Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
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("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + \cdots + 1936 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 229.1 | ||
Root | \(-0.657798 - 2.02449i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.229 |
Dual form | 418.2.f.h.115.1 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | ||||
\(3\) | −1.72214 | + | 1.25121i | −0.994276 | + | 0.722384i | −0.960853 | − | 0.277057i | \(-0.910641\pi\) |
−0.0334229 | + | 0.999441i | \(0.510641\pi\) | |||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | −0.137434 | − | 0.422980i | −0.0614625 | − | 0.189162i | 0.915611 | − | 0.402066i | \(-0.131708\pi\) |
−0.977073 | + | 0.212904i | \(0.931708\pi\) | |||||||
\(6\) | −0.657798 | − | 2.02449i | −0.268545 | − | 0.826496i | ||||
\(7\) | −0.658492 | − | 0.478423i | −0.248887 | − | 0.180827i | 0.456347 | − | 0.889802i | \(-0.349158\pi\) |
−0.705233 | + | 0.708975i | \(0.749158\pi\) | |||||||
\(8\) | 0.809017 | − | 0.587785i | 0.286031 | − | 0.207813i | ||||
\(9\) | 0.473189 | − | 1.45633i | 0.157730 | − | 0.485442i | ||||
\(10\) | 0.444747 | 0.140641 | ||||||||
\(11\) | −2.12947 | − | 2.54271i | −0.642060 | − | 0.766654i | ||||
\(12\) | 2.12868 | 0.614497 | ||||||||
\(13\) | 0.164234 | − | 0.505460i | 0.0455503 | − | 0.140189i | −0.925695 | − | 0.378271i | \(-0.876519\pi\) |
0.971245 | + | 0.238082i | \(0.0765187\pi\) | |||||||
\(14\) | 0.658492 | − | 0.478423i | 0.175990 | − | 0.127864i | ||||
\(15\) | 0.765915 | + | 0.556470i | 0.197758 | + | 0.143680i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −1.81738 | − | 5.59332i | −0.440779 | − | 1.35658i | −0.887047 | − | 0.461679i | \(-0.847247\pi\) |
0.446268 | − | 0.894899i | \(-0.352753\pi\) | |||||||
\(18\) | 1.23883 | + | 0.900059i | 0.291994 | + | 0.212146i | ||||
\(19\) | 0.809017 | − | 0.587785i | 0.185601 | − | 0.134847i | ||||
\(20\) | −0.137434 | + | 0.422980i | −0.0307313 | + | 0.0945811i | ||||
\(21\) | 1.73262 | 0.378089 | ||||||||
\(22\) | 3.07630 | − | 1.23951i | 0.655869 | − | 0.264264i | ||||
\(23\) | 6.69536 | 1.39608 | 0.698040 | − | 0.716059i | \(-0.254056\pi\) | ||||
0.698040 | + | 0.716059i | \(0.254056\pi\) | |||||||
\(24\) | −0.657798 | + | 2.02449i | −0.134272 | + | 0.413248i | ||||
\(25\) | 3.88506 | − | 2.82266i | 0.777012 | − | 0.564532i | ||||
\(26\) | 0.429970 | + | 0.312391i | 0.0843240 | + | 0.0612650i | ||||
\(27\) | −0.966126 | − | 2.97343i | −0.185931 | − | 0.572237i | ||||
\(28\) | 0.251522 | + | 0.774104i | 0.0475331 | + | 0.146292i | ||||
\(29\) | 3.37106 | + | 2.44922i | 0.625991 | + | 0.454809i | 0.855009 | − | 0.518613i | \(-0.173552\pi\) |
−0.229018 | + | 0.973422i | \(0.573552\pi\) | |||||||
\(30\) | −0.765915 | + | 0.556470i | −0.139836 | + | 0.101597i | ||||
\(31\) | −1.79257 | + | 5.51696i | −0.321955 | + | 0.990876i | 0.650841 | + | 0.759214i | \(0.274416\pi\) |
−0.972796 | + | 0.231662i | \(0.925584\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.84869 | + | 1.71448i | 1.19220 | + | 0.298453i | ||||
\(34\) | 5.88116 | 1.00861 | ||||||||
\(35\) | −0.111864 | + | 0.344281i | −0.0189084 | + | 0.0581940i | ||||
\(36\) | −1.23883 | + | 0.900059i | −0.206471 | + | 0.150010i | ||||
\(37\) | −1.92167 | − | 1.39618i | −0.315921 | − | 0.229530i | 0.418512 | − | 0.908211i | \(-0.362552\pi\) |
−0.734433 | + | 0.678681i | \(0.762552\pi\) | |||||||
\(38\) | 0.309017 | + | 0.951057i | 0.0501292 | + | 0.154282i | ||||
\(39\) | 0.349601 | + | 1.07596i | 0.0559809 | + | 0.172292i | ||||
\(40\) | −0.359808 | − | 0.261416i | −0.0568906 | − | 0.0413335i | ||||
\(41\) | 8.29803 | − | 6.02887i | 1.29594 | − | 0.941552i | 0.296028 | − | 0.955179i | \(-0.404338\pi\) |
0.999907 | + | 0.0136272i | \(0.00433781\pi\) | |||||||
\(42\) | −0.535409 | + | 1.64782i | −0.0826154 | + | 0.254264i | ||||
\(43\) | −10.2461 | −1.56252 | −0.781258 | − | 0.624208i | \(-0.785422\pi\) | ||||
−0.781258 | + | 0.624208i | \(0.785422\pi\) | |||||||
\(44\) | 0.228214 | + | 3.30876i | 0.0344046 | + | 0.498815i | ||||
\(45\) | −0.681029 | −0.101522 | ||||||||
\(46\) | −2.06898 | + | 6.36767i | −0.305055 | + | 0.938861i | ||||
\(47\) | −5.12692 | + | 3.72493i | −0.747838 | + | 0.543336i | −0.895156 | − | 0.445753i | \(-0.852936\pi\) |
