Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.2 | ||
Root | \(-0.293939 - 0.213559i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.u.148.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.421292 | + | 1.29660i | −0.297898 | + | 0.916836i | 0.684334 | + | 0.729168i | \(0.260093\pi\) |
−0.982233 | + | 0.187668i | \(0.939907\pi\) | |||||||
\(3\) | −0.293939 | + | 0.213559i | −0.169706 | + | 0.123298i | −0.669396 | − | 0.742906i | \(-0.733447\pi\) |
0.499691 | + | 0.866204i | \(0.333447\pi\) | |||||||
\(4\) | 0.114343 | + | 0.0830753i | 0.0571717 | + | 0.0415376i | ||||
\(5\) | 0.970726 | + | 2.98759i | 0.434122 | + | 1.33609i | 0.893984 | + | 0.448100i | \(0.147899\pi\) |
−0.459862 | + | 0.887991i | \(0.652101\pi\) | |||||||
\(6\) | −0.153067 | − | 0.471092i | −0.0624894 | − | 0.192323i | ||||
\(7\) | 0.809017 | + | 0.587785i | 0.305780 | + | 0.222162i | ||||
\(8\) | −2.36180 | + | 1.71595i | −0.835022 | + | 0.606679i | ||||
\(9\) | −0.886258 | + | 2.72762i | −0.295419 | + | 0.909208i | ||||
\(10\) | −4.28267 | −1.35430 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.0513514 | −0.0148239 | ||||||||
\(13\) | −1.47649 | + | 4.54416i | −0.409503 | + | 1.26032i | 0.507572 | + | 0.861609i | \(0.330543\pi\) |
−0.917076 | + | 0.398713i | \(0.869457\pi\) | |||||||
\(14\) | −1.10296 | + | 0.801344i | −0.294777 | + | 0.214168i | ||||
\(15\) | −0.923360 | − | 0.670861i | −0.238411 | − | 0.173215i | ||||
\(16\) | −1.14254 | − | 3.51639i | −0.285636 | − | 0.879098i | ||||
\(17\) | −1.47649 | − | 4.54416i | −0.358100 | − | 1.10212i | −0.954190 | − | 0.299202i | \(-0.903280\pi\) |
0.596090 | − | 0.802918i | \(-0.296720\pi\) | |||||||
\(18\) | −3.16327 | − | 2.29825i | −0.745590 | − | 0.541703i | ||||
\(19\) | 5.67067 | − | 4.11998i | 1.30094 | − | 0.945188i | 0.300976 | − | 0.953632i | \(-0.402688\pi\) |
0.999964 | + | 0.00844358i | \(0.00268771\pi\) | |||||||
\(20\) | −0.137199 | + | 0.422254i | −0.0306786 | + | 0.0944189i | ||||
\(21\) | −0.363328 | −0.0792847 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.14134 | 1.07204 | 0.536021 | − | 0.844204i | \(-0.319927\pi\) | ||||
0.536021 | + | 0.844204i | \(0.319927\pi\) | |||||||
\(24\) | 0.327768 | − | 1.00877i | 0.0669054 | − | 0.205914i | ||||
\(25\) | −3.93829 | + | 2.86133i | −0.787658 | + | 0.572267i | ||||
\(26\) | −5.26993 | − | 3.82883i | −1.03352 | − | 0.750895i | ||||
\(27\) | −0.658827 | − | 2.02766i | −0.126791 | − | 0.390223i | ||||
\(28\) | 0.0436753 | + | 0.134419i | 0.00825385 | + | 0.0254027i | ||||
\(29\) | −5.67067 | − | 4.11998i | −1.05302 | − | 0.765061i | −0.0802326 | − | 0.996776i | \(-0.525566\pi\) |
−0.972784 | + | 0.231715i | \(0.925566\pi\) | |||||||
\(30\) | 1.25884 | − | 0.914603i | 0.229832 | − | 0.166983i | ||||
\(31\) | −1.12379 | + | 3.45868i | −0.201839 | + | 0.621197i | 0.797989 | + | 0.602672i | \(0.205897\pi\) |
−0.999828 | + | 0.0185255i | \(0.994103\pi\) | |||||||
\(32\) | −0.797984 | −0.141065 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.51399 | 1.11714 | ||||||||
\(35\) | −0.970726 | + | 2.98759i | −0.164083 | + | 0.504995i | ||||
\(36\) | −0.327936 | + | 0.238259i | −0.0546560 | + | 0.0397099i | ||||
\(37\) | 7.98337 | + | 5.80026i | 1.31246 | + | 0.953557i | 0.999993 | + | 0.00362773i | \(0.00115474\pi\) |
0.312465 | + | 0.949929i | \(0.398845\pi\) | |||||||
\(38\) | 2.95297 | + | 9.08831i | 0.479035 | + | 1.47432i | ||||
\(39\) | −0.536449 | − | 1.65102i | −0.0859006 | − | 0.264375i | ||||
\(40\) | −7.41920 | − | 5.39037i | −1.17308 | − | 0.852292i | ||||
\(41\) | 2.60665 | − | 1.89384i | 0.407090 | − | 0.295768i | −0.365333 | − | 0.930877i | \(-0.619045\pi\) |
0.772423 | + | 0.635109i | \(0.219045\pi\) | |||||||
\(42\) | 0.153067 | − | 0.471092i | 0.0236188 | − | 0.0726911i | ||||
\(43\) | 4.28267 | 0.653101 | 0.326551 | − | 0.945180i | \(-0.394114\pi\) | ||||
0.326551 | + | 0.945180i | \(0.394114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.00933 | −1.34303 | ||||||||
\(46\) | −2.16600 | + | 6.66627i | −0.319360 | + | 0.982888i | ||||
\(47\) | 0.629422 | − | 0.457302i | 0.0918106 | − | 0.0667043i | −0.540933 | − | 0.841066i | \(-0.681929\pi\) |
0.632744 | + | 0.774361i | \(0.281929\pi\) | |||||||
\(48\) | 1.08679 | + | 0.789603i | 0.156865 | + | 0.113969i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | −2.05084 | − | 6.31185i | −0.290033 | − | 0.892630i | ||||
\(51\) | 1.40444 | + | 1.02039i | 0.196661 | + | 0.142883i | ||||
\(52\) | −0.546333 | + | 0.396934i | −0.0757628 | + | 0.0550449i | ||||
\(53\) | 0.705385 | − | 2.17095i | 0.0968920 | − | 0.298203i | −0.890850 | − | 0.454297i | \(-0.849890\pi\) |
0.987742 | + | 0.156094i | \(0.0498904\pi\) | |||||||
\(54\) | 2.90663 | 0.395542 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.91934 | −0.390114 | ||||||||
\(57\) | −0.786970 | + | 2.42204i | −0.104237 | + | 0.320807i | ||||
\(58\) | 7.73098 | − | 5.61689i | 1.01513 | − | 0.737533i | ||||
\(59\) | 0.293939 | + | 0.213559i | 0.0382676 | + | 0.0278030i | 0.606755 | − | 0.794889i | \(-0.292471\pi\) |
−0.568487 | + | 0.822692i | \(0.692471\pi\) | |||||||
\(60\) | −0.0498482 | − | 0.153417i | −0.00643537 | − | 0.0198060i | ||||
\(61\) | 0.995650 | + | 3.06430i | 0.127480 | + | 0.392343i | 0.994345 | − | 0.106200i | \(-0.0338685\pi\) |
−0.866865 | + | 0.498543i | \(0.833868\pi\) | |||||||
\(62\) | −4.01109 | − | 2.91423i | −0.509409 | − | 0.370107i | ||||
\(63\) | −2.32025 | + | 1.68576i | −0.292325 | + | 0.212386i | ||||
\(64\) | 2.62127 | − | 8.06745i | 0.327659 | − | 1.00843i | ||||
\(65\) | −15.0093 | −1.86168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.59465 | −0.805665 | −0.402832 | − | 0.915274i | \(-0.631974\pi\) | ||||
−0.402832 | + | 0.915274i | \(0.631974\pi\) | |||||||
\(68\) | 0.208681 | − | 0.642253i | 0.0253063 | − | 0.0778847i | ||||
\(69\) | −1.51124 | + | 1.09798i | −0.181932 | + | 0.132181i | ||||
\(70\) | −3.46475 | − | 2.51729i | −0.414117 | − | 0.300874i | ||||
\(71\) | −4.68470 | − | 14.4180i | −0.555971 | − | 1.71110i | −0.693365 | − | 0.720587i | \(-0.743873\pi\) |
0.137394 | − | 0.990516i | \(-0.456127\pi\) | |||||||
\(72\) | −2.58729 | − | 7.96287i | −0.304915 | − | 0.938433i | ||||
\(73\) | 2.60665 | + | 1.89384i | 0.305085 | + | 0.221657i | 0.729785 | − | 0.683677i | \(-0.239620\pi\) |
−0.424700 | + | 0.905334i | \(0.639620\pi\) | |||||||
\(74\) | −10.8840 | + | 7.90766i | −1.26523 | + | 0.919247i | ||||
\(75\) | 0.546552 | − | 1.68211i | 0.0631104 | − | 0.194234i | ||||
\(76\) | 0.990671 | 0.113638 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.36672 | 0.267978 | ||||||||
\(79\) | −1.14872 | + | 3.53539i | −0.129241 | + | 0.397762i | −0.994650 | − | 0.103304i | \(-0.967059\pi\) |
0.865409 | + | 0.501066i | \(0.167059\pi\) | |||||||
\(80\) | 9.39643 | − | 6.82691i | 1.05055 | − | 0.763271i | ||||
\(81\) | −6.33408 | − | 4.60198i | −0.703787 | − | 0.511331i | ||||
\(82\) | 1.35740 | + | 4.17764i | 0.149900 | + | 0.461343i | ||||
\(83\) | 0.480835 | + | 1.47986i | 0.0527785 | + | 0.162436i | 0.973972 | − | 0.226670i | \(-0.0727840\pi\) |
−0.921193 | + | 0.389106i | \(0.872784\pi\) | |||||||
\(84\) | −0.0415442 | − | 0.0301836i | −0.00453284 | − | 0.00329330i | ||||
\(85\) | 12.1428 | − | 8.82226i | 1.31707 | − | 0.956909i | ||||
\(86\) | −1.80425 | + | 5.55292i | −0.194558 | + | 0.598787i | ||||
\(87\) | 2.54669 | 0.273034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.58532 | −0.592043 | −0.296021 | − | 0.955181i | \(-0.595660\pi\) | ||||
−0.296021 | + | 0.955181i | \(0.595660\pi\) | |||||||
\(90\) | 3.79555 | − | 11.6815i | 0.400087 | − | 1.23134i | ||||
\(91\) | −3.86549 | + | 2.80844i | −0.405213 | + | 0.294405i | ||||
\(92\) | 0.587877 | + | 0.427118i | 0.0612905 | + | 0.0445301i | ||||
\(93\) | −0.408306 | − | 1.25664i | −0.0423393 | − | 0.130307i | ||||
\(94\) | 0.327768 | + | 1.00877i | 0.0338067 | + | 0.104046i | ||||
\(95\) | 17.8135 | + | 12.9422i | 1.82762 | + | 1.32785i | ||||
\(96\) | 0.234558 | − | 0.170417i | 0.0239395 | − | 0.0173931i | ||||
\(97\) | 1.90066 | − | 5.84963i | 0.192983 | − | 0.593940i | −0.807011 | − | 0.590536i | \(-0.798916\pi\) |
0.999994 | − | 0.00340410i | \(-0.00108356\pi\) | |||||||
\(98\) | −1.36333 | −0.137717 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.688023 | −0.0688023 | ||||||||
\(101\) | −3.33635 | + | 10.2682i | −0.331980 | + | 1.02173i | 0.636211 | + | 0.771515i | \(0.280501\pi\) |
−0.968191 | + | 0.250213i | \(0.919499\pi\) | |||||||
\(102\) | −1.91471 | + | 1.39112i | −0.189585 | + | 0.137742i | ||||
\(103\) | 10.7119 | + | 7.78266i | 1.05548 | + | 0.766848i | 0.973246 | − | 0.229765i | \(-0.0737958\pi\) |
0.0822298 | + | 0.996613i | \(0.473796\pi\) | |||||||
\(104\) | −4.31037 | − | 13.2660i | −0.422667 | − | 1.30083i | ||||
\(105\) | −0.352692 | − | 1.08548i | −0.0344192 | − | 0.105932i | ||||
\(106\) | 2.51769 | + | 1.82921i | 0.244539 | + | 0.177668i | ||||
\(107\) | −11.3413 | + | 8.23996i | −1.09641 | + | 0.796587i | −0.980470 | − | 0.196669i | \(-0.936987\pi\) |
−0.115938 | + | 0.993256i | \(0.536987\pi\) | |||||||
\(108\) | 0.0931160 | − | 0.286582i | 0.00896009 | − | 0.0275763i | ||||
\(109\) | −15.5747 | −1.49178 | −0.745892 | − | 0.666067i | \(-0.767976\pi\) | ||||
−0.745892 | + | 0.666067i | \(0.767976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.58532 | −0.340304 | ||||||||
\(112\) | 1.14254 | − | 3.51639i | 0.107960 | − | 0.332268i | ||||
\(113\) | −3.34286 | + | 2.42873i | −0.314470 | + | 0.228476i | −0.733812 | − | 0.679352i | \(-0.762261\pi\) |
0.419342 | + | 0.907828i | \(0.362261\pi\) | |||||||
\(114\) | −2.80888 | − | 2.04077i | −0.263076 | − | 0.191136i | ||||
\(115\) | 4.99083 | + | 15.3602i | 0.465397 | + | 1.43235i | ||||
