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 | 83.3 | ||
Root | \(0.611750 + 0.253395i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.83 |
Dual form | 105.3.k.c.62.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
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 | ||||
\(7\) | 5.49694 | − | 4.33402i | 0.785277 | − | 0.619145i | ||||
\(8\) | −4.94975 | + | 4.94975i | −0.618718 | + | 0.618718i | ||||
\(9\) | −8.95332 | − | 0.915476i | −0.994813 | − | 0.101720i | ||||
\(10\) | −1.13835 | − | 4.86869i | −0.113835 | − | 0.486869i | ||||
\(11\) | − | 13.9031i | − | 1.26392i | −0.775003 | − | 0.631958i | \(-0.782252\pi\) | ||
0.775003 | − | 0.631958i | \(-0.217748\pi\) | |||||||
\(12\) | −8.98832 | − | 0.458333i | −0.749027 | − | 0.0381944i | ||||
\(13\) | −14.6307 | + | 14.6307i | −1.12543 | + | 1.12543i | −0.134524 | + | 0.990910i | \(0.542951\pi\) |
−0.990910 | + | 0.134524i | \(0.957049\pi\) | |||||||
\(14\) | −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 | −0.549413 | − | 0.835551i | \(-0.685149\pi\) |
0.835551 | + | 0.549413i | \(0.185149\pi\) | |||||||
\(18\) | 5.68361 | + | 6.97829i | 0.315756 | + | 0.387683i | ||||
\(19\) | 21.7515 | 1.14481 | 0.572407 | − | 0.819970i | \(-0.306010\pi\) | ||||
0.572407 | + | 0.819970i | \(0.306010\pi\) | |||||||
\(20\) | 7.91326 | − | 12.7429i | 0.395663 | − | 0.637143i | ||||
\(21\) | −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 | \(-0.767357\pi\) |
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 | ||||
\(28\) | −13.0020 | − | 16.4908i | −0.464359 | − | 0.588957i | ||||
\(29\) | 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 | \(-0.910268\pi\) | ||
0.960529 | − | 0.278181i | \(-0.0897315\pi\) | |||||||
\(32\) | 23.3345 | + | 23.3345i | 0.729204 | + | 0.729204i | ||||
\(33\) | −41.6551 | − | 2.12408i | −1.26228 | − | 0.0643660i | ||||
\(34\) | −6.87923 | −0.202330 | ||||||||
\(35\) | 34.7809 | − | 3.90969i | 0.993741 | − | 0.111705i | ||||
\(36\) | −2.74643 | + | 26.8600i | −0.0762897 | + | 0.746110i | ||||
\(37\) | −6.50714 | + | 6.50714i | −0.175869 | + | 0.175869i | −0.789552 | − | 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 | \(-0.394352\pi\) | ||||
0.325844 | + | 0.945424i | \(0.394352\pi\) | |||||||
\(42\) | −3.52576 | + | 20.7019i | −0.0839468 | + | 0.492903i | ||||
\(43\) | 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 | −0.876470 | − | 0.481457i | \(-0.840108\pi\) |
0.481457 | + | 0.876470i | \(0.340108\pi\) | |||||||
\(48\) | −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 | \(0.0808953\pi\) | ||||
−0.967880 | + | 0.251413i | \(0.919105\pi\) | |||||||
\(60\) | −36.9700 | − | 25.6558i | −0.616167 | − | 0.427597i | ||||
\(61\) | − | 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 | ||||
\(63\) | −53.1835 | + | 33.7715i | −0.844183 | + | 0.536056i | ||||
\(64\) | − | 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 | ||||
\(70\) | −27.3584 | − | 21.8293i | −0.390834 | − | 0.311847i | ||||
\(71\) | − | 16.0345i | − | 0.225838i | −0.993604 | − | 0.112919i | \(-0.963980\pi\) | ||
0.993604 | − | 0.112919i | \(-0.0360200\pi\) | |||||||
\(72\) | 48.8480 | − | 39.7853i | 0.678445 | − | 0.552573i | ||||
\(73\) | −57.3597 | + | 57.3597i | −0.785749 | + | 0.785749i | −0.980794 | − | 0.195045i | \(-0.937515\pi\) |
0.195045 | + | 0.980794i | \(0.437515\pi\) | |||||||
\(74\) | 9.20249 | 0.124358 | ||||||||
\(75\) | 68.8312 | − | 29.7869i | 0.917750 | − | 0.397159i | ||||
\(76\) | − | 65.2544i | − | 0.858610i | ||||||
\(77\) | −60.2561 | − | 76.4243i | −0.782547 | − | 0.992523i | ||||
\(78\) | 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 | 0.320974 | − | 0.947088i | \(-0.395990\pi\) |
−0.947088 | + | 0.320974i | \(0.895990\pi\) | |||||||
\(84\) | −51.3947 | + | 36.4361i | −0.611841 | + | 0.433763i | ||||
\(85\) | 33.4929 | − | 7.83095i | 0.394034 | − | 0.0921288i | ||||
\(86\) | − | 46.8879i | − | 0.545208i | ||||||
\(87\) | 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 | \(0.434935\pi\) | ||||
−0.202987 | + | 0.979181i | \(0.565065\pi\) | |||||||
\(90\) | 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 | 0.787775 | − | 0.615963i | \(-0.211233\pi\) |
−0.615963 | + | 0.787775i | \(0.711233\pi\) | |||||||
\(98\) | −41.7760 | + | 25.6079i | −0.426286 | + | 0.261305i | ||||
\(99\) | −12.7279 | + | 124.479i | −0.128565 | + | 1.25736i | ||||
\(100\) | 67.2250 | − | 33.2536i | 0.672250 | − | 0.332536i | ||||
\(101\) | −113.114 | −1.11994 | −0.559968 | − | 0.828514i | \(-0.689187\pi\) | ||||
−0.559968 | + | 0.828514i | \(0.689187\pi\) | |||||||
\(102\) | −1.05099 | + | 20.6109i | −0.0103038 | + | 0.202068i | ||||