0.147318 | + | 0.989089i | \(0.452936\pi\) | |||||||
\(48\) | −1.72214 | − | 1.25121i | −0.248569 | − | 0.180596i | ||||
\(49\) | −1.95839 | − | 6.02732i | −0.279771 | − | 0.861046i | ||||
\(50\) | 1.48396 | + | 4.56716i | 0.209864 | + | 0.645894i | ||||
\(51\) | 10.1282 | + | 7.35854i | 1.41823 | + | 1.03040i | ||||
\(52\) | −0.429970 | + | 0.312391i | −0.0596261 | + | 0.0433209i | ||||
\(53\) | 2.87949 | − | 8.86217i | 0.395529 | − | 1.21731i | −0.533020 | − | 0.846102i | \(-0.678943\pi\) |
0.928549 | − | 0.371210i | \(-0.121057\pi\) | |||||||
\(54\) | 3.12645 | 0.425456 | ||||||||
\(55\) | −0.782850 | + | 1.25018i | −0.105559 | + | 0.168574i | ||||
\(56\) | −0.813941 | −0.108768 | ||||||||
\(57\) | −0.657798 | + | 2.02449i | −0.0871275 | + | 0.268151i | ||||
\(58\) | −3.37106 | + | 2.44922i | −0.442642 | + | 0.321598i | ||||
\(59\) | −2.73342 | − | 1.98595i | −0.355862 | − | 0.258549i | 0.395462 | − | 0.918482i | \(-0.370584\pi\) |
−0.751324 | + | 0.659934i | \(0.770584\pi\) | |||||||
\(60\) | −0.292554 | − | 0.900388i | −0.0377685 | − | 0.116240i | ||||
\(61\) | −1.47351 | − | 4.53500i | −0.188664 | − | 0.580647i | 0.811329 | − | 0.584590i | \(-0.198745\pi\) |
−0.999992 | + | 0.00394334i | \(0.998745\pi\) | |||||||
\(62\) | −4.69301 | − | 3.40967i | −0.596013 | − | 0.433029i | ||||
\(63\) | −1.00833 | + | 0.732596i | −0.127038 | + | 0.0922984i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −0.236370 | −0.0293181 | ||||||||
\(66\) | −3.74693 | + | 5.98369i | −0.461215 | + | 0.736541i | ||||
\(67\) | −1.23043 | −0.150321 | −0.0751604 | − | 0.997171i | \(-0.523947\pi\) | ||||
−0.0751604 | + | 0.997171i | \(0.523947\pi\) | |||||||
\(68\) | −1.81738 | + | 5.59332i | −0.220390 | + | 0.678289i | ||||
\(69\) | −11.5303 | + | 8.37728i | −1.38809 | + | 1.00851i | ||||
\(70\) | −0.292863 | − | 0.212777i | −0.0350038 | − | 0.0254317i | ||||
\(71\) | −3.57970 | − | 11.0172i | −0.424832 | − | 1.30750i | −0.903155 | − | 0.429315i | \(-0.858755\pi\) |
0.478323 | − | 0.878184i | \(-0.341245\pi\) | |||||||
\(72\) | −0.473189 | − | 1.45633i | −0.0557659 | − | 0.171630i | ||||
\(73\) | −9.98343 | − | 7.25339i | −1.16847 | − | 0.848945i | −0.177647 | − | 0.984094i | \(-0.556848\pi\) |
−0.990825 | + | 0.135150i | \(0.956848\pi\) | |||||||
\(74\) | 1.92167 | − | 1.39618i | 0.223390 | − | 0.162302i | ||||
\(75\) | −3.15888 | + | 9.72202i | −0.364756 | + | 1.12260i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0.185753 | + | 2.69314i | 0.0211685 | + | 0.306912i | ||||
\(78\) | −1.13133 | −0.128098 | ||||||||
\(79\) | −1.07228 | + | 3.30013i | −0.120640 | + | 0.371293i | −0.993082 | − | 0.117426i | \(-0.962536\pi\) |
0.872441 | + | 0.488719i | \(0.162536\pi\) | |||||||
\(80\) | 0.359808 | − | 0.261416i | 0.0402277 | − | 0.0292272i | ||||
\(81\) | 9.10065 | + | 6.61201i | 1.01118 | + | 0.734668i | ||||
\(82\) | 3.16957 | + | 9.75492i | 0.350020 | + | 1.07725i | ||||
\(83\) | −3.97579 | − | 12.2362i | −0.436400 | − | 1.34310i | −0.891645 | − | 0.452735i | \(-0.850449\pi\) |
0.455246 | − | 0.890366i | \(-0.349551\pi\) | |||||||
\(84\) | −1.40172 | − | 1.01841i | −0.152940 | − | 0.111117i | ||||
\(85\) | −2.11609 | + | 1.53743i | −0.229522 | + | 0.166757i | ||||
\(86\) | 3.16622 | − | 9.74463i | 0.341422 | − | 1.05079i | ||||
\(87\) | −8.86991 | −0.950954 | ||||||||
\(88\) | −3.21734 | − | 0.805420i | −0.342970 | − | 0.0858580i | ||||
\(89\) | 7.40160 | 0.784568 | 0.392284 | − | 0.919844i | \(-0.371685\pi\) | ||||
0.392284 | + | 0.919844i | \(0.371685\pi\) | |||||||
\(90\) | 0.210449 | − | 0.647697i | 0.0221833 | − | 0.0682733i | ||||
\(91\) | −0.349970 | + | 0.254268i | −0.0366868 | + | 0.0266545i | ||||
\(92\) | −5.41666 | − | 3.93543i | −0.564726 | − | 0.410297i | ||||
\(93\) | −3.81580 | − | 11.7438i | −0.395681 | − | 1.21778i | ||||
\(94\) | −1.95831 | − | 6.02706i | −0.201984 | − | 0.621643i | ||||
\(95\) | −0.359808 | − | 0.261416i | −0.0369155 | − | 0.0268207i | ||||
\(96\) | 1.72214 | − | 1.25121i | 0.175765 | − | 0.127701i | ||||
\(97\) | −4.39716 | + | 13.5331i | −0.446464 | + | 1.37408i | 0.434405 | + | 0.900718i | \(0.356959\pi\) |
−0.880870 | + | 0.473359i | \(0.843041\pi\) | |||||||
\(98\) | 6.33750 | 0.640184 | ||||||||
\(99\) | −4.71065 | + | 1.89803i | −0.473438 | + | 0.190759i | ||||
