Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(53,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 53.1 | ||
Root | \(-0.862625 - 1.49411i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.53 |
Dual form | 91.2.e.c.79.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36263 | − | 2.36014i | −0.963521 | − | 1.66887i | −0.713536 | − | 0.700619i | \(-0.752907\pi\) |
−0.249986 | − | 0.968250i | \(-0.580426\pi\) | |||||||
\(3\) | 0.673208 | − | 1.16603i | 0.388677 | − | 0.673208i | −0.603595 | − | 0.797291i | \(-0.706266\pi\) |
0.992272 | + | 0.124083i | \(0.0395989\pi\) | |||||||
\(4\) | −2.71349 | + | 4.69991i | −1.35675 | + | 2.34996i | ||||
\(5\) | −1.09358 | − | 1.89414i | −0.489065 | − | 0.847085i | 0.510856 | − | 0.859666i | \(-0.329328\pi\) |
−0.999921 | + | 0.0125813i | \(0.995995\pi\) | |||||||
\(6\) | −3.66932 | −1.49799 | ||||||||
\(7\) | −2.19729 | − | 1.47375i | −0.830496 | − | 0.557025i | ||||
\(8\) | 9.33940 | 3.30198 | ||||||||
\(9\) | 0.593582 | + | 1.02811i | 0.197861 | + | 0.342705i | ||||
\(10\) | −2.98028 | + | 5.16200i | −0.942449 | + | 1.63237i | ||||
\(11\) | 0.524077 | − | 0.907729i | 0.158015 | − | 0.273691i | −0.776138 | − | 0.630564i | \(-0.782824\pi\) |
0.934153 | + | 0.356873i | \(0.116157\pi\) | |||||||
\(12\) | 3.65349 | + | 6.32803i | 1.05467 | + | 1.82675i | ||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −0.484172 | + | 7.19406i | −0.129400 | + | 1.92269i | ||||
\(15\) | −2.94483 | −0.760352 | ||||||||
\(16\) | −7.29912 | − | 12.6424i | −1.82478 | − | 3.16061i | ||||
\(17\) | 2.64562 | − | 4.58236i | 0.641658 | − | 1.11138i | −0.343404 | − | 0.939188i | \(-0.611580\pi\) |
0.985063 | − | 0.172197i | \(-0.0550865\pi\) | |||||||
\(18\) | 1.61766 | − | 2.80187i | 0.381286 | − | 0.660407i | ||||
\(19\) | −0.378453 | − | 0.655500i | −0.0868231 | − | 0.150382i | 0.819344 | − | 0.573303i | \(-0.194338\pi\) |
−0.906167 | + | 0.422921i | \(0.861005\pi\) | |||||||
\(20\) | 11.8697 | 2.65415 | ||||||||
\(21\) | −3.19767 | + | 1.56996i | −0.697788 | + | 0.342594i | ||||
\(22\) | −2.85648 | −0.609005 | ||||||||
\(23\) | −0.326792 | − | 0.566020i | −0.0681408 | − | 0.118023i | 0.829942 | − | 0.557850i | \(-0.188373\pi\) |
−0.898083 | + | 0.439826i | \(0.855040\pi\) | |||||||
\(24\) | 6.28736 | − | 10.8900i | 1.28340 | − | 2.22292i | ||||
\(25\) | 0.108157 | − | 0.187333i | 0.0216314 | − | 0.0374667i | ||||
\(26\) | −1.36263 | − | 2.36014i | −0.267233 | − | 0.462861i | ||||
\(27\) | 5.63766 | 1.08497 | ||||||||
\(28\) | 12.8888 | − | 6.32803i | 2.43576 | − | 1.19589i | ||||
\(29\) | −3.10408 | −0.576414 | −0.288207 | − | 0.957568i | \(-0.593059\pi\) | ||||
−0.288207 | + | 0.957568i | \(0.593059\pi\) | |||||||
\(30\) | 4.01270 | + | 6.95021i | 0.732616 | + | 1.26893i | ||||
\(31\) | −0.513956 | + | 0.890198i | −0.0923092 | + | 0.159884i | −0.908482 | − | 0.417923i | \(-0.862758\pi\) |
0.816173 | + | 0.577807i | \(0.196091\pi\) | |||||||
\(32\) | −10.5525 | + | 18.2775i | −1.86544 | + | 3.23104i | ||||
\(33\) | −0.705626 | − | 1.22218i | −0.122834 | − | 0.212754i | ||||
\(34\) | −14.4200 | −2.47301 | ||||||||
\(35\) | −0.388575 | + | 5.77363i | −0.0656811 | + | 0.975922i | ||||
\(36\) | −6.44273 | −1.07379 | ||||||||
\(37\) | 5.44661 | + | 9.43381i | 0.895418 | + | 1.55091i | 0.833287 | + | 0.552841i | \(0.186456\pi\) |
0.0621309 | + | 0.998068i | \(0.480210\pi\) | |||||||
\(38\) | −1.03138 | + | 1.78640i | −0.167312 | + | 0.289793i | ||||
\(39\) | 0.673208 | − | 1.16603i | 0.107800 | − | 0.186714i | ||||
\(40\) | −10.2134 | − | 17.6901i | −1.61488 | − | 2.79706i | ||||
\(41\) | 7.32040 | 1.14325 | 0.571627 | − | 0.820514i | \(-0.306312\pi\) | ||||
0.571627 | + | 0.820514i | \(0.306312\pi\) | |||||||
\(42\) | 8.06254 | + | 5.40766i | 1.24408 | + | 0.834420i | ||||
\(43\) | 0.887771 | 0.135384 | 0.0676919 | − | 0.997706i | \(-0.478437\pi\) | ||||
0.0676919 | + | 0.997706i | \(0.478437\pi\) | |||||||
\(44\) | 2.84416 | + | 4.92623i | 0.428774 | + | 0.742658i | ||||
\(45\) | 1.29826 | − | 2.24865i | 0.193533 | − | 0.335210i | ||||
\(46\) | −0.890590 | + | 1.54255i | −0.131310 | + | 0.227436i | ||||
\(47\) | −1.16875 | − | 2.02434i | −0.170480 | − | 0.295281i | 0.768108 | − | 0.640321i | \(-0.221199\pi\) |
−0.938588 | + | 0.345040i | \(0.887865\pi\) | |||||||
\(48\) | −19.6553 | −2.83700 | ||||||||
\(49\) | 2.65613 | + | 6.47650i | 0.379447 | + | 0.925214i | ||||
\(50\) | −0.589510 | −0.0833692 | ||||||||
\(51\) | −3.56211 | − | 6.16976i | −0.498795 | − | 0.863939i | ||||
\(52\) | −2.71349 | + | 4.69991i | −0.376294 | + | 0.651760i | ||||
\(53\) | −2.44407 | + | 4.23325i | −0.335719 | + | 0.581482i | −0.983623 | − | 0.180240i | \(-0.942313\pi\) |
0.647904 | + | 0.761722i | \(0.275646\pi\) | |||||||
\(54\) | −7.68202 | − | 13.3057i | −1.04539 | − | 1.81067i | ||||
\(55\) | −2.29249 | −0.309119 | ||||||||
\(56\) | −20.5213 | − | 13.7639i | −2.74228 | − | 1.83928i | ||||
\(57\) | −1.01911 | −0.134985 | ||||||||
\(58\) | 4.22970 | + | 7.32606i | 0.555387 | + | 0.961959i | ||||
\(59\) | 0.524077 | − | 0.907729i | 0.0682291 | − | 0.118176i | −0.829893 | − | 0.557923i | \(-0.811598\pi\) |
0.898122 | + | 0.439747i | \(0.144932\pi\) | |||||||
\(60\) | 7.99079 | − | 13.8404i | 1.03161 | − | 1.78679i | ||||
\(61\) | 6.24989 | + | 10.8251i | 0.800217 | + | 1.38602i | 0.919473 | + | 0.393153i | \(0.128616\pi\) |
−0.119256 | + | 0.992864i | \(0.538051\pi\) | |||||||
\(62\) | 2.80132 | 0.355768 | ||||||||
\(63\) | 0.210913 | − | 3.13385i | 0.0265726 | − | 0.394828i | ||||
\(64\) | 28.3200 | 3.54000 | ||||||||
\(65\) | −1.09358 | − | 1.89414i | −0.135642 | − | 0.234939i | ||||
\(66\) | −1.92301 | + | 3.33075i | −0.236706 | + | 0.409987i | ||||
\(67\) | −2.23944 | + | 3.87883i | −0.273592 | + | 0.473875i | −0.969779 | − | 0.243986i | \(-0.921545\pi\) |
0.696187 | + | 0.717860i | \(0.254878\pi\) | |||||||
\(68\) | 14.3578 | + | 24.8684i | 1.74114 | + | 3.01574i | ||||
\(69\) | −0.879996 | −0.105939 | ||||||||
\(70\) | 14.1560 | − | 6.95021i | 1.69197 | − | 0.830708i | ||||
\(71\) | −6.60274 | −0.783601 | −0.391801 | − | 0.920050i | \(-0.628148\pi\) | ||||
−0.391801 | + | 0.920050i | \(0.628148\pi\) | |||||||
\(72\) | 5.54370 | + | 9.60197i | 0.653331 | + | 1.13160i | ||||
\(73\) | 4.14174 | − | 7.17370i | 0.484754 | − | 0.839618i | −0.515093 | − | 0.857134i | \(-0.672243\pi\) |
0.999847 | + | 0.0175164i | \(0.00557593\pi\) | |||||||
\(74\) | 14.8434 | − | 25.7095i | 1.72551 | − | 2.98867i | ||||
\(75\) | −0.145624 | − | 0.252229i | −0.0168152 | − | 0.0291249i | ||||
\(76\) | 4.10772 | 0.471188 | ||||||||
\(77\) | −2.48931 | + | 1.22218i | −0.283683 | + | 0.139280i | ||||
\(78\) | −3.66932 | −0.415469 | ||||||||
\(79\) | −1.07007 | − | 1.85342i | −0.120392 | − | 0.208526i | 0.799530 | − | 0.600626i | \(-0.205082\pi\) |
−0.919922 | + | 0.392100i | \(0.871749\pi\) | |||||||
\(80\) | −15.9644 | + | 27.6511i | −1.78487 | + | 3.09149i | ||||
\(81\) | 2.01457 | − | 3.48935i | 0.223842 | − | 0.387705i | ||||
\(82\) | −9.97496 | − | 17.2771i | −1.10155 | − | 1.90794i | ||||
\(83\) | −6.66558 | −0.731642 | −0.365821 | − | 0.930685i | \(-0.619212\pi\) | ||||
−0.365821 | + | 0.930685i | \(0.619212\pi\) | |||||||
\(84\) | 1.29817 | − | 19.2888i | 0.141642 | − | 2.10458i | ||||
\(85\) | −11.5728 | −1.25525 | ||||||||
\(86\) | −1.20970 | − | 2.09526i | −0.130445 | − | 0.225938i | ||||
\(87\) | −2.08969 | + | 3.61946i | −0.224039 | + | 0.388047i | ||||
\(88\) | 4.89457 | − | 8.47765i | 0.521763 | − | 0.903720i | ||||
\(89\) | 2.88388 | + | 4.99503i | 0.305691 | + | 0.529472i | 0.977415 | − | 0.211329i | \(-0.0677792\pi\) |
−0.671724 | + | 0.740802i | \(0.734446\pi\) | |||||||
\(90\) | −7.07617 | −0.745894 | ||||||||
\(91\) | −2.19729 | − | 1.47375i | −0.230338 | − | 0.154491i | ||||
\(92\) | 3.54699 | 0.369800 | ||||||||
\(93\) | 0.691998 | + | 1.19858i | 0.0717569 | + | 0.124287i | ||||
\(94\) | −3.18515 | + | 5.51684i | −0.328523 | + | 0.569019i | ||||
\(95\) | −0.827739 | + | 1.43369i | −0.0849242 | + | 0.147093i | ||||
\(96\) | 14.2081 | + | 24.6091i | 1.45011 | + | 2.51166i | ||||
\(97\) | −2.88777 | −0.293209 | −0.146604 | − | 0.989195i | \(-0.546834\pi\) | ||||
−0.146604 | + | 0.989195i | \(0.546834\pi\) | |||||||
\(98\) | 11.6661 | − | 15.0939i | 1.17845 | − | 1.52471i | ||||
\(99\) | 1.24433 | 0.125060 | ||||||||
\(100\) | 0.586967 | + | 1.01666i | 0.0586967 | + | 0.101666i | ||||
\(101\) | 5.62716 | − | 9.74653i | 0.559924 | − | 0.969816i | −0.437579 | − | 0.899180i | \(-0.644164\pi\) |
0.997502 | − | 0.0706359i | \(-0.0225028\pi\) | |||||||
\(102\) | −9.70764 | + | 16.8141i | −0.961200 | + | 1.66485i | ||||
\(103\) | −10.1167 | − | 17.5226i | −0.996828 | − | 1.72656i | −0.567341 | − | 0.823483i | \(-0.692028\pi\) |
−0.429487 | − | 0.903073i | \(-0.641306\pi\) | |||||||
\(104\) | 9.33940 | 0.915804 | ||||||||
\(105\) | 6.47064 | + | 4.33994i | 0.631470 | + | 0.423535i | ||||
\(106\) | 13.3214 | 1.29389 | ||||||||
\(107\) | −4.52758 | − | 7.84201i | −0.437698 | − | 0.758115i | 0.559813 | − | 0.828619i | \(-0.310873\pi\) |
−0.997512 | + | 0.0705034i | \(0.977539\pi\) | |||||||
\(108\) | −15.2978 | + | 26.4965i | −1.47203 | + | 2.54963i | ||||
\(109\) | −7.55070 | + | 13.0782i | −0.723226 | + | 1.25266i | 0.236474 | + | 0.971638i | \(0.424008\pi\) |
−0.959700 | + | 0.281026i | \(0.909325\pi\) | |||||||
\(110\) | 3.12380 | + | 5.41058i | 0.297843 | + | 0.515879i | ||||
\(111\) | 14.6668 | 1.39211 | ||||||||
\(112\) | −2.59354 | + | 38.5361i | −0.245067 | + | 3.64132i | ||||
\(113\) | 3.10408 | 0.292008 | 0.146004 | − | 0.989284i | \(-0.453359\pi\) | ||||
0.146004 | + | 0.989284i | \(0.453359\pi\) | |||||||
\(114\) | 1.38867 | + | 2.40524i | 0.130061 | + | 0.225271i | ||||
