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 | 83.7 | ||
Root | \(-0.253395 + 0.611750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.83 |
Dual form | 105.3.k.c.62.7 |
$q$-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 | 0.861430 | − | 0.507877i | \(-0.169569\pi\) |
−0.507877 | + | 0.861430i | \(0.669569\pi\) | |||||||
\(3\) | 0.854662 | + | 2.87568i | 0.284887 | + | 0.958561i | ||||
\(4\) | − | 3.00000i | − | 0.750000i | ||||||
\(5\) | 4.57796 | − | 2.01054i | 0.915592 | − | 0.402108i | ||||
\(6\) | −1.42908 | + | 2.63775i | −0.238180 | + | 0.439625i | ||||
\(7\) | 3.94887 | + | 5.77983i | 0.564125 | + | 0.825689i | ||||
\(8\) | 4.94975 | − | 4.94975i | 0.618718 | − | 0.618718i | ||||
\(9\) | −7.53910 | + | 4.91548i | −0.837678 | + | 0.546164i | ||||
\(10\) | 4.65877 | + | 1.81544i | 0.465877 | + | 0.181544i | ||||
\(11\) | − | 2.58936i | − | 0.235396i | −0.993049 | − | 0.117698i | \(-0.962449\pi\) | ||
0.993049 | − | 0.117698i | \(-0.0375515\pi\) | |||||||
\(12\) | 8.62705 | − | 2.56399i | 0.718921 | − | 0.213666i | ||||
\(13\) | −8.94114 | + | 8.94114i | −0.687780 | + | 0.687780i | −0.961741 | − | 0.273961i | \(-0.911666\pi\) |
0.273961 | + | 0.961741i | \(0.411666\pi\) | |||||||
\(14\) | −1.29468 | + | 6.87923i | −0.0924770 | + | 0.491374i | ||||
\(15\) | 9.69428 | + | 11.4464i | 0.646285 | + | 0.763096i | ||||
\(16\) | −5.00000 | −0.312500 | ||||||||
\(17\) | −0.581460 | + | 0.581460i | −0.0342036 | + | 0.0342036i | −0.724002 | − | 0.689798i | \(-0.757699\pi\) |
0.689798 | + | 0.724002i | \(0.257699\pi\) | |||||||
\(18\) | −8.80672 | − | 1.85519i | −0.489262 | − | 0.103066i | ||||
\(19\) | −16.5793 | −0.872596 | −0.436298 | − | 0.899802i | \(-0.643711\pi\) | ||||
−0.436298 | + | 0.899802i | \(0.643711\pi\) | |||||||
\(20\) | −6.03161 | − | 13.7339i | −0.301581 | − | 0.686694i | ||||
\(21\) | −13.2460 | + | 16.2955i | −0.630762 | + | 0.775977i | ||||
\(22\) | 1.83095 | − | 1.83095i | 0.0832251 | − | 0.0832251i | ||||
\(23\) | 26.5115 | − | 26.5115i | 1.15267 | − | 1.15267i | 0.166657 | − | 0.986015i | \(-0.446703\pi\) |
0.986015 | − | 0.166657i | \(-0.0532972\pi\) | |||||||
\(24\) | 18.4643 | + | 10.0035i | 0.769344 | + | 0.416814i | ||||
\(25\) | 16.9155 | − | 18.4083i | 0.676619 | − | 0.736333i | ||||
\(26\) | −12.6447 | −0.486334 | ||||||||
\(27\) | −20.5787 | − | 17.4790i | −0.762176 | − | 0.647370i | ||||
\(28\) | 17.3395 | − | 11.8466i | 0.619267 | − | 0.423094i | ||||
\(29\) | −11.5528 | −0.398372 | −0.199186 | − | 0.979962i | \(-0.563830\pi\) | ||||
−0.199186 | + | 0.979962i | \(0.563830\pi\) | |||||||
\(30\) | −1.23896 | + | 14.9487i | −0.0412987 | + | 0.498291i | ||||
\(31\) | − | 30.8307i | − | 0.994539i | −0.867596 | − | 0.497270i | \(-0.834336\pi\) | ||
0.867596 | − | 0.497270i | \(-0.165664\pi\) | |||||||
\(32\) | −23.3345 | − | 23.3345i | −0.729204 | − | 0.729204i | ||||
\(33\) | 7.44617 | − | 2.21303i | 0.225642 | − | 0.0670614i | ||||
\(34\) | −0.822309 | −0.0241856 | ||||||||
\(35\) | 29.6984 | + | 18.5205i | 0.848524 | + | 0.529156i | ||||
\(36\) | 14.7464 | + | 22.6173i | 0.409623 | + | 0.628259i | ||||
\(37\) | −41.4929 | + | 41.4929i | −1.12143 | + | 1.12143i | −0.129902 | + | 0.991527i | \(0.541466\pi\) |
−0.991527 | + | 0.129902i | \(0.958534\pi\) | |||||||
\(38\) | −11.7233 | − | 11.7233i | −0.308509 | − | 0.308509i | ||||
\(39\) | −33.3536 | − | 18.0702i | −0.855219 | − | 0.463339i | ||||
\(40\) | 12.7081 | − | 32.6114i | 0.317703 | − | 0.815285i | ||||
\(41\) | 17.1489 | 0.418267 | 0.209133 | − | 0.977887i | \(-0.432936\pi\) | ||||
0.209133 | + | 0.977887i | \(0.432936\pi\) | |||||||
\(42\) | −20.8890 | + | 2.15633i | −0.497357 | + | 0.0513413i | ||||
\(43\) | −25.1548 | − | 25.1548i | −0.584994 | − | 0.584994i | 0.351277 | − | 0.936272i | \(-0.385748\pi\) |
−0.936272 | + | 0.351277i | \(0.885748\pi\) | |||||||
\(44\) | −7.76807 | −0.176547 | ||||||||
\(45\) | −24.6310 | + | 37.6605i | −0.547355 | + | 0.836900i | ||||
\(46\) | 37.4929 | 0.815062 | ||||||||
\(47\) | −45.2473 | + | 45.2473i | −0.962709 | + | 0.962709i | −0.999329 | − | 0.0366205i | \(-0.988341\pi\) |
0.0366205 | + | 0.999329i | \(0.488341\pi\) | |||||||
\(48\) | −4.27331 | − | 14.3784i | −0.0890273 | − | 0.299550i | ||||
\(49\) | −17.8128 | + | 45.6476i | −0.363526 | + | 0.931584i | ||||
\(50\) | 24.9777 | − | 1.05561i | 0.499554 | − | 0.0211122i | ||||
\(51\) | −2.16905 | − | 1.17514i | −0.0425304 | − | 0.0230420i | ||||
\(52\) | 26.8234 | + | 26.8234i | 0.515835 | + | 0.515835i | ||||
\(53\) | 34.1600 | − | 34.1600i | 0.644528 | − | 0.644528i | −0.307137 | − | 0.951665i | \(-0.599371\pi\) |
0.951665 | + | 0.307137i | \(0.0993710\pi\) | |||||||
\(54\) | −2.19185 | − | 26.9109i | −0.0405897 | − | 0.498350i | ||||
\(55\) | −5.20600 | − | 11.8540i | −0.0946545 | − | 0.215527i | ||||
\(56\) | 48.1546 | + | 9.06275i | 0.859904 | + | 0.161835i | ||||
\(57\) | −14.1697 | − | 47.6769i | −0.248592 | − | 0.836436i | ||||
\(58\) | −8.16905 | − | 8.16905i | −0.140846 | − | 0.140846i | ||||
\(59\) | − | 47.6223i | − | 0.807158i | −0.914945 | − | 0.403579i | \(-0.867766\pi\) | ||
0.914945 | − | 0.403579i | \(-0.132234\pi\) | |||||||
\(60\) | 34.3393 | − | 29.0828i | 0.572322 | − | 0.484714i | ||||
\(61\) | 78.9936i | 1.29498i | 0.762075 | + | 0.647488i | \(0.224181\pi\) | ||||
−0.762075 | + | 0.647488i | \(0.775819\pi\) | |||||||
\(62\) | 21.8006 | − | 21.8006i | 0.351623 | − | 0.351623i | ||||
\(63\) | −58.1816 | − | 24.1641i | −0.923517 | − | 0.383557i | ||||
\(64\) | − | 13.0000i | − | 0.203125i | ||||||
\(65\) | −22.9557 | + | 58.9087i | −0.353165 | + | 0.906288i | ||||
\(66\) | 6.83008 | + | 3.70039i | 0.103486 | + | 0.0560665i | ||||
\(67\) | 72.4786 | − | 72.4786i | 1.08177 | − | 1.08177i | 0.0854251 | − | 0.996345i | \(-0.472775\pi\) |
0.996345 | − | 0.0854251i | \(-0.0272248\pi\) | |||||||
\(68\) | 1.74438 | + | 1.74438i | 0.0256527 | + | 0.0256527i | ||||
\(69\) | 98.8969 | + | 53.5802i | 1.43329 | + | 0.776524i | ||||
\(70\) | 7.90396 | + | 34.0959i | 0.112914 | + | 0.487084i | ||||
\(71\) | 49.0193i | 0.690413i | 0.938527 | + | 0.345207i | \(0.112191\pi\) | ||||
−0.938527 | + | 0.345207i | \(0.887809\pi\) | |||||||
\(72\) | −12.9863 | + | 61.6470i | −0.180365 | + | 0.856209i | ||||
\(73\) | −26.0359 | + | 26.0359i | −0.356656 | + | 0.356656i | −0.862579 | − | 0.505923i | \(-0.831152\pi\) |
0.505923 | + | 0.862579i | \(0.331152\pi\) | |||||||
\(74\) | −58.6798 | −0.792970 | ||||||||
\(75\) | 67.3935 | + | 32.9106i | 0.898581 | + | 0.438808i | ||||
\(76\) | 49.7380i | 0.654447i | ||||||||
\(77\) | 14.9660 | − | 10.2250i | 0.194364 | − | 0.132793i | ||||
\(78\) | −10.8069 | − | 36.3621i | −0.138550 | − | 0.466181i | ||||
\(79\) | 75.8024i | 0.959524i | 0.877399 | + | 0.479762i | \(0.159277\pi\) | ||||
−0.877399 | + | 0.479762i | \(0.840723\pi\) | |||||||
\(80\) | −22.8898 | + | 10.0527i | −0.286123 | + | 0.125659i | ||||
\(81\) | 32.6762 | − | 74.1166i | 0.403410 | − | 0.915019i | ||||
\(82\) | 12.1261 | + | 12.1261i | 0.147880 | + | 0.147880i | ||||
\(83\) | 53.6785 | + | 53.6785i | 0.646729 | + | 0.646729i | 0.952201 | − | 0.305472i | \(-0.0988143\pi\) |
−0.305472 | + | 0.952201i | \(0.598814\pi\) | |||||||
\(84\) | 48.8865 | + | 39.7380i | 0.581983 | + | 0.473071i | ||||
\(85\) | −1.49286 | + | 3.83095i | −0.0175630 | + | 0.0450700i | ||||
\(86\) | − | 35.5742i | − | 0.413654i | ||||||
\(87\) | −9.87373 | − | 33.2221i | −0.113491 | − | 0.381864i | ||||
\(88\) | −12.8167 | − | 12.8167i | −0.145644 | − | 0.145644i | ||||
\(89\) | − | 14.0533i | − | 0.157903i | −0.996878 | − | 0.0789514i | \(-0.974843\pi\) | ||
0.996878 | − | 0.0789514i | \(-0.0251572\pi\) | |||||||
\(90\) | −44.0467 | + | 9.21327i | −0.489408 | + | 0.102370i | ||||
\(91\) | −86.9857 | − | 16.3708i | −0.955887 | − | 0.179899i | ||||
\(92\) | −79.5344 | − | 79.5344i | −0.864504 | − | 0.864504i | ||||
\(93\) | 88.6594 | − | 26.3499i | 0.953327 | − | 0.283332i | ||||
\(94\) | −63.9894 | −0.680738 | ||||||||
\(95\) | −75.8995 | + | 33.3333i | −0.798942 | + | 0.350877i | ||||
\(96\) | 47.1596 | − | 87.0458i | 0.491245 | − | 0.906727i | ||||
\(97\) | 25.9664 | + | 25.9664i | 0.267695 | + | 0.267695i | 0.828171 | − | 0.560476i | \(-0.189382\pi\) |
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(98\) | −44.8733 | + | 19.6822i | −0.457891 | + | 0.200839i | ||||
\(99\) | 12.7279 | + | 19.5214i | 0.128565 | + | 0.197186i | ||||
\(100\) | −55.2250 | − | 50.7464i | −0.552250 | − | 0.507464i | ||||
\(101\) | 23.6924 | 0.234579 | 0.117289 | − | 0.993098i | \(-0.462580\pi\) | ||||
0.117289 | + | 0.993098i | \(0.462580\pi\) | |||||||
\(102\) | −0.702797 | − | 2.36470i | −0.00689016 | − | 0.0231833i | ||||
\(103\) | 78.6519 | − | 78.6519i | 0.763611 | − | 0.763611i | −0.213362 | − | 0.976973i | \(-0.568441\pi\) |
0.976973 | + | 0.213362i | \(0.0684415\pi\) | |||||||
\(104\) | 88.5128i | 0.851085i | ||||||||
\(105\) | −27.8769 | + | 101.232i | −0.265494 | + | 0.964112i | ||||
\(106\) | 48.3095 | 0.455750 | ||||||||
\(107\) | 124.868 | + | 124.868i | 1.16699 | + | 1.16699i | 0.982911 | + | 0.184083i | \(0.0589315\pi\) |
0.184083 | + | 0.982911i | \(0.441069\pi\) | |||||||
\(108\) | −52.4370 | + | 61.7362i | −0.485528 | + | 0.571632i | ||||
\(109\) | − | 72.9857i | − | 0.669594i | −0.942290 | − | 0.334797i | \(-0.891332\pi\) | ||
0.942290 | − | 0.334797i | \(-0.108668\pi\) | |||||||
\(110\) | 4.70083 | − | 12.0632i | 0.0427348 | − | 0.109666i | ||||
\(111\) | −154.783 | − | 83.8579i | −1.39444 | − | 0.755477i | ||||
\(112\) | −19.7444 | − | 28.8991i | −0.176289 | − | 0.258028i | ||||
\(113\) | −51.8276 | + | 51.8276i | −0.458651 | + | 0.458651i | −0.898212 | − | 0.439562i | \(-0.855134\pi\) |
0.439562 | + | 0.898212i | \(0.355134\pi\) | |||||||
\(114\) | 23.6931 | − | 43.7321i | 0.207834 | − | 0.383615i | ||||
\(115\) | 68.0662 | − | 174.671i | 0.591880 | − | 1.51888i | ||||
\(116\) | 34.6583i | 0.298779i | ||||||||
