Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 551.1 | ||
Character | \(\chi\) | \(=\) | 630.551 |
Dual form | 630.2.t.b.311.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −1.71805 | + | 0.219817i | −0.991914 | + | 0.126912i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.37796 | − | 1.04939i | 0.562551 | − | 0.428412i | ||||
\(7\) | −2.11261 | + | 1.59276i | −0.798491 | + | 0.602007i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.90336 | − | 0.755312i | 0.967787 | − | 0.251771i | ||||
\(10\) | 0.866025 | − | 0.500000i | 0.273861 | − | 0.158114i | ||||
\(11\) | 0.767810i | 0.231504i | 0.993278 | + | 0.115752i | \(0.0369277\pi\) | ||||
−0.993278 | + | 0.115752i | \(0.963072\pi\) | |||||||
\(12\) | −0.668655 | + | 1.59778i | −0.193024 | + | 0.461239i | ||||
\(13\) | −3.78024 | + | 2.18252i | −1.04845 | + | 0.605323i | −0.922215 | − | 0.386677i | \(-0.873623\pi\) |
−0.126236 | + | 0.992000i | \(0.540290\pi\) | |||||||
\(14\) | 1.03319 | − | 2.43568i | 0.276132 | − | 0.650962i | ||||
\(15\) | 1.71805 | − | 0.219817i | 0.443597 | − | 0.0567566i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.15157 | − | 1.99457i | −0.279296 | − | 0.483755i | 0.691914 | − | 0.721980i | \(-0.256768\pi\) |
−0.971210 | + | 0.238225i | \(0.923434\pi\) | |||||||
\(18\) | −2.13673 | + | 2.10580i | −0.503632 | + | 0.496342i | ||||
\(19\) | 4.19206 | + | 2.42029i | 0.961725 | + | 0.555252i | 0.896703 | − | 0.442632i | \(-0.145955\pi\) |
0.0650212 | + | 0.997884i | \(0.479288\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | 3.27944 | − | 3.20083i | 0.715632 | − | 0.698477i | ||||
\(22\) | −0.383905 | − | 0.664943i | −0.0818489 | − | 0.141766i | ||||
\(23\) | − | 5.59780i | − | 1.16722i | −0.812033 | − | 0.583611i | \(-0.801639\pi\) | ||
0.812033 | − | 0.583611i | \(-0.198361\pi\) | |||||||
\(24\) | −0.219817 | − | 1.71805i | −0.0448700 | − | 0.350695i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.18252 | − | 3.78024i | 0.428028 | − | 0.741367i | ||||
\(27\) | −4.82207 | + | 1.93587i | −0.928009 | + | 0.372558i | ||||
\(28\) | 0.323069 | + | 2.62595i | 0.0610542 | + | 0.496258i | ||||
\(29\) | −9.12141 | − | 5.26625i | −1.69380 | − | 0.977918i | −0.951397 | − | 0.307968i | \(-0.900351\pi\) |
−0.742407 | − | 0.669949i | \(-0.766316\pi\) | |||||||
\(30\) | −1.37796 | + | 1.04939i | −0.251580 | + | 0.191592i | ||||
\(31\) | 6.97950 | + | 4.02962i | 1.25356 | + | 0.723741i | 0.971814 | − | 0.235749i | \(-0.0757544\pi\) |
0.281742 | + | 0.959490i | \(0.409088\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −0.168778 | − | 1.31913i | −0.0293805 | − | 0.229632i | ||||
\(34\) | 1.99457 | + | 1.15157i | 0.342066 | + | 0.197492i | ||||
\(35\) | 2.11261 | − | 1.59276i | 0.357096 | − | 0.269226i | ||||
\(36\) | 0.797561 | − | 2.89204i | 0.132927 | − | 0.482007i | ||||
\(37\) | 4.15617 | − | 7.19869i | 0.683269 | − | 1.18346i | −0.290708 | − | 0.956812i | \(-0.593891\pi\) |
0.973977 | − | 0.226645i | \(-0.0727759\pi\) | |||||||
\(38\) | −4.84057 | −0.785245 | ||||||||
\(39\) | 6.01487 | − | 4.58064i | 0.963151 | − | 0.733489i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | −2.65381 | − | 4.59654i | −0.414456 | − | 0.717859i | 0.580915 | − | 0.813964i | \(-0.302695\pi\) |
−0.995371 | + | 0.0961053i | \(0.969361\pi\) | |||||||
\(42\) | −1.23966 | + | 4.41172i | −0.191284 | + | 0.680742i | ||||
\(43\) | 5.94724 | − | 10.3009i | 0.906945 | − | 1.57087i | 0.0886598 | − | 0.996062i | \(-0.471742\pi\) |
0.818285 | − | 0.574813i | \(-0.194925\pi\) | |||||||
\(44\) | 0.664943 | + | 0.383905i | 0.100244 | + | 0.0578759i | ||||
\(45\) | −2.90336 | + | 0.755312i | −0.432807 | + | 0.112595i | ||||
\(46\) | 2.79890 | + | 4.84784i | 0.412675 | + | 0.714775i | ||||
\(47\) | 3.23073 | + | 5.59578i | 0.471250 | + | 0.816229i | 0.999459 | − | 0.0328853i | \(-0.0104696\pi\) |
−0.528209 | + | 0.849114i | \(0.677136\pi\) | |||||||
\(48\) | 1.04939 | + | 1.37796i | 0.151466 | + | 0.198892i | ||||
\(49\) | 1.92622 | − | 6.72976i | 0.275174 | − | 0.961394i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 2.41689 | + | 3.17363i | 0.338432 | + | 0.444397i | ||||
\(52\) | 4.36505i | 0.605323i | ||||||||
\(53\) | 6.48067 | − | 3.74161i | 0.890188 | − | 0.513950i | 0.0161839 | − | 0.999869i | \(-0.494848\pi\) |
0.874004 | + | 0.485919i | \(0.161515\pi\) | |||||||
\(54\) | 3.20810 | − | 4.08755i | 0.436568 | − | 0.556245i | ||||
\(55\) | − | 0.767810i | − | 0.103532i | ||||||
\(56\) | −1.59276 | − | 2.11261i | −0.212842 | − | 0.282309i | ||||
\(57\) | −7.73417 | − | 3.23668i | −1.02442 | − | 0.428708i | ||||
\(58\) | 10.5325 | 1.38298 | ||||||||
\(59\) | 5.71736 | − | 9.90276i | 0.744337 | − | 1.28923i | −0.206167 | − | 0.978517i | \(-0.566099\pi\) |
0.950504 | − | 0.310712i | \(-0.100568\pi\) | |||||||
\(60\) | 0.668655 | − | 1.59778i | 0.0863230 | − | 0.206272i | ||||
\(61\) | −8.22722 | + | 4.74999i | −1.05339 | + | 0.608174i | −0.923596 | − | 0.383368i | \(-0.874764\pi\) |
−0.129792 | + | 0.991541i | \(0.541431\pi\) | |||||||
\(62\) | −8.05924 | −1.02352 | ||||||||
\(63\) | −4.93063 | + | 6.22004i | −0.621201 | + | 0.783651i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.78024 | − | 2.18252i | 0.468881 | − | 0.270709i | ||||
\(66\) | 0.805733 | + | 1.05801i | 0.0991788 | + | 0.130232i | ||||
\(67\) | −6.85237 | + | 11.8687i | −0.837151 | + | 1.44999i | 0.0551168 | + | 0.998480i | \(0.482447\pi\) |
−0.892267 | + | 0.451507i | \(0.850886\pi\) | |||||||
\(68\) | −2.30313 | −0.279296 | ||||||||
\(69\) | 1.23049 | + | 9.61728i | 0.148134 | + | 1.15778i | ||||
\(70\) | −1.03319 | + | 2.43568i | −0.123490 | + | 0.291119i | ||||
\(71\) | − | 7.50583i | − | 0.890779i | −0.895337 | − | 0.445389i | \(-0.853065\pi\) | ||
0.895337 | − | 0.445389i | \(-0.146935\pi\) | |||||||
\(72\) | 0.755312 | + | 2.90336i | 0.0890144 | + | 0.342164i | ||||
\(73\) | 10.1185 | − | 5.84190i | 1.18428 | − | 0.683742i | 0.227277 | − | 0.973830i | \(-0.427018\pi\) |
0.957000 | + | 0.290088i | \(0.0936845\pi\) | |||||||
\(74\) | 8.31233i | 0.966289i | ||||||||
\(75\) | −1.71805 | + | 0.219817i | −0.198383 | + | 0.0253823i | ||||
\(76\) | 4.19206 | − | 2.42029i | 0.480862 | − | 0.277626i | ||||
\(77\) | −1.22294 | − | 1.62208i | −0.139367 | − | 0.184853i | ||||
\(78\) | −2.91871 | + | 6.97439i | −0.330479 | + | 0.789694i | ||||
\(79\) | 0.555218 | + | 0.961666i | 0.0624669 | + | 0.108196i | 0.895568 | − | 0.444926i | \(-0.146770\pi\) |
−0.833101 | + | 0.553121i | \(0.813437\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | 7.85901 | − | 4.38589i | 0.873223 | − | 0.487321i | ||||
\(82\) | 4.59654 | + | 2.65381i | 0.507603 | + | 0.293065i | ||||
\(83\) | −0.254578 | + | 0.440942i | −0.0279435 | + | 0.0483996i | −0.879659 | − | 0.475605i | \(-0.842229\pi\) |
0.851715 | + | 0.524005i | \(0.175563\pi\) | |||||||
\(84\) | −1.13228 | − | 4.44049i | −0.123541 | − | 0.484497i | ||||
\(85\) | 1.15157 | + | 1.99457i | 0.124905 | + | 0.216342i | ||||
\(86\) | 11.8945i | 1.28261i | ||||||||
\(87\) | 16.8286 | + | 7.04261i | 1.80422 | + | 0.755047i | ||||
\(88\) | −0.767810 | −0.0818489 | ||||||||
\(89\) | 2.80167 | − | 4.85263i | 0.296976 | − | 0.514378i | −0.678467 | − | 0.734631i | \(-0.737355\pi\) |
0.975443 | + | 0.220254i | \(0.0706885\pi\) | |||||||
\(90\) | 2.13673 | − | 2.10580i | 0.225231 | − | 0.221971i | ||||
\(91\) | 4.50993 | − | 10.6318i | 0.472769 | − | 1.11452i | ||||
\(92\) | −4.84784 | − | 2.79890i | −0.505422 | − | 0.291806i | ||||
\(93\) | −12.8769 | − | 5.38885i | −1.33527 | − | 0.558798i | ||||
\(94\) | −5.59578 | − | 3.23073i | −0.577161 | − | 0.333224i | ||||
\(95\) | −4.19206 | − | 2.42029i | −0.430096 | − | 0.248316i | ||||
\(96\) | −1.59778 | − | 0.668655i | −0.163073 | − | 0.0682443i | ||||
\(97\) | −7.61423 | − | 4.39608i | −0.773107 | − | 0.446354i | 0.0608745 | − | 0.998145i | \(-0.480611\pi\) |
−0.833982 | + | 0.551792i | \(0.813944\pi\) | |||||||
\(98\) | 1.69673 | + | 6.79125i | 0.171395 | + | 0.686020i | ||||
\(99\) | 0.579937 | + | 2.22923i | 0.0582858 | + | 0.224046i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −11.8515 | −1.17927 | −0.589633 | − | 0.807671i | \(-0.700728\pi\) | ||||
−0.589633 | + | 0.807671i | \(0.700728\pi\) | |||||||
\(102\) | −3.67990 | − | 1.54000i | −0.364365 | − | 0.152483i | ||||
\(103\) | − | 0.878126i | − | 0.0865244i | −0.999064 | − | 0.0432622i | \(-0.986225\pi\) | ||
0.999064 | − | 0.0432622i | \(-0.0137751\pi\) | |||||||
\(104\) | −2.18252 | − | 3.78024i | −0.214014 | − | 0.370683i | ||||
\(105\) | −3.27944 | + | 3.20083i | −0.320040 | + | 0.312369i | ||||
\(106\) | −3.74161 | + | 6.48067i | −0.363418 | + | 0.629458i | ||||
\(107\) | 5.55184 | + | 3.20536i | 0.536717 | + | 0.309874i | 0.743747 | − | 0.668461i | \(-0.233047\pi\) |
−0.207031 | + | 0.978334i | \(0.566380\pi\) | |||||||
\(108\) | −0.734525 | + | 5.14397i | −0.0706797 | + | 0.494979i | ||||
\(109\) | −4.36380 | − | 7.55832i | −0.417976 | − | 0.723955i | 0.577760 | − | 0.816207i | \(-0.303927\pi\) |
−0.995736 | + | 0.0922513i | \(0.970594\pi\) | |||||||
\(110\) | 0.383905 | + | 0.664943i | 0.0366039 | + | 0.0633999i | ||||
\(111\) | −5.55808 | + | 13.2813i | −0.527550 | + | 1.26060i | ||||
\(112\) | 2.43568 | + | 1.03319i | 0.230150 | + | 0.0976273i | ||||
\(113\) | −0.697613 | + | 0.402767i | −0.0656259 | + | 0.0378891i | −0.532454 | − | 0.846459i | \(-0.678730\pi\) |
0.466828 | + | 0.884348i | \(0.345397\pi\) | |||||||
\(114\) | 8.31633 | − | 1.06404i | 0.778895 | − | 0.0996567i | ||||
\(115\) | 5.59780i | 0.521998i | ||||||||
\(116\) | −9.12141 | + | 5.26625i | −0.846902 | + | 0.488959i | ||||
\(117\) | −9.32692 | + | 9.19192i | −0.862274 | + | 0.849793i | ||||
\(118\) | 11.4347i | 1.05265i | ||||||||
\(119\) | 5.60969 | + | 2.37958i | 0.514239 | + | 0.218135i | ||||
\(120\) | 0.219817 | + | 1.71805i | 0.0200665 | + | 0.156835i | ||||
\(121\) | 10.4105 | 0.946406 | ||||||||
\(122\) | 4.74999 | − | 8.22722i | 0.430044 | − | 0.744857i | ||||
\(123\) | 5.56977 | + | 7.31371i | 0.502209 | + | 0.659455i | ||||