\(115\) | −0.714748 | + | 1.23798i | −0.0666506 | + | 0.115442i | ||||
\(116\) | 8.42292 | − | 14.5889i | 0.782048 | − | 1.35455i | ||||
\(117\) | 0.593582 | + | 1.02811i | 0.0548767 | + | 0.0950492i | ||||
\(118\) | −2.85648 | −0.262961 | ||||||||
\(119\) | −12.5664 | + | 6.16976i | −1.15196 | + | 0.565581i | ||||
\(120\) | −27.5030 | −2.51067 | ||||||||
\(121\) | 4.95069 | + | 8.57484i | 0.450062 | + | 0.779531i | ||||
\(122\) | 17.0325 | − | 29.5012i | 1.54205 | − | 2.67091i | ||||
\(123\) | 4.92815 | − | 8.53581i | 0.444356 | − | 0.769648i | ||||
\(124\) | −2.78923 | − | 4.83109i | −0.250481 | − | 0.433845i | ||||
\(125\) | −11.4089 | −1.02045 | ||||||||
\(126\) | −7.68371 | + | 3.77248i | −0.684519 | + | 0.336079i | ||||
\(127\) | 8.78914 | 0.779910 | 0.389955 | − | 0.920834i | \(-0.372491\pi\) | ||||
0.389955 | + | 0.920834i | \(0.372491\pi\) | |||||||
\(128\) | −17.4846 | − | 30.2841i | −1.54543 | − | 2.67676i | ||||
\(129\) | 0.597654 | − | 1.03517i | 0.0526205 | − | 0.0911414i | ||||
\(130\) | −2.98028 | + | 5.16200i | −0.261388 | + | 0.452738i | ||||
\(131\) | 5.25723 | + | 9.10580i | 0.459327 | + | 0.795577i | 0.998925 | − | 0.0463451i | \(-0.0147574\pi\) |
−0.539599 | + | 0.841922i | \(0.681424\pi\) | |||||||
\(132\) | 7.65885 | 0.666618 | ||||||||
\(133\) | −0.134473 | + | 1.99807i | −0.0116603 | + | 0.173254i | ||||
\(134\) | 12.2061 | 1.05445 | ||||||||
\(135\) | −6.16525 | − | 10.6785i | −0.530620 | − | 0.919061i | ||||
\(136\) | 24.7086 | − | 42.7965i | 2.11874 | − | 3.66977i | ||||
\(137\) | −4.36583 | + | 7.56183i | −0.372998 | + | 0.646051i | −0.990025 | − | 0.140891i | \(-0.955003\pi\) |
0.617028 | + | 0.786942i | \(0.288337\pi\) | |||||||
\(138\) | 1.19910 | + | 2.07691i | 0.102075 | + | 0.176798i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −26.0812 | − | 17.4930i | −2.20426 | − | 1.47843i | ||||
\(141\) | −3.14726 | −0.265047 | ||||||||
\(142\) | 8.99706 | + | 15.5834i | 0.755016 | + | 1.30773i | ||||
\(143\) | 0.524077 | − | 0.907729i | 0.0438256 | − | 0.0759081i | ||||
\(144\) | 8.66525 | − | 15.0087i | 0.722104 | − | 1.25072i | ||||
\(145\) | 3.39457 | + | 5.87957i | 0.281904 | + | 0.488272i | ||||
\(146\) | −22.5745 | −1.86828 | ||||||||
\(147\) | 9.33992 | + | 1.26290i | 0.770343 | + | 0.104163i | ||||
\(148\) | −59.1174 | −4.85942 | ||||||||
\(149\) | −7.69632 | − | 13.3304i | −0.630507 | − | 1.09207i | −0.987448 | − | 0.157944i | \(-0.949514\pi\) |
0.356941 | − | 0.934127i | \(-0.383820\pi\) | |||||||
\(150\) | −0.396863 | + | 0.687386i | −0.0324037 | + | 0.0561248i | ||||
\(151\) | 6.83786 | − | 11.8435i | 0.556457 | − | 0.963812i | −0.441331 | − | 0.897344i | \(-0.645494\pi\) |
0.997789 | − | 0.0664680i | \(-0.0211730\pi\) | |||||||
\(152\) | −3.53453 | − | 6.12198i | −0.286688 | − | 0.496558i | ||||
\(153\) | 6.28158 | 0.507836 | ||||||||
\(154\) | 6.27651 | + | 4.20974i | 0.505776 | + | 0.339231i | ||||
\(155\) | 2.24821 | 0.180581 | ||||||||
\(156\) | 3.65349 | + | 6.32803i | 0.292514 | + | 0.506648i | ||||
\(157\) | −1.69378 | + | 2.93371i | −0.135178 | + | 0.234136i | −0.925666 | − | 0.378343i | \(-0.876494\pi\) |
0.790487 | + | 0.612478i | \(0.209827\pi\) | |||||||
\(158\) | −2.91621 | + | 5.05102i | −0.232001 | + | 0.401838i | ||||
\(159\) | 3.29074 | + | 5.69972i | 0.260972 | + | 0.452017i | ||||
\(160\) | 46.1602 | 3.64928 | ||||||||
\(161\) | −0.116117 | + | 1.72532i | −0.00915128 | + | 0.135974i | ||||
\(162\) | −10.9804 | −0.862705 | ||||||||
\(163\) | 6.90502 | + | 11.9598i | 0.540843 | + | 0.936767i | 0.998856 | + | 0.0478219i | \(0.0152280\pi\) |
−0.458013 | + | 0.888946i | \(0.651439\pi\) | |||||||
\(164\) | −19.8639 | + | 34.4052i | −1.55111 | + | 2.68660i | ||||
\(165\) | −1.54332 | + | 2.67311i | −0.120147 | + | 0.208101i | ||||
\(166\) | 9.08268 | + | 15.7317i | 0.704953 | + | 1.22101i | ||||
\(167\) | 16.3783 | 1.26739 | 0.633695 | − | 0.773583i | \(-0.281538\pi\) | ||||
0.633695 | + | 0.773583i | \(0.281538\pi\) | |||||||
\(168\) | −29.8643 | + | 14.6625i | −2.30408 | + | 1.13124i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 15.7694 | + | 27.3134i | 1.20946 | + | 2.09485i | ||||
\(171\) | 0.449286 | − | 0.778186i | 0.0343578 | − | 0.0595094i | ||||
\(172\) | −2.40896 | + | 4.17244i | −0.183682 | + | 0.318146i | ||||
\(173\) | −2.06273 | − | 3.57275i | −0.156826 | − | 0.271631i | 0.776896 | − | 0.629629i | \(-0.216793\pi\) |
−0.933723 | + | 0.357997i | \(0.883460\pi\) | |||||||
\(174\) | 11.3899 | 0.863465 | ||||||||
\(175\) | −0.513734 | + | 0.252229i | −0.0388346 | + | 0.0190667i | ||||
\(176\) | −15.3012 | −1.15337 | ||||||||
\(177\) | −0.705626 | − | 1.22218i | −0.0530381 | − | 0.0918647i | ||||
\(178\) | 7.85930 | − | 13.6127i | 0.589080 | − | 1.02032i | ||||
\(179\) | −7.20679 | + | 12.4825i | −0.538661 | + | 0.932988i | 0.460316 | + | 0.887755i | \(0.347736\pi\) |
−0.998976 | + | 0.0452324i | \(0.985597\pi\) | |||||||
\(180\) | 7.04565 | + | 12.2034i | 0.525152 | + | 0.909589i | ||||
\(181\) | 18.1014 | 1.34547 | 0.672733 | − | 0.739885i | \(-0.265120\pi\) | ||||
0.672733 | + | 0.739885i | \(0.265120\pi\) | |||||||
\(182\) | −0.484172 | + | 7.19406i | −0.0358892 | + | 0.533259i | ||||
\(183\) | 16.8299 | 1.24410 | ||||||||
\(184\) | −3.05204 | − | 5.28629i | −0.225000 | − | 0.389711i | ||||
\(185\) | 11.9126 | − | 20.6333i | 0.875834 | − | 1.51699i | ||||
\(186\) | 1.88587 | − | 3.26642i | 0.138279 | − | 0.239506i | ||||
\(187\) | −2.77302 | − | 4.80302i | −0.202784 | − | 0.351232i | ||||
\(188\) | 12.6856 | 0.925195 | ||||||||
\(189\) | −12.3876 | − | 8.30850i | −0.901062 | − | 0.604355i | ||||
\(190\) | 4.51159 | 0.327305 | ||||||||
\(191\) | −2.77068 | − | 4.79895i | −0.200479 | − | 0.347240i | 0.748204 | − | 0.663469i | \(-0.230917\pi\) |
−0.948683 | + | 0.316229i | \(0.897583\pi\) | |||||||
\(192\) | 19.0653 | − | 33.0220i | 1.37592 | − | 2.38316i | ||||
\(193\) | 4.37044 | − | 7.56983i | 0.314591 | − | 0.544888i | −0.664759 | − | 0.747058i | \(-0.731466\pi\) |
0.979351 | + | 0.202170i | \(0.0647992\pi\) | |||||||
\(194\) | 3.93495 | + | 6.81553i | 0.282513 | + | 0.489327i | ||||
\(195\) | −2.94483 | −0.210884 | ||||||||
\(196\) | −37.6463 | − | 5.09038i | −2.68902 | − | 0.363598i | ||||
\(197\) | −5.46874 | −0.389632 | −0.194816 | − | 0.980840i | \(-0.562411\pi\) | ||||
−0.194816 | + | 0.980840i | \(0.562411\pi\) | |||||||
\(198\) | −1.69556 | − | 2.93679i | −0.120498 | − | 0.208709i | ||||
\(199\) | −9.76839 | + | 16.9193i | −0.692463 | + | 1.19938i | 0.278566 | + | 0.960417i | \(0.410141\pi\) |
−0.971029 | + | 0.238963i | \(0.923192\pi\) | |||||||
\(200\) | 1.01012 | − | 1.74958i | 0.0714264 | − | 0.123714i | ||||
\(201\) | 3.01522 | + | 5.22252i | 0.212677 | + | 0.368368i | ||||
\(202\) | −30.6708 | −2.15799 | ||||||||
\(203\) | 6.82056 | + | 4.57464i | 0.478709 | + | 0.321077i | ||||
\(204\) | 38.6631 | 2.70696 | ||||||||
\(205\) | −8.00546 | − | 13.8659i | −0.559125 | − | 0.968433i | ||||
\(206\) | −27.5705 | + | 47.7536i | −1.92093 | + | 3.32715i | ||||
\(207\) | 0.387956 | − | 0.671959i | 0.0269648 | − | 0.0467044i | ||||
\(208\) | −7.29912 | − | 12.6424i | −0.506103 | − | 0.876596i | ||||
\(209\) | −0.793355 | −0.0548775 | ||||||||
\(210\) | 1.42581 | − | 21.1853i | 0.0983899 | − | 1.46192i | ||||
\(211\) | 16.6905 | 1.14902 | 0.574511 | − | 0.818497i | \(-0.305192\pi\) | ||||
0.574511 | + | 0.818497i | \(0.305192\pi\) | |||||||
\(212\) | −13.2639 | − | 22.9738i | −0.910971 | − | 1.57785i | ||||
\(213\) | −4.44502 | + | 7.69900i | −0.304568 | + | 0.527527i | ||||
\(214\) | −12.3388 | + | 21.3714i | −0.843463 | + | 1.46092i | ||||
\(215\) | −0.970850 | − | 1.68156i | −0.0662114 | − | 0.114682i | ||||
\(216\) | 52.6524 | 3.58254 | ||||||||
\(217\) | 2.44124 | − | 1.19858i | 0.165722 | − | 0.0813647i | ||||
\(218\) | 41.1551 | 2.78737 | ||||||||
\(219\) | −5.57650 | − | 9.65878i | −0.376825 | − | 0.652680i | ||||
\(220\) | 6.22065 | − | 10.7745i | 0.419396 | − | 0.726415i | ||||
\(221\) | 2.64562 | − | 4.58236i | 0.177964 | − | 0.308243i | ||||
\(222\) | −19.9854 | − | 34.6157i | −1.34133 | − | 2.32325i | ||||
\(223\) | −5.34217 | −0.357738 | −0.178869 | − | 0.983873i | \(-0.557244\pi\) | ||||
−0.178869 | + | 0.983873i | \(0.557244\pi\) | |||||||
\(224\) | 50.1233 | − | 24.6091i | 3.34901 | − | 1.64427i | ||||
\(225\) | 0.256800 | 0.0171200 | ||||||||
\(226\) | −4.22970 | − | 7.32606i | −0.281356 | − | 0.487322i | ||||
\(227\) | −10.0608 | + | 17.4258i | −0.667757 | + | 1.15659i | 0.310774 | + | 0.950484i | \(0.399412\pi\) |
−0.978530 | + | 0.206104i | \(0.933921\pi\) | |||||||
\(228\) | 2.76535 | − | 4.78973i | 0.183140 | − | 0.317208i | ||||
\(229\) | −12.6249 | − | 21.8669i | −0.834275 | − | 1.44501i | −0.894619 | − | 0.446829i | \(-0.852553\pi\) |
0.0603445 | − | 0.998178i | \(-0.480780\pi\) | |||||||
\(230\) | 3.89573 | 0.256877 | ||||||||
\(231\) | −0.250725 | + | 3.72540i | −0.0164965 | + | 0.245113i | ||||
\(232\) | −28.9903 | −1.90331 | ||||||||
\(233\) | 0.396678 | + | 0.687066i | 0.0259872 | + | 0.0450112i | 0.878727 | − | 0.477326i | \(-0.158394\pi\) |
−0.852739 | + | 0.522337i | \(0.825060\pi\) | |||||||
\(234\) | 1.61766 | − | 2.80187i | 0.105750 | − | 0.183164i | ||||
\(235\) | −2.55626 | + | 4.42757i | −0.166752 | + | 0.288823i | ||||
\(236\) | 2.84416 | + | 4.92623i | 0.185139 | + | 0.320671i | ||||
\(237\) | −2.88152 | −0.187175 | ||||||||
\(238\) | 31.6848 | + | 21.2514i | 2.05382 | + | 1.37753i | ||||
\(239\) | 20.0488 | 1.29685 | 0.648425 | − | 0.761279i | \(-0.275428\pi\) | ||||
0.648425 | + | 0.761279i | \(0.275428\pi\) | |||||||
\(240\) | 21.4947 | + | 37.2299i | 1.38748 | + | 2.40318i | ||||
\(241\) | −6.90602 | + | 11.9616i | −0.444856 | + | 0.770513i | −0.998042 | − | 0.0625446i | \(-0.980078\pi\) |