\(117\) | 23.4582 | − | 111.358i | 0.200498 | − | 0.951779i | ||||
\(118\) | 33.6740 | − | 33.6740i | 0.285373 | − | 0.285373i | ||||
\(119\) | −5.65685 | − | 1.06463i | −0.0475366 | − | 0.00894644i | ||||
\(120\) | 104.641 | + | 8.67273i | 0.872010 | + | 0.0722727i | ||||
\(121\) | 114.295 | 0.944589 | ||||||||
\(122\) | −55.8569 | + | 55.8569i | −0.457843 | + | 0.457843i | ||||
\(123\) | 14.6565 | + | 49.3149i | 0.119159 | + | 0.400934i | ||||
\(124\) | −92.4922 | −0.745905 | ||||||||
\(125\) | 40.4278 | − | 118.282i | 0.323422 | − | 0.946255i | ||||
\(126\) | −24.0540 | − | 58.2272i | −0.190905 | − | 0.462121i | ||||
\(127\) | 21.6476 | − | 21.6476i | 0.170454 | − | 0.170454i | −0.616725 | − | 0.787179i | \(-0.711541\pi\) |
0.787179 | + | 0.616725i | \(0.211541\pi\) | |||||||
\(128\) | −84.1457 | + | 84.1457i | −0.657388 | + | 0.657388i | ||||
\(129\) | 50.8383 | − | 93.8359i | 0.394095 | − | 0.727410i | ||||
\(130\) | −57.8869 | + | 25.4226i | −0.445284 | + | 0.195559i | ||||
\(131\) | −217.662 | −1.66154 | −0.830771 | − | 0.556614i | \(-0.812100\pi\) | ||||
−0.830771 | + | 0.556614i | \(0.812100\pi\) | |||||||
\(132\) | −6.63908 | − | 22.3385i | −0.0502960 | − | 0.169231i | ||||
\(133\) | −65.4696 | − | 95.8256i | −0.492253 | − | 0.720493i | ||||
\(134\) | 102.500 | 0.764927 | ||||||||
\(135\) | −129.351 | − | 38.6439i | −0.958155 | − | 0.286251i | ||||
\(136\) | 5.75616i | 0.0423247i | ||||||||
\(137\) | 32.1683 | + | 32.1683i | 0.234805 | + | 0.234805i | 0.814695 | − | 0.579890i | \(-0.196904\pi\) |
−0.579890 | + | 0.814695i | \(0.696904\pi\) | |||||||
\(138\) | 32.0437 | + | 107.818i | 0.232201 | + | 0.781287i | ||||
\(139\) | −112.569 | −0.809851 | −0.404925 | − | 0.914350i | \(-0.632702\pi\) | ||||
−0.404925 | + | 0.914350i | \(0.632702\pi\) | |||||||
\(140\) | 55.5614 | − | 89.0951i | 0.396867 | − | 0.636393i | ||||
\(141\) | −168.788 | − | 91.4457i | −1.19708 | − | 0.648551i | ||||
\(142\) | −34.6619 | + | 34.6619i | −0.244098 | + | 0.244098i | ||||
\(143\) | 23.1518 | + | 23.1518i | 0.161901 | + | 0.161901i | ||||
\(144\) | 37.6955 | − | 24.5774i | 0.261774 | − | 0.170676i | ||||
\(145\) | −52.8882 | + | 23.2273i | −0.364746 | + | 0.160188i | ||||
\(146\) | −36.8203 | −0.252194 | ||||||||
\(147\) | −146.492 | − | 12.2106i | −0.996544 | − | 0.0830654i | ||||
\(148\) | 124.479 | + | 124.479i | 0.841071 | + | 0.841071i | ||||
\(149\) | −24.7386 | −0.166031 | −0.0830155 | − | 0.996548i | \(-0.526455\pi\) | ||||
−0.0830155 | + | 0.996548i | \(0.526455\pi\) | |||||||
\(150\) | 24.3831 | + | 70.9258i | 0.162554 | + | 0.472838i | ||||
\(151\) | −116.676 | −0.772690 | −0.386345 | − | 0.922354i | \(-0.626263\pi\) | ||||
−0.386345 | + | 0.922354i | \(0.626263\pi\) | |||||||
\(152\) | −82.0634 | + | 82.0634i | −0.539891 | + | 0.539891i | ||||
\(153\) | 1.52554 | − | 7.24185i | 0.00997082 | − | 0.0473323i | ||||
\(154\) | 17.8128 | + | 3.35238i | 0.115667 | + | 0.0217687i | ||||
\(155\) | −61.9863 | − | 141.142i | −0.399912 | − | 0.910593i | ||||
\(156\) | −54.2107 | + | 100.061i | −0.347505 | + | 0.641414i | ||||
\(157\) | 142.879 | + | 142.879i | 0.910055 | + | 0.910055i | 0.996276 | − | 0.0862209i | \(-0.0274791\pi\) |
−0.0862209 | + | 0.996276i | \(0.527479\pi\) | |||||||
\(158\) | −53.6004 | + | 53.6004i | −0.339243 | + | 0.339243i | ||||
\(159\) | 127.429 | + | 69.0380i | 0.801437 | + | 0.434202i | ||||
\(160\) | −153.740 | − | 59.9096i | −0.960872 | − | 0.374435i | ||||
\(161\) | 257.922 | + | 48.5412i | 1.60200 | + | 0.301498i | ||||
\(162\) | 75.5139 | − | 29.3028i | 0.466135 | − | 0.180881i | ||||
\(163\) | 97.1548 | + | 97.1548i | 0.596041 | + | 0.596041i | 0.939257 | − | 0.343215i | \(-0.111516\pi\) |
−0.343215 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(164\) | − | 51.4468i | − | 0.313700i | ||||||
\(165\) | 29.6389 | − | 25.1020i | 0.179630 | − | 0.152133i | ||||
\(166\) | 75.9128i | 0.457306i | ||||||||
\(167\) | 207.245 | − | 207.245i | 1.24099 | − | 1.24099i | 0.281396 | − | 0.959592i | \(-0.409203\pi\) |
0.959592 | − | 0.281396i | \(-0.0907974\pi\) | |||||||
\(168\) | 15.0943 | + | 146.223i | 0.0898473 | + | 0.870375i | ||||
\(169\) | 9.11189i | 0.0539165i | ||||||||
\(170\) | −3.76450 | + | 1.65328i | −0.0221441 | + | 0.00972520i | ||||
\(171\) | 124.993 | − | 81.4952i | 0.730954 | − | 0.476580i | ||||
\(172\) | −75.4643 | + | 75.4643i | −0.438746 | + | 0.438746i | ||||
\(173\) | −115.444 | − | 115.444i | −0.667307 | − | 0.667307i | 0.289785 | − | 0.957092i | \(-0.406416\pi\) |
−0.957092 | + | 0.289785i | \(0.906416\pi\) | |||||||
\(174\) | 16.5098 | − | 30.4734i | 0.0948840 | − | 0.175134i | ||||
\(175\) | 173.194 | + | 25.0763i | 0.989680 | + | 0.143293i | ||||
\(176\) | 12.9468i | 0.0735613i | ||||||||
\(177\) | 136.947 | − | 40.7010i | 0.773710 | − | 0.229949i | ||||
\(178\) | 9.93722 | − | 9.93722i | 0.0558271 | − | 0.0558271i | ||||
\(179\) | 236.871 | 1.32330 | 0.661650 | − | 0.749813i | \(-0.269857\pi\) | ||||
0.661650 | + | 0.749813i | \(0.269857\pi\) | |||||||
\(180\) | 112.982 | + | 73.8930i | 0.627675 | + | 0.410516i | ||||
\(181\) | 227.866i | 1.25893i | 0.777030 | + | 0.629463i | \(0.216725\pi\) | ||||
−0.777030 | + | 0.629463i | \(0.783275\pi\) | |||||||
\(182\) | −49.9323 | − | 73.0841i | −0.274353 | − | 0.401561i | ||||
\(183\) | −227.160 | + | 67.5128i | −1.24131 | + | 0.368923i | ||||
\(184\) | − | 262.450i | − | 1.42636i | ||||||
\(185\) | −106.530 | + | 273.376i | −0.575837 | + | 1.47771i | ||||
\(186\) | 81.3238 | + | 44.0595i | 0.437225 | + | 0.236879i | ||||
\(187\) | 1.50561 | + | 1.50561i | 0.00805138 | + | 0.00805138i | ||||
\(188\) | 135.742 | + | 135.742i | 0.722032 | + | 0.722032i | ||||
\(189\) | 19.7627 | − | 187.964i | 0.104565 | − | 0.994518i | ||||
\(190\) | −77.2393 | − | 30.0988i | −0.406523 | − | 0.158415i | ||||
\(191\) | − | 370.941i | − | 1.94210i | −0.238872 | − | 0.971051i | \(-0.576778\pi\) | ||
0.238872 | − | 0.971051i | \(-0.423222\pi\) | |||||||
\(192\) | 37.3839 | − | 11.1106i | 0.194708 | − | 0.0578678i | ||||
\(193\) | 81.6333 | + | 81.6333i | 0.422971 | + | 0.422971i | 0.886225 | − | 0.463255i | \(-0.153318\pi\) |
−0.463255 | + | 0.886225i | \(0.653318\pi\) | |||||||
\(194\) | 36.7220i | 0.189289i | ||||||||
\(195\) | −189.022 | − | 15.6663i | −0.969345 | − | 0.0803399i | ||||
\(196\) | 136.943 | + | 53.4383i | 0.698688 | + | 0.272645i | ||||
\(197\) | 182.194 | + | 182.194i | 0.924845 | + | 0.924845i | 0.997367 | − | 0.0725218i | \(-0.0231047\pi\) |
−0.0725218 | + | 0.997367i | \(0.523105\pi\) | |||||||
\(198\) | −4.80374 | + | 22.8037i | −0.0242613 | + | 0.115170i | ||||
\(199\) | −31.2360 | −0.156965 | −0.0784824 | − | 0.996915i | \(-0.525007\pi\) | ||||
−0.0784824 | + | 0.996915i | \(0.525007\pi\) | |||||||
\(200\) | −7.38926 | − | 174.844i | −0.0369463 | − | 0.874220i | ||||
\(201\) | 270.370 | + | 146.481i | 1.34512 | + | 0.728760i | ||||
\(202\) | 16.7531 | + | 16.7531i | 0.0829360 | + | 0.0829360i | ||||
\(203\) | −45.6205 | − | 66.7731i | −0.224731 | − | 0.328931i | ||||
\(204\) | −3.52543 | + | 6.50714i | −0.0172815 | + | 0.0318978i | ||||
\(205\) | 78.5071 | − | 34.4786i | 0.382962 | − | 0.168188i | ||||
\(206\) | 111.231 | 0.539954 | ||||||||
\(207\) | −69.5562 | + | 330.189i | −0.336020 | + | 1.59512i | ||||
\(208\) | 44.7057 | − | 44.7057i | 0.214931 | − | 0.214931i | ||||
\(209\) | 42.9298i | 0.205406i | ||||||||
\(210\) | −91.2937 | + | 51.8697i | −0.434732 | + | 0.246999i | ||||
\(211\) | −96.5905 | −0.457775 | −0.228887 | − | 0.973453i | \(-0.573509\pi\) | ||||
−0.228887 | + | 0.973453i | \(0.573509\pi\) | |||||||
\(212\) | −102.480 | − | 102.480i | −0.483396 | − | 0.483396i | ||||
\(213\) | −140.964 | + | 41.8950i | −0.661803 | + | 0.196690i | ||||
\(214\) | 176.590i | 0.825189i | ||||||||
\(215\) | −165.732 | − | 64.5829i | −0.770847 | − | 0.300386i | ||||
\(216\) | −188.376 | + | 15.3429i | −0.872112 | + | 0.0710320i | ||||
\(217\) | 178.196 | − | 121.747i | 0.821181 | − | 0.561044i | ||||
\(218\) | 51.6087 | − | 51.6087i | 0.236737 | − | 0.236737i | ||||
\(219\) | −97.1228 | − | 52.6190i | −0.443483 | − | 0.240270i | ||||
\(220\) | −35.5619 | + | 15.6180i | −0.161645 | + | 0.0709909i | ||||
\(221\) | − | 10.3978i | − | 0.0470491i | ||||||
\(222\) | −50.1514 | − | 168.744i | −0.225907 | − | 0.760110i | ||||
\(223\) | 79.9490 | − | 79.9490i | 0.358516 | − | 0.358516i | −0.504750 | − | 0.863266i | \(-0.668415\pi\) |
0.863266 | + | 0.504750i | \(0.168415\pi\) | |||||||
\(224\) | 42.7244 | − | 227.015i | 0.190734 | − | 1.01346i | ||||
\(225\) | −37.0418 | + | 221.930i | −0.164630 | + | 0.986355i | ||||
\(226\) | −73.2952 | −0.324315 | ||||||||
\(227\) | −56.7824 | + | 56.7824i | −0.250143 | + | 0.250143i | −0.821029 | − | 0.570886i | \(-0.806600\pi\) |
0.570886 | + | 0.821029i | \(0.306600\pi\) | |||||||
\(228\) | −143.031 | + | 42.5092i | −0.627327 | + | 0.186444i | ||||
\(229\) | −153.812 | −0.671668 | −0.335834 | − | 0.941921i | \(-0.609018\pi\) | ||||
−0.335834 | + | 0.941921i | \(0.609018\pi\) | |||||||
\(230\) | 171.641 | − | 75.3808i | 0.746265 | − | 0.327743i | ||||
\(231\) | 42.1949 | + | 34.2986i | 0.182662 | + | 0.148479i | ||||
\(232\) | −57.1833 | + | 57.1833i | −0.246480 | + | 0.246480i | ||||
\(233\) | 50.2938 | − | 50.2938i | 0.215853 | − | 0.215853i | −0.590895 | − | 0.806748i | \(-0.701225\pi\) |
0.806748 | + | 0.590895i | \(0.201225\pi\) | |||||||
\(234\) | 95.3296 | − | 62.1547i | 0.407392 | − | 0.265618i | ||||
\(235\) | −116.169 | + | 298.112i | −0.494336 | + | 1.26856i | ||||
\(236\) | −142.867 | −0.605368 | ||||||||
\(237\) | −217.984 | + | 64.7854i | −0.919762 | + | 0.273356i | ||||
\(238\) | −3.24720 | − | 4.75280i | −0.0136437 | − | 0.0199698i | ||||
\(239\) | −131.741 | −0.551216 | −0.275608 | − | 0.961270i | \(-0.588879\pi\) | ||||
−0.275608 | + | 0.961270i | \(0.588879\pi\) | |||||||
\(240\) | −48.4714 | − | 57.2322i | −0.201964 | − | 0.238467i | ||||
\(241\) | − | 103.031i | − | 0.427516i | −0.976887 | − | 0.213758i | \(-0.931430\pi\) | ||
