Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,3,Mod(31,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.h (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.67576647683\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(1.93649 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.31 |
Dual form | 245.3.h.b.166.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | 0.963525 | − | 0.267617i | \(-0.0862360\pi\) |
−0.713525 | + | 0.700629i | \(0.752903\pi\) | |||||||
\(3\) | −3.87298 | − | 2.23607i | −1.29099 | − | 0.745356i | −0.312164 | − | 0.950028i | \(-0.601054\pi\) |
−0.978831 | + | 0.204672i | \(0.934387\pi\) | |||||||
\(4\) | 1.50000 | − | 2.59808i | 0.375000 | − | 0.649519i | ||||
\(5\) | 1.93649 | − | 1.11803i | 0.387298 | − | 0.223607i | ||||
\(6\) | − | 4.47214i | − | 0.745356i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(10\) | 1.93649 | + | 1.11803i | 0.193649 | + | 0.111803i | ||||
\(11\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | −0.907894 | − | 0.419200i | \(-0.862311\pi\) |
0.816985 | + | 0.576659i | \(0.195644\pi\) | |||||||
\(12\) | −11.6190 | + | 6.70820i | −0.968246 | + | 0.559017i | ||||
\(13\) | − | 13.4164i | − | 1.03203i | −0.856579 | − | 0.516016i | \(-0.827415\pi\) | ||
0.856579 | − | 0.516016i | \(-0.172585\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.0000 | −0.666667 | ||||||||
\(16\) | −2.50000 | − | 4.33013i | −0.156250 | − | 0.270633i | ||||
\(17\) | −23.2379 | − | 13.4164i | −1.36694 | − | 0.789200i | −0.376400 | − | 0.926457i | \(-0.622838\pi\) |
−0.990535 | + | 0.137257i | \(0.956171\pi\) | |||||||
\(18\) | −5.50000 | + | 9.52628i | −0.305556 | + | 0.529238i | ||||
\(19\) | −11.6190 | + | 6.70820i | −0.611524 | + | 0.353063i | −0.773562 | − | 0.633721i | \(-0.781527\pi\) |
0.162038 | + | 0.986785i | \(0.448193\pi\) | |||||||
\(20\) | − | 6.70820i | − | 0.335410i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.0909091 | ||||||||
\(23\) | −13.0000 | − | 22.5167i | −0.565217 | − | 0.978985i | −0.997029 | − | 0.0770216i | \(-0.975459\pi\) |
0.431812 | − | 0.901964i | \(-0.357874\pi\) | |||||||
\(24\) | −27.1109 | − | 15.6525i | −1.12962 | − | 0.652186i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.100000 | − | 0.173205i | ||||
\(26\) | 11.6190 | − | 6.70820i | 0.446883 | − | 0.258008i | ||||
\(27\) | − | 8.94427i | − | 0.331269i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −22.0000 | −0.758621 | −0.379310 | − | 0.925270i | \(-0.623839\pi\) | ||||
−0.379310 | + | 0.925270i | \(0.623839\pi\) | |||||||
\(30\) | −5.00000 | − | 8.66025i | −0.166667 | − | 0.288675i | ||||
\(31\) | 46.4758 | + | 26.8328i | 1.49922 | + | 0.865575i | 1.00000 | 0.000900703i | \(-0.000286703\pi\) | |
0.499220 | + | 0.866475i | \(0.333620\pi\) | |||||||
\(32\) | 16.5000 | − | 28.5788i | 0.515625 | − | 0.893089i | ||||
\(33\) | 7.74597 | − | 4.47214i | 0.234726 | − | 0.135519i | ||||
\(34\) | − | 26.8328i | − | 0.789200i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 33.0000 | 0.916667 | ||||||||
\(37\) | −7.00000 | − | 12.1244i | −0.189189 | − | 0.327685i | 0.755791 | − | 0.654813i | \(-0.227253\pi\) |
−0.944980 | + | 0.327128i | \(0.893919\pi\) | |||||||
\(38\) | −11.6190 | − | 6.70820i | −0.305762 | − | 0.176532i | ||||
\(39\) | −30.0000 | + | 51.9615i | −0.769231 | + | 1.33235i | ||||
\(40\) | 13.5554 | − | 7.82624i | 0.338886 | − | 0.195656i | ||||
\(41\) | − | 26.8328i | − | 0.654459i | −0.944945 | − | 0.327229i | \(-0.893885\pi\) | ||
0.944945 | − | 0.327229i | \(-0.106115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.0000 | −0.790698 | −0.395349 | − | 0.918531i | \(-0.629376\pi\) | ||||
−0.395349 | + | 0.918531i | \(0.629376\pi\) | |||||||
\(44\) | 3.00000 | + | 5.19615i | 0.0681818 | + | 0.118094i | ||||
\(45\) | 21.3014 | + | 12.2984i | 0.473365 | + | 0.273297i | ||||
\(46\) | 13.0000 | − | 22.5167i | 0.282609 | − | 0.489493i | ||||
\(47\) | −23.2379 | + | 13.4164i | −0.494423 | + | 0.285455i | −0.726408 | − | 0.687264i | \(-0.758812\pi\) |
0.231984 | + | 0.972720i | \(0.425478\pi\) | |||||||
\(48\) | 22.3607i | 0.465847i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.00000 | 0.100000 | ||||||||
\(51\) | 60.0000 | + | 103.923i | 1.17647 | + | 2.03771i | ||||
\(52\) | −34.8569 | − | 20.1246i | −0.670324 | − | 0.387012i | ||||
\(53\) | 17.0000 | − | 29.4449i | 0.320755 | − | 0.555563i | −0.659889 | − | 0.751363i | \(-0.729397\pi\) |
0.980644 | + | 0.195799i | \(0.0627301\pi\) | |||||||
\(54\) | 7.74597 | − | 4.47214i | 0.143444 | − | 0.0828173i | ||||
\(55\) | 4.47214i | 0.0813116i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60.0000 | 1.05263 | ||||||||
\(58\) | −11.0000 | − | 19.0526i | −0.189655 | − | 0.328492i | ||||
\(59\) | 34.8569 | + | 20.1246i | 0.590794 | + | 0.341095i | 0.765411 | − | 0.643541i | \(-0.222536\pi\) |
−0.174617 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(60\) | −15.0000 | + | 25.9808i | −0.250000 | + | 0.433013i | ||||
\(61\) | 81.3327 | − | 46.9574i | 1.33332 | − | 0.769794i | 0.347515 | − | 0.937674i | \(-0.387026\pi\) |
0.985807 | + | 0.167881i | \(0.0536923\pi\) | |||||||
\(62\) | 53.6656i | 0.865575i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | −15.0000 | − | 25.9808i | −0.230769 | − | 0.399704i | ||||
\(66\) | 7.74597 | + | 4.47214i | 0.117363 | + | 0.0677596i | ||||
\(67\) | −7.00000 | + | 12.1244i | −0.104478 | + | 0.180961i | −0.913525 | − | 0.406783i | \(-0.866650\pi\) |
0.809047 | + | 0.587744i | \(0.199984\pi\) | |||||||
\(68\) | −69.7137 | + | 40.2492i | −1.02520 | + | 0.591900i | ||||
\(69\) | 116.276i | 1.68515i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 62.0000 | 0.873239 | 0.436620 | − | 0.899646i | \(-0.356176\pi\) | ||||
0.436620 | + | 0.899646i | \(0.356176\pi\) | |||||||
\(72\) | 38.5000 | + | 66.6840i | 0.534722 | + | 0.926166i | ||||
\(73\) | 46.4758 | + | 26.8328i | 0.636655 | + | 0.367573i | 0.783325 | − | 0.621613i | \(-0.213522\pi\) |
−0.146670 | + | 0.989185i | \(0.546856\pi\) | |||||||
\(74\) | 7.00000 | − | 12.1244i | 0.0945946 | − | 0.163843i | ||||
\(75\) | −19.3649 | + | 11.1803i | −0.258199 | + | 0.149071i | ||||
\(76\) | 40.2492i | 0.529595i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −60.0000 | −0.769231 | ||||||||
\(79\) | −19.0000 | − | 32.9090i | −0.240506 | − | 0.416569i | 0.720352 | − | 0.693608i | \(-0.243980\pi\) |
−0.960859 | + | 0.277039i | \(0.910647\pi\) | |||||||
\(80\) | −9.68246 | − | 5.59017i | −0.121031 | − | 0.0698771i | ||||
\(81\) | 29.5000 | − | 51.0955i | 0.364198 | − | 0.630809i | ||||
\(82\) | 23.2379 | − | 13.4164i | 0.283389 | − | 0.163615i | ||||
\(83\) | 40.2492i | 0.484930i | 0.970160 | + | 0.242465i | \(0.0779560\pi\) | ||||
−0.970160 | + | 0.242465i | \(0.922044\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60.0000 | −0.705882 | ||||||||
\(86\) | −17.0000 | − | 29.4449i | −0.197674 | − | 0.342382i | ||||
\(87\) | 85.2056 | + | 49.1935i | 0.979375 | + | 0.565442i | ||||
\(88\) | −7.00000 | + | 12.1244i | −0.0795455 | + | 0.137777i | ||||
\(89\) | −23.2379 | + | 13.4164i | −0.261100 | + | 0.150746i | −0.624836 | − | 0.780756i | \(-0.714834\pi\) |
0.363736 | + | 0.931502i | \(0.381501\pi\) | |||||||
\(90\) | 24.5967i | 0.273297i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −78.0000 | −0.847826 | ||||||||
\(93\) | −120.000 | − | 207.846i | −1.29032 | − | 2.23490i | ||||
\(94\) | −23.2379 | − | 13.4164i | −0.247212 | − | 0.142728i | ||||
\(95\) | −15.0000 | + | 25.9808i | −0.157895 | + | 0.273482i | ||||
\(96\) | −127.808 | + | 73.7902i | −1.33134 | + | 0.768648i | ||||
\(97\) | − | 26.8328i | − | 0.276627i | −0.990388 | − | 0.138313i | \(-0.955832\pi\) | ||
0.990388 | − | 0.138313i | \(-0.0441681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.0000 | −0.222222 | ||||||||
\(100\) | −7.50000 | − | 12.9904i | −0.0750000 | − | 0.129904i | ||||
\(101\) | −58.0948 | − | 33.5410i | −0.575196 | − | 0.332089i | 0.184026 | − | 0.982921i | \(-0.441087\pi\) |
−0.759222 | + | 0.650832i | \(0.774420\pi\) | |||||||
\(102\) | −60.0000 | + | 103.923i | −0.588235 | + | 1.01885i | ||||
\(103\) | 139.427 | − | 80.4984i | 1.35366 | − | 0.781538i | 0.364903 | − | 0.931045i | \(-0.381102\pi\) |
0.988761 | + | 0.149507i | \(0.0477687\pi\) | |||||||
\(104\) | − | 93.9149i | − | 0.903027i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 34.0000 | 0.320755 | ||||||||
\(107\) | 53.0000 | + | 91.7987i | 0.495327 | + | 0.857932i | 0.999985 | − | 0.00538742i | \(-0.00171488\pi\) |
−0.504658 | + | 0.863319i | \(0.668382\pi\) | |||||||
\(108\) | −23.2379 | − | 13.4164i | −0.215166 | − | 0.124226i | ||||
\(109\) | 71.0000 | − | 122.976i | 0.651376 | − | 1.12822i | −0.331413 | − | 0.943486i | \(-0.607525\pi\) |
0.982789 | − | 0.184731i | \(-0.0591413\pi\) | |||||||
\(110\) | −3.87298 | + | 2.23607i | −0.0352089 | + | 0.0203279i | ||||
\(111\) | 62.6099i | 0.564053i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −34.0000 | −0.300885 | −0.150442 | − | 0.988619i | \(-0.548070\pi\) | ||||
−0.150442 | + | 0.988619i | \(0.548070\pi\) | |||||||
\(114\) | 30.0000 | + | 51.9615i | 0.263158 | + | 0.455803i | ||||
\(115\) | −50.3488 | − | 29.0689i | −0.437816 | − | 0.252773i | ||||
