Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(37,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(2.19691 - 2.19691i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.37 |
Dual form | 570.2.m.a.493.4 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.25884 | + | 1.84806i | 0.562970 | + | 0.826477i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.10690 | + | 3.10690i | 1.17430 | + | 1.17430i | 0.981175 | + | 0.193123i | \(0.0618615\pi\) |
0.193123 | + | 0.981175i | \(0.438138\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −2.19691 | − | 0.416642i | −0.694724 | − | 0.131754i | ||||
\(11\) | −3.82217 | −1.15243 | −0.576214 | − | 0.817299i | \(-0.695470\pi\) | ||||
−0.576214 | + | 0.817299i | \(0.695470\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | 0.0891314 | + | 0.0891314i | 0.0247206 | + | 0.0247206i | 0.719359 | − | 0.694638i | \(-0.244436\pi\) |
−0.694638 | + | 0.719359i | \(0.744436\pi\) | |||||||
\(14\) | −4.39382 | −1.17430 | ||||||||
\(15\) | 0.416642 | − | 2.19691i | 0.107576 | − | 0.567239i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.83065 | − | 1.83065i | −0.443998 | − | 0.443998i | 0.449355 | − | 0.893353i | \(-0.351654\pi\) |
−0.893353 | + | 0.449355i | \(0.851654\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | 2.70268 | + | 3.41987i | 0.620038 | + | 0.784572i | ||||
\(20\) | 1.84806 | − | 1.25884i | 0.413239 | − | 0.281485i | ||||
\(21\) | − | 4.39382i | − | 0.958810i | ||||||
\(22\) | 2.70268 | − | 2.70268i | 0.576214 | − | 0.576214i | ||||
\(23\) | 2.58922 | − | 2.58922i | 0.539890 | − | 0.539890i | −0.383607 | − | 0.923497i | \(-0.625318\pi\) |
0.923497 | + | 0.383607i | \(0.125318\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −1.83065 | + | 4.65282i | −0.366130 | + | 0.930564i | ||||
\(26\) | −0.126051 | −0.0247206 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 3.10690 | − | 3.10690i | 0.587149 | − | 0.587149i | ||||
\(29\) | −3.60048 | −0.668591 | −0.334296 | − | 0.942468i | \(-0.608498\pi\) | ||||
−0.334296 | + | 0.942468i | \(0.608498\pi\) | |||||||
\(30\) | 1.25884 | + | 1.84806i | 0.229832 | + | 0.337408i | ||||
\(31\) | 3.60048i | 0.646664i | 0.946286 | + | 0.323332i | \(0.104803\pi\) | ||||
−0.946286 | + | 0.323332i | \(0.895197\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 2.70268 | + | 2.70268i | 0.470477 | + | 0.470477i | ||||
\(34\) | 2.58893 | 0.443998 | ||||||||
\(35\) | −1.83065 | + | 9.65282i | −0.309436 | + | 1.63162i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.07188 | + | 7.07188i | −1.16261 | + | 1.16261i | −0.178707 | + | 0.983902i | \(0.557192\pi\) |
−0.983902 | + | 0.178707i | \(0.942808\pi\) | |||||||
\(38\) | −4.32930 | − | 0.507128i | −0.702305 | − | 0.0822670i | ||||
\(39\) | − | 0.126051i | − | 0.0201843i | ||||||
\(40\) | −0.416642 | + | 2.19691i | −0.0658769 | + | 0.347362i | ||||
\(41\) | 11.2134i | 1.75124i | 0.483002 | + | 0.875619i | \(0.339546\pi\) | ||||
−0.483002 | + | 0.875619i | \(0.660454\pi\) | |||||||
\(42\) | 3.10690 | + | 3.10690i | 0.479405 | + | 0.479405i | ||||
\(43\) | 7.93755 | − | 7.93755i | 1.21046 | − | 1.21046i | 0.239591 | − | 0.970874i | \(-0.422987\pi\) |
0.970874 | − | 0.239591i | \(-0.0770132\pi\) | |||||||
\(44\) | 3.82217i | 0.576214i | ||||||||
\(45\) | −1.84806 | + | 1.25884i | −0.275492 | + | 0.187657i | ||||
\(46\) | 3.66171i | 0.539890i | ||||||||
\(47\) | −0.463170 | − | 0.463170i | −0.0675603 | − | 0.0675603i | 0.672519 | − | 0.740080i | \(-0.265212\pi\) |
−0.740080 | + | 0.672519i | \(0.765212\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 12.3056i | 1.75795i | ||||||||
\(50\) | −1.99558 | − | 4.58450i | −0.282217 | − | 0.648347i | ||||
\(51\) | 2.58893i | 0.362523i | ||||||||
\(52\) | 0.0891314 | − | 0.0891314i | 0.0123603 | − | 0.0123603i | ||||
\(53\) | 3.21910 | + | 3.21910i | 0.442178 | + | 0.442178i | 0.892743 | − | 0.450566i | \(-0.148778\pi\) |
−0.450566 | + | 0.892743i | \(0.648778\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −4.81150 | − | 7.06360i | −0.648782 | − | 0.952455i | ||||
\(56\) | 4.39382i | 0.587149i | ||||||||
\(57\) | 0.507128 | − | 4.32930i | 0.0671707 | − | 0.573430i | ||||
\(58\) | 2.54592 | − | 2.54592i | 0.334296 | − | 0.334296i | ||||
\(59\) | −9.40851 | −1.22488 | −0.612442 | − | 0.790516i | \(-0.709813\pi\) | ||||
−0.612442 | + | 0.790516i | \(0.709813\pi\) | |||||||
\(60\) | −2.19691 | − | 0.416642i | −0.283620 | − | 0.0537882i | ||||
\(61\) | 8.21380 | 1.05167 | 0.525834 | − | 0.850587i | \(-0.323753\pi\) | ||||
0.525834 | + | 0.850587i | \(0.323753\pi\) | |||||||
\(62\) | −2.54592 | − | 2.54592i | −0.323332 | − | 0.323332i | ||||
\(63\) | −3.10690 | + | 3.10690i | −0.391432 | + | 0.391432i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.0525181 | + | 0.276922i | −0.00651406 | + | 0.0343480i | ||||
\(66\) | −3.82217 | −0.470477 | ||||||||
\(67\) | 8.78764 | − | 8.78764i | 1.07358 | − | 1.07358i | 0.0765120 | − | 0.997069i | \(-0.475622\pi\) |
0.997069 | − | 0.0765120i | \(-0.0243783\pi\) | |||||||
\(68\) | −1.83065 | + | 1.83065i | −0.221999 | + | 0.221999i | ||||
\(69\) | −3.66171 | −0.440818 | ||||||||
\(70\) | −5.53111 | − | 8.12004i | −0.661094 | − | 0.970530i | ||||
\(71\) | 1.66657i | 0.197785i | 0.995098 | + | 0.0988926i | \(0.0315300\pi\) | ||||
−0.995098 | + | 0.0988926i | \(0.968470\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −3.64373 | + | 3.64373i | −0.426466 | + | 0.426466i | −0.887423 | − | 0.460957i | \(-0.847506\pi\) |
0.460957 | + | 0.887423i | \(0.347506\pi\) | |||||||
\(74\) | − | 10.0011i | − | 1.16261i | ||||||
\(75\) | 4.58450 | − | 1.99558i | 0.529373 | − | 0.230429i | ||||
\(76\) | 3.41987 | − | 2.70268i | 0.392286 | − | 0.310019i | ||||
\(77\) | −11.8751 | − | 11.8751i | −1.35329 | − | 1.35329i | ||||
\(78\) | 0.0891314 | + | 0.0891314i | 0.0100921 | + | 0.0100921i | ||||
\(79\) | 8.82758 | 0.993180 | 0.496590 | − | 0.867985i | \(-0.334585\pi\) | ||||
0.496590 | + | 0.867985i | \(0.334585\pi\) | |||||||
\(80\) | −1.25884 | − | 1.84806i | −0.140742 | − | 0.206619i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −7.92907 | − | 7.92907i | −0.875619 | − | 0.875619i | ||||
\(83\) | −0.347181 | + | 0.347181i | −0.0381081 | + | 0.0381081i | −0.725904 | − | 0.687796i | \(-0.758578\pi\) |
0.687796 | + | 0.725904i | \(0.258578\pi\) | |||||||
\(84\) | −4.39382 | −0.479405 | ||||||||
\(85\) | 1.07866 | − | 5.68764i | 0.116997 | − | 0.616911i | ||||
\(86\) | 11.2254i | 1.21046i | ||||||||
\(87\) | 2.54592 | + | 2.54592i | 0.272951 | + | 0.272951i | ||||
\(88\) | −2.70268 | − | 2.70268i | −0.288107 | − | 0.288107i | ||||
\(89\) | 9.79832 | 1.03862 | 0.519310 | − | 0.854586i | \(-0.326189\pi\) | ||||
0.519310 | + | 0.854586i | \(0.326189\pi\) | |||||||
\(90\) | 0.416642 | − | 2.19691i | 0.0439179 | − | 0.231575i | ||||
\(91\) | 0.553844i | 0.0580587i | ||||||||
\(92\) | −2.58922 | − | 2.58922i | −0.269945 | − | 0.269945i | ||||
\(93\) | 2.54592 | − | 2.54592i | 0.264000 | − | 0.264000i | ||||
\(94\) | 0.655021 | 0.0675603 | ||||||||
\(95\) | −2.91788 | + | 9.29978i | −0.299368 | + | 0.954138i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 6.88409 | − | 6.88409i | 0.698973 | − | 0.698973i | −0.265216 | − | 0.964189i | \(-0.585443\pi\) |
0.964189 | + | 0.265216i | \(0.0854432\pi\) | |||||||
\(98\) | −8.70140 | − | 8.70140i | −0.878974 | − | 0.878974i | ||||
\(99\) | − | 3.82217i | − | 0.384143i | ||||||
\(100\) | 4.65282 | + | 1.83065i | 0.465282 | + | 0.183065i | ||||
\(101\) | −3.89174 | −0.387242 | −0.193621 | − | 0.981076i | \(-0.562023\pi\) | ||||
−0.193621 | + | 0.981076i | \(0.562023\pi\) | |||||||
\(102\) | −1.83065 | − | 1.83065i | −0.181261 | − | 0.181261i | ||||
\(103\) | −9.40518 | − | 9.40518i | −0.926720 | − | 0.926720i | 0.0707726 | − | 0.997492i | \(-0.477454\pi\) |
−0.997492 | + | 0.0707726i | \(0.977454\pi\) | |||||||
\(104\) | 0.126051i | 0.0123603i | ||||||||
\(105\) | 8.12004 | − | 5.53111i | 0.792435 | − | 0.539781i | ||||
\(106\) | −4.55250 | −0.442178 | ||||||||
\(107\) | 7.00983 | − | 7.00983i | 0.677666 | − | 0.677666i | −0.281806 | − | 0.959472i | \(-0.590933\pi\) |
0.959472 | + | 0.281806i | \(0.0909333\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | −17.7935 | −1.70431 | −0.852153 | − | 0.523293i | \(-0.824703\pi\) | ||||
−0.852153 | + | 0.523293i | \(0.824703\pi\) | |||||||
\(110\) | 8.39696 | + | 1.59248i | 0.800619 | + | 0.151837i | ||||
\(111\) | 10.0011 | 0.949267 | ||||||||
\(112\) | −3.10690 | − | 3.10690i | −0.293574 | − | 0.293574i | ||||
\(113\) | 12.4493 | + | 12.4493i | 1.17114 | + | 1.17114i | 0.981939 | + | 0.189197i | \(0.0605884\pi\) |
0.189197 | + | 0.981939i | \(0.439412\pi\) | |||||||
\(114\) | 2.70268 | + | 3.41987i | 0.253129 | + | 0.320300i | ||||
\(115\) | 8.04445 | + | 1.52562i | 0.750148 | + | 0.142265i | ||||
\(116\) | 3.60048i | 0.334296i | ||||||||
\(117\) | −0.0891314 | + | 0.0891314i | −0.00824020 | + | 0.00824020i | ||||
\(118\) | 6.65282 | − | 6.65282i | 0.612442 | − | 0.612442i | ||||
\(119\) | − | 11.3753i | − | 1.04277i | ||||||
\(120\) | 1.84806 | − | 1.25884i | 0.168704 | − | 0.114916i | ||||
\(121\) | 3.60898 | 0.328089 | ||||||||
\(122\) | −5.80803 | + | 5.80803i | −0.525834 | + | 0.525834i | ||||
\(123\) | 7.92907 | − | 7.92907i | 0.714940 | − | 0.714940i | ||||
\(124\) | 3.60048 | 0.323332 | ||||||||
