Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(165,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.e (of order \(3\), 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: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 247.2 | ||
Root | \(-0.309017 + 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.247 |
Dual form | 287.2.e.a.165.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | − | 0.535233i | 0.218508 | − | 0.378467i | −0.735844 | − | 0.677151i | \(-0.763214\pi\) |
0.954352 | + | 0.298684i | \(0.0965477\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0.809017 | + | 1.40126i | 0.404508 | + | 0.700629i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | −0.309017 | − | 0.535233i | −0.0977198 | − | 0.169256i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | 0.809017 | − | 1.40126i | 0.233543 | − | 0.404508i | ||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | −1.54508 | + | 0.535233i | −0.412941 | + | 0.143047i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.927051 | + | 1.60570i | −0.231763 | + | 0.401425i | ||||
\(17\) | 0.118034 | + | 0.204441i | 0.0286274 | + | 0.0495842i | 0.879984 | − | 0.475003i | \(-0.157553\pi\) |
−0.851357 | + | 0.524587i | \(0.824220\pi\) | |||||||
\(18\) | −0.618034 | − | 1.07047i | −0.145672 | − | 0.252311i | ||||
\(19\) | 3.73607 | − | 6.47106i | 0.857113 | − | 1.48456i | −0.0175582 | − | 0.999846i | \(-0.505589\pi\) |
0.874671 | − | 0.484717i | \(-0.161077\pi\) | |||||||
\(20\) | 1.61803 | 0.361803 | ||||||||
\(21\) | −0.500000 | + | 2.59808i | −0.109109 | + | 0.566947i | ||||
\(22\) | −0.618034 | −0.131765 | ||||||||
\(23\) | −2.35410 | + | 4.07742i | −0.490864 | + | 0.850202i | −0.999945 | − | 0.0105172i | \(-0.996652\pi\) |
0.509081 | + | 0.860719i | \(0.329986\pi\) | |||||||
\(24\) | −1.11803 | − | 1.93649i | −0.228218 | − | 0.395285i | ||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 1.38197 | − | 2.39364i | 0.271026 | − | 0.469431i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0.809017 | − | 4.20378i | 0.152890 | − | 0.794439i | ||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | −0.309017 | + | 0.535233i | −0.0564185 | + | 0.0977198i | ||||
\(31\) | −2.11803 | − | 3.66854i | −0.380410 | − | 0.658890i | 0.610711 | − | 0.791854i | \(-0.290884\pi\) |
−0.991121 | + | 0.132964i | \(0.957550\pi\) | |||||||
\(32\) | 2.80902 | + | 4.86536i | 0.496569 | + | 0.860082i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 0.145898 | 0.0250213 | ||||||||
\(35\) | −2.50000 | + | 0.866025i | −0.422577 | + | 0.146385i | ||||
\(36\) | 3.23607 | 0.539345 | ||||||||
\(37\) | −2.73607 | + | 4.73901i | −0.449807 | + | 0.779088i | −0.998373 | − | 0.0570188i | \(-0.981840\pi\) |
0.548566 | + | 0.836107i | \(0.315174\pi\) | |||||||
\(38\) | −2.30902 | − | 3.99933i | −0.374572 | − | 0.648778i | ||||
\(39\) | −2.23607 | − | 3.87298i | −0.358057 | − | 0.620174i | ||||
\(40\) | 1.11803 | − | 1.93649i | 0.176777 | − | 0.306186i | ||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 1.23607 | + | 1.07047i | 0.190729 | + | 0.165177i | ||||
\(43\) | 2.47214 | 0.376997 | 0.188499 | − | 0.982073i | \(-0.439638\pi\) | ||||
0.188499 | + | 0.982073i | \(0.439638\pi\) | |||||||
\(44\) | 0.809017 | − | 1.40126i | 0.121964 | − | 0.211248i | ||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 1.45492 | + | 2.51999i | 0.214516 | + | 0.371552i | ||||
\(47\) | −2.73607 | + | 4.73901i | −0.399097 | + | 0.691255i | −0.993615 | − | 0.112827i | \(-0.964010\pi\) |
0.594518 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(48\) | 1.85410 | 0.267617 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 2.47214 | 0.349613 | ||||||||
\(51\) | 0.118034 | − | 0.204441i | 0.0165281 | − | 0.0286274i | ||||
\(52\) | 3.61803 | + | 6.26662i | 0.501731 | + | 0.869024i | ||||
\(53\) | 2.88197 | + | 4.99171i | 0.395868 | + | 0.685664i | 0.993212 | − | 0.116321i | \(-0.0371103\pi\) |
−0.597343 | + | 0.801986i | \(0.703777\pi\) | |||||||
\(54\) | −1.54508 | + | 2.67617i | −0.210259 | + | 0.364180i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −4.47214 | − | 3.87298i | −0.597614 | − | 0.517549i | ||||
\(57\) | −7.47214 | −0.989709 | ||||||||
\(58\) | −1.38197 | + | 2.39364i | −0.181461 | + | 0.314300i | ||||
\(59\) | 2.35410 | + | 4.07742i | 0.306478 | + | 0.530835i | 0.977589 | − | 0.210521i | \(-0.0675161\pi\) |
−0.671111 | + | 0.741357i | \(0.734183\pi\) | |||||||
\(60\) | −0.809017 | − | 1.40126i | −0.104444 | − | 0.180902i | ||||
\(61\) | −0.263932 | + | 0.457144i | −0.0337930 | + | 0.0585312i | −0.882427 | − | 0.470449i | \(-0.844092\pi\) |
0.848634 | + | 0.528980i | \(0.177425\pi\) | |||||||
\(62\) | −2.61803 | −0.332491 | ||||||||
\(63\) | −5.00000 | + | 1.73205i | −0.629941 | + | 0.218218i | ||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 2.23607 | − | 3.87298i | 0.277350 | − | 0.480384i | ||||
\(66\) | 0.309017 | + | 0.535233i | 0.0380374 | + | 0.0658826i | ||||
\(67\) | 5.97214 | + | 10.3440i | 0.729613 | + | 1.26373i | 0.957047 | + | 0.289933i | \(0.0936329\pi\) |
−0.227435 | + | 0.973793i | \(0.573034\pi\) | |||||||
\(68\) | −0.190983 | + | 0.330792i | −0.0231601 | + | 0.0401145i | ||||
\(69\) | 4.70820 | 0.566801 | ||||||||
\(70\) | −0.309017 | + | 1.60570i | −0.0369346 | + | 0.191918i | ||||
\(71\) | −5.52786 | −0.656037 | −0.328018 | − | 0.944671i | \(-0.606381\pi\) | ||||
−0.328018 | + | 0.944671i | \(0.606381\pi\) | |||||||
\(72\) | 2.23607 | − | 3.87298i | 0.263523 | − | 0.456435i | ||||
\(73\) | 5.73607 | + | 9.93516i | 0.671356 | + | 1.16282i | 0.977520 | + | 0.210844i | \(0.0676211\pi\) |
−0.306164 | + | 0.951979i | \(0.599046\pi\) | |||||||
\(74\) | 1.69098 | + | 2.92887i | 0.196573 | + | 0.340474i | ||||
\(75\) | 2.00000 | − | 3.46410i | 0.230940 | − | 0.400000i | ||||
\(76\) | 12.0902 | 1.38684 | ||||||||
\(77\) | −0.500000 | + | 2.59808i | −0.0569803 | + | 0.296078i | ||||
\(78\) | −2.76393 | −0.312954 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 0.927051 | + | 1.60570i | 0.103647 | + | 0.179523i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.309017 | + | 0.535233i | −0.0341252 | + | 0.0591066i | ||||
\(83\) | −10.4721 | −1.14947 | −0.574733 | − | 0.818341i | \(-0.694894\pi\) | ||||
−0.574733 | + | 0.818341i | \(0.694894\pi\) | |||||||
\(84\) | −4.04508 | + | 1.40126i | −0.441355 | + | 0.152890i | ||||
\(85\) | 0.236068 | 0.0256052 | ||||||||
\(86\) | 0.763932 | − | 1.32317i | 0.0823769 | − | 0.142681i | ||||
\(87\) | 2.23607 | + | 3.87298i | 0.239732 | + | 0.415227i | ||||
\(88\) | −1.11803 | − | 1.93649i | −0.119183 | − | 0.206431i | ||||
\(89\) | 4.88197 | − | 8.45581i | 0.517487 | − | 0.896314i | −0.482306 | − | 0.876003i | \(-0.660201\pi\) |
0.999794 | − | 0.0203118i | \(-0.00646588\pi\) | |||||||
\(90\) | −1.23607 | −0.130293 | ||||||||
\(91\) | −8.94427 | − | 7.74597i | −0.937614 | − | 0.811998i | ||||
\(92\) | −7.61803 | −0.794235 | ||||||||
\(93\) | −2.11803 | + | 3.66854i | −0.219630 | + | 0.380410i | ||||
\(94\) | 1.69098 | + | 2.92887i | 0.174412 | + | 0.302090i | ||||
\(95\) | −3.73607 | − | 6.47106i | −0.383312 | − | 0.663917i | ||||
\(96\) | 2.80902 | − | 4.86536i | 0.286694 | − | 0.496569i | ||||
\(97\) | −0.472136 | −0.0479381 | −0.0239691 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239691 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(98\) | 4.01722 | + | 1.60570i | 0.405801 | + | 0.162200i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −3.23607 | + | 5.60503i | −0.323607 | + | 0.560503i | ||||
\(101\) | −8.35410 | − | 14.4697i | −0.831264 | − | 1.43979i | −0.897036 | − | 0.441957i | \(-0.854284\pi\) |
0.0657719 | − | 0.997835i | \(-0.479049\pi\) | |||||||
\(102\) | −0.0729490 | − | 0.126351i | −0.00722303 | − | 0.0125107i | ||||
\(103\) | 2.59017 | − | 4.48631i | 0.255217 | − | 0.442049i | −0.709737 | − | 0.704466i | \(-0.751186\pi\) |
0.964954 | + | 0.262417i | \(0.0845197\pi\) | |||||||
\(104\) | 10.0000 | 0.980581 | ||||||||
\(105\) | 2.00000 | + | 1.73205i | 0.195180 | + | 0.169031i | ||||
\(106\) | 3.56231 | 0.346002 | ||||||||
\(107\) | 7.35410 | − | 12.7377i | 0.710948 | − | 1.23140i | −0.253554 | − | 0.967321i | \(-0.581600\pi\) |
0.964502 | − | 0.264077i | \(-0.0850672\pi\) | |||||||
\(108\) | −4.04508 | − | 7.00629i | −0.389238 | − | 0.674181i | ||||
\(109\) | 4.88197 | + | 8.45581i | 0.467608 | + | 0.809920i | 0.999315 | − | 0.0370081i | \(-0.0117827\pi\) |
−0.531707 | + | 0.846928i | \(0.678449\pi\) | |||||||
\(110\) | −0.309017 | + | 0.535233i | −0.0294636 | + | 0.0510325i | ||||
\(111\) | 5.47214 | 0.519392 | ||||||||
\(112\) | 4.63525 | − | 1.60570i | 0.437990 | − | 0.151724i | ||||
\(113\) | −15.8885 | −1.49467 | −0.747334 | − | 0.664448i | \(-0.768667\pi\) | ||||
−0.747334 | + | 0.664448i | \(0.768667\pi\) | |||||||
\(114\) | −2.30902 | + | 3.99933i | −0.216259 | + | 0.374572i | ||||
\(115\) | 2.35410 | + | 4.07742i | 0.219521 | + | 0.380222i | ||||
\(116\) | −3.61803 | − | 6.26662i | −0.335926 | − | 0.581841i | ||||
\(117\) | 4.47214 | − | 7.74597i | 0.413449 | − | 0.716115i | ||||
\(118\) | 2.90983 | 0.267872 | ||||||||
\(119\) | 0.118034 | − | 0.613323i | 0.0108202 | − | 0.0562232i | ||||
\(120\) | −2.23607 | −0.204124 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0.163119 | + | 0.282530i | 0.0147681 | + | 0.0255791i | ||||
\(123\) | 0.500000 | + | 0.866025i | 0.0450835 | + | 0.0780869i | ||||
\(124\) | 3.42705 | − | 5.93583i | 0.307758 | − | 0.533053i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | −0.618034 | + | 3.21140i | −0.0550588 | + | 0.286094i | ||||