\(116\) | −33.0000 | + | 57.1577i | −0.284483 | + | 0.492739i | ||||
\(117\) | 127.808 | − | 73.7902i | 1.09238 | − | 0.630686i | ||||
\(118\) | 40.2492i | 0.341095i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −70.0000 | −0.583333 | ||||||||
\(121\) | 58.5000 | + | 101.325i | 0.483471 | + | 0.837396i | ||||
\(122\) | 81.3327 | + | 46.9574i | 0.666661 | + | 0.384897i | ||||
\(123\) | −60.0000 | + | 103.923i | −0.487805 | + | 0.844903i | ||||
\(124\) | 139.427 | − | 80.4984i | 1.12441 | − | 0.649181i | ||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 194.000 | 1.52756 | 0.763780 | − | 0.645477i | \(-0.223341\pi\) | ||||
0.763780 | + | 0.645477i | \(0.223341\pi\) | |||||||
\(128\) | −59.5000 | − | 103.057i | −0.464844 | − | 0.805133i | ||||
\(129\) | 131.681 | + | 76.0263i | 1.02079 | + | 0.589351i | ||||
\(130\) | 15.0000 | − | 25.9808i | 0.115385 | − | 0.199852i | ||||
\(131\) | −104.571 | + | 60.3738i | −0.798248 | + | 0.460869i | −0.842858 | − | 0.538136i | \(-0.819129\pi\) |
0.0446099 | + | 0.999004i | \(0.485796\pi\) | |||||||
\(132\) | − | 26.8328i | − | 0.203279i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.0000 | −0.104478 | ||||||||
\(135\) | −10.0000 | − | 17.3205i | −0.0740741 | − | 0.128300i | ||||
\(136\) | −162.665 | − | 93.9149i | −1.19607 | − | 0.690550i | ||||
\(137\) | 83.0000 | − | 143.760i | 0.605839 | − | 1.04934i | −0.386079 | − | 0.922466i | \(-0.626171\pi\) |
0.991918 | − | 0.126879i | \(-0.0404959\pi\) | |||||||
\(138\) | −100.698 | + | 58.1378i | −0.729693 | + | 0.421288i | ||||
\(139\) | − | 93.9149i | − | 0.675646i | −0.941210 | − | 0.337823i | \(-0.890309\pi\) | ||
0.941210 | − | 0.337823i | \(-0.109691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 120.000 | 0.851064 | ||||||||
\(142\) | 31.0000 | + | 53.6936i | 0.218310 | + | 0.378124i | ||||
\(143\) | 23.2379 | + | 13.4164i | 0.162503 | + | 0.0938210i | ||||
\(144\) | 27.5000 | − | 47.6314i | 0.190972 | − | 0.330774i | ||||
\(145\) | −42.6028 | + | 24.5967i | −0.293813 | + | 0.169633i | ||||
\(146\) | 53.6656i | 0.367573i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −42.0000 | −0.283784 | ||||||||
\(149\) | 71.0000 | + | 122.976i | 0.476510 | + | 0.825340i | 0.999638 | − | 0.0269147i | \(-0.00856824\pi\) |
−0.523128 | + | 0.852254i | \(0.675235\pi\) | |||||||
\(150\) | −19.3649 | − | 11.1803i | −0.129099 | − | 0.0745356i | ||||
\(151\) | −1.00000 | + | 1.73205i | −0.00662252 | + | 0.0114705i | −0.869318 | − | 0.494254i | \(-0.835441\pi\) |
0.862695 | + | 0.505724i | \(0.168775\pi\) | |||||||
\(152\) | −81.3327 | + | 46.9574i | −0.535083 | + | 0.308930i | ||||
\(153\) | − | 295.161i | − | 1.92916i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 120.000 | 0.774194 | ||||||||
\(156\) | 90.0000 | + | 155.885i | 0.576923 | + | 0.999260i | ||||
\(157\) | 58.0948 | + | 33.5410i | 0.370030 | + | 0.213637i | 0.673472 | − | 0.739213i | \(-0.264802\pi\) |
−0.303441 | + | 0.952850i | \(0.598136\pi\) | |||||||
\(158\) | 19.0000 | − | 32.9090i | 0.120253 | − | 0.208285i | ||||
\(159\) | −131.681 | + | 76.0263i | −0.828185 | + | 0.478153i | ||||
\(160\) | − | 73.7902i | − | 0.461189i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 59.0000 | 0.364198 | ||||||||
\(163\) | 17.0000 | + | 29.4449i | 0.104294 | + | 0.180643i | 0.913450 | − | 0.406952i | \(-0.133408\pi\) |
−0.809155 | + | 0.587595i | \(0.800075\pi\) | |||||||
\(164\) | −69.7137 | − | 40.2492i | −0.425084 | − | 0.245422i | ||||
\(165\) | 10.0000 | − | 17.3205i | 0.0606061 | − | 0.104973i | ||||
\(166\) | −34.8569 | + | 20.1246i | −0.209981 | + | 0.121233i | ||||
\(167\) | − | 107.331i | − | 0.642702i | −0.946960 | − | 0.321351i | \(-0.895863\pi\) | ||
0.946960 | − | 0.321351i | \(-0.104137\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.0650888 | ||||||||
\(170\) | −30.0000 | − | 51.9615i | −0.176471 | − | 0.305656i | ||||
\(171\) | −127.808 | − | 73.7902i | −0.747418 | − | 0.431522i | ||||
\(172\) | −51.0000 | + | 88.3346i | −0.296512 | + | 0.513573i | ||||
\(173\) | 127.808 | − | 73.7902i | 0.738777 | − | 0.426533i | −0.0828474 | − | 0.996562i | \(-0.526401\pi\) |
0.821625 | + | 0.570029i | \(0.193068\pi\) | |||||||
\(174\) | 98.3870i | 0.565442i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.0000 | 0.0568182 | ||||||||
\(177\) | −90.0000 | − | 155.885i | −0.508475 | − | 0.880704i | ||||
\(178\) | −23.2379 | − | 13.4164i | −0.130550 | − | 0.0753731i | ||||
\(179\) | −109.000 | + | 188.794i | −0.608939 | + | 1.05471i | 0.382477 | + | 0.923965i | \(0.375071\pi\) |
−0.991416 | + | 0.130748i | \(0.958262\pi\) | |||||||
\(180\) | 63.9042 | − | 36.8951i | 0.355023 | − | 0.204973i | ||||
\(181\) | − | 254.912i | − | 1.40835i | −0.710025 | − | 0.704176i | \(-0.751317\pi\) | ||
0.710025 | − | 0.704176i | \(-0.248683\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −420.000 | −2.29508 | ||||||||
\(184\) | −91.0000 | − | 157.617i | −0.494565 | − | 0.856612i | ||||
\(185\) | −27.1109 | − | 15.6525i | −0.146545 | − | 0.0846080i | ||||
\(186\) | 120.000 | − | 207.846i | 0.645161 | − | 1.11745i | ||||
\(187\) | 46.4758 | − | 26.8328i | 0.248534 | − | 0.143491i | ||||
\(188\) | 80.4984i | 0.428183i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −30.0000 | −0.157895 | ||||||||
\(191\) | 29.0000 | + | 50.2295i | 0.151832 | + | 0.262982i | 0.931901 | − | 0.362712i | \(-0.118149\pi\) |
−0.780069 | + | 0.625694i | \(0.784816\pi\) | |||||||
\(192\) | −50.3488 | − | 29.0689i | −0.262233 | − | 0.151400i | ||||
\(193\) | −103.000 | + | 178.401i | −0.533679 | + | 0.924359i | 0.465547 | + | 0.885023i | \(0.345858\pi\) |
−0.999226 | + | 0.0393357i | \(0.987476\pi\) | |||||||
\(194\) | 23.2379 | − | 13.4164i | 0.119783 | − | 0.0691567i | ||||
\(195\) | 134.164i | 0.688021i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −226.000 | −1.14721 | −0.573604 | − | 0.819133i | \(-0.694455\pi\) | ||||
−0.573604 | + | 0.819133i | \(0.694455\pi\) | |||||||
\(198\) | −11.0000 | − | 19.0526i | −0.0555556 | − | 0.0962250i | ||||
\(199\) | −116.190 | − | 67.0820i | −0.583867 | − | 0.337096i | 0.178802 | − | 0.983885i | \(-0.442778\pi\) |
−0.762669 | + | 0.646789i | \(0.776111\pi\) | |||||||
\(200\) | 17.5000 | − | 30.3109i | 0.0875000 | − | 0.151554i | ||||
\(201\) | 54.2218 | − | 31.3050i | 0.269760 | − | 0.155746i | ||||
\(202\) | − | 67.0820i | − | 0.332089i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 360.000 | 1.76471 | ||||||||
\(205\) | −30.0000 | − | 51.9615i | −0.146341 | − | 0.253471i | ||||
\(206\) | 139.427 | + | 80.4984i | 0.676832 | + | 0.390769i | ||||
\(207\) | 143.000 | − | 247.683i | 0.690821 | − | 1.19654i | ||||
\(208\) | −58.0948 | + | 33.5410i | −0.279302 | + | 0.161255i | ||||
\(209\) | − | 26.8328i | − | 0.128387i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −118.000 | −0.559242 | −0.279621 | − | 0.960111i | \(-0.590209\pi\) | ||||
−0.279621 | + | 0.960111i | \(0.590209\pi\) | |||||||
\(212\) | −51.0000 | − | 88.3346i | −0.240566 | − | 0.416673i | ||||
\(213\) | −240.125 | − | 138.636i | −1.12735 | − | 0.650874i | ||||
\(214\) | −53.0000 | + | 91.7987i | −0.247664 | + | 0.428966i | ||||
\(215\) | −65.8407 | + | 38.0132i | −0.306236 | + | 0.176805i | ||||
\(216\) | − | 62.6099i | − | 0.289861i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 142.000 | 0.651376 | ||||||||
\(219\) | −120.000 | − | 207.846i | −0.547945 | − | 0.949069i | ||||
\(220\) | 11.6190 | + | 6.70820i | 0.0528134 | + | 0.0304918i | ||||
\(221\) | −180.000 | + | 311.769i | −0.814480 | + | 1.41072i | ||||
\(222\) | −54.2218 | + | 31.3050i | −0.244242 | + | 0.141013i | ||||
\(223\) | 80.4984i | 0.360980i | 0.983577 | + | 0.180490i | \(0.0577683\pi\) | ||||
−0.983577 | + | 0.180490i | \(0.942232\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 55.0000 | 0.244444 | ||||||||
\(226\) | −17.0000 | − | 29.4449i | −0.0752212 | − | 0.130287i | ||||
\(227\) | −220.760 | − | 127.456i | −0.972511 | − | 0.561480i | −0.0725103 | − | 0.997368i | \(-0.523101\pi\) |
−0.900001 | + | 0.435888i | \(0.856434\pi\) | |||||||
\(228\) | 90.0000 | − | 155.885i | 0.394737 | − | 0.683704i | ||||
\(229\) | 11.6190 | − | 6.70820i | 0.0507378 | − | 0.0292935i | −0.474417 | − | 0.880300i | \(-0.657341\pi\) |
0.525154 | + | 0.851007i | \(0.324008\pi\) | |||||||
\(230\) | − | 58.1378i | − | 0.252773i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −154.000 | −0.663793 | ||||||||
\(233\) | 107.000 | + | 185.329i | 0.459227 | + | 0.795405i | 0.998920 | − | 0.0464567i | \(-0.0147930\pi\) |
−0.539693 | + | 0.841862i | \(0.681460\pi\) | |||||||
\(234\) | 127.808 | + | 73.7902i | 0.546190 | + | 0.315343i | ||||
\(235\) | −30.0000 | + | 51.9615i | −0.127660 | + | 0.221113i | ||||
\(236\) | 104.571 | − | 60.3738i | 0.443096 | − | 0.255821i | ||||
\(237\) | 169.941i | 0.717051i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 98.0000 | 0.410042 | 0.205021 | − | 0.978758i | \(-0.434274\pi\) | ||||
0.205021 | + | 0.978758i | \(0.434274\pi\) | |||||||
\(240\) | 25.0000 | + | 43.3013i | 0.104167 | + | 0.180422i | ||||
\(241\) | 139.427 | + | 80.4984i | 0.578537 | + | 0.334018i | 0.760552 | − | 0.649277i | \(-0.224929\pi\) |