\(125\) | −10.9032 | + | 2.47400i | −0.975210 | + | 0.221281i | ||||
\(126\) | − | 4.39382i | − | 0.391432i | ||||||
\(127\) | −0.0636986 | + | 0.0636986i | −0.00565234 | + | 0.00565234i | −0.709927 | − | 0.704275i | \(-0.751272\pi\) |
0.704275 | + | 0.709927i | \(0.251272\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −11.2254 | −0.988340 | ||||||||
\(130\) | −0.158678 | − | 0.232949i | −0.0139170 | − | 0.0204310i | ||||
\(131\) | 2.44811 | 0.213893 | 0.106946 | − | 0.994265i | \(-0.465893\pi\) | ||||
0.106946 | + | 0.994265i | \(0.465893\pi\) | |||||||
\(132\) | 2.70268 | − | 2.70268i | 0.235238 | − | 0.235238i | ||||
\(133\) | −2.22823 | + | 19.0221i | −0.193212 | + | 1.64943i | ||||
\(134\) | 12.4276i | 1.07358i | ||||||||
\(135\) | 2.19691 | + | 0.416642i | 0.189080 | + | 0.0358588i | ||||
\(136\) | − | 2.58893i | − | 0.221999i | ||||||
\(137\) | 3.02688 | + | 3.02688i | 0.258604 | + | 0.258604i | 0.824486 | − | 0.565882i | \(-0.191464\pi\) |
−0.565882 | + | 0.824486i | \(0.691464\pi\) | |||||||
\(138\) | 2.58922 | − | 2.58922i | 0.220409 | − | 0.220409i | ||||
\(139\) | 3.96170i | 0.336027i | 0.985785 | + | 0.168013i | \(0.0537352\pi\) | ||||
−0.985785 | + | 0.168013i | \(0.946265\pi\) | |||||||
\(140\) | 9.65282 | + | 1.83065i | 0.815812 | + | 0.154718i | ||||
\(141\) | 0.655021i | 0.0551627i | ||||||||
\(142\) | −1.17844 | − | 1.17844i | −0.0988926 | − | 0.0988926i | ||||
\(143\) | −0.340675 | − | 0.340675i | −0.0284887 | − | 0.0284887i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −4.53242 | − | 6.65389i | −0.376397 | − | 0.552576i | ||||
\(146\) | − | 5.15301i | − | 0.426466i | ||||||
\(147\) | 8.70140 | − | 8.70140i | 0.717679 | − | 0.717679i | ||||
\(148\) | 7.07188 | + | 7.07188i | 0.581305 | + | 0.581305i | ||||
\(149\) | − | 22.3940i | − | 1.83459i | −0.398211 | − | 0.917294i | \(-0.630369\pi\) | ||
0.398211 | − | 0.917294i | \(-0.369631\pi\) | |||||||
\(150\) | −1.83065 | + | 4.65282i | −0.149472 | + | 0.379901i | ||||
\(151\) | − | 11.2995i | − | 0.919539i | −0.888038 | − | 0.459769i | \(-0.847932\pi\) | ||
0.888038 | − | 0.459769i | \(-0.152068\pi\) | |||||||
\(152\) | −0.507128 | + | 4.32930i | −0.0411335 | + | 0.351152i | ||||
\(153\) | 1.83065 | − | 1.83065i | 0.147999 | − | 0.147999i | ||||
\(154\) | 16.7939 | 1.35329 | ||||||||
\(155\) | −6.65389 | + | 4.53242i | −0.534454 | + | 0.364053i | ||||
\(156\) | −0.126051 | −0.0100921 | ||||||||
\(157\) | −4.57916 | − | 4.57916i | −0.365457 | − | 0.365457i | 0.500361 | − | 0.865817i | \(-0.333201\pi\) |
−0.865817 | + | 0.500361i | \(0.833201\pi\) | |||||||
\(158\) | −6.24204 | + | 6.24204i | −0.496590 | + | 0.496590i | ||||
\(159\) | − | 4.55250i | − | 0.361037i | ||||||
\(160\) | 2.19691 | + | 0.416642i | 0.173681 | + | 0.0329384i | ||||
\(161\) | 16.0889 | 1.26798 | ||||||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 7.54592 | − | 7.54592i | 0.591042 | − | 0.591042i | −0.346871 | − | 0.937913i | \(-0.612756\pi\) |
0.937913 | + | 0.346871i | \(0.112756\pi\) | |||||||
\(164\) | 11.2134 | 0.875619 | ||||||||
\(165\) | −1.59248 | + | 8.39696i | −0.123974 | + | 0.653702i | ||||
\(166\) | − | 0.490988i | − | 0.0381081i | ||||||
\(167\) | 15.1275 | − | 15.1275i | 1.17060 | − | 1.17060i | 0.188531 | − | 0.982067i | \(-0.439627\pi\) |
0.982067 | − | 0.188531i | \(-0.0603726\pi\) | |||||||
\(168\) | 3.10690 | − | 3.10690i | 0.239702 | − | 0.239702i | ||||
\(169\) | − | 12.9841i | − | 0.998778i | ||||||
\(170\) | 3.25904 | + | 4.78449i | 0.249957 | + | 0.366954i | ||||
\(171\) | −3.41987 | + | 2.70268i | −0.261524 | + | 0.206679i | ||||
\(172\) | −7.93755 | − | 7.93755i | −0.605232 | − | 0.605232i | ||||
\(173\) | −2.32458 | − | 2.32458i | −0.176735 | − | 0.176735i | 0.613196 | − | 0.789931i | \(-0.289884\pi\) |
−0.789931 | + | 0.613196i | \(0.789884\pi\) | |||||||
\(174\) | −3.60048 | −0.272951 | ||||||||
\(175\) | −20.1435 | + | 8.76820i | −1.52270 | + | 0.662813i | ||||
\(176\) | 3.82217 | 0.288107 | ||||||||
\(177\) | 6.65282 | + | 6.65282i | 0.500056 | + | 0.500056i | ||||
\(178\) | −6.92846 | + | 6.92846i | −0.519310 | + | 0.519310i | ||||
\(179\) | −0.515834 | −0.0385553 | −0.0192776 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192776 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(180\) | 1.25884 | + | 1.84806i | 0.0938283 | + | 0.137746i | ||||
\(181\) | − | 4.86127i | − | 0.361336i | −0.983544 | − | 0.180668i | \(-0.942174\pi\) | ||
0.983544 | − | 0.180668i | \(-0.0578259\pi\) | |||||||
\(182\) | −0.391627 | − | 0.391627i | −0.0290293 | − | 0.0290293i | ||||
\(183\) | −5.80803 | − | 5.80803i | −0.429342 | − | 0.429342i | ||||
\(184\) | 3.66171 | 0.269945 | ||||||||
\(185\) | −21.9716 | − | 4.16690i | −1.61538 | − | 0.306356i | ||||
\(186\) | 3.60048i | 0.264000i | ||||||||
\(187\) | 6.99705 | + | 6.99705i | 0.511675 | + | 0.511675i | ||||
\(188\) | −0.463170 | + | 0.463170i | −0.0337801 | + | 0.0337801i | ||||
\(189\) | 4.39382 | 0.319603 | ||||||||
\(190\) | −4.51269 | − | 8.63919i | −0.327385 | − | 0.626753i | ||||
\(191\) | −15.3369 | −1.10974 | −0.554870 | − | 0.831937i | \(-0.687232\pi\) | ||||
−0.554870 | + | 0.831937i | \(0.687232\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | 17.1600 | + | 17.1600i | 1.23521 | + | 1.23521i | 0.961938 | + | 0.273268i | \(0.0881046\pi\) |
0.273268 | + | 0.961938i | \(0.411895\pi\) | |||||||
\(194\) | 9.73557i | 0.698973i | ||||||||
\(195\) | 0.232949 | − | 0.158678i | 0.0166819 | − | 0.0113631i | ||||
\(196\) | 12.3056 | 0.878974 | ||||||||
\(197\) | −6.25052 | − | 6.25052i | −0.445331 | − | 0.445331i | 0.448468 | − | 0.893799i | \(-0.351970\pi\) |
−0.893799 | + | 0.448468i | \(0.851970\pi\) | |||||||
\(198\) | 2.70268 | + | 2.70268i | 0.192071 | + | 0.192071i | ||||
\(199\) | 10.4094i | 0.737904i | 0.929448 | + | 0.368952i | \(0.120283\pi\) | ||||
−0.929448 | + | 0.368952i | \(0.879717\pi\) | |||||||
\(200\) | −4.58450 | + | 1.99558i | −0.324173 | + | 0.141109i | ||||
\(201\) | −12.4276 | −0.876575 | ||||||||
\(202\) | 2.75187 | − | 2.75187i | 0.193621 | − | 0.193621i | ||||
\(203\) | −11.1863 | − | 11.1863i | −0.785125 | − | 0.785125i | ||||
\(204\) | 2.58893 | 0.181261 | ||||||||
\(205\) | −20.7230 | + | 14.1159i | −1.44736 | + | 0.985894i | ||||
\(206\) | 13.3009 | 0.926720 | ||||||||
\(207\) | 2.58922 | + | 2.58922i | 0.179963 | + | 0.179963i | ||||
\(208\) | −0.0891314 | − | 0.0891314i | −0.00618015 | − | 0.00618015i | ||||
\(209\) | −10.3301 | − | 13.0713i | −0.714549 | − | 0.904162i | ||||
\(210\) | −1.83065 | + | 9.65282i | −0.126327 | + | 0.666108i | ||||
\(211\) | − | 13.0551i | − | 0.898752i | −0.893343 | − | 0.449376i | \(-0.851646\pi\) | ||
0.893343 | − | 0.449376i | \(-0.148354\pi\) | |||||||
\(212\) | 3.21910 | − | 3.21910i | 0.221089 | − | 0.221089i | ||||
\(213\) | 1.17844 | − | 1.17844i | 0.0807455 | − | 0.0807455i | ||||
\(214\) | 9.91340i | 0.677666i | ||||||||
\(215\) | 24.6612 | + | 4.67697i | 1.68188 | + | 0.318967i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −11.1863 | + | 11.1863i | −0.759376 | + | 0.759376i | ||||
\(218\) | 12.5819 | − | 12.5819i | 0.852153 | − | 0.852153i | ||||
\(219\) | 5.15301 | 0.348208 | ||||||||
\(220\) | −7.06360 | + | 4.81150i | −0.476228 | + | 0.324391i | ||||
\(221\) | − | 0.326337i | − | 0.0219518i | ||||||
\(222\) | −7.07188 | + | 7.07188i | −0.474633 | + | 0.474633i | ||||
\(223\) | 11.5414 | + | 11.5414i | 0.772872 | + | 0.772872i | 0.978608 | − | 0.205736i | \(-0.0659587\pi\) |
−0.205736 | + | 0.978608i | \(0.565959\pi\) | |||||||
\(224\) | 4.39382 | 0.293574 | ||||||||
\(225\) | −4.65282 | − | 1.83065i | −0.310188 | − | 0.122043i | ||||
\(226\) | −17.6060 | −1.17114 | ||||||||
\(227\) | 16.4312 | − | 16.4312i | 1.09058 | − | 1.09058i | 0.0951099 | − | 0.995467i | \(-0.469680\pi\) |
0.995467 | − | 0.0951099i | \(-0.0303202\pi\) | |||||||
\(228\) | −4.32930 | − | 0.507128i | −0.286715 | − | 0.0335854i | ||||
\(229\) | 15.5194i | 1.02555i | 0.858522 | + | 0.512777i | \(0.171383\pi\) | ||||
−0.858522 | + | 0.512777i | \(0.828617\pi\) | |||||||
\(230\) | −6.76706 | + | 4.60950i | −0.446207 | + | 0.303942i | ||||
\(231\) | 16.7939i | 1.10496i | ||||||||
\(232\) | −2.54592 | − | 2.54592i | −0.167148 | − | 0.167148i | ||||
\(233\) | −1.69112 | + | 1.69112i | −0.110789 | + | 0.110789i | −0.760328 | − | 0.649539i | \(-0.774962\pi\) |
0.649539 | + | 0.760328i | \(0.274962\pi\) | |||||||
\(234\) | − | 0.126051i | − | 0.00824020i | ||||||
\(235\) | 0.272909 | − | 1.43902i | 0.0178026 | − | 0.0938714i | ||||
\(236\) | 9.40851i | 0.612442i | ||||||||
\(237\) | −6.24204 | − | 6.24204i | −0.405464 | − | 0.405464i | ||||
\(238\) | 8.04354 | + | 8.04354i | 0.521385 | + | 0.521385i | ||||
\(239\) | 12.9971i | 0.840714i | 0.907359 | + | 0.420357i | \(0.138095\pi\) | ||||
−0.907359 | + | 0.420357i | \(0.861905\pi\) | |||||||
\(240\) | −0.416642 | + | 2.19691i | −0.0268941 | + | 0.141810i | ||||
\(241\) | − | 8.64001i | − | 0.556552i | −0.960501 | − | 0.278276i | \(-0.910237\pi\) | ||
0.960501 | − | 0.278276i | \(-0.0897630\pi\) | |||||||
\(242\) | −2.55194 | + | 2.55194i | −0.164045 | + | 0.164045i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 8.21380i | − | 0.525834i | ||||||
\(245\) | −22.7416 | + | 15.4908i | −1.45290 | + | 0.989672i | ||||
\(246\) | 11.2134i | 0.714940i | ||||||||
\(247\) | −0.0639239 | + | 0.545712i | −0.00406738 | + | 0.0347228i | ||||
