Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(24,475)]
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([9, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.u (of order \(18\), degree \(6\), not 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: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 74.2 | ||
Character | \(\chi\) | \(=\) | 475.74 |
Dual form | 475.2.u.c.199.2 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44009 | − | 0.253927i | −1.01830 | − | 0.179554i | −0.360510 | − | 0.932755i | \(-0.617397\pi\) |
−0.657789 | + | 0.753202i | \(0.728508\pi\) | |||||||
\(3\) | 0.970838 | − | 1.15700i | 0.560513 | − | 0.667994i | −0.409142 | − | 0.912471i | \(-0.634172\pi\) |
0.969655 | + | 0.244477i | \(0.0786163\pi\) | |||||||
\(4\) | 0.130002 | + | 0.0473169i | 0.0650011 | + | 0.0236585i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.69189 | + | 1.41966i | −0.690711 | + | 0.579575i | ||||
\(7\) | 3.52622 | − | 2.03586i | 1.33278 | − | 0.769484i | 0.347059 | − | 0.937843i | \(-0.387180\pi\) |
0.985726 | + | 0.168360i | \(0.0538470\pi\) | |||||||
\(8\) | 2.35759 | + | 1.36116i | 0.833535 | + | 0.481241i | ||||
\(9\) | 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 | \(0.136823\pi\) | |||||||
\(12\) | 0.180957 | − | 0.104475i | 0.0522377 | − | 0.0301595i | ||||
\(13\) | 3.27390 | + | 3.90168i | 0.908017 | + | 1.08213i | 0.996292 | + | 0.0860363i | \(0.0274201\pi\) |
−0.0882750 | + | 0.996096i | \(0.528135\pi\) | |||||||
\(14\) | −5.59504 | + | 2.03643i | −1.49534 | + | 0.544258i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.26147 | − | 2.73670i | −0.815368 | − | 0.684175i | ||||
\(17\) | −0.262435 | − | 0.0462744i | −0.0636498 | − | 0.0112232i | 0.141733 | − | 0.989905i | \(-0.454733\pi\) |
−0.205382 | + | 0.978682i | \(0.565844\pi\) | |||||||
\(18\) | − | 1.05115i | − | 0.247758i | ||||||
\(19\) | −0.399960 | + | 4.34051i | −0.0917571 | + | 0.995781i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.06789 | − | 6.05632i | 0.233033 | − | 1.32160i | ||||
\(22\) | −0.583716 | + | 0.695646i | −0.124449 | + | 0.148312i | ||||
\(23\) | 1.99799 | − | 5.48944i | 0.416610 | − | 1.14463i | −0.537000 | − | 0.843582i | \(-0.680442\pi\) |
0.953610 | − | 0.301045i | \(-0.0973353\pi\) | |||||||
\(24\) | 3.86370 | − | 1.40627i | 0.788674 | − | 0.287054i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.72398 | − | 6.45012i | −0.730332 | − | 1.26497i | ||||
\(27\) | 4.86425 | + | 2.80837i | 0.936125 | + | 0.540472i | ||||
\(28\) | 0.554747 | − | 0.0978169i | 0.104837 | − | 0.0184856i | ||||
\(29\) | −0.708058 | − | 4.01560i | −0.131483 | − | 0.745678i | −0.977244 | − | 0.212116i | \(-0.931964\pi\) |
0.845761 | − | 0.533561i | \(-0.179147\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.24496 | + | 5.62043i | 0.582811 | + | 1.00946i | 0.995144 | + | 0.0984257i | \(0.0313807\pi\) |
−0.412333 | + | 0.911033i | \(0.635286\pi\) | |||||||
\(32\) | 0.502163 | + | 0.598455i | 0.0887708 | + | 0.105793i | ||||
\(33\) | −0.320794 | − | 0.881374i | −0.0558431 | − | 0.153428i | ||||
\(34\) | 0.366180 | + | 0.133279i | 0.0627994 | + | 0.0228571i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0172687 | + | 0.0979357i | −0.00287812 | + | 0.0163226i | ||||
\(37\) | − | 8.83927i | − | 1.45317i | −0.687078 | − | 0.726584i | \(-0.741107\pi\) | ||
0.687078 | − | 0.726584i | \(-0.258893\pi\) | |||||||
\(38\) | 1.67815 | − | 6.14918i | 0.272232 | − | 0.997528i | ||||
\(39\) | 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 | \(0.836005\pi\) | |||||||
\(42\) | −3.07573 | + | 8.45050i | −0.474595 | + | 1.30394i | ||||
\(43\) | −0.615885 | − | 1.69213i | −0.0939215 | − | 0.258047i | 0.883832 | − | 0.467804i | \(-0.154955\pi\) |
−0.977753 | + | 0.209757i | \(0.932733\pi\) | |||||||
\(44\) | 0.0658134 | − | 0.0552240i | 0.00992175 | − | 0.00832533i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.27121 | + | 7.39795i | −0.629756 | + | 1.09077i | ||||
\(47\) | −11.3711 | + | 2.00502i | −1.65864 | + | 0.292463i | −0.922968 | − | 0.384877i | \(-0.874244\pi\) |
−0.735671 | + | 0.677339i | \(0.763133\pi\) | |||||||
\(48\) | −6.33272 | + | 1.11663i | −0.914050 | + | 0.161172i | ||||
\(49\) | 4.78947 | − | 8.29561i | 0.684210 | − | 1.18509i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.308321 | + | 0.258712i | −0.0431736 | + | 0.0362269i | ||||
\(52\) | 0.240999 | + | 0.662139i | 0.0334205 | + | 0.0918221i | ||||
\(53\) | 0.862891 | − | 2.37077i | 0.118527 | − | 0.325651i | −0.866215 | − | 0.499672i | \(-0.833454\pi\) |
0.984742 | + | 0.174021i | \(0.0556761\pi\) | |||||||
\(54\) | −6.29184 | − | 5.27948i | −0.856212 | − | 0.718447i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.0845 | 1.48123 | ||||||||
\(57\) | 4.63367 | + | 4.67668i | 0.613745 | + | 0.619442i | ||||
\(58\) | 5.96263i | 0.782931i | ||||||||
\(59\) | −0.154624 | + | 0.876916i | −0.0201303 | + | 0.114165i | −0.993217 | − | 0.116274i | \(-0.962905\pi\) |
0.973087 | + | 0.230439i | \(0.0740161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.03905 | − | 0.742153i | −0.261073 | − | 0.0950229i | 0.208167 | − | 0.978093i | \(-0.433250\pi\) |
−0.469241 | + | 0.883070i | \(0.655472\pi\) | |||||||
\(62\) | −3.24586 | − | 8.91792i | −0.412224 | − | 1.13258i | ||||
\(63\) | 1.88135 | + | 2.24211i | 0.237028 | + | 0.282479i | ||||
\(64\) | 3.68635 | + | 6.38495i | 0.460794 | + | 0.798119i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.238168 | + | 1.35072i | 0.0293165 | + | 0.166262i | ||||
\(67\) | 13.8649 | − | 2.44476i | 1.69387 | − | 0.298674i | 0.758322 | − | 0.651881i | \(-0.226020\pi\) |
0.935546 | + | 0.353206i | \(0.114909\pi\) | |||||||
\(68\) | −0.0319276 | − | 0.0184334i | −0.00387179 | − | 0.00223538i | ||||
\(69\) | −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 | \(0.357736\pi\) | |||||||
\(72\) | −0.669290 | + | 1.83886i | −0.0788766 | + | 0.216712i | ||||
\(73\) | 1.15493 | − | 1.37639i | 0.135174 | − | 0.161095i | −0.694211 | − | 0.719772i | \(-0.744246\pi\) |
0.829385 | + | 0.558677i | \(0.188691\pi\) | |||||||
\(74\) | −2.24453 | + | 12.7294i | −0.260922 | + | 1.47976i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.257375 | + | 0.545351i | −0.0295230 | + | 0.0625561i | ||||
\(77\) | − | 2.52856i | − | 0.288157i | ||||||
\(78\) | −11.0782 | − | 1.95338i | −1.25435 | − | 0.221177i | ||||
\(79\) | −3.94242 | − | 3.30809i | −0.443557 | − | 0.372189i | 0.393481 | − | 0.919333i | \(-0.371271\pi\) |
−0.837039 | + | 0.547144i | \(0.815715\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.94525 | − | 2.16389i | 0.660584 | − | 0.240433i | ||||
\(82\) | 4.21177 | + | 5.01940i | 0.465113 | + | 0.554300i | ||||
\(83\) | −11.9367 | + | 6.89167i | −1.31023 | + | 0.756459i | −0.982133 | − | 0.188187i | \(-0.939739\pi\) |
−0.328092 | + | 0.944646i | \(0.606406\pi\) | |||||||
\(84\) | 0.425395 | − | 0.736806i | 0.0464144 | − | 0.0803921i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.457253 | + | 2.59321i | 0.0493069 | + | 0.279633i | ||||
\(87\) | −5.33345 | − | 3.07927i | −0.571806 | − | 0.330132i | ||||
\(88\) | 1.46408 | − | 0.845286i | 0.156071 | − | 0.0901078i | ||||
\(89\) | 0.000572418 | 0 | 0.000480315i | 6.06762e−5 | 0 | 5.09133e-5i | −0.642757 | − | 0.766070i | \(-0.722210\pi\) |
0.642818 | + | 0.766019i | \(0.277765\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.4878 | + | 7.09297i | 2.04287 | + | 0.743545i | ||||
\(92\) | 0.519487 | − | 0.619100i | 0.0541603 | − | 0.0645457i | ||||
\(93\) | 9.65316 | + | 1.70211i | 1.00099 | + | 0.176501i | ||||
\(94\) | 16.8845 | 1.74150 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.17993 | 0.120426 | ||||||||
\(97\) | −10.2642 | − | 1.80985i | −1.04217 | − | 0.183762i | −0.373736 | − | 0.927535i | \(-0.621923\pi\) |
−0.668432 | + | 0.743773i | \(0.733034\pi\) | |||||||
\(98\) | −9.00376 | + | 10.7303i | −0.909517 | + | 1.08392i | ||||
\(99\) | 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 | \(0.485788\pi\) | |||||||
\(102\) | 0.509705 | − | 0.294278i | 0.0504683 | − | 0.0291379i | ||||
\(103\) | −6.75822 | − | 3.90186i | −0.665908 | − | 0.384462i | 0.128617 | − | 0.991694i | \(-0.458946\pi\) |
−0.794524 | + | 0.607232i | \(0.792280\pi\) | |||||||
\(104\) | 2.40772 | + | 13.6549i | 0.236097 | + | 1.33897i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.84465 | + | 3.19502i | −0.179168 | + | 0.310328i | ||||
\(107\) | 4.93993 | − | 2.85207i | 0.477561 | − | 0.275720i | −0.241839 | − | 0.970316i | \(-0.577750\pi\) |
0.719399 | + | 0.694597i | \(0.244417\pi\) | |||||||
\(108\) | 0.499479 | + | 0.595256i | 0.0480624 | + | 0.0572786i | ||||
\(109\) | −6.32712 | + | 2.30288i | −0.606029 | + | 0.220576i | −0.626765 | − | 0.779209i | \(-0.715621\pi\) |
0.0207361 | + | 0.999785i | \(0.493399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.2270 | − | 8.58150i | −0.970707 | − | 0.814520i | ||||
\(112\) | −17.0722 | − | 3.01029i | −1.61317 | − | 0.284446i | ||||
\(113\) | 4.78878i | 0.450490i | 0.974302 | + | 0.225245i | \(0.0723183\pi\) | ||||