−0.182015 | + | 0.983296i | \(0.558262\pi\) | |||||||
\(242\) | −58.5000 | + | 101.325i | −0.241736 | + | 0.418698i | ||||
\(243\) | −298.220 | + | 172.177i | −1.22724 | + | 0.708548i | ||||
\(244\) | − | 281.745i | − | 1.15469i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −120.000 | −0.487805 | ||||||||
\(247\) | 90.0000 | + | 155.885i | 0.364372 | + | 0.631112i | ||||
\(248\) | 325.331 | + | 187.830i | 1.31182 | + | 0.757378i | ||||
\(249\) | 90.0000 | − | 155.885i | 0.361446 | − | 0.626042i | ||||
\(250\) | 9.68246 | − | 5.59017i | 0.0387298 | − | 0.0223607i | ||||
\(251\) | 335.410i | 1.33630i | 0.744029 | + | 0.668148i | \(0.232913\pi\) | ||||
−0.744029 | + | 0.668148i | \(0.767087\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 52.0000 | 0.205534 | ||||||||
\(254\) | 97.0000 | + | 168.009i | 0.381890 | + | 0.661452i | ||||
\(255\) | 232.379 | + | 134.164i | 0.911290 | + | 0.526134i | ||||
\(256\) | 85.5000 | − | 148.090i | 0.333984 | − | 0.578478i | ||||
\(257\) | −116.190 | + | 67.0820i | −0.452099 | + | 0.261020i | −0.708716 | − | 0.705494i | \(-0.750725\pi\) |
0.256617 | + | 0.966513i | \(0.417392\pi\) | |||||||
\(258\) | 152.053i | 0.589351i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −90.0000 | −0.346154 | ||||||||
\(261\) | −121.000 | − | 209.578i | −0.463602 | − | 0.802981i | ||||
\(262\) | −104.571 | − | 60.3738i | −0.399124 | − | 0.230434i | ||||
\(263\) | 17.0000 | − | 29.4449i | 0.0646388 | − | 0.111958i | −0.831895 | − | 0.554933i | \(-0.812744\pi\) |
0.896534 | + | 0.442976i | \(0.146077\pi\) | |||||||
\(264\) | 54.2218 | − | 31.3050i | 0.205385 | − | 0.118579i | ||||
\(265\) | − | 76.0263i | − | 0.286892i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 120.000 | 0.449438 | ||||||||
\(268\) | 21.0000 | + | 36.3731i | 0.0783582 | + | 0.135720i | ||||
\(269\) | −220.760 | − | 127.456i | −0.820669 | − | 0.473814i | 0.0299779 | − | 0.999551i | \(-0.490456\pi\) |
−0.850647 | + | 0.525737i | \(0.823790\pi\) | |||||||
\(270\) | 10.0000 | − | 17.3205i | 0.0370370 | − | 0.0641500i | ||||
\(271\) | 278.855 | − | 160.997i | 1.02898 | − | 0.594084i | 0.112291 | − | 0.993675i | \(-0.464181\pi\) |
0.916694 | + | 0.399591i | \(0.130848\pi\) | |||||||
\(272\) | 134.164i | 0.493250i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 166.000 | 0.605839 | ||||||||
\(275\) | 5.00000 | + | 8.66025i | 0.0181818 | + | 0.0314918i | ||||
\(276\) | 302.093 | + | 174.413i | 1.09454 | + | 0.631932i | ||||
\(277\) | −7.00000 | + | 12.1244i | −0.0252708 | + | 0.0437702i | −0.878384 | − | 0.477955i | \(-0.841378\pi\) |
0.853113 | + | 0.521725i | \(0.174711\pi\) | |||||||
\(278\) | 81.3327 | − | 46.9574i | 0.292563 | − | 0.168912i | ||||
\(279\) | 590.322i | 2.11585i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.00711744 | 0.00355872 | − | 0.999994i | \(-0.498867\pi\) | ||||
0.00355872 | + | 0.999994i | \(0.498867\pi\) | |||||||
\(282\) | 60.0000 | + | 103.923i | 0.212766 | + | 0.368521i | ||||
\(283\) | 81.3327 | + | 46.9574i | 0.287395 | + | 0.165927i | 0.636766 | − | 0.771057i | \(-0.280272\pi\) |
−0.349372 | + | 0.936984i | \(0.613605\pi\) | |||||||
\(284\) | 93.0000 | − | 161.081i | 0.327465 | − | 0.567186i | ||||
\(285\) | 116.190 | − | 67.0820i | 0.407682 | − | 0.235376i | ||||
\(286\) | 26.8328i | 0.0938210i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 363.000 | 1.26042 | ||||||||
\(289\) | 215.500 | + | 373.257i | 0.745675 | + | 1.29155i | ||||
\(290\) | −42.6028 | − | 24.5967i | −0.146906 | − | 0.0848164i | ||||
\(291\) | −60.0000 | + | 103.923i | −0.206186 | + | 0.357124i | ||||
\(292\) | 139.427 | − | 80.4984i | 0.477491 | − | 0.275680i | ||||
\(293\) | 335.410i | 1.14474i | 0.819994 | + | 0.572372i | \(0.193977\pi\) | ||||
−0.819994 | + | 0.572372i | \(0.806023\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 90.0000 | 0.305085 | ||||||||
\(296\) | −49.0000 | − | 84.8705i | −0.165541 | − | 0.286725i | ||||
\(297\) | 15.4919 | + | 8.94427i | 0.0521614 | + | 0.0301154i | ||||
\(298\) | −71.0000 | + | 122.976i | −0.238255 | + | 0.412670i | ||||
\(299\) | −302.093 | + | 174.413i | −1.01034 | + | 0.583322i | ||||
\(300\) | 67.0820i | 0.223607i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.00000 | −0.00662252 | ||||||||
\(303\) | 150.000 | + | 259.808i | 0.495050 | + | 0.857451i | ||||
\(304\) | 58.0948 | + | 33.5410i | 0.191101 | + | 0.110332i | ||||
\(305\) | 105.000 | − | 181.865i | 0.344262 | − | 0.596280i | ||||
\(306\) | 255.617 | − | 147.580i | 0.835349 | − | 0.482289i | ||||
\(307\) | 201.246i | 0.655525i | 0.944760 | + | 0.327762i | \(0.106295\pi\) | ||||
−0.944760 | + | 0.327762i | \(0.893705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −720.000 | −2.33010 | ||||||||
\(310\) | 60.0000 | + | 103.923i | 0.193548 | + | 0.335236i | ||||
\(311\) | 441.520 | + | 254.912i | 1.41968 | + | 0.819652i | 0.996270 | − | 0.0862870i | \(-0.0275002\pi\) |
0.423408 | + | 0.905939i | \(0.360834\pi\) | |||||||
\(312\) | −210.000 | + | 363.731i | −0.673077 | + | 1.16580i | ||||
\(313\) | 278.855 | − | 160.997i | 0.890910 | − | 0.514367i | 0.0166699 | − | 0.999861i | \(-0.494694\pi\) |
0.874240 | + | 0.485494i | \(0.161360\pi\) | |||||||
\(314\) | 67.0820i | 0.213637i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −114.000 | −0.360759 | ||||||||
\(317\) | −187.000 | − | 323.894i | −0.589905 | − | 1.02175i | −0.994244 | − | 0.107137i | \(-0.965832\pi\) |
0.404339 | − | 0.914609i | \(-0.367502\pi\) | |||||||
\(318\) | −131.681 | − | 76.0263i | −0.414093 | − | 0.239076i | ||||
\(319\) | 22.0000 | − | 38.1051i | 0.0689655 | − | 0.119452i | ||||
\(320\) | 25.1744 | − | 14.5344i | 0.0786700 | − | 0.0454201i | ||||
\(321\) | − | 474.046i | − | 1.47678i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 360.000 | 1.11455 | ||||||||
\(324\) | −88.5000 | − | 153.286i | −0.273148 | − | 0.473106i | ||||
\(325\) | −58.0948 | − | 33.5410i | −0.178753 | − | 0.103203i | ||||
\(326\) | −17.0000 | + | 29.4449i | −0.0521472 | + | 0.0903217i | ||||
\(327\) | −549.964 | + | 317.522i | −1.68185 | + | 0.971014i | ||||
\(328\) | − | 187.830i | − | 0.572652i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 20.0000 | 0.0606061 | ||||||||
\(331\) | −241.000 | − | 417.424i | −0.728097 | − | 1.26110i | −0.957687 | − | 0.287813i | \(-0.907072\pi\) |
0.229590 | − | 0.973287i | \(-0.426261\pi\) | |||||||
\(332\) | 104.571 | + | 60.3738i | 0.314972 | + | 0.181849i | ||||
\(333\) | 77.0000 | − | 133.368i | 0.231231 | − | 0.400504i | ||||
\(334\) | 92.9516 | − | 53.6656i | 0.278298 | − | 0.160676i | ||||
\(335\) | 31.3050i | 0.0934476i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 494.000 | 1.46588 | 0.732938 | − | 0.680296i | \(-0.238149\pi\) | ||||
0.732938 | + | 0.680296i | \(0.238149\pi\) | |||||||
\(338\) | −5.50000 | − | 9.52628i | −0.0162722 | − | 0.0281843i | ||||
\(339\) | 131.681 | + | 76.0263i | 0.388441 | + | 0.224266i | ||||
\(340\) | −90.0000 | + | 155.885i | −0.264706 | + | 0.458484i | ||||
\(341\) | −92.9516 | + | 53.6656i | −0.272585 | + | 0.157377i | ||||
\(342\) | − | 147.580i | − | 0.431522i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −238.000 | −0.691860 | ||||||||
\(345\) | 130.000 | + | 225.167i | 0.376812 | + | 0.652657i | ||||
\(346\) | 127.808 | + | 73.7902i | 0.369389 | + | 0.213267i | ||||
\(347\) | 173.000 | − | 299.645i | 0.498559 | − | 0.863530i | −0.501440 | − | 0.865193i | \(-0.667196\pi\) |
0.999999 | + | 0.00166304i | \(0.000529361\pi\) | |||||||
\(348\) | 255.617 | − | 147.580i | 0.734531 | − | 0.424082i | ||||
\(349\) | − | 335.410i | − | 0.961061i | −0.876978 | − | 0.480530i | \(-0.840444\pi\) | ||
0.876978 | − | 0.480530i | \(-0.159556\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −120.000 | −0.341880 | ||||||||
\(352\) | 33.0000 | + | 57.1577i | 0.0937500 | + | 0.162380i | ||||
\(353\) | −23.2379 | − | 13.4164i | −0.0658297 | − | 0.0380068i | 0.466724 | − | 0.884403i | \(-0.345434\pi\) |
−0.532554 | + | 0.846396i | \(0.678768\pi\) | |||||||
\(354\) | 90.0000 | − | 155.885i | 0.254237 | − | 0.440352i | ||||
\(355\) | 120.062 | − | 69.3181i | 0.338204 | − | 0.195262i | ||||
\(356\) | 80.4984i | 0.226119i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −218.000 | −0.608939 | ||||||||
\(359\) | −169.000 | − | 292.717i | −0.470752 | − | 0.815367i | 0.528688 | − | 0.848816i | \(-0.322684\pi\) |
−0.999440 | + | 0.0334495i | \(0.989351\pi\) | |||||||
\(360\) | 149.110 | + | 86.0886i | 0.414194 | + | 0.239135i | ||||
\(361\) | −90.5000 | + | 156.751i | −0.250693 | + | 0.434212i | ||||
\(362\) | 220.760 | − | 127.456i | 0.609834 | − | 0.352088i | ||||
\(363\) | − | 523.240i | − | 1.44143i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 120.000 | 0.328767 | ||||||||
\(366\) | −210.000 | − | 363.731i | −0.573770 | − | 0.993800i | ||||
\(367\) | −255.617 | − | 147.580i | −0.696504 | − | 0.402127i | 0.109540 | − | 0.993982i | \(-0.465062\pi\) |
−0.806044 | + | 0.591856i | \(0.798396\pi\) | |||||||
\(368\) | −65.0000 | + | 112.583i | −0.176630 | + | 0.305933i | ||||
\(369\) | 255.617 | − | 147.580i | 0.692729 | − | 0.399947i | ||||