\(127\) | −11.4164 | −1.01304 | −0.506521 | − | 0.862228i | \(-0.669069\pi\) | ||||
−0.506521 | + | 0.862228i | \(0.669069\pi\) | |||||||
\(128\) | −5.69098 | + | 9.85707i | −0.503017 | + | 0.871250i | ||||
\(129\) | −1.23607 | − | 2.14093i | −0.108830 | − | 0.188499i | ||||
\(130\) | −1.38197 | − | 2.39364i | −0.121206 | − | 0.209936i | ||||
\(131\) | −8.82624 | + | 15.2875i | −0.771152 | + | 1.33567i | 0.165780 | + | 0.986163i | \(0.446986\pi\) |
−0.936932 | + | 0.349512i | \(0.886348\pi\) | |||||||
\(132\) | −1.61803 | −0.140832 | ||||||||
\(133\) | −18.6803 | + | 6.47106i | −1.61979 | + | 0.561112i | ||||
\(134\) | 7.38197 | 0.637705 | ||||||||
\(135\) | −2.50000 | + | 4.33013i | −0.215166 | + | 0.372678i | ||||
\(136\) | 0.263932 | + | 0.457144i | 0.0226320 | + | 0.0391997i | ||||
\(137\) | 7.82624 | + | 13.5554i | 0.668641 | + | 1.15812i | 0.978284 | + | 0.207267i | \(0.0664569\pi\) |
−0.309644 | + | 0.950853i | \(0.600210\pi\) | |||||||
\(138\) | 1.45492 | − | 2.51999i | 0.123851 | − | 0.214516i | ||||
\(139\) | −0.944272 | −0.0800921 | −0.0400460 | − | 0.999198i | \(-0.512750\pi\) | ||||
−0.0400460 | + | 0.999198i | \(0.512750\pi\) | |||||||
\(140\) | −3.23607 | − | 2.80252i | −0.273498 | − | 0.236856i | ||||
\(141\) | 5.47214 | 0.460837 | ||||||||
\(142\) | −1.70820 | + | 2.95870i | −0.143349 | + | 0.248288i | ||||
\(143\) | −2.23607 | − | 3.87298i | −0.186989 | − | 0.323875i | ||||
\(144\) | 1.85410 | + | 3.21140i | 0.154508 | + | 0.267617i | ||||
\(145\) | −2.23607 | + | 3.87298i | −0.185695 | + | 0.321634i | ||||
\(146\) | 7.09017 | 0.586787 | ||||||||
\(147\) | 5.50000 | − | 4.33013i | 0.453632 | − | 0.357143i | ||||
\(148\) | −8.85410 | −0.727803 | ||||||||
\(149\) | 10.5902 | − | 18.3427i | 0.867581 | − | 1.50269i | 0.00311867 | − | 0.999995i | \(-0.499007\pi\) |
0.864462 | − | 0.502698i | \(-0.167659\pi\) | |||||||
\(150\) | −1.23607 | − | 2.14093i | −0.100925 | − | 0.174806i | ||||
\(151\) | 5.97214 | + | 10.3440i | 0.486006 | + | 0.841786i | 0.999871 | − | 0.0160847i | \(-0.00512015\pi\) |
−0.513865 | + | 0.857871i | \(0.671787\pi\) | |||||||
\(152\) | 8.35410 | − | 14.4697i | 0.677607 | − | 1.17365i | ||||
\(153\) | 0.472136 | 0.0381699 | ||||||||
\(154\) | 1.23607 | + | 1.07047i | 0.0996052 | + | 0.0862606i | ||||
\(155\) | −4.23607 | −0.340249 | ||||||||
\(156\) | 3.61803 | − | 6.26662i | 0.289675 | − | 0.501731i | ||||
\(157\) | −1.11803 | − | 1.93649i | −0.0892288 | − | 0.154549i | 0.817957 | − | 0.575280i | \(-0.195107\pi\) |
−0.907185 | + | 0.420731i | \(0.861774\pi\) | |||||||
\(158\) | −0.309017 | − | 0.535233i | −0.0245841 | − | 0.0425809i | ||||
\(159\) | 2.88197 | − | 4.99171i | 0.228555 | − | 0.395868i | ||||
\(160\) | 5.61803 | 0.444145 | ||||||||
\(161\) | 11.7705 | − | 4.07742i | 0.927646 | − | 0.321346i | ||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | 9.35410 | − | 16.2018i | 0.732670 | − | 1.26902i | −0.223068 | − | 0.974803i | \(-0.571607\pi\) |
0.955738 | − | 0.294219i | \(-0.0950594\pi\) | |||||||
\(164\) | −0.809017 | − | 1.40126i | −0.0631736 | − | 0.109420i | ||||
\(165\) | 0.500000 | + | 0.866025i | 0.0389249 | + | 0.0674200i | ||||
\(166\) | −3.23607 | + | 5.60503i | −0.251168 | + | 0.435035i | ||||
\(167\) | 6.47214 | 0.500829 | 0.250414 | − | 0.968139i | \(-0.419433\pi\) | ||||
0.250414 | + | 0.968139i | \(0.419433\pi\) | |||||||
\(168\) | −1.11803 | + | 5.80948i | −0.0862582 | + | 0.448211i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0.0729490 | − | 0.126351i | 0.00559493 | − | 0.00969071i | ||||
\(171\) | −7.47214 | − | 12.9421i | −0.571409 | − | 0.989709i | ||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | −8.44427 | + | 14.6259i | −0.642006 | + | 1.11199i | 0.342978 | + | 0.939343i | \(0.388564\pi\) |
−0.984984 | + | 0.172644i | \(0.944769\pi\) | |||||||
\(174\) | 2.76393 | 0.209533 | ||||||||
\(175\) | 2.00000 | − | 10.3923i | 0.151186 | − | 0.785584i | ||||
\(176\) | 1.85410 | 0.139758 | ||||||||
\(177\) | 2.35410 | − | 4.07742i | 0.176945 | − | 0.306478i | ||||
\(178\) | −3.01722 | − | 5.22598i | −0.226150 | − | 0.391704i | ||||
\(179\) | −8.20820 | − | 14.2170i | −0.613510 | − | 1.06263i | −0.990644 | − | 0.136472i | \(-0.956424\pi\) |
0.377134 | − | 0.926159i | \(-0.376910\pi\) | |||||||
\(180\) | 1.61803 | − | 2.80252i | 0.120601 | − | 0.208887i | ||||
\(181\) | 5.41641 | 0.402598 | 0.201299 | − | 0.979530i | \(-0.435484\pi\) | ||||
0.201299 | + | 0.979530i | \(0.435484\pi\) | |||||||
\(182\) | −6.90983 | + | 2.39364i | −0.512191 | + | 0.177428i | ||||
\(183\) | 0.527864 | 0.0390208 | ||||||||
\(184\) | −5.26393 | + | 9.11740i | −0.388062 | + | 0.672143i | ||||
\(185\) | 2.73607 | + | 4.73901i | 0.201160 | + | 0.348419i | ||||
\(186\) | 1.30902 | + | 2.26728i | 0.0959818 | + | 0.166245i | ||||
\(187\) | 0.118034 | − | 0.204441i | 0.00863150 | − | 0.0149502i | ||||
\(188\) | −8.85410 | −0.645752 | ||||||||
\(189\) | 10.0000 | + | 8.66025i | 0.727393 | + | 0.629941i | ||||
\(190\) | −4.61803 | −0.335027 | ||||||||
\(191\) | 1.73607 | − | 3.00696i | 0.125617 | − | 0.217576i | −0.796357 | − | 0.604827i | \(-0.793242\pi\) |
0.921974 | + | 0.387251i | \(0.126575\pi\) | |||||||
\(192\) | 0.118034 | + | 0.204441i | 0.00851837 | + | 0.0147542i | ||||
\(193\) | −11.5902 | − | 20.0748i | −0.834279 | − | 1.44501i | −0.894616 | − | 0.446835i | \(-0.852551\pi\) |
0.0603377 | − | 0.998178i | \(-0.480782\pi\) | |||||||
\(194\) | −0.145898 | + | 0.252703i | −0.0104749 | + | 0.0181430i | ||||
\(195\) | −4.47214 | −0.320256 | ||||||||
\(196\) | −8.89919 | + | 7.00629i | −0.635656 | + | 0.500449i | ||||
\(197\) | 14.9443 | 1.06474 | 0.532368 | − | 0.846513i | \(-0.321302\pi\) | ||||
0.532368 | + | 0.846513i | \(0.321302\pi\) | |||||||
\(198\) | −0.618034 | + | 1.07047i | −0.0439218 | + | 0.0760747i | ||||
\(199\) | −0.0278640 | − | 0.0482619i | −0.00197523 | − | 0.00342120i | 0.865036 | − | 0.501710i | \(-0.167295\pi\) |
−0.867011 | + | 0.498288i | \(0.833962\pi\) | |||||||
\(200\) | 4.47214 | + | 7.74597i | 0.316228 | + | 0.547723i | ||||
\(201\) | 5.97214 | − | 10.3440i | 0.421242 | − | 0.729613i | ||||
\(202\) | −10.3262 | −0.726552 | ||||||||
\(203\) | 8.94427 | + | 7.74597i | 0.627765 | + | 0.543660i | ||||
\(204\) | 0.381966 | 0.0267430 | ||||||||
\(205\) | −0.500000 | + | 0.866025i | −0.0349215 | + | 0.0604858i | ||||
\(206\) | −1.60081 | − | 2.77269i | −0.111534 | − | 0.193182i | ||||
\(207\) | 4.70820 | + | 8.15485i | 0.327243 | + | 0.566801i | ||||
\(208\) | −4.14590 | + | 7.18091i | −0.287466 | + | 0.497906i | ||||
\(209\) | −7.47214 | −0.516858 | ||||||||
\(210\) | 1.54508 | − | 0.535233i | 0.106621 | − | 0.0369346i | ||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | −4.66312 | + | 8.07676i | −0.320264 | + | 0.554714i | ||||
\(213\) | 2.76393 | + | 4.78727i | 0.189382 | + | 0.328018i | ||||
\(214\) | −4.54508 | − | 7.87232i | −0.310696 | − | 0.538141i | ||||
\(215\) | 1.23607 | − | 2.14093i | 0.0842991 | − | 0.146010i | ||||
\(216\) | −11.1803 | −0.760726 | ||||||||
\(217\) | −2.11803 | + | 11.0056i | −0.143782 | + | 0.747111i | ||||
\(218\) | 6.03444 | 0.408704 | ||||||||
\(219\) | 5.73607 | − | 9.93516i | 0.387608 | − | 0.671356i | ||||
\(220\) | −0.809017 | − | 1.40126i | −0.0545439 | − | 0.0944728i | ||||
\(221\) | 0.527864 | + | 0.914287i | 0.0355080 | + | 0.0615016i | ||||
\(222\) | 1.69098 | − | 2.92887i | 0.113491 | − | 0.196573i | ||||
\(223\) | 0.944272 | 0.0632331 | 0.0316166 | − | 0.999500i | \(-0.489934\pi\) | ||||
0.0316166 | + | 0.999500i | \(0.489934\pi\) | |||||||
\(224\) | 2.80902 | − | 14.5961i | 0.187685 | − | 0.975242i | ||||
\(225\) | 8.00000 | 0.533333 | ||||||||
\(226\) | −4.90983 | + | 8.50408i | −0.326597 | + | 0.565683i | ||||
\(227\) | −1.73607 | − | 3.00696i | −0.115227 | − | 0.199579i | 0.802644 | − | 0.596459i | \(-0.203426\pi\) |
−0.917870 | + | 0.396880i | \(0.870093\pi\) | |||||||
\(228\) | −6.04508 | − | 10.4704i | −0.400346 | − | 0.693419i | ||||
\(229\) | −10.0623 | + | 17.4284i | −0.664936 | + | 1.15170i | 0.314367 | + | 0.949302i | \(0.398208\pi\) |
−0.979303 | + | 0.202401i | \(0.935126\pi\) | |||||||
\(230\) | 2.90983 | 0.191869 | ||||||||
\(231\) | 2.50000 | − | 0.866025i | 0.164488 | − | 0.0569803i | ||||
\(232\) | −10.0000 | −0.656532 | ||||||||
\(233\) | −8.35410 | + | 14.4697i | −0.547295 | + | 0.947943i | 0.451163 | + | 0.892441i | \(0.351009\pi\) |
−0.998459 | + | 0.0555020i | \(0.982324\pi\) | |||||||
\(234\) | −2.76393 | − | 4.78727i | −0.180684 | − | 0.312954i | ||||
\(235\) | 2.73607 | + | 4.73901i | 0.178481 | + | 0.309139i | ||||
\(236\) | −3.80902 | + | 6.59741i | −0.247946 | + | 0.429455i | ||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −0.291796 | − | 0.252703i | −0.0189143 | − | 0.0163803i | ||||
\(239\) | 6.47214 | 0.418648 | 0.209324 | − | 0.977846i | \(-0.432874\pi\) | ||||
0.209324 | + | 0.977846i | \(0.432874\pi\) | |||||||
\(240\) | 0.927051 | − | 1.60570i | 0.0598409 | − | 0.103647i | ||||
\(241\) | 3.73607 | + | 6.47106i | 0.240661 | + | 0.416838i | 0.960903 | − | 0.276886i | \(-0.0893024\pi\) |
−0.720242 | + | 0.693723i | \(0.755969\pi\) | |||||||
\(242\) | −3.09017 | − | 5.35233i | −0.198644 | − | 0.344061i | ||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | −0.854102 | −0.0546783 | ||||||||
\(245\) | 6.50000 | + | 2.59808i | 0.415270 | + | 0.165985i | ||||
\(246\) | 0.618034 | 0.0394044 | ||||||||
\(247\) | 16.7082 | − | 28.9395i | 1.06312 | − | 1.84137i | ||||
