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 | 83.2 | ||
Root | \(-0.611750 - 0.253395i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.83 |
Dual form | 105.3.k.c.62.2 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 | \(-0.330431\pi\) |
−0.861430 | + | 0.507877i | \(0.830431\pi\) | |||||||
\(3\) | −0.152778 | + | 2.99611i | −0.0509259 | + | 0.998702i | ||||
\(4\) | − | 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 | \(-0.217748\pi\) | |||||||
\(12\) | 8.98832 | + | 0.458333i | 0.749027 | + | 0.0381944i | ||||
\(13\) | 14.6307 | − | 14.6307i | 1.12543 | − | 1.12543i | 0.134524 | − | 0.990910i | \(-0.457049\pi\) |
0.990910 | − | 0.134524i | \(-0.0429507\pi\) | |||||||
\(14\) | −6.95153 | + | 0.822309i | −0.496538 | + | 0.0587364i | ||||
\(15\) | 8.55193 | − | 12.3233i | 0.570129 | − | 0.821555i | ||||
\(16\) | −5.00000 | −0.312500 | ||||||||
\(17\) | −4.86435 | + | 4.86435i | −0.286138 | + | 0.286138i | −0.835551 | − | 0.549413i | \(-0.814851\pi\) |
0.549413 | + | 0.835551i | \(0.314851\pi\) | |||||||
\(18\) | 5.68361 | + | 6.97829i | 0.315756 | + | 0.387683i | ||||
\(19\) | −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 | ||||
\(21\) | 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 | \(-0.767357\pi\) |
0.667516 | + | 0.744595i | \(0.267357\pi\) | |||||||
\(24\) | −14.0738 | − | 15.5862i | −0.586407 | − | 0.649424i | ||||
\(25\) | 11.0845 | + | 22.4083i | 0.443381 | + | 0.896333i | ||||
\(26\) | −20.6909 | −0.795802 | ||||||||
\(27\) | 4.11073 | − | 26.6852i | 0.152249 | − | 0.988342i | ||||
\(28\) | −16.4908 | − | 13.0020i | −0.588957 | − | 0.464359i | ||||
\(29\) | 28.0452 | 0.967076 | 0.483538 | − | 0.875323i | \(-0.339352\pi\) | ||||
0.483538 | + | 0.875323i | \(0.339352\pi\) | |||||||
\(30\) | −14.7610 | + | 2.66678i | −0.492035 | + | 0.0888928i | ||||
\(31\) | 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 | ||||
\(33\) | 41.6551 | + | 2.12408i | 1.26228 | + | 0.0643660i | ||||
\(34\) | 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 | −0.789552 | − | 0.613683i | \(-0.789687\pi\) |
0.613683 | + | 0.789552i | \(0.289687\pi\) | |||||||
\(38\) | 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 | \(0.605648\pi\) | |||||||
\(42\) | −1.40169 | − | 20.9532i | −0.0333735 | − | 0.498885i | ||||
\(43\) | 33.1548 | + | 33.1548i | 0.771041 | + | 0.771041i | 0.978289 | − | 0.207248i | \(-0.0664506\pi\) |
−0.207248 | + | 0.978289i | \(0.566451\pi\) | |||||||
\(44\) | −41.7092 | −0.947936 | ||||||||
\(45\) | 35.6155 | + | 27.5052i | 0.791455 | + | 0.611227i | ||||
\(46\) | 2.50714 | 0.0545031 | ||||||||
\(47\) | 18.5656 | − | 18.5656i | 0.395012 | − | 0.395012i | −0.481457 | − | 0.876470i | \(-0.659892\pi\) |
0.876470 | + | 0.481457i | \(0.159892\pi\) | |||||||
\(48\) | 0.763888 | − | 14.9805i | 0.0159143 | − | 0.312095i | ||||
\(49\) | −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 | \(-0.527095\pi\) |
0.996379 | + | 0.0850185i | \(0.0270949\pi\) | |||||||
\(54\) | −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 | ||||
\(57\) | 3.32314 | − | 65.1697i | 0.0583006 | − | 1.14333i | ||||
\(58\) | −19.8310 | − | 19.8310i | −0.341913 | − | 0.341913i | ||||
\(59\) | − | 29.6668i | − | 0.502826i | −0.967880 | − | 0.251413i | \(-0.919105\pi\) | ||
0.967880 | − | 0.251413i | \(-0.0808953\pi\) | |||||||
\(60\) | −36.9700 | − | 25.6558i | −0.616167 | − | 0.427597i | ||||
\(61\) | 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 | ||||
\(63\) | −43.8361 | + | 45.2481i | −0.695812 | + | 0.718224i | ||||
\(64\) | − | 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 | −0.906646 | − | 0.421892i | \(-0.861366\pi\) |
0.421892 | + | 0.906646i | \(0.361366\pi\) | |||||||
\(68\) | 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 | \(-0.0360200\pi\) | |||||||
\(72\) | 48.8480 | − | 39.7853i | 0.678445 | − | 0.552573i | ||||
\(73\) | 57.3597 | − | 57.3597i | 0.785749 | − | 0.785749i | −0.195045 | − | 0.980794i | \(-0.562485\pi\) |
0.980794 | + | 0.195045i | \(0.0624853\pi\) | |||||||
\(74\) | 9.20249 | 0.124358 | ||||||||
\(75\) | −68.8312 | + | 29.7869i | −0.917750 | + | 0.397159i | ||||
\(76\) | 65.2544i | 0.858610i | ||||||||
\(77\) | −76.4243 | − | 60.2561i | −0.992523 | − | 0.782547i | ||||
\(78\) | 3.16110 | − | 61.9921i | 0.0405269 | − | 0.794770i | ||||
\(79\) | − | 75.8024i | − | 0.959524i | −0.877399 | − | 0.479762i | \(-0.840723\pi\) | ||
0.877399 | − | 0.479762i | \(-0.159277\pi\) | |||||||
\(80\) | 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 | \(-0.104010\pi\) |
−0.320974 | + | 0.947088i | \(0.604010\pi\) | |||||||
\(84\) | 41.4750 | − | 47.4218i | 0.493749 | − | 0.564545i | ||||
\(85\) | 33.4929 | − | 7.83095i | 0.394034 | − | 0.0921288i | ||||
\(86\) | − | 46.8879i | − | 0.545208i | ||||||
\(87\) | −4.28468 | + | 84.0264i | −0.0492492 | + | 0.965821i | ||||
\(88\) | 68.8167 | + | 68.8167i | 0.782008 | + | 0.782008i | ||||
\(89\) | − | 174.294i | − | 1.95836i | −0.202987 | − | 0.979181i | \(-0.565065\pi\) | ||
0.202987 | − | 0.979181i | \(-0.434935\pi\) | |||||||
\(90\) | −5.73481 | − | 44.6331i | −0.0637201 | − | 0.495923i | ||||
\(91\) | −17.0143 | − | 143.833i | −0.186970 | − | 1.58058i | ||||
\(92\) | 5.31846 | + | 5.31846i | 0.0578093 | + | 0.0578093i | ||||
\(93\) | −51.6745 | − | 2.63499i | −0.555640 | − | 0.0283332i | ||||
\(94\) | −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 | \(-0.288767\pi\) |
−0.787775 | + | 0.615963i | \(0.788767\pi\) | |||||||
\(98\) | −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 | \(-0.310813\pi\) | ||||
0.559968 | + | 0.828514i | \(0.310813\pi\) | |||||||
\(102\) | −1.05099 | + | 20.6109i | −0.0103038 | + | 0.202068i | ||||
\(103\) | −16.1826 | + | 16.1826i | −0.157113 | + | 0.157113i | −0.781286 | − | 0.624173i | \(-0.785436\pi\) |
0.624173 | + | 0.781286i | \(0.285436\pi\) | |||||||
\(104\) | 144.836i | 1.39265i | ||||||||
\(105\) | −30.6764 | − | 100.419i | −0.292156 | − | 0.956371i | ||||
\(106\) | −68.3095 | −0.644429 | ||||||||
\(107\) | 139.010 | + | 139.010i | 1.29916 | + | 1.29916i | 0.928945 | + | 0.370218i | \(0.120717\pi\) |
0.370218 | + | 0.928945i | \(0.379283\pi\) | |||||||
\(108\) | −80.0557 | − | 12.3322i | −0.741257 | − | 0.114187i | ||||
\(109\) | − | 3.01429i | − | 0.0276540i | −0.999904 | − | 0.0138270i | \(-0.995599\pi\) | ||
0.999904 | − | 0.0138270i | \(-0.00440141\pi\) | |||||||
