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.t.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 | \(-0.739907\pi\) |
0.982233 | − | 0.187668i | \(-0.0600929\pi\) | |||||||
\(3\) | −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 | \(-0.669457\pi\) |
0.917076 | − | 0.398713i | \(-0.130543\pi\) | |||||||
\(14\) | −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 | \(0.0967203\pi\) |
−0.596090 | + | 0.802918i | \(0.703280\pi\) | |||||||
\(18\) | 3.16327 | + | 2.29825i | 0.745590 | + | 0.541703i | ||||
\(19\) | −5.67067 | + | 4.11998i | −1.30094 | + | 0.945188i | −0.999964 | − | 0.00844358i | \(-0.997312\pi\) |
−0.300976 | + | 0.953632i | \(0.597312\pi\) | |||||||
\(20\) | −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 | 0.972784 | − | 0.231715i | \(-0.0744337\pi\) |
0.0802326 | + | 0.996776i | \(0.474434\pi\) | |||||||
\(30\) | −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 | −0.772423 | − | 0.635109i | \(-0.780955\pi\) |
0.365333 | + | 0.930877i | \(0.380955\pi\) | |||||||
\(42\) | 0.153067 | − | 0.471092i | 0.0236188 | − | 0.0726911i | ||||
\(43\) | −4.28267 | −0.653101 | −0.326551 | − | 0.945180i | \(-0.605886\pi\) | ||||
−0.326551 | + | 0.945180i | \(0.605886\pi\) | |||||||
\(44\) | 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 | 0.866865 | − | 0.498543i | \(-0.166132\pi\) |
−0.994345 | + | 0.106200i | \(0.966132\pi\) | |||||||
\(62\) | 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 | 0.424700 | − | 0.905334i | \(-0.360380\pi\) |
−0.729785 | + | 0.683677i | \(0.760380\pi\) | |||||||
\(74\) | 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 | −0.865409 | − | 0.501066i | \(-0.832941\pi\) |
0.994650 | + | 0.103304i | \(0.0329414\pi\) | |||||||
\(80\) | 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 | 0.921193 | − | 0.389106i | \(-0.127216\pi\) |
−0.973972 | + | 0.226670i | \(0.927216\pi\) | |||||||
\(84\) | 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 | \(-0.719499\pi\) |
0.968191 | − | 0.250213i | \(-0.0805007\pi\) | |||||||
\(102\) | −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 | 0.115938 | − | 0.993256i | \(-0.463013\pi\) |
0.980470 | + | 0.196669i | \(0.0630126\pi\) | |||||||
\(108\) | 0.0931160 | − | 0.286582i | 0.00896009 | − | 0.0275763i | ||||
\(109\) | 15.5747 | 1.49178 | 0.745892 | − | 0.666067i | \(-0.232024\pi\) | ||||
0.745892 | + | 0.666067i | \(0.232024\pi\) | |||||||
\(110\) | 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 | \(-0.668521\pi\) |
−0.0987337 | − | 0.995114i | \(-0.531479\pi\) | |||||||
\(128\) | −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 | \(-0.727620\pi\) | ||||
−0.655686 | + | 0.755034i | \(0.727620\pi\) | |||||||
\(132\) | 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 | 0.719583 | − | 0.694406i | \(-0.244333\pi\) |
−0.438056 | + | 0.898948i | \(0.644333\pi\) | |||||||
\(140\) | 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 | \(-0.905303\pi\) |
0.601181 | − | 0.799113i | \(-0.294697\pi\) | |||||||
\(150\) | −1.95077 | − | 1.41732i | −0.159280 | − | 0.115724i | ||||
\(151\) | −5.52507 | + | 4.01420i | −0.449624 | + | 0.326671i | −0.789447 | − | 0.613819i | \(-0.789633\pi\) |
0.339824 | + | 0.940489i | \(0.389633\pi\) | |||||||
\(152\) | −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 | −0.957588 | − | 0.288140i | \(-0.906963\pi\) |
0.944070 | + | 0.329746i | \(0.106963\pi\) | |||||||
\(168\) | 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 | −0.974171 | − | 0.225813i | \(-0.927496\pi\) |
−0.0862745 | + | 0.996271i | \(0.527496\pi\) | |||||||
\(174\) | −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 | 0.975377 | − | 0.220545i | \(-0.0707836\pi\) |
−0.918729 | + | 0.394887i | \(0.870784\pi\) | |||||||