−0.974302 | + | 0.225245i | \(0.927682\pi\) | |||||||
\(114\) | −5.48538 | − | 7.91147i | −0.513753 | − | 0.740977i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.0979567 | − | 0.555540i | 0.00909505 | − | 0.0515806i | ||||
\(117\) | −2.35337 | + | 2.80464i | −0.217569 | + | 0.259289i | ||||
\(118\) | 0.445346 | − | 1.22358i | 0.0409974 | − | 0.112639i | ||||
\(119\) | −1.01961 | + | 0.371108i | −0.0934676 | + | 0.0340194i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.30718 | + | 9.19230i | 0.482471 | + | 0.835664i | ||||
\(122\) | 2.74796 | + | 1.58654i | 0.248789 | + | 0.143638i | ||||
\(123\) | −6.66483 | + | 1.17519i | −0.600948 | + | 0.105963i | ||||
\(124\) | 0.155910 | + | 0.884210i | 0.0140011 | + | 0.0794044i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.13999 | − | 3.70657i | −0.190646 | − | 0.330208i | ||||
\(127\) | 11.8894 | + | 14.1693i | 1.05502 | + | 1.25732i | 0.965242 | + | 0.261356i | \(0.0841698\pi\) |
0.0897732 | + | 0.995962i | \(0.471386\pi\) | |||||||
\(128\) | −4.22177 | − | 11.5992i | −0.373155 | − | 1.02524i | ||||
\(129\) | −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 | \(0.728775\pi\) | |||||||
\(132\) | − | 0.129760i | − | 0.0112941i | ||||||
\(133\) | 7.42634 | + | 16.1198i | 0.643945 | + | 1.39777i | ||||
\(134\) | −20.5875 | −1.77849 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.555728 | − | 0.466311i | −0.0476533 | − | 0.0399858i | ||||
\(137\) | −0.806027 | + | 2.21454i | −0.0688635 | + | 0.189201i | −0.969350 | − | 0.245682i | \(-0.920988\pi\) |
0.900487 | + | 0.434883i | \(0.143210\pi\) | |||||||
\(138\) | 4.41278 | + | 12.1240i | 0.375640 | + | 1.03206i | ||||
\(139\) | −2.93433 | + | 2.46220i | −0.248887 | + | 0.208841i | −0.758693 | − | 0.651448i | \(-0.774162\pi\) |
0.509806 | + | 0.860289i | \(0.329717\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.71964 | + | 15.1029i | −0.734326 | + | 1.27189i | ||||
\(142\) | −2.37137 | + | 0.418137i | −0.199001 | + | 0.0350893i | ||||
\(143\) | 3.11491 | − | 0.549242i | 0.260482 | − | 0.0459299i | ||||
\(144\) | 1.53022 | − | 2.65042i | 0.127519 | − | 0.220869i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.01271 | + | 1.68887i | −0.166573 | + | 0.139772i | ||||
\(147\) | −4.94821 | − | 13.5951i | −0.408122 | − | 1.12130i | ||||
\(148\) | 0.418247 | − | 1.14913i | 0.0343797 | − | 0.0944575i | ||||
\(149\) | −13.9310 | − | 11.6895i | −1.14127 | − | 0.957638i | −0.141789 | − | 0.989897i | \(-0.545286\pi\) |
−0.999480 | + | 0.0322585i | \(0.989730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.29340 | −0.186634 | −0.0933170 | − | 0.995636i | \(-0.529747\pi\) | ||||
−0.0933170 | + | 0.995636i | \(0.529747\pi\) | |||||||
\(152\) | −6.85106 | + | 9.68875i | −0.555694 | + | 0.785861i | ||||
\(153\) | − | 0.191556i | − | 0.0154863i | ||||||
\(154\) | −0.642071 | + | 3.64137i | −0.0517396 | + | 0.293430i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00006 | + | 0.363994i | 0.0800693 | + | 0.0291428i | ||||
\(157\) | 7.12925 | + | 19.5874i | 0.568976 | + | 1.56325i | 0.806106 | + | 0.591771i | \(0.201571\pi\) |
−0.237130 | + | 0.971478i | \(0.576207\pi\) | |||||||
\(158\) | 4.83744 | + | 5.76504i | 0.384846 | + | 0.458642i | ||||
\(159\) | −1.90526 | − | 3.30000i | −0.151097 | − | 0.261707i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.13039 | − | 23.4246i | −0.325520 | − | 1.84612i | ||||
\(162\) | −9.11119 | + | 1.60655i | −0.715842 | + | 0.126222i | ||||
\(163\) | −6.85624 | − | 3.95845i | −0.537022 | − | 0.310050i | 0.206849 | − | 0.978373i | \(-0.433679\pi\) |
−0.743871 | + | 0.668323i | \(0.767012\pi\) | |||||||
\(164\) | −0.309952 | − | 0.536852i | −0.0242031 | − | 0.0419211i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.9400 | − | 6.89358i | 1.47003 | − | 0.535046i | ||||
\(167\) | 4.82025 | − | 13.2435i | 0.373002 | − | 1.02482i | −0.601192 | − | 0.799105i | \(-0.705307\pi\) |
0.974194 | − | 0.225711i | \(-0.0724705\pi\) | |||||||
\(168\) | 10.7613 | − | 12.8248i | 0.830249 | − | 0.989452i | ||||
\(169\) | −2.24728 | + | 12.7450i | −0.172868 | + | 0.980382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.12260 | + | 0.258662i | −0.238791 | + | 0.0197803i | ||||
\(172\) | − | 0.249122i | − | 0.0189954i | ||||||
\(173\) | 10.3531 | + | 1.82553i | 0.787130 | + | 0.138792i | 0.552744 | − | 0.833351i | \(-0.313581\pi\) |
0.234386 | + | 0.972144i | \(0.424692\pi\) | |||||||
\(174\) | 6.89876 | + | 5.78874i | 0.522993 | + | 0.438843i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.48451 | + | 0.904289i | −0.187277 | + | 0.0681633i | ||||
\(177\) | 0.864477 | + | 1.03024i | 0.0649780 | + | 0.0774378i | ||||
\(178\) | −0.000946300 | 0 | 0.000546346i | −7.09282e−5 | 0 | 4.09504e-5i | ||||
\(179\) | 2.50164 | − | 4.33298i | 0.186982 | − | 0.323862i | −0.757261 | − | 0.653113i | \(-0.773463\pi\) |
0.944243 | + | 0.329251i | \(0.106796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.60022 | − | 26.0891i | −0.341932 | − | 1.93919i | −0.343395 | − | 0.939191i | \(-0.611577\pi\) |
0.00146347 | − | 0.999999i | \(-0.499534\pi\) | |||||||
\(182\) | −26.2631 | − | 15.1630i | −1.94675 | − | 1.12396i | ||||
\(183\) | −2.83825 | + | 1.63867i | −0.209810 | + | 0.121134i | ||||
\(184\) | 12.1824 | − | 10.2223i | 0.898101 | − | 0.753596i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.4692 | − | 4.90240i | −0.987612 | − | 0.359461i | ||||
\(187\) | −0.106373 | + | 0.126771i | −0.00777879 | + | 0.00927041i | ||||
\(188\) | −1.57313 | − | 0.277386i | −0.114733 | − | 0.0202305i | ||||
\(189\) | 22.8699 | 1.66354 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.143815 | −0.0104061 | −0.00520303 | − | 0.999986i | \(-0.501656\pi\) | ||||
−0.00520303 | + | 0.999986i | \(0.501656\pi\) | |||||||
\(192\) | 10.9662 | + | 1.93364i | 0.791420 | + | 0.139549i | ||||
\(193\) | 1.32488 | − | 1.57893i | 0.0953669 | − | 0.113654i | −0.716250 | − | 0.697843i | \(-0.754143\pi\) |
0.811617 | + | 0.584190i | \(0.198588\pi\) | |||||||
\(194\) | 14.3218 | + | 5.21270i | 1.02824 | + | 0.374250i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.01516 | − | 0.851824i | 0.0725118 | − | 0.0608446i | ||||
\(197\) | 15.8035 | − | 9.12413i | 1.12595 | − | 0.650068i | 0.183037 | − | 0.983106i | \(-0.441407\pi\) |
0.942913 | + | 0.333038i | \(0.108074\pi\) | |||||||
\(198\) | −0.565314 | − | 0.326384i | −0.0401751 | − | 0.0231951i | ||||
\(199\) | −1.38971 | − | 7.88142i | −0.0985137 | − | 0.558699i | −0.993614 | − | 0.112834i | \(-0.964007\pi\) |
0.895100 | − | 0.445865i | \(-0.147104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6320 | − | 18.4151i | 0.749922 | − | 1.29890i | ||||
\(202\) | 15.4750 | − | 8.93451i | 1.08882 | − | 0.628630i | ||||
\(203\) | −10.6720 | − | 12.7184i | −0.749026 | − | 0.892654i | ||||
\(204\) | −0.0523239 | + | 0.0190443i | −0.00366341 | + | 0.00133337i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.74168 | + | 7.33514i | 0.609062 | + | 0.511063i | ||||
\(207\) | 4.13541 | + | 0.729184i | 0.287431 | + | 0.0506818i | ||||
\(208\) | − | 21.6849i | − | 1.50358i | ||||||
\(209\) | 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 | \(0.894466\pi\) | |||||||
\(212\) | 0.224356 | − | 0.267377i | 0.0154088 | − | 0.0183635i | ||||
\(213\) | 0.850628 | − | 2.33708i | 0.0582841 | − | 0.160134i | ||||
\(214\) | −7.83817 | + | 2.85286i | −0.535806 | + | 0.195018i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.64528 | + | 13.2420i | 0.520195 | + | 0.901004i | ||||
\(217\) | 22.8848 | + | 13.2126i | 1.55352 | + | 0.896928i | ||||
\(218\) | 9.69641 | − | 1.70974i | 0.656724 | − | 0.115798i | ||||
\(219\) | −0.471235 | − | 2.67251i | −0.0318431 | − | 0.180591i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.678638 | − | 1.17544i | −0.0456501 | − | 0.0790684i | ||||
\(222\) | 12.5488 | + | 14.9551i | 0.842220 | + | 1.00372i | ||||
\(223\) | 1.67798 | + | 4.61022i | 0.112366 | + | 0.308723i | 0.983111 | − | 0.183012i | \(-0.0585848\pi\) |
−0.870744 | + | 0.491736i | \(0.836363\pi\) | |||||||
\(224\) | 2.98911 | + | 1.08795i | 0.199718 | + | 0.0726915i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.21600 | − | 6.89629i | 0.0808872 | − | 0.458734i | ||||
\(227\) | 2.65246i | 0.176050i | 0.996118 | + | 0.0880250i | \(0.0280555\pi\) | ||||
−0.996118 | + | 0.0880250i | \(0.971944\pi\) | |||||||
\(228\) | 0.381101 | + | 0.827231i | 0.0252390 | + | 0.0547847i | ||||
\(229\) | 23.1372 | 1.52895 | 0.764473 | − | 0.644655i | \(-0.222999\pi\) | ||||
0.764473 | + | 0.644655i | \(0.222999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.92555 | − | 2.45482i | −0.192487 | − | 0.161516i | ||||
\(232\) | 3.79654 | − | 10.4309i | 0.249255 | − | 0.684823i | ||||
\(233\) | −9.88772 | − | 27.1663i | −0.647766 | − | 1.77972i | −0.625824 | − | 0.779964i | \(-0.715237\pi\) |
−0.0219420 | − | 0.999759i | \(-0.506985\pi\) | |||||||
\(234\) | 4.10124 | − | 3.44135i | 0.268107 | − | 0.224968i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.0615945 | + | 0.106685i | −0.00400946 | + | 0.00694458i | ||||