\(110\) | 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 | \(-0.917147\pi\) |
0.257361 | + | 0.966315i | \(0.417147\pi\) | |||||||
\(114\) | −48.4318 | + | 43.7321i | −0.424840 | + | 0.383615i | ||||
\(115\) | 12.2065 | − | 2.85400i | 0.106144 | − | 0.0248174i | ||||
\(116\) | − | 84.1356i | − | 0.725307i | ||||||
\(117\) | −144.387 | + | 117.599i | −1.23408 | + | 1.00512i | ||||
\(118\) | −20.9776 | + | 20.9776i | −0.177776 | + | 0.177776i | ||||
\(119\) | 5.65685 | + | 47.8212i | 0.0475366 | + | 0.401859i | ||||
\(120\) | 18.6675 | + | 103.327i | 0.155562 | + | 0.861061i | ||||
\(121\) | −72.2952 | −0.597481 | ||||||||
\(122\) | 14.8999 | − | 14.8999i | 0.122131 | − | 0.122131i | ||||
\(123\) | 4.08209 | − | 80.0535i | 0.0331877 | − | 0.650842i | ||||
\(124\) | 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 | −0.930485 | − | 0.366330i | \(-0.880614\pi\) |
0.366330 | + | 0.930485i | \(0.380614\pi\) | |||||||
\(128\) | 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 | \(0.401907\pi\) | |||||||
\(132\) | 6.37223 | − | 124.965i | 0.0482745 | − | 0.946706i | ||||
\(133\) | −94.2712 | + | 119.566i | −0.708806 | + | 0.898996i | ||||
\(134\) | 45.9316 | 0.342773 | ||||||||
\(135\) | −87.8499 | + | 102.506i | −0.650740 | + | 0.759301i | ||||
\(136\) | − | 48.1546i | − | 0.354078i | ||||||
\(137\) | −7.42967 | − | 7.42967i | −0.0542312 | − | 0.0542312i | 0.679471 | − | 0.733702i | \(-0.262209\pi\) |
−0.733702 | + | 0.679471i | \(0.762209\pi\) | |||||||
\(138\) | −0.383035 | + | 7.51167i | −0.00277562 | + | 0.0544324i | ||||
\(139\) | 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 | ||||||||
\(147\) | 144.504 | − | 26.9739i | 0.983021 | − | 0.183496i | ||||
\(148\) | 19.5214 | + | 19.5214i | 0.131902 | + | 0.131902i | ||||
\(149\) | −24.7386 | −0.166031 | −0.0830155 | − | 0.996548i | \(-0.526455\pi\) | ||||
−0.0830155 | + | 0.996548i | \(0.526455\pi\) | |||||||
\(150\) | 69.7336 | + | 27.6085i | 0.464890 | + | 0.184057i | ||||
\(151\) | −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 | ||||
\(153\) | 48.0053 | − | 39.0989i | 0.313760 | − | 0.255548i | ||||
\(154\) | 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 | \(-0.0876988\pi\) |
−0.272042 | + | 0.962285i | \(0.587699\pi\) | |||||||
\(158\) | −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 | ||||
\(162\) | −44.4987 | − | 67.6821i | −0.274684 | − | 0.417791i | ||||
\(163\) | 38.8452 | + | 38.8452i | 0.238314 | + | 0.238314i | 0.816152 | − | 0.577837i | \(-0.196103\pi\) |
−0.577837 | + | 0.816152i | \(0.696103\pi\) | |||||||
\(164\) | 80.1575i | 0.488765i | ||||||||
\(165\) | −171.332 | − | 118.898i | −1.03838 | − | 0.720594i | ||||
\(166\) | − | 73.4931i | − | 0.442730i | ||||||
\(167\) | −138.252 | + | 138.252i | −0.827855 | + | 0.827855i | −0.987220 | − | 0.159365i | \(-0.949055\pi\) |
0.159365 | + | 0.987220i | \(0.449055\pi\) | |||||||
\(168\) | −146.672 | + | 9.81182i | −0.873049 | + | 0.0584037i | ||||
\(169\) | − | 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 | \(-0.214857\pi\) |
−0.624893 | + | 0.780711i | \(0.714857\pi\) | |||||||
\(174\) | 62.4454 | − | 56.3859i | 0.358882 | − | 0.324057i | ||||
\(175\) | 171.218 | + | 36.1871i | 0.978387 | + | 0.206784i | ||||
\(176\) | 69.5153i | 0.394973i | ||||||||
\(177\) | 88.8848 | + | 4.53242i | 0.502174 | + | 0.0256069i | ||||
\(178\) | −123.245 | + | 123.245i | −0.692386 | + | 0.692386i | ||||
\(179\) | −187.393 | −1.04689 | −0.523445 | − | 0.852059i | \(-0.675354\pi\) | ||||
−0.523445 | + | 0.852059i | \(0.675354\pi\) | |||||||
\(180\) | 82.5157 | − | 106.846i | 0.458420 | − | 0.593591i | ||||
\(181\) | 179.581i | 0.992158i | 0.868277 | + | 0.496079i | \(0.165227\pi\) | ||||
−0.868277 | + | 0.496079i | \(0.834773\pi\) | |||||||
\(182\) | −89.6745 | + | 113.736i | −0.492717 | + | 0.624925i | ||||
\(183\) | −63.1331 | − | 3.21928i | −0.344990 | − | 0.0175917i | ||||
\(184\) | − | 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 | \(0.909576\pi\) | |||||||
\(192\) | 38.9494 | + | 1.98611i | 0.202861 | + | 0.0103443i | ||||
\(193\) | −81.6333 | − | 81.6333i | −0.422971 | − | 0.422971i | 0.463255 | − | 0.886225i | \(-0.346682\pi\) |
−0.886225 | + | 0.463255i | \(0.846682\pi\) | |||||||
\(194\) | 23.5689i | 0.121489i | ||||||||
\(195\) | −55.1781 | − | 305.419i | −0.282964 | − | 1.56625i | ||||
\(196\) | −142.943 | + | 34.2979i | −0.729300 | + | 0.174989i | ||||
\(197\) | −165.702 | − | 165.702i | −0.841127 | − | 0.841127i | 0.147878 | − | 0.989006i | \(-0.452756\pi\) |
−0.989006 | + | 0.147878i | \(0.952756\pi\) | |||||||
\(198\) | 97.0196 | − | 79.0196i | 0.489998 | − | 0.399089i | ||||
\(199\) | −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 | ||||||||
\(207\) | 17.4956 | − | 14.2496i | 0.0845197 | − | 0.0688388i | ||||
\(208\) | −73.1533 | + | 73.1533i | −0.351698 | + | 0.351698i | ||||
\(209\) | 302.412i | 1.44695i | ||||||||
\(210\) | −49.3154 | + | 92.6984i | −0.234835 | + | 0.441421i | ||||
\(211\) | 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 | ||||
\(213\) | 48.0411 | + | 2.44971i | 0.225545 | + | 0.0115010i | ||||
\(214\) | − | 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 | ||||||||
\(222\) | −1.40593 | + | 27.5717i | −0.00633304 | + | 0.124197i | ||||
\(223\) | 173.529 | − | 173.529i | 0.778155 | − | 0.778155i | −0.201362 | − | 0.979517i | \(-0.564537\pi\) |
0.979517 | + | 0.201362i | \(0.0645368\pi\) | |||||||
\(224\) | 229.401 | − | 27.1362i | 1.02411 | − | 0.121144i | ||||
\(225\) | −78.7290 | − | 210.777i | −0.349907 | − | 0.936785i | ||||
\(226\) | 113.295 | 0.501306 | ||||||||
\(227\) | −191.389 | + | 191.389i | −0.843123 | + | 0.843123i | −0.989264 | − | 0.146140i | \(-0.953315\pi\) |
0.146140 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(228\) | −195.509 | − | 9.96941i | −0.857496 | − | 0.0437255i | ||||
\(229\) | 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 | ||||
\(231\) | 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 | \(-0.662049\pi\) |
0.873187 | + | 0.487385i | \(0.162049\pi\) | |||||||
\(234\) | 185.252 | + | 18.9420i | 0.791675 | + | 0.0809487i | ||||
\(235\) | −127.831 | + | 29.8881i | −0.543961 | + | 0.127183i | ||||
\(236\) | −89.0003 | −0.377120 | ||||||||
\(237\) | 227.112 | + | 11.5809i | 0.958279 | + | 0.0488646i | ||||
\(238\) | 29.8147 | − | 37.8147i | 0.125272 | − | 0.158885i | ||||