\(103\) | 16.1826 | − | 16.1826i | 0.157113 | − | 0.157113i | −0.624173 | − | 0.781286i | \(-0.714564\pi\) |
0.781286 | + | 0.624173i | \(0.214564\pi\) | |||||||
\(104\) | − | 144.836i | − | 1.39265i | ||||||
\(105\) | −6.40009 | − | 104.805i | −0.0609533 | − | 0.998141i | ||||
\(106\) | −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 | ||||
\(112\) | −27.4847 | + | 21.6701i | −0.245399 | + | 0.193483i | ||||
\(113\) | −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 | ||||
\(126\) | 61.4865 | + | 13.7264i | 0.487988 | + | 0.108939i | ||||
\(127\) | −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 | \(-0.598093\pi\) | ||||
−0.303314 | + | 0.952891i | \(0.598093\pi\) | |||||||
\(132\) | −6.37223 | + | 124.965i | −0.0482745 | + | 0.946706i | ||||
\(133\) | 119.566 | − | 94.2712i | 0.898996 | − | 0.708806i | ||||
\(134\) | 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 | \(-0.723561\pi\) | ||||
−0.646003 | + | 0.763335i | \(0.723561\pi\) | |||||||
\(140\) | −11.7291 | − | 104.343i | −0.0837790 | − | 0.745306i | ||||
\(141\) | 52.7881 | + | 58.4609i | 0.374384 | + | 0.414616i | ||||
\(142\) | −11.3381 | + | 11.3381i | −0.0798457 | + | 0.0798457i | ||||
\(143\) | 203.411 | + | 203.411i | 1.42245 | + | 1.42245i | ||||
\(144\) | 44.7666 | + | 4.57738i | 0.310879 | + | 0.0317874i | ||||
\(145\) | 119.125 | + | 73.9763i | 0.821554 | + | 0.510181i | ||||
\(146\) | 81.1188 | 0.555609 | ||||||||
\(147\) | −141.011 | − | 41.5328i | −0.959257 | − | 0.282536i | ||||
\(148\) | 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 | 0.272042 | − | 0.962285i | \(-0.412301\pi\) |
−0.962285 | + | 0.272042i | \(0.912301\pi\) | |||||||
\(158\) | −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 | −0.159365 | − | 0.987220i | \(-0.550945\pi\) |
0.987220 | + | 0.159365i | \(0.0509447\pi\) | |||||||
\(168\) | 144.913 | + | 24.6804i | 0.862579 | + | 0.146907i | ||||
\(169\) | − | 259.112i | − | 1.53321i | ||||||
\(170\) | −29.2203 | − | 18.1457i | −0.171884 | − | 0.106739i | ||||
\(171\) | −194.748 | − | 19.9129i | −1.13888 | − | 0.116450i | ||||
\(172\) | 99.4643 | − | 99.4643i | 0.578281 | − | 0.578281i | ||||
\(173\) | −26.9566 | − | 26.9566i | −0.155818 | − | 0.155818i | 0.624893 | − | 0.780711i | \(-0.285143\pi\) |
−0.780711 | + | 0.624893i | \(0.785143\pi\) | |||||||
\(174\) | −62.4454 | + | 56.3859i | −0.358882 | + | 0.324057i | ||||
\(175\) | 158.049 | + | 75.1367i | 0.903137 | + | 0.429352i | ||||
\(176\) | 69.5153i | 0.394973i | ||||||||
\(177\) | 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 | \(-0.834773\pi\) | ||
0.868277 | − | 0.496079i | \(-0.165227\pi\) | |||||||
\(182\) | 113.736 | − | 89.6745i | 0.624925 | − | 0.492717i | ||||
\(183\) | −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 | ||||
\(189\) | 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 | \(0.909576\pi\) | |||||||
\(192\) | −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 | \(-0.313538\pi\) | ||||
0.552857 | + | 0.833276i | \(0.313538\pi\) | |||||||
\(200\) | −165.781 | − | 56.0500i | −0.828906 | − | 0.280250i | ||||
\(201\) | 92.3473 | + | 102.271i | 0.459439 | + | 0.508812i | ||||
\(202\) | 79.9833 | + | 79.9833i | 0.395957 | + | 0.395957i | ||||
\(203\) | 154.163 | − | 121.548i | 0.759422 | − | 0.598760i | ||||
\(204\) | −45.9518 | + | 41.4929i | −0.225254 | + | 0.203396i | ||||
\(205\) | 113.493 | + | 70.4786i | 0.553624 | + | 0.343798i | ||||
\(206\) | −22.8856 | −0.111095 | ||||||||
\(207\) | 17.4956 | − | 14.2496i | 0.0845197 | − | 0.0688388i | ||||
\(208\) | 73.1533 | − | 73.1533i | 0.351698 | − | 0.351698i | ||||
\(209\) | − | 302.412i | − | 1.44695i | ||||||
\(210\) | −69.5826 | + | 78.6337i | −0.331346 | + | 0.374446i | ||||
\(211\) | 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 | ||||
\(217\) | −74.7497 | − | 94.8069i | −0.344469 | − | 0.436898i | ||||
\(218\) | −2.13142 | + | 2.13142i | −0.00977717 | + | 0.00977717i | ||||
\(219\) | 163.092 | + | 180.619i | 0.744715 | + | 0.824744i | ||||
\(220\) | −177.165 | − | 110.019i | −0.805294 | − | 0.500084i | ||||
\(221\) | 142.337i | 0.644060i | ||||||||
\(222\) | 1.40593 | − | 27.5717i | 0.00633304 | − | 0.124197i | ||||
\(223\) | −173.529 | + | 173.529i | −0.778155 | + | 0.778155i | −0.979517 | − | 0.201362i | \(-0.935463\pi\) |
0.201362 | + | 0.979517i | \(0.435463\pi\) | |||||||
\(224\) | 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 | −0.146140 | − | 0.989264i | \(-0.546685\pi\) |
0.989264 | + | 0.146140i | \(0.0466851\pi\) | |||||||
\(228\) | −195.509 | − | 9.96941i | −0.857496 | − | 0.0437255i | ||||
\(229\) | −123.490 | −0.539259 | −0.269630 | − | 0.962964i | \(-0.586901\pi\) | ||||
−0.269630 | + | 0.962964i | \(0.586901\pi\) | |||||||