\(124\) | 6.97950 | − | 4.02962i | 0.626778 | − | 0.361870i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.16003 | − | 7.85203i | 0.103344 | − | 0.699514i | ||||
\(127\) | −12.6479 | −1.12232 | −0.561162 | − | 0.827706i | \(-0.689645\pi\) | ||||
−0.561162 | + | 0.827706i | \(0.689645\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −7.95330 | + | 19.0047i | −0.700249 | + | 1.67327i | ||||
\(130\) | −2.18252 | + | 3.78024i | −0.191420 | + | 0.331549i | ||||
\(131\) | −9.92603 | −0.867241 | −0.433620 | − | 0.901096i | \(-0.642764\pi\) | ||||
−0.433620 | + | 0.901096i | \(0.642764\pi\) | |||||||
\(132\) | −1.22679 | − | 0.513400i | −0.106779 | − | 0.0446858i | ||||
\(133\) | −12.7111 | + | 1.56384i | −1.10219 | + | 0.135602i | ||||
\(134\) | − | 13.7047i | − | 1.18391i | ||||||
\(135\) | 4.82207 | − | 1.93587i | 0.415018 | − | 0.166613i | ||||
\(136\) | 1.99457 | − | 1.15157i | 0.171033 | − | 0.0987461i | ||||
\(137\) | 14.3935i | 1.22972i | 0.788637 | + | 0.614859i | \(0.210787\pi\) | ||||
−0.788637 | + | 0.614859i | \(0.789213\pi\) | |||||||
\(138\) | −5.87428 | − | 7.71356i | −0.500052 | − | 0.656622i | ||||
\(139\) | −8.82052 | + | 5.09253i | −0.748147 | + | 0.431943i | −0.825024 | − | 0.565098i | \(-0.808838\pi\) |
0.0768772 | + | 0.997041i | \(0.475505\pi\) | |||||||
\(140\) | −0.323069 | − | 2.62595i | −0.0273043 | − | 0.221933i | ||||
\(141\) | −6.78059 | − | 8.90364i | −0.571028 | − | 0.749822i | ||||
\(142\) | 3.75292 | + | 6.50024i | 0.314938 | + | 0.545488i | ||||
\(143\) | −1.67576 | − | 2.90251i | −0.140135 | − | 0.242720i | ||||
\(144\) | −2.10580 | − | 2.13673i | −0.175483 | − | 0.178061i | ||||
\(145\) | 9.12141 | + | 5.26625i | 0.757492 | + | 0.437338i | ||||
\(146\) | −5.84190 | + | 10.1185i | −0.483479 | + | 0.837410i | ||||
\(147\) | −1.83001 | + | 11.9855i | −0.150937 | + | 0.988543i | ||||
\(148\) | −4.15617 | − | 7.19869i | −0.341635 | − | 0.591729i | ||||
\(149\) | 8.95303i | 0.733461i | 0.930327 | + | 0.366730i | \(0.119523\pi\) | ||||
−0.930327 | + | 0.366730i | \(0.880477\pi\) | |||||||
\(150\) | 1.37796 | − | 1.04939i | 0.112510 | − | 0.0856823i | ||||
\(151\) | −5.00718 | −0.407479 | −0.203739 | − | 0.979025i | \(-0.565310\pi\) | ||||
−0.203739 | + | 0.979025i | \(0.565310\pi\) | |||||||
\(152\) | −2.42029 | + | 4.19206i | −0.196311 | + | 0.340021i | ||||
\(153\) | −4.84994 | − | 4.92117i | −0.392094 | − | 0.397853i | ||||
\(154\) | 1.87014 | + | 0.793294i | 0.150700 | + | 0.0639255i | ||||
\(155\) | −6.97950 | − | 4.02962i | −0.560607 | − | 0.323667i | ||||
\(156\) | −0.959514 | − | 7.49935i | −0.0768226 | − | 0.600429i | ||||
\(157\) | −2.81741 | − | 1.62663i | −0.224854 | − | 0.129819i | 0.383342 | − | 0.923607i | \(-0.374773\pi\) |
−0.608196 | + | 0.793787i | \(0.708106\pi\) | |||||||
\(158\) | −0.961666 | − | 0.555218i | −0.0765060 | − | 0.0441708i | ||||
\(159\) | −10.3116 | + | 7.85283i | −0.817764 | + | 0.622770i | ||||
\(160\) | −0.866025 | − | 0.500000i | −0.0684653 | − | 0.0395285i | ||||
\(161\) | 8.91596 | + | 11.8260i | 0.702676 | + | 0.932016i | ||||
\(162\) | −4.61315 | + | 7.72779i | −0.362444 | + | 0.607153i | ||||
\(163\) | 2.40931 | − | 4.17306i | 0.188712 | − | 0.326859i | −0.756109 | − | 0.654446i | \(-0.772902\pi\) |
0.944821 | + | 0.327587i | \(0.106235\pi\) | |||||||
\(164\) | −5.30763 | −0.414456 | ||||||||
\(165\) | 0.168778 | + | 1.31913i | 0.0131394 | + | 0.102694i | ||||
\(166\) | − | 0.509156i | − | 0.0395181i | ||||||
\(167\) | −4.97259 | − | 8.61278i | −0.384791 | − | 0.666477i | 0.606949 | − | 0.794740i | \(-0.292393\pi\) |
−0.991740 | + | 0.128263i | \(0.959060\pi\) | |||||||
\(168\) | 3.20083 | + | 3.27944i | 0.246949 | + | 0.253014i | ||||
\(169\) | 3.02683 | − | 5.24262i | 0.232833 | − | 0.403278i | ||||
\(170\) | −1.99457 | − | 1.15157i | −0.152977 | − | 0.0883212i | ||||
\(171\) | 13.9991 | + | 3.86065i | 1.07054 | + | 0.295231i | ||||
\(172\) | −5.94724 | − | 10.3009i | −0.453472 | − | 0.785437i | ||||
\(173\) | −8.31317 | − | 14.3988i | −0.632039 | − | 1.09472i | −0.987134 | − | 0.159893i | \(-0.948885\pi\) |
0.355096 | − | 0.934830i | \(-0.384448\pi\) | |||||||
\(174\) | −18.0953 | + | 2.31523i | −1.37180 | + | 0.175517i | ||||
\(175\) | −2.11261 | + | 1.59276i | −0.159698 | + | 0.120401i | ||||
\(176\) | 0.664943 | − | 0.383905i | 0.0501220 | − | 0.0289379i | ||||
\(177\) | −7.64589 | + | 18.2702i | −0.574700 | + | 1.37327i | ||||
\(178\) | 5.60333i | 0.419988i | ||||||||
\(179\) | 4.07453 | − | 2.35243i | 0.304545 | − | 0.175829i | −0.339938 | − | 0.940448i | \(-0.610406\pi\) |
0.644483 | + | 0.764619i | \(0.277073\pi\) | |||||||
\(180\) | −0.797561 | + | 2.89204i | −0.0594467 | + | 0.215560i | ||||
\(181\) | 8.33408i | 0.619467i | 0.950823 | + | 0.309734i | \(0.100240\pi\) | ||||
−0.950823 | + | 0.309734i | \(0.899760\pi\) | |||||||
\(182\) | 1.41021 | + | 11.4624i | 0.104532 | + | 0.849650i | ||||
\(183\) | 13.0906 | − | 9.96918i | 0.967685 | − | 0.736943i | ||||
\(184\) | 5.59780 | 0.412675 | ||||||||
\(185\) | −4.15617 | + | 7.19869i | −0.305567 | + | 0.529258i | ||||
\(186\) | 13.8461 | − | 1.77156i | 1.01525 | − | 0.129897i | ||||
\(187\) | 1.53145 | − | 0.884185i | 0.111991 | − | 0.0646580i | ||||
\(188\) | 6.46146 | 0.471250 | ||||||||
\(189\) | 7.10377 | − | 11.7702i | 0.516723 | − | 0.856152i | ||||
\(190\) | 4.84057 | 0.351172 | ||||||||
\(191\) | 3.28474 | − | 1.89645i | 0.237676 | − | 0.137222i | −0.376432 | − | 0.926444i | \(-0.622849\pi\) |
0.614108 | + | 0.789222i | \(0.289516\pi\) | |||||||
\(192\) | 1.71805 | − | 0.219817i | 0.123989 | − | 0.0158640i | ||||
\(193\) | 10.7480 | − | 18.6160i | 0.773656 | − | 1.34001i | −0.161892 | − | 0.986809i | \(-0.551759\pi\) |
0.935547 | − | 0.353202i | \(-0.114907\pi\) | |||||||
\(194\) | 8.79215 | 0.631240 | ||||||||
\(195\) | −6.01487 | + | 4.58064i | −0.430734 | + | 0.328026i | ||||
\(196\) | −4.86503 | − | 5.03304i | −0.347502 | − | 0.359503i | ||||
\(197\) | 13.3908i | 0.954054i | 0.878889 | + | 0.477027i | \(0.158286\pi\) | ||||
−0.878889 | + | 0.477027i | \(0.841714\pi\) | |||||||
\(198\) | −1.61686 | − | 1.64060i | −0.114905 | − | 0.116592i | ||||
\(199\) | 0.485507 | − | 0.280308i | 0.0344167 | − | 0.0198705i | −0.482693 | − | 0.875790i | \(-0.660341\pi\) |
0.517110 | + | 0.855919i | \(0.327008\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 9.16375 | − | 21.8972i | 0.646361 | − | 1.54451i | ||||
\(202\) | 10.2637 | − | 5.92574i | 0.722150 | − | 0.416933i | ||||
\(203\) | 27.6578 | − | 3.40272i | 1.94120 | − | 0.238824i | ||||
\(204\) | 3.95689 | − | 0.506269i | 0.277038 | − | 0.0354459i | ||||
\(205\) | 2.65381 | + | 4.59654i | 0.185350 | + | 0.321036i | ||||
\(206\) | 0.439063 | + | 0.760480i | 0.0305910 | + | 0.0529851i | ||||
\(207\) | −4.22809 | − | 16.2524i | −0.293872 | − | 1.12962i | ||||
\(208\) | 3.78024 | + | 2.18252i | 0.262113 | + | 0.151331i | ||||
\(209\) | −1.85832 | + | 3.21871i | −0.128543 | + | 0.222643i | ||||
\(210\) | 1.23966 | − | 4.41172i | 0.0855450 | − | 0.304437i | ||||
\(211\) | 1.76537 | + | 3.05771i | 0.121533 | + | 0.210501i | 0.920372 | − | 0.391043i | \(-0.127886\pi\) |
−0.798839 | + | 0.601544i | \(0.794552\pi\) | |||||||
\(212\) | − | 7.48323i | − | 0.513950i | ||||||
\(213\) | 1.64991 | + | 12.8954i | 0.113050 | + | 0.883576i | ||||
\(214\) | −6.41071 | −0.438227 | ||||||||
\(215\) | −5.94724 | + | 10.3009i | −0.405598 | + | 0.702516i | ||||
\(216\) | −1.93587 | − | 4.82207i | −0.131719 | − | 0.328101i | ||||
\(217\) | −21.1632 | + | 2.60369i | −1.43665 | + | 0.176750i | ||||
\(218\) | 7.55832 | + | 4.36380i | 0.511914 | + | 0.295554i | ||||
\(219\) | −16.0998 | + | 12.2609i | −1.08793 | + | 0.828512i | ||||
\(220\) | −0.664943 | − | 0.383905i | −0.0448305 | − | 0.0258829i | ||||
\(221\) | 8.70641 | + | 5.02665i | 0.585656 | + | 0.338129i | ||||
\(222\) | −1.82719 | − | 14.2810i | −0.122633 | − | 0.958475i | ||||
\(223\) | 22.1791 | + | 12.8051i | 1.48522 | + | 0.857495i | 0.999859 | − | 0.0168159i | \(-0.00535291\pi\) |
0.485366 | + | 0.874311i | \(0.338686\pi\) | |||||||
\(224\) | −2.62595 | + | 0.323069i | −0.175454 | + | 0.0215859i | ||||
\(225\) | 2.90336 | − | 0.755312i | 0.193557 | − | 0.0503542i | ||||
\(226\) | 0.402767 | − | 0.697613i | 0.0267917 | − | 0.0464045i | ||||
\(227\) | 11.1386 | 0.739295 | 0.369647 | − | 0.929172i | \(-0.379479\pi\) | ||||
0.369647 | + | 0.929172i | \(0.379479\pi\) | |||||||
\(228\) | −6.67013 | + | 5.07965i | −0.441740 | + | 0.336408i | ||||
\(229\) | − | 3.80842i | − | 0.251668i | −0.992051 | − | 0.125834i | \(-0.959839\pi\) | ||
0.992051 | − | 0.125834i | \(-0.0401606\pi\) | |||||||
\(230\) | −2.79890 | − | 4.84784i | −0.184554 | − | 0.319657i | ||||
\(231\) | 2.45763 | + | 2.51799i | 0.161700 | + | 0.165671i | ||||
\(232\) | 5.26625 | − | 9.12141i | 0.345746 | − | 0.598850i | ||||
\(233\) | 2.04230 | + | 1.17912i | 0.133795 | + | 0.0772468i | 0.565404 | − | 0.824814i | \(-0.308720\pi\) |
−0.431608 | + | 0.902061i | \(0.642054\pi\) | |||||||
\(234\) | 3.48139 | − | 12.6239i | 0.227586 | − | 0.825250i | ||||
\(235\) | −3.23073 | − | 5.59578i | −0.210749 | − | 0.365029i | ||||
\(236\) | −5.71736 | − | 9.90276i | −0.372168 | − | 0.644615i | ||||
\(237\) | −1.16528 | − | 1.53014i | −0.0756931 | − | 0.0993932i | ||||
\(238\) | −6.04792 | + | 0.744070i | −0.392029 | + | 0.0482309i | ||||
\(239\) | 10.1968 | − | 5.88712i | 0.659576 | − | 0.380806i | −0.132540 | − | 0.991178i | \(-0.542313\pi\) |
0.792115 | + | 0.610372i | \(0.208980\pi\) | |||||||
\(240\) | −1.04939 | − | 1.37796i | −0.0677378 | − | 0.0889471i | ||||
\(241\) | − | 18.8137i | − | 1.21189i | −0.795505 | − | 0.605947i | \(-0.792794\pi\) | ||
0.795505 | − | 0.605947i | \(-0.207206\pi\) | |||||||
\(242\) | −9.01573 | + | 5.20523i | −0.579553 | + | 0.334605i | ||||
\(243\) | −12.5380 | + | 9.26270i | −0.804315 | + | 0.594203i | ||||
\(244\) | 9.49997i | 0.608174i | ||||||||
\(245\) | −1.92622 | + | 6.72976i | −0.123062 | + | 0.429949i | ||||