\(370\) | − | 31.3050i | − | 0.0846080i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −720.000 | −1.93548 | ||||||||
\(373\) | −43.0000 | − | 74.4782i | −0.115282 | − | 0.199673i | 0.802611 | − | 0.596503i | \(-0.203444\pi\) |
−0.917892 | + | 0.396830i | \(0.870110\pi\) | |||||||
\(374\) | 46.4758 | + | 26.8328i | 0.124267 | + | 0.0717455i | ||||
\(375\) | −25.0000 | + | 43.3013i | −0.0666667 | + | 0.115470i | ||||
\(376\) | −162.665 | + | 93.9149i | −0.432620 | + | 0.249774i | ||||
\(377\) | 295.161i | 0.782920i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −262.000 | −0.691293 | −0.345646 | − | 0.938365i | \(-0.612340\pi\) | ||||
−0.345646 | + | 0.938365i | \(0.612340\pi\) | |||||||
\(380\) | 45.0000 | + | 77.9423i | 0.118421 | + | 0.205111i | ||||
\(381\) | −751.359 | − | 433.797i | −1.97207 | − | 1.13858i | ||||
\(382\) | −29.0000 | + | 50.2295i | −0.0759162 | + | 0.131491i | ||||
\(383\) | −487.996 | + | 281.745i | −1.27414 | + | 0.735625i | −0.975765 | − | 0.218823i | \(-0.929778\pi\) |
−0.298376 | + | 0.954448i | \(0.596445\pi\) | |||||||
\(384\) | 532.184i | 1.38590i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −206.000 | −0.533679 | ||||||||
\(387\) | −187.000 | − | 323.894i | −0.483204 | − | 0.836934i | ||||
\(388\) | −69.7137 | − | 40.2492i | −0.179674 | − | 0.103735i | ||||
\(389\) | −349.000 | + | 604.486i | −0.897172 | + | 1.55395i | −0.0660793 | + | 0.997814i | \(0.521049\pi\) |
−0.831093 | + | 0.556134i | \(0.812284\pi\) | |||||||
\(390\) | −116.190 | + | 67.0820i | −0.297922 | + | 0.172005i | ||||
\(391\) | 697.653i | 1.78428i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 540.000 | 1.37405 | ||||||||
\(394\) | −113.000 | − | 195.722i | −0.286802 | − | 0.496756i | ||||
\(395\) | −73.5867 | − | 42.4853i | −0.186295 | − | 0.107558i | ||||
\(396\) | −33.0000 | + | 57.1577i | −0.0833333 | + | 0.144338i | ||||
\(397\) | 267.236 | − | 154.289i | 0.673138 | − | 0.388636i | −0.124126 | − | 0.992266i | \(-0.539613\pi\) |
0.797265 | + | 0.603630i | \(0.206280\pi\) | |||||||
\(398\) | − | 134.164i | − | 0.337096i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −25.0000 | −0.0625000 | ||||||||
\(401\) | 269.000 | + | 465.922i | 0.670823 | + | 1.16190i | 0.977671 | + | 0.210141i | \(0.0673923\pi\) |
−0.306848 | + | 0.951758i | \(0.599274\pi\) | |||||||
\(402\) | 54.2218 | + | 31.3050i | 0.134880 | + | 0.0778730i | ||||
\(403\) | 360.000 | − | 623.538i | 0.893300 | − | 1.54724i | ||||
\(404\) | −174.284 | + | 100.623i | −0.431397 | + | 0.249067i | ||||
\(405\) | − | 131.928i | − | 0.325748i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.0000 | 0.0687961 | ||||||||
\(408\) | 420.000 | + | 727.461i | 1.02941 | + | 1.78299i | ||||
\(409\) | −255.617 | − | 147.580i | −0.624980 | − | 0.360832i | 0.153825 | − | 0.988098i | \(-0.450841\pi\) |
−0.778805 | + | 0.627266i | \(0.784174\pi\) | |||||||
\(410\) | 30.0000 | − | 51.9615i | 0.0731707 | − | 0.126735i | ||||
\(411\) | −642.915 | + | 371.187i | −1.56427 | + | 0.903132i | ||||
\(412\) | − | 482.991i | − | 1.17231i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 286.000 | 0.690821 | ||||||||
\(415\) | 45.0000 | + | 77.9423i | 0.108434 | + | 0.187813i | ||||
\(416\) | −383.425 | − | 221.371i | −0.921696 | − | 0.532141i | ||||
\(417\) | −210.000 | + | 363.731i | −0.503597 | + | 0.872256i | ||||
\(418\) | 23.2379 | − | 13.4164i | 0.0555931 | − | 0.0320967i | ||||
\(419\) | − | 818.401i | − | 1.95322i | −0.215009 | − | 0.976612i | \(-0.568978\pi\) | ||
0.215009 | − | 0.976612i | \(-0.431022\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −118.000 | −0.280285 | −0.140143 | − | 0.990131i | \(-0.544756\pi\) | ||||
−0.140143 | + | 0.990131i | \(0.544756\pi\) | |||||||
\(422\) | −59.0000 | − | 102.191i | −0.139810 | − | 0.242159i | ||||
\(423\) | −255.617 | − | 147.580i | −0.604295 | − | 0.348890i | ||||
\(424\) | 119.000 | − | 206.114i | 0.280660 | − | 0.486118i | ||||
\(425\) | −116.190 | + | 67.0820i | −0.273387 | + | 0.157840i | ||||
\(426\) | − | 277.272i | − | 0.650874i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 318.000 | 0.742991 | ||||||||
\(429\) | −60.0000 | − | 103.923i | −0.139860 | − | 0.242245i | ||||
\(430\) | −65.8407 | − | 38.0132i | −0.153118 | − | 0.0884027i | ||||
\(431\) | 359.000 | − | 621.806i | 0.832947 | − | 1.44271i | −0.0627447 | − | 0.998030i | \(-0.519985\pi\) |
0.895691 | − | 0.444676i | \(-0.146681\pi\) | |||||||
\(432\) | −38.7298 | + | 22.3607i | −0.0896524 | + | 0.0517608i | ||||
\(433\) | 509.823i | 1.17742i | 0.808344 | + | 0.588711i | \(0.200364\pi\) | ||||
−0.808344 | + | 0.588711i | \(0.799636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 220.000 | 0.505747 | ||||||||
\(436\) | −213.000 | − | 368.927i | −0.488532 | − | 0.846162i | ||||
\(437\) | 302.093 | + | 174.413i | 0.691288 | + | 0.399115i | ||||
\(438\) | 120.000 | − | 207.846i | 0.273973 | − | 0.474534i | ||||
\(439\) | −23.2379 | + | 13.4164i | −0.0529337 | + | 0.0305613i | −0.526233 | − | 0.850340i | \(-0.676396\pi\) |
0.473300 | + | 0.880902i | \(0.343063\pi\) | |||||||
\(440\) | 31.3050i | 0.0711476i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −360.000 | −0.814480 | ||||||||
\(443\) | 317.000 | + | 549.060i | 0.715576 | + | 1.23941i | 0.962737 | + | 0.270439i | \(0.0871689\pi\) |
−0.247161 | + | 0.968974i | \(0.579498\pi\) | |||||||
\(444\) | 162.665 | + | 93.9149i | 0.366363 | + | 0.211520i | ||||
\(445\) | −30.0000 | + | 51.9615i | −0.0674157 | + | 0.116767i | ||||
\(446\) | −69.7137 | + | 40.2492i | −0.156309 | + | 0.0902449i | ||||
\(447\) | − | 635.043i | − | 1.42068i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 338.000 | 0.752784 | 0.376392 | − | 0.926461i | \(-0.377165\pi\) | ||||
0.376392 | + | 0.926461i | \(0.377165\pi\) | |||||||
\(450\) | 27.5000 | + | 47.6314i | 0.0611111 | + | 0.105848i | ||||
\(451\) | 46.4758 | + | 26.8328i | 0.103051 | + | 0.0594963i | ||||
\(452\) | −51.0000 | + | 88.3346i | −0.112832 | + | 0.195431i | ||||
\(453\) | 7.74597 | − | 4.47214i | 0.0170993 | − | 0.00987226i | ||||
\(454\) | − | 254.912i | − | 0.561480i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 420.000 | 0.921053 | ||||||||
\(457\) | 233.000 | + | 403.568i | 0.509847 | + | 0.883081i | 0.999935 | + | 0.0114077i | \(0.00363126\pi\) |
−0.490088 | + | 0.871673i | \(0.663035\pi\) | |||||||
\(458\) | 11.6190 | + | 6.70820i | 0.0253689 | + | 0.0146467i | ||||
\(459\) | −120.000 | + | 207.846i | −0.261438 | + | 0.452824i | ||||
\(460\) | −151.046 | + | 87.2067i | −0.328362 | + | 0.189580i | ||||
\(461\) | − | 442.741i | − | 0.960394i | −0.877161 | − | 0.480197i | \(-0.840565\pi\) | ||
0.877161 | − | 0.480197i | \(-0.159435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 206.000 | 0.444924 | 0.222462 | − | 0.974941i | \(-0.428591\pi\) | ||||
0.222462 | + | 0.974941i | \(0.428591\pi\) | |||||||
\(464\) | 55.0000 | + | 95.2628i | 0.118534 | + | 0.205308i | ||||
\(465\) | −464.758 | − | 268.328i | −0.999480 | − | 0.577050i | ||||
\(466\) | −107.000 | + | 185.329i | −0.229614 | + | 0.397703i | ||||
\(467\) | 313.712 | − | 181.122i | 0.671759 | − | 0.387840i | −0.124984 | − | 0.992159i | \(-0.539888\pi\) |
0.796743 | + | 0.604318i | \(0.206554\pi\) | |||||||
\(468\) | − | 442.741i | − | 0.946029i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −60.0000 | −0.127660 | ||||||||
\(471\) | −150.000 | − | 259.808i | −0.318471 | − | 0.551609i | ||||
\(472\) | 243.998 | + | 140.872i | 0.516945 | + | 0.298458i | ||||
\(473\) | 34.0000 | − | 58.8897i | 0.0718816 | − | 0.124503i | ||||
\(474\) | −147.173 | + | 84.9706i | −0.310492 | + | 0.179263i | ||||
\(475\) | 67.0820i | 0.141225i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 374.000 | 0.784067 | ||||||||
\(478\) | 49.0000 | + | 84.8705i | 0.102510 | + | 0.177553i | ||||
\(479\) | −185.903 | − | 107.331i | −0.388107 | − | 0.224074i | 0.293233 | − | 0.956041i | \(-0.405269\pi\) |
−0.681340 | + | 0.731967i | \(0.738602\pi\) | |||||||
\(480\) | −165.000 | + | 285.788i | −0.343750 | + | 0.595392i | ||||
\(481\) | −162.665 | + | 93.9149i | −0.338181 | + | 0.195249i | ||||
\(482\) | 160.997i | 0.334018i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 351.000 | 0.725207 | ||||||||
\(485\) | −30.0000 | − | 51.9615i | −0.0618557 | − | 0.107137i | ||||
\(486\) | −298.220 | − | 172.177i | −0.613621 | − | 0.354274i | ||||
\(487\) | 83.0000 | − | 143.760i | 0.170431 | − | 0.295196i | −0.768139 | − | 0.640283i | \(-0.778817\pi\) |
0.938571 | + | 0.345087i | \(0.112151\pi\) | |||||||
\(488\) | 569.329 | − | 328.702i | 1.16666 | − | 0.673570i | ||||
\(489\) | − | 152.053i | − | 0.310946i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −838.000 | −1.70672 | −0.853360 | − | 0.521321i | \(-0.825439\pi\) | ||||
−0.853360 | + | 0.521321i | \(0.825439\pi\) | |||||||
\(492\) | 180.000 | + | 311.769i | 0.365854 | + | 0.633677i | ||||
\(493\) | 511.234 | + | 295.161i | 1.03699 | + | 0.598704i | ||||
\(494\) | −90.0000 | + | 155.885i | −0.182186 | + | 0.315556i | ||||
\(495\) | −42.6028 | + | 24.5967i | −0.0860663 | + | 0.0496904i | ||||
\(496\) | − | 268.328i | − | 0.540984i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 180.000 | 0.361446 | ||||||||