\(116\) | −0.306134 | − | 0.942184i | −0.0284239 | − | 0.0874796i | ||||
\(117\) | −11.0862 | − | 8.05459i | −1.02492 | − | 0.744647i | ||||
\(118\) | −0.400735 | + | 0.291151i | −0.0368906 | + | 0.0268026i | ||||
\(119\) | 1.47649 | − | 4.54416i | 0.135349 | − | 0.416562i | ||||
\(120\) | 3.33195 | 0.304164 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.39263 | −0.397690 | ||||||||
\(123\) | −0.361748 | + | 1.11335i | −0.0326177 | + | 0.100387i | ||||
\(124\) | −0.415829 | + | 0.302118i | −0.0373426 | + | 0.0271310i | ||||
\(125\) | 0.335483 | + | 0.243743i | 0.0300065 | + | 0.0218010i | ||||
\(126\) | −1.20826 | − | 3.71865i | −0.107640 | − | 0.331283i | ||||
\(127\) | 6.80414 | + | 20.9410i | 0.603770 | + | 1.85821i | 0.505036 | + | 0.863098i | \(0.331479\pi\) |
0.0987337 | + | 0.995114i | \(0.468521\pi\) | |||||||
\(128\) | 8.06479 | + | 5.85941i | 0.712833 | + | 0.517904i | ||||
\(129\) | −1.25884 | + | 0.914603i | −0.110835 | + | 0.0805263i | ||||
\(130\) | 6.32330 | − | 19.4611i | 0.554590 | − | 1.70685i | ||||
\(131\) | 15.0093 | 1.31137 | 0.655686 | − | 0.755034i | \(-0.272380\pi\) | ||||
0.655686 | + | 0.755034i | \(0.272380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.00933 | 0.607786 | ||||||||
\(134\) | 2.77827 | − | 8.55064i | 0.240006 | − | 0.738662i | ||||
\(135\) | 5.41827 | − | 3.93660i | 0.466331 | − | 0.338809i | ||||
\(136\) | 11.2847 | + | 8.19881i | 0.967655 | + | 0.703042i | ||||
\(137\) | −3.30566 | − | 10.1738i | −0.282422 | − | 0.869205i | −0.987160 | − | 0.159737i | \(-0.948935\pi\) |
0.704738 | − | 0.709468i | \(-0.251065\pi\) | |||||||
\(138\) | −0.786970 | − | 2.42204i | −0.0669913 | − | 0.206178i | ||||
\(139\) | −3.31916 | − | 2.41151i | −0.281527 | − | 0.204541i | 0.438056 | − | 0.898948i | \(-0.355667\pi\) |
−0.719583 | + | 0.694406i | \(0.755667\pi\) | |||||||
\(140\) | −0.359191 | + | 0.260967i | −0.0303572 | + | 0.0220558i | ||||
\(141\) | −0.0873505 | + | 0.268837i | −0.00735624 | + | 0.0226402i | ||||
\(142\) | 20.6680 | 1.73442 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.6040 | 0.883665 | ||||||||
\(145\) | 6.80414 | − | 20.9410i | 0.565053 | − | 1.73905i | ||||
\(146\) | −3.55371 | + | 2.58192i | −0.294108 | + | 0.213682i | ||||
\(147\) | −0.293939 | − | 0.213559i | −0.0242437 | − | 0.0176140i | ||||
\(148\) | 0.430987 | + | 1.32644i | 0.0354269 | + | 0.109033i | ||||
\(149\) | 4.33200 | + | 13.3325i | 0.354892 | + | 1.09224i | 0.956072 | + | 0.293131i | \(0.0946972\pi\) |
−0.601181 | + | 0.799113i | \(0.705303\pi\) | |||||||
\(150\) | 1.95077 | + | 1.41732i | 0.159280 | + | 0.115724i | ||||
\(151\) | 5.52507 | − | 4.01420i | 0.449624 | − | 0.326671i | −0.339824 | − | 0.940489i | \(-0.610367\pi\) |
0.789447 | + | 0.613819i | \(0.210367\pi\) | |||||||
\(152\) | −6.32330 | + | 19.4611i | −0.512888 | + | 1.57851i | ||||
\(153\) | 13.7033 | 1.10785 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4240 | −0.917598 | ||||||||
\(156\) | 0.0758196 | − | 0.233349i | 0.00607043 | − | 0.0186829i | ||||
\(157\) | 18.9655 | − | 13.7793i | 1.51361 | − | 1.09970i | 0.549071 | − | 0.835776i | \(-0.314982\pi\) |
0.964542 | − | 0.263928i | \(-0.0850182\pi\) | |||||||
\(158\) | −4.10005 | − | 2.97886i | −0.326182 | − | 0.236985i | ||||
\(159\) | 0.256286 | + | 0.788768i | 0.0203248 | + | 0.0625533i | ||||
\(160\) | −0.774624 | − | 2.38405i | −0.0612394 | − | 0.188475i | ||||
\(161\) | 4.15943 | + | 3.02200i | 0.327809 | + | 0.238167i | ||||
\(162\) | 8.63544 | − | 6.27401i | 0.678464 | − | 0.492933i | ||||
\(163\) | −0.306134 | + | 0.942184i | −0.0239783 | + | 0.0737976i | −0.962330 | − | 0.271886i | \(-0.912353\pi\) |
0.938351 | + | 0.345683i | \(0.112353\pi\) | |||||||
\(164\) | 0.455384 | 0.0355595 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.12136 | −0.164649 | ||||||||
\(167\) | 0.174701 | − | 0.537675i | 0.0135188 | − | 0.0416065i | −0.944070 | − | 0.329746i | \(-0.893037\pi\) |
0.957588 | + | 0.288140i | \(0.0930368\pi\) | |||||||
\(168\) | 0.858108 | − | 0.623452i | 0.0662045 | − | 0.0481004i | ||||
\(169\) | −7.95212 | − | 5.77755i | −0.611701 | − | 0.444427i | ||||
\(170\) | 6.32330 | + | 19.4611i | 0.484975 | + | 1.49260i | ||||
\(171\) | 6.21208 | + | 19.1188i | 0.475049 | + | 1.46205i | ||||
\(172\) | 0.489695 | + | 0.355784i | 0.0373389 | + | 0.0271283i | ||||
\(173\) | 13.9480 | − | 10.1338i | 1.06045 | − | 0.770459i | 0.0862745 | − | 0.996271i | \(-0.472504\pi\) |
0.974171 | + | 0.225813i | \(0.0725038\pi\) | |||||||
\(174\) | −1.07290 | + | 3.30204i | −0.0813362 | + | 0.250327i | ||||
\(175\) | −4.86799 | −0.367986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.132007 | −0.00992228 | ||||||||
\(178\) | 2.35305 | − | 7.24194i | 0.176368 | − | 0.542806i | ||||
\(179\) | −9.15913 | + | 6.65450i | −0.684585 | + | 0.497380i | −0.874876 | − | 0.484347i | \(-0.839057\pi\) |
0.190290 | + | 0.981728i | \(0.439057\pi\) | |||||||
\(180\) | −1.03016 | − | 0.748453i | −0.0767833 | − | 0.0557864i | ||||
\(181\) | 4.59735 | + | 14.1492i | 0.341718 | + | 1.05170i | 0.963317 | + | 0.268365i | \(0.0864832\pi\) |
−0.621599 | + | 0.783335i | \(0.713517\pi\) | |||||||
\(182\) | −2.01293 | − | 6.19518i | −0.149209 | − | 0.459217i | ||||
\(183\) | −0.947068 | − | 0.688085i | −0.0700093 | − | 0.0508647i | ||||
\(184\) | −12.1428 | + | 8.82226i | −0.895179 | + | 0.650386i | ||||
\(185\) | −9.57912 | + | 29.4815i | −0.704271 | + | 2.16752i | ||||
\(186\) | 1.80137 | 0.132083 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.109961 | 0.00801970 | ||||||||
\(189\) | 0.658827 | − | 2.02766i | 0.0479226 | − | 0.147491i | ||||
\(190\) | −24.2856 | + | 17.6445i | −1.76186 | + | 1.28007i | ||||
\(191\) | −3.11418 | − | 2.26258i | −0.225334 | − | 0.163715i | 0.469390 | − | 0.882991i | \(-0.344474\pi\) |
−0.694724 | + | 0.719276i | \(0.744474\pi\) | |||||||
\(192\) | 0.952382 | + | 2.93113i | 0.0687323 | + | 0.211536i | ||||
\(193\) | −0.786970 | − | 2.42204i | −0.0566473 | − | 0.174342i | 0.918729 | − | 0.394887i | \(-0.129216\pi\) |
−0.975377 | + | 0.220545i | \(0.929216\pi\) | |||||||
\(194\) | 6.78391 | + | 4.92880i | 0.487056 | + | 0.353867i | ||||
\(195\) | 4.41182 | − | 3.20538i | 0.315937 | − | 0.229542i | ||||
\(196\) | −0.0436753 | + | 0.134419i | −0.00311966 | + | 0.00960133i | ||||
\(197\) | −10.5467 | −0.751420 | −0.375710 | − | 0.926737i | \(-0.622601\pi\) | ||||
−0.375710 | + | 0.926737i | \(0.622601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6846 | 0.828302 | 0.414151 | − | 0.910208i | \(-0.364079\pi\) | ||||
0.414151 | + | 0.910208i | \(0.364079\pi\) | |||||||
\(200\) | 4.39155 | − | 13.5158i | 0.310529 | − | 0.955711i | ||||
\(201\) | 1.93842 | − | 1.40835i | 0.136726 | − | 0.0993371i | ||||
\(202\) | −11.9082 | − | 8.65185i | −0.837861 | − | 0.608742i | ||||
\(203\) | −2.16600 | − | 6.66627i | −0.152024 | − | 0.467880i | ||||
\(204\) | 0.0758196 | + | 0.233349i | 0.00530843 | + | 0.0163377i | ||||
\(205\) | 8.18835 | + | 5.94919i | 0.571899 | + | 0.415509i | ||||
\(206\) | −14.6039 | + | 10.6103i | −1.01750 | + | 0.739256i | ||||
\(207\) | −4.55655 | + | 14.0236i | −0.316702 | + | 0.974709i | ||||
\(208\) | 17.6660 | 1.22492 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.55602 | 0.107375 | ||||||||
\(211\) | 3.43381 | − | 10.5682i | 0.236393 | − | 0.727543i | −0.760541 | − | 0.649290i | \(-0.775066\pi\) |
0.996934 | − | 0.0782524i | \(-0.0249340\pi\) | |||||||
\(212\) | 0.261008 | − | 0.189634i | 0.0179261 | − | 0.0130241i | ||||
\(213\) | 4.45611 | + | 3.23755i | 0.305328 | + | 0.221833i | ||||
\(214\) | −5.90594 | − | 18.1766i | −0.403722 | − | 1.24253i | ||||
\(215\) | 4.15730 | + | 12.7949i | 0.283526 | + | 0.872602i | ||||
\(216\) | 5.03537 | + | 3.65841i | 0.342614 | + | 0.248923i | ||||
\(217\) | −2.94213 | + | 2.13758i | −0.199725 | + | 0.145109i | ||||
\(218\) | 6.56148 | − | 20.1942i | 0.444399 | − | 1.36772i | ||||
\(219\) | −1.17064 | −0.0791046 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.8294 | 1.53567 | ||||||||
\(222\) | 1.51047 | − | 4.64873i | 0.101376 | − | 0.312003i | ||||
\(223\) | −22.6854 | + | 16.4819i | −1.51913 | + | 1.10371i | −0.557209 | + | 0.830372i | \(0.688128\pi\) |
−0.961918 | + | 0.273338i | \(0.911872\pi\) | |||||||
\(224\) | −0.645582 | − | 0.469043i | −0.0431348 | − | 0.0313393i | ||||
\(225\) | −4.31430 | − | 13.2780i | −0.287620 | − | 0.885203i | ||||
\(226\) | −1.74078 | − | 5.35757i | −0.115795 | − | 0.356380i | ||||
\(227\) | 18.6149 | + | 13.5245i | 1.23552 | + | 0.897656i | 0.997291 | − | 0.0735543i | \(-0.0234342\pi\) |
0.238226 | + | 0.971210i | \(0.423434\pi\) | |||||||
\(228\) | −0.291197 | + | 0.211567i | −0.0192850 | + | 0.0140114i | ||||
\(229\) | 4.14825 | − | 12.7670i | 0.274124 | − | 0.843666i | −0.715326 | − | 0.698791i | \(-0.753722\pi\) |
0.989450 | − | 0.144876i | \(-0.0462782\pi\) | |||||||
\(230\) | −22.0187 | −1.45187 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.4626 | 1.34344 | ||||||||
\(233\) | −1.09310 | + | 3.36423i | −0.0716116 | + | 0.220398i | −0.980456 | − | 0.196737i | \(-0.936966\pi\) |
0.908845 | + | 0.417135i | \(0.136966\pi\) | |||||||
\(234\) | 15.1141 | − | 10.9811i | 0.988041 | − | 0.717854i | ||||
\(235\) | 1.97722 | + | 1.43654i | 0.128980 | + | 0.0937094i | ||||
\(236\) | 0.0158685 | + | 0.0488381i | 0.00103295 | + | 0.00317909i | ||||
\(237\) | −0.417361 | − | 1.28451i | −0.0271105 | − | 0.0834377i | ||||
\(238\) | 5.26993 | + | 3.82883i | 0.341599 | + | 0.248186i | ||||
\(239\) | −17.8135 | + | 12.9422i | −1.15226 | + | 0.837164i | −0.988779 | − | 0.149383i | \(-0.952271\pi\) |
−0.163478 | + | 0.986547i | \(0.552271\pi\) | |||||||
\(240\) | −1.30403 | + | 4.01338i | −0.0841746 | + | 0.259063i | ||||