\(246\) | −8.48042 | − | 3.54897i | −0.540692 | − | 0.226274i | ||||
\(247\) | −21.1293 | −1.34443 | ||||||||
\(248\) | −4.02962 | + | 6.97950i | −0.255881 | + | 0.443199i | ||||
\(249\) | 0.340450 | − | 0.813518i | 0.0215751 | − | 0.0515546i | ||||
\(250\) | 0.866025 | − | 0.500000i | 0.0547723 | − | 0.0316228i | ||||
\(251\) | −3.35759 | −0.211929 | −0.105965 | − | 0.994370i | \(-0.533793\pi\) | ||||
−0.105965 | + | 0.994370i | \(0.533793\pi\) | |||||||
\(252\) | 2.92140 | + | 7.38007i | 0.184031 | + | 0.464901i | ||||
\(253\) | 4.29805 | 0.270216 | ||||||||
\(254\) | 10.9534 | − | 6.32397i | 0.687280 | − | 0.396801i | ||||
\(255\) | −2.41689 | − | 3.17363i | −0.151351 | − | 0.198741i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.3362 | 0.707132 | 0.353566 | − | 0.935410i | \(-0.384969\pi\) | ||||
0.353566 | + | 0.935410i | \(0.384969\pi\) | |||||||
\(258\) | −2.61461 | − | 20.4352i | −0.162779 | − | 1.27224i | ||||
\(259\) | 2.68545 | + | 21.8278i | 0.166866 | + | 1.35631i | ||||
\(260\) | − | 4.36505i | − | 0.270709i | ||||||
\(261\) | −30.4604 | − | 8.40030i | −1.88545 | − | 0.519966i | ||||
\(262\) | 8.59619 | − | 4.96301i | 0.531074 | − | 0.306616i | ||||
\(263\) | − | 25.7820i | − | 1.58978i | −0.606750 | − | 0.794892i | \(-0.707527\pi\) | ||
0.606750 | − | 0.794892i | \(-0.292473\pi\) | |||||||
\(264\) | 1.31913 | − | 0.168778i | 0.0811870 | − | 0.0103876i | ||||
\(265\) | −6.48067 | + | 3.74161i | −0.398104 | + | 0.229846i | ||||
\(266\) | 10.2262 | − | 7.70988i | 0.627011 | − | 0.472723i | ||||
\(267\) | −3.74670 | + | 8.95289i | −0.229294 | + | 0.547908i | ||||
\(268\) | 6.85237 | + | 11.8687i | 0.418575 | + | 0.724994i | ||||
\(269\) | 2.94884 | + | 5.10754i | 0.179794 | + | 0.311412i | 0.941810 | − | 0.336146i | \(-0.109124\pi\) |
−0.762016 | + | 0.647558i | \(0.775790\pi\) | |||||||
\(270\) | −3.20810 | + | 4.08755i | −0.195239 | + | 0.248760i | ||||
\(271\) | −8.76680 | − | 5.06151i | −0.532545 | − | 0.307465i | 0.209507 | − | 0.977807i | \(-0.432814\pi\) |
−0.742052 | + | 0.670342i | \(0.766147\pi\) | |||||||
\(272\) | −1.15157 | + | 1.99457i | −0.0698240 | + | 0.120939i | ||||
\(273\) | −5.41120 | + | 19.2574i | −0.327501 | + | 1.16551i | ||||
\(274\) | −7.19674 | − | 12.4651i | −0.434771 | − | 0.753045i | ||||
\(275\) | 0.767810i | 0.0463007i | ||||||||
\(276\) | 8.94405 | + | 3.74300i | 0.538369 | + | 0.225302i | ||||
\(277\) | 10.3900 | 0.624277 | 0.312139 | − | 0.950037i | \(-0.398955\pi\) | ||||
0.312139 | + | 0.950037i | \(0.398955\pi\) | |||||||
\(278\) | 5.09253 | − | 8.82052i | 0.305430 | − | 0.529020i | ||||
\(279\) | 23.3076 | + | 6.42773i | 1.39539 | + | 0.384818i | ||||
\(280\) | 1.59276 | + | 2.11261i | 0.0951857 | + | 0.126252i | ||||
\(281\) | −14.3149 | − | 8.26473i | −0.853957 | − | 0.493032i | 0.00802696 | − | 0.999968i | \(-0.497445\pi\) |
−0.861984 | + | 0.506935i | \(0.830778\pi\) | |||||||
\(282\) | 10.3240 | + | 4.32049i | 0.614784 | + | 0.257281i | ||||
\(283\) | −9.00009 | − | 5.19621i | −0.535000 | − | 0.308882i | 0.208050 | − | 0.978118i | \(-0.433288\pi\) |
−0.743050 | + | 0.669236i | \(0.766622\pi\) | |||||||
\(284\) | −6.50024 | − | 3.75292i | −0.385718 | − | 0.222695i | ||||
\(285\) | 7.73417 | + | 3.23668i | 0.458133 | + | 0.191724i | ||||
\(286\) | 2.90251 | + | 1.67576i | 0.171629 | + | 0.0990901i | ||||
\(287\) | 12.9277 | + | 5.48379i | 0.763095 | + | 0.323698i | ||||
\(288\) | 2.89204 | + | 0.797561i | 0.170415 | + | 0.0469967i | ||||
\(289\) | 5.84779 | − | 10.1287i | 0.343987 | − | 0.595804i | ||||
\(290\) | −10.5325 | −0.618490 | ||||||||
\(291\) | 14.0479 | + | 5.87892i | 0.823504 | + | 0.344628i | ||||
\(292\) | − | 11.6838i | − | 0.683742i | ||||||
\(293\) | −12.7786 | − | 22.1332i | −0.746533 | − | 1.29303i | −0.949475 | − | 0.313843i | \(-0.898384\pi\) |
0.202942 | − | 0.979191i | \(-0.434950\pi\) | |||||||
\(294\) | −4.40789 | − | 11.2947i | −0.257073 | − | 0.658721i | ||||
\(295\) | −5.71736 | + | 9.90276i | −0.332878 | + | 0.576561i | ||||
\(296\) | 7.19869 | + | 4.15617i | 0.418415 | + | 0.241572i | ||||
\(297\) | −1.48638 | − | 3.70244i | −0.0862486 | − | 0.214837i | ||||
\(298\) | −4.47651 | − | 7.75355i | −0.259318 | − | 0.449151i | ||||
\(299\) | 12.2173 | + | 21.1611i | 0.706547 | + | 1.22378i | ||||
\(300\) | −0.668655 | + | 1.59778i | −0.0386048 | + | 0.0922479i | ||||
\(301\) | 3.84273 | + | 31.2343i | 0.221491 | + | 1.80032i | ||||
\(302\) | 4.33635 | − | 2.50359i | 0.249529 | − | 0.144065i | ||||
\(303\) | 20.3614 | − | 2.60516i | 1.16973 | − | 0.149662i | ||||
\(304\) | − | 4.84057i | − | 0.277626i | ||||||
\(305\) | 8.22722 | − | 4.74999i | 0.471089 | − | 0.271983i | ||||
\(306\) | 6.66076 | + | 1.83689i | 0.380770 | + | 0.105008i | ||||
\(307\) | 9.33336i | 0.532683i | 0.963879 | + | 0.266342i | \(0.0858149\pi\) | ||||
−0.963879 | + | 0.266342i | \(0.914185\pi\) | |||||||
\(308\) | −2.01623 | + | 0.248055i | −0.114886 | + | 0.0141343i | ||||
\(309\) | 0.193027 | + | 1.50866i | 0.0109809 | + | 0.0858247i | ||||
\(310\) | 8.05924 | 0.457734 | ||||||||
\(311\) | −2.68289 | + | 4.64689i | −0.152132 | + | 0.263501i | −0.932011 | − | 0.362429i | \(-0.881947\pi\) |
0.779879 | + | 0.625931i | \(0.215281\pi\) | |||||||
\(312\) | 4.58064 | + | 6.01487i | 0.259328 | + | 0.340525i | ||||
\(313\) | 22.0455 | − | 12.7280i | 1.24608 | − | 0.719427i | 0.275758 | − | 0.961227i | \(-0.411071\pi\) |
0.970326 | + | 0.241800i | \(0.0777378\pi\) | |||||||
\(314\) | 3.25327 | 0.183592 | ||||||||
\(315\) | 4.93063 | − | 6.22004i | 0.277809 | − | 0.350460i | ||||
\(316\) | 1.11044 | 0.0624669 | ||||||||
\(317\) | 6.48372 | − | 3.74338i | 0.364162 | − | 0.210249i | −0.306743 | − | 0.951792i | \(-0.599239\pi\) |
0.670905 | + | 0.741543i | \(0.265906\pi\) | |||||||
\(318\) | 5.00370 | − | 11.9566i | 0.280594 | − | 0.670490i | ||||
\(319\) | 4.04348 | − | 7.00351i | 0.226391 | − | 0.392121i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −10.2429 | − | 4.28656i | −0.571703 | − | 0.239252i | ||||
\(322\) | −13.6344 | − | 5.78360i | −0.759817 | − | 0.322307i | ||||
\(323\) | − | 11.1485i | − | 0.620319i | ||||||
\(324\) | 0.131212 | − | 8.99904i | 0.00728955 | − | 0.499947i | ||||
\(325\) | −3.78024 | + | 2.18252i | −0.209690 | + | 0.121065i | ||||
\(326\) | 4.81863i | 0.266879i | ||||||||
\(327\) | 9.15865 | + | 12.0263i | 0.506474 | + | 0.665056i | ||||
\(328\) | 4.59654 | − | 2.65381i | 0.253801 | − | 0.146532i | ||||
\(329\) | −15.7380 | − | 6.67592i | −0.867665 | − | 0.368055i | ||||
\(330\) | −0.805733 | − | 1.05801i | −0.0443541 | − | 0.0582417i | ||||
\(331\) | −3.71433 | − | 6.43342i | −0.204158 | − | 0.353613i | 0.745706 | − | 0.666275i | \(-0.232112\pi\) |
−0.949864 | + | 0.312663i | \(0.898779\pi\) | |||||||
\(332\) | 0.254578 | + | 0.440942i | 0.0139718 | + | 0.0241998i | ||||
\(333\) | 6.62959 | − | 24.0396i | 0.363299 | − | 1.31736i | ||||
\(334\) | 8.61278 | + | 4.97259i | 0.471270 | + | 0.272088i | ||||
\(335\) | 6.85237 | − | 11.8687i | 0.374385 | − | 0.648454i | ||||
\(336\) | −4.41172 | − | 1.23966i | −0.240679 | − | 0.0676293i | ||||
\(337\) | −12.9171 | − | 22.3731i | −0.703641 | − | 1.21874i | −0.967180 | − | 0.254093i | \(-0.918223\pi\) |
0.263539 | − | 0.964649i | \(-0.415110\pi\) | |||||||
\(338\) | 6.05365i | 0.329275i | ||||||||
\(339\) | 1.11000 | − | 0.845320i | 0.0602867 | − | 0.0459115i | ||||
\(340\) | 2.30313 | 0.124905 | ||||||||
\(341\) | −3.09398 | + | 5.35894i | −0.167549 | + | 0.290203i | ||||
\(342\) | −14.0539 | + | 3.65615i | −0.759950 | + | 0.197702i | ||||
\(343\) | 6.64956 | + | 17.2854i | 0.359043 | + | 0.933321i | ||||
\(344\) | 10.3009 | + | 5.94724i | 0.555388 | + | 0.320653i | ||||
\(345\) | −1.23049 | − | 9.61728i | −0.0662476 | − | 0.517777i | ||||
\(346\) | 14.3988 | + | 8.31317i | 0.774086 | + | 0.446919i | ||||
\(347\) | 15.9560 | + | 9.21220i | 0.856562 | + | 0.494537i | 0.862860 | − | 0.505444i | \(-0.168671\pi\) |
−0.00629718 | + | 0.999980i | \(0.502004\pi\) | |||||||
\(348\) | 14.5134 | − | 11.0527i | 0.777999 | − | 0.592487i | ||||
\(349\) | −1.37452 | − | 0.793577i | −0.0735761 | − | 0.0424792i | 0.462761 | − | 0.886483i | \(-0.346859\pi\) |
−0.536337 | + | 0.844004i | \(0.680192\pi\) | |||||||
\(350\) | 1.03319 | − | 2.43568i | 0.0552264 | − | 0.130192i | ||||
\(351\) | 14.0035 | − | 17.8424i | 0.747453 | − | 0.952355i | ||||
\(352\) | −0.383905 | + | 0.664943i | −0.0204622 | + | 0.0354416i | ||||
\(353\) | −9.20537 | −0.489952 | −0.244976 | − | 0.969529i | \(-0.578780\pi\) | ||||
−0.244976 | + | 0.969529i | \(0.578780\pi\) | |||||||
\(354\) | −2.51355 | − | 19.6454i | −0.133594 | − | 1.04414i | ||||
\(355\) | 7.50583i | 0.398368i | ||||||||
\(356\) | −2.80167 | − | 4.85263i | −0.148488 | − | 0.257189i | ||||
\(357\) | −10.1608 | − | 2.85511i | −0.537765 | − | 0.151109i | ||||
\(358\) | −2.35243 | + | 4.07453i | −0.124330 | + | 0.215346i | ||||
\(359\) | 22.3751 | + | 12.9183i | 1.18091 | + | 0.681801i | 0.956226 | − | 0.292629i | \(-0.0945302\pi\) |
0.224689 | + | 0.974431i | \(0.427864\pi\) | |||||||
\(360\) | −0.755312 | − | 2.90336i | −0.0398085 | − | 0.153021i | ||||
\(361\) | 2.21558 | + | 3.83750i | 0.116610 | + | 0.201974i | ||||
\(362\) | −4.16704 | − | 7.21752i | −0.219015 | − | 0.379345i | ||||
\(363\) | −17.8857 | + | 2.28840i | −0.938754 | + | 0.120110i | ||||
\(364\) | −6.95248 | − | 9.22163i | −0.364409 | − | 0.483345i | ||||
\(365\) | −10.1185 | + | 5.84190i | −0.529625 | + | 0.305779i | ||||
\(366\) | −6.35221 | + | 15.1789i | −0.332035 | + | 0.793412i | ||||
\(367\) | − | 22.2564i | − | 1.16178i | −0.813984 | − | 0.580888i | \(-0.802706\pi\) | ||
0.813984 | − | 0.580888i | \(-0.197294\pi\) | |||||||
\(368\) | −4.84784 | + | 2.79890i | −0.252711 | + | 0.145903i | ||||
\(369\) | −11.1768 | − | 11.3410i | −0.581841 | − | 0.590386i | ||||
\(370\) | − | 8.31233i | − | 0.432137i | ||||||
\(371\) | −7.73160 | + | 18.2267i | −0.401405 | + | 0.946284i | ||||
\(372\) | −11.1053 | + | 8.45728i | −0.575784 | + | 0.438490i | ||||