\(194\) | −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 | \(-0.377399\pi\) | ||||
0.375710 | + | 0.926737i | \(0.377399\pi\) | |||||||
\(198\) | 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 | \(0.224934\pi\) |
−0.996934 | + | 0.0782524i | \(0.975066\pi\) | |||||||
\(212\) | 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 | −0.238226 | − | 0.971210i | \(-0.576566\pi\) |
−0.997291 | + | 0.0735543i | \(0.976566\pi\) | |||||||
\(228\) | 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 | −0.908845 | − | 0.417135i | \(-0.863034\pi\) |
0.980456 | + | 0.196737i | \(0.0630344\pi\) | |||||||
\(234\) | 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 | 0.163478 | − | 0.986547i | \(-0.447729\pi\) |
0.988779 | + | 0.149383i | \(0.0477287\pi\) | |||||||
\(240\) | −1.30403 | + | 4.01338i | −0.0841746 | + | 0.259063i | ||||
\(241\) | 0.315366 | 0.0203145 | 0.0101573 | − | 0.999948i | \(-0.496767\pi\) | ||||
0.0101573 | + | 0.999948i | \(0.496767\pi\) | |||||||
\(242\) | 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 | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 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 | 0.876310 | − | 0.481747i | \(-0.159998\pi\) |
−0.187374 | + | 0.982289i | \(0.559998\pi\) | |||||||
\(272\) | 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 | −0.879506 | − | 0.475887i | \(-0.842127\pi\) |
0.991255 | + | 0.131960i | \(0.0421271\pi\) | |||||||
\(278\) | 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 | \(0.111440\pi\) |
−0.558335 | + | 0.829615i | \(0.688560\pi\) | |||||||
\(282\) | 0.311775 | + | 0.226518i | 0.0185659 | + | 0.0134889i | ||||
\(283\) | 8.02218 | − | 5.82845i | 0.476869 | − | 0.346466i | −0.323243 | − | 0.946316i | \(-0.604773\pi\) |
0.800112 | + | 0.599850i | \(0.204773\pi\) | |||||||
\(284\) | 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 | −0.267441 | − | 0.963574i | \(-0.586178\pi\) |
−0.999057 | + | 0.0434095i | \(0.986178\pi\) | |||||||
\(294\) | −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 | \(-0.610260\pi\) | ||||
−0.339507 | + | 0.940603i | \(0.610260\pi\) | |||||||
\(308\) | 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 | 0.609401 | − | 0.792862i | \(-0.291410\pi\) |
−0.565742 | + | 0.824582i | \(0.691410\pi\) | |||||||
\(338\) | −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 | \(0.0336698\pi\) |
−0.742437 | + | 0.669916i | \(0.766330\pi\) | |||||||
\(348\) | −0.291197 | − | 0.211567i | −0.0156098 | − | 0.0113412i | ||||
\(349\) | −24.0305 | + | 17.4592i | −1.28632 | + | 0.934567i | −0.999724 | − | 0.0234839i | \(-0.992524\pi\) |
−0.286597 | + | 0.958051i | \(0.592524\pi\) | |||||||
\(350\) | 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 | 0.898080 | − | 0.439833i | \(-0.144962\pi\) |
−0.140784 | + | 0.990040i | \(0.544962\pi\) | |||||||
\(360\) | −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 | \(-0.504659\pi\) | ||||
−0.0146362 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(374\) | 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 | \(0.401243\pi\) |
−0.806715 | + | 0.590941i | \(0.798757\pi\) | |||||||
\(410\) | −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 | \(-0.620391\pi\) |
0.844985 | − | 0.534791i | \(-0.179609\pi\) | |||||||
\(432\) | −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 | \(-0.272423\pi\) | ||||
0.655583 | + | 0.755123i | \(0.272423\pi\) | |||||||
\(440\) | 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 | 0.993683 | − | 0.112223i | \(-0.0357970\pi\) |
−0.869869 | + | 0.493282i | \(0.835797\pi\) | |||||||
\(458\) | −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 | \(-0.572269\pi\) | ||||
−0.225095 | + | 0.974337i | \(0.572269\pi\) | |||||||