\(100\) | −4.80220 | −0.480220 | ||||||||
\(101\) | 1.08313 | − | 3.33352i | 0.107775 | − | 0.331698i | −0.882597 | − | 0.470131i | \(-0.844207\pi\) |
0.990372 | + | 0.138433i | \(0.0442067\pi\) | |||||||
\(102\) | −10.1282 | + | 7.35854i | −1.00284 | + | 0.728604i | ||||
\(103\) | −0.561557 | − | 0.407995i | −0.0553319 | − | 0.0402009i | 0.559776 | − | 0.828644i | \(-0.310887\pi\) |
−0.615107 | + | 0.788443i | \(0.710887\pi\) | |||||||
\(104\) | −0.164234 | − | 0.505460i | −0.0161044 | − | 0.0495644i | ||||
\(105\) | −0.238122 | − | 0.732863i | −0.0232383 | − | 0.0715201i | ||||
\(106\) | 7.53861 | + | 5.47712i | 0.732214 | + | 0.531985i | ||||
\(107\) | −6.98246 | + | 5.07306i | −0.675020 | + | 0.490431i | −0.871702 | − | 0.490037i | \(-0.836983\pi\) |
0.196682 | + | 0.980467i | \(0.436983\pi\) | |||||||
\(108\) | −0.966126 | + | 2.97343i | −0.0929655 | + | 0.286118i | ||||
\(109\) | 8.10360 | 0.776184 | 0.388092 | − | 0.921621i | \(-0.373134\pi\) | ||||
0.388092 | + | 0.921621i | \(0.373134\pi\) | |||||||
\(110\) | −0.947076 | − | 1.13086i | −0.0903002 | − | 0.107823i | ||||
\(111\) | 5.05629 | 0.479922 | ||||||||
\(112\) | 0.251522 | − | 0.774104i | 0.0237666 | − | 0.0731460i | ||||
\(113\) | −3.77212 | + | 2.74061i | −0.354851 | + | 0.257814i | −0.750901 | − | 0.660414i | \(-0.770381\pi\) |
0.396050 | + | 0.918229i | \(0.370381\pi\) | |||||||
\(114\) | −1.72214 | − | 1.25121i | −0.161293 | − | 0.117186i | ||||
\(115\) | −0.920173 | − | 2.83200i | −0.0858066 | − | 0.264085i | ||||
\(116\) | −1.28763 | − | 3.96292i | −0.119554 | − | 0.367948i | ||||
\(117\) | −0.658401 | − | 0.478356i | −0.0608692 | − | 0.0442240i | ||||
\(118\) | 2.73342 | − | 1.98595i | 0.251632 | − | 0.182821i | ||||
\(119\) | −1.47924 | + | 4.55263i | −0.135602 | + | 0.417339i | ||||
\(120\) | 0.946723 | 0.0864236 | ||||||||
\(121\) | −1.93070 | + | 10.8292i | −0.175518 | + | 0.984476i | ||||
\(122\) | 4.76838 | 0.431709 | ||||||||
\(123\) | −6.74699 | + | 20.7651i | −0.608356 | + | 1.87233i | ||||
\(124\) | 4.69301 | − | 3.40967i | 0.421445 | − | 0.306197i | ||||
\(125\) | −3.52691 | − | 2.56245i | −0.315456 | − | 0.229192i | ||||
\(126\) | −0.385148 | − | 1.18536i | −0.0343117 | − | 0.105601i | ||||
\(127\) | 1.77843 | + | 5.47344i | 0.157810 | + | 0.485689i | 0.998435 | − | 0.0559287i | \(-0.0178119\pi\) |
−0.840625 | + | 0.541618i | \(0.817812\pi\) | |||||||
\(128\) | 0.809017 | + | 0.587785i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | 17.6452 | − | 12.8200i | 1.55357 | − | 1.12874i | ||||
\(130\) | 0.0730425 | − | 0.224802i | 0.00640625 | − | 0.0197164i | ||||
\(131\) | −0.970302 | −0.0847756 | −0.0423878 | − | 0.999101i | \(-0.513497\pi\) | ||||
−0.0423878 | + | 0.999101i | \(0.513497\pi\) | |||||||
\(132\) | −4.53296 | − | 5.41260i | −0.394544 | − | 0.471107i | ||||
\(133\) | −0.813941 | −0.0705777 | ||||||||
\(134\) | 0.380224 | − | 1.17021i | 0.0328463 | − | 0.101091i | ||||
\(135\) | −1.12492 | + | 0.817303i | −0.0968178 | + | 0.0703422i | ||||
\(136\) | −4.75796 | − | 3.45686i | −0.407992 | − | 0.296423i | ||||
\(137\) | 0.663405 | + | 2.04175i | 0.0566785 | + | 0.174438i | 0.975388 | − | 0.220496i | \(-0.0707674\pi\) |
−0.918709 | + | 0.394934i | \(0.870767\pi\) | |||||||
\(138\) | −4.40419 | − | 13.5547i | −0.374910 | − | 1.15385i | ||||
\(139\) | 7.91878 | + | 5.75333i | 0.671663 | + | 0.487991i | 0.870581 | − | 0.492025i | \(-0.163743\pi\) |
−0.198919 | + | 0.980016i | \(0.563743\pi\) | |||||||
\(140\) | 0.292863 | − | 0.212777i | 0.0247514 | − | 0.0179829i | ||||
\(141\) | 4.16861 | − | 12.8297i | 0.351060 | − | 1.08045i | ||||
\(142\) | 11.5841 | 0.972120 | ||||||||
\(143\) | −1.63497 | + | 0.658764i | −0.136723 | + | 0.0550886i | ||||
\(144\) | 1.53127 | 0.127606 | ||||||||
\(145\) | 0.572670 | − | 1.76250i | 0.0475577 | − | 0.146367i | ||||
\(146\) | 9.98343 | − | 7.25339i | 0.826234 | − | 0.600294i | ||||
\(147\) | 10.9140 | + | 7.92952i | 0.900175 | + | 0.654015i | ||||
\(148\) | 0.734014 | + | 2.25906i | 0.0603356 | + | 0.185694i | ||||
\(149\) | 0.386032 | + | 1.18808i | 0.0316250 | + | 0.0973316i | 0.965623 | − | 0.259946i | \(-0.0837049\pi\) |
−0.933998 | + | 0.357278i | \(0.883705\pi\) | |||||||
\(150\) | −8.27005 | − | 6.00854i | −0.675247 | − | 0.490595i | ||||
