Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 295.2 | ||
Root | \(1.40126 - 1.01807i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.295 |
Dual form | 462.2.j.g.379.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | ||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0.330792 | + | 1.01807i | 0.147935 | + | 0.455296i | 0.997377 | − | 0.0723856i | \(-0.0230612\pi\) |
−0.849442 | + | 0.527682i | \(0.823061\pi\) | |||||||
\(6\) | −0.309017 | − | 0.951057i | −0.126156 | − | 0.388267i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | 0.809017 | − | 0.587785i | 0.286031 | − | 0.207813i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | −1.07047 | −0.338511 | ||||||||
\(11\) | −3.25134 | − | 0.654803i | −0.980317 | − | 0.197430i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.12387 | + | 6.53660i | −0.589055 | + | 1.81293i | −0.00671890 | + | 0.999977i | \(0.502139\pi\) |
−0.582336 | + | 0.812948i | \(0.697861\pi\) | |||||||
\(14\) | 0.809017 | − | 0.587785i | 0.216219 | − | 0.157092i | ||||
\(15\) | −0.866025 | − | 0.629204i | −0.223607 | − | 0.162460i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −2.18850 | − | 6.73551i | −0.530789 | − | 1.63360i | −0.752575 | − | 0.658506i | \(-0.771189\pi\) |
0.221786 | − | 0.975095i | \(-0.428811\pi\) | |||||||
\(18\) | 0.809017 | + | 0.587785i | 0.190687 | + | 0.138542i | ||||
\(19\) | −4.70378 | + | 3.41749i | −1.07912 | + | 0.784027i | −0.977529 | − | 0.210800i | \(-0.932393\pi\) |
−0.101591 | + | 0.994826i | \(0.532393\pi\) | |||||||
\(20\) | 0.330792 | − | 1.01807i | 0.0739674 | − | 0.227648i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.62747 | − | 2.88987i | 0.346979 | − | 0.616122i | ||||
\(23\) | −2.29850 | −0.479270 | −0.239635 | − | 0.970863i | \(-0.577028\pi\) | ||||
−0.239635 | + | 0.970863i | \(0.577028\pi\) | |||||||
\(24\) | −0.309017 | + | 0.951057i | −0.0630778 | + | 0.194134i | ||||
\(25\) | 3.11803 | − | 2.26538i | 0.623607 | − | 0.453077i | ||||
\(26\) | −5.56036 | − | 4.03984i | −1.09048 | − | 0.792277i | ||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | 0.309017 | + | 0.951057i | 0.0583987 | + | 0.179733i | ||||
\(29\) | −3.14275 | − | 2.28334i | −0.583594 | − | 0.424006i | 0.256424 | − | 0.966564i | \(-0.417456\pi\) |
−0.840018 | + | 0.542559i | \(0.817456\pi\) | |||||||
\(30\) | 0.866025 | − | 0.629204i | 0.158114 | − | 0.114876i | ||||
\(31\) | 1.10570 | − | 3.40299i | 0.198589 | − | 0.611196i | −0.801326 | − | 0.598227i | \(-0.795872\pi\) |
0.999916 | − | 0.0129682i | \(-0.00412803\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.01528 | − | 1.38135i | 0.524892 | − | 0.240461i | ||||
\(34\) | 7.08214 | 1.21458 | ||||||||
\(35\) | 0.330792 | − | 1.01807i | 0.0559141 | − | 0.172086i | ||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | −2.63799 | − | 1.91661i | −0.433683 | − | 0.315089i | 0.349437 | − | 0.936960i | \(-0.386373\pi\) |
−0.783120 | + | 0.621871i | \(0.786373\pi\) | |||||||
\(38\) | −1.79668 | − | 5.52962i | −0.291460 | − | 0.897023i | ||||
\(39\) | −2.12387 | − | 6.53660i | −0.340091 | − | 1.04669i | ||||
\(40\) | 0.866025 | + | 0.629204i | 0.136931 | + | 0.0994859i | ||||
\(41\) | 3.92055 | − | 2.84845i | 0.612287 | − | 0.444853i | −0.237932 | − | 0.971282i | \(-0.576469\pi\) |
0.850219 | + | 0.526429i | \(0.176469\pi\) | |||||||
\(42\) | −0.309017 | + | 0.951057i | −0.0476824 | + | 0.146751i | ||||
\(43\) | −5.20419 | −0.793631 | −0.396816 | − | 0.917898i | \(-0.629885\pi\) | ||||
−0.396816 | + | 0.917898i | \(0.629885\pi\) | |||||||
\(44\) | 2.24551 | + | 2.44084i | 0.338523 | + | 0.367970i | ||||
\(45\) | 1.07047 | 0.159576 | ||||||||
\(46\) | 0.710276 | − | 2.18600i | 0.104724 | − | 0.322309i | ||||
\(47\) | −8.22489 | + | 5.97573i | −1.19972 | + | 0.871650i | −0.994257 | − | 0.107015i | \(-0.965871\pi\) |
−0.205465 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(48\) | −0.809017 | − | 0.587785i | −0.116772 | − | 0.0848395i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 1.19098 | + | 3.66547i | 0.168430 | + | 0.518376i | ||||
\(51\) | 5.72957 | + | 4.16277i | 0.802300 | + | 0.582905i | ||||
\(52\) | 5.56036 | − | 4.03984i | 0.771083 | − | 0.560225i | ||||
\(53\) | −3.18336 | + | 9.79737i | −0.437268 | + | 1.34577i | 0.453476 | + | 0.891268i | \(0.350184\pi\) |
−0.890744 | + | 0.454505i | \(0.849816\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.408882 | − | 3.52671i | −0.0551336 | − | 0.475542i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.79668 | − | 5.52962i | 0.237976 | − | 0.732416i | ||||
\(58\) | 3.14275 | − | 2.28334i | 0.412663 | − | 0.299817i | ||||
\(59\) | −0.410699 | − | 0.298390i | −0.0534685 | − | 0.0388471i | 0.560730 | − | 0.827999i | \(-0.310521\pi\) |
−0.614198 | + | 0.789152i | \(0.710521\pi\) | |||||||
\(60\) | 0.330792 | + | 1.01807i | 0.0427051 | + | 0.131433i | ||||
\(61\) | 2.47019 | + | 7.60246i | 0.316275 | + | 0.973396i | 0.975226 | + | 0.221210i | \(0.0710005\pi\) |
−0.658951 | + | 0.752186i | \(0.728999\pi\) | |||||||
\(62\) | 2.89476 | + | 2.10317i | 0.367635 | + | 0.267102i | ||||
\(63\) | −0.809017 | + | 0.587785i | −0.101927 | + | 0.0740540i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −7.35730 | −0.912560 | ||||||||
\(66\) | 0.381966 | + | 3.29456i | 0.0470168 | + | 0.405532i | ||||
\(67\) | 3.79167 | 0.463226 | 0.231613 | − | 0.972808i | \(-0.425600\pi\) | ||||
0.231613 | + | 0.972808i | \(0.425600\pi\) | |||||||
\(68\) | −2.18850 | + | 6.73551i | −0.265395 | + | 0.816801i | ||||
\(69\) | 1.85953 | − | 1.35102i | 0.223861 | − | 0.162644i | ||||
\(70\) | 0.866025 | + | 0.629204i | 0.103510 | + | 0.0752043i | ||||
\(71\) | −4.39364 | − | 13.5222i | −0.521429 | − | 1.60479i | −0.771272 | − | 0.636506i | \(-0.780379\pi\) |
0.249843 | − | 0.968286i | \(-0.419621\pi\) | |||||||
\(72\) | −0.309017 | − | 0.951057i | −0.0364180 | − | 0.112083i | ||||
\(73\) | 10.4174 | + | 7.56869i | 1.21926 | + | 0.885848i | 0.996039 | − | 0.0889190i | \(-0.0283412\pi\) |
0.223226 | + | 0.974767i | \(0.428341\pi\) | |||||||
\(74\) | 2.63799 | − | 1.91661i | 0.306660 | − | 0.222802i | ||||
\(75\) | −1.19098 | + | 3.66547i | −0.137523 | + | 0.423252i | ||||
\(76\) | 5.81419 | 0.666933 | ||||||||
\(77\) | 2.24551 | + | 2.44084i | 0.255899 | + | 0.278159i | ||||
\(78\) | 6.87298 | 0.778212 | ||||||||
\(79\) | −2.77491 | + | 8.54029i | −0.312201 | + | 0.960857i | 0.664690 | + | 0.747120i | \(0.268564\pi\) |
−0.976891 | + | 0.213738i | \(0.931436\pi\) | |||||||
\(80\) | −0.866025 | + | 0.629204i | −0.0968246 | + | 0.0703472i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 1.49752 | + | 4.60888i | 0.165373 | + | 0.508966i | ||||
\(83\) | −0.553656 | − | 1.70398i | −0.0607717 | − | 0.187036i | 0.916062 | − | 0.401037i | \(-0.131350\pi\) |
−0.976833 | + | 0.214001i | \(0.931350\pi\) | |||||||
\(84\) | −0.809017 | − | 0.587785i | −0.0882710 | − | 0.0641326i | ||||
\(85\) | 6.13331 | − | 4.45611i | 0.665251 | − | 0.483333i | ||||
\(86\) | 1.60818 | − | 4.94948i | 0.173415 | − | 0.533716i | ||||
\(87\) | 3.88465 | 0.416478 | ||||||||
\(88\) | −3.01528 | + | 1.38135i | −0.321429 | + | 0.147252i | ||||
\(89\) | 6.23110 | 0.660496 | 0.330248 | − | 0.943894i | \(-0.392868\pi\) | ||||
0.330248 | + | 0.943894i | \(0.392868\pi\) | |||||||
\(90\) | −0.330792 | + | 1.01807i | −0.0348686 | + | 0.107314i | ||||
\(91\) | 5.56036 | − | 4.03984i | 0.582884 | − | 0.423490i | ||||
\(92\) | 1.85953 | + | 1.35102i | 0.193869 | + | 0.140854i | ||||
\(93\) | 1.10570 | + | 3.40299i | 0.114656 | + | 0.352874i | ||||
\(94\) | −3.14163 | − | 9.66893i | −0.324034 | − | 0.997274i | ||||
\(95\) | −5.03523 | − | 3.65831i | −0.516604 | − | 0.375335i | ||||
\(96\) | 0.809017 | − | 0.587785i | 0.0825700 | − | 0.0599906i | ||||
\(97\) | −5.17839 | + | 15.9375i | −0.525786 | + | 1.61820i | 0.236969 | + | 0.971517i | \(0.423846\pi\) |
−0.762756 | + | 0.646687i | \(0.776154\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −1.62747 | + | 2.88987i | −0.163567 | + | 0.290442i | ||||
\(100\) | −3.85410 | −0.385410 | ||||||||
\(101\) | −4.42096 | + | 13.6063i | −0.439902 | + | 1.35388i | 0.448077 | + | 0.893995i | \(0.352109\pi\) |
−0.887979 | + | 0.459885i | \(0.847891\pi\) | |||||||
\(102\) | −5.72957 | + | 4.16277i | −0.567312 | + | 0.412176i | ||||
\(103\) | 5.22849 | + | 3.79872i | 0.515179 | + | 0.374299i | 0.814785 | − | 0.579764i | \(-0.196855\pi\) |
−0.299606 | + | 0.954063i | \(0.596855\pi\) | |||||||
\(104\) | 2.12387 | + | 6.53660i | 0.208262 | + | 0.640966i | ||||
\(105\) | 0.330792 | + | 1.01807i | 0.0322820 | + | 0.0993538i | ||||
\(106\) | −8.33414 | − | 6.05511i | −0.809484 | − | 0.588124i | ||||
\(107\) | −5.38424 | + | 3.91188i | −0.520514 | + | 0.378176i | −0.816798 | − | 0.576924i | \(-0.804253\pi\) |
0.296283 | + | 0.955100i | \(0.404253\pi\) | |||||||
\(108\) | 0.309017 | − | 0.951057i | 0.0297352 | − | 0.0915155i | ||||
\(109\) | −13.4250 | −1.28588 | −0.642941 | − | 0.765915i | \(-0.722286\pi\) | ||||
−0.642941 | + | 0.765915i | \(0.722286\pi\) | |||||||
\(110\) | 3.48045 | + | 0.700944i | 0.331848 | + | 0.0668324i | ||||
\(111\) | 3.26074 | 0.309495 | ||||||||
\(112\) | 0.309017 | − | 0.951057i | 0.0291994 | − | 0.0898664i | ||||
\(113\) | 10.5186 | − | 7.64223i | 0.989509 | − | 0.718921i | 0.0296957 | − | 0.999559i | \(-0.490546\pi\) |
0.959814 | + | 0.280638i | \(0.0905462\pi\) | |||||||
\(114\) | 4.70378 | + | 3.41749i | 0.440549 | + | 0.320078i | ||||
\(115\) | −0.760326 | − | 2.34004i | −0.0709008 | − | 0.218210i | ||||
\(116\) | 1.20042 | + | 3.69452i | 0.111457 | + | 0.343028i | ||||
\(117\) | 5.56036 | + | 4.03984i | 0.514055 | + | 0.373483i | ||||
\(118\) | 0.410699 | − | 0.298390i | 0.0378079 | − | 0.0274691i | ||||
\(119\) | −2.18850 | + | 6.73551i | −0.200619 | + | 0.617443i | ||||
\(120\) | −1.07047 | −0.0977198 | ||||||||
\(121\) | 10.1425 | + | 4.25798i | 0.922042 | + | 0.387089i | ||||
\(122\) | −7.99370 | −0.723716 | ||||||||