\(373\) | −32.7801 | −1.69729 | −0.848644 | − | 0.528965i | \(-0.822580\pi\) | ||||
−0.848644 | + | 0.528965i | \(0.822580\pi\) | |||||||
\(374\) | −0.884185 | + | 1.53145i | −0.0457201 | + | 0.0791896i | ||||
\(375\) | 1.71805 | − | 0.219817i | 0.0887195 | − | 0.0113513i | ||||
\(376\) | −5.59578 | + | 3.23073i | −0.288581 | + | 0.166612i | ||||
\(377\) | 45.9749 | 2.36783 | ||||||||
\(378\) | −0.266971 | + | 13.7451i | −0.0137315 | + | 0.706973i | ||||
\(379\) | −26.7133 | −1.37217 | −0.686085 | − | 0.727522i | \(-0.740672\pi\) | ||||
−0.686085 | + | 0.727522i | \(0.740672\pi\) | |||||||
\(380\) | −4.19206 | + | 2.42029i | −0.215048 | + | 0.124158i | ||||
\(381\) | 21.7297 | − | 2.78024i | 1.11325 | − | 0.142436i | ||||
\(382\) | −1.89645 | + | 3.28474i | −0.0970307 | + | 0.168062i | ||||
\(383\) | −1.81734 | −0.0928615 | −0.0464307 | − | 0.998922i | \(-0.514785\pi\) | ||||
−0.0464307 | + | 0.998922i | \(0.514785\pi\) | |||||||
\(384\) | −1.37796 | + | 1.04939i | −0.0703188 | + | 0.0535515i | ||||
\(385\) | 1.22294 | + | 1.62208i | 0.0623267 | + | 0.0826689i | ||||
\(386\) | 21.4959i | 1.09411i | ||||||||
\(387\) | 9.48656 | − | 34.3993i | 0.482229 | − | 1.74861i | ||||
\(388\) | −7.61423 | + | 4.39608i | −0.386554 | + | 0.223177i | ||||
\(389\) | 29.9694i | 1.51951i | 0.650209 | + | 0.759755i | \(0.274681\pi\) | ||||
−0.650209 | + | 0.759755i | \(0.725319\pi\) | |||||||
\(390\) | 2.91871 | − | 6.97439i | 0.147795 | − | 0.353162i | ||||
\(391\) | −11.1652 | + | 6.44624i | −0.564650 | + | 0.326001i | ||||
\(392\) | 6.72976 | + | 1.92622i | 0.339904 | + | 0.0972888i | ||||
\(393\) | 17.0534 | − | 2.18191i | 0.860228 | − | 0.110063i | ||||
\(394\) | −6.69540 | − | 11.5968i | −0.337309 | − | 0.584237i | ||||
\(395\) | −0.555218 | − | 0.961666i | −0.0279360 | − | 0.0483867i | ||||
\(396\) | 2.22054 | + | 0.612375i | 0.111586 | + | 0.0307730i | ||||
\(397\) | 0.811242 | + | 0.468371i | 0.0407151 | + | 0.0235069i | 0.520219 | − | 0.854033i | \(-0.325850\pi\) |
−0.479504 | + | 0.877540i | \(0.659184\pi\) | |||||||
\(398\) | −0.280308 | + | 0.485507i | −0.0140506 | + | 0.0243363i | ||||
\(399\) | 21.4945 | − | 5.48087i | 1.07607 | − | 0.274387i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 5.80877i | 0.290076i | 0.989426 | + | 0.145038i | \(0.0463305\pi\) | ||||
−0.989426 | + | 0.145038i | \(0.953670\pi\) | |||||||
\(402\) | 3.01254 | + | 23.5454i | 0.150252 | + | 1.17434i | ||||
\(403\) | −35.1790 | −1.75239 | ||||||||
\(404\) | −5.92574 | + | 10.2637i | −0.294816 | + | 0.510637i | ||||
\(405\) | −7.85901 | + | 4.38589i | −0.390517 | + | 0.217937i | ||||
\(406\) | −22.2510 | + | 16.7758i | −1.10430 | + | 0.832567i | ||||
\(407\) | 5.52723 | + | 3.19115i | 0.273975 | + | 0.158179i | ||||
\(408\) | −3.17363 | + | 2.41689i | −0.157118 | + | 0.119654i | ||||
\(409\) | −18.9501 | − | 10.9409i | −0.937023 | − | 0.540990i | −0.0479969 | − | 0.998847i | \(-0.515284\pi\) |
−0.889026 | + | 0.457857i | \(0.848617\pi\) | |||||||
\(410\) | −4.59654 | − | 2.65381i | −0.227007 | − | 0.131062i | ||||
\(411\) | −3.16394 | − | 24.7286i | −0.156065 | − | 1.21977i | ||||
\(412\) | −0.760480 | − | 0.439063i | −0.0374661 | − | 0.0216311i | ||||
\(413\) | 3.69420 | + | 30.0270i | 0.181780 | + | 1.47753i | ||||
\(414\) | 11.7879 | + | 11.9610i | 0.579341 | + | 0.587850i | ||||
\(415\) | 0.254578 | − | 0.440942i | 0.0124967 | − | 0.0216450i | ||||
\(416\) | −4.36505 | −0.214014 | ||||||||
\(417\) | 14.0346 | − | 10.6881i | 0.687279 | − | 0.523399i | ||||
\(418\) | − | 3.71664i | − | 0.181787i | ||||||
\(419\) | −7.97218 | − | 13.8082i | −0.389467 | − | 0.674576i | 0.602911 | − | 0.797808i | \(-0.294007\pi\) |
−0.992378 | + | 0.123232i | \(0.960674\pi\) | |||||||
\(420\) | 1.13228 | + | 4.44049i | 0.0552494 | + | 0.216674i | ||||
\(421\) | 8.26978 | − | 14.3237i | 0.403044 | − | 0.698093i | −0.591047 | − | 0.806637i | \(-0.701285\pi\) |
0.994092 | + | 0.108544i | \(0.0346187\pi\) | |||||||
\(422\) | −3.05771 | − | 1.76537i | −0.148847 | − | 0.0859368i | ||||
\(423\) | 13.6065 | + | 13.8064i | 0.661572 | + | 0.671289i | ||||
\(424\) | 3.74161 | + | 6.48067i | 0.181709 | + | 0.314729i | ||||
\(425\) | −1.15157 | − | 1.99457i | −0.0558592 | − | 0.0967510i | ||||
\(426\) | −7.87655 | − | 10.3428i | −0.381620 | − | 0.501108i | ||||
\(427\) | 9.81528 | − | 23.1389i | 0.474995 | − | 1.11977i | ||||
\(428\) | 5.55184 | − | 3.20536i | 0.268358 | − | 0.154937i | ||||
\(429\) | 3.51706 | + | 4.61828i | 0.169805 | + | 0.222973i | ||||
\(430\) | − | 11.8945i | − | 0.573602i | ||||||
\(431\) | −10.5417 | + | 6.08623i | −0.507774 | + | 0.293163i | −0.731918 | − | 0.681393i | \(-0.761375\pi\) |
0.224144 | + | 0.974556i | \(0.428041\pi\) | |||||||
\(432\) | 4.08755 | + | 3.20810i | 0.196662 | + | 0.154350i | ||||
\(433\) | 8.54538i | 0.410665i | 0.978692 | + | 0.205332i | \(0.0658276\pi\) | ||||
−0.978692 | + | 0.205332i | \(0.934172\pi\) | |||||||
\(434\) | 17.0260 | − | 12.8364i | 0.817274 | − | 0.616169i | ||||
\(435\) | −16.8286 | − | 7.04261i | −0.806870 | − | 0.337667i | ||||
\(436\) | −8.72759 | −0.417976 | ||||||||
\(437\) | 13.5483 | − | 23.4663i | 0.648102 | − | 1.12255i | ||||
\(438\) | 7.81243 | − | 18.6681i | 0.373292 | − | 0.891998i | ||||
\(439\) | 5.69997 | − | 3.29088i | 0.272045 | − | 0.157065i | −0.357772 | − | 0.933809i | \(-0.616463\pi\) |
0.629816 | + | 0.776744i | \(0.283130\pi\) | |||||||
\(440\) | 0.767810 | 0.0366039 | ||||||||
\(441\) | 0.509438 | − | 20.9938i | 0.0242589 | − | 0.999706i | ||||
\(442\) | −10.0533 | −0.478186 | ||||||||
\(443\) | −23.4466 | + | 13.5369i | −1.11398 | + | 0.643157i | −0.939857 | − | 0.341567i | \(-0.889042\pi\) |
−0.174123 | + | 0.984724i | \(0.555709\pi\) | |||||||
\(444\) | 8.72288 | + | 11.4541i | 0.413969 | + | 0.543587i | ||||
\(445\) | −2.80167 | + | 4.85263i | −0.132812 | + | 0.230037i | ||||
\(446\) | −25.6103 | −1.21268 | ||||||||
\(447\) | −1.96803 | − | 15.3817i | −0.0930847 | − | 0.727530i | ||||
\(448\) | 2.11261 | − | 1.59276i | 0.0998113 | − | 0.0752509i | ||||
\(449\) | − | 17.9654i | − | 0.847841i | −0.905700 | − | 0.423920i | \(-0.860654\pi\) | ||
0.905700 | − | 0.423920i | \(-0.139346\pi\) | |||||||
\(450\) | −2.13673 | + | 2.10580i | −0.100726 | + | 0.0992684i | ||||
\(451\) | 3.52927 | − | 2.03763i | 0.166187 | − | 0.0959480i | ||||
\(452\) | 0.805534i | 0.0378891i | ||||||||
\(453\) | 8.60257 | − | 1.10067i | 0.404184 | − | 0.0517138i | ||||
\(454\) | −9.64631 | + | 5.56930i | −0.452724 | + | 0.261380i | ||||
\(455\) | −4.50993 | + | 10.6318i | −0.211429 | + | 0.498429i | ||||
\(456\) | 3.23668 | − | 7.73417i | 0.151571 | − | 0.362186i | ||||
\(457\) | 2.57466 | + | 4.45944i | 0.120438 | + | 0.208604i | 0.919940 | − | 0.392058i | \(-0.128237\pi\) |
−0.799503 | + | 0.600662i | \(0.794904\pi\) | |||||||
\(458\) | 1.90421 | + | 3.29819i | 0.0889780 | + | 0.154114i | ||||
\(459\) | 9.41418 | + | 7.38870i | 0.439416 | + | 0.344875i | ||||
\(460\) | 4.84784 | + | 2.79890i | 0.226032 | + | 0.130499i | ||||
\(461\) | 5.46051 | − | 9.45788i | 0.254321 | − | 0.440498i | −0.710390 | − | 0.703809i | \(-0.751481\pi\) |
0.964711 | + | 0.263311i | \(0.0848146\pi\) | |||||||
\(462\) | −3.38736 | − | 0.951827i | −0.157594 | − | 0.0442830i | ||||
\(463\) | 14.8704 | + | 25.7563i | 0.691088 | + | 1.19700i | 0.971482 | + | 0.237114i | \(0.0762015\pi\) |
−0.280394 | + | 0.959885i | \(0.590465\pi\) | |||||||
\(464\) | 10.5325i | 0.488959i | ||||||||
\(465\) | 12.8769 | + | 5.38885i | 0.597151 | + | 0.249902i | ||||
\(466\) | −2.35824 | −0.109243 | ||||||||
\(467\) | −4.55724 | + | 7.89337i | −0.210884 | + | 0.365262i | −0.951991 | − | 0.306125i | \(-0.900968\pi\) |
0.741107 | + | 0.671386i | \(0.234301\pi\) | |||||||
\(468\) | 3.29698 | + | 12.6733i | 0.152403 | + | 0.585824i | ||||
\(469\) | −4.42757 | − | 35.9880i | −0.204446 | − | 1.66177i | ||||
\(470\) | 5.59578 | + | 3.23073i | 0.258114 | + | 0.149022i | ||||
\(471\) | 5.19800 | + | 2.17531i | 0.239511 | + | 0.100233i | ||||
\(472\) | 9.90276 | + | 5.71736i | 0.455811 | + | 0.263163i | ||||
\(473\) | 7.90915 | + | 4.56635i | 0.363663 | + | 0.209961i | ||||
\(474\) | 1.77423 | + | 0.742499i | 0.0814932 | + | 0.0341041i | ||||
\(475\) | 4.19206 | + | 2.42029i | 0.192345 | + | 0.111050i | ||||
\(476\) | 4.86562 | − | 3.66834i | 0.223015 | − | 0.168138i | ||||
\(477\) | 15.9896 | − | 15.7582i | 0.732114 | − | 0.721518i | ||||
\(478\) | −5.88712 | + | 10.1968i | −0.269271 | + | 0.466390i | ||||
\(479\) | −37.2972 | −1.70415 | −0.852076 | − | 0.523419i | \(-0.824656\pi\) | ||||
−0.852076 | + | 0.523419i | \(0.824656\pi\) | |||||||
\(480\) | 1.59778 | + | 0.668655i | 0.0729283 | + | 0.0305198i | ||||
\(481\) | 36.2837i | 1.65440i | ||||||||
\(482\) | 9.40683 | + | 16.2931i | 0.428469 | + | 0.742130i | ||||
\(483\) | −17.9176 | − | 18.3576i | −0.815278 | − | 0.835302i | ||||
\(484\) | 5.20523 | − | 9.01573i | 0.236602 | − | 0.409806i | ||||
\(485\) | 7.61423 | + | 4.39608i | 0.345744 | + | 0.199615i | ||||
\(486\) | 6.22691 | − | 14.2908i | 0.282458 | − | 0.648242i | ||||
\(487\) | −9.44574 | − | 16.3605i | −0.428027 | − | 0.741365i | 0.568671 | − | 0.822565i | \(-0.307458\pi\) |
−0.996698 | + | 0.0812005i | \(0.974125\pi\) | |||||||
\(488\) | −4.74999 | − | 8.22722i | −0.215022 | − | 0.372429i | ||||
\(489\) | −3.22200 | + | 7.69911i | −0.145704 | + | 0.348166i | ||||
\(490\) | −1.69673 | − | 6.79125i | −0.0766502 | − | 0.306798i | ||||
\(491\) | −30.1458 | + | 17.4047i | −1.36046 | + | 0.785462i | −0.989685 | − | 0.143260i | \(-0.954241\pi\) |
−0.370776 | + | 0.928723i | \(0.620908\pi\) | |||||||
\(492\) | 9.11874 | − | 1.16671i | 0.411105 | − | 0.0525993i | ||||
\(493\) | 24.2578i | 1.09251i | ||||||||
\(494\) | 18.2986 | − | 10.5647i | 0.823291 | − | 0.475327i | ||||
\(495\) | −0.579937 | − | 2.22923i | −0.0260662 | − | 0.100196i | ||||
\(496\) | − | 8.05924i | − | 0.361870i | ||||||
\(497\) | 11.9550 | + | 15.8569i | 0.536255 | + | 0.711278i | ||||
\(498\) | 0.111921 | + | 0.874752i | 0.00501531 | + | 0.0391986i | ||||