\(237\) | −7.65490 | + | 1.34977i | −0.497239 | + | 0.0876767i | ||||
\(238\) | 1.56257 | − | 0.275523i | 0.101286 | − | 0.0178595i | ||||
\(239\) | −10.3736 | + | 17.9677i | −0.671016 | + | 1.16223i | 0.306601 | + | 0.951838i | \(0.400808\pi\) |
−0.977616 | + | 0.210395i | \(0.932525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.74748 | − | 3.98361i | 0.305812 | − | 0.256607i | −0.476946 | − | 0.878932i | \(-0.658256\pi\) |
0.782759 | + | 0.622326i | \(0.213812\pi\) | |||||||
\(242\) | −5.30865 | − | 14.5854i | −0.341253 | − | 0.937585i | ||||
\(243\) | −2.49487 | + | 6.85461i | −0.160046 | + | 0.439724i | ||||
\(244\) | −0.229964 | − | 0.192963i | −0.0147220 | − | 0.0123532i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.89639 | 0.630971 | ||||||||
\(247\) | −18.2447 | + | 12.6499i | −1.16088 | + | 0.804893i | ||||
\(248\) | 17.6676i | 1.12189i | ||||||||
\(249\) | −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 | \(0.690178\pi\) | |||||||
\(252\) | 0.138490 | + | 0.380499i | 0.00872408 | + | 0.0239692i | ||||
\(253\) | −2.33187 | − | 2.77902i | −0.146604 | − | 0.174715i | ||||
\(254\) | −13.5239 | − | 23.4241i | −0.848565 | − | 1.46976i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.573868 | + | 3.25456i | 0.0358667 | + | 0.203410i | ||||
\(257\) | −19.8510 | + | 3.50026i | −1.23827 | + | 0.218340i | −0.754174 | − | 0.656675i | \(-0.771962\pi\) |
−0.484096 | + | 0.875015i | \(0.660851\pi\) | |||||||
\(258\) | 3.44426 | + | 1.98855i | 0.214430 | + | 0.123801i | ||||
\(259\) | −17.9955 | − | 31.1692i | −1.11819 | − | 1.93676i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.75429 | − | 1.00248i | 0.170486 | − | 0.0620518i | ||||
\(262\) | 9.79493 | − | 26.9114i | 0.605133 | − | 1.66259i | ||||
\(263\) | 6.86869 | − | 8.18579i | 0.423542 | − | 0.504758i | −0.511506 | − | 0.859280i | \(-0.670912\pi\) |
0.935048 | + | 0.354522i | \(0.115357\pi\) | |||||||
\(264\) | 0.443387 | − | 2.51457i | 0.0272886 | − | 0.154761i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.60135 | − | 25.0998i | −0.404754 | − | 1.53897i | ||||
\(267\) | − | 0.00112860i | − | 6.90689e-5i | ||||||
\(268\) | 1.91815 | + | 0.338221i | 0.117169 | + | 0.0206601i | ||||
\(269\) | 18.3284 | + | 15.3793i | 1.11750 | + | 0.937693i | 0.998475 | − | 0.0551980i | \(-0.0175790\pi\) |
0.119024 | + | 0.992891i | \(0.462023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.4040 | + | 8.88231i | −1.48243 | + | 0.539562i | −0.951446 | − | 0.307817i | \(-0.900402\pi\) |
−0.530989 | + | 0.847379i | \(0.678179\pi\) | |||||||
\(272\) | 0.729285 | + | 0.869129i | 0.0442194 | + | 0.0526987i | ||||
\(273\) | 27.1260 | − | 15.6612i | 1.64174 | − | 0.947860i | ||||
\(274\) | 1.72309 | − | 2.98447i | 0.104095 | − | 0.180299i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.211961 | − | 1.20209i | −0.0127586 | − | 0.0723574i | ||||
\(277\) | 1.58803 | + | 0.916850i | 0.0954156 | + | 0.0550882i | 0.546949 | − | 0.837166i | \(-0.315789\pi\) |
−0.451533 | + | 0.892254i | \(0.649123\pi\) | |||||||
\(278\) | 4.85093 | − | 2.80069i | 0.290940 | − | 0.167974i | ||||
\(279\) | −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 | \(0.477277\pi\) | |||||||
\(282\) | 16.3921 | − | 19.5354i | 0.976136 | − | 1.16331i | ||||
\(283\) | −10.3762 | − | 1.82961i | −0.616803 | − | 0.108759i | −0.143488 | − | 0.989652i | \(-0.545832\pi\) |
−0.473315 | + | 0.880893i | \(0.656943\pi\) | |||||||
\(284\) | 0.227811 | 0.0135181 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.62522 | −0.273495 | ||||||||
\(287\) | −17.9675 | − | 3.16816i | −1.06059 | − | 0.187011i | ||||
\(288\) | −0.360969 | + | 0.430186i | −0.0212703 | + | 0.0253489i | ||||
\(289\) | −15.9080 | − | 5.79005i | −0.935767 | − | 0.340591i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0588 | + | 10.1186i | −0.706901 | + | 0.593161i | ||||
\(292\) | 0.215270 | − | 0.124286i | 0.0125977 | − | 0.00727331i | ||||
\(293\) | 20.7017 | + | 11.9521i | 1.20941 | + | 0.698251i | 0.962630 | − | 0.270822i | \(-0.0872953\pi\) |
0.246776 | + | 0.969072i | \(0.420629\pi\) | |||||||
\(294\) | 3.67372 | + | 20.8347i | 0.214256 | + | 1.21510i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.0316 | − | 20.8394i | 0.699325 | − | 1.21127i | ||||
\(297\) | 3.02072 | − | 1.74402i | 0.175280 | − | 0.101198i | ||||
\(298\) | 17.0936 | + | 20.3714i | 0.990206 | + | 1.18008i | ||||
\(299\) | 27.9593 | − | 10.1763i | 1.61693 | − | 0.588513i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.61668 | − | 4.71296i | −0.323740 | − | 0.271650i | ||||
\(302\) | 3.30271 | + | 0.582356i | 0.190049 | + | 0.0335108i | ||||
\(303\) | 18.4561i | 1.06028i | ||||||||
\(304\) | 13.1831 | − | 13.0619i | 0.756105 | − | 0.749151i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0486412 | + | 0.275858i | −0.00278063 | + | 0.0157697i | ||||
\(307\) | −10.0716 | + | 12.0029i | −0.574817 | + | 0.685040i | −0.972612 | − | 0.232434i | \(-0.925331\pi\) |
0.397795 | + | 0.917474i | \(0.369775\pi\) | |||||||
\(308\) | 0.119644 | − | 0.328719i | 0.00681734 | − | 0.0187305i | ||||
\(309\) | −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 | \(0.801585\pi\) | |||||||
\(312\) | 18.1362 | + | 10.4709i | 1.02676 | + | 0.592800i | ||||
\(313\) | 1.15525 | − | 0.203702i | 0.0652987 | − | 0.0115139i | −0.140903 | − | 0.990023i | \(-0.545001\pi\) |
0.206202 | + | 0.978509i | \(0.433890\pi\) | |||||||
\(314\) | −5.29299 | − | 30.0180i | −0.298701 | − | 1.69402i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.355995 | − | 0.616602i | −0.0200263 | − | 0.0346866i | ||||
\(317\) | −0.843086 | − | 1.00475i | −0.0473524 | − | 0.0564324i | 0.741848 | − | 0.670568i | \(-0.233949\pi\) |
−0.789201 | + | 0.614135i | \(0.789505\pi\) | |||||||
\(318\) | 1.90579 | + | 5.23610i | 0.106871 | + | 0.293626i | ||||
\(319\) | −2.37947 | − | 0.866056i | −0.133225 | − | 0.0484898i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.49603 | − | 8.48439i | 0.0835000 | − | 0.473552i | ||||
\(322\) | 34.7824i | 1.93835i | ||||||||
\(323\) | 0.305818 | − | 1.12059i | 0.0170162 | − | 0.0623515i | ||||
\(324\) | 0.875285 | 0.0486270 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.86847 | + | 7.44153i | 0.491179 | + | 0.412148i | ||||
\(327\) | −3.47817 | + | 9.55620i | −0.192343 | + | 0.528459i | ||||
\(328\) | −4.17204 | − | 11.4626i | −0.230362 | − | 0.632915i | ||||
\(329\) | −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 | \(0.0529462\pi\) | |||||||
\(332\) | −1.87789 | + | 0.331123i | −0.103063 | + | 0.0181727i | ||||
\(333\) | 6.25738 | − | 1.10335i | 0.342902 | − | 0.0604629i | ||||
\(334\) | −10.3045 | + | 17.8479i | −0.563837 | + | 0.976595i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −20.0572 | + | 16.8300i | −1.09421 | + | 0.918153i | ||||
\(337\) | −5.20541 | − | 14.3017i | −0.283557 | − | 0.779066i | −0.996931 | − | 0.0782827i | \(-0.975056\pi\) |
0.713374 | − | 0.700783i | \(-0.247166\pi\) | |||||||
\(338\) | 6.47258 | − | 17.7833i | 0.352062 | − | 0.967283i | ||||
\(339\) | 5.54061 | + | 4.64913i | 0.300925 | + | 0.252506i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.03027 | 0.218251 | ||||||||
\(342\) | 4.56251 | + | 0.420417i | 0.246713 | + | 0.0227335i | ||||
\(343\) | − | 10.5007i | − | 0.566987i | ||||||
\(344\) | 0.851248 | − | 4.82766i | 0.0458962 | − | 0.260290i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.4458 | − | 5.25786i | −0.776613 | − | 0.282664i | ||||
\(347\) | −6.84652 | − | 18.8107i | −0.367541 | − | 1.00981i | −0.976294 | − | 0.216450i | \(-0.930552\pi\) |
0.608753 | − | 0.793360i | \(-0.291670\pi\) | |||||||
\(348\) | −0.547659 | − | 0.652675i | −0.0293576 | − | 0.0349870i | ||||
\(349\) | 11.1408 | + | 19.2964i | 0.596353 | + | 1.03291i | 0.993354 | + | 0.115095i | \(0.0367174\pi\) |
−0.397002 | + | 0.917818i | \(0.629949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.96768 | + | 28.1731i | 0.265155 | + | 1.50377i | ||||
\(352\) | 0.477776 | − | 0.0842448i | 0.0254655 | − | 0.00449026i | ||||
\(353\) | −22.7029 | − | 13.1075i | −1.20835 | − | 0.697642i | −0.245952 | − | 0.969282i | \(-0.579101\pi\) |
−0.962399 | + | 0.271640i | \(0.912434\pi\) | |||||||
\(354\) | −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 | ||||
\(357\) | −0.560505 | + | 1.53997i | −0.0296651 | + | 0.0815041i | ||||
\(358\) | −4.70286 | + | 5.60465i | −0.248554 | + | 0.296215i | ||||
\(359\) | −4.91047 | + | 27.8486i | −0.259164 | + | 1.46979i | 0.525988 | + | 0.850492i | \(0.323696\pi\) |
−0.785152 | + | 0.619303i | \(0.787415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6801 | − | 3.47206i | −0.983161 | − | 0.182740i | ||||
\(362\) | 38.7389i | 2.03607i | ||||||||
\(363\) | 15.7879 | + | 2.78383i | 0.828649 | + | 0.146113i | ||||
\(364\) | 2.19784 | + | 1.84420i | 0.115198 | + | 0.0966626i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.50345 | − | 1.63912i | 0.235399 | − | 0.0856783i | ||||
\(367\) | −6.16747 | − | 7.35010i | −0.321939 | − | 0.383672i | 0.580666 | − | 0.814142i | \(-0.302792\pi\) |