\(241\) | −0.315366 | −0.0203145 | −0.0101573 | − | 0.999948i | \(-0.503233\pi\) | ||||
−0.0101573 | + | 0.999948i | \(0.503233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.24065 | 0.592788 | ||||||||
\(244\) | −0.140721 | + | 0.433096i | −0.00900876 | + | 0.0277261i | ||||
\(245\) | −2.54139 | + | 1.84643i | −0.162364 | + | 0.117964i | ||||
\(246\) | −1.29116 | − | 0.938086i | −0.0823217 | − | 0.0598102i | ||||
\(247\) | 10.3492 | + | 31.8515i | 0.658502 | + | 2.02666i | ||||
\(248\) | −3.28074 | − | 10.0971i | −0.208327 | − | 0.641165i | ||||
\(249\) | −0.457373 | − | 0.332301i | −0.0289849 | − | 0.0210587i | ||||
\(250\) | −0.457373 | + | 0.332301i | −0.0289268 | + | 0.0210166i | ||||
\(251\) | 5.76193 | − | 17.7334i | 0.363690 | − | 1.11932i | −0.587108 | − | 0.809509i | \(-0.699733\pi\) |
0.950797 | − | 0.309813i | \(-0.100267\pi\) | |||||||
\(252\) | −0.405351 | −0.0255347 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −30.0187 | −1.88354 | ||||||||
\(255\) | −1.68517 | + | 5.18641i | −0.105529 | + | 0.324786i | ||||
\(256\) | 2.73021 | − | 1.98362i | 0.170638 | − | 0.123976i | ||||
\(257\) | 6.91442 | + | 5.02362i | 0.431309 | + | 0.313365i | 0.782172 | − | 0.623062i | \(-0.214112\pi\) |
−0.350863 | + | 0.936427i | \(0.614112\pi\) | |||||||
\(258\) | −0.655536 | − | 2.01753i | −0.0408119 | − | 0.125606i | ||||
\(259\) | 3.04938 | + | 9.38502i | 0.189479 | + | 0.583157i | ||||
\(260\) | −1.71622 | − | 1.24690i | −0.106435 | − | 0.0773297i | ||||
\(261\) | 16.2634 | − | 11.8161i | 1.00668 | − | 0.731397i | ||||
\(262\) | −6.32330 | + | 19.4611i | −0.390655 | + | 1.20231i | ||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.17064 | 0.440489 | ||||||||
\(266\) | −2.95297 | + | 9.08831i | −0.181058 | + | 0.557240i | ||||
\(267\) | 1.64174 | − | 1.19280i | 0.100473 | − | 0.0729979i | ||||
\(268\) | −0.754054 | − | 0.547852i | −0.0460612 | − | 0.0334654i | ||||
\(269\) | 2.33494 | + | 7.18620i | 0.142364 | + | 0.438150i | 0.996663 | − | 0.0816318i | \(-0.0260132\pi\) |
−0.854299 | + | 0.519782i | \(0.826013\pi\) | |||||||
\(270\) | 2.82154 | + | 8.68380i | 0.171713 | + | 0.528479i | ||||
\(271\) | −11.3413 | − | 8.23996i | −0.688937 | − | 0.500542i | 0.187374 | − | 0.982289i | \(-0.440002\pi\) |
−0.876310 | + | 0.481747i | \(0.840002\pi\) | |||||||
\(272\) | −14.2921 | + | 10.3838i | −0.866584 | + | 0.629610i | ||||
\(273\) | 0.536449 | − | 1.65102i | 0.0324674 | − | 0.0999243i | ||||
\(274\) | 14.5840 | 0.881052 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.264015 | −0.0158918 | ||||||||
\(277\) | −1.85987 | + | 5.72408i | −0.111749 | + | 0.343927i | −0.991255 | − | 0.131960i | \(-0.957873\pi\) |
0.879506 | + | 0.475887i | \(0.157873\pi\) | |||||||
\(278\) | 4.52510 | − | 3.28768i | 0.271397 | − | 0.197182i | ||||
\(279\) | −8.43800 | − | 6.13057i | −0.505170 | − | 0.367028i | ||||
\(280\) | −2.83388 | − | 8.72180i | −0.169357 | − | 0.521227i | ||||
\(281\) | −6.38678 | − | 19.6565i | −0.381003 | − | 1.17261i | −0.939338 | − | 0.342992i | \(-0.888560\pi\) |
0.558335 | − | 0.829615i | \(-0.311440\pi\) | |||||||
\(282\) | −0.311775 | − | 0.226518i | −0.0185659 | − | 0.0134889i | ||||
\(283\) | −8.02218 | + | 5.82845i | −0.476869 | + | 0.346466i | −0.800112 | − | 0.599850i | \(-0.795227\pi\) |
0.323243 | + | 0.946316i | \(0.395227\pi\) | |||||||
\(284\) | 0.662117 | − | 2.03779i | 0.0392894 | − | 0.120920i | ||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.22199 | 0.190188 | ||||||||
\(288\) | 0.707220 | − | 2.17660i | 0.0416733 | − | 0.128257i | ||||
\(289\) | −4.71605 | + | 3.42641i | −0.277415 | + | 0.201554i | ||||
\(290\) | 24.2856 | + | 17.6445i | 1.42610 | + | 1.03612i | ||||
\(291\) | 0.690563 | + | 2.12534i | 0.0404815 | + | 0.124589i | ||||
\(292\) | 0.140721 | + | 0.433096i | 0.00823509 | + | 0.0253450i | ||||
\(293\) | 21.6790 | + | 15.7507i | 1.26650 | + | 0.920165i | 0.999057 | − | 0.0434095i | \(-0.0138220\pi\) |
0.267441 | + | 0.963574i | \(0.413822\pi\) | |||||||
\(294\) | 0.400735 | − | 0.291151i | 0.0233713 | − | 0.0169803i | ||||
\(295\) | −0.352692 | + | 1.08548i | −0.0205345 | + | 0.0631988i | ||||
\(296\) | −28.8081 | −1.67443 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.1120 | −1.10713 | ||||||||
\(299\) | −7.59111 | + | 23.3630i | −0.439005 | + | 1.35112i | ||||
\(300\) | 0.202237 | − | 0.146934i | 0.0116761 | − | 0.00848321i | ||||
\(301\) | 3.46475 | + | 2.51729i | 0.199705 | + | 0.145094i | ||||
\(302\) | 2.87715 | + | 8.85496i | 0.165561 | + | 0.509546i | ||||
\(303\) | −1.21219 | − | 3.73074i | −0.0696386 | − | 0.214325i | ||||
\(304\) | −20.9664 | − | 15.2330i | −1.20251 | − | 0.873673i | ||||
\(305\) | −8.18835 | + | 5.94919i | −0.468864 | + | 0.340649i | ||||
\(306\) | −5.77308 | + | 17.7677i | −0.330025 | + | 1.01571i | ||||
\(307\) | 11.8973 | 0.679015 | 0.339507 | − | 0.940603i | \(-0.389740\pi\) | ||||
0.339507 | + | 0.940603i | \(0.389740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.81070 | −0.273671 | ||||||||
\(310\) | 4.81284 | − | 14.8124i | 0.273351 | − | 0.841287i | ||||
\(311\) | 17.1840 | − | 12.4849i | 0.974418 | − | 0.707956i | 0.0179637 | − | 0.999839i | \(-0.494282\pi\) |
0.956454 | + | 0.291883i | \(0.0942817\pi\) | |||||||
\(312\) | 4.10005 | + | 2.97886i | 0.232120 | + | 0.168645i | ||||
\(313\) | −3.92370 | − | 12.0759i | −0.221780 | − | 0.682570i | −0.998602 | − | 0.0528499i | \(-0.983170\pi\) |
0.776822 | − | 0.629720i | \(-0.216830\pi\) | |||||||
\(314\) | 9.87620 | + | 30.3958i | 0.557346 | + | 1.71533i | ||||
\(315\) | −7.28870 | − | 5.29555i | −0.410672 | − | 0.298370i | ||||
\(316\) | −0.425052 | + | 0.308818i | −0.0239110 | + | 0.0173724i | ||||
\(317\) | −3.66741 | + | 11.2871i | −0.205982 | + | 0.633948i | 0.793689 | + | 0.608323i | \(0.208158\pi\) |
−0.999672 | + | 0.0256251i | \(0.991842\pi\) | |||||||
\(318\) | −1.13069 | −0.0634059 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 26.6468 | 1.48960 | ||||||||
\(321\) | 1.57394 | − | 4.84409i | 0.0878487 | − | 0.270371i | ||||
\(322\) | −5.67067 | + | 4.11998i | −0.316014 | + | 0.229598i | ||||
\(323\) | −27.0945 | − | 19.6853i | −1.50758 | − | 1.09532i | ||||
\(324\) | −0.341949 | − | 1.05241i | −0.0189972 | − | 0.0584673i | ||||
\(325\) | −7.18752 | − | 22.1209i | −0.398692 | − | 1.22705i | ||||
\(326\) | −1.09267 | − | 0.793869i | −0.0605172 | − | 0.0439683i | ||||
\(327\) | 4.57800 | − | 3.32611i | 0.253164 | − | 0.183934i | ||||
\(328\) | −2.90665 | + | 8.94574i | −0.160493 | + | 0.493946i | ||||
\(329\) | 0.778008 | 0.0428930 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8867 | −0.653349 | −0.326675 | − | 0.945137i | \(-0.605928\pi\) | ||||
−0.326675 | + | 0.945137i | \(0.605928\pi\) | |||||||
\(332\) | −0.0679594 | + | 0.209158i | −0.00372976 | + | 0.0114790i | ||||
\(333\) | −22.8963 | + | 16.6351i | −1.25471 | + | 0.911598i | ||||
\(334\) | 0.623550 | + | 0.453036i | 0.0341191 | + | 0.0247890i | ||||
\(335\) | −6.40160 | − | 19.7021i | −0.349757 | − | 1.07644i | ||||
\(336\) | 0.415119 | + | 1.27760i | 0.0226466 | + | 0.0696990i | ||||
\(337\) | −0.801470 | − | 0.582302i | −0.0436588 | − | 0.0317200i | 0.565742 | − | 0.824582i | \(-0.308590\pi\) |
−0.609401 | + | 0.792862i | \(0.708590\pi\) | |||||||
\(338\) | 10.8413 | − | 7.87670i | 0.589692 | − | 0.428436i | ||||
\(339\) | 0.463919 | − | 1.42780i | 0.0251966 | − | 0.0775473i | ||||
\(340\) | 2.12136 | 0.115047 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −27.4066 | −1.48198 | ||||||||
\(343\) | −0.309017 | + | 0.951057i | −0.0166853 | + | 0.0513522i | ||||
\(344\) | −10.1148 | + | 7.34884i | −0.545354 | + | 0.396223i | ||||
\(345\) | −4.74731 | − | 3.44912i | −0.255586 | − | 0.185694i | ||||
\(346\) | 7.26334 | + | 22.3543i | 0.390480 | + | 1.20177i | ||||
\(347\) | −4.69375 | − | 14.4459i | −0.251974 | − | 0.775496i | −0.994411 | − | 0.105580i | \(-0.966330\pi\) |
0.742437 | − | 0.669916i | \(-0.233670\pi\) | |||||||
\(348\) | 0.291197 | + | 0.211567i | 0.0156098 | + | 0.0113412i | ||||
\(349\) | 24.0305 | − | 17.4592i | 1.28632 | − | 0.934567i | 0.286597 | − | 0.958051i | \(-0.407476\pi\) |
0.999724 | + | 0.0234839i | \(0.00747586\pi\) | |||||||
\(350\) | 2.05084 | − | 6.31185i | 0.109622 | − | 0.337383i | ||||
\(351\) | 10.1867 | 0.543728 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.71601 | −0.357457 | −0.178729 | − | 0.983898i | \(-0.557198\pi\) | ||||
−0.178729 | + | 0.983898i | \(0.557198\pi\) | |||||||
\(354\) | 0.0556136 | − | 0.171161i | 0.00295583 | − | 0.00909711i | ||||
\(355\) | 38.5275 | − | 27.9919i | 2.04483 | − | 1.48565i | ||||
\(356\) | −0.638644 | − | 0.464002i | −0.0338481 | − | 0.0245921i | ||||
\(357\) | 0.536449 | + | 1.65102i | 0.0283919 | + | 0.0873812i | ||||
\(358\) | −4.76957 | − | 14.6792i | −0.252080 | − | 0.775821i | ||||
\(359\) | −14.3487 | − | 10.4250i | −0.757296 | − | 0.550208i | 0.140784 | − | 0.990040i | \(-0.455038\pi\) |
−0.898080 | + | 0.439833i | \(0.855038\pi\) | |||||||
\(360\) | 21.2782 | − | 15.4595i | 1.12146 | − | 0.814789i | ||||
\(361\) | 9.31089 | − | 28.6560i | 0.490047 | − | 1.50821i | ||||
\(362\) | −20.2827 | −1.06603 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.675305 | −0.0353956 | ||||||||
\(365\) | −3.12767 | + | 9.62599i | −0.163710 | + | 0.503847i | ||||
\(366\) | 1.29116 | − | 0.938086i | 0.0674903 | − | 0.0490346i | ||||
\(367\) | 6.55248 | + | 4.76066i | 0.342037 | + | 0.248504i | 0.745521 | − | 0.666482i | \(-0.232201\pi\) |
−0.403484 | + | 0.914987i | \(0.632201\pi\) | |||||||
\(368\) | −5.87421 | − | 18.0789i | −0.306214 | − | 0.942430i | ||||
\(369\) | 2.85552 | + | 8.78838i | 0.148652 | + | 0.457505i | ||||
\(370\) | −34.1902 | − | 24.8406i | −1.77746 | − | 1.29140i | ||||