\(151\) | 11.2071 | − | 8.14242i | 0.912020 | − | 0.662621i | −0.0295053 | − | 0.999565i | \(-0.509393\pi\) |
0.941525 | + | 0.336944i | \(0.109393\pi\) | |||||||
\(152\) | 0.309017 | − | 0.951057i | 0.0250646 | − | 0.0771409i | ||||
\(153\) | −9.00566 | −0.728065 | ||||||||
\(154\) | −2.61873 | − | 0.655564i | −0.211023 | − | 0.0528269i | ||||
\(155\) | 2.57992 | 0.207224 | ||||||||
\(156\) | 0.349601 | − | 1.07596i | 0.0279905 | − | 0.0861458i | ||||
\(157\) | −14.0038 | + | 10.1744i | −1.11763 | + | 0.812002i | −0.983847 | − | 0.179009i | \(-0.942711\pi\) |
−0.133778 | + | 0.991011i | \(0.542711\pi\) | |||||||
\(158\) | −2.80726 | − | 2.03959i | −0.223333 | − | 0.162261i | ||||
\(159\) | 6.12951 | + | 18.8647i | 0.486102 | + | 1.49607i | ||||
\(160\) | 0.137434 | + | 0.422980i | 0.0108651 | + | 0.0334395i | ||||
\(161\) | −4.40885 | − | 3.20321i | −0.347466 | − | 0.252449i | ||||
\(162\) | −9.10065 | + | 6.61201i | −0.715015 | + | 0.519489i | ||||
\(163\) | −3.08190 | + | 9.48513i | −0.241393 | + | 0.742932i | 0.754815 | + | 0.655937i | \(0.227726\pi\) |
−0.996209 | + | 0.0869951i | \(0.972274\pi\) | |||||||
\(164\) | −10.2569 | −0.800932 | ||||||||
\(165\) | −0.216056 | − | 3.13248i | −0.0168199 | − | 0.243864i | ||||
\(166\) | 12.8659 | 0.998590 | ||||||||
\(167\) | 7.07592 | − | 21.7774i | 0.547551 | − | 1.68519i | −0.167294 | − | 0.985907i | \(-0.553503\pi\) |
0.714845 | − | 0.699282i | \(-0.246497\pi\) | |||||||
\(168\) | 1.40172 | − | 1.01841i | 0.108145 | − | 0.0785719i | ||||
\(169\) | 10.2887 | + | 7.47518i | 0.791439 | + | 0.575014i | ||||
\(170\) | −0.808274 | − | 2.48761i | −0.0619918 | − | 0.190791i | ||||
\(171\) | −0.473189 | − | 1.45633i | −0.0361857 | − | 0.111368i | ||||
\(172\) | 8.28927 | + | 6.02251i | 0.632051 | + | 0.459212i | ||||
\(173\) | 6.26926 | − | 4.55488i | 0.476643 | − | 0.346301i | −0.323382 | − | 0.946269i | \(-0.604820\pi\) |
0.800024 | + | 0.599967i | \(0.204820\pi\) | |||||||
\(174\) | 2.74095 | − | 8.43579i | 0.207791 | − | 0.639515i | ||||
\(175\) | −3.90871 | −0.295471 | ||||||||
\(176\) | 1.76021 | − | 2.81099i | 0.132681 | − | 0.211886i | ||||
\(177\) | 7.19216 | 0.540596 | ||||||||
\(178\) | −2.28722 | + | 7.03934i | −0.171434 | + | 0.527621i | ||||
\(179\) | −10.6619 | + | 7.74632i | −0.796908 | + | 0.578987i | −0.910005 | − | 0.414597i | \(-0.863923\pi\) |
0.113098 | + | 0.993584i | \(0.463923\pi\) | |||||||
\(180\) | 0.550964 | + | 0.400299i | 0.0410664 | + | 0.0298365i | ||||
\(181\) | −2.83113 | − | 8.71331i | −0.210436 | − | 0.647655i | −0.999446 | − | 0.0332754i | \(-0.989406\pi\) |
0.789010 | − | 0.614380i | \(-0.210594\pi\) | |||||||
\(182\) | −0.133677 | − | 0.411414i | −0.00990877 | − | 0.0304961i | ||||
\(183\) | 8.21180 | + | 5.96623i | 0.607034 | + | 0.441036i | ||||
\(184\) | 5.41666 | − | 3.93543i | 0.399322 | − | 0.290124i | ||||
\(185\) | −0.326450 | + | 1.00471i | −0.0240011 | + | 0.0738678i | ||||
\(186\) | 12.3482 | 0.905414 | ||||||||
\(187\) | −10.3521 | + | 16.5319i | −0.757020 | + | 1.20893i | ||||
\(188\) | 6.33722 | 0.462189 | ||||||||
\(189\) | −0.786370 | + | 2.42020i | −0.0572000 | + | 0.176043i | ||||
\(190\) | 0.359808 | − | 0.261416i | 0.0261032 | − | 0.0189651i | ||||
\(191\) | 11.7816 | + | 8.55983i | 0.852486 | + | 0.619367i | 0.925830 | − | 0.377939i | \(-0.123367\pi\) |
−0.0733442 | + | 0.997307i | \(0.523367\pi\) | |||||||
\(192\) | 0.657798 | + | 2.02449i | 0.0474725 | + | 0.146105i | ||||
\(193\) | −0.751094 | − | 2.31163i | −0.0540649 | − | 0.166395i | 0.920378 | − | 0.391030i | \(-0.127881\pi\) |
−0.974443 | + | 0.224635i | \(0.927881\pi\) | |||||||
\(194\) | −11.5119 | − | 8.36390i | −0.826508 | − | 0.600493i | ||||
\(195\) | 0.407062 | − | 0.295748i | 0.0291503 | − | 0.0211790i | ||||
\(196\) | −1.95839 | + | 6.02732i | −0.139885 | + | 0.430523i | ||||
\(197\) | −10.9047 | −0.776928 | −0.388464 | − | 0.921464i | \(-0.626994\pi\) | ||||
−0.388464 | + | 0.921464i | \(0.626994\pi\) | |||||||
\(198\) | −0.349458 | − | 5.06662i | −0.0248349 | − | 0.360069i | ||||
\(199\) | −15.3004 | −1.08461 | −0.542307 | − | 0.840180i | \(-0.682449\pi\) | ||||
−0.542307 | + | 0.840180i | \(0.682449\pi\) | |||||||
\(200\) | 1.48396 | − | 4.56716i | 0.104932 | − | 0.322947i | ||||
\(201\) | 2.11897 | − | 1.53952i | 0.149460 | − | 0.108589i | ||||