\(239\) | 49.2786 | 0.206187 | 0.103093 | − | 0.994672i | \(-0.467126\pi\) | ||||
0.103093 | + | 0.994672i | \(0.467126\pi\) | |||||||
\(240\) | −42.7597 | + | 61.6167i | −0.178165 | + | 0.256736i | ||||
\(241\) | − | 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 | ||||
\(243\) | −61.2344 | + | 235.158i | −0.251993 | + | 0.967729i | ||||
\(244\) | 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 | \(-0.741631\pi\) | ||||
−0.688274 | + | 0.725450i | \(0.741631\pi\) | |||||||
\(252\) | 135.744 | + | 131.508i | 0.538668 | + | 0.521859i | ||||
\(253\) | 24.6476 | + | 24.6476i | 0.0974214 | + | 0.0974214i | ||||
\(254\) | 101.325 | 0.398917 | ||||||||
\(255\) | 18.3454 | + | 101.545i | 0.0719428 | + | 0.398214i | ||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | 216.568 | − | 216.568i | 0.842676 | − | 0.842676i | −0.146530 | − | 0.989206i | \(-0.546810\pi\) |
0.989206 | + | 0.146530i | \(0.0468104\pi\) | |||||||
\(258\) | 140.481 | + | 7.16342i | 0.544501 | + | 0.0277652i | ||||
\(259\) | 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 | \(-0.927231\pi\) |
0.226623 | + | 0.973982i | \(0.427231\pi\) | |||||||
\(264\) | −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 | ||||
\(267\) | 522.204 | + | 26.6283i | 1.95582 | + | 0.0997313i | ||||
\(268\) | 97.4357 | + | 97.4357i | 0.363566 | + | 0.363566i | ||||
\(269\) | − | 349.961i | − | 1.30097i | −0.759519 | − | 0.650485i | \(-0.774566\pi\) | ||
0.759519 | − | 0.650485i | \(-0.225434\pi\) | |||||||
\(270\) | 134.602 | − | 10.3632i | 0.498525 | − | 0.0383822i | ||||
\(271\) | 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 | ||||
\(273\) | 433.539 | − | 29.0021i | 1.58806 | − | 0.106235i | ||||
\(274\) | 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 | −0.425484 | − | 0.904966i | \(-0.639896\pi\) |
0.904966 | + | 0.425484i | \(0.139896\pi\) | |||||||
\(278\) | −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 | \(-0.0813658\pi\) | |||||||
\(282\) | 4.01128 | − | 78.6649i | 0.0142244 | − | 0.278954i | ||||
\(283\) | −120.235 | + | 120.235i | −0.424858 | + | 0.424858i | −0.886873 | − | 0.462014i | \(-0.847127\pi\) |
0.462014 | + | 0.886873i | \(0.347127\pi\) | |||||||
\(284\) | −48.1035 | −0.169378 | ||||||||
\(285\) | −186.017 | + | 268.050i | −0.652691 | + | 0.940528i | ||||
\(286\) | 287.666i | 1.00583i | ||||||||
\(287\) | −115.801 | + | 146.874i | −0.403489 | + | 0.511755i | ||||
\(288\) | −187.559 | − | 230.284i | −0.651247 | − | 0.799596i | ||||
\(289\) | 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 | 0.934962 | + | 0.354747i | \(0.115433\pi\) |
0.354747 | + | 0.934962i | \(0.384567\pi\) | |||||||
\(294\) | −121.253 | − | 83.1064i | −0.412426 | − | 0.282675i | ||||
\(295\) | −78.2536 | + | 126.013i | −0.265266 | + | 0.427163i | ||||
\(296\) | − | 64.4174i | − | 0.217626i | ||||||
\(297\) | −371.007 | − | 57.1518i | −1.24918 | − | 0.192430i | ||||
\(298\) | 17.4929 | + | 17.4929i | 0.0587009 | + | 0.0587009i | ||||
\(299\) | 51.8750i | 0.173495i | ||||||||
\(300\) | 89.3608 | + | 206.494i | 0.297869 | + | 0.688312i | ||||
\(301\) | 325.943 | − | 38.5564i | 1.08287 | − | 0.128094i | ||||
\(302\) | 115.487 | + | 115.487i | 0.382409 | + | 0.382409i | ||||
\(303\) | −17.2812 | + | 338.900i | −0.0570337 | + | 1.11848i | ||||
\(304\) | 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 | \(-0.319962\pi\) |
−0.844264 | + | 0.535928i | \(0.819962\pi\) | |||||||
\(308\) | −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 | \(-0.384140\pi\) | ||||
0.356000 | + | 0.934486i | \(0.384140\pi\) | |||||||
\(312\) | −433.944 | − | 22.1277i | −1.39085 | − | 0.0709221i | ||||
\(313\) | 225.950 | − | 225.950i | 0.721885 | − | 0.721885i | −0.247104 | − | 0.968989i | \(-0.579479\pi\) |
0.968989 | + | 0.247104i | \(0.0794790\pi\) | |||||||
\(314\) | − | 153.256i | − | 0.488076i | ||||||
\(315\) | 305.553 | − | 76.5679i | 0.970008 | − | 0.243073i | ||||
\(316\) | −227.407 | −0.719643 | ||||||||
\(317\) | 96.2271 | + | 96.2271i | 0.303556 | + | 0.303556i | 0.842403 | − | 0.538848i | \(-0.181140\pi\) |
−0.538848 | + | 0.842403i | \(0.681140\pi\) | |||||||
\(318\) | 10.4362 | − | 204.663i | 0.0328181 | − | 0.643593i | ||||
\(319\) | − | 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 | ||||||
\(327\) | 9.03113 | + | 0.460516i | 0.0276181 | + | 0.00140830i | ||||
\(328\) | 132.253 | − | 132.253i | 0.403211 | − | 0.403211i | ||||
\(329\) | −21.5903 | − | 182.517i | −0.0656240 | − | 0.554764i | ||||
\(330\) | 37.0765 | + | 205.224i | 0.112353 | + | 0.621890i | ||||
\(331\) | 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 | ||||
\(333\) | 64.2177 | − | 52.3034i | 0.192846 | − | 0.157067i | ||||
\(334\) | 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 | −0.525588 | − | 0.850739i | \(-0.676155\pi\) |
0.850739 | + | 0.525588i | \(0.176155\pi\) | |||||||
\(338\) | −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 | ||||||||
\(342\) | −123.627 | − | 151.788i | −0.361482 | − | 0.443825i | ||||
\(343\) | −311.465 | − | 143.661i | −0.908061 | − | 0.418837i | ||||
\(344\) | −328.215 | −0.954114 | ||||||||
\(345\) | 6.68601 | + | 37.0081i | 0.0193797 | + | 0.107270i | ||||
\(346\) | − | 38.1223i | − | 0.110180i | ||||||
\(347\) | −268.600 | − | 268.600i | −0.774062 | − | 0.774062i | 0.204752 | − | 0.978814i | \(-0.434361\pi\) |
−0.978814 | + | 0.204752i | \(0.934361\pi\) | |||||||
\(348\) | 252.079 | + | 12.8540i | 0.724366 | + | 0.0369369i | ||||
\(349\) | −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 | \(-0.0901715\pi\) |
−0.279509 | + | 0.960143i | \(0.590172\pi\) | |||||||
\(354\) | −59.6461 | − | 66.0559i | −0.168492 | − | 0.186599i | ||||
\(355\) | −42.2950 | + | 68.1084i | −0.119141 | + | 0.191855i | ||||
\(356\) | −522.883 | −1.46877 | ||||||||
\(357\) | −144.142 | + | 9.64254i | −0.403758 | + | 0.0270099i | ||||
\(358\) | 132.507 | + | 132.507i | 0.370132 | + | 0.370132i | ||||
\(359\) | −161.739 | −0.450526 | −0.225263 | − | 0.974298i | \(-0.572324\pi\) | ||||
−0.225263 | + | 0.974298i | \(0.572324\pi\) | |||||||
\(360\) | −312.432 | + | 40.1437i | −0.867865 | + | 0.111510i | ||||
\(361\) | 112.126 | 0.310599 | ||||||||
\(362\) | 126.983 | − | 126.983i | 0.350781 | − | 0.350781i | ||||
\(363\) | 11.0451 | − | 216.604i | 0.0304272 | − | 0.596706i | ||||
\(364\) | −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 | \(-0.187628\pi\) |