0.553186 | + | 0.833058i | \(0.313412\pi\) | |||||||
\(242\) | 13.4919 | − | 23.3686i | 0.867289 | − | 1.50219i | ||||
\(243\) | 5.74404 | + | 9.94897i | 0.368480 | + | 0.638227i | ||||
\(244\) | −67.8362 | −4.34277 | ||||||||
\(245\) | 9.36269 | − | 12.1137i | 0.598161 | − | 0.773913i | ||||
\(246\) | −26.8609 | −1.71259 | ||||||||
\(247\) | −0.378453 | − | 0.655500i | −0.0240804 | − | 0.0417085i | ||||
\(248\) | −4.80004 | + | 8.31392i | −0.304803 | + | 0.527934i | ||||
\(249\) | −4.48732 | + | 7.77227i | −0.284372 | + | 0.492547i | ||||
\(250\) | 15.5461 | + | 26.9266i | 0.983222 | + | 1.70299i | ||||
\(251\) | −26.1095 | −1.64802 | −0.824010 | − | 0.566576i | \(-0.808268\pi\) | ||||
−0.824010 | + | 0.566576i | \(0.808268\pi\) | |||||||
\(252\) | 14.1565 | + | 9.49496i | 0.891776 | + | 0.598126i | ||||
\(253\) | −0.685057 | −0.0430692 | ||||||||
\(254\) | −11.9763 | − | 20.7436i | −0.751460 | − | 1.30157i | ||||
\(255\) | −7.79092 | + | 13.4943i | −0.487886 | + | 0.845044i | ||||
\(256\) | −19.3298 | + | 33.4801i | −1.20811 | + | 2.09251i | ||||
\(257\) | −5.30990 | − | 9.19701i | −0.331222 | − | 0.573694i | 0.651530 | − | 0.758623i | \(-0.274128\pi\) |
−0.982752 | + | 0.184930i | \(0.940794\pi\) | |||||||
\(258\) | −3.25752 | −0.202804 | ||||||||
\(259\) | 1.93531 | − | 28.7557i | 0.120254 | − | 1.78679i | ||||
\(260\) | 11.8697 | 0.736128 | ||||||||
\(261\) | −1.84253 | − | 3.19135i | −0.114050 | − | 0.197540i | ||||
\(262\) | 14.3273 | − | 24.8156i | 0.885142 | − | 1.53311i | ||||
\(263\) | −5.17888 | + | 8.97008i | −0.319343 | + | 0.553119i | −0.980351 | − | 0.197260i | \(-0.936796\pi\) |
0.661008 | + | 0.750379i | \(0.270129\pi\) | |||||||
\(264\) | −6.59013 | − | 11.4144i | −0.405594 | − | 0.702510i | ||||
\(265\) | 10.6912 | 0.656753 | ||||||||
\(266\) | 4.89894 | − | 2.40524i | 0.300374 | − | 0.147475i | ||||
\(267\) | 7.76581 | 0.475260 | ||||||||
\(268\) | −12.1534 | − | 21.0504i | −0.742389 | − | 1.28586i | ||||
\(269\) | −5.98503 | + | 10.3664i | −0.364914 | + | 0.632049i | −0.988762 | − | 0.149496i | \(-0.952235\pi\) |
0.623849 | + | 0.781545i | \(0.285568\pi\) | |||||||
\(270\) | −16.8018 | + | 29.1016i | −1.02253 | + | 1.77107i | ||||
\(271\) | 1.37845 | + | 2.38755i | 0.0837351 | + | 0.145033i | 0.904852 | − | 0.425727i | \(-0.139982\pi\) |
−0.821116 | + | 0.570761i | \(0.806648\pi\) | |||||||
\(272\) | −77.2429 | −4.68354 | ||||||||
\(273\) | −3.19767 | + | 1.56996i | −0.193532 | + | 0.0950184i | ||||
\(274\) | 23.7959 | 1.43757 | ||||||||
\(275\) | −0.113365 | − | 0.196354i | −0.00683618 | − | 0.0118406i | ||||
\(276\) | 2.38786 | − | 4.13590i | 0.143733 | − | 0.248952i | ||||
\(277\) | 11.9637 | − | 20.7218i | 0.718831 | − | 1.24505i | −0.242632 | − | 0.970118i | \(-0.578011\pi\) |
0.961463 | − | 0.274933i | \(-0.0886558\pi\) | |||||||
\(278\) | 5.45050 | + | 9.44054i | 0.326899 | + | 0.566206i | ||||
\(279\) | −1.22030 | −0.0730574 | ||||||||
\(280\) | −3.62906 | + | 53.9223i | −0.216878 | + | 3.22247i | ||||
\(281\) | −3.87870 | −0.231384 | −0.115692 | − | 0.993285i | \(-0.536909\pi\) | ||||
−0.115692 | + | 0.993285i | \(0.536909\pi\) | |||||||
\(282\) | 4.28854 | + | 7.42796i | 0.255379 | + | 0.442329i | ||||
\(283\) | 3.10499 | − | 5.37801i | 0.184573 | − | 0.319689i | −0.758860 | − | 0.651254i | \(-0.774243\pi\) |
0.943432 | + | 0.331565i | \(0.107577\pi\) | |||||||
\(284\) | 17.9165 | − | 31.0323i | 1.06315 | − | 1.84143i | ||||
\(285\) | 1.11448 | + | 1.93034i | 0.0660162 | + | 0.114343i | ||||
\(286\) | −2.85648 | −0.168907 | ||||||||
\(287\) | −16.0850 | − | 10.7884i | −0.949468 | − | 0.636821i | ||||
\(288\) | −25.0551 | −1.47639 | ||||||||
\(289\) | −5.49866 | − | 9.52395i | −0.323450 | − | 0.560232i | ||||
\(290\) | 9.25106 | − | 16.0233i | 0.543241 | − | 0.940920i | ||||
\(291\) | −1.94407 | + | 3.36723i | −0.113963 | + | 0.197390i | ||||
\(292\) | 22.4772 | + | 38.9316i | 1.31538 | + | 2.27830i | ||||
\(293\) | 16.5754 | 0.968347 | 0.484174 | − | 0.874972i | \(-0.339120\pi\) | ||||
0.484174 | + | 0.874972i | \(0.339120\pi\) | |||||||
\(294\) | −9.74618 | − | 23.7643i | −0.568409 | − | 1.38596i | ||||
\(295\) | −2.29249 | −0.133474 | ||||||||
\(296\) | 50.8681 | + | 88.1062i | 2.95665 | + | 5.12107i | ||||
\(297\) | 2.95457 | − | 5.11747i | 0.171442 | − | 0.296946i | ||||
\(298\) | −20.9744 | + | 36.3287i | −1.21501 | + | 2.10447i | ||||
\(299\) | −0.326792 | − | 0.566020i | −0.0188989 | − | 0.0327338i | ||||
\(300\) | 1.58060 | 0.0912561 | ||||||||
\(301\) | −1.95069 | − | 1.30835i | −0.112436 | − | 0.0754121i | ||||
\(302\) | −37.2698 | −2.14463 | ||||||||
\(303\) | −7.57650 | − | 13.1229i | −0.435259 | − | 0.753890i | ||||
\(304\) | −5.52475 | + | 9.56914i | −0.316866 | + | 0.548828i | ||||
\(305\) | 13.6695 | − | 23.6763i | 0.782716 | − | 1.35570i | ||||
\(306\) | −8.55944 | − | 14.8254i | −0.489311 | − | 0.847511i | ||||
\(307\) | −7.05788 | −0.402815 | −0.201407 | − | 0.979508i | \(-0.564551\pi\) | ||||
−0.201407 | + | 0.979508i | \(0.564551\pi\) | |||||||
\(308\) | 1.01060 | − | 15.0159i | 0.0575841 | − | 0.855612i | ||||
\(309\) | −27.2426 | −1.54978 | ||||||||
\(310\) | −3.06347 | − | 5.30609i | −0.173993 | − | 0.301365i | ||||
\(311\) | −10.5551 | + | 18.2820i | −0.598525 | + | 1.03668i | 0.394514 | + | 0.918890i | \(0.370913\pi\) |
−0.993039 | + | 0.117785i | \(0.962420\pi\) | |||||||
\(312\) | 6.28736 | − | 10.8900i | 0.355952 | − | 0.616526i | ||||
\(313\) | −0.990260 | − | 1.71518i | −0.0559728 | − | 0.0969477i | 0.836681 | − | 0.547690i | \(-0.184493\pi\) |
−0.892654 | + | 0.450742i | \(0.851159\pi\) | |||||||
\(314\) | 9.23194 | 0.520989 | ||||||||
\(315\) | −6.16660 | + | 3.02762i | −0.347449 | + | 0.170587i | ||||
\(316\) | 11.6145 | 0.653368 | ||||||||
\(317\) | 9.02297 | + | 15.6282i | 0.506781 | + | 0.877770i | 0.999969 | + | 0.00784727i | \(0.00249789\pi\) |
−0.493189 | + | 0.869922i | \(0.664169\pi\) | |||||||
\(318\) | 8.96808 | − | 15.5332i | 0.502905 | − | 0.871057i | ||||
\(319\) | −1.62678 | + | 2.81767i | −0.0910822 | + | 0.157759i | ||||
\(320\) | −30.9703 | − | 53.6421i | −1.73129 | − | 2.99868i | ||||
\(321\) | −12.1920 | −0.680492 | ||||||||
\(322\) | 4.23021 | − | 2.07691i | 0.235740 | − | 0.115742i | ||||
\(323\) | −4.00498 | −0.222843 | ||||||||
\(324\) | 10.9331 | + | 18.9366i | 0.607393 | + | 1.05204i | ||||
\(325\) | 0.108157 | − | 0.187333i | 0.00599947 | − | 0.0103914i | ||||
\(326\) | 18.8179 | − | 32.5936i | 1.04223 | − | 1.80519i | ||||
\(327\) | 10.1664 | + | 17.6087i | 0.562202 | + | 0.973763i | ||||
\(328\) | 68.3682 | 3.77500 | ||||||||
\(329\) | −0.415285 | + | 6.17051i | −0.0228954 | + | 0.340191i | ||||
\(330\) | 8.41187 | 0.463058 | ||||||||
\(331\) | 7.33689 | + | 12.7079i | 0.403272 | + | 0.698488i | 0.994119 | − | 0.108296i | \(-0.0345395\pi\) |
−0.590847 | + | 0.806784i | \(0.701206\pi\) | |||||||
\(332\) | 18.0870 | − | 31.3276i | 0.992653 | − | 1.71933i | ||||
\(333\) | −6.46602 | + | 11.1995i | −0.354336 | + | 0.613728i | ||||
\(334\) | −22.3175 | − | 38.6550i | −1.22116 | − | 2.11511i | ||||
\(335\) | 9.79606 | 0.535216 | ||||||||
\(336\) | 43.1883 | + | 28.9670i | 2.35611 | + | 1.58028i | ||||
\(337\) | 12.8080 | 0.697698 | 0.348849 | − | 0.937179i | \(-0.386573\pi\) | ||||
0.348849 | + | 0.937179i | \(0.386573\pi\) | |||||||
\(338\) | −1.36263 | − | 2.36014i | −0.0741170 | − | 0.128374i | ||||
\(339\) | 2.08969 | − | 3.61946i | 0.113497 | − | 0.196582i | ||||
\(340\) | 31.4028 | − | 54.3913i | 1.70306 | − | 2.94978i | ||||
\(341\) | 0.538705 | + | 0.933065i | 0.0291725 | + | 0.0505283i | ||||
\(342\) | −2.44883 | −0.132418 | ||||||||
\(343\) | 3.70846 | − | 18.1452i | 0.200238 | − | 0.979747i | ||||
\(344\) | 8.29125 | 0.447034 | ||||||||
\(345\) | 0.962348 | + | 1.66684i | 0.0518111 | + | 0.0897394i | ||||
\(346\) | −5.62146 | + | 9.73665i | −0.302211 | + | 0.523445i | ||||
\(347\) | −10.1027 | + | 17.4984i | −0.542342 | + | 0.939363i | 0.456428 | + | 0.889761i | \(0.349129\pi\) |
−0.998769 | + | 0.0496025i | \(0.984205\pi\) | |||||||
\(348\) | −11.3408 | − | 19.6428i | −0.607928 | − | 1.05296i | ||||
\(349\) | −18.4434 | −0.987252 | −0.493626 | − | 0.869674i | \(-0.664329\pi\) | ||||
−0.493626 | + | 0.869674i | \(0.664329\pi\) | |||||||
\(350\) | 1.29532 | + | 0.868789i | 0.0692378 | + | 0.0464387i | ||||
\(351\) | 5.63766 | 0.300916 | ||||||||
\(352\) | 11.0607 | + | 19.1576i | 0.589536 | + | 1.02111i | ||||
\(353\) | 4.07218 | − | 7.05322i | 0.216740 | − | 0.375405i | −0.737069 | − | 0.675817i | \(-0.763791\pi\) |
0.953810 | + | 0.300412i | \(0.0971242\pi\) | |||||||
\(354\) | −1.92301 | + | 3.33075i | −0.102207 | + | 0.177027i | ||||
\(355\) | 7.22064 | + | 12.5065i | 0.383232 | + | 0.663777i | ||||
\(356\) | −31.3016 | −1.65898 | ||||||||
\(357\) | −1.26570 | + | 18.8064i | −0.0669879 | + | 0.995339i | ||||
\(358\) | 39.2806 | 2.07604 | ||||||||
\(359\) | 16.3050 | + | 28.2411i | 0.860545 | + | 1.49051i | 0.871404 | + | 0.490566i | \(0.163210\pi\) |
−0.0108595 | + | 0.999941i | \(0.503457\pi\) | |||||||
\(360\) | 12.1250 | − | 21.0011i | 0.639043 | − | 1.10685i | ||||
\(361\) | 9.21355 | − | 15.9583i | 0.484923 | − | 0.839912i | ||||
\(362\) | −24.6654 | − | 42.7218i | −1.29639 | − | 2.24541i | ||||
\(363\) | 13.3314 | 0.699715 | ||||||||
\(364\) | 12.8888 | − | 6.32803i | 0.675557 | − | 0.331679i | ||||
\(365\) | −18.1173 | −0.948304 | ||||||||
\(366\) | −22.9329 | − | 39.7209i | −1.19872 | − | 2.07624i | ||||
\(367\) | 1.58006 | − | 2.73675i | 0.0824786 | − | 0.142857i | −0.821835 | − | 0.569725i | \(-0.807050\pi\) |
0.904314 | + | 0.426868i | \(0.140383\pi\) | |||||||
\(368\) | −4.77059 | + | 8.26290i | −0.248684 | + | 0.430733i | ||||
\(369\) | 4.34526 | + | 7.52621i | 0.226205 | + | 0.391799i | ||||