\(499\) | 24.4326 | 1.09376 | 0.546878 | − | 0.837212i | \(-0.315816\pi\) | ||||
0.546878 | + | 0.837212i | \(0.315816\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 10.4364 | + | 13.7041i | 0.466263 | + | 0.612253i | ||||
\(502\) | 2.90776 | − | 1.67879i | 0.129780 | − | 0.0749283i | ||||
\(503\) | −13.5009 | −0.601977 | −0.300988 | − | 0.953628i | \(-0.597317\pi\) | ||||
−0.300988 | + | 0.953628i | \(0.597317\pi\) | |||||||
\(504\) | −6.22004 | − | 4.93063i | −0.277063 | − | 0.219628i | ||||
\(505\) | 11.8515 | 0.527384 | ||||||||
\(506\) | −3.72222 | + | 2.14902i | −0.165473 | + | 0.0955358i | ||||
\(507\) | −4.04781 | + | 9.67241i | −0.179769 | + | 0.429567i | ||||
\(508\) | −6.32397 | + | 10.9534i | −0.280581 | + | 0.485980i | ||||
\(509\) | −27.3443 | −1.21202 | −0.606008 | − | 0.795459i | \(-0.707230\pi\) | ||||
−0.606008 | + | 0.795459i | \(0.707230\pi\) | |||||||
\(510\) | 3.67990 | + | 1.54000i | 0.162949 | + | 0.0681925i | ||||
\(511\) | −12.0716 | + | 28.4579i | −0.534016 | + | 1.25891i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −24.8998 | − | 3.55552i | −1.09935 | − | 0.156980i | ||||
\(514\) | −9.81743 | + | 5.66810i | −0.433028 | + | 0.250009i | ||||
\(515\) | 0.878126i | 0.0386949i | ||||||||
\(516\) | 12.4819 | + | 16.3901i | 0.549487 | + | 0.721535i | ||||
\(517\) | −4.29650 | + | 2.48059i | −0.188960 | + | 0.109096i | ||||
\(518\) | −13.2396 | − | 17.5607i | −0.581713 | − | 0.771572i | ||||
\(519\) | 17.4475 | + | 22.9105i | 0.765861 | + | 1.00566i | ||||
\(520\) | 2.18252 | + | 3.78024i | 0.0957100 | + | 0.165775i | ||||
\(521\) | 5.24997 | + | 9.09321i | 0.230005 | + | 0.398381i | 0.957809 | − | 0.287404i | \(-0.0927923\pi\) |
−0.727804 | + | 0.685785i | \(0.759459\pi\) | |||||||
\(522\) | 30.5796 | − | 7.95533i | 1.33843 | − | 0.348195i | ||||
\(523\) | −15.4653 | − | 8.92889i | −0.676250 | − | 0.390433i | 0.122191 | − | 0.992507i | \(-0.461008\pi\) |
−0.798441 | + | 0.602074i | \(0.794341\pi\) | |||||||
\(524\) | −4.96301 | + | 8.59619i | −0.216810 | + | 0.375526i | ||||
\(525\) | 3.27944 | − | 3.20083i | 0.143126 | − | 0.139695i | ||||
\(526\) | 12.8910 | + | 22.3278i | 0.562074 | + | 0.973540i | ||||
\(527\) | − | 18.5615i | − | 0.808552i | ||||||
\(528\) | −1.05801 | + | 0.805733i | −0.0460441 | + | 0.0350650i | ||||
\(529\) | −8.33538 | −0.362408 | ||||||||
\(530\) | 3.74161 | − | 6.48067i | 0.162525 | − | 0.281502i | ||||
\(531\) | 9.11988 | − | 33.0697i | 0.395769 | − | 1.43510i | ||||
\(532\) | −5.00124 | + | 11.7901i | −0.216831 | + | 0.511164i | ||||
\(533\) | 20.0641 | + | 11.5840i | 0.869074 | + | 0.501760i | ||||
\(534\) | −1.23171 | − | 9.62678i | −0.0533013 | − | 0.416592i | ||||
\(535\) | −5.55184 | − | 3.20536i | −0.240027 | − | 0.138580i | ||||
\(536\) | −11.8687 | − | 6.85237i | −0.512648 | − | 0.295977i | ||||
\(537\) | −6.48312 | + | 4.93724i | −0.279767 | + | 0.213057i | ||||
\(538\) | −5.10754 | − | 2.94884i | −0.220202 | − | 0.127134i | ||||
\(539\) | 5.16718 | + | 1.47897i | 0.222566 | + | 0.0637038i | ||||
\(540\) | 0.734525 | − | 5.14397i | 0.0316089 | − | 0.221361i | ||||
\(541\) | 4.16365 | − | 7.21166i | 0.179009 | − | 0.310053i | −0.762532 | − | 0.646950i | \(-0.776044\pi\) |
0.941542 | + | 0.336897i | \(0.109377\pi\) | |||||||
\(542\) | 10.1230 | 0.434821 | ||||||||
\(543\) | −1.83198 | − | 14.3183i | −0.0786176 | − | 0.614458i | ||||
\(544\) | − | 2.30313i | − | 0.0987461i | ||||||
\(545\) | 4.36380 | + | 7.55832i | 0.186924 | + | 0.323763i | ||||
\(546\) | −4.94244 | − | 19.3830i | −0.211517 | − | 0.829514i | ||||
\(547\) | 15.3348 | − | 26.5606i | 0.655667 | − | 1.13565i | −0.326059 | − | 0.945349i | \(-0.605721\pi\) |
0.981726 | − | 0.190299i | \(-0.0609459\pi\) | |||||||
\(548\) | 12.4651 | + | 7.19674i | 0.532483 | + | 0.307429i | ||||
\(549\) | −20.2989 | + | 20.0050i | −0.866334 | + | 0.853795i | ||||
\(550\) | −0.383905 | − | 0.664943i | −0.0163698 | − | 0.0283533i | ||||
\(551\) | −25.4917 | − | 44.1529i | −1.08598 | − | 1.88098i | ||||
\(552\) | −9.61728 | + | 1.23049i | −0.409338 | + | 0.0523733i | ||||
\(553\) | −2.70466 | − | 1.14729i | −0.115014 | − | 0.0487878i | ||||
\(554\) | −8.99804 | + | 5.19502i | −0.382290 | + | 0.220715i | ||||
\(555\) | 5.55808 | − | 13.2813i | 0.235928 | − | 0.563759i | ||||
\(556\) | 10.1851i | 0.431943i | ||||||||
\(557\) | −1.82492 | + | 1.05362i | −0.0773242 | + | 0.0446432i | −0.538164 | − | 0.842840i | \(-0.680882\pi\) |
0.460839 | + | 0.887484i | \(0.347548\pi\) | |||||||
\(558\) | −23.3989 | + | 6.08724i | −0.990553 | + | 0.257694i | ||||
\(559\) | 51.9199i | 2.19598i | ||||||||
\(560\) | −2.43568 | − | 1.03319i | −0.102926 | − | 0.0436603i | ||||
\(561\) | −2.43675 | + | 1.85571i | −0.102880 | + | 0.0783482i | ||||
\(562\) | 16.5295 | 0.697253 | ||||||||
\(563\) | 5.74415 | − | 9.94915i | 0.242087 | − | 0.419307i | −0.719222 | − | 0.694781i | \(-0.755501\pi\) |
0.961309 | + | 0.275474i | \(0.0888347\pi\) | |||||||
\(564\) | −11.1011 | + | 1.42034i | −0.467440 | + | 0.0598071i | ||||
\(565\) | 0.697613 | − | 0.402767i | 0.0293488 | − | 0.0169445i | ||||
\(566\) | 10.3924 | 0.436826 | ||||||||
\(567\) | −9.61732 | + | 21.7832i | −0.403889 | + | 0.914808i | ||||
\(568\) | 7.50583 | 0.314938 | ||||||||
\(569\) | 39.7209 | − | 22.9329i | 1.66519 | − | 0.961395i | 0.695007 | − | 0.719003i | \(-0.255401\pi\) |
0.970178 | − | 0.242392i | \(-0.0779320\pi\) | |||||||
\(570\) | −8.31633 | + | 1.06404i | −0.348333 | + | 0.0445678i | ||||
\(571\) | 6.79295 | − | 11.7657i | 0.284276 | − | 0.492381i | −0.688157 | − | 0.725562i | \(-0.741580\pi\) |
0.972433 | + | 0.233181i | \(0.0749134\pi\) | |||||||
\(572\) | −3.35153 | −0.140135 | ||||||||
\(573\) | −5.22647 | + | 3.98023i | −0.218339 | + | 0.166276i | ||||
\(574\) | −13.9376 | + | 1.71473i | −0.581743 | + | 0.0715713i | ||||
\(575\) | − | 5.59780i | − | 0.233444i | ||||||
\(576\) | −2.90336 | + | 0.755312i | −0.120973 | + | 0.0314714i | ||||
\(577\) | −17.2122 | + | 9.93748i | −0.716554 | + | 0.413703i | −0.813483 | − | 0.581589i | \(-0.802431\pi\) |
0.0969291 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(578\) | 11.6956i | 0.486472i | ||||||||
\(579\) | −14.3734 | + | 34.3458i | −0.597337 | + | 1.42736i | ||||
\(580\) | 9.12141 | − | 5.26625i | 0.378746 | − | 0.218669i | ||||
\(581\) | −0.164492 | − | 1.33702i | −0.00682428 | − | 0.0554689i | ||||
\(582\) | −15.1053 | + | 1.93267i | −0.626135 | + | 0.0801116i | ||||
\(583\) | 2.87285 | + | 4.97592i | 0.118981 | + | 0.206082i | ||||
\(584\) | 5.84190 | + | 10.1185i | 0.241739 | + | 0.418705i | ||||
\(585\) | 9.32692 | − | 9.19192i | 0.385621 | − | 0.380039i | ||||
\(586\) | 22.1332 | + | 12.7786i | 0.914313 | + | 0.527879i | ||||
\(587\) | 11.8126 | − | 20.4600i | 0.487558 | − | 0.844475i | −0.512340 | − | 0.858783i | \(-0.671221\pi\) |
0.999898 | + | 0.0143079i | \(0.00455451\pi\) | |||||||
\(588\) | 9.46470 | + | 7.57756i | 0.390318 | + | 0.312494i | ||||
\(589\) | 19.5057 | + | 33.7848i | 0.803717 | + | 1.39208i | ||||
\(590\) | − | 11.4347i | − | 0.470760i | ||||||
\(591\) | −2.94353 | − | 23.0060i | −0.121081 | − | 0.946340i | ||||
\(592\) | −8.31233 | −0.341635 | ||||||||
\(593\) | −23.9443 | + | 41.4727i | −0.983274 | + | 1.70308i | −0.333907 | + | 0.942606i | \(0.608367\pi\) |
−0.649367 | + | 0.760475i | \(0.724966\pi\) | |||||||
\(594\) | 3.13846 | + | 2.46322i | 0.128773 | + | 0.101067i | ||||
\(595\) | −5.60969 | − | 2.37958i | −0.229975 | − | 0.0975531i | ||||
\(596\) | 7.75355 | + | 4.47651i | 0.317598 | + | 0.183365i | ||||
\(597\) | −0.772507 | + | 0.588304i | −0.0316166 | + | 0.0240777i | ||||
\(598\) | −21.1611 | − | 12.2173i | −0.865340 | − | 0.499604i | ||||
\(599\) | 12.9010 | + | 7.44842i | 0.527123 | + | 0.304334i | 0.739844 | − | 0.672779i | \(-0.234899\pi\) |
−0.212721 | + | 0.977113i | \(0.568233\pi\) | |||||||
\(600\) | −0.219817 | − | 1.71805i | −0.00897401 | − | 0.0701389i | ||||
\(601\) | 13.3073 | + | 7.68296i | 0.542815 | + | 0.313394i | 0.746219 | − | 0.665700i | \(-0.231867\pi\) |
−0.203404 | + | 0.979095i | \(0.565200\pi\) | |||||||
\(602\) | −18.9451 | − | 25.1283i | −0.772143 | − | 1.02415i | ||||
\(603\) | −10.9304 | + | 39.6347i | −0.445119 | + | 1.61405i | ||||
\(604\) | −2.50359 | + | 4.33635i | −0.101870 | + | 0.176443i | ||||
\(605\) | −10.4105 | −0.423246 | ||||||||
\(606\) | −16.3309 | + | 12.4368i | −0.663397 | + | 0.505211i | ||||
\(607\) | − | 8.96232i | − | 0.363769i | −0.983320 | − | 0.181885i | \(-0.941780\pi\) | ||
0.983320 | − | 0.181885i | \(-0.0582197\pi\) | |||||||
\(608\) | 2.42029 | + | 4.19206i | 0.0981556 | + | 0.170011i | ||||
\(609\) | −46.7694 | + | 11.9257i | −1.89519 | + | 0.483254i | ||||
\(610\) | −4.74999 | + | 8.22722i | −0.192321 | + | 0.333110i | ||||
\(611\) | −24.4259 | − | 14.1023i | −0.988165 | − | 0.570517i | ||||
\(612\) | −6.68683 | + | 1.73959i | −0.270299 | + | 0.0703186i | ||||
\(613\) | −10.8226 | − | 18.7452i | −0.437119 | − | 0.757113i | 0.560347 | − | 0.828258i | \(-0.310668\pi\) |
−0.997466 | + | 0.0711452i | \(0.977335\pi\) | |||||||
\(614\) | −4.66668 | − | 8.08293i | −0.188332 | − | 0.326200i | ||||
\(615\) | −5.56977 | − | 7.31371i | −0.224595 | − | 0.294917i | ||||
\(616\) | 1.62208 | − | 1.22294i | 0.0653555 | − | 0.0492736i | ||||
\(617\) | −28.3642 | + | 16.3761i | −1.14190 | + | 0.659277i | −0.946901 | − | 0.321527i | \(-0.895804\pi\) |
−0.195000 | + | 0.980803i | \(0.562471\pi\) | |||||||
\(618\) | −0.921497 | − | 1.21003i | −0.0370681 | − | 0.0486743i | ||||
\(619\) | − | 13.1574i | − | 0.528839i | −0.964408 | − | 0.264420i | \(-0.914820\pi\) | ||
0.964408 | − | 0.264420i | \(-0.0851804\pi\) | |||||||
\(620\) | −6.97950 | + | 4.02962i | −0.280304 | + | 0.161833i | ||||
\(621\) | 10.8366 | + | 26.9930i | 0.434858 | + | 1.08319i | ||||
\(622\) | − | 5.36577i | − | 0.215148i | ||||||
\(623\) | 1.81026 | + | 14.7141i | 0.0725266 | + | 0.589507i | ||||