−0.555904 | + | 0.831247i | \(0.687628\pi\) | |||||||
\(368\) | 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 | ||||
\(372\) | −7.90497 | + | 155.024i | −0.0212499 | + | 0.416730i | ||||
\(373\) | −369.464 | − | 369.464i | −0.990521 | − | 0.990521i | 0.00943464 | − | 0.999955i | \(-0.496997\pi\) |
−0.999955 | + | 0.00943464i | \(0.996997\pi\) | |||||||
\(374\) | − | 95.6424i | − | 0.255728i | ||||||
\(375\) | 370.939 | + | 55.0362i | 0.989172 | + | 0.146763i | ||||
\(376\) | 183.790i | 0.488803i | ||||||||
\(377\) | 410.320 | − | 410.320i | 1.08838 | − | 1.08838i | ||||
\(378\) | −6.63236 | + | 188.884i | −0.0175459 | + | 0.499692i | ||||
\(379\) | 261.209i | 0.689207i | 0.938748 | + | 0.344604i | \(0.111987\pi\) | ||||
−0.938748 | + | 0.344604i | \(0.888013\pi\) | |||||||
\(380\) | 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 | \(-0.152200\pi\) |
−0.460138 | + | 0.887847i | \(0.652200\pi\) | |||||||
\(384\) | 239.254 | + | 264.965i | 0.623057 | + | 0.690013i | ||||
\(385\) | 165.680 | + | 457.533i | 0.430339 | + | 1.18840i | ||||
\(386\) | 115.447i | 0.299085i | ||||||||
\(387\) | −266.493 | − | 327.197i | −0.688612 | − | 0.845472i | ||||
\(388\) | −49.9973 | + | 49.9973i | −0.128859 | + | 0.128859i | ||||
\(389\) | 401.000 | 1.03085 | 0.515425 | − | 0.856935i | \(-0.327634\pi\) | ||||
0.515425 | + | 0.856935i | \(0.327634\pi\) | |||||||
\(390\) | −176.947 | + | 254.980i | −0.453710 | + | 0.653796i | ||||
\(391\) | − | 17.2472i | − | 0.0441105i | ||||||
\(392\) | 292.432 | + | 179.255i | 0.746001 | + | 0.457283i | ||||
\(393\) | −12.1410 | + | 238.096i | −0.0308931 | + | 0.605841i | ||||
\(394\) | 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 | \(-0.432185\pi\) |
−0.977391 | + | 0.211440i | \(0.932185\pi\) | |||||||
\(398\) | 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 | \(0.740996\pi\) | |||||||
\(402\) | −7.01732 | + | 137.616i | −0.0174560 | + | 0.342329i | ||||
\(403\) | 252.338 | + | 252.338i | 0.626149 | + | 0.626149i | ||||
\(404\) | − | 339.341i | − | 0.839952i | ||||||
\(405\) | −293.696 | − | 278.868i | −0.725176 | − | 0.688563i | ||||
\(406\) | −194.957 | + | 23.0618i | −0.480190 | + | 0.0568025i | ||||
\(407\) | 90.4693 | + | 90.4693i | 0.222283 | + | 0.222283i | ||||
\(408\) | 144.276 | + | 7.35694i | 0.353619 | + | 0.0180317i | ||||
\(409\) | −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 | ||||||||
\(417\) | −27.4372 | + | 538.068i | −0.0657965 | + | 1.29033i | ||||
\(418\) | 213.838 | − | 213.838i | 0.511573 | − | 0.511573i | ||||
\(419\) | 343.927i | 0.820828i | 0.911899 | + | 0.410414i | \(0.134616\pi\) | ||||
−0.911899 | + | 0.410414i | \(0.865384\pi\) | |||||||
\(420\) | −301.257 | + | 92.0291i | −0.717278 | + | 0.219117i | ||||
\(421\) | 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 | ||||
\(423\) | −183.220 | + | 149.227i | −0.433144 | + | 0.352783i | ||||
\(424\) | 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 | \(0.828164\pi\) | |||||||
\(432\) | −20.5537 | + | 133.426i | −0.0475779 | + | 0.308857i | ||||
\(433\) | 487.352 | − | 487.352i | 1.12553 | − | 1.12553i | 0.134629 | − | 0.990896i | \(-0.457016\pi\) |
0.990896 | − | 0.134629i | \(-0.0429843\pi\) | |||||||
\(434\) | −14.1825 | − | 119.895i | −0.0326787 | − | 0.276255i | ||||
\(435\) | 239.841 | − | 345.610i | 0.551358 | − | 0.794506i | ||||
\(436\) | −9.04287 | −0.0207405 | ||||||||
\(437\) | 38.5614 | − | 38.5614i | 0.0882412 | − | 0.0882412i | ||||
\(438\) | 12.3931 | − | 243.041i | 0.0282948 | − | 0.554888i | ||||
\(439\) | −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 | ||||
\(441\) | 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 | \(-0.847019\pi\) |
0.462315 | + | 0.886716i | \(0.347019\pi\) | |||||||
\(444\) | −61.4707 | + | 55.5059i | −0.138448 | + | 0.125013i | ||||
\(445\) | −459.745 | + | 740.336i | −1.03314 | + | 1.66368i | ||||
\(446\) | −245.406 | −0.550239 | ||||||||
\(447\) | 3.77951 | − | 74.1196i | 0.00845528 | − | 0.165816i | ||||
\(448\) | −71.4602 | − | 56.3422i | −0.159509 | − | 0.125764i | ||||
\(449\) | 397.613 | 0.885552 | 0.442776 | − | 0.896632i | \(-0.353994\pi\) | ||||
0.442776 | + | 0.896632i | \(0.353994\pi\) | |||||||
\(450\) | −93.3717 | + | 204.711i | −0.207493 | + | 0.454914i | ||||
\(451\) | 371.478i | 0.823677i | ||||||||
\(452\) | 240.335 | + | 240.335i | 0.531716 | + | 0.531716i | ||||
\(453\) | 24.9522 | − | 489.336i | 0.0550821 | − | 1.08021i | ||||
\(454\) | 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 | −0.775842 | − | 0.630927i | \(-0.782675\pi\) |
0.630927 | + | 0.775842i | \(0.282675\pi\) | |||||||
\(458\) | −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 | \(0.433386\pi\) | |||||||
\(462\) | −291.313 | + | 19.4878i | −0.630548 | + | 0.0421813i | ||||
\(463\) | 42.9857 | + | 42.9857i | 0.0928417 | + | 0.0928417i | 0.752002 | − | 0.659161i | \(-0.229088\pi\) |
−0.659161 | + | 0.752002i | \(0.729088\pi\) | |||||||
\(464\) | −140.226 | −0.302211 | ||||||||
\(465\) | 212.543 | + | 147.497i | 0.457082 | + | 0.317198i | ||||
\(466\) | −127.126 | −0.272803 | ||||||||
\(467\) | −252.836 | + | 252.836i | −0.541405 | + | 0.541405i | −0.923941 | − | 0.382536i | \(-0.875051\pi\) |
0.382536 | + | 0.923941i | \(0.375051\pi\) | |||||||
\(468\) | 352.797 | + | 433.161i | 0.753839 | + | 0.925557i | ||||
\(469\) | 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 | ||||
\(477\) | −476.684 | + | 388.245i | −0.999337 | + | 0.813930i | ||||
\(478\) | −34.8452 | − | 34.8452i | −0.0728980 | − | 0.0728980i | ||||
\(479\) | 91.5191i | 0.191063i | 0.995426 | + | 0.0955314i | \(0.0304550\pi\) | ||||
−0.995426 | + | 0.0955314i | \(0.969545\pi\) | |||||||
\(480\) | 487.114 | − | 88.0038i | 1.01482 | − | 0.183341i | ||||
\(481\) | 190.408i | 0.395858i | ||||||||
\(482\) | −298.161 | + | 298.161i | −0.618592 | + | 0.618592i | ||||
\(483\) | −52.5326 | + | 3.51424i | −0.108763 | + | 0.00727585i | ||||
\(484\) | 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 | −0.398358 | − | 0.917230i | \(-0.630420\pi\) |
0.917230 | + | 0.398358i | \(0.130420\pi\) | |||||||
\(488\) | −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 | \(-0.176913\pi\) | |||||||
\(492\) | −240.161 | − | 12.2463i | −0.488131 | − | 0.0248908i | ||||
\(493\) | −136.422 | + | 136.422i | −0.276717 | + | 0.276717i | ||||
\(494\) | 450.057 | 0.911046 | ||||||||