−0.902605 | + | 0.430470i | \(0.858348\pi\) | |||||||
\(368\) | −21.5394 | + | 12.4358i | −1.12282 | + | 0.648258i | ||||
\(369\) | 1.61047 | − | 2.78942i | 0.0838378 | − | 0.145211i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.78383 | − | 10.1166i | −0.0926117 | − | 0.525227i | ||||
\(372\) | 1.17439 | + | 0.678036i | 0.0608895 | + | 0.0351545i | ||||
\(373\) | −11.2930 | + | 6.52003i | −0.584731 | + | 0.337595i | −0.763011 | − | 0.646385i | \(-0.776280\pi\) |
0.178280 | + | 0.983980i | \(0.442947\pi\) | |||||||
\(374\) | 0.185378 | − | 0.155551i | 0.00958568 | − | 0.00804334i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −29.5375 | − | 10.7508i | −1.52328 | − | 0.554428i | ||||
\(377\) | 13.3495 | − | 15.9093i | 0.687533 | − | 0.819370i | ||||
\(378\) | −32.9347 | − | 5.80728i | −1.69398 | − | 0.298694i | ||||
\(379\) | −9.93895 | −0.510530 | −0.255265 | − | 0.966871i | \(-0.582163\pi\) | ||||
−0.255265 | + | 0.966871i | \(0.582163\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.9365 | 1.43123 | ||||||||
\(382\) | 0.207106 | + | 0.0365184i | 0.0105965 | + | 0.00186845i | ||||
\(383\) | −11.5885 | + | 13.8106i | −0.592144 | + | 0.705689i | −0.976017 | − | 0.217697i | \(-0.930146\pi\) |
0.383873 | + | 0.923386i | \(0.374590\pi\) | |||||||
\(384\) | −17.5189 | − | 6.37637i | −0.894009 | − | 0.325393i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.30888 | + | 1.93738i | −0.117519 | + | 0.0986102i | ||||
\(387\) | 1.12099 | − | 0.647205i | 0.0569833 | − | 0.0328993i | ||||
\(388\) | −1.24873 | − | 0.720954i | −0.0633946 | − | 0.0366009i | ||||
\(389\) | −4.22852 | − | 23.9811i | −0.214395 | − | 1.21589i | −0.881954 | − | 0.471336i | \(-0.843772\pi\) |
0.667559 | − | 0.744557i | \(-0.267339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.778363 | + | 1.34816i | −0.0393635 | + | 0.0681796i | ||||
\(392\) | 22.5832 | − | 13.0384i | 1.14063 | − | 0.658541i | ||||
\(393\) | 19.0133 | + | 22.6592i | 0.959094 | + | 1.14300i | ||||
\(394\) | −25.0753 | + | 9.12667i | −1.26328 | + | 0.459795i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0473085 | + | 0.0396965i | 0.00237734 | + | 0.00199483i | ||||
\(397\) | −19.6684 | − | 3.46808i | −0.987131 | − | 0.174058i | −0.343300 | − | 0.939226i | \(-0.611545\pi\) |
−0.643831 | + | 0.765168i | \(0.722656\pi\) | |||||||
\(398\) | 11.7029i | 0.586611i | ||||||||
\(399\) | 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 | \(0.921230\pi\) | |||||||
\(402\) | −19.9871 | + | 23.8198i | −0.996868 | + | 1.18802i | ||||
\(403\) | −11.3055 | + | 31.0615i | −0.563166 | + | 1.54728i | ||||
\(404\) | −1.58859 | + | 0.578201i | −0.0790355 | + | 0.0287666i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.1391 | + | 21.0255i | 0.602453 | + | 1.04348i | ||||
\(407\) | −4.75382 | − | 2.74462i | −0.235638 | − | 0.136046i | ||||
\(408\) | −1.07904 | + | 0.190264i | −0.0534206 | + | 0.00941949i | ||||
\(409\) | −1.44702 | − | 8.20643i | −0.0715503 | − | 0.405782i | −0.999456 | − | 0.0329680i | \(-0.989504\pi\) |
0.927906 | − | 0.372814i | \(-0.121607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.77970 | + | 3.08253i | 0.0877862 | + | 0.152050i | ||||
\(412\) | −0.693960 | − | 0.827029i | −0.0341890 | − | 0.0407448i | ||||
\(413\) | 1.24004 | + | 3.40699i | 0.0610185 | + | 0.167647i | ||||
\(414\) | −5.77021 | − | 2.10018i | −0.283590 | − | 0.103218i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.690949 | + | 3.91856i | −0.0338765 | + | 0.192123i | ||||
\(417\) | 5.78542i | 0.283313i | ||||||||
\(418\) | −2.78600 | − | 2.81186i | −0.136268 | − | 0.137532i | ||||
\(419\) | 11.6553 | 0.569397 | 0.284698 | − | 0.958617i | \(-0.408107\pi\) | ||||
0.284698 | + | 0.958617i | \(0.408107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2337 | + | 13.6217i | 0.791182 | + | 0.663881i | 0.946038 | − | 0.324056i | \(-0.105047\pi\) |
−0.154855 | + | 0.987937i | \(0.549491\pi\) | |||||||
\(422\) | 7.04336 | − | 19.3515i | 0.342866 | − | 0.942015i | ||||
\(423\) | −2.83874 | − | 7.79937i | −0.138024 | − | 0.379218i | ||||
\(424\) | 5.26134 | − | 4.41479i | 0.255513 | − | 0.214401i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.81843 | + | 3.14962i | −0.0881033 | + | 0.152599i | ||||
\(427\) | −8.70105 | + | 1.53423i | −0.421073 | + | 0.0742465i | ||||
\(428\) | 0.777153 | − | 0.137033i | 0.0375651 | − | 0.00662374i | ||||
\(429\) | 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 | \(0.274771\pi\) | |||||||
\(432\) | −8.17893 | − | 22.4714i | −0.393509 | − | 1.08116i | ||||
\(433\) | −4.43639 | + | 12.1889i | −0.213199 | + | 0.585761i | −0.999485 | − | 0.0321031i | \(-0.989780\pi\) |
0.786285 | + | 0.617864i | \(0.212002\pi\) | |||||||
\(434\) | −29.6013 | − | 24.8384i | −1.42091 | − | 1.19228i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.931506 | −0.0446110 | ||||||||
\(437\) | 23.0278 | + | 10.8679i | 1.10157 | + | 0.519880i | ||||
\(438\) | 3.96832i | 0.189614i | ||||||||
\(439\) | 0.946035 | − | 5.36523i | 0.0451518 | − | 0.256068i | −0.953874 | − | 0.300209i | \(-0.902944\pi\) |
0.999025 | + | 0.0441401i | \(0.0140548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.47035 | + | 2.35502i | 0.308112 | + | 0.112144i | ||||
\(442\) | 0.678827 | + | 1.86506i | 0.0322885 | + | 0.0887119i | ||||
\(443\) | −15.9043 | − | 18.9540i | −0.755636 | − | 0.900532i | 0.241928 | − | 0.970294i | \(-0.422220\pi\) |
−0.997564 | + | 0.0697627i | \(0.977776\pi\) | |||||||
\(444\) | −0.923487 | − | 1.59953i | −0.0438267 | − | 0.0759102i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.24579 | − | 7.06523i | −0.0589899 | − | 0.334549i | ||||
\(447\) | −27.0494 | + | 4.76954i | −1.27939 | + | 0.225591i | ||||
\(448\) | 25.9978 | + | 15.0098i | 1.22828 | + | 0.709147i | ||||
\(449\) | 17.2809 | + | 29.9315i | 0.815538 | + | 1.41255i | 0.908941 | + | 0.416925i | \(0.136892\pi\) |
−0.0934033 | + | 0.995628i | \(0.529775\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.61481 | + | 0.951713i | −0.123127 | + | 0.0448144i | ||||
\(452\) | −0.226590 | + | 0.622552i | −0.0106579 | + | 0.0292824i | ||||
\(453\) | −2.22652 | + | 2.65346i | −0.104611 | + | 0.124670i | ||||
\(454\) | 0.673532 | − | 3.81979i | 0.0316104 | − | 0.179272i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.55861 | + | 17.3329i | 0.213476 | + | 0.811686i | ||||
\(457\) | − | 11.6425i | − | 0.544613i | −0.962211 | − | 0.272307i | \(-0.912214\pi\) | ||
0.962211 | − | 0.272307i | \(-0.0877865\pi\) | |||||||
\(458\) | −33.3197 | − | 5.87515i | −1.55693 | − | 0.274528i | ||||
\(459\) | −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 | \(0.411068\pi\) | |||||||
\(462\) | 3.58971 | + | 4.27805i | 0.167008 | + | 0.199033i | ||||
\(463\) | 7.35009 | − | 4.24358i | 0.341588 | − | 0.197216i | −0.319386 | − | 0.947625i | \(-0.603477\pi\) |
0.660974 | + | 0.750409i | \(0.270143\pi\) | |||||||
\(464\) | −8.68018 | + | 15.0345i | −0.402967 | + | 0.697960i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.34098 | + | 41.6327i | 0.340064 | + | 1.92860i | ||||
\(467\) | −15.5280 | − | 8.96512i | −0.718552 | − | 0.414856i | 0.0956676 | − | 0.995413i | \(-0.469501\pi\) |
−0.814219 | + | 0.580557i | \(0.802835\pi\) | |||||||
\(468\) | −0.438650 | + | 0.253255i | −0.0202766 | + | 0.0117067i | ||||
\(469\) | 43.9135 | − | 36.8478i | 2.02774 | − | 1.70147i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.5840 | + | 10.7677i | 1.36316 | + | 0.496149i | ||||
\(472\) | −1.55816 | + | 1.85694i | −0.0717201 | + | 0.0854727i | ||||
\(473\) | −1.10127 | − | 0.194184i | −0.0506365 | − | 0.00892859i | ||||
\(474\) | 11.3665 | 0.522081 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.150111 | −0.00688034 | ||||||||
\(477\) | 1.78599 | + | 0.314919i | 0.0817751 | + | 0.0144192i | ||||
\(478\) | 19.5015 | − | 23.2410i | 0.891978 | − | 1.06302i | ||||
\(479\) | 3.18514 | + | 1.15929i | 0.145533 | + | 0.0529695i | 0.413759 | − | 0.910386i | \(-0.364215\pi\) |
−0.268227 | + | 0.963356i | \(0.586438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.4881 | − | 28.9389i | 1.57252 | − | 1.31950i | ||||
\(482\) | −7.84836 | + | 4.53125i | −0.357483 | + | 0.206393i | ||||
\(483\) | −31.1122 | − | 17.9626i | −1.41565 | − | 0.817327i | ||||
\(484\) | 0.254993 | + | 1.44614i | 0.0115906 | + | 0.0657336i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.33342 | − | 9.23776i | 0.241929 | − | 0.419033i | ||||
\(487\) | −9.66655 | + | 5.58098i | −0.438033 | + | 0.252899i | −0.702763 | − | 0.711424i | \(-0.748051\pi\) |
0.264730 | + | 0.964323i | \(0.414717\pi\) | |||||||
\(488\) | −3.79706 | − | 4.52516i | −0.171885 | − | 0.204844i | ||||
\(489\) | −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 | \(0.548674\pi\) | |||||||
\(492\) | −0.922050 | − | 0.162582i | −0.0415692 | − | 0.00732977i | ||||
\(493\) | 1.08660i | 0.0489379i | ||||||||
\(494\) | 29.4862 | − | 13.5842i | 1.32665 | − | 0.611181i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.79810 | − | 27.2114i | 0.215441 | − | 1.22183i | ||||
