Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(101,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\), degree \(6\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 226.3 | ||
Root | \(0.731154 - 1.26640i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.226 |
Dual form | 475.2.l.b.351.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.253927 | − | 1.44009i | 0.179554 | − | 1.01830i | −0.753202 | − | 0.657789i | \(-0.771492\pi\) |
0.932755 | − | 0.360510i | \(-0.117397\pi\) | |||||||
\(3\) | −1.15700 | − | 0.970838i | −0.667994 | − | 0.560513i | 0.244477 | − | 0.969655i | \(-0.421384\pi\) |
−0.912471 | + | 0.409142i | \(0.865828\pi\) | |||||||
\(4\) | −0.130002 | − | 0.0473169i | −0.0650011 | − | 0.0236585i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.69189 | + | 1.41966i | −0.690711 | + | 0.579575i | ||||
\(7\) | 2.03586 | + | 3.52622i | 0.769484 | + | 1.33278i | 0.937843 | + | 0.347059i | \(0.112820\pi\) |
−0.168360 | + | 0.985726i | \(0.553847\pi\) | |||||||
\(8\) | 1.36116 | − | 2.35759i | 0.481241 | − | 0.833535i | ||||
\(9\) | −0.124823 | − | 0.707907i | −0.0416077 | − | 0.235969i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.310503 | − | 0.537807i | 0.0936201 | − | 0.162155i | −0.815412 | − | 0.578881i | \(-0.803489\pi\) |
0.909032 | + | 0.416727i | \(0.136823\pi\) | |||||||
\(12\) | 0.104475 | + | 0.180957i | 0.0301595 | + | 0.0522377i | ||||
\(13\) | 3.90168 | − | 3.27390i | 1.08213 | − | 0.908017i | 0.0860363 | − | 0.996292i | \(-0.472580\pi\) |
0.996096 | + | 0.0882750i | \(0.0281354\pi\) | |||||||
\(14\) | 5.59504 | − | 2.03643i | 1.49534 | − | 0.544258i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.26147 | − | 2.73670i | −0.815368 | − | 0.684175i | ||||
\(17\) | 0.0462744 | − | 0.262435i | 0.0112232 | − | 0.0636498i | −0.978682 | − | 0.205382i | \(-0.934156\pi\) |
0.989905 | + | 0.141733i | \(0.0452673\pi\) | |||||||
\(18\) | −1.05115 | −0.247758 | ||||||||
\(19\) | 0.399960 | − | 4.34051i | 0.0917571 | − | 0.995781i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.06789 | − | 6.05632i | 0.233033 | − | 1.32160i | ||||
\(22\) | −0.695646 | − | 0.583716i | −0.148312 | − | 0.124449i | ||||
\(23\) | −5.48944 | − | 1.99799i | −1.14463 | − | 0.416610i | −0.301045 | − | 0.953610i | \(-0.597335\pi\) |
−0.843582 | + | 0.537000i | \(0.819558\pi\) | |||||||
\(24\) | −3.86370 | + | 1.40627i | −0.788674 | + | 0.287054i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.72398 | − | 6.45012i | −0.730332 | − | 1.26497i | ||||
\(27\) | −2.80837 | + | 4.86425i | −0.540472 | + | 0.936125i | ||||
\(28\) | −0.0978169 | − | 0.554747i | −0.0184856 | − | 0.104837i | ||||
\(29\) | 0.708058 | + | 4.01560i | 0.131483 | + | 0.745678i | 0.977244 | + | 0.212116i | \(0.0680356\pi\) |
−0.845761 | + | 0.533561i | \(0.820853\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.24496 | + | 5.62043i | 0.582811 | + | 1.00946i | 0.995144 | + | 0.0984257i | \(0.0313807\pi\) |
−0.412333 | + | 0.911033i | \(0.635286\pi\) | |||||||
\(32\) | −0.598455 | + | 0.502163i | −0.105793 | + | 0.0887708i | ||||
\(33\) | −0.881374 | + | 0.320794i | −0.153428 | + | 0.0558431i | ||||
\(34\) | −0.366180 | − | 0.133279i | −0.0627994 | − | 0.0228571i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0172687 | + | 0.0979357i | −0.00287812 | + | 0.0163226i | ||||
\(37\) | 8.83927 | 1.45317 | 0.726584 | − | 0.687078i | \(-0.241107\pi\) | ||||
0.726584 | + | 0.687078i | \(0.241107\pi\) | |||||||
\(38\) | −6.14918 | − | 1.67815i | −0.997528 | − | 0.272232i | ||||
\(39\) | −7.69267 | −1.23181 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.43252 | − | 2.88022i | −0.536069 | − | 0.449815i | 0.334122 | − | 0.942530i | \(-0.391560\pi\) |
−0.870191 | + | 0.492714i | \(0.836005\pi\) | |||||||
\(42\) | −8.45050 | − | 3.07573i | −1.30394 | − | 0.474595i | ||||
\(43\) | −1.69213 | + | 0.615885i | −0.258047 | + | 0.0939215i | −0.467804 | − | 0.883832i | \(-0.654955\pi\) |
0.209757 | + | 0.977753i | \(0.432733\pi\) | |||||||
\(44\) | −0.0658134 | + | 0.0552240i | −0.00992175 | + | 0.00832533i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.27121 | + | 7.39795i | −0.629756 | + | 1.09077i | ||||
\(47\) | −2.00502 | − | 11.3711i | −0.292463 | − | 1.65864i | −0.677339 | − | 0.735671i | \(-0.736867\pi\) |
0.384877 | − | 0.922968i | \(-0.374244\pi\) | |||||||
\(48\) | 1.11663 | + | 6.33272i | 0.161172 | + | 0.914050i | ||||
\(49\) | −4.78947 | + | 8.29561i | −0.684210 | + | 1.18509i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.308321 | + | 0.258712i | −0.0431736 | + | 0.0362269i | ||||
\(52\) | −0.662139 | + | 0.240999i | −0.0918221 | + | 0.0334205i | ||||
\(53\) | −2.37077 | − | 0.862891i | −0.325651 | − | 0.118527i | 0.174021 | − | 0.984742i | \(-0.444324\pi\) |
−0.499672 | + | 0.866215i | \(0.666546\pi\) | |||||||
\(54\) | 6.29184 | + | 5.27948i | 0.856212 | + | 0.718447i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.0845 | 1.48123 | ||||||||
\(57\) | −4.67668 | + | 4.63367i | −0.619442 | + | 0.613745i | ||||
\(58\) | 5.96263 | 0.782931 | ||||||||
\(59\) | 0.154624 | − | 0.876916i | 0.0201303 | − | 0.114165i | −0.973087 | − | 0.230439i | \(-0.925984\pi\) |
0.993217 | + | 0.116274i | \(0.0370950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.03905 | − | 0.742153i | −0.261073 | − | 0.0950229i | 0.208167 | − | 0.978093i | \(-0.433250\pi\) |
−0.469241 | + | 0.883070i | \(0.655472\pi\) | |||||||
\(62\) | 8.91792 | − | 3.24586i | 1.13258 | − | 0.412224i | ||||
\(63\) | 2.24211 | − | 1.88135i | 0.282479 | − | 0.237028i | ||||
\(64\) | −3.68635 | − | 6.38495i | −0.460794 | − | 0.798119i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.238168 | + | 1.35072i | 0.0293165 | + | 0.166262i | ||||
\(67\) | 2.44476 | + | 13.8649i | 0.298674 | + | 1.69387i | 0.651881 | + | 0.758322i | \(0.273980\pi\) |
−0.353206 | + | 0.935546i | \(0.614909\pi\) | |||||||
\(68\) | −0.0184334 | + | 0.0319276i | −0.00223538 | + | 0.00387179i | ||||
\(69\) | 4.41155 | + | 7.64103i | 0.531088 | + | 0.919872i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.54737 | − | 0.563198i | 0.183639 | − | 0.0668393i | −0.248564 | − | 0.968616i | \(-0.579959\pi\) |
0.432203 | + | 0.901776i | \(0.357736\pi\) | |||||||
\(72\) | −1.83886 | − | 0.669290i | −0.216712 | − | 0.0788766i | ||||
\(73\) | −1.37639 | − | 1.15493i | −0.161095 | − | 0.135174i | 0.558677 | − | 0.829385i | \(-0.311309\pi\) |
−0.719772 | + | 0.694211i | \(0.755754\pi\) | |||||||
\(74\) | 2.24453 | − | 12.7294i | 0.260922 | − | 1.47976i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.257375 | + | 0.545351i | −0.0295230 | + | 0.0625561i | ||||
\(77\) | 2.52856 | 0.288157 | ||||||||
\(78\) | −1.95338 | + | 11.0782i | −0.221177 | + | 1.25435i | ||||
\(79\) | 3.94242 | + | 3.30809i | 0.443557 | + | 0.372189i | 0.837039 | − | 0.547144i | \(-0.184285\pi\) |
−0.393481 | + | 0.919333i | \(0.628729\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.94525 | − | 2.16389i | 0.660584 | − | 0.240433i | ||||
\(82\) | −5.01940 | + | 4.21177i | −0.554300 | + | 0.465113i | ||||
\(83\) | 6.89167 | + | 11.9367i | 0.756459 | + | 1.31023i | 0.944646 | + | 0.328092i | \(0.106406\pi\) |
−0.188187 | + | 0.982133i | \(0.560261\pi\) | |||||||
\(84\) | −0.425395 | + | 0.736806i | −0.0464144 | + | 0.0803921i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.457253 | + | 2.59321i | 0.0493069 | + | 0.279633i | ||||
\(87\) | 3.07927 | − | 5.33345i | 0.330132 | − | 0.571806i | ||||
\(88\) | −0.845286 | − | 1.46408i | −0.0901078 | − | 0.156071i | ||||
\(89\) | −0.000572418 | 0 | 0.000480315i | −6.06762e−5 | 0 | 5.09133e-5i | −0.642818 | − | 0.766019i | \(-0.722235\pi\) |
0.642757 | + | 0.766070i | \(0.277790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.4878 | + | 7.09297i | 2.04287 | + | 0.743545i | ||||
\(92\) | 0.619100 | + | 0.519487i | 0.0645457 | + | 0.0541603i | ||||
\(93\) | 1.70211 | − | 9.65316i | 0.176501 | − | 1.00099i | ||||
\(94\) | −16.8845 | −1.74150 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.17993 | 0.120426 | ||||||||
\(97\) | 1.80985 | − | 10.2642i | 0.183762 | − | 1.04217i | −0.743773 | − | 0.668432i | \(-0.766966\pi\) |
0.927535 | − | 0.373736i | \(-0.121923\pi\) | |||||||
\(98\) | 10.7303 | + | 9.00376i | 1.08392 | + | 0.909517i | ||||
\(99\) | −0.419475 | − | 0.152676i | −0.0421588 | − | 0.0153445i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.36086 | + | 7.85469i | −0.931440 | + | 0.781571i | −0.976075 | − | 0.217432i | \(-0.930232\pi\) |
0.0446350 | + | 0.999003i | \(0.485788\pi\) | |||||||
\(102\) | 0.294278 | + | 0.509705i | 0.0291379 | + | 0.0504683i | ||||
\(103\) | −3.90186 | + | 6.75822i | −0.384462 | + | 0.665908i | −0.991694 | − | 0.128617i | \(-0.958946\pi\) |
0.607232 | + | 0.794524i | \(0.292280\pi\) | |||||||
\(104\) | −2.40772 | − | 13.6549i | −0.236097 | − | 1.33897i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.84465 | + | 3.19502i | −0.179168 | + | 0.310328i | ||||
\(107\) | 2.85207 | + | 4.93993i | 0.275720 | + | 0.477561i | 0.970316 | − | 0.241839i | \(-0.0777505\pi\) |
−0.694597 | + | 0.719399i | \(0.744417\pi\) | |||||||
\(108\) | 0.595256 | − | 0.499479i | 0.0572786 | − | 0.0480624i | ||||
\(109\) | 6.32712 | − | 2.30288i | 0.606029 | − | 0.220576i | −0.0207361 | − | 0.999785i | \(-0.506601\pi\) |
0.626765 | + | 0.779209i | \(0.284379\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.2270 | − | 8.58150i | −0.970707 | − | 0.814520i | ||||
\(112\) | 3.01029 | − | 17.0722i | 0.284446 | − | 1.61317i | ||||
\(113\) | 4.78878 | 0.450490 | 0.225245 | − | 0.974302i | \(-0.427682\pi\) | ||||