\(462\) | 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 | 0.923549 | − | 0.383480i | \(-0.125275\pi\) |
−0.972571 | + | 0.232606i | \(0.925275\pi\) | |||||||
\(480\) | −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 | 0.467533 | − | 0.883976i | \(-0.345143\pi\) |
−0.696235 | + | 0.717814i | \(0.745143\pi\) | |||||||
\(492\) | 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 | −0.114962 | − | 0.993370i | \(-0.536675\pi\) |
0.909226 | + | 0.416304i | \(0.136675\pi\) | |||||||
\(504\) | 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 | \(0.0324032\pi\) |
−0.745097 | + | 0.666956i | \(0.767597\pi\) | |||||||
\(524\) | −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 | \(0.397900\pi\) |
−0.812877 | + | 0.582435i | \(0.802100\pi\) | |||||||
\(542\) | 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 | −0.843233 | − | 0.537548i | \(-0.819351\pi\) |
0.250665 | + | 0.968074i | \(0.419351\pi\) | |||||||
\(548\) | 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 | 0.922951 | − | 0.384918i | \(-0.125770\pi\) |
−0.0808715 | + | 0.996725i | \(0.525770\pi\) | |||||||
\(558\) | −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 | \(-0.797565\pi\) |
0.999971 | − | 0.00765038i | \(-0.00243521\pi\) | |||||||
\(564\) | −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 | −0.363321 | − | 0.931664i | \(-0.618357\pi\) |
0.773793 | + | 0.633439i | \(0.218357\pi\) | |||||||
\(570\) | 3.37033 | − | 10.3728i | 0.141168 | − | 0.434470i | ||||
\(571\) | −38.9439 | −1.62975 | −0.814877 | − | 0.579634i | \(-0.803195\pi\) | ||||
−0.814877 | + | 0.579634i | \(0.803195\pi\) | |||||||
\(572\) | 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 | \(-0.375330\pi\) | ||||
0.381726 | + | 0.924276i | \(0.375330\pi\) | |||||||
\(594\) | 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 | −0.0334095 | − | 0.999442i | \(-0.510637\pi\) |
−0.960850 | + | 0.277070i | \(0.910637\pi\) | |||||||
\(602\) | 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 | −0.828130 | − | 0.560536i | \(-0.810595\pi\) |
0.999446 | + | 0.0332795i | \(0.0105951\pi\) | |||||||
\(608\) | −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 | \(0.663406\pi\) |
−0.980226 | + | 0.197882i | \(0.936594\pi\) | |||||||
\(614\) | −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 | \(-0.382620\pi\) | ||||
0.360460 | + | 0.932775i | \(0.382620\pi\) | |||||||
\(660\) | 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 | \(0.209875\pi\) |
−0.999519 | + | 0.0310171i | \(0.990125\pi\) | |||||||
\(674\) | 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 | 0.970376 | − | 0.241599i | \(-0.0776717\pi\) |
−0.927059 | + | 0.374916i | \(0.877672\pi\) | |||||||
\(678\) | −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 | −0.469477 | − | 0.882945i | \(-0.655558\pi\) |
0.694654 | + | 0.719344i | \(0.255558\pi\) | |||||||
\(702\) | −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 | 0.0224928 | − | 0.999747i | \(-0.492840\pi\) |
−0.943865 | + | 0.330331i | \(0.892840\pi\) | |||||||
\(734\) | 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 | \(0.234040\pi\) |
−0.994288 | + | 0.106735i | \(0.965960\pi\) | |||||||
\(740\) | −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 | \(0.0935915\pi\) |
−0.603953 | + | 0.797020i | \(0.706409\pi\) | |||||||
\(744\) | −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 | −0.985473 | − | 0.169833i | \(-0.945677\pi\) |
0.897090 | + | 0.441848i | \(0.145677\pi\) | |||||||
\(762\) | 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 | \(-0.157433\pi\) | ||||
0.880163 | + | 0.474672i | \(0.157433\pi\) | |||||||
\(770\) | 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 | \(0.173408\pi\) |