\(370\) | −64.9298 | −3.37554 | ||||||||
\(371\) | 11.6091 | − | 5.69972i | 0.602713 | − | 0.295915i | ||||
\(372\) | −7.51094 | −0.389424 | ||||||||
\(373\) | 0.738849 | + | 1.27972i | 0.0382561 | + | 0.0662616i | 0.884520 | − | 0.466503i | \(-0.154486\pi\) |
−0.846263 | + | 0.532765i | \(0.821153\pi\) | |||||||
\(374\) | −7.55718 | + | 13.0894i | −0.390773 | + | 0.676838i | ||||
\(375\) | −7.68059 | + | 13.3032i | −0.396624 | + | 0.686972i | ||||
\(376\) | −10.9155 | − | 18.9061i | −0.562922 | − | 0.975010i | ||||
\(377\) | −3.10408 | −0.159868 | ||||||||
\(378\) | −2.72960 | + | 40.5577i | −0.140395 | + | 2.08606i | ||||
\(379\) | 10.7254 | 0.550927 | 0.275463 | − | 0.961312i | \(-0.411169\pi\) | ||||
0.275463 | + | 0.961312i | \(0.411169\pi\) | |||||||
\(380\) | −4.49213 | − | 7.78060i | −0.230441 | − | 0.399136i | ||||
\(381\) | 5.91692 | − | 10.2484i | 0.303133 | − | 0.525042i | ||||
\(382\) | −7.55079 | + | 13.0784i | −0.386332 | + | 0.669147i | ||||
\(383\) | 10.7054 | + | 18.5424i | 0.547023 | + | 0.947471i | 0.998477 | + | 0.0551766i | \(0.0175722\pi\) |
−0.451454 | + | 0.892294i | \(0.649094\pi\) | |||||||
\(384\) | −47.0830 | −2.40269 | ||||||||
\(385\) | 5.03725 | + | 3.37855i | 0.256722 | + | 0.172187i | ||||
\(386\) | −23.8211 | −1.21246 | ||||||||
\(387\) | 0.526965 | + | 0.912730i | 0.0267871 | + | 0.0463967i | ||||
\(388\) | 7.83595 | − | 13.5723i | 0.397810 | − | 0.689027i | ||||
\(389\) | −17.3909 | + | 30.1220i | −0.881755 | + | 1.52725i | −0.0323675 | + | 0.999476i | \(0.510305\pi\) |
−0.849388 | + | 0.527769i | \(0.823029\pi\) | |||||||
\(390\) | 4.01270 | + | 6.95021i | 0.203191 | + | 0.351937i | ||||
\(391\) | −3.45828 | −0.174893 | ||||||||
\(392\) | 24.8066 | + | 60.4866i | 1.25292 | + | 3.05503i | ||||
\(393\) | 14.1568 | 0.714119 | ||||||||
\(394\) | 7.45185 | + | 12.9070i | 0.375419 | + | 0.650244i | ||||
\(395\) | −2.34042 | + | 4.05373i | −0.117759 | + | 0.203965i | ||||
\(396\) | −3.37649 | + | 5.84825i | −0.169675 | + | 0.293886i | ||||
\(397\) | −2.22605 | − | 3.85564i | −0.111722 | − | 0.193509i | 0.804742 | − | 0.593624i | \(-0.202303\pi\) |
−0.916465 | + | 0.400115i | \(0.868970\pi\) | |||||||
\(398\) | 53.2426 | 2.66881 | ||||||||
\(399\) | 2.23928 | + | 1.50191i | 0.112104 | + | 0.0751897i | ||||
\(400\) | −3.15780 | −0.157890 | ||||||||
\(401\) | 6.87687 | + | 11.9111i | 0.343415 | + | 0.594811i | 0.985064 | − | 0.172186i | \(-0.0550831\pi\) |
−0.641650 | + | 0.766998i | \(0.721750\pi\) | |||||||
\(402\) | 8.21724 | − | 14.2327i | 0.409839 | − | 0.709861i | ||||
\(403\) | −0.513956 | + | 0.890198i | −0.0256020 | + | 0.0443439i | ||||
\(404\) | 30.5385 | + | 52.8943i | 1.51935 | + | 2.63159i | ||||
\(405\) | −8.81241 | −0.437892 | ||||||||
\(406\) | 1.50291 | − | 22.3310i | 0.0745882 | − | 1.10827i | ||||
\(407\) | 11.4178 | 0.565959 | ||||||||
\(408\) | −33.2680 | − | 57.6219i | −1.64701 | − | 2.85271i | ||||
\(409\) | 1.74603 | − | 3.02422i | 0.0863358 | − | 0.149538i | −0.819624 | − | 0.572902i | \(-0.805818\pi\) |
0.905960 | + | 0.423364i | \(0.139151\pi\) | |||||||
\(410\) | −21.8169 | + | 37.7879i | −1.07746 | + | 1.86621i | ||||
\(411\) | 5.87822 | + | 10.1814i | 0.289951 | + | 0.502210i | ||||
\(412\) | 109.806 | 5.40977 | ||||||||
\(413\) | −2.48931 | + | 1.22218i | −0.122491 | + | 0.0601396i | ||||
\(414\) | −2.11455 | −0.103925 | ||||||||
\(415\) | 7.28935 | + | 12.6255i | 0.357820 | + | 0.619763i | ||||
\(416\) | −10.5525 | + | 18.2775i | −0.517380 | + | 0.896128i | ||||
\(417\) | −2.69283 | + | 4.66412i | −0.131869 | + | 0.228403i | ||||
\(418\) | 1.08105 | + | 1.87243i | 0.0528757 | + | 0.0915834i | ||||
\(419\) | −3.56737 | −0.174278 | −0.0871388 | − | 0.996196i | \(-0.527772\pi\) | ||||
−0.0871388 | + | 0.996196i | \(0.527772\pi\) | |||||||
\(420\) | −37.9554 | + | 18.6350i | −1.85203 | + | 0.909295i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | −22.7429 | − | 39.3919i | −1.10711 | − | 1.91757i | ||||
\(423\) | 1.38750 | − | 2.40323i | 0.0674627 | − | 0.116849i | ||||
\(424\) | −22.8262 | + | 39.5361i | −1.10854 | + | 1.92004i | ||||
\(425\) | −0.572285 | − | 0.991227i | −0.0277599 | − | 0.0480816i | ||||
\(426\) | 24.2276 | 1.17383 | ||||||||
\(427\) | 2.22073 | − | 32.9967i | 0.107469 | − | 1.59682i | ||||
\(428\) | 49.1423 | 2.37538 | ||||||||
\(429\) | −0.705626 | − | 1.22218i | −0.0340680 | − | 0.0590074i | ||||
\(430\) | −2.64581 | + | 4.58268i | −0.127592 | + | 0.220996i | ||||
\(431\) | 5.68211 | − | 9.84171i | 0.273698 | − | 0.474059i | −0.696108 | − | 0.717937i | \(-0.745087\pi\) |
0.969806 | + | 0.243879i | \(0.0784198\pi\) | |||||||
\(432\) | −41.1500 | − | 71.2738i | −1.97983 | − | 3.42916i | ||||
\(433\) | −21.2136 | −1.01946 | −0.509731 | − | 0.860334i | \(-0.670255\pi\) | ||||
−0.509731 | + | 0.860334i | \(0.670255\pi\) | |||||||
\(434\) | −6.15529 | − | 4.12844i | −0.295464 | − | 0.198171i | ||||
\(435\) | 9.14101 | 0.438278 | ||||||||
\(436\) | −40.9776 | − | 70.9752i | −1.96247 | − | 3.39910i | ||||
\(437\) | −0.247351 | + | 0.428424i | −0.0118324 | + | 0.0204943i | ||||
\(438\) | −15.1974 | + | 26.3226i | −0.726158 | + | 1.25774i | ||||
\(439\) | 12.2503 | + | 21.2182i | 0.584676 | + | 1.01269i | 0.994916 | + | 0.100711i | \(0.0321118\pi\) |
−0.410239 | + | 0.911978i | \(0.634555\pi\) | |||||||
\(440\) | −21.4105 | −1.02070 | ||||||||
\(441\) | −5.08195 | + | 6.57513i | −0.241997 | + | 0.313102i | ||||
\(442\) | −14.4200 | −0.685888 | ||||||||
\(443\) | −20.2344 | − | 35.0470i | −0.961366 | − | 1.66513i | −0.719077 | − | 0.694930i | \(-0.755435\pi\) |
−0.242288 | − | 0.970204i | \(-0.577898\pi\) | |||||||
\(444\) | −39.7983 | + | 68.9327i | −1.88874 | + | 3.27140i | ||||
\(445\) | 6.30753 | − | 10.9250i | 0.299005 | − | 0.517893i | ||||
\(446\) | 7.27937 | + | 12.6082i | 0.344688 | + | 0.597017i | ||||
\(447\) | −20.7249 | −0.980254 | ||||||||
\(448\) | −62.2272 | − | 41.7366i | −2.93996 | − | 1.97187i | ||||
\(449\) | −27.7638 | −1.31025 | −0.655127 | − | 0.755519i | \(-0.727385\pi\) | ||||
−0.655127 | + | 0.755519i | \(0.727385\pi\) | |||||||
\(450\) | −0.349922 | − | 0.606083i | −0.0164955 | − | 0.0285710i | ||||
\(451\) | 3.83646 | − | 6.64494i | 0.180652 | − | 0.312898i | ||||
\(452\) | −8.42292 | + | 14.5889i | −0.396181 | + | 0.686205i | ||||
\(453\) | −9.20661 | − | 15.9463i | −0.432564 | − | 0.749223i | ||||
\(454\) | 54.8362 | 2.57359 | ||||||||
\(455\) | −0.388575 | + | 5.77363i | −0.0182167 | + | 0.270672i | ||||
\(456\) | −9.51789 | −0.445716 | ||||||||
\(457\) | 5.59696 | + | 9.69422i | 0.261815 | + | 0.453476i | 0.966724 | − | 0.255821i | \(-0.0823457\pi\) |
−0.704910 | + | 0.709297i | \(0.749012\pi\) | |||||||
\(458\) | −34.4059 | + | 59.5928i | −1.60768 | + | 2.78459i | ||||
\(459\) | 14.9151 | − | 25.8338i | 0.696179 | − | 1.20582i | ||||
\(460\) | −3.87893 | − | 6.71850i | −0.180856 | − | 0.313252i | ||||
\(461\) | −9.29773 | −0.433038 | −0.216519 | − | 0.976278i | \(-0.569470\pi\) | ||||
−0.216519 | + | 0.976278i | \(0.569470\pi\) | |||||||
\(462\) | 9.13409 | − | 4.48457i | 0.424956 | − | 0.208641i | ||||
\(463\) | 28.2439 | 1.31260 | 0.656302 | − | 0.754499i | \(-0.272120\pi\) | ||||
0.656302 | + | 0.754499i | \(0.272120\pi\) | |||||||
\(464\) | 22.6571 | + | 39.2432i | 1.05183 | + | 1.82182i | ||||
\(465\) | 1.51351 | − | 2.62148i | 0.0701875 | − | 0.121568i | ||||
\(466\) | 1.08105 | − | 1.87243i | 0.0500785 | − | 0.0867385i | ||||
\(467\) | −11.1303 | − | 19.2783i | −0.515050 | − | 0.892093i | −0.999847 | − | 0.0174663i | \(-0.994440\pi\) |
0.484797 | − | 0.874626i | \(-0.338893\pi\) | |||||||
\(468\) | −6.44273 | −0.297815 | ||||||||
\(469\) | 10.6371 | − | 5.22252i | 0.491177 | − | 0.241154i | ||||
\(470\) | 13.9329 | 0.642676 | ||||||||
\(471\) | 2.28053 | + | 3.95000i | 0.105081 | + | 0.182006i | ||||
\(472\) | 4.89457 | − | 8.47765i | 0.225291 | − | 0.390215i | ||||
\(473\) | 0.465261 | − | 0.805855i | 0.0213927 | − | 0.0370533i | ||||
\(474\) | 3.92643 | + | 6.80078i | 0.180347 | + | 0.312370i | ||||
\(475\) | −0.163729 | −0.00751242 | ||||||||
\(476\) | 5.10165 | − | 75.8027i | 0.233834 | − | 3.47441i | ||||
\(477\) | −5.80302 | −0.265702 | ||||||||
\(478\) | −27.3190 | − | 47.3179i | −1.24954 | − | 2.16427i | ||||
\(479\) | 16.4382 | − | 28.4718i | 0.751081 | − | 1.30091i | −0.196219 | − | 0.980560i | \(-0.562866\pi\) |
0.947299 | − | 0.320350i | \(-0.103800\pi\) | |||||||
\(480\) | 31.0754 | − | 53.8242i | 1.41839 | − | 2.45673i | ||||
\(481\) | 5.44661 | + | 9.43381i | 0.248344 | + | 0.430145i | ||||
\(482\) | 37.6413 | 1.71451 | ||||||||
\(483\) | 1.93360 | + | 1.29689i | 0.0879820 | + | 0.0590107i | ||||
\(484\) | −53.7346 | −2.44248 | ||||||||
\(485\) | 3.15801 | + | 5.46984i | 0.143398 | + | 0.248373i | ||||
\(486\) | 15.6539 | − | 27.1134i | 0.710078 | − | 1.22989i | ||||
\(487\) | 13.9462 | − | 24.1555i | 0.631962 | − | 1.09459i | −0.355188 | − | 0.934795i | \(-0.615583\pi\) |
0.987150 | − | 0.159796i | \(-0.0510836\pi\) | |||||||
\(488\) | 58.3703 | + | 101.100i | 2.64230 | + | 4.57660i | ||||
\(489\) | 18.5941 | 0.840852 | ||||||||
\(490\) | −41.3477 | − | 5.59086i | −1.86790 | − | 0.252569i | ||||
\(491\) | 10.6571 | 0.480948 | 0.240474 | − | 0.970656i | \(-0.422697\pi\) | ||||
0.240474 | + | 0.970656i | \(0.422697\pi\) | |||||||
\(492\) | 26.7450 | + | 46.3237i | 1.20576 | + | 2.08844i | ||||
\(493\) | −8.21224 | + | 14.2240i | −0.369861 | + | 0.640618i | ||||
\(494\) | −1.03138 | + | 1.78640i | −0.0464040 | + | 0.0803740i | ||||
\(495\) | −1.36078 | − | 2.35694i | −0.0611625 | − | 0.105936i | ||||
\(496\) | 15.0057 | 0.673776 | ||||||||
\(497\) | 14.5081 | + | 9.73078i | 0.650777 | + | 0.436485i | ||||
\(498\) | 24.4581 | 1.09600 | ||||||||