\(497\) | 4.30978 | − | 5.13620i | 0.193320 | − | 0.230390i | ||||
\(498\) | 10.4118 | − | 28.6061i | 0.466562 | − | 1.28187i | ||||
\(499\) | 0.921587 | − | 0.335430i | 0.0412559 | − | 0.0150159i | −0.321310 | − | 0.946974i | \(-0.604123\pi\) |
0.362566 | + | 0.931958i | \(0.381901\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.6431 | − | 18.4343i | −0.475498 | − | 0.823586i | ||||
\(502\) | 9.86516 | + | 5.69566i | 0.440304 | + | 0.254210i | ||||
\(503\) | 3.51768 | − | 0.620262i | 0.156846 | − | 0.0276561i | −0.0946739 | − | 0.995508i | \(-0.530181\pi\) |
0.251520 | + | 0.967852i | \(0.419070\pi\) | |||||||
\(504\) | 1.38360 | + | 7.84680i | 0.0616305 | + | 0.349524i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.65245 | + | 4.59417i | 0.117916 | + | 0.204236i | ||||
\(507\) | 12.5642 | + | 14.9734i | 0.557994 | + | 0.664991i | ||||
\(508\) | 0.875205 | + | 2.40461i | 0.0388310 | + | 0.106687i | ||||
\(509\) | −12.2069 | − | 4.44293i | −0.541059 | − | 0.196929i | 0.0570105 | − | 0.998374i | \(-0.481843\pi\) |
−0.598070 | + | 0.801444i | \(0.704065\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.27039 | − | 7.20474i | 0.0561988 | − | 0.318719i | ||||
\(512\) | 19.8547i | 0.877460i | ||||||||
\(513\) | −14.1353 | + | 19.9901i | −0.624088 | + | 0.882584i | ||||
\(514\) | 29.4761 | 1.30013 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.288234 | − | 0.241857i | −0.0126888 | − | 0.0106472i | ||||
\(517\) | −2.45243 | + | 6.73799i | −0.107858 | + | 0.296337i | ||||
\(518\) | 18.0005 | + | 49.4561i | 0.790898 | + | 2.17298i | ||||
\(519\) | 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 | \(0.999241\pi\) | |||||||
\(522\) | −4.22098 | + | 0.744273i | −0.184747 | + | 0.0325760i | ||||
\(523\) | 1.94240 | − | 0.342497i | 0.0849352 | − | 0.0149764i | −0.131019 | − | 0.991380i | \(-0.541825\pi\) |
0.215954 | + | 0.976403i | \(0.430714\pi\) | |||||||
\(524\) | −1.35471 | + | 2.34642i | −0.0591807 | + | 0.102504i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.9702 | + | 10.0441i | −0.521923 | + | 0.437946i | ||||
\(527\) | −0.591508 | − | 1.62515i | −0.0257665 | − | 0.0707929i | ||||
\(528\) | −1.36580 | + | 3.75250i | −0.0594387 | + | 0.163306i | ||||
\(529\) | −8.52294 | − | 7.15159i | −0.370563 | − | 0.310939i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.640075 | −0.0277769 | ||||||||
\(532\) | 0.202699 | + | 2.44701i | 0.00878810 | + | 0.106091i | ||||
\(533\) | − | 22.8222i | − | 0.988538i | ||||||
\(534\) | −0.000286581 | 0.00162528i | −1.24016e−5 | 7.03328e-5i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 36.0155 | + | 13.1086i | 1.55563 | + | 0.566204i | ||||
\(537\) | −2.58456 | − | 7.10102i | −0.111532 | − | 0.306431i | ||||
\(538\) | −22.4893 | − | 26.8017i | −0.969583 | − | 1.15550i | ||||
\(539\) | −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 | \(-0.257114\pi\) | |||||||
\(542\) | 37.3994 | − | 6.59452i | 1.60644 | − | 0.283259i | ||||
\(543\) | −34.6512 | − | 20.0059i | −1.48702 | − | 0.858534i | ||||
\(544\) | −0.104092 | − | 0.180293i | −0.00446291 | − | 0.00772999i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −43.0408 | + | 15.6656i | −1.84198 | + | 0.670425i | ||||
\(547\) | 2.85466 | − | 7.84310i | 0.122056 | − | 0.335347i | −0.863584 | − | 0.504205i | \(-0.831786\pi\) |
0.985640 | + | 0.168858i | \(0.0540079\pi\) | |||||||
\(548\) | −0.209571 | + | 0.249757i | −0.00895241 | + | 0.0106691i | ||||
\(549\) | 0.270855 | − | 1.53609i | 0.0115598 | − | 0.0655589i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.7129 | − | 1.46726i | 0.754597 | − | 0.0625072i | ||||
\(552\) | − | 24.0192i | − | 1.02233i | ||||||
\(553\) | −20.6366 | − | 3.63880i | −0.877559 | − | 0.154737i | ||||
\(554\) | −2.05410 | − | 1.72359i | −0.0872703 | − | 0.0732285i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.497974 | + | 0.181248i | −0.0211188 | + | 0.00768661i | ||||
\(557\) | 15.3198 | + | 18.2574i | 0.649120 | + | 0.773591i | 0.985781 | − | 0.168035i | \(-0.0537421\pi\) |
−0.336661 | + | 0.941626i | \(0.609298\pi\) | |||||||
\(558\) | 5.90790 | − | 3.41093i | 0.250101 | − | 0.144396i | ||||
\(559\) | 4.58581 | − | 7.94285i | 0.193959 | − | 0.335947i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0434025 | + | 0.246148i | 0.00183246 | + | 0.0103924i | ||||
\(562\) | −17.3299 | − | 10.0054i | −0.731019 | − | 0.422054i | ||||
\(563\) | 16.9979 | − | 9.81371i | 0.716374 | − | 0.413599i | −0.0970426 | − | 0.995280i | \(-0.530938\pi\) |
0.813417 | + | 0.581681i | \(0.197605\pi\) | |||||||
\(564\) | −1.84819 | + | 1.55082i | −0.0778230 | + | 0.0653012i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.4782 | + | 5.26962i | 0.608562 | + | 0.221499i | ||||
\(567\) | 16.5589 | − | 19.7341i | 0.695407 | − | 0.828753i | ||||
\(568\) | 4.41467 | + | 0.778426i | 0.185236 | + | 0.0326620i | ||||
\(569\) | −23.7705 | −0.996510 | −0.498255 | − | 0.867030i | \(-0.666026\pi\) | ||||
−0.498255 | + | 0.867030i | \(0.666026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5361 | −0.733865 | −0.366933 | − | 0.930248i | \(-0.619592\pi\) | ||||
−0.366933 | + | 0.930248i | \(0.619592\pi\) | |||||||
\(572\) | 0.430933 | + | 0.0759852i | 0.0180182 | + | 0.00317710i | ||||
\(573\) | −0.139621 | + | 0.166393i | −0.00583273 | + | 0.00695118i | ||||
\(574\) | 25.0704 | + | 9.12489i | 1.04642 | + | 0.380866i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.05981 | + | 3.40658i | −0.169159 | + | 0.141941i | ||||
\(577\) | −22.4543 | + | 12.9640i | −0.934786 | + | 0.539699i | −0.888322 | − | 0.459221i | \(-0.848128\pi\) |
−0.0464636 | + | 0.998920i | \(0.514795\pi\) | |||||||
\(578\) | 21.4388 | + | 12.3777i | 0.891737 | + | 0.514844i | ||||
\(579\) | −0.540578 | − | 3.06577i | −0.0224656 | − | 0.127409i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.0610 | + | 48.6030i | −1.16417 | + | 2.01639i | ||||
\(582\) | 19.9352 | − | 11.5096i | 0.826341 | − | 0.477088i | ||||
\(583\) | −1.00709 | − | 1.20020i | −0.0417093 | − | 0.0497072i | ||||
\(584\) | 4.59634 | − | 1.67293i | 0.190198 | − | 0.0692264i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.7774 | − | 22.4689i | −1.10616 | − | 0.928182i | ||||
\(587\) | −3.98064 | − | 0.701894i | −0.164299 | − | 0.0289703i | 0.0908937 | − | 0.995861i | \(-0.471028\pi\) |
−0.255192 | + | 0.966890i | \(0.582139\pi\) | |||||||
\(588\) | − | 2.00153i | − | 0.0825416i | ||||||
\(589\) | −25.6934 | + | 11.8368i | −1.05868 | + | 0.487728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.78598 | − | 27.1426i | 0.196869 | − | 1.11650i | ||||
\(592\) | −24.1905 | + | 28.8291i | −0.994221 | + | 1.18487i | ||||
\(593\) | −6.44918 | + | 17.7190i | −0.264836 | + | 0.727631i | 0.733988 | + | 0.679162i | \(0.237657\pi\) |
−0.998825 | + | 0.0484695i | \(0.984566\pi\) | |||||||
\(594\) | −4.79298 | + | 1.74450i | −0.196658 | + | 0.0715777i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.25795 | − | 2.17883i | −0.0515275 | − | 0.0892482i | ||||
\(597\) | −10.4680 | − | 6.04369i | −0.428426 | − | 0.247352i | ||||
\(598\) | −42.8480 | + | 7.55526i | −1.75219 | + | 0.308958i | ||||
\(599\) | 6.74122 | + | 38.2313i | 0.275439 | + | 1.56209i | 0.737565 | + | 0.675276i | \(0.235976\pi\) |
−0.462126 | + | 0.886814i | \(0.652913\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.179210 | − | 0.310400i | −0.00731011 | − | 0.0126615i | 0.862347 | − | 0.506317i | \(-0.168994\pi\) |
−0.869657 | + | 0.493656i | \(0.835660\pi\) | |||||||
\(602\) | 6.89180 | + | 8.21332i | 0.280889 | + | 0.334750i | ||||
\(603\) | 3.46132 | + | 9.50989i | 0.140956 | + | 0.387273i | ||||
\(604\) | −0.298147 | − | 0.108517i | −0.0121314 | − | 0.00441548i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.68652 | − | 26.5785i | 0.190377 | − | 1.07968i | ||||
\(607\) | 4.56885i | 0.185444i | 0.995692 | + | 0.0927219i | \(0.0295568\pi\) | ||||
−0.995692 | + | 0.0927219i | \(0.970443\pi\) | |||||||
\(608\) | −2.79844 | + | 1.94029i | −0.113492 | + | 0.0786890i | ||||
\(609\) | −25.0759 | −1.01613 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.0507 | − | 37.8020i | −1.82256 | − | 1.52931i | ||||
\(612\) | 0.00906382 | − | 0.0249026i | 0.000366383 | − | 0.00100663i | ||||
\(613\) | 5.77762 | + | 15.8739i | 0.233356 | + | 0.641140i | 1.00000 | 0.000932984i | \(-0.000296978\pi\) | |
−0.766644 | + | 0.642073i | \(0.778075\pi\) | |||||||
\(614\) | 17.5519 | − | 14.7278i | 0.708337 | − | 0.594365i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.44177 | − | 5.96132i | 0.138673 | − | 0.240188i | ||||
\(617\) | −23.9952 | + | 4.23101i | −0.966011 | + | 0.170334i | −0.634334 | − | 0.773059i | \(-0.718726\pi\) |
−0.331677 | + | 0.943393i | \(0.607615\pi\) | |||||||
\(618\) | 16.9735 | − | 2.99289i | 0.682774 | − | 0.120392i | ||||
\(619\) | −16.6616 | + | 28.8588i | −0.669687 | + | 1.15993i | 0.308305 | + | 0.951288i | \(0.400238\pi\) |
−0.977992 | + | 0.208644i | \(0.933095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.1351 | − | 21.0909i | 1.00864 | − | 0.846348i | ||||