0.976887 | − | 0.213758i | \(-0.0685704\pi\) | |||||||
\(242\) | 80.8189 | + | 80.8189i | 0.333963 | + | 0.333963i | ||||
\(243\) | 241.063 | + | 30.6217i | 0.992028 | + | 0.126015i | ||||
\(244\) | 236.981 | 0.971232 | ||||||||
\(245\) | 10.2300 | + | 244.786i | 0.0417551 | + | 0.999128i | ||||
\(246\) | −24.5071 | + | 45.2346i | −0.0996225 | + | 0.183881i | ||||
\(247\) | 148.238 | − | 148.238i | 0.600154 | − | 0.600154i | ||||
\(248\) | −152.604 | − | 152.604i | −0.615340 | − | 0.615340i | ||||
\(249\) | −108.485 | + | 200.239i | −0.435684 | + | 0.804174i | ||||
\(250\) | 112.225 | − | 55.0512i | 0.448899 | − | 0.220205i | ||||
\(251\) | −363.395 | −1.44779 | −0.723895 | − | 0.689910i | \(-0.757650\pi\) | ||||
−0.723895 | + | 0.689910i | \(0.757650\pi\) | |||||||
\(252\) | −72.4924 | + | 174.545i | −0.287668 | + | 0.692638i | ||||
\(253\) | −68.6476 | − | 68.6476i | −0.271334 | − | 0.271334i | ||||
\(254\) | 30.6144 | 0.120529 | ||||||||
\(255\) | −12.2925 | − | 1.01881i | −0.0482058 | − | 0.00399533i | ||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | 86.9159 | − | 86.9159i | 0.338194 | − | 0.338194i | −0.517493 | − | 0.855687i | \(-0.673135\pi\) |
0.855687 | + | 0.517493i | \(0.173135\pi\) | |||||||
\(258\) | 102.300 | − | 30.4039i | 0.396512 | − | 0.117845i | ||||
\(259\) | −403.672 | − | 75.9714i | −1.55858 | − | 0.293326i | ||||
\(260\) | 176.726 | + | 68.8671i | 0.679716 | + | 0.264874i | ||||
\(261\) | 87.0976 | − | 56.7874i | 0.333707 | − | 0.217576i | ||||
\(262\) | −153.910 | − | 153.910i | −0.587444 | − | 0.587444i | ||||
\(263\) | 97.6009 | − | 97.6009i | 0.371106 | − | 0.371106i | −0.496774 | − | 0.867880i | \(-0.665482\pi\) |
0.867880 | + | 0.496774i | \(0.165482\pi\) | |||||||
\(264\) | 25.9027 | − | 47.8106i | 0.0981164 | − | 0.181101i | ||||
\(265\) | 87.7032 | − | 225.063i | 0.330955 | − | 0.849295i | ||||
\(266\) | 21.4649 | − | 114.053i | 0.0806951 | − | 0.428770i | ||||
\(267\) | 40.4130 | − | 12.0109i | 0.151359 | − | 0.0449845i | ||||
\(268\) | −217.436 | − | 217.436i | −0.811327 | − | 0.811327i | ||||
\(269\) | − | 119.813i | − | 0.445403i | −0.974887 | − | 0.222701i | \(-0.928512\pi\) | ||
0.974887 | − | 0.222701i | \(-0.0714875\pi\) | |||||||
\(270\) | −64.1395 | − | 118.790i | −0.237554 | − | 0.439964i | ||||
\(271\) | − | 246.646i | − | 0.910132i | −0.890458 | − | 0.455066i | \(-0.849616\pi\) | ||
0.890458 | − | 0.455066i | \(-0.150384\pi\) | |||||||
\(272\) | 2.90730 | − | 2.90730i | 0.0106886 | − | 0.0106886i | ||||
\(273\) | −27.2662 | − | 264.135i | −0.0998761 | − | 0.967527i | ||||
\(274\) | 45.4929i | 0.166032i | ||||||||
\(275\) | −47.6657 | − | 43.8002i | −0.173330 | − | 0.159273i | ||||
\(276\) | 160.741 | − | 296.691i | 0.582393 | − | 1.07497i | ||||
\(277\) | 51.1833 | − | 51.1833i | 0.184777 | − | 0.184777i | −0.608656 | − | 0.793434i | \(-0.708291\pi\) |
0.793434 | + | 0.608656i | \(0.208291\pi\) | |||||||
\(278\) | −79.5985 | − | 79.5985i | −0.286325 | − | 0.286325i | ||||
\(279\) | 151.548 | + | 232.436i | 0.543182 | + | 0.833104i | ||||
\(280\) | 238.671 | − | 55.3277i | 0.852396 | − | 0.197599i | ||||
\(281\) | − | 6.33365i | − | 0.0225397i | −0.999936 | − | 0.0112698i | \(-0.996413\pi\) | ||
0.999936 | − | 0.0112698i | \(-0.00358738\pi\) | |||||||
\(282\) | −54.6893 | − | 184.013i | −0.193934 | − | 0.652529i | ||||
\(283\) | −242.152 | + | 242.152i | −0.855661 | + | 0.855661i | −0.990823 | − | 0.135163i | \(-0.956844\pi\) |
0.135163 | + | 0.990823i | \(0.456844\pi\) | |||||||
\(284\) | 147.058 | 0.517810 | ||||||||
\(285\) | −160.725 | − | 189.774i | −0.563946 | − | 0.665874i | ||||
\(286\) | 32.7416i | 0.114481i | ||||||||
\(287\) | 67.7190 | + | 99.1178i | 0.235955 | + | 0.345358i | ||||
\(288\) | 290.622 | + | 61.2211i | 1.00910 | + | 0.212573i | ||||
\(289\) | 288.324i | 0.997660i | ||||||||
\(290\) | −53.8218 | − | 20.9734i | −0.185592 | − | 0.0723221i | ||||
\(291\) | −52.4786 | + | 96.8635i | −0.180339 | + | 0.332864i | ||||
\(292\) | 78.1076 | + | 78.1076i | 0.267492 | + | 0.267492i | ||||
\(293\) | 333.360 | + | 333.360i | 1.13775 | + | 1.13775i | 0.988853 | + | 0.148895i | \(0.0475717\pi\) |
0.148895 | + | 0.988853i | \(0.452428\pi\) | |||||||
\(294\) | −94.9513 | − | 112.220i | −0.322963 | − | 0.381700i | ||||
\(295\) | −95.7464 | − | 218.013i | −0.324564 | − | 0.739027i | ||||
\(296\) | 410.758i | 1.38770i | ||||||||
\(297\) | −45.2594 | + | 53.2857i | −0.152388 | + | 0.179413i | ||||
\(298\) | −17.4929 | − | 17.4929i | −0.0587009 | − | 0.0587009i | ||||
\(299\) | 474.085i | 1.58557i | ||||||||
\(300\) | 98.7319 | − | 202.181i | 0.329106 | − | 0.673935i | ||||
\(301\) | 46.0572 | − | 244.723i | 0.153014 | − | 0.813034i | ||||
\(302\) | −82.5025 | − | 82.5025i | −0.273187 | − | 0.273187i | ||||
\(303\) | 20.2490 | + | 68.1319i | 0.0668285 | + | 0.224858i | ||||
\(304\) | 82.8966 | 0.272686 | ||||||||
\(305\) | 158.820 | + | 361.630i | 0.520720 | + | 1.18567i | ||||
\(306\) | 6.19947 | − | 4.04204i | 0.0202597 | − | 0.0132093i | ||||
\(307\) | −115.748 | − | 115.748i | −0.377030 | − | 0.377030i | 0.492999 | − | 0.870030i | \(-0.335901\pi\) |
−0.870030 | + | 0.492999i | \(0.835901\pi\) | |||||||
\(308\) | −30.6751 | − | 44.8981i | −0.0995946 | − | 0.145773i | ||||
\(309\) | 293.399 | + | 158.957i | 0.949511 | + | 0.514424i | ||||
\(310\) | 55.9714 | − | 143.633i | 0.180553 | − | 0.463333i | ||||
\(311\) | 87.4973 | 0.281342 | 0.140671 | − | 0.990056i | \(-0.455074\pi\) | ||||
0.140671 | + | 0.990056i | \(0.455074\pi\) | |||||||
\(312\) | −254.535 | + | 75.6486i | −0.815817 | + | 0.242463i | ||||
\(313\) | −74.9574 | + | 74.9574i | −0.239481 | + | 0.239481i | −0.816635 | − | 0.577154i | \(-0.804163\pi\) |
0.577154 | + | 0.816635i | \(0.304163\pi\) | |||||||
\(314\) | 202.061i | 0.643506i | ||||||||
\(315\) | −314.936 | + | 6.35383i | −0.999797 | + | 0.0201709i | ||||
\(316\) | 227.407 | 0.719643 | ||||||||
\(317\) | −393.091 | − | 393.091i | −1.24003 | − | 1.24003i | −0.959986 | − | 0.280048i | \(-0.909650\pi\) |
−0.280048 | − | 0.959986i | \(-0.590350\pi\) | |||||||
\(318\) | 41.2883 | + | 138.923i | 0.129838 | + | 0.436864i | ||||
\(319\) | 29.9143i | 0.0937751i | ||||||||
\(320\) | −26.1370 | − | 59.5135i | −0.0816781 | − | 0.185980i | ||||
\(321\) | −252.361 | + | 465.802i | −0.786173 | + | 1.45110i | ||||
\(322\) | 148.055 | + | 216.702i | 0.459797 | + | 0.672988i | ||||
\(323\) | 9.64022 | − | 9.64022i | 0.0298459 | − | 0.0298459i | ||||
\(324\) | −222.350 | − | 98.0286i | −0.686265 | − | 0.302557i | ||||
\(325\) | 13.3478 | + | 315.835i | 0.0410703 | + | 0.971801i | ||||
\(326\) | 137.398i | 0.421465i | ||||||||
\(327\) | 209.884 | − | 62.3781i | 0.641846 | − | 0.190759i | ||||
\(328\) | 84.8829 | − | 84.8829i | 0.258789 | − | 0.258789i | ||||
\(329\) | −440.198 | − | 82.8456i | −1.33799 | − | 0.251810i | ||||
\(330\) | 38.7076 | + | 3.20811i | 0.117296 | + | 0.00972155i | ||||
\(331\) | 244.986 | 0.740138 | 0.370069 | − | 0.929004i | \(-0.379334\pi\) | ||||
0.370069 | + | 0.929004i | \(0.379334\pi\) | |||||||
\(332\) | 161.035 | − | 161.035i | 0.485047 | − | 0.485047i | ||||
\(333\) | 108.862 | − | 516.776i | 0.326912 | − | 1.55188i | ||||
\(334\) | 293.089 | 0.877511 | ||||||||
\(335\) | 186.083 | − | 477.525i | 0.555472 | − | 1.42545i | ||||
\(336\) | 66.2300 | − | 81.4776i | 0.197113 | − | 0.242493i | ||||
\(337\) | −333.576 | + | 333.576i | −0.989840 | + | 0.989840i | −0.999949 | − | 0.0101086i | \(-0.996782\pi\) |
0.0101086 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(338\) | −6.44308 | + | 6.44308i | −0.0190624 | + | 0.0190624i | ||||
\(339\) | −193.335 | − | 104.745i | −0.570309 | − | 0.308981i | ||||
\(340\) | 11.4929 | + | 4.47857i | 0.0338025 | + | 0.0131723i | ||||
\(341\) | −79.8317 | −0.234111 | ||||||||
\(342\) | 146.009 | + | 30.7577i | 0.426928 | + | 0.0899348i | ||||
\(343\) | −334.176 | + | 77.3019i | −0.974273 | + | 0.225370i | ||||
\(344\) | −249.019 | −0.723894 | ||||||||
\(345\) | 560.471 | + | 46.4522i | 1.62455 | + | 0.134644i | ||||
\(346\) | − | 163.263i | − | 0.471857i | ||||||
\(347\) | −226.173 | − | 226.173i | −0.651796 | − | 0.651796i | 0.301629 | − | 0.953425i | \(-0.402469\pi\) |
−0.953425 | + | 0.301629i | \(0.902469\pi\) | |||||||
\(348\) | −99.6664 | + | 29.6212i | −0.286398 | + | 0.0851183i | ||||
\(349\) | 247.335 | 0.708696 | 0.354348 | − | 0.935114i | \(-0.384703\pi\) | ||||
0.354348 | + | 0.935114i | \(0.384703\pi\) | |||||||
\(350\) | 104.735 | + | 140.198i | 0.299243 | + | 0.400567i | ||||
\(351\) | 340.280 | − | 27.7152i | 0.969458 | − | 0.0789607i | ||||
\(352\) | −60.4214 | + | 60.4214i | −0.171652 | + | 0.171652i | ||||
\(353\) | −276.422 | − | 276.422i | −0.783065 | − | 0.783065i | 0.197281 | − | 0.980347i | \(-0.436789\pi\) |
−0.980347 | + | 0.197281i | \(0.936789\pi\) | |||||||
\(354\) | 125.616 | + | 68.0559i | 0.354847 | + | 0.192248i | ||||
\(355\) | 98.5552 | + | 224.409i | 0.277620 | + | 0.632137i | ||||
\(356\) | −42.1600 | −0.118427 | ||||||||
\(357\) | −1.77317 | − | 17.1772i | −0.00496687 | − | 0.0481154i | ||||
\(358\) | 167.493 | + | 167.493i | 0.467857 | + | 0.467857i | ||||
\(359\) | 392.633 | 1.09368 | 0.546842 | − | 0.837236i | \(-0.315830\pi\) | ||||
0.546842 | + | 0.837236i | \(0.315830\pi\) | |||||||
\(360\) | 64.4929 | + | 308.327i | 0.179147 | + | 0.856464i | ||||
\(361\) | −86.1262 | −0.238577 | ||||||||
\(362\) | −161.125 | + | 161.125i | −0.445098 | + | 0.445098i | ||||
\(363\) | 97.6838 | + | 328.677i | 0.269101 | + | 0.905446i | ||||
\(364\) | −49.1124 | + | 260.957i | −0.134924 | + | 0.716915i | ||||
\(365\) | −66.8451 | + | 171.537i | −0.183137 | + | 0.469965i | ||||
\(366\) | −208.365 | − | 112.888i | −0.569305 | − | 0.308437i | ||||
\(367\) | 232.458 | + | 232.458i | 0.633401 | + | 0.633401i | 0.948919 | − | 0.315519i | \(-0.102179\pi\) |
−0.315519 | + | 0.948919i | \(0.602179\pi\) | |||||||