\(624\) | −6.97439 | − | 2.91871i | −0.279199 | − | 0.116842i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.7280 | + | 22.0455i | −0.508712 | + | 0.881115i | ||||
\(627\) | 2.48515 | − | 5.93838i | 0.0992475 | − | 0.237156i | ||||
\(628\) | −2.81741 | + | 1.62663i | −0.112427 | + | 0.0649097i | ||||
\(629\) | −19.1444 | −0.763338 | ||||||||
\(630\) | −1.16003 | + | 7.85203i | −0.0462167 | + | 0.312832i | ||||
\(631\) | −32.3439 | −1.28759 | −0.643795 | − | 0.765198i | \(-0.722641\pi\) | ||||
−0.643795 | + | 0.765198i | \(0.722641\pi\) | |||||||
\(632\) | −0.961666 | + | 0.555218i | −0.0382530 | + | 0.0220854i | ||||
\(633\) | −3.70512 | − | 4.86522i | −0.147265 | − | 0.193375i | ||||
\(634\) | −3.74338 | + | 6.48372i | −0.148669 | + | 0.257502i | ||||
\(635\) | 12.6479 | 0.501918 | ||||||||
\(636\) | 1.64494 | + | 12.8565i | 0.0652262 | + | 0.509794i | ||||
\(637\) | 7.40629 | + | 29.6442i | 0.293448 | + | 1.17454i | ||||
\(638\) | 8.08696i | 0.320166i | ||||||||
\(639\) | −5.66925 | − | 21.7921i | −0.224272 | − | 0.862084i | ||||
\(640\) | −0.866025 | + | 0.500000i | −0.0342327 | + | 0.0197642i | ||||
\(641\) | 28.0300i | 1.10712i | 0.832810 | + | 0.553559i | \(0.186731\pi\) | ||||
−0.832810 | + | 0.553559i | \(0.813269\pi\) | |||||||
\(642\) | 11.0139 | − | 1.40919i | 0.434684 | − | 0.0556161i | ||||
\(643\) | −11.6003 | + | 6.69742i | −0.457470 | + | 0.264121i | −0.710980 | − | 0.703212i | \(-0.751748\pi\) |
0.253510 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(644\) | 14.6996 | − | 1.80847i | 0.579244 | − | 0.0712638i | ||||
\(645\) | 7.95330 | − | 19.0047i | 0.313161 | − | 0.748311i | ||||
\(646\) | 5.57425 | + | 9.65488i | 0.219316 | + | 0.379866i | ||||
\(647\) | −10.5813 | − | 18.3274i | −0.415995 | − | 0.720524i | 0.579537 | − | 0.814946i | \(-0.303233\pi\) |
−0.995532 | + | 0.0944214i | \(0.969900\pi\) | |||||||
\(648\) | 4.38589 | + | 7.85901i | 0.172294 | + | 0.308731i | ||||
\(649\) | 7.60344 | + | 4.38985i | 0.298461 | + | 0.172317i | ||||
\(650\) | 2.18252 | − | 3.78024i | 0.0856057 | − | 0.148273i | ||||
\(651\) | 35.7870 | − | 9.12528i | 1.40260 | − | 0.357648i | ||||
\(652\) | −2.40931 | − | 4.17306i | −0.0943560 | − | 0.163429i | ||||
\(653\) | 21.0984i | 0.825645i | 0.910811 | + | 0.412823i | \(0.135457\pi\) | ||||
−0.910811 | + | 0.412823i | \(0.864543\pi\) | |||||||
\(654\) | −13.9448 | − | 5.83575i | −0.545284 | − | 0.228196i | ||||
\(655\) | 9.92603 | 0.387842 | ||||||||
\(656\) | −2.65381 | + | 4.59654i | −0.103614 | + | 0.179465i | ||||
\(657\) | 24.9651 | − | 24.6037i | 0.973981 | − | 0.959883i | ||||
\(658\) | 16.9675 | − | 2.08749i | 0.661461 | − | 0.0813790i | ||||
\(659\) | 24.0800 | + | 13.9026i | 0.938025 | + | 0.541569i | 0.889341 | − | 0.457245i | \(-0.151164\pi\) |
0.0486845 | + | 0.998814i | \(0.484497\pi\) | |||||||
\(660\) | 1.22679 | + | 0.513400i | 0.0477528 | + | 0.0199841i | ||||
\(661\) | 8.80674 | + | 5.08458i | 0.342543 | + | 0.197767i | 0.661396 | − | 0.750037i | \(-0.269964\pi\) |
−0.318853 | + | 0.947804i | \(0.603298\pi\) | |||||||
\(662\) | 6.43342 | + | 3.71433i | 0.250042 | + | 0.144362i | ||||
\(663\) | −16.0630 | − | 6.72219i | −0.623833 | − | 0.261068i | ||||
\(664\) | −0.440942 | − | 0.254578i | −0.0171119 | − | 0.00987953i | ||||
\(665\) | 12.7111 | − | 1.56384i | 0.492916 | − | 0.0606430i | ||||
\(666\) | 6.27841 | + | 24.1337i | 0.243283 | + | 0.935162i | ||||
\(667\) | −29.4794 | + | 51.0598i | −1.14145 | + | 1.97704i | ||||
\(668\) | −9.94518 | −0.384791 | ||||||||
\(669\) | −40.9196 | − | 17.1244i | −1.58204 | − | 0.662069i | ||||
\(670\) | 13.7047i | 0.529461i | ||||||||
\(671\) | −3.64709 | − | 6.31694i | −0.140794 | − | 0.243863i | ||||
\(672\) | 4.44049 | − | 1.13228i | 0.171296 | − | 0.0436785i | ||||
\(673\) | −5.29232 | + | 9.16657i | −0.204004 | + | 0.353345i | −0.949815 | − | 0.312812i | \(-0.898729\pi\) |
0.745811 | + | 0.666158i | \(0.232062\pi\) | |||||||
\(674\) | 22.3731 | + | 12.9171i | 0.861781 | + | 0.497549i | ||||
\(675\) | −4.82207 | + | 1.93587i | −0.185602 | + | 0.0745117i | ||||
\(676\) | −3.02683 | − | 5.24262i | −0.116416 | − | 0.201639i | ||||
\(677\) | −16.5653 | − | 28.6920i | −0.636657 | − | 1.10272i | −0.986162 | − | 0.165787i | \(-0.946983\pi\) |
0.349505 | − | 0.936935i | \(-0.386350\pi\) | |||||||
\(678\) | −0.538625 | + | 1.28707i | −0.0206858 | + | 0.0494295i | ||||
\(679\) | 23.0878 | − | 2.84047i | 0.886027 | − | 0.109007i | ||||
\(680\) | −1.99457 | + | 1.15157i | −0.0764884 | + | 0.0441606i | ||||
\(681\) | −19.1366 | + | 2.44846i | −0.733317 | + | 0.0938251i | ||||
\(682\) | − | 6.18797i | − | 0.236949i | ||||||
\(683\) | −15.1376 | + | 8.73972i | −0.579225 | + | 0.334416i | −0.760826 | − | 0.648957i | \(-0.775206\pi\) |
0.181600 | + | 0.983372i | \(0.441872\pi\) | |||||||
\(684\) | 10.3430 | − | 10.1933i | 0.395474 | − | 0.389750i | ||||
\(685\) | − | 14.3935i | − | 0.549947i | ||||||
\(686\) | −14.4014 | − | 11.6448i | −0.549847 | − | 0.444599i | ||||
\(687\) | 0.837158 | + | 6.54305i | 0.0319396 | + | 0.249633i | ||||
\(688\) | −11.8945 | −0.453472 | ||||||||
\(689\) | −16.3323 | + | 28.2884i | −0.622212 | + | 1.07770i | ||||
\(690\) | 5.87428 | + | 7.71356i | 0.223630 | + | 0.293650i | ||||
\(691\) | 16.5287 | − | 9.54285i | 0.628782 | − | 0.363027i | −0.151498 | − | 0.988457i | \(-0.548410\pi\) |
0.780280 | + | 0.625430i | \(0.215077\pi\) | |||||||
\(692\) | −16.6263 | −0.632039 | ||||||||
\(693\) | −4.77581 | − | 3.78579i | −0.181418 | − | 0.143810i | ||||
\(694\) | −18.4244 | −0.699380 | ||||||||
\(695\) | 8.82052 | − | 5.09253i | 0.334581 | − | 0.193171i | ||||
\(696\) | −7.04261 | + | 16.8286i | −0.266949 | + | 0.637887i | ||||
\(697\) | −6.11209 | + | 10.5864i | −0.231512 | + | 0.400990i | ||||
\(698\) | 1.58715 | 0.0600747 | ||||||||
\(699\) | −3.76795 | − | 1.57685i | −0.142517 | − | 0.0596420i | ||||
\(700\) | 0.323069 | + | 2.62595i | 0.0122108 | + | 0.0992517i | ||||
\(701\) | − | 14.4247i | − | 0.544815i | −0.962182 | − | 0.272407i | \(-0.912180\pi\) | ||
0.962182 | − | 0.272407i | \(-0.0878198\pi\) | |||||||
\(702\) | −3.20624 | + | 22.4537i | −0.121012 | + | 0.847460i | ||||
\(703\) | 34.8458 | − | 20.1182i | 1.31423 | − | 0.758773i | ||||
\(704\) | − | 0.767810i | − | 0.0289379i | ||||||
\(705\) | 6.78059 | + | 8.90364i | 0.255372 | + | 0.335331i | ||||
\(706\) | 7.97208 | − | 4.60268i | 0.300033 | − | 0.173224i | ||||
\(707\) | 25.0375 | − | 18.8766i | 0.941632 | − | 0.709927i | ||||
\(708\) | 11.9995 | + | 15.7566i | 0.450968 | + | 0.592170i | ||||
\(709\) | −11.9719 | − | 20.7360i | −0.449615 | − | 0.778755i | 0.548746 | − | 0.835989i | \(-0.315105\pi\) |
−0.998361 | + | 0.0572336i | \(0.981772\pi\) | |||||||
\(710\) | −3.75292 | − | 6.50024i | −0.140844 | − | 0.243950i | ||||
\(711\) | 2.33836 | + | 2.37270i | 0.0876952 | + | 0.0889832i | ||||
\(712\) | 4.85263 | + | 2.80167i | 0.181860 | + | 0.104997i | ||||
\(713\) | 22.5570 | − | 39.0699i | 0.844766 | − | 1.46318i | ||||
\(714\) | 10.2270 | − | 2.60778i | 0.382738 | − | 0.0975939i | ||||
\(715\) | 1.67576 | + | 2.90251i | 0.0626701 | + | 0.108548i | ||||
\(716\) | − | 4.70486i | − | 0.175829i | ||||||
\(717\) | −16.2245 | + | 12.3558i | −0.605914 | + | 0.461435i | ||||
\(718\) | −25.8366 | −0.964213 | ||||||||
\(719\) | −7.04096 | + | 12.1953i | −0.262584 | + | 0.454808i | −0.966928 | − | 0.255051i | \(-0.917908\pi\) |
0.704344 | + | 0.709859i | \(0.251241\pi\) | |||||||
\(720\) | 2.10580 | + | 2.13673i | 0.0784785 | + | 0.0796311i | ||||
\(721\) | 1.39865 | + | 1.85514i | 0.0520883 | + | 0.0690889i | ||||
\(722\) | −3.83750 | − | 2.21558i | −0.142817 | − | 0.0824554i | ||||
\(723\) | 4.13557 | + | 32.3227i | 0.153803 | + | 1.20209i | ||||
\(724\) | 7.21752 | + | 4.16704i | 0.268237 | + | 0.154867i | ||||
\(725\) | −9.12141 | − | 5.26625i | −0.338761 | − | 0.195584i | ||||
\(726\) | 14.3452 | − | 10.9246i | 0.532402 | − | 0.405451i | ||||
\(727\) | 10.6031 | + | 6.12171i | 0.393248 | + | 0.227042i | 0.683566 | − | 0.729888i | \(-0.260428\pi\) |
−0.290319 | + | 0.956930i | \(0.593761\pi\) | |||||||
\(728\) | 10.6318 | + | 4.50993i | 0.394042 | + | 0.167149i | ||||
\(729\) | 19.5048 | − | 18.6698i | 0.722400 | − | 0.691475i | ||||
\(730\) | 5.84190 | − | 10.1185i | 0.216218 | − | 0.374501i | ||||
\(731\) | −27.3946 | −1.01322 | ||||||||
\(732\) | −2.08826 | − | 16.3214i | −0.0771843 | − | 0.603256i | ||||
\(733\) | − | 31.9863i | − | 1.18144i | −0.806877 | − | 0.590720i | \(-0.798844\pi\) | ||
0.806877 | − | 0.590720i | \(-0.201156\pi\) | |||||||
\(734\) | 11.1282 | + | 19.2746i | 0.410750 | + | 0.711439i | ||||
\(735\) | 1.83001 | − | 11.9855i | 0.0675011 | − | 0.442090i | ||||
\(736\) | 2.79890 | − | 4.84784i | 0.103169 | − | 0.178694i | ||||
\(737\) | −9.11288 | − | 5.26132i | −0.335677 | − | 0.193803i | ||||
\(738\) | 15.3499 | + | 4.23315i | 0.565037 | + | 0.155825i | ||||
\(739\) | −17.7732 | − | 30.7841i | −0.653798 | − | 1.13241i | −0.982194 | − | 0.187871i | \(-0.939841\pi\) |
0.328396 | − | 0.944540i | \(-0.393492\pi\) | |||||||
\(740\) | 4.15617 | + | 7.19869i | 0.152784 | + | 0.264629i | ||||
\(741\) | 36.3012 | − | 4.64460i | 1.33356 | − | 0.170624i | ||||
\(742\) | −2.41760 | − | 19.6506i | −0.0887527 | − | 0.721396i | ||||
\(743\) | 19.6903 | − | 11.3682i | 0.722366 | − | 0.417058i | −0.0932570 | − | 0.995642i | \(-0.529728\pi\) |
0.815623 | + | 0.578584i | \(0.196394\pi\) | |||||||
\(744\) | 5.38885 | − | 12.8769i | 0.197565 | − | 0.472090i | ||||
\(745\) | − | 8.95303i | − | 0.328014i | ||||||
\(746\) | 28.3884 | − | 16.3900i | 1.03937 | − | 0.600082i | ||||
\(747\) | −0.406082 | + | 1.47250i | −0.0148578 | + | 0.0538759i | ||||
\(748\) | − | 1.76837i | − | 0.0646580i | ||||||
\(749\) | −16.8342 | + | 2.07110i | −0.615109 | + | 0.0756763i | ||||
\(750\) | −1.37796 | + | 1.04939i | −0.0503161 | + | 0.0383183i | ||||
\(751\) | 14.4519 | 0.527357 | 0.263678 | − | 0.964611i | \(-0.415064\pi\) | ||||
0.263678 | + | 0.964611i | \(0.415064\pi\) | |||||||
\(752\) | 3.23073 | − | 5.59578i | 0.117813 | − | 0.204057i | ||||