\(622\) | −1.75654 | − | 4.82605i | −0.0704307 | − | 0.193507i | ||||
\(623\) | 0.00104061 | − | 0.00285906i | 4.16913e−5 | − | 0.000114546i | ||||
\(624\) | −25.0894 | − | 21.0525i | −1.00438 | − | 0.842776i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.71540 | −0.0685610 | ||||||||
\(627\) | 3.95392 | − | 1.03990i | 0.157904 | − | 0.0415294i | ||||
\(628\) | 2.88375i | 0.115074i | ||||||||
\(629\) | −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 | \(0.879643\pi\) | |||||||
\(632\) | −4.79180 | − | 13.1654i | −0.190608 | − | 0.523690i | ||||
\(633\) | 13.6721 | + | 16.2938i | 0.543418 | + | 0.647621i | ||||
\(634\) | 0.958988 | + | 1.66102i | 0.0380863 | + | 0.0659674i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0915416 | − | 0.519158i | −0.00362986 | − | 0.0205860i | ||||
\(637\) | 48.0471 | − | 8.47200i | 1.90370 | − | 0.335673i | ||||
\(638\) | 3.20674 | + | 1.85141i | 0.126956 | + | 0.0732981i | ||||
\(639\) | 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 | \(0.344452\pi\) | |||||||
\(642\) | −4.30883 | + | 11.8384i | −0.170056 | + | 0.467225i | ||||
\(643\) | 9.82279 | − | 11.7063i | 0.387373 | − | 0.461653i | −0.536754 | − | 0.843739i | \(-0.680350\pi\) |
0.924127 | + | 0.382086i | \(0.124794\pi\) | |||||||
\(644\) | 0.571420 | − | 3.24069i | 0.0225171 | − | 0.127701i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.724955 | + | 1.53610i | −0.0285230 | + | 0.0604372i | ||||
\(647\) | 23.8972i | 0.939495i | 0.882801 | + | 0.469748i | \(0.155655\pi\) | ||||
−0.882801 | + | 0.469748i | \(0.844345\pi\) | |||||||
\(648\) | 16.9619 | + | 2.99084i | 0.666326 | + | 0.117491i | ||||
\(649\) | 0.423600 | + | 0.355443i | 0.0166278 | + | 0.0139523i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.5044 | − | 13.6505i | 1.46991 | − | 0.535005i | ||||
\(652\) | −0.704025 | − | 0.839024i | −0.0275718 | − | 0.0328587i | ||||
\(653\) | 23.5046 | − | 13.5704i | 0.919805 | − | 0.531050i | 0.0362323 | − | 0.999343i | \(-0.488464\pi\) |
0.883573 | + | 0.468294i | \(0.155131\pi\) | |||||||
\(654\) | 7.43547 | − | 12.8786i | 0.290750 | − | 0.503594i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.31275 | + | 18.7875i | 0.129341 | + | 0.733530i | ||||
\(657\) | 1.11852 | + | 0.645778i | 0.0436376 | + | 0.0251942i | ||||
\(658\) | 59.5384 | − | 34.3745i | 2.32105 | − | 1.34006i | ||||
\(659\) | 35.1081 | − | 29.4592i | 1.36762 | − | 1.14757i | 0.394073 | − | 0.919079i | \(-0.371066\pi\) |
0.973546 | − | 0.228490i | \(-0.0733787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.2794 | − | 6.28920i | −0.672092 | − | 0.244622i | −0.0166438 | − | 0.999861i | \(-0.505298\pi\) |
−0.655448 | + | 0.755240i | \(0.727520\pi\) | |||||||
\(662\) | −11.9608 | + | 14.2543i | −0.464870 | + | 0.554010i | ||||
\(663\) | −2.01883 | − | 0.355973i | −0.0784047 | − | 0.0138249i | ||||
\(664\) | −37.5226 | −1.45616 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.29138 | −0.360034 | ||||||||
\(667\) | −23.4581 | − | 4.13629i | −0.908300 | − | 0.160158i | ||||
\(668\) | 1.25329 | − | 1.49361i | 0.0484911 | − | 0.0577895i | ||||
\(669\) | 6.96308 | + | 2.53435i | 0.269208 | + | 0.0979837i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.03226 | + | 0.866173i | −0.0398501 | + | 0.0334382i | ||||
\(672\) | 4.16069 | − | 2.40218i | 0.160502 | − | 0.0926660i | ||||
\(673\) | −5.04007 | − | 2.90989i | −0.194280 | − | 0.112168i | 0.399704 | − | 0.916644i | \(-0.369113\pi\) |
−0.593985 | + | 0.804476i | \(0.702446\pi\) | |||||||
\(674\) | 3.86467 | + | 21.9176i | 0.148862 | + | 0.844236i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.895204 | + | 1.55054i | −0.0344309 | + | 0.0596361i | ||||
\(677\) | 15.4877 | − | 8.94182i | 0.595240 | − | 0.343662i | −0.171926 | − | 0.985110i | \(-0.554999\pi\) |
0.767167 | + | 0.641448i | \(0.221666\pi\) | |||||||
\(678\) | −6.79846 | − | 8.10209i | −0.261093 | − | 0.311159i | ||||
\(679\) | −39.8783 | + | 14.5145i | −1.53039 | + | 0.557016i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.06890 | + | 2.57511i | 0.117600 | + | 0.0986784i | ||||
\(682\) | −5.80396 | − | 1.02340i | −0.222245 | − | 0.0391878i | ||||
\(683\) | 13.4534i | 0.514779i | 0.966308 | + | 0.257390i | \(0.0828624\pi\) | ||||
−0.966308 | + | 0.257390i | \(0.917138\pi\) | |||||||
\(684\) | −0.418184 | − | 0.114125i | −0.0159897 | − | 0.00436369i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.66642 | + | 15.1220i | −0.101804 | + | 0.577362i | ||||
\(687\) | 22.4624 | − | 26.7697i | 0.856995 | − | 1.02133i | ||||
\(688\) | −2.62216 | + | 7.20433i | −0.0999689 | + | 0.274662i | ||||
\(689\) | 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 | \(0.847355\pi\) | |||||||
\(692\) | 1.25955 | + | 0.727199i | 0.0478807 | + | 0.0276439i | ||||
\(693\) | 1.78999 | − | 0.315623i | 0.0679960 | − | 0.0119895i | ||||
\(694\) | 5.08309 | + | 28.8276i | 0.192951 | + | 1.09428i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.38274 | − | 14.5193i | −0.317747 | − | 0.550354i | ||||
\(697\) | 0.767532 | + | 0.914709i | 0.0290723 | + | 0.0346471i | ||||
\(698\) | −11.1439 | − | 30.6176i | −0.421802 | − | 1.15889i | ||||
\(699\) | −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 | \(0.0367528\pi\) | |||||||
\(702\) | − | 41.8333i | − | 1.57890i | ||||||
\(703\) | 38.3670 | + | 3.53535i | 1.44704 | + | 0.133338i | ||||
\(704\) | 4.57849 | 0.172558 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.3659 | + | 24.6409i | 1.10520 | + | 0.927372i | ||||
\(707\) | −17.0173 | + | 46.7548i | −0.640003 | + | 1.75839i | ||||
\(708\) | 0.0636359 | + | 0.174838i | 0.00239158 | + | 0.00657083i | ||||
\(709\) | 21.5824 | − | 18.1098i | 0.810544 | − | 0.680127i | −0.140193 | − | 0.990124i | \(-0.544772\pi\) |
0.950738 | + | 0.309997i | \(0.100328\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.84971 | − | 3.20379i | 0.0693696 | − | 0.120152i | ||||
\(712\) | 0.00200331 | 0.000353238i | 7.50773e−5 | 1.32382e-5i | ||||||
\(713\) | 37.3364 | − | 6.58341i | 1.39826 | − | 0.246551i | ||||
\(714\) | 1.19822 | − | 2.07538i | 0.0448423 | − | 0.0776691i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.530243 | − | 0.444926i | 0.0198161 | − | 0.0166277i | ||||
\(717\) | 10.7175 | + | 29.4460i | 0.400251 | + | 1.09968i | ||||
\(718\) | 14.1431 | − | 38.8577i | 0.527814 | − | 1.45016i | ||||
\(719\) | 0.929140 | + | 0.779641i | 0.0346511 | + | 0.0290757i | 0.659949 | − | 0.751311i | \(-0.270578\pi\) |
−0.625298 | + | 0.780386i | \(0.715022\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.7746 | −1.18335 | ||||||||
\(722\) | 26.0194 | + | 9.74346i | 0.968341 | + | 0.362614i | ||||
\(723\) | − | 9.36027i | − | 0.348112i | ||||||
\(724\) | 0.636420 | − | 3.60931i | 0.0236523 | − | 0.134139i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.0291 | − | 8.01795i | −0.817578 | − | 0.297574i | ||||
\(727\) | −12.2347 | − | 33.6146i | −0.453761 | − | 1.24670i | −0.930058 | − | 0.367413i | \(-0.880244\pi\) |
0.476297 | − | 0.879284i | \(-0.341979\pi\) | |||||||
\(728\) | 36.2896 | + | 43.2482i | 1.34498 | + | 1.60289i | ||||
\(729\) | 14.9989 | + | 25.9788i | 0.555514 | + | 0.962178i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0833274 | + | 0.472573i | 0.00308198 | + | 0.0174788i | ||||
\(732\) | −0.446516 | + | 0.0787328i | −0.0165037 | + | 0.00291005i | ||||
\(733\) | 32.7765 | + | 18.9235i | 1.21063 | + | 0.698957i | 0.962896 | − | 0.269872i | \(-0.0869813\pi\) |
0.247732 | + | 0.968828i | \(0.420315\pi\) | |||||||
\(734\) | 7.01533 | + | 12.1509i | 0.258941 | + | 0.448498i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.28850 | − | 1.56089i | 0.158076 | − | 0.0575350i | ||||
\(737\) | 2.99028 | − | 8.21574i | 0.110149 | − | 0.302631i | ||||
\(738\) | −3.02754 | + | 3.60808i | −0.111445 | + | 0.132815i | ||||
\(739\) | −1.31048 | + | 7.43210i | −0.0482067 | + | 0.273394i | −0.999378 | − | 0.0352702i | \(-0.988771\pi\) |
0.951171 | + | 0.308664i | \(0.0998819\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.07676 | + | 33.3901i | −0.113028 | + | 1.22662i | ||||
\(742\) | 15.0218i | 0.551467i | ||||||||
\(743\) | 9.03644 | + | 1.59337i | 0.331515 | + | 0.0584550i | 0.336928 | − | 0.941530i | \(-0.390612\pi\) |
−0.00541343 | + | 0.999985i | \(0.501723\pi\) | |||||||
\(744\) | 20.4414 | + | 17.1523i | 0.749417 | + | 0.628835i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.9186 | − | 6.52185i | 0.656047 | − | 0.238782i | ||||
\(747\) | −6.36864 | − | 7.58984i | −0.233016 | − | 0.277698i | ||||
\(748\) | −0.0198272 | + | 0.0114472i | −0.000724954 | + | 0.000418552i | ||||
\(749\) | 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 | \(0.883254\pi\) | |||||||
\(752\) | 42.5735 | + | 24.5798i | 1.55250 | + | 0.896335i | ||||
\(753\) | −10.1893 | + | 5.88280i | −0.371319 | + | 0.214381i | ||||
\(754\) | −23.2643 | + | 19.5211i | −0.847235 | + | 0.710915i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.97313 | + | 1.08213i | 0.108132 | + | 0.0393568i | ||||