\(248\) | −4.73607 | − | 8.20311i | −0.300741 | − | 0.520898i | ||||
\(249\) | 5.23607 | + | 9.06914i | 0.331822 | + | 0.574733i | ||||
\(250\) | 2.78115 | − | 4.81710i | 0.175896 | − | 0.304660i | ||||
\(251\) | −26.8328 | −1.69367 | −0.846836 | − | 0.531854i | \(-0.821496\pi\) | ||||
−0.846836 | + | 0.531854i | \(0.821496\pi\) | |||||||
\(252\) | −6.47214 | − | 5.60503i | −0.407706 | − | 0.353084i | ||||
\(253\) | 4.70820 | 0.296002 | ||||||||
\(254\) | −3.52786 | + | 6.11044i | −0.221358 | + | 0.383403i | ||||
\(255\) | −0.118034 | − | 0.204441i | −0.00739158 | − | 0.0128026i | ||||
\(256\) | 3.28115 | + | 5.68312i | 0.205072 | + | 0.355195i | ||||
\(257\) | 7.35410 | − | 12.7377i | 0.458736 | − | 0.794555i | −0.540158 | − | 0.841564i | \(-0.681636\pi\) |
0.998894 | + | 0.0470090i | \(0.0149689\pi\) | |||||||
\(258\) | −1.52786 | −0.0951207 | ||||||||
\(259\) | 13.6803 | − | 4.73901i | 0.850055 | − | 0.294468i | ||||
\(260\) | 7.23607 | 0.448762 | ||||||||
\(261\) | −4.47214 | + | 7.74597i | −0.276818 | + | 0.479463i | ||||
\(262\) | 5.45492 | + | 9.44819i | 0.337006 | + | 0.583711i | ||||
\(263\) | 0.736068 | + | 1.27491i | 0.0453879 | + | 0.0786141i | 0.887827 | − | 0.460178i | \(-0.152214\pi\) |
−0.842439 | + | 0.538792i | \(0.818881\pi\) | |||||||
\(264\) | −1.11803 | + | 1.93649i | −0.0688102 | + | 0.119183i | ||||
\(265\) | 5.76393 | 0.354076 | ||||||||
\(266\) | −2.30902 | + | 11.9980i | −0.141575 | + | 0.735645i | ||||
\(267\) | −9.76393 | −0.597543 | ||||||||
\(268\) | −9.66312 | + | 16.7370i | −0.590269 | + | 1.02238i | ||||
\(269\) | 5.26393 | + | 9.11740i | 0.320948 | + | 0.555898i | 0.980684 | − | 0.195600i | \(-0.0626653\pi\) |
−0.659736 | + | 0.751497i | \(0.729332\pi\) | |||||||
\(270\) | 1.54508 | + | 2.67617i | 0.0940309 | + | 0.162866i | ||||
\(271\) | −4.82624 | + | 8.35929i | −0.293173 | + | 0.507791i | −0.974558 | − | 0.224134i | \(-0.928045\pi\) |
0.681385 | + | 0.731925i | \(0.261378\pi\) | |||||||
\(272\) | −0.437694 | −0.0265391 | ||||||||
\(273\) | −2.23607 | + | 11.6190i | −0.135333 | + | 0.703211i | ||||
\(274\) | 9.67376 | 0.584413 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 3.80902 | + | 6.59741i | 0.229276 | + | 0.397117i | ||||
\(277\) | 10.9721 | + | 19.0043i | 0.659252 | + | 1.14186i | 0.980810 | + | 0.194968i | \(0.0624602\pi\) |
−0.321558 | + | 0.946890i | \(0.604206\pi\) | |||||||
\(278\) | −0.291796 | + | 0.505406i | −0.0175008 | + | 0.0303122i | ||||
\(279\) | −8.47214 | −0.507214 | ||||||||
\(280\) | −5.59017 | + | 1.93649i | −0.334077 | + | 0.115728i | ||||
\(281\) | 4.47214 | 0.266785 | 0.133393 | − | 0.991063i | \(-0.457413\pi\) | ||||
0.133393 | + | 0.991063i | \(0.457413\pi\) | |||||||
\(282\) | 1.69098 | − | 2.92887i | 0.100697 | − | 0.174412i | ||||
\(283\) | 5.59017 | + | 9.68246i | 0.332301 | + | 0.575562i | 0.982963 | − | 0.183805i | \(-0.0588416\pi\) |
−0.650662 | + | 0.759368i | \(0.725508\pi\) | |||||||
\(284\) | −4.47214 | − | 7.74597i | −0.265372 | − | 0.459639i | ||||
\(285\) | −3.73607 | + | 6.47106i | −0.221306 | + | 0.383312i | ||||
\(286\) | −2.76393 | −0.163435 | ||||||||
\(287\) | 2.00000 | + | 1.73205i | 0.118056 | + | 0.102240i | ||||
\(288\) | 11.2361 | 0.662092 | ||||||||
\(289\) | 8.47214 | − | 14.6742i | 0.498361 | − | 0.863186i | ||||
\(290\) | 1.38197 | + | 2.39364i | 0.0811518 | + | 0.140559i | ||||
\(291\) | 0.236068 | + | 0.408882i | 0.0138385 | + | 0.0239691i | ||||
\(292\) | −9.28115 | + | 16.0754i | −0.543138 | + | 0.940743i | ||||
\(293\) | −24.8328 | −1.45075 | −0.725374 | − | 0.688355i | \(-0.758333\pi\) | ||||
−0.725374 | + | 0.688355i | \(0.758333\pi\) | |||||||
\(294\) | −0.618034 | − | 4.28187i | −0.0360445 | − | 0.249723i | ||||
\(295\) | 4.70820 | 0.274122 | ||||||||
\(296\) | −6.11803 | + | 10.5967i | −0.355604 | + | 0.615923i | ||||
\(297\) | 2.50000 | + | 4.33013i | 0.145065 | + | 0.251259i | ||||
\(298\) | −6.54508 | − | 11.3364i | −0.379147 | − | 0.656701i | ||||
\(299\) | −10.5279 | + | 18.2348i | −0.608842 | + | 1.05455i | ||||
\(300\) | 6.47214 | 0.373669 | ||||||||
\(301\) | −4.94427 | − | 4.28187i | −0.284983 | − | 0.246803i | ||||
\(302\) | 7.38197 | 0.424784 | ||||||||
\(303\) | −8.35410 | + | 14.4697i | −0.479931 | + | 0.831264i | ||||
\(304\) | 6.92705 | + | 11.9980i | 0.397294 | + | 0.688133i | ||||
\(305\) | 0.263932 | + | 0.457144i | 0.0151127 | + | 0.0261760i | ||||
\(306\) | 0.145898 | − | 0.252703i | 0.00834044 | − | 0.0144461i | ||||
\(307\) | 25.8885 | 1.47754 | 0.738769 | − | 0.673959i | \(-0.235408\pi\) | ||||
0.738769 | + | 0.673959i | \(0.235408\pi\) | |||||||
\(308\) | −4.04508 | + | 1.40126i | −0.230490 | + | 0.0798441i | ||||
\(309\) | −5.18034 | −0.294699 | ||||||||
\(310\) | −1.30902 | + | 2.26728i | −0.0743472 | + | 0.128773i | ||||
\(311\) | −15.9164 | − | 27.5680i | −0.902537 | − | 1.56324i | −0.824190 | − | 0.566313i | \(-0.808369\pi\) |
−0.0783466 | − | 0.996926i | \(-0.524964\pi\) | |||||||
\(312\) | −5.00000 | − | 8.66025i | −0.283069 | − | 0.490290i | ||||
\(313\) | 15.3541 | − | 26.5941i | 0.867865 | − | 1.50319i | 0.00369130 | − | 0.999993i | \(-0.498825\pi\) |
0.864174 | − | 0.503193i | \(-0.167842\pi\) | |||||||
\(314\) | −1.38197 | −0.0779889 | ||||||||
\(315\) | −1.00000 | + | 5.19615i | −0.0563436 | + | 0.292770i | ||||
\(316\) | 1.61803 | 0.0910215 | ||||||||
\(317\) | −15.1180 | + | 26.1852i | −0.849113 | + | 1.47071i | 0.0328871 | + | 0.999459i | \(0.489530\pi\) |
−0.882001 | + | 0.471248i | \(0.843804\pi\) | |||||||
\(318\) | −1.78115 | − | 3.08505i | −0.0998821 | − | 0.173001i | ||||
\(319\) | 2.23607 | + | 3.87298i | 0.125196 | + | 0.216845i | ||||
\(320\) | −0.118034 | + | 0.204441i | −0.00659830 | + | 0.0114286i | ||||
\(321\) | −14.7082 | −0.820932 | ||||||||
\(322\) | 1.45492 | − | 7.55996i | 0.0810792 | − | 0.421300i | ||||
\(323\) | 1.76393 | 0.0981478 | ||||||||
\(324\) | 0.809017 | − | 1.40126i | 0.0449454 | − | 0.0778477i | ||||
\(325\) | 8.94427 | + | 15.4919i | 0.496139 | + | 0.859338i | ||||
\(326\) | −5.78115 | − | 10.0133i | −0.320188 | − | 0.554583i | ||||
\(327\) | 4.88197 | − | 8.45581i | 0.269973 | − | 0.467608i | ||||
\(328\) | −2.23607 | −0.123466 | ||||||||
\(329\) | 13.6803 | − | 4.73901i | 0.754222 | − | 0.261270i | ||||
\(330\) | 0.618034 | 0.0340217 | ||||||||
\(331\) | −10.9164 | + | 18.9078i | −0.600020 | + | 1.03927i | 0.392797 | + | 0.919625i | \(0.371507\pi\) |
−0.992817 | + | 0.119640i | \(0.961826\pi\) | |||||||
\(332\) | −8.47214 | − | 14.6742i | −0.464969 | − | 0.805350i | ||||
\(333\) | 5.47214 | + | 9.47802i | 0.299871 | + | 0.519392i | ||||
\(334\) | 2.00000 | − | 3.46410i | 0.109435 | − | 0.189547i | ||||
\(335\) | 11.9443 | 0.652585 | ||||||||
\(336\) | −3.70820 | − | 3.21140i | −0.202299 | − | 0.175196i | ||||
\(337\) | 0.472136 | 0.0257189 | 0.0128594 | − | 0.999917i | \(-0.495907\pi\) | ||||
0.0128594 | + | 0.999917i | \(0.495907\pi\) | |||||||
\(338\) | 2.16312 | − | 3.74663i | 0.117658 | − | 0.203790i | ||||
\(339\) | 7.94427 | + | 13.7599i | 0.431474 | + | 0.747334i | ||||
\(340\) | 0.190983 | + | 0.330792i | 0.0103575 | + | 0.0179397i | ||||
\(341\) | −2.11803 | + | 3.66854i | −0.114698 | + | 0.198663i | ||||
\(342\) | −9.23607 | −0.499429 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 5.52786 | 0.298042 | ||||||||
\(345\) | 2.35410 | − | 4.07742i | 0.126741 | − | 0.219521i | ||||
\(346\) | 5.21885 | + | 9.03931i | 0.280567 | + | 0.485956i | ||||
\(347\) | 1.50000 | + | 2.59808i | 0.0805242 | + | 0.139472i | 0.903475 | − | 0.428640i | \(-0.141007\pi\) |
−0.822951 | + | 0.568112i | \(0.807674\pi\) | |||||||
\(348\) | −3.61803 | + | 6.26662i | −0.193947 | + | 0.335926i | ||||
\(349\) | −11.5279 | −0.617072 | −0.308536 | − | 0.951213i | \(-0.599839\pi\) | ||||
−0.308536 | + | 0.951213i | \(0.599839\pi\) | |||||||
\(350\) | −4.94427 | − | 4.28187i | −0.264282 | − | 0.228875i | ||||
\(351\) | −22.3607 | −1.19352 | ||||||||
\(352\) | 2.80902 | − | 4.86536i | 0.149721 | − | 0.259325i | ||||
\(353\) | −8.26393 | − | 14.3136i | −0.439845 | − | 0.761833i | 0.557832 | − | 0.829954i | \(-0.311633\pi\) |
−0.997677 | + | 0.0681202i | \(0.978300\pi\) | |||||||
\(354\) | −1.45492 | − | 2.51999i | −0.0773279 | − | 0.133936i | ||||
\(355\) | −2.76393 | + | 4.78727i | −0.146694 | + | 0.254082i | ||||
\(356\) | 15.7984 | 0.837312 | ||||||||
\(357\) | −0.590170 | + | 0.204441i | −0.0312351 | + | 0.0108202i | ||||
\(358\) | −10.1459 | −0.536227 | ||||||||
\(359\) | −8.82624 | + | 15.2875i | −0.465831 | + | 0.806843i | −0.999239 | − | 0.0390154i | \(-0.987578\pi\) |
0.533408 | + | 0.845858i | \(0.320911\pi\) | |||||||
\(360\) | −2.23607 | − | 3.87298i | −0.117851 | − | 0.204124i | ||||
\(361\) | −18.4164 | − | 31.8982i | −0.969285 | − | 1.67885i | ||||
\(362\) | 1.67376 | − | 2.89904i | 0.0879710 | − | 0.152370i | ||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 3.61803 | − | 18.7999i | 0.189637 | − | 0.985380i | ||||
\(365\) | 11.4721 | 0.600479 | ||||||||
\(366\) | 0.163119 | − | 0.282530i | 0.00852636 | − | 0.0147681i | ||||
\(367\) | −8.59017 | − | 14.8786i | −0.448403 | − | 0.776657i | 0.549879 | − | 0.835244i | \(-0.314674\pi\) |
−0.998282 | + | 0.0585871i | \(0.981340\pi\) | |||||||
\(368\) | −4.36475 | − | 7.55996i | −0.227528 | − | 0.394090i | ||||
\(369\) | −1.00000 | + | 1.73205i | −0.0520579 | + | 0.0901670i | ||||
\(370\) | 3.38197 | 0.175820 | ||||||||
\(371\) | 2.88197 | − | 14.9751i | 0.149624 | − | 0.777470i | ||||
\(372\) | −6.85410 | −0.355369 | ||||||||