\(202\) | 2.83566 | + | 2.06023i | 0.199516 | + | 0.144957i | ||||
\(203\) | −1.04806 | − | 3.22559i | −0.0735591 | − | 0.226392i | ||||
\(204\) | −3.86862 | − | 11.9064i | −0.270857 | − | 0.833613i | ||||
\(205\) | −3.69053 | − | 2.68132i | −0.257758 | − | 0.187272i | ||||
\(206\) | 0.561557 | − | 0.407995i | 0.0391255 | − | 0.0284264i | ||||
\(207\) | 3.16817 | − | 9.75063i | 0.220203 | − | 0.677716i | ||||
\(208\) | 0.531472 | 0.0368509 | ||||||||
\(209\) | −3.21734 | − | 0.805420i | −0.222548 | − | 0.0557120i | ||||
\(210\) | 0.770577 | 0.0531749 | ||||||||
\(211\) | −1.73393 | + | 5.33647i | −0.119368 | + | 0.367378i | −0.992833 | − | 0.119509i | \(-0.961868\pi\) |
0.873465 | + | 0.486887i | \(0.161868\pi\) | |||||||
\(212\) | −7.53861 | + | 5.47712i | −0.517754 | + | 0.376170i | ||||
\(213\) | 19.9495 | + | 14.4942i | 1.36692 | + | 0.993123i | ||||
\(214\) | −2.66706 | − | 8.20838i | −0.182317 | − | 0.561113i | ||||
\(215\) | 1.40817 | + | 4.33389i | 0.0960362 | + | 0.295569i | ||||
\(216\) | −2.52935 | − | 1.83768i | −0.172100 | − | 0.125038i | ||||
\(217\) | 3.81983 | − | 2.77527i | 0.259307 | − | 0.188398i | ||||
\(218\) | −2.50415 | + | 7.70698i | −0.169603 | + | 0.521983i | ||||
\(219\) | 26.2683 | 1.77505 | ||||||||
\(220\) | 1.36817 | − | 0.551268i | 0.0922423 | − | 0.0371665i | ||||
\(221\) | −3.12567 | −0.210255 | ||||||||
\(222\) | −1.56248 | + | 4.80882i | −0.104867 | + | 0.322747i | ||||
\(223\) | 19.4052 | − | 14.0987i | 1.29947 | − | 0.944121i | 0.299521 | − | 0.954090i | \(-0.403173\pi\) |
0.999950 | + | 0.00996822i | \(0.00317304\pi\) | |||||||
\(224\) | 0.658492 | + | 0.478423i | 0.0439974 | + | 0.0319660i | ||||
\(225\) | −2.27235 | − | 6.99357i | −0.151490 | − | 0.466238i | ||||
\(226\) | −1.44082 | − | 4.43439i | −0.0958420 | − | 0.294971i | ||||
\(227\) | 2.85398 | + | 2.07354i | 0.189425 | + | 0.137625i | 0.678456 | − | 0.734641i | \(-0.262649\pi\) |
−0.489031 | + | 0.872267i | \(0.662649\pi\) | |||||||
\(228\) | 1.72214 | − | 1.25121i | 0.114051 | − | 0.0828631i | ||||
\(229\) | −6.04800 | + | 18.6138i | −0.399663 | + | 1.23004i | 0.525607 | + | 0.850728i | \(0.323838\pi\) |
−0.925270 | + | 0.379309i | \(0.876162\pi\) | |||||||
\(230\) | 2.97774 | 0.196347 | ||||||||
\(231\) | −3.68957 | − | 4.40554i | −0.242756 | − | 0.289863i | ||||
\(232\) | 4.16686 | 0.273568 | ||||||||
\(233\) | 5.93372 | − | 18.2621i | 0.388731 | − | 1.19639i | −0.545007 | − | 0.838432i | \(-0.683473\pi\) |
0.933737 | − | 0.357959i | \(-0.116527\pi\) | |||||||
\(234\) | 0.658401 | − | 0.478356i | 0.0430410 | − | 0.0312711i | ||||
\(235\) | 2.28018 | + | 1.65665i | 0.148743 | + | 0.108068i | ||||
\(236\) | 1.04408 | + | 3.21333i | 0.0679635 | + | 0.209170i | ||||
\(237\) | −2.28253 | − | 7.02491i | −0.148266 | − | 0.456317i | ||||
\(238\) | −3.87270 | − | 2.81368i | −0.251030 | − | 0.182384i | ||||
\(239\) | 15.6786 | − | 11.3912i | 1.01417 | − | 0.736836i | 0.0490884 | − | 0.998794i | \(-0.484368\pi\) |
0.965079 | + | 0.261959i | \(0.0843684\pi\) | |||||||
\(240\) | −0.292554 | + | 0.900388i | −0.0188843 | + | 0.0581198i | ||||
\(241\) | 5.20964 | 0.335582 | 0.167791 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167791 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(242\) | −9.70260 | − | 5.18262i | −0.623707 | − | 0.333152i | ||||
\(243\) | −14.5662 | −0.934423 | ||||||||
\(244\) | −1.47351 | + | 4.53500i | −0.0943318 | + | 0.290324i | ||||
\(245\) | −2.28028 | + | 1.65672i | −0.145682 | + | 0.105844i | ||||
\(246\) | −17.6638 | − | 12.8335i | −1.12621 | − | 0.818236i | ||||
\(247\) | −0.164234 | − | 0.505460i | −0.0104499 | − | 0.0321616i | ||||
\(248\) | 1.79257 | + | 5.51696i | 0.113828 | + | 0.350327i | ||||
\(249\) | 22.1569 | + | 16.0979i | 1.40414 | + | 1.02016i | ||||
\(250\) | 3.52691 | − | 2.56245i | 0.223061 | − | 0.162064i | ||||
\(251\) | 4.20242 | − | 12.9337i | 0.265255 | − | 0.816370i | −0.726380 | − | 0.687293i | \(-0.758799\pi\) |
0.991635 | − | 0.129077i | \(-0.0412013\pi\) | |||||||
\(252\) | 1.24637 | 0.0785137 | ||||||||
\(253\) | −14.2576 | − | 17.0243i | −0.896367 | − | 1.07031i | ||||
\(254\) | −5.75512 | −0.361108 | ||||||||
\(255\) | 1.72056 | − | 5.29532i | 0.107745 | − | 0.331606i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 8.86110 | + | 6.43797i | 0.552740 | + | 0.401589i | 0.828795 | − | 0.559553i | \(-0.189027\pi\) |