\(248\) | −2.54592 | + | 2.54592i | −0.161666 | + | 0.161666i | ||||
\(249\) | 0.490988 | 0.0311151 | ||||||||
\(250\) | 5.96033 | − | 9.45910i | 0.376964 | − | 0.598246i | ||||
\(251\) | 23.6590 | 1.49334 | 0.746670 | − | 0.665194i | \(-0.231651\pi\) | ||||
0.746670 | + | 0.665194i | \(0.231651\pi\) | |||||||
\(252\) | 3.10690 | + | 3.10690i | 0.195716 | + | 0.195716i | ||||
\(253\) | −9.89644 | + | 9.89644i | −0.622184 | + | 0.622184i | ||||
\(254\) | − | 0.0900835i | − | 0.00565234i | ||||||
\(255\) | −4.78449 | + | 3.25904i | −0.299617 | + | 0.204089i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.63732 | − | 8.63732i | 0.538781 | − | 0.538781i | −0.384390 | − | 0.923171i | \(-0.625588\pi\) |
0.923171 | + | 0.384390i | \(0.125588\pi\) | |||||||
\(258\) | 7.93755 | − | 7.93755i | 0.494170 | − | 0.494170i | ||||
\(259\) | −43.9432 | −2.73050 | ||||||||
\(260\) | 0.276922 | + | 0.0525181i | 0.0171740 | + | 0.00325703i | ||||
\(261\) | − | 3.60048i | − | 0.222864i | ||||||
\(262\) | −1.73108 | + | 1.73108i | −0.106946 | + | 0.106946i | ||||
\(263\) | 10.9291 | − | 10.9291i | 0.673915 | − | 0.673915i | −0.284701 | − | 0.958616i | \(-0.591894\pi\) |
0.958616 | + | 0.284701i | \(0.0918943\pi\) | |||||||
\(264\) | 3.82217i | 0.235238i | ||||||||
\(265\) | −1.89676 | + | 10.0014i | −0.116517 | + | 0.614383i | ||||
\(266\) | −11.8751 | − | 15.0263i | −0.728109 | − | 0.921321i | ||||
\(267\) | −6.92846 | − | 6.92846i | −0.424015 | − | 0.424015i | ||||
\(268\) | −8.78764 | − | 8.78764i | −0.536790 | − | 0.536790i | ||||
\(269\) | −13.8523 | −0.844591 | −0.422296 | − | 0.906458i | \(-0.638776\pi\) | ||||
−0.422296 | + | 0.906458i | \(0.638776\pi\) | |||||||
\(270\) | −1.84806 | + | 1.25884i | −0.112469 | + | 0.0766105i | ||||
\(271\) | 14.8370 | 0.901284 | 0.450642 | − | 0.892705i | \(-0.351195\pi\) | ||||
0.450642 | + | 0.892705i | \(0.351195\pi\) | |||||||
\(272\) | 1.83065 | + | 1.83065i | 0.110999 | + | 0.110999i | ||||
\(273\) | 0.391627 | − | 0.391627i | 0.0237024 | − | 0.0237024i | ||||
\(274\) | −4.28065 | −0.258604 | ||||||||
\(275\) | 6.99705 | − | 17.7839i | 0.421938 | − | 1.07241i | ||||
\(276\) | 3.66171i | 0.220409i | ||||||||
\(277\) | −8.95723 | − | 8.95723i | −0.538188 | − | 0.538188i | 0.384808 | − | 0.922996i | \(-0.374268\pi\) |
−0.922996 | + | 0.384808i | \(0.874268\pi\) | |||||||
\(278\) | −2.80134 | − | 2.80134i | −0.168013 | − | 0.168013i | ||||
\(279\) | −3.60048 | −0.215555 | ||||||||
\(280\) | −8.12004 | + | 5.53111i | −0.485265 | + | 0.330547i | ||||
\(281\) | − | 6.13940i | − | 0.366246i | −0.983090 | − | 0.183123i | \(-0.941379\pi\) | ||
0.983090 | − | 0.183123i | \(-0.0586207\pi\) | |||||||
\(282\) | −0.463170 | − | 0.463170i | −0.0275814 | − | 0.0275814i | ||||
\(283\) | −22.7963 | + | 22.7963i | −1.35510 | + | 1.35510i | −0.475246 | + | 0.879853i | \(0.657641\pi\) |
−0.879853 | + | 0.475246i | \(0.842359\pi\) | |||||||
\(284\) | 1.66657 | 0.0988926 | ||||||||
\(285\) | 8.63919 | − | 4.51269i | 0.511742 | − | 0.267308i | ||||
\(286\) | 0.481788 | 0.0284887 | ||||||||
\(287\) | −34.8389 | + | 34.8389i | −2.05647 | + | 2.05647i | ||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 10.2974i | − | 0.605732i | ||||||
\(290\) | 7.90992 | + | 1.50011i | 0.464486 | + | 0.0880894i | ||||
\(291\) | −9.73557 | −0.570709 | ||||||||
\(292\) | 3.64373 | + | 3.64373i | 0.213233 | + | 0.213233i | ||||
\(293\) | 0.341431 | + | 0.341431i | 0.0199466 | + | 0.0199466i | 0.717010 | − | 0.697063i | \(-0.245510\pi\) |
−0.697063 | + | 0.717010i | \(0.745510\pi\) | |||||||
\(294\) | 12.3056i | 0.717679i | ||||||||
\(295\) | −11.8438 | − | 17.3875i | −0.689572 | − | 1.01234i | ||||
\(296\) | −10.0011 | −0.581305 | ||||||||
\(297\) | −2.70268 | + | 2.70268i | −0.156826 | + | 0.156826i | ||||
\(298\) | 15.8349 | + | 15.8349i | 0.917294 | + | 0.917294i | ||||
\(299\) | 0.461562 | 0.0266928 | ||||||||
\(300\) | −1.99558 | − | 4.58450i | −0.115215 | − | 0.264686i | ||||
\(301\) | 49.3223 | 2.84289 | ||||||||
\(302\) | 7.98994 | + | 7.98994i | 0.459769 | + | 0.459769i | ||||
\(303\) | 2.75187 | + | 2.75187i | 0.158091 | + | 0.158091i | ||||
\(304\) | −2.70268 | − | 3.41987i | −0.155009 | − | 0.196143i | ||||
\(305\) | 10.3398 | + | 15.1796i | 0.592058 | + | 0.869181i | ||||
\(306\) | 2.58893i | 0.147999i | ||||||||
\(307\) | −18.0543 | + | 18.0543i | −1.03041 | + | 1.03041i | −0.0308888 | + | 0.999523i | \(0.509834\pi\) |
−0.999523 | + | 0.0308888i | \(0.990166\pi\) | |||||||
\(308\) | −11.8751 | + | 11.8751i | −0.676646 | + | 0.676646i | ||||
\(309\) | 13.3009i | 0.756664i | ||||||||
\(310\) | 1.50011 | − | 7.90992i | 0.0852005 | − | 0.449253i | ||||
\(311\) | 5.73086 | 0.324967 | 0.162484 | − | 0.986711i | \(-0.448049\pi\) | ||||
0.162484 | + | 0.986711i | \(0.448049\pi\) | |||||||
\(312\) | 0.0891314 | − | 0.0891314i | 0.00504607 | − | 0.00504607i | ||||
\(313\) | 22.1761 | − | 22.1761i | 1.25347 | − | 1.25347i | 0.299312 | − | 0.954155i | \(-0.403243\pi\) |
0.954155 | − | 0.299312i | \(-0.0967572\pi\) | |||||||
\(314\) | 6.47591 | 0.365457 | ||||||||
\(315\) | −9.65282 | − | 1.83065i | −0.543875 | − | 0.103145i | ||||
\(316\) | − | 8.82758i | − | 0.496590i | ||||||
\(317\) | 11.0630 | − | 11.0630i | 0.621359 | − | 0.621359i | −0.324520 | − | 0.945879i | \(-0.605203\pi\) |
0.945879 | + | 0.324520i | \(0.105203\pi\) | |||||||
\(318\) | 3.21910 | + | 3.21910i | 0.180518 | + | 0.180518i | ||||
\(319\) | 13.7616 | 0.770503 | ||||||||
\(320\) | −1.84806 | + | 1.25884i | −0.103310 | + | 0.0703712i | ||||
\(321\) | −9.91340 | −0.553312 | ||||||||
\(322\) | −11.3766 | + | 11.3766i | −0.633991 | + | 0.633991i | ||||
\(323\) | 1.31292 | − | 11.2082i | 0.0730527 | − | 0.623643i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −0.577881 | + | 0.251544i | −0.0320550 | + | 0.0139531i | ||||
\(326\) | 10.6715i | 0.591042i | ||||||||
\(327\) | 12.5819 | + | 12.5819i | 0.695780 | + | 0.695780i | ||||
\(328\) | −7.92907 | + | 7.92907i | −0.437810 | + | 0.437810i | ||||
\(329\) | − | 2.87804i | − | 0.158672i | ||||||
\(330\) | −4.81150 | − | 7.06360i | −0.264864 | − | 0.388838i | ||||
\(331\) | − | 11.7959i | − | 0.648364i | −0.945995 | − | 0.324182i | \(-0.894911\pi\) | ||
0.945995 | − | 0.324182i | \(-0.105089\pi\) | |||||||
\(332\) | 0.347181 | + | 0.347181i | 0.0190540 | + | 0.0190540i | ||||
\(333\) | −7.07188 | − | 7.07188i | −0.387537 | − | 0.387537i | ||||
\(334\) | 21.3935i | 1.17060i | ||||||||
\(335\) | 27.3023 | + | 5.17786i | 1.49168 | + | 0.282897i | ||||
\(336\) | 4.39382i | 0.239702i | ||||||||
\(337\) | −10.9001 | + | 10.9001i | −0.593765 | + | 0.593765i | −0.938646 | − | 0.344881i | \(-0.887919\pi\) |
0.344881 | + | 0.938646i | \(0.387919\pi\) | |||||||
\(338\) | 9.18115 | + | 9.18115i | 0.499389 | + | 0.499389i | ||||
\(339\) | − | 17.6060i | − | 0.956229i | ||||||
\(340\) | −5.68764 | − | 1.07866i | −0.308456 | − | 0.0584983i | ||||
\(341\) | − | 13.7616i | − | 0.745234i | ||||||
\(342\) | 0.507128 | − | 4.32930i | 0.0274223 | − | 0.234102i | ||||
\(343\) | −16.4841 | + | 16.4841i | −0.890057 | + | 0.890057i | ||||
\(344\) | 11.2254 | 0.605232 | ||||||||
\(345\) | −4.60950 | − | 6.76706i | −0.248167 | − | 0.364326i | ||||
\(346\) | 3.28746 | 0.176735 | ||||||||
\(347\) | 15.9014 | + | 15.9014i | 0.853630 | + | 0.853630i | 0.990578 | − | 0.136948i | \(-0.0437295\pi\) |
−0.136948 | + | 0.990578i | \(0.543729\pi\) | |||||||
\(348\) | 2.54592 | − | 2.54592i | 0.136476 | − | 0.136476i | ||||
\(349\) | − | 14.0170i | − | 0.750311i | −0.926962 | − | 0.375155i | \(-0.877589\pi\) | ||
0.926962 | − | 0.375155i | \(-0.122411\pi\) | |||||||
\(350\) | 8.04354 | − | 20.4436i | 0.429945 | − | 1.09276i | ||||
\(351\) | 0.126051 | 0.00672810 | ||||||||
\(352\) | −2.70268 | + | 2.70268i | −0.144053 | + | 0.144053i | ||||
\(353\) | −1.70112 | + | 1.70112i | −0.0905412 | + | 0.0905412i | −0.750927 | − | 0.660386i | \(-0.770393\pi\) |
0.660386 | + | 0.750927i | \(0.270393\pi\) | |||||||
\(354\) | −9.40851 | −0.500056 | ||||||||
\(355\) | −3.07992 | + | 2.09794i | −0.163465 | + | 0.111347i | ||||
\(356\) | − | 9.79832i | − | 0.519310i | ||||||
\(357\) | −8.04354 | + | 8.04354i | −0.425709 | + | 0.425709i | ||||
\(358\) | 0.364750 | − | 0.364750i | 0.0192776 | − | 0.0192776i | ||||
\(359\) | 36.9693i | 1.95117i | 0.219633 | + | 0.975583i | \(0.429514\pi\) | ||||
−0.219633 | + | 0.975583i | \(0.570486\pi\) | |||||||
\(360\) | −2.19691 | − | 0.416642i | −0.115787 | − | 0.0219590i | ||||
\(361\) | −4.39102 | + | 18.4856i | −0.231106 | + | 0.972929i | ||||
\(362\) | 3.43744 | + | 3.43744i | 0.180668 | + | 0.180668i | ||||
\(363\) | −2.55194 | − | 2.55194i | −0.133942 | − | 0.133942i | ||||
\(364\) | 0.553844 | 0.0290293 | ||||||||
\(365\) | −11.3207 | − | 2.14696i | −0.592552 | − | 0.112377i | ||||
\(366\) | 8.21380 | 0.429342 | ||||||||
\(367\) | −11.7866 | − | 11.7866i | −0.615255 | − | 0.615255i | 0.329055 | − | 0.944311i | \(-0.393270\pi\) |
−0.944311 | + | 0.329055i | \(0.893270\pi\) | |||||||
\(368\) | −2.58922 | + | 2.58922i | −0.134972 | + | 0.134972i | ||||
\(369\) | −11.2134 | −0.583746 | ||||||||
\(370\) | 18.4827 | − | 12.5898i | 0.960871 | − | 0.654514i | ||||
\(371\) | 20.0029i | 1.03850i | ||||||||
\(372\) | −2.54592 | − | 2.54592i | −0.132000 | − | 0.132000i | ||||
\(373\) | 9.29229 | + | 9.29229i | 0.481137 | + | 0.481137i | 0.905495 | − | 0.424358i | \(-0.139500\pi\) |