\(123\) | −1.49752 | + | 4.60888i | −0.135027 | + | 0.415569i | ||||
\(124\) | −2.89476 | + | 2.10317i | −0.259957 | + | 0.188870i | ||||
\(125\) | 7.66788 | + | 5.57104i | 0.685836 | + | 0.498289i | ||||
\(126\) | −0.309017 | − | 0.951057i | −0.0275294 | − | 0.0847268i | ||||
\(127\) | 3.91968 | + | 12.0635i | 0.347816 | + | 1.07047i | 0.960059 | + | 0.279797i | \(0.0902672\pi\) |
−0.612244 | + | 0.790669i | \(0.709733\pi\) | |||||||
\(128\) | 0.809017 | + | 0.587785i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | 4.21028 | − | 3.05894i | 0.370694 | − | 0.269325i | ||||
\(130\) | 2.27353 | − | 6.99721i | 0.199402 | − | 0.613695i | ||||
\(131\) | 0.283254 | 0.0247480 | 0.0123740 | − | 0.999923i | \(-0.496061\pi\) | ||||
0.0123740 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(132\) | −3.25134 | − | 0.654803i | −0.282993 | − | 0.0569933i | ||||
\(133\) | 5.81419 | 0.504154 | ||||||||
\(134\) | −1.17169 | + | 3.60609i | −0.101219 | + | 0.311519i | ||||
\(135\) | −0.866025 | + | 0.629204i | −0.0745356 | + | 0.0541533i | ||||
\(136\) | −5.72957 | − | 4.16277i | −0.491306 | − | 0.356955i | ||||
\(137\) | 1.64564 | + | 5.06477i | 0.140597 | + | 0.432713i | 0.996419 | − | 0.0845584i | \(-0.0269479\pi\) |
−0.855822 | + | 0.517271i | \(0.826948\pi\) | |||||||
\(138\) | 0.710276 | + | 2.18600i | 0.0604627 | + | 0.186085i | ||||
\(139\) | −14.5449 | − | 10.5675i | −1.23368 | − | 0.896321i | −0.236520 | − | 0.971627i | \(-0.576007\pi\) |
−0.997161 | + | 0.0753053i | \(0.976007\pi\) | |||||||
\(140\) | −0.866025 | + | 0.629204i | −0.0731925 | + | 0.0531775i | ||||
\(141\) | 3.14163 | − | 9.66893i | 0.264573 | − | 0.814271i | ||||
\(142\) | 14.2181 | 1.19316 | ||||||||
\(143\) | 11.1856 | − | 19.8620i | 0.935387 | − | 1.66094i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.28501 | − | 3.95486i | 0.106715 | − | 0.328434i | ||||
\(146\) | −10.4174 | + | 7.56869i | −0.862150 | + | 0.626389i | ||||
\(147\) | −0.809017 | − | 0.587785i | −0.0667266 | − | 0.0484797i | ||||
\(148\) | 1.00762 | + | 3.10115i | 0.0828261 | + | 0.254913i | ||||
\(149\) | −3.23607 | − | 9.95959i | −0.265109 | − | 0.815922i | −0.991668 | − | 0.128818i | \(-0.958882\pi\) |
0.726559 | − | 0.687104i | \(-0.241118\pi\) | |||||||
\(150\) | −3.11803 | − | 2.26538i | −0.254586 | − | 0.184968i | ||||
\(151\) | −4.14784 | + | 3.01358i | −0.337547 | + | 0.245242i | −0.743626 | − | 0.668596i | \(-0.766896\pi\) |
0.406079 | + | 0.913838i | \(0.366896\pi\) | |||||||
\(152\) | −1.79668 | + | 5.52962i | −0.145730 | + | 0.448511i | ||||
\(153\) | −7.08214 | −0.572557 | ||||||||
\(154\) | −3.01528 | + | 1.38135i | −0.242978 | + | 0.111312i | ||||
\(155\) | 3.83026 | 0.307653 | ||||||||
\(156\) | −2.12387 | + | 6.53660i | −0.170046 | + | 0.523346i | ||||
\(157\) | 8.60503 | − | 6.25192i | 0.686756 | − | 0.498958i | −0.188836 | − | 0.982009i | \(-0.560471\pi\) |
0.875592 | + | 0.483051i | \(0.160471\pi\) | |||||||
\(158\) | −7.26480 | − | 5.27819i | −0.577957 | − | 0.419910i | ||||
\(159\) | −3.18336 | − | 9.79737i | −0.252457 | − | 0.776982i | ||||
\(160\) | −0.330792 | − | 1.01807i | −0.0261514 | − | 0.0804858i | ||||
\(161\) | 1.85953 | + | 1.35102i | 0.146551 | + | 0.106476i | ||||
\(162\) | 0.809017 | − | 0.587785i | 0.0635624 | − | 0.0461808i | ||||
\(163\) | 0.145898 | − | 0.449028i | 0.0114276 | − | 0.0351706i | −0.945180 | − | 0.326549i | \(-0.894114\pi\) |
0.956608 | + | 0.291379i | \(0.0941140\pi\) | |||||||
\(164\) | −4.84607 | −0.378414 | ||||||||
\(165\) | 2.40374 | + | 2.61283i | 0.187131 | + | 0.203409i | ||||
\(166\) | 1.79167 | 0.139061 | ||||||||
\(167\) | −6.55854 | + | 20.1851i | −0.507515 | + | 1.56197i | 0.288985 | + | 0.957334i | \(0.406682\pi\) |
−0.796501 | + | 0.604638i | \(0.793318\pi\) | |||||||
\(168\) | 0.809017 | − | 0.587785i | 0.0624170 | − | 0.0453486i | ||||
\(169\) | −27.6990 | − | 20.1245i | −2.13070 | − | 1.54804i | ||||
\(170\) | 2.34272 | + | 7.21014i | 0.179678 | + | 0.552992i | ||||
\(171\) | 1.79668 | + | 5.52962i | 0.137396 | + | 0.422861i | ||||
\(172\) | 4.21028 | + | 3.05894i | 0.321030 | + | 0.233242i | ||||
\(173\) | 14.4774 | − | 10.5184i | 1.10069 | − | 0.799700i | 0.119520 | − | 0.992832i | \(-0.461864\pi\) |
0.981173 | + | 0.193132i | \(0.0618645\pi\) | |||||||
\(174\) | −1.20042 | + | 3.69452i | −0.0910039 | + | 0.280081i | ||||
\(175\) | −3.85410 | −0.291343 | ||||||||
\(176\) | −0.381966 | − | 3.29456i | −0.0287918 | − | 0.248337i | ||||
\(177\) | 0.507652 | 0.0381575 | ||||||||
\(178\) | −1.92552 | + | 5.92613i | −0.144324 | + | 0.444182i | ||||
\(179\) | 10.3429 | − | 7.51457i | 0.773066 | − | 0.561665i | −0.129824 | − | 0.991537i | \(-0.541441\pi\) |
0.902890 | + | 0.429872i | \(0.141441\pi\) | |||||||
\(180\) | −0.866025 | − | 0.629204i | −0.0645497 | − | 0.0468981i | ||||
\(181\) | 0.785453 | + | 2.41738i | 0.0583823 | + | 0.179682i | 0.975995 | − | 0.217794i | \(-0.0698861\pi\) |
−0.917612 | + | 0.397476i | \(0.869886\pi\) | |||||||
\(182\) | 2.12387 | + | 6.53660i | 0.157432 | + | 0.484525i | ||||
\(183\) | −6.46704 | − | 4.69858i | −0.478058 | − | 0.347329i | ||||
\(184\) | −1.85953 | + | 1.35102i | −0.137086 | + | 0.0995988i | ||||
\(185\) | 1.07863 | − | 3.31967i | 0.0793022 | − | 0.244067i | ||||
\(186\) | −3.57812 | −0.262360 | ||||||||
\(187\) | 2.70514 | + | 23.3325i | 0.197819 | + | 1.70624i | ||||
\(188\) | 10.1665 | 0.741470 | ||||||||
\(189\) | 0.309017 | − | 0.951057i | 0.0224777 | − | 0.0691792i | ||||
\(190\) | 5.03523 | − | 3.65831i | 0.365294 | − | 0.265402i | ||||
\(191\) | −6.16138 | − | 4.47650i | −0.445822 | − | 0.323908i | 0.342122 | − | 0.939655i | \(-0.388854\pi\) |
−0.787944 | + | 0.615747i | \(0.788854\pi\) | |||||||
\(192\) | 0.309017 | + | 0.951057i | 0.0223014 | + | 0.0686366i | ||||
\(193\) | −4.15414 | − | 12.7851i | −0.299021 | − | 0.920293i | −0.981841 | − | 0.189706i | \(-0.939247\pi\) |
0.682820 | − | 0.730587i | \(-0.260753\pi\) | |||||||
\(194\) | −13.5572 | − | 9.84989i | −0.973351 | − | 0.707181i | ||||
\(195\) | 5.95218 | − | 4.32451i | 0.426244 | − | 0.309685i | ||||
\(196\) | 0.309017 | − | 0.951057i | 0.0220726 | − | 0.0679326i | ||||
\(197\) | −6.97391 | −0.496870 | −0.248435 | − | 0.968649i | \(-0.579916\pi\) | ||||
−0.248435 | + | 0.968649i | \(0.579916\pi\) | |||||||
\(198\) | −2.24551 | − | 2.44084i | −0.159581 | − | 0.173463i | ||||
\(199\) | 24.6592 | 1.74804 | 0.874021 | − | 0.485887i | \(-0.161503\pi\) | ||||
0.874021 | + | 0.485887i | \(0.161503\pi\) | |||||||
\(200\) | 1.19098 | − | 3.66547i | 0.0842152 | − | 0.259188i | ||||
\(201\) | −3.06753 | + | 2.22869i | −0.216367 | + | 0.157200i | ||||
\(202\) | −11.5742 | − | 8.40917i | −0.814360 | − | 0.591667i | ||||
\(203\) | 1.20042 | + | 3.69452i | 0.0842532 | + | 0.259305i | ||||
\(204\) | −2.18850 | − | 6.73551i | −0.153226 | − | 0.471580i | ||||
\(205\) | 4.19682 | + | 3.04917i | 0.293118 | + | 0.212963i | ||||
\(206\) | −5.22849 | + | 3.79872i | −0.364286 | + | 0.264669i | ||||
\(207\) | −0.710276 | + | 2.18600i | −0.0493676 | + | 0.151938i | ||||
\(208\) | −6.87298 | −0.476556 | ||||||||
\(209\) | 17.5314 | − | 8.03140i | 1.21267 | − | 0.555543i | ||||
\(210\) | −1.07047 | −0.0738692 | ||||||||
\(211\) | 6.73763 | − | 20.7363i | 0.463838 | − | 1.42755i | −0.396601 | − | 0.917991i | \(-0.629810\pi\) |
0.860438 | − | 0.509554i | \(-0.170190\pi\) | |||||||
\(212\) | 8.33414 | − | 6.05511i | 0.572391 | − | 0.415867i | ||||
\(213\) | 11.5027 | + | 8.35719i | 0.788151 | + | 0.572625i | ||||
\(214\) | −2.05660 | − | 6.32956i | −0.140586 | − | 0.432680i | ||||
\(215\) | −1.72150 | − | 5.29825i | −0.117406 | − | 0.361337i | ||||
\(216\) | 0.809017 | + | 0.587785i | 0.0550466 | + | 0.0399937i | ||||
\(217\) | −2.89476 | + | 2.10317i | −0.196509 | + | 0.142772i | ||||
\(218\) | 4.14856 | − | 12.7679i | 0.280976 | − | 0.864754i | ||||
\(219\) | −12.8766 | −0.870121 | ||||||||
\(220\) | −1.74216 | + | 3.09350i | −0.117456 | + | 0.208564i | ||||
\(221\) | 48.6754 | 3.27426 | ||||||||
\(222\) | −1.00762 | + | 3.10115i | −0.0676272 | + | 0.208135i | ||||
\(223\) | 6.81009 | − | 4.94782i | 0.456038 | − | 0.331331i | −0.335937 | − | 0.941884i | \(-0.609053\pi\) |
0.791975 | + | 0.610554i | \(0.209053\pi\) | |||||||
\(224\) | 0.809017 | + | 0.587785i | 0.0540547 | + | 0.0392731i | ||||
\(225\) | −1.19098 | − | 3.66547i | −0.0793989 | − | 0.244365i | ||||
\(226\) | 4.01776 | + | 12.3654i | 0.267257 | + | 0.822533i | ||||
\(227\) | −17.0949 | − | 12.4202i | −1.13463 | − | 0.824357i | −0.148268 | − | 0.988947i | \(-0.547370\pi\) |
−0.986362 | + | 0.164590i | \(0.947370\pi\) | |||||||
\(228\) | −4.70378 | + | 3.41749i | −0.311515 | + | 0.226329i | ||||
\(229\) | −1.91899 | + | 5.90604i | −0.126810 | + | 0.390282i | −0.994227 | − | 0.107301i | \(-0.965779\pi\) |
0.867416 | + | 0.497583i | \(0.165779\pi\) | |||||||
\(230\) | 2.46047 | 0.162238 | ||||||||
\(231\) | −3.25134 | − | 0.654803i | −0.213923 | − | 0.0430829i | ||||
\(232\) | −3.88465 | −0.255040 | ||||||||
\(233\) | −6.05759 | + | 18.6434i | −0.396846 | + | 1.22137i | 0.530668 | + | 0.847580i | \(0.321941\pi\) |
−0.927514 | + | 0.373787i | \(0.878059\pi\) | |||||||
\(234\) | −5.56036 | + | 4.03984i | −0.363492 | + | 0.264092i | ||||
\(235\) | −8.80446 | − | 6.39682i | −0.574340 | − | 0.417282i | ||||
\(236\) | 0.156873 | + | 0.482806i | 0.0102116 | + | 0.0314280i | ||||
\(237\) | −2.77491 | − | 8.54029i | −0.180250 | − | 0.554751i | ||||
\(238\) | −5.72957 | − | 4.16277i | −0.371393 | − | 0.269833i | ||||
\(239\) | −10.7383 | + | 7.80183i | −0.694603 | + | 0.504658i | −0.878170 | − | 0.478349i | \(-0.841235\pi\) |
0.183567 | + | 0.983007i | \(0.441235\pi\) | |||||||
\(240\) | 0.330792 | − | 1.01807i | 0.0213525 | − | 0.0657164i | ||||
\(241\) | −23.8051 | −1.53342 | −0.766710 | − | 0.641994i | \(-0.778108\pi\) | ||||
−0.766710 | + | 0.641994i | \(0.778108\pi\) | |||||||
\(242\) | −7.18377 | + | 8.33027i | −0.461790 | + | 0.535490i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.47019 | − | 7.60246i | 0.158138 | − | 0.486698i | ||||