\(371\) | 1.84672 | − | 1.34172i | 0.0958770 | − | 0.0696587i | ||||
\(372\) | 0.0577084 | − | 0.177608i | 0.00299204 | − | 0.00920855i | ||||
\(373\) | 0.565344 | 0.0292724 | 0.0146362 | − | 0.999893i | \(-0.495341\pi\) | ||||
0.0146362 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.150665 | −0.00778030 | ||||||||
\(376\) | −0.701862 | + | 2.16011i | −0.0361958 | + | 0.111399i | ||||
\(377\) | 27.0945 | − | 19.6853i | 1.39544 | − | 1.01384i | ||||
\(378\) | 2.35151 | + | 1.70847i | 0.120949 | + | 0.0878743i | ||||
\(379\) | −6.96402 | − | 21.4330i | −0.357718 | − | 1.10094i | −0.954417 | − | 0.298477i | \(-0.903521\pi\) |
0.596699 | − | 0.802465i | \(-0.296479\pi\) | |||||||
\(380\) | 0.961671 | + | 2.95972i | 0.0493327 | + | 0.151830i | ||||
\(381\) | −6.47214 | − | 4.70228i | −0.331578 | − | 0.240905i | ||||
\(382\) | 4.24565 | − | 3.08464i | 0.217226 | − | 0.157824i | ||||
\(383\) | 6.61028 | − | 20.3443i | 0.337770 | − | 1.03955i | −0.627572 | − | 0.778558i | \(-0.715951\pi\) |
0.965342 | − | 0.260989i | \(-0.0840487\pi\) | |||||||
\(384\) | −3.62188 | −0.184828 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.47197 | 0.176719 | ||||||||
\(387\) | −3.79555 | + | 11.6815i | −0.192939 | + | 0.593805i | ||||
\(388\) | 0.703287 | − | 0.510968i | 0.0357040 | − | 0.0259405i | ||||
\(389\) | −8.63925 | − | 6.27678i | −0.438027 | − | 0.318245i | 0.346823 | − | 0.937930i | \(-0.387260\pi\) |
−0.784851 | + | 0.619685i | \(0.787260\pi\) | |||||||
\(390\) | 2.29743 | + | 7.07078i | 0.116335 | + | 0.358043i | ||||
\(391\) | −7.59111 | − | 23.3630i | −0.383899 | − | 1.18152i | ||||
\(392\) | −2.36180 | − | 1.71595i | −0.119289 | − | 0.0866684i | ||||
\(393\) | −4.41182 | + | 3.20538i | −0.222547 | + | 0.161690i | ||||
\(394\) | 4.44323 | − | 13.6749i | 0.223847 | − | 0.688929i | ||||
\(395\) | −11.6774 | −0.587553 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.9160 | −1.20031 | −0.600154 | − | 0.799885i | \(-0.704894\pi\) | ||||
−0.600154 | + | 0.799885i | \(0.704894\pi\) | |||||||
\(398\) | −4.92264 | + | 15.1503i | −0.246750 | + | 0.759417i | ||||
\(399\) | −2.06031 | + | 1.49691i | −0.103145 | + | 0.0749390i | ||||
\(400\) | 14.5612 | + | 10.5794i | 0.728062 | + | 0.528968i | ||||
\(401\) | 3.60274 | + | 11.0881i | 0.179912 | + | 0.553713i | 0.999824 | − | 0.0187772i | \(-0.00597733\pi\) |
−0.819911 | + | 0.572491i | \(0.805977\pi\) | |||||||
\(402\) | 1.00942 | + | 3.10669i | 0.0503455 | + | 0.154947i | ||||
\(403\) | −14.0575 | − | 10.2134i | −0.700255 | − | 0.508765i | ||||
\(404\) | −1.23453 | + | 0.896936i | −0.0614200 | + | 0.0446242i | ||||
\(405\) | 7.60016 | − | 23.3909i | 0.377655 | − | 1.16230i | ||||
\(406\) | 9.55602 | 0.474257 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.06794 | −0.250900 | ||||||||
\(409\) | 10.1405 | − | 31.2092i | 0.501415 | − | 1.54320i | −0.305300 | − | 0.952256i | \(-0.598757\pi\) |
0.806715 | − | 0.590941i | \(-0.201243\pi\) | |||||||
\(410\) | −11.1634 | + | 8.11069i | −0.551322 | + | 0.400559i | ||||
\(411\) | 3.14437 | + | 2.28452i | 0.155100 | + | 0.112687i | ||||
\(412\) | 0.578289 | + | 1.77979i | 0.0284902 | + | 0.0876840i | ||||
\(413\) | 0.112275 | + | 0.345546i | 0.00552467 | + | 0.0170032i | ||||
\(414\) | −16.2634 | − | 11.8161i | −0.799304 | − | 0.580728i | ||||
\(415\) | −3.95445 | + | 2.87308i | −0.194116 | + | 0.141034i | ||||
\(416\) | 1.17821 | − | 3.62616i | 0.0577666 | − | 0.177787i | ||||
\(417\) | 1.49063 | 0.0729964 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.7967 | 0.527452 | 0.263726 | − | 0.964598i | \(-0.415049\pi\) | ||||
0.263726 | + | 0.964598i | \(0.415049\pi\) | |||||||
\(420\) | 0.0498482 | − | 0.153417i | 0.00243234 | − | 0.00748598i | ||||
\(421\) | 0.931974 | − | 0.677119i | 0.0454216 | − | 0.0330008i | −0.564843 | − | 0.825199i | \(-0.691063\pi\) |
0.610264 | + | 0.792198i | \(0.291063\pi\) | |||||||
\(422\) | 12.2561 | + | 8.90456i | 0.596617 | + | 0.433467i | ||||
\(423\) | 0.689516 | + | 2.12211i | 0.0335254 | + | 0.103181i | ||||
\(424\) | 2.05926 | + | 6.33775i | 0.100007 | + | 0.307788i | ||||
\(425\) | 18.8172 | + | 13.6715i | 0.912767 | + | 0.663164i | ||||
\(426\) | −6.07514 | + | 4.41385i | −0.294341 | + | 0.213852i | ||||
\(427\) | −0.995650 | + | 3.06430i | −0.0481829 | + | 0.148292i | ||||
\(428\) | −1.98134 | −0.0957718 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.3413 | −0.884495 | ||||||||
\(431\) | −9.87620 | + | 30.3958i | −0.475720 | + | 1.46411i | 0.369265 | + | 0.929324i | \(0.379609\pi\) |
−0.844985 | + | 0.534791i | \(0.820391\pi\) | |||||||
\(432\) | −6.37730 | + | 4.63338i | −0.306828 | + | 0.222924i | ||||
\(433\) | 3.58665 | + | 2.60585i | 0.172363 | + | 0.125229i | 0.670622 | − | 0.741799i | \(-0.266027\pi\) |
−0.498259 | + | 0.867028i | \(0.666027\pi\) | |||||||
\(434\) | −1.53210 | − | 4.71532i | −0.0735431 | − | 0.226342i | ||||
\(435\) | 2.47214 | + | 7.60845i | 0.118530 | + | 0.364797i | ||||
\(436\) | −1.78086 | − | 1.29387i | −0.0852877 | − | 0.0619652i | ||||
\(437\) | 29.1548 | − | 21.1822i | 1.39466 | − | 1.01328i | ||||
\(438\) | 0.493181 | − | 1.51786i | 0.0235651 | − | 0.0725259i | ||||
\(439\) | −27.4720 | −1.31117 | −0.655583 | − | 0.755123i | \(-0.727577\pi\) | ||||
−0.655583 | + | 0.755123i | \(0.727577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.86799 | −0.136571 | ||||||||
\(442\) | −9.61782 | + | 29.6006i | −0.457473 | + | 1.40796i | ||||
\(443\) | 6.30283 | − | 4.57927i | 0.299456 | − | 0.217568i | −0.427903 | − | 0.903825i | \(-0.640747\pi\) |
0.727359 | + | 0.686257i | \(0.240747\pi\) | |||||||
\(444\) | −0.409957 | − | 0.297852i | −0.0194557 | − | 0.0141354i | ||||
\(445\) | −5.42182 | − | 16.6866i | −0.257019 | − | 0.791022i | ||||
\(446\) | −11.8133 | − | 36.3576i | −0.559377 | − | 1.72158i | ||||
\(447\) | −4.12063 | − | 2.99381i | −0.194899 | − | 0.141602i | ||||
\(448\) | 6.86258 | − | 4.98596i | 0.324227 | − | 0.235564i | ||||
\(449\) | 6.33813 | − | 19.5067i | 0.299115 | − | 0.920580i | −0.682694 | − | 0.730705i | \(-0.739192\pi\) |
0.981808 | − | 0.189875i | \(-0.0608084\pi\) | |||||||
\(450\) | 19.0339 | 0.897268 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.584002 | −0.0274691 | ||||||||
\(453\) | −0.766764 | + | 2.35986i | −0.0360257 | + | 0.110876i | ||||
\(454\) | −25.3783 | + | 18.4384i | −1.19106 | + | 0.865357i | ||||
\(455\) | −12.1428 | − | 8.82226i | −0.569263 | − | 0.413594i | ||||
\(456\) | −2.29743 | − | 7.07078i | −0.107587 | − | 0.331119i | ||||
\(457\) | −2.64684 | − | 8.14613i | −0.123814 | − | 0.381060i | 0.869869 | − | 0.493282i | \(-0.164203\pi\) |
−0.993683 | + | 0.112223i | \(0.964203\pi\) | |||||||
\(458\) | 14.8061 | + | 10.7573i | 0.691843 | + | 0.502653i | ||||
\(459\) | −8.24125 | + | 5.98762i | −0.384669 | + | 0.279478i | ||||
\(460\) | −0.705385 | + | 2.17095i | −0.0328887 | + | 0.101221i | ||||
\(461\) | 9.66598 | 0.450189 | 0.225095 | − | 0.974337i | \(-0.427731\pi\) | ||||
0.225095 | + | 0.974337i | \(0.427731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4240 | 0.530919 | 0.265459 | − | 0.964122i | \(-0.414476\pi\) | ||||
0.265459 | + | 0.964122i | \(0.414476\pi\) | |||||||
\(464\) | −8.00847 | + | 24.6475i | −0.371784 | + | 1.14423i | ||||
\(465\) | 3.35796 | − | 2.43970i | 0.155722 | − | 0.113138i | ||||
\(466\) | −3.90155 | − | 2.83464i | −0.180736 | − | 0.131312i | ||||
\(467\) | 5.63050 | + | 17.3289i | 0.260548 | + | 0.801885i | 0.992686 | + | 0.120728i | \(0.0385230\pi\) |
−0.732137 | + | 0.681157i | \(0.761477\pi\) | |||||||
\(468\) | −0.598495 | − | 1.84198i | −0.0276654 | − | 0.0851454i | ||||
\(469\) | −5.33518 | − | 3.87624i | −0.246356 | − | 0.178988i | ||||
\(470\) | −2.69561 | + | 1.95847i | −0.124339 | + | 0.0903376i | ||||
\(471\) | −2.63202 | + | 8.10051i | −0.121277 | + | 0.373252i | ||||
\(472\) | −1.06068 | −0.0488218 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.84132 | 0.0845749 | ||||||||
\(475\) | −10.5441 | + | 32.4513i | −0.483796 | + | 1.48897i | ||||
\(476\) | 0.546333 | − | 0.396934i | 0.0250411 | − | 0.0181935i | ||||
\(477\) | 5.29638 | + | 3.84805i | 0.242505 | + | 0.176190i | ||||
\(478\) | −9.27628 | − | 28.5494i | −0.424287 | − | 1.30582i | ||||
\(479\) | 1.07290 | + | 3.30204i | 0.0490220 | + | 0.150874i | 0.972571 | − | 0.232606i | \(-0.0747254\pi\) |
−0.923549 | + | 0.383480i | \(0.874725\pi\) | |||||||
\(480\) | 0.736827 | + | 0.535336i | 0.0336314 | + | 0.0244346i | ||||
\(481\) | −38.1446 | + | 27.7137i | −1.73925 | + | 1.26364i | ||||
\(482\) | 0.132861 | − | 0.408905i | 0.00605166 | − | 0.0186251i | ||||
\(483\) | −1.86799 | −0.0849966 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.3213 | 0.877335 | ||||||||
\(486\) | −3.89301 | + | 11.9814i | −0.176590 | + | 0.543489i | ||||
\(487\) | 22.2167 | − | 16.1414i | 1.00673 | − | 0.731435i | 0.0432123 | − | 0.999066i | \(-0.486241\pi\) |
0.963521 | + | 0.267631i | \(0.0862408\pi\) | |||||||
\(488\) | −7.60970 | − | 5.52877i | −0.344475 | − | 0.250276i | ||||
\(489\) | −0.111227 | − | 0.342322i | −0.00502987 | − | 0.0154803i | ||||
\(490\) | −1.32342 | − | 4.07306i | −0.0597860 | − | 0.184002i | ||||
\(491\) | 5.06769 | + | 3.68190i | 0.228702 | + | 0.166162i | 0.696235 | − | 0.717814i | \(-0.254857\pi\) |
−0.467533 | + | 0.883976i | \(0.654857\pi\) | |||||||
\(492\) | −0.133855 | + | 0.0972513i | −0.00603465 | + | 0.00438443i | ||||
\(493\) | −10.3492 | + | 31.8515i | −0.466103 | + | 1.43452i | ||||
\(494\) | −45.6587 | −2.05428 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.4461 | 0.603746 | ||||||||
\(497\) | 4.68470 | − | 14.4180i | 0.210137 | − | 0.646736i | ||||
\(498\) | 0.623550 | − | 0.453036i | 0.0279419 | − | 0.0203010i | ||||