\(230\) | 10.6494 | + | 6.61323i | 0.0463017 | + | 0.0287532i | ||||
\(231\) | −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 | \(-0.662049\pi\) |
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 | ||||
\(238\) | −37.8147 | + | 29.8147i | −0.158885 | + | 0.125272i | ||||
\(239\) | 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 | \(0.339021\pi\) | ||||
−0.484445 | + | 0.874822i | \(0.660979\pi\) | |||||||
\(242\) | 51.1204 | + | 51.1204i | 0.211242 | + | 0.211242i | ||||
\(243\) | 61.2344 | − | 235.158i | 0.251993 | − | 0.967729i | ||||
\(244\) | −63.2151 | −0.259078 | ||||||||
\(245\) | 174.244 | − | 172.232i | 0.711200 | − | 0.702990i | ||||
\(246\) | −59.4929 | + | 53.7199i | −0.241841 | + | 0.218374i | ||||
\(247\) | −318.238 | + | 318.238i | −1.28841 | + | 1.28841i | ||||
\(248\) | 85.3694 | + | 85.3694i | 0.344231 | + | 0.344231i | ||||
\(249\) | −163.640 | + | 147.761i | −0.657187 | + | 0.593417i | ||||
\(250\) | 96.4812 | − | 79.4756i | 0.385925 | − | 0.317902i | ||||
\(251\) | 345.514 | 1.37655 | 0.688274 | − | 0.725450i | \(-0.258369\pi\) | ||||
0.688274 | + | 0.725450i | \(0.258369\pi\) | |||||||
\(252\) | 101.315 | + | 159.551i | 0.402042 | + | 0.633137i | ||||
\(253\) | 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 | −0.989206 | − | 0.146530i | \(-0.953190\pi\) |
0.146530 | + | 0.989206i | \(0.453190\pi\) | |||||||
\(258\) | −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 | \(0.225434\pi\) | ||||
−0.759519 | + | 0.650485i | \(0.774566\pi\) | |||||||
\(270\) | 134.602 | − | 10.3632i | 0.498525 | − | 0.0383822i | ||||
\(271\) | − | 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 | ||||
\(273\) | 428.340 | + | 72.9511i | 1.56901 | + | 0.267220i | ||||
\(274\) | 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 | ||||
\(280\) | −152.805 | + | 191.509i | −0.545732 | + | 0.683960i | ||||
\(281\) | − | 142.098i | − | 0.505687i | −0.967507 | − | 0.252844i | \(-0.918634\pi\) | ||
0.967507 | − | 0.252844i | \(-0.0813658\pi\) | |||||||
\(282\) | 4.01128 | − | 78.6649i | 0.0142244 | − | 0.278954i | ||||
\(283\) | 120.235 | − | 120.235i | 0.424858 | − | 0.424858i | −0.462014 | − | 0.886873i | \(-0.652873\pi\) |
0.886873 | + | 0.462014i | \(0.152873\pi\) | |||||||
\(284\) | −48.1035 | −0.169378 | ||||||||
\(285\) | 186.017 | − | 268.050i | 0.652691 | − | 0.940528i | ||||
\(286\) | − | 287.666i | − | 1.00583i | ||||||
\(287\) | 146.874 | − | 115.801i | 0.511755 | − | 0.403489i | ||||
\(288\) | −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 | \(-0.884567\pi\) |
−0.354747 | − | 0.934962i | \(-0.615433\pi\) | |||||||
\(294\) | 70.3415 | + | 129.078i | 0.239257 | + | 0.439040i | ||||
\(295\) | −78.2536 | + | 126.013i | −0.265266 | + | 0.427163i | ||||
\(296\) | − | 64.4174i | − | 0.217626i | ||||||
\(297\) | 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 | 0.844264 | − | 0.535928i | \(-0.180038\pi\) |
−0.535928 | + | 0.844264i | \(0.680038\pi\) | |||||||
\(308\) | −229.273 | + | 180.768i | −0.744392 | + | 0.586910i | ||||
\(309\) | −46.0125 | − | 50.9571i | −0.148908 | − | 0.164910i | ||||
\(310\) | −83.9714 | + | 19.6333i | −0.270876 | + | 0.0633333i | ||||
\(311\) | −221.432 | −0.712001 | −0.356000 | − | 0.934486i | \(-0.615860\pi\) | ||||
−0.356000 | + | 0.934486i | \(0.615860\pi\) | |||||||
\(312\) | −433.944 | − | 22.1277i | −1.39085 | − | 0.0709221i | ||||
\(313\) | −225.950 | + | 225.950i | −0.721885 | + | 0.721885i | −0.968989 | − | 0.247104i | \(-0.920521\pi\) |
0.247104 | + | 0.968989i | \(0.420521\pi\) | |||||||
\(314\) | 153.256i | 0.488076i | ||||||||
\(315\) | −314.984 | + | 3.16355i | −0.999950 | + | 0.0100430i | ||||
\(316\) | −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 | ||||
\(322\) | 13.7816 | − | 10.8660i | 0.0428000 | − | 0.0337453i | ||||
\(323\) | 105.807 | − | 105.807i | 0.327575 | − | 0.327575i | ||||
\(324\) | 49.1793 | − | 237.971i | 0.151788 | − | 0.734480i | ||||
\(325\) | −490.022 | − | 165.675i | −1.50776 | − | 0.509768i | ||||
\(326\) | − | 54.9355i | − | 0.168514i | ||||||
\(327\) | −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 | ||||
\(336\) | 60.7268 | + | 85.6578i | 0.180735 | + | 0.254934i | ||||
\(337\) | 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 | ||||
\(343\) | −143.661 | − | 311.465i | −0.418837 | − | 0.908061i | ||||
\(344\) | −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 | \(-0.356463\pi\) | ||||
0.435807 | + | 0.900040i | \(0.356463\pi\) | |||||||
\(350\) | −58.6279 | − | 164.887i | −0.167508 | − | 0.471106i | ||||
\(351\) | −330.280 | − | 450.565i | −0.940968 | − | 1.28366i | ||||
\(352\) | 324.421 | − | 324.421i | 0.921652 | − | 0.921652i | ||||