−0.424358 | + | 0.905495i | \(0.639500\pi\) | |||||||
\(374\) | −9.89533 | −0.511675 | ||||||||
\(375\) | 9.45910 | + | 5.96033i | 0.488466 | + | 0.307790i | ||||
\(376\) | − | 0.655021i | − | 0.0337801i | ||||||
\(377\) | −0.320915 | − | 0.320915i | −0.0165280 | − | 0.0165280i | ||||
\(378\) | −3.10690 | + | 3.10690i | −0.159802 | + | 0.159802i | ||||
\(379\) | 9.08999 | 0.466921 | 0.233461 | − | 0.972366i | \(-0.424995\pi\) | ||||
0.233461 | + | 0.972366i | \(0.424995\pi\) | |||||||
\(380\) | 9.29978 | + | 2.91788i | 0.477069 | + | 0.149684i | ||||
\(381\) | 0.0900835 | 0.00461512 | ||||||||
\(382\) | 10.8448 | − | 10.8448i | 0.554870 | − | 0.554870i | ||||
\(383\) | 2.91923 | + | 2.91923i | 0.149166 | + | 0.149166i | 0.777745 | − | 0.628579i | \(-0.216363\pi\) |
−0.628579 | + | 0.777745i | \(0.716363\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 6.99705 | − | 36.8947i | 0.356603 | − | 1.88033i | ||||
\(386\) | −24.2679 | −1.23521 | ||||||||
\(387\) | 7.93755 | + | 7.93755i | 0.403488 | + | 0.403488i | ||||
\(388\) | −6.88409 | − | 6.88409i | −0.349487 | − | 0.349487i | ||||
\(389\) | 25.2850i | 1.28200i | 0.767540 | + | 0.641001i | \(0.221481\pi\) | ||||
−0.767540 | + | 0.641001i | \(0.778519\pi\) | |||||||
\(390\) | −0.0525181 | + | 0.276922i | −0.00265936 | + | 0.0140225i | ||||
\(391\) | −9.47991 | −0.479420 | ||||||||
\(392\) | −8.70140 | + | 8.70140i | −0.439487 | + | 0.439487i | ||||
\(393\) | −1.73108 | − | 1.73108i | −0.0873213 | − | 0.0873213i | ||||
\(394\) | 8.83957 | 0.445331 | ||||||||
\(395\) | 11.1125 | + | 16.3139i | 0.559130 | + | 0.820841i | ||||
\(396\) | −3.82217 | −0.192071 | ||||||||
\(397\) | 11.4572 | + | 11.4572i | 0.575020 | + | 0.575020i | 0.933527 | − | 0.358507i | \(-0.116714\pi\) |
−0.358507 | + | 0.933527i | \(0.616714\pi\) | |||||||
\(398\) | −7.36057 | − | 7.36057i | −0.368952 | − | 0.368952i | ||||
\(399\) | 15.0263 | − | 11.8751i | 0.752255 | − | 0.594498i | ||||
\(400\) | 1.83065 | − | 4.65282i | 0.0915324 | − | 0.232641i | ||||
\(401\) | 7.22311i | 0.360705i | 0.983602 | + | 0.180352i | \(0.0577238\pi\) | ||||
−0.983602 | + | 0.180352i | \(0.942276\pi\) | |||||||
\(402\) | 8.78764 | − | 8.78764i | 0.438287 | − | 0.438287i | ||||
\(403\) | −0.320915 | + | 0.320915i | −0.0159859 | + | 0.0159859i | ||||
\(404\) | 3.89174i | 0.193621i | ||||||||
\(405\) | −1.25884 | − | 1.84806i | −0.0625522 | − | 0.0918308i | ||||
\(406\) | 15.8198 | 0.785125 | ||||||||
\(407\) | 27.0299 | − | 27.0299i | 1.33982 | − | 1.33982i | ||||
\(408\) | −1.83065 | + | 1.83065i | −0.0906306 | + | 0.0906306i | ||||
\(409\) | 17.4019 | 0.860470 | 0.430235 | − | 0.902717i | \(-0.358431\pi\) | ||||
0.430235 | + | 0.902717i | \(0.358431\pi\) | |||||||
\(410\) | 4.67197 | − | 24.6348i | 0.230732 | − | 1.21663i | ||||
\(411\) | − | 4.28065i | − | 0.211149i | ||||||
\(412\) | −9.40518 | + | 9.40518i | −0.463360 | + | 0.463360i | ||||
\(413\) | −29.2313 | − | 29.2313i | −1.43838 | − | 1.43838i | ||||
\(414\) | −3.66171 | −0.179963 | ||||||||
\(415\) | −1.07866 | − | 0.204566i | −0.0529491 | − | 0.0100418i | ||||
\(416\) | 0.126051 | 0.00618015 | ||||||||
\(417\) | 2.80134 | − | 2.80134i | 0.137182 | − | 0.137182i | ||||
\(418\) | 16.5473 | + | 1.93833i | 0.809356 | + | 0.0948068i | ||||
\(419\) | 1.67485i | 0.0818218i | 0.999163 | + | 0.0409109i | \(0.0130260\pi\) | ||||
−0.999163 | + | 0.0409109i | \(0.986974\pi\) | |||||||
\(420\) | −5.53111 | − | 8.12004i | −0.269891 | − | 0.396217i | ||||
\(421\) | − | 26.3045i | − | 1.28200i | −0.767540 | − | 0.641001i | \(-0.778520\pi\) | ||
0.767540 | − | 0.641001i | \(-0.221480\pi\) | |||||||
\(422\) | 9.23137 | + | 9.23137i | 0.449376 | + | 0.449376i | ||||
\(423\) | 0.463170 | − | 0.463170i | 0.0225201 | − | 0.0225201i | ||||
\(424\) | 4.55250i | 0.221089i | ||||||||
\(425\) | 11.8690 | − | 5.16640i | 0.575729 | − | 0.250607i | ||||
\(426\) | 1.66657i | 0.0807455i | ||||||||
\(427\) | 25.5194 | + | 25.5194i | 1.23497 | + | 1.23497i | ||||
\(428\) | −7.00983 | − | 7.00983i | −0.338833 | − | 0.338833i | ||||
\(429\) | 0.481788i | 0.0232609i | ||||||||
\(430\) | −20.7452 | + | 14.1310i | −1.00042 | + | 0.681455i | ||||
\(431\) | − | 9.18675i | − | 0.442510i | −0.975216 | − | 0.221255i | \(-0.928985\pi\) | ||
0.975216 | − | 0.221255i | \(-0.0710154\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −7.28482 | − | 7.28482i | −0.350086 | − | 0.350086i | 0.510055 | − | 0.860142i | \(-0.329625\pi\) |
−0.860142 | + | 0.510055i | \(0.829625\pi\) | |||||||
\(434\) | − | 15.8198i | − | 0.759376i | ||||||
\(435\) | −1.50011 | + | 7.90992i | −0.0719247 | + | 0.379251i | ||||
\(436\) | 17.7935i | 0.852153i | ||||||||
\(437\) | 15.8526 | + | 1.85696i | 0.758335 | + | 0.0888302i | ||||
\(438\) | −3.64373 | + | 3.64373i | −0.174104 | + | 0.174104i | ||||
\(439\) | −11.5269 | −0.550148 | −0.275074 | − | 0.961423i | \(-0.588702\pi\) | ||||
−0.275074 | + | 0.961423i | \(0.588702\pi\) | |||||||
\(440\) | 1.59248 | − | 8.39696i | 0.0759183 | − | 0.400309i | ||||
\(441\) | −12.3056 | −0.585983 | ||||||||
\(442\) | 0.230755 | + | 0.230755i | 0.0109759 | + | 0.0109759i | ||||
\(443\) | 1.68879 | − | 1.68879i | 0.0802367 | − | 0.0802367i | −0.665849 | − | 0.746086i | \(-0.731931\pi\) |
0.746086 | + | 0.665849i | \(0.231931\pi\) | |||||||
\(444\) | − | 10.0011i | − | 0.474633i | ||||||
\(445\) | 12.3345 | + | 18.1079i | 0.584712 | + | 0.858396i | ||||
\(446\) | −16.3221 | −0.772872 | ||||||||
\(447\) | −15.8349 | + | 15.8349i | −0.748967 | + | 0.748967i | ||||
\(448\) | −3.10690 | + | 3.10690i | −0.146787 | + | 0.146787i | ||||
\(449\) | 10.9876 | 0.518538 | 0.259269 | − | 0.965805i | \(-0.416518\pi\) | ||||
0.259269 | + | 0.965805i | \(0.416518\pi\) | |||||||
\(450\) | 4.58450 | − | 1.99558i | 0.216116 | − | 0.0940723i | ||||
\(451\) | − | 42.8595i | − | 2.01818i | ||||||
\(452\) | 12.4493 | − | 12.4493i | 0.585568 | − | 0.585568i | ||||
\(453\) | −7.98994 | + | 7.98994i | −0.375400 | + | 0.375400i | ||||
\(454\) | 23.2372i | 1.09058i | ||||||||
\(455\) | −1.02354 | + | 0.697201i | −0.0479842 | + | 0.0326853i | ||||
\(456\) | 3.41987 | − | 2.70268i | 0.160150 | − | 0.126565i | ||||
\(457\) | −24.3188 | − | 24.3188i | −1.13759 | − | 1.13759i | −0.988882 | − | 0.148703i | \(-0.952490\pi\) |
−0.148703 | − | 0.988882i | \(-0.547510\pi\) | |||||||
\(458\) | −10.9739 | − | 10.9739i | −0.512777 | − | 0.512777i | ||||
\(459\) | −2.58893 | −0.120841 | ||||||||
\(460\) | 1.52562 | − | 8.04445i | 0.0711325 | − | 0.375074i | ||||
\(461\) | 20.8769 | 0.972332 | 0.486166 | − | 0.873866i | \(-0.338395\pi\) | ||||
0.486166 | + | 0.873866i | \(0.338395\pi\) | |||||||
\(462\) | −11.8751 | − | 11.8751i | −0.552479 | − | 0.552479i | ||||
\(463\) | −16.5161 | + | 16.5161i | −0.767568 | + | 0.767568i | −0.977678 | − | 0.210110i | \(-0.932618\pi\) |
0.210110 | + | 0.977678i | \(0.432618\pi\) | |||||||
\(464\) | 3.60048 | 0.167148 | ||||||||
\(465\) | 7.90992 | + | 1.50011i | 0.366814 | + | 0.0695659i | ||||
\(466\) | − | 2.39161i | − | 0.110789i | ||||||
\(467\) | −14.6317 | − | 14.6317i | −0.677074 | − | 0.677074i | 0.282263 | − | 0.959337i | \(-0.408915\pi\) |
−0.959337 | + | 0.282263i | \(0.908915\pi\) | |||||||
\(468\) | 0.0891314 | + | 0.0891314i | 0.00412010 | + | 0.00412010i | ||||
\(469\) | 54.6046 | 2.52141 | ||||||||
\(470\) | 0.824566 | + | 1.21052i | 0.0380344 | + | 0.0558370i | ||||
\(471\) | 6.47591i | 0.298394i | ||||||||
\(472\) | −6.65282 | − | 6.65282i | −0.306221 | − | 0.306221i | ||||
\(473\) | −30.3387 | + | 30.3387i | −1.39497 | + | 1.39497i | ||||
\(474\) | 8.82758 | 0.405464 | ||||||||
\(475\) | −20.8597 | + | 6.31451i | −0.957109 | + | 0.289730i | ||||
\(476\) | −11.3753 | −0.521385 | ||||||||
\(477\) | −3.21910 | + | 3.21910i | −0.147393 | + | 0.147393i | ||||
\(478\) | −9.19036 | − | 9.19036i | −0.420357 | − | 0.420357i | ||||
\(479\) | − | 28.1296i | − | 1.28527i | −0.766171 | − | 0.642636i | \(-0.777841\pi\) | ||
0.766171 | − | 0.642636i | \(-0.222159\pi\) | |||||||
\(480\) | −1.25884 | − | 1.84806i | −0.0574579 | − | 0.0843520i | ||||
\(481\) | −1.26065 | −0.0574808 | ||||||||
\(482\) | 6.10941 | + | 6.10941i | 0.278276 | + | 0.278276i | ||||
\(483\) | −11.3766 | − | 11.3766i | −0.517652 | − | 0.517652i | ||||
\(484\) | − | 3.60898i | − | 0.164045i | ||||||
\(485\) | 21.3882 | + | 4.05625i | 0.971186 | + | 0.184185i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 11.6398 | − | 11.6398i | 0.527451 | − | 0.527451i | −0.392361 | − | 0.919811i | \(-0.628342\pi\) |
0.919811 | + | 0.392361i | \(0.128342\pi\) | |||||||
\(488\) | 5.80803 | + | 5.80803i | 0.262917 | + | 0.262917i | ||||
\(489\) | −10.6715 | −0.482584 | ||||||||
\(490\) | 5.12704 | − | 27.0344i | 0.231616 | − | 1.22129i | ||||
\(491\) | 5.55189 | 0.250553 | 0.125277 | − | 0.992122i | \(-0.460018\pi\) | ||||
0.125277 | + | 0.992122i | \(0.460018\pi\) | |||||||
\(492\) | −7.92907 | − | 7.92907i | −0.357470 | − | 0.357470i | ||||
\(493\) | 6.59121 | + | 6.59121i | 0.296853 | + | 0.296853i | ||||
\(494\) | −0.340675 | − | 0.431077i | −0.0153277 | − | 0.0193951i | ||||
\(495\) | 7.06360 | − | 4.81150i | 0.317485 | − | 0.216261i | ||||
\(496\) | − | 3.60048i | − | 0.161666i | ||||||
\(497\) | −5.17786 | + | 5.17786i | −0.232259 | + | 0.232259i | ||||
\(498\) | −0.347181 | + | 0.347181i | −0.0155576 | + | 0.0155576i | ||||