\(499\) | 16.7208 | + | 12.1484i | 0.748526 | + | 0.543836i | 0.895370 | − | 0.445324i | \(-0.146911\pi\) |
−0.146844 | + | 0.989160i | \(0.546911\pi\) | |||||||
\(500\) | 0.0181112 | + | 0.0557407i | 0.000809959 | + | 0.00249280i | ||||
\(501\) | 0.0634738 | + | 0.195352i | 0.00283580 | + | 0.00872770i | ||||
\(502\) | 20.5657 | + | 14.9419i | 0.917893 | + | 0.666888i | ||||
\(503\) | −17.8135 | + | 12.9422i | −0.794263 | + | 0.577066i | −0.909226 | − | 0.416304i | \(-0.863325\pi\) |
0.114962 | + | 0.993370i | \(0.463325\pi\) | |||||||
\(504\) | 2.58729 | − | 7.96287i | 0.115247 | − | 0.354694i | ||||
\(505\) | −33.9160 | −1.50924 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.57128 | 0.158606 | ||||||||
\(508\) | −0.961671 | + | 2.95972i | −0.0426672 | + | 0.131316i | ||||
\(509\) | −17.3324 | + | 12.5927i | −0.768245 | + | 0.558162i | −0.901428 | − | 0.432929i | \(-0.857480\pi\) |
0.133183 | + | 0.991091i | \(0.457480\pi\) | |||||||
\(510\) | −6.01476 | − | 4.36998i | −0.266338 | − | 0.193506i | ||||
\(511\) | 0.995650 | + | 3.06430i | 0.0440450 | + | 0.135557i | ||||
\(512\) | 7.58269 | + | 23.3371i | 0.335111 | + | 1.03137i | ||||
\(513\) | −12.0899 | − | 8.78383i | −0.533782 | − | 0.387815i | ||||
\(514\) | −9.42662 | + | 6.84884i | −0.415790 | + | 0.302089i | ||||
\(515\) | −12.8530 | + | 39.5576i | −0.566373 | + | 1.74312i | ||||
\(516\) | −0.219921 | −0.00968149 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.4533 | −0.591105 | ||||||||
\(519\) | −1.93569 | + | 5.95743i | −0.0849672 | + | 0.261502i | ||||
\(520\) | 35.4490 | − | 25.7552i | 1.55454 | − | 1.12944i | ||||
\(521\) | −11.2820 | − | 8.19682i | −0.494271 | − | 0.359109i | 0.312553 | − | 0.949900i | \(-0.398816\pi\) |
−0.806825 | + | 0.590791i | \(0.798816\pi\) | |||||||
\(522\) | 8.46910 | + | 26.0652i | 0.370682 | + | 1.14084i | ||||
\(523\) | −5.71104 | − | 17.5768i | −0.249726 | − | 0.768578i | −0.994823 | − | 0.101622i | \(-0.967597\pi\) |
0.745097 | − | 0.666956i | \(-0.232403\pi\) | |||||||
\(524\) | 1.71622 | + | 1.24690i | 0.0749733 | + | 0.0544713i | ||||
\(525\) | 1.43089 | − | 1.03960i | 0.0624492 | − | 0.0453720i | ||||
\(526\) | −6.74067 | + | 20.7456i | −0.293907 | + | 0.904553i | ||||
\(527\) | 17.3760 | 0.756912 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.43334 | 0.149276 | ||||||||
\(530\) | −3.02093 | + | 9.29747i | −0.131221 | + | 0.403856i | ||||
\(531\) | −0.843014 | + | 0.612486i | −0.0365837 | + | 0.0265796i | ||||
\(532\) | 0.801470 | + | 0.582302i | 0.0347481 | + | 0.0252460i | ||||
\(533\) | 4.75723 | + | 14.6412i | 0.206058 | + | 0.634182i | ||||
\(534\) | 0.854929 | + | 2.63120i | 0.0369964 | + | 0.113863i | ||||
\(535\) | −35.6269 | − | 25.8845i | −1.54029 | − | 1.11908i | ||||
\(536\) | 15.5752 | − | 11.3161i | 0.672748 | − | 0.488780i | ||||
\(537\) | 1.27110 | − | 3.91203i | 0.0548518 | − | 0.168816i | ||||
\(538\) | −10.3013 | −0.444122 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.946578 | 0.0407342 | ||||||||
\(541\) | 11.5737 | − | 35.6202i | 0.497593 | − | 1.53143i | −0.315284 | − | 0.948997i | \(-0.602100\pi\) |
0.812877 | − | 0.582435i | \(-0.197900\pi\) | |||||||
\(542\) | 15.4620 | − | 11.2338i | 0.664148 | − | 0.482532i | ||||
\(543\) | −4.37302 | − | 3.17719i | −0.187664 | − | 0.136346i | ||||
\(544\) | 1.17821 | + | 3.62616i | 0.0505154 | + | 0.155470i | ||||
\(545\) | −15.1187 | − | 46.5307i | −0.647616 | − | 1.99316i | ||||
\(546\) | 1.91471 | + | 1.39112i | 0.0819422 | + | 0.0595345i | ||||
\(547\) | 13.8590 | − | 10.0692i | 0.592569 | − | 0.430526i | −0.250665 | − | 0.968074i | \(-0.580649\pi\) |
0.843233 | + | 0.537548i | \(0.180649\pi\) | |||||||
\(548\) | 0.467210 | − | 1.43792i | 0.0199582 | − | 0.0614250i | ||||
\(549\) | −9.24065 | −0.394381 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.1307 | −2.09304 | ||||||||
\(552\) | 1.68517 | − | 5.18641i | 0.0717254 | − | 0.220748i | ||||
\(553\) | −3.00738 | + | 2.18499i | −0.127887 | + | 0.0929152i | ||||
\(554\) | −6.63831 | − | 4.82302i | −0.282035 | − | 0.204910i | ||||
\(555\) | −3.48036 | − | 10.7115i | −0.147733 | − | 0.454676i | ||||
\(556\) | −0.179187 | − | 0.551480i | −0.00759921 | − | 0.0233879i | ||||
\(557\) | −19.8738 | − | 14.4391i | −0.842079 | − | 0.611806i | 0.0808715 | − | 0.996725i | \(-0.474230\pi\) |
−0.922951 | + | 0.384918i | \(0.874230\pi\) | |||||||
\(558\) | 11.5038 | − | 8.35798i | 0.486993 | − | 0.353821i | ||||
\(559\) | −6.32330 | + | 19.4611i | −0.267447 | + | 0.823118i | ||||
\(560\) | 11.6146 | 0.490807 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.1773 | 1.18859 | ||||||||
\(563\) | −4.63814 | + | 14.2747i | −0.195474 | + | 0.601608i | 0.804497 | + | 0.593957i | \(0.202435\pi\) |
−0.999971 | + | 0.00765038i | \(0.997565\pi\) | |||||||
\(564\) | −0.0323217 | + | 0.0234831i | −0.00136099 | + | 0.000988816i | ||||
\(565\) | −10.5011 | − | 7.62947i | −0.441783 | − | 0.320974i | ||||
\(566\) | −4.17751 | − | 12.8570i | −0.175594 | − | 0.540422i | ||||
\(567\) | −2.41941 | − | 7.44616i | −0.101605 | − | 0.312709i | ||||
\(568\) | 35.8049 | + | 26.0138i | 1.50234 | + | 1.09151i | ||||
\(569\) | −9.79129 | + | 7.11379i | −0.410472 | + | 0.298226i | −0.773793 | − | 0.633439i | \(-0.781643\pi\) |
0.363321 | + | 0.931664i | \(0.381643\pi\) | |||||||
\(570\) | 3.37033 | − | 10.3728i | 0.141168 | − | 0.434470i | ||||
\(571\) | 38.9439 | 1.62975 | 0.814877 | − | 0.579634i | \(-0.196805\pi\) | ||||
0.814877 | + | 0.579634i | \(0.196805\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.39857 | 0.0584262 | ||||||||
\(574\) | −1.35740 | + | 4.17764i | −0.0566567 | + | 0.174371i | ||||
\(575\) | −20.2481 | + | 14.7111i | −0.844403 | + | 0.613494i | ||||
\(576\) | 19.6818 | + | 14.2997i | 0.820076 | + | 0.595820i | ||||
\(577\) | 11.7892 | + | 36.2834i | 0.490791 | + | 1.51050i | 0.823415 | + | 0.567440i | \(0.192066\pi\) |
−0.332624 | + | 0.943060i | \(0.607934\pi\) | |||||||
\(578\) | −2.45586 | − | 7.55836i | −0.102150 | − | 0.314386i | ||||
\(579\) | 0.748570 | + | 0.543868i | 0.0311095 | + | 0.0226024i | ||||
\(580\) | 2.51769 | − | 1.82921i | 0.104541 | − | 0.0759537i | ||||
\(581\) | −0.480835 | + | 1.47986i | −0.0199484 | + | 0.0613949i | ||||
\(582\) | −3.04664 | −0.126287 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.40610 | −0.389227 | ||||||||
\(585\) | 13.3021 | − | 40.9398i | 0.549976 | − | 1.69265i | ||||
\(586\) | −29.5555 | + | 21.4734i | −1.22093 | + | 0.887056i | ||||
\(587\) | 28.1511 | + | 20.4530i | 1.16192 | + | 0.844184i | 0.990020 | − | 0.140930i | \(-0.0450093\pi\) |
0.171900 | + | 0.985114i | \(0.445009\pi\) | |||||||
\(588\) | −0.0158685 | − | 0.0488381i | −0.000654404 | − | 0.00201405i | ||||
\(589\) | 7.87704 | + | 24.2430i | 0.324568 | + | 0.998917i | ||||
\(590\) | −1.25884 | − | 0.914603i | −0.0518258 | − | 0.0376536i | ||||
\(591\) | 3.10008 | − | 2.25234i | 0.127520 | − | 0.0926489i | ||||
\(592\) | 11.2746 | − | 34.6997i | 0.463384 | − | 1.42615i | ||||
\(593\) | −18.5913 | −0.763452 | −0.381726 | − | 0.924276i | \(-0.624670\pi\) | ||||
−0.381726 | + | 0.924276i | \(0.624670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0093 | 0.615322 | ||||||||
\(596\) | −0.612269 | + | 1.88437i | −0.0250795 | + | 0.0771868i | ||||
\(597\) | −3.43457 | + | 2.49536i | −0.140567 | + | 0.102128i | ||||
\(598\) | −27.0945 | − | 19.6853i | −1.10798 | − | 0.804992i | ||||
\(599\) | 7.62285 | + | 23.4607i | 0.311461 | + | 0.958579i | 0.977187 | + | 0.212382i | \(0.0681221\pi\) |
−0.665726 | + | 0.746197i | \(0.731878\pi\) | |||||||
\(600\) | 1.59557 | + | 4.91067i | 0.0651390 | + | 0.200477i | ||||
\(601\) | 24.3746 | + | 17.7092i | 0.994259 | + | 0.722372i | 0.960850 | − | 0.277070i | \(-0.0893634\pi\) |
0.0334095 | + | 0.999442i | \(0.489363\pi\) | |||||||
\(602\) | −4.72360 | + | 3.43189i | −0.192519 | + | 0.139874i | ||||
\(603\) | 5.84456 | − | 17.9877i | 0.238009 | − | 0.732516i | ||||
\(604\) | 0.965235 | 0.0392749 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.34797 | 0.217247 | ||||||||
\(607\) | −4.22078 | + | 12.9902i | −0.171316 | + | 0.527256i | −0.999446 | − | 0.0332795i | \(-0.989405\pi\) |
0.828130 | + | 0.560536i | \(0.189405\pi\) | |||||||
\(608\) | −4.52510 | + | 3.28768i | −0.183517 | + | 0.133333i | ||||
\(609\) | 2.06031 | + | 1.49691i | 0.0834881 | + | 0.0606577i | ||||
\(610\) | −4.26404 | − | 13.1234i | −0.172646 | − | 0.531350i | ||||
\(611\) | 1.14872 | + | 3.53539i | 0.0464721 | + | 0.143027i | ||||
\(612\) | 1.56688 | + | 1.13840i | 0.0633374 | + | 0.0460173i | ||||
\(613\) | 36.4284 | − | 26.4668i | 1.47133 | − | 1.06898i | 0.491104 | − | 0.871101i | \(-0.336594\pi\) |
0.980226 | − | 0.197882i | \(-0.0634064\pi\) | |||||||
\(614\) | −5.01223 | + | 15.4261i | −0.202277 | + | 0.622545i | ||||
\(615\) | −3.67738 | −0.148286 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.26401 | −0.332697 | −0.166348 | − | 0.986067i | \(-0.553198\pi\) | ||||
−0.166348 | + | 0.986067i | \(0.553198\pi\) | |||||||
\(618\) | 2.02671 | − | 6.23757i | 0.0815262 | − | 0.250912i | ||||
\(619\) | −34.8282 | + | 25.3042i | −1.39986 | + | 1.01706i | −0.405164 | + | 0.914244i | \(0.632785\pi\) |
−0.994700 | + | 0.102816i | \(0.967215\pi\) | |||||||
\(620\) | −1.30626 | − | 0.949053i | −0.0524606 | − | 0.0381149i | ||||
\(621\) | −3.38725 | − | 10.4249i | −0.135926 | − | 0.418336i | ||||
\(622\) | 8.94851 | + | 27.5407i | 0.358802 | + | 1.10428i | ||||
\(623\) | −4.51862 | − | 3.28297i | −0.181035 | − | 0.131529i | ||||
\(624\) | −5.19271 | + | 3.77273i | −0.207875 | + | 0.151030i | ||||
\(625\) | −7.92400 | + | 24.3876i | −0.316960 | + | 0.975503i | ||||
\(626\) | 17.3107 | 0.691873 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.31330 | 0.132215 | ||||||||