\(753\) | 5.76849 | − | 0.738056i | 0.210215 | − | 0.0268963i | ||||
\(754\) | −39.8154 | + | 22.9874i | −1.44999 | + | 0.837153i | ||||
\(755\) | 5.00718 | 0.182230 | ||||||||
\(756\) | −6.64136 | − | 12.0371i | −0.241544 | − | 0.437786i | ||||
\(757\) | 29.2971 | 1.06482 | 0.532410 | − | 0.846487i | \(-0.321287\pi\) | ||||
0.532410 | + | 0.846487i | \(0.321287\pi\) | |||||||
\(758\) | 23.1344 | − | 13.3566i | 0.840278 | − | 0.485135i | ||||
\(759\) | −7.38424 | + | 0.944786i | −0.268031 | + | 0.0342936i | ||||
\(760\) | 2.42029 | − | 4.19206i | 0.0877930 | − | 0.152062i | ||||
\(761\) | 48.9328 | 1.77381 | 0.886906 | − | 0.461949i | \(-0.152850\pi\) | ||||
0.886906 | + | 0.461949i | \(0.152850\pi\) | |||||||
\(762\) | −17.4284 | + | 13.2726i | −0.631364 | + | 0.480816i | ||||
\(763\) | 21.2576 | + | 9.01727i | 0.769576 | + | 0.326447i | ||||
\(764\) | − | 3.79290i | − | 0.137222i | ||||||
\(765\) | 4.84994 | + | 4.92117i | 0.175350 | + | 0.177925i | ||||
\(766\) | 1.57386 | − | 0.908668i | 0.0568658 | − | 0.0328315i | ||||
\(767\) | 49.9131i | 1.80226i | ||||||||
\(768\) | 0.668655 | − | 1.59778i | 0.0241280 | − | 0.0576549i | ||||
\(769\) | 44.0886 | − | 25.4546i | 1.58988 | − | 0.917915i | 0.596549 | − | 0.802577i | \(-0.296538\pi\) |
0.993326 | − | 0.115339i | \(-0.0367953\pi\) | |||||||
\(770\) | −1.87014 | − | 0.793294i | −0.0673951 | − | 0.0285883i | ||||
\(771\) | −19.4761 | + | 2.49189i | −0.701414 | + | 0.0897433i | ||||
\(772\) | −10.7480 | − | 18.6160i | −0.386828 | − | 0.670005i | ||||
\(773\) | −10.7757 | − | 18.6640i | −0.387574 | − | 0.671297i | 0.604549 | − | 0.796568i | \(-0.293353\pi\) |
−0.992123 | + | 0.125271i | \(0.960020\pi\) | |||||||
\(774\) | 8.98404 | + | 34.5339i | 0.322925 | + | 1.24130i | ||||
\(775\) | 6.97950 | + | 4.02962i | 0.250711 | + | 0.144748i | ||||
\(776\) | 4.39608 | − | 7.61423i | 0.157810 | − | 0.273335i | ||||
\(777\) | −9.41186 | − | 36.9108i | −0.337648 | − | 1.32417i | ||||
\(778\) | −14.9847 | − | 25.9543i | −0.537228 | − | 0.930507i | ||||
\(779\) | − | 25.6920i | − | 0.920510i | ||||||
\(780\) | 0.959514 | + | 7.49935i | 0.0343561 | + | 0.268520i | ||||
\(781\) | 5.76306 | 0.206218 | ||||||||
\(782\) | 6.44624 | − | 11.1652i | 0.230517 | − | 0.399268i | ||||
\(783\) | 54.1789 | + | 7.73638i | 1.93620 | + | 0.276476i | ||||
\(784\) | −6.79125 | + | 1.69673i | −0.242545 | + | 0.0605973i | ||||
\(785\) | 2.81741 | + | 1.62663i | 0.100558 | + | 0.0580570i | ||||
\(786\) | −13.6777 | + | 10.4163i | −0.487867 | + | 0.371536i | ||||
\(787\) | −21.3479 | − | 12.3252i | −0.760971 | − | 0.439347i | 0.0686734 | − | 0.997639i | \(-0.478123\pi\) |
−0.829644 | + | 0.558293i | \(0.811457\pi\) | |||||||
\(788\) | 11.5968 | + | 6.69540i | 0.413118 | + | 0.238514i | ||||
\(789\) | 5.66733 | + | 44.2946i | 0.201762 | + | 1.57693i | ||||
\(790\) | 0.961666 | + | 0.555218i | 0.0342145 | + | 0.0197538i | ||||
\(791\) | 0.832270 | − | 1.96202i | 0.0295921 | − | 0.0697614i | ||||
\(792\) | −2.22923 | + | 0.579937i | −0.0792122 | + | 0.0206072i | ||||
\(793\) | 20.7339 | − | 35.9122i | 0.736283 | − | 1.27528i | ||||
\(794\) | −0.936742 | −0.0332437 | ||||||||
\(795\) | 10.3116 | − | 7.85283i | 0.365715 | − | 0.278511i | ||||
\(796\) | − | 0.560615i | − | 0.0198705i | ||||||
\(797\) | 1.27405 | + | 2.20672i | 0.0451293 | + | 0.0781662i | 0.887708 | − | 0.460407i | \(-0.152297\pi\) |
−0.842578 | + | 0.538574i | \(0.818963\pi\) | |||||||
\(798\) | −15.8744 | + | 15.4938i | −0.561947 | + | 0.548476i | ||||
\(799\) | 7.44080 | − | 12.8878i | 0.263237 | − | 0.455939i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 4.46900 | − | 16.2051i | 0.157904 | − | 0.572578i | ||||
\(802\) | −2.90439 | − | 5.03054i | −0.102557 | − | 0.177635i | ||||
\(803\) | 4.48547 | + | 7.76906i | 0.158289 | + | 0.274164i | ||||
\(804\) | −14.3816 | − | 18.8846i | −0.507201 | − | 0.666009i | ||||
\(805\) | −8.91596 | − | 11.8260i | −0.314246 | − | 0.416810i | ||||
\(806\) | 30.4659 | − | 17.5895i | 1.07311 | − | 0.619563i | ||||
\(807\) | −6.18897 | − | 8.12678i | −0.217862 | − | 0.286076i | ||||
\(808\) | − | 11.8515i | − | 0.416933i | ||||||
\(809\) | −3.56339 | + | 2.05733i | −0.125282 | + | 0.0723318i | −0.561331 | − | 0.827591i | \(-0.689711\pi\) |
0.436049 | + | 0.899923i | \(0.356377\pi\) | |||||||
\(810\) | 4.61315 | − | 7.72779i | 0.162090 | − | 0.271527i | ||||
\(811\) | 36.4586i | 1.28024i | 0.768277 | + | 0.640118i | \(0.221115\pi\) | ||||
−0.768277 | + | 0.640118i | \(0.778885\pi\) | |||||||
\(812\) | 10.8821 | − | 25.6537i | 0.381886 | − | 0.900270i | ||||
\(813\) | 16.1744 | + | 6.76882i | 0.567260 | + | 0.237393i | ||||
\(814\) | −6.38229 | −0.223699 | ||||||||
\(815\) | −2.40931 | + | 4.17306i | −0.0843946 | + | 0.146176i | ||||
\(816\) | 1.54000 | − | 3.67990i | 0.0539109 | − | 0.128822i | ||||
\(817\) | 49.8623 | − | 28.7880i | 1.74446 | − | 1.00717i | ||||
\(818\) | 21.8817 | 0.765076 | ||||||||
\(819\) | 5.06358 | − | 34.2745i | 0.176936 | − | 1.19765i | ||||
\(820\) | 5.30763 | 0.185350 | ||||||||
\(821\) | 28.0297 | − | 16.1829i | 0.978243 | − | 0.564789i | 0.0765035 | − | 0.997069i | \(-0.475624\pi\) |
0.901739 | + | 0.432281i | \(0.142291\pi\) | |||||||
\(822\) | 15.1044 | + | 19.8337i | 0.526826 | + | 0.691779i | ||||
\(823\) | 3.84178 | − | 6.65416i | 0.133916 | − | 0.231949i | −0.791267 | − | 0.611471i | \(-0.790578\pi\) |
0.925183 | + | 0.379522i | \(0.123911\pi\) | |||||||
\(824\) | 0.878126 | 0.0305910 | ||||||||
\(825\) | −0.168778 | − | 1.31913i | −0.00587610 | − | 0.0459263i | ||||
\(826\) | −18.2128 | − | 24.1571i | −0.633704 | − | 0.840532i | ||||
\(827\) | − | 8.88863i | − | 0.309088i | −0.987986 | − | 0.154544i | \(-0.950609\pi\) | ||
0.987986 | − | 0.154544i | \(-0.0493908\pi\) | |||||||
\(828\) | −16.1891 | − | 4.46459i | −0.562609 | − | 0.155155i | ||||
\(829\) | 15.5068 | − | 8.95287i | 0.538574 | − | 0.310946i | −0.205927 | − | 0.978567i | \(-0.566021\pi\) |
0.744501 | + | 0.667621i | \(0.232688\pi\) | |||||||
\(830\) | 0.509156i | 0.0176730i | ||||||||
\(831\) | −17.8506 | + | 2.28391i | −0.619230 | + | 0.0792281i | ||||
\(832\) | 3.78024 | − | 2.18252i | 0.131056 | − | 0.0756654i | ||||
\(833\) | −15.6412 | + | 3.90779i | −0.541934 | + | 0.135397i | ||||
\(834\) | −6.81029 | + | 16.2735i | −0.235821 | + | 0.563505i | ||||
\(835\) | 4.97259 | + | 8.61278i | 0.172084 | + | 0.298058i | ||||
\(836\) | 1.85832 | + | 3.21871i | 0.0642714 | + | 0.111321i | ||||
\(837\) | −41.4565 | − | 5.91971i | −1.43295 | − | 0.204615i | ||||
\(838\) | 13.8082 | + | 7.97218i | 0.476997 | + | 0.275395i | ||||
\(839\) | −15.0745 | + | 26.1098i | −0.520430 | + | 0.901412i | 0.479287 | + | 0.877658i | \(0.340895\pi\) |
−0.999718 | + | 0.0237538i | \(0.992438\pi\) | |||||||
\(840\) | −3.20083 | − | 3.27944i | −0.110439 | − | 0.113151i | ||||
\(841\) | 40.9667 | + | 70.9565i | 1.41265 | + | 2.44678i | ||||
\(842\) | 16.5396i | 0.569991i | ||||||||
\(843\) | 26.4104 | + | 11.0525i | 0.909624 | + | 0.380669i | ||||
\(844\) | 3.53074 | 0.121533 | ||||||||
\(845\) | −3.02683 | + | 5.24262i | −0.104126 | + | 0.180352i | ||||
\(846\) | −18.6868 | − | 5.15340i | −0.642465 | − | 0.177178i | ||||
\(847\) | −21.9932 | + | 16.5814i | −0.755696 | + | 0.569743i | ||||
\(848\) | −6.48067 | − | 3.74161i | −0.222547 | − | 0.128488i | ||||
\(849\) | 16.6048 | + | 6.94894i | 0.569875 | + | 0.238487i | ||||
\(850\) | 1.99457 | + | 1.15157i | 0.0684133 | + | 0.0394984i | ||||
\(851\) | −40.2968 | − | 23.2654i | −1.38136 | − | 0.797527i | ||||
\(852\) | 11.9927 | + | 5.01882i | 0.410862 | + | 0.171942i | ||||
\(853\) | −11.2347 | − | 6.48634i | −0.384668 | − | 0.222088i | 0.295180 | − | 0.955442i | \(-0.404621\pi\) |
−0.679847 | + | 0.733354i | \(0.737954\pi\) | |||||||
\(854\) | 3.06914 | + | 24.9465i | 0.105024 | + | 0.853651i | ||||
\(855\) | −13.9991 | − | 3.86065i | −0.478760 | − | 0.132031i | ||||
\(856\) | −3.20536 | + | 5.55184i | −0.109557 | + | 0.189758i | ||||
\(857\) | −26.4584 | −0.903800 | −0.451900 | − | 0.892069i | \(-0.649254\pi\) | ||||
−0.451900 | + | 0.892069i | \(0.649254\pi\) | |||||||
\(858\) | −5.35501 | − | 2.24102i | −0.182817 | − | 0.0765071i | ||||
\(859\) | 30.5959i | 1.04392i | 0.852970 | + | 0.521959i | \(0.174799\pi\) | ||||
−0.852970 | + | 0.521959i | \(0.825201\pi\) | |||||||
\(860\) | 5.94724 | + | 10.3009i | 0.202799 | + | 0.351258i | ||||
\(861\) | −23.4157 | − | 6.57968i | −0.798006 | − | 0.224235i | ||||
\(862\) | 6.08623 | − | 10.5417i | 0.207298 | − | 0.359050i | ||||
\(863\) | −42.9051 | − | 24.7713i | −1.46051 | − | 0.843223i | −0.461471 | − | 0.887155i | \(-0.652678\pi\) |
−0.999035 | + | 0.0439320i | \(0.986012\pi\) | |||||||
\(864\) | −5.14397 | − | 0.734525i | −0.175002 | − | 0.0249890i | ||||
\(865\) | 8.31317 | + | 14.3988i | 0.282656 | + | 0.489575i | ||||
\(866\) | −4.27269 | − | 7.40052i | −0.145192 | − | 0.251480i | ||||
\(867\) | −7.82031 | + | 18.6869i | −0.265592 | + | 0.634642i | ||||
\(868\) | −8.32673 | + | 19.6297i | −0.282628 | + | 0.666275i | ||||
\(869\) | −0.738377 | + | 0.426302i | −0.0250477 | + | 0.0144613i | ||||
\(870\) | 18.0953 | − | 2.31523i | 0.613488 | − | 0.0784935i | ||||
\(871\) | − | 59.8219i | − | 2.02699i | ||||||
\(872\) | 7.55832 | − | 4.36380i | 0.255957 | − | 0.147777i | ||||
\(873\) | −25.4273 | − | 7.01227i | −0.860582 | − | 0.237329i | ||||
\(874\) | 27.0966i | 0.916555i | ||||||||
\(875\) | 2.11261 | − | 1.59276i | 0.0714192 | − | 0.0538452i | ||||
\(876\) | 2.56830 | + | 20.0733i | 0.0867748 | + | 0.678214i | ||||
\(877\) | −44.1241 | −1.48997 | −0.744983 | − | 0.667083i | \(-0.767543\pi\) | ||||
−0.744983 | + | 0.667083i | \(0.767543\pi\) | |||||||
\(878\) | −3.29088 | + | 5.69997i | −0.111062 | + | 0.192365i | ||||
\(879\) | 26.8195 | + | 35.2168i | 0.904598 | + | 1.18783i | ||||
\(880\) | −0.664943 | + | 0.383905i | −0.0224152 | + | 0.0129414i | ||||
\(881\) | 14.2789 | 0.481068 | 0.240534 | − | 0.970641i | \(-0.422677\pi\) | ||||
0.240534 | + | 0.970641i | \(0.422677\pi\) | |||||||