\(495\) | 382.407 | − | 495.164i | 0.772539 | − | 1.00033i | ||||
\(496\) | − | 86.2361i | − | 0.173863i | ||||||
\(497\) | −88.1406 | − | 69.4937i | −0.177345 | − | 0.139826i | ||||
\(498\) | 220.193 | + | 11.2281i | 0.442155 | + | 0.0225464i | ||||
\(499\) | − | 217.267i | − | 0.435404i | −0.976015 | − | 0.217702i | \(-0.930144\pi\) | ||
0.976015 | − | 0.217702i | \(-0.0698561\pi\) | |||||||
\(500\) | −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 | \(-0.244299\pi\) |
−0.694329 | + | 0.719657i | \(0.744299\pi\) | |||||||
\(504\) | −6.98904 | − | 440.945i | −0.0138671 | − | 0.874890i | ||||
\(505\) | −480.463 | − | 298.365i | −0.951412 | − | 0.590823i | ||||
\(506\) | − | 34.8570i | − | 0.0688873i | ||||||
\(507\) | 776.327 | + | 39.5865i | 1.53122 | + | 0.0780798i | ||||
\(508\) | 214.943 | + | 214.943i | 0.423116 | + | 0.423116i | ||||
\(509\) | 611.593i | 1.20156i | 0.799415 | + | 0.600779i | \(0.205143\pi\) | ||||
−0.799415 | + | 0.600779i | \(0.794857\pi\) | |||||||
\(510\) | 58.8307 | − | 84.7750i | 0.115354 | − | 0.166226i | ||||
\(511\) | −66.7048 | − | 563.900i | −0.130538 | − | 1.10352i | ||||
\(512\) | −215.668 | − | 215.668i | −0.421226 | − | 0.421226i | ||||
\(513\) | −89.4144 | + | 580.443i | −0.174297 | + | 1.13147i | ||||
\(514\) | −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 | \(-0.731397\pi\) | ||||
−0.664597 | + | 0.747202i | \(0.731397\pi\) | |||||||
\(522\) | 159.398 | + | 195.708i | 0.305360 | + | 0.374919i | ||||
\(523\) | −583.903 | + | 583.903i | −1.11645 | + | 1.11645i | −0.124191 | + | 0.992258i | \(0.539634\pi\) |
−0.992258 | + | 0.124191i | \(0.960366\pi\) | |||||||
\(524\) | − | 238.405i | − | 0.454971i | ||||||
\(525\) | −134.579 | + | 507.458i | −0.256340 | + | 0.966587i | ||||
\(526\) | 277.971 | 0.528463 | ||||||||
\(527\) | −83.8965 | − | 83.8965i | −0.159196 | − | 0.159196i | ||||
\(528\) | −208.275 | − | 10.6204i | −0.394461 | − | 0.0201144i | ||||
\(529\) | 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 | ||||||
\(537\) | 28.6295 | − | 561.451i | 0.0533138 | − | 1.04553i | ||||
\(538\) | −247.460 | + | 247.460i | −0.459963 | + | 0.459963i | ||||
\(539\) | −662.448 | + | 158.948i | −1.22903 | + | 0.294895i | ||||
\(540\) | 307.517 | + | 263.550i | 0.569476 | + | 0.488055i | ||||
\(541\) | 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 | ||||
\(543\) | −538.043 | − | 27.4359i | −0.990871 | − | 0.0505265i | ||||
\(544\) | −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 | −0.472193 | − | 0.881495i | \(-0.656538\pi\) |
0.881495 | + | 0.472193i | \(0.156538\pi\) | |||||||
\(548\) | −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 | ||||||||
\(552\) | 52.5817 | + | 2.68125i | 0.0952567 | + | 0.00485733i | ||||
\(553\) | −416.681 | − | 328.529i | −0.753492 | − | 0.594084i | ||||
\(554\) | −187.831 | −0.339045 | ||||||||
\(555\) | 24.5411 | + | 135.838i | 0.0442181 | + | 0.244754i | ||||
\(556\) | − | 538.767i | − | 0.969005i | ||||||
\(557\) | 245.854 | + | 245.854i | 0.441390 | + | 0.441390i | 0.892479 | − | 0.451089i | \(-0.148964\pi\) |
−0.451089 | + | 0.892479i | \(0.648964\pi\) | |||||||
\(558\) | −120.356 | + | 98.0265i | −0.215692 | + | 0.175675i | ||||
\(559\) | 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 | \(-0.420527\pi\) |
−0.968993 | + | 0.247086i | \(0.920527\pi\) | |||||||
\(564\) | 175.383 | − | 158.364i | 0.310962 | − | 0.280788i | ||||
\(565\) | 551.600 | − | 128.969i | 0.976283 | − | 0.228264i | ||||
\(566\) | 170.038 | 0.300420 | ||||||||
\(567\) | 433.902 | − | 364.990i | 0.765260 | − | 0.643721i | ||||
\(568\) | 79.3667 | + | 79.3667i | 0.139730 | + | 0.139730i | ||||
\(569\) | −690.156 | −1.21293 | −0.606464 | − | 0.795111i | \(-0.707413\pi\) | ||||
−0.606464 | + | 0.795111i | \(0.707413\pi\) | |||||||
\(570\) | 321.074 | − | 58.0064i | 0.563288 | − | 0.101766i | ||||
\(571\) | 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 | ||||
\(573\) | −320.771 | − | 16.3568i | −0.559810 | − | 0.0285459i | ||||
\(574\) | 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 | \(-0.149063\pi\) |
−0.451366 | + | 0.892339i | \(0.649063\pi\) | |||||||
\(578\) | 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 | ||||
\(582\) | −70.6151 | − | 3.60081i | −0.121332 | − | 0.00618695i | ||||
\(583\) | −671.548 | − | 671.548i | −1.15188 | − | 1.15188i | ||||
\(584\) | 567.832i | 0.972315i | ||||||||
\(585\) | 923.497 | − | 118.658i | 1.57863 | − | 0.202835i | ||||
\(586\) | − | 534.410i | − | 0.911962i | ||||||
\(587\) | 195.495 | − | 195.495i | 0.333040 | − | 0.333040i | −0.520700 | − | 0.853740i | \(-0.674329\pi\) |
0.853740 | + | 0.520700i | \(0.174329\pi\) | |||||||
\(588\) | −80.9216 | − | 433.512i | −0.137622 | − | 0.737265i | ||||
\(589\) | − | 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 | \(-0.180403\pi\) |
−0.536897 | + | 0.843648i | \(0.680403\pi\) | |||||||
\(594\) | 221.929 | + | 302.754i | 0.373618 | + | 0.509686i | ||||
\(595\) | 102.112 | − | 218.048i | 0.171617 | − | 0.366466i | ||||
\(596\) | 74.2159i | 0.124523i | ||||||||
\(597\) | 33.6167 | − | 659.255i | 0.0563094 | − | 1.10428i | ||||
\(598\) | 36.6812 | − | 36.6812i | 0.0613397 | − | 0.0613397i | ||||
\(599\) | −376.201 | −0.628048 | −0.314024 | − | 0.949415i | \(-0.601677\pi\) | ||||
−0.314024 | + | 0.949415i | \(0.601677\pi\) | |||||||
\(600\) | 193.259 | − | 488.135i | 0.322099 | − | 0.813558i | ||||
\(601\) | 1122.87i | 1.86834i | 0.356832 | + | 0.934169i | \(0.383857\pi\) | ||||
−0.356832 | + | 0.934169i | \(0.616143\pi\) | |||||||
\(602\) | −257.740 | − | 203.213i | −0.428139 | − | 0.337563i | ||||
\(603\) | 320.524 | − | 261.058i | 0.531549 | − | 0.432931i | ||||
\(604\) | 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 | \(-0.202404\pi\) |
−0.593879 | + | 0.804554i | \(0.702404\pi\) | |||||||
\(608\) | −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 | ||||||
\(612\) | −117.297 | − | 144.016i | −0.191661 | − | 0.235320i | ||||
\(613\) | 668.817 | + | 668.817i | 1.09105 | + | 1.09105i | 0.995416 | + | 0.0956388i | \(0.0304894\pi\) |
0.0956388 | + | 0.995416i | \(0.469511\pi\) | |||||||
\(614\) | 133.868i | 0.218026i | ||||||||
\(615\) | −228.501 | + | 329.269i | −0.371546 | + | 0.535397i | ||||
\(616\) | 676.533 | − | 80.0283i | 1.09827 | − | 0.129916i | ||||
\(617\) | 416.614 | + | 416.614i | 0.675225 | + | 0.675225i | 0.958916 | − | 0.283691i | \(-0.0915589\pi\) |