\(499\) | − | 27.8562i | − | 1.24701i | −0.781818 | − | 0.623507i | \(-0.785707\pi\) | ||
0.781818 | − | 0.623507i | \(-0.214293\pi\) | |||||||
\(500\) | 2.47400 | + | 10.9032i | 0.110641 | + | 0.487605i | ||||
\(501\) | −21.3935 | −0.955789 | ||||||||
\(502\) | −16.7294 | + | 16.7294i | −0.746670 | + | 0.746670i | ||||
\(503\) | 20.5340 | − | 20.5340i | 0.915564 | − | 0.915564i | −0.0811388 | − | 0.996703i | \(-0.525856\pi\) |
0.996703 | + | 0.0811388i | \(0.0258557\pi\) | |||||||
\(504\) | −4.39382 | −0.195716 | ||||||||
\(505\) | −4.89907 | − | 7.19216i | −0.218006 | − | 0.320047i | ||||
\(506\) | − | 13.9957i | − | 0.622184i | ||||||
\(507\) | −9.18115 | + | 9.18115i | −0.407749 | + | 0.407749i | ||||
\(508\) | 0.0636986 | + | 0.0636986i | 0.00282617 | + | 0.00282617i | ||||
\(509\) | 27.6636 | 1.22617 | 0.613085 | − | 0.790017i | \(-0.289928\pi\) | ||||
0.613085 | + | 0.790017i | \(0.289928\pi\) | |||||||
\(510\) | 1.07866 | − | 5.68764i | 0.0477637 | − | 0.251853i | ||||
\(511\) | −22.6414 | −1.00160 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.32930 | + | 0.507128i | 0.191143 | + | 0.0223902i | ||||
\(514\) | 12.2150i | 0.538781i | ||||||||
\(515\) | 5.54173 | − | 29.2209i | 0.244198 | − | 1.28763i | ||||
\(516\) | 11.2254i | 0.494170i | ||||||||
\(517\) | 1.77031 | + | 1.77031i | 0.0778583 | + | 0.0778583i | ||||
\(518\) | 31.0725 | − | 31.0725i | 1.36525 | − | 1.36525i | ||||
\(519\) | 3.28746i | 0.144303i | ||||||||
\(520\) | −0.232949 | + | 0.158678i | −0.0102155 | + | 0.00695848i | ||||
\(521\) | 23.2591i | 1.01900i | 0.860471 | + | 0.509500i | \(0.170170\pi\) | ||||
−0.860471 | + | 0.509500i | \(0.829830\pi\) | |||||||
\(522\) | 2.54592 | + | 2.54592i | 0.111432 | + | 0.111432i | ||||
\(523\) | 8.81162 | + | 8.81162i | 0.385305 | + | 0.385305i | 0.873009 | − | 0.487704i | \(-0.162165\pi\) |
−0.487704 | + | 0.873009i | \(0.662165\pi\) | |||||||
\(524\) | − | 2.44811i | − | 0.106946i | ||||||
\(525\) | 20.4436 | + | 8.04354i | 0.892234 | + | 0.351049i | ||||
\(526\) | 15.4560i | 0.673915i | ||||||||
\(527\) | 6.59121 | − | 6.59121i | 0.287117 | − | 0.287117i | ||||
\(528\) | −2.70268 | − | 2.70268i | −0.117619 | − | 0.117619i | ||||
\(529\) | 9.59187i | 0.417038i | ||||||||
\(530\) | −5.73086 | − | 8.41329i | −0.248933 | − | 0.365450i | ||||
\(531\) | − | 9.40851i | − | 0.408294i | ||||||
\(532\) | 19.0221 | + | 2.22823i | 0.824715 | + | 0.0966059i | ||||
\(533\) | −0.999466 | + | 0.999466i | −0.0432917 | + | 0.0432917i | ||||
\(534\) | 9.79832 | 0.424015 | ||||||||
\(535\) | 21.7788 | + | 4.13034i | 0.941581 | + | 0.178570i | ||||
\(536\) | 12.4276 | 0.536790 | ||||||||
\(537\) | 0.364750 | + | 0.364750i | 0.0157401 | + | 0.0157401i | ||||
\(538\) | 9.79507 | − | 9.79507i | 0.422296 | − | 0.422296i | ||||
\(539\) | − | 47.0342i | − | 2.02591i | ||||||
\(540\) | 0.416642 | − | 2.19691i | 0.0179294 | − | 0.0945399i | ||||
\(541\) | −16.3738 | −0.703966 | −0.351983 | − | 0.936006i | \(-0.614493\pi\) | ||||
−0.351983 | + | 0.936006i | \(0.614493\pi\) | |||||||
\(542\) | −10.4913 | + | 10.4913i | −0.450642 | + | 0.450642i | ||||
\(543\) | −3.43744 | + | 3.43744i | −0.147515 | + | 0.147515i | ||||
\(544\) | −2.58893 | −0.110999 | ||||||||
\(545\) | −22.3991 | − | 32.8834i | −0.959473 | − | 1.40857i | ||||
\(546\) | 0.553844i | 0.0237024i | ||||||||
\(547\) | −20.3289 | + | 20.3289i | −0.869199 | + | 0.869199i | −0.992384 | − | 0.123185i | \(-0.960689\pi\) |
0.123185 | + | 0.992384i | \(0.460689\pi\) | |||||||
\(548\) | 3.02688 | − | 3.02688i | 0.129302 | − | 0.129302i | ||||
\(549\) | 8.21380i | 0.350556i | ||||||||
\(550\) | 7.62743 | + | 17.5228i | 0.325235 | + | 0.747173i | ||||
\(551\) | −9.73094 | − | 12.3132i | −0.414552 | − | 0.524558i | ||||
\(552\) | −2.58922 | − | 2.58922i | −0.110205 | − | 0.110205i | ||||
\(553\) | 27.4264 | + | 27.4264i | 1.16629 | + | 1.16629i | ||||
\(554\) | 12.6674 | 0.538188 | ||||||||
\(555\) | 12.5898 | + | 18.4827i | 0.534409 | + | 0.784548i | ||||
\(556\) | 3.96170 | 0.168013 | ||||||||
\(557\) | −12.6433 | − | 12.6433i | −0.535713 | − | 0.535713i | 0.386554 | − | 0.922267i | \(-0.373665\pi\) |
−0.922267 | + | 0.386554i | \(0.873665\pi\) | |||||||
\(558\) | 2.54592 | − | 2.54592i | 0.107777 | − | 0.107777i | ||||
\(559\) | 1.41497 | 0.0598468 | ||||||||
\(560\) | 1.83065 | − | 9.65282i | 0.0773590 | − | 0.407906i | ||||
\(561\) | − | 9.89533i | − | 0.417781i | ||||||
\(562\) | 4.34121 | + | 4.34121i | 0.183123 | + | 0.183123i | ||||
\(563\) | −20.5997 | − | 20.5997i | −0.868176 | − | 0.868176i | 0.124095 | − | 0.992270i | \(-0.460397\pi\) |
−0.992270 | + | 0.124095i | \(0.960397\pi\) | |||||||
\(564\) | 0.655021 | 0.0275814 | ||||||||
\(565\) | −7.33541 | + | 38.6789i | −0.308603 | + | 1.62723i | ||||
\(566\) | − | 32.2388i | − | 1.35510i | ||||||
\(567\) | −3.10690 | − | 3.10690i | −0.130477 | − | 0.130477i | ||||
\(568\) | −1.17844 | + | 1.17844i | −0.0494463 | + | 0.0494463i | ||||
\(569\) | −39.5742 | −1.65904 | −0.829519 | − | 0.558478i | \(-0.811386\pi\) | ||||
−0.829519 | + | 0.558478i | \(0.811386\pi\) | |||||||
\(570\) | −2.91788 | + | 9.29978i | −0.122217 | + | 0.389525i | ||||
\(571\) | −15.5508 | −0.650780 | −0.325390 | − | 0.945580i | \(-0.605496\pi\) | ||||
−0.325390 | + | 0.945580i | \(0.605496\pi\) | |||||||
\(572\) | −0.340675 | + | 0.340675i | −0.0142444 | + | 0.0142444i | ||||
\(573\) | 10.8448 | + | 10.8448i | 0.453049 | + | 0.453049i | ||||
\(574\) | − | 49.2696i | − | 2.05647i | ||||||
\(575\) | 7.30722 | + | 16.7871i | 0.304732 | + | 0.700072i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 2.21358 | + | 2.21358i | 0.0921525 | + | 0.0921525i | 0.751680 | − | 0.659528i | \(-0.229244\pi\) |
−0.659528 | + | 0.751680i | \(0.729244\pi\) | |||||||
\(578\) | 7.28140 | + | 7.28140i | 0.302866 | + | 0.302866i | ||||
\(579\) | − | 24.2679i | − | 1.00854i | ||||||
\(580\) | −6.65389 | + | 4.53242i | −0.276288 | + | 0.188198i | ||||
\(581\) | −2.15731 | −0.0895004 | ||||||||
\(582\) | 6.88409 | − | 6.88409i | 0.285355 | − | 0.285355i | ||||
\(583\) | −12.3040 | − | 12.3040i | −0.509578 | − | 0.509578i | ||||
\(584\) | −5.15301 | −0.213233 | ||||||||
\(585\) | −0.276922 | − | 0.0525181i | −0.0114493 | − | 0.00217135i | ||||
\(586\) | −0.482856 | −0.0199466 | ||||||||
\(587\) | −0.773553 | − | 0.773553i | −0.0319279 | − | 0.0319279i | 0.690963 | − | 0.722891i | \(-0.257187\pi\) |
−0.722891 | + | 0.690963i | \(0.757187\pi\) | |||||||
\(588\) | −8.70140 | − | 8.70140i | −0.358840 | − | 0.358840i | ||||
\(589\) | −12.3132 | + | 9.73094i | −0.507355 | + | 0.400956i | ||||
\(590\) | 20.6696 | + | 3.91998i | 0.850955 | + | 0.161383i | ||||
\(591\) | 8.83957i | 0.363611i | ||||||||
\(592\) | 7.07188 | − | 7.07188i | 0.290652 | − | 0.290652i | ||||
\(593\) | 6.83126 | − | 6.83126i | 0.280526 | − | 0.280526i | −0.552793 | − | 0.833319i | \(-0.686438\pi\) |
0.833319 | + | 0.552793i | \(0.186438\pi\) | |||||||
\(594\) | − | 3.82217i | − | 0.156826i | ||||||
\(595\) | 21.0222 | − | 14.3196i | 0.861826 | − | 0.587048i | ||||
\(596\) | −22.3940 | −0.917294 | ||||||||
\(597\) | 7.36057 | − | 7.36057i | 0.301248 | − | 0.301248i | ||||
\(598\) | −0.326373 | + | 0.326373i | −0.0133464 | + | 0.0133464i | ||||
\(599\) | 4.89411 | 0.199968 | 0.0999840 | − | 0.994989i | \(-0.468121\pi\) | ||||
0.0999840 | + | 0.994989i | \(0.468121\pi\) | |||||||
\(600\) | 4.65282 | + | 1.83065i | 0.189951 | + | 0.0747359i | ||||
\(601\) | 18.8596i | 0.769299i | 0.923063 | + | 0.384650i | \(0.125678\pi\) | ||||
−0.923063 | + | 0.384650i | \(0.874322\pi\) | |||||||
\(602\) | −34.8761 | + | 34.8761i | −1.42145 | + | 1.42145i | ||||
\(603\) | 8.78764 | + | 8.78764i | 0.357860 | + | 0.357860i | ||||
\(604\) | −11.2995 | −0.459769 | ||||||||
\(605\) | 4.54313 | + | 6.66962i | 0.184705 | + | 0.271159i | ||||
\(606\) | −3.89174 | −0.158091 | ||||||||
\(607\) | 16.5646 | − | 16.5646i | 0.672335 | − | 0.672335i | −0.285919 | − | 0.958254i | \(-0.592299\pi\) |
0.958254 | + | 0.285919i | \(0.0922988\pi\) | |||||||
\(608\) | 4.32930 | + | 0.507128i | 0.175576 | + | 0.0205668i | ||||
\(609\) | 15.8198i | 0.641052i | ||||||||
\(610\) | −18.0450 | − | 3.42221i | −0.730619 | − | 0.138561i | ||||
\(611\) | − | 0.0825659i | − | 0.00334026i | ||||||
\(612\) | −1.83065 | − | 1.83065i | −0.0739996 | − | 0.0739996i | ||||
\(613\) | 29.1371 | − | 29.1371i | 1.17684 | − | 1.17684i | 0.196291 | − | 0.980546i | \(-0.437110\pi\) |
0.980546 | − | 0.196291i | \(-0.0628899\pi\) | |||||||
\(614\) | − | 25.5326i | − | 1.03041i | ||||||
\(615\) | 24.6348 | + | 4.67197i | 0.993372 | + | 0.188392i | ||||
\(616\) | − | 16.7939i | − | 0.676646i | ||||||
\(617\) | 18.0432 | + | 18.0432i | 0.726393 | + | 0.726393i | 0.969899 | − | 0.243506i | \(-0.0782977\pi\) |
−0.243506 | + | 0.969899i | \(0.578298\pi\) | |||||||
\(618\) | −9.40518 | − | 9.40518i | −0.378332 | − | 0.378332i | ||||
\(619\) | 2.38578i | 0.0958924i | 0.998850 | + | 0.0479462i | \(0.0152676\pi\) | ||||
−0.998850 | + | 0.0479462i | \(0.984732\pi\) | |||||||
\(620\) | 4.53242 | + | 6.65389i | 0.182026 | + | 0.267227i | ||||
\(621\) | − | 3.66171i | − | 0.146939i | ||||||
\(622\) | −4.05233 | + | 4.05233i | −0.162484 | + | 0.162484i | ||||
\(623\) | 30.4424 | + | 30.4424i | 1.21965 | + | 1.21965i | ||||
\(624\) | 0.126051i | 0.00504607i | ||||||||
\(625\) | −18.2974 | − | 17.0354i | −0.731898 | − | 0.681414i | ||||