\(499\) | 12.2557 | + | 21.2275i | 0.548641 | + | 0.950274i | 0.998368 | + | 0.0571077i | \(0.0181878\pi\) |
−0.449727 | + | 0.893166i | \(0.648479\pi\) | |||||||
\(500\) | 30.9581 | − | 53.6210i | 1.38449 | − | 2.39800i | ||||
\(501\) | 11.0260 | − | 19.0976i | 0.492605 | − | 0.853217i | ||||
\(502\) | 35.5775 | + | 61.6221i | 1.58790 | + | 2.75033i | ||||
\(503\) | −38.0054 | −1.69458 | −0.847288 | − | 0.531134i | \(-0.821766\pi\) | ||||
−0.847288 | + | 0.531134i | \(0.821766\pi\) | |||||||
\(504\) | 1.96980 | − | 29.2683i | 0.0877421 | − | 1.30371i | ||||
\(505\) | −24.6151 | −1.09536 | ||||||||
\(506\) | 0.933476 | + | 1.61683i | 0.0414981 | + | 0.0718768i | ||||
\(507\) | 0.673208 | − | 1.16603i | 0.0298982 | − | 0.0517852i | ||||
\(508\) | −23.8493 | + | 41.3082i | −1.05814 | + | 1.83275i | ||||
\(509\) | −19.9250 | − | 34.5112i | −0.883161 | − | 1.52968i | −0.847807 | − | 0.530305i | \(-0.822077\pi\) |
−0.0353545 | − | 0.999375i | \(-0.511256\pi\) | |||||||
\(510\) | 42.4644 | 1.88036 | ||||||||
\(511\) | −19.6728 | + | 9.65878i | −0.870274 | + | 0.427279i | ||||
\(512\) | 35.4186 | 1.56530 | ||||||||
\(513\) | −2.13359 | − | 3.69549i | −0.0942004 | − | 0.163160i | ||||
\(514\) | −14.4708 | + | 25.0642i | −0.638279 | + | 1.10553i | ||||
\(515\) | −22.1269 | + | 38.3249i | −0.975027 | + | 1.68880i | ||||
\(516\) | 3.24346 | + | 5.61784i | 0.142786 | + | 0.247312i | ||||
\(517\) | −2.45007 | −0.107754 | ||||||||
\(518\) | −70.5045 | + | 34.6157i | −3.09779 | + | 1.52093i | ||||
\(519\) | −5.55459 | −0.243819 | ||||||||
\(520\) | −10.2134 | − | 17.6901i | −0.447887 | − | 0.775764i | ||||
\(521\) | 9.81670 | − | 17.0030i | 0.430077 | − | 0.744916i | −0.566802 | − | 0.823854i | \(-0.691820\pi\) |
0.996880 | + | 0.0789382i | \(0.0251530\pi\) | |||||||
\(522\) | −5.02135 | + | 8.69724i | −0.219779 | + | 0.380668i | ||||
\(523\) | −11.4162 | − | 19.7734i | −0.499195 | − | 0.864632i | 0.500804 | − | 0.865561i | \(-0.333038\pi\) |
−1.00000 | 0.000928862i | \(0.999704\pi\) | ||||||||
\(524\) | −57.0619 | −2.49276 | ||||||||
\(525\) | −0.0517436 | + | 0.768832i | −0.00225828 | + | 0.0335546i | ||||
\(526\) | 28.2275 | 1.23078 | ||||||||
\(527\) | 2.71947 | + | 4.71026i | 0.118462 | + | 0.205182i | ||||
\(528\) | −10.3009 | + | 17.8417i | −0.448289 | + | 0.776459i | ||||
\(529\) | 11.2864 | − | 19.5486i | 0.490714 | − | 0.849941i | ||||
\(530\) | −14.5681 | − | 25.2326i | −0.632796 | − | 1.09603i | ||||
\(531\) | 1.24433 | 0.0539994 | ||||||||
\(532\) | −9.02584 | − | 6.05375i | −0.391320 | − | 0.262463i | ||||
\(533\) | 7.32040 | 0.317082 | ||||||||
\(534\) | −10.5819 | − | 18.3284i | −0.457923 | − | 0.793146i | ||||
\(535\) | −9.90257 | + | 17.1518i | −0.428125 | + | 0.741535i | ||||
\(536\) | −20.9151 | + | 36.2260i | −0.903394 | + | 1.56472i | ||||
\(537\) | 9.70333 | + | 16.8067i | 0.418730 | + | 0.725261i | ||||
\(538\) | 32.6214 | 1.40641 | ||||||||
\(539\) | 7.27092 | + | 0.983142i | 0.313181 | + | 0.0423469i | ||||
\(540\) | 66.9175 | 2.87967 | ||||||||
\(541\) | 4.82334 | + | 8.35427i | 0.207372 | + | 0.359178i | 0.950886 | − | 0.309542i | \(-0.100176\pi\) |
−0.743514 | + | 0.668720i | \(0.766842\pi\) | |||||||
\(542\) | 3.75663 | − | 6.50667i | 0.161361 | − | 0.279486i | ||||
\(543\) | 12.1860 | − | 21.1068i | 0.522952 | − | 0.905779i | ||||
\(544\) | 55.8360 | + | 96.7108i | 2.39395 | + | 4.14644i | ||||
\(545\) | 33.0292 | 1.41482 | ||||||||
\(546\) | 8.06254 | + | 5.40766i | 0.345045 | + | 0.231426i | ||||
\(547\) | −43.8570 | −1.87519 | −0.937596 | − | 0.347728i | \(-0.886953\pi\) | ||||
−0.937596 | + | 0.347728i | \(0.886953\pi\) | |||||||
\(548\) | −23.6933 | − | 41.0380i | −1.01213 | − | 1.75306i | ||||
\(549\) | −7.41965 | + | 12.8512i | −0.316663 | + | 0.548476i | ||||
\(550\) | −0.308949 | + | 0.535115i | −0.0131736 | + | 0.0228174i | ||||
\(551\) | 1.17475 | + | 2.03473i | 0.0500461 | + | 0.0866823i | ||||
\(552\) | −8.21864 | −0.349808 | ||||||||
\(553\) | −0.380221 | + | 5.64950i | −0.0161686 | + | 0.240241i | ||||
\(554\) | −65.2083 | −2.77044 | ||||||||
\(555\) | −16.0394 | − | 27.7810i | −0.680833 | − | 1.17924i | ||||
\(556\) | 10.8540 | − | 18.7996i | 0.460311 | − | 0.797282i | ||||
\(557\) | −7.45977 | + | 12.9207i | −0.316080 | + | 0.547467i | −0.979667 | − | 0.200633i | \(-0.935700\pi\) |
0.663586 | + | 0.748100i | \(0.269034\pi\) | |||||||
\(558\) | 1.66281 | + | 2.88007i | 0.0703924 | + | 0.121923i | ||||
\(559\) | 0.887771 | 0.0375487 | ||||||||
\(560\) | 75.8290 | − | 37.2299i | 3.20436 | − | 1.57325i | ||||
\(561\) | −7.46729 | −0.315269 | ||||||||
\(562\) | 5.28521 | + | 9.15426i | 0.222943 | + | 0.386149i | ||||
\(563\) | 8.63486 | − | 14.9560i | 0.363916 | − | 0.630321i | −0.624686 | − | 0.780876i | \(-0.714773\pi\) |
0.988602 | + | 0.150555i | \(0.0481062\pi\) | |||||||
\(564\) | 8.54007 | − | 14.7918i | 0.359602 | − | 0.622849i | ||||
\(565\) | −3.39457 | − | 5.87957i | −0.142811 | − | 0.247355i | ||||
\(566\) | −16.9238 | −0.711359 | ||||||||
\(567\) | −9.56902 | + | 4.69811i | −0.401861 | + | 0.197302i | ||||
\(568\) | −61.6657 | −2.58743 | ||||||||
\(569\) | −13.2662 | − | 22.9777i | −0.556148 | − | 0.963277i | −0.997813 | − | 0.0660972i | \(-0.978945\pi\) |
0.441665 | − | 0.897180i | \(-0.354388\pi\) | |||||||
\(570\) | 3.03724 | − | 5.26065i | 0.127216 | − | 0.220345i | ||||
\(571\) | 0.992844 | − | 1.71966i | 0.0415492 | − | 0.0719654i | −0.844503 | − | 0.535551i | \(-0.820104\pi\) |
0.886052 | + | 0.463586i | \(0.153437\pi\) | |||||||
\(572\) | 2.84416 | + | 4.92623i | 0.118920 | + | 0.205976i | ||||
\(573\) | −7.46097 | −0.311686 | ||||||||
\(574\) | −3.54433 | + | 52.6634i | −0.147938 | + | 2.19813i | ||||
\(575\) | −0.141379 | −0.00589593 | ||||||||
\(576\) | 16.8103 | + | 29.1162i | 0.700428 | + | 1.21318i | ||||
\(577\) | −5.94915 | + | 10.3042i | −0.247666 | + | 0.428971i | −0.962878 | − | 0.269937i | \(-0.912997\pi\) |
0.715212 | + | 0.698908i | \(0.246330\pi\) | |||||||
\(578\) | −14.9852 | + | 25.9551i | −0.623303 | + | 1.07959i | ||||
\(579\) | −5.88443 | − | 10.1921i | −0.244549 | − | 0.423571i | ||||
\(580\) | −36.8446 | −1.52989 | ||||||||
\(581\) | 14.6462 | + | 9.82339i | 0.607626 | + | 0.407543i | ||||
\(582\) | 10.5962 | 0.439225 | ||||||||
\(583\) | 2.56176 | + | 4.43711i | 0.106097 | + | 0.183766i | ||||
\(584\) | 38.6814 | − | 66.9981i | 1.60065 | − | 2.77240i | ||||
\(585\) | 1.29826 | − | 2.24865i | 0.0536765 | − | 0.0929704i | ||||
\(586\) | −22.5861 | − | 39.1203i | −0.933024 | − | 1.61604i | ||||
\(587\) | 33.5122 | 1.38320 | 0.691598 | − | 0.722283i | \(-0.256907\pi\) | ||||
0.691598 | + | 0.722283i | \(0.256907\pi\) | |||||||
\(588\) | −31.2793 | + | 40.4699i | −1.28994 | + | 1.66895i | ||||
\(589\) | 0.778033 | 0.0320583 | ||||||||
\(590\) | 3.12380 | + | 5.41058i | 0.128605 | + | 0.222750i | ||||
\(591\) | −3.68160 | + | 6.37672i | −0.151441 | + | 0.262303i | ||||
\(592\) | 79.5109 | − | 137.717i | 3.26788 | − | 5.66013i | ||||
\(593\) | −17.6408 | − | 30.5547i | −0.724419 | − | 1.25473i | −0.959213 | − | 0.282686i | \(-0.908775\pi\) |
0.234793 | − | 0.972045i | \(-0.424559\pi\) | |||||||
\(594\) | −16.1039 | −0.660751 | ||||||||
\(595\) | 25.4288 | + | 17.0554i | 1.04248 | + | 0.699205i | ||||
\(596\) | 83.5357 | 3.42176 | ||||||||
\(597\) | 13.1523 | + | 22.7805i | 0.538288 | + | 0.932343i | ||||
\(598\) | −0.890590 | + | 1.54255i | −0.0364189 | + | 0.0630794i | ||||
\(599\) | 12.5034 | − | 21.6565i | 0.510876 | − | 0.884863i | −0.489045 | − | 0.872259i | \(-0.662655\pi\) |
0.999921 | − | 0.0126040i | \(-0.00401207\pi\) | |||||||
\(600\) | −1.36004 | − | 2.35566i | −0.0555236 | − | 0.0961696i | ||||
\(601\) | −28.4688 | −1.16127 | −0.580634 | − | 0.814165i | \(-0.697195\pi\) | ||||
−0.580634 | + | 0.814165i | \(0.697195\pi\) | |||||||
\(602\) | −0.429834 | + | 6.38668i | −0.0175187 | + | 0.260301i | ||||
\(603\) | −5.31717 | −0.216532 | ||||||||
\(604\) | 37.1090 | + | 64.2747i | 1.50994 | + | 2.61530i | ||||
\(605\) | 10.8280 | − | 18.7546i | 0.440219 | − | 0.762482i | ||||
\(606\) | −20.6479 | + | 35.7631i | −0.838762 | + | 1.45278i | ||||
\(607\) | −18.0234 | − | 31.2175i | −0.731549 | − | 1.26708i | −0.956221 | − | 0.292646i | \(-0.905464\pi\) |
0.224672 | − | 0.974434i | \(-0.427869\pi\) | |||||||
\(608\) | 15.9745 | 0.647853 | ||||||||
\(609\) | 9.92583 | − | 4.87330i | 0.402215 | − | 0.197476i | ||||
\(610\) | −74.5058 | −3.01665 | ||||||||
\(611\) | −1.16875 | − | 2.02434i | −0.0472827 | − | 0.0818961i | ||||
\(612\) | −17.0450 | + | 29.5229i | −0.689005 | + | 1.19339i | ||||
\(613\) | −9.16264 | + | 15.8702i | −0.370075 | + | 0.640989i | −0.989577 | − | 0.144006i | \(-0.954001\pi\) |
0.619501 | + | 0.784996i | \(0.287335\pi\) | |||||||
\(614\) | 9.61725 | + | 16.6576i | 0.388121 | + | 0.672245i | ||||
\(615\) | −21.5573 | −0.869276 | ||||||||
\(616\) | −23.2487 | + | 11.4144i | −0.936717 | + | 0.459901i | ||||
\(617\) | 44.3782 | 1.78660 | 0.893299 | − | 0.449463i | \(-0.148385\pi\) | ||||
0.893299 | + | 0.449463i | \(0.148385\pi\) | |||||||
\(618\) | 37.1214 | + | 64.2962i | 1.49324 | + | 2.58637i | ||||
\(619\) | 12.5043 | − | 21.6580i | 0.502588 | − | 0.870509i | −0.497407 | − | 0.867517i | \(-0.665714\pi\) |
0.999996 | − | 0.00299144i | \(-0.000952205\pi\) | |||||||
\(620\) | −6.10051 | + | 10.5664i | −0.245002 | + | 0.424357i | ||||
\(621\) | −1.84234 | − | 3.19103i | −0.0739307 | − | 0.128052i | ||||
\(622\) | 57.5306 | 2.30677 | ||||||||
\(623\) | 1.02471 | − | 15.2256i | 0.0410541 | − | 0.610002i | ||||
\(624\) | −19.6553 | −0.786842 | ||||||||
\(625\) | 11.9358 | + | 20.6734i | 0.477433 | + | 0.826938i | ||||
\(626\) | −2.69871 | + | 4.67429i | −0.107862 | + | 0.186822i | ||||
\(627\) | −0.534093 | + | 0.925076i | −0.0213296 | + | 0.0369440i | ||||