−0.283691 | + | 0.958916i | \(0.591559\pi\) | |||||||
\(618\) | −3.49641 | + | 68.5679i | −0.00565763 | + | 0.110951i | ||||
\(619\) | 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 | ||||||||
\(627\) | −906.059 | − | 46.2018i | −1.44507 | − | 0.0736870i | ||||
\(628\) | 325.105 | − | 325.105i | 0.517683 | − | 0.517683i | ||||
\(629\) | − | 63.3061i | − | 0.100646i | ||||||
\(630\) | −270.200 | − | 161.917i | −0.428889 | − | 0.257010i | ||||
\(631\) | −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 | ||||
\(633\) | −42.2568 | + | 828.695i | −0.0667564 | + | 1.30915i | ||||
\(634\) | − | 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 | \(-0.0466304\pi\) | |||||||
\(642\) | 589.006 | + | 30.0346i | 0.917455 | + | 0.0467829i | ||||
\(643\) | −767.988 | + | 767.988i | −1.19438 | + | 1.19438i | −0.218559 | + | 0.975824i | \(0.570136\pi\) |
−0.975824 | + | 0.218559i | \(0.929864\pi\) | |||||||
\(644\) | 52.2855 | − | 6.18494i | 0.0811886 | − | 0.00960395i | ||||
\(645\) | 692.114 | − | 125.040i | 1.07305 | − | 0.193860i | ||||
\(646\) | −149.633 | −0.231631 | ||||||||
\(647\) | −573.588 | + | 573.588i | −0.886535 | + | 0.886535i | −0.994188 | − | 0.107654i | \(-0.965666\pi\) |
0.107654 | + | 0.994188i | \(0.465666\pi\) | |||||||
\(648\) | −473.774 | + | 311.491i | −0.731133 | + | 0.480696i | ||||
\(649\) | −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 | \(-0.700721\pi\) |
0.807683 | + | 0.589616i | \(0.200721\pi\) | |||||||
\(654\) | −6.06034 | − | 6.71161i | −0.00926658 | − | 0.0102624i | ||||
\(655\) | −337.551 | − | 209.618i | −0.515345 | − | 0.320027i | ||||
\(656\) | 133.596 | 0.203652 | ||||||||
\(657\) | −566.071 | + | 461.048i | −0.861600 | + | 0.701747i | ||||
\(658\) | −113.793 | + | 144.326i | −0.172937 | + | 0.219340i | ||||
\(659\) | 960.106 | 1.45691 | 0.728457 | − | 0.685092i | \(-0.240238\pi\) | ||||
0.728457 | + | 0.685092i | \(0.240238\pi\) | |||||||
\(660\) | −356.694 | + | 513.996i | −0.540446 | + | 0.778782i | ||||
\(661\) | 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 | ||||
\(663\) | −426.458 | − | 21.7459i | −0.643224 | − | 0.0327993i | ||||
\(664\) | −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 | ||||||||
\(672\) | 46.2557 | + | 691.455i | 0.0688329 | + | 1.02895i | ||||
\(673\) | −442.857 | − | 442.857i | −0.658034 | − | 0.658034i | 0.296880 | − | 0.954915i | \(-0.404054\pi\) |
−0.954915 | + | 0.296880i | \(0.904054\pi\) | |||||||
\(674\) | −154.964 | −0.229917 | ||||||||
\(675\) | 643.537 | − | 203.679i | 0.953388 | − | 0.301746i | ||||
\(676\) | −777.336 | −1.14990 | ||||||||
\(677\) | −447.410 | + | 447.410i | −0.660872 | + | 0.660872i | −0.955586 | − | 0.294714i | \(-0.904776\pi\) |
0.294714 | + | 0.955586i | \(0.404776\pi\) | |||||||
\(678\) | −17.3090 | + | 339.445i | −0.0255295 | + | 0.500656i | ||||
\(679\) | −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 | \(-0.683731\pi\) |
0.837990 | + | 0.545686i | \(0.183731\pi\) | |||||||
\(684\) | 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 | ||||
\(687\) | −18.8666 | + | 369.991i | −0.0274622 | + | 0.538560i | ||||
\(688\) | −165.774 | − | 165.774i | −0.240950 | − | 0.240950i | ||||
\(689\) | − | 1413.38i | − | 2.05135i | ||||||
\(690\) | 21.4409 | − | 30.8964i | 0.0310738 | − | 0.0447773i | ||||
\(691\) | − | 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 | ||||
\(693\) | 629.088 | + | 609.457i | 0.907775 | + | 0.879447i | ||||
\(694\) | 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 | \(0.998155\pi\) | |||||||
\(702\) | −85.0546 | + | 552.141i | −0.121160 | + | 0.786525i | ||||
\(703\) | 141.540 | − | 141.540i | 0.201337 | − | 0.201337i | ||||
\(704\) | −180.740 | −0.256733 | ||||||||
\(705\) | −70.0183 | − | 387.561i | −0.0993167 | − | 0.549733i | ||||
\(706\) | − | 339.785i | − | 0.481281i | ||||||
\(707\) | 490.236 | − | 621.778i | 0.693403 | − | 0.879459i | ||||
\(708\) | 13.5972 | − | 266.654i | 0.0192052 | − | 0.376631i | ||||
\(709\) | 854.167i | 1.20475i | 0.798214 | + | 0.602374i | \(0.205778\pi\) | ||||
−0.798214 | + | 0.602374i | \(0.794222\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | −7.52867 | + | 147.644i | −0.0105002 | + | 0.205919i | ||||
\(718\) | 114.367 | + | 114.367i | 0.159285 | + | 0.159285i | ||||
\(719\) | 1236.22i | 1.71936i | 0.510837 | + | 0.859678i | \(0.329336\pi\) | ||||
−0.510837 | + | 0.859678i | \(0.670664\pi\) | |||||||
\(720\) | −178.077 | − | 137.526i | −0.247330 | − | 0.191009i | ||||
\(721\) | 18.8191 | + | 159.090i | 0.0261014 | + | 0.220652i | ||||
\(722\) | −79.2852 | − | 79.2852i | −0.109813 | − | 0.109813i | ||||
\(723\) | 1263.35 | + | 64.4208i | 1.74737 | + | 0.0891021i | ||||
\(724\) | 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 | \(-0.0380815\pi\) |
−0.119351 | + | 0.992852i | \(0.538081\pi\) | |||||||
\(728\) | 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 | ||||||||
\(732\) | −9.65785 | + | 189.399i | −0.0131938 | + | 0.258742i | ||||
\(733\) | 174.851 | − | 174.851i | 0.238542 | − | 0.238542i | −0.577704 | − | 0.816246i | \(-0.696051\pi\) |
0.816246 | + | 0.577704i | \(0.196051\pi\) | |||||||
\(734\) | − | 142.908i | − | 0.194697i | ||||||
\(735\) | −684.948 | − | 266.591i | −0.931902 | − | 0.362709i | ||||
\(736\) | −82.7358 | −0.112413 | ||||||||
\(737\) | 451.552 | + | 451.552i | 0.612689 | + | 0.612689i | ||||
\(738\) | −151.861 | − | 186.454i | −0.205774 | − | 0.252648i | ||||
\(739\) | − | 1448.98i | − | 1.96073i | −0.197187 | − | 0.980366i | \(-0.563181\pi\) | ||
0.197187 | − | 0.980366i | \(-0.436819\pi\) | |||||||
\(740\) | −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 | \(-0.740639\pi\) |
0.727592 | + | 0.686010i | \(0.240639\pi\) | |||||||
\(744\) | 268.818 | − | 242.733i | 0.361315 | − | 0.326254i | ||||
\(745\) | 105.080 | + | 65.2544i | 0.141047 | + | 0.0875898i | ||||
\(746\) | 522.501i | 0.700404i | ||||||||
\(747\) | −417.706 | − | 512.856i | −0.559179 | − | 0.686555i | ||||
\(748\) | 202.888 | − | 202.888i | 0.271241 | − | 0.271241i | ||||
\(749\) | 1366.61 | − | 161.658i | 1.82457 | − | 0.215832i | ||||
\(750\) | −223.377 | − | 301.210i | −0.297836 | − | 0.401614i | ||||
\(751\) | 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 | ||||
\(753\) | 52.7867 | − | 1035.20i | 0.0701019 | − | 1.37476i | ||||