\(499\) | 131.000 | + | 226.899i | 0.262525 | + | 0.454707i | 0.966912 | − | 0.255109i | \(-0.0821114\pi\) |
−0.704387 | + | 0.709816i | \(0.748778\pi\) | |||||||
\(500\) | −29.0474 | − | 16.7705i | −0.0580948 | − | 0.0335410i | ||||
\(501\) | −240.000 | + | 415.692i | −0.479042 | + | 0.829725i | ||||
\(502\) | −290.474 | + | 167.705i | −0.578633 | + | 0.334074i | ||||
\(503\) | 429.325i | 0.853529i | 0.904363 | + | 0.426764i | \(0.140347\pi\) | ||||
−0.904363 | + | 0.426764i | \(0.859653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −150.000 | −0.297030 | ||||||||
\(506\) | 26.0000 | + | 45.0333i | 0.0513834 | + | 0.0889987i | ||||
\(507\) | 42.6028 | + | 24.5967i | 0.0840292 | + | 0.0485143i | ||||
\(508\) | 291.000 | − | 504.027i | 0.572835 | − | 0.992179i | ||||
\(509\) | 778.470 | − | 449.450i | 1.52941 | − | 0.883005i | 0.530023 | − | 0.847983i | \(-0.322183\pi\) |
0.999387 | − | 0.0350222i | \(-0.0111502\pi\) | |||||||
\(510\) | 268.328i | 0.526134i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | 60.0000 | + | 103.923i | 0.116959 | + | 0.202579i | ||||
\(514\) | −116.190 | − | 67.0820i | −0.226050 | − | 0.130510i | ||||
\(515\) | 180.000 | − | 311.769i | 0.349515 | − | 0.605377i | ||||
\(516\) | 395.044 | − | 228.079i | 0.765590 | − | 0.442013i | ||||
\(517\) | − | 53.6656i | − | 0.103802i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −660.000 | −1.27168 | ||||||||
\(520\) | −105.000 | − | 181.865i | −0.201923 | − | 0.349741i | ||||
\(521\) | −627.423 | − | 362.243i | −1.20427 | − | 0.695284i | −0.242766 | − | 0.970085i | \(-0.578055\pi\) |
−0.961501 | + | 0.274801i | \(0.911388\pi\) | |||||||
\(522\) | 121.000 | − | 209.578i | 0.231801 | − | 0.401491i | ||||
\(523\) | −453.139 | + | 261.620i | −0.866423 | + | 0.500229i | −0.866158 | − | 0.499771i | \(-0.833418\pi\) |
−0.000264858 | 1.00000i | \(0.500084\pi\) | ||||||||
\(524\) | 362.243i | 0.691303i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.0000 | 0.0646388 | ||||||||
\(527\) | −720.000 | − | 1247.08i | −1.36622 | − | 2.36637i | ||||
\(528\) | −38.7298 | − | 22.3607i | −0.0733520 | − | 0.0423498i | ||||
\(529\) | −73.5000 | + | 127.306i | −0.138941 | + | 0.240654i | ||||
\(530\) | 65.8407 | − | 38.0132i | 0.124228 | − | 0.0717229i | ||||
\(531\) | 442.741i | 0.833788i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −360.000 | −0.675422 | ||||||||
\(534\) | 60.0000 | + | 103.923i | 0.112360 | + | 0.194612i | ||||
\(535\) | 205.268 | + | 118.512i | 0.383679 | + | 0.221517i | ||||
\(536\) | −49.0000 | + | 84.8705i | −0.0914179 | + | 0.158340i | ||||
\(537\) | 844.310 | − | 487.463i | 1.57227 | − | 0.907752i | ||||
\(538\) | − | 254.912i | − | 0.473814i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −60.0000 | −0.111111 | ||||||||
\(541\) | −421.000 | − | 729.193i | −0.778189 | − | 1.34786i | −0.932985 | − | 0.359916i | \(-0.882805\pi\) |
0.154796 | − | 0.987946i | \(-0.450528\pi\) | |||||||
\(542\) | 278.855 | + | 160.997i | 0.514492 | + | 0.297042i | ||||
\(543\) | −570.000 | + | 987.269i | −1.04972 | + | 1.81817i | ||||
\(544\) | −766.851 | + | 442.741i | −1.40965 | + | 0.813863i | ||||
\(545\) | − | 317.522i | − | 0.582609i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 134.000 | 0.244973 | 0.122486 | − | 0.992470i | \(-0.460913\pi\) | ||||
0.122486 | + | 0.992470i | \(0.460913\pi\) | |||||||
\(548\) | −249.000 | − | 431.281i | −0.454380 | − | 0.787008i | ||||
\(549\) | 894.659 | + | 516.532i | 1.62962 | + | 0.940859i | ||||
\(550\) | −5.00000 | + | 8.66025i | −0.00909091 | + | 0.0157459i | ||||
\(551\) | 255.617 | − | 147.580i | 0.463915 | − | 0.267841i | ||||
\(552\) | 813.929i | 1.47451i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.0000 | −0.0252708 | ||||||||
\(555\) | 70.0000 | + | 121.244i | 0.126126 | + | 0.218457i | ||||
\(556\) | −243.998 | − | 140.872i | −0.438845 | − | 0.253367i | ||||
\(557\) | 353.000 | − | 611.414i | 0.633752 | − | 1.09769i | −0.353026 | − | 0.935614i | \(-0.614847\pi\) |
0.986778 | − | 0.162077i | \(-0.0518195\pi\) | |||||||
\(558\) | −511.234 | + | 295.161i | −0.916190 | + | 0.528962i | ||||
\(559\) | 456.158i | 0.816025i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −240.000 | −0.427807 | ||||||||
\(562\) | 1.00000 | + | 1.73205i | 0.00177936 | + | 0.00308194i | ||||
\(563\) | 11.6190 | + | 6.70820i | 0.0206376 | + | 0.0119151i | 0.510283 | − | 0.860006i | \(-0.329541\pi\) |
−0.489646 | + | 0.871921i | \(0.662874\pi\) | |||||||
\(564\) | 180.000 | − | 311.769i | 0.319149 | − | 0.552782i | ||||
\(565\) | −65.8407 | + | 38.0132i | −0.116532 | + | 0.0672799i | ||||
\(566\) | 93.9149i | 0.165927i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 434.000 | 0.764085 | ||||||||
\(569\) | 41.0000 | + | 71.0141i | 0.0720562 | + | 0.124805i | 0.899802 | − | 0.436298i | \(-0.143711\pi\) |
−0.827746 | + | 0.561103i | \(0.810377\pi\) | |||||||
\(570\) | 116.190 | + | 67.0820i | 0.203841 | + | 0.117688i | ||||
\(571\) | 59.0000 | − | 102.191i | 0.103327 | − | 0.178968i | −0.809726 | − | 0.586808i | \(-0.800384\pi\) |
0.913054 | + | 0.407839i | \(0.133718\pi\) | |||||||
\(572\) | 69.7137 | − | 40.2492i | 0.121877 | − | 0.0703658i | ||||
\(573\) | − | 259.384i | − | 0.452677i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −130.000 | −0.226087 | ||||||||
\(576\) | 71.5000 | + | 123.842i | 0.124132 | + | 0.215003i | ||||
\(577\) | 766.851 | + | 442.741i | 1.32903 | + | 0.767316i | 0.985150 | − | 0.171697i | \(-0.0549250\pi\) |
0.343881 | + | 0.939013i | \(0.388258\pi\) | |||||||
\(578\) | −215.500 | + | 373.257i | −0.372837 | + | 0.645773i | ||||
\(579\) | 797.835 | − | 460.630i | 1.37795 | − | 0.795561i | ||||
\(580\) | 147.580i | 0.254449i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −120.000 | −0.206186 | ||||||||
\(583\) | 34.0000 | + | 58.8897i | 0.0583190 | + | 0.101012i | ||||
\(584\) | 325.331 | + | 187.830i | 0.557073 | + | 0.321626i | ||||
\(585\) | 165.000 | − | 285.788i | 0.282051 | − | 0.488527i | ||||
\(586\) | −290.474 | + | 167.705i | −0.495689 | + | 0.286186i | ||||
\(587\) | − | 791.568i | − | 1.34850i | −0.738504 | − | 0.674249i | \(-0.764468\pi\) | ||
0.738504 | − | 0.674249i | \(-0.235532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −720.000 | −1.22241 | ||||||||
\(590\) | 45.0000 | + | 77.9423i | 0.0762712 | + | 0.132106i | ||||
\(591\) | 875.294 | + | 505.351i | 1.48104 | + | 0.855078i | ||||
\(592\) | −35.0000 | + | 60.6218i | −0.0591216 | + | 0.102402i | ||||
\(593\) | −116.190 | + | 67.0820i | −0.195935 | + | 0.113123i | −0.594758 | − | 0.803905i | \(-0.702752\pi\) |
0.398823 | + | 0.917028i | \(0.369419\pi\) | |||||||
\(594\) | 17.8885i | 0.0301154i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 426.000 | 0.714765 | ||||||||
\(597\) | 300.000 | + | 519.615i | 0.502513 | + | 0.870377i | ||||
\(598\) | −302.093 | − | 174.413i | −0.505172 | − | 0.291661i | ||||
\(599\) | −199.000 | + | 344.678i | −0.332220 | + | 0.575423i | −0.982947 | − | 0.183890i | \(-0.941131\pi\) |
0.650727 | + | 0.759312i | \(0.274464\pi\) | |||||||
\(600\) | −135.554 | + | 78.2624i | −0.225924 | + | 0.130437i | ||||
\(601\) | 134.164i | 0.223235i | 0.993751 | + | 0.111617i | \(0.0356031\pi\) | ||||
−0.993751 | + | 0.111617i | \(0.964397\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −154.000 | −0.255390 | ||||||||
\(604\) | 3.00000 | + | 5.19615i | 0.00496689 | + | 0.00860290i | ||||
\(605\) | 226.570 | + | 130.810i | 0.374495 | + | 0.216215i | ||||
\(606\) | −150.000 | + | 259.808i | −0.247525 | + | 0.428725i | ||||
\(607\) | −813.327 | + | 469.574i | −1.33991 | + | 0.773598i | −0.986794 | − | 0.161980i | \(-0.948212\pi\) |
−0.353118 | + | 0.935579i | \(0.614879\pi\) | |||||||
\(608\) | 442.741i | 0.728193i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 210.000 | 0.344262 | ||||||||
\(611\) | 180.000 | + | 311.769i | 0.294599 | + | 0.510260i | ||||
\(612\) | −766.851 | − | 442.741i | −1.25302 | − | 0.723434i | ||||
\(613\) | −103.000 | + | 178.401i | −0.168026 | + | 0.291030i | −0.937726 | − | 0.347376i | \(-0.887073\pi\) |
0.769700 | + | 0.638406i | \(0.220406\pi\) | |||||||
\(614\) | −174.284 | + | 100.623i | −0.283851 | + | 0.163881i | ||||
\(615\) | 268.328i | 0.436306i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 494.000 | 0.800648 | 0.400324 | − | 0.916374i | \(-0.368898\pi\) | ||||
0.400324 | + | 0.916374i | \(0.368898\pi\) | |||||||
\(618\) | −360.000 | − | 623.538i | −0.582524 | − | 1.00896i | ||||
\(619\) | −104.571 | − | 60.3738i | −0.168935 | − | 0.0975345i | 0.413149 | − | 0.910664i | \(-0.364429\pi\) |
−0.582083 | + | 0.813129i | \(0.697762\pi\) | |||||||
\(620\) | 180.000 | − | 311.769i | 0.290323 | − | 0.502853i | ||||
\(621\) | −201.395 | + | 116.276i | −0.324308 | + | 0.187239i | ||||
\(622\) | 509.823i | 0.819652i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 300.000 | 0.480769 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 278.855 | + | 160.997i | 0.445455 | + | 0.257184i | ||||
\(627\) | −60.0000 | + | 103.923i | −0.0956938 | + | 0.165746i | ||||
\(628\) | 174.284 | − | 100.623i | 0.277523 | − | 0.160228i | ||||