\(626\) | 31.3617i | 1.25347i | ||||||||
\(627\) | −1.93833 | + | 16.5473i | −0.0774094 | + | 0.660836i | ||||
\(628\) | −4.57916 | + | 4.57916i | −0.182728 | + | 0.182728i | ||||
\(629\) | 25.8923 | 1.03239 | ||||||||
\(630\) | 8.12004 | − | 5.53111i | 0.323510 | − | 0.220365i | ||||
\(631\) | −14.5023 | −0.577326 | −0.288663 | − | 0.957431i | \(-0.593211\pi\) | ||||
−0.288663 | + | 0.957431i | \(0.593211\pi\) | |||||||
\(632\) | 6.24204 | + | 6.24204i | 0.248295 | + | 0.248295i | ||||
\(633\) | −9.23137 | + | 9.23137i | −0.366914 | + | 0.366914i | ||||
\(634\) | 15.6454i | 0.621359i | ||||||||
\(635\) | −0.197905 | − | 0.0375326i | −0.00785363 | − | 0.00148943i | ||||
\(636\) | −4.55250 | −0.180518 | ||||||||
\(637\) | −1.09682 | + | 1.09682i | −0.0434575 | + | 0.0434575i | ||||
\(638\) | −9.73094 | + | 9.73094i | −0.385252 | + | 0.385252i | ||||
\(639\) | −1.66657 | −0.0659284 | ||||||||
\(640\) | 0.416642 | − | 2.19691i | 0.0164692 | − | 0.0868405i | ||||
\(641\) | 12.7084i | 0.501950i | 0.967994 | + | 0.250975i | \(0.0807512\pi\) | ||||
−0.967994 | + | 0.250975i | \(0.919249\pi\) | |||||||
\(642\) | 7.00983 | − | 7.00983i | 0.276656 | − | 0.276656i | ||||
\(643\) | −1.79680 | + | 1.79680i | −0.0708588 | + | 0.0708588i | −0.741648 | − | 0.670789i | \(-0.765956\pi\) |
0.670789 | + | 0.741648i | \(0.265956\pi\) | |||||||
\(644\) | − | 16.0889i | − | 0.633991i | ||||||
\(645\) | −14.1310 | − | 20.7452i | −0.556406 | − | 0.816841i | ||||
\(646\) | 6.99705 | + | 8.85380i | 0.275295 | + | 0.348348i | ||||
\(647\) | 7.42896 | + | 7.42896i | 0.292063 | + | 0.292063i | 0.837895 | − | 0.545832i | \(-0.183786\pi\) |
−0.545832 | + | 0.837895i | \(0.683786\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 35.9609 | 1.41159 | ||||||||
\(650\) | 0.230755 | − | 0.586492i | 0.00905095 | − | 0.0230041i | ||||
\(651\) | 15.8198 | 0.620028 | ||||||||
\(652\) | −7.54592 | − | 7.54592i | −0.295521 | − | 0.295521i | ||||
\(653\) | −32.4125 | + | 32.4125i | −1.26840 | + | 1.26840i | −0.321486 | + | 0.946914i | \(0.604182\pi\) |
−0.946914 | + | 0.321486i | \(0.895818\pi\) | |||||||
\(654\) | −17.7935 | −0.695780 | ||||||||
\(655\) | 3.08178 | + | 4.52426i | 0.120415 | + | 0.176777i | ||||
\(656\) | − | 11.2134i | − | 0.437810i | ||||||
\(657\) | −3.64373 | − | 3.64373i | −0.142155 | − | 0.142155i | ||||
\(658\) | 2.03508 | + | 2.03508i | 0.0793358 | + | 0.0793358i | ||||
\(659\) | −41.3365 | −1.61024 | −0.805122 | − | 0.593110i | \(-0.797900\pi\) | ||||
−0.805122 | + | 0.593110i | \(0.797900\pi\) | |||||||
\(660\) | 8.39696 | + | 1.59248i | 0.326851 | + | 0.0619871i | ||||
\(661\) | − | 2.43023i | − | 0.0945250i | −0.998883 | − | 0.0472625i | \(-0.984950\pi\) | ||
0.998883 | − | 0.0472625i | \(-0.0150497\pi\) | |||||||
\(662\) | 8.34099 | + | 8.34099i | 0.324182 | + | 0.324182i | ||||
\(663\) | −0.230755 | + | 0.230755i | −0.00896177 | + | 0.00896177i | ||||
\(664\) | −0.490988 | −0.0190540 | ||||||||
\(665\) | −37.9590 | + | 19.8279i | −1.47199 | + | 0.768894i | ||||
\(666\) | 10.0011 | 0.387537 | ||||||||
\(667\) | −9.32242 | + | 9.32242i | −0.360966 | + | 0.360966i | ||||
\(668\) | −15.1275 | − | 15.1275i | −0.585299 | − | 0.585299i | ||||
\(669\) | − | 16.3221i | − | 0.631047i | ||||||
\(670\) | −22.9669 | + | 15.6443i | −0.887290 | + | 0.604394i | ||||
\(671\) | −31.3945 | −1.21197 | ||||||||
\(672\) | −3.10690 | − | 3.10690i | −0.119851 | − | 0.119851i | ||||
\(673\) | −19.4040 | − | 19.4040i | −0.747968 | − | 0.747968i | 0.226129 | − | 0.974097i | \(-0.427393\pi\) |
−0.974097 | + | 0.226129i | \(0.927393\pi\) | |||||||
\(674\) | − | 15.4150i | − | 0.593765i | ||||||
\(675\) | 1.99558 | + | 4.58450i | 0.0768097 | + | 0.176458i | ||||
\(676\) | −12.9841 | −0.499389 | ||||||||
\(677\) | −18.9654 | + | 18.9654i | −0.728899 | + | 0.728899i | −0.970401 | − | 0.241501i | \(-0.922360\pi\) |
0.241501 | + | 0.970401i | \(0.422360\pi\) | |||||||
\(678\) | 12.4493 | + | 12.4493i | 0.478114 | + | 0.478114i | ||||
\(679\) | 42.7763 | 1.64160 | ||||||||
\(680\) | 4.78449 | − | 3.25904i | 0.183477 | − | 0.124979i | ||||
\(681\) | −23.2372 | −0.890452 | ||||||||
\(682\) | 9.73094 | + | 9.73094i | 0.372617 | + | 0.372617i | ||||
\(683\) | 11.9597 | + | 11.9597i | 0.457626 | + | 0.457626i | 0.897876 | − | 0.440249i | \(-0.145110\pi\) |
−0.440249 | + | 0.897876i | \(0.645110\pi\) | |||||||
\(684\) | 2.70268 | + | 3.41987i | 0.103340 | + | 0.130762i | ||||
\(685\) | −1.78350 | + | 9.40420i | −0.0681440 | + | 0.359316i | ||||
\(686\) | − | 23.3120i | − | 0.890057i | ||||||
\(687\) | 10.9739 | − | 10.9739i | 0.418680 | − | 0.418680i | ||||
\(688\) | −7.93755 | + | 7.93755i | −0.302616 | + | 0.302616i | ||||
\(689\) | 0.573846i | 0.0218618i | ||||||||
\(690\) | 8.04445 | + | 1.52562i | 0.306247 | + | 0.0580795i | ||||
\(691\) | 3.66130 | 0.139282 | 0.0696412 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696412 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(692\) | −2.32458 | + | 2.32458i | −0.0883674 | + | 0.0883674i | ||||
\(693\) | 11.8751 | − | 11.8751i | 0.451098 | − | 0.451098i | ||||
\(694\) | −22.4879 | −0.853630 | ||||||||
\(695\) | −7.32145 | + | 4.98714i | −0.277718 | + | 0.189173i | ||||
\(696\) | 3.60048i | 0.136476i | ||||||||
\(697\) | 20.5278 | − | 20.5278i | 0.777546 | − | 0.777546i | ||||
\(698\) | 9.91149 | + | 9.91149i | 0.375155 | + | 0.375155i | ||||
\(699\) | 2.39161 | 0.0904590 | ||||||||
\(700\) | 8.76820 | + | 20.1435i | 0.331407 | + | 0.761352i | ||||
\(701\) | −25.2380 | −0.953225 | −0.476612 | − | 0.879113i | \(-0.658136\pi\) | ||||
−0.476612 | + | 0.879113i | \(0.658136\pi\) | |||||||
\(702\) | −0.0891314 | + | 0.0891314i | −0.00336405 | + | 0.00336405i | ||||
\(703\) | −43.2979 | − | 5.07186i | −1.63301 | − | 0.191289i | ||||
\(704\) | − | 3.82217i | − | 0.144053i | ||||||
\(705\) | −1.21052 | + | 0.824566i | −0.0455907 | + | 0.0310550i | ||||
\(706\) | − | 2.40574i | − | 0.0905412i | ||||||
\(707\) | −12.0912 | − | 12.0912i | −0.454737 | − | 0.454737i | ||||
\(708\) | 6.65282 | − | 6.65282i | 0.250028 | − | 0.250028i | ||||
\(709\) | − | 7.14208i | − | 0.268226i | −0.990966 | − | 0.134113i | \(-0.957181\pi\) | ||
0.990966 | − | 0.134113i | \(-0.0428186\pi\) | |||||||
\(710\) | 0.694362 | − | 3.66130i | 0.0260589 | − | 0.137406i | ||||
\(711\) | 8.82758i | 0.331060i | ||||||||
\(712\) | 6.92846 | + | 6.92846i | 0.259655 | + | 0.259655i | ||||
\(713\) | 9.32242 | + | 9.32242i | 0.349128 | + | 0.349128i | ||||
\(714\) | − | 11.3753i | − | 0.425709i | ||||||
\(715\) | 0.200733 | − | 1.05844i | 0.00750699 | − | 0.0395836i | ||||
\(716\) | 0.515834i | 0.0192776i | ||||||||
\(717\) | 9.19036 | − | 9.19036i | 0.343220 | − | 0.343220i | ||||
\(718\) | −26.1412 | − | 26.1412i | −0.975583 | − | 0.975583i | ||||
\(719\) | 30.1848i | 1.12570i | 0.826558 | + | 0.562852i | \(0.190296\pi\) | ||||
−0.826558 | + | 0.562852i | \(0.809704\pi\) | |||||||
\(720\) | 1.84806 | − | 1.25884i | 0.0688731 | − | 0.0469142i | ||||
\(721\) | − | 58.4419i | − | 2.17649i | ||||||
\(722\) | −9.96641 | − | 16.1762i | −0.370911 | − | 0.602017i | ||||
\(723\) | −6.10941 | + | 6.10941i | −0.227211 | + | 0.227211i | ||||
\(724\) | −4.86127 | −0.180668 | ||||||||
\(725\) | 6.59121 | − | 16.7524i | 0.244791 | − | 0.622167i | ||||
\(726\) | 3.60898 | 0.133942 | ||||||||
\(727\) | 10.1806 | + | 10.1806i | 0.377576 | + | 0.377576i | 0.870227 | − | 0.492651i | \(-0.163972\pi\) |
−0.492651 | + | 0.870227i | \(0.663972\pi\) | |||||||
\(728\) | −0.391627 | + | 0.391627i | −0.0145147 | + | 0.0145147i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 9.52307 | − | 6.48681i | 0.352465 | − | 0.240088i | ||||
\(731\) | −29.0617 | −1.07489 | ||||||||
\(732\) | −5.80803 | + | 5.80803i | −0.214671 | + | 0.214671i | ||||
\(733\) | −12.6028 | + | 12.6028i | −0.465495 | + | 0.465495i | −0.900451 | − | 0.434957i | \(-0.856764\pi\) |
0.434957 | + | 0.900451i | \(0.356764\pi\) | |||||||
\(734\) | 16.6688 | 0.615255 | ||||||||
\(735\) | 27.0344 | + | 5.12704i | 0.997178 | + | 0.189114i | ||||
\(736\) | − | 3.66171i | − | 0.134972i | ||||||
\(737\) | −33.5878 | + | 33.5878i | −1.23722 | + | 1.23722i | ||||
\(738\) | 7.92907 | − | 7.92907i | 0.291873 | − | 0.291873i | ||||
\(739\) | − | 30.9906i | − | 1.14001i | −0.821642 | − | 0.570003i | \(-0.806942\pi\) | ||
0.821642 | − | 0.570003i | \(-0.193058\pi\) | |||||||
\(740\) | −4.16690 | + | 21.9716i | −0.153178 | + | 0.807692i | ||||
\(741\) | 0.431077 | − | 0.340675i | 0.0158360 | − | 0.0125150i | ||||
\(742\) | −14.1442 | − | 14.1442i | −0.519248 | − | 0.519248i | ||||
\(743\) | 33.1976 | + | 33.1976i | 1.21790 | + | 1.21790i | 0.968366 | + | 0.249536i | \(0.0802779\pi\) |
0.249536 | + | 0.968366i | \(0.419722\pi\) | |||||||
\(744\) | 3.60048 | 0.132000 | ||||||||
\(745\) | 41.3854 | − | 28.1904i | 1.51625 | − | 1.03282i | ||||
\(746\) | −13.1413 | −0.481137 | ||||||||
\(747\) | −0.347181 | − | 0.347181i | −0.0127027 | − | 0.0127027i | ||||
\(748\) | 6.99705 | − | 6.99705i | 0.255838 | − | 0.255838i | ||||
\(749\) | 43.5577 | 1.59156 | ||||||||
\(750\) | −10.9032 | + | 2.47400i | −0.398128 | + | 0.0903378i | ||||
\(751\) | 11.6085i | 0.423600i | 0.977313 | + | 0.211800i | \(0.0679325\pi\) | ||||
−0.977313 | + | 0.211800i | \(0.932067\pi\) | |||||||
\(752\) | 0.463170 | + | 0.463170i | 0.0168901 | + | 0.0168901i | ||||
\(753\) | −16.7294 | − | 16.7294i | −0.609654 | − | 0.609654i | ||||