0.225245 | + | 0.974302i | \(0.427682\pi\) | |||||||
\(114\) | 5.48538 | + | 7.91147i | 0.513753 | + | 0.740977i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.0979567 | − | 0.555540i | 0.00909505 | − | 0.0515806i | ||||
\(117\) | −2.80464 | − | 2.35337i | −0.259289 | − | 0.217569i | ||||
\(118\) | −1.22358 | − | 0.445346i | −0.112639 | − | 0.0409974i | ||||
\(119\) | 1.01961 | − | 0.371108i | 0.0934676 | − | 0.0340194i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.30718 | + | 9.19230i | 0.482471 | + | 0.835664i | ||||
\(122\) | −1.58654 | + | 2.74796i | −0.143638 | + | 0.248789i | ||||
\(123\) | 1.17519 | + | 6.66483i | 0.105963 | + | 0.600948i | ||||
\(124\) | −0.155910 | − | 0.884210i | −0.0140011 | − | 0.0794044i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.13999 | − | 3.70657i | −0.190646 | − | 0.330208i | ||||
\(127\) | −14.1693 | + | 11.8894i | −1.25732 | + | 1.05502i | −0.261356 | + | 0.965242i | \(0.584170\pi\) |
−0.995962 | + | 0.0897732i | \(0.971386\pi\) | |||||||
\(128\) | −11.5992 | + | 4.22177i | −1.02524 | + | 0.373155i | ||||
\(129\) | 2.55572 | + | 0.930204i | 0.225018 | + | 0.0818999i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.40080 | + | 19.2869i | −0.297129 | + | 1.68510i | 0.361291 | + | 0.932453i | \(0.382336\pi\) |
−0.658420 | + | 0.752650i | \(0.728775\pi\) | |||||||
\(132\) | 0.129760 | 0.0112941 | ||||||||
\(133\) | 16.1198 | − | 7.42634i | 1.39777 | − | 0.643945i | ||||
\(134\) | 20.5875 | 1.77849 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.555728 | − | 0.466311i | −0.0476533 | − | 0.0399858i | ||||
\(137\) | −2.21454 | − | 0.806027i | −0.189201 | − | 0.0688635i | 0.245682 | − | 0.969350i | \(-0.420988\pi\) |
−0.434883 | + | 0.900487i | \(0.643210\pi\) | |||||||
\(138\) | 12.1240 | − | 4.41278i | 1.03206 | − | 0.375640i | ||||
\(139\) | 2.93433 | − | 2.46220i | 0.248887 | − | 0.208841i | −0.509806 | − | 0.860289i | \(-0.670283\pi\) |
0.758693 | + | 0.651448i | \(0.225838\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.71964 | + | 15.1029i | −0.734326 | + | 1.27189i | ||||
\(142\) | −0.418137 | − | 2.37137i | −0.0350893 | − | 0.199001i | ||||
\(143\) | −0.549242 | − | 3.11491i | −0.0459299 | − | 0.260482i | ||||
\(144\) | −1.53022 | + | 2.65042i | −0.127519 | + | 0.220869i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.01271 | + | 1.68887i | −0.166573 | + | 0.139772i | ||||
\(147\) | 13.5951 | − | 4.94821i | 1.12130 | − | 0.408122i | ||||
\(148\) | −1.14913 | − | 0.418247i | −0.0944575 | − | 0.0343797i | ||||
\(149\) | 13.9310 | + | 11.6895i | 1.14127 | + | 0.957638i | 0.999480 | − | 0.0322585i | \(-0.0102700\pi\) |
0.141789 | + | 0.989897i | \(0.454714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.29340 | −0.186634 | −0.0933170 | − | 0.995636i | \(-0.529747\pi\) | ||||
−0.0933170 | + | 0.995636i | \(0.529747\pi\) | |||||||
\(152\) | −9.68875 | − | 6.85106i | −0.785861 | − | 0.555694i | ||||
\(153\) | −0.191556 | −0.0154863 | ||||||||
\(154\) | 0.642071 | − | 3.64137i | 0.0517396 | − | 0.293430i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00006 | + | 0.363994i | 0.0800693 | + | 0.0291428i | ||||
\(157\) | −19.5874 | + | 7.12925i | −1.56325 | + | 0.568976i | −0.971478 | − | 0.237130i | \(-0.923793\pi\) |
−0.591771 | + | 0.806106i | \(0.701571\pi\) | |||||||
\(158\) | 5.76504 | − | 4.83744i | 0.458642 | − | 0.384846i | ||||
\(159\) | 1.90526 | + | 3.30000i | 0.151097 | + | 0.261707i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.13039 | − | 23.4246i | −0.325520 | − | 1.84612i | ||||
\(162\) | −1.60655 | − | 9.11119i | −0.126222 | − | 0.715842i | ||||
\(163\) | −3.95845 | + | 6.85624i | −0.310050 | + | 0.537022i | −0.978373 | − | 0.206849i | \(-0.933679\pi\) |
0.668323 | + | 0.743871i | \(0.267012\pi\) | |||||||
\(164\) | 0.309952 | + | 0.536852i | 0.0242031 | + | 0.0419211i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.9400 | − | 6.89358i | 1.47003 | − | 0.535046i | ||||
\(167\) | 13.2435 | + | 4.82025i | 1.02482 | + | 0.373002i | 0.799105 | − | 0.601192i | \(-0.205307\pi\) |
0.225711 | + | 0.974194i | \(0.427530\pi\) | |||||||
\(168\) | −12.8248 | − | 10.7613i | −0.989452 | − | 0.830249i | ||||
\(169\) | 2.24728 | − | 12.7450i | 0.172868 | − | 0.980382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.12260 | + | 0.258662i | −0.238791 | + | 0.0197803i | ||||
\(172\) | 0.249122 | 0.0189954 | ||||||||
\(173\) | 1.82553 | − | 10.3531i | 0.138792 | − | 0.787130i | −0.833351 | − | 0.552744i | \(-0.813581\pi\) |
0.972144 | − | 0.234386i | \(-0.0753081\pi\) | |||||||
\(174\) | −6.89876 | − | 5.78874i | −0.522993 | − | 0.438843i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.48451 | + | 0.904289i | −0.187277 | + | 0.0681633i | ||||
\(177\) | −1.03024 | + | 0.864477i | −0.0774378 | + | 0.0649780i | ||||
\(178\) | 0.000546346 | 0 | 0.000946300i | 4.09504e−5 | 0 | 7.09282e-5i | ||||
\(179\) | −2.50164 | + | 4.33298i | −0.186982 | + | 0.323862i | −0.944243 | − | 0.329251i | \(-0.893204\pi\) |
0.757261 | + | 0.653113i | \(0.226537\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.60022 | − | 26.0891i | −0.341932 | − | 1.93919i | −0.343395 | − | 0.939191i | \(-0.611577\pi\) |
0.00146347 | − | 0.999999i | \(-0.499534\pi\) | |||||||
\(182\) | 15.1630 | − | 26.2631i | 1.12396 | − | 1.94675i | ||||
\(183\) | 1.63867 | + | 2.83825i | 0.121134 | + | 0.209810i | ||||
\(184\) | −12.1824 | + | 10.2223i | −0.898101 | + | 0.753596i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.4692 | − | 4.90240i | −0.987612 | − | 0.359461i | ||||
\(187\) | −0.126771 | − | 0.106373i | −0.00927041 | − | 0.00777879i | ||||
\(188\) | −0.277386 | + | 1.57313i | −0.0202305 | + | 0.114733i | ||||
\(189\) | −22.8699 | −1.66354 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.143815 | −0.0104061 | −0.00520303 | − | 0.999986i | \(-0.501656\pi\) | ||||
−0.00520303 | + | 0.999986i | \(0.501656\pi\) | |||||||
\(192\) | −1.93364 | + | 10.9662i | −0.139549 | + | 0.791420i | ||||
\(193\) | −1.57893 | − | 1.32488i | −0.113654 | − | 0.0953669i | 0.584190 | − | 0.811617i | \(-0.301412\pi\) |
−0.697843 | + | 0.716250i | \(0.745857\pi\) | |||||||
\(194\) | −14.3218 | − | 5.21270i | −1.02824 | − | 0.374250i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.01516 | − | 0.851824i | 0.0725118 | − | 0.0608446i | ||||
\(197\) | 9.12413 | + | 15.8035i | 0.650068 | + | 1.12595i | 0.983106 | + | 0.183037i | \(0.0585928\pi\) |
−0.333038 | + | 0.942913i | \(0.608074\pi\) | |||||||
\(198\) | −0.326384 | + | 0.565314i | −0.0231951 | + | 0.0401751i | ||||
\(199\) | 1.38971 | + | 7.88142i | 0.0985137 | + | 0.558699i | 0.993614 | + | 0.112834i | \(0.0359928\pi\) |
−0.895100 | + | 0.445865i | \(0.852896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6320 | − | 18.4151i | 0.749922 | − | 1.29890i | ||||
\(202\) | 8.93451 | + | 15.4750i | 0.628630 | + | 1.08882i | ||||
\(203\) | −12.7184 | + | 10.6720i | −0.892654 | + | 0.749026i | ||||
\(204\) | 0.0523239 | − | 0.0190443i | 0.00366341 | − | 0.00133337i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.74168 | + | 7.33514i | 0.609062 | + | 0.511063i | ||||
\(207\) | −0.729184 | + | 4.13541i | −0.0506818 | + | 0.287431i | ||||
\(208\) | −21.6849 | −1.50358 | ||||||||
\(209\) | −2.21017 | − | 1.56284i | −0.152880 | − | 0.108104i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.44545 | + | 13.8689i | −0.168352 | + | 0.954772i | 0.777189 | + | 0.629268i | \(0.216645\pi\) |
−0.945541 | + | 0.325504i | \(0.894466\pi\) | |||||||
\(212\) | 0.267377 | + | 0.224356i | 0.0183635 | + | 0.0154088i | ||||
\(213\) | −2.33708 | − | 0.850628i | −0.160134 | − | 0.0582841i | ||||
\(214\) | 7.83817 | − | 2.85286i | 0.535806 | − | 0.195018i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.64528 | + | 13.2420i | 0.520195 | + | 0.901004i | ||||
\(217\) | −13.2126 | + | 22.8848i | −0.896928 | + | 1.55352i | ||||
\(218\) | −1.70974 | − | 9.69641i | −0.115798 | − | 0.656724i | ||||
\(219\) | 0.471235 | + | 2.67251i | 0.0318431 | + | 0.180591i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.678638 | − | 1.17544i | −0.0456501 | − | 0.0790684i | ||||
\(222\) | −14.9551 | + | 12.5488i | −1.00372 | + | 0.842220i | ||||
\(223\) | 4.61022 | − | 1.67798i | 0.308723 | − | 0.112366i | −0.183012 | − | 0.983111i | \(-0.558585\pi\) |
0.491736 | + | 0.870744i | \(0.336363\pi\) | |||||||
\(224\) | −2.98911 | − | 1.08795i | −0.199718 | − | 0.0726915i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.21600 | − | 6.89629i | 0.0808872 | − | 0.458734i | ||||
\(227\) | −2.65246 | −0.176050 | −0.0880250 | − | 0.996118i | \(-0.528056\pi\) | ||||
−0.0880250 | + | 0.996118i | \(0.528056\pi\) | |||||||
\(228\) | 0.827231 | − | 0.381101i | 0.0547847 | − | 0.0252390i | ||||
\(229\) | −23.1372 | −1.52895 | −0.764473 | − | 0.644655i | \(-0.777001\pi\) | ||||
−0.764473 | + | 0.644655i | \(0.777001\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.92555 | − | 2.45482i | −0.192487 | − | 0.161516i | ||||
\(232\) | 10.4309 | + | 3.79654i | 0.684823 | + | 0.249255i | ||||
\(233\) | −27.1663 | + | 9.88772i | −1.77972 | + | 0.647766i | −0.779964 | + | 0.625824i | \(0.784763\pi\) |
−0.999759 | + | 0.0219420i | \(0.993015\pi\) | |||||||
\(234\) | −4.10124 | + | 3.44135i | −0.268107 | + | 0.224968i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.0615945 | + | 0.106685i | −0.00400946 | + | 0.00694458i | ||||
\(237\) | −1.34977 | − | 7.65490i | −0.0876767 | − | 0.497239i | ||||
\(238\) | −0.275523 | − | 1.56257i | −0.0178595 | − | 0.101286i | ||||
\(239\) | 10.3736 | − | 17.9677i | 0.671016 | − | 1.16223i | −0.306601 | − | 0.951838i | \(-0.599192\pi\) |