\(368\) | −132.557 | + | 132.557i | −0.360210 | + | 0.360210i | ||||
\(369\) | −129.288 | + | 84.2951i | −0.350373 | + | 0.228442i | ||||
\(370\) | −268.634 | + | 117.978i | −0.726037 | + | 0.318859i | ||||
\(371\) | 332.332 | + | 62.5453i | 0.895774 | + | 0.168586i | ||||
\(372\) | −79.0496 | − | 265.978i | −0.212499 | − | 0.714995i | ||||
\(373\) | −194.536 | − | 194.536i | −0.521543 | − | 0.521543i | 0.396494 | − | 0.918037i | \(-0.370227\pi\) |
−0.918037 | + | 0.396494i | \(0.870227\pi\) | |||||||
\(374\) | 2.12925i | 0.00569319i | ||||||||
\(375\) | 374.693 | + | 15.1664i | 0.999182 | + | 0.0404437i | ||||
\(376\) | 447.926i | 1.19129i | ||||||||
\(377\) | 103.295 | − | 103.295i | 0.273992 | − | 0.273992i | ||||
\(378\) | 146.885 | − | 118.936i | 0.388584 | − | 0.314646i | ||||
\(379\) | − | 345.209i | − | 0.910843i | −0.890276 | − | 0.455422i | \(-0.849489\pi\) | ||
0.890276 | − | 0.455422i | \(-0.150511\pi\) | |||||||
\(380\) | 100.000 | + | 227.698i | 0.263158 | + | 0.599207i | ||||
\(381\) | 80.7531 | + | 43.7503i | 0.211950 | + | 0.114830i | ||||
\(382\) | 262.295 | − | 262.295i | 0.686637 | − | 0.686637i | ||||
\(383\) | 46.7051 | + | 46.7051i | 0.121945 | + | 0.121945i | 0.765446 | − | 0.643500i | \(-0.222518\pi\) |
−0.643500 | + | 0.765446i | \(0.722518\pi\) | |||||||
\(384\) | −313.893 | − | 170.060i | −0.817428 | − | 0.442865i | ||||
\(385\) | 47.9561 | − | 76.8996i | 0.124561 | − | 0.199739i | ||||
\(386\) | 115.447i | 0.299085i | ||||||||
\(387\) | 313.292 | + | 65.9967i | 0.809540 | + | 0.170534i | ||||
\(388\) | 77.8991 | − | 77.8991i | 0.200771 | − | 0.200771i | ||||
\(389\) | −747.341 | −1.92119 | −0.960593 | − | 0.277960i | \(-0.910342\pi\) | ||||
−0.960593 | + | 0.277960i | \(0.910342\pi\) | |||||||
\(390\) | −122.581 | − | 144.737i | −0.314311 | − | 0.371120i | ||||
\(391\) | 30.8307i | 0.0788509i | ||||||||
\(392\) | 137.775 | + | 314.113i | 0.351468 | + | 0.801309i | ||||
\(393\) | −186.028 | − | 625.927i | −0.473353 | − | 1.59269i | ||||
\(394\) | 257.662i | 0.653964i | ||||||||
\(395\) | 152.404 | + | 347.020i | 0.385832 | + | 0.878533i | ||||
\(396\) | 58.5643 | − | 38.1838i | 0.147890 | − | 0.0964237i | ||||
\(397\) | −320.867 | − | 320.867i | −0.808230 | − | 0.808230i | 0.176135 | − | 0.984366i | \(-0.443640\pi\) |
−0.984366 | + | 0.176135i | \(0.943640\pi\) | |||||||
\(398\) | −22.0872 | − | 22.0872i | −0.0554954 | − | 0.0554954i | ||||
\(399\) | 219.610 | − | 270.168i | 0.550400 | − | 0.677114i | ||||
\(400\) | −84.5774 | + | 92.0417i | −0.211443 | + | 0.230104i | ||||
\(401\) | 472.603i | 1.17856i | 0.807928 | + | 0.589281i | \(0.200589\pi\) | ||||
−0.807928 | + | 0.589281i | \(0.799411\pi\) | |||||||
\(402\) | 87.6030 | + | 294.758i | 0.217918 | + | 0.733229i | ||||
\(403\) | 275.662 | + | 275.662i | 0.684025 | + | 0.684025i | ||||
\(404\) | − | 71.0773i | − | 0.175934i | ||||||
\(405\) | 0.576206 | − | 405.000i | 0.00142273 | − | 0.999999i | ||||
\(406\) | 14.9571 | − | 79.4742i | 0.0368402 | − | 0.195749i | ||||
\(407\) | 107.440 | + | 107.440i | 0.263980 | + | 0.263980i | ||||
\(408\) | −16.5529 | + | 4.91958i | −0.0405708 | + | 0.0120578i | ||||
\(409\) | −121.806 | −0.297813 | −0.148907 | − | 0.988851i | \(-0.547575\pi\) | ||||
−0.148907 | + | 0.988851i | \(0.547575\pi\) | |||||||
\(410\) | 79.8930 | + | 31.1329i | 0.194861 | + | 0.0759339i | ||||
\(411\) | −65.0128 | + | 119.999i | −0.158182 | + | 0.291968i | ||||
\(412\) | −235.956 | − | 235.956i | −0.572708 | − | 0.572708i | ||||
\(413\) | 275.249 | − | 188.054i | 0.666462 | − | 0.455338i | ||||
\(414\) | −282.663 | + | 184.295i | −0.682760 | + | 0.445158i | ||||
\(415\) | 353.661 | + | 137.815i | 0.852194 | + | 0.332085i | ||||
\(416\) | 417.275 | 1.00306 | ||||||||
\(417\) | −96.2087 | − | 323.713i | −0.230716 | − | 0.776291i | ||||
\(418\) | −30.3559 | + | 30.3559i | −0.0726219 | + | 0.0726219i | ||||
\(419\) | − | 91.1169i | − | 0.217463i | −0.994071 | − | 0.108731i | \(-0.965321\pi\) | ||
0.994071 | − | 0.108731i | \(-0.0346788\pi\) | |||||||
\(420\) | 303.695 | + | 83.6308i | 0.723084 | + | 0.199121i | ||||
\(421\) | 61.3238 | 0.145662 | 0.0728311 | − | 0.997344i | \(-0.476797\pi\) | ||||
0.0728311 | + | 0.997344i | \(0.476797\pi\) | |||||||
\(422\) | −68.2998 | − | 68.2998i | −0.161848 | − | 0.161848i | ||||
\(423\) | 118.712 | − | 563.536i | 0.280643 | − | 1.33224i | ||||
\(424\) | − | 338.167i | − | 0.797563i | ||||||
\(425\) | 0.868036 | + | 20.5394i | 0.00204244 | + | 0.0483280i | ||||
\(426\) | −129.301 | − | 70.0524i | −0.303523 | − | 0.164442i | ||||
\(427\) | −456.569 | + | 311.936i | −1.06925 | + | 0.730528i | ||||
\(428\) | 374.605 | − | 374.605i | 0.875245 | − | 0.875245i | ||||
\(429\) | −46.7903 | + | 86.3643i | −0.109068 | + | 0.201315i | ||||
\(430\) | −71.5233 | − | 162.857i | −0.166333 | − | 0.378738i | ||||
\(431\) | − | 179.188i | − | 0.415749i | −0.978156 | − | 0.207874i | \(-0.933346\pi\) | ||
0.978156 | − | 0.207874i | \(-0.0666545\pi\) | |||||||
\(432\) | 102.894 | + | 87.3950i | 0.238180 | + | 0.202303i | ||||
\(433\) | 234.230 | − | 234.230i | 0.540947 | − | 0.540947i | −0.382860 | − | 0.923806i | \(-0.625061\pi\) |
0.923806 | + | 0.382860i | \(0.125061\pi\) | |||||||
\(434\) | 212.092 | + | 39.9159i | 0.488690 | + | 0.0919721i | ||||
\(435\) | −111.996 | − | 132.238i | −0.257462 | − | 0.303996i | ||||
\(436\) | −218.957 | −0.502195 | ||||||||
\(437\) | −439.542 | + | 439.542i | −1.00582 | + | 1.00582i | ||||
\(438\) | −31.4689 | − | 105.883i | −0.0718468 | − | 0.241743i | ||||
\(439\) | 526.311 | 1.19889 | 0.599443 | − | 0.800417i | \(-0.295389\pi\) | ||||
0.599443 | + | 0.800417i | \(0.295389\pi\) | |||||||
\(440\) | −84.4426 | − | 32.9058i | −0.191915 | − | 0.0747859i | ||||
\(441\) | −90.0873 | − | 431.700i | −0.204280 | − | 0.978913i | ||||
\(442\) | 7.35238 | − | 7.35238i | 0.0166344 | − | 0.0166344i | ||||
\(443\) | −207.809 | + | 207.809i | −0.469094 | + | 0.469094i | −0.901621 | − | 0.432527i | \(-0.857622\pi\) |
0.432527 | + | 0.901621i | \(0.357622\pi\) | |||||||
\(444\) | −251.574 | + | 464.348i | −0.566608 | + | 1.04583i | ||||
\(445\) | −28.2548 | − | 64.3357i | −0.0634939 | − | 0.144575i | ||||
\(446\) | 113.065 | 0.253509 | ||||||||
\(447\) | −21.1432 | − | 71.1405i | −0.0473002 | − | 0.159151i | ||||
\(448\) | 75.1377 | − | 51.3354i | 0.167718 | − | 0.114588i | ||||
\(449\) | −315.151 | −0.701895 | −0.350947 | − | 0.936395i | \(-0.614140\pi\) | ||||
−0.350947 | + | 0.936395i | \(0.614140\pi\) | |||||||
\(450\) | −183.121 | + | 130.736i | −0.406935 | + | 0.290524i | ||||
\(451\) | − | 44.4047i | − | 0.0984583i | ||||||
\(452\) | 155.483 | + | 155.483i | 0.343988 | + | 0.343988i | ||||
\(453\) | −99.7188 | − | 335.524i | −0.220130 | − | 0.740670i | ||||
\(454\) | −80.3024 | −0.176878 | ||||||||
\(455\) | −431.131 | + | 99.9431i | −0.947542 | + | 0.219655i | ||||
\(456\) | −306.125 | − | 165.852i | −0.671327 | − | 0.363710i | ||||
\(457\) | −357.774 | + | 357.774i | −0.782875 | + | 0.782875i | −0.980315 | − | 0.197440i | \(-0.936737\pi\) |
0.197440 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(458\) | −108.761 | − | 108.761i | −0.237470 | − | 0.237470i | ||||
\(459\) | 22.1291 | − | 1.80237i | 0.0482115 | − | 0.00392674i | ||||
\(460\) | −524.012 | − | 204.198i | −1.13916 | − | 0.443910i | ||||
\(461\) | −563.655 | −1.22268 | −0.611339 | − | 0.791369i | \(-0.709369\pi\) | ||||
−0.611339 | + | 0.791369i | \(0.709369\pi\) | |||||||
\(462\) | 5.58352 | + | 54.0891i | 0.0120855 | + | 0.117076i | ||||
\(463\) | −26.9857 | − | 26.9857i | −0.0582845 | − | 0.0582845i | 0.677364 | − | 0.735648i | \(-0.263122\pi\) |
−0.735648 | + | 0.677364i | \(0.763122\pi\) | |||||||
\(464\) | 57.7639 | 0.124491 | ||||||||
\(465\) | 352.902 | − | 298.882i | 0.758929 | − | 0.642756i | ||||
\(466\) | 71.1262 | 0.152631 | ||||||||
\(467\) | 271.529 | − | 271.529i | 0.581432 | − | 0.581432i | −0.353864 | − | 0.935297i | \(-0.615133\pi\) |
0.935297 | + | 0.353864i | \(0.115133\pi\) | |||||||
\(468\) | −334.075 | − | 70.3747i | −0.713835 | − | 0.150373i | ||||
\(469\) | 705.122 | + | 132.705i | 1.50346 | + | 0.282953i | ||||
\(470\) | −292.941 | + | 128.653i | −0.623278 | + | 0.273730i | ||||
\(471\) | −288.761 | + | 532.987i | −0.613080 | + | 1.13161i | ||||
\(472\) | −235.718 | − | 235.718i | −0.499403 | − | 0.499403i | ||||
\(473\) | −65.1347 | + | 65.1347i | −0.137705 | + | 0.137705i | ||||
\(474\) | −199.948 | − | 108.327i | −0.421831 | − | 0.228539i | ||||
\(475\) | −280.447 | + | 305.198i | −0.590415 | + | 0.642521i | ||||
\(476\) | −3.19388 | + | 16.9706i | −0.00670983 | + | 0.0356524i | ||||
\(477\) | −89.6231 | + | 425.448i | −0.187889 | + | 0.891925i | ||||
\(478\) | −93.1548 | − | 93.1548i | −0.194884 | − | 0.194884i | ||||
\(479\) | − | 517.973i | − | 1.08136i | −0.841227 | − | 0.540682i | \(-0.818166\pi\) | ||
0.841227 | − | 0.540682i | \(-0.181834\pi\) | |||||||
\(480\) | 40.8857 | − | 493.309i | 0.0851786 | − | 1.02773i | ||||
\(481\) | − | 741.987i | − | 1.54259i | ||||||
\(482\) | 72.8542 | − | 72.8542i | 0.151150 | − | 0.151150i | ||||
\(483\) | 80.8471 | + | 783.188i | 0.167385 | + | 1.62151i | ||||
\(484\) | − | 342.886i | − | 0.708442i | ||||||
\(485\) | 171.079 | + | 66.6667i | 0.352741 | + | 0.137457i | ||||
\(486\) | 148.804 | + | 192.110i | 0.306182 | + | 0.395288i | ||||
\(487\) | 369.310 | − | 369.310i | 0.758336 | − | 0.758336i | −0.217684 | − | 0.976019i | \(-0.569850\pi\) |
0.976019 | + | 0.217684i | \(0.0698501\pi\) | |||||||
\(488\) | 390.998 | + | 390.998i | 0.801226 | + | 0.801226i | ||||
\(489\) | −196.352 | + | 362.421i | −0.401537 | + | 0.741147i | ||||
\(490\) | −165.856 | + | 180.324i | −0.338482 | + | 0.368008i | ||||
\(491\) | − | 421.951i | − | 0.859370i | −0.902979 | − | 0.429685i | \(-0.858625\pi\) | ||
0.902979 | − | 0.429685i | \(-0.141375\pi\) | |||||||
\(492\) | 147.945 | − | 43.9696i | 0.300700 | − | 0.0893692i | ||||
\(493\) | 6.71748 | − | 6.71748i | 0.0136257 | − | 0.0136257i | ||||