\(628\) | −9.19212 | − | 15.9212i | −0.366806 | − | 0.635326i | ||||
\(629\) | 57.6388 | 2.29821 | ||||||||
\(630\) | 15.5484 | + | 10.4285i | 0.619462 | + | 0.415482i | ||||
\(631\) | −18.4638 | −0.735032 | −0.367516 | − | 0.930017i | \(-0.619792\pi\) | ||||
−0.367516 | + | 0.930017i | \(0.619792\pi\) | |||||||
\(632\) | −9.99382 | − | 17.3098i | −0.397533 | − | 0.688547i | ||||
\(633\) | 11.2362 | − | 19.4616i | 0.446598 | − | 0.773531i | ||||
\(634\) | 24.5899 | − | 42.5909i | 0.976588 | − | 1.69150i | ||||
\(635\) | −9.61165 | − | 16.6479i | −0.381427 | − | 0.660650i | ||||
\(636\) | −35.7176 | −1.41629 | ||||||||
\(637\) | 2.65613 | + | 6.47650i | 0.105240 | + | 0.256608i | ||||
\(638\) | 8.86677 | 0.351039 | ||||||||
\(639\) | −3.91927 | − | 6.78837i | −0.155044 | − | 0.268544i | ||||
\(640\) | −38.2416 | + | 66.2364i | −1.51163 | + | 2.61822i | ||||
\(641\) | 10.6284 | − | 18.4088i | 0.419795 | − | 0.727106i | −0.576124 | − | 0.817362i | \(-0.695435\pi\) |
0.995919 | + | 0.0902567i | \(0.0287687\pi\) | |||||||
\(642\) | 16.6132 | + | 28.7748i | 0.655669 | + | 1.13565i | ||||
\(643\) | −36.0554 | −1.42188 | −0.710942 | − | 0.703251i | \(-0.751731\pi\) | ||||
−0.710942 | + | 0.703251i | \(0.751731\pi\) | |||||||
\(644\) | −7.79376 | − | 5.22738i | −0.307117 | − | 0.205988i | ||||
\(645\) | −2.61434 | −0.102939 | ||||||||
\(646\) | 5.45729 | + | 9.45230i | 0.214714 | + | 0.371896i | ||||
\(647\) | −19.9117 | + | 34.4881i | −0.782809 | + | 1.35587i | 0.147490 | + | 0.989064i | \(0.452881\pi\) |
−0.930299 | + | 0.366802i | \(0.880453\pi\) | |||||||
\(648\) | 18.8149 | − | 32.5884i | 0.739120 | − | 1.28019i | ||||
\(649\) | −0.549314 | − | 0.951440i | −0.0215625 | − | 0.0373473i | ||||
\(650\) | −0.589510 | −0.0231225 | ||||||||
\(651\) | 0.245883 | − | 3.65345i | 0.00963691 | − | 0.143190i | ||||
\(652\) | −74.9469 | −2.93515 | ||||||||
\(653\) | 16.2335 | + | 28.1172i | 0.635265 | + | 1.10031i | 0.986459 | + | 0.164008i | \(0.0524423\pi\) |
−0.351195 | + | 0.936303i | \(0.614224\pi\) | |||||||
\(654\) | 27.7059 | − | 47.9881i | 1.08339 | − | 1.87648i | ||||
\(655\) | 11.4984 | − | 19.9159i | 0.449281 | − | 0.778177i | ||||
\(656\) | −53.4324 | − | 92.5477i | −2.08619 | − | 3.61338i | ||||
\(657\) | 9.83384 | 0.383655 | ||||||||
\(658\) | 15.1291 | − | 7.42796i | 0.589794 | − | 0.289572i | ||||
\(659\) | 23.5230 | 0.916327 | 0.458164 | − | 0.888868i | \(-0.348507\pi\) | ||||
0.458164 | + | 0.888868i | \(0.348507\pi\) | |||||||
\(660\) | −8.37558 | − | 14.5069i | −0.326019 | − | 0.564682i | ||||
\(661\) | −7.01944 | + | 12.1580i | −0.273025 | + | 0.472893i | −0.969635 | − | 0.244557i | \(-0.921357\pi\) |
0.696610 | + | 0.717450i | \(0.254691\pi\) | |||||||
\(662\) | 19.9949 | − | 34.6321i | 0.777122 | − | 1.34602i | ||||
\(663\) | −3.56211 | − | 6.16976i | −0.138341 | − | 0.239614i | ||||
\(664\) | −62.2525 | −2.41587 | ||||||||
\(665\) | 3.93167 | − | 1.93034i | 0.152464 | − | 0.0748553i | ||||
\(666\) | 35.2431 | 1.36564 | ||||||||
\(667\) | 1.01439 | + | 1.75698i | 0.0392773 | + | 0.0680303i | ||||
\(668\) | −44.4424 | + | 76.9765i | −1.71953 | + | 2.97831i | ||||
\(669\) | −3.59639 | + | 6.22913i | −0.139044 | + | 0.240832i | ||||
\(670\) | −13.3484 | − | 23.1200i | −0.515692 | − | 0.893205i | ||||
\(671\) | 13.1017 | 0.505786 | ||||||||
\(672\) | 5.04846 | − | 75.0124i | 0.194748 | − | 2.89367i | ||||
\(673\) | −47.1937 | −1.81918 | −0.909592 | − | 0.415502i | \(-0.863606\pi\) | ||||
−0.909592 | + | 0.415502i | \(0.863606\pi\) | |||||||
\(674\) | −17.4526 | − | 30.2287i | −0.672247 | − | 1.16437i | ||||
\(675\) | 0.609753 | − | 1.05612i | 0.0234694 | − | 0.0406502i | ||||
\(676\) | −2.71349 | + | 4.69991i | −0.104365 | + | 0.180766i | ||||
\(677\) | 4.79438 | + | 8.30411i | 0.184263 | + | 0.319153i | 0.943328 | − | 0.331862i | \(-0.107677\pi\) |
−0.759065 | + | 0.651015i | \(0.774344\pi\) | |||||||
\(678\) | −11.3899 | −0.437426 | ||||||||
\(679\) | 6.34526 | + | 4.25585i | 0.243509 | + | 0.163325i | ||||
\(680\) | −108.083 | −4.14481 | ||||||||
\(681\) | 13.5460 | + | 23.4623i | 0.519083 | + | 0.899078i | ||||
\(682\) | 1.46811 | − | 2.54284i | 0.0562167 | − | 0.0973702i | ||||
\(683\) | −23.6581 | + | 40.9769i | −0.905250 | + | 1.56794i | −0.0846691 | + | 0.996409i | \(0.526983\pi\) |
−0.820581 | + | 0.571530i | \(0.806350\pi\) | |||||||
\(684\) | 2.43827 | + | 4.22321i | 0.0932296 | + | 0.161478i | ||||
\(685\) | 19.0976 | 0.729680 | ||||||||
\(686\) | −47.8783 | + | 15.9726i | −1.82800 | + | 0.609837i | ||||
\(687\) | −33.9967 | −1.29705 | ||||||||
\(688\) | −6.47994 | − | 11.2236i | −0.247045 | − | 0.427895i | ||||
\(689\) | −2.44407 | + | 4.23325i | −0.0931117 | + | 0.161274i | ||||
\(690\) | 2.62264 | − | 4.54254i | 0.0998421 | − | 0.172932i | ||||
\(691\) | 13.5559 | + | 23.4796i | 0.515692 | + | 0.893205i | 0.999834 | + | 0.0182158i | \(0.00579859\pi\) |
−0.484142 | + | 0.874990i | \(0.660868\pi\) | |||||||
\(692\) | 22.3888 | 0.851095 | ||||||||
\(693\) | −2.73415 | − | 1.83383i | −0.103862 | − | 0.0696615i | ||||
\(694\) | 55.0648 | 2.09023 | ||||||||
\(695\) | 4.37433 | + | 7.57656i | 0.165928 | + | 0.287395i | ||||
\(696\) | −19.5165 | + | 33.8036i | −0.739771 | + | 1.28132i | ||||
\(697\) | 19.3670 | − | 33.5447i | 0.733578 | − | 1.27059i | ||||
\(698\) | 25.1314 | + | 43.5289i | 0.951238 | + | 1.64759i | ||||
\(699\) | 1.06819 | 0.0404025 | ||||||||
\(700\) | 0.208563 | − | 3.09893i | 0.00788293 | − | 0.117128i | ||||
\(701\) | −1.79821 | −0.0679176 | −0.0339588 | − | 0.999423i | \(-0.510811\pi\) | ||||
−0.0339588 | + | 0.999423i | \(0.510811\pi\) | |||||||
\(702\) | −7.68202 | − | 13.3057i | −0.289939 | − | 0.502190i | ||||
\(703\) | 4.12258 | − | 7.14051i | 0.155486 | − | 0.269310i | ||||
\(704\) | 14.8419 | − | 25.7069i | 0.559375 | − | 0.968866i | ||||
\(705\) | 3.44179 | + | 5.96135i | 0.129625 | + | 0.224517i | ||||
\(706\) | −22.1954 | −0.835336 | ||||||||
\(707\) | −26.7284 | + | 13.1229i | −1.00523 | + | 0.493537i | ||||
\(708\) | 7.65885 | 0.287837 | ||||||||
\(709\) | 14.1615 | + | 24.5284i | 0.531846 | + | 0.921185i | 0.999309 | + | 0.0371721i | \(0.0118350\pi\) |
−0.467462 | + | 0.884013i | \(0.654832\pi\) | |||||||
\(710\) | 19.6780 | − | 34.0834i | 0.738504 | − | 1.27913i | ||||
\(711\) | 1.27035 | − | 2.20031i | 0.0476418 | − | 0.0825180i | ||||
\(712\) | 26.9337 | + | 46.6506i | 1.00938 | + | 1.74831i | ||||
\(713\) | 0.671827 | 0.0251601 | ||||||||
\(714\) | 46.1103 | − | 22.6388i | 1.72563 | − | 0.847236i | ||||
\(715\) | −2.29249 | −0.0857341 | ||||||||
\(716\) | −39.1112 | − | 67.7425i | −1.46165 | − | 2.53166i | ||||
\(717\) | 13.4970 | − | 23.3775i | 0.504055 | − | 0.873050i | ||||
\(718\) | 44.4352 | − | 76.9640i | 1.65831 | − | 2.87227i | ||||
\(719\) | 20.9485 | + | 36.2839i | 0.781249 | + | 1.35316i | 0.931215 | + | 0.364471i | \(0.118750\pi\) |
−0.149966 | + | 0.988691i | \(0.547916\pi\) | |||||||
\(720\) | −37.9046 | −1.41262 | ||||||||
\(721\) | −3.59469 | + | 53.4117i | −0.133873 | + | 1.98916i | ||||
\(722\) | −50.2184 | −1.86894 | ||||||||
\(723\) | 9.29838 | + | 16.1053i | 0.345810 | + | 0.598961i | ||||
\(724\) | −49.1180 | + | 85.0749i | −1.82546 | + | 3.16179i | ||||
\(725\) | −0.335728 | + | 0.581499i | −0.0124686 | + | 0.0215963i | ||||
\(726\) | −18.1657 | − | 31.4638i | −0.674191 | − | 1.16773i | ||||
\(727\) | 19.5123 | 0.723670 | 0.361835 | − | 0.932242i | \(-0.382150\pi\) | ||||
0.361835 | + | 0.932242i | \(0.382150\pi\) | |||||||
\(728\) | −20.5213 | − | 13.7639i | −0.760571 | − | 0.510125i | ||||
\(729\) | 27.5552 | 1.02056 | ||||||||
\(730\) | 24.6871 | + | 42.7593i | 0.913711 | + | 1.58259i | ||||
\(731\) | 2.34871 | − | 4.06808i | 0.0868701 | − | 0.150463i | ||||
\(732\) | −45.6679 | + | 79.0991i | −1.68793 | + | 2.92359i | ||||
\(733\) | −8.87698 | − | 15.3754i | −0.327879 | − | 0.567902i | 0.654212 | − | 0.756311i | \(-0.273000\pi\) |
−0.982091 | + | 0.188409i | \(0.939667\pi\) | |||||||
\(734\) | −8.61213 | −0.317880 | ||||||||
\(735\) | −7.82185 | − | 19.0722i | −0.288513 | − | 0.703488i | ||||
\(736\) | 13.7939 | 0.508450 | ||||||||
\(737\) | 2.34728 | + | 4.06562i | 0.0864633 | + | 0.149759i | ||||
\(738\) | 11.8419 | − | 20.5108i | 0.435907 | − | 0.755013i | ||||
\(739\) | −22.1571 | + | 38.3772i | −0.815061 | + | 1.41173i | 0.0942227 | + | 0.995551i | \(0.469963\pi\) |
−0.909284 | + | 0.416176i | \(0.863370\pi\) | |||||||
\(740\) | 64.6497 | + | 111.977i | 2.37657 | + | 4.11634i | ||||
\(741\) | −1.01911 | −0.0374380 | ||||||||
\(742\) | −29.2709 | − | 19.6324i | −1.07457 | − | 0.720729i | ||||
\(743\) | −7.16727 | −0.262941 | −0.131471 | − | 0.991320i | \(-0.541970\pi\) | ||||
−0.131471 | + | 0.991320i | \(0.541970\pi\) | |||||||
\(744\) | 6.46285 | + | 11.1940i | 0.236940 | + | 0.410392i | ||||
\(745\) | −16.8331 | + | 29.1558i | −0.616718 | + | 1.06819i | ||||
\(746\) | 2.01355 | − | 3.48757i | 0.0737212 | − | 0.127689i | ||||
\(747\) | −3.95657 | − | 6.85297i | −0.144763 | − | 0.250737i | ||||
\(748\) | 30.0983 | 1.10050 | ||||||||
\(749\) | −1.60875 | + | 23.9036i | −0.0587826 | + | 0.873420i | ||||
\(750\) | 41.8630 | 1.52862 | ||||||||
\(751\) | 16.9532 | + | 29.3639i | 0.618632 | + | 1.07150i | 0.989736 | + | 0.142911i | \(0.0456462\pi\) |
−0.371103 | + | 0.928592i | \(0.621020\pi\) | |||||||
\(752\) | −17.0618 | + | 29.5518i | −0.622178 | + | 1.07764i | ||||
\(753\) | −17.5772 | + | 30.4445i | −0.640547 | + | 1.10946i | ||||
\(754\) | 4.22970 | + | 7.32606i | 0.154037 | + | 0.266799i | ||||
\(755\) | −29.9110 | −1.08857 | ||||||||
\(756\) | 72.6628 | − | 35.6753i | 2.64272 | − | 1.29750i | ||||
\(757\) | −0.906670 | −0.0329535 | −0.0164767 | − | 0.999864i | \(-0.505245\pi\) | ||||