\(353\) | −240.264 | − | 240.264i | −0.680635 | − | 0.680635i | 0.279509 | − | 0.960143i | \(-0.409828\pi\) |
−0.960143 | + | 0.279509i | \(0.909828\pi\) | |||||||
\(354\) | −59.6461 | − | 66.0559i | −0.168492 | − | 0.186599i | ||||
\(355\) | 42.2950 | − | 68.1084i | 0.119141 | − | 0.191855i | ||||
\(356\) | 522.883 | 1.46877 | ||||||||
\(357\) | −142.413 | − | 24.2545i | −0.398916 | − | 0.0679399i | ||||
\(358\) | 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 | 0.555904 | − | 0.831247i | \(-0.312372\pi\) |
−0.831247 | + | 0.555904i | \(0.812372\pi\) | |||||||
\(368\) | 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 | ||||
\(378\) | 50.5194 | − | 182.123i | 0.133649 | − | 0.481807i | ||||
\(379\) | 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 | 0.460138 | − | 0.887847i | \(-0.347800\pi\) |
−0.887847 | + | 0.460138i | \(0.847800\pi\) | |||||||
\(384\) | −239.254 | − | 264.965i | −0.623057 | − | 0.690013i | ||||
\(385\) | −54.3566 | − | 483.562i | −0.141186 | − | 1.25600i | ||||
\(386\) | 115.447i | 0.299085i | ||||||||
\(387\) | −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 | ||||||||
\(392\) | 179.255 | + | 292.432i | 0.457283 | + | 0.746001i | ||||
\(393\) | −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 | 0.977391 | − | 0.211440i | \(-0.0678154\pi\) |
−0.211440 | + | 0.977391i | \(0.567815\pi\) | |||||||
\(398\) | −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 | \(0.740996\pi\) | |||||||
\(402\) | 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 | \(-0.361485\pi\) | ||||
0.421552 | + | 0.906804i | \(0.361485\pi\) | |||||||
\(410\) | −30.4157 | − | 130.087i | −0.0741846 | − | 0.317286i | ||||
\(411\) | −23.3952 | + | 21.1250i | −0.0569226 | + | 0.0513991i | ||||
\(412\) | −48.5478 | − | 48.5478i | −0.117834 | − | 0.117834i | ||||
\(413\) | 128.576 | + | 163.076i | 0.311323 | + | 0.394858i | ||||
\(414\) | −22.4473 | − | 2.29523i | −0.0542204 | − | 0.00554403i | ||||
\(415\) | −83.6607 | − | 357.815i | −0.201592 | − | 0.862206i | ||||
\(416\) | −682.799 | −1.64134 | ||||||||
\(417\) | −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 | \(-0.865384\pi\) | ||
0.911899 | − | 0.410414i | \(-0.134616\pi\) | |||||||
\(420\) | −314.414 | + | 19.2003i | −0.748605 | + | 0.0457149i | ||||
\(421\) | 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 | ||||
\(427\) | −91.3251 | − | 115.830i | −0.213876 | − | 0.271264i | ||||
\(428\) | 417.031 | − | 417.031i | 0.974372 | − | 0.974372i | ||||
\(429\) | 640.518 | − | 578.364i | 1.49305 | − | 1.34817i | ||||
\(430\) | 123.679 | − | 199.162i | 0.287625 | − | 0.463167i | ||||
\(431\) | 443.066i | 1.02800i | 0.857791 | + | 0.513998i | \(0.171836\pi\) | ||||
−0.857791 | + | 0.513998i | \(0.828164\pi\) | |||||||
\(432\) | 20.5537 | − | 133.426i | 0.0475779 | − | 0.308857i | ||||
\(433\) | −487.352 | + | 487.352i | −1.12553 | + | 1.12553i | −0.134629 | + | 0.990896i | \(0.542984\pi\) |
−0.990896 | + | 0.134629i | \(0.957016\pi\) | |||||||
\(434\) | −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 | \(-0.444959\pi\) | ||||
0.172056 | + | 0.985087i | \(0.444959\pi\) | |||||||
\(440\) | 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 | \(-0.847019\pi\) |
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 | ||||
\(448\) | −56.3422 | − | 71.4602i | −0.125764 | − | 0.159509i | ||||
\(449\) | 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 | ||||||||
\(455\) | −451.667 | + | 566.069i | −0.992674 | + | 1.24411i | ||||
\(456\) | 306.125 | + | 339.022i | 0.671327 | + | 0.743470i | ||||
\(457\) | −66.2262 | + | 66.2262i | −0.144915 | + | 0.144915i | −0.775842 | − | 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 | \(-0.566614\pi\) | ||||
−0.207750 | + | 0.978182i | \(0.566614\pi\) | |||||||
\(462\) | 287.820 | + | 49.0189i | 0.622987 | + | 0.106102i | ||||
\(463\) | 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 | −0.382536 | − | 0.923941i | \(-0.624949\pi\) |
0.923941 | + | 0.382536i | \(0.124949\pi\) | |||||||
\(468\) | −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 | \(-0.969545\pi\) | ||
0.995426 | − | 0.0955314i | \(-0.0304550\pi\) | |||||||
\(480\) | 487.114 | − | 88.0038i | 1.01482 | − | 0.183341i | ||||
\(481\) | − | 190.408i | − | 0.395858i | ||||||
\(482\) | 298.161 | − | 298.161i | 0.618592 | − | 0.618592i | ||||
\(483\) | 51.9027 | + | 8.83960i | 0.107459 | + | 0.0183015i | ||||
\(484\) | 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 | ||||
\(490\) | −244.996 | − | 1.42238i | −0.499992 | − | 0.00290281i | ||||
\(491\) | − | 518.117i | − | 1.05523i | −0.849484 | − | 0.527614i | \(-0.823087\pi\) | ||
0.849484 | − | 0.527614i | \(-0.176913\pi\) | |||||||