\(373\) | 8.97214 | − | 15.5402i | 0.464560 | − | 0.804641i | −0.534622 | − | 0.845091i | \(-0.679546\pi\) |
0.999182 | + | 0.0404505i | \(0.0128793\pi\) | |||||||
\(374\) | −0.0729490 | − | 0.126351i | −0.00377210 | − | 0.00653348i | ||||
\(375\) | −4.50000 | − | 7.79423i | −0.232379 | − | 0.402492i | ||||
\(376\) | −6.11803 | + | 10.5967i | −0.315514 | + | 0.546485i | ||||
\(377\) | −20.0000 | −1.03005 | ||||||||
\(378\) | 7.72542 | − | 2.67617i | 0.397353 | − | 0.137647i | ||||
\(379\) | 4.58359 | 0.235443 | 0.117722 | − | 0.993047i | \(-0.462441\pi\) | ||||
0.117722 | + | 0.993047i | \(0.462441\pi\) | |||||||
\(380\) | 6.04508 | − | 10.4704i | 0.310106 | − | 0.537120i | ||||
\(381\) | 5.70820 | + | 9.88690i | 0.292440 | + | 0.506521i | ||||
\(382\) | −1.07295 | − | 1.85840i | −0.0548968 | − | 0.0950841i | ||||
\(383\) | 7.44427 | − | 12.8939i | 0.380385 | − | 0.658845i | −0.610733 | − | 0.791837i | \(-0.709125\pi\) |
0.991117 | + | 0.132992i | \(0.0424583\pi\) | |||||||
\(384\) | 11.3820 | 0.580834 | ||||||||
\(385\) | 2.00000 | + | 1.73205i | 0.101929 | + | 0.0882735i | ||||
\(386\) | −14.3262 | −0.729186 | ||||||||
\(387\) | 2.47214 | − | 4.28187i | 0.125666 | − | 0.217659i | ||||
\(388\) | −0.381966 | − | 0.661585i | −0.0193914 | − | 0.0335869i | ||||
\(389\) | 0.500000 | + | 0.866025i | 0.0253510 | + | 0.0439092i | 0.878423 | − | 0.477885i | \(-0.158596\pi\) |
−0.853072 | + | 0.521794i | \(0.825263\pi\) | |||||||
\(390\) | −1.38197 | + | 2.39364i | −0.0699786 | + | 0.121206i | ||||
\(391\) | −1.11146 | −0.0562088 | ||||||||
\(392\) | 2.23607 | + | 15.4919i | 0.112938 | + | 0.782461i | ||||
\(393\) | 17.6525 | 0.890450 | ||||||||
\(394\) | 4.61803 | − | 7.99867i | 0.232653 | − | 0.402967i | ||||
\(395\) | −0.500000 | − | 0.866025i | −0.0251577 | − | 0.0435745i | ||||
\(396\) | −1.61803 | − | 2.80252i | −0.0813093 | − | 0.140832i | ||||
\(397\) | 1.82624 | − | 3.16314i | 0.0916563 | − | 0.158753i | −0.816552 | − | 0.577272i | \(-0.804117\pi\) |
0.908208 | + | 0.418519i | \(0.137451\pi\) | |||||||
\(398\) | −0.0344419 | −0.00172641 | ||||||||
\(399\) | 14.9443 | + | 12.9421i | 0.748149 | + | 0.647916i | ||||
\(400\) | −7.41641 | −0.370820 | ||||||||
\(401\) | 4.97214 | − | 8.61199i | 0.248297 | − | 0.430062i | −0.714757 | − | 0.699373i | \(-0.753463\pi\) |
0.963053 | + | 0.269311i | \(0.0867959\pi\) | |||||||
\(402\) | −3.69098 | − | 6.39297i | −0.184090 | − | 0.318852i | ||||
\(403\) | −9.47214 | − | 16.4062i | −0.471841 | − | 0.817252i | ||||
\(404\) | 13.5172 | − | 23.4125i | 0.672507 | − | 1.16482i | ||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 6.90983 | − | 2.39364i | 0.342929 | − | 0.118794i | ||||
\(407\) | 5.47214 | 0.271244 | ||||||||
\(408\) | 0.263932 | − | 0.457144i | 0.0130666 | − | 0.0226320i | ||||
\(409\) | −6.44427 | − | 11.1618i | −0.318649 | − | 0.551916i | 0.661558 | − | 0.749894i | \(-0.269896\pi\) |
−0.980206 | + | 0.197979i | \(0.936562\pi\) | |||||||
\(410\) | 0.309017 | + | 0.535233i | 0.0152613 | + | 0.0264333i | ||||
\(411\) | 7.82624 | − | 13.5554i | 0.386040 | − | 0.668641i | ||||
\(412\) | 8.38197 | 0.412950 | ||||||||
\(413\) | 2.35410 | − | 12.2323i | 0.115838 | − | 0.601911i | ||||
\(414\) | 5.81966 | 0.286021 | ||||||||
\(415\) | −5.23607 | + | 9.06914i | −0.257028 | + | 0.445186i | ||||
\(416\) | 12.5623 | + | 21.7586i | 0.615918 | + | 1.06680i | ||||
\(417\) | 0.472136 | + | 0.817763i | 0.0231206 | + | 0.0400460i | ||||
\(418\) | −2.30902 | + | 3.99933i | −0.112938 | + | 0.195614i | ||||
\(419\) | 17.8885 | 0.873913 | 0.436956 | − | 0.899483i | \(-0.356056\pi\) | ||||
0.436956 | + | 0.899483i | \(0.356056\pi\) | |||||||
\(420\) | −0.809017 | + | 4.20378i | −0.0394760 | + | 0.205123i | ||||
\(421\) | −7.52786 | −0.366886 | −0.183443 | − | 0.983030i | \(-0.558724\pi\) | ||||
−0.183443 | + | 0.983030i | \(0.558724\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.47214 | + | 9.47802i | 0.266064 | + | 0.460837i | ||||
\(424\) | 6.44427 | + | 11.1618i | 0.312962 | + | 0.542065i | ||||
\(425\) | −0.472136 | + | 0.817763i | −0.0229020 | + | 0.0396674i | ||||
\(426\) | 3.41641 | 0.165526 | ||||||||
\(427\) | 1.31966 | − | 0.457144i | 0.0638628 | − | 0.0221227i | ||||
\(428\) | 23.7984 | 1.15034 | ||||||||
\(429\) | −2.23607 | + | 3.87298i | −0.107958 | + | 0.186989i | ||||
\(430\) | −0.763932 | − | 1.32317i | −0.0368401 | − | 0.0638089i | ||||
\(431\) | 16.8262 | + | 29.1439i | 0.810491 | + | 1.40381i | 0.912521 | + | 0.409031i | \(0.134133\pi\) |
−0.102029 | + | 0.994781i | \(0.532534\pi\) | |||||||
\(432\) | 4.63525 | − | 8.02850i | 0.223014 | − | 0.386271i | ||||
\(433\) | −10.9443 | −0.525948 | −0.262974 | − | 0.964803i | \(-0.584703\pi\) | ||||
−0.262974 | + | 0.964803i | \(0.584703\pi\) | |||||||
\(434\) | 5.23607 | + | 4.53457i | 0.251339 | + | 0.217666i | ||||
\(435\) | 4.47214 | 0.214423 | ||||||||
\(436\) | −7.89919 | + | 13.6818i | −0.378302 | + | 0.655239i | ||||
\(437\) | 17.5902 | + | 30.4671i | 0.841452 | + | 1.45744i | ||||
\(438\) | −3.54508 | − | 6.14027i | −0.169391 | − | 0.293393i | ||||
\(439\) | 4.79180 | − | 8.29963i | 0.228700 | − | 0.396120i | −0.728723 | − | 0.684808i | \(-0.759886\pi\) |
0.957423 | + | 0.288689i | \(0.0932192\pi\) | |||||||
\(440\) | −2.23607 | −0.106600 | ||||||||
\(441\) | 13.0000 | + | 5.19615i | 0.619048 | + | 0.247436i | ||||
\(442\) | 0.652476 | 0.0310351 | ||||||||
\(443\) | 6.11803 | − | 10.5967i | 0.290677 | − | 0.503467i | −0.683293 | − | 0.730144i | \(-0.739453\pi\) |
0.973970 | + | 0.226677i | \(0.0727863\pi\) | |||||||
\(444\) | 4.42705 | + | 7.66788i | 0.210099 | + | 0.363901i | ||||
\(445\) | −4.88197 | − | 8.45581i | −0.231427 | − | 0.400844i | ||||
\(446\) | 0.291796 | − | 0.505406i | 0.0138169 | − | 0.0239316i | ||||
\(447\) | −21.1803 | −1.00180 | ||||||||
\(448\) | 0.472136 | + | 0.408882i | 0.0223063 | + | 0.0193178i | ||||
\(449\) | 38.9443 | 1.83789 | 0.918947 | − | 0.394381i | \(-0.129041\pi\) | ||||
0.918947 | + | 0.394381i | \(0.129041\pi\) | |||||||
\(450\) | 2.47214 | − | 4.28187i | 0.116538 | − | 0.201849i | ||||
\(451\) | 0.500000 | + | 0.866025i | 0.0235441 | + | 0.0407795i | ||||
\(452\) | −12.8541 | − | 22.2640i | −0.604606 | − | 1.04721i | ||||
\(453\) | 5.97214 | − | 10.3440i | 0.280595 | − | 0.486006i | ||||
\(454\) | −2.14590 | −0.100712 | ||||||||
\(455\) | −11.1803 | + | 3.87298i | −0.524142 | + | 0.181568i | ||||
\(456\) | −16.7082 | −0.782433 | ||||||||
\(457\) | 10.8820 | − | 18.8481i | 0.509037 | − | 0.881678i | −0.490908 | − | 0.871211i | \(-0.663335\pi\) |
0.999945 | − | 0.0104665i | \(-0.00333166\pi\) | |||||||
\(458\) | 6.21885 | + | 10.7714i | 0.290588 | + | 0.503313i | ||||
\(459\) | −0.590170 | − | 1.02220i | −0.0275468 | − | 0.0477124i | ||||
\(460\) | −3.80902 | + | 6.59741i | −0.177596 | + | 0.307606i | ||||
\(461\) | −21.0557 | −0.980663 | −0.490332 | − | 0.871536i | \(-0.663124\pi\) | ||||
−0.490332 | + | 0.871536i | \(0.663124\pi\) | |||||||
\(462\) | 0.309017 | − | 1.60570i | 0.0143768 | − | 0.0747039i | ||||
\(463\) | −37.8885 | −1.76083 | −0.880415 | − | 0.474204i | \(-0.842736\pi\) | ||||
−0.880415 | + | 0.474204i | \(0.842736\pi\) | |||||||
\(464\) | 4.14590 | − | 7.18091i | 0.192468 | − | 0.333365i | ||||
\(465\) | 2.11803 | + | 3.66854i | 0.0982215 | + | 0.170125i | ||||
\(466\) | 5.16312 | + | 8.94278i | 0.239177 | + | 0.414266i | ||||
\(467\) | −15.5902 | + | 27.0030i | −0.721427 | + | 1.24955i | 0.239001 | + | 0.971019i | \(0.423180\pi\) |
−0.960428 | + | 0.278529i | \(0.910153\pi\) | |||||||
\(468\) | 14.4721 | 0.668975 | ||||||||
\(469\) | 5.97214 | − | 31.0321i | 0.275768 | − | 1.43293i | ||||
\(470\) | 3.38197 | 0.155998 | ||||||||
\(471\) | −1.11803 | + | 1.93649i | −0.0515163 | + | 0.0892288i | ||||
\(472\) | 5.26393 | + | 9.11740i | 0.242292 | + | 0.419662i | ||||
\(473\) | −1.23607 | − | 2.14093i | −0.0568345 | − | 0.0984402i | ||||
\(474\) | −0.309017 | + | 0.535233i | −0.0141936 | + | 0.0245841i | ||||
\(475\) | 29.8885 | 1.37138 | ||||||||
\(476\) | 0.954915 | − | 0.330792i | 0.0437685 | − | 0.0151618i | ||||
\(477\) | 11.5279 | 0.527825 | ||||||||
\(478\) | 2.00000 | − | 3.46410i | 0.0914779 | − | 0.158444i | ||||
\(479\) | −10.5000 | − | 18.1865i | −0.479757 | − | 0.830964i | 0.519973 | − | 0.854183i | \(-0.325942\pi\) |
−0.999730 | + | 0.0232187i | \(0.992609\pi\) | |||||||
\(480\) | −2.80902 | − | 4.86536i | −0.128213 | − | 0.222072i | ||||
\(481\) | −12.2361 | + | 21.1935i | −0.557917 | + | 0.966340i | ||||
\(482\) | 4.61803 | 0.210346 | ||||||||
\(483\) | −9.41641 | − | 8.15485i | −0.428461 | − | 0.371058i | ||||
\(484\) | 16.1803 | 0.735470 | ||||||||
\(485\) | −0.236068 | + | 0.408882i | −0.0107193 | + | 0.0185664i | ||||
\(486\) | 4.94427 | + | 8.56373i | 0.224277 | + | 0.388459i | ||||
\(487\) | −20.7705 | − | 35.9756i | −0.941202 | − | 1.63021i | −0.763183 | − | 0.646182i | \(-0.776365\pi\) |
−0.178018 | − | 0.984027i | \(-0.556969\pi\) | |||||||
\(488\) | −0.590170 | + | 1.02220i | −0.0267157 | + | 0.0462730i | ||||
\(489\) | −18.7082 | −0.846014 | ||||||||
\(490\) | 3.39919 | − | 2.67617i | 0.153560 | − | 0.120897i | ||||
\(491\) | 32.3607 | 1.46042 | 0.730209 | − | 0.683224i | \(-0.239423\pi\) | ||||
0.730209 | + | 0.683224i | \(0.239423\pi\) | |||||||
\(492\) | −0.809017 | + | 1.40126i | −0.0364733 | + | 0.0631736i | ||||
\(493\) | −0.527864 | − | 0.914287i | −0.0237738 | − | 0.0411774i | ||||
\(494\) | −10.3262 | − | 17.8856i | −0.464599 | − | 0.804710i | ||||
\(495\) | −1.00000 | + | 1.73205i | −0.0449467 | + | 0.0778499i | ||||