0.977616 | − | 0.210395i | \(-0.0674750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.74748 | − | 3.98361i | 0.305812 | − | 0.256607i | −0.476946 | − | 0.878932i | \(-0.658256\pi\) |
0.782759 | + | 0.622326i | \(0.213812\pi\) | |||||||
\(242\) | 14.5854 | − | 5.30865i | 0.937585 | − | 0.341253i | ||||
\(243\) | 6.85461 | + | 2.49487i | 0.439724 | + | 0.160046i | ||||
\(244\) | 0.229964 | + | 0.192963i | 0.0147220 | + | 0.0123532i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.89639 | 0.630971 | ||||||||
\(247\) | −12.6499 | − | 18.2447i | −0.804893 | − | 1.16088i | ||||
\(248\) | 17.6676 | 1.12189 | ||||||||
\(249\) | 3.61496 | − | 20.5015i | 0.229089 | − | 1.29923i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.32016 | − | 2.66432i | −0.462044 | − | 0.168170i | 0.100501 | − | 0.994937i | \(-0.467956\pi\) |
−0.562545 | + | 0.826767i | \(0.690178\pi\) | |||||||
\(252\) | −0.380499 | + | 0.138490i | −0.0239692 | + | 0.00872408i | ||||
\(253\) | −2.77902 | + | 2.33187i | −0.174715 | + | 0.146604i | ||||
\(254\) | 13.5239 | + | 23.4241i | 0.848565 | + | 1.46976i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.573868 | + | 3.25456i | 0.0358667 | + | 0.203410i | ||||
\(257\) | −3.50026 | − | 19.8510i | −0.218340 | − | 1.23827i | −0.875015 | − | 0.484096i | \(-0.839149\pi\) |
0.656675 | − | 0.754174i | \(-0.271962\pi\) | |||||||
\(258\) | 1.98855 | − | 3.44426i | 0.123801 | − | 0.214430i | ||||
\(259\) | 17.9955 | + | 31.1692i | 1.11819 | + | 1.93676i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.75429 | − | 1.00248i | 0.170486 | − | 0.0620518i | ||||
\(262\) | 26.9114 | + | 9.79493i | 1.66259 | + | 0.605133i | ||||
\(263\) | −8.18579 | − | 6.86869i | −0.504758 | − | 0.423542i | 0.354522 | − | 0.935048i | \(-0.384643\pi\) |
−0.859280 | + | 0.511506i | \(0.829088\pi\) | |||||||
\(264\) | −0.443387 | + | 2.51457i | −0.0272886 | + | 0.154761i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.60135 | − | 25.0998i | −0.404754 | − | 1.53897i | ||||
\(267\) | 0.00112860 | 6.90689e−5 | ||||||||
\(268\) | 0.338221 | − | 1.91815i | 0.0206601 | − | 0.117169i | ||||
\(269\) | −18.3284 | − | 15.3793i | −1.11750 | − | 0.937693i | −0.119024 | − | 0.992891i | \(-0.537977\pi\) |
−0.998475 | + | 0.0551980i | \(0.982421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.4040 | + | 8.88231i | −1.48243 | + | 0.539562i | −0.951446 | − | 0.307817i | \(-0.900402\pi\) |
−0.530989 | + | 0.847379i | \(0.678179\pi\) | |||||||
\(272\) | −0.869129 | + | 0.729285i | −0.0526987 | + | 0.0442194i | ||||
\(273\) | −15.6612 | − | 27.1260i | −0.947860 | − | 1.64174i | ||||
\(274\) | −1.72309 | + | 2.98447i | −0.104095 | + | 0.180299i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.211961 | − | 1.20209i | −0.0127586 | − | 0.0723574i | ||||
\(277\) | −0.916850 | + | 1.58803i | −0.0550882 | + | 0.0954156i | −0.892254 | − | 0.451533i | \(-0.850877\pi\) |
0.837166 | + | 0.546949i | \(0.184211\pi\) | |||||||
\(278\) | −2.80069 | − | 4.85093i | −0.167974 | − | 0.290940i | ||||
\(279\) | 3.57369 | − | 2.99869i | 0.213951 | − | 0.179527i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.8592 | + | 4.68035i | 0.767114 | + | 0.279207i | 0.695789 | − | 0.718247i | \(-0.255055\pi\) |
0.0713251 | + | 0.997453i | \(0.477277\pi\) | |||||||
\(282\) | 19.5354 | + | 16.3921i | 1.16331 | + | 0.976136i | ||||
\(283\) | −1.82961 | + | 10.3762i | −0.108759 | + | 0.616803i | 0.880893 | + | 0.473315i | \(0.156943\pi\) |
−0.989652 | + | 0.143488i | \(0.954168\pi\) | |||||||
\(284\) | −0.227811 | −0.0135181 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.62522 | −0.273495 | ||||||||
\(287\) | 3.16816 | − | 17.9675i | 0.187011 | − | 1.06059i | ||||
\(288\) | 0.430186 | + | 0.360969i | 0.0253489 | + | 0.0212703i | ||||
\(289\) | 15.9080 | + | 5.79005i | 0.935767 | + | 0.340591i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0588 | + | 10.1186i | −0.706901 | + | 0.593161i | ||||
\(292\) | 0.124286 | + | 0.215270i | 0.00727331 | + | 0.0125977i | ||||
\(293\) | 11.9521 | − | 20.7017i | 0.698251 | − | 1.20941i | −0.270822 | − | 0.962630i | \(-0.587295\pi\) |
0.969072 | − | 0.246776i | \(-0.0793713\pi\) | |||||||
\(294\) | −3.67372 | − | 20.8347i | −0.214256 | − | 1.21510i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.0316 | − | 20.8394i | 0.699325 | − | 1.21127i | ||||
\(297\) | 1.74402 | + | 3.02072i | 0.101198 | + | 0.175280i | ||||
\(298\) | 20.3714 | − | 17.0936i | 1.18008 | − | 0.990206i | ||||
\(299\) | −27.9593 | + | 10.1763i | −1.61693 | + | 0.588513i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.61668 | − | 4.71296i | −0.323740 | − | 0.271650i | ||||
\(302\) | −0.582356 | + | 3.30271i | −0.0335108 | + | 0.190049i | ||||
\(303\) | 18.4561 | 1.06028 | ||||||||
\(304\) | −13.1831 | + | 13.0619i | −0.756105 | + | 0.749151i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0486412 | + | 0.275858i | −0.00278063 | + | 0.0157697i | ||||
\(307\) | −12.0029 | − | 10.0716i | −0.685040 | − | 0.574817i | 0.232434 | − | 0.972612i | \(-0.425331\pi\) |
−0.917474 | + | 0.397795i | \(0.869775\pi\) | |||||||
\(308\) | −0.328719 | − | 0.119644i | −0.0187305 | − | 0.00681734i | ||||
\(309\) | 11.0756 | − | 4.03118i | 0.630068 | − | 0.229326i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.75605 | + | 3.04157i | 0.0995764 | + | 0.172471i | 0.911509 | − | 0.411279i | \(-0.134918\pi\) |
−0.811933 | + | 0.583751i | \(0.801585\pi\) | |||||||
\(312\) | −10.4709 | + | 18.1362i | −0.592800 | + | 1.02676i | ||||
\(313\) | −0.203702 | − | 1.15525i | −0.0115139 | − | 0.0652987i | 0.978509 | − | 0.206202i | \(-0.0661104\pi\) |
−0.990023 | + | 0.140903i | \(0.954999\pi\) | |||||||
\(314\) | 5.29299 | + | 30.0180i | 0.298701 | + | 1.69402i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.355995 | − | 0.616602i | −0.0200263 | − | 0.0346866i | ||||
\(317\) | 1.00475 | − | 0.843086i | 0.0564324 | − | 0.0473524i | −0.614135 | − | 0.789201i | \(-0.710495\pi\) |
0.670568 | + | 0.741848i | \(0.266051\pi\) | |||||||
\(318\) | 5.23610 | − | 1.90579i | 0.293626 | − | 0.106871i | ||||
\(319\) | 2.37947 | + | 0.866056i | 0.133225 | + | 0.0484898i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.49603 | − | 8.48439i | 0.0835000 | − | 0.473552i | ||||
\(322\) | −34.7824 | −1.93835 | ||||||||
\(323\) | −1.12059 | − | 0.305818i | −0.0623515 | − | 0.0170162i | ||||
\(324\) | −0.875285 | −0.0486270 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.86847 | + | 7.44153i | 0.491179 | + | 0.412148i | ||||
\(327\) | −9.55620 | − | 3.47817i | −0.528459 | − | 0.192343i | ||||
\(328\) | −11.4626 | + | 4.17204i | −0.632915 | + | 0.230362i | ||||
\(329\) | 36.0148 | − | 30.2200i | 1.98556 | − | 1.66609i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.36245 | − | 11.0201i | 0.349712 | − | 0.605718i | −0.636487 | − | 0.771288i | \(-0.719613\pi\) |
0.986198 | + | 0.165570i | \(0.0529462\pi\) | |||||||
\(332\) | −0.331123 | − | 1.87789i | −0.0181727 | − | 0.103063i | ||||
\(333\) | −1.10335 | − | 6.25738i | −0.0604629 | − | 0.342902i | ||||
\(334\) | 10.3045 | − | 17.8479i | 0.563837 | − | 0.976595i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −20.0572 | + | 16.8300i | −1.09421 | + | 0.918153i | ||||
\(337\) | 14.3017 | − | 5.20541i | 0.779066 | − | 0.283557i | 0.0782827 | − | 0.996931i | \(-0.475056\pi\) |
0.700783 | + | 0.713374i | \(0.252834\pi\) | |||||||
\(338\) | −17.7833 | − | 6.47258i | −0.967283 | − | 0.352062i | ||||
\(339\) | −5.54061 | − | 4.64913i | −0.300925 | − | 0.252506i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.03027 | 0.218251 | ||||||||
\(342\) | −0.420417 | + | 4.56251i | −0.0227335 | + | 0.246713i | ||||
\(343\) | −10.5007 | −0.566987 | ||||||||
\(344\) | −0.851248 | + | 4.82766i | −0.0458962 | + | 0.260290i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.4458 | − | 5.25786i | −0.776613 | − | 0.282664i | ||||
\(347\) | 18.8107 | − | 6.84652i | 1.00981 | − | 0.367541i | 0.216450 | − | 0.976294i | \(-0.430552\pi\) |
0.793360 | + | 0.608753i | \(0.208330\pi\) | |||||||
\(348\) | −0.652675 | + | 0.547659i | −0.0349870 | + | 0.0293576i | ||||
\(349\) | −11.1408 | − | 19.2964i | −0.596353 | − | 1.03291i | −0.993354 | − | 0.115095i | \(-0.963283\pi\) |
0.397002 | − | 0.917818i | \(-0.370051\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.96768 | + | 28.1731i | 0.265155 | + | 1.50377i | ||||
\(352\) | 0.0842448 | + | 0.477776i | 0.00449026 | + | 0.0254655i | ||||
\(353\) | −13.1075 | + | 22.7029i | −0.697642 | + | 1.20835i | 0.271640 | + | 0.962399i | \(0.412434\pi\) |
−0.969282 | + | 0.245952i | \(0.920899\pi\) | |||||||
\(354\) | 0.983319 | + | 1.70316i | 0.0522628 | + | 0.0905219i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.71426e−5 | 0 | 3.53570e-5i | 5.14855e−6 | 0 | 1.87392e-6i | ||||
\(357\) | −1.53997 | − | 0.560505i | −0.0815041 | − | 0.0296651i | ||||
\(358\) | 5.60465 | + | 4.70286i | 0.296215 | + | 0.248554i | ||||
\(359\) | 4.91047 | − | 27.8486i | 0.259164 | − | 1.46979i | −0.525988 | − | 0.850492i | \(-0.676304\pi\) |
0.785152 | − | 0.619303i | \(-0.212585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6801 | − | 3.47206i | −0.983161 | − | 0.182740i | ||||
\(362\) | −38.7389 | −2.03607 | ||||||||
\(363\) | 2.78383 | − | 15.7879i | 0.146113 | − | 0.828649i | ||||
\(364\) | −2.19784 | − | 1.84420i | −0.115198 | − | 0.0966626i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.50345 | − | 1.63912i | 0.235399 | − | 0.0856783i | ||||
\(367\) | 7.35010 | − | 6.16747i | 0.383672 | − | 0.321939i | −0.430470 | − | 0.902605i | \(-0.641652\pi\) |
