 | + | 76.6905i | 0.564282 | + | 0.0961034i | ||||
\(799\) | − | 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 | ||||
\(805\) | 37.2150 | + | 79.4677i | 0.0462298 | + | 0.0987177i | ||||
\(806\) | − | 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 | \(0.290873\pi\) | ||||
−0.610738 | + | 0.791833i | \(0.709127\pi\) | |||||||
\(812\) | 462.488 | − | 364.645i | 0.569567 | − | 0.449070i | ||||
\(813\) | −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 | ||||
\(819\) | −284.010 | + | 1272.21i | −0.346777 | + | 1.55337i | ||||
\(820\) | 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 | \(-0.809419\pi\) | ||||
−0.826054 | + | 0.563591i | \(0.809419\pi\) | |||||||
\(830\) | 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 | ||||
\(833\) | −287.387 | + | 176.162i | −0.345002 | + | 0.211480i | ||||
\(834\) | −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 | \(-0.816310\pi\) | ||
0.838059 | − | 0.545580i | \(-0.183690\pi\) | |||||||
\(840\) | −277.413 | − | 680.637i | −0.330253 | − | 0.810282i | ||||
\(841\) | −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 | ||||
\(847\) | −313.329 | − | 397.402i | −0.369928 | − | 0.469188i | ||||
\(848\) | 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 | 0.855015 | − | 0.518604i | \(-0.173548\pi\) |
−0.518604 | + | 0.855015i | \(0.673548\pi\) | |||||||
\(854\) | 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 | 0.259509 | − | 0.965741i | \(-0.416439\pi\) |
−0.965741 | + | 0.259509i | \(0.916439\pi\) | |||||||
\(858\) | −43.9490 | + | 861.880i | −0.0512226 | + | 1.00452i | ||||
\(859\) | 1440.15 | 1.67654 | 0.838272 | − | 0.545253i | \(-0.183566\pi\) | ||||
0.838272 | + | 0.545253i | \(0.183566\pi\) | |||||||
\(860\) | 684.848 | + | 160.124i | 0.796335 | + | 0.186191i | ||||
\(861\) | −324.514 | − | 457.741i | −0.376904 | − | 0.531639i | ||||
\(862\) | 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 | ||||
\(868\) | 224.249 | + | 284.421i | 0.258352 | + | 0.327674i | ||||
\(869\) | 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 | ||||||||
\(875\) | 631.815 | − | 605.339i | 0.722074 | − | 0.691816i | ||||
\(876\) | 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 | \(-0.548807\pi\) | ||||
−0.152732 | + | 0.988268i | \(0.548807\pi\) | |||||||
\(882\) | 191.030 | + | 397.478i | 0.216588 | + | 0.450655i | ||||
\(883\) | 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 | 0.470020 | − | 0.882656i | \(-0.344247\pi\) |
−0.882656 | + | 0.470020i | \(0.844247\pi\) | |||||||
\(888\) | −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 | ||||
\(903\) | −970.669 | − | 165.316i | −1.07494 | − | 0.183074i | ||||
\(904\) | 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 | ||||
\(910\) | 680.912 | + | 246.569i | 0.748254 | + | 0.270955i | ||||
\(911\) | 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 | ||||||||
\(917\) | −344.417 | − | 436.832i | −0.375591 | − | 0.476371i | ||||
\(918\) | −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 | ||||
\(924\) | −506.574 | − | 714.543i | −0.548240 | − | 0.773315i | ||||
\(925\) | −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 | \(-0.840663\pi\) | ||
0.877308 | − | 0.479927i | \(-0.159337\pi\) | |||||||
\(930\) | 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 | −0.398652 | − | 0.917102i | \(-0.630522\pi\) |
0.917102 | + | 0.398652i | \(0.130522\pi\) | |||||||
\(938\) | −199.068 | − | 252.483i | −0.212226 | − | 0.269172i | ||||
\(939\) | −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 | \(-0.243837\pi\) | ||||
0.720665 | + | 0.693284i | \(0.243837\pi\) | |||||||
\(942\) | −23.4141 | + | 459.171i | −0.0248557 | + | 0.487443i | ||||
\(943\) | 47.3683 | + | 47.3683i | 0.0502314 | + | 0.0502314i | ||||
\(944\) | 148.334i | 0.157133i | ||||||||
\(945\) | −829.192 | − | 453.283i | −0.877452 | − | 0.479664i | ||||
\(946\) | −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 | ||||
\(952\) | −264.703 | + | 208.703i | −0.278049 | + | 0.219226i | ||||
\(953\) | 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 | ||||
\(966\) | −30.4502 | − | 42.9513i | −0.0315219 | − | 0.0444630i | ||||
\(967\) | −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 | \(-0.560454\pi\) | ||||
−0.188783 | + | 0.982019i | \(0.560454\pi\) | |||||||
\(972\) | 183.703 | − | 705.474i | 0.188995 | − | 0.725797i | ||||
\(973\) | 778.341 | + | 987.189i | 0.799939 | + | 1.01458i | ||||
\(974\) | 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 | ||||||||
\(980\) | −697.636 | + | 231.364i | −0.711873 | + | 0.236085i | ||||
\(981\) | −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 | −0.947834 | − | 0.318765i | \(-0.896732\pi\) |
0.318765 | + | 0.947834i | \(0.396732\pi\) | |||||||
\(984\) | −376.039 | − | 416.450i | −0.382154 | − | 0.423222i | ||||
\(985\) | 266.758 | − | 1140.92i | 0.270820 | − | 1.15829i | ||||
\(986\) | −192.929 | −0.195669 | ||||||||
\(987\) | −92.5714 | + | 543.543i | −0.0937907 | + | 0.550702i | ||||
\(988\) | 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 | −0.748986 | − | 0.662585i | \(-0.769459\pi\) |
0.662585 | + | 0.748986i | \(0.269459\pi\) | |||||||
\(998\) | 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.62.5 | yes | 16 | |
3.2 | odd | 2 | inner | 105.3.k.c.62.2 | ✓ | 16 | |
5.3 | odd | 4 | inner | 105.3.k.c.83.3 | yes | 16 | |
7.6 | odd | 2 | inner | 105.3.k.c.62.8 | yes | 16 | |
15.8 | even | 4 | inner | 105.3.k.c.83.8 | yes | 16 | |
21.20 | even | 2 | inner | 105.3.k.c.62.3 | yes | 16 | |
35.13 | even | 4 | inner | 105.3.k.c.83.2 | yes | 16 | |
105.83 | odd | 4 | inner | 105.3.k.c.83.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.c.62.2 | ✓ | 16 | 3.2 | odd | 2 | inner | |
105.3.k.c.62.3 | yes | 16 | 21.20 | even | 2 | inner | |
105.3.k.c.62.5 | yes | 16 | 1.1 | even | 1 | trivial | |
105.3.k.c.62.8 | yes | 16 | 7.6 | odd | 2 | inner | |
105.3.k.c.83.2 | yes | 16 | 35.13 | even | 4 | inner | |
105.3.k.c.83.3 | yes | 16 | 5.3 | odd | 4 | inner | |
105.3.k.c.83.5 | yes | 16 | 105.83 | odd | 4 | inner | |
105.3.k.c.83.8 | yes | 16 | 15.8 | even | 4 | inner |