−0.0164767 | + | 0.999864i | \(0.505245\pi\) | |||||||
\(758\) | −14.6147 | − | 25.3134i | −0.530830 | − | 0.919424i | ||||
\(759\) | −0.461186 | + | 0.798798i | −0.0167400 | + | 0.0289945i | ||||
\(760\) | −7.73059 | + | 13.3898i | −0.280418 | + | 0.485698i | ||||
\(761\) | −10.1247 | − | 17.5365i | −0.367020 | − | 0.635697i | 0.622079 | − | 0.782955i | \(-0.286288\pi\) |
−0.989098 | + | 0.147258i | \(0.952955\pi\) | |||||||
\(762\) | −32.2502 | −1.16830 | ||||||||
\(763\) | 35.8650 | − | 17.6087i | 1.29840 | − | 0.637477i | ||||
\(764\) | 30.0729 | 1.08800 | ||||||||
\(765\) | −6.86942 | − | 11.8982i | −0.248364 | − | 0.430180i | ||||
\(766\) | 29.1750 | − | 50.5326i | 1.05414 | − | 1.82582i | ||||
\(767\) | 0.524077 | − | 0.907729i | 0.0189233 | − | 0.0327762i | ||||
\(768\) | 26.0259 | + | 45.0782i | 0.939129 | + | 1.62662i | ||||
\(769\) | −36.9094 | −1.33099 | −0.665494 | − | 0.746403i | \(-0.731779\pi\) | ||||
−0.665494 | + | 0.746403i | \(0.731779\pi\) | |||||||
\(770\) | 1.10996 | − | 16.4923i | 0.0400001 | − | 0.594341i | ||||
\(771\) | −14.2987 | −0.514954 | ||||||||
\(772\) | 23.7183 | + | 41.0814i | 0.853642 | + | 1.47855i | ||||
\(773\) | 4.94018 | − | 8.55665i | 0.177686 | − | 0.307761i | −0.763402 | − | 0.645924i | \(-0.776472\pi\) |
0.941088 | + | 0.338163i | \(0.109806\pi\) | |||||||
\(774\) | 1.43611 | − | 2.48742i | 0.0516199 | − | 0.0894083i | ||||
\(775\) | 0.111176 | + | 0.192562i | 0.00399355 | + | 0.00691704i | ||||
\(776\) | −26.9701 | −0.968169 | ||||||||
\(777\) | −32.2272 | − | 21.6152i | −1.15614 | − | 0.775441i | ||||
\(778\) | 94.7893 | 3.39836 | ||||||||
\(779\) | −2.77043 | − | 4.79852i | −0.0992609 | − | 0.171925i | ||||
\(780\) | 7.99079 | − | 13.8404i | 0.286116 | − | 0.495568i | ||||
\(781\) | −3.46035 | + | 5.99350i | −0.123821 | + | 0.214464i | ||||
\(782\) | 4.71233 | + | 8.16200i | 0.168513 | + | 0.291873i | ||||
\(783\) | −17.4998 | −0.625391 | ||||||||
\(784\) | 62.4913 | − | 80.8526i | 2.23183 | − | 2.88759i | ||||
\(785\) | 7.40915 | 0.264444 | ||||||||
\(786\) | −19.2905 | − | 33.4121i | −0.688069 | − | 1.19177i | ||||
\(787\) | −18.8411 | + | 32.6337i | −0.671611 | + | 1.16326i | 0.305836 | + | 0.952084i | \(0.401064\pi\) |
−0.977447 | + | 0.211180i | \(0.932269\pi\) | |||||||
\(788\) | 14.8394 | − | 25.7026i | 0.528632 | − | 0.915617i | ||||
\(789\) | 6.97292 | + | 12.0775i | 0.248243 | + | 0.429969i | ||||
\(790\) | 12.7565 | 0.453854 | ||||||||
\(791\) | −6.82056 | − | 4.57464i | −0.242511 | − | 0.162656i | ||||
\(792\) | 11.6213 | 0.412945 | ||||||||
\(793\) | 6.24989 | + | 10.8251i | 0.221940 | + | 0.384412i | ||||
\(794\) | −6.06656 | + | 10.5076i | −0.215294 | + | 0.372900i | ||||
\(795\) | 7.19738 | − | 12.4662i | 0.255265 | − | 0.442131i | ||||
\(796\) | −53.0129 | − | 91.8211i | −1.87899 | − | 3.25451i | ||||
\(797\) | 28.3837 | 1.00540 | 0.502701 | − | 0.864460i | \(-0.332340\pi\) | ||||
0.502701 | + | 0.864460i | \(0.332340\pi\) | |||||||
\(798\) | 0.493425 | − | 7.33155i | 0.0174671 | − | 0.259534i | ||||
\(799\) | −12.3683 | −0.437560 | ||||||||
\(800\) | 2.28266 | + | 3.95368i | 0.0807041 | + | 0.139784i | ||||
\(801\) | −3.42364 | + | 5.92992i | −0.120968 | + | 0.209524i | ||||
\(802\) | 18.7412 | − | 32.4607i | 0.661775 | − | 1.14623i | ||||
\(803\) | −4.34118 | − | 7.51915i | −0.153197 | − | 0.265345i | ||||
\(804\) | −32.7272 | −1.15420 | ||||||||
\(805\) | 3.39498 | − | 1.66684i | 0.119657 | − | 0.0587482i | ||||
\(806\) | 2.80132 | 0.0986722 | ||||||||
\(807\) | 8.05834 | + | 13.9574i | 0.283667 | + | 0.491325i | ||||
\(808\) | 52.5543 | − | 91.0268i | 1.84886 | − | 3.20231i | ||||
\(809\) | 5.87327 | − | 10.1728i | 0.206493 | − | 0.357657i | −0.744114 | − | 0.668052i | \(-0.767128\pi\) |
0.950607 | + | 0.310396i | \(0.100461\pi\) | |||||||
\(810\) | 12.0080 | + | 20.7985i | 0.421919 | + | 0.730784i | ||||
\(811\) | 2.01940 | 0.0709108 | 0.0354554 | − | 0.999371i | \(-0.488712\pi\) | ||||
0.0354554 | + | 0.999371i | \(0.488712\pi\) | |||||||
\(812\) | −40.0080 | + | 19.6428i | −1.40400 | + | 0.689326i | ||||
\(813\) | 3.71194 | 0.130184 | ||||||||
\(814\) | −15.5582 | − | 26.9475i | −0.545313 | − | 0.944511i | ||||
\(815\) | 15.1024 | − | 26.1581i | 0.529014 | − | 0.916280i | ||||
\(816\) | −52.0005 | + | 90.0676i | −1.82038 | + | 3.15300i | ||||
\(817\) | −0.335980 | − | 0.581934i | −0.0117544 | − | 0.0203593i | ||||
\(818\) | −9.51676 | −0.332746 | ||||||||
\(819\) | 0.210913 | − | 3.13385i | 0.00736991 | − | 0.109506i | ||||
\(820\) | 86.8910 | 3.03437 | ||||||||
\(821\) | 7.54208 | + | 13.0633i | 0.263220 | + | 0.455911i | 0.967096 | − | 0.254412i | \(-0.0818820\pi\) |
−0.703875 | + | 0.710323i | \(0.748549\pi\) | |||||||
\(822\) | 16.0196 | − | 27.7468i | 0.558748 | − | 0.967780i | ||||
\(823\) | 7.38828 | − | 12.7969i | 0.257539 | − | 0.446071i | −0.708043 | − | 0.706170i | \(-0.750422\pi\) |
0.965582 | + | 0.260098i | \(0.0837550\pi\) | |||||||
\(824\) | −94.4839 | − | 163.651i | −3.29150 | − | 5.70105i | ||||
\(825\) | −0.305274 | −0.0106283 | ||||||||
\(826\) | 6.27651 | + | 4.20974i | 0.218388 | + | 0.146476i | ||||
\(827\) | 13.0407 | 0.453471 | 0.226736 | − | 0.973956i | \(-0.427195\pi\) | ||||
0.226736 | + | 0.973956i | \(0.427195\pi\) | |||||||
\(828\) | 2.10543 | + | 3.64671i | 0.0731688 | + | 0.126732i | ||||
\(829\) | 12.7291 | − | 22.0474i | 0.442099 | − | 0.765738i | −0.555746 | − | 0.831352i | \(-0.687567\pi\) |
0.997845 | + | 0.0656144i | \(0.0209007\pi\) | |||||||
\(830\) | 19.8653 | − | 34.4077i | 0.689535 | − | 1.19431i | ||||
\(831\) | −16.1082 | − | 27.9002i | −0.558786 | − | 0.967845i | ||||
\(832\) | 28.3200 | 0.981820 | ||||||||
\(833\) | 36.7047 | + | 4.96305i | 1.27174 | + | 0.171960i | ||||
\(834\) | 14.6773 | 0.508233 | ||||||||
\(835\) | −17.9110 | − | 31.0228i | −0.619835 | − | 1.07359i | ||||
\(836\) | 2.15277 | − | 3.72870i | 0.0744549 | − | 0.128960i | ||||
\(837\) | −2.89751 | + | 5.01864i | −0.100153 | + | 0.173469i | ||||
\(838\) | 4.86099 | + | 8.41948i | 0.167920 | + | 0.290846i | ||||
\(839\) | 32.1703 | 1.11064 | 0.555321 | − | 0.831636i | \(-0.312596\pi\) | ||||
0.555321 | + | 0.831636i | \(0.312596\pi\) | |||||||
\(840\) | 60.4319 | + | 40.5325i | 2.08510 | + | 1.39850i | ||||
\(841\) | −19.3647 | −0.667747 | ||||||||
\(842\) | 13.6263 | + | 23.6014i | 0.469592 | + | 0.813357i | ||||
\(843\) | −2.61117 | + | 4.52268i | −0.0899335 | + | 0.155769i | ||||
\(844\) | −45.2896 | + | 78.4439i | −1.55893 | + | 2.70015i | ||||
\(845\) | −1.09358 | − | 1.89414i | −0.0376204 | − | 0.0651604i | ||||
\(846\) | −7.56259 | −0.260007 | ||||||||
\(847\) | 1.75909 | − | 26.1374i | 0.0604431 | − | 0.898093i | ||||
\(848\) | 71.3582 | 2.45045 | ||||||||
\(849\) | −4.18061 | − | 7.24104i | −0.143478 | − | 0.248512i | ||||
\(850\) | −1.55962 | + | 2.70134i | −0.0534946 | + | 0.0926553i | ||||
\(851\) | 3.55982 | − | 6.16579i | 0.122029 | − | 0.211360i | ||||
\(852\) | −24.1231 | − | 41.7824i | −0.826442 | − | 1.43144i | ||||
\(853\) | −19.3910 | −0.663934 | −0.331967 | − | 0.943291i | \(-0.607712\pi\) | ||||
−0.331967 | + | 0.943291i | \(0.607712\pi\) | |||||||
\(854\) | −80.9027 | + | 39.7209i | −2.76843 | + | 1.35922i | ||||
\(855\) | −1.96532 | −0.0672127 | ||||||||
\(856\) | −42.2849 | − | 73.2396i | −1.44527 | − | 2.50328i | ||||
\(857\) | −8.71210 | + | 15.0898i | −0.297600 | + | 0.515458i | −0.975586 | − | 0.219616i | \(-0.929519\pi\) |
0.677987 | + | 0.735074i | \(0.262853\pi\) | |||||||
\(858\) | −1.92301 | + | 3.33075i | −0.0656504 | + | 0.113710i | ||||
\(859\) | 17.7459 | + | 30.7367i | 0.605481 | + | 1.04872i | 0.991975 | + | 0.126432i | \(0.0403524\pi\) |
−0.386495 | + | 0.922292i | \(0.626314\pi\) | |||||||
\(860\) | 10.5376 | 0.359329 | ||||||||
\(861\) | −23.4082 | + | 11.4927i | −0.797749 | + | 0.391672i | ||||
\(862\) | −30.9704 | −1.05486 | ||||||||
\(863\) | −28.0010 | − | 48.4991i | −0.953164 | − | 1.65093i | −0.738516 | − | 0.674236i | \(-0.764473\pi\) |
−0.214648 | − | 0.976691i | \(-0.568860\pi\) | |||||||
\(864\) | −59.4916 | + | 103.042i | −2.02394 | + | 3.50557i | ||||
\(865\) | −4.51153 | + | 7.81420i | −0.153397 | + | 0.265691i | ||||
\(866\) | 28.9062 | + | 50.0670i | 0.982273 | + | 1.70135i | ||||
\(867\) | −14.8070 | −0.502871 | ||||||||
\(868\) | −0.991079 | + | 14.7259i | −0.0336394 | + | 0.499830i | ||||
\(869\) | −2.24320 | −0.0760953 | ||||||||
\(870\) | −12.4558 | − | 21.5740i | −0.422290 | − | 0.731428i | ||||
\(871\) | −2.23944 | + | 3.87883i | −0.0758807 | + | 0.131429i | ||||
\(872\) | −70.5190 | + | 122.143i | −2.38808 | + | 4.13627i | ||||
\(873\) | −1.71413 | − | 2.96896i | −0.0580145 | − | 0.100484i | ||||
\(874\) | 1.34819 | 0.0456031 | ||||||||
\(875\) | 25.0687 | + | 16.8139i | 0.847476 | + | 0.568414i | ||||
\(876\) | 60.5272 | 2.04503 | ||||||||
\(877\) | −12.6031 | − | 21.8292i | −0.425577 | − | 0.737120i | 0.570898 | − | 0.821021i | \(-0.306595\pi\) |
−0.996474 | + | 0.0839011i | \(0.973262\pi\) | |||||||
\(878\) | 33.3852 | − | 57.8249i | 1.12670 | − | 1.95150i | ||||
\(879\) | 11.1587 | − | 19.3275i | 0.376374 | − | 0.651899i | ||||
\(880\) | 16.7331 | + | 28.9826i | 0.564074 | + | 0.977004i | ||||
\(881\) | −18.6082 | −0.626925 | −0.313463 | − | 0.949601i | \(-0.601489\pi\) | ||||
−0.313463 | + | 0.949601i | \(0.601489\pi\) | |||||||
\(882\) | 22.4430 | + | 3.03465i | 0.755695 | + | 0.102182i | ||||
\(883\) | −11.2552 | −0.378768 | −0.189384 | − | 0.981903i | \(-0.560649\pi\) | ||||
−0.189384 | + | 0.981903i | \(0.560649\pi\) | |||||||
\(884\) | 14.3578 | + | 24.8684i | 0.482904 | + | 0.836415i | ||||
\(885\) | −1.54332 | + | 2.67311i | −0.0518781 | + | 0.0898556i | ||||
\(886\) | −55.1438 | + | 95.5119i | −1.85259 | + | 3.20879i | ||||