0.814142 | + | 0.580666i | \(0.197208\pi\) | |||||||
\(368\) | 12.4358 | + | 21.5394i | 0.648258 | + | 1.12282i | ||||
\(369\) | −1.61047 | + | 2.78942i | −0.0838378 | + | 0.145211i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.78383 | − | 10.1166i | −0.0926117 | − | 0.525227i | ||||
\(372\) | −0.678036 | + | 1.17439i | −0.0351545 | + | 0.0608895i | ||||
\(373\) | 6.52003 | + | 11.2930i | 0.337595 | + | 0.584731i | 0.983980 | − | 0.178280i | \(-0.0570534\pi\) |
−0.646385 | + | 0.763011i | \(0.723720\pi\) | |||||||
\(374\) | −0.185378 | + | 0.155551i | −0.00958568 | + | 0.00804334i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −29.5375 | − | 10.7508i | −1.52328 | − | 0.554428i | ||||
\(377\) | 15.9093 | + | 13.3495i | 0.819370 | + | 0.687533i | ||||
\(378\) | −5.80728 | + | 32.9347i | −0.298694 | + | 1.69398i | ||||
\(379\) | 9.93895 | 0.510530 | 0.255265 | − | 0.966871i | \(-0.417837\pi\) | ||||
0.255265 | + | 0.966871i | \(0.417837\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.9365 | 1.43123 | ||||||||
\(382\) | −0.0365184 | + | 0.207106i | −0.00186845 | + | 0.0105965i | ||||
\(383\) | 13.8106 | + | 11.5885i | 0.705689 | + | 0.592144i | 0.923386 | − | 0.383873i | \(-0.125410\pi\) |
−0.217697 | + | 0.976017i | \(0.569854\pi\) | |||||||
\(384\) | 17.5189 | + | 6.37637i | 0.894009 | + | 0.325393i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.30888 | + | 1.93738i | −0.117519 | + | 0.0986102i | ||||
\(387\) | 0.647205 | + | 1.12099i | 0.0328993 | + | 0.0569833i | ||||
\(388\) | −0.720954 | + | 1.24873i | −0.0366009 | + | 0.0633946i | ||||
\(389\) | 4.22852 | + | 23.9811i | 0.214395 | + | 1.21589i | 0.881954 | + | 0.471336i | \(0.156228\pi\) |
−0.667559 | + | 0.744557i | \(0.732661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.778363 | + | 1.34816i | −0.0393635 | + | 0.0681796i | ||||
\(392\) | 13.0384 | + | 22.5832i | 0.658541 | + | 1.14063i | ||||
\(393\) | 22.6592 | − | 19.0133i | 1.14300 | − | 0.959094i | ||||
\(394\) | 25.0753 | − | 9.12667i | 1.26328 | − | 0.459795i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0473085 | + | 0.0396965i | 0.00237734 | + | 0.00199483i | ||||
\(397\) | 3.46808 | − | 19.6684i | 0.174058 | − | 0.987131i | −0.765168 | − | 0.643831i | \(-0.777344\pi\) |
0.939226 | − | 0.343300i | \(-0.111545\pi\) | |||||||
\(398\) | 11.7029 | 0.586611 | ||||||||
\(399\) | −25.8604 | − | 7.05749i | −1.29464 | − | 0.353316i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.84848 | + | 16.1545i | −0.142246 | + | 0.806718i | 0.827291 | + | 0.561774i | \(0.189881\pi\) |
−0.969537 | + | 0.244944i | \(0.921230\pi\) | |||||||
\(402\) | −23.8198 | − | 19.9871i | −1.18802 | − | 0.996868i | ||||
\(403\) | 31.0615 | + | 11.3055i | 1.54728 | + | 0.563166i | ||||
\(404\) | 1.58859 | − | 0.578201i | 0.0790355 | − | 0.0287666i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.1391 | + | 21.0255i | 0.602453 | + | 1.04348i | ||||
\(407\) | 2.74462 | − | 4.75382i | 0.136046 | − | 0.235638i | ||||
\(408\) | 0.190264 | + | 1.07904i | 0.00941949 | + | 0.0534206i | ||||
\(409\) | 1.44702 | + | 8.20643i | 0.0715503 | + | 0.405782i | 0.999456 | + | 0.0329680i | \(0.0104960\pi\) |
−0.927906 | + | 0.372814i | \(0.878393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.77970 | + | 3.08253i | 0.0877862 | + | 0.152050i | ||||
\(412\) | 0.827029 | − | 0.693960i | 0.0407448 | − | 0.0341890i | ||||
\(413\) | 3.40699 | − | 1.24004i | 0.167647 | − | 0.0610185i | ||||
\(414\) | 5.77021 | + | 2.10018i | 0.283590 | + | 0.103218i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.690949 | + | 3.91856i | −0.0338765 | + | 0.192123i | ||||
\(417\) | −5.78542 | −0.283313 | ||||||||
\(418\) | −2.81186 | + | 2.78600i | −0.137532 | + | 0.136268i | ||||
\(419\) | −11.6553 | −0.569397 | −0.284698 | − | 0.958617i | \(-0.591893\pi\) | ||||
−0.284698 | + | 0.958617i | \(0.591893\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2337 | + | 13.6217i | 0.791182 | + | 0.663881i | 0.946038 | − | 0.324056i | \(-0.105047\pi\) |
−0.154855 | + | 0.987937i | \(0.549491\pi\) | |||||||
\(422\) | 19.3515 | + | 7.04336i | 0.942015 | + | 0.342866i | ||||
\(423\) | −7.79937 | + | 2.83874i | −0.379218 | + | 0.138024i | ||||
\(424\) | −5.26134 | + | 4.41479i | −0.255513 | + | 0.214401i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.81843 | + | 3.14962i | −0.0881033 | + | 0.152599i | ||||
\(427\) | −1.53423 | − | 8.70105i | −0.0742465 | − | 0.421073i | ||||
\(428\) | −0.137033 | − | 0.777153i | −0.00662374 | − | 0.0375651i | ||||
\(429\) | −2.38860 | + | 4.13717i | −0.115322 | + | 0.199744i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.300492 | − | 0.252142i | 0.0144742 | − | 0.0121453i | −0.635522 | − | 0.772083i | \(-0.719215\pi\) |
0.649996 | + | 0.759938i | \(0.274771\pi\) | |||||||
\(432\) | 22.4714 | − | 8.17893i | 1.08116 | − | 0.393509i | ||||
\(433\) | 12.1889 | + | 4.43639i | 0.585761 | + | 0.213199i | 0.617864 | − | 0.786285i | \(-0.287998\pi\) |
−0.0321031 | + | 0.999485i | \(0.510220\pi\) | |||||||
\(434\) | 29.6013 | + | 24.8384i | 1.42091 | + | 1.19228i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.931506 | −0.0446110 | ||||||||
\(437\) | −10.8679 | + | 23.0278i | −0.519880 | + | 1.10157i | ||||
\(438\) | 3.96832 | 0.189614 | ||||||||
\(439\) | −0.946035 | + | 5.36523i | −0.0451518 | + | 0.256068i | −0.999025 | − | 0.0441401i | \(-0.985945\pi\) |
0.953874 | + | 0.300209i | \(0.0970563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.47035 | + | 2.35502i | 0.308112 | + | 0.112144i | ||||
\(442\) | −1.86506 | + | 0.678827i | −0.0887119 | + | 0.0322885i | ||||
\(443\) | −18.9540 | + | 15.9043i | −0.900532 | + | 0.755636i | −0.970294 | − | 0.241928i | \(-0.922220\pi\) |
0.0697627 | + | 0.997564i | \(0.477776\pi\) | |||||||
\(444\) | 0.923487 | + | 1.59953i | 0.0438267 | + | 0.0759102i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.24579 | − | 7.06523i | −0.0589899 | − | 0.334549i | ||||
\(447\) | −4.76954 | − | 27.0494i | −0.225591 | − | 1.27939i | ||||
\(448\) | 15.0098 | − | 25.9978i | 0.709147 | − | 1.22828i | ||||
\(449\) | −17.2809 | − | 29.9315i | −0.815538 | − | 1.41255i | −0.908941 | − | 0.416925i | \(-0.863108\pi\) |
0.0934033 | − | 0.995628i | \(-0.470225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.61481 | + | 0.951713i | −0.123127 | + | 0.0448144i | ||||
\(452\) | −0.622552 | − | 0.226590i | −0.0292824 | − | 0.0106579i | ||||
\(453\) | 2.65346 | + | 2.22652i | 0.124670 | + | 0.104611i | ||||
\(454\) | −0.673532 | + | 3.81979i | −0.0316104 | + | 0.179272i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.55861 | + | 17.3329i | 0.213476 | + | 0.811686i | ||||
\(457\) | 11.6425 | 0.544613 | 0.272307 | − | 0.962211i | \(-0.412214\pi\) | ||||
0.272307 | + | 0.962211i | \(0.412214\pi\) | |||||||
\(458\) | −5.87515 | + | 33.3197i | −0.274528 | + | 1.55693i | ||||
\(459\) | 1.14659 | + | 0.962106i | 0.0535184 | + | 0.0449072i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.80943 | + | 1.02255i | −0.130848 | + | 0.0476248i | −0.406614 | − | 0.913600i | \(-0.633291\pi\) |
0.275766 | + | 0.961225i | \(0.411068\pi\) | |||||||
\(462\) | −4.27805 | + | 3.58971i | −0.199033 | + | 0.167008i | ||||
\(463\) | −4.24358 | − | 7.35009i | −0.197216 | − | 0.341588i | 0.750409 | − | 0.660974i | \(-0.229857\pi\) |
−0.947625 | + | 0.319386i | \(0.896523\pi\) | |||||||
\(464\) | 8.68018 | − | 15.0345i | 0.402967 | − | 0.697960i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.34098 | + | 41.6327i | 0.340064 | + | 1.92860i | ||||
\(467\) | 8.96512 | − | 15.5280i | 0.414856 | − | 0.718552i | −0.580557 | − | 0.814219i | \(-0.697165\pi\) |
0.995413 | + | 0.0956676i | \(0.0304986\pi\) | |||||||
\(468\) | 0.253255 | + | 0.438650i | 0.0117067 | + | 0.0202766i | ||||
\(469\) | −43.9135 | + | 36.8478i | −2.02774 | + | 1.70147i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.5840 | + | 10.7677i | 1.36316 | + | 0.496149i | ||||
\(472\) | −1.85694 | − | 1.55816i | −0.0854727 | − | 0.0717201i | ||||
\(473\) | −0.194184 | + | 1.10127i | −0.00892859 | + | 0.0506365i | ||||
\(474\) | −11.3665 | −0.522081 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.150111 | −0.00688034 | ||||||||
\(477\) | −0.314919 | + | 1.78599i | −0.0144192 | + | 0.0817751i | ||||
\(478\) | −23.2410 | − | 19.5015i | −1.06302 | − | 0.891978i | ||||
\(479\) | −3.18514 | − | 1.15929i | −0.145533 | − | 0.0529695i | 0.268227 | − | 0.963356i | \(-0.413562\pi\) |
−0.413759 | + | 0.910386i | \(0.635785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.4881 | − | 28.9389i | 1.57252 | − | 1.31950i | ||||
\(482\) | −4.53125 | − | 7.84836i | −0.206393 | − | 0.357483i | ||||
\(483\) | −17.9626 | + | 31.1122i | −0.817327 | + | 1.41565i | ||||
\(484\) | −0.254993 | − | 1.44614i | −0.0115906 | − | 0.0657336i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.33342 | − | 9.23776i | 0.241929 | − | 0.419033i | ||||
\(487\) | −5.58098 | − | 9.66655i | −0.252899 | − | 0.438033i | 0.711424 | − | 0.702763i | \(-0.248051\pi\) |
−0.964323 | + | 0.264730i | \(0.914717\pi\) | |||||||
\(488\) | −4.52516 | + | 3.79706i | −0.204844 | + | 0.171885i | ||||
\(489\) | 11.2362 | − | 4.08965i | 0.508120 | − | 0.184940i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6060 | + | 14.7732i | 0.794547 | + | 0.666704i | 0.946866 | − | 0.321627i | \(-0.104230\pi\) |
−0.152320 | + | 0.988331i | \(0.548674\pi\) | |||||||
\(492\) | 0.162582 | − | 0.922050i | 0.00732977 | − | 0.0415692i | ||||
\(493\) | 1.08660 | 0.0489379 | ||||||||
\(494\) | −29.4862 | + | 13.5842i | −1.32665 | + | 0.611181i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.79810 | − | 27.2114i | 0.215441 | − | 1.22183i | ||||