\(496\) | 7.85410 | 0.352660 | ||||||||
\(497\) | 11.0557 | + | 9.57454i | 0.495917 | + | 0.429477i | ||||
\(498\) | 6.47214 | 0.290023 | ||||||||
\(499\) | 16.9721 | − | 29.3966i | 0.759777 | − | 1.31597i | −0.183187 | − | 0.983078i | \(-0.558641\pi\) |
0.942964 | − | 0.332895i | \(-0.108025\pi\) | |||||||
\(500\) | 7.28115 | + | 12.6113i | 0.325623 | + | 0.563996i | ||||
\(501\) | −3.23607 | − | 5.60503i | −0.144577 | − | 0.250414i | ||||
\(502\) | −8.29180 | + | 14.3618i | −0.370081 | + | 0.640999i | ||||
\(503\) | 4.00000 | 0.178351 | 0.0891756 | − | 0.996016i | \(-0.471577\pi\) | ||||
0.0891756 | + | 0.996016i | \(0.471577\pi\) | |||||||
\(504\) | −11.1803 | + | 3.87298i | −0.498012 | + | 0.172516i | ||||
\(505\) | −16.7082 | −0.743505 | ||||||||
\(506\) | 1.45492 | − | 2.51999i | 0.0646789 | − | 0.112027i | ||||
\(507\) | −3.50000 | − | 6.06218i | −0.155440 | − | 0.269231i | ||||
\(508\) | −9.23607 | − | 15.9973i | −0.409784 | − | 0.709767i | ||||
\(509\) | −13.5902 | + | 23.5389i | −0.602374 | + | 1.04334i | 0.390087 | + | 0.920778i | \(0.372445\pi\) |
−0.992461 | + | 0.122564i | \(0.960888\pi\) | |||||||
\(510\) | −0.145898 | −0.00646047 | ||||||||
\(511\) | 5.73607 | − | 29.8055i | 0.253749 | − | 1.31852i | ||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | −18.6803 | + | 32.3553i | −0.824757 | + | 1.42852i | ||||
\(514\) | −4.54508 | − | 7.87232i | −0.200475 | − | 0.347233i | ||||
\(515\) | −2.59017 | − | 4.48631i | −0.114137 | − | 0.197690i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | 5.47214 | 0.240664 | ||||||||
\(518\) | 1.69098 | − | 8.78661i | 0.0742975 | − | 0.386061i | ||||
\(519\) | 16.8885 | 0.741325 | ||||||||
\(520\) | 5.00000 | − | 8.66025i | 0.219265 | − | 0.379777i | ||||
\(521\) | −4.17376 | − | 7.22917i | −0.182856 | − | 0.316716i | 0.759996 | − | 0.649928i | \(-0.225201\pi\) |
−0.942852 | + | 0.333212i | \(0.891867\pi\) | |||||||
\(522\) | 2.76393 | + | 4.78727i | 0.120974 | + | 0.209533i | ||||
\(523\) | −5.88197 | + | 10.1879i | −0.257200 | + | 0.445484i | −0.965491 | − | 0.260437i | \(-0.916133\pi\) |
0.708290 | + | 0.705921i | \(0.249467\pi\) | |||||||
\(524\) | −28.5623 | −1.24775 | ||||||||
\(525\) | −10.0000 | + | 3.46410i | −0.436436 | + | 0.151186i | ||||
\(526\) | 0.909830 | 0.0396705 | ||||||||
\(527\) | 0.500000 | − | 0.866025i | 0.0217803 | − | 0.0377247i | ||||
\(528\) | −0.927051 | − | 1.60570i | −0.0403447 | − | 0.0698791i | ||||
\(529\) | 0.416408 | + | 0.721240i | 0.0181047 | + | 0.0313582i | ||||
\(530\) | 1.78115 | − | 3.08505i | 0.0773683 | − | 0.134006i | ||||
\(531\) | 9.41641 | 0.408637 | ||||||||
\(532\) | −24.1803 | − | 20.9408i | −1.04835 | − | 0.907898i | ||||
\(533\) | −4.47214 | −0.193710 | ||||||||
\(534\) | −3.01722 | + | 5.22598i | −0.130568 | + | 0.226150i | ||||
\(535\) | −7.35410 | − | 12.7377i | −0.317946 | − | 0.550698i | ||||
\(536\) | 13.3541 | + | 23.1300i | 0.576809 | + | 0.999063i | ||||
\(537\) | −8.20820 | + | 14.2170i | −0.354210 | + | 0.613510i | ||||
\(538\) | 6.50658 | 0.280518 | ||||||||
\(539\) | 5.50000 | − | 4.33013i | 0.236902 | − | 0.186512i | ||||
\(540\) | −8.09017 | −0.348145 | ||||||||
\(541\) | −14.7361 | + | 25.5236i | −0.633553 | + | 1.09735i | 0.353267 | + | 0.935523i | \(0.385071\pi\) |
−0.986820 | + | 0.161823i | \(0.948263\pi\) | |||||||
\(542\) | 2.98278 | + | 5.16632i | 0.128121 | + | 0.221913i | ||||
\(543\) | −2.70820 | − | 4.69075i | −0.116220 | − | 0.201299i | ||||
\(544\) | −0.663119 | + | 1.14856i | −0.0284310 | + | 0.0492439i | ||||
\(545\) | 9.76393 | 0.418241 | ||||||||
\(546\) | 5.52786 | + | 4.78727i | 0.236571 | + | 0.204876i | ||||
\(547\) | −18.4721 | −0.789812 | −0.394906 | − | 0.918722i | \(-0.629223\pi\) | ||||
−0.394906 | + | 0.918722i | \(0.629223\pi\) | |||||||
\(548\) | −12.6631 | + | 21.9332i | −0.540942 | + | 0.936938i | ||||
\(549\) | 0.527864 | + | 0.914287i | 0.0225287 | + | 0.0390208i | ||||
\(550\) | −1.23607 | − | 2.14093i | −0.0527061 | − | 0.0912897i | ||||
\(551\) | −16.7082 | + | 28.9395i | −0.711793 | + | 1.23286i | ||||
\(552\) | 10.5279 | 0.448096 | ||||||||
\(553\) | −2.50000 | + | 0.866025i | −0.106311 | + | 0.0368271i | ||||
\(554\) | 13.5623 | 0.576207 | ||||||||
\(555\) | 2.73607 | − | 4.73901i | 0.116140 | − | 0.201160i | ||||
\(556\) | −0.763932 | − | 1.32317i | −0.0323979 | − | 0.0561149i | ||||
\(557\) | −3.59017 | − | 6.21836i | −0.152120 | − | 0.263480i | 0.779886 | − | 0.625921i | \(-0.215277\pi\) |
−0.932007 | + | 0.362441i | \(0.881943\pi\) | |||||||
\(558\) | −2.61803 | + | 4.53457i | −0.110830 | + | 0.191964i | ||||
\(559\) | 11.0557 | 0.467607 | ||||||||
\(560\) | 0.927051 | − | 4.81710i | 0.0391751 | − | 0.203560i | ||||
\(561\) | −0.236068 | −0.00996680 | ||||||||
\(562\) | 1.38197 | − | 2.39364i | 0.0582947 | − | 0.100969i | ||||
\(563\) | 5.50000 | + | 9.52628i | 0.231797 | + | 0.401485i | 0.958337 | − | 0.285640i | \(-0.0922060\pi\) |
−0.726540 | + | 0.687124i | \(0.758873\pi\) | |||||||
\(564\) | 4.42705 | + | 7.66788i | 0.186412 | + | 0.322876i | ||||
\(565\) | −7.94427 | + | 13.7599i | −0.334218 | + | 0.578883i | ||||
\(566\) | 6.90983 | 0.290442 | ||||||||
\(567\) | −0.500000 | + | 2.59808i | −0.0209980 | + | 0.109109i | ||||
\(568\) | −12.3607 | −0.518643 | ||||||||
\(569\) | 6.02786 | − | 10.4406i | 0.252701 | − | 0.437691i | −0.711567 | − | 0.702618i | \(-0.752014\pi\) |
0.964269 | + | 0.264927i | \(0.0853477\pi\) | |||||||
\(570\) | 2.30902 | + | 3.99933i | 0.0967141 | + | 0.167514i | ||||
\(571\) | 18.7361 | + | 32.4518i | 0.784080 | + | 1.35807i | 0.929547 | + | 0.368703i | \(0.120198\pi\) |
−0.145467 | + | 0.989363i | \(0.546468\pi\) | |||||||
\(572\) | 3.61803 | − | 6.26662i | 0.151278 | − | 0.262020i | ||||
\(573\) | −3.47214 | −0.145051 | ||||||||
\(574\) | 1.54508 | − | 0.535233i | 0.0644906 | − | 0.0223402i | ||||
\(575\) | −18.8328 | −0.785383 | ||||||||
\(576\) | −0.236068 | + | 0.408882i | −0.00983617 | + | 0.0170367i | ||||
\(577\) | −17.7705 | − | 30.7794i | −0.739796 | − | 1.28136i | −0.952587 | − | 0.304267i | \(-0.901589\pi\) |
0.212791 | − | 0.977098i | \(-0.431745\pi\) | |||||||
\(578\) | −5.23607 | − | 9.06914i | −0.217792 | − | 0.377226i | ||||
\(579\) | −11.5902 | + | 20.0748i | −0.481671 | + | 0.834279i | ||||
\(580\) | −7.23607 | −0.300461 | ||||||||
\(581\) | 20.9443 | + | 18.1383i | 0.868915 | + | 0.752502i | ||||
\(582\) | 0.291796 | 0.0120953 | ||||||||
\(583\) | 2.88197 | − | 4.99171i | 0.119359 | − | 0.206736i | ||||
\(584\) | 12.8262 | + | 22.2157i | 0.530754 | + | 0.919292i | ||||
\(585\) | −4.47214 | − | 7.74597i | −0.184900 | − | 0.320256i | ||||
\(586\) | −7.67376 | + | 13.2913i | −0.317000 | + | 0.549060i | ||||
\(587\) | −16.0000 | −0.660391 | −0.330195 | − | 0.943913i | \(-0.607115\pi\) | ||||
−0.330195 | + | 0.943913i | \(0.607115\pi\) | |||||||
\(588\) | 10.5172 | + | 4.20378i | 0.433723 | + | 0.173361i | ||||
\(589\) | −31.6525 | −1.30422 | ||||||||
\(590\) | 1.45492 | − | 2.51999i | 0.0598979 | − | 0.103746i | ||||
\(591\) | −7.47214 | − | 12.9421i | −0.307363 | − | 0.532368i | ||||
\(592\) | −5.07295 | − | 8.78661i | −0.208497 | − | 0.361127i | ||||
\(593\) | 6.11803 | − | 10.5967i | 0.251238 | − | 0.435156i | −0.712629 | − | 0.701541i | \(-0.752496\pi\) |
0.963867 | + | 0.266385i | \(0.0858291\pi\) | |||||||
\(594\) | 3.09017 | 0.126791 | ||||||||
\(595\) | −0.472136 | − | 0.408882i | −0.0193557 | − | 0.0167625i | ||||
\(596\) | 34.2705 | 1.40377 | ||||||||
\(597\) | −0.0278640 | + | 0.0482619i | −0.00114040 | + | 0.00197523i | ||||
\(598\) | 6.50658 | + | 11.2697i | 0.266074 | + | 0.460853i | ||||
\(599\) | −11.0623 | − | 19.1605i | −0.451994 | − | 0.782876i | 0.546516 | − | 0.837449i | \(-0.315954\pi\) |
−0.998510 | + | 0.0545727i | \(0.982620\pi\) | |||||||
\(600\) | 4.47214 | − | 7.74597i | 0.182574 | − | 0.316228i | ||||
\(601\) | −8.47214 | −0.345586 | −0.172793 | − | 0.984958i | \(-0.555279\pi\) | ||||
−0.172793 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(602\) | −3.81966 | + | 1.32317i | −0.155678 | + | 0.0539283i | ||||
\(603\) | 23.8885 | 0.972817 | ||||||||
\(604\) | −9.66312 | + | 16.7370i | −0.393187 | + | 0.681019i | ||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | 5.16312 | + | 8.94278i | 0.209737 | + | 0.363276i | ||||
\(607\) | −3.40983 | + | 5.90600i | −0.138401 | + | 0.239717i | −0.926891 | − | 0.375330i | \(-0.877530\pi\) |
0.788491 | + | 0.615047i | \(0.210863\pi\) | |||||||
\(608\) | 41.9787 | 1.70246 | ||||||||
\(609\) | 2.23607 | − | 11.6190i | 0.0906100 | − | 0.470824i | ||||
\(610\) | 0.326238 | 0.0132090 | ||||||||
\(611\) | −12.2361 | + | 21.1935i | −0.495018 | + | 0.857397i | ||||
\(612\) | 0.381966 | + | 0.661585i | 0.0154401 | + | 0.0267430i | ||||
\(613\) | −4.55573 | − | 7.89075i | −0.184004 | − | 0.318704i | 0.759236 | − | 0.650815i | \(-0.225573\pi\) |
−0.943240 | + | 0.332110i | \(0.892239\pi\) | |||||||
\(614\) | 8.00000 | − | 13.8564i | 0.322854 | − | 0.559199i | ||||
\(615\) | 1.00000 | 0.0403239 | ||||||||
\(616\) | −1.11803 | + | 5.80948i | −0.0450469 | + | 0.234070i | ||||
\(617\) | −1.41641 | −0.0570224 | −0.0285112 | − | 0.999593i | \(-0.509077\pi\) | ||||
−0.0285112 | + | 0.999593i | \(0.509077\pi\) | |||||||
\(618\) | −1.60081 | + | 2.77269i | −0.0643941 | + | 0.111534i | ||||
\(619\) | 13.1180 | + | 22.7211i | 0.527258 | + | 0.913238i | 0.999495 | + | 0.0317666i | \(0.0101133\pi\) |
−0.472237 | + | 0.881472i | \(0.656553\pi\) | |||||||
\(620\) | −3.42705 | − | 5.93583i | −0.137634 | − | 0.238389i | ||||