\(757\) | 34.1163 | − | 40.6582i | 1.23998 | − | 1.47775i | 0.417779 | − | 0.908549i | \(-0.362809\pi\) |
0.822199 | − | 0.569199i | \(-0.192747\pi\) | |||||||
\(758\) | 14.3130 | + | 2.52377i | 0.519872 | + | 0.0916675i | ||||
\(759\) | −5.47919 | −0.198882 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.6886 | −0.604960 | −0.302480 | − | 0.953156i | \(-0.597815\pi\) | ||||
−0.302480 | + | 0.953156i | \(0.597815\pi\) | |||||||
\(762\) | −40.2312 | − | 7.09384i | −1.45742 | − | 0.256983i | ||||
\(763\) | −17.6225 | + | 21.0016i | −0.637976 | + | 0.760310i | ||||
\(764\) | −0.0186962 | − | 0.00680487i | −0.000676405 | − | 0.000246191i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.1954 | − | 16.9459i | 0.729689 | − | 0.612281i | ||||
\(767\) | −3.92767 | + | 2.26764i | −0.141820 | + | 0.0818799i | ||||
\(768\) | 4.32266 | + | 2.49569i | 0.155981 | + | 0.0900554i | ||||
\(769\) | 1.07276 | + | 6.08395i | 0.0386849 | + | 0.219393i | 0.998022 | − | 0.0628711i | \(-0.0200257\pi\) |
−0.959337 | + | 0.282264i | \(0.908915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2223 | + | 26.3657i | −0.548217 | + | 0.949539i | ||||
\(772\) | 0.246947 | − | 0.142575i | 0.00888783 | − | 0.00513139i | ||||
\(773\) | −18.0982 | − | 21.5686i | −0.650948 | − | 0.775769i | 0.335109 | − | 0.942179i | \(-0.391227\pi\) |
−0.986057 | + | 0.166410i | \(0.946782\pi\) | |||||||
\(774\) | −1.77868 | + | 0.647385i | −0.0639332 | + | 0.0232698i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −21.7352 | − | 18.2380i | −0.780249 | − | 0.654707i | ||||
\(777\) | −53.5335 | − | 9.43940i | −1.92050 | − | 0.338637i | ||||
\(778\) | 35.6088i | 1.27664i | ||||||||
\(779\) | 13.8745 | − | 13.7469i | 0.497106 | − | 0.492534i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.177572 | − | 1.00706i | 0.00635403 | − | 0.0360355i | ||||
\(782\) | 1.46325 | − | 1.74383i | 0.0523257 | − | 0.0623594i | ||||
\(783\) | 7.83313 | − | 21.5214i | 0.279933 | − | 0.769111i | ||||
\(784\) | −38.3233 | + | 13.9486i | −1.36869 | + | 0.498163i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.6271 | − | 37.4593i | −0.771414 | − | 1.33613i | ||||
\(787\) | −4.73601 | − | 2.73433i | −0.168820 | − | 0.0974685i | 0.413209 | − | 0.910636i | \(-0.364408\pi\) |
−0.582030 | + | 0.813168i | \(0.697741\pi\) | |||||||
\(788\) | 2.48621 | − | 0.438386i | 0.0885676 | − | 0.0156169i | ||||
\(789\) | −2.80257 | − | 15.8941i | −0.0997740 | − | 0.565847i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.74930 | + | 16.8863i | 0.346645 | + | 0.600407i | ||||
\(792\) | 0.781134 | + | 0.930919i | 0.0277564 | + | 0.0330788i | ||||
\(793\) | −3.78000 | − | 10.3855i | −0.134232 | − | 0.368798i | ||||
\(794\) | 27.4437 | + | 9.98870i | 0.973942 | + | 0.354486i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.192260 | − | 1.09036i | 0.00681447 | − | 0.0386468i | ||||
\(797\) | − | 47.2273i | − | 1.67288i | −0.548061 | − | 0.836439i | \(-0.684634\pi\) | ||
0.548061 | − | 0.836439i | \(-0.315366\pi\) | |||||||
\(798\) | −35.4493 | − | 16.7301i | −1.25489 | − | 0.592239i | ||||
\(799\) | 3.07694 | 0.108854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.000411469 | 0 | 0.000345264i | 1.45386e−5 | 0 | 1.21993e-5i | ||||
\(802\) | 8.20414 | − | 22.5407i | 0.289698 | − | 0.795939i | ||||
\(803\) | −0.381624 | − | 1.04850i | −0.0134672 | − | 0.0370009i | ||||
\(804\) | 2.25353 | − | 1.89094i | 0.0794759 | − | 0.0666882i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.1683 | − | 41.8607i | 0.851292 | − | 1.47448i | ||||
\(807\) | 35.5877 | − | 6.27507i | 1.25275 | − | 0.220893i | ||||
\(808\) | −32.7606 | + | 5.77657i | −1.15251 | + | 0.203219i | ||||
\(809\) | −3.06691 | + | 5.31204i | −0.107827 | + | 0.186762i | −0.914890 | − | 0.403704i | \(-0.867723\pi\) |
0.807063 | + | 0.590466i | \(0.201056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6831 | − | 17.3552i | 0.726281 | − | 0.609422i | −0.202834 | − | 0.979213i | \(-0.565015\pi\) |
0.929115 | + | 0.369791i | \(0.120571\pi\) | |||||||
\(812\) | −0.785586 | − | 2.15838i | −0.0275687 | − | 0.0757443i | ||||
\(813\) | −13.4154 | + | 36.8586i | −0.470500 | + | 1.29269i | ||||
\(814\) | 6.14901 | + | 5.15963i | 0.215523 | + | 0.180845i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.71360 | 0.0599880 | ||||||||
\(817\) | 7.59103 | − | 1.99647i | 0.265577 | − | 0.0698476i | ||||
\(818\) | 12.1855i | 0.426055i | ||||||||
\(819\) | −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 | \(0.321414\pi\) | |||||||
\(822\) | −1.78020 | − | 4.89105i | −0.0620914 | − | 0.170595i | ||||
\(823\) | −19.3760 | − | 23.0915i | −0.675407 | − | 0.804918i | 0.314102 | − | 0.949389i | \(-0.398296\pi\) |
−0.989509 | + | 0.144471i | \(0.953852\pi\) | |||||||
\(824\) | −10.6221 | − | 18.3980i | −0.370038 | − | 0.640925i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.920649 | − | 5.22126i | −0.0320335 | − | 0.181671i | ||||
\(827\) | 20.1600 | − | 3.55475i | 0.701032 | − | 0.123611i | 0.188239 | − | 0.982123i | \(-0.439722\pi\) |
0.512793 | + | 0.858512i | \(0.328611\pi\) | |||||||
\(828\) | 0.503109 | + | 0.290470i | 0.0174843 | + | 0.0100945i | ||||
\(829\) | −10.4604 | − | 18.1179i | −0.363303 | − | 0.629259i | 0.625199 | − | 0.780465i | \(-0.285018\pi\) |
−0.988502 | + | 0.151206i | \(0.951684\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.60252 | − | 0.947238i | 0.0902803 | − | 0.0328593i | ||||
\(832\) | −12.8433 | + | 35.2867i | −0.445262 | + | 1.22335i | ||||
\(833\) | −1.64080 | + | 1.95543i | −0.0568503 | + | 0.0677515i | ||||
\(834\) | 1.46907 | − | 8.33154i | 0.0508699 | − | 0.288498i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.213378 | + | 0.307751i | 0.00737982 | + | 0.0106438i | ||||
\(837\) | 36.4522i | 1.25997i | ||||||||
\(838\) | −16.7847 | − | 2.95959i | −0.579816 | − | 0.102237i | ||||
\(839\) | −3.25369 | − | 2.73017i | −0.112330 | − | 0.0942559i | 0.584893 | − | 0.811111i | \(-0.301137\pi\) |
−0.697222 | + | 0.716855i | \(0.745581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6274 | − | 4.23203i | 0.400945 | − | 0.145932i | ||||
\(842\) | −19.9191 | − | 23.7387i | −0.686458 | − | 0.818089i | ||||
\(843\) | 17.8993 | − | 10.3342i | 0.616486 | − | 0.355928i | ||||
\(844\) | −0.974147 | + | 1.68727i | −0.0335315 | + | 0.0580783i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.10757 | + | 11.9526i | 0.0724599 | + | 0.410941i | ||||
\(847\) | 37.4285 | + | 21.6094i | 1.28606 | + | 0.742506i | ||||
\(848\) | −9.30239 | + | 5.37074i | −0.319446 | + | 0.184432i | ||||
\(849\) | −12.1905 | + | 10.2290i | −0.418377 | + | 0.351060i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48.5226 | − | 17.6608i | −1.66334 | − | 0.605404i | ||||
\(852\) | 0.221167 | − | 0.263577i | 0.00757706 | − | 0.00902999i | ||||
\(853\) | 1.64409 | + | 0.289897i | 0.0562926 | + | 0.00992590i | 0.201724 | − | 0.979443i | \(-0.435346\pi\) |
−0.145431 | + | 0.989368i | \(0.546457\pi\) | |||||||
\(854\) | 12.9199 | 0.442110 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.5284 | 0.530751 | ||||||||
\(857\) | 0.843653 | + | 0.148759i | 0.0288186 | + | 0.00508150i | 0.188039 | − | 0.982162i | \(-0.439787\pi\) |
−0.159220 | + | 0.987243i | \(0.550898\pi\) | |||||||
\(858\) | −4.49034 | + | 5.35138i | −0.153298 | + | 0.182693i | ||||
\(859\) | −49.8985 | − | 18.1616i | −1.70251 | − | 0.619665i | −0.706407 | − | 0.707806i | \(-0.749685\pi\) |
−0.996108 | + | 0.0881416i | \(0.971907\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.1091 | + | 17.7127i | −0.719397 | + | 0.603646i | ||||
\(862\) | −0.496761 | + | 0.286805i | −0.0169198 | + | 0.00976863i | ||||
\(863\) | 25.6004 | + | 14.7804i | 0.871447 | + | 0.503130i | 0.867829 | − | 0.496864i | \(-0.165515\pi\) |
0.00361786 | + | 0.999993i | \(0.498848\pi\) | |||||||
\(864\) | 0.761961 | + | 4.32130i | 0.0259224 | + | 0.147013i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.48391 | − | 16.4266i | 0.322276 | − | 0.558199i | ||||
\(867\) | −22.1432 | + | 12.7844i | −0.752023 | + | 0.434181i | ||||
\(868\) | 2.34990 | + | 2.80050i | 0.0797609 | + | 0.0950553i | ||||
\(869\) | −3.00324 | + | 1.09309i | −0.101878 | + | 0.0370806i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.9310 | + | 46.0926i | 1.86127 | + | 1.56179i | ||||
\(872\) | −18.0514 | − | 3.18294i | −0.611296 | − | 0.107788i | ||||
\(873\) | − | 7.49198i | − | 0.253565i | ||||||
\(874\) | −30.4026 | − | 21.4981i | −1.02838 | − | 0.727185i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0651933 | − | 0.369730i | 0.00220268 | − | 0.0124920i | ||||
\(877\) | −5.65060 | + | 6.73412i | −0.190807 | + | 0.227395i | −0.852963 | − | 0.521971i | \(-0.825197\pi\) |
0.662156 | + | 0.749366i | \(0.269641\pi\) | |||||||
\(878\) | −2.72476 | + | 7.48620i | −0.0919560 | + | 0.252647i | ||||
\(879\) | 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 | \(0.985242\pi\) | |||||||
\(882\) | −8.71990 | − | 5.03444i | −0.293614 | − | 0.169518i | ||||
\(883\) | −8.51936 | + | 1.50219i | −0.286699 | + | 0.0505528i | −0.315148 | − | 0.949042i | \(-0.602054\pi\) |