\(245\) | −0.866025 | + | 0.629204i | −0.0553283 | + | 0.0401984i | ||||
\(246\) | −3.92055 | − | 2.84845i | −0.249965 | − | 0.181610i | ||||
\(247\) | −12.3486 | − | 38.0050i | −0.785721 | − | 2.41820i | ||||
\(248\) | −1.10570 | − | 3.40299i | −0.0702120 | − | 0.216090i | ||||
\(249\) | 1.44949 | + | 1.05312i | 0.0918578 | + | 0.0667386i | ||||
\(250\) | −7.66788 | + | 5.57104i | −0.484959 | + | 0.352343i | ||||
\(251\) | 0.0931899 | − | 0.286809i | 0.00588209 | − | 0.0181032i | −0.948072 | − | 0.318055i | \(-0.896970\pi\) |
0.953954 | + | 0.299951i | \(0.0969705\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 7.47321 | + | 1.50506i | 0.469837 | + | 0.0946226i | ||||
\(254\) | −12.6844 | −0.795887 | ||||||||
\(255\) | −2.34272 | + | 7.21014i | −0.146707 | + | 0.451516i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 10.5015 | + | 7.62981i | 0.655068 | + | 0.475935i | 0.864994 | − | 0.501783i | \(-0.167322\pi\) |
−0.209926 | + | 0.977717i | \(0.567322\pi\) | |||||||
\(258\) | 1.60818 | + | 4.94948i | 0.100121 | + | 0.308141i | ||||
\(259\) | 1.00762 | + | 3.10115i | 0.0626107 | + | 0.192696i | ||||
\(260\) | 5.95218 | + | 4.32451i | 0.369138 | + | 0.268195i | ||||
\(261\) | −3.14275 | + | 2.28334i | −0.194531 | + | 0.141335i | ||||
\(262\) | −0.0875302 | + | 0.269390i | −0.00540763 | + | 0.0166430i | ||||
\(263\) | −2.73287 | −0.168516 | −0.0842581 | − | 0.996444i | \(-0.526852\pi\) | ||||
−0.0842581 | + | 0.996444i | \(0.526852\pi\) | |||||||
\(264\) | 1.62747 | − | 2.88987i | 0.100164 | − | 0.177859i | ||||
\(265\) | −11.0275 | −0.677413 | ||||||||
\(266\) | −1.79668 | + | 5.52962i | −0.110162 | + | 0.339043i | ||||
\(267\) | −5.04107 | + | 3.66255i | −0.308508 | + | 0.224144i | ||||
\(268\) | −3.06753 | − | 2.22869i | −0.187379 | − | 0.136139i | ||||
\(269\) | −7.72212 | − | 23.7662i | −0.470826 | − | 1.44905i | −0.851505 | − | 0.524346i | \(-0.824310\pi\) |
0.380679 | − | 0.924707i | \(-0.375690\pi\) | |||||||
\(270\) | −0.330792 | − | 1.01807i | −0.0201314 | − | 0.0619580i | ||||
\(271\) | 9.51279 | + | 6.91145i | 0.577861 | + | 0.419841i | 0.837952 | − | 0.545743i | \(-0.183753\pi\) |
−0.260091 | + | 0.965584i | \(0.583753\pi\) | |||||||
\(272\) | 5.72957 | − | 4.16277i | 0.347406 | − | 0.252405i | ||||
\(273\) | −2.12387 | + | 6.53660i | −0.128542 | + | 0.395613i | ||||
\(274\) | −5.32542 | −0.321720 | ||||||||
\(275\) | −11.6212 | + | 5.32385i | −0.700783 | + | 0.321040i | ||||
\(276\) | −2.29850 | −0.138353 | ||||||||
\(277\) | 6.48406 | − | 19.9559i | 0.389589 | − | 1.19903i | −0.543506 | − | 0.839405i | \(-0.682904\pi\) |
0.933096 | − | 0.359628i | \(-0.117096\pi\) | |||||||
\(278\) | 14.5449 | − | 10.5675i | 0.872344 | − | 0.633795i | ||||
\(279\) | −2.89476 | − | 2.10317i | −0.173305 | − | 0.125913i | ||||
\(280\) | −0.330792 | − | 1.01807i | −0.0197686 | − | 0.0608416i | ||||
\(281\) | −3.63083 | − | 11.1745i | −0.216597 | − | 0.666617i | −0.999036 | − | 0.0438902i | \(-0.986025\pi\) |
0.782439 | − | 0.622727i | \(-0.213975\pi\) | |||||||
\(282\) | 8.22489 | + | 5.97573i | 0.489785 | + | 0.355849i | ||||
\(283\) | −11.2499 | + | 8.17356i | −0.668739 | + | 0.485868i | −0.869603 | − | 0.493752i | \(-0.835625\pi\) |
0.200864 | + | 0.979619i | \(0.435625\pi\) | |||||||
\(284\) | −4.39364 | + | 13.5222i | −0.260714 | + | 0.802396i | ||||
\(285\) | 6.22389 | 0.368671 | ||||||||
\(286\) | 15.4333 | + | 16.7758i | 0.912593 | + | 0.991976i | ||||
\(287\) | −4.84607 | −0.286054 | ||||||||
\(288\) | −0.309017 | + | 0.951057i | −0.0182090 | + | 0.0560415i | ||||
\(289\) | −26.8243 | + | 19.4890i | −1.57790 | + | 1.14641i | ||||
\(290\) | 3.36421 | + | 2.44424i | 0.197553 | + | 0.143531i | ||||
\(291\) | −5.17839 | − | 15.9375i | −0.303563 | − | 0.934270i | ||||
\(292\) | −3.97909 | − | 12.2464i | −0.232859 | − | 0.716666i | ||||
\(293\) | −1.11642 | − | 0.811129i | −0.0652222 | − | 0.0473867i | 0.554696 | − | 0.832053i | \(-0.312834\pi\) |
−0.619919 | + | 0.784666i | \(0.712834\pi\) | |||||||
\(294\) | 0.809017 | − | 0.587785i | 0.0471828 | − | 0.0342803i | ||||
\(295\) | 0.167927 | − | 0.516827i | 0.00977711 | − | 0.0300909i | ||||
\(296\) | −3.26074 | −0.189526 | ||||||||
\(297\) | −0.381966 | − | 3.29456i | −0.0221639 | − | 0.191170i | ||||
\(298\) | 10.4721 | 0.606635 | ||||||||
\(299\) | 4.88171 | − | 15.0244i | 0.282317 | − | 0.868881i | ||||
\(300\) | 3.11803 | − | 2.26538i | 0.180020 | − | 0.130792i | ||||
\(301\) | 4.21028 | + | 3.05894i | 0.242676 | + | 0.176315i | ||||
\(302\) | −1.58434 | − | 4.87608i | −0.0911683 | − | 0.280587i | ||||
\(303\) | −4.42096 | − | 13.6063i | −0.253978 | − | 0.781663i | ||||
\(304\) | −4.70378 | − | 3.41749i | −0.269780 | − | 0.196007i | ||||
\(305\) | −6.92275 | + | 5.02967i | −0.396396 | + | 0.287998i | ||||
\(306\) | 2.18850 | − | 6.73551i | 0.125108 | − | 0.385044i | ||||
\(307\) | −16.0206 | −0.914345 | −0.457173 | − | 0.889378i | \(-0.651138\pi\) | ||||
−0.457173 | + | 0.889378i | \(0.651138\pi\) | |||||||
\(308\) | −0.381966 | − | 3.29456i | −0.0217645 | − | 0.187725i | ||||
\(309\) | −6.46277 | −0.367654 | ||||||||
\(310\) | −1.18361 | + | 3.64279i | −0.0672248 | + | 0.206897i | ||||
\(311\) | 1.20621 | − | 0.876364i | 0.0683980 | − | 0.0496940i | −0.553061 | − | 0.833141i | \(-0.686540\pi\) |
0.621459 | + | 0.783447i | \(0.286540\pi\) | |||||||
\(312\) | −5.56036 | − | 4.03984i | −0.314793 | − | 0.228711i | ||||
\(313\) | 1.97226 | + | 6.07000i | 0.111479 | + | 0.343097i | 0.991196 | − | 0.132400i | \(-0.0422684\pi\) |
−0.879718 | + | 0.475497i | \(0.842268\pi\) | |||||||
\(314\) | 3.28683 | + | 10.1158i | 0.185487 | + | 0.570869i | ||||
\(315\) | −0.866025 | − | 0.629204i | −0.0487950 | − | 0.0354516i | ||||
\(316\) | 7.26480 | − | 5.27819i | 0.408677 | − | 0.296921i | ||||
\(317\) | 1.40776 | − | 4.33264i | 0.0790676 | − | 0.243345i | −0.903708 | − | 0.428150i | \(-0.859165\pi\) |
0.982775 | + | 0.184805i | \(0.0591654\pi\) | |||||||
\(318\) | 10.3016 | 0.577683 | ||||||||
\(319\) | 8.72302 | + | 9.48181i | 0.488395 | + | 0.530879i | ||||
\(320\) | 1.07047 | 0.0598409 | ||||||||
\(321\) | 2.05660 | − | 6.32956i | 0.114788 | − | 0.353281i | ||||
\(322\) | −1.85953 | + | 1.35102i | −0.103627 | + | 0.0752896i | ||||
\(323\) | 33.3128 | + | 24.2031i | 1.85357 | + | 1.34670i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | 8.18561 | + | 25.1927i | 0.454056 | + | 1.39744i | ||||
\(326\) | 0.381966 | + | 0.277515i | 0.0211551 | + | 0.0153701i | ||||
\(327\) | 10.8611 | − | 7.89102i | 0.600618 | − | 0.436375i | ||||
\(328\) | 1.49752 | − | 4.60888i | 0.0826866 | − | 0.254483i | ||||
\(329\) | 10.1665 | 0.560498 | ||||||||
\(330\) | −3.22775 | + | 1.47868i | −0.177682 | + | 0.0813988i | ||||
\(331\) | 9.56098 | 0.525519 | 0.262759 | − | 0.964861i | \(-0.415367\pi\) | ||||
0.262759 | + | 0.964861i | \(0.415367\pi\) | |||||||
\(332\) | −0.553656 | + | 1.70398i | −0.0303858 | + | 0.0935180i | ||||
\(333\) | −2.63799 | + | 1.91661i | −0.144561 | + | 0.105030i | ||||
\(334\) | −17.1705 | − | 12.4751i | −0.939527 | − | 0.682607i | ||||
\(335\) | 1.25426 | + | 3.86020i | 0.0685273 | + | 0.210905i | ||||
\(336\) | 0.309017 | + | 0.951057i | 0.0168583 | + | 0.0518844i | ||||
\(337\) | −3.88867 | − | 2.82528i | −0.211829 | − | 0.153903i | 0.476812 | − | 0.879005i | \(-0.341792\pi\) |
−0.688641 | + | 0.725102i | \(0.741792\pi\) | |||||||
\(338\) | 27.6990 | − | 20.1245i | 1.50663 | − | 1.09463i | ||||
\(339\) | −4.01776 | + | 12.3654i | −0.218215 | + | 0.671596i | ||||
\(340\) | −7.58119 | −0.411148 | ||||||||
\(341\) | −5.82330 | + | 10.3403i | −0.315349 | + | 0.559958i | ||||
\(342\) | −5.81419 | −0.314395 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | −4.21028 | + | 3.05894i | −0.227003 | + | 0.164927i | ||||
\(345\) | 1.99056 | + | 1.44623i | 0.107168 | + | 0.0778622i | ||||
\(346\) | 5.52986 | + | 17.0191i | 0.297287 | + | 0.914955i | ||||
\(347\) | 10.4322 | + | 32.1071i | 0.560032 | + | 1.72360i | 0.682270 | + | 0.731100i | \(0.260993\pi\) |
−0.122238 | + | 0.992501i | \(0.539007\pi\) | |||||||
\(348\) | −3.14275 | − | 2.28334i | −0.168469 | − | 0.122400i | ||||
\(349\) | −26.0727 | + | 18.9429i | −1.39564 | + | 1.01399i | −0.400419 | + | 0.916332i | \(0.631136\pi\) |
−0.995220 | + | 0.0976592i | \(0.968864\pi\) | |||||||
\(350\) | 1.19098 | − | 3.66547i | 0.0636607 | − | 0.195928i | ||||
\(351\) | −6.87298 | −0.366853 | ||||||||
\(352\) | 3.25134 | + | 0.654803i | 0.173297 | + | 0.0349011i | ||||
\(353\) | −8.35904 | −0.444907 | −0.222453 | − | 0.974943i | \(-0.571406\pi\) | ||||
−0.222453 | + | 0.974943i | \(0.571406\pi\) | |||||||
\(354\) | −0.156873 | + | 0.482806i | −0.00833771 | + | 0.0256608i | ||||
\(355\) | 12.3132 | − | 8.94609i | 0.653519 | − | 0.474809i | ||||
\(356\) | −5.04107 | − | 3.66255i | −0.267176 | − | 0.194115i | ||||
\(357\) | −2.18850 | − | 6.73551i | −0.115828 | − | 0.356481i | ||||
\(358\) | 3.95064 | + | 12.1588i | 0.208798 | + | 0.642614i | ||||
\(359\) | 10.2223 | + | 7.42696i | 0.539514 | + | 0.391980i | 0.823904 | − | 0.566729i | \(-0.191791\pi\) |
−0.284391 | + | 0.958708i | \(0.591791\pi\) | |||||||
\(360\) | 0.866025 | − | 0.629204i | 0.0456435 | − | 0.0331620i | ||||
\(361\) | 4.57492 | − | 14.0802i | 0.240785 | − | 0.741061i | ||||
\(362\) | −2.54178 | −0.133593 | ||||||||
\(363\) | −10.7082 | + | 2.51682i | −0.562035 | + | 0.132099i | ||||
\(364\) | −6.87298 | −0.360242 | ||||||||
\(365\) | −4.25949 | + | 13.1093i | −0.222952 | + | 0.686175i | ||||
\(366\) | 6.46704 | − | 4.69858i | 0.338038 | − | 0.245599i | ||||
\(367\) | 4.69728 | + | 3.41277i | 0.245196 | + | 0.178145i | 0.703595 | − | 0.710601i | \(-0.251577\pi\) |
−0.458399 | + | 0.888746i | \(0.651577\pi\) | |||||||
\(368\) | −0.710276 | − | 2.18600i | −0.0370257 | − | 0.113953i | ||||
\(369\) | −1.49752 | − | 4.60888i | −0.0779576 | − | 0.239929i | ||||
\(370\) | 2.82388 | + | 2.05167i | 0.146807 | + | 0.106661i | ||||