\(494\) | 209.640 | 0.424373 | ||||||||
\(495\) | 97.5165 | + | 63.7784i | 0.197003 | + | 0.128845i | ||||
\(496\) | 154.154i | 0.310794i | ||||||||
\(497\) | −283.323 | + | 193.571i | −0.570067 | + | 0.389479i | ||||
\(498\) | −218.301 | + | 64.8798i | −0.438356 | + | 0.130281i | ||||
\(499\) | 109.267i | 0.218971i | 0.993988 | + | 0.109486i | \(0.0349204\pi\) | ||||
−0.993988 | + | 0.109486i | \(0.965080\pi\) | |||||||
\(500\) | −354.846 | − | 121.283i | −0.709691 | − | 0.242567i | ||||
\(501\) | 773.095 | + | 418.846i | 1.54310 | + | 0.836021i | ||||
\(502\) | −256.959 | − | 256.959i | −0.511871 | − | 0.511871i | ||||
\(503\) | −134.096 | − | 134.096i | −0.266592 | − | 0.266592i | 0.561133 | − | 0.827725i | \(-0.310365\pi\) |
−0.827725 | + | 0.561133i | \(0.810365\pi\) | |||||||
\(504\) | −407.590 | + | 168.378i | −0.808711 | + | 0.334083i | ||||
\(505\) | 108.463 | − | 47.6345i | 0.214778 | − | 0.0943258i | ||||
\(506\) | − | 97.0824i | − | 0.191862i | ||||||
\(507\) | −26.2029 | + | 7.78759i | −0.0516823 | + | 0.0153601i | ||||
\(508\) | −64.9428 | − | 64.9428i | −0.127840 | − | 0.127840i | ||||
\(509\) | − | 459.197i | − | 0.902154i | −0.892485 | − | 0.451077i | \(-0.851040\pi\) | ||
0.892485 | − | 0.451077i | \(-0.148960\pi\) | |||||||
\(510\) | −7.97170 | − | 9.41251i | −0.0156308 | − | 0.0184559i | ||||
\(511\) | −253.295 | − | 47.6704i | −0.495685 | − | 0.0932885i | ||||
\(512\) | 215.668 | + | 215.668i | 0.421226 | + | 0.421226i | ||||
\(513\) | 341.181 | + | 289.790i | 0.665071 | + | 0.564893i | ||||
\(514\) | 122.918 | 0.239139 | ||||||||
\(515\) | 201.933 | − | 518.198i | 0.392103 | − | 1.00621i | ||||
\(516\) | −281.508 | − | 152.515i | −0.545558 | − | 0.295571i | ||||
\(517\) | 117.161 | + | 117.161i | 0.226618 | + | 0.226618i | ||||
\(518\) | −231.719 | − | 339.159i | −0.447334 | − | 0.654747i | ||||
\(519\) | 233.315 | − | 430.646i | 0.449547 | − | 0.829762i | ||||
\(520\) | 177.958 | + | 405.208i | 0.342228 | + | 0.779247i | ||||
\(521\) | 303.734 | 0.582983 | 0.291491 | − | 0.956573i | \(-0.405848\pi\) | ||||
0.291491 | + | 0.956573i | \(0.405848\pi\) | |||||||
\(522\) | 101.742 | + | 21.4325i | 0.194908 | + | 0.0410585i | ||||
\(523\) | −249.060 | + | 249.060i | −0.476215 | + | 0.476215i | −0.903919 | − | 0.427704i | \(-0.859323\pi\) |
0.427704 | + | 0.903919i | \(0.359323\pi\) | |||||||
\(524\) | 652.986i | 1.24616i | ||||||||
\(525\) | 75.9109 | + | 519.483i | 0.144592 | + | 0.989491i | ||||
\(526\) | 138.029 | 0.262412 | ||||||||
\(527\) | 17.9268 | + | 17.9268i | 0.0340168 | + | 0.0340168i | ||||
\(528\) | −37.2308 | + | 11.0651i | −0.0705130 | + | 0.0209567i | ||||
\(529\) | − | 876.714i | − | 1.65730i | ||||||
\(530\) | 221.159 | − | 97.1281i | 0.417281 | − | 0.183261i | ||||
\(531\) | 234.086 | + | 359.029i | 0.440840 | + | 0.676138i | ||||
\(532\) | −287.477 | + | 196.409i | −0.540370 | + | 0.369190i | ||||
\(533\) | −153.331 | + | 153.331i | −0.287675 | + | 0.287675i | ||||
\(534\) | 37.0692 | + | 20.0833i | 0.0694181 | + | 0.0376092i | ||||
\(535\) | 822.695 | + | 320.590i | 1.53775 | + | 0.599234i | ||||
\(536\) | − | 717.501i | − | 1.33862i | ||||||
\(537\) | 202.444 | + | 681.165i | 0.376992 | + | 1.26846i | ||||
\(538\) | 84.7209 | − | 84.7209i | 0.157474 | − | 0.157474i | ||||
\(539\) | 118.198 | + | 46.1237i | 0.219291 | + | 0.0855726i | ||||
\(540\) | −115.932 | + | 388.053i | −0.214688 | + | 0.718616i | ||||
\(541\) | −198.562 | −0.367028 | −0.183514 | − | 0.983017i | \(-0.558747\pi\) | ||||
−0.183514 | + | 0.983017i | \(0.558747\pi\) | |||||||
\(542\) | 174.405 | − | 174.405i | 0.321780 | − | 0.321780i | ||||
\(543\) | −655.270 | + | 194.748i | −1.20676 | + | 0.358653i | ||||
\(544\) | 27.1362 | 0.0498827 | ||||||||
\(545\) | −146.741 | − | 334.126i | −0.269249 | − | 0.613075i | ||||
\(546\) | 167.491 | − | 206.052i | 0.306761 | − | 0.377384i | ||||
\(547\) | 492.112 | − | 492.112i | 0.899656 | − | 0.899656i | −0.0957494 | − | 0.995405i | \(-0.530525\pi\) |
0.995405 | + | 0.0957494i | \(0.0305247\pi\) | |||||||
\(548\) | 96.5049 | − | 96.5049i | 0.176104 | − | 0.176104i | ||||
\(549\) | −388.291 | − | 595.541i | −0.707270 | − | 1.08477i | ||||
\(550\) | −2.73335 | − | 64.6762i | −0.00496972 | − | 0.117593i | ||||
\(551\) | 191.537 | 0.347617 | ||||||||
\(552\) | 754.723 | − | 224.306i | 1.36725 | − | 0.406352i | ||||
\(553\) | −438.125 | + | 299.334i | −0.792269 | + | 0.541291i | ||||
\(554\) | 72.3842 | 0.130657 | ||||||||
\(555\) | −877.189 | − | 72.7019i | −1.58052 | − | 0.130994i | ||||
\(556\) | 337.708i | 0.607388i | ||||||||
\(557\) | −328.316 | − | 328.316i | −0.589437 | − | 0.589437i | 0.348042 | − | 0.937479i | \(-0.386847\pi\) |
−0.937479 | + | 0.348042i | \(0.886847\pi\) | |||||||
\(558\) | −57.1967 | + | 271.517i | −0.102503 | + | 0.486590i | ||||
\(559\) | 449.825 | 0.804695 | ||||||||
\(560\) | −148.492 | − | 92.6023i | −0.265164 | − | 0.165361i | ||||
\(561\) | −3.04287 | + | 5.61644i | −0.00542400 | + | 0.0100115i | ||||
\(562\) | 4.47857 | − | 4.47857i | 0.00796898 | − | 0.00796898i | ||||
\(563\) | 510.844 | + | 510.844i | 0.907361 | + | 0.907361i | 0.996059 | − | 0.0886978i | \(-0.0282706\pi\) |
−0.0886978 | + | 0.996059i | \(0.528271\pi\) | |||||||
\(564\) | −274.337 | + | 506.364i | −0.486414 | + | 0.897809i | ||||
\(565\) | −133.063 | + | 341.466i | −0.235510 | + | 0.604364i | ||||
\(566\) | −342.455 | −0.605043 | ||||||||
\(567\) | 557.415 | − | 103.814i | 0.983095 | − | 0.183094i | ||||
\(568\) | 242.633 | + | 242.633i | 0.427171 | + | 0.427171i | ||||
\(569\) | 789.111 | 1.38684 | 0.693419 | − | 0.720534i | \(-0.256103\pi\) | ||||
0.693419 | + | 0.720534i | \(0.256103\pi\) | |||||||
\(570\) | 20.5411 | − | 247.840i | 0.0360371 | − | 0.434807i | ||||
\(571\) | −320.476 | −0.561254 | −0.280627 | − | 0.959817i | \(-0.590542\pi\) | ||||
−0.280627 | + | 0.959817i | \(0.590542\pi\) | |||||||
\(572\) | 69.4554 | − | 69.4554i | 0.121426 | − | 0.121426i | ||||
\(573\) | 1066.71 | − | 317.030i | 1.86162 | − | 0.553280i | ||||
\(574\) | −22.2023 | + | 117.971i | −0.0386800 | + | 0.205525i | ||||
\(575\) | −39.5778 | − | 936.485i | −0.0688309 | − | 1.62867i | ||||
\(576\) | 63.9012 | + | 98.0084i | 0.110940 | + | 0.170153i | ||||
\(577\) | −313.311 | − | 313.311i | −0.542999 | − | 0.542999i | 0.381408 | − | 0.924407i | \(-0.375439\pi\) |
−0.924407 | + | 0.381408i | \(0.875439\pi\) | |||||||
\(578\) | −203.876 | + | 203.876i | −0.352726 | + | 0.352726i | ||||
\(579\) | −164.983 | + | 304.520i | −0.284944 | + | 0.525942i | ||||
\(580\) | 69.6819 | + | 158.665i | 0.120141 | + | 0.273560i | ||||
\(581\) | −98.2827 | + | 522.222i | −0.169161 | + | 0.898833i | ||||
\(582\) | −105.601 | + | 31.3849i | −0.181445 | + | 0.0539260i | ||||
\(583\) | −88.4524 | − | 88.4524i | −0.151719 | − | 0.151719i | ||||
\(584\) | 257.742i | 0.441339i | ||||||||
\(585\) | −116.499 | − | 556.957i | −0.199143 | − | 0.952064i | ||||
\(586\) | 471.443i | 0.804510i | ||||||||
\(587\) | −149.545 | + | 149.545i | −0.254762 | + | 0.254762i | −0.822920 | − | 0.568158i | \(-0.807656\pi\) |
0.568158 | + | 0.822920i | \(0.307656\pi\) | |||||||
\(588\) | −36.6318 | + | 439.476i | −0.0622991 | + | 0.747408i | ||||
\(589\) | 511.152i | 0.867831i | ||||||||
\(590\) | 86.4556 | − | 221.861i | 0.146535 | − | 0.376036i | ||||
\(591\) | −368.219 | + | 679.648i | −0.623044 | + | 1.15000i | ||||
\(592\) | 207.464 | − | 207.464i | 0.350446 | − | 0.350446i | ||||
\(593\) | 198.048 | + | 198.048i | 0.333977 | + | 0.333977i | 0.854095 | − | 0.520118i | \(-0.174112\pi\) |
−0.520118 | + | 0.854095i | \(0.674112\pi\) | |||||||
\(594\) | −69.6819 | + | 5.67547i | −0.117310 | + | 0.00955466i | ||||
\(595\) | −28.0373 | + | 6.49950i | −0.0471216 | + | 0.0109235i | ||||
\(596\) | 74.2159i | 0.124523i | ||||||||
\(597\) | −26.6962 | − | 89.8248i | −0.0447173 | − | 0.150460i | ||||
\(598\) | −335.229 | + | 335.229i | −0.560584 | + | 0.560584i | ||||
\(599\) | 475.156 | 0.793248 | 0.396624 | − | 0.917981i | \(-0.370182\pi\) | ||||
0.396624 | + | 0.917981i | \(0.370182\pi\) | |||||||
\(600\) | 496.480 | − | 170.682i | 0.827467 | − | 0.284469i | ||||
\(601\) | − | 373.965i | − | 0.622237i | −0.950371 | − | 0.311119i | \(-0.899296\pi\) | ||
0.950371 | − | 0.311119i | \(-0.100704\pi\) | |||||||
\(602\) | 205.613 | − | 140.478i | 0.341549 | − | 0.233352i | ||||
\(603\) | −190.157 | + | 902.690i | −0.315351 | + | 1.49700i | ||||
\(604\) | 350.029i | 0.579518i | ||||||||
\(605\) | 523.239 | − | 229.795i | 0.864858 | − | 0.379826i | ||||
\(606\) | −33.8583 | + | 62.4948i | −0.0558718 | + | 0.103127i | ||||
\(607\) | 632.018 | + | 632.018i | 1.04122 | + | 1.04122i | 0.999113 | + | 0.0421025i | \(0.0134056\pi\) |
0.0421025 | + | 0.999113i | \(0.486594\pi\) | |||||||
\(608\) | 386.871 | + | 386.871i | 0.636300 | + | 0.636300i | ||||
\(609\) | 153.028 | − | 188.258i | 0.251278 | − | 0.309127i | ||||
\(610\) | −143.408 | + | 368.013i | −0.235096 | + | 0.603300i | ||||
\(611\) | − | 809.125i | − | 1.32426i | ||||||
\(612\) | −21.7255 | − | 4.57661i | −0.0354992 | − | 0.00747812i | ||||
\(613\) | 587.183 | + | 587.183i | 0.957885 | + | 0.957885i | 0.999148 | − | 0.0412636i | \(-0.0131383\pi\) |
−0.0412636 | + | 0.999148i | \(0.513138\pi\) | |||||||
\(614\) | − | 163.693i | − | 0.266601i | ||||||
\(615\) | 166.247 | + | 196.294i | 0.270320 | + | 0.319177i | ||||
\(616\) | 23.4667 | − | 124.689i | 0.0380953 | − | 0.202418i | ||||
\(617\) | 111.144 | + | 111.144i | 0.180136 | + | 0.180136i | 0.791415 | − | 0.611279i | \(-0.209345\pi\) |
−0.611279 | + | 0.791415i | \(0.709345\pi\) | |||||||
\(618\) | 95.0646 | + | 319.864i | 0.153826 | + | 0.517579i | ||||
\(619\) | −716.455 | −1.15744 | −0.578720 | − | 0.815526i | \(-0.696448\pi\) | ||||
−0.578720 | + | 0.815526i | \(0.696448\pi\) | |||||||
\(620\) | −423.426 | + | 185.959i | −0.682945 | + | 0.299934i | ||||
\(621\) | −1008.97 | + | 82.1785i | −1.62474 | + | 0.132333i | ||||