\(629\) | 375.659i | 0.597233i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 542.000 | 0.858954 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(632\) | −133.000 | − | 230.363i | −0.210443 | − | 0.364498i | ||||
\(633\) | 457.012 | + | 263.856i | 0.721978 | + | 0.416834i | ||||
\(634\) | 187.000 | − | 323.894i | 0.294953 | − | 0.510873i | ||||
\(635\) | 375.679 | − | 216.899i | 0.591621 | − | 0.341573i | ||||
\(636\) | 456.158i | 0.717229i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 44.0000 | 0.0689655 | ||||||||
\(639\) | 341.000 | + | 590.629i | 0.533646 | + | 0.924303i | ||||
\(640\) | −230.443 | − | 133.046i | −0.360066 | − | 0.207884i | ||||
\(641\) | 149.000 | − | 258.076i | 0.232449 | − | 0.402614i | −0.726079 | − | 0.687611i | \(-0.758659\pi\) |
0.958528 | + | 0.284997i | \(0.0919927\pi\) | |||||||
\(642\) | 410.536 | − | 237.023i | 0.639465 | − | 0.369195i | ||||
\(643\) | 1006.23i | 1.56490i | 0.622714 | + | 0.782450i | \(0.286030\pi\) | ||||
−0.622714 | + | 0.782450i | \(0.713970\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 340.000 | 0.527132 | ||||||||
\(646\) | 180.000 | + | 311.769i | 0.278638 | + | 0.482615i | ||||
\(647\) | −557.710 | − | 321.994i | −0.861993 | − | 0.497672i | 0.00268605 | − | 0.999996i | \(-0.499145\pi\) |
−0.864679 | + | 0.502324i | \(0.832478\pi\) | |||||||
\(648\) | 206.500 | − | 357.668i | 0.318673 | − | 0.551958i | ||||
\(649\) | −69.7137 | + | 40.2492i | −0.107417 | + | 0.0620173i | ||||
\(650\) | − | 67.0820i | − | 0.103203i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 102.000 | 0.156442 | ||||||||
\(653\) | 77.0000 | + | 133.368i | 0.117917 | + | 0.204239i | 0.918942 | − | 0.394392i | \(-0.129045\pi\) |
−0.801025 | + | 0.598631i | \(0.795712\pi\) | |||||||
\(654\) | −549.964 | − | 317.522i | −0.840923 | − | 0.485507i | ||||
\(655\) | −135.000 | + | 233.827i | −0.206107 | + | 0.356988i | ||||
\(656\) | −116.190 | + | 67.0820i | −0.177118 | + | 0.102259i | ||||
\(657\) | 590.322i | 0.898511i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 338.000 | 0.512898 | 0.256449 | − | 0.966558i | \(-0.417447\pi\) | ||||
0.256449 | + | 0.966558i | \(0.417447\pi\) | |||||||
\(660\) | −30.0000 | − | 51.9615i | −0.0454545 | − | 0.0787296i | ||||
\(661\) | 499.615 | + | 288.453i | 0.755847 | + | 0.436388i | 0.827803 | − | 0.561019i | \(-0.189591\pi\) |
−0.0719557 | + | 0.997408i | \(0.522924\pi\) | |||||||
\(662\) | 241.000 | − | 417.424i | 0.364048 | − | 0.630550i | ||||
\(663\) | 1394.27 | − | 804.984i | 2.10298 | − | 1.21415i | ||||
\(664\) | 281.745i | 0.424314i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 154.000 | 0.231231 | ||||||||
\(667\) | 286.000 | + | 495.367i | 0.428786 | + | 0.742678i | ||||
\(668\) | −278.855 | − | 160.997i | −0.417447 | − | 0.241013i | ||||
\(669\) | 180.000 | − | 311.769i | 0.269058 | − | 0.466023i | ||||
\(670\) | −27.1109 | + | 15.6525i | −0.0404640 | + | 0.0233619i | ||||
\(671\) | 187.830i | 0.279925i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −814.000 | −1.20951 | −0.604755 | − | 0.796412i | \(-0.706729\pi\) | ||||
−0.604755 | + | 0.796412i | \(0.706729\pi\) | |||||||
\(674\) | 247.000 | + | 427.817i | 0.366469 | + | 0.634743i | ||||
\(675\) | −38.7298 | − | 22.3607i | −0.0573775 | − | 0.0331269i | ||||
\(676\) | −16.5000 | + | 28.5788i | −0.0244083 | + | 0.0422764i | ||||
\(677\) | −592.566 | + | 342.118i | −0.875283 | + | 0.505345i | −0.869100 | − | 0.494636i | \(-0.835301\pi\) |
−0.00618263 | + | 0.999981i | \(0.501968\pi\) | |||||||
\(678\) | 152.053i | 0.224266i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −420.000 | −0.617647 | ||||||||
\(681\) | 570.000 | + | 987.269i | 0.837004 | + | 1.44973i | ||||
\(682\) | −92.9516 | − | 53.6656i | −0.136293 | − | 0.0786886i | ||||
\(683\) | −463.000 | + | 801.940i | −0.677892 | + | 1.17414i | 0.297723 | + | 0.954652i | \(0.403773\pi\) |
−0.975615 | + | 0.219490i | \(0.929561\pi\) | |||||||
\(684\) | −383.425 | + | 221.371i | −0.560563 | + | 0.323641i | ||||
\(685\) | − | 371.187i | − | 0.541879i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −60.0000 | −0.0873362 | ||||||||
\(688\) | 85.0000 | + | 147.224i | 0.123547 | + | 0.213989i | ||||
\(689\) | −395.044 | − | 228.079i | −0.573359 | − | 0.331029i | ||||
\(690\) | −130.000 | + | 225.167i | −0.188406 | + | 0.326328i | ||||
\(691\) | 499.615 | − | 288.453i | 0.723032 | − | 0.417443i | −0.0928359 | − | 0.995681i | \(-0.529593\pi\) |
0.815867 | + | 0.578239i | \(0.196260\pi\) | |||||||
\(692\) | − | 442.741i | − | 0.639800i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 346.000 | 0.498559 | ||||||||
\(695\) | −105.000 | − | 181.865i | −0.151079 | − | 0.261677i | ||||
\(696\) | 596.439 | + | 344.354i | 0.856953 | + | 0.494762i | ||||
\(697\) | −360.000 | + | 623.538i | −0.516499 | + | 0.894603i | ||||
\(698\) | 290.474 | − | 167.705i | 0.416152 | − | 0.240265i | ||||
\(699\) | − | 957.037i | − | 1.36915i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 362.000 | 0.516405 | 0.258203 | − | 0.966091i | \(-0.416870\pi\) | ||||
0.258203 | + | 0.966091i | \(0.416870\pi\) | |||||||
\(702\) | −60.0000 | − | 103.923i | −0.0854701 | − | 0.148039i | ||||
\(703\) | 162.665 | + | 93.9149i | 0.231387 | + | 0.133592i | ||||
\(704\) | −13.0000 | + | 22.5167i | −0.0184659 | + | 0.0319839i | ||||
\(705\) | 232.379 | − | 134.164i | 0.329616 | − | 0.190304i | ||||
\(706\) | − | 26.8328i | − | 0.0380068i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −540.000 | −0.762712 | ||||||||
\(709\) | −529.000 | − | 916.255i | −0.746121 | − | 1.29232i | −0.949669 | − | 0.313255i | \(-0.898581\pi\) |
0.203548 | − | 0.979065i | \(-0.434753\pi\) | |||||||
\(710\) | 120.062 | + | 69.3181i | 0.169102 | + | 0.0976311i | ||||
\(711\) | 209.000 | − | 361.999i | 0.293952 | − | 0.509140i | ||||
\(712\) | −162.665 | + | 93.9149i | −0.228463 | + | 0.131903i | ||||
\(713\) | − | 1395.31i | − | 1.95695i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 60.0000 | 0.0839161 | ||||||||
\(716\) | 327.000 | + | 566.381i | 0.456704 | + | 0.791034i | ||||
\(717\) | −379.552 | − | 219.135i | −0.529362 | − | 0.305627i | ||||
\(718\) | 169.000 | − | 292.717i | 0.235376 | − | 0.407683i | ||||
\(719\) | −418.282 | + | 241.495i | −0.581755 | + | 0.335877i | −0.761831 | − | 0.647776i | \(-0.775699\pi\) |
0.180075 | + | 0.983653i | \(0.442366\pi\) | |||||||
\(720\) | − | 122.984i | − | 0.170811i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −181.000 | −0.250693 | ||||||||
\(723\) | −360.000 | − | 623.538i | −0.497925 | − | 0.862432i | ||||
\(724\) | −662.280 | − | 382.368i | −0.914752 | − | 0.528132i | ||||
\(725\) | −55.0000 | + | 95.2628i | −0.0758621 | + | 0.131397i | ||||
\(726\) | 453.139 | − | 261.620i | 0.624158 | − | 0.360358i | ||||
\(727\) | 1126.98i | 1.55018i | 0.631853 | + | 0.775088i | \(0.282295\pi\) | ||||
−0.631853 | + | 0.775088i | \(0.717705\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1009.00 | 1.38409 | ||||||||
\(730\) | 60.0000 | + | 103.923i | 0.0821918 | + | 0.142360i | ||||
\(731\) | 790.089 | + | 456.158i | 1.08083 | + | 0.624019i | ||||
\(732\) | −630.000 | + | 1091.19i | −0.860656 | + | 1.49070i | ||||
\(733\) | −1127.04 | + | 650.696i | −1.53757 | + | 0.887716i | −0.538589 | + | 0.842569i | \(0.681042\pi\) |
−0.998980 | + | 0.0451472i | \(0.985624\pi\) | |||||||
\(734\) | − | 295.161i | − | 0.402127i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −858.000 | −1.16576 | ||||||||
\(737\) | −14.0000 | − | 24.2487i | −0.0189959 | − | 0.0329019i | ||||
\(738\) | 255.617 | + | 147.580i | 0.346364 | + | 0.199974i | ||||
\(739\) | 491.000 | − | 850.437i | 0.664411 | − | 1.15079i | −0.315033 | − | 0.949081i | \(-0.602016\pi\) |
0.979445 | − | 0.201714i | \(-0.0646510\pi\) | |||||||
\(740\) | −81.3327 | + | 46.9574i | −0.109909 | + | 0.0634560i | ||||
\(741\) | − | 804.984i | − | 1.08635i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −694.000 | −0.934051 | −0.467026 | − | 0.884244i | \(-0.654674\pi\) | ||||
−0.467026 | + | 0.884244i | \(0.654674\pi\) | |||||||
\(744\) | −840.000 | − | 1454.92i | −1.12903 | − | 1.95554i | ||||
\(745\) | 274.982 | + | 158.761i | 0.369103 | + | 0.213102i | ||||
\(746\) | 43.0000 | − | 74.4782i | 0.0576408 | − | 0.0998367i | ||||
\(747\) | −383.425 | + | 221.371i | −0.513287 | + | 0.296346i | ||||
\(748\) | − | 160.997i | − | 0.215236i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −50.0000 | −0.0666667 | ||||||||
\(751\) | −121.000 | − | 209.578i | −0.161119 | − | 0.279065i | 0.774152 | − | 0.633000i | \(-0.218177\pi\) |
−0.935270 | + | 0.353935i | \(0.884843\pi\) | |||||||
\(752\) | 116.190 | + | 67.0820i | 0.154507 | + | 0.0892048i | ||||
\(753\) | 750.000 | − | 1299.04i | 0.996016 | − | 1.72515i | ||||
\(754\) | −255.617 | + | 147.580i | −0.339014 | + | 0.195730i | ||||
\(755\) | 4.47214i | 0.00592336i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −106.000 | −0.140026 | −0.0700132 | − | 0.997546i | \(-0.522304\pi\) | ||||
−0.0700132 | + | 0.997546i | \(0.522304\pi\) | |||||||
\(758\) | −131.000 | − | 226.899i | −0.172823 | − | 0.299339i | ||||