\(621\) | 11.7705 | − | 20.3871i | 0.472334 | − | 0.818107i | ||||
\(622\) | −19.6738 | −0.788846 | ||||||||
\(623\) | −24.4098 | + | 8.45581i | −0.977959 | + | 0.338775i | ||||
\(624\) | 8.29180 | 0.331937 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | −9.48936 | − | 16.4360i | −0.379271 | − | 0.656917i | ||||
\(627\) | 3.73607 | + | 6.47106i | 0.149204 | + | 0.258429i | ||||
\(628\) | 1.80902 | − | 3.13331i | 0.0721876 | − | 0.125033i | ||||
\(629\) | −1.29180 | −0.0515073 | ||||||||
\(630\) | 2.47214 | + | 2.14093i | 0.0984923 | + | 0.0852968i | ||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 1.11803 | − | 1.93649i | 0.0444730 | − | 0.0770295i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.34346 | + | 16.1833i | 0.371076 | + | 0.642723i | ||||
\(635\) | −5.70820 | + | 9.88690i | −0.226523 | + | 0.392350i | ||||
\(636\) | 9.32624 | 0.369809 | ||||||||
\(637\) | 4.47214 | + | 30.9839i | 0.177192 | + | 1.22763i | ||||
\(638\) | 2.76393 | 0.109425 | ||||||||
\(639\) | −5.52786 | + | 9.57454i | −0.218679 | + | 0.378763i | ||||
\(640\) | 5.69098 | + | 9.85707i | 0.224956 | + | 0.389635i | ||||
\(641\) | −19.8820 | − | 34.4366i | −0.785290 | − | 1.36016i | −0.928825 | − | 0.370518i | \(-0.879180\pi\) |
0.143535 | − | 0.989645i | \(-0.454153\pi\) | |||||||
\(642\) | −4.54508 | + | 7.87232i | −0.179380 | + | 0.310696i | ||||
\(643\) | −43.7771 | −1.72640 | −0.863200 | − | 0.504862i | \(-0.831543\pi\) | ||||
−0.863200 | + | 0.504862i | \(0.831543\pi\) | |||||||
\(644\) | 15.2361 | + | 13.1948i | 0.600385 | + | 0.519949i | ||||
\(645\) | −2.47214 | −0.0973403 | ||||||||
\(646\) | 0.545085 | − | 0.944115i | 0.0214461 | − | 0.0371457i | ||||
\(647\) | 11.1180 | + | 19.2570i | 0.437095 | + | 0.757071i | 0.997464 | − | 0.0711723i | \(-0.0226740\pi\) |
−0.560369 | + | 0.828243i | \(0.689341\pi\) | |||||||
\(648\) | −1.11803 | − | 1.93649i | −0.0439205 | − | 0.0760726i | ||||
\(649\) | 2.35410 | − | 4.07742i | 0.0924066 | − | 0.160053i | ||||
\(650\) | 11.0557 | 0.433641 | ||||||||
\(651\) | 10.5902 | − | 3.66854i | 0.415061 | − | 0.143782i | ||||
\(652\) | 30.2705 | 1.18548 | ||||||||
\(653\) | −22.5344 | + | 39.0308i | −0.881841 | + | 1.52739i | −0.0325486 | + | 0.999470i | \(0.510362\pi\) |
−0.849292 | + | 0.527923i | \(0.822971\pi\) | |||||||
\(654\) | −3.01722 | − | 5.22598i | −0.117983 | − | 0.204352i | ||||
\(655\) | 8.82624 | + | 15.2875i | 0.344870 | + | 0.597332i | ||||
\(656\) | 0.927051 | − | 1.60570i | 0.0361953 | − | 0.0626920i | ||||
\(657\) | 22.9443 | 0.895141 | ||||||||
\(658\) | 1.69098 | − | 8.78661i | 0.0659214 | − | 0.342538i | ||||
\(659\) | −7.05573 | −0.274852 | −0.137426 | − | 0.990512i | \(-0.543883\pi\) | ||||
−0.137426 | + | 0.990512i | \(0.543883\pi\) | |||||||
\(660\) | −0.809017 | + | 1.40126i | −0.0314909 | + | 0.0545439i | ||||
\(661\) | −23.6803 | − | 41.0156i | −0.921058 | − | 1.59532i | −0.797781 | − | 0.602948i | \(-0.793993\pi\) |
−0.123278 | − | 0.992372i | \(-0.539341\pi\) | |||||||
\(662\) | 6.74671 | + | 11.6856i | 0.262218 | + | 0.454176i | ||||
\(663\) | 0.527864 | − | 0.914287i | 0.0205005 | − | 0.0355080i | ||||
\(664\) | −23.4164 | −0.908733 | ||||||||
\(665\) | −3.73607 | + | 19.4132i | −0.144879 | + | 0.752811i | ||||
\(666\) | 6.76393 | 0.262097 | ||||||||
\(667\) | 10.5279 | − | 18.2348i | 0.407641 | − | 0.706054i | ||||
\(668\) | 5.23607 | + | 9.06914i | 0.202590 | + | 0.350895i | ||||
\(669\) | −0.472136 | − | 0.817763i | −0.0182538 | − | 0.0316166i | ||||
\(670\) | 3.69098 | − | 6.39297i | 0.142595 | − | 0.246982i | ||||
\(671\) | 0.527864 | 0.0203780 | ||||||||
\(672\) | −14.0451 | + | 4.86536i | −0.541801 | + | 0.187685i | ||||
\(673\) | −18.5836 | −0.716345 | −0.358172 | − | 0.933655i | \(-0.616600\pi\) | ||||
−0.358172 | + | 0.933655i | \(0.616600\pi\) | |||||||
\(674\) | 0.145898 | − | 0.252703i | 0.00561978 | − | 0.00973375i | ||||
\(675\) | −10.0000 | − | 17.3205i | −0.384900 | − | 0.666667i | ||||
\(676\) | 5.66312 | + | 9.80881i | 0.217812 | + | 0.377262i | ||||
\(677\) | 0.972136 | − | 1.68379i | 0.0373622 | − | 0.0647133i | −0.846740 | − | 0.532008i | \(-0.821438\pi\) |
0.884102 | + | 0.467294i | \(0.154771\pi\) | |||||||
\(678\) | 9.81966 | 0.377122 | ||||||||
\(679\) | 0.944272 | + | 0.817763i | 0.0362378 | + | 0.0313829i | ||||
\(680\) | 0.527864 | 0.0202427 | ||||||||
\(681\) | −1.73607 | + | 3.00696i | −0.0665263 | + | 0.115227i | ||||
\(682\) | 1.30902 | + | 2.26728i | 0.0501249 | + | 0.0868188i | ||||
\(683\) | −3.26393 | − | 5.65330i | −0.124891 | − | 0.216317i | 0.796799 | − | 0.604244i | \(-0.206525\pi\) |
−0.921690 | + | 0.387927i | \(0.873191\pi\) | |||||||
\(684\) | 12.0902 | − | 20.9408i | 0.462279 | − | 0.800691i | ||||
\(685\) | 15.6525 | 0.598050 | ||||||||
\(686\) | −5.25329 | − | 10.1694i | −0.200572 | − | 0.388271i | ||||
\(687\) | 20.1246 | 0.767802 | ||||||||
\(688\) | −2.29180 | + | 3.96951i | −0.0873739 | + | 0.151336i | ||||
\(689\) | 12.8885 | + | 22.3236i | 0.491014 | + | 0.850462i | ||||
\(690\) | −1.45492 | − | 2.51999i | −0.0553877 | − | 0.0959343i | ||||
\(691\) | −1.31966 | + | 2.28572i | −0.0502022 | + | 0.0869528i | −0.890035 | − | 0.455893i | \(-0.849320\pi\) |
0.839832 | + | 0.542846i | \(0.182653\pi\) | |||||||
\(692\) | −27.3262 | −1.03879 | ||||||||
\(693\) | 4.00000 | + | 3.46410i | 0.151947 | + | 0.131590i | ||||
\(694\) | 1.85410 | 0.0703807 | ||||||||
\(695\) | −0.472136 | + | 0.817763i | −0.0179091 | + | 0.0310195i | ||||
\(696\) | 5.00000 | + | 8.66025i | 0.189525 | + | 0.328266i | ||||
\(697\) | −0.118034 | − | 0.204441i | −0.00447086 | − | 0.00774375i | ||||
\(698\) | −3.56231 | + | 6.17009i | −0.134835 | + | 0.233542i | ||||
\(699\) | 16.7082 | 0.631962 | ||||||||
\(700\) | 16.1803 | − | 5.60503i | 0.611559 | − | 0.211850i | ||||
\(701\) | 2.36068 | 0.0891616 | 0.0445808 | − | 0.999006i | \(-0.485805\pi\) | ||||
0.0445808 | + | 0.999006i | \(0.485805\pi\) | |||||||
\(702\) | −6.90983 | + | 11.9682i | −0.260795 | + | 0.451710i | ||||
\(703\) | 20.4443 | + | 35.4105i | 0.771070 | + | 1.33553i | ||||
\(704\) | 0.118034 | + | 0.204441i | 0.00444857 | + | 0.00770516i | ||||
\(705\) | 2.73607 | − | 4.73901i | 0.103046 | − | 0.178481i | ||||
\(706\) | −10.2148 | −0.384438 | ||||||||
\(707\) | −8.35410 | + | 43.4092i | −0.314188 | + | 1.63257i | ||||
\(708\) | 7.61803 | 0.286303 | ||||||||
\(709\) | 1.06231 | − | 1.83997i | 0.0398957 | − | 0.0691014i | −0.845388 | − | 0.534153i | \(-0.820631\pi\) |
0.885284 | + | 0.465051i | \(0.153964\pi\) | |||||||
\(710\) | 1.70820 | + | 2.95870i | 0.0641078 | + | 0.111038i | ||||
\(711\) | −1.00000 | − | 1.73205i | −0.0375029 | − | 0.0649570i | ||||
\(712\) | 10.9164 | − | 18.9078i | 0.409110 | − | 0.708599i | ||||
\(713\) | 19.9443 | 0.746919 | ||||||||
\(714\) | −0.0729490 | + | 0.379054i | −0.00273005 | + | 0.0141857i | ||||
\(715\) | −4.47214 | −0.167248 | ||||||||
\(716\) | 13.2812 | − | 23.0036i | 0.496340 | − | 0.859686i | ||||
\(717\) | −3.23607 | − | 5.60503i | −0.120853 | − | 0.209324i | ||||
\(718\) | 5.45492 | + | 9.44819i | 0.203576 | + | 0.352603i | ||||
\(719\) | −21.6803 | + | 37.5515i | −0.808540 | + | 1.40043i | 0.105335 | + | 0.994437i | \(0.466409\pi\) |
−0.913875 | + | 0.405996i | \(0.866925\pi\) | |||||||
\(720\) | 3.70820 | 0.138197 | ||||||||
\(721\) | −12.9508 | + | 4.48631i | −0.482315 | + | 0.167079i | ||||
\(722\) | −22.7639 | −0.847186 | ||||||||
\(723\) | 3.73607 | − | 6.47106i | 0.138946 | − | 0.240661i | ||||
\(724\) | 4.38197 | + | 7.58979i | 0.162854 | + | 0.282072i | ||||
\(725\) | −8.94427 | − | 15.4919i | −0.332182 | − | 0.575356i | ||||
\(726\) | −3.09017 | + | 5.35233i | −0.114687 | + | 0.198644i | ||||
\(727\) | 24.9443 | 0.925132 | 0.462566 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462566 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(728\) | −20.0000 | − | 17.3205i | −0.741249 | − | 0.641941i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 3.54508 | − | 6.14027i | 0.131209 | − | 0.227261i | ||||
\(731\) | 0.291796 | + | 0.505406i | 0.0107925 | + | 0.0186931i | ||||
\(732\) | 0.427051 | + | 0.739674i | 0.0157843 | + | 0.0273391i | ||||
\(733\) | 17.9164 | − | 31.0321i | 0.661758 | − | 1.14620i | −0.318396 | − | 0.947958i | \(-0.603144\pi\) |
0.980154 | − | 0.198240i | \(-0.0635225\pi\) | |||||||
\(734\) | −10.6180 | −0.391919 | ||||||||
\(735\) | −1.00000 | − | 6.92820i | −0.0368856 | − | 0.255551i | ||||
\(736\) | −26.4508 | −0.974991 | ||||||||
\(737\) | 5.97214 | − | 10.3440i | 0.219986 | − | 0.381028i | ||||
\(738\) | 0.618034 | + | 1.07047i | 0.0227501 | + | 0.0394044i | ||||
\(739\) | 6.17376 | + | 10.6933i | 0.227106 | + | 0.393358i | 0.956949 | − | 0.290256i | \(-0.0937404\pi\) |
−0.729844 | + | 0.683614i | \(0.760407\pi\) | |||||||
\(740\) | −4.42705 | + | 7.66788i | −0.162742 | + | 0.281877i | ||||
\(741\) | −33.4164 | −1.22758 | ||||||||
\(742\) | −7.12461 | − | 6.17009i | −0.261553 | − | 0.226511i | ||||
\(743\) | 44.7214 | 1.64067 | 0.820334 | − | 0.571885i | \(-0.193788\pi\) | ||||
0.820334 | + | 0.571885i | \(0.193788\pi\) | |||||||
\(744\) | −4.73607 | + | 8.20311i | −0.173633 | + | 0.300741i | ||||
\(745\) | −10.5902 | − | 18.3427i | −0.387994 | − | 0.672025i | ||||
\(746\) | −5.54508 | − | 9.60437i | −0.203020 | − | 0.351641i | ||||
\(747\) | −10.4721 | + | 18.1383i | −0.383155 | + | 0.663645i | ||||
\(748\) | 0.381966 | 0.0139661 | ||||||||
\(749\) | −36.7705 | + | 12.7377i | −1.34357 | + | 0.465425i | ||||