\(754\) | −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 | −0.555401 | − | 0.831582i | \(-0.687435\pi\) |
0.831582 | + | 0.555401i | \(0.187435\pi\) | |||||||
\(758\) | 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 | \(0.345305\pi\) | |||||||
\(762\) | −15.4802 | + | 303.581i | −0.0203152 | + | 0.398400i | ||||
\(763\) | −16.5694 | − | 13.0640i | −0.0217161 | − | 0.0171219i | ||||
\(764\) | 321.188 | 0.420403 | ||||||||
\(765\) | −307.041 | + | 39.4511i | −0.401361 | + | 0.0515701i | ||||
\(766\) | − | 231.666i | − | 0.302436i | ||||||
\(767\) | −434.044 | − | 434.044i | −0.565898 | − | 0.565898i | ||||
\(768\) | 26.1250 | − | 512.334i | 0.0340169 | − | 0.667102i | ||||
\(769\) | 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 | \(-0.159292\pi\) |
−0.479804 | + | 0.877376i | \(0.659292\pi\) | |||||||
\(774\) | −42.9248 | + | 419.802i | −0.0554583 | + | 0.542380i | ||||
\(775\) | −386.481 | + | 191.177i | −0.498686 | + | 0.246680i | ||||
\(776\) | 164.983 | 0.212606 | ||||||||
\(777\) | −192.821 | + | 12.8990i | −0.248161 | + | 0.0166011i | ||||
\(778\) | −283.550 | − | 283.550i | −0.364460 | − | 0.364460i | ||||
\(779\) | 581.181 | 0.746061 | ||||||||
\(780\) | −916.256 | + | 165.534i | −1.17469 | + | 0.212223i | ||||
\(781\) | −222.929 | −0.285440 | ||||||||
\(782\) | −12.1956 | + | 12.1956i | −0.0155954 | + | 0.0155954i | ||||
\(783\) | 115.286 | − | 748.393i | 0.147237 | − | 0.955802i | ||||
\(784\) | 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 | \(-0.306453\pi\) |
−0.820766 | + | 0.571265i | \(0.806453\pi\) | |||||||
\(788\) | −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 | ||||
\(792\) | −553.137 | − | 679.137i | −0.698406 | − | 0.857497i | ||||
\(793\) | 308.293 | + | 308.293i | 0.388768 | + | 0.388768i | ||||
\(794\) | 430.037i | 0.541609i | ||||||||
\(795\) | −182.167 | − | 1008.32i | −0.229140 | − | 1.26833i | ||||
\(796\) | 660.111i | 0.829285i | ||||||||
\(797\) | 941.657 | − | 941.657i | 1.18150 | − | 1.18150i | 0.202147 | − | 0.979355i | \(-0.435208\pi\) |
0.979355 | − | 0.202147i | \(-0.0647918\pi\) | |||||||
\(798\) | 30.4888 | + | 455.762i | 0.0382065 | + | 0.571130i | ||||
\(799\) | 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 | ||||||
\(807\) | 1048.52 | + | 53.4662i | 1.29928 | + | 0.0662530i | ||||
\(808\) | −559.883 | + | 559.883i | −0.692925 | + | 0.692925i | ||||
\(809\) | −1461.04 | −1.80598 | −0.902990 | − | 0.429662i | \(-0.858633\pi\) | ||||
−0.902990 | + | 0.429662i | \(0.858633\pi\) | |||||||
\(810\) | 10.4851 | + | 404.864i | 0.0129446 | + | 0.499832i | ||||
\(811\) | − | 1284.35i | − | 1.58367i | −0.610738 | − | 0.791833i | \(-0.709127\pi\) | ||
0.610738 | − | 0.791833i | \(-0.290873\pi\) | |||||||
\(812\) | −462.488 | − | 364.645i | −0.569567 | − | 0.449070i | ||||
\(813\) | −413.396 | − | 21.0799i | −0.508482 | − | 0.0259285i | ||||
\(814\) | − | 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 | \(-0.158065\pi\) | |||||||
\(822\) | −31.4805 | − | 1.60526i | −0.0382975 | − | 0.00195287i | ||||
\(823\) | −361.067 | − | 361.067i | −0.438720 | − | 0.438720i | 0.452861 | − | 0.891581i | \(-0.350403\pi\) |
−0.891581 | + | 0.452861i | \(0.850403\pi\) | |||||||
\(824\) | − | 160.200i | − | 0.194417i | ||||||
\(825\) | 414.130 | + | 956.965i | 0.501975 | + | 1.15996i | ||||
\(826\) | 24.3953 | + | 206.229i | 0.0295342 | + | 0.249672i | ||||
\(827\) | −711.346 | − | 711.346i | −0.860152 | − | 0.860152i | 0.131203 | − | 0.991356i | \(-0.458116\pi\) |
−0.991356 | + | 0.131203i | \(0.958116\pi\) | |||||||
\(828\) | −42.7489 | − | 52.4867i | −0.0516291 | − | 0.0633898i | ||||
\(829\) | −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 | ||||||||
\(837\) | 460.246 | + | 70.8987i | 0.549876 | + | 0.0847057i | ||||
\(838\) | 243.193 | − | 243.193i | 0.290206 | − | 0.290206i | ||||
\(839\) | − | 915.483i | − | 1.09116i | −0.838059 | − | 0.545580i | \(-0.816310\pi\) | ||
0.838059 | − | 0.545580i | \(-0.183690\pi\) | |||||||
\(840\) | 648.889 | + | 345.208i | 0.772486 | + | 0.410962i | ||||
\(841\) | −54.4667 | −0.0647642 | ||||||||
\(842\) | −10.3776 | − | 10.3776i | −0.0123250 | − | 0.0123250i | ||||
\(843\) | 425.741 | + | 21.7094i | 0.505031 | + | 0.0257526i | ||||
\(844\) | − | 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 | ||||||
\(852\) | 7.34913 | − | 144.123i | 0.00862574 | − | 0.169159i | ||||
\(853\) | 286.958 | − | 286.958i | 0.336411 | − | 0.336411i | −0.518604 | − | 0.855015i | \(-0.673548\pi\) |
0.855015 | + | 0.518604i | \(0.173548\pi\) | |||||||
\(854\) | −17.3275 | − | 146.481i | −0.0202898 | − | 0.171523i | ||||
\(855\) | −774.689 | − | 598.279i | −0.906069 | − | 0.699742i | ||||
\(856\) | −1376.13 | −1.60763 | ||||||||
\(857\) | 605.241 | − | 605.241i | 0.706232 | − | 0.706232i | −0.259509 | − | 0.965741i | \(-0.583561\pi\) |
0.965741 | + | 0.259509i | \(0.0835606\pi\) | |||||||
\(858\) | −861.880 | − | 43.9490i | −1.00452 | − | 0.0512226i | ||||
\(859\) | 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 | ||||
\(861\) | −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 | \(-0.535483\pi\) |
0.993793 | + | 0.111242i | \(0.0354830\pi\) | |||||||
\(864\) | 718.609 | − | 526.765i | 0.831724 | − | 0.609682i | ||||
\(865\) | −43.3965 | − | 185.606i | −0.0501693 | − | 0.214573i | ||||
\(866\) | −689.220 | −0.795866 | ||||||||
\(867\) | −724.088 | − | 36.9227i | −0.835165 | − | 0.0425867i | ||||
\(868\) | 224.249 | − | 284.421i | 0.258352 | − | 0.327674i | ||||
\(869\) | −1053.89 | −1.21276 | ||||||||
\(870\) | −413.976 | + | 74.7905i | −0.475835 | + | 0.0859661i | ||||
\(871\) | 950.365i | 1.09112i | ||||||||
\(872\) | 14.9200 | + | 14.9200i | 0.0171101 | + | 0.0171101i | ||||
\(873\) | 133.957 | + | 164.471i | 0.153444 | + | 0.188397i | ||||
\(874\) | −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 | −0.719302 | − | 0.694697i | \(-0.755538\pi\) |
0.694697 | + | 0.719302i | \(0.255538\pi\) | |||||||
\(878\) | 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 | \(0.451193\pi\) | |||||||
\(882\) | 267.520 | − | 350.591i | 0.303311 | − | 0.397495i | ||||
\(883\) | 659.321 | + | 659.321i | 0.746683 | + | 0.746683i | 0.973855 | − | 0.227171i | \(-0.0729478\pi\) |
−0.227171 | + | 0.973855i | \(0.572948\pi\) | |||||||
\(884\) | 427.012 | 0.483045 | ||||||||
\(885\) | −365.593 | − | 253.708i | −0.413100 | − | 0.286676i | ||||
\(886\) | 265.886 | 0.300097 | ||||||||