\(629\) | 14.5699 | − | 44.8417i | 0.580942 | − | 1.78796i | ||||
\(630\) | 9.93689 | − | 7.21957i | 0.395895 | − | 0.287635i | ||||
\(631\) | −0.840272 | − | 0.610493i | −0.0334507 | − | 0.0243034i | 0.570934 | − | 0.820996i | \(-0.306581\pi\) |
−0.604385 | + | 0.796692i | \(0.706581\pi\) | |||||||
\(632\) | −3.35350 | − | 10.3210i | −0.133395 | − | 0.410548i | ||||
\(633\) | 1.24760 | + | 3.83971i | 0.0495876 | + | 0.152615i | ||||
\(634\) | −13.0899 | − | 9.51035i | −0.519865 | − | 0.377704i | ||||
\(635\) | −55.9581 | + | 40.6559i | −2.22063 | + | 1.61338i | ||||
\(636\) | −0.0362225 | + | 0.111481i | −0.00143631 | + | 0.00442052i | ||||
\(637\) | −4.77801 | −0.189312 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 43.4787 | 1.71999 | ||||||||
\(640\) | −9.67681 | + | 29.7821i | −0.382509 | + | 1.17724i | ||||
\(641\) | −27.2164 | + | 19.7739i | −1.07498 | + | 0.781020i | −0.976801 | − | 0.214148i | \(-0.931302\pi\) |
−0.0981811 | + | 0.995169i | \(0.531302\pi\) | |||||||
\(642\) | 5.61777 | + | 4.08155i | 0.221716 | + | 0.161086i | ||||
\(643\) | −6.49905 | − | 20.0020i | −0.256298 | − | 0.788803i | −0.993571 | − | 0.113209i | \(-0.963887\pi\) |
0.737274 | − | 0.675594i | \(-0.236113\pi\) | |||||||
\(644\) | 0.224549 | + | 0.691091i | 0.00884848 | + | 0.0272328i | ||||
\(645\) | −3.95445 | − | 2.87308i | −0.155706 | − | 0.113127i | ||||
\(646\) | 36.9387 | − | 26.8375i | 1.45333 | − | 1.05591i | ||||
\(647\) | 7.79650 | − | 23.9952i | 0.306512 | − | 0.943347i | −0.672597 | − | 0.740009i | \(-0.734821\pi\) |
0.979109 | − | 0.203338i | \(-0.0651789\pi\) | |||||||
\(648\) | 22.8566 | 0.897892 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 31.7101 | 1.24377 | ||||||||
\(651\) | 0.408306 | − | 1.25664i | 0.0160028 | − | 0.0492515i | ||||
\(652\) | −0.113277 | + | 0.0823003i | −0.00443626 | + | 0.00322313i | ||||
\(653\) | −16.6971 | − | 12.1311i | −0.653408 | − | 0.474729i | 0.211023 | − | 0.977481i | \(-0.432321\pi\) |
−0.864430 | + | 0.502753i | \(0.832321\pi\) | |||||||
\(654\) | 2.38397 | + | 7.33711i | 0.0932206 | + | 0.286904i | ||||
\(655\) | 14.5699 | + | 44.8417i | 0.569295 | + | 1.75211i | ||||
\(656\) | −9.63769 | − | 7.00219i | −0.376289 | − | 0.273390i | ||||
\(657\) | −7.47584 | + | 5.43152i | −0.291660 | + | 0.211904i | ||||
\(658\) | −0.327768 | + | 1.00877i | −0.0127777 | + | 0.0393258i | ||||
\(659\) | −18.5067 | −0.720920 | −0.360460 | − | 0.932775i | \(-0.617380\pi\) | ||||
−0.360460 | + | 0.932775i | \(0.617380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8001 | 0.653446 | 0.326723 | − | 0.945120i | \(-0.394056\pi\) | ||||
0.326723 | + | 0.945120i | \(0.394056\pi\) | |||||||
\(662\) | 5.00775 | − | 15.4123i | 0.194632 | − | 0.599014i | ||||
\(663\) | −6.71043 | + | 4.87541i | −0.260612 | + | 0.189345i | ||||
\(664\) | −3.67500 | − | 2.67004i | −0.142618 | − | 0.103618i | ||||
\(665\) | 6.80414 | + | 20.9410i | 0.263853 | + | 0.812057i | ||||
\(666\) | −11.9231 | − | 36.6956i | −0.462011 | − | 1.42192i | ||||
\(667\) | −29.1548 | − | 21.1822i | −1.12888 | − | 0.820178i | ||||
\(668\) | 0.0646434 | − | 0.0469662i | 0.00250113 | − | 0.00181717i | ||||
\(669\) | 3.14826 | − | 9.68934i | 0.121719 | − | 0.374612i | ||||
\(670\) | 28.2427 | 1.09111 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.289930 | 0.0111843 | ||||||||
\(673\) | 5.42511 | − | 16.6968i | 0.209123 | − | 0.643613i | −0.790396 | − | 0.612596i | \(-0.790125\pi\) |
0.999519 | − | 0.0310171i | \(-0.00987464\pi\) | |||||||
\(674\) | 1.09267 | − | 0.793869i | 0.0420879 | − | 0.0305787i | ||||
\(675\) | 8.39646 | + | 6.10039i | 0.323180 | + | 0.234804i | ||||
\(676\) | −0.429300 | − | 1.32125i | −0.0165115 | − | 0.0508173i | ||||
\(677\) | −1.12708 | − | 3.46881i | −0.0433173 | − | 0.133317i | 0.927059 | − | 0.374916i | \(-0.122328\pi\) |
−0.970376 | + | 0.241599i | \(0.922328\pi\) | |||||||
\(678\) | 1.65584 | + | 1.20304i | 0.0635921 | + | 0.0462024i | ||||
\(679\) | 4.97599 | − | 3.61527i | 0.190961 | − | 0.138741i | ||||
\(680\) | −13.5403 | + | 41.6728i | −0.519248 | + | 1.59808i | ||||
\(681\) | −8.35994 | −0.320354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.4720 | 1.05119 | 0.525593 | − | 0.850736i | \(-0.323844\pi\) | ||||
0.525593 | + | 0.850736i | \(0.323844\pi\) | |||||||
\(684\) | −0.877991 | + | 2.70218i | −0.0335708 | + | 0.103320i | ||||
\(685\) | 27.1862 | − | 19.7519i | 1.03873 | − | 0.754682i | ||||
\(686\) | −1.10296 | − | 0.801344i | −0.0421110 | − | 0.0305955i | ||||
\(687\) | 1.50718 | + | 4.63861i | 0.0575023 | + | 0.176974i | ||||
\(688\) | −4.89314 | − | 15.0595i | −0.186549 | − | 0.574140i | ||||
\(689\) | 8.82365 | + | 6.41075i | 0.336154 | + | 0.244230i | ||||
\(690\) | 6.47214 | − | 4.70228i | 0.246390 | − | 0.179013i | ||||
\(691\) | −1.84071 | + | 5.66512i | −0.0700239 | + | 0.215511i | −0.979944 | − | 0.199271i | \(-0.936142\pi\) |
0.909920 | + | 0.414783i | \(0.136142\pi\) | |||||||
\(692\) | 2.43673 | 0.0926304 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.7080 | 0.786065 | ||||||||
\(695\) | 3.98260 | − | 12.2572i | 0.151069 | − | 0.464942i | ||||
\(696\) | −6.01476 | + | 4.36998i | −0.227989 | + | 0.165644i | ||||
\(697\) | −12.4546 | − | 9.04878i | −0.471751 | − | 0.342747i | ||||
\(698\) | 12.5137 | + | 38.5134i | 0.473652 | + | 1.45775i | ||||
\(699\) | −0.397155 | − | 1.22232i | −0.0150218 | − | 0.0462323i | ||||
\(700\) | −0.556622 | − | 0.404410i | −0.0210384 | − | 0.0152853i | ||||
\(701\) | −5.96186 | + | 4.33155i | −0.225176 | + | 0.163600i | −0.694654 | − | 0.719344i | \(-0.744442\pi\) |
0.469477 | + | 0.882945i | \(0.344442\pi\) | |||||||
\(702\) | −4.29159 | + | 13.2082i | −0.161976 | + | 0.498510i | ||||
\(703\) | 69.1680 | 2.60872 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.887968 | −0.0334428 | ||||||||
\(706\) | 2.82940 | − | 8.70799i | 0.106486 | − | 0.327730i | ||||
\(707\) | −8.73469 | + | 6.34612i | −0.328502 | + | 0.238670i | ||||
\(708\) | −0.0150942 | − | 0.0109666i | −0.000567273 | − | 0.000412148i | ||||
\(709\) | −10.7278 | − | 33.0169i | −0.402892 | − | 1.23998i | −0.922642 | − | 0.385657i | \(-0.873975\pi\) |
0.519750 | − | 0.854318i | \(-0.326025\pi\) | |||||||
\(710\) | 20.0630 | + | 61.7476i | 0.752952 | + | 2.31735i | ||||
\(711\) | −8.62515 | − | 6.26654i | −0.323468 | − | 0.235013i | ||||
\(712\) | 13.1914 | − | 9.58412i | 0.494369 | − | 0.359180i | ||||
\(713\) | −5.77780 | + | 17.7822i | −0.216380 | + | 0.665950i | ||||
\(714\) | −2.36672 | −0.0885722 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.60011 | −0.0597989 | ||||||||
\(717\) | 2.47214 | − | 7.60845i | 0.0923236 | − | 0.284143i | ||||
\(718\) | 19.5620 | − | 14.2126i | 0.730048 | − | 0.530411i | ||||
\(719\) | 3.28623 | + | 2.38758i | 0.122556 | + | 0.0890418i | 0.647375 | − | 0.762172i | \(-0.275867\pi\) |
−0.524819 | + | 0.851214i | \(0.675867\pi\) | |||||||
\(720\) | 10.2936 | + | 31.6803i | 0.383618 | + | 1.18066i | ||||
\(721\) | 4.09159 | + | 12.5926i | 0.152379 | + | 0.468973i | ||||
\(722\) | 33.2328 | + | 24.1451i | 1.23680 | + | 0.898586i | ||||
\(723\) | 0.0926983 | − | 0.0673493i | 0.00344749 | − | 0.00250475i | ||||
\(724\) | −0.649771 | + | 1.99979i | −0.0241485 | + | 0.0743216i | ||||
\(725\) | 34.1214 | 1.26724 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5433 | −1.13279 | −0.566394 | − | 0.824135i | \(-0.691662\pi\) | ||||
−0.566394 | + | 0.824135i | \(0.691662\pi\) | |||||||
\(728\) | 4.31037 | − | 13.2660i | 0.159753 | − | 0.491669i | ||||
\(729\) | 16.2861 | − | 11.8325i | 0.603188 | − | 0.438242i | ||||
\(730\) | −11.1634 | − | 8.11069i | −0.413176 | − | 0.300190i | ||||
\(731\) | −6.32330 | − | 19.4611i | −0.233876 | − | 0.719796i | ||||
\(732\) | −0.0511280 | − | 0.157356i | −0.00188975 | − | 0.00581604i | ||||
\(733\) | 24.9452 | + | 18.1238i | 0.921372 | + | 0.669416i | 0.943865 | − | 0.330331i | \(-0.107160\pi\) |
−0.0224928 | + | 0.999747i | \(0.507160\pi\) | |||||||
\(734\) | −8.93318 | + | 6.49034i | −0.329730 | + | 0.239563i | ||||
\(735\) | 0.352692 | − | 1.08548i | 0.0130092 | − | 0.0400384i | ||||
\(736\) | −4.10270 | −0.151228 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.5980 | −0.463740 | ||||||||
\(739\) | 6.86761 | − | 21.1363i | 0.252629 | − | 0.777513i | −0.741658 | − | 0.670778i | \(-0.765960\pi\) |
0.994288 | − | 0.106735i | \(-0.0340396\pi\) | |||||||
\(740\) | −3.54449 | + | 2.57522i | −0.130298 | + | 0.0946671i | ||||
\(741\) | −9.84419 | − | 7.15222i | −0.361635 | − | 0.262744i | ||||
\(742\) | 0.961671 | + | 2.95972i | 0.0353040 | + | 0.108655i | ||||
\(743\) | −9.62568 | − | 29.6248i | −0.353132 | − | 1.08683i | −0.957085 | − | 0.289808i | \(-0.906409\pi\) |
0.603953 | − | 0.797020i | \(-0.293591\pi\) | |||||||
\(744\) | 3.12066 | + | 2.26729i | 0.114409 | + | 0.0831229i | ||||
\(745\) | −35.6269 | + | 25.8845i | −1.30527 | + | 0.948334i | ||||
\(746\) | −0.238175 | + | 0.733027i | −0.00872020 | + | 0.0268380i | ||||
\(747\) | −4.46264 | −0.163280 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0187 | −0.512231 | ||||||||
\(750\) | 0.0634738 | − | 0.195352i | 0.00231774 | − | 0.00713326i | ||||
\(751\) | −9.69959 | + | 7.04716i | −0.353943 | + | 0.257155i | −0.750521 | − | 0.660846i | \(-0.770198\pi\) |
0.396578 | + | 0.918001i | \(0.370198\pi\) | |||||||
\(752\) | −2.32719 | − | 1.69080i | −0.0848640 | − | 0.0616573i | ||||
\(753\) | 2.09347 | + | 6.44305i | 0.0762904 | + | 0.234798i | ||||
\(754\) | 14.1093 | + | 43.4240i | 0.513831 | + | 1.58141i | ||||
\(755\) | 17.3561 | + | 12.6099i | 0.631653 | + | 0.458923i | ||||
\(756\) | 0.243781 | − | 0.177117i | 0.00886622 | − | 0.00644169i | ||||