\(750\) | −5.56231 | −0.203107 | ||||||||
\(751\) | 15.7361 | − | 27.2557i | 0.574217 | − | 0.994573i | −0.421909 | − | 0.906638i | \(-0.638640\pi\) |
0.996126 | − | 0.0879353i | \(-0.0280269\pi\) | |||||||
\(752\) | −5.07295 | − | 8.78661i | −0.184991 | − | 0.320415i | ||||
\(753\) | 13.4164 | + | 23.2379i | 0.488921 | + | 0.846836i | ||||
\(754\) | −6.18034 | + | 10.7047i | −0.225075 | + | 0.389841i | ||||
\(755\) | 11.9443 | 0.434697 | ||||||||
\(756\) | −4.04508 | + | 21.0189i | −0.147118 | + | 0.764449i | ||||
\(757\) | 14.9443 | 0.543159 | 0.271579 | − | 0.962416i | \(-0.412454\pi\) | ||||
0.271579 | + | 0.962416i | \(0.412454\pi\) | |||||||
\(758\) | 1.41641 | − | 2.45329i | 0.0514463 | − | 0.0891075i | ||||
\(759\) | −2.35410 | − | 4.07742i | −0.0854485 | − | 0.148001i | ||||
\(760\) | −8.35410 | − | 14.4697i | −0.303035 | − | 0.524872i | ||||
\(761\) | 23.1525 | − | 40.1013i | 0.839277 | − | 1.45367i | −0.0512238 | − | 0.998687i | \(-0.516312\pi\) |
0.890500 | − | 0.454983i | \(-0.150354\pi\) | |||||||
\(762\) | 7.05573 | 0.255602 | ||||||||
\(763\) | 4.88197 | − | 25.3674i | 0.176739 | − | 0.918363i | ||||
\(764\) | 5.61803 | 0.203253 | ||||||||
\(765\) | 0.236068 | − | 0.408882i | 0.00853506 | − | 0.0147832i | ||||
\(766\) | −4.60081 | − | 7.96884i | −0.166234 | − | 0.287926i | ||||
\(767\) | 10.5279 | + | 18.2348i | 0.380139 | + | 0.658420i | ||||
\(768\) | 3.28115 | − | 5.68312i | 0.118398 | − | 0.205072i | ||||
\(769\) | 36.8328 | 1.32823 | 0.664113 | − | 0.747633i | \(-0.268810\pi\) | ||||
0.664113 | + | 0.747633i | \(0.268810\pi\) | |||||||
\(770\) | 1.54508 | − | 0.535233i | 0.0556810 | − | 0.0192885i | ||||
\(771\) | −14.7082 | −0.529703 | ||||||||
\(772\) | 18.7533 | − | 32.4816i | 0.674946 | − | 1.16904i | ||||
\(773\) | −10.8262 | − | 18.7516i | −0.389393 | − | 0.674448i | 0.602975 | − | 0.797760i | \(-0.293982\pi\) |
−0.992368 | + | 0.123312i | \(0.960648\pi\) | |||||||
\(774\) | −1.52786 | − | 2.64634i | −0.0549179 | − | 0.0951207i | ||||
\(775\) | 8.47214 | − | 14.6742i | 0.304328 | − | 0.527112i | ||||
\(776\) | −1.05573 | −0.0378984 | ||||||||
\(777\) | −10.9443 | − | 9.47802i | −0.392624 | − | 0.340022i | ||||
\(778\) | 0.618034 | 0.0221576 | ||||||||
\(779\) | −3.73607 | + | 6.47106i | −0.133859 | + | 0.231850i | ||||
\(780\) | −3.61803 | − | 6.26662i | −0.129546 | − | 0.224381i | ||||
\(781\) | 2.76393 | + | 4.78727i | 0.0989013 | + | 0.171302i | ||||
\(782\) | −0.343459 | + | 0.594888i | −0.0122821 | + | 0.0212732i | ||||
\(783\) | 22.3607 | 0.799106 | ||||||||
\(784\) | −12.0517 | − | 4.81710i | −0.430417 | − | 0.172039i | ||||
\(785\) | −2.23607 | −0.0798087 | ||||||||
\(786\) | 5.45492 | − | 9.44819i | 0.194570 | − | 0.337006i | ||||
\(787\) | 10.8262 | + | 18.7516i | 0.385914 | + | 0.668422i | 0.991895 | − | 0.127056i | \(-0.0405529\pi\) |
−0.605982 | + | 0.795479i | \(0.707220\pi\) | |||||||
\(788\) | 12.0902 | + | 20.9408i | 0.430694 | + | 0.745985i | ||||
\(789\) | 0.736068 | − | 1.27491i | 0.0262047 | − | 0.0453879i | ||||
\(790\) | −0.618034 | −0.0219887 | ||||||||
\(791\) | 31.7771 | + | 27.5198i | 1.12986 | + | 0.978490i | ||||
\(792\) | −4.47214 | −0.158910 | ||||||||
\(793\) | −1.18034 | + | 2.04441i | −0.0419151 | + | 0.0725991i | ||||
\(794\) | −1.12868 | − | 1.95493i | −0.0400553 | − | 0.0693777i | ||||
\(795\) | −2.88197 | − | 4.99171i | −0.102213 | − | 0.177038i | ||||
\(796\) | 0.0450850 | − | 0.0780895i | 0.00159799 | − | 0.00276781i | ||||
\(797\) | −28.8328 | −1.02131 | −0.510655 | − | 0.859785i | \(-0.670597\pi\) | ||||
−0.510655 | + | 0.859785i | \(0.670597\pi\) | |||||||
\(798\) | 11.5451 | − | 3.99933i | 0.408692 | − | 0.141575i | ||||
\(799\) | −1.29180 | −0.0457005 | ||||||||
\(800\) | −11.2361 | + | 19.4614i | −0.397255 | + | 0.688066i | ||||
\(801\) | −9.76393 | − | 16.9116i | −0.344992 | − | 0.597543i | ||||
\(802\) | −3.07295 | − | 5.32250i | −0.108510 | − | 0.187944i | ||||
\(803\) | 5.73607 | − | 9.93516i | 0.202421 | − | 0.350604i | ||||
\(804\) | 19.3262 | 0.681584 | ||||||||
\(805\) | 2.35410 | − | 12.2323i | 0.0829712 | − | 0.431131i | ||||
\(806\) | −11.7082 | −0.412404 | ||||||||
\(807\) | 5.26393 | − | 9.11740i | 0.185299 | − | 0.320948i | ||||
\(808\) | −18.6803 | − | 32.3553i | −0.657172 | − | 1.13826i | ||||
\(809\) | −12.8262 | − | 22.2157i | −0.450947 | − | 0.781062i | 0.547499 | − | 0.836807i | \(-0.315580\pi\) |
−0.998445 | + | 0.0557444i | \(0.982247\pi\) | |||||||
\(810\) | −0.309017 | + | 0.535233i | −0.0108578 | + | 0.0188062i | ||||
\(811\) | −36.7214 | −1.28946 | −0.644731 | − | 0.764410i | \(-0.723030\pi\) | ||||
−0.644731 | + | 0.764410i | \(0.723030\pi\) | |||||||
\(812\) | −3.61803 | + | 18.7999i | −0.126968 | + | 0.659746i | ||||
\(813\) | 9.65248 | 0.338527 | ||||||||
\(814\) | 1.69098 | − | 2.92887i | 0.0592689 | − | 0.102657i | ||||
\(815\) | −9.35410 | − | 16.2018i | −0.327660 | − | 0.567524i | ||||
\(816\) | 0.218847 | + | 0.379054i | 0.00766118 | + | 0.0132696i | ||||
\(817\) | 9.23607 | − | 15.9973i | 0.323129 | − | 0.559676i | ||||
\(818\) | −7.96556 | −0.278509 | ||||||||
\(819\) | −22.3607 | + | 7.74597i | −0.781345 | + | 0.270666i | ||||
\(820\) | −1.61803 | −0.0565042 | ||||||||
\(821\) | 10.5000 | − | 18.1865i | 0.366453 | − | 0.634714i | −0.622556 | − | 0.782576i | \(-0.713906\pi\) |
0.989008 | + | 0.147861i | \(0.0472389\pi\) | |||||||
\(822\) | −4.83688 | − | 8.37772i | −0.168706 | − | 0.292207i | ||||
\(823\) | 2.26393 | + | 3.92125i | 0.0789157 | + | 0.136686i | 0.902782 | − | 0.430098i | \(-0.141521\pi\) |
−0.823867 | + | 0.566784i | \(0.808188\pi\) | |||||||
\(824\) | 5.79180 | − | 10.0317i | 0.201767 | − | 0.349470i | ||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | −5.81966 | − | 5.03997i | −0.202492 | − | 0.175363i | ||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | −7.61803 | + | 13.1948i | −0.264745 | + | 0.458552i | ||||
\(829\) | 6.97214 | + | 12.0761i | 0.242152 | + | 0.419420i | 0.961327 | − | 0.275409i | \(-0.0888133\pi\) |
−0.719175 | + | 0.694829i | \(0.755480\pi\) | |||||||
\(830\) | 3.23607 | + | 5.60503i | 0.112326 | + | 0.194554i | ||||
\(831\) | 10.9721 | − | 19.0043i | 0.380619 | − | 0.659252i | ||||
\(832\) | −1.05573 | −0.0366008 | ||||||||
\(833\) | −1.29837 | + | 1.02220i | −0.0449860 | + | 0.0354173i | ||||
\(834\) | 0.583592 | 0.0202081 | ||||||||
\(835\) | 3.23607 | − | 5.60503i | 0.111989 | − | 0.193970i | ||||
\(836\) | −6.04508 | − | 10.4704i | −0.209074 | − | 0.362126i | ||||
\(837\) | 10.5902 | + | 18.3427i | 0.366050 | + | 0.634017i | ||||
\(838\) | 5.52786 | − | 9.57454i | 0.190957 | − | 0.330747i | ||||
\(839\) | 3.05573 | 0.105495 | 0.0527477 | − | 0.998608i | \(-0.483202\pi\) | ||||
0.0527477 | + | 0.998608i | \(0.483202\pi\) | |||||||
\(840\) | 4.47214 | + | 3.87298i | 0.154303 | + | 0.133631i | ||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | −2.32624 | + | 4.02916i | −0.0801675 | + | 0.138854i | ||||
\(843\) | −2.23607 | − | 3.87298i | −0.0770143 | − | 0.133393i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.50000 | − | 6.06218i | 0.120404 | − | 0.208545i | ||||
\(846\) | 6.76393 | 0.232549 | ||||||||
\(847\) | −25.0000 | + | 8.66025i | −0.859010 | + | 0.297570i | ||||
\(848\) | −10.6869 | −0.366990 | ||||||||
\(849\) | 5.59017 | − | 9.68246i | 0.191854 | − | 0.332301i | ||||
\(850\) | 0.291796 | + | 0.505406i | 0.0100085 | + | 0.0173353i | ||||
\(851\) | −12.8820 | − | 22.3122i | −0.441588 | − | 0.764853i | ||||
\(852\) | −4.47214 | + | 7.74597i | −0.153213 | + | 0.265372i | ||||
\(853\) | 1.05573 | 0.0361474 | 0.0180737 | − | 0.999837i | \(-0.494247\pi\) | ||||
0.0180737 | + | 0.999837i | \(0.494247\pi\) | |||||||
\(854\) | 0.163119 | − | 0.847591i | 0.00558182 | − | 0.0290040i | ||||
\(855\) | −14.9443 | −0.511083 | ||||||||
\(856\) | 16.4443 | − | 28.4823i | 0.562054 | − | 0.973505i | ||||
\(857\) | −26.1525 | − | 45.2974i | −0.893352 | − | 1.54733i | −0.835832 | − | 0.548986i | \(-0.815014\pi\) |
−0.0575200 | − | 0.998344i | \(-0.518319\pi\) | |||||||
\(858\) | 1.38197 | + | 2.39364i | 0.0471795 | + | 0.0817174i | ||||
\(859\) | 21.3541 | − | 36.9864i | 0.728593 | − | 1.26196i | −0.228886 | − | 0.973453i | \(-0.573508\pi\) |
0.957478 | − | 0.288506i | \(-0.0931585\pi\) | |||||||
\(860\) | 4.00000 | 0.136399 | ||||||||
\(861\) | 0.500000 | − | 2.59808i | 0.0170400 | − | 0.0885422i | ||||
\(862\) | 20.7984 | 0.708395 | ||||||||
\(863\) | −11.5902 | + | 20.0748i | −0.394534 | + | 0.683353i | −0.993042 | − | 0.117764i | \(-0.962427\pi\) |
0.598508 | + | 0.801117i | \(0.295761\pi\) | |||||||
\(864\) | −14.0451 | − | 24.3268i | −0.477823 | − | 0.827615i | ||||
\(865\) | 8.44427 | + | 14.6259i | 0.287114 | + | 0.497296i | ||||
\(866\) | −3.38197 | + | 5.85774i | −0.114924 | + | 0.199054i | ||||
\(867\) | −16.9443 | −0.575458 | ||||||||
\(868\) | −17.1353 | + | 5.93583i | −0.581608 | + | 0.201475i | ||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 1.38197 | − | 2.39364i | 0.0468530 | − | 0.0811518i | ||||
\(871\) | 26.7082 | + | 46.2600i | 0.904973 | + | 1.56746i | ||||
\(872\) | 10.9164 | + | 18.9078i | 0.369676 | + | 0.640298i | ||||
\(873\) | −0.472136 | + | 0.817763i | −0.0159794 | + | 0.0276771i | ||||
\(874\) | 21.7426 | 0.735456 | ||||||||
\(875\) | −18.0000 | − | 15.5885i | −0.608511 | − | 0.526986i | ||||
\(876\) | 18.5623 | 0.627162 | ||||||||
\(877\) | 3.73607 | − | 6.47106i | 0.126158 | − | 0.218512i | −0.796027 | − | 0.605261i | \(-0.793069\pi\) |
0.922185 | + | 0.386749i | \(0.126402\pi\) | |||||||