\(492\) | −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 | ||||||||
\(497\) | −69.4937 | − | 88.1406i | −0.139826 | − | 0.177345i | ||||
\(498\) | 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 | 0.694329 | − | 0.719657i | \(-0.255701\pi\) |
−0.719657 | + | 0.694329i | \(0.755701\pi\) | |||||||
\(504\) | 96.0845 | − | 430.405i | 0.190644 | − | 0.853979i | ||||
\(505\) | −480.463 | − | 298.365i | −0.951412 | − | 0.590823i | ||||
\(506\) | − | 34.8570i | − | 0.0688873i | ||||||
\(507\) | −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 | \(-0.794857\pi\) | ||
0.799415 | − | 0.600779i | \(-0.205143\pi\) | |||||||
\(510\) | −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 | ||||
\(518\) | 50.5855 | − | 39.8837i | 0.0976554 | − | 0.0769956i | ||||
\(519\) | −84.8831 | + | 76.6464i | −0.163551 | + | 0.147681i | ||||
\(520\) | 382.042 | − | 615.208i | 0.734695 | − | 1.18309i | ||||
\(521\) | 692.510 | 1.32919 | 0.664597 | − | 0.747202i | \(-0.268603\pi\) | ||||
0.664597 | + | 0.747202i | \(0.268603\pi\) | |||||||
\(522\) | 159.398 | + | 195.708i | 0.305360 | + | 0.374919i | ||||
\(523\) | 583.903 | − | 583.903i | 1.11645 | − | 1.11645i | 0.124191 | − | 0.992258i | \(-0.460366\pi\) |
0.992258 | − | 0.124191i | \(-0.0396337\pi\) | |||||||
\(524\) | 238.405i | 0.454971i | ||||||||
\(525\) | 249.264 | − | 462.053i | 0.474788 | − | 0.880100i | ||||
\(526\) | 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 | ||||
\(532\) | −282.814 | − | 358.699i | −0.531604 | − | 0.674247i | ||||
\(533\) | −390.919 | + | 390.919i | −0.733431 | + | 0.733431i | ||||
\(534\) | −350.425 | − | 388.083i | −0.656227 | − | 0.726748i | ||||
\(535\) | 223.788 | + | 957.138i | 0.418296 | + | 1.78904i | ||||
\(536\) | − | 321.521i | − | 0.599853i | ||||||
\(537\) | −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 | ||||
\(546\) | −251.298 | − | 354.467i | −0.460253 | − | 0.649206i | ||||
\(547\) | 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 | ||||
\(553\) | −328.529 | − | 416.681i | −0.594084 | − | 0.753492i | ||||
\(554\) | −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 | ||||||||
\(560\) | −173.905 | + | 19.5484i | −0.310544 | + | 0.0349079i | ||||
\(561\) | −212.957 | + | 192.293i | −0.379603 | + | 0.342768i | ||||
\(562\) | −100.479 | + | 100.479i | −0.178787 | + | 0.178787i | ||||
\(563\) | 406.434 | + | 406.434i | 0.721907 | + | 0.721907i | 0.968993 | − | 0.247086i | \(-0.0794732\pi\) |
−0.247086 | + | 0.968993i | \(0.579473\pi\) | |||||||
\(564\) | 175.383 | − | 158.364i | 0.310962 | − | 0.280788i | ||||
\(565\) | −551.600 | + | 128.969i | −0.976283 | + | 0.228264i | ||||
\(566\) | −170.038 | −0.300420 | ||||||||
\(567\) | 507.086 | − | 253.679i | 0.894331 | − | 0.447405i | ||||
\(568\) | 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 | 0.451366 | − | 0.892339i | \(-0.350937\pi\) |
−0.892339 | + | 0.451366i | \(0.850937\pi\) | |||||||
\(578\) | 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 | −0.853740 | − | 0.520700i | \(-0.825671\pi\) |
0.520700 | + | 0.853740i | \(0.325671\pi\) | |||||||
\(588\) | −124.599 | + | 423.032i | −0.211902 | + | 0.719442i | ||||
\(589\) | − | 375.152i | − | 0.636931i | ||||||
\(590\) | 144.438 | − | 33.7711i | 0.244811 | − | 0.0572391i | ||||
\(591\) | −521.777 | + | 471.146i | −0.882871 | + | 0.797201i | ||||
\(592\) | 32.5357 | − | 32.5357i | 0.0549590 | − | 0.0549590i | ||||
\(593\) | −181.904 | − | 181.904i | −0.306751 | − | 0.306751i | 0.536897 | − | 0.843648i | \(-0.319597\pi\) |
−0.843648 | + | 0.536897i | \(0.819597\pi\) | |||||||
\(594\) | −221.929 | − | 302.754i | −0.373618 | − | 0.509686i | ||||
\(595\) | 150.169 | − | 188.205i | 0.252384 | − | 0.316311i | ||||
\(596\) | 74.2159i | 0.124523i | ||||||||
\(597\) | 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 | \(-0.616143\pi\) | ||
0.356832 | − | 0.934169i | \(-0.383857\pi\) | |||||||
\(602\) | −203.213 | − | 257.740i | −0.337563 | − | 0.428139i | ||||
\(603\) | 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 | 0.593879 | − | 0.804554i | \(-0.297596\pi\) |
−0.804554 | + | 0.593879i | \(0.797596\pi\) | |||||||
\(608\) | 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 | ||||||
\(612\) | 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 | \(-0.872546\pi\) | ||||
−0.920902 | + | 0.389794i | \(0.872546\pi\) | |||||||
\(620\) | −219.779 | − | 136.482i | −0.354482 | − | 0.220132i | ||||
\(621\) | −40.0205 | − | 54.5957i | −0.0644453 | − | 0.0879157i | ||||
\(622\) | 156.576 | + | 156.576i | 0.251730 | + | 0.251730i | ||||
\(623\) | 755.394 | + | 958.085i | 1.21251 | + | 1.53786i | ||||
\(624\) | −207.999 | − | 230.351i | −0.333331 | − | 0.369153i | ||||