−0.276055 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(258\) | 6.73987 | + | 20.7432i | 0.419606 | + | 1.29141i | ||||
\(259\) | 0.597444 | + | 1.83874i | 0.0371234 | + | 0.114254i | ||||
\(260\) | 0.191228 | + | 0.138935i | 0.0118594 | + | 0.00861639i | ||||
\(261\) | 5.16201 | − | 3.75042i | 0.319521 | − | 0.232145i | ||||
\(262\) | 0.299840 | − | 0.922812i | 0.0185242 | − | 0.0570115i | ||||
\(263\) | 27.8602 | 1.71793 | 0.858966 | − | 0.512032i | \(-0.171107\pi\) | ||||
0.858966 | + | 0.512032i | \(0.171107\pi\) | |||||||
\(264\) | 6.54845 | − | 2.63852i | 0.403029 | − | 0.162389i | ||||
\(265\) | −4.14426 | −0.254580 | ||||||||
\(266\) | 0.251522 | − | 0.774104i | 0.0154218 | − | 0.0474634i | ||||
\(267\) | −12.7466 | + | 9.26092i | −0.780077 | + | 0.566759i | ||||
\(268\) | 0.995438 | + | 0.723228i | 0.0608061 | + | 0.0441782i | ||||
\(269\) | 3.99223 | + | 12.2868i | 0.243411 | + | 0.749141i | 0.995894 | + | 0.0905294i | \(0.0288559\pi\) |
−0.752483 | + | 0.658611i | \(0.771144\pi\) | |||||||
\(270\) | −0.429682 | − | 1.32242i | −0.0261496 | − | 0.0804802i | ||||
\(271\) | −6.55792 | − | 4.76461i | −0.398365 | − | 0.289429i | 0.370509 | − | 0.928829i | \(-0.379183\pi\) |
−0.768875 | + | 0.639399i | \(0.779183\pi\) | |||||||
\(272\) | 4.75796 | − | 3.45686i | 0.288494 | − | 0.209603i | ||||
\(273\) | 0.284555 | − | 0.875769i | 0.0172220 | − | 0.0530040i | ||||
\(274\) | −2.14682 | −0.129694 | ||||||||
\(275\) | −15.4503 | − | 3.86779i | −0.931690 | − | 0.233236i | ||||
\(276\) | 14.2523 | 0.857886 | ||||||||
\(277\) | 7.25063 | − | 22.3151i | 0.435648 | − | 1.34079i | −0.456773 | − | 0.889583i | \(-0.650995\pi\) |
0.892421 | − | 0.451204i | \(-0.149005\pi\) | |||||||
\(278\) | −7.91878 | + | 5.75333i | −0.474937 | + | 0.345062i | ||||
\(279\) | 7.18627 | + | 5.22113i | 0.430231 | + | 0.312581i | ||||
\(280\) | 0.111864 | + | 0.344281i | 0.00668513 | + | 0.0205747i | ||||
\(281\) | −4.44071 | − | 13.6671i | −0.264911 | − | 0.815311i | −0.991714 | − | 0.128465i | \(-0.958995\pi\) |
0.726803 | − | 0.686846i | \(-0.241005\pi\) | |||||||
\(282\) | 10.9136 | + | 7.92917i | 0.649893 | + | 0.472175i | ||||
\(283\) | 9.45652 | − | 6.87056i | 0.562132 | − | 0.408412i | −0.270107 | − | 0.962830i | \(-0.587059\pi\) |
0.832238 | + | 0.554418i | \(0.187059\pi\) | |||||||
\(284\) | −3.57970 | + | 11.0172i | −0.212416 | + | 0.653749i | ||||
\(285\) | 0.946723 | 0.0560791 | ||||||||
\(286\) | −0.121289 | − | 1.75851i | −0.00717200 | − | 0.103983i | ||||
\(287\) | −8.34854 | −0.492799 | ||||||||
\(288\) | −0.473189 | + | 1.45633i | −0.0278829 | + | 0.0858149i | ||||
\(289\) | −14.2290 | + | 10.3380i | −0.837002 | + | 0.608118i | ||||
\(290\) | 1.49927 | + | 1.08928i | 0.0880402 | + | 0.0639649i | ||||
\(291\) | −9.36015 | − | 28.8076i | −0.548702 | − | 1.68873i | ||||
\(292\) | 3.81333 | + | 11.7362i | 0.223158 | + | 0.686811i | ||||
\(293\) | −19.9706 | − | 14.5095i | −1.16670 | − | 0.847656i | −0.176088 | − | 0.984374i | \(-0.556344\pi\) |
−0.990610 | + | 0.136719i | \(0.956344\pi\) | |||||||
\(294\) | −10.9140 | + | 7.92952i | −0.636520 | + | 0.462459i | ||||
\(295\) | −0.464349 | + | 1.42912i | −0.0270355 | + | 0.0832066i | ||||
\(296\) | −2.37532 | −0.138063 | ||||||||
\(297\) | −5.50322 | + | 8.78841i | −0.319329 | + | 0.509955i | ||||
\(298\) | −1.24923 | −0.0723657 | ||||||||
\(299\) | 1.09960 | − | 3.38423i | 0.0635918 | − | 0.195715i | ||||
\(300\) | 8.27005 | − | 6.00854i | 0.477471 | − | 0.346903i | ||||
\(301\) | 6.74698 | + | 4.90197i | 0.388890 | + | 0.282545i | ||||
\(302\) | 4.28073 | + | 13.1747i | 0.246328 | + | 0.758120i | ||||
\(303\) | 2.30563 | + | 7.09599i | 0.132455 | + | 0.407654i | ||||
\(304\) | 0.809017 | + | 0.587785i | 0.0464003 | + | 0.0337118i | ||||
\(305\) | −1.71570 | + | 1.24653i | −0.0982407 | + | 0.0713761i | ||||
\(306\) | 2.78290 | − | 8.56489i | 0.159088 | − | 0.489622i | ||||
\(307\) | −11.2527 | −0.642226 | −0.321113 | − | 0.947041i | \(-0.604057\pi\) | ||||
−0.321113 | + | 0.947041i | \(0.604057\pi\) | |||||||
\(308\) | 1.43271 | − | 2.28798i | 0.0816363 | − | 0.130370i | ||||
\(309\) | 1.47756 | 0.0840557 | ||||||||
\(310\) | −0.797240 | + | 2.45365i | −0.0452802 | + | 0.139358i | ||||