\(887\) | 366.008 | − | 366.008i | 0.412636 | − | 0.412636i | −0.470020 | − | 0.882656i | \(-0.655753\pi\) |
0.882656 | + | 0.470020i | \(0.155753\pi\) | |||||||
\(888\) | 193.002 | + | 9.84154i | 0.217344 | + | 0.0110828i | ||||
\(889\) | 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 | ||||
\(897\) | −155.423 | − | 7.92533i | −0.173270 | − | 0.00883538i | ||||
\(898\) | −281.155 | − | 281.155i | −0.313090 | − | 0.313090i | ||||
\(899\) | 483.702i | 0.538044i | ||||||||
\(900\) | −632.330 | + | 236.187i | −0.702588 | + | 0.262430i | ||||
\(901\) | 469.917i | 0.521550i | ||||||||
\(902\) | 262.675 | − | 262.675i | 0.291214 | − | 0.291214i | ||||
\(903\) | 65.7222 | + | 982.450i | 0.0727821 | + | 1.08798i | ||||
\(904\) | − | 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 | −0.670342 | − | 0.742052i | \(-0.733853\pi\) |
0.742052 | + | 0.670342i | \(0.233853\pi\) | |||||||
\(908\) | 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 | \(0.657236\pi\) | |||||||
\(912\) | −16.6157 | + | 325.849i | −0.0182189 | + | 0.357290i | ||||
\(913\) | 722.507 | − | 722.507i | 0.791355 | − | 0.791355i | ||||
\(914\) | 93.6580 | 0.102470 | ||||||||
\(915\) | 259.674 | + | 180.204i | 0.283796 | + | 0.196944i | ||||
\(916\) | − | 370.471i | − | 0.404445i | ||||||
\(917\) | 344.417 | − | 436.832i | 0.375591 | − | 0.476371i | ||||
\(918\) | 28.2787 | − | 183.574i | 0.0308046 | − | 0.199972i | ||||
\(919\) | − | 18.0596i | − | 0.0196513i | −0.999952 | − | 0.00982566i | \(-0.996872\pi\) | ||
0.999952 | − | 0.00982566i | \(-0.00312766\pi\) | |||||||
\(920\) | −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 | ||||||
\(927\) | 159.703 | − | 130.073i | 0.172279 | − | 0.140316i | ||||
\(928\) | 654.421 | + | 654.421i | 0.705195 | + | 0.705195i | ||||
\(929\) | − | 891.704i | − | 0.959854i | −0.877308 | − | 0.479927i | \(-0.840663\pi\) | ||
0.877308 | − | 0.479927i | \(-0.159337\pi\) | |||||||
\(930\) | −45.9946 | − | 254.587i | −0.0494566 | − | 0.273749i | ||||
\(931\) | 248.676 | + | 1036.41i | 0.267107 | + | 1.11322i | ||||
\(932\) | −269.675 | − | 269.675i | −0.289351 | − | 0.289351i | ||||
\(933\) | −33.8299 | + | 663.435i | −0.0362592 | + | 0.711077i | ||||
\(934\) | 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 | \(-0.130522\pi\) |
−0.398652 | + | 0.917102i | \(0.630522\pi\) | |||||||
\(938\) | 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 | \(-0.756163\pi\) | ||||
−0.720665 | + | 0.693284i | \(0.756163\pi\) | |||||||
\(942\) | 459.171 | + | 23.4141i | 0.487443 | + | 0.0248557i | ||||
\(943\) | 47.3683 | − | 47.3683i | 0.0502314 | − | 0.0502314i | ||||
\(944\) | 148.334i | 0.157133i | ||||||||
\(945\) | 182.724 | + | 927.166i | 0.193359 | + | 0.981128i | ||||
\(946\) | −651.886 | −0.689097 | ||||||||
\(947\) | 757.557 | + | 757.557i | 0.799955 | + | 0.799955i | 0.983088 | − | 0.183133i | \(-0.0586240\pi\) |
−0.183133 | + | 0.983088i | \(0.558624\pi\) | |||||||
\(948\) | 34.7427 | − | 681.336i | 0.0366484 | − | 0.718709i | ||||
\(949\) | − | 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 | −0.147800 | + | 0.989017i | \(0.547219\pi\) |
−0.989017 | + | 0.147800i | \(0.952781\pi\) | |||||||
\(954\) | 611.597 | + | 62.5357i | 0.641087 | + | 0.0655511i | ||||
\(955\) | 282.405 | − | 454.762i | 0.295712 | − | 0.476190i | ||||
\(956\) | − | 147.836i | − | 0.154640i | ||||||
\(957\) | 1168.22 | + | 59.5702i | 1.22072 | + | 0.0622468i | ||||
\(958\) | 64.7138 | − | 64.7138i | 0.0675509 | − | 0.0675509i | ||||
\(959\) | −73.0408 | + | 8.64012i | −0.0761635 | + | 0.00900951i | ||||
\(960\) | −160.203 | − | 111.175i | −0.166878 | − | 0.115807i | ||||
\(961\) | 663.533 | 0.690461 | ||||||||
\(962\) | 134.638 | − | 134.638i | 0.139957 | − | 0.139957i | ||||
\(963\) | −1117.34 | − | 1371.87i | −1.16027 | − | 1.42457i | ||||
\(964\) | −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 | −0.0151989 | + | 0.999884i | \(0.504838\pi\) |
−0.999884 | + | 0.0151989i | \(0.995162\pi\) | |||||||
\(968\) | 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 | \(0.439546\pi\) | |||||||
\(972\) | 705.474 | + | 183.703i | 0.725797 | + | 0.188995i | ||||
\(973\) | 778.341 | − | 987.189i | 0.799939 | − | 1.01458i | ||||
\(974\) | −357.358 | −0.366898 | ||||||||
\(975\) | −571.244 | + | 1442.85i | −0.585891 | + | 1.47984i | ||||
\(976\) | − | 105.359i | − | 0.107949i | ||||||
\(977\) | 576.937 | + | 576.937i | 0.590519 | + | 0.590519i | 0.937772 | − | 0.347253i | \(-0.112885\pi\) |
−0.347253 | + | 0.937772i | \(0.612885\pi\) | |||||||
\(978\) | 164.593 | + | 8.39291i | 0.168295 | + | 0.00858170i | ||||
\(979\) | −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 | \(-0.103268\pi\) |
−0.318765 | + | 0.947834i | \(0.603268\pi\) | |||||||
\(984\) | 376.039 | + | 416.450i | 0.382154 | + | 0.423222i | ||||
\(985\) | 266.758 | + | 1140.92i | 0.270820 | + | 1.15829i | ||||
\(986\) | 192.929 | 0.195669 | ||||||||
\(987\) | 550.140 | − | 36.8023i | 0.557386 | − | 0.0372870i | ||||
\(988\) | 954.714 | + | 954.714i | 0.966310 | + | 0.966310i | ||||
\(989\) | −117.555 | −0.118862 | ||||||||
\(990\) | −620.537 | + | 79.7315i | −0.626805 | + | 0.0805369i | ||||
\(991\) | −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 | ||||
\(993\) | −26.7383 | + | 524.362i | −0.0269267 | + | 0.528058i | ||||
\(994\) | 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 | \(-0.269459\pi\) |
−0.748986 | + | 0.662585i | \(0.769459\pi\) | |||||||
\(998\) | −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.83.2 | yes | 16 | |
3.2 | odd | 2 | inner | 105.3.k.c.83.5 | yes | 16 | |
5.2 | odd | 4 | inner | 105.3.k.c.62.8 | yes | 16 | |
7.6 | odd | 2 | inner | 105.3.k.c.83.3 | yes | 16 | |
15.2 | even | 4 | inner | 105.3.k.c.62.3 | yes | 16 | |
21.20 | even | 2 | inner | 105.3.k.c.83.8 | yes | 16 | |
35.27 | even | 4 | inner | 105.3.k.c.62.5 | yes | 16 | |
105.62 | odd | 4 | inner | 105.3.k.c.62.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.c.62.2 | ✓ | 16 | 105.62 | odd | 4 | inner | |
105.3.k.c.62.3 | yes | 16 | 15.2 | even | 4 | inner | |
105.3.k.c.62.5 | yes | 16 | 35.27 | even | 4 | inner | |
105.3.k.c.62.8 | yes | 16 | 5.2 | odd | 4 | inner | |
105.3.k.c.83.2 | yes | 16 | 1.1 | even | 1 | trivial | |
105.3.k.c.83.3 | yes | 16 | 7.6 | odd | 2 | inner | |
105.3.k.c.83.5 | yes | 16 | 3.2 | odd | 2 | inner | |
105.3.k.c.83.8 | yes | 16 | 21.20 | even | 2 | inner |