\(625\) | −379.267 | + | 496.771i | −0.606827 | + | 0.794834i | ||||
\(626\) | 319.542 | 0.510450 | ||||||||
\(627\) | −906.059 | − | 46.2018i | −1.44507 | − | 0.0736870i | ||||
\(628\) | −325.105 | + | 325.105i | −0.517683 | + | 0.517683i | ||||
\(629\) | 63.3061i | 0.100646i | ||||||||
\(630\) | 224.964 | + | 220.490i | 0.357086 | + | 0.349985i | ||||
\(631\) | −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 | ||||
\(637\) | 529.849 | + | 864.382i | 0.831788 | + | 1.35696i | ||||
\(638\) | −275.711 | + | 275.711i | −0.432149 | + | 0.432149i | ||||
\(639\) | −14.6792 | + | 143.562i | −0.0229721 | + | 0.224666i | ||||
\(640\) | 579.374 | − | 135.463i | 0.905272 | − | 0.211661i | ||||
\(641\) | − | 187.134i | − | 0.291941i | −0.989289 | − | 0.145970i | \(-0.953370\pi\) | ||
0.989289 | − | 0.145970i | \(-0.0466304\pi\) | |||||||
\(642\) | −589.006 | − | 30.0346i | −0.917455 | − | 0.0467829i | ||||
\(643\) | 767.988 | − | 767.988i | 1.19438 | − | 1.19438i | 0.218559 | − | 0.975824i | \(-0.429864\pi\) |
0.975824 | − | 0.218559i | \(-0.0701356\pi\) | |||||||
\(644\) | 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 | −0.107654 | − | 0.994188i | \(-0.534334\pi\) |
0.994188 | + | 0.107654i | \(0.0343337\pi\) | |||||||
\(648\) | −473.774 | + | 311.491i | −0.731133 | + | 0.480696i | ||||
\(649\) | 412.459 | 0.635530 | ||||||||
\(650\) | 229.348 | + | 463.648i | 0.352844 | + | 0.713304i | ||||
\(651\) | −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 | \(-0.700721\pi\) |
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 | ||||
\(658\) | 144.326 | − | 113.793i | 0.219340 | − | 0.172937i | ||||
\(659\) | 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 | \(-0.977146\pi\) | ||
0.997424 | − | 0.0717364i | \(-0.0228540\pi\) | |||||||
\(662\) | −123.754 | − | 123.754i | −0.186939 | − | 0.186939i | ||||
\(663\) | 426.458 | + | 21.7459i | 0.643224 | + | 0.0327993i | ||||
\(664\) | 514.452 | 0.774777 | ||||||||
\(665\) | 756.537 | − | 85.0414i | 1.13765 | − | 0.127882i | ||||
\(666\) | −82.3928 | − | 8.42466i | −0.123713 | − | 0.0126496i | ||||
\(667\) | −49.7191 | + | 49.7191i | −0.0745413 | + | 0.0745413i | ||||
\(668\) | −414.755 | − | 414.755i | −0.620891 | − | 0.620891i | ||||
\(669\) | 493.399 | + | 546.421i | 0.737517 | + | 0.816773i | ||||
\(670\) | 195.100 | + | 121.156i | 0.291194 | + | 0.180830i | ||||
\(671\) | −292.961 | −0.436604 | ||||||||
\(672\) | 116.350 | − | 683.163i | 0.173140 | − | 1.01661i | ||||
\(673\) | −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 | −0.294714 | − | 0.955586i | \(-0.595224\pi\) |
0.955586 | + | 0.294714i | \(0.0952243\pi\) | |||||||
\(678\) | 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 | \(0.0479031\pi\) | ||||
−0.988697 | + | 0.149925i | \(0.952097\pi\) | |||||||
\(692\) | −80.8697 | + | 80.8697i | −0.116864 | + | 0.116864i | ||||
\(693\) | 469.527 | + | 739.414i | 0.677529 | + | 1.06698i | ||||
\(694\) | 379.857i | 0.547345i | ||||||||
\(695\) | −762.825 | − | 473.711i | −1.09759 | − | 0.681599i | ||||
\(696\) | 394.702 | + | 437.118i | 0.567100 | + | 0.628043i | ||||
\(697\) | 129.971 | − | 129.971i | 0.186473 | − | 0.186473i | ||||
\(698\) | −215.097 | − | 215.097i | −0.308162 | − | 0.308162i | ||||
\(699\) | −255.592 | − | 283.059i | −0.365654 | − | 0.404948i | ||||
\(700\) | 225.410 | − | 474.147i | 0.322014 | − | 0.677353i | ||||
\(701\) | 8.12497i | 0.0115905i | 0.999983 | + | 0.00579527i | \(0.00184470\pi\) | ||||
−0.999983 | + | 0.00579527i | \(0.998155\pi\) | |||||||
\(702\) | −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 | ||||||||
\(707\) | −621.778 | + | 490.236i | −0.879459 | + | 0.693403i | ||||
\(708\) | 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 | ||||
\(714\) | 83.5508 | + | 117.852i | 0.117018 | + | 0.165059i | ||||
\(715\) | 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 | \(-0.670664\pi\) | ||
0.510837 | − | 0.859678i | \(-0.329336\pi\) | |||||||
\(720\) | 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 | 0.119351 | − | 0.992852i | \(-0.461919\pi\) |
−0.992852 | + | 0.119351i | \(0.961919\pi\) | |||||||
\(728\) | −627.722 | − | 796.155i | −0.862255 | − | 1.09362i | ||||
\(729\) | −695.204 | − | 219.392i | −0.953640 | − | 0.300949i | ||||
\(730\) | 344.562 | + | 213.971i | 0.472003 | + | 0.293112i | ||||
\(731\) | 322.553 | 0.441249 | ||||||||
\(732\) | −9.65785 | + | 189.399i | −0.0131938 | + | 0.258742i | ||||
\(733\) | −174.851 | + | 174.851i | −0.238542 | + | 0.238542i | −0.816246 | − | 0.577704i | \(-0.803949\pi\) |
0.577704 | + | 0.816246i | \(0.303949\pi\) | |||||||
\(734\) | 142.908i | 0.194697i | ||||||||