\(371\) | 8.33414 | − | 6.05511i | 0.432687 | − | 0.314366i | ||||
\(372\) | 1.10570 | − | 3.40299i | 0.0573278 | − | 0.176437i | ||||
\(373\) | 31.9384 | 1.65371 | 0.826853 | − | 0.562417i | \(-0.190129\pi\) | ||||
0.826853 | + | 0.562417i | \(0.190129\pi\) | |||||||
\(374\) | −23.0265 | − | 4.63740i | −1.19067 | − | 0.239794i | ||||
\(375\) | −9.47802 | −0.489443 | ||||||||
\(376\) | −3.14163 | + | 9.66893i | −0.162017 | + | 0.498637i | ||||
\(377\) | 21.6001 | − | 15.6934i | 1.11246 | − | 0.808250i | ||||
\(378\) | 0.809017 | + | 0.587785i | 0.0416113 | + | 0.0302324i | ||||
\(379\) | −0.906889 | − | 2.79112i | −0.0465838 | − | 0.143370i | 0.925059 | − | 0.379823i | \(-0.124015\pi\) |
−0.971643 | + | 0.236453i | \(0.924015\pi\) | |||||||
\(380\) | 1.92329 | + | 5.91927i | 0.0986626 | + | 0.303652i | ||||
\(381\) | −10.2619 | − | 7.45568i | −0.525731 | − | 0.381966i | ||||
\(382\) | 6.16138 | − | 4.47650i | 0.315243 | − | 0.229038i | ||||
\(383\) | −0.304288 | + | 0.936501i | −0.0155484 | + | 0.0478530i | −0.958530 | − | 0.284993i | \(-0.908009\pi\) |
0.942981 | + | 0.332846i | \(0.108009\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −1.74216 | + | 3.09350i | −0.0887885 | + | 0.157660i | ||||
\(386\) | 13.4431 | 0.684234 | ||||||||
\(387\) | −1.60818 | + | 4.94948i | −0.0817485 | + | 0.251596i | ||||
\(388\) | 13.5572 | − | 9.84989i | 0.688263 | − | 0.500052i | ||||
\(389\) | −2.73533 | − | 1.98733i | −0.138687 | − | 0.100762i | 0.516279 | − | 0.856421i | \(-0.327317\pi\) |
−0.654965 | + | 0.755659i | \(0.727317\pi\) | |||||||
\(390\) | 2.27353 | + | 6.99721i | 0.115125 | + | 0.354317i | ||||
\(391\) | 5.03027 | + | 15.4816i | 0.254392 | + | 0.782937i | ||||
\(392\) | 0.809017 | + | 0.587785i | 0.0408615 | + | 0.0296876i | ||||
\(393\) | −0.229157 | + | 0.166492i | −0.0115594 | + | 0.00839842i | ||||
\(394\) | 2.15506 | − | 6.63258i | 0.108570 | − | 0.334145i | ||||
\(395\) | −9.61256 | −0.483660 | ||||||||
\(396\) | 3.01528 | − | 1.38135i | 0.151523 | − | 0.0694152i | ||||
\(397\) | −14.6427 | −0.734896 | −0.367448 | − | 0.930044i | \(-0.619768\pi\) | ||||
−0.367448 | + | 0.930044i | \(0.619768\pi\) | |||||||
\(398\) | −7.62011 | + | 23.4523i | −0.381961 | + | 1.17556i | ||||
\(399\) | −4.70378 | + | 3.41749i | −0.235483 | + | 0.171089i | ||||
\(400\) | 3.11803 | + | 2.26538i | 0.155902 | + | 0.113269i | ||||
\(401\) | −6.85968 | − | 21.1119i | −0.342556 | − | 1.05428i | −0.962879 | − | 0.269933i | \(-0.912998\pi\) |
0.620323 | − | 0.784347i | \(-0.287002\pi\) | |||||||
\(402\) | −1.17169 | − | 3.60609i | −0.0584386 | − | 0.179856i | ||||
\(403\) | 19.8956 | + | 14.4550i | 0.991072 | + | 0.720056i | ||||
\(404\) | 11.5742 | − | 8.40917i | 0.575839 | − | 0.418372i | ||||
\(405\) | 0.330792 | − | 1.01807i | 0.0164372 | − | 0.0505885i | ||||
\(406\) | −3.88465 | −0.192792 | ||||||||
\(407\) | 7.32201 | + | 7.95893i | 0.362939 | + | 0.394510i | ||||
\(408\) | 7.08214 | 0.350618 | ||||||||
\(409\) | 6.47659 | − | 19.9329i | 0.320247 | − | 0.985619i | −0.653294 | − | 0.757105i | \(-0.726613\pi\) |
0.973541 | − | 0.228514i | \(-0.0733867\pi\) | |||||||
\(410\) | −4.19682 | + | 3.04917i | −0.207266 | + | 0.150588i | ||||
\(411\) | −4.30835 | − | 3.13020i | −0.212515 | − | 0.154401i | ||||
\(412\) | −1.99711 | − | 6.14646i | −0.0983904 | − | 0.302814i | ||||
\(413\) | 0.156873 | + | 0.482806i | 0.00771922 | + | 0.0237573i | ||||
\(414\) | −1.85953 | − | 1.35102i | −0.0913907 | − | 0.0663992i | ||||
\(415\) | 1.55163 | − | 1.12733i | 0.0761666 | − | 0.0553383i | ||||
\(416\) | 2.12387 | − | 6.53660i | 0.104131 | − | 0.320483i | ||||
\(417\) | 17.9785 | 0.880409 | ||||||||
\(418\) | 2.22082 | + | 19.1552i | 0.108624 | + | 0.936910i | ||||
\(419\) | −22.3088 | −1.08986 | −0.544929 | − | 0.838482i | \(-0.683443\pi\) | ||||
−0.544929 | + | 0.838482i | \(0.683443\pi\) | |||||||
\(420\) | 0.330792 | − | 1.01807i | 0.0161410 | − | 0.0496769i | ||||
\(421\) | −11.9980 | + | 8.71706i | −0.584747 | + | 0.424844i | −0.840432 | − | 0.541917i | \(-0.817699\pi\) |
0.255685 | + | 0.966760i | \(0.417699\pi\) | |||||||
\(422\) | 17.6393 | + | 12.8157i | 0.858670 | + | 0.623860i | ||||
\(423\) | 3.14163 | + | 9.66893i | 0.152751 | + | 0.470120i | ||||
\(424\) | 3.18336 | + | 9.79737i | 0.154598 | + | 0.475803i | ||||
\(425\) | −22.0823 | − | 16.0438i | −1.07115 | − | 0.778237i | ||||
\(426\) | −11.5027 | + | 8.35719i | −0.557307 | + | 0.404907i | ||||
\(427\) | 2.47019 | − | 7.60246i | 0.119541 | − | 0.367909i | ||||
\(428\) | 6.65529 | 0.321696 | ||||||||
\(429\) | 2.62525 | + | 22.6434i | 0.126748 | + | 1.09324i | ||||
\(430\) | 5.57091 | 0.268653 | ||||||||
\(431\) | 1.77035 | − | 5.44859i | 0.0852749 | − | 0.262449i | −0.899323 | − | 0.437286i | \(-0.855940\pi\) |
0.984597 | + | 0.174837i | \(0.0559398\pi\) | |||||||
\(432\) | −0.809017 | + | 0.587785i | −0.0389238 | + | 0.0282798i | ||||
\(433\) | 3.76588 | + | 2.73607i | 0.180977 | + | 0.131487i | 0.674585 | − | 0.738197i | \(-0.264322\pi\) |
−0.493609 | + | 0.869684i | \(0.664322\pi\) | |||||||
\(434\) | −1.10570 | − | 3.40299i | −0.0530753 | − | 0.163349i | ||||
\(435\) | 1.28501 | + | 3.95486i | 0.0616117 | + | 0.189621i | ||||
\(436\) | 10.8611 | + | 7.89102i | 0.520150 | + | 0.377911i | ||||
\(437\) | 10.8116 | − | 7.85511i | 0.517190 | − | 0.375761i | ||||
\(438\) | 3.97909 | − | 12.2464i | 0.190128 | − | 0.585155i | ||||
\(439\) | −3.00895 | −0.143609 | −0.0718047 | − | 0.997419i | \(-0.522876\pi\) | ||||
−0.0718047 | + | 0.997419i | \(0.522876\pi\) | |||||||
\(440\) | −2.40374 | − | 2.61283i | −0.114594 | − | 0.124562i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −15.0415 | + | 46.2931i | −0.715452 | + | 2.20194i | ||||
\(443\) | −4.15033 | + | 3.01539i | −0.197188 | + | 0.143265i | −0.681998 | − | 0.731354i | \(-0.738889\pi\) |
0.484810 | + | 0.874619i | \(0.338889\pi\) | |||||||
\(444\) | −2.63799 | − | 1.91661i | −0.125194 | − | 0.0909584i | ||||
\(445\) | 2.06120 | + | 6.34372i | 0.0977103 | + | 0.300721i | ||||
\(446\) | 2.60122 | + | 8.00574i | 0.123172 | + | 0.379083i | ||||
\(447\) | 8.47214 | + | 6.15537i | 0.400718 | + | 0.291139i | ||||
\(448\) | −0.809017 | + | 0.587785i | −0.0382225 | + | 0.0277702i | ||||
\(449\) | 1.15959 | − | 3.56886i | 0.0547245 | − | 0.168425i | −0.919959 | − | 0.392016i | \(-0.871778\pi\) |
0.974683 | + | 0.223591i | \(0.0717779\pi\) | |||||||
\(450\) | 3.85410 | 0.181684 | ||||||||
\(451\) | −14.6122 | + | 6.69409i | −0.688063 | + | 0.315212i | ||||
\(452\) | −13.0017 | −0.611550 | ||||||||
\(453\) | 1.58434 | − | 4.87608i | 0.0744386 | − | 0.229098i | ||||
\(454\) | 17.0949 | − | 12.4202i | 0.802305 | − | 0.582909i | ||||
\(455\) | 5.95218 | + | 4.32451i | 0.279042 | + | 0.202736i | ||||
\(456\) | −1.79668 | − | 5.52962i | −0.0841374 | − | 0.258948i | ||||
\(457\) | 6.68850 | + | 20.5851i | 0.312875 | + | 0.962930i | 0.976620 | + | 0.214971i | \(0.0689658\pi\) |
−0.663746 | + | 0.747958i | \(0.731034\pi\) | |||||||
\(458\) | −5.02397 | − | 3.65013i | −0.234755 | − | 0.170559i | ||||
\(459\) | 5.72957 | − | 4.16277i | 0.267433 | − | 0.194302i | ||||
\(460\) | −0.760326 | + | 2.34004i | −0.0354504 | + | 0.109105i | ||||
\(461\) | 4.96761 | 0.231365 | 0.115682 | − | 0.993286i | \(-0.463095\pi\) | ||||
0.115682 | + | 0.993286i | \(0.463095\pi\) | |||||||
\(462\) | 1.62747 | − | 2.88987i | 0.0757170 | − | 0.134449i | ||||
\(463\) | −14.3253 | −0.665754 | −0.332877 | − | 0.942970i | \(-0.608019\pi\) | ||||
−0.332877 | + | 0.942970i | \(0.608019\pi\) | |||||||
\(464\) | 1.20042 | − | 3.69452i | 0.0557283 | − | 0.171514i | ||||
\(465\) | −3.09874 | + | 2.25137i | −0.143701 | + | 0.104405i | ||||
\(466\) | −15.8590 | − | 11.5222i | −0.734653 | − | 0.533757i | ||||
\(467\) | 1.86879 | + | 5.75155i | 0.0864773 | + | 0.266150i | 0.984939 | − | 0.172902i | \(-0.0553144\pi\) |
−0.898462 | + | 0.439052i | \(0.855314\pi\) | |||||||
\(468\) | −2.12387 | − | 6.53660i | −0.0981759 | − | 0.302154i | ||||
\(469\) | −3.06753 | − | 2.22869i | −0.141645 | − | 0.102911i | ||||
\(470\) | 8.80446 | − | 6.39682i | 0.406120 | − | 0.295063i | ||||
\(471\) | −3.28683 | + | 10.1158i | −0.151449 | + | 0.466113i | ||||
\(472\) | −0.507652 | −0.0233666 | ||||||||
\(473\) | 16.9206 | + | 3.40772i | 0.778010 | + | 0.156687i | ||||
\(474\) | 8.97979 | 0.412455 | ||||||||
\(475\) | −6.92460 | + | 21.3117i | −0.317722 | + | 0.977849i | ||||
\(476\) | 5.72957 | − | 4.16277i | 0.262614 | − | 0.190800i | ||||
\(477\) | 8.33414 | + | 6.05511i | 0.381594 | + | 0.277244i | ||||
\(478\) | −4.10166 | − | 12.6236i | −0.187606 | − | 0.577391i | ||||
\(479\) | 1.39446 | + | 4.29170i | 0.0637144 | + | 0.196093i | 0.977846 | − | 0.209324i | \(-0.0671264\pi\) |
−0.914132 | + | 0.405417i | \(0.867126\pi\) | |||||||
\(480\) | 0.866025 | + | 0.629204i | 0.0395285 | + | 0.0287191i | ||||
\(481\) | 18.1309 | − | 13.1729i | 0.826697 | − | 0.600630i | ||||
\(482\) | 7.35617 | − | 22.6400i | 0.335065 | − | 1.03122i | ||||
\(483\) | −2.29850 | −0.104585 | ||||||||
\(484\) | −5.70265 | − | 9.40637i | −0.259211 | − | 0.427562i | ||||
\(485\) | −17.9385 | −0.814545 | ||||||||
\(486\) | −0.309017 | + | 0.951057i | −0.0140173 | + | 0.0431408i | ||||
\(487\) | 0.573025 | − | 0.416327i | 0.0259662 | − | 0.0188656i | −0.574726 | − | 0.818346i | \(-0.694892\pi\) |
0.600693 | + | 0.799480i | \(0.294892\pi\) | |||||||
\(488\) | 6.46704 | + | 4.69858i | 0.292749 | + | 0.212695i | ||||
\(489\) | 0.145898 | + | 0.449028i | 0.00659774 | + | 0.0203057i | ||||
\(490\) | −0.330792 | − | 1.01807i | −0.0149437 | − | 0.0459919i | ||||
\(491\) | 32.8358 | + | 23.8566i | 1.48186 | + | 1.07663i | 0.976953 | + | 0.213456i | \(0.0684722\pi\) |
0.504904 | + | 0.863175i | \(0.331528\pi\) | |||||||
\(492\) | 3.92055 | − | 2.84845i | 0.176752 | − | 0.128418i | ||||
\(493\) | −8.50156 | + | 26.1651i | −0.382891 | + | 1.17842i | ||||
\(494\) | 39.9608 | 1.79792 | ||||||||