\(887\) | 19.6056 | + | 33.9579i | 0.658292 | + | 1.14020i | 0.981057 | + | 0.193717i | \(0.0620543\pi\) |
−0.322765 | + | 0.946479i | \(0.604612\pi\) | |||||||
\(888\) | 136.979 | 4.59672 | ||||||||
\(889\) | −19.3123 | − | 12.9530i | −0.647712 | − | 0.434429i | ||||
\(890\) | −34.3792 | −1.15239 | ||||||||
\(891\) | −2.11159 | − | 3.65738i | −0.0707408 | − | 0.122527i | ||||
\(892\) | 14.4959 | − | 25.1077i | 0.485360 | − | 0.840668i | ||||
\(893\) | −0.884638 | + | 1.53224i | −0.0296033 | + | 0.0512744i | ||||
\(894\) | 28.2403 | + | 48.9136i | 0.944496 | + | 1.63592i | ||||
\(895\) | 31.5249 | 1.05376 | ||||||||
\(896\) | −6.21266 | + | 92.3107i | −0.207551 | + | 3.08389i | ||||
\(897\) | −0.879996 | −0.0293822 | ||||||||
\(898\) | 37.8316 | + | 65.5263i | 1.26246 | + | 2.18664i | ||||
\(899\) | 1.59536 | − | 2.76325i | 0.0532083 | − | 0.0921595i | ||||
\(900\) | −0.696826 | + | 1.20694i | −0.0232275 | + | 0.0402312i | ||||
\(901\) | 12.9322 | + | 22.3992i | 0.430834 | + | 0.746226i | ||||
\(902\) | −20.9106 | −0.696247 | ||||||||
\(903\) | −2.83879 | + | 1.39377i | −0.0944692 | + | 0.0463816i | ||||
\(904\) | 28.9903 | 0.964203 | ||||||||
\(905\) | −19.7954 | − | 34.2866i | −0.658020 | − | 1.13972i | ||||
\(906\) | −25.0903 | + | 43.4577i | −0.833570 | + | 1.44378i | ||||
\(907\) | −10.7985 | + | 18.7035i | −0.358558 | + | 0.621040i | −0.987720 | − | 0.156234i | \(-0.950065\pi\) |
0.629162 | + | 0.777274i | \(0.283398\pi\) | |||||||
\(908\) | −54.5997 | − | 94.5694i | −1.81195 | − | 3.13840i | ||||
\(909\) | 13.3607 | 0.443147 | ||||||||
\(910\) | 14.1560 | − | 6.95021i | 0.469268 | − | 0.230397i | ||||
\(911\) | −32.4434 | −1.07490 | −0.537449 | − | 0.843297i | \(-0.680612\pi\) | ||||
−0.537449 | + | 0.843297i | \(0.680612\pi\) | |||||||
\(912\) | 7.43861 | + | 12.8840i | 0.246317 | + | 0.426634i | ||||
\(913\) | −3.49328 | + | 6.05054i | −0.115611 | + | 0.200244i | ||||
\(914\) | 15.2531 | − | 26.4192i | 0.504528 | − | 0.873868i | ||||
\(915\) | −18.4049 | − | 31.8782i | −0.608447 | − | 1.05386i | ||||
\(916\) | 137.030 | 4.52760 | ||||||||
\(917\) | 1.86802 | − | 27.7559i | 0.0616873 | − | 0.916580i | ||||
\(918\) | −81.2950 | −2.68313 | ||||||||
\(919\) | −17.8686 | − | 30.9493i | −0.589430 | − | 1.02092i | −0.994307 | − | 0.106552i | \(-0.966019\pi\) |
0.404877 | − | 0.914371i | \(-0.367314\pi\) | |||||||
\(920\) | −6.67532 | + | 11.5620i | −0.220079 | + | 0.381187i | ||||
\(921\) | −4.75142 | + | 8.22971i | −0.156565 | + | 0.271178i | ||||
\(922\) | 12.6693 | + | 21.9439i | 0.417242 | + | 0.722684i | ||||
\(923\) | −6.60274 | −0.217332 | ||||||||
\(924\) | −16.8287 | − | 11.2872i | −0.553623 | − | 0.371323i | ||||
\(925\) | 2.35636 | 0.0774765 | ||||||||
\(926\) | −38.4858 | − | 66.6594i | −1.26472 | − | 2.19056i | ||||
\(927\) | 12.0102 | − | 20.8022i | 0.394466 | − | 0.683235i | ||||
\(928\) | 32.7559 | − | 56.7349i | 1.07527 | − | 1.86241i | ||||
\(929\) | −5.88847 | − | 10.1991i | −0.193194 | − | 0.334622i | 0.753113 | − | 0.657891i | \(-0.228551\pi\) |
−0.946307 | + | 0.323269i | \(0.895218\pi\) | |||||||
\(930\) | −8.24941 | −0.270509 | ||||||||
\(931\) | 3.24012 | − | 4.19214i | 0.106191 | − | 0.137392i | ||||
\(932\) | −4.30553 | −0.141032 | ||||||||
\(933\) | 14.2116 | + | 24.6151i | 0.465265 | + | 0.805863i | ||||
\(934\) | −30.3329 | + | 52.5382i | −0.992523 | + | 1.71910i | ||||
\(935\) | −6.06506 | + | 10.5050i | −0.198349 | + | 0.343550i | ||||
\(936\) | 5.54370 | + | 9.60197i | 0.181202 | + | 0.313850i | ||||
\(937\) | 18.9937 | 0.620497 | 0.310248 | − | 0.950655i | \(-0.399588\pi\) | ||||
0.310248 | + | 0.950655i | \(0.399588\pi\) | |||||||
\(938\) | −26.8203 | − | 17.9887i | −0.875713 | − | 0.587352i | ||||
\(939\) | −2.66660 | −0.0870213 | ||||||||
\(940\) | −13.8728 | − | 24.0284i | −0.452480 | − | 0.783719i | ||||
\(941\) | −3.40932 | + | 5.90511i | −0.111141 | + | 0.192501i | −0.916230 | − | 0.400652i | \(-0.868784\pi\) |
0.805090 | + | 0.593153i | \(0.202117\pi\) | |||||||
\(942\) | 6.21502 | − | 10.7647i | 0.202496 | − | 0.350734i | ||||
\(943\) | −2.39225 | − | 4.14349i | −0.0779023 | − | 0.134931i | ||||
\(944\) | −15.3012 | −0.498012 | ||||||||
\(945\) | −2.19065 | + | 32.5498i | −0.0712620 | + | 1.05884i | ||||
\(946\) | −2.53590 | −0.0824493 | ||||||||
\(947\) | −0.529958 | − | 0.917914i | −0.0172213 | − | 0.0298282i | 0.857286 | − | 0.514840i | \(-0.172149\pi\) |
−0.874508 | + | 0.485012i | \(0.838815\pi\) | |||||||
\(948\) | 7.81899 | − | 13.5429i | 0.253949 | − | 0.439853i | ||||
\(949\) | 4.14174 | − | 7.17370i | 0.134446 | − | 0.232868i | ||||
\(950\) | 0.223102 | + | 0.386424i | 0.00723838 | + | 0.0125372i | ||||
\(951\) | 24.2973 | 0.787895 | ||||||||
\(952\) | −117.363 | + | 57.6219i | −3.80376 | + | 1.86753i | ||||
\(953\) | −40.4127 | −1.30910 | −0.654548 | − | 0.756020i | \(-0.727141\pi\) | ||||
−0.654548 | + | 0.756020i | \(0.727141\pi\) | |||||||
\(954\) | 7.90735 | + | 13.6959i | 0.256010 | + | 0.443422i | ||||
\(955\) | −6.05993 | + | 10.4961i | −0.196095 | + | 0.339646i | ||||
\(956\) | −54.4023 | + | 94.2276i | −1.75950 | + | 3.04754i | ||||
\(957\) | 2.19032 | + | 3.79375i | 0.0708031 | + | 0.122635i | ||||
\(958\) | −89.5964 | −2.89473 | ||||||||
\(959\) | 20.7372 | − | 10.1814i | 0.669639 | − | 0.328774i | ||||
\(960\) | −83.3978 | −2.69165 | ||||||||
\(961\) | 14.9717 | + | 25.9317i | 0.482958 | + | 0.836508i | ||||
\(962\) | 14.8434 | − | 25.7095i | 0.478570 | − | 0.828907i | ||||
\(963\) | 5.37498 | − | 9.30975i | 0.173206 | − | 0.300002i | ||||
\(964\) | −37.4789 | − | 64.9154i | −1.20711 | − | 2.09078i | ||||
\(965\) | −19.1177 | −0.615422 | ||||||||
\(966\) | 0.426069 | − | 6.33074i | 0.0137086 | − | 0.203688i | ||||
\(967\) | −36.2949 | −1.16717 | −0.583583 | − | 0.812053i | \(-0.698350\pi\) | ||||
−0.583583 | + | 0.812053i | \(0.698350\pi\) | |||||||
\(968\) | 46.2365 | + | 80.0839i | 1.48610 | + | 2.57399i | ||||
\(969\) | −2.69618 | + | 4.66993i | −0.0866139 | + | 0.150020i | ||||
\(970\) | 8.60638 | − | 14.9067i | 0.276334 | − | 0.478625i | ||||
\(971\) | 10.7218 | + | 18.5708i | 0.344080 | + | 0.595964i | 0.985186 | − | 0.171488i | \(-0.0548575\pi\) |
−0.641106 | + | 0.767452i | \(0.721524\pi\) | |||||||
\(972\) | −62.3457 | −1.99974 | ||||||||
\(973\) | 8.78914 | + | 5.89500i | 0.281767 | + | 0.188985i | ||||
\(974\) | −76.0137 | −2.43564 | ||||||||
\(975\) | −0.145624 | − | 0.252229i | −0.00466371 | − | 0.00807778i | ||||
\(976\) | 91.2374 | − | 158.028i | 2.92044 | − | 5.05835i | ||||
\(977\) | 19.9138 | − | 34.4918i | 0.637100 | − | 1.10349i | −0.348966 | − | 0.937135i | \(-0.613467\pi\) |
0.986066 | − | 0.166354i | \(-0.0531994\pi\) | |||||||
\(978\) | −25.3367 | − | 43.8845i | −0.810179 | − | 1.40327i | ||||
\(979\) | 6.04551 | 0.193215 | ||||||||
\(980\) | 31.5275 | + | 76.8742i | 1.00711 | + | 2.45565i | ||||
\(981\) | −17.9278 | −0.572392 | ||||||||
\(982\) | −14.5216 | − | 25.1522i | −0.463403 | − | 0.802638i | ||||
\(983\) | −7.94071 | + | 13.7537i | −0.253269 | + | 0.438675i | −0.964424 | − | 0.264360i | \(-0.914839\pi\) |
0.711155 | + | 0.703036i | \(0.248173\pi\) | |||||||
\(984\) | 46.0260 | − | 79.7194i | 1.46725 | − | 2.54136i | ||||
\(985\) | 5.98052 | + | 10.3586i | 0.190555 | + | 0.330051i | ||||
\(986\) | 44.7608 | 1.42548 | ||||||||
\(987\) | 6.91543 | + | 4.63827i | 0.220120 | + | 0.147638i | ||||
\(988\) | 4.10772 | 0.130684 | ||||||||
\(989\) | −0.290116 | − | 0.502496i | −0.00922516 | − | 0.0159785i | ||||
\(990\) | −3.70846 | + | 6.42325i | −0.117863 | + | 0.204144i | ||||
\(991\) | 8.83435 | − | 15.3016i | 0.280633 | − | 0.486070i | −0.690908 | − | 0.722943i | \(-0.742789\pi\) |
0.971541 | + | 0.236873i | \(0.0761225\pi\) | |||||||
\(992\) | −10.8471 | − | 18.7877i | −0.344394 | − | 0.596509i | ||||
\(993\) | 19.7570 | 0.626970 | ||||||||
\(994\) | 3.19686 | − | 47.5005i | 0.101398 | − | 1.50662i | ||||
\(995\) | 42.7301 | 1.35464 | ||||||||
\(996\) | −24.3526 | − | 42.1800i | −0.771643 | − | 1.33652i | ||||
\(997\) | 12.4304 | − | 21.5301i | 0.393675 | − | 0.681865i | −0.599256 | − | 0.800558i | \(-0.704537\pi\) |
0.992931 | + | 0.118692i | \(0.0378701\pi\) | |||||||
\(998\) | 33.3999 | − | 57.8503i | 1.05725 | − | 1.83122i | ||||
\(999\) | 30.7062 | + | 53.1847i | 0.971500 | + | 1.68269i |
(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 | 91.2.e.c.53.1 | ✓ | 10 | |
3.2 | odd | 2 | 819.2.j.h.235.5 | 10 | |||
4.3 | odd | 2 | 1456.2.r.p.417.2 | 10 | |||
7.2 | even | 3 | inner | 91.2.e.c.79.1 | yes | 10 | |
7.3 | odd | 6 | 637.2.a.k.1.5 | 5 | |||
7.4 | even | 3 | 637.2.a.l.1.5 | 5 | |||
7.5 | odd | 6 | 637.2.e.m.79.1 | 10 | |||
7.6 | odd | 2 | 637.2.e.m.508.1 | 10 | |||
13.12 | even | 2 | 1183.2.e.f.508.5 | 10 | |||
21.2 | odd | 6 | 819.2.j.h.352.5 | 10 | |||
21.11 | odd | 6 | 5733.2.a.bl.1.1 | 5 | |||
21.17 | even | 6 | 5733.2.a.bm.1.1 | 5 | |||
28.23 | odd | 6 | 1456.2.r.p.625.2 | 10 | |||
91.25 | even | 6 | 8281.2.a.bw.1.1 | 5 | |||
91.38 | odd | 6 | 8281.2.a.bx.1.1 | 5 | |||
91.51 | even | 6 | 1183.2.e.f.170.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
91.2.e.c.79.1 | yes | 10 | 7.2 | even | 3 | inner | |
637.2.a.k.1.5 | 5 | 7.3 | odd | 6 | |||
637.2.a.l.1.5 | 5 | 7.4 | even | 3 | |||
637.2.e.m.79.1 | 10 | 7.5 | odd | 6 | |||
637.2.e.m.508.1 | 10 | 7.6 | odd | 2 | |||
819.2.j.h.235.5 | 10 | 3.2 | odd | 2 | |||
819.2.j.h.352.5 | 10 | 21.2 | odd | 6 | |||
1183.2.e.f.170.5 | 10 | 91.51 | even | 6 | |||
1183.2.e.f.508.5 | 10 | 13.12 | even | 2 | |||
1456.2.r.p.417.2 | 10 | 4.3 | odd | 2 | |||
1456.2.r.p.625.2 | 10 | 28.23 | odd | 6 | |||
5733.2.a.bl.1.1 | 5 | 21.11 | odd | 6 | |||
5733.2.a.bm.1.1 | 5 | 21.17 | even | 6 | |||
8281.2.a.bw.1.1 | 5 | 91.25 | even | 6 | |||
8281.2.a.bx.1.1 | 5 | 91.38 | odd | 6 |