\(622\) | 61.8700 | + | 61.8700i | 0.0994694 | + | 0.0994694i | ||||
\(623\) | 81.2259 | − | 55.4949i | 0.130379 | − | 0.0890769i | ||||
\(624\) | 166.768 | + | 90.3512i | 0.267256 | + | 0.144794i | ||||
\(625\) | −52.7333 | − | 622.771i | −0.0843734 | − | 0.996434i | ||||
\(626\) | −106.006 | −0.169338 | ||||||||
\(627\) | −123.452 | + | 36.6905i | −0.196894 | + | 0.0585175i | ||||
\(628\) | 428.636 | − | 428.636i | 0.682541 | − | 0.682541i | ||||
\(629\) | − | 48.2529i | − | 0.0767137i | ||||||
\(630\) | −227.186 | − | 218.200i | −0.360613 | − | 0.346350i | ||||
\(631\) | 4.81666 | 0.00763338 | 0.00381669 | − | 0.999993i | \(-0.498785\pi\) | ||||
0.00381669 | + | 0.999993i | \(0.498785\pi\) | |||||||
\(632\) | 375.203 | + | 375.203i | 0.593675 | + | 0.593675i | ||||
\(633\) | −82.5522 | − | 277.764i | −0.130414 | − | 0.438805i | ||||
\(634\) | − | 555.914i | − | 0.876836i | ||||||
\(635\) | 55.5786 | − | 142.625i | 0.0875254 | − | 0.224607i | ||||
\(636\) | 207.114 | − | 382.286i | 0.325651 | − | 0.601078i | ||||
\(637\) | −248.875 | − | 567.409i | −0.390699 | − | 0.890751i | ||||
\(638\) | −21.1526 | + | 21.1526i | −0.0331545 | + | 0.0331545i | ||||
\(639\) | −240.953 | − | 369.562i | −0.377079 | − | 0.578344i | ||||
\(640\) | −216.038 | + | 554.394i | −0.337559 | + | 0.866241i | ||||
\(641\) | 121.164i | 0.189024i | 0.995524 | + | 0.0945120i | \(0.0301291\pi\) | ||||
−0.995524 | + | 0.0945120i | \(0.969871\pi\) | |||||||
\(642\) | −507.818 | + | 150.925i | −0.790994 | + | 0.235086i | ||||
\(643\) | −524.336 | + | 524.336i | −0.815453 | + | 0.815453i | −0.985445 | − | 0.169993i | \(-0.945626\pi\) |
0.169993 | + | 0.985445i | \(0.445626\pi\) | |||||||
\(644\) | 145.624 | − | 773.766i | 0.226124 | − | 1.20150i | ||||
\(645\) | 44.0751 | − | 531.790i | 0.0683334 | − | 0.824480i | ||||
\(646\) | 13.6333 | 0.0211042 | ||||||||
\(647\) | −305.897 | + | 305.897i | −0.472792 | + | 0.472792i | −0.902817 | − | 0.430025i | \(-0.858505\pi\) |
0.430025 | + | 0.902817i | \(0.358505\pi\) | |||||||
\(648\) | −205.119 | − | 528.597i | −0.316542 | − | 0.815736i | ||||
\(649\) | −123.311 | −0.190002 | ||||||||
\(650\) | −213.891 | + | 232.768i | −0.329063 | + | 0.358104i | ||||
\(651\) | 502.402 | + | 408.384i | 0.771739 | + | 0.627317i | ||||
\(652\) | 291.464 | − | 291.464i | 0.447031 | − | 0.447031i | ||||
\(653\) | −307.322 | + | 307.322i | −0.470631 | + | 0.470631i | −0.902119 | − | 0.431488i | \(-0.857989\pi\) |
0.431488 | + | 0.902119i | \(0.357989\pi\) | |||||||
\(654\) | 192.518 | + | 104.302i | 0.294370 | + | 0.159484i | ||||
\(655\) | −996.449 | + | 437.618i | −1.52130 | + | 0.668119i | ||||
\(656\) | −85.7446 | −0.130708 | ||||||||
\(657\) | 68.3085 | − | 324.266i | 0.103970 | − | 0.493555i | ||||
\(658\) | −252.686 | − | 369.847i | −0.384021 | − | 0.562078i | ||||
\(659\) | 903.538 | 1.37107 | 0.685537 | − | 0.728038i | \(-0.259568\pi\) | ||||
0.685537 | + | 0.728038i | \(0.259568\pi\) | |||||||
\(660\) | −75.3059 | − | 88.9167i | −0.114100 | − | 0.134722i | ||||
\(661\) | − | 1162.10i | − | 1.75809i | −0.476737 | − | 0.879046i | \(-0.658180\pi\) | ||
0.476737 | − | 0.879046i | \(-0.341820\pi\) | |||||||
\(662\) | 173.231 | + | 173.231i | 0.261678 | + | 0.261678i | ||||
\(663\) | 29.9009 | − | 8.88664i | 0.0450994 | − | 0.0134037i | ||||
\(664\) | 531.390 | 0.800286 | ||||||||
\(665\) | −492.379 | − | 307.057i | −0.740419 | − | 0.461739i | ||||
\(666\) | 442.393 | − | 288.439i | 0.664254 | − | 0.433092i | ||||
\(667\) | −306.281 | + | 306.281i | −0.459192 | + | 0.459192i | ||||
\(668\) | −621.735 | − | 621.735i | −0.930741 | − | 0.930741i | ||||
\(669\) | 298.237 | + | 161.579i | 0.445796 | + | 0.241523i | ||||
\(670\) | 469.242 | − | 206.080i | 0.700361 | − | 0.307583i | ||||
\(671\) | 204.543 | 0.304832 | ||||||||
\(672\) | 689.337 | − | 71.1590i | 1.02580 | − | 0.105891i | ||||
\(673\) | 256.857 | + | 256.857i | 0.381660 | + | 0.381660i | 0.871700 | − | 0.490040i | \(-0.163018\pi\) |
−0.490040 | + | 0.871700i | \(0.663018\pi\) | |||||||
\(674\) | −471.748 | −0.699923 | ||||||||
\(675\) | −669.858 | + | 83.1546i | −0.992383 | + | 0.123192i | ||||
\(676\) | 27.3357 | 0.0404374 | ||||||||
\(677\) | 248.270 | − | 248.270i | 0.366721 | − | 0.366721i | −0.499559 | − | 0.866280i | \(-0.666504\pi\) |
0.866280 | + | 0.499559i | \(0.166504\pi\) | |||||||
\(678\) | −62.6427 | − | 210.774i | −0.0923933 | − | 0.310876i | ||||
\(679\) | −47.5432 | + | 252.619i | −0.0700194 | + | 0.372046i | ||||
\(680\) | 11.5730 | + | 26.3515i | 0.0170191 | + | 0.0387522i | ||||
\(681\) | −211.818 | − | 114.758i | −0.311039 | − | 0.168514i | ||||
\(682\) | −56.4496 | − | 56.4496i | −0.0827706 | − | 0.0827706i | ||||
\(683\) | −216.136 | + | 216.136i | −0.316450 | + | 0.316450i | −0.847402 | − | 0.530952i | \(-0.821835\pi\) |
0.530952 | + | 0.847402i | \(0.321835\pi\) | |||||||
\(684\) | −244.486 | − | 374.980i | −0.357435 | − | 0.548216i | ||||
\(685\) | 211.941 | + | 82.5897i | 0.309403 | + | 0.120569i | ||||
\(686\) | −290.959 | − | 181.637i | −0.424138 | − | 0.264777i | ||||
\(687\) | −131.457 | − | 442.314i | −0.191350 | − | 0.643835i | ||||
\(688\) | 125.774 | + | 125.774i | 0.182811 | + | 0.182811i | ||||
\(689\) | 610.859i | 0.886587i | ||||||||
\(690\) | 363.466 | + | 429.160i | 0.526763 | + | 0.621970i | ||||
\(691\) | − | 167.027i | − | 0.241717i | −0.992670 | − | 0.120859i | \(-0.961435\pi\) | ||
0.992670 | − | 0.120859i | \(-0.0385648\pi\) | |||||||
\(692\) | −346.332 | + | 346.332i | −0.500480 | + | 0.500480i | ||||
\(693\) | −62.5695 | + | 150.653i | −0.0902879 | + | 0.217392i | ||||
\(694\) | − | 319.857i | − | 0.460889i | ||||||
\(695\) | −515.338 | + | 226.325i | −0.741493 | + | 0.325647i | ||||
\(696\) | −213.314 | − | 115.569i | −0.306485 | − | 0.166047i | ||||
\(697\) | −9.97142 | + | 9.97142i | −0.0143062 | + | 0.0143062i | ||||
\(698\) | 174.892 | + | 174.892i | 0.250562 | + | 0.250562i | ||||
\(699\) | 187.613 | + | 101.645i | 0.268402 | + | 0.145415i | ||||
\(700\) | 75.2290 | − | 519.582i | 0.107470 | − | 0.742260i | ||||
\(701\) | 602.095i | 0.858908i | 0.903089 | + | 0.429454i | \(0.141294\pi\) | ||||
−0.903089 | + | 0.429454i | \(0.858706\pi\) | |||||||
\(702\) | 260.212 | + | 221.017i | 0.370672 | + | 0.314838i | ||||
\(703\) | 687.923 | − | 687.923i | 0.978554 | − | 0.978554i | ||||
\(704\) | −33.6616 | −0.0478148 | ||||||||
\(705\) | −956.561 | − | 79.2803i | −1.35682 | − | 0.112454i | ||||
\(706\) | − | 390.920i | − | 0.553711i | ||||||
\(707\) | 93.5584 | + | 136.938i | 0.132332 | + | 0.193689i | ||||
\(708\) | −122.103 | − | 410.840i | −0.172462 | − | 0.580282i | ||||
\(709\) | 37.8334i | 0.0533616i | 0.999644 | + | 0.0266808i | \(0.00849377\pi\) | ||||
−0.999644 | + | 0.0266808i | \(0.991506\pi\) | |||||||
\(710\) | −88.9918 | + | 228.370i | −0.125341 | + | 0.321648i | ||||
\(711\) | −372.605 | − | 571.482i | −0.524057 | − | 0.803772i | ||||
\(712\) | −69.5605 | − | 69.5605i | −0.0976973 | − | 0.0976973i | ||||
\(713\) | −817.367 | − | 817.367i | −1.14638 | − | 1.14638i | ||||
\(714\) | 10.8923 | − | 13.3999i | 0.0152553 | − | 0.0187674i | ||||
\(715\) | 152.536 | + | 59.4405i | 0.213337 | + | 0.0831336i | ||||
\(716\) | − | 710.612i | − | 0.992475i | ||||||
\(717\) | −112.594 | − | 378.845i | −0.157035 | − | 0.528375i | ||||
\(718\) | 277.633 | + | 277.633i | 0.386676 | + | 0.386676i | ||||
\(719\) | − | 408.265i | − | 0.567824i | −0.958850 | − | 0.283912i | \(-0.908368\pi\) | ||
0.958850 | − | 0.283912i | \(-0.0916324\pi\) | |||||||
\(720\) | 123.155 | − | 188.303i | 0.171049 | − | 0.261531i | ||||
\(721\) | 765.181 | + | 144.008i | 1.06128 | + | 0.199734i | ||||
\(722\) | −60.9004 | − | 60.9004i | −0.0843496 | − | 0.0843496i | ||||
\(723\) | 296.286 | − | 88.0571i | 0.409800 | − | 0.121794i | ||||
\(724\) | 683.597 | 0.944195 | ||||||||
\(725\) | −195.421 | + | 212.667i | −0.269546 | + | 0.293334i | ||||
\(726\) | −163.337 | + | 301.483i | −0.224982 | + | 0.415265i | ||||
\(727\) | −660.880 | − | 660.880i | −0.909051 | − | 0.909051i | 0.0871447 | − | 0.996196i | \(-0.472226\pi\) |
−0.996196 | + | 0.0871447i | \(0.972226\pi\) | |||||||
\(728\) | −511.589 | + | 349.526i | −0.702732 | + | 0.480118i | ||||
\(729\) | 117.969 | + | 719.392i | 0.161823 | + | 0.986820i | ||||
\(730\) | −168.562 | + | 74.0286i | −0.230907 | + | 0.101409i | ||||
\(731\) | 29.2530 | 0.0400178 | ||||||||
\(732\) | 202.538 | + | 681.481i | 0.276692 | + | 0.930985i | ||||
\(733\) | −526.757 | + | 526.757i | −0.718632 | + | 0.718632i | −0.968325 | − | 0.249693i | \(-0.919670\pi\) |
0.249693 | + | 0.968325i | \(0.419670\pi\) | |||||||
\(734\) | 328.745i | 0.447882i | ||||||||
\(735\) | −695.185 | + | 238.628i | −0.945829 | + | 0.324664i | ||||
\(736\) | −1237.26 | −1.68107 | ||||||||
\(737\) | −187.673 | − | 187.673i | −0.254644 | − | 0.254644i | ||||
\(738\) | −151.026 | − | 31.8144i | −0.204642 | − | 0.0431090i | ||||
\(739\) | 276.981i | 0.374805i | 0.982283 | + | 0.187402i | \(0.0600069\pi\) | ||||
−0.982283 | + | 0.187402i | \(0.939993\pi\) | |||||||
\(740\) | 820.127 | + | 319.589i | 1.10828 | + | 0.431877i | ||||
\(741\) | 552.979 | + | 299.592i | 0.746261 | + | 0.404308i | ||||
\(742\) | 190.768 | + | 279.221i | 0.257100 | + | 0.376308i | ||||
\(743\) | −698.839 | + | 698.839i | −0.940563 | + | 0.940563i | −0.998330 | − | 0.0577666i | \(-0.981602\pi\) |
0.0577666 | + | 0.998330i | \(0.481602\pi\) | |||||||
\(744\) | 308.416 | − | 569.267i | 0.414538 | − | 0.765143i | ||||
\(745\) | −113.253 | + | 49.7380i | −0.152017 | + | 0.0667624i | ||||
\(746\) | − | 275.115i | − | 0.368787i | ||||||
\(747\) | −668.543 | − | 140.832i | −0.894971 | − | 0.188531i | ||||
\(748\) | 4.51683 | − | 4.51683i | 0.00603854 | − | 0.00603854i | ||||
\(749\) | −228.628 | + | 1214.81i | −0.305244 | + | 1.62190i | ||||
\(750\) | 254.224 | + | 275.672i | 0.338965 | + | 0.367563i | ||||
\(751\) | 488.791 | 0.650853 | 0.325426 | − | 0.945567i | \(-0.394492\pi\) | ||||