\(311\) | −2.75641 | + | 2.00265i | −0.156302 | + | 0.113560i | −0.663187 | − | 0.748454i | \(-0.730797\pi\) |
0.506886 | + | 0.862013i | \(0.330797\pi\) | |||||||
\(312\) | 0.915267 | + | 0.664980i | 0.0518168 | + | 0.0376471i | ||||
\(313\) | 6.37884 | + | 19.6321i | 0.360554 | + | 1.10967i | 0.952719 | + | 0.303853i | \(0.0982733\pi\) |
−0.592165 | + | 0.805817i | \(0.701727\pi\) | |||||||
\(314\) | −5.34898 | − | 16.4625i | −0.301860 | − | 0.929031i | ||||
\(315\) | 0.448452 | + | 0.325820i | 0.0252674 | + | 0.0183579i | ||||
\(316\) | 2.80726 | − | 2.03959i | 0.157920 | − | 0.114736i | ||||
\(317\) | −8.09693 | + | 24.9198i | −0.454769 | + | 1.39963i | 0.416637 | + | 0.909073i | \(0.363209\pi\) |
−0.871406 | + | 0.490562i | \(0.836791\pi\) | |||||||
\(318\) | −19.8355 | −1.11232 | ||||||||
\(319\) | −0.950938 | − | 13.7872i | −0.0532423 | − | 0.771933i | ||||
\(320\) | −0.444747 | −0.0248621 | ||||||||
\(321\) | 5.67732 | − | 17.4730i | 0.316877 | − | 0.975248i | ||||
\(322\) | 4.40885 | − | 3.20321i | 0.245695 | − | 0.178508i | ||||
\(323\) | −4.75796 | − | 3.45686i | −0.264740 | − | 0.192345i | ||||
\(324\) | −3.47614 | − | 10.6985i | −0.193119 | − | 0.594359i | ||||
\(325\) | −0.788683 | − | 2.42732i | −0.0437483 | − | 0.134643i | ||||
\(326\) | −8.06853 | − | 5.86213i | −0.446875 | − | 0.324673i | ||||
\(327\) | −13.9555 | + | 10.1393i | −0.771742 | + | 0.560703i | ||||
\(328\) | 3.16957 | − | 9.75492i | 0.175010 | − | 0.538626i | ||||
\(329\) | 5.15813 | 0.284377 | ||||||||
\(330\) | 3.04593 | + | 0.762510i | 0.167673 | + | 0.0419748i | ||||
\(331\) | 22.7831 | 1.25227 | 0.626137 | − | 0.779713i | \(-0.284635\pi\) | ||||
0.626137 | + | 0.779713i | \(0.284635\pi\) | |||||||
\(332\) | −3.97579 | + | 12.2362i | −0.218200 | + | 0.671550i | ||||
\(333\) | −2.94260 | + | 2.13793i | −0.161254 | + | 0.117158i | ||||
\(334\) | 18.5250 | + | 13.4592i | 1.01364 | + | 0.736455i | ||||
\(335\) | 0.169103 | + | 0.520446i | 0.00923910 | + | 0.0284350i | ||||
\(336\) | 0.535409 | + | 1.64782i | 0.0292090 | + | 0.0898959i | ||||
\(337\) | 13.4952 | + | 9.80482i | 0.735129 | + | 0.534103i | 0.891182 | − | 0.453646i | \(-0.149877\pi\) |
−0.156053 | + | 0.987749i | \(0.549877\pi\) | |||||||
\(338\) | −10.2887 | + | 7.47518i | −0.559632 | + | 0.406596i | ||||
\(339\) | 3.06705 | − | 9.43940i | 0.166579 | − | 0.512678i | ||||
\(340\) | 2.61563 | 0.141852 | ||||||||
\(341\) | 17.8452 | − | 7.19024i | 0.966374 | − | 0.389373i | ||||
\(342\) | 1.53127 | 0.0828017 | ||||||||
\(343\) | −3.35467 | + | 10.3246i | −0.181135 | + | 0.557477i | ||||
\(344\) | −8.28927 | + | 6.02251i | −0.446928 | + | 0.324712i | ||||
\(345\) | 5.12808 | + | 3.72577i | 0.276087 | + | 0.200589i | ||||
\(346\) | 2.39464 | + | 7.36995i | 0.128737 | + | 0.396211i | ||||
\(347\) | 7.68261 | + | 23.6447i | 0.412424 | + | 1.26931i | 0.914534 | + | 0.404508i | \(0.132557\pi\) |
−0.502110 | + | 0.864804i | \(0.667443\pi\) | |||||||
\(348\) | 7.17591 | + | 5.21360i | 0.384669 | + | 0.279478i | ||||
\(349\) | −15.8230 | + | 11.4961i | −0.846987 | + | 0.615372i | −0.924314 | − | 0.381634i | \(-0.875362\pi\) |
0.0773266 | + | 0.997006i | \(0.475362\pi\) | |||||||
\(350\) | 1.20786 | − | 3.71740i | 0.0645627 | − | 0.198704i | ||||
\(351\) | −1.66162 | −0.0886907 | ||||||||
\(352\) | 2.12947 | + | 2.54271i | 0.113501 | + | 0.135527i | ||||
\(353\) | −17.1793 | −0.914360 | −0.457180 | − | 0.889374i | \(-0.651141\pi\) | ||||
−0.457180 | + | 0.889374i | \(0.651141\pi\) | |||||||
\(354\) | −2.22250 | + | 6.84015i | −0.118125 | + | 0.363550i | ||||
\(355\) | −4.16807 | + | 3.02828i | −0.221218 | + | 0.160724i | ||||
\(356\) | −5.98802 | − | 4.35055i | −0.317364 | − | 0.230579i | ||||
\(357\) | −3.14883 | − | 9.69109i | −0.166654 | − | 0.512907i | ||||
\(358\) | −4.07248 | − | 12.5338i | −0.215237 | − | 0.662432i | ||||
\(359\) | −15.3867 | − | 11.1791i | −0.812080 | − | 0.590011i | 0.102353 | − | 0.994748i | \(-0.467363\pi\) |
−0.914433 | + | 0.404738i | \(0.867363\pi\) | |||||||
\(360\) | −0.550964 | + | 0.400299i | −0.0290383 | + | 0.0210976i | ||||
\(361\) | 0.309017 | − | 0.951057i | 0.0162641 | − | 0.0500556i | ||||
\(362\) | 9.16172 | 0.481529 | ||||||||
\(363\) | −10.2247 | − | 21.0651i | −0.536656 | − | 1.10563i | ||||
\(364\) | 0.432587 | 0.0226737 | ||||||||