−0.387301 | + | 0.921953i | \(0.626592\pi\) | |||||||
\(788\) | 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 | \(0.0732346\pi\) |
−0.653655 | + | 0.756792i | \(0.726765\pi\) | |||||||
\(810\) | −27.1268 | − | 19.7088i | −0.953139 | − | 0.692496i | ||||
\(811\) | −2.00741 | + | 1.45847i | −0.0704898 | + | 0.0512138i | −0.622472 | − | 0.782642i | \(-0.713872\pi\) |
0.551982 | + | 0.833856i | \(0.313872\pi\) | |||||||
\(812\) | 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 | 0.372019 | − | 0.928225i | \(-0.378666\pi\) |
−0.767834 | + | 0.640648i | \(0.778666\pi\) | |||||||
\(822\) | 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 | −0.988161 | − | 0.153420i | \(-0.950971\pi\) |
0.889617 | + | 0.456707i | \(0.150971\pi\) | |||||||
\(828\) | −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 | \(-0.938678\pi\) |
0.681514 | − | 0.731805i | \(-0.261322\pi\) | |||||||
\(854\) | 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 | \(-0.427596\pi\) | ||||
0.225509 | + | 0.974241i | \(0.427596\pi\) | |||||||
\(858\) | 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 | −0.164048 | − | 0.986452i | \(-0.552455\pi\) |
0.887479 | + | 0.460849i | \(0.152455\pi\) | |||||||
\(878\) | 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 | 0.0849861 | − | 0.996382i | \(-0.472915\pi\) |
−0.921354 | + | 0.388726i | \(0.872915\pi\) | |||||||
\(888\) | −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 | \(-0.870667\pi\) |
0.510843 | − | 0.859674i | \(-0.329333\pi\) | |||||||
\(920\) | 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 | −0.829602 | − | 0.558355i | \(-0.811433\pi\) |
0.999355 | + | 0.0359089i | \(0.0114326\pi\) | |||||||
\(938\) | 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 | 0.907812 | − | 0.419378i | \(-0.137752\pi\) |
−0.980939 | + | 0.194314i | \(0.937752\pi\) | |||||||
\(942\) | 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 | 0.677511 | − | 0.735512i | \(-0.263058\pi\) |
−0.490151 | + | 0.871637i | \(0.663058\pi\) | |||||||
\(954\) | 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 | \(-0.582609\pi\) | ||||
−0.256620 | + | 0.966512i | \(0.582609\pi\) | |||||||
\(968\) | 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 | 0.848301 | − | 0.529514i | \(-0.177626\pi\) |
−0.241458 | + | 0.970411i | \(0.577626\pi\) | |||||||
\(998\) | 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.t.372.2 | 12 | ||
11.2 | odd | 10 | 847.2.f.u.729.2 | 12 | |||
11.3 | even | 5 | inner | 847.2.f.t.323.2 | 12 | ||
11.4 | even | 5 | 847.2.a.j.1.2 | yes | 3 | ||
11.5 | even | 5 | inner | 847.2.f.t.148.2 | 12 | ||
11.6 | odd | 10 | 847.2.f.u.148.2 | 12 | |||
11.7 | odd | 10 | 847.2.a.i.1.2 | ✓ | 3 | ||
11.8 | odd | 10 | 847.2.f.u.323.2 | 12 | |||
11.9 | even | 5 | inner | 847.2.f.t.729.2 | 12 | ||
11.10 | odd | 2 | 847.2.f.u.372.2 | 12 | |||
33.26 | odd | 10 | 7623.2.a.bz.1.2 | 3 | |||
33.29 | even | 10 | 7623.2.a.ce.1.2 | 3 | |||
77.48 | odd | 10 | 5929.2.a.y.1.2 | 3 | |||
77.62 | even | 10 | 5929.2.a.t.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.2 | ✓ | 3 | 11.7 | odd | 10 | ||
847.2.a.j.1.2 | yes | 3 | 11.4 | even | 5 | ||
847.2.f.t.148.2 | 12 | 11.5 | even | 5 | inner | ||
847.2.f.t.323.2 | 12 | 11.3 | even | 5 | inner | ||
847.2.f.t.372.2 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.t.729.2 | 12 | 11.9 | even | 5 | inner | ||
847.2.f.u.148.2 | 12 | 11.6 | odd | 10 | |||
847.2.f.u.323.2 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.372.2 | 12 | 11.10 | odd | 2 | |||
847.2.f.u.729.2 | 12 | 11.2 | odd | 10 | |||
5929.2.a.t.1.2 | 3 | 77.62 | even | 10 | |||
5929.2.a.y.1.2 | 3 | 77.48 | odd | 10 | |||
7623.2.a.bz.1.2 | 3 | 33.26 | odd | 10 | |||
7623.2.a.ce.1.2 | 3 | 33.29 | even | 10 |