\(759\) | −201.395 | − | 116.276i | −0.265343 | − | 0.153196i | ||||
\(760\) | −105.000 | + | 181.865i | −0.138158 | + | 0.239296i | ||||
\(761\) | 952.754 | − | 550.073i | 1.25198 | − | 0.722829i | 0.280475 | − | 0.959861i | \(-0.409508\pi\) |
0.971502 | + | 0.237033i | \(0.0761748\pi\) | |||||||
\(762\) | − | 867.594i | − | 1.13858i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 174.000 | 0.227749 | ||||||||
\(765\) | −330.000 | − | 571.577i | −0.431373 | − | 0.747159i | ||||
\(766\) | −487.996 | − | 281.745i | −0.637070 | − | 0.367813i | ||||
\(767\) | 270.000 | − | 467.654i | 0.352021 | − | 0.609718i | ||||
\(768\) | −662.280 | + | 382.368i | −0.862344 | + | 0.497875i | ||||
\(769\) | 1126.98i | 1.46551i | 0.680492 | + | 0.732756i | \(0.261766\pi\) | ||||
−0.680492 | + | 0.732756i | \(0.738234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 600.000 | 0.778210 | ||||||||
\(772\) | 309.000 | + | 535.204i | 0.400259 | + | 0.693269i | ||||
\(773\) | −708.756 | − | 409.200i | −0.916890 | − | 0.529367i | −0.0342484 | − | 0.999413i | \(-0.510904\pi\) |
−0.882642 | + | 0.470047i | \(0.844237\pi\) | |||||||
\(774\) | 187.000 | − | 323.894i | 0.241602 | − | 0.418467i | ||||
\(775\) | 232.379 | − | 134.164i | 0.299844 | − | 0.173115i | ||||
\(776\) | − | 187.830i | − | 0.242049i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −698.000 | −0.897172 | ||||||||
\(779\) | 180.000 | + | 311.769i | 0.231065 | + | 0.400217i | ||||
\(780\) | 348.569 | + | 201.246i | 0.446883 | + | 0.258008i | ||||
\(781\) | −62.0000 | + | 107.387i | −0.0793854 | + | 0.137500i | ||||
\(782\) | −604.185 | + | 348.827i | −0.772616 | + | 0.446070i | ||||
\(783\) | 196.774i | 0.251308i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 150.000 | 0.191083 | ||||||||
\(786\) | 270.000 | + | 467.654i | 0.343511 | + | 0.594979i | ||||
\(787\) | −592.566 | − | 342.118i | −0.752943 | − | 0.434712i | 0.0738130 | − | 0.997272i | \(-0.476483\pi\) |
−0.826756 | + | 0.562560i | \(0.809817\pi\) | |||||||
\(788\) | −339.000 | + | 587.165i | −0.430203 | + | 0.745134i | ||||
\(789\) | −131.681 | + | 76.0263i | −0.166897 | + | 0.0963578i | ||||
\(790\) | − | 84.9706i | − | 0.107558i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −154.000 | −0.194444 | ||||||||
\(793\) | −630.000 | − | 1091.19i | −0.794451 | − | 1.37603i | ||||
\(794\) | 267.236 | + | 154.289i | 0.336569 | + | 0.194318i | ||||
\(795\) | −170.000 | + | 294.449i | −0.213836 | + | 0.370376i | ||||
\(796\) | −348.569 | + | 201.246i | −0.437900 | + | 0.252822i | ||||
\(797\) | 308.577i | 0.387174i | 0.981083 | + | 0.193587i | \(0.0620121\pi\) | ||||
−0.981083 | + | 0.193587i | \(0.937988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 720.000 | 0.901126 | ||||||||
\(800\) | −82.5000 | − | 142.894i | −0.103125 | − | 0.178618i | ||||
\(801\) | −255.617 | − | 147.580i | −0.319122 | − | 0.184245i | ||||
\(802\) | −269.000 | + | 465.922i | −0.335411 | + | 0.580950i | ||||
\(803\) | −92.9516 | + | 53.6656i | −0.115755 | + | 0.0668314i | ||||
\(804\) | − | 187.830i | − | 0.233619i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 720.000 | 0.893300 | ||||||||
\(807\) | 570.000 | + | 987.269i | 0.706320 | + | 1.22338i | ||||
\(808\) | −406.663 | − | 234.787i | −0.503296 | − | 0.290578i | ||||
\(809\) | −679.000 | + | 1176.06i | −0.839308 | + | 1.45372i | 0.0511665 | + | 0.998690i | \(0.483706\pi\) |
−0.890474 | + | 0.455034i | \(0.849627\pi\) | |||||||
\(810\) | 114.253 | − | 65.9640i | 0.141053 | − | 0.0814370i | ||||
\(811\) | − | 308.577i | − | 0.380490i | −0.981737 | − | 0.190245i | \(-0.939072\pi\) | ||
0.981737 | − | 0.190245i | \(-0.0609282\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1440.00 | −1.77122 | ||||||||
\(814\) | 14.0000 | + | 24.2487i | 0.0171990 | + | 0.0297896i | ||||
\(815\) | 65.8407 | + | 38.0132i | 0.0807862 | + | 0.0466419i | ||||
\(816\) | 300.000 | − | 519.615i | 0.367647 | − | 0.636783i | ||||
\(817\) | 395.044 | − | 228.079i | 0.483530 | − | 0.279166i | ||||
\(818\) | − | 295.161i | − | 0.360832i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −180.000 | −0.219512 | ||||||||
\(821\) | −241.000 | − | 417.424i | −0.293544 | − | 0.508434i | 0.681101 | − | 0.732190i | \(-0.261502\pi\) |
−0.974645 | + | 0.223756i | \(0.928168\pi\) | |||||||
\(822\) | −642.915 | − | 371.187i | −0.782135 | − | 0.451566i | ||||
\(823\) | −463.000 | + | 801.940i | −0.562576 | + | 0.974410i | 0.434695 | + | 0.900578i | \(0.356856\pi\) |
−0.997271 | + | 0.0738323i | \(0.976477\pi\) | |||||||
\(824\) | 975.992 | − | 563.489i | 1.18446 | − | 0.683846i | ||||
\(825\) | − | 44.7214i | − | 0.0542077i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −226.000 | −0.273277 | −0.136638 | − | 0.990621i | \(-0.543630\pi\) | ||||
−0.136638 | + | 0.990621i | \(0.543630\pi\) | |||||||
\(828\) | −429.000 | − | 743.050i | −0.518116 | − | 0.897403i | ||||
\(829\) | 1266.47 | + | 731.194i | 1.52770 | + | 0.882020i | 0.999458 | + | 0.0329276i | \(0.0104831\pi\) |
0.528245 | + | 0.849092i | \(0.322850\pi\) | |||||||
\(830\) | −45.0000 | + | 77.9423i | −0.0542169 | + | 0.0939064i | ||||
\(831\) | 54.2218 | − | 31.3050i | 0.0652488 | − | 0.0376714i | ||||
\(832\) | − | 174.413i | − | 0.209631i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −420.000 | −0.503597 | ||||||||
\(835\) | −120.000 | − | 207.846i | −0.143713 | − | 0.248917i | ||||
\(836\) | −69.7137 | − | 40.2492i | −0.0833896 | − | 0.0481450i | ||||
\(837\) | 240.000 | − | 415.692i | 0.286738 | − | 0.496645i | ||||
\(838\) | 708.756 | − | 409.200i | 0.845771 | − | 0.488306i | ||||
\(839\) | − | 831.817i | − | 0.991439i | −0.868483 | − | 0.495719i | \(-0.834904\pi\) | ||
0.868483 | − | 0.495719i | \(-0.165096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −357.000 | −0.424495 | ||||||||
\(842\) | −59.0000 | − | 102.191i | −0.0700713 | − | 0.121367i | ||||
\(843\) | −7.74597 | − | 4.47214i | −0.00918857 | − | 0.00530502i | ||||
\(844\) | −177.000 | + | 306.573i | −0.209716 | + | 0.363238i | ||||
\(845\) | −21.3014 | + | 12.2984i | −0.0252088 | + | 0.0145543i | ||||
\(846\) | − | 295.161i | − | 0.348890i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −170.000 | −0.200472 | ||||||||
\(849\) | −210.000 | − | 363.731i | −0.247350 | − | 0.428422i | ||||
\(850\) | −116.190 | − | 67.0820i | −0.136694 | − | 0.0789200i | ||||
\(851\) | −182.000 | + | 315.233i | −0.213866 | + | 0.370427i | ||||
\(852\) | −720.375 | + | 415.909i | −0.845510 | + | 0.488156i | ||||
\(853\) | − | 40.2492i | − | 0.0471855i | −0.999722 | − | 0.0235927i | \(-0.992489\pi\) | ||
0.999722 | − | 0.0235927i | \(-0.00751050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −330.000 | −0.385965 | ||||||||
\(856\) | 371.000 | + | 642.591i | 0.433411 | + | 0.750690i | ||||
\(857\) | −232.379 | − | 134.164i | −0.271154 | − | 0.156551i | 0.358258 | − | 0.933623i | \(-0.383371\pi\) |
−0.629412 | + | 0.777072i | \(0.716704\pi\) | |||||||
\(858\) | 60.0000 | − | 103.923i | 0.0699301 | − | 0.121122i | ||||
\(859\) | −267.236 | + | 154.289i | −0.311101 | + | 0.179614i | −0.647419 | − | 0.762134i | \(-0.724152\pi\) |
0.336318 | + | 0.941748i | \(0.390818\pi\) | |||||||
\(860\) | 228.079i | 0.265208i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 718.000 | 0.832947 | ||||||||
\(863\) | 257.000 | + | 445.137i | 0.297798 | + | 0.515802i | 0.975632 | − | 0.219413i | \(-0.0704144\pi\) |
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(864\) | −255.617 | − | 147.580i | −0.295853 | − | 0.170811i | ||||
\(865\) | 165.000 | − | 285.788i | 0.190751 | − | 0.330391i | ||||
\(866\) | −441.520 | + | 254.912i | −0.509838 | + | 0.294355i | ||||
\(867\) | − | 1927.49i | − | 2.22317i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 76.0000 | 0.0874568 | ||||||||
\(870\) | 110.000 | + | 190.526i | 0.126437 | + | 0.218995i | ||||
\(871\) | 162.665 | + | 93.9149i | 0.186757 | + | 0.107824i | ||||
\(872\) | 497.000 | − | 860.829i | 0.569954 | − | 0.987190i | ||||
\(873\) | 255.617 | − | 147.580i | 0.292803 | − | 0.169050i | ||||
\(874\) | 348.827i | 0.399115i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −720.000 | −0.821918 | ||||||||
\(877\) | 653.000 | + | 1131.03i | 0.744584 | + | 1.28966i | 0.950389 | + | 0.311064i | \(0.100685\pi\) |
−0.205805 | + | 0.978593i | \(0.565981\pi\) | |||||||
\(878\) | −23.2379 | − | 13.4164i | −0.0264669 | − | 0.0152806i | ||||
\(879\) | 750.000 | − | 1299.04i | 0.853242 | − | 1.47786i | ||||
\(880\) | 19.3649 | − | 11.1803i | 0.0220056 | − | 0.0127049i | ||||
\(881\) | − | 1126.98i | − | 1.27920i | −0.768706 | − | 0.639602i | \(-0.779099\pi\) | ||
0.768706 | − | 0.639602i | \(-0.220901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1526.00 | 1.72820 | 0.864100 | − | 0.503321i | \(-0.167889\pi\) | ||||
0.864100 | + | 0.503321i | \(0.167889\pi\) | |||||||
\(884\) | 540.000 | + | 935.307i | 0.610860 | + | 1.05804i | ||||
\(885\) | −348.569 | − | 201.246i | −0.393863 | − | 0.227397i | ||||
\(886\) | −317.000 | + | 549.060i | −0.357788 | + | 0.619707i | ||||
\(887\) | 1347.80 | − | 778.152i | 1.51950 | − | 0.877285i | 0.519766 | − | 0.854309i | \(-0.326019\pi\) |