\(495\) | −3.48045 | − | 0.700944i | −0.156435 | − | 0.0315051i | ||||
\(496\) | 3.57812 | 0.160662 | ||||||||
\(497\) | −4.39364 | + | 13.5222i | −0.197081 | + | 0.606554i | ||||
\(498\) | −1.44949 | + | 1.05312i | −0.0649533 | + | 0.0471913i | ||||
\(499\) | −4.72017 | − | 3.42941i | −0.211304 | − | 0.153521i | 0.477099 | − | 0.878849i | \(-0.341688\pi\) |
−0.688404 | + | 0.725328i | \(0.741688\pi\) | |||||||
\(500\) | −2.92887 | − | 9.01413i | −0.130983 | − | 0.403124i | ||||
\(501\) | −6.55854 | − | 20.1851i | −0.293014 | − | 0.901805i | ||||
\(502\) | 0.243974 | + | 0.177258i | 0.0108891 | + | 0.00791140i | ||||
\(503\) | −17.4126 | + | 12.6510i | −0.776391 | + | 0.564081i | −0.903894 | − | 0.427757i | \(-0.859304\pi\) |
0.127502 | + | 0.991838i | \(0.459304\pi\) | |||||||
\(504\) | −0.309017 | + | 0.951057i | −0.0137647 | + | 0.0423634i | ||||
\(505\) | −15.3147 | −0.681494 | ||||||||
\(506\) | −3.74075 | + | 6.64236i | −0.166297 | + | 0.295289i | ||||
\(507\) | 34.2379 | 1.52056 | ||||||||
\(508\) | 3.91968 | − | 12.0635i | 0.173908 | − | 0.535233i | ||||
\(509\) | −13.7717 | + | 10.0057i | −0.610420 | + | 0.443496i | −0.849562 | − | 0.527488i | \(-0.823134\pi\) |
0.239142 | + | 0.970985i | \(0.423134\pi\) | |||||||
\(510\) | −6.13331 | − | 4.45611i | −0.271588 | − | 0.197320i | ||||
\(511\) | −3.97909 | − | 12.2464i | −0.176025 | − | 0.541748i | ||||
\(512\) | −0.309017 | − | 0.951057i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | −4.70378 | − | 3.41749i | −0.207677 | − | 0.150886i | ||||
\(514\) | −10.5015 | + | 7.62981i | −0.463203 | + | 0.336537i | ||||
\(515\) | −2.13783 | + | 6.57958i | −0.0942043 | + | 0.289931i | ||||
\(516\) | −5.20419 | −0.229102 | ||||||||
\(517\) | 30.6549 | − | 14.0435i | 1.34820 | − | 0.617631i | ||||
\(518\) | −3.26074 | −0.143269 | ||||||||
\(519\) | −5.52986 | + | 17.0191i | −0.242734 | + | 0.747058i | ||||
\(520\) | −5.95218 | + | 4.32451i | −0.261020 | + | 0.189642i | ||||
\(521\) | −3.55614 | − | 2.58368i | −0.155797 | − | 0.113193i | 0.507156 | − | 0.861855i | \(-0.330697\pi\) |
−0.662953 | + | 0.748661i | \(0.730697\pi\) | |||||||
\(522\) | −1.20042 | − | 3.69452i | −0.0525411 | − | 0.161705i | ||||
\(523\) | −8.16872 | − | 25.1407i | −0.357193 | − | 1.09933i | −0.954727 | − | 0.297484i | \(-0.903853\pi\) |
0.597534 | − | 0.801844i | \(-0.296147\pi\) | |||||||
\(524\) | −0.229157 | − | 0.166492i | −0.0100108 | − | 0.00727325i | ||||
\(525\) | 3.11803 | − | 2.26538i | 0.136082 | − | 0.0988695i | ||||
\(526\) | 0.844504 | − | 2.59912i | 0.0368221 | − | 0.113327i | ||||
\(527\) | −25.3407 | −1.10386 | ||||||||
\(528\) | 2.24551 | + | 2.44084i | 0.0977232 | + | 0.106224i | ||||
\(529\) | −17.7169 | −0.770300 | ||||||||
\(530\) | 3.40768 | − | 10.4878i | 0.148020 | − | 0.455559i | ||||
\(531\) | −0.410699 | + | 0.298390i | −0.0178228 | + | 0.0129490i | ||||
\(532\) | −4.70378 | − | 3.41749i | −0.203935 | − | 0.148167i | ||||
\(533\) | 10.2924 | + | 31.6768i | 0.445814 | + | 1.37207i | ||||
\(534\) | −1.92552 | − | 5.92613i | −0.0833253 | − | 0.256449i | ||||
\(535\) | −5.76365 | − | 4.18754i | −0.249184 | − | 0.181043i | ||||
\(536\) | 3.06753 | − | 2.22869i | 0.132497 | − | 0.0962646i | ||||
\(537\) | −3.95064 | + | 12.1588i | −0.170483 | + | 0.524692i | ||||
\(538\) | 24.9893 | 1.07737 | ||||||||
\(539\) | −0.381966 | − | 3.29456i | −0.0164524 | − | 0.141907i | ||||
\(540\) | 1.07047 | 0.0460655 | ||||||||
\(541\) | 7.13141 | − | 21.9482i | 0.306603 | − | 0.943628i | −0.672471 | − | 0.740124i | \(-0.734767\pi\) |
0.979074 | − | 0.203504i | \(-0.0652331\pi\) | |||||||
\(542\) | −9.51279 | + | 6.91145i | −0.408609 | + | 0.296872i | ||||
\(543\) | −2.05634 | − | 1.49402i | −0.0882461 | − | 0.0641146i | ||||
\(544\) | 2.18850 | + | 6.73551i | 0.0938312 | + | 0.288783i | ||||
\(545\) | −4.44089 | − | 13.6677i | −0.190227 | − | 0.585458i | ||||
\(546\) | −5.56036 | − | 4.03984i | −0.237961 | − | 0.172889i | ||||
\(547\) | 3.13044 | − | 2.27440i | 0.133848 | − | 0.0972464i | −0.518847 | − | 0.854867i | \(-0.673638\pi\) |
0.652695 | + | 0.757621i | \(0.273638\pi\) | |||||||
\(548\) | 1.64564 | − | 5.06477i | 0.0702984 | − | 0.216356i | ||||
\(549\) | 7.99370 | 0.341163 | ||||||||
\(550\) | −1.47214 | − | 12.6976i | −0.0627721 | − | 0.541426i | ||||
\(551\) | 22.5861 | 0.962200 | ||||||||
\(552\) | 0.710276 | − | 2.18600i | 0.0302313 | − | 0.0930425i | ||||
\(553\) | 7.26480 | − | 5.27819i | 0.308931 | − | 0.224451i | ||||
\(554\) | 16.9755 | + | 12.3334i | 0.721219 | + | 0.523997i | ||||
\(555\) | 1.07863 | + | 3.31967i | 0.0457852 | + | 0.140912i | ||||
\(556\) | 5.55565 | + | 17.0985i | 0.235612 | + | 0.725139i | ||||
\(557\) | 13.4192 | + | 9.74963i | 0.568591 | + | 0.413105i | 0.834593 | − | 0.550867i | \(-0.185703\pi\) |
−0.266002 | + | 0.963972i | \(0.585703\pi\) | |||||||
\(558\) | 2.89476 | − | 2.10317i | 0.122545 | − | 0.0890341i | ||||
\(559\) | 11.0530 | − | 34.0177i | 0.467492 | − | 1.43879i | ||||
\(560\) | 1.07047 | 0.0452355 | ||||||||
\(561\) | −15.9030 | − | 17.2863i | −0.671425 | − | 0.729830i | ||||
\(562\) | 11.7496 | 0.495627 | ||||||||
\(563\) | 3.32053 | − | 10.2195i | 0.139944 | − | 0.430702i | −0.856383 | − | 0.516342i | \(-0.827293\pi\) |
0.996326 | + | 0.0856397i | \(0.0272934\pi\) | |||||||
\(564\) | −8.22489 | + | 5.97573i | −0.346330 | + | 0.251624i | ||||
\(565\) | 11.2598 | + | 8.18075i | 0.473705 | + | 0.344167i | ||||
\(566\) | −4.29709 | − | 13.2251i | −0.180620 | − | 0.555892i | ||||
\(567\) | 0.309017 | + | 0.951057i | 0.0129775 | + | 0.0399406i | ||||
\(568\) | −11.5027 | − | 8.35719i | −0.482642 | − | 0.350660i | ||||
\(569\) | 9.67653 | − | 7.03041i | 0.405661 | − | 0.294730i | −0.366182 | − | 0.930543i | \(-0.619335\pi\) |
0.771843 | + | 0.635813i | \(0.219335\pi\) | |||||||
\(570\) | −1.92329 | + | 5.91927i | −0.0805577 | + | 0.247931i | ||||
\(571\) | 8.27920 | 0.346474 | 0.173237 | − | 0.984880i | \(-0.444577\pi\) | ||||
0.173237 | + | 0.984880i | \(0.444577\pi\) | |||||||
\(572\) | −20.7239 | + | 9.49396i | −0.866511 | + | 0.396963i | ||||
\(573\) | 7.61588 | 0.318158 | ||||||||
\(574\) | 1.49752 | − | 4.60888i | 0.0625052 | − | 0.192371i | ||||
\(575\) | −7.16680 | + | 5.20699i | −0.298876 | + | 0.217146i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | −0.351208 | − | 1.08091i | −0.0146210 | − | 0.0449988i | 0.943480 | − | 0.331430i | \(-0.107531\pi\) |
−0.958101 | + | 0.286431i | \(0.907531\pi\) | |||||||
\(578\) | −10.2460 | − | 31.5338i | −0.426176 | − | 1.31163i | ||||
\(579\) | 10.8757 | + | 7.90164i | 0.451977 | + | 0.328381i | ||||
\(580\) | −3.36421 | + | 2.44424i | −0.139691 | + | 0.101492i | ||||
\(581\) | −0.553656 | + | 1.70398i | −0.0229695 | + | 0.0706930i | ||||
\(582\) | 16.7576 | 0.694626 | ||||||||
\(583\) | 16.7655 | − | 29.7702i | 0.694358 | − | 1.23295i | ||||
\(584\) | 12.8766 | 0.532838 | ||||||||
\(585\) | −2.27353 | + | 6.99721i | −0.0939989 | + | 0.289299i | ||||
\(586\) | 1.11642 | − | 0.811129i | 0.0461190 | − | 0.0335074i | ||||
\(587\) | −9.04007 | − | 6.56799i | −0.373124 | − | 0.271090i | 0.385381 | − | 0.922757i | \(-0.374070\pi\) |
−0.758505 | + | 0.651667i | \(0.774070\pi\) | |||||||
\(588\) | 0.309017 | + | 0.951057i | 0.0127436 | + | 0.0392209i | ||||
\(589\) | 6.42874 | + | 19.7856i | 0.264892 | + | 0.815253i | ||||
\(590\) | 0.439640 | + | 0.319417i | 0.0180997 | + | 0.0131502i | ||||
\(591\) | 5.64201 | − | 4.09916i | 0.232081 | − | 0.168617i | ||||
\(592\) | 1.00762 | − | 3.10115i | 0.0414131 | − | 0.127456i | ||||
\(593\) | −13.0875 | −0.537440 | −0.268720 | − | 0.963218i | \(-0.586601\pi\) | ||||
−0.268720 | + | 0.963218i | \(0.586601\pi\) | |||||||
\(594\) | 3.25134 | + | 0.654803i | 0.133404 | + | 0.0268669i | ||||
\(595\) | −7.58119 | −0.310798 | ||||||||
\(596\) | −3.23607 | + | 9.95959i | −0.132555 | + | 0.407961i | ||||
\(597\) | −19.9497 | + | 14.4943i | −0.816487 | + | 0.593212i | ||||
\(598\) | 12.7805 | + | 9.28557i | 0.522633 | + | 0.379715i | ||||
\(599\) | −8.57349 | − | 26.3865i | −0.350303 | − | 1.07812i | −0.958683 | − | 0.284476i | \(-0.908180\pi\) |
0.608380 | − | 0.793646i | \(-0.291820\pi\) | |||||||
\(600\) | 1.19098 | + | 3.66547i | 0.0486217 | + | 0.149642i | ||||
\(601\) | −21.1077 | − | 15.3357i | −0.861002 | − | 0.625554i | 0.0671555 | − | 0.997743i | \(-0.478608\pi\) |
−0.928157 | + | 0.372188i | \(0.878608\pi\) | |||||||
\(602\) | −4.21028 | + | 3.05894i | −0.171598 | + | 0.124673i | ||||
\(603\) | 1.17169 | − | 3.60609i | 0.0477149 | − | 0.146851i | ||||
\(604\) | 5.12702 | 0.208615 | ||||||||
\(605\) | −0.979885 | + | 11.7343i | −0.0398380 | + | 0.477067i | ||||
\(606\) | 14.3065 | 0.581163 | ||||||||
\(607\) | 13.8113 | − | 42.5068i | 0.560583 | − | 1.72530i | −0.120141 | − | 0.992757i | \(-0.538335\pi\) |
0.680724 | − | 0.732540i | \(-0.261665\pi\) | |||||||
\(608\) | 4.70378 | − | 3.41749i | 0.190763 | − | 0.138598i | ||||
\(609\) | −3.14275 | − | 2.28334i | −0.127351 | − | 0.0925257i | ||||
\(610\) | −2.64426 | − | 8.13818i | −0.107063 | − | 0.329505i | ||||
\(611\) | −21.5923 | − | 66.4544i | −0.873533 | − | 2.68846i | ||||
\(612\) | 5.72957 | + | 4.16277i | 0.231604 | + | 0.168270i | ||||
\(613\) | −30.6941 | + | 22.3006i | −1.23972 | + | 0.900712i | −0.997580 | − | 0.0695281i | \(-0.977851\pi\) |
−0.242144 | + | 0.970240i | \(0.577851\pi\) | |||||||
\(614\) | 4.95064 | − | 15.2365i | 0.199792 | − | 0.614896i | ||||
\(615\) | −5.18755 | −0.209182 | ||||||||
\(616\) | 3.25134 | + | 0.654803i | 0.131000 | + | 0.0263828i | ||||
\(617\) | −27.2763 | −1.09810 | −0.549052 | − | 0.835788i | \(-0.685011\pi\) | ||||
−0.549052 | + | 0.835788i | \(0.685011\pi\) | |||||||
\(618\) | 1.99711 | − | 6.14646i | 0.0803354 | − | 0.247247i | ||||
\(619\) | 32.4572 | − | 23.5815i | 1.30456 | − | 0.947822i | 0.304576 | − | 0.952488i | \(-0.401485\pi\) |
0.999989 | + | 0.00466642i | \(0.00148537\pi\) | |||||||
\(620\) | −3.09874 | − | 2.25137i | −0.124448 | − | 0.0904171i | ||||