\(757\) | −3.53927 | + | 10.8927i | −0.128637 | + | 0.395904i | −0.994546 | − | 0.104297i | \(-0.966741\pi\) |
0.865909 | + | 0.500201i | \(0.166741\pi\) | |||||||
\(758\) | 30.7240 | 1.11595 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −64.2800 | −2.33168 | ||||||||
\(761\) | 2.43816 | − | 7.50387i | 0.0883831 | − | 0.272015i | −0.897090 | − | 0.441848i | \(-0.854323\pi\) |
0.985473 | + | 0.169833i | \(0.0543229\pi\) | |||||||
\(762\) | 8.82365 | − | 6.41075i | 0.319647 | − | 0.232237i | ||||
\(763\) | −12.6002 | − | 9.15456i | −0.456157 | − | 0.331417i | ||||
\(764\) | −0.168121 | − | 0.517422i | −0.00608239 | − | 0.0187197i | ||||
\(765\) | 13.3021 | + | 40.9398i | 0.480940 | + | 1.48018i | ||||
\(766\) | 23.5937 | + | 17.1418i | 0.852474 | + | 0.619359i | ||||
\(767\) | −1.40444 | + | 1.02039i | −0.0507114 | + | 0.0368440i | ||||
\(768\) | −0.378896 | + | 1.16612i | −0.0136722 | + | 0.0420788i | ||||
\(769\) | −48.8153 | −1.76033 | −0.880163 | − | 0.474672i | \(-0.842567\pi\) | ||||
−0.880163 | + | 0.474672i | \(0.842567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.10525 | −0.111833 | ||||||||
\(772\) | 0.111227 | − | 0.342322i | 0.00400316 | − | 0.0123204i | ||||
\(773\) | 2.58568 | − | 1.87861i | 0.0930005 | − | 0.0675688i | −0.540313 | − | 0.841464i | \(-0.681694\pi\) |
0.633314 | + | 0.773895i | \(0.281694\pi\) | |||||||
\(774\) | −13.5472 | − | 9.84265i | −0.486946 | − | 0.353787i | ||||
\(775\) | −5.47062 | − | 16.8368i | −0.196510 | − | 0.604797i | ||||
\(776\) | 5.54868 | + | 17.0771i | 0.199186 | + | 0.613032i | ||||
\(777\) | −2.90059 | − | 2.10740i | −0.104058 | − | 0.0756025i | ||||
\(778\) | 11.7781 | − | 8.55731i | 0.422266 | − | 0.306794i | ||||
\(779\) | 6.97884 | − | 21.4787i | 0.250043 | − | 0.769553i | ||||
\(780\) | 0.770750 | 0.0275973 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 33.4906 | 1.19762 | ||||||||
\(783\) | −4.61793 | + | 14.2125i | −0.165031 | + | 0.507914i | ||||
\(784\) | 2.99122 | − | 2.17325i | 0.106829 | − | 0.0776160i | ||||
\(785\) | 59.5771 | + | 43.2853i | 2.12640 | + | 1.54492i | ||||
\(786\) | −2.29743 | − | 7.07078i | −0.0819468 | − | 0.252206i | ||||
\(787\) | −13.1274 | − | 40.4021i | −0.467943 | − | 1.44018i | −0.855243 | − | 0.518226i | \(-0.826592\pi\) |
0.387301 | − | 0.921953i | \(-0.373408\pi\) | |||||||
\(788\) | −1.20594 | − | 0.876169i | −0.0429599 | − | 0.0312122i | ||||
\(789\) | −4.70302 | + | 3.41694i | −0.167432 | + | 0.121646i | ||||
\(790\) | 4.91958 | − | 15.1409i | 0.175031 | − | 0.538689i | ||||
\(791\) | −4.13201 | −0.146917 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.3947 | −0.546682 | ||||||||
\(794\) | 10.0756 | − | 31.0095i | 0.357569 | − | 1.10049i | ||||
\(795\) | −2.10773 | + | 1.53135i | −0.0747534 | + | 0.0543116i | ||||
\(796\) | 1.33606 | + | 0.970704i | 0.0473554 | + | 0.0344057i | ||||
\(797\) | −8.91782 | − | 27.4462i | −0.315885 | − | 0.972195i | −0.975389 | − | 0.220493i | \(-0.929233\pi\) |
0.659503 | − | 0.751702i | \(-0.270767\pi\) | |||||||
\(798\) | −1.07290 | − | 3.30204i | −0.0379802 | − | 0.116891i | ||||
\(799\) | −3.00738 | − | 2.18499i | −0.106394 | − | 0.0772994i | ||||
\(800\) | 3.14269 | − | 2.28330i | 0.111111 | − | 0.0807268i | ||||
\(801\) | 4.95004 | − | 15.2346i | 0.174901 | − | 0.538290i | ||||
\(802\) | −15.8947 | −0.561260 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.338644 | 0.0119431 | ||||||||
\(805\) | −4.99083 | + | 15.3602i | −0.175904 | + | 0.541376i | ||||
\(806\) | 19.1650 | − | 13.9242i | 0.675059 | − | 0.490459i | ||||
\(807\) | −2.22101 | − | 1.61366i | −0.0781831 | − | 0.0568033i | ||||
\(808\) | −9.73996 | − | 29.9765i | −0.342651 | − | 1.05457i | ||||
\(809\) | −9.10157 | − | 28.0118i | −0.319994 | − | 0.984841i | −0.973650 | − | 0.228049i | \(-0.926765\pi\) |
0.653655 | − | 0.756792i | \(-0.273235\pi\) | |||||||
\(810\) | 27.1268 | + | 19.7088i | 0.953139 | + | 0.692496i | ||||
\(811\) | 2.00741 | − | 1.45847i | 0.0704898 | − | 0.0512138i | −0.551982 | − | 0.833856i | \(-0.686128\pi\) |
0.622472 | + | 0.782642i | \(0.286128\pi\) | |||||||
\(812\) | 0.306134 | − | 0.942184i | 0.0107432 | − | 0.0330642i | ||||
\(813\) | 5.09337 | 0.178632 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.11203 | −0.109010 | ||||||||
\(816\) | 1.98344 | − | 6.10440i | 0.0694343 | − | 0.213697i | ||||
\(817\) | 24.2856 | − | 17.6445i | 0.849646 | − | 0.617304i | ||||
\(818\) | 36.1938 | + | 26.2964i | 1.26549 | + | 0.919431i | ||||
\(819\) | −4.23455 | − | 13.0326i | −0.147967 | − | 0.455396i | ||||
\(820\) | 0.442053 | + | 1.36050i | 0.0154372 | + | 0.0475107i | ||||
\(821\) | 11.3413 | + | 8.23996i | 0.395815 | + | 0.287577i | 0.767834 | − | 0.640648i | \(-0.221334\pi\) |
−0.372019 | + | 0.928225i | \(0.621334\pi\) | |||||||
\(822\) | −4.28680 | + | 3.11454i | −0.149519 | + | 0.108632i | ||||
\(823\) | −13.2238 | + | 40.6988i | −0.460954 | + | 1.41867i | 0.403046 | + | 0.915180i | \(0.367952\pi\) |
−0.864000 | + | 0.503492i | \(0.832048\pi\) | |||||||
\(824\) | −38.6540 | −1.34658 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.495336 | −0.0172349 | ||||||||
\(827\) | 2.83388 | − | 8.72180i | 0.0985438 | − | 0.303287i | −0.889617 | − | 0.456707i | \(-0.849029\pi\) |
0.988161 | + | 0.153420i | \(0.0490288\pi\) | |||||||
\(828\) | −1.68603 | + | 1.22497i | −0.0585935 | + | 0.0425707i | ||||
\(829\) | −23.6211 | − | 17.1617i | −0.820395 | − | 0.596052i | 0.0964304 | − | 0.995340i | \(-0.469257\pi\) |
−0.916826 | + | 0.399288i | \(0.869257\pi\) | |||||||
\(830\) | −2.05926 | − | 6.33775i | −0.0714780 | − | 0.219987i | ||||
\(831\) | −0.675742 | − | 2.07972i | −0.0234412 | − | 0.0721447i | ||||
\(832\) | 32.7895 | + | 23.8229i | 1.13677 | + | 0.825912i | ||||
\(833\) | 3.86549 | − | 2.80844i | 0.133931 | − | 0.0973068i | ||||
\(834\) | −0.627989 | + | 1.93275i | −0.0217455 | + | 0.0669257i | ||||
\(835\) | 1.77594 | 0.0614588 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.75341 | 0.267997 | ||||||||
\(838\) | −4.54854 | + | 13.9990i | −0.157127 | + | 0.483587i | ||||
\(839\) | −15.9640 | + | 11.5985i | −0.551139 | + | 0.400426i | −0.828205 | − | 0.560425i | \(-0.810638\pi\) |
0.277066 | + | 0.960851i | \(0.410638\pi\) | |||||||
\(840\) | 2.69561 | + | 1.95847i | 0.0930073 | + | 0.0675737i | ||||
\(841\) | 6.22072 | + | 19.1454i | 0.214508 | + | 0.660187i | ||||
\(842\) | 0.485321 | + | 1.49366i | 0.0167253 | + | 0.0514751i | ||||
\(843\) | 6.07514 | + | 4.41385i | 0.209239 | + | 0.152021i | ||||
\(844\) | 1.27059 | − | 0.923135i | 0.0437354 | − | 0.0317756i | ||||
\(845\) | 9.54162 | − | 29.3661i | 0.328242 | − | 1.01022i | ||||
\(846\) | −3.04202 | −0.104587 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.43984 | −0.289825 | ||||||||
\(849\) | 1.11331 | − | 3.42642i | 0.0382087 | − | 0.117594i | ||||
\(850\) | −25.6540 | + | 18.6387i | −0.879924 | + | 0.639303i | ||||
\(851\) | 41.0452 | + | 29.8211i | 1.40701 | + | 1.02225i | ||||
\(852\) | 0.240566 | + | 0.740385i | 0.00824164 | + | 0.0253652i | ||||
\(853\) | 8.76146 | + | 26.9650i | 0.299987 | + | 0.923264i | 0.981501 | + | 0.191459i | \(0.0613219\pi\) |
−0.681514 | + | 0.731805i | \(0.738678\pi\) | |||||||
\(854\) | −3.55371 | − | 2.58192i | −0.121606 | − | 0.0883516i | ||||
\(855\) | −51.0889 | + | 37.1183i | −1.74720 | + | 1.26942i | ||||
\(856\) | 12.6466 | − | 38.9223i | 0.432252 | − | 1.33034i | ||||
\(857\) | −13.2033 | −0.451017 | −0.225509 | − | 0.974241i | \(-0.572404\pi\) | ||||
−0.225509 | + | 0.974241i | \(0.572404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.8260 | −0.710573 | −0.355286 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355286 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(860\) | −0.587577 | + | 1.80838i | −0.0200362 | + | 0.0616651i | ||||
\(861\) | −0.947068 | + | 0.688085i | −0.0322760 | + | 0.0234499i | ||||
\(862\) | −35.2505 | − | 25.6110i | −1.20064 | − | 0.872314i | ||||
\(863\) | 10.7983 | + | 33.2337i | 0.367577 | + | 1.13129i | 0.948351 | + | 0.317222i | \(0.102750\pi\) |
−0.580774 | + | 0.814065i | \(0.697250\pi\) | |||||||
\(864\) | 0.525733 | + | 1.61804i | 0.0178858 | + | 0.0550468i | ||||
\(865\) | 43.8153 | + | 31.8337i | 1.48976 | + | 1.08238i | ||||
\(866\) | −4.88977 | + | 3.55263i | −0.166161 | + | 0.120723i | ||||
\(867\) | 0.654489 | − | 2.01431i | 0.0222276 | − | 0.0684096i | ||||
\(868\) | −0.513993 | −0.0174461 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.9066 | −0.369769 | ||||||||
\(871\) | 9.73690 | − | 29.9671i | 0.329922 | − | 1.01540i | ||||
\(872\) | 36.7842 | − | 26.7253i | 1.24567 | − | 0.905034i | ||||
\(873\) | 14.2711 | + | 10.3686i | 0.483004 | + | 0.350923i | ||||
\(874\) | 15.1822 | + | 46.7261i | 0.513546 | + | 1.58053i | ||||
\(875\) | 0.128143 | + | 0.394384i | 0.00433203 | + | 0.0133326i | ||||
\(876\) | −0.133855 | − | 0.0972513i | −0.00452254 | − | 0.00328582i | ||||
\(877\) | −21.4238 | + | 15.5653i | −0.723431 | + | 0.525603i | −0.887479 | − | 0.460849i | \(-0.847545\pi\) |
0.164048 | + | 0.986452i | \(0.447545\pi\) | |||||||
\(878\) | 11.5737 | − | 35.6202i | 0.390594 | − | 1.20212i | ||||
\(879\) | −9.73599 | −0.328387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.2627 | 0.581595 | 0.290798 | − | 0.956785i | \(-0.406079\pi\) | ||||
0.290798 | + | 0.956785i | \(0.406079\pi\) | |||||||
\(882\) | 1.20826 | − | 3.71865i | 0.0406843 | − | 0.125213i | ||||
\(883\) | 36.0843 | − | 26.2168i | 1.21433 | − | 0.882265i | 0.218717 | − | 0.975788i | \(-0.429813\pi\) |
0.995617 | + | 0.0935234i | \(0.0298130\pi\) | |||||||
\(884\) | 2.61038 | + | 1.89656i | 0.0877967 | + | 0.0637881i | ||||
\(885\) | −0.128143 | − | 0.394384i | −0.00430748 | − | 0.0132571i | ||||