\(754\) | 0.453843 | 0.0165280 | ||||||||
\(755\) | 20.8821 | − | 14.2242i | 0.759978 | − | 0.517673i | ||||
\(756\) | − | 4.39382i | − | 0.159802i | ||||||
\(757\) | 33.9555 | + | 33.9555i | 1.23413 | + | 1.23413i | 0.962362 | + | 0.271772i | \(0.0876098\pi\) |
0.271772 | + | 0.962362i | \(0.412390\pi\) | |||||||
\(758\) | −6.42759 | + | 6.42759i | −0.233461 | + | 0.233461i | ||||
\(759\) | 13.9957 | 0.508011 | ||||||||
\(760\) | −8.63919 | + | 4.51269i | −0.313376 | + | 0.163692i | ||||
\(761\) | −1.91340 | −0.0693607 | −0.0346803 | − | 0.999398i | \(-0.511041\pi\) | ||||
−0.0346803 | + | 0.999398i | \(0.511041\pi\) | |||||||
\(762\) | −0.0636986 | + | 0.0636986i | −0.00230756 | + | 0.00230756i | ||||
\(763\) | −55.2825 | − | 55.2825i | −2.00136 | − | 2.00136i | ||||
\(764\) | 15.3369i | 0.554870i | ||||||||
\(765\) | 5.68764 | + | 1.07866i | 0.205637 | + | 0.0389989i | ||||
\(766\) | −4.12842 | −0.149166 | ||||||||
\(767\) | −0.838593 | − | 0.838593i | −0.0302798 | − | 0.0302798i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 17.5747i | 0.633760i | 0.948466 | + | 0.316880i | \(0.102635\pi\) | ||||
−0.948466 | + | 0.316880i | \(0.897365\pi\) | |||||||
\(770\) | 21.1408 | + | 31.0362i | 0.761863 | + | 1.11847i | ||||
\(771\) | −12.2150 | −0.439913 | ||||||||
\(772\) | 17.1600 | − | 17.1600i | 0.617603 | − | 0.617603i | ||||
\(773\) | −28.9882 | − | 28.9882i | −1.04263 | − | 1.04263i | −0.999050 | − | 0.0435843i | \(-0.986122\pi\) |
−0.0435843 | − | 0.999050i | \(-0.513878\pi\) | |||||||
\(774\) | −11.2254 | −0.403488 | ||||||||
\(775\) | −16.7524 | − | 6.59121i | −0.601763 | − | 0.236763i | ||||
\(776\) | 9.73557 | 0.349487 | ||||||||
\(777\) | 31.0725 | + | 31.0725i | 1.11472 | + | 1.11472i | ||||
\(778\) | −17.8792 | − | 17.8792i | −0.641001 | − | 0.641001i | ||||
\(779\) | −38.3484 | + | 30.3062i | −1.37397 | + | 1.08583i | ||||
\(780\) | −0.158678 | − | 0.232949i | −0.00568157 | − | 0.00834093i | ||||
\(781\) | − | 6.36991i | − | 0.227933i | ||||||
\(782\) | 6.70331 | − | 6.70331i | 0.239710 | − | 0.239710i | ||||
\(783\) | −2.54592 | + | 2.54592i | −0.0909838 | + | 0.0909838i | ||||
\(784\) | − | 12.3056i | − | 0.439487i | ||||||
\(785\) | 2.69813 | − | 14.2270i | 0.0963006 | − | 0.507783i | ||||
\(786\) | 2.44811 | 0.0873213 | ||||||||
\(787\) | 1.82074 | − | 1.82074i | 0.0649024 | − | 0.0649024i | −0.673911 | − | 0.738813i | \(-0.735387\pi\) |
0.738813 | + | 0.673911i | \(0.235387\pi\) | |||||||
\(788\) | −6.25052 | + | 6.25052i | −0.222666 | + | 0.222666i | ||||
\(789\) | −15.4560 | −0.550249 | ||||||||
\(790\) | −19.3934 | − | 3.67794i | −0.689986 | − | 0.130855i | ||||
\(791\) | 77.3577i | 2.75052i | ||||||||
\(792\) | 2.70268 | − | 2.70268i | 0.0960356 | − | 0.0960356i | ||||
\(793\) | 0.732107 | + | 0.732107i | 0.0259979 | + | 0.0259979i | ||||
\(794\) | −16.2029 | −0.575020 | ||||||||
\(795\) | 8.41329 | − | 5.73086i | 0.298389 | − | 0.203253i | ||||
\(796\) | 10.4094 | 0.368952 | ||||||||
\(797\) | 2.79855 | − | 2.79855i | 0.0991296 | − | 0.0991296i | −0.655803 | − | 0.754932i | \(-0.727670\pi\) |
0.754932 | + | 0.655803i | \(0.227670\pi\) | |||||||
\(798\) | −2.22823 | + | 19.0221i | −0.0788784 | + | 0.673377i | ||||
\(799\) | 1.69580i | 0.0599932i | ||||||||
\(800\) | 1.99558 | + | 4.58450i | 0.0705543 | + | 0.162087i | ||||
\(801\) | 9.79832i | 0.346207i | ||||||||
\(802\) | −5.10751 | − | 5.10751i | −0.180352 | − | 0.180352i | ||||
\(803\) | 13.9270 | − | 13.9270i | 0.491471 | − | 0.491471i | ||||
\(804\) | 12.4276i | 0.438287i | ||||||||
\(805\) | 20.2533 | + | 29.7332i | 0.713836 | + | 1.04796i | ||||
\(806\) | − | 0.453843i | − | 0.0159859i | ||||||
\(807\) | 9.79507 | + | 9.79507i | 0.344803 | + | 0.344803i | ||||
\(808\) | −2.75187 | − | 2.75187i | −0.0968106 | − | 0.0968106i | ||||
\(809\) | 45.2384i | 1.59050i | 0.606282 | + | 0.795249i | \(0.292660\pi\) | ||||
−0.606282 | + | 0.795249i | \(0.707340\pi\) | |||||||
\(810\) | 2.19691 | + | 0.416642i | 0.0771915 | + | 0.0146393i | ||||
\(811\) | 42.6013i | 1.49593i | 0.663737 | + | 0.747966i | \(0.268970\pi\) | ||||
−0.663737 | + | 0.747966i | \(0.731030\pi\) | |||||||
\(812\) | −11.1863 | + | 11.1863i | −0.392563 | + | 0.392563i | ||||
\(813\) | −10.4913 | − | 10.4913i | −0.367948 | − | 0.367948i | ||||
\(814\) | 38.2261i | 1.33982i | ||||||||
\(815\) | 23.4444 | + | 4.44621i | 0.821222 | + | 0.155744i | ||||
\(816\) | − | 2.58893i | − | 0.0906306i | ||||||
\(817\) | 48.5980 | + | 5.69271i | 1.70023 | + | 0.199163i | ||||
\(818\) | −12.3050 | + | 12.3050i | −0.430235 | + | 0.430235i | ||||
\(819\) | −0.553844 | −0.0193529 | ||||||||
\(820\) | 14.1159 | + | 20.7230i | 0.492947 | + | 0.723679i | ||||
\(821\) | 52.7865 | 1.84226 | 0.921130 | − | 0.389255i | \(-0.127268\pi\) | ||||
0.921130 | + | 0.389255i | \(0.127268\pi\) | |||||||
\(822\) | 3.02688 | + | 3.02688i | 0.105574 | + | 0.105574i | ||||
\(823\) | −24.2470 | + | 24.2470i | −0.845199 | + | 0.845199i | −0.989529 | − | 0.144331i | \(-0.953897\pi\) |
0.144331 | + | 0.989529i | \(0.453897\pi\) | |||||||
\(824\) | − | 13.3009i | − | 0.463360i | ||||||
\(825\) | −17.5228 | + | 7.62743i | −0.610064 | + | 0.265553i | ||||
\(826\) | 41.3393 | 1.43838 | ||||||||
\(827\) | 8.09237 | − | 8.09237i | 0.281399 | − | 0.281399i | −0.552268 | − | 0.833667i | \(-0.686237\pi\) |
0.833667 | + | 0.552268i | \(0.186237\pi\) | |||||||
\(828\) | 2.58922 | − | 2.58922i | 0.0899816 | − | 0.0899816i | ||||
\(829\) | −8.26535 | −0.287067 | −0.143534 | − | 0.989645i | \(-0.545847\pi\) | ||||
−0.143534 | + | 0.989645i | \(0.545847\pi\) | |||||||
\(830\) | 0.907375 | − | 0.618075i | 0.0314955 | − | 0.0214537i | ||||
\(831\) | 12.6674i | 0.439429i | ||||||||
\(832\) | −0.0891314 | + | 0.0891314i | −0.00309007 | + | 0.00309007i | ||||
\(833\) | 22.5273 | − | 22.5273i | 0.780525 | − | 0.780525i | ||||
\(834\) | 3.96170i | 0.137182i | ||||||||
\(835\) | 46.9995 | + | 8.91341i | 1.62648 | + | 0.308461i | ||||
\(836\) | −13.0713 | + | 10.3301i | −0.452081 | + | 0.357274i | ||||
\(837\) | 2.54592 | + | 2.54592i | 0.0879999 | + | 0.0879999i | ||||
\(838\) | −1.18430 | − | 1.18430i | −0.0409109 | − | 0.0409109i | ||||
\(839\) | −36.8428 | −1.27196 | −0.635978 | − | 0.771707i | \(-0.719403\pi\) | ||||
−0.635978 | + | 0.771707i | \(0.719403\pi\) | |||||||
\(840\) | 9.65282 | + | 1.83065i | 0.333054 | + | 0.0631634i | ||||
\(841\) | −16.0366 | −0.552985 | ||||||||
\(842\) | 18.6001 | + | 18.6001i | 0.641001 | + | 0.641001i | ||||
\(843\) | −4.34121 | + | 4.34121i | −0.149519 | + | 0.149519i | ||||
\(844\) | −13.0551 | −0.449376 | ||||||||
\(845\) | 23.9954 | − | 16.3449i | 0.825467 | − | 0.562282i | ||||
\(846\) | 0.655021i | 0.0225201i | ||||||||
\(847\) | 11.2127 | + | 11.2127i | 0.385275 | + | 0.385275i | ||||
\(848\) | −3.21910 | − | 3.21910i | −0.110544 | − | 0.110544i | ||||
\(849\) | 32.2388 | 1.10643 | ||||||||
\(850\) | −4.73942 | + | 12.0458i | −0.162561 | + | 0.413168i | ||||
\(851\) | 36.6213i | 1.25536i | ||||||||
\(852\) | −1.17844 | − | 1.17844i | −0.0403727 | − | 0.0403727i | ||||
\(853\) | 25.7405 | − | 25.7405i | 0.881338 | − | 0.881338i | −0.112333 | − | 0.993671i | \(-0.535832\pi\) |
0.993671 | + | 0.112333i | \(0.0358324\pi\) | |||||||
\(854\) | −36.0899 | −1.23497 | ||||||||
\(855\) | −9.29978 | − | 2.91788i | −0.318046 | − | 0.0997894i | ||||
\(856\) | 9.91340 | 0.338833 | ||||||||
\(857\) | 4.80004 | − | 4.80004i | 0.163966 | − | 0.163966i | −0.620355 | − | 0.784321i | \(-0.713011\pi\) |
0.784321 | + | 0.620355i | \(0.213011\pi\) | |||||||
\(858\) | −0.340675 | − | 0.340675i | −0.0116305 | − | 0.0116305i | ||||
\(859\) | − | 32.4106i | − | 1.10584i | −0.833235 | − | 0.552918i | \(-0.813514\pi\) | ||
0.833235 | − | 0.552918i | \(-0.186486\pi\) | |||||||
\(860\) | 4.67697 | − | 24.6612i | 0.159483 | − | 0.840938i | ||||
\(861\) | 49.2696 | 1.67910 | ||||||||
\(862\) | 6.49601 | + | 6.49601i | 0.221255 | + | 0.221255i | ||||
\(863\) | 22.4852 | + | 22.4852i | 0.765406 | + | 0.765406i | 0.977294 | − | 0.211888i | \(-0.0679611\pi\) |
−0.211888 | + | 0.977294i | \(0.567961\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 1.36969 | − | 7.22225i | 0.0465709 | − | 0.245564i | ||||
\(866\) | 10.3023 | 0.350086 | ||||||||
\(867\) | −7.28140 | + | 7.28140i | −0.247289 | + | 0.247289i | ||||
\(868\) | 11.1863 | + | 11.1863i | 0.379688 | + | 0.379688i | ||||
\(869\) | −33.7405 | −1.14457 | ||||||||
\(870\) | −4.53242 | − | 6.65389i | −0.153663 | − | 0.225588i | ||||
\(871\) | 1.56651 | 0.0530791 | ||||||||
\(872\) | −12.5819 | − | 12.5819i | −0.426076 | − | 0.426076i | ||||
\(873\) | 6.88409 | + | 6.88409i | 0.232991 | + | 0.232991i | ||||
\(874\) | −12.5226 | + | 9.89644i | −0.423582 | + | 0.334752i | ||||
\(875\) | −41.5615 | − | 26.1886i | −1.40504 | − | 0.885336i | ||||
\(876\) | − | 5.15301i | − | 0.174104i | ||||||
\(877\) | −35.3194 | + | 35.3194i | −1.19265 | + | 1.19265i | −0.216334 | + | 0.976320i | \(0.569410\pi\) |
−0.976320 | + | 0.216334i | \(0.930590\pi\) | |||||||
\(878\) | 8.15073 | − | 8.15073i | 0.275074 | − | 0.275074i | ||||
\(879\) | − | 0.482856i | − | 0.0162863i | ||||||
\(880\) | 4.81150 | + | 7.06360i | 0.162196 | + | 0.238114i | ||||
\(881\) | 31.6981 | 1.06794 | 0.533968 | − | 0.845505i | \(-0.320700\pi\) | ||||
0.533968 | + | 0.845505i | \(0.320700\pi\) | |||||||