\(621\) | −0.710276 | − | 2.18600i | −0.0285024 | − | 0.0877213i | ||||
\(622\) | 0.460732 | + | 1.41799i | 0.0184737 | + | 0.0568561i | ||||
\(623\) | −5.04107 | − | 3.66255i | −0.201966 | − | 0.146737i | ||||
\(624\) | 5.56036 | − | 4.03984i | 0.222593 | − | 0.161723i | ||||
\(625\) | 2.81966 | − | 8.67802i | 0.112786 | − | 0.347121i | ||||
\(626\) | −6.38237 | −0.255091 | ||||||||
\(627\) | −9.46244 | + | 16.8022i | −0.377893 | + | 0.671016i | ||||
\(628\) | −10.6364 | −0.424439 | ||||||||
\(629\) | −7.13612 | + | 21.9627i | −0.284536 | + | 0.875711i | ||||
\(630\) | 0.866025 | − | 0.629204i | 0.0345033 | − | 0.0250681i | ||||
\(631\) | 27.5546 | + | 20.0196i | 1.09693 | + | 0.796966i | 0.980556 | − | 0.196240i | \(-0.0628731\pi\) |
0.116373 | + | 0.993206i | \(0.462873\pi\) | |||||||
\(632\) | 2.77491 | + | 8.54029i | 0.110380 | + | 0.339714i | ||||
\(633\) | 6.73763 | + | 20.7363i | 0.267797 | + | 0.824194i | ||||
\(634\) | 3.68556 | + | 2.67772i | 0.146372 | + | 0.106346i | ||||
\(635\) | −10.9850 | + | 7.98105i | −0.435925 | + | 0.316718i | ||||
\(636\) | −3.18336 | + | 9.79737i | −0.126228 | + | 0.388491i | ||||
\(637\) | −6.87298 | −0.272318 | ||||||||
\(638\) | −11.7133 | + | 5.36605i | −0.463734 | + | 0.212444i | ||||
\(639\) | −14.2181 | −0.562459 | ||||||||
\(640\) | −0.330792 | + | 1.01807i | −0.0130757 | + | 0.0402429i | ||||
\(641\) | −40.1489 | + | 29.1699i | −1.58579 | + | 1.15214i | −0.676132 | + | 0.736781i | \(0.736345\pi\) |
−0.909656 | + | 0.415362i | \(0.863655\pi\) | |||||||
\(642\) | 5.38424 | + | 3.91188i | 0.212499 | + | 0.154390i | ||||
\(643\) | −3.73962 | − | 11.5094i | −0.147476 | − | 0.453886i | 0.849845 | − | 0.527033i | \(-0.176696\pi\) |
−0.997321 | + | 0.0731475i | \(0.976696\pi\) | |||||||
\(644\) | −0.710276 | − | 2.18600i | −0.0279888 | − | 0.0861406i | ||||
\(645\) | 4.50696 | + | 3.27450i | 0.177461 | + | 0.128933i | ||||
\(646\) | −33.3128 | + | 24.2031i | −1.31067 | + | 0.952260i | ||||
\(647\) | −8.39964 | + | 25.8514i | −0.330224 | + | 1.01633i | 0.638803 | + | 0.769370i | \(0.279430\pi\) |
−0.969027 | + | 0.246955i | \(0.920570\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 1.13994 | + | 1.23910i | 0.0447465 | + | 0.0486388i | ||||
\(650\) | −26.4892 | −1.03899 | ||||||||
\(651\) | 1.10570 | − | 3.40299i | 0.0433358 | − | 0.133374i | ||||
\(652\) | −0.381966 | + | 0.277515i | −0.0149589 | + | 0.0108683i | ||||
\(653\) | 4.84934 | + | 3.52325i | 0.189769 | + | 0.137876i | 0.678613 | − | 0.734496i | \(-0.262581\pi\) |
−0.488844 | + | 0.872371i | \(0.662581\pi\) | |||||||
\(654\) | 4.14856 | + | 12.7679i | 0.162221 | + | 0.499266i | ||||
\(655\) | 0.0936981 | + | 0.288373i | 0.00366109 | + | 0.0112677i | ||||
\(656\) | 3.92055 | + | 2.84845i | 0.153072 | + | 0.111213i | ||||
\(657\) | 10.4174 | − | 7.56869i | 0.406422 | − | 0.295283i | ||||
\(658\) | −3.14163 | + | 9.66893i | −0.122473 | + | 0.376934i | ||||
\(659\) | −37.0565 | −1.44352 | −0.721758 | − | 0.692146i | \(-0.756666\pi\) | ||||
−0.721758 | + | 0.692146i | \(0.756666\pi\) | |||||||
\(660\) | −0.408882 | − | 3.52671i | −0.0159157 | − | 0.137277i | ||||
\(661\) | −0.424601 | −0.0165150 | −0.00825752 | − | 0.999966i | \(-0.502628\pi\) | ||||
−0.00825752 | + | 0.999966i | \(0.502628\pi\) | |||||||
\(662\) | −2.95450 | + | 9.09303i | −0.114830 | + | 0.353411i | ||||
\(663\) | −39.3792 | + | 28.6107i | −1.52936 | + | 1.11115i | ||||
\(664\) | −1.44949 | − | 1.05312i | −0.0562512 | − | 0.0408689i | ||||
\(665\) | 1.92329 | + | 5.91927i | 0.0745819 | + | 0.229540i | ||||
\(666\) | −1.00762 | − | 3.10115i | −0.0390446 | − | 0.120167i | ||||
\(667\) | 7.22361 | + | 5.24826i | 0.279699 | + | 0.203213i | ||||
\(668\) | 17.1705 | − | 12.4751i | 0.664346 | − | 0.482676i | ||||
\(669\) | −2.60122 | + | 8.00574i | −0.100569 | + | 0.309520i | ||||
\(670\) | −4.05885 | −0.156807 | ||||||||
\(671\) | −3.05332 | − | 26.3357i | −0.117872 | − | 1.01668i | ||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 0.423778 | − | 1.30426i | 0.0163354 | − | 0.0502753i | −0.942557 | − | 0.334047i | \(-0.891586\pi\) |
0.958892 | + | 0.283771i | \(0.0915857\pi\) | |||||||
\(674\) | 3.88867 | − | 2.82528i | 0.149786 | − | 0.108826i | ||||
\(675\) | 3.11803 | + | 2.26538i | 0.120013 | + | 0.0871947i | ||||
\(676\) | 10.5801 | + | 32.5622i | 0.406927 | + | 1.25239i | ||||
\(677\) | −0.231575 | − | 0.712714i | −0.00890015 | − | 0.0273918i | 0.946508 | − | 0.322681i | \(-0.104584\pi\) |
−0.955408 | + | 0.295289i | \(0.904584\pi\) | |||||||
\(678\) | −10.5186 | − | 7.64223i | −0.403965 | − | 0.293498i | ||||
\(679\) | 13.5572 | − | 9.84989i | 0.520278 | − | 0.378004i | ||||
\(680\) | 2.34272 | − | 7.21014i | 0.0898390 | − | 0.276496i | ||||
\(681\) | 21.1305 | 0.809722 | ||||||||
\(682\) | −8.03470 | − | 8.73361i | −0.307664 | − | 0.334427i | ||||
\(683\) | 23.8913 | 0.914174 | 0.457087 | − | 0.889422i | \(-0.348893\pi\) | ||||
0.457087 | + | 0.889422i | \(0.348893\pi\) | |||||||
\(684\) | 1.79668 | − | 5.52962i | 0.0686979 | − | 0.211430i | ||||
\(685\) | −4.61195 | + | 3.35077i | −0.176213 | + | 0.128027i | ||||
\(686\) | 0.809017 | + | 0.587785i | 0.0308884 | + | 0.0224417i | ||||
\(687\) | −1.91899 | − | 5.90604i | −0.0732139 | − | 0.225329i | ||||
\(688\) | −1.60818 | − | 4.94948i | −0.0613114 | − | 0.188697i | ||||
\(689\) | −57.2804 | − | 41.6167i | −2.18221 | − | 1.58547i | ||||
\(690\) | −1.99056 | + | 1.44623i | −0.0757793 | + | 0.0550569i | ||||
\(691\) | −9.95200 | + | 30.6291i | −0.378592 | + | 1.16519i | 0.562431 | + | 0.826844i | \(0.309866\pi\) |
−0.941023 | + | 0.338342i | \(0.890134\pi\) | |||||||
\(692\) | −17.8950 | −0.680266 | ||||||||
\(693\) | 3.01528 | − | 1.38135i | 0.114541 | − | 0.0524730i | ||||
\(694\) | −33.7594 | −1.28149 | ||||||||
\(695\) | 5.94713 | − | 18.3034i | 0.225588 | − | 0.694287i | ||||
\(696\) | 3.14275 | − | 2.28334i | 0.119126 | − | 0.0865498i | ||||
\(697\) | −27.7659 | − | 20.1731i | −1.05171 | − | 0.764110i | ||||
\(698\) | −9.95888 | − | 30.6503i | −0.376949 | − | 1.16013i | ||||
\(699\) | −6.05759 | − | 18.6434i | −0.229119 | − | 0.705157i | ||||
\(700\) | 3.11803 | + | 2.26538i | 0.117851 | + | 0.0856235i | ||||
\(701\) | −4.10892 | + | 2.98531i | −0.155192 | + | 0.112754i | −0.662671 | − | 0.748910i | \(-0.730577\pi\) |
0.507479 | + | 0.861664i | \(0.330577\pi\) | |||||||
\(702\) | 2.12387 | − | 6.53660i | 0.0801603 | − | 0.246708i | ||||
\(703\) | 18.9585 | 0.715035 | ||||||||
\(704\) | −1.62747 | + | 2.88987i | −0.0613378 | + | 0.108916i | ||||
\(705\) | 10.8829 | 0.409874 | ||||||||
\(706\) | 2.58308 | − | 7.94991i | 0.0972156 | − | 0.299199i | ||||
\(707\) | 11.5742 | − | 8.40917i | 0.435294 | − | 0.316259i | ||||
\(708\) | −0.410699 | − | 0.298390i | −0.0154350 | − | 0.0112142i | ||||
\(709\) | −3.78680 | − | 11.6546i | −0.142216 | − | 0.437697i | 0.854426 | − | 0.519573i | \(-0.173909\pi\) |
−0.996643 | + | 0.0818759i | \(0.973909\pi\) | |||||||
\(710\) | 4.70324 | + | 14.4751i | 0.176509 | + | 0.543240i | ||||
\(711\) | 7.26480 | + | 5.27819i | 0.272451 | + | 0.197947i | ||||
\(712\) | 5.04107 | − | 3.66255i | 0.188922 | − | 0.137260i | ||||
\(713\) | −2.54145 | + | 7.82178i | −0.0951780 | + | 0.292928i | ||||
\(714\) | 7.08214 | 0.265042 | ||||||||
\(715\) | 23.9211 | + | 4.81758i | 0.894598 | + | 0.180167i | ||||
\(716\) | −12.7846 | −0.477781 | ||||||||
\(717\) | 4.10166 | − | 12.6236i | 0.153179 | − | 0.471438i | ||||
\(718\) | −10.2223 | + | 7.42696i | −0.381494 | + | 0.277172i | ||||
\(719\) | −17.1987 | − | 12.4956i | −0.641402 | − | 0.466006i | 0.218929 | − | 0.975741i | \(-0.429744\pi\) |
−0.860332 | + | 0.509735i | \(0.829744\pi\) | |||||||
\(720\) | 0.330792 | + | 1.01807i | 0.0123279 | + | 0.0379414i | ||||
\(721\) | −1.99711 | − | 6.14646i | −0.0743761 | − | 0.228906i | ||||
\(722\) | 11.9773 | + | 8.70202i | 0.445749 | + | 0.323856i | ||||
\(723\) | 19.2587 | − | 13.9923i | 0.716239 | − | 0.520378i | ||||
\(724\) | 0.785453 | − | 2.41738i | 0.0291911 | − | 0.0898411i | ||||
\(725\) | −14.9718 | −0.556040 | ||||||||
\(726\) | 0.915382 | − | 10.9618i | 0.0339730 | − | 0.406832i | ||||
\(727\) | −27.9895 | −1.03807 | −0.519037 | − | 0.854752i | \(-0.673709\pi\) | ||||
−0.519037 | + | 0.854752i | \(0.673709\pi\) | |||||||
\(728\) | 2.12387 | − | 6.53660i | 0.0787158 | − | 0.242262i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | −11.1515 | − | 8.10202i | −0.412735 | − | 0.299869i | ||||
\(731\) | 11.3894 | + | 35.0529i | 0.421251 | + | 1.29648i | ||||
\(732\) | 2.47019 | + | 7.60246i | 0.0913009 | + | 0.280995i | ||||
\(733\) | −27.3088 | − | 19.8410i | −1.00867 | − | 0.732843i | −0.0447419 | − | 0.998999i | \(-0.514247\pi\) |
−0.963930 | + | 0.266155i | \(0.914247\pi\) | |||||||
\(734\) | −4.69728 | + | 3.41277i | −0.173380 | + | 0.125968i | ||||
\(735\) | 0.330792 | − | 1.01807i | 0.0122015 | − | 0.0375522i | ||||
\(736\) | 2.29850 | 0.0847238 | ||||||||
\(737\) | −12.3280 | − | 2.48280i | −0.454108 | − | 0.0914550i | ||||
\(738\) | 4.84607 | 0.178386 | ||||||||
\(739\) | 5.83522 | − | 17.9590i | 0.214652 | − | 0.660631i | −0.784526 | − | 0.620096i | \(-0.787094\pi\) |
0.999178 | − | 0.0405352i | \(-0.0129063\pi\) | |||||||
\(740\) | −2.82388 | + | 2.05167i | −0.103808 | + | 0.0754209i | ||||
\(741\) | 32.3290 | + | 23.4884i | 1.18763 | + | 0.862867i | ||||
\(742\) | 3.18336 | + | 9.79737i | 0.116865 | + | 0.359673i | ||||
\(743\) | 15.2479 | + | 46.9281i | 0.559390 | + | 1.72162i | 0.684059 | + | 0.729426i | \(0.260213\pi\) |
−0.124669 | + | 0.992198i | \(0.539787\pi\) | |||||||
\(744\) | 2.89476 | + | 2.10317i | 0.106127 | + | 0.0771058i | ||||
\(745\) | 9.06914 | − | 6.58911i | 0.332267 | − | 0.241406i | ||||
\(746\) | −9.86950 | + | 30.3752i | −0.361348 | + | 1.11212i | ||||
\(747\) | −1.79167 | −0.0655538 | ||||||||
\(748\) | 11.5260 | − | 20.4664i | 0.421432 | − | 0.748327i | ||||
\(749\) | 6.65529 | 0.243179 | ||||||||
\(750\) | 2.92887 | − | 9.01413i | 0.106947 | − | 0.329150i | ||||