\(886\) | 3.28217 | + | 10.1015i | 0.110267 | + | 0.339366i | ||||
\(887\) | 24.9092 | + | 18.0976i | 0.836368 | + | 0.607657i | 0.921354 | − | 0.388726i | \(-0.127085\pi\) |
−0.0849861 | + | 0.996382i | \(0.527085\pi\) | |||||||
\(888\) | 8.46781 | − | 6.15222i | 0.284161 | − | 0.206455i | ||||
\(889\) | −6.80414 | + | 20.9410i | −0.228204 | + | 0.702338i | ||||
\(890\) | 23.9201 | 0.801803 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.96316 | −0.132697 | ||||||||
\(893\) | 1.68517 | − | 5.18641i | 0.0563919 | − | 0.173557i | ||||
\(894\) | 5.61777 | − | 4.08155i | 0.187886 | − | 0.136507i | ||||
\(895\) | −28.7719 | − | 20.9040i | −0.961739 | − | 0.698744i | ||||
\(896\) | 3.08047 | + | 9.48073i | 0.102911 | + | 0.316729i | ||||
\(897\) | −2.75806 | − | 8.48845i | −0.0920891 | − | 0.283421i | ||||
\(898\) | 22.6223 | + | 16.4361i | 0.754916 | + | 0.548478i | ||||
\(899\) | 20.6224 | − | 14.9830i | 0.687794 | − | 0.499712i | ||||
\(900\) | 0.609766 | − | 1.87667i | 0.0203255 | − | 0.0625556i | ||||
\(901\) | −10.9066 | −0.363352 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.55602 | −0.0517810 | ||||||||
\(904\) | 3.72760 | − | 11.4724i | 0.123978 | − | 0.381565i | ||||
\(905\) | −37.8091 | + | 27.4699i | −1.25682 | + | 0.913132i | ||||
\(906\) | −2.73676 | − | 1.98837i | −0.0909229 | − | 0.0660593i | ||||
\(907\) | 7.34845 | + | 22.6162i | 0.244001 | + | 0.750959i | 0.995799 | + | 0.0915649i | \(0.0291869\pi\) |
−0.751798 | + | 0.659394i | \(0.770813\pi\) | |||||||
\(908\) | 1.00494 | + | 3.09288i | 0.0333501 | + | 0.102641i | ||||
\(909\) | −25.0510 | − | 18.2006i | −0.830890 | − | 0.603677i | ||||
\(910\) | 16.5546 | − | 12.0276i | 0.548780 | − | 0.398712i | ||||
\(911\) | 15.1505 | − | 46.6284i | 0.501958 | − | 1.54487i | −0.303868 | − | 0.952714i | \(-0.598278\pi\) |
0.805825 | − | 0.592153i | \(-0.201722\pi\) | |||||||
\(912\) | 9.41600 | 0.311795 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11.6774 | 0.386253 | ||||||||
\(915\) | 1.13637 | − | 3.49739i | 0.0375673 | − | 0.115620i | ||||
\(916\) | 1.53495 | − | 1.11520i | 0.0507160 | − | 0.0368474i | ||||
\(917\) | 12.1428 | + | 8.82226i | 0.400991 | + | 0.291337i | ||||
\(918\) | −4.29159 | − | 13.2082i | −0.141644 | − | 0.435934i | ||||
\(919\) | 12.3607 | + | 38.0423i | 0.407741 | + | 1.25490i | 0.918585 | + | 0.395225i | \(0.129333\pi\) |
−0.510843 | + | 0.859674i | \(0.670667\pi\) | |||||||
\(920\) | −38.1446 | − | 27.7137i | −1.25759 | − | 0.913693i | ||||
\(921\) | −3.49708 | + | 2.54077i | −0.115233 | + | 0.0837214i | ||||
\(922\) | −4.07219 | + | 12.5329i | −0.134111 | + | 0.412750i | ||||
\(923\) | 72.4346 | 2.38421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.0373 | −1.57946 | ||||||||
\(926\) | −4.81284 | + | 14.8124i | −0.158160 | + | 0.486765i | ||||
\(927\) | −30.7217 | + | 22.3206i | −1.00903 | + | 0.733105i | ||||
\(928\) | 4.52510 | + | 3.28768i | 0.148544 | + | 0.107923i | ||||
\(929\) | −17.4854 | − | 53.8146i | −0.573678 | − | 1.76560i | −0.640637 | − | 0.767844i | \(-0.721330\pi\) |
0.0669595 | − | 0.997756i | \(-0.478670\pi\) | |||||||
\(930\) | 1.74864 | + | 5.38176i | 0.0573402 | + | 0.176475i | ||||
\(931\) | 5.67067 | + | 4.11998i | 0.185849 | + | 0.135027i | ||||
\(932\) | −0.404473 | + | 0.293867i | −0.0132490 | + | 0.00962594i | ||||
\(933\) | −2.38479 | + | 7.33961i | −0.0780744 | + | 0.240288i | ||||
\(934\) | −24.8408 | −0.812814 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 40.0046 | 1.30759 | ||||||||
\(937\) | −5.19622 | + | 15.9923i | −0.169753 | + | 0.522446i | −0.999355 | − | 0.0359089i | \(-0.988567\pi\) |
0.829602 | + | 0.558355i | \(0.188567\pi\) | |||||||
\(938\) | 7.27361 | − | 5.28458i | 0.237492 | − | 0.172548i | ||||
\(939\) | 3.73224 | + | 2.71163i | 0.121797 | + | 0.0884908i | ||||
\(940\) | 0.106742 | + | 0.328517i | 0.00348153 | + | 0.0107150i | ||||
\(941\) | 2.24325 | + | 6.90401i | 0.0731278 | + | 0.225064i | 0.980939 | − | 0.194314i | \(-0.0622481\pi\) |
−0.907812 | + | 0.419378i | \(0.862248\pi\) | |||||||
\(942\) | −9.39430 | − | 6.82536i | −0.306083 | − | 0.222382i | ||||
\(943\) | 13.4016 | − | 9.73687i | 0.436418 | − | 0.317076i | ||||
\(944\) | 0.415119 | − | 1.27760i | 0.0135110 | − | 0.0415825i | ||||
\(945\) | 6.69735 | 0.217865 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.6040 | −0.832017 | −0.416009 | − | 0.909361i | \(-0.636571\pi\) | ||||
−0.416009 | + | 0.909361i | \(0.636571\pi\) | |||||||
\(948\) | 0.0589883 | − | 0.181547i | 0.00191585 | − | 0.00589638i | ||||
\(949\) | −12.4546 | + | 9.04878i | −0.404293 | + | 0.293736i | ||||
\(950\) | −37.6343 | − | 27.3430i | −1.22102 | − | 0.887123i | ||||
\(951\) | −1.33247 | − | 4.10093i | −0.0432084 | − | 0.132982i | ||||
\(952\) | 4.31037 | + | 13.2660i | 0.139700 | + | 0.429952i | ||||
\(953\) | −5.78394 | − | 4.20228i | −0.187360 | − | 0.136125i | 0.490151 | − | 0.871637i | \(-0.336942\pi\) |
−0.677511 | + | 0.735512i | \(0.736942\pi\) | |||||||
\(954\) | −7.22071 | + | 5.24615i | −0.233779 | + | 0.169850i | ||||
\(955\) | 3.73665 | − | 11.5002i | 0.120915 | − | 0.372139i | ||||
\(956\) | −3.11203 | −0.100650 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.73344 | −0.152930 | ||||||||
\(959\) | 3.30566 | − | 10.1738i | 0.106745 | − | 0.328529i | ||||
\(960\) | −7.83251 | + | 5.69065i | −0.252793 | + | 0.183665i | ||||
\(961\) | 14.3800 | + | 10.4477i | 0.463870 | + | 0.337021i | ||||
\(962\) | −19.8636 | − | 61.1339i | −0.640429 | − | 1.97104i | ||||
\(963\) | −12.4242 | − | 38.2376i | −0.400363 | − | 1.23219i | ||||
\(964\) | −0.0360600 | − | 0.0261991i | −0.00116142 | − | 0.000843817i | ||||
\(965\) | 6.47214 | − | 4.70228i | 0.208345 | − | 0.151372i | ||||
\(966\) | 0.786970 | − | 2.42204i | 0.0253203 | − | 0.0779280i | ||||
\(967\) | 15.9600 | 0.513241 | 0.256620 | − | 0.966512i | \(-0.417391\pi\) | ||||
0.256620 | + | 0.966512i | \(0.417391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.1681 | 0.390895 | ||||||||
\(970\) | −8.13990 | + | 25.0520i | −0.261357 | + | 0.804373i | ||||
\(971\) | 24.6571 | − | 17.9145i | 0.791285 | − | 0.574903i | −0.117059 | − | 0.993125i | \(-0.537347\pi\) |
0.908345 | + | 0.418222i | \(0.137347\pi\) | |||||||
\(972\) | 1.05661 | + | 0.767670i | 0.0338907 | + | 0.0246230i | ||||
\(973\) | −1.26780 | − | 3.90190i | −0.0406440 | − | 0.125089i | ||||
\(974\) | 11.5692 | + | 35.6064i | 0.370702 | + | 1.14090i | ||||
\(975\) | 6.83681 | + | 4.96723i | 0.218953 | + | 0.159079i | ||||
\(976\) | 9.63769 | − | 7.00219i | 0.308495 | − | 0.224135i | ||||
\(977\) | 1.27686 | − | 3.92977i | 0.0408504 | − | 0.125725i | −0.928552 | − | 0.371204i | \(-0.878945\pi\) |
0.969402 | + | 0.245479i | \(0.0789452\pi\) | |||||||
\(978\) | 0.490715 | 0.0156913 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.443984 | −0.0141826 | ||||||||
\(981\) | 13.8032 | − | 42.4818i | 0.440702 | − | 1.35634i | ||||
\(982\) | −6.90893 | + | 5.01963i | −0.220473 | + | 0.160183i | ||||
\(983\) | 20.2453 | + | 14.7091i | 0.645726 | + | 0.469147i | 0.861812 | − | 0.507227i | \(-0.169329\pi\) |
−0.216087 | + | 0.976374i | \(0.569329\pi\) | |||||||
\(984\) | −1.05607 | − | 3.25024i | −0.0336662 | − | 0.103614i | ||||
\(985\) | −10.2379 | − | 31.5092i | −0.326208 | − | 1.00397i | ||||
\(986\) | −36.9387 | − | 26.8375i | −1.17637 | − | 0.854681i | ||||
\(987\) | −0.228687 | + | 0.166151i | −0.00727918 | + | 0.00528863i | ||||
\(988\) | −1.46271 | + | 4.50176i | −0.0465351 | + | 0.143220i | ||||
\(989\) | 22.0187 | 0.700153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5747 | −0.875938 | −0.437969 | − | 0.898990i | \(-0.644302\pi\) | ||||
−0.437969 | + | 0.898990i | \(0.644302\pi\) | |||||||
\(992\) | 0.896769 | − | 2.75997i | 0.0284724 | − | 0.0876292i | ||||
\(993\) | 3.49395 | − | 2.53850i | 0.110877 | − | 0.0805569i | ||||
\(994\) | 16.7208 | + | 12.1484i | 0.530352 | + | 0.385323i | ||||
\(995\) | 11.3426 | + | 34.9089i | 0.359584 | + | 1.10669i | ||||
\(996\) | −0.0246916 | − | 0.0759928i | −0.000782382 | − | 0.00240792i | ||||
\(997\) | −19.1613 | − | 13.9215i | −0.606844 | − | 0.440898i | 0.241458 | − | 0.970411i | \(-0.422374\pi\) |
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(998\) | −22.7959 | + | 16.5622i | −0.721593 | + | 0.524268i | ||||
\(999\) | 6.50130 | − | 20.0089i | 0.205692 | − | 0.633055i |
(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 | 847.2.f.u.372.2 | 12 | ||
11.2 | odd | 10 | 847.2.f.t.729.2 | 12 | |||
11.3 | even | 5 | inner | 847.2.f.u.323.2 | 12 | ||
11.4 | even | 5 | 847.2.a.i.1.2 | ✓ | 3 | ||
11.5 | even | 5 | inner | 847.2.f.u.148.2 | 12 | ||
11.6 | odd | 10 | 847.2.f.t.148.2 | 12 | |||
11.7 | odd | 10 | 847.2.a.j.1.2 | yes | 3 | ||
11.8 | odd | 10 | 847.2.f.t.323.2 | 12 | |||
11.9 | even | 5 | inner | 847.2.f.u.729.2 | 12 | ||
11.10 | odd | 2 | 847.2.f.t.372.2 | 12 | |||
33.26 | odd | 10 | 7623.2.a.ce.1.2 | 3 | |||
33.29 | even | 10 | 7623.2.a.bz.1.2 | 3 | |||
77.48 | odd | 10 | 5929.2.a.t.1.2 | 3 | |||
77.62 | even | 10 | 5929.2.a.y.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.2 | ✓ | 3 | 11.4 | even | 5 | ||
847.2.a.j.1.2 | yes | 3 | 11.7 | odd | 10 | ||
847.2.f.t.148.2 | 12 | 11.6 | odd | 10 | |||
847.2.f.t.323.2 | 12 | 11.8 | odd | 10 | |||
847.2.f.t.372.2 | 12 | 11.10 | odd | 2 | |||
847.2.f.t.729.2 | 12 | 11.2 | odd | 10 | |||
847.2.f.u.148.2 | 12 | 11.5 | even | 5 | inner | ||
847.2.f.u.323.2 | 12 | 11.3 | even | 5 | inner | ||
847.2.f.u.372.2 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.u.729.2 | 12 | 11.9 | even | 5 | inner | ||
5929.2.a.t.1.2 | 3 | 77.48 | odd | 10 | |||
5929.2.a.y.1.2 | 3 | 77.62 | even | 10 | |||
7623.2.a.bz.1.2 | 3 | 33.29 | even | 10 | |||
7623.2.a.ce.1.2 | 3 | 33.26 | odd | 10 |