\(497\) | 5.13620 | + | 4.30978i | 0.230390 | + | 0.193320i | ||||
\(498\) | −28.6061 | − | 10.4118i | −1.28187 | − | 0.466562i | ||||
\(499\) | −0.921587 | + | 0.335430i | −0.0412559 | + | 0.0150159i | −0.362566 | − | 0.931958i | \(-0.618099\pi\) |
0.321310 | + | 0.946974i | \(0.395877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6431 | − | 18.4343i | −0.475498 | − | 0.823586i | ||||
\(502\) | −5.69566 | + | 9.86516i | −0.254210 | + | 0.440304i | ||||
\(503\) | −0.620262 | − | 3.51768i | −0.0276561 | − | 0.156846i | 0.967852 | − | 0.251520i | \(-0.0809303\pi\) |
−0.995508 | + | 0.0946739i | \(0.969819\pi\) | |||||||
\(504\) | −1.38360 | − | 7.84680i | −0.0616305 | − | 0.349524i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.65245 | + | 4.59417i | 0.117916 | + | 0.204236i | ||||
\(507\) | −14.9734 | + | 12.5642i | −0.664991 | + | 0.557994i | ||||
\(508\) | 2.40461 | − | 0.875205i | 0.106687 | − | 0.0388310i | ||||
\(509\) | 12.2069 | + | 4.44293i | 0.541059 | + | 0.196929i | 0.598070 | − | 0.801444i | \(-0.295935\pi\) |
−0.0570105 | + | 0.998374i | \(0.518157\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.27039 | − | 7.20474i | 0.0561988 | − | 0.318719i | ||||
\(512\) | −19.8547 | −0.877460 | ||||||||
\(513\) | 19.9901 | + | 14.1353i | 0.882584 | + | 0.624088i | ||||
\(514\) | −29.4761 | −1.30013 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.288234 | − | 0.241857i | −0.0126888 | − | 0.0106472i | ||||
\(517\) | −6.73799 | − | 2.45243i | −0.296337 | − | 0.107858i | ||||
\(518\) | 49.4561 | − | 18.0005i | 2.17298 | − | 0.790898i | ||||
\(519\) | −12.1633 | + | 10.2062i | −0.533909 | + | 0.448003i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4598 | + | 19.8490i | −0.502064 | + | 0.869601i | 0.497933 | + | 0.867216i | \(0.334093\pi\) |
−0.999997 | + | 0.00238537i | \(0.999241\pi\) | |||||||
\(522\) | −0.744273 | − | 4.22098i | −0.0325760 | − | 0.184747i | ||||
\(523\) | −0.342497 | − | 1.94240i | −0.0149764 | − | 0.0849352i | 0.976403 | − | 0.215954i | \(-0.0692862\pi\) |
−0.991380 | + | 0.131019i | \(0.958175\pi\) | |||||||
\(524\) | 1.35471 | − | 2.34642i | 0.0591807 | − | 0.102504i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.9702 | + | 10.0441i | −0.521923 | + | 0.437946i | ||||
\(527\) | 1.62515 | − | 0.591508i | 0.0707929 | − | 0.0257665i | ||||
\(528\) | 3.75250 | + | 1.36580i | 0.163306 | + | 0.0594387i | ||||
\(529\) | 8.52294 | + | 7.15159i | 0.370563 | + | 0.310939i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.640075 | −0.0277769 | ||||||||
\(532\) | −2.44701 | + | 0.202699i | −0.106091 | + | 0.00878810i | ||||
\(533\) | −22.8222 | −0.988538 | ||||||||
\(534\) | 0.000286581 | − | 0.00162528i | 1.24016e−5 | − | 7.03328e-5i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 36.0155 | + | 13.1086i | 1.55563 | + | 0.566204i | ||||
\(537\) | 7.10102 | − | 2.58456i | 0.306431 | − | 0.111532i | ||||
\(538\) | −26.8017 | + | 22.4893i | −1.15550 | + | 0.969583i | ||||
\(539\) | 2.97429 | + | 5.15162i | 0.128112 | + | 0.221896i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.78002 | − | 27.1088i | −0.205509 | − | 1.16550i | −0.896637 | − | 0.442767i | \(-0.853997\pi\) |
0.691128 | − | 0.722733i | \(-0.257114\pi\) | |||||||
\(542\) | 6.59452 | + | 37.3994i | 0.283259 | + | 1.60644i | ||||
\(543\) | −20.0059 | + | 34.6512i | −0.858534 | + | 1.48702i | ||||
\(544\) | 0.104092 | + | 0.180293i | 0.00446291 | + | 0.00772999i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −43.0408 | + | 15.6656i | −1.84198 | + | 0.670425i | ||||
\(547\) | 7.84310 | + | 2.85466i | 0.335347 | + | 0.122056i | 0.504205 | − | 0.863584i | \(-0.331786\pi\) |
−0.168858 | + | 0.985640i | \(0.554008\pi\) | |||||||
\(548\) | 0.249757 | + | 0.209571i | 0.0106691 | + | 0.00895241i | ||||
\(549\) | −0.270855 | + | 1.53609i | −0.0115598 | + | 0.0655589i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.7129 | − | 1.46726i | 0.754597 | − | 0.0625072i | ||||
\(552\) | 24.0192 | 1.02233 | ||||||||
\(553\) | −3.63880 | + | 20.6366i | −0.154737 | + | 0.877559i | ||||
\(554\) | 2.05410 | + | 1.72359i | 0.0872703 | + | 0.0732285i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.497974 | + | 0.181248i | −0.0211188 | + | 0.00768661i | ||||
\(557\) | −18.2574 | + | 15.3198i | −0.773591 | + | 0.649120i | −0.941626 | − | 0.336661i | \(-0.890702\pi\) |
0.168035 | + | 0.985781i | \(0.446258\pi\) | |||||||
\(558\) | −3.41093 | − | 5.90790i | −0.144396 | − | 0.250101i | ||||
\(559\) | −4.58581 | + | 7.94285i | −0.193959 | + | 0.335947i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0434025 | + | 0.246148i | 0.00183246 | + | 0.0103924i | ||||
\(562\) | 10.0054 | − | 17.3299i | 0.422054 | − | 0.731019i | ||||
\(563\) | −9.81371 | − | 16.9979i | −0.413599 | − | 0.716374i | 0.581681 | − | 0.813417i | \(-0.302395\pi\) |
−0.995280 | + | 0.0970426i | \(0.969062\pi\) | |||||||
\(564\) | 1.84819 | − | 1.55082i | 0.0778230 | − | 0.0653012i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.4782 | + | 5.26962i | 0.608562 | + | 0.221499i | ||||
\(567\) | 19.7341 | + | 16.5589i | 0.828753 | + | 0.695407i | ||||
\(568\) | 0.778426 | − | 4.41467i | 0.0326620 | − | 0.185236i | ||||
\(569\) | 23.7705 | 0.996510 | 0.498255 | − | 0.867030i | \(-0.333974\pi\) | ||||
0.498255 | + | 0.867030i | \(0.333974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5361 | −0.733865 | −0.366933 | − | 0.930248i | \(-0.619592\pi\) | ||||
−0.366933 | + | 0.930248i | \(0.619592\pi\) | |||||||
\(572\) | −0.0759852 | + | 0.430933i | −0.00317710 | + | 0.0180182i | ||||
\(573\) | 0.166393 | + | 0.139621i | 0.00695118 | + | 0.00583273i | ||||
\(574\) | −25.0704 | − | 9.12489i | −1.04642 | − | 0.380866i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.05981 | + | 3.40658i | −0.169159 | + | 0.141941i | ||||
\(577\) | −12.9640 | − | 22.4543i | −0.539699 | − | 0.934786i | −0.998920 | − | 0.0464636i | \(-0.985205\pi\) |
0.459221 | − | 0.888322i | \(-0.348128\pi\) | |||||||
\(578\) | 12.3777 | − | 21.4388i | 0.514844 | − | 0.891737i | ||||
\(579\) | 0.540578 | + | 3.06577i | 0.0224656 | + | 0.127409i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.0610 | + | 48.6030i | −1.16417 | + | 2.01639i | ||||
\(582\) | 11.5096 | + | 19.9352i | 0.477088 | + | 0.826341i | ||||
\(583\) | −1.20020 | + | 1.00709i | −0.0497072 | + | 0.0417093i | ||||
\(584\) | −4.59634 | + | 1.67293i | −0.190198 | + | 0.0692264i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.7774 | − | 22.4689i | −1.10616 | − | 0.928182i | ||||
\(587\) | 0.701894 | − | 3.98064i | 0.0289703 | − | 0.164299i | −0.966890 | − | 0.255192i | \(-0.917861\pi\) |
0.995861 | + | 0.0908937i | \(0.0289723\pi\) | |||||||
\(588\) | −2.00153 | −0.0825416 | ||||||||
\(589\) | 25.6934 | − | 11.8368i | 1.05868 | − | 0.487728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.78598 | − | 27.1426i | 0.196869 | − | 1.11650i | ||||
\(592\) | −28.8291 | − | 24.1905i | −1.18487 | − | 0.994221i | ||||
\(593\) | 17.7190 | + | 6.44918i | 0.727631 | + | 0.264836i | 0.679162 | − | 0.733988i | \(-0.262343\pi\) |
0.0484695 | + | 0.998825i | \(0.484566\pi\) | |||||||
\(594\) | 4.79298 | − | 1.74450i | 0.196658 | − | 0.0715777i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.25795 | − | 2.17883i | −0.0515275 | − | 0.0892482i | ||||
\(597\) | 6.04369 | − | 10.4680i | 0.247352 | − | 0.428426i | ||||
\(598\) | 7.55526 | + | 42.8480i | 0.308958 | + | 1.75219i | ||||
\(599\) | −6.74122 | − | 38.2313i | −0.275439 | − | 1.56209i | −0.737565 | − | 0.675276i | \(-0.764024\pi\) |
0.462126 | − | 0.886814i | \(-0.347087\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.179210 | − | 0.310400i | −0.00731011 | − | 0.0126615i | 0.862347 | − | 0.506317i | \(-0.168994\pi\) |
−0.869657 | + | 0.493656i | \(0.835660\pi\) | |||||||
\(602\) | −8.21332 | + | 6.89180i | −0.334750 | + | 0.280889i | ||||
\(603\) | 9.50989 | − | 3.46132i | 0.387273 | − | 0.140956i | ||||
\(604\) | 0.298147 | + | 0.108517i | 0.0121314 | + | 0.00441548i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.68652 | − | 26.5785i | 0.190377 | − | 1.07968i | ||||
\(607\) | −4.56885 | −0.185444 | −0.0927219 | − | 0.995692i | \(-0.529557\pi\) | ||||
−0.0927219 | + | 0.995692i | \(0.529557\pi\) | |||||||
\(608\) | 1.94029 | + | 2.79844i | 0.0786890 | + | 0.113492i | ||||
\(609\) | 25.0759 | 1.01613 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.0507 | − | 37.8020i | −1.82256 | − | 1.52931i | ||||
\(612\) | 0.0249026 | + | 0.00906382i | 0.00100663 | + | 0.000366383i | ||||
\(613\) | 15.8739 | − | 5.77762i | 0.641140 | − | 0.233356i | −0.000932984 | − | 1.00000i | \(-0.500297\pi\) |
0.642073 | + | 0.766644i | \(0.278075\pi\) | |||||||
\(614\) | −17.5519 | + | 14.7278i | −0.708337 | + | 0.594365i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.44177 | − | 5.96132i | 0.138673 | − | 0.240188i | ||||
\(617\) | −4.23101 | − | 23.9952i | −0.170334 | − | 0.966011i | −0.943393 | − | 0.331677i | \(-0.892385\pi\) |
0.773059 | − | 0.634334i | \(-0.218726\pi\) | |||||||
\(618\) | −2.99289 | − | 16.9735i | −0.120392 | − | 0.682774i | ||||
\(619\) | 16.6616 | − | 28.8588i | 0.669687 | − | 1.15993i | −0.308305 | − | 0.951288i | \(-0.599762\pi\) |
0.977992 | − | 0.208644i | \(-0.0669049\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.1351 | − | 21.0909i | 1.00864 | − | 0.846348i | ||||
\(622\) | 4.82605 | − | 1.75654i | 0.193507 | − | 0.0704307i | ||||
\(623\) | −0.00285906 | − | 0.00104061i | −0.000114546 | − | 4.16913e-5i | ||||