\(751\) | 18.9891 | − | 13.7964i | 0.692922 | − | 0.503437i | −0.184697 | − | 0.982795i | \(-0.559130\pi\) |
0.877619 | + | 0.479358i | \(0.159130\pi\) | |||||||
\(752\) | −8.22489 | − | 5.97573i | −0.299931 | − | 0.217912i | ||||
\(753\) | 0.0931899 | + | 0.286809i | 0.00339603 | + | 0.0104519i | ||||
\(754\) | 8.25049 | + | 25.3924i | 0.300465 | + | 0.924737i | ||||
\(755\) | −4.44013 | − | 3.22594i | −0.161593 | − | 0.117404i | ||||
\(756\) | −0.809017 | + | 0.587785i | −0.0294237 | + | 0.0213775i | ||||
\(757\) | 11.4730 | − | 35.3101i | 0.416992 | − | 1.28337i | −0.493466 | − | 0.869765i | \(-0.664270\pi\) |
0.910457 | − | 0.413603i | \(-0.135730\pi\) | |||||||
\(758\) | 2.93476 | 0.106595 | ||||||||
\(759\) | −6.93061 | + | 3.17502i | −0.251565 | + | 0.115246i | ||||
\(760\) | −6.22389 | −0.225764 | ||||||||
\(761\) | 2.65437 | − | 8.16932i | 0.0962209 | − | 0.296138i | −0.891349 | − | 0.453318i | \(-0.850240\pi\) |
0.987570 | + | 0.157180i | \(0.0502403\pi\) | |||||||
\(762\) | 10.2619 | − | 7.45568i | 0.371748 | − | 0.270091i | ||||
\(763\) | 10.8611 | + | 7.89102i | 0.393197 | + | 0.285674i | ||||
\(764\) | 2.35344 | + | 7.24313i | 0.0851444 | + | 0.262047i | ||||
\(765\) | −2.34272 | − | 7.21014i | −0.0847011 | − | 0.260683i | ||||
\(766\) | −0.796636 | − | 0.578790i | −0.0287836 | − | 0.0209125i | ||||
\(767\) | 2.82273 | − | 2.05083i | 0.101923 | − | 0.0740513i | ||||
\(768\) | 0.309017 | − | 0.951057i | 0.0111507 | − | 0.0343183i | ||||
\(769\) | −52.0121 | −1.87561 | −0.937803 | − | 0.347168i | \(-0.887143\pi\) | ||||
−0.937803 | + | 0.347168i | \(0.887143\pi\) | |||||||
\(770\) | −2.40374 | − | 2.61283i | −0.0866248 | − | 0.0941600i | ||||
\(771\) | −12.9806 | −0.467485 | ||||||||
\(772\) | −4.15414 | + | 12.7851i | −0.149511 | + | 0.460146i | ||||
\(773\) | 2.14672 | − | 1.55968i | 0.0772122 | − | 0.0560979i | −0.548510 | − | 0.836144i | \(-0.684805\pi\) |
0.625722 | + | 0.780046i | \(0.284805\pi\) | |||||||
\(774\) | −4.21028 | − | 3.05894i | −0.151335 | − | 0.109951i | ||||
\(775\) | −4.26148 | − | 13.1155i | −0.153077 | − | 0.471122i | ||||
\(776\) | 5.17839 | + | 15.9375i | 0.185894 | + | 0.572121i | ||||
\(777\) | −2.63799 | − | 1.91661i | −0.0946374 | − | 0.0687581i | ||||
\(778\) | 2.73533 | − | 1.98733i | 0.0980662 | − | 0.0712493i | ||||
\(779\) | −8.70684 | + | 26.7969i | −0.311955 | + | 0.960099i | ||||
\(780\) | −7.35730 | −0.263433 | ||||||||
\(781\) | 5.43083 | + | 46.8423i | 0.194330 | + | 1.67615i | ||||
\(782\) | −16.2783 | −0.582110 | ||||||||
\(783\) | 1.20042 | − | 3.69452i | 0.0428996 | − | 0.132032i | ||||
\(784\) | −0.809017 | + | 0.587785i | −0.0288935 | + | 0.0209923i | ||||
\(785\) | 9.21140 | + | 6.69247i | 0.328769 | + | 0.238865i | ||||
\(786\) | −0.0875302 | − | 0.269390i | −0.00312210 | − | 0.00960883i | ||||
\(787\) | 10.3016 | + | 31.7049i | 0.367211 | + | 1.13016i | 0.948585 | + | 0.316522i | \(0.102515\pi\) |
−0.581375 | + | 0.813636i | \(0.697485\pi\) | |||||||
\(788\) | 5.64201 | + | 4.09916i | 0.200988 | + | 0.146027i | ||||
\(789\) | 2.21094 | − | 1.60634i | 0.0787116 | − | 0.0571873i | ||||
\(790\) | 2.97044 | − | 9.14209i | 0.105684 | − | 0.325261i | ||||
\(791\) | −13.0017 | −0.462289 | ||||||||
\(792\) | 0.381966 | + | 3.29456i | 0.0135726 | + | 0.117067i | ||||
\(793\) | −54.9406 | −1.95100 | ||||||||
\(794\) | 4.52484 | − | 13.9260i | 0.160581 | − | 0.494217i | ||||
\(795\) | 8.92142 | − | 6.48179i | 0.316410 | − | 0.229885i | ||||
\(796\) | −19.9497 | − | 14.4943i | −0.707098 | − | 0.513737i | ||||
\(797\) | 8.76659 | + | 26.9808i | 0.310529 | + | 0.955709i | 0.977556 | + | 0.210675i | \(0.0675663\pi\) |
−0.667028 | + | 0.745033i | \(0.732434\pi\) | |||||||
\(798\) | −1.79668 | − | 5.52962i | −0.0636019 | − | 0.195746i | ||||
\(799\) | 58.2498 | + | 42.3209i | 2.06073 | + | 1.49721i | ||||
\(800\) | −3.11803 | + | 2.26538i | −0.110239 | + | 0.0800934i | ||||
\(801\) | 1.92552 | − | 5.92613i | 0.0680348 | − | 0.209390i | ||||
\(802\) | 22.1984 | 0.783853 | ||||||||
\(803\) | −28.9146 | − | 31.4297i | −1.02037 | − | 1.10913i | ||||
\(804\) | 3.79167 | 0.133722 | ||||||||
\(805\) | −0.760326 | + | 2.34004i | −0.0267980 | + | 0.0824757i | ||||
\(806\) | −19.8956 | + | 14.4550i | −0.700794 | + | 0.509156i | ||||
\(807\) | 20.2168 | + | 14.6883i | 0.711664 | + | 0.517054i | ||||
\(808\) | 4.42096 | + | 13.6063i | 0.155529 | + | 0.478669i | ||||
\(809\) | −9.33527 | − | 28.7310i | −0.328211 | − | 1.01013i | −0.969971 | − | 0.243223i | \(-0.921795\pi\) |
0.641760 | − | 0.766906i | \(-0.278205\pi\) | |||||||
\(810\) | 0.866025 | + | 0.629204i | 0.0304290 | + | 0.0221080i | ||||
\(811\) | 31.4385 | − | 22.8414i | 1.10396 | − | 0.802071i | 0.122254 | − | 0.992499i | \(-0.460988\pi\) |
0.981701 | + | 0.190428i | \(0.0609877\pi\) | |||||||
\(812\) | 1.20042 | − | 3.69452i | 0.0421266 | − | 0.129652i | ||||
\(813\) | −11.7585 | −0.412387 | ||||||||
\(814\) | −9.83202 | + | 4.50420i | −0.344612 | + | 0.157872i | ||||
\(815\) | 0.505406 | 0.0177036 | ||||||||
\(816\) | −2.18850 | + | 6.73551i | −0.0766128 | + | 0.235790i | ||||
\(817\) | 24.4793 | − | 17.7853i | 0.856423 | − | 0.622228i | ||||
\(818\) | 16.9559 | + | 12.3192i | 0.592851 | + | 0.430731i | ||||
\(819\) | −2.12387 | − | 6.53660i | −0.0742140 | − | 0.228407i | ||||
\(820\) | −1.60304 | − | 4.93366i | −0.0559806 | − | 0.172291i | ||||
\(821\) | 19.4618 | + | 14.1398i | 0.679221 | + | 0.493483i | 0.873099 | − | 0.487543i | \(-0.162107\pi\) |
−0.193878 | + | 0.981026i | \(0.562107\pi\) | |||||||
\(822\) | 4.30835 | − | 3.13020i | 0.150271 | − | 0.109178i | ||||
\(823\) | 0.925820 | − | 2.84938i | 0.0322720 | − | 0.0993231i | −0.933623 | − | 0.358257i | \(-0.883371\pi\) |
0.965895 | + | 0.258934i | \(0.0833712\pi\) | |||||||
\(824\) | 6.46277 | 0.225141 | ||||||||
\(825\) | 6.27245 | − | 11.1378i | 0.218379 | − | 0.387770i | ||||
\(826\) | −0.507652 | −0.0176635 | ||||||||
\(827\) | −0.0102920 | + | 0.0316754i | −0.000357886 | + | 0.00110146i | −0.951235 | − | 0.308466i | \(-0.900184\pi\) |
0.950877 | + | 0.309568i | \(0.100184\pi\) | |||||||
\(828\) | 1.85953 | − | 1.35102i | 0.0646230 | − | 0.0469513i | ||||
\(829\) | 7.49283 | + | 5.44386i | 0.260237 | + | 0.189073i | 0.710251 | − | 0.703948i | \(-0.248581\pi\) |
−0.450015 | + | 0.893021i | \(0.648581\pi\) | |||||||
\(830\) | 0.592671 | + | 1.82405i | 0.0205719 | + | 0.0633138i | ||||
\(831\) | 6.48406 | + | 19.9559i | 0.224930 | + | 0.692262i | ||||
\(832\) | 5.56036 | + | 4.03984i | 0.192771 | + | 0.140056i | ||||
\(833\) | 5.72957 | − | 4.16277i | 0.198518 | − | 0.144232i | ||||
\(834\) | −5.55565 | + | 17.0985i | −0.192376 | + | 0.592074i | ||||
\(835\) | −22.7195 | −0.786239 | ||||||||
\(836\) | −18.9039 | − | 3.80714i | −0.653806 | − | 0.131673i | ||||
\(837\) | 3.57812 | 0.123678 | ||||||||
\(838\) | 6.89381 | − | 21.2170i | 0.238143 | − | 0.732928i | ||||
\(839\) | 2.43698 | − | 1.77057i | 0.0841338 | − | 0.0611268i | −0.544923 | − | 0.838486i | \(-0.683441\pi\) |
0.629057 | + | 0.777359i | \(0.283441\pi\) | |||||||
\(840\) | 0.866025 | + | 0.629204i | 0.0298807 | + | 0.0217096i | ||||
\(841\) | −4.29826 | − | 13.2287i | −0.148216 | − | 0.456162i | ||||
\(842\) | −4.58283 | − | 14.1045i | −0.157935 | − | 0.486073i | ||||
\(843\) | 9.50563 | + | 6.90624i | 0.327391 | + | 0.237864i | ||||
\(844\) | −17.6393 | + | 12.8157i | −0.607171 | + | 0.441136i | ||||
\(845\) | 11.3256 | − | 34.8567i | 0.389614 | − | 1.19911i | ||||
\(846\) | −10.1665 | −0.349532 | ||||||||
\(847\) | −5.70265 | − | 9.40637i | −0.195945 | − | 0.323207i | ||||
\(848\) | −10.3016 | −0.353757 | ||||||||
\(849\) | 4.29709 | − | 13.2251i | 0.147476 | − | 0.453884i | ||||
\(850\) | 22.0823 | − | 16.0438i | 0.757418 | − | 0.550296i | ||||
\(851\) | 6.06342 | + | 4.40534i | 0.207851 | + | 0.151013i | ||||
\(852\) | −4.39364 | − | 13.5222i | −0.150523 | − | 0.463264i | ||||
\(853\) | −12.0965 | − | 37.2293i | −0.414177 | − | 1.27471i | −0.912985 | − | 0.407993i | \(-0.866229\pi\) |
0.498808 | − | 0.866713i | \(-0.333771\pi\) | |||||||
\(854\) | 6.46704 | + | 4.69858i | 0.221298 | + | 0.160782i | ||||
\(855\) | −5.03523 | + | 3.65831i | −0.172201 | + | 0.125112i | ||||
\(856\) | −2.05660 | + | 6.32956i | −0.0702930 | + | 0.216340i | ||||
\(857\) | −5.97666 | −0.204159 | −0.102079 | − | 0.994776i | \(-0.532550\pi\) | ||||
−0.102079 | + | 0.994776i | \(0.532550\pi\) | |||||||
\(858\) | −22.3464 | − | 4.50045i | −0.762894 | − | 0.153643i | ||||
\(859\) | −4.14359 | −0.141378 | −0.0706888 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706888 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(860\) | −1.72150 | + | 5.29825i | −0.0587028 | + | 0.180669i | ||||
\(861\) | 3.92055 | − | 2.84845i | 0.133612 | − | 0.0970748i | ||||
\(862\) | 4.63484 | + | 3.36741i | 0.157863 | + | 0.114694i | ||||
\(863\) | 0.746156 | + | 2.29643i | 0.0253994 | + | 0.0781715i | 0.962953 | − | 0.269670i | \(-0.0869147\pi\) |
−0.937553 | + | 0.347842i | \(0.886915\pi\) | |||||||
\(864\) | −0.309017 | − | 0.951057i | −0.0105130 | − | 0.0323556i | ||||
\(865\) | 15.4975 | + | 11.2596i | 0.526931 | + | 0.382838i | ||||
\(866\) | −3.76588 | + | 2.73607i | −0.127970 | + | 0.0929755i | ||||
\(867\) | 10.2460 | − | 31.5338i | 0.347971 | − | 1.07095i | ||||
\(868\) | 3.57812 | 0.121449 | ||||||||
\(869\) | 14.6144 | − | 25.9504i | 0.495759 | − | 0.880307i | ||||
\(870\) | −4.15839 | −0.140983 | ||||||||
\(871\) | −8.05301 | + | 24.7846i | −0.272866 | + | 0.839795i | ||||
\(872\) | −10.8611 | + | 7.89102i | −0.367802 | + | 0.267224i | ||||
\(873\) | 13.5572 | + | 9.84989i | 0.458842 | + | 0.333368i | ||||
\(874\) | 4.12967 | + | 12.7098i | 0.139688 | + | 0.429916i | ||||
\(875\) | −2.92887 | − | 9.01413i | −0.0990138 | − | 0.304733i | ||||
\(876\) | 10.4174 | + | 7.56869i | 0.351971 | + | 0.255722i | ||||
\(877\) | 16.4440 | − | 11.9473i | 0.555274 | − | 0.403430i | −0.274452 | − | 0.961601i | \(-0.588497\pi\) |