\(882\) | 10.0557 | + | 18.4359i | 0.338594 | + | 0.620769i | ||||
\(883\) | −2.99831 | −0.100901 | −0.0504505 | − | 0.998727i | \(-0.516066\pi\) | ||||
−0.0504505 | + | 0.998727i | \(0.516066\pi\) | |||||||
\(884\) | 8.70641 | − | 5.02665i | 0.292828 | − | 0.169064i | ||||
\(885\) | 7.64589 | − | 18.2702i | 0.257014 | − | 0.614145i | ||||
\(886\) | 13.5369 | − | 23.4466i | 0.454781 | − | 0.787703i | ||||
\(887\) | 36.0244 | 1.20958 | 0.604791 | − | 0.796384i | \(-0.293257\pi\) | ||||
0.604791 | + | 0.796384i | \(0.293257\pi\) | |||||||
\(888\) | −13.2813 | − | 5.55808i | −0.445690 | − | 0.186517i | ||||
\(889\) | 26.7201 | − | 20.1452i | 0.896164 | − | 0.675647i | ||||
\(890\) | − | 5.60333i | − | 0.187824i | ||||||
\(891\) | 3.36753 | + | 6.03423i | 0.112817 | + | 0.202154i | ||||
\(892\) | 22.1791 | − | 12.8051i | 0.742612 | − | 0.428748i | ||||
\(893\) | 31.2772i | 1.04665i | ||||||||
\(894\) | 9.39522 | + | 12.3369i | 0.314223 | + | 0.412609i | ||||
\(895\) | −4.07453 | + | 2.35243i | −0.136197 | + | 0.0786331i | ||||
\(896\) | −1.03319 | + | 2.43568i | −0.0345165 | + | 0.0813702i | ||||
\(897\) | −25.6415 | − | 33.6701i | −0.856145 | − | 1.12421i | ||||
\(898\) | 8.98271 | + | 15.5585i | 0.299757 | + | 0.519194i | ||||
\(899\) | −42.4419 | − | 73.5116i | −1.41552 | − | 2.45175i | ||||
\(900\) | 0.797561 | − | 2.89204i | 0.0265854 | − | 0.0964013i | ||||
\(901\) | −14.9258 | − | 8.61744i | −0.497252 | − | 0.287089i | ||||
\(902\) | −2.03763 | + | 3.52927i | −0.0678455 | + | 0.117512i | ||||
\(903\) | −13.4678 | − | 52.8173i | −0.448181 | − | 1.75765i | ||||
\(904\) | −0.402767 | − | 0.697613i | −0.0133958 | − | 0.0232023i | ||||
\(905\) | − | 8.33408i | − | 0.277034i | ||||||
\(906\) | −6.89971 | + | 5.25449i | −0.229227 | + | 0.174569i | ||||
\(907\) | 21.0929 | 0.700378 | 0.350189 | − | 0.936679i | \(-0.386117\pi\) | ||||
0.350189 | + | 0.936679i | \(0.386117\pi\) | |||||||
\(908\) | 5.56930 | − | 9.64631i | 0.184824 | − | 0.320124i | ||||
\(909\) | −34.4091 | + | 8.95156i | −1.14128 | + | 0.296905i | ||||
\(910\) | −1.41021 | − | 11.4624i | −0.0467480 | − | 0.379975i | ||||
\(911\) | −23.7590 | − | 13.7172i | −0.787169 | − | 0.454472i | 0.0517958 | − | 0.998658i | \(-0.483505\pi\) |
−0.838965 | + | 0.544185i | \(0.816839\pi\) | |||||||
\(912\) | 1.06404 | + | 8.31633i | 0.0352340 | + | 0.275381i | ||||
\(913\) | −0.338560 | − | 0.195467i | −0.0112047 | − | 0.00646903i | ||||
\(914\) | −4.45944 | − | 2.57466i | −0.147505 | − | 0.0851622i | ||||
\(915\) | −13.0906 | + | 9.96918i | −0.432762 | + | 0.329571i | ||||
\(916\) | −3.29819 | − | 1.90421i | −0.108975 | − | 0.0629169i | ||||
\(917\) | 20.9698 | − | 15.8098i | 0.692484 | − | 0.522085i | ||||
\(918\) | −11.8473 | − | 1.69171i | −0.391018 | − | 0.0558347i | ||||
\(919\) | 2.13518 | − | 3.69824i | 0.0704332 | − | 0.121994i | −0.828658 | − | 0.559755i | \(-0.810895\pi\) |
0.899091 | + | 0.437761i | \(0.144229\pi\) | |||||||
\(920\) | −5.59780 | −0.184554 | ||||||||
\(921\) | −2.05164 | − | 16.0351i | −0.0676037 | − | 0.528376i | ||||
\(922\) | 10.9210i | 0.359665i | ||||||||
\(923\) | 16.3817 | + | 28.3739i | 0.539209 | + | 0.933938i | ||||
\(924\) | 3.40945 | − | 0.869374i | 0.112163 | − | 0.0286003i | ||||
\(925\) | 4.15617 | − | 7.19869i | 0.136654 | − | 0.236691i | ||||
\(926\) | −25.7563 | − | 14.8704i | −0.846406 | − | 0.488673i | ||||
\(927\) | −0.663260 | − | 2.54952i | −0.0217843 | − | 0.0837371i | ||||
\(928\) | −5.26625 | − | 9.12141i | −0.172873 | − | 0.299425i | ||||
\(929\) | 5.90039 | + | 10.2198i | 0.193585 | + | 0.335300i | 0.946436 | − | 0.322892i | \(-0.104655\pi\) |
−0.752850 | + | 0.658192i | \(0.771322\pi\) | |||||||
\(930\) | −13.8461 | + | 1.77156i | −0.454033 | + | 0.0580917i | ||||
\(931\) | 24.3628 | − | 23.5496i | 0.798458 | − | 0.771806i | ||||
\(932\) | 2.04230 | − | 1.17912i | 0.0668977 | − | 0.0386234i | ||||
\(933\) | 3.58785 | − | 8.57332i | 0.117461 | − | 0.280678i | ||||
\(934\) | − | 9.11448i | − | 0.298235i | ||||||
\(935\) | −1.53145 | + | 0.884185i | −0.0500839 | + | 0.0289159i | ||||
\(936\) | −9.19192 | − | 9.32692i | −0.300447 | − | 0.304860i | ||||
\(937\) | − | 52.8223i | − | 1.72563i | −0.505520 | − | 0.862815i | \(-0.668699\pi\) | ||
0.505520 | − | 0.862815i | \(-0.331301\pi\) | |||||||
\(938\) | 21.8284 | + | 28.9527i | 0.712722 | + | 0.945341i | ||||
\(939\) | −35.0773 | + | 26.7132i | −1.14470 | + | 0.871752i | ||||
\(940\) | −6.46146 | −0.210749 | ||||||||
\(941\) | −20.6789 | + | 35.8169i | −0.674113 | + | 1.16760i | 0.302615 | + | 0.953113i | \(0.402140\pi\) |
−0.976727 | + | 0.214484i | \(0.931193\pi\) | |||||||
\(942\) | −5.58926 | + | 0.715124i | −0.182108 | + | 0.0233000i | ||||
\(943\) | −25.7305 | + | 14.8555i | −0.837901 | + | 0.483762i | ||||
\(944\) | −11.4347 | −0.372168 | ||||||||
\(945\) | −7.10377 | + | 11.7702i | −0.231086 | + | 0.382883i | ||||
\(946\) | −9.13270 | −0.296930 | ||||||||
\(947\) | 16.5721 | − | 9.56789i | 0.538520 | − | 0.310914i | −0.205959 | − | 0.978561i | \(-0.566031\pi\) |
0.744479 | + | 0.667646i | \(0.232698\pi\) | |||||||
\(948\) | −1.90778 | + | 0.244093i | −0.0619618 | + | 0.00792778i | ||||
\(949\) | −25.5002 | + | 44.1676i | −0.827771 | + | 1.43374i | ||||
\(950\) | −4.84057 | −0.157049 | ||||||||
\(951\) | −10.3165 | + | 7.85653i | −0.334535 | + | 0.254765i | ||||
\(952\) | −2.37958 | + | 5.60969i | −0.0771225 | + | 0.181811i | ||||
\(953\) | − | 16.1271i | − | 0.522407i | −0.965284 | − | 0.261203i | \(-0.915881\pi\) | ||
0.965284 | − | 0.261203i | \(-0.0841193\pi\) | |||||||
\(954\) | −5.96833 | + | 21.6418i | −0.193232 | + | 0.700679i | ||||
\(955\) | −3.28474 | + | 1.89645i | −0.106292 | + | 0.0613676i | ||||
\(956\) | − | 11.7742i | − | 0.380806i | ||||||
\(957\) | −5.40739 | + | 12.9212i | −0.174796 | + | 0.417682i | ||||
\(958\) | 32.3003 | − | 18.6486i | 1.04358 | − | 0.602508i | ||||
\(959\) | −22.9254 | − | 30.4078i | −0.740299 | − | 0.981918i | ||||
\(960\) | −1.71805 | + | 0.219817i | −0.0554497 | + | 0.00709457i | ||||
\(961\) | 16.9757 | + | 29.4027i | 0.547602 | + | 0.948474i | ||||
\(962\) | −18.1419 | − | 31.4226i | −0.584917 | − | 1.01311i | ||||
\(963\) | 18.5400 | + | 5.11293i | 0.597445 | + | 0.164762i | ||||
\(964\) | −16.2931 | − | 9.40683i | −0.524765 | − | 0.302973i | ||||
\(965\) | −10.7480 | + | 18.6160i | −0.345989 | + | 0.599271i | ||||
\(966\) | 24.6959 | + | 6.93940i | 0.794578 | + | 0.223271i | ||||
\(967\) | 23.6109 | + | 40.8952i | 0.759274 | + | 1.31510i | 0.943221 | + | 0.332165i | \(0.107779\pi\) |
−0.183948 | + | 0.982936i | \(0.558888\pi\) | |||||||
\(968\) | 10.4105i | 0.334605i | ||||||||
\(969\) | 2.45063 | + | 19.1536i | 0.0787257 | + | 0.615303i | ||||
\(970\) | −8.79215 | −0.282299 | ||||||||
\(971\) | 12.0076 | − | 20.7978i | 0.385343 | − | 0.667434i | −0.606474 | − | 0.795104i | \(-0.707416\pi\) |
0.991817 | + | 0.127670i | \(0.0407497\pi\) | |||||||
\(972\) | 1.75272 | + | 15.4896i | 0.0562185 | + | 0.496829i | ||||
\(973\) | 10.5231 | − | 24.8075i | 0.337355 | − | 0.795292i | ||||
\(974\) | 16.3605 | + | 9.44574i | 0.524224 | + | 0.302661i | ||||
\(975\) | 6.01487 | − | 4.58064i | 0.192630 | − | 0.146698i | ||||
\(976\) | 8.22722 | + | 4.74999i | 0.263347 | + | 0.152043i | ||||
\(977\) | 9.29422 | + | 5.36602i | 0.297348 | + | 0.171674i | 0.641251 | − | 0.767331i | \(-0.278416\pi\) |
−0.343903 | + | 0.939005i | \(0.611749\pi\) | |||||||
\(978\) | −1.05922 | − | 8.27862i | −0.0338701 | − | 0.264721i | ||||
\(979\) | 3.72590 | + | 2.15115i | 0.119080 | + | 0.0687510i | ||||
\(980\) | 4.86503 | + | 5.03304i | 0.155408 | + | 0.160774i | ||||
\(981\) | −18.3786 | − | 18.6485i | −0.586782 | − | 0.595400i | ||||
\(982\) | 17.4047 | − | 30.1458i | 0.555406 | − | 0.961991i | ||||
\(983\) | 54.3759 | 1.73432 | 0.867162 | − | 0.498027i | \(-0.165942\pi\) | ||||
0.867162 | + | 0.498027i | \(0.165942\pi\) | |||||||
\(984\) | −7.31371 | + | 5.56977i | −0.233153 | + | 0.177558i | ||||
\(985\) | − | 13.3908i | − | 0.426666i | ||||||
\(986\) | −12.1289 | − | 21.0078i | −0.386262 | − | 0.669026i | ||||
\(987\) | 28.5061 | + | 8.01004i | 0.907359 | + | 0.254962i | ||||
\(988\) | −10.5647 | + | 18.2986i | −0.336107 | + | 0.582154i | ||||
\(989\) | −57.6625 | − | 33.2914i | −1.83356 | − | 1.05861i | ||||
\(990\) | 1.61686 | + | 1.64060i | 0.0513870 | + | 0.0521417i | ||||
\(991\) | 1.44414 | + | 2.50132i | 0.0458746 | + | 0.0794571i | 0.888051 | − | 0.459745i | \(-0.152059\pi\) |
−0.842176 | + | 0.539202i | \(0.818726\pi\) | |||||||
\(992\) | 4.02962 | + | 6.97950i | 0.127941 | + | 0.221599i | ||||
\(993\) | 7.79557 | + | 10.2364i | 0.247385 | + | 0.324843i | ||||
\(994\) | −18.2818 | − | 7.75496i | −0.579863 | − | 0.245972i | ||||
\(995\) | −0.485507 | + | 0.280308i | −0.0153916 | + | 0.00888635i | ||||
\(996\) | −0.534303 | − | 0.701597i | −0.0169300 | − | 0.0222310i | ||||
\(997\) | 10.0200i | 0.317337i | 0.987332 | + | 0.158668i | \(0.0507201\pi\) | ||||
−0.987332 | + | 0.158668i | \(0.949280\pi\) | |||||||
\(998\) | −21.1593 | + | 12.2163i | −0.669786 | + | 0.386701i | ||||
\(999\) | −6.10561 | + | 42.7584i | −0.193173 | + | 1.35282i |
(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 | 630.2.t.b.551.1 | yes | 28 | |
3.2 | odd | 2 | 1890.2.t.b.1601.11 | 28 | |||
7.3 | odd | 6 | 630.2.bk.b.101.3 | yes | 28 | ||
9.4 | even | 3 | 1890.2.bk.b.341.6 | 28 | |||
9.5 | odd | 6 | 630.2.bk.b.131.10 | yes | 28 | ||
21.17 | even | 6 | 1890.2.bk.b.521.6 | 28 | |||
63.31 | odd | 6 | 1890.2.t.b.1151.11 | 28 | |||
63.59 | even | 6 | inner | 630.2.t.b.311.1 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.1 | ✓ | 28 | 63.59 | even | 6 | inner | |
630.2.t.b.551.1 | yes | 28 | 1.1 | even | 1 | trivial | |
630.2.bk.b.101.3 | yes | 28 | 7.3 | odd | 6 | ||
630.2.bk.b.131.10 | yes | 28 | 9.5 | odd | 6 | ||
1890.2.t.b.1151.11 | 28 | 63.31 | odd | 6 | |||
1890.2.t.b.1601.11 | 28 | 3.2 | odd | 2 | |||
1890.2.bk.b.341.6 | 28 | 9.4 | even | 3 | |||
1890.2.bk.b.521.6 | 28 | 21.17 | even | 6 |