\(735\) | −489.406 | − | 548.367i | −0.665859 | − | 0.746078i | ||||
\(736\) | −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 | ||||
\(742\) | −375.493 | + | 296.055i | −0.506055 | + | 0.398995i | ||||
\(743\) | 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 | ||||
\(756\) | 493.509 | − | 279.173i | 0.652790 | − | 0.369277i | ||||
\(757\) | 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 | \(-0.654695\pi\) | ||||
−0.467084 | + | 0.884213i | \(0.654695\pi\) | |||||||
\(762\) | 15.4802 | − | 303.581i | 0.0203152 | − | 0.398400i | ||||
\(763\) | −13.0640 | − | 16.5694i | −0.0171219 | − | 0.0217161i | ||||
\(764\) | 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 | \(-0.551606\pi\) | ||||
−0.161417 | + | 0.986886i | \(0.551606\pi\) | |||||||
\(770\) | −303.494 | + | 380.366i | −0.394148 | + | 0.493982i | ||||
\(771\) | 615.774 | + | 681.947i | 0.798669 | + | 0.884497i | ||||
\(772\) | −244.900 | + | 244.900i | −0.317228 | + | 0.317228i | ||||
\(773\) | −307.323 | − | 307.323i | −0.397572 | − | 0.397572i | 0.479804 | − | 0.877376i | \(-0.340708\pi\) |
−0.877376 | + | 0.479804i | \(0.840708\pi\) | |||||||
\(774\) | −42.9248 | + | 419.802i | −0.0554583 | + | 0.542380i | ||||
\(775\) | 386.481 | − | 191.177i | 0.498686 | − | 0.246680i | ||||
\(776\) | −164.983 | −0.212606 | ||||||||
\(777\) | 190.509 | + | 32.4458i | 0.245186 | + | 0.0417578i | ||||
\(778\) | −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 | 0.820766 | − | 0.571265i | \(-0.193547\pi\) |
−0.571265 | + | 0.820766i | \(0.693547\pi\) | |||||||
\(788\) | −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 | \(0.564792\pi\) |
−0.979355 | + | 0.202147i | \(0.935208\pi\) | |||||||
\(798\) | −76.6905 | + | 450.297i | −0.0961034 | + | 0.564282i | ||||
\(799\) | 180.619i | 0.226056i | ||||||||
\(800\) | −264.236 | + | 781.540i | −0.330295 | + | 0.976925i | ||||
\(801\) | 159.562 | − | 1560.51i | 0.199204 | − | 1.94821i | ||||
\(802\) | 412.181 | − | 412.181i | 0.513941 | − | 0.513941i | ||||
\(803\) | 797.475 | + | 797.475i | 0.993120 | + | 0.993120i | ||||
\(804\) | 306.814 | − | 277.042i | 0.381609 | − | 0.344579i | ||||
\(805\) | −54.7292 | + | 68.5915i | −0.0679865 | + | 0.0852068i | ||||
\(806\) | − | 356.860i | − | 0.442754i | ||||||
\(807\) | 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 | \(0.290873\pi\) | ||||
−0.610738 | + | 0.791833i | \(0.709127\pi\) | |||||||
\(812\) | −364.645 | − | 462.488i | −0.449070 | − | 0.569567i | ||||
\(813\) | −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 | ||||
\(819\) | 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 | \(-0.158065\pi\) | |||||||
\(822\) | 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 | \(-0.190581\pi\) | ||||
0.826054 | + | 0.563591i | \(0.190581\pi\) | |||||||
\(830\) | −193.857 | + | 312.171i | −0.233562 | + | 0.376109i | ||||
\(831\) | −377.642 | − | 418.224i | −0.454442 | − | 0.503278i | ||||
\(832\) | 190.198 | + | 190.198i | 0.228604 | + | 0.228604i | ||||
\(833\) | −176.162 | − | 287.387i | −0.211480 | − | 0.345002i | ||||
\(834\) | 399.872 | − | 361.070i | 0.479463 | − | 0.432938i | ||||
\(835\) | 951.914 | − | 222.567i | 1.14002 | − | 0.266547i | ||||
\(836\) | −907.236 | −1.08521 | ||||||||
\(837\) | 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 | \(0.183690\pi\) | ||||
−0.838059 | + | 0.545580i | \(0.816310\pi\) | |||||||
\(840\) | 550.436 | + | 487.078i | 0.655281 | + | 0.579855i | ||||
\(841\) | −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 | ||||
\(847\) | −397.402 | + | 313.329i | −0.469188 | + | 0.369928i | ||||
\(848\) | −241.511 | + | 241.511i | −0.284800 | + | 0.284800i | ||||
\(849\) | −341.868 | − | 378.606i | −0.402671 | − | 0.445943i | ||||
\(850\) | −76.2530 | − | 154.152i | −0.0897094 | − | 0.181355i | ||||
\(851\) | − | 23.0720i | − | 0.0271116i | ||||||
\(852\) | −7.34913 | + | 144.123i | −0.00862574 | + | 0.169159i | ||||
\(853\) | −286.958 | + | 286.958i | −0.336411 | + | 0.336411i | −0.855015 | − | 0.518604i | \(-0.826452\pi\) |
0.518604 | + | 0.855015i | \(0.326452\pi\) | |||||||
\(854\) | −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 | −0.965741 | − | 0.259509i | \(-0.916439\pi\) |
0.259509 | + | 0.965741i | \(0.416439\pi\) | |||||||
\(858\) | −861.880 | − | 43.9490i | −1.00452 | − | 0.0512226i | ||||
\(859\) | −1440.15 | −1.67654 | −0.838272 | − | 0.545253i | \(-0.816434\pi\) | ||||
−0.838272 | + | 0.545253i | \(0.816434\pi\) | |||||||
\(860\) | 684.848 | − | 160.124i | 0.796335 | − | 0.186191i | ||||
\(861\) | −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 | \(-0.535483\pi\) |
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 | ||||