0.325426 | + | 0.945567i | \(0.394492\pi\) | |||||||
\(752\) | 226.237 | − | 226.237i | 0.300846 | − | 0.300846i | ||||
\(753\) | −310.580 | − | 1045.01i | −0.412457 | − | 1.38780i | ||||
\(754\) | 146.081 | 0.193742 | ||||||||
\(755\) | −534.139 | + | 234.582i | −0.707469 | + | 0.310704i | ||||
\(756\) | −563.892 | − | 59.2882i | −0.745889 | − | 0.0784236i | ||||
\(757\) | −269.069 | + | 269.069i | −0.355441 | + | 0.355441i | −0.862129 | − | 0.506688i | \(-0.830870\pi\) |
0.506688 | + | 0.862129i | \(0.330870\pi\) | |||||||
\(758\) | 244.100 | − | 244.100i | 0.322032 | − | 0.322032i | ||||
\(759\) | 138.738 | − | 256.079i | 0.182791 | − | 0.337390i | ||||
\(760\) | −210.692 | + | 540.675i | −0.277226 | + | 0.711414i | ||||
\(761\) | 973.280 | 1.27895 | 0.639475 | − | 0.768812i | \(-0.279152\pi\) | ||||
0.639475 | + | 0.768812i | \(0.279152\pi\) | |||||||
\(762\) | 26.1649 | + | 88.0372i | 0.0343372 | + | 0.115534i | ||||
\(763\) | 421.845 | − | 288.211i | 0.552876 | − | 0.377734i | ||||
\(764\) | −1112.82 | −1.45658 | ||||||||
\(765\) | −7.57616 | − | 36.2200i | −0.00990347 | − | 0.0473465i | ||||
\(766\) | 66.0510i | 0.0862285i | ||||||||
\(767\) | 425.798 | + | 425.798i | 0.555147 | + | 0.555147i | ||||
\(768\) | −146.147 | − | 491.742i | −0.190296 | − | 0.640289i | ||||
\(769\) | −1055.77 | −1.37292 | −0.686458 | − | 0.727169i | \(-0.740835\pi\) | ||||
−0.686458 | + | 0.727169i | \(0.740835\pi\) | |||||||
\(770\) | 88.2863 | − | 20.4662i | 0.114658 | − | 0.0265795i | ||||
\(771\) | 324.226 | + | 175.659i | 0.420527 | + | 0.227832i | ||||
\(772\) | 244.900 | − | 244.900i | 0.317228 | − | 0.317228i | ||||
\(773\) | 545.306 | + | 545.306i | 0.705441 | + | 0.705441i | 0.965573 | − | 0.260132i | \(-0.0837661\pi\) |
−0.260132 | + | 0.965573i | \(0.583766\pi\) | |||||||
\(774\) | 174.864 | + | 268.198i | 0.225923 | + | 0.346509i | ||||
\(775\) | −567.542 | − | 521.516i | −0.732312 | − | 0.672924i | ||||
\(776\) | 257.054 | 0.331255 | ||||||||
\(777\) | −126.533 | − | 1225.76i | −0.162848 | − | 1.57756i | ||||
\(778\) | −528.450 | − | 528.450i | −0.679242 | − | 0.679242i | ||||
\(779\) | −284.318 | −0.364978 | ||||||||
\(780\) | −46.9988 | + | 567.067i | −0.0602549 | + | 0.727008i | ||||
\(781\) | 126.929 | 0.162521 | ||||||||
\(782\) | −21.8006 | + | 21.8006i | −0.0278780 | + | 0.0278780i | ||||
\(783\) | 237.742 | + | 201.931i | 0.303629 | + | 0.257894i | ||||
\(784\) | 89.0639 | − | 228.238i | 0.113602 | − | 0.291120i | ||||
\(785\) | 941.356 | + | 366.830i | 1.19918 | + | 0.467300i | ||||
\(786\) | 311.056 | − | 574.139i | 0.395745 | − | 0.730456i | ||||
\(787\) | 366.303 | + | 366.303i | 0.465442 | + | 0.465442i | 0.900434 | − | 0.434992i | \(-0.143249\pi\) |
−0.434992 | + | 0.900434i | \(0.643249\pi\) | |||||||
\(788\) | 546.583 | − | 546.583i | 0.693634 | − | 0.693634i | ||||
\(789\) | 364.085 | + | 197.254i | 0.461451 | + | 0.250004i | ||||
\(790\) | −137.615 | + | 353.146i | −0.174196 | + | 0.447020i | ||||
\(791\) | −504.215 | − | 94.8938i | −0.637440 | − | 0.119967i | ||||
\(792\) | 159.626 | + | 33.6262i | 0.201548 | + | 0.0424573i | ||||
\(793\) | −706.293 | − | 706.293i | −0.890659 | − | 0.890659i | ||||
\(794\) | − | 453.775i | − | 0.571505i | ||||||
\(795\) | 722.167 | + | 59.8536i | 0.908386 | + | 0.0752876i | ||||
\(796\) | 93.7080i | 0.117724i | ||||||||
\(797\) | −124.772 | + | 124.772i | −0.156552 | + | 0.156552i | −0.781037 | − | 0.624485i | \(-0.785309\pi\) |
0.624485 | + | 0.781037i | \(0.285309\pi\) | |||||||
\(798\) | 346.325 | − | 35.7506i | 0.433992 | − | 0.0448002i | ||||
\(799\) | − | 52.6190i | − | 0.0658561i | ||||||
\(800\) | −824.264 | + | 34.8351i | −1.03033 | + | 0.0435438i | ||||
\(801\) | 69.0789 | + | 105.950i | 0.0862408 | + | 0.132272i | ||||
\(802\) | −334.181 | + | 334.181i | −0.416684 | + | 0.416684i | ||||
\(803\) | 67.4162 | + | 67.4162i | 0.0839554 | + | 0.0839554i | ||||
\(804\) | 439.442 | − | 811.110i | 0.546570 | − | 1.00884i | ||||
\(805\) | 1278.35 | − | 296.342i | 1.58801 | − | 0.368127i | ||||
\(806\) | 389.845i | 0.483678i | ||||||||
\(807\) | 344.545 | − | 102.400i | 0.426946 | − | 0.126890i | ||||
\(808\) | 117.272 | − | 117.272i | 0.145138 | − | 0.145138i | ||||
\(809\) | −89.2503 | −0.110322 | −0.0551609 | − | 0.998477i | \(-0.517567\pi\) | ||||
−0.0551609 | + | 0.998477i | \(0.517567\pi\) | |||||||
\(810\) | 286.785 | − | 285.971i | 0.354056 | − | 0.353050i | ||||
\(811\) | 959.059i | 1.18256i | 0.806465 | + | 0.591282i | \(0.201378\pi\) | ||||
−0.806465 | + | 0.591282i | \(0.798622\pi\) | |||||||
\(812\) | −200.319 | + | 136.861i | −0.246698 | + | 0.168549i | ||||
\(813\) | 709.275 | − | 210.799i | 0.872417 | − | 0.259285i | ||||
\(814\) | 151.943i | 0.186662i | ||||||||
\(815\) | 640.104 | + | 249.438i | 0.785404 | + | 0.306058i | ||||
\(816\) | 10.8452 | + | 5.87572i | 0.0132907 | + | 0.00720063i | ||||
\(817\) | 417.049 | + | 417.049i | 0.510464 | + | 0.510464i | ||||
\(818\) | −86.1295 | − | 86.1295i | −0.105293 | − | 0.105293i | ||||
\(819\) | 736.265 | − | 304.155i | 0.898980 | − | 0.371374i | ||||
\(820\) | −103.436 | − | 235.521i | −0.126141 | − | 0.287221i | ||||
\(821\) | 699.817i | 0.852396i | 0.904630 | + | 0.426198i | \(0.140147\pi\) | ||||
−0.904630 | + | 0.426198i | \(0.859853\pi\) | |||||||
\(822\) | −130.823 | + | 38.8810i | −0.159152 | + | 0.0473005i | ||||
\(823\) | 945.067 | + | 945.067i | 1.14832 | + | 1.14832i | 0.986883 | + | 0.161436i | \(0.0516125\pi\) |
0.161436 | + | 0.986883i | \(0.448387\pi\) | |||||||
\(824\) | − | 778.614i | − | 0.944920i | ||||||
\(825\) | 85.2174 | − | 174.506i | 0.103294 | − | 0.211522i | ||||
\(826\) | 327.605 | + | 61.6556i | 0.396616 | + | 0.0746435i | ||||
\(827\) | −459.616 | − | 459.616i | −0.555763 | − | 0.555763i | 0.372335 | − | 0.928098i | \(-0.378557\pi\) |
−0.928098 | + | 0.372335i | \(0.878557\pi\) | |||||||
\(828\) | 990.567 | + | 208.669i | 1.19634 | + | 0.252015i | ||||
\(829\) | 197.279 | 0.237972 | 0.118986 | − | 0.992896i | \(-0.462036\pi\) | ||||
0.118986 | + | 0.992896i | \(0.462036\pi\) | |||||||
\(830\) | 152.626 | + | 347.526i | 0.183886 | + | 0.418706i | ||||
\(831\) | 190.932 | + | 103.443i | 0.229761 | + | 0.124480i | ||||
\(832\) | 116.235 | + | 116.235i | 0.139705 | + | 0.139705i | ||||
\(833\) | −16.1849 | − | 36.8997i | −0.0194296 | − | 0.0442974i | ||||
\(834\) | 160.870 | − | 296.930i | 0.192890 | − | 0.356031i | ||||
\(835\) | 532.086 | − | 1365.43i | 0.637228 | − | 1.63525i | ||||
\(836\) | 128.789 | 0.154054 | ||||||||
\(837\) | −538.890 | + | 634.457i | −0.643835 | + | 0.758014i | ||||
\(838\) | 64.4294 | − | 64.4294i | 0.0768847 | − | 0.0768847i | ||||
\(839\) | − | 1160.48i | − | 1.38317i | −0.722296 | − | 0.691584i | \(-0.756913\pi\) | ||
0.722296 | − | 0.691584i | \(-0.243087\pi\) | |||||||
\(840\) | 363.088 | + | 639.056i | 0.432248 | + | 0.760780i | ||||
\(841\) | −707.533 | −0.841300 | ||||||||
\(842\) | 43.3625 | + | 43.3625i | 0.0514994 | + | 0.0514994i | ||||
\(843\) | 18.2136 | − | 5.41313i | 0.0216057 | − | 0.00642127i | ||||
\(844\) | 289.771i | 0.343331i | ||||||||
\(845\) | 18.3198 | + | 41.7139i | 0.0216802 | + | 0.0493656i | ||||
\(846\) | 482.422 | − | 314.538i | 0.570239 | − | 0.371795i | ||||
\(847\) | 451.338 | + | 660.607i | 0.532866 | + | 0.779937i | ||||
\(848\) | −170.800 | + | 170.800i | −0.201415 | + | 0.201415i | ||||
\(849\) | −903.310 | − | 489.394i | −1.06397 | − | 0.576436i | ||||
\(850\) | −13.9098 | + | 15.1373i | −0.0163644 | + | 0.0178086i | ||||
\(851\) | 2200.07i | 2.58528i | ||||||||
\(852\) | 125.685 | + | 422.892i | 0.147518 | + | 0.496352i | ||||
\(853\) | −727.157 | + | 727.157i | −0.852470 | + | 0.852470i | −0.990437 | − | 0.137967i | \(-0.955943\pi\) |
0.137967 | + | 0.990437i | \(0.455943\pi\) | |||||||
\(854\) | −543.415 | − | 102.271i | −0.636317 | − | 0.119756i | ||||
\(855\) | 408.365 | − | 624.386i | 0.477620 | − | 0.730276i | ||||
\(856\) | 1236.13 | 1.44408 | ||||||||
\(857\) | 330.023 | − | 330.023i | 0.385091 | − | 0.385091i | −0.487841 | − | 0.872932i | \(-0.662216\pi\) |
0.872932 | + | 0.487841i | \(0.162216\pi\) | |||||||
\(858\) | −94.1545 | + | 27.9830i | −0.109737 | + | 0.0326142i | ||||
\(859\) | −900.965 | −1.04885 | −0.524427 | − | 0.851456i | \(-0.675720\pi\) | ||||
−0.524427 | + | 0.851456i | \(0.675720\pi\) | |||||||
\(860\) | −193.749 | + | 497.196i | −0.225289 | + | 0.578135i | ||||
\(861\) | −227.155 | + | 279.451i | −0.263826 | + | 0.324565i | ||||
\(862\) | 126.705 | − | 126.705i | 0.146989 | − | 0.146989i | ||||
\(863\) | −35.9749 | + | 35.9749i | −0.0416859 | + | 0.0416859i | −0.727642 | − | 0.685957i | \(-0.759384\pi\) |
0.685957 | + | 0.727642i | \(0.259384\pi\) | |||||||
\(864\) | 72.3309 | + | 888.059i | 0.0837163 | + | 1.02785i | ||||
\(865\) | −760.604 | − | 296.394i | −0.879310 | − | 0.342652i | ||||
\(866\) | 331.251 | 0.382507 | ||||||||
\(867\) | −829.128 | + | 246.420i | −0.956318 | + | 0.284221i | ||||
\(868\) | −365.240 | − | 534.589i | −0.420783 | − | 0.615886i | ||||
\(869\) | 196.279 | 0.225868 | ||||||||
\(870\) | 14.3134 | − | 172.700i | 0.0164522 | − | 0.198505i | ||||
\(871\) | 1296.08i | 1.48804i | ||||||||
\(872\) | −361.261 | − | 361.261i | −0.414290 | − | 0.414290i | ||||
\(873\) | −323.400 | − | 68.1261i | −0.370447 | − | 0.0780368i | ||||
\(874\) | −621.606 | −0.711220 | ||||||||
\(875\) | 843.293 | − | 233.415i | 0.963763 | − | 0.266760i | ||||
\(876\) | −157.857 | + | 291.368i | −0.180202 | + | 0.332612i | ||||
\(877\) | −406.421 | + | 406.421i | −0.463422 | + | 0.463422i | −0.899775 | − | 0.436353i | \(-0.856270\pi\) |
0.436353 | + | 0.899775i | \(0.356270\pi\) | |||||||
\(878\) | 372.158 | + | 372.158i | 0.423870 | + | 0.423870i | ||||
\(879\) | −673.728 | + | 1243.55i | −0.766471 | + | 1.41473i | ||||
\(880\) | 26.0300 | + | 59.2699i | 0.0295795 | + | 0.0673522i | ||||
\(881\) | 5.04486 | 0.00572629 | 0.00286315 | − | 0.999996i | \(-0.499089\pi\) | ||||