\(624\) | 25.0894 | + | 21.0525i | 1.00438 | + | 0.842776i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.71540 | −0.0685610 | ||||||||
\(627\) | 1.03990 | + | 3.95392i | 0.0415294 | + | 0.157904i | ||||
\(628\) | 2.88375 | 0.115074 | ||||||||
\(629\) | 0.409032 | − | 2.31973i | 0.0163092 | − | 0.0924939i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.2681 | − | 12.8365i | −1.40400 | − | 0.511014i | −0.474637 | − | 0.880181i | \(-0.657421\pi\) |
−0.929363 | + | 0.369167i | \(0.879643\pi\) | |||||||
\(632\) | 13.1654 | − | 4.79180i | 0.523690 | − | 0.190608i | ||||
\(633\) | 16.2938 | − | 13.6721i | 0.647621 | − | 0.543418i | ||||
\(634\) | −0.958988 | − | 1.66102i | −0.0380863 | − | 0.0659674i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0915416 | − | 0.519158i | −0.00362986 | − | 0.0205860i | ||||
\(637\) | 8.47200 | + | 48.0471i | 0.335673 | + | 1.90370i | ||||
\(638\) | 1.85141 | − | 3.20674i | 0.0732981 | − | 0.126956i | ||||
\(639\) | −0.591839 | − | 1.02510i | −0.0234128 | − | 0.0405522i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.62106 | − | 2.40987i | 0.261516 | − | 0.0951841i | −0.207935 | − | 0.978143i | \(-0.566674\pi\) |
0.469451 | + | 0.882959i | \(0.344452\pi\) | |||||||
\(642\) | −11.8384 | − | 4.30883i | −0.467225 | − | 0.170056i | ||||
\(643\) | −11.7063 | − | 9.82279i | −0.461653 | − | 0.387373i | 0.382086 | − | 0.924127i | \(-0.375206\pi\) |
−0.843739 | + | 0.536754i | \(0.819650\pi\) | |||||||
\(644\) | −0.571420 | + | 3.24069i | −0.0225171 | + | 0.127701i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.724955 | + | 1.53610i | −0.0285230 | + | 0.0604372i | ||||
\(647\) | −23.8972 | −0.939495 | −0.469748 | − | 0.882801i | \(-0.655655\pi\) | ||||
−0.469748 | + | 0.882801i | \(0.655655\pi\) | |||||||
\(648\) | 2.99084 | − | 16.9619i | 0.117491 | − | 0.666326i | ||||
\(649\) | −0.423600 | − | 0.355443i | −0.0166278 | − | 0.0139523i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.5044 | − | 13.6505i | 1.46991 | − | 0.535005i | ||||
\(652\) | 0.839024 | − | 0.704025i | 0.0328587 | − | 0.0275718i | ||||
\(653\) | −13.5704 | − | 23.5046i | −0.531050 | − | 0.919805i | −0.999343 | − | 0.0362323i | \(-0.988464\pi\) |
0.468294 | − | 0.883573i | \(-0.344869\pi\) | |||||||
\(654\) | −7.43547 | + | 12.8786i | −0.290750 | + | 0.503594i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.31275 | + | 18.7875i | 0.129341 | + | 0.733530i | ||||
\(657\) | −0.645778 | + | 1.11852i | −0.0251942 | + | 0.0436376i | ||||
\(658\) | −34.3745 | − | 59.5384i | −1.34006 | − | 2.32105i | ||||
\(659\) | −35.1081 | + | 29.4592i | −1.36762 | + | 1.14757i | −0.394073 | + | 0.919079i | \(0.628934\pi\) |
−0.973546 | + | 0.228490i | \(0.926621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.2794 | − | 6.28920i | −0.672092 | − | 0.244622i | −0.0166438 | − | 0.999861i | \(-0.505298\pi\) |
−0.655448 | + | 0.755240i | \(0.727520\pi\) | |||||||
\(662\) | −14.2543 | − | 11.9608i | −0.554010 | − | 0.464870i | ||||
\(663\) | −0.355973 | + | 2.01883i | −0.0138249 | + | 0.0784047i | ||||
\(664\) | 37.5226 | 1.45616 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.29138 | −0.360034 | ||||||||
\(667\) | 4.13629 | − | 23.4581i | 0.160158 | − | 0.908300i | ||||
\(668\) | −1.49361 | − | 1.25329i | −0.0577895 | − | 0.0484911i | ||||
\(669\) | −6.96308 | − | 2.53435i | −0.269208 | − | 0.0979837i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.03226 | + | 0.866173i | −0.0398501 | + | 0.0334382i | ||||
\(672\) | 2.40218 | + | 4.16069i | 0.0926660 | + | 0.160502i | ||||
\(673\) | −2.90989 | + | 5.04007i | −0.112168 | + | 0.194280i | −0.916644 | − | 0.399704i | \(-0.869113\pi\) |
0.804476 | + | 0.593985i | \(0.202446\pi\) | |||||||
\(674\) | −3.86467 | − | 21.9176i | −0.148862 | − | 0.844236i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.895204 | + | 1.55054i | −0.0344309 | + | 0.0596361i | ||||
\(677\) | 8.94182 | + | 15.4877i | 0.343662 | + | 0.595240i | 0.985110 | − | 0.171926i | \(-0.0549992\pi\) |
−0.641448 | + | 0.767167i | \(0.721666\pi\) | |||||||
\(678\) | −8.10209 | + | 6.79846i | −0.311159 | + | 0.261093i | ||||
\(679\) | 39.8783 | − | 14.5145i | 1.53039 | − | 0.557016i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.06890 | + | 2.57511i | 0.117600 | + | 0.0986784i | ||||
\(682\) | 1.02340 | − | 5.80396i | 0.0391878 | − | 0.222245i | ||||
\(683\) | 13.4534 | 0.514779 | 0.257390 | − | 0.966308i | \(-0.417138\pi\) | ||||
0.257390 | + | 0.966308i | \(0.417138\pi\) | |||||||
\(684\) | 0.418184 | + | 0.114125i | 0.0159897 | + | 0.00436369i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.66642 | + | 15.1220i | −0.101804 | + | 0.577362i | ||||
\(687\) | 26.7697 | + | 22.4624i | 1.02133 | + | 0.856995i | ||||
\(688\) | 7.20433 | + | 2.62216i | 0.274662 | + | 0.0999689i | ||||
\(689\) | −12.0750 | + | 4.39495i | −0.460022 | + | 0.167434i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.15757 | − | 2.00498i | −0.0440362 | − | 0.0762729i | 0.843167 | − | 0.537651i | \(-0.180688\pi\) |
−0.887203 | + | 0.461379i | \(0.847355\pi\) | |||||||
\(692\) | −0.727199 | + | 1.25955i | −0.0276439 | + | 0.0478807i | ||||
\(693\) | −0.315623 | − | 1.78999i | −0.0119895 | − | 0.0679960i | ||||
\(694\) | −5.08309 | − | 28.8276i | −0.192951 | − | 1.09428i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.38274 | − | 14.5193i | −0.317747 | − | 0.550354i | ||||
\(697\) | −0.914709 | + | 0.767532i | −0.0346471 | + | 0.0290723i | ||||
\(698\) | −30.6176 | + | 11.1439i | −1.15889 | + | 0.421802i | ||||
\(699\) | 41.0308 | + | 14.9340i | 1.55193 | + | 0.564855i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.542849 | − | 3.07865i | 0.0205031 | − | 0.116279i | −0.972839 | − | 0.231485i | \(-0.925642\pi\) |
0.993342 | + | 0.115206i | \(0.0367528\pi\) | |||||||
\(702\) | 41.8333 | 1.57890 | ||||||||
\(703\) | 3.53535 | − | 38.3670i | 0.133338 | − | 1.44704i | ||||
\(704\) | −4.57849 | −0.172558 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.3659 | + | 24.6409i | 1.10520 | + | 0.927372i | ||||
\(707\) | −46.7548 | − | 17.0173i | −1.75839 | − | 0.640003i | ||||
\(708\) | 0.174838 | − | 0.0636359i | 0.00657083 | − | 0.00239158i | ||||
\(709\) | −21.5824 | + | 18.1098i | −0.810544 | + | 0.680127i | −0.950738 | − | 0.309997i | \(-0.899672\pi\) |
0.140193 | + | 0.990124i | \(0.455228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.84971 | − | 3.20379i | 0.0693696 | − | 0.120152i | ||||
\(712\) | 0.000353238 | 0.00200331i | 1.32382e−5 | 7.50773e-5i | ||||||
\(713\) | −6.58341 | − | 37.3364i | −0.246551 | − | 1.39826i | ||||
\(714\) | −1.19822 | + | 2.07538i | −0.0448423 | + | 0.0776691i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.530243 | − | 0.444926i | 0.0198161 | − | 0.0166277i | ||||
\(717\) | −29.4460 | + | 10.7175i | −1.09968 | + | 0.400251i | ||||
\(718\) | −38.8577 | − | 14.1431i | −1.45016 | − | 0.527814i | ||||
\(719\) | −0.929140 | − | 0.779641i | −0.0346511 | − | 0.0290757i | 0.625298 | − | 0.780386i | \(-0.284978\pi\) |
−0.659949 | + | 0.751311i | \(0.729422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.7746 | −1.18335 | ||||||||
\(722\) | −9.74346 | + | 26.0194i | −0.362614 | + | 0.968341i | ||||
\(723\) | −9.36027 | −0.348112 | ||||||||
\(724\) | −0.636420 | + | 3.60931i | −0.0236523 | + | 0.134139i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.0291 | − | 8.01795i | −0.817578 | − | 0.297574i | ||||
\(727\) | 33.6146 | − | 12.2347i | 1.24670 | − | 0.453761i | 0.367413 | − | 0.930058i | \(-0.380244\pi\) |
0.879284 | + | 0.476297i | \(0.158021\pi\) | |||||||
\(728\) | 43.2482 | − | 36.2896i | 1.60289 | − | 1.34498i | ||||
\(729\) | −14.9989 | − | 25.9788i | −0.555514 | − | 0.962178i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0833274 | + | 0.472573i | 0.00308198 | + | 0.0174788i | ||||
\(732\) | −0.0787328 | − | 0.446516i | −0.00291005 | − | 0.0165037i | ||||
\(733\) | 18.9235 | − | 32.7765i | 0.698957 | − | 1.21063i | −0.269872 | − | 0.962896i | \(-0.586981\pi\) |
0.968828 | − | 0.247732i | \(-0.0796854\pi\) | |||||||
\(734\) | −7.01533 | − | 12.1509i | −0.258941 | − | 0.448498i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.28850 | − | 1.56089i | 0.158076 | − | 0.0575350i | ||||
\(737\) | 8.21574 | + | 2.99028i | 0.302631 | + | 0.110149i | ||||
\(738\) | 3.60808 | + | 3.02754i | 0.132815 | + | 0.111445i | ||||
\(739\) | 1.31048 | − | 7.43210i | 0.0482067 | − | 0.273394i | −0.951171 | − | 0.308664i | \(-0.900118\pi\) |
0.999378 | + | 0.0352702i | \(0.0112292\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.07676 | + | 33.3901i | −0.113028 | + | 1.22662i | ||||
\(742\) | −15.0218 | −0.551467 | ||||||||
\(743\) | 1.59337 | − | 9.03644i | 0.0584550 | − | 0.331515i | −0.941530 | − | 0.336928i | \(-0.890612\pi\) |
0.999985 | + | 0.00541343i | \(0.00172316\pi\) | |||||||
\(744\) | −20.4414 | − | 17.1523i | −0.749417 | − | 0.628835i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.9186 | − | 6.52185i | 0.656047 | − | 0.238782i | ||||
\(747\) | 7.58984 | − | 6.36864i | 0.277698 | − | 0.233016i | ||||
\(748\) | 0.0114472 | + | 0.0198272i | 0.000418552 | + | 0.000724954i | ||||
\(749\) | −11.6128 | + | 20.1140i | −0.424324 | + | 0.734950i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.81833 | + | 10.3123i | 0.0663519 | + | 0.376300i | 0.999843 | + | 0.0177006i | \(0.00563457\pi\) |
−0.933491 | + | 0.358600i | \(0.883254\pi\) | |||||||
\(752\) | −24.5798 | + | 42.5735i | −0.896335 | + | 1.55250i | ||||
\(753\) | 5.88280 | + | 10.1893i | 0.214381 | + | 0.371319i | ||||