\(882\) | 8.70140 | − | 8.70140i | 0.292991 | − | 0.292991i | ||||
\(883\) | 5.19260 | − | 5.19260i | 0.174745 | − | 0.174745i | −0.614316 | − | 0.789060i | \(-0.710568\pi\) |
0.789060 | + | 0.614316i | \(0.210568\pi\) | |||||||
\(884\) | −0.326337 | −0.0109759 | ||||||||
\(885\) | −3.91998 | + | 20.6696i | −0.131769 | + | 0.694802i | ||||
\(886\) | 2.38830i | 0.0802367i | ||||||||
\(887\) | −38.1720 | + | 38.1720i | −1.28169 | + | 1.28169i | −0.341986 | + | 0.939705i | \(0.611100\pi\) |
−0.939705 | + | 0.341986i | \(0.888900\pi\) | |||||||
\(888\) | 7.07188 | + | 7.07188i | 0.237317 | + | 0.237317i | ||||
\(889\) | −0.395810 | −0.0132751 | ||||||||
\(890\) | −21.5260 | − | 4.08239i | −0.721554 | − | 0.136842i | ||||
\(891\) | 3.82217 | 0.128048 | ||||||||
\(892\) | 11.5414 | − | 11.5414i | 0.386436 | − | 0.386436i | ||||
\(893\) | 0.332179 | − | 2.83578i | 0.0111160 | − | 0.0948958i | ||||
\(894\) | − | 22.3940i | − | 0.748967i | ||||||
\(895\) | −0.649352 | − | 0.953293i | −0.0217055 | − | 0.0318651i | ||||
\(896\) | − | 4.39382i | − | 0.146787i | ||||||
\(897\) | −0.326373 | − | 0.326373i | −0.0108973 | − | 0.0108973i | ||||
\(898\) | −7.76942 | + | 7.76942i | −0.259269 | + | 0.259269i | ||||
\(899\) | − | 12.9634i | − | 0.432354i | ||||||
\(900\) | −1.83065 | + | 4.65282i | −0.0610216 | + | 0.155094i | ||||
\(901\) | − | 11.7861i | − | 0.392652i | ||||||
\(902\) | 30.3062 | + | 30.3062i | 1.00909 | + | 1.00909i | ||||
\(903\) | −34.8761 | − | 34.8761i | −1.16061 | − | 1.16061i | ||||
\(904\) | 17.6060i | 0.585568i | ||||||||
\(905\) | 8.98392 | − | 6.11956i | 0.298636 | − | 0.203421i | ||||
\(906\) | − | 11.2995i | − | 0.375400i | ||||||
\(907\) | −2.04159 | + | 2.04159i | −0.0677900 | + | 0.0677900i | −0.740189 | − | 0.672399i | \(-0.765264\pi\) |
0.672399 | + | 0.740189i | \(0.265264\pi\) | |||||||
\(908\) | −16.4312 | − | 16.4312i | −0.545288 | − | 0.545288i | ||||
\(909\) | − | 3.89174i | − | 0.129081i | ||||||
\(910\) | 0.230755 | − | 1.21675i | 0.00764945 | − | 0.0403347i | ||||
\(911\) | − | 52.8342i | − | 1.75047i | −0.483695 | − | 0.875237i | \(-0.660705\pi\) | ||
0.483695 | − | 0.875237i | \(-0.339295\pi\) | |||||||
\(912\) | −0.507128 | + | 4.32930i | −0.0167927 | + | 0.143357i | ||||
\(913\) | 1.32698 | − | 1.32698i | 0.0439168 | − | 0.0439168i | ||||
\(914\) | 34.3920 | 1.13759 | ||||||||
\(915\) | 3.42221 | − | 18.0450i | 0.113135 | − | 0.596548i | ||||
\(916\) | 15.5194 | 0.512777 | ||||||||
\(917\) | 7.60604 | + | 7.60604i | 0.251173 | + | 0.251173i | ||||
\(918\) | 1.83065 | − | 1.83065i | 0.0604204 | − | 0.0604204i | ||||
\(919\) | 3.57090i | 0.117793i | 0.998264 | + | 0.0588965i | \(0.0187582\pi\) | ||||
−0.998264 | + | 0.0588965i | \(0.981242\pi\) | |||||||
\(920\) | 4.60950 | + | 6.76706i | 0.151971 | + | 0.223103i | ||||
\(921\) | 25.5326 | 0.841328 | ||||||||
\(922\) | −14.7622 | + | 14.7622i | −0.486166 | + | 0.486166i | ||||
\(923\) | −0.148543 | + | 0.148543i | −0.00488937 | + | 0.00488937i | ||||
\(924\) | 16.7939 | 0.552479 | ||||||||
\(925\) | −19.9580 | − | 45.8503i | −0.656216 | − | 1.50755i | ||||
\(926\) | − | 23.3573i | − | 0.767568i | ||||||
\(927\) | 9.40518 | − | 9.40518i | 0.308907 | − | 0.308907i | ||||
\(928\) | −2.54592 | + | 2.54592i | −0.0835739 | + | 0.0835739i | ||||
\(929\) | 14.0100i | 0.459653i | 0.973232 | + | 0.229826i | \(0.0738159\pi\) | ||||
−0.973232 | + | 0.229826i | \(0.926184\pi\) | |||||||
\(930\) | −6.65389 | + | 4.53242i | −0.218190 | + | 0.148624i | ||||
\(931\) | −42.0837 | + | 33.2582i | −1.37924 | + | 1.08999i | ||||
\(932\) | 1.69112 | + | 1.69112i | 0.0553946 | + | 0.0553946i | ||||
\(933\) | −4.05233 | − | 4.05233i | −0.132667 | − | 0.132667i | ||||
\(934\) | 20.6923 | 0.677074 | ||||||||
\(935\) | −4.12281 | + | 21.7391i | −0.134830 | + | 0.710946i | ||||
\(936\) | −0.126051 | −0.00412010 | ||||||||
\(937\) | 0.588249 | + | 0.588249i | 0.0192173 | + | 0.0192173i | 0.716650 | − | 0.697433i | \(-0.245674\pi\) |
−0.697433 | + | 0.716650i | \(0.745674\pi\) | |||||||
\(938\) | −38.6113 | + | 38.6113i | −1.26070 | + | 1.26070i | ||||
\(939\) | −31.3617 | −1.02345 | ||||||||
\(940\) | −1.43902 | − | 0.272909i | −0.0469357 | − | 0.00890132i | ||||
\(941\) | − | 52.7538i | − | 1.71972i | −0.510526 | − | 0.859862i | \(-0.670549\pi\) | ||
0.510526 | − | 0.859862i | \(-0.329451\pi\) | |||||||
\(942\) | −4.57916 | − | 4.57916i | −0.149197 | − | 0.149197i | ||||
\(943\) | 29.0340 | + | 29.0340i | 0.945476 | + | 0.945476i | ||||
\(944\) | 9.40851 | 0.306221 | ||||||||
\(945\) | 5.53111 | + | 8.12004i | 0.179927 | + | 0.264145i | ||||
\(946\) | − | 42.9053i | − | 1.39497i | ||||||
\(947\) | −16.9932 | − | 16.9932i | −0.552205 | − | 0.552205i | 0.374872 | − | 0.927077i | \(-0.377687\pi\) |
−0.927077 | + | 0.374872i | \(0.877687\pi\) | |||||||
\(948\) | −6.24204 | + | 6.24204i | −0.202732 | + | 0.202732i | ||||
\(949\) | −0.649541 | −0.0210850 | ||||||||
\(950\) | 10.2850 | − | 19.2151i | 0.333689 | − | 0.623419i | ||||
\(951\) | −15.6454 | −0.507337 | ||||||||
\(952\) | 8.04354 | − | 8.04354i | 0.260693 | − | 0.260693i | ||||
\(953\) | −15.6870 | − | 15.6870i | −0.508151 | − | 0.508151i | 0.405807 | − | 0.913959i | \(-0.366990\pi\) |
−0.913959 | + | 0.405807i | \(0.866990\pi\) | |||||||
\(954\) | − | 4.55250i | − | 0.147393i | ||||||
\(955\) | −19.3067 | − | 28.3435i | −0.624750 | − | 0.917174i | ||||
\(956\) | 12.9971 | 0.420357 | ||||||||
\(957\) | −9.73094 | − | 9.73094i | −0.314557 | − | 0.314557i | ||||
\(958\) | 19.8906 | + | 19.8906i | 0.642636 | + | 0.642636i | ||||
\(959\) | 18.8084i | 0.607355i | ||||||||
\(960\) | 2.19691 | + | 0.416642i | 0.0709049 | + | 0.0134471i | ||||
\(961\) | 18.0366 | 0.581825 | ||||||||
\(962\) | 0.891416 | − | 0.891416i | 0.0287404 | − | 0.0287404i | ||||
\(963\) | 7.00983 | + | 7.00983i | 0.225889 | + | 0.225889i | ||||
\(964\) | −8.64001 | −0.278276 | ||||||||
\(965\) | −10.1110 | + | 53.3145i | −0.325486 | + | 1.71625i | ||||
\(966\) | 16.0889 | 0.517652 | ||||||||
\(967\) | −33.2376 | − | 33.2376i | −1.06885 | − | 1.06885i | −0.997448 | − | 0.0714018i | \(-0.977253\pi\) |
−0.0714018 | − | 0.997448i | \(-0.522747\pi\) | |||||||
\(968\) | 2.55194 | + | 2.55194i | 0.0820224 | + | 0.0820224i | ||||
\(969\) | −8.85380 | + | 6.99705i | −0.284425 | + | 0.224778i | ||||
\(970\) | −17.9919 | + | 12.2555i | −0.577686 | + | 0.393501i | ||||
\(971\) | 35.6664i | 1.14459i | 0.820048 | + | 0.572294i | \(0.193946\pi\) | ||||
−0.820048 | + | 0.572294i | \(0.806054\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −12.3086 | + | 12.3086i | −0.394595 | + | 0.394595i | ||||
\(974\) | 16.4612i | 0.527451i | ||||||||
\(975\) | 0.586492 | + | 0.230755i | 0.0187828 | + | 0.00739007i | ||||
\(976\) | −8.21380 | −0.262917 | ||||||||
\(977\) | 31.4909 | − | 31.4909i | 1.00748 | − | 1.00748i | 0.00751053 | − | 0.999972i | \(-0.497609\pi\) |
0.999972 | − | 0.00751053i | \(-0.00239070\pi\) | |||||||
\(978\) | 7.54592 | − | 7.54592i | 0.241292 | − | 0.241292i | ||||
\(979\) | −37.4508 | −1.19693 | ||||||||
\(980\) | 15.4908 | + | 22.7416i | 0.494836 | + | 0.726452i | ||||
\(981\) | − | 17.7935i | − | 0.568102i | ||||||
\(982\) | −3.92578 | + | 3.92578i | −0.125277 | + | 0.125277i | ||||
\(983\) | 5.10301 | + | 5.10301i | 0.162761 | + | 0.162761i | 0.783789 | − | 0.621028i | \(-0.213285\pi\) |
−0.621028 | + | 0.783789i | \(0.713285\pi\) | |||||||
\(984\) | 11.2134 | 0.357470 | ||||||||
\(985\) | 3.68293 | − | 19.4197i | 0.117348 | − | 0.618764i | ||||
\(986\) | −9.32137 | −0.296853 | ||||||||
\(987\) | −2.03508 | + | 2.03508i | −0.0647774 | + | 0.0647774i | ||||
\(988\) | 0.545712 | + | 0.0639239i | 0.0173614 | + | 0.00203369i | ||||
\(989\) | − | 41.1041i | − | 1.30704i | ||||||
\(990\) | −1.59248 | + | 8.39696i | −0.0506122 | + | 0.266873i | ||||
\(991\) | 12.3920i | 0.393644i | 0.980439 | + | 0.196822i | \(0.0630621\pi\) | ||||
−0.980439 | + | 0.196822i | \(0.936938\pi\) | |||||||
\(992\) | 2.54592 | + | 2.54592i | 0.0808331 | + | 0.0808331i | ||||
\(993\) | −8.34099 | + | 8.34099i | −0.264693 | + | 0.264693i | ||||
\(994\) | − | 7.32260i | − | 0.232259i | ||||||
\(995\) | −19.2372 | + | 13.1038i | −0.609861 | + | 0.415418i | ||||
\(996\) | − | 0.490988i | − | 0.0155576i | ||||||
\(997\) | −22.8719 | − | 22.8719i | −0.724359 | − | 0.724359i | 0.245131 | − | 0.969490i | \(-0.421169\pi\) |
−0.969490 | + | 0.245131i | \(0.921169\pi\) | |||||||
\(998\) | 19.6973 | + | 19.6973i | 0.623507 | + | 0.623507i | ||||
\(999\) | 10.0011i | 0.316422i |
(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 | 570.2.m.a.37.4 | ✓ | 20 | |
3.2 | odd | 2 | 1710.2.p.d.37.7 | 20 | |||
5.3 | odd | 4 | inner | 570.2.m.a.493.9 | yes | 20 | |
15.8 | even | 4 | 1710.2.p.d.1063.2 | 20 | |||
19.18 | odd | 2 | inner | 570.2.m.a.37.9 | yes | 20 | |
57.56 | even | 2 | 1710.2.p.d.37.2 | 20 | |||
95.18 | even | 4 | inner | 570.2.m.a.493.4 | yes | 20 | |
285.113 | odd | 4 | 1710.2.p.d.1063.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.a.37.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
570.2.m.a.37.9 | yes | 20 | 19.18 | odd | 2 | inner | |
570.2.m.a.493.4 | yes | 20 | 95.18 | even | 4 | inner | |
570.2.m.a.493.9 | yes | 20 | 5.3 | odd | 4 | inner | |
1710.2.p.d.37.2 | 20 | 57.56 | even | 2 | |||
1710.2.p.d.37.7 | 20 | 3.2 | odd | 2 | |||
1710.2.p.d.1063.2 | 20 | 15.8 | even | 4 | |||
1710.2.p.d.1063.7 | 20 | 285.113 | odd | 4 |