0.00286315 | + | 0.999996i | \(0.499089\pi\) | |||||||
\(882\) | 241.557 | − | 368.960i | 0.273874 | − | 0.418322i | ||||
\(883\) | −215.321 | − | 215.321i | −0.243852 | − | 0.243852i | 0.574590 | − | 0.818442i | \(-0.305162\pi\) |
−0.818442 | + | 0.574590i | \(0.805162\pi\) | |||||||
\(884\) | −31.1935 | −0.0352868 | ||||||||
\(885\) | 545.106 | − | 461.664i | 0.615939 | − | 0.521654i | ||||
\(886\) | −293.886 | −0.331699 | ||||||||
\(887\) | 735.406 | − | 735.406i | 0.829094 | − | 0.829094i | −0.158298 | − | 0.987391i | \(-0.550601\pi\) |
0.987391 | + | 0.158298i | \(0.0506006\pi\) | |||||||
\(888\) | −1181.21 | + | 351.060i | −1.33019 | + | 0.395337i | ||||
\(889\) | 210.603 | + | 39.6357i | 0.236899 | + | 0.0445846i | ||||
\(890\) | 25.5130 | − | 65.4713i | 0.0286663 | − | 0.0735633i | ||||
\(891\) | −191.914 | − | 84.6103i | −0.215392 | − | 0.0949611i | ||||
\(892\) | −239.847 | − | 239.847i | −0.268887 | − | 0.268887i | ||||
\(893\) | 750.170 | − | 750.170i | 0.840056 | − | 0.840056i | ||||
\(894\) | 35.3534 | − | 65.2544i | 0.0395452 | − | 0.0729915i | ||||
\(895\) | 1084.38 | − | 476.237i | 1.21160 | − | 0.532109i | ||||
\(896\) | −818.628 | − | 154.067i | −0.913648 | − | 0.171949i | ||||
\(897\) | −1363.32 | + | 405.183i | −1.51987 | + | 0.451709i | ||||
\(898\) | −222.845 | − | 222.845i | −0.248157 | − | 0.248157i | ||||
\(899\) | 356.180i | 0.396196i | ||||||||
\(900\) | 665.790 | + | 111.125i | 0.739767 | + | 0.123473i | ||||
\(901\) | 39.7254i | 0.0440903i | ||||||||
\(902\) | 31.3989 | − | 31.3989i | 0.0348103 | − | 0.0348103i | ||||
\(903\) | 743.109 | − | 76.7099i | 0.822934 | − | 0.0849500i | ||||
\(904\) | 513.067i | 0.567552i | ||||||||
\(905\) | 458.133 | + | 1043.16i | 0.506224 | + | 1.15266i | ||||
\(906\) | 166.739 | − | 307.763i | 0.184039 | − | 0.339694i | ||||
\(907\) | −553.040 | + | 553.040i | −0.609747 | + | 0.609747i | −0.942880 | − | 0.333133i | \(-0.891894\pi\) |
0.333133 | + | 0.942880i | \(0.391894\pi\) | |||||||
\(908\) | 170.347 | + | 170.347i | 0.187607 | + | 0.187607i | ||||
\(909\) | −178.620 | + | 116.460i | −0.196501 | + | 0.128118i | ||||
\(910\) | −375.526 | − | 234.185i | −0.412666 | − | 0.257347i | ||||
\(911\) | − | 466.216i | − | 0.511763i | −0.966708 | − | 0.255881i | \(-0.917634\pi\) | ||
0.966708 | − | 0.255881i | \(-0.0823656\pi\) | |||||||
\(912\) | 70.8486 | + | 238.384i | 0.0776849 | + | 0.261386i | ||||
\(913\) | 138.993 | − | 138.993i | 0.152237 | − | 0.152237i | ||||
\(914\) | −505.969 | −0.553576 | ||||||||
\(915\) | −904.195 | + | 765.786i | −0.988191 | + | 0.836924i | ||||
\(916\) | 461.436i | 0.503751i | ||||||||
\(917\) | −859.520 | − | 1258.05i | −0.937318 | − | 1.37192i | ||||
\(918\) | 16.9221 | + | 14.3731i | 0.0184336 | + | 0.0156570i | ||||
\(919\) | − | 1125.94i | − | 1.22518i | −0.790401 | − | 0.612590i | \(-0.790128\pi\) | ||
0.790401 | − | 0.612590i | \(-0.209872\pi\) | |||||||
\(920\) | −527.666 | − | 1201.49i | −0.573550 | − | 1.30596i | ||||
\(921\) | 233.930 | − | 431.781i | 0.253995 | − | 0.468818i | ||||
\(922\) | −398.564 | − | 398.564i | −0.432282 | − | 0.432282i | ||||
\(923\) | −438.289 | − | 438.289i | −0.474853 | − | 0.474853i | ||||
\(924\) | 102.896 | − | 126.585i | 0.111359 | − | 0.136996i | ||||
\(925\) | 61.9428 | + | 1465.69i | 0.0669652 | + | 1.58453i | ||||
\(926\) | − | 38.1636i | − | 0.0412133i | ||||||
\(927\) | −206.353 | + | 979.577i | −0.222603 | + | 1.05672i | ||||
\(928\) | 269.579 | + | 269.579i | 0.290494 | + | 0.290494i | ||||
\(929\) | 1846.32i | 1.98743i | 0.111954 | + | 0.993713i | \(0.464289\pi\) | ||||
−0.111954 | + | 0.993713i | \(0.535711\pi\) | |||||||
\(930\) | 460.881 | + | 38.1981i | 0.495571 | + | 0.0410732i | ||||
\(931\) | 295.324 | − | 756.806i | 0.317211 | − | 0.812896i | ||||
\(932\) | −150.881 | − | 150.881i | −0.161890 | − | 0.161890i | ||||
\(933\) | 74.7807 | + | 251.615i | 0.0801508 | + | 0.269683i | ||||
\(934\) | 384.000 | 0.411135 | ||||||||
\(935\) | 9.91970 | + | 3.86554i | 0.0106093 | + | 0.00413426i | ||||
\(936\) | −435.083 | − | 667.307i | −0.464832 | − | 0.712935i | ||||
\(937\) | 814.593 | + | 814.593i | 0.869363 | + | 0.869363i | 0.992402 | − | 0.123039i | \(-0.0392640\pi\) |
−0.123039 | + | 0.992402i | \(0.539264\pi\) | |||||||
\(938\) | 404.760 | + | 592.433i | 0.431514 | + | 0.631592i | ||||
\(939\) | −279.617 | − | 151.490i | −0.297782 | − | 0.161332i | ||||
\(940\) | 894.336 | + | 348.507i | 0.951421 | + | 0.370752i | ||||
\(941\) | −1318.27 | −1.40093 | −0.700464 | − | 0.713687i | \(-0.747024\pi\) | ||||
−0.700464 | + | 0.713687i | \(0.747024\pi\) | |||||||
\(942\) | −581.063 | + | 172.694i | −0.616840 | + | 0.183327i | ||||
\(943\) | 454.643 | − | 454.643i | 0.482124 | − | 0.482124i | ||||
\(944\) | 238.111i | 0.252237i | ||||||||
\(945\) | −287.435 | − | 900.225i | −0.304165 | − | 0.952620i | ||||
\(946\) | −92.1143 | −0.0973724 | ||||||||
\(947\) | 347.435 | + | 347.435i | 0.366880 | + | 0.366880i | 0.866338 | − | 0.499458i | \(-0.166468\pi\) |
−0.499458 | + | 0.866338i | \(0.666468\pi\) | |||||||
\(948\) | 194.356 | + | 653.951i | 0.205017 | + | 0.689821i | ||||
\(949\) | − | 465.581i | − | 0.490602i | ||||||
\(950\) | −414.113 | + | 17.5013i | −0.435909 | + | 0.0184224i | ||||
\(951\) | 794.444 | − | 1466.36i | 0.835378 | − | 1.54192i | ||||
\(952\) | −33.2696 | + | 22.7304i | −0.0349471 | + | 0.0238764i | ||||
\(953\) | 992.679 | − | 992.679i | 1.04164 | − | 1.04164i | 0.0425407 | − | 0.999095i | \(-0.486455\pi\) |
0.999095 | − | 0.0425407i | \(-0.0135452\pi\) | |||||||
\(954\) | −364.211 | + | 237.464i | −0.381772 | + | 0.248914i | ||||
\(955\) | −745.792 | − | 1698.16i | −0.780934 | − | 1.77817i | ||||
\(956\) | 395.222i | 0.413412i | ||||||||
\(957\) | −86.0240 | + | 25.5666i | −0.0898892 | + | 0.0267154i | ||||
\(958\) | 366.262 | − | 366.262i | 0.382320 | − | 0.382320i | ||||
\(959\) | −58.8986 | + | 312.956i | −0.0614167 | + | 0.326336i | ||||
\(960\) | 148.804 | − | 126.026i | 0.155004 | − | 0.131277i | ||||
\(961\) | 10.4667 | 0.0108915 | ||||||||
\(962\) | 524.664 | − | 524.664i | 0.545389 | − | 0.545389i | ||||
\(963\) | −1555.18 | − | 327.608i | −1.61494 | − | 0.340195i | ||||
\(964\) | −309.094 | −0.320637 | ||||||||
\(965\) | 537.841 | + | 209.587i | 0.557348 | + | 0.217189i | ||||
\(966\) | −496.630 | + | 610.965i | −0.514110 | + | 0.632469i | ||||
\(967\) | 1047.59 | − | 1047.59i | 1.08334 | − | 1.08334i | 0.0871396 | − | 0.996196i | \(-0.472227\pi\) |
0.996196 | − | 0.0871396i | \(-0.0277726\pi\) | |||||||
\(968\) | 565.733 | − | 565.733i | 0.584434 | − | 0.584434i | ||||
\(969\) | 35.9613 | + | 19.4831i | 0.0371118 | + | 0.0201064i | ||||
\(970\) | 73.8310 | + | 168.112i | 0.0761144 | + | 0.173311i | ||||
\(971\) | 379.480 | 0.390813 | 0.195407 | − | 0.980722i | \(-0.437397\pi\) | ||||
0.195407 | + | 0.980722i | \(0.437397\pi\) | |||||||
\(972\) | 91.8652 | − | 723.189i | 0.0945115 | − | 0.744021i | ||||
\(973\) | −444.522 | − | 650.631i | −0.456857 | − | 0.668685i | ||||
\(974\) | 522.283 | 0.536224 | ||||||||
\(975\) | −896.834 | + | 308.317i | −0.919830 | + | 0.316222i | ||||
\(976\) | − | 394.968i | − | 0.404680i | ||||||
\(977\) | 305.408 | + | 305.408i | 0.312598 | + | 0.312598i | 0.845915 | − | 0.533318i | \(-0.179055\pi\) |
−0.533318 | + | 0.845915i | \(0.679055\pi\) | |||||||
\(978\) | −395.112 | + | 117.429i | −0.404000 | + | 0.120070i | ||||
\(979\) | −36.3891 | −0.0371697 | ||||||||
\(980\) | 734.359 | − | 30.6900i | 0.749346 | − | 0.0313163i | ||||
\(981\) | 358.760 | + | 550.247i | 0.365708 | + | 0.560904i | ||||
\(982\) | 298.364 | − | 298.364i | 0.303833 | − | 0.303833i | ||||
\(983\) | −522.805 | − | 522.805i | −0.531846 | − | 0.531846i | 0.389275 | − | 0.921121i | \(-0.372726\pi\) |
−0.921121 | + | 0.389275i | \(0.872726\pi\) | |||||||
\(984\) | 316.642 | + | 171.550i | 0.321791 | + | 0.174339i | ||||
\(985\) | 1200.39 | + | 467.771i | 1.21867 | + | 0.474894i | ||||
\(986\) | 9.49996 | 0.00963484 | ||||||||
\(987\) | −137.982 | − | 1336.67i | −0.139800 | − | 1.35428i | ||||
\(988\) | −444.714 | − | 444.714i | −0.450116 | − | 0.450116i | ||||
\(989\) | −1333.78 | −1.34861 | ||||||||
\(990\) | 23.8564 | + | 114.053i | 0.0240974 | + | 0.115205i | ||||
\(991\) | −1178.96 | −1.18967 | −0.594833 | − | 0.803849i | \(-0.702782\pi\) | ||||
−0.594833 | + | 0.803849i | \(0.702782\pi\) | |||||||
\(992\) | −719.420 | + | 719.420i | −0.725222 | + | 0.725222i | ||||
\(993\) | 209.380 | + | 704.501i | 0.210856 | + | 0.709467i | ||||
\(994\) | −337.215 | − | 63.4643i | −0.339251 | − | 0.0638474i | ||||
\(995\) | −142.997 | + | 62.8012i | −0.143716 | + | 0.0631167i | ||||
\(996\) | 600.718 | + | 325.456i | 0.603130 | + | 0.326763i | ||||
\(997\) | 266.821 | + | 266.821i | 0.267624 | + | 0.267624i | 0.828142 | − | 0.560518i | \(-0.189398\pi\) |
−0.560518 | + | 0.828142i | \(0.689398\pi\) | |||||||
\(998\) | −77.2632 | + | 77.2632i | −0.0774180 | + | 0.0774180i | ||||
\(999\) | 1579.12 | − | 128.617i | 1.58071 | − | 0.128746i |
(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.83.7 | yes | 16 | |
3.2 | odd | 2 | inner | 105.3.k.c.83.1 | yes | 16 | |
5.2 | odd | 4 | inner | 105.3.k.c.62.4 | yes | 16 | |
7.6 | odd | 2 | inner | 105.3.k.c.83.6 | yes | 16 | |
15.2 | even | 4 | inner | 105.3.k.c.62.6 | yes | 16 | |
21.20 | even | 2 | inner | 105.3.k.c.83.4 | yes | 16 | |
35.27 | even | 4 | inner | 105.3.k.c.62.1 | ✓ | 16 | |
105.62 | odd | 4 | inner | 105.3.k.c.62.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.c.62.1 | ✓ | 16 | 35.27 | even | 4 | inner | |
105.3.k.c.62.4 | yes | 16 | 5.2 | odd | 4 | inner | |
105.3.k.c.62.6 | yes | 16 | 15.2 | even | 4 | inner | |
105.3.k.c.62.7 | yes | 16 | 105.62 | odd | 4 | inner | |
105.3.k.c.83.1 | yes | 16 | 3.2 | odd | 2 | inner | |
105.3.k.c.83.4 | yes | 16 | 21.20 | even | 2 | inner | |
105.3.k.c.83.6 | yes | 16 | 7.6 | odd | 2 | inner | |
105.3.k.c.83.7 | yes | 16 | 1.1 | even | 1 | trivial |