0.829726 | + | 0.558171i | \(0.188497\pi\) | |||||||
\(878\) | 0.929817 | − | 2.86168i | 0.0313798 | − | 0.0965771i | ||||
\(879\) | 1.37998 | 0.0465454 | ||||||||
\(880\) | 3.22775 | − | 1.47868i | 0.108807 | − | 0.0498464i | ||||
\(881\) | 33.4251 | 1.12612 | 0.563060 | − | 0.826416i | \(-0.309624\pi\) | ||||
0.563060 | + | 0.826416i | \(0.309624\pi\) | |||||||
\(882\) | −0.309017 | + | 0.951057i | −0.0104051 | + | 0.0320237i | ||||
\(883\) | 26.2444 | − | 19.0677i | 0.883194 | − | 0.641678i | −0.0509007 | − | 0.998704i | \(-0.516209\pi\) |
0.934094 | + | 0.357026i | \(0.116209\pi\) | |||||||
\(884\) | −39.3792 | − | 28.6107i | −1.32447 | − | 0.962281i | ||||
\(885\) | 0.167927 | + | 0.516827i | 0.00564482 | + | 0.0173730i | ||||
\(886\) | −1.58528 | − | 4.87900i | −0.0532586 | − | 0.163913i | ||||
\(887\) | 7.37964 | + | 5.36162i | 0.247784 | + | 0.180026i | 0.704744 | − | 0.709462i | \(-0.251062\pi\) |
−0.456960 | + | 0.889487i | \(0.651062\pi\) | |||||||
\(888\) | 2.63799 | − | 1.91661i | 0.0885252 | − | 0.0643173i | ||||
\(889\) | 3.91968 | − | 12.0635i | 0.131462 | − | 0.404598i | ||||
\(890\) | −6.67019 | −0.223585 | ||||||||
\(891\) | 2.24551 | + | 2.44084i | 0.0752274 | + | 0.0817712i | ||||
\(892\) | −8.41774 | −0.281847 | ||||||||
\(893\) | 18.2660 | − | 56.2170i | 0.611249 | − | 1.88123i | ||||
\(894\) | −8.47214 | + | 6.15537i | −0.283351 | + | 0.205866i | ||||
\(895\) | 11.0717 | + | 8.04409i | 0.370088 | + | 0.268884i | ||||
\(896\) | −0.309017 | − | 0.951057i | −0.0103235 | − | 0.0317726i | ||||
\(897\) | 4.88171 | + | 15.0244i | 0.162996 | + | 0.501649i | ||||
\(898\) | 3.03585 | + | 2.20568i | 0.101308 | + | 0.0736043i | ||||
\(899\) | −11.2451 | + | 8.17007i | −0.375046 | + | 0.272487i | ||||
\(900\) | −1.19098 | + | 3.66547i | −0.0396994 | + | 0.122182i | ||||
\(901\) | 72.9571 | 2.43055 | ||||||||
\(902\) | −1.85103 | − | 15.9656i | −0.0616327 | − | 0.531598i | ||||
\(903\) | −5.20419 | −0.173184 | ||||||||
\(904\) | 4.01776 | − | 12.3654i | 0.133629 | − | 0.411267i | ||||
\(905\) | −2.20125 | + | 1.59930i | −0.0731719 | + | 0.0531625i | ||||
\(906\) | 4.14784 | + | 3.01358i | 0.137803 | + | 0.100120i | ||||
\(907\) | 0.253053 | + | 0.778816i | 0.00840248 | + | 0.0258602i | 0.955170 | − | 0.296058i | \(-0.0956723\pi\) |
−0.946767 | + | 0.321919i | \(0.895672\pi\) | |||||||
\(908\) | 6.52968 | + | 20.0963i | 0.216695 | + | 0.666919i | ||||
\(909\) | 11.5742 | + | 8.40917i | 0.383893 | + | 0.278915i | ||||
\(910\) | −5.95218 | + | 4.32451i | −0.197313 | + | 0.143356i | ||||
\(911\) | −7.04494 | + | 21.6821i | −0.233409 | + | 0.718360i | 0.763919 | + | 0.645312i | \(0.223273\pi\) |
−0.997328 | + | 0.0730479i | \(0.976727\pi\) | |||||||
\(912\) | 5.81419 | 0.192527 | ||||||||
\(913\) | 0.684357 | + | 5.90276i | 0.0226489 | + | 0.195353i | ||||
\(914\) | −21.6444 | −0.715934 | ||||||||
\(915\) | 2.64426 | − | 8.13818i | 0.0874164 | − | 0.269040i | ||||
\(916\) | 5.02397 | − | 3.65013i | 0.165997 | − | 0.120604i | ||||
\(917\) | −0.229157 | − | 0.166492i | −0.00756743 | − | 0.00549806i | ||||
\(918\) | 2.18850 | + | 6.73551i | 0.0722313 | + | 0.222305i | ||||
\(919\) | 17.2494 | + | 53.0883i | 0.569006 | + | 1.75122i | 0.655738 | + | 0.754989i | \(0.272358\pi\) |
−0.0867314 | + | 0.996232i | \(0.527642\pi\) | |||||||
\(920\) | −1.99056 | − | 1.44623i | −0.0656268 | − | 0.0476807i | ||||
\(921\) | 12.9610 | − | 9.41668i | 0.427078 | − | 0.310290i | ||||
\(922\) | −1.53508 | + | 4.72448i | −0.0505550 | + | 0.155592i | ||||
\(923\) | 97.7208 | 3.21652 | ||||||||
\(924\) | 2.24551 | + | 2.44084i | 0.0738718 | + | 0.0802977i | ||||
\(925\) | −12.5672 | −0.413207 | ||||||||
\(926\) | 4.42677 | − | 13.6242i | 0.145473 | − | 0.447719i | ||||
\(927\) | 5.22849 | − | 3.79872i | 0.171726 | − | 0.124766i | ||||
\(928\) | 3.14275 | + | 2.28334i | 0.103166 | + | 0.0749544i | ||||
\(929\) | 9.99045 | + | 30.7474i | 0.327776 | + | 1.00879i | 0.970172 | + | 0.242418i | \(0.0779405\pi\) |
−0.642396 | + | 0.766373i | \(0.722059\pi\) | |||||||
\(930\) | −1.18361 | − | 3.64279i | −0.0388122 | − | 0.119452i | ||||
\(931\) | −4.70378 | − | 3.41749i | −0.154160 | − | 0.112004i | ||||
\(932\) | 15.8590 | − | 11.5222i | 0.519478 | − | 0.377423i | ||||
\(933\) | −0.460732 | + | 1.41799i | −0.0150837 | + | 0.0464228i | ||||
\(934\) | −6.04754 | −0.197881 | ||||||||
\(935\) | −22.8594 | + | 10.4722i | −0.747581 | + | 0.342479i | ||||
\(936\) | 6.87298 | 0.224650 | ||||||||
\(937\) | 3.69697 | − | 11.3781i | 0.120775 | − | 0.371707i | −0.872333 | − | 0.488913i | \(-0.837394\pi\) |
0.993108 | + | 0.117206i | \(0.0373937\pi\) | |||||||
\(938\) | 3.06753 | − | 2.22869i | 0.100158 | − | 0.0727692i | ||||
\(939\) | −5.16345 | − | 3.75147i | −0.168503 | − | 0.122424i | ||||
\(940\) | 3.36301 | + | 10.3503i | 0.109689 | + | 0.337588i | ||||
\(941\) | −3.75840 | − | 11.5672i | −0.122520 | − | 0.377079i | 0.870921 | − | 0.491423i | \(-0.163523\pi\) |
−0.993441 | + | 0.114345i | \(0.963523\pi\) | |||||||
\(942\) | −8.60503 | − | 6.25192i | −0.280367 | − | 0.203699i | ||||
\(943\) | −9.01139 | + | 6.54716i | −0.293451 | + | 0.213205i | ||||
\(944\) | 0.156873 | − | 0.482806i | 0.00510579 | − | 0.0157140i | ||||
\(945\) | 1.07047 | 0.0348223 | ||||||||
\(946\) | −8.46968 | + | 15.0394i | −0.275373 | + | 0.488973i | ||||
\(947\) | 0.662536 | 0.0215295 | 0.0107648 | − | 0.999942i | \(-0.496573\pi\) | ||||
0.0107648 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(948\) | −2.77491 | + | 8.54029i | −0.0901248 | + | 0.277376i | ||||
\(949\) | −71.5986 | + | 52.0195i | −2.32419 | + | 1.68862i | ||||
\(950\) | −18.1288 | − | 13.1714i | −0.588177 | − | 0.427336i | ||||
\(951\) | 1.40776 | + | 4.33264i | 0.0456497 | + | 0.140495i | ||||
\(952\) | 2.18850 | + | 6.73551i | 0.0709297 | + | 0.218299i | ||||
\(953\) | −43.6292 | − | 31.6985i | −1.41329 | − | 1.02681i | −0.992834 | − | 0.119501i | \(-0.961871\pi\) |
−0.420455 | − | 0.907314i | \(-0.638129\pi\) | |||||||
\(954\) | −8.33414 | + | 6.05511i | −0.269828 | + | 0.196041i | ||||
\(955\) | 2.51927 | − | 7.75353i | 0.0815218 | − | 0.250898i | ||||
\(956\) | 13.2733 | 0.429288 | ||||||||
\(957\) | −12.6303 | − | 2.54368i | −0.408281 | − | 0.0822255i | ||||
\(958\) | −4.51256 | −0.145794 | ||||||||
\(959\) | 1.64564 | − | 5.06477i | 0.0531406 | − | 0.163550i | ||||
\(960\) | −0.866025 | + | 0.629204i | −0.0279508 | + | 0.0203075i | ||||
\(961\) | 14.7217 | + | 10.6960i | 0.474895 | + | 0.345031i | ||||
\(962\) | 6.92538 | + | 21.3141i | 0.223283 | + | 0.687195i | ||||
\(963\) | 2.05660 | + | 6.32956i | 0.0662729 | + | 0.203967i | ||||
\(964\) | 19.2587 | + | 13.9923i | 0.620281 | + | 0.450661i | ||||
\(965\) | 11.6420 | − | 8.45844i | 0.374770 | − | 0.272287i | ||||
\(966\) | 0.710276 | − | 2.18600i | 0.0228527 | − | 0.0703335i | ||||
\(967\) | 55.7169 | 1.79173 | 0.895867 | − | 0.444322i | \(-0.146555\pi\) | ||||
0.895867 | + | 0.444322i | \(0.146555\pi\) | |||||||
\(968\) | 10.7082 | − | 2.51682i | 0.344175 | − | 0.0808936i | ||||
\(969\) | −41.1769 | −1.32279 | ||||||||
\(970\) | 5.54330 | − | 17.0605i | 0.177985 | − | 0.547780i | ||||
\(971\) | −22.1000 | + | 16.0566i | −0.709223 | + | 0.515281i | −0.882923 | − | 0.469518i | \(-0.844428\pi\) |
0.173700 | + | 0.984799i | \(0.444428\pi\) | |||||||
\(972\) | −0.809017 | − | 0.587785i | −0.0259492 | − | 0.0188532i | ||||
\(973\) | 5.55565 | + | 17.0985i | 0.178106 | + | 0.548154i | ||||
\(974\) | 0.218876 | + | 0.673631i | 0.00701324 | + | 0.0215845i | ||||
\(975\) | −21.4302 | − | 15.5699i | −0.686316 | − | 0.498637i | ||||
\(976\) | −6.46704 | + | 4.69858i | −0.207005 | + | 0.150398i | ||||
\(977\) | −4.78177 | + | 14.7168i | −0.152982 | + | 0.470831i | −0.997951 | − | 0.0639848i | \(-0.979619\pi\) |
0.844969 | + | 0.534816i | \(0.179619\pi\) | |||||||
\(978\) | −0.472136 | −0.0150972 | ||||||||
\(979\) | −20.2595 | − | 4.08014i | −0.647495 | − | 0.130402i | ||||
\(980\) | 1.07047 | 0.0341948 | ||||||||
\(981\) | −4.14856 | + | 12.7679i | −0.132453 | + | 0.407649i | ||||
\(982\) | −32.8358 | + | 23.8566i | −1.04783 | + | 0.761294i | ||||
\(983\) | 19.7819 | + | 14.3724i | 0.630944 | + | 0.458408i | 0.856727 | − | 0.515770i | \(-0.172494\pi\) |
−0.225783 | + | 0.974178i | \(0.572494\pi\) | |||||||
\(984\) | 1.49752 | + | 4.60888i | 0.0477391 | + | 0.146926i | ||||
\(985\) | −2.30691 | − | 7.09995i | −0.0735044 | − | 0.226223i | ||||
\(986\) | −22.2574 | − | 16.1709i | −0.708819 | − | 0.514987i | ||||
\(987\) | −8.22489 | + | 5.97573i | −0.261801 | + | 0.190210i | ||||
\(988\) | −12.3486 | + | 38.0050i | −0.392860 | + | 1.20910i | ||||
\(989\) | 11.9618 | 0.380364 | ||||||||
\(990\) | 1.74216 | − | 3.09350i | 0.0553694 | − | 0.0983180i | ||||
\(991\) | 59.1364 | 1.87853 | 0.939264 | − | 0.343194i | \(-0.111509\pi\) | ||||
0.939264 | + | 0.343194i | \(0.111509\pi\) | |||||||
\(992\) | −1.10570 | + | 3.40299i | −0.0351060 | + | 0.108045i | ||||
\(993\) | −7.73499 | + | 5.61980i | −0.245463 | + | 0.178339i | ||||
\(994\) | −11.5027 | − | 8.35719i | −0.364843 | − | 0.265074i | ||||
\(995\) | 8.15707 | + | 25.1049i | 0.258596 | + | 0.795878i | ||||
\(996\) | −0.553656 | − | 1.70398i | −0.0175433 | − | 0.0539927i | ||||
\(997\) | 13.5068 | + | 9.81323i | 0.427763 | + | 0.310788i | 0.780754 | − | 0.624839i | \(-0.214835\pi\) |
−0.352991 | + | 0.935627i | \(0.614835\pi\) | |||||||
\(998\) | 4.72017 | − | 3.42941i | 0.149415 | − | 0.108556i | ||||
\(999\) | 1.00762 | − | 3.10115i | 0.0318798 | − | 0.0981159i |
(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 | 462.2.j.g.295.2 | ✓ | 8 | |
11.4 | even | 5 | 5082.2.a.bz.1.3 | 4 | |||
11.5 | even | 5 | inner | 462.2.j.g.379.2 | yes | 8 | |
11.7 | odd | 10 | 5082.2.a.ce.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.g.295.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
462.2.j.g.379.2 | yes | 8 | 11.5 | even | 5 | inner | |
5082.2.a.bz.1.3 | 4 | 11.4 | even | 5 | |||
5082.2.a.ce.1.3 | 4 | 11.7 | odd | 10 |