\(754\) | 23.2643 | − | 19.5211i | 0.847235 | − | 0.710915i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.97313 | + | 1.08213i | 0.108132 | + | 0.0393568i | ||||
\(757\) | 40.6582 | + | 34.1163i | 1.47775 | + | 1.23998i | 0.908549 | + | 0.417779i | \(0.137191\pi\) |
0.569199 | + | 0.822199i | \(0.307253\pi\) | |||||||
\(758\) | 2.52377 | − | 14.3130i | 0.0916675 | − | 0.519872i | ||||
\(759\) | 5.47919 | 0.198882 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.6886 | −0.604960 | −0.302480 | − | 0.953156i | \(-0.597815\pi\) | ||||
−0.302480 | + | 0.953156i | \(0.597815\pi\) | |||||||
\(762\) | 7.09384 | − | 40.2312i | 0.256983 | − | 1.45742i | ||||
\(763\) | 21.0016 | + | 17.6225i | 0.760310 | + | 0.637976i | ||||
\(764\) | 0.0186962 | + | 0.00680487i | 0.000676405 | + | 0.000246191i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.1954 | − | 16.9459i | 0.729689 | − | 0.612281i | ||||
\(767\) | −2.26764 | − | 3.92767i | −0.0818799 | − | 0.141820i | ||||
\(768\) | 2.49569 | − | 4.32266i | 0.0900554 | − | 0.155981i | ||||
\(769\) | −1.07276 | − | 6.08395i | −0.0386849 | − | 0.219393i | 0.959337 | − | 0.282264i | \(-0.0910854\pi\) |
−0.998022 | + | 0.0628711i | \(0.979974\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2223 | + | 26.3657i | −0.548217 | + | 0.949539i | ||||
\(772\) | 0.142575 | + | 0.246947i | 0.00513139 | + | 0.00888783i | ||||
\(773\) | −21.5686 | + | 18.0982i | −0.775769 | + | 0.650948i | −0.942179 | − | 0.335109i | \(-0.891227\pi\) |
0.166410 | + | 0.986057i | \(0.446782\pi\) | |||||||
\(774\) | 1.77868 | − | 0.647385i | 0.0639332 | − | 0.0232698i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −21.7352 | − | 18.2380i | −0.780249 | − | 0.654707i | ||||
\(777\) | 9.43940 | − | 53.5335i | 0.338637 | − | 1.92050i | ||||
\(778\) | 35.6088 | 1.27664 | ||||||||
\(779\) | −13.8745 | + | 13.7469i | −0.497106 | + | 0.492534i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.177572 | − | 1.00706i | 0.00635403 | − | 0.0360355i | ||||
\(782\) | 1.74383 | + | 1.46325i | 0.0623594 | + | 0.0523257i | ||||
\(783\) | −21.5214 | − | 7.83313i | −0.769111 | − | 0.279933i | ||||
\(784\) | 38.3233 | − | 13.9486i | 1.36869 | − | 0.498163i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.6271 | − | 37.4593i | −0.771414 | − | 1.33613i | ||||
\(787\) | 2.73433 | − | 4.73601i | 0.0974685 | − | 0.168820i | −0.813168 | − | 0.582030i | \(-0.802259\pi\) |
0.910636 | + | 0.413209i | \(0.135592\pi\) | |||||||
\(788\) | −0.438386 | − | 2.48621i | −0.0156169 | − | 0.0885676i | ||||
\(789\) | 2.80257 | + | 15.8941i | 0.0997740 | + | 0.565847i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.74930 | + | 16.8863i | 0.346645 | + | 0.600407i | ||||
\(792\) | −0.930919 | + | 0.781134i | −0.0330788 | + | 0.0277564i | ||||
\(793\) | −10.3855 | + | 3.78000i | −0.368798 | + | 0.134232i | ||||
\(794\) | −27.4437 | − | 9.98870i | −0.973942 | − | 0.354486i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.192260 | − | 1.09036i | 0.00681447 | − | 0.0386468i | ||||
\(797\) | 47.2273 | 1.67288 | 0.836439 | − | 0.548061i | \(-0.184634\pi\) | ||||
0.836439 | + | 0.548061i | \(0.184634\pi\) | |||||||
\(798\) | −16.7301 | + | 35.4493i | −0.592239 | + | 1.25489i | ||||
\(799\) | −3.07694 | −0.108854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.000411469 | 0 | 0.000345264i | 1.45386e−5 | 0 | 1.21993e-5i | ||||
\(802\) | 22.5407 | + | 8.20414i | 0.795939 | + | 0.289698i | ||||
\(803\) | −1.04850 | + | 0.381624i | −0.0370009 | + | 0.0134672i | ||||
\(804\) | −2.25353 | + | 1.89094i | −0.0794759 | + | 0.0666882i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.1683 | − | 41.8607i | 0.851292 | − | 1.47448i | ||||
\(807\) | 6.27507 | + | 35.5877i | 0.220893 | + | 1.25275i | ||||
\(808\) | 5.77657 | + | 32.7606i | 0.203219 | + | 1.15251i | ||||
\(809\) | 3.06691 | − | 5.31204i | 0.107827 | − | 0.186762i | −0.807063 | − | 0.590466i | \(-0.798944\pi\) |
0.914890 | + | 0.403704i | \(0.132277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6831 | − | 17.3552i | 0.726281 | − | 0.609422i | −0.202834 | − | 0.979213i | \(-0.565015\pi\) |
0.929115 | + | 0.369791i | \(0.120571\pi\) | |||||||
\(812\) | 2.15838 | − | 0.785586i | 0.0757443 | − | 0.0275687i | ||||
\(813\) | 36.8586 | + | 13.4154i | 1.29269 | + | 0.470500i | ||||
\(814\) | −6.14901 | − | 5.15963i | −0.215523 | − | 0.180845i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.71360 | 0.0599880 | ||||||||
\(817\) | 1.99647 | + | 7.59103i | 0.0698476 | + | 0.265577i | ||||
\(818\) | 12.1855 | 0.426055 | ||||||||
\(819\) | 2.58864 | − | 14.6809i | 0.0904543 | − | 0.512992i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.5186 | + | 15.4755i | 1.48391 | + | 0.540099i | 0.951838 | − | 0.306600i | \(-0.0991914\pi\) |
0.532072 | + | 0.846699i | \(0.321414\pi\) | |||||||
\(822\) | 4.89105 | − | 1.78020i | 0.170595 | − | 0.0620914i | ||||
\(823\) | −23.0915 | + | 19.3760i | −0.804918 | + | 0.675407i | −0.949389 | − | 0.314102i | \(-0.898296\pi\) |
0.144471 | + | 0.989509i | \(0.453852\pi\) | |||||||
\(824\) | 10.6221 | + | 18.3980i | 0.370038 | + | 0.640925i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.920649 | − | 5.22126i | −0.0320335 | − | 0.181671i | ||||
\(827\) | 3.55475 | + | 20.1600i | 0.123611 | + | 0.701032i | 0.982123 | + | 0.188239i | \(0.0602779\pi\) |
−0.858512 | + | 0.512793i | \(0.828611\pi\) | |||||||
\(828\) | 0.290470 | − | 0.503109i | 0.0100945 | − | 0.0174843i | ||||
\(829\) | 10.4604 | + | 18.1179i | 0.363303 | + | 0.629259i | 0.988502 | − | 0.151206i | \(-0.0483156\pi\) |
−0.625199 | + | 0.780465i | \(0.714982\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.60252 | − | 0.947238i | 0.0902803 | − | 0.0328593i | ||||
\(832\) | −35.2867 | − | 12.8433i | −1.22335 | − | 0.445262i | ||||
\(833\) | 1.95543 | + | 1.64080i | 0.0677515 | + | 0.0568503i | ||||
\(834\) | −1.46907 | + | 8.33154i | −0.0508699 | + | 0.288498i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.213378 | + | 0.307751i | 0.00737982 | + | 0.0106438i | ||||
\(837\) | −36.4522 | −1.25997 | ||||||||
\(838\) | −2.95959 | + | 16.7847i | −0.102237 | + | 0.579816i | ||||
\(839\) | 3.25369 | + | 2.73017i | 0.112330 | + | 0.0942559i | 0.697222 | − | 0.716855i | \(-0.254419\pi\) |
−0.584893 | + | 0.811111i | \(0.698863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6274 | − | 4.23203i | 0.400945 | − | 0.145932i | ||||
\(842\) | 23.7387 | − | 19.9191i | 0.818089 | − | 0.686458i | ||||
\(843\) | −10.3342 | − | 17.8993i | −0.355928 | − | 0.616486i | ||||
\(844\) | 0.974147 | − | 1.68727i | 0.0335315 | − | 0.0580783i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.10757 | + | 11.9526i | 0.0724599 | + | 0.410941i | ||||
\(847\) | −21.6094 | + | 37.4285i | −0.742506 | + | 1.28606i | ||||
\(848\) | 5.37074 | + | 9.30239i | 0.184432 | + | 0.319446i | ||||
\(849\) | 12.1905 | − | 10.2290i | 0.418377 | − | 0.351060i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48.5226 | − | 17.6608i | −1.66334 | − | 0.605404i | ||||
\(852\) | 0.263577 | + | 0.221167i | 0.00902999 | + | 0.00757706i | ||||
\(853\) | 0.289897 | − | 1.64409i | 0.00992590 | − | 0.0562926i | −0.979443 | − | 0.201724i | \(-0.935346\pi\) |
0.989368 | + | 0.145431i | \(0.0464569\pi\) | |||||||
\(854\) | −12.9199 | −0.442110 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.5284 | 0.530751 | ||||||||
\(857\) | −0.148759 | + | 0.843653i | −0.00508150 | + | 0.0288186i | −0.987243 | − | 0.159220i | \(-0.949102\pi\) |
0.982162 | + | 0.188039i | \(0.0602131\pi\) | |||||||
\(858\) | 5.35138 | + | 4.49034i | 0.182693 | + | 0.153298i | ||||
\(859\) | 49.8985 | + | 18.1616i | 1.70251 | + | 0.619665i | 0.996108 | − | 0.0881416i | \(-0.0280928\pi\) |
0.706407 | + | 0.707806i | \(0.250315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.1091 | + | 17.7127i | −0.719397 | + | 0.603646i | ||||
\(862\) | −0.286805 | − | 0.496761i | −0.00976863 | − | 0.0169198i | ||||
\(863\) | 14.7804 | − | 25.6004i | 0.503130 | − | 0.871447i | −0.496864 | − | 0.867829i | \(-0.665515\pi\) |
0.999993 | − | 0.00361786i | \(-0.00115160\pi\) | |||||||
\(864\) | −0.761961 | − | 4.32130i | −0.0259224 | − | 0.147013i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.48391 | − | 16.4266i | 0.322276 | − | 0.558199i | ||||
\(867\) | −12.7844 | − | 22.1432i | −0.434181 | − | 0.752023i | ||||
\(868\) | 2.80050 | − | 2.34990i | 0.0950553 | − | 0.0797609i | ||||
\(869\) | 3.00324 | − | 1.09309i | 0.101878 | − | 0.0370806i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.9310 | + | 46.0926i | 1.86127 | + | 1.56179i | ||||
\(872\) | 3.18294 | − | 18.0514i | 0.107788 | − | 0.611296i | ||||
\(873\) | −7.49198 | −0.253565 | ||||||||
\(874\) | 30.4026 | + | 21.4981i | 1.02838 | + | 0.727185i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0651933 | − | 0.369730i | 0.00220268 | − | 0.0124920i | ||||
\(877\) | −6.73412 | − | 5.65060i | −0.227395 | − | 0.190807i | 0.521971 | − | 0.852963i | \(-0.325197\pi\) |
−0.749366 | + | 0.662156i | \(0.769641\pi\) | |||||||
\(878\) | 7.48620 | + | 2.72476i | 0.252647 | + | 0.0919560i | ||||
\(879\) | −33.9266 | + | 12.3483i | −1.14432 | + | 0.416497i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6335 | − | 23.6139i | −0.459324 | − | 0.795572i | 0.539602 | − | 0.841920i | \(-0.318575\pi\) |
−0.998925 | + | 0.0463485i | \(0.985242\pi\) | |||||||
\(882\) | 5.03444 | − | 8.71990i | 0.169518 | − | 0.293614i | ||||
\(883\) | 1.50219 | + | 8.51936i | 0.0505528 | + | 0.286699i | 0.999595 | − | 0.0284490i | \(-0.00905681\pi\) |
−0.949042 | + | 0.315148i | \(0.897946\pi\) | |||||||