\(878\) | −2.96149 | − | 5.12946i | −0.0999455 | − | 0.173111i | ||||
\(879\) | 12.4164 | + | 21.5058i | 0.418795 | + | 0.725374i | ||||
\(880\) | 0.927051 | − | 1.60570i | 0.0312509 | − | 0.0541281i | ||||
\(881\) | 15.5279 | 0.523147 | 0.261574 | − | 0.965184i | \(-0.415759\pi\) | ||||
0.261574 | + | 0.965184i | \(0.415759\pi\) | |||||||
\(882\) | 6.79837 | − | 5.35233i | 0.228913 | − | 0.180222i | ||||
\(883\) | −43.4164 | −1.46108 | −0.730539 | − | 0.682871i | \(-0.760731\pi\) | ||||
−0.730539 | + | 0.682871i | \(0.760731\pi\) | |||||||
\(884\) | −0.854102 | + | 1.47935i | −0.0287266 | + | 0.0497559i | ||||
\(885\) | −2.35410 | − | 4.07742i | −0.0791323 | − | 0.137061i | ||||
\(886\) | −3.78115 | − | 6.54915i | −0.127030 | − | 0.220023i | ||||
\(887\) | 5.55573 | − | 9.62280i | 0.186543 | − | 0.323102i | −0.757552 | − | 0.652774i | \(-0.773605\pi\) |
0.944095 | + | 0.329672i | \(0.106938\pi\) | |||||||
\(888\) | 12.2361 | 0.410616 | ||||||||
\(889\) | 22.8328 | + | 19.7738i | 0.765788 | + | 0.663192i | ||||
\(890\) | −6.03444 | −0.202275 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | 0.763932 | + | 1.32317i | 0.0255783 | + | 0.0443030i | ||||
\(893\) | 20.4443 | + | 35.4105i | 0.684141 | + | 1.18497i | ||||
\(894\) | −6.54508 | + | 11.3364i | −0.218900 | + | 0.379147i | ||||
\(895\) | −16.4164 | −0.548740 | ||||||||
\(896\) | 28.4549 | − | 9.85707i | 0.950612 | − | 0.329302i | ||||
\(897\) | 21.0557 | 0.703030 | ||||||||
\(898\) | 12.0344 | − | 20.8443i | 0.401595 | − | 0.695582i | ||||
\(899\) | 9.47214 | + | 16.4062i | 0.315913 | + | 0.547178i | ||||
\(900\) | 6.47214 | + | 11.2101i | 0.215738 | + | 0.373669i | ||||
\(901\) | −0.680340 | + | 1.17838i | −0.0226654 | + | 0.0392576i | ||||
\(902\) | 0.618034 | 0.0205783 | ||||||||
\(903\) | −1.23607 | + | 6.42280i | −0.0411338 | + | 0.213737i | ||||
\(904\) | −35.5279 | −1.18164 | ||||||||
\(905\) | 2.70820 | − | 4.69075i | 0.0900237 | − | 0.155926i | ||||
\(906\) | −3.69098 | − | 6.39297i | −0.122625 | − | 0.212392i | ||||
\(907\) | 22.8262 | + | 39.5362i | 0.757933 | + | 1.31278i | 0.943903 | + | 0.330223i | \(0.107124\pi\) |
−0.185970 | + | 0.982555i | \(0.559543\pi\) | |||||||
\(908\) | 2.80902 | − | 4.86536i | 0.0932205 | − | 0.161463i | ||||
\(909\) | −33.4164 | −1.10835 | ||||||||
\(910\) | −1.38197 | + | 7.18091i | −0.0458117 | + | 0.238045i | ||||
\(911\) | −20.5836 | −0.681965 | −0.340982 | − | 0.940070i | \(-0.610760\pi\) | ||||
−0.340982 | + | 0.940070i | \(0.610760\pi\) | |||||||
\(912\) | 6.92705 | − | 11.9980i | 0.229378 | − | 0.397294i | ||||
\(913\) | 5.23607 | + | 9.06914i | 0.173289 | + | 0.300145i | ||||
\(914\) | −6.72542 | − | 11.6488i | −0.222457 | − | 0.385307i | ||||
\(915\) | 0.263932 | − | 0.457144i | 0.00872532 | − | 0.0151127i | ||||
\(916\) | −32.5623 | −1.07589 | ||||||||
\(917\) | 44.1312 | − | 15.2875i | 1.45734 | − | 0.504837i | ||||
\(918\) | −0.729490 | −0.0240768 | ||||||||
\(919\) | 10.9721 | − | 19.0043i | 0.361937 | − | 0.626894i | −0.626342 | − | 0.779548i | \(-0.715449\pi\) |
0.988280 | + | 0.152654i | \(0.0487821\pi\) | |||||||
\(920\) | 5.26393 | + | 9.11740i | 0.173547 | + | 0.300592i | ||||
\(921\) | −12.9443 | − | 22.4201i | −0.426528 | − | 0.738769i | ||||
\(922\) | −6.50658 | + | 11.2697i | −0.214283 | + | 0.371149i | ||||
\(923\) | −24.7214 | −0.813713 | ||||||||
\(924\) | 3.23607 | + | 2.80252i | 0.106459 | + | 0.0921960i | ||||
\(925\) | −21.8885 | −0.719691 | ||||||||
\(926\) | −11.7082 | + | 20.2792i | −0.384755 | + | 0.666416i | ||||
\(927\) | −5.18034 | − | 8.97261i | −0.170145 | − | 0.294699i | ||||
\(928\) | −12.5623 | − | 21.7586i | −0.412378 | − | 0.714259i | ||||
\(929\) | −13.7705 | + | 23.8512i | −0.451796 | + | 0.782533i | −0.998498 | − | 0.0547941i | \(-0.982550\pi\) |
0.546702 | + | 0.837327i | \(0.315883\pi\) | |||||||
\(930\) | 2.61803 | 0.0858487 | ||||||||
\(931\) | 48.5689 | + | 19.4132i | 1.59178 | + | 0.636241i | ||||
\(932\) | −27.0344 | −0.885543 | ||||||||
\(933\) | −15.9164 | + | 27.5680i | −0.521080 | + | 0.902537i | ||||
\(934\) | 9.63525 | + | 16.6888i | 0.315275 | + | 0.546073i | ||||
\(935\) | −0.118034 | − | 0.204441i | −0.00386012 | − | 0.00668593i | ||||
\(936\) | 10.0000 | − | 17.3205i | 0.326860 | − | 0.566139i | ||||
\(937\) | 2.58359 | 0.0844023 | 0.0422011 | − | 0.999109i | \(-0.486563\pi\) | ||||
0.0422011 | + | 0.999109i | \(0.486563\pi\) | |||||||
\(938\) | −14.7639 | − | 12.7859i | −0.482059 | − | 0.417476i | ||||
\(939\) | −30.7082 | −1.00212 | ||||||||
\(940\) | −4.42705 | + | 7.66788i | −0.144394 | + | 0.250099i | ||||
\(941\) | −3.79180 | − | 6.56758i | −0.123609 | − | 0.214097i | 0.797579 | − | 0.603214i | \(-0.206114\pi\) |
−0.921188 | + | 0.389117i | \(0.872780\pi\) | |||||||
\(942\) | 0.690983 | + | 1.19682i | 0.0225134 | + | 0.0389944i | ||||
\(943\) | 2.35410 | − | 4.07742i | 0.0766601 | − | 0.132779i | ||||
\(944\) | −8.72949 | −0.284121 | ||||||||
\(945\) | 12.5000 | − | 4.33013i | 0.406625 | − | 0.140859i | ||||
\(946\) | −1.52786 | −0.0496751 | ||||||||
\(947\) | −8.64590 | + | 14.9751i | −0.280954 | + | 0.486626i | −0.971620 | − | 0.236547i | \(-0.923984\pi\) |
0.690666 | + | 0.723174i | \(0.257317\pi\) | |||||||
\(948\) | −0.809017 | − | 1.40126i | −0.0262757 | − | 0.0455108i | ||||
\(949\) | 25.6525 | + | 44.4314i | 0.832715 | + | 1.44230i | ||||
\(950\) | 9.23607 | − | 15.9973i | 0.299658 | − | 0.519022i | ||||
\(951\) | 30.2361 | 0.980472 | ||||||||
\(952\) | 0.263932 | − | 1.37143i | 0.00855409 | − | 0.0444483i | ||||
\(953\) | 8.11146 | 0.262756 | 0.131378 | − | 0.991332i | \(-0.458060\pi\) | ||||
0.131378 | + | 0.991332i | \(0.458060\pi\) | |||||||
\(954\) | 3.56231 | − | 6.17009i | 0.115334 | − | 0.199764i | ||||
\(955\) | −1.73607 | − | 3.00696i | −0.0561778 | − | 0.0973029i | ||||
\(956\) | 5.23607 | + | 9.06914i | 0.169347 | + | 0.293317i | ||||
\(957\) | 2.23607 | − | 3.87298i | 0.0722818 | − | 0.125196i | ||||
\(958\) | −12.9787 | −0.419323 | ||||||||
\(959\) | 7.82624 | − | 40.6663i | 0.252722 | − | 1.31318i | ||||
\(960\) | 0.236068 | 0.00761906 | ||||||||
\(961\) | 6.52786 | − | 11.3066i | 0.210576 | − | 0.364729i | ||||
\(962\) | 7.56231 | + | 13.0983i | 0.243819 | + | 0.422306i | ||||
\(963\) | −14.7082 | − | 25.4754i | −0.473965 | − | 0.820932i | ||||
\(964\) | −6.04508 | + | 10.4704i | −0.194699 | + | 0.337229i | ||||
\(965\) | −23.1803 | −0.746202 | ||||||||
\(966\) | −7.27458 | + | 2.51999i | −0.234056 | + | 0.0810792i | ||||
\(967\) | −41.3050 | −1.32828 | −0.664139 | − | 0.747609i | \(-0.731202\pi\) | ||||
−0.664139 | + | 0.747609i | \(0.731202\pi\) | |||||||
\(968\) | 11.1803 | − | 19.3649i | 0.359350 | − | 0.622412i | ||||
\(969\) | −0.881966 | − | 1.52761i | −0.0283328 | − | 0.0490739i | ||||
\(970\) | 0.145898 | + | 0.252703i | 0.00468450 | + | 0.00811380i | ||||
\(971\) | 12.3885 | − | 21.4576i | 0.397567 | − | 0.688607i | −0.595858 | − | 0.803090i | \(-0.703188\pi\) |
0.993425 | + | 0.114483i | \(0.0365212\pi\) | |||||||
\(972\) | −25.8885 | −0.830375 | ||||||||
\(973\) | 1.88854 | + | 1.63553i | 0.0605439 | + | 0.0524326i | ||||
\(974\) | −25.6738 | −0.822640 | ||||||||
\(975\) | 8.94427 | − | 15.4919i | 0.286446 | − | 0.496139i | ||||
\(976\) | −0.489357 | − | 0.847591i | −0.0156639 | − | 0.0271307i | ||||
\(977\) | 3.82624 | + | 6.62724i | 0.122412 | + | 0.212024i | 0.920718 | − | 0.390228i | \(-0.127604\pi\) |
−0.798306 | + | 0.602252i | \(0.794270\pi\) | |||||||
\(978\) | −5.78115 | + | 10.0133i | −0.184861 | + | 0.320188i | ||||
\(979\) | −9.76393 | −0.312057 | ||||||||
\(980\) | 1.61803 | + | 11.2101i | 0.0516862 | + | 0.358092i | ||||
\(981\) | 19.5279 | 0.623477 | ||||||||
\(982\) | 10.0000 | − | 17.3205i | 0.319113 | − | 0.552720i | ||||
\(983\) | 4.93769 | + | 8.55234i | 0.157488 | + | 0.272777i | 0.933962 | − | 0.357372i | \(-0.116327\pi\) |
−0.776474 | + | 0.630149i | \(0.782994\pi\) | |||||||
\(984\) | 1.11803 | + | 1.93649i | 0.0356416 | + | 0.0617331i | ||||
\(985\) | 7.47214 | − | 12.9421i | 0.238082 | − | 0.412370i | ||||
\(986\) | −0.652476 | −0.0207791 | ||||||||
\(987\) | −10.9443 | − | 9.47802i | −0.348360 | − | 0.301689i | ||||
\(988\) | 54.0689 | 1.72016 | ||||||||
\(989\) | −5.81966 | + | 10.0799i | −0.185054 | + | 0.320524i | ||||
\(990\) | 0.618034 | + | 1.07047i | 0.0196424 | + | 0.0340217i | ||||
\(991\) | 9.79180 | + | 16.9599i | 0.311047 | + | 0.538749i | 0.978589 | − | 0.205823i | \(-0.0659871\pi\) |
−0.667543 | + | 0.744572i | \(0.732654\pi\) | |||||||
\(992\) | 11.8992 | − | 20.6100i | 0.377800 | − | 0.654368i | ||||
\(993\) | 21.8328 | 0.692843 | ||||||||
\(994\) | 8.54102 | − | 2.95870i | 0.270905 | − | 0.0938441i | ||||
\(995\) | −0.0557281 | −0.00176670 | ||||||||
\(996\) | −8.47214 | + | 14.6742i | −0.268450 | + | 0.464969i | ||||
\(997\) | −8.53444 | − | 14.7821i | −0.270288 | − | 0.468153i | 0.698647 | − | 0.715466i | \(-0.253786\pi\) |
−0.968936 | + | 0.247313i | \(0.920452\pi\) | |||||||
\(998\) | −10.4894 | − | 18.1681i | −0.332035 | − | 0.575101i | ||||
\(999\) | 13.6803 | − | 23.6950i | 0.432827 | − | 0.749678i |
(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 | 287.2.e.a.247.2 | yes | 4 | |
7.2 | even | 3 | 2009.2.a.f.1.1 | 2 | |||
7.4 | even | 3 | inner | 287.2.e.a.165.2 | ✓ | 4 | |
7.5 | odd | 6 | 2009.2.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.a.165.2 | ✓ | 4 | 7.4 | even | 3 | inner | |
287.2.e.a.247.2 | yes | 4 | 1.1 | even | 1 | trivial | |
2009.2.a.e.1.1 | 2 | 7.5 | odd | 6 | |||
2009.2.a.f.1.1 | 2 | 7.2 | even | 3 |