\(868\) | −284.421 | + | 224.249i | −0.327674 | + | 0.258352i | ||||
\(869\) | −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 | ||||||||
\(875\) | 473.140 | + | 736.046i | 0.540731 | + | 0.841195i | ||||
\(876\) | 541.857 | − | 489.277i | 0.618558 | − | 0.558536i | ||||
\(877\) | −21.5786 | + | 21.5786i | −0.0246050 | + | 0.0246050i | −0.719302 | − | 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 | \(-0.548807\pi\) | ||||
−0.152732 | + | 0.988268i | \(0.548807\pi\) | |||||||
\(882\) | 397.478 | − | 191.030i | 0.450655 | − | 0.216588i | ||||
\(883\) | 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 | −0.882656 | − | 0.470020i | \(-0.844247\pi\) |
0.470020 | + | 0.882656i | \(0.344247\pi\) | |||||||
\(888\) | −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 | ||||
\(903\) | 165.316 | − | 970.669i | 0.183074 | − | 1.07494i | ||||
\(904\) | − | 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 | ||||
\(910\) | 719.648 | − | 80.8948i | 0.790822 | − | 0.0888954i | ||||
\(911\) | 1604.19i | 1.76091i | 0.474126 | + | 0.880457i | \(0.342764\pi\) | ||||
−0.474126 | + | 0.880457i | \(0.657236\pi\) | |||||||
\(912\) | −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 | ||||||||
\(917\) | −436.832 | + | 344.417i | −0.476371 | + | 0.375591i | ||||
\(918\) | 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 | ||||
\(924\) | 506.574 | + | 714.543i | 0.548240 | + | 0.773315i | ||||
\(925\) | −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 | \(0.159337\pi\) | ||||
−0.877308 | + | 0.479927i | \(0.840663\pi\) | |||||||
\(930\) | 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 | 0.398652 | − | 0.917102i | \(-0.369478\pi\) |
−0.917102 | + | 0.398652i | \(0.869478\pi\) | |||||||
\(938\) | 252.483 | − | 199.068i | 0.269172 | − | 0.212226i | ||||
\(939\) | 642.450 | + | 711.490i | 0.684186 | + | 0.757711i | ||||
\(940\) | 89.6643 | + | 383.493i | 0.0953876 | + | 0.407971i | ||||
\(941\) | 1356.29 | 1.44133 | 0.720665 | − | 0.693284i | \(-0.243837\pi\) | ||||
0.720665 | + | 0.693284i | \(0.243837\pi\) | |||||||
\(942\) | 459.171 | + | 23.4141i | 0.487443 | + | 0.0248557i | ||||
\(943\) | −47.3683 | + | 47.3683i | −0.0502314 | + | 0.0502314i | ||||
\(944\) | − | 148.334i | − | 0.157133i | ||||||
\(945\) | −38.6442 | + | 944.210i | −0.0408933 | + | 0.999164i | ||||
\(946\) | −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 | ||||
\(952\) | 208.703 | + | 264.703i | 0.219226 | + | 0.278049i | ||||
\(953\) | −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 | ||||
\(966\) | −30.4502 | − | 42.9513i | −0.0315219 | − | 0.0444630i | ||||
\(967\) | −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 | \(-0.560454\pi\) | ||||
−0.188783 | + | 0.982019i | \(0.560454\pi\) | |||||||
\(972\) | −705.474 | − | 183.703i | −0.725797 | − | 0.188995i | ||||
\(973\) | −987.189 | + | 778.341i | −1.01458 | + | 0.799939i | ||||
\(974\) | −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 | ||||||||
\(980\) | −516.697 | − | 522.732i | −0.527242 | − | 0.533400i | ||||
\(981\) | −2.75951 | + | 26.9879i | −0.00281295 | + | 0.0275106i | ||||
\(982\) | −366.364 | + | 366.364i | −0.373080 | + | 0.373080i | ||||
\(983\) | −618.375 | − | 618.375i | −0.629069 | − | 0.629069i | 0.318765 | − | 0.947834i | \(-0.396732\pi\) |
−0.947834 | + | 0.318765i | \(0.896732\pi\) | |||||||
\(984\) | 376.039 | + | 416.450i | 0.382154 | + | 0.423222i | ||||
\(985\) | −266.758 | − | 1140.92i | −0.270820 | − | 1.15829i | ||||
\(986\) | −192.929 | −0.195669 | ||||||||
\(987\) | 543.543 | + | 92.5714i | 0.550702 | + | 0.0937907i | ||||
\(988\) | 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 | 0.748986 | − | 0.662585i | \(-0.230541\pi\) |
−0.662585 | + | 0.748986i | \(0.730541\pi\) | |||||||
\(998\) | −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.83.3 | yes | 16 | |
3.2 | odd | 2 | inner | 105.3.k.c.83.8 | yes | 16 | |
5.2 | odd | 4 | inner | 105.3.k.c.62.5 | yes | 16 | |
7.6 | odd | 2 | inner | 105.3.k.c.83.2 | yes | 16 | |
15.2 | even | 4 | inner | 105.3.k.c.62.2 | ✓ | 16 | |
21.20 | even | 2 | inner | 105.3.k.c.83.5 | yes | 16 | |
35.27 | even | 4 | inner | 105.3.k.c.62.8 | yes | 16 | |
105.62 | odd | 4 | inner | 105.3.k.c.62.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.c.62.2 | ✓ | 16 | 15.2 | even | 4 | inner | |
105.3.k.c.62.3 | yes | 16 | 105.62 | odd | 4 | inner | |
105.3.k.c.62.5 | yes | 16 | 5.2 | odd | 4 | inner | |
105.3.k.c.62.8 | yes | 16 | 35.27 | even | 4 | inner | |
105.3.k.c.83.2 | yes | 16 | 7.6 | odd | 2 | inner | |
105.3.k.c.83.3 | yes | 16 | 1.1 | even | 1 | trivial | |
105.3.k.c.83.5 | yes | 16 | 21.20 | even | 2 | inner | |
105.3.k.c.83.8 | yes | 16 | 3.2 | odd | 2 | inner |