0.0284490 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(884\) | −0.0326065 | − | 0.184920i | −0.00109667 | − | 0.00621955i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0907 | + | 31.3340i | 0.607769 | + | 1.05269i | ||||
\(887\) | 25.4862 | + | 30.3733i | 0.855744 | + | 1.01984i | 0.999543 | + | 0.0302292i | \(0.00962373\pi\) |
−0.143799 | + | 0.989607i | \(0.545932\pi\) | |||||||
\(888\) | −12.4304 | − | 34.1523i | −0.417137 | − | 1.14607i | ||||
\(889\) | 70.7713 | + | 25.7587i | 2.37359 | + | 0.863918i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.682260 | − | 3.86929i | 0.0228566 | − | 0.129626i | ||||
\(892\) | 0.678737i | 0.0227258i | ||||||||
\(893\) | −4.15486 | − | 50.1581i | −0.139037 | − | 1.67848i | ||||
\(894\) | 40.1648 | 1.34331 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −38.5013 | − | 32.3064i | −1.28624 | − | 1.07928i | ||||
\(897\) | 15.3699 | − | 42.2284i | 0.513186 | − | 1.40997i | ||||
\(898\) | −17.2857 | − | 47.4922i | −0.576832 | − | 1.58483i | ||||
\(899\) | 20.2718 | − | 17.0100i | 0.676101 | − | 0.567316i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.336159 | + | 0.582244i | −0.0111991 | + | 0.0193974i | ||||
\(902\) | 4.00723 | − | 0.706583i | 0.133426 | − | 0.0235266i | ||||
\(903\) | −10.9058 | + | 1.92298i | −0.362921 | + | 0.0639929i | ||||
\(904\) | −6.51828 | + | 11.2900i | −0.216795 | + | 0.375499i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.88018 | − | 3.25585i | 0.128910 | − | 0.108169i | ||||
\(907\) | 11.4157 | + | 31.3645i | 0.379053 | + | 1.04144i | 0.971750 | + | 0.236014i | \(0.0758412\pi\) |
−0.592696 | + | 0.805426i | \(0.701937\pi\) | |||||||
\(908\) | −0.125506 | + | 0.344826i | −0.00416508 | + | 0.0114435i | ||||
\(909\) | −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 | \(0.779052\pi\) | |||||||
\(912\) | −2.31391 | − | 27.9339i | −0.0766212 | − | 0.924982i | ||||
\(913\) | 8.55953i | 0.283279i | ||||||||
\(914\) | −2.95635 | + | 16.7663i | −0.0977873 | + | 0.554579i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.00788 | + | 1.09478i | 0.0993833 | + | 0.0361726i | ||||
\(917\) | 27.2735 | + | 74.9333i | 0.900650 | + | 2.47452i | ||||
\(918\) | 1.40689 | + | 1.67667i | 0.0464345 | + | 0.0553384i | ||||
\(919\) | 4.25997 | + | 7.37849i | 0.140524 | + | 0.243394i | 0.927694 | − | 0.373342i | \(-0.121788\pi\) |
−0.787170 | + | 0.616736i | \(0.788455\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.10942 | + | 23.3057i | 0.135410 | + | 0.767948i | ||||
\(922\) | 4.30549 | − | 0.759174i | 0.141794 | − | 0.0250021i | ||||
\(923\) | 7.26337 | + | 4.19351i | 0.239077 | + | 0.138031i | ||||
\(924\) | −0.264173 | − | 0.457561i | −0.00869065 | − | 0.0150526i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.6624 | + | 4.24475i | −0.383249 | + | 0.139491i | ||||
\(927\) | 1.91857 | − | 5.27123i | 0.0630142 | − | 0.173130i | ||||
\(928\) | 2.04759 | − | 2.44023i | 0.0672155 | − | 0.0801044i | ||||
\(929\) | 8.18896 | − | 46.4419i | 0.268671 | − | 1.52371i | −0.489702 | − | 0.871890i | \(-0.662894\pi\) |
0.758373 | − | 0.651820i | \(-0.225994\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.0916 | + | 24.1067i | 1.11731 | + | 0.790064i | ||||
\(932\) | − | 3.99954i | − | 0.131009i | ||||||
\(933\) | 5.22393 | + | 0.921119i | 0.171024 | + | 0.0301561i | ||||
\(934\) | 20.0853 | + | 16.8536i | 0.657212 | + | 0.551466i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.36584 | + | 3.40889i | −0.306132 | + | 0.111423i | ||||
\(937\) | −18.9625 | − | 22.5986i | −0.619477 | − | 0.738264i | 0.361504 | − | 0.932371i | \(-0.382264\pi\) |
−0.980980 | + | 0.194107i | \(0.937819\pi\) | |||||||
\(938\) | −72.5961 | + | 41.9134i | −2.37035 | + | 1.36852i | ||||
\(939\) | 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 | \(0.993927\pi\) | |||||||
\(942\) | −39.8695 | − | 23.0187i | −1.29902 | − | 0.749989i | ||||
\(943\) | −22.6690 | + | 13.0879i | −0.738203 | + | 0.426201i | ||||
\(944\) | 2.90416 | − | 2.43688i | 0.0945223 | − | 0.0793137i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.53662 | + | 0.559286i | 0.0499600 | + | 0.0181839i | ||||
\(947\) | 6.33765 | − | 7.55292i | 0.205946 | − | 0.245437i | −0.653178 | − | 0.757204i | \(-0.726565\pi\) |
0.859124 | + | 0.511768i | \(0.171009\pi\) | |||||||
\(948\) | −1.05902 | − | 0.186734i | −0.0343954 | − | 0.00606484i | ||||
\(949\) | 9.15138 | 0.297066 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.98099 | −0.0642381 | ||||||||
\(952\) | −2.90896 | − | 0.512928i | −0.0942800 | − | 0.0166241i | ||||
\(953\) | 34.5014 | − | 41.1172i | 1.11761 | − | 1.33192i | 0.180223 | − | 0.983626i | \(-0.442318\pi\) |
0.937387 | − | 0.348290i | \(-0.113237\pi\) | |||||||
\(954\) | −2.49203 | − | 0.907025i | −0.0806825 | − | 0.0293660i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.19877 | + | 1.84499i | −0.0711134 | + | 0.0596712i | ||||
\(957\) | −3.31210 | + | 1.91224i | −0.107065 | + | 0.0618141i | ||||
\(958\) | −4.29251 | − | 2.47828i | −0.138685 | − | 0.0800697i | ||||
\(959\) | 1.66627 | + | 9.44991i | 0.0538068 | + | 0.305154i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.55948 | + | 9.62930i | −0.179338 | + | 0.310623i | ||||
\(962\) | −57.0144 | + | 32.9173i | −1.83822 | + | 1.06130i | ||||
\(963\) | 2.63561 | + | 3.14100i | 0.0849315 | + | 0.101217i | ||||
\(964\) | 0.805675 | − | 0.293242i | 0.0259491 | − | 0.00944468i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 40.2432 | + | 33.7681i | 1.29480 | + | 1.08647i | ||||
\(967\) | 33.7173 | + | 5.94528i | 1.08428 | + | 0.191187i | 0.687106 | − | 0.726557i | \(-0.258881\pi\) |
0.397171 | + | 0.917745i | \(0.369992\pi\) | |||||||
\(968\) | 28.8956i | 0.928739i | ||||||||
\(969\) | −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 | \(-0.0174555\pi\) | |||||||
\(972\) | −0.648679 | + | 0.773065i | −0.0208064 | + | 0.0247961i | ||||
\(973\) | −5.33440 | + | 14.6561i | −0.171013 | + | 0.469855i | ||||
\(974\) | 15.3379 | − | 5.58254i | 0.491458 | − | 0.178876i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.61925 | + | 8.00078i | 0.147859 | + | 0.256099i | ||||
\(977\) | −39.5060 | − | 22.8088i | −1.26391 | − | 0.729717i | −0.290079 | − | 0.957003i | \(-0.593682\pi\) |
−0.973828 | + | 0.227285i | \(0.927015\pi\) | |||||||
\(978\) | 17.2197 | − | 3.03629i | 0.550625 | − | 0.0970900i | ||||
\(979\) | −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 | ||||
\(982\) | −21.6029 | − | 25.7454i | −0.689377 | − | 0.821568i | ||||
\(983\) | 6.90400 | + | 18.9686i | 0.220203 | + | 0.605004i | 0.999773 | − | 0.0213117i | \(-0.00678425\pi\) |
−0.779569 | + | 0.626316i | \(0.784562\pi\) | |||||||
\(984\) | −17.3126 | − | 6.30126i | −0.551905 | − | 0.200877i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.275917 | − | 1.56480i | 0.00878698 | − | 0.0498334i | ||||
\(987\) | 71.0079i | 2.26021i | ||||||||
\(988\) | −2.97041 | + | 0.781229i | −0.0945013 | + | 0.0248542i | ||||
\(989\) | −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 | \(0.778413\pi\) | |||||||
\(992\) | −1.73408 | + | 4.76433i | −0.0550569 | + | 0.151268i | ||||
\(993\) | −6.57332 | − | 18.0601i | −0.208598 | − | 0.573118i | ||||
\(994\) | −7.51070 | + | 6.30223i | −0.238225 | + | 0.199894i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.44002 | + | 2.49419i | −0.0456288 | + | 0.0790314i | ||||
\(997\) | −30.7526 | + | 5.42251i | −0.973945 | + | 0.171733i | −0.637905 | − | 0.770115i | \(-0.720199\pi\) |
−0.336040 | + | 0.941848i | \(0.609088\pi\) | |||||||
\(998\) | −1.41235 | + | 0.249035i | −0.0447070 | + | 0.00788305i | ||||
\(999\) | 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.u.c.74.2 | 36 | ||
5.2 | odd | 4 | 475.2.l.b.226.3 | 18 | |||
5.3 | odd | 4 | 95.2.k.b.36.1 | ✓ | 18 | ||
5.4 | even | 2 | inner | 475.2.u.c.74.5 | 36 | ||
15.8 | even | 4 | 855.2.bs.b.226.3 | 18 | |||
19.9 | even | 9 | inner | 475.2.u.c.199.5 | 36 | ||
95.3 | even | 36 | 1805.2.a.u.1.7 | 9 | |||
95.9 | even | 18 | inner | 475.2.u.c.199.2 | 36 | ||
95.22 | even | 36 | 9025.2.a.cd.1.3 | 9 | |||
95.28 | odd | 36 | 95.2.k.b.66.1 | yes | 18 | ||
95.47 | odd | 36 | 475.2.l.b.351.3 | 18 | |||
95.73 | odd | 36 | 1805.2.a.t.1.3 | 9 | |||
95.92 | odd | 36 | 9025.2.a.ce.1.7 | 9 | |||
285.218 | even | 36 | 855.2.bs.b.541.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.36.1 | ✓ | 18 | 5.3 | odd | 4 | ||
95.2.k.b.66.1 | yes | 18 | 95.28 | odd | 36 | ||
475.2.l.b.226.3 | 18 | 5.2 | odd | 4 | |||
475.2.l.b.351.3 | 18 | 95.47 | odd | 36 | |||
475.2.u.c.74.2 | 36 | 1.1 | even | 1 | trivial | ||
475.2.u.c.74.5 | 36 | 5.4 | even | 2 | inner | ||
475.2.u.c.199.2 | 36 | 95.9 | even | 18 | inner | ||
475.2.u.c.199.5 | 36 | 19.9 | even | 9 | inner | ||
855.2.bs.b.226.3 | 18 | 15.8 | even | 4 | |||
855.2.bs.b.541.3 | 18 | 285.218 | even | 36 | |||
1805.2.a.t.1.3 | 9 | 95.73 | odd | 36 | |||
1805.2.a.u.1.7 | 9 | 95.3 | even | 36 | |||
9025.2.a.cd.1.3 | 9 | 95.22 | even | 36 | |||
9025.2.a.ce.1.7 | 9 | 95.92 | odd | 36 |