\(884\) | 0.0326065 | + | 0.184920i | 0.00109667 | + | 0.00621955i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0907 | + | 31.3340i | 0.607769 | + | 1.05269i | ||||
\(887\) | −30.3733 | + | 25.4862i | −1.01984 | + | 0.855744i | −0.989607 | − | 0.143799i | \(-0.954068\pi\) |
−0.0302292 | + | 0.999543i | \(0.509624\pi\) | |||||||
\(888\) | −34.1523 | + | 12.4304i | −1.14607 | + | 0.417137i | ||||
\(889\) | −70.7713 | − | 25.7587i | −2.37359 | − | 0.863918i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.682260 | − | 3.86929i | 0.0228566 | − | 0.129626i | ||||
\(892\) | −0.678737 | −0.0227258 | ||||||||
\(893\) | −50.1581 | + | 4.15486i | −1.67848 | + | 0.139037i | ||||
\(894\) | −40.1648 | −1.34331 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −38.5013 | − | 32.3064i | −1.28624 | − | 1.07928i | ||||
\(897\) | 42.2284 | + | 15.3699i | 1.40997 | + | 0.513186i | ||||
\(898\) | −47.4922 | + | 17.2857i | −1.58483 | + | 0.576832i | ||||
\(899\) | −20.2718 | + | 17.0100i | −0.676101 | + | 0.567316i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.336159 | + | 0.582244i | −0.0111991 | + | 0.0193974i | ||||
\(902\) | 0.706583 | + | 4.00723i | 0.0235266 | + | 0.133426i | ||||
\(903\) | 1.92298 | + | 10.9058i | 0.0639929 | + | 0.362921i | ||||
\(904\) | 6.51828 | − | 11.2900i | 0.216795 | − | 0.375499i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.88018 | − | 3.25585i | 0.128910 | − | 0.108169i | ||||
\(907\) | −31.3645 | + | 11.4157i | −1.04144 | + | 0.379053i | −0.805426 | − | 0.592696i | \(-0.798063\pi\) |
−0.236014 | + | 0.971750i | \(0.575841\pi\) | |||||||
\(908\) | 0.344826 | + | 0.125506i | 0.0114435 | + | 0.00416508i | ||||
\(909\) | 6.72884 | + | 5.64617i | 0.223182 | + | 0.187272i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.3977 | −1.53722 | −0.768611 | − | 0.639716i | \(-0.779052\pi\) | ||||
−0.768611 | + | 0.639716i | \(0.779052\pi\) | |||||||
\(912\) | 27.9339 | − | 2.31391i | 0.924982 | − | 0.0766212i | ||||
\(913\) | 8.55953 | 0.283279 | ||||||||
\(914\) | 2.95635 | − | 16.7663i | 0.0977873 | − | 0.554579i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.00788 | + | 1.09478i | 0.0993833 | + | 0.0361726i | ||||
\(917\) | −74.9333 | + | 27.2735i | −2.47452 | + | 0.900650i | ||||
\(918\) | 1.67667 | − | 1.40689i | 0.0553384 | − | 0.0464345i | ||||
\(919\) | −4.25997 | − | 7.37849i | −0.140524 | − | 0.243394i | 0.787170 | − | 0.616736i | \(-0.211545\pi\) |
−0.927694 | + | 0.373342i | \(0.878212\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.10942 | + | 23.3057i | 0.135410 | + | 0.767948i | ||||
\(922\) | 0.759174 | + | 4.30549i | 0.0250021 | + | 0.141794i | ||||
\(923\) | 4.19351 | − | 7.26337i | 0.138031 | − | 0.239077i | ||||
\(924\) | 0.264173 | + | 0.457561i | 0.00869065 | + | 0.0150526i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.6624 | + | 4.24475i | −0.383249 | + | 0.139491i | ||||
\(927\) | 5.27123 | + | 1.91857i | 0.173130 | + | 0.0630142i | ||||
\(928\) | −2.44023 | − | 2.04759i | −0.0801044 | − | 0.0672155i | ||||
\(929\) | −8.18896 | + | 46.4419i | −0.268671 | + | 1.52371i | 0.489702 | + | 0.871890i | \(0.337106\pi\) |
−0.758373 | + | 0.651820i | \(0.774006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.0916 | + | 24.1067i | 1.11731 | + | 0.790064i | ||||
\(932\) | 3.99954 | 0.131009 | ||||||||
\(933\) | 0.921119 | − | 5.22393i | 0.0301561 | − | 0.171024i | ||||
\(934\) | −20.0853 | − | 16.8536i | −0.657212 | − | 0.551466i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.36584 | + | 3.40889i | −0.306132 | + | 0.111423i | ||||
\(937\) | 22.5986 | − | 18.9625i | 0.738264 | − | 0.619477i | −0.194107 | − | 0.980980i | \(-0.562181\pi\) |
0.932371 | + | 0.361504i | \(0.117736\pi\) | |||||||
\(938\) | 41.9134 | + | 72.5961i | 1.36852 | + | 2.37035i | ||||
\(939\) | −0.885879 | + | 1.53439i | −0.0289096 | + | 0.0500729i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.64948 | − | 9.35464i | −0.0537714 | − | 0.304953i | 0.946047 | − | 0.324031i | \(-0.105038\pi\) |
−0.999818 | + | 0.0190779i | \(0.993927\pi\) | |||||||
\(942\) | 23.0187 | − | 39.8695i | 0.749989 | − | 1.29902i | ||||
\(943\) | 13.0879 | + | 22.6690i | 0.426201 | + | 0.738203i | ||||
\(944\) | −2.90416 | + | 2.43688i | −0.0945223 | + | 0.0793137i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.53662 | + | 0.559286i | 0.0499600 | + | 0.0181839i | ||||
\(947\) | 7.55292 | + | 6.33765i | 0.245437 | + | 0.205946i | 0.757204 | − | 0.653178i | \(-0.226565\pi\) |
−0.511768 | + | 0.859124i | \(0.671009\pi\) | |||||||
\(948\) | −0.186734 | + | 1.05902i | −0.00606484 | + | 0.0343954i | ||||
\(949\) | −9.15138 | −0.297066 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.98099 | −0.0642381 | ||||||||
\(952\) | 0.512928 | − | 2.90896i | 0.0166241 | − | 0.0942800i | ||||
\(953\) | −41.1172 | − | 34.5014i | −1.33192 | − | 1.11761i | −0.983626 | − | 0.180223i | \(-0.942318\pi\) |
−0.348290 | − | 0.937387i | \(-0.613237\pi\) | |||||||
\(954\) | 2.49203 | + | 0.907025i | 0.0806825 | + | 0.0293660i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.19877 | + | 1.84499i | −0.0711134 | + | 0.0596712i | ||||
\(957\) | −1.91224 | − | 3.31210i | −0.0618141 | − | 0.107065i | ||||
\(958\) | −2.47828 | + | 4.29251i | −0.0800697 | + | 0.138685i | ||||
\(959\) | −1.66627 | − | 9.44991i | −0.0538068 | − | 0.305154i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.55948 | + | 9.62930i | −0.179338 | + | 0.310623i | ||||
\(962\) | −32.9173 | − | 57.0144i | −1.06130 | − | 1.83822i | ||||
\(963\) | 3.14100 | − | 2.63561i | 0.101217 | − | 0.0849315i | ||||
\(964\) | −0.805675 | + | 0.293242i | −0.0259491 | + | 0.00944468i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 40.2432 | + | 33.7681i | 1.29480 | + | 1.08647i | ||||
\(967\) | −5.94528 | + | 33.7173i | −0.191187 | + | 1.08428i | 0.726557 | + | 0.687106i | \(0.241119\pi\) |
−0.917745 | + | 0.397171i | \(0.869992\pi\) | |||||||
\(968\) | 28.8956 | 0.928739 | ||||||||
\(969\) | 0.999627 | + | 1.44175i | 0.0321126 | + | 0.0463155i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.46056 | − | 13.9545i | 0.0789630 | − | 0.447821i | −0.919534 | − | 0.393011i | \(-0.871433\pi\) |
0.998497 | − | 0.0548105i | \(-0.0174555\pi\) | |||||||
\(972\) | −0.773065 | − | 0.648679i | −0.0247961 | − | 0.0208064i | ||||
\(973\) | 14.6561 | + | 5.33440i | 0.469855 | + | 0.171013i | ||||
\(974\) | −15.3379 | + | 5.58254i | −0.491458 | + | 0.178876i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.61925 | + | 8.00078i | 0.147859 | + | 0.256099i | ||||
\(977\) | 22.8088 | − | 39.5060i | 0.729717 | − | 1.26391i | −0.227285 | − | 0.973828i | \(-0.572985\pi\) |
0.957003 | − | 0.290079i | \(-0.0936817\pi\) | |||||||
\(978\) | −3.03629 | − | 17.2197i | −0.0970900 | − | 0.550625i | ||||
\(979\) | 8.05795e−5 | 0 | 0.000456989i | 2.57533e−6 | 0 | 1.46054e-5i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.42000 | − | 4.19156i | −0.0772646 | − | 0.133826i | ||||
\(982\) | 25.7454 | − | 21.6029i | 0.821568 | − | 0.689377i | ||||
\(983\) | 18.9686 | − | 6.90400i | 0.605004 | − | 0.220203i | −0.0213117 | − | 0.999773i | \(-0.506784\pi\) |
0.626316 | + | 0.779569i | \(0.284562\pi\) | |||||||
\(984\) | 17.3126 | + | 6.30126i | 0.551905 | + | 0.200877i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.275917 | − | 1.56480i | 0.00878698 | − | 0.0498334i | ||||
\(987\) | −71.0079 | −2.26021 | ||||||||
\(988\) | 0.781229 | + | 2.97041i | 0.0248542 | + | 0.0945013i | ||||
\(989\) | 10.5194 | 0.334496 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.46987 | − | 7.10707i | −0.269054 | − | 0.225763i | 0.498271 | − | 0.867021i | \(-0.333968\pi\) |
−0.767325 | + | 0.641258i | \(0.778413\pi\) | |||||||
\(992\) | −4.76433 | − | 1.73408i | −0.151268 | − | 0.0550569i | ||||
\(993\) | −18.0601 | + | 6.57332i | −0.573118 | + | 0.208598i | ||||
\(994\) | 7.51070 | − | 6.30223i | 0.238225 | − | 0.199894i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.44002 | + | 2.49419i | −0.0456288 | + | 0.0790314i | ||||
\(997\) | −5.42251 | − | 30.7526i | −0.171733 | − | 0.973945i | −0.941848 | − | 0.336040i | \(-0.890912\pi\) |
0.770115 | − | 0.637905i | \(-0.220199\pi\) | |||||||
\(998\) | 0.249035 | + | 1.41235i | 0.00788305 | + | 0.0447070i | ||||
\(999\) | −24.8240 | + | 42.9964i | −0.785396 | + | 1.36035i |
(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 | 475.2.l.b.226.3 | 18 | ||
5.2 | odd | 4 | 475.2.u.c.74.5 | 36 | |||
5.3 | odd | 4 | 475.2.u.c.74.2 | 36 | |||
5.4 | even | 2 | 95.2.k.b.36.1 | ✓ | 18 | ||
15.14 | odd | 2 | 855.2.bs.b.226.3 | 18 | |||
19.3 | odd | 18 | 9025.2.a.cd.1.3 | 9 | |||
19.9 | even | 9 | inner | 475.2.l.b.351.3 | 18 | ||
19.16 | even | 9 | 9025.2.a.ce.1.7 | 9 | |||
95.9 | even | 18 | 95.2.k.b.66.1 | yes | 18 | ||
95.28 | odd | 36 | 475.2.u.c.199.5 | 36 | |||
95.47 | odd | 36 | 475.2.u.c.199.2 | 36 | |||
95.54 | even | 18 | 1805.2.a.t.1.3 | 9 | |||
95.79 | odd | 18 | 1805.2.a.u.1.7 | 9 | |||
285.104 | odd | 18 | 855.2.bs.b.541.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.36.1 | ✓ | 18 | 5.4 | even | 2 | ||
95.2.k.b.66.1 | yes | 18 | 95.9 | even | 18 | ||
475.2.l.b.226.3 | 18 | 1.1 | even | 1 | trivial | ||
475.2.l.b.351.3 | 18 | 19.9 | even | 9 | inner | ||
475.2.u.c.74.2 | 36 | 5.3 | odd | 4 | |||
475.2.u.c.74.5 | 36 | 5.2 | odd | 4 | |||
475.2.u.c.199.2 | 36 | 95.47 | odd | 36 | |||
475.2.u.c.199.5 | 36 | 95.28 | odd | 36 | |||
855.2.bs.b.226.3 | 18 | 15.14 | odd | 2 | |||
855.2.bs.b.541.3 | 18 | 285.104 | odd | 18 | |||
1805.2.a.t.1.3 | 9 | 95.54 | even | 18 | |||
1805.2.a.u.1.7 | 9 | 95.79 | odd | 18 | |||
9025.2.a.cd.1.3 | 9 | 19.3 | odd | 18 | |||
9025.2.a.ce.1.7 | 9 | 19.16 | even | 9 |