0.999736 | − | 0.0229761i | \(-0.00731417\pi\) | |||||||
\(888\) | 438.269i | 0.493547i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −60.0000 | −0.0674157 | ||||||||
\(891\) | 59.0000 | + | 102.191i | 0.0662177 | + | 0.114692i | ||||
\(892\) | 209.141 | + | 120.748i | 0.234463 | + | 0.135367i | ||||
\(893\) | 180.000 | − | 311.769i | 0.201568 | − | 0.349126i | ||||
\(894\) | 549.964 | − | 317.522i | 0.615172 | − | 0.355170i | ||||
\(895\) | 487.463i | 0.544651i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1560.00 | 1.73913 | ||||||||
\(898\) | 169.000 | + | 292.717i | 0.188196 | + | 0.325965i | ||||
\(899\) | −1022.47 | − | 590.322i | −1.13734 | − | 0.656643i | ||||
\(900\) | 82.5000 | − | 142.894i | 0.0916667 | − | 0.158771i | ||||
\(901\) | −790.089 | + | 456.158i | −0.876902 | + | 0.506280i | ||||
\(902\) | 53.6656i | 0.0594963i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −238.000 | −0.263274 | ||||||||
\(905\) | −285.000 | − | 493.634i | −0.314917 | − | 0.545452i | ||||
\(906\) | 7.74597 | + | 4.47214i | 0.00854963 | + | 0.00493613i | ||||
\(907\) | −367.000 | + | 635.663i | −0.404631 | + | 0.700841i | −0.994278 | − | 0.106820i | \(-0.965933\pi\) |
0.589648 | + | 0.807661i | \(0.299267\pi\) | |||||||
\(908\) | −662.280 | + | 382.368i | −0.729383 | + | 0.421110i | ||||
\(909\) | − | 737.902i | − | 0.811774i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1202.00 | 1.31943 | 0.659715 | − | 0.751516i | \(-0.270677\pi\) | ||||
0.659715 | + | 0.751516i | \(0.270677\pi\) | |||||||
\(912\) | −150.000 | − | 259.808i | −0.164474 | − | 0.284877i | ||||
\(913\) | −69.7137 | − | 40.2492i | −0.0763567 | − | 0.0440846i | ||||
\(914\) | −233.000 | + | 403.568i | −0.254923 | + | 0.441540i | ||||
\(915\) | −813.327 | + | 469.574i | −0.888881 | + | 0.513196i | ||||
\(916\) | − | 40.2492i | − | 0.0439402i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −240.000 | −0.261438 | ||||||||
\(919\) | 641.000 | + | 1110.24i | 0.697497 | + | 1.20810i | 0.969332 | + | 0.245757i | \(0.0790364\pi\) |
−0.271834 | + | 0.962344i | \(0.587630\pi\) | |||||||
\(920\) | −352.441 | − | 203.482i | −0.383089 | − | 0.221176i | ||||
\(921\) | 450.000 | − | 779.423i | 0.488599 | − | 0.846279i | ||||
\(922\) | 383.425 | − | 221.371i | 0.415863 | − | 0.240098i | ||||
\(923\) | − | 831.817i | − | 0.901210i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −70.0000 | −0.0756757 | ||||||||
\(926\) | 103.000 | + | 178.401i | 0.111231 | + | 0.192658i | ||||
\(927\) | 1533.70 | + | 885.483i | 1.65448 | + | 0.955214i | ||||
\(928\) | −363.000 | + | 628.734i | −0.391164 | + | 0.677516i | ||||
\(929\) | −975.992 | + | 563.489i | −1.05058 | + | 0.606554i | −0.922813 | − | 0.385249i | \(-0.874115\pi\) |
−0.127771 | + | 0.991804i | \(0.540782\pi\) | |||||||
\(930\) | − | 536.656i | − | 0.577050i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 642.000 | 0.688841 | ||||||||
\(933\) | −1140.00 | − | 1974.54i | −1.22186 | − | 2.11633i | ||||
\(934\) | 313.712 | + | 181.122i | 0.335880 | + | 0.193920i | ||||
\(935\) | 60.0000 | − | 103.923i | 0.0641711 | − | 0.111148i | ||||
\(936\) | 894.659 | − | 516.532i | 0.955832 | − | 0.551850i | ||||
\(937\) | 214.663i | 0.229096i | 0.993418 | + | 0.114548i | \(0.0365419\pi\) | ||||
−0.993418 | + | 0.114548i | \(0.963458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1440.00 | −1.53355 | ||||||||
\(940\) | 90.0000 | + | 155.885i | 0.0957447 | + | 0.165835i | ||||
\(941\) | −731.994 | − | 422.617i | −0.777889 | − | 0.449115i | 0.0577924 | − | 0.998329i | \(-0.481594\pi\) |
−0.835682 | + | 0.549214i | \(0.814927\pi\) | |||||||
\(942\) | 150.000 | − | 259.808i | 0.159236 | − | 0.275804i | ||||
\(943\) | −604.185 | + | 348.827i | −0.640706 | + | 0.369912i | ||||
\(944\) | − | 201.246i | − | 0.213184i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 68.0000 | 0.0718816 | ||||||||
\(947\) | −367.000 | − | 635.663i | −0.387540 | − | 0.671238i | 0.604578 | − | 0.796546i | \(-0.293342\pi\) |
−0.992118 | + | 0.125307i | \(0.960008\pi\) | |||||||
\(948\) | 441.520 | + | 254.912i | 0.465739 | + | 0.268894i | ||||
\(949\) | 360.000 | − | 623.538i | 0.379347 | − | 0.657048i | ||||
\(950\) | −58.0948 | + | 33.5410i | −0.0611524 | + | 0.0353063i | ||||
\(951\) | 1672.58i | 1.75876i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −934.000 | −0.980063 | −0.490031 | − | 0.871705i | \(-0.663015\pi\) | ||||
−0.490031 | + | 0.871705i | \(0.663015\pi\) | |||||||
\(954\) | 187.000 | + | 323.894i | 0.196017 | + | 0.339511i | ||||
\(955\) | 112.317 | + | 64.8460i | 0.117609 | + | 0.0679015i | ||||
\(956\) | 147.000 | − | 254.611i | 0.153766 | − | 0.266330i | ||||
\(957\) | −170.411 | + | 98.3870i | −0.178068 | + | 0.102808i | ||||
\(958\) | − | 214.663i | − | 0.224074i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −130.000 | −0.135417 | ||||||||
\(961\) | 959.500 | + | 1661.90i | 0.998439 | + | 1.72935i | ||||
\(962\) | −162.665 | − | 93.9149i | −0.169091 | − | 0.0976246i | ||||
\(963\) | −583.000 | + | 1009.79i | −0.605400 | + | 1.04858i | ||||
\(964\) | 418.282 | − | 241.495i | 0.433903 | − | 0.250514i | ||||
\(965\) | 460.630i | 0.477337i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 314.000 | 0.324716 | 0.162358 | − | 0.986732i | \(-0.448090\pi\) | ||||
0.162358 | + | 0.986732i | \(0.448090\pi\) | |||||||
\(968\) | 409.500 | + | 709.275i | 0.423037 | + | 0.732722i | ||||
\(969\) | −1394.27 | − | 804.984i | −1.43888 | − | 0.830737i | ||||
\(970\) | 30.0000 | − | 51.9615i | 0.0309278 | − | 0.0535686i | ||||
\(971\) | −127.808 | + | 73.7902i | −0.131626 | + | 0.0759941i | −0.564367 | − | 0.825524i | \(-0.690880\pi\) |
0.432741 | + | 0.901518i | \(0.357546\pi\) | |||||||
\(972\) | 1033.06i | 1.06282i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 166.000 | 0.170431 | ||||||||
\(975\) | 150.000 | + | 259.808i | 0.153846 | + | 0.266469i | ||||
\(976\) | −406.663 | − | 234.787i | −0.416663 | − | 0.240561i | ||||
\(977\) | 743.000 | − | 1286.91i | 0.760491 | − | 1.31721i | −0.182106 | − | 0.983279i | \(-0.558292\pi\) |
0.942598 | − | 0.333931i | \(-0.108375\pi\) | |||||||
\(978\) | 131.681 | − | 76.0263i | 0.134644 | − | 0.0777365i | ||||
\(979\) | − | 53.6656i | − | 0.0548168i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1562.00 | 1.59225 | ||||||||
\(982\) | −419.000 | − | 725.729i | −0.426680 | − | 0.739032i | ||||
\(983\) | 836.564 | + | 482.991i | 0.851032 | + | 0.491344i | 0.860999 | − | 0.508607i | \(-0.169839\pi\) |
−0.00996696 | + | 0.999950i | \(0.503173\pi\) | |||||||
\(984\) | −420.000 | + | 727.461i | −0.426829 | + | 0.739290i | ||||
\(985\) | −437.647 | + | 252.676i | −0.444312 | + | 0.256524i | ||||
\(986\) | 590.322i | 0.598704i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 540.000 | 0.546559 | ||||||||
\(989\) | 442.000 | + | 765.566i | 0.446916 | + | 0.774081i | ||||
\(990\) | −42.6028 | − | 24.5967i | −0.0430331 | − | 0.0248452i | ||||
\(991\) | 29.0000 | − | 50.2295i | 0.0292634 | − | 0.0506856i | −0.851023 | − | 0.525129i | \(-0.824017\pi\) |
0.880286 | + | 0.474443i | \(0.157351\pi\) | |||||||
\(992\) | 1533.70 | − | 885.483i | 1.54607 | − | 0.892624i | ||||
\(993\) | 2155.57i | 2.17076i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −300.000 | −0.301508 | ||||||||
\(996\) | −270.000 | − | 467.654i | −0.271084 | − | 0.469532i | ||||
\(997\) | 546.091 | + | 315.286i | 0.547734 | + | 0.316234i | 0.748207 | − | 0.663465i | \(-0.230915\pi\) |
−0.200474 | + | 0.979699i | \(0.564248\pi\) | |||||||
\(998\) | −131.000 | + | 226.899i | −0.131263 | + | 0.227353i | ||||
\(999\) | −108.444 | + | 62.6099i | −0.108552 | + | 0.0626726i |
(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 | 245.3.h.b.31.1 | 4 | ||
7.2 | even | 3 | inner | 245.3.h.b.166.2 | 4 | ||
7.3 | odd | 6 | 35.3.d.a.6.1 | ✓ | 2 | ||
7.4 | even | 3 | 35.3.d.a.6.2 | yes | 2 | ||
7.5 | odd | 6 | inner | 245.3.h.b.166.1 | 4 | ||
7.6 | odd | 2 | inner | 245.3.h.b.31.2 | 4 | ||
21.11 | odd | 6 | 315.3.h.b.181.1 | 2 | |||
21.17 | even | 6 | 315.3.h.b.181.2 | 2 | |||
28.3 | even | 6 | 560.3.f.a.321.2 | 2 | |||
28.11 | odd | 6 | 560.3.f.a.321.1 | 2 | |||
35.3 | even | 12 | 175.3.c.d.174.4 | 4 | |||
35.4 | even | 6 | 175.3.d.f.76.1 | 2 | |||
35.17 | even | 12 | 175.3.c.d.174.1 | 4 | |||
35.18 | odd | 12 | 175.3.c.d.174.3 | 4 | |||
35.24 | odd | 6 | 175.3.d.f.76.2 | 2 | |||
35.32 | odd | 12 | 175.3.c.d.174.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.3.d.a.6.1 | ✓ | 2 | 7.3 | odd | 6 | ||
35.3.d.a.6.2 | yes | 2 | 7.4 | even | 3 | ||
175.3.c.d.174.1 | 4 | 35.17 | even | 12 | |||
175.3.c.d.174.2 | 4 | 35.32 | odd | 12 | |||
175.3.c.d.174.3 | 4 | 35.18 | odd | 12 | |||
175.3.c.d.174.4 | 4 | 35.3 | even | 12 | |||
175.3.d.f.76.1 | 2 | 35.4 | even | 6 | |||
175.3.d.f.76.2 | 2 | 35.24 | odd | 6 | |||
245.3.h.b.31.1 | 4 | 1.1 | even | 1 | trivial | ||
245.3.h.b.31.2 | 4 | 7.6 | odd | 2 | inner | ||
245.3.h.b.166.1 | 4 | 7.5 | odd | 6 | inner | ||
245.3.h.b.166.2 | 4 | 7.2 | even | 3 | inner | ||
315.3.h.b.181.1 | 2 | 21.11 | odd | 6 | |||
315.3.h.b.181.2 | 2 | 21.17 | even | 6 | |||
560.3.f.a.321.1 | 2 | 28.11 | odd | 6 | |||
560.3.f.a.321.2 | 2 | 28.3 | even | 6 |