\(365\) | −1.69597 | + | 5.21965i | −0.0887710 | + | 0.273209i | ||||
\(366\) | −8.21180 | + | 5.96623i | −0.429238 | + | 0.311860i | ||||
\(367\) | −3.39444 | − | 2.46621i | −0.177188 | − | 0.128735i | 0.495656 | − | 0.868519i | \(-0.334928\pi\) |
−0.672844 | + | 0.739784i | \(0.734928\pi\) | |||||||
\(368\) | 2.06898 | + | 6.36767i | 0.107853 | + | 0.331938i | ||||
\(369\) | −4.85347 | − | 14.9374i | −0.252662 | − | 0.777612i | ||||
\(370\) | −0.854658 | − | 0.620946i | −0.0444316 | − | 0.0322814i | ||||
\(371\) | −6.13599 | + | 4.45806i | −0.318565 | + | 0.231451i | ||||
\(372\) | −3.81580 | + | 11.7438i | −0.197840 | + | 0.608890i | ||||
\(373\) | −30.5753 | −1.58313 | −0.791564 | − | 0.611086i | \(-0.790733\pi\) | ||||
−0.791564 | + | 0.611086i | \(0.790733\pi\) | |||||||
\(374\) | −12.5238 | − | 14.9541i | −0.647589 | − | 0.773256i | ||||
\(375\) | 9.27997 | 0.479216 | ||||||||
\(376\) | −1.95831 | + | 6.02706i | −0.100992 | + | 0.310822i | ||||
\(377\) | 1.79162 | − | 1.30169i | 0.0922733 | − | 0.0670405i | ||||
\(378\) | −2.05874 | − | 1.49576i | −0.105890 | − | 0.0769338i | ||||
\(379\) | 8.62627 | + | 26.5489i | 0.443102 | + | 1.36373i | 0.884552 | + | 0.466441i | \(0.154464\pi\) |
−0.441451 | + | 0.897286i | \(0.645536\pi\) | |||||||
\(380\) | 0.137434 | + | 0.422980i | 0.00705024 | + | 0.0216984i | ||||
\(381\) | −9.91110 | − | 7.20084i | −0.507761 | − | 0.368910i | ||||
\(382\) | −11.7816 | + | 8.55983i | −0.602799 | + | 0.437959i | ||||
\(383\) | −4.12024 | + | 12.6808i | −0.210535 | + | 0.647959i | 0.788906 | + | 0.614514i | \(0.210648\pi\) |
−0.999441 | + | 0.0334448i | \(0.989352\pi\) | |||||||
\(384\) | −2.12868 | −0.108629 | ||||||||
\(385\) | 1.11361 | − | 0.448700i | 0.0567550 | − | 0.0228679i | ||||
\(386\) | 2.43059 | 0.123714 | ||||||||
\(387\) | −4.84835 | + | 14.9217i | −0.246455 | + | 0.758512i | ||||
\(388\) | 11.5119 | − | 8.36390i | 0.584430 | − | 0.424613i | ||||
\(389\) | 4.85839 | + | 3.52983i | 0.246330 | + | 0.178969i | 0.704099 | − | 0.710102i | \(-0.251351\pi\) |
−0.457769 | + | 0.889071i | \(0.651351\pi\) | |||||||
\(390\) | 0.155484 | + | 0.478530i | 0.00787324 | + | 0.0242313i | ||||
\(391\) | −12.1680 | − | 37.4493i | −0.615363 | − | 1.89389i | ||||
\(392\) | −5.12714 | − | 3.72509i | −0.258960 | − | 0.188145i | ||||
\(393\) | 1.67099 | − | 1.21405i | 0.0842904 | − | 0.0612406i | ||||
\(394\) | 3.36974 | − | 10.3710i | 0.169765 | − | 0.522483i | ||||
\(395\) | 1.54325 | 0.0776495 | ||||||||
\(396\) | 4.92663 | + | 1.23332i | 0.247572 | + | 0.0619765i | ||||
\(397\) | −27.7223 | −1.39134 | −0.695671 | − | 0.718360i | \(-0.744893\pi\) | ||||
−0.695671 | + | 0.718360i | \(0.744893\pi\) | |||||||
\(398\) | 4.72807 | − | 14.5515i | 0.236997 | − | 0.729402i | ||||
\(399\) | 1.40172 | − | 1.01841i | 0.0701737 | − | 0.0509842i | ||||
\(400\) | 3.88506 | + | 2.82266i | 0.194253 | + | 0.141133i | ||||
\(401\) | 9.01192 | + | 27.7358i | 0.450034 | + | 1.38506i | 0.876868 | + | 0.480732i | \(0.159629\pi\) |
−0.426834 | + | 0.904330i | \(0.640371\pi\) | |||||||
\(402\) | 0.809374 | + | 2.49100i | 0.0403679 | + | 0.124240i | ||||
\(403\) | 2.49420 | + | 1.81214i | 0.124245 | + | 0.0902693i | ||||
\(404\) | −2.83566 | + | 2.06023i | −0.141079 | + | 0.102500i | ||||
\(405\) | 1.54600 | − | 4.75811i | 0.0768215 | − | 0.236432i | ||||
\(406\) | 3.39158 | 0.168321 | ||||||||
\(407\) | 0.542082 | + | 7.85937i | 0.0268700 | + | 0.389574i | ||||
\(408\) | 12.5191 | 0.619788 | ||||||||
\(409\) | 3.47106 | − | 10.6828i | 0.171633 | − | 0.528231i | −0.827831 | − | 0.560978i | \(-0.810425\pi\) |
0.999464 | + | 0.0327463i | \(0.0104253\pi\) | |||||||
\(410\) | 3.69053 | − | 2.68132i | 0.182262 | − | 0.132421i | ||||
\(411\) | −3.69712 | − | 2.68612i | −0.182366 | − | 0.132496i | ||||
\(412\) | 0.214496 | + | 0.660150i | 0.0105674 | + | 0.0325232i | ||||
\(413\) | 0.849816 | + | 2.61547i | 0.0418167 | + | 0.128699i | ||||
\(414\) | 8.29438 | + | 6.02622i | 0.407647 | + | 0.296173i | ||||
\(415\) | −4.62926 | + | 3.36336i | −0.227242 | + | 0.165101i | ||||
\(416\) | −0.164234 | + | 0.505460i | −0.00805222 | + | 0.0247822i | ||||
\(417\) | −20.8358 | −1.02034 | ||||||||
\(418\) | 1.76021 | − | 2.81099i | 0.0860948 | − | 0.137490i | ||||
\(419\) | −20.2013 | −0.986897 | −0.493449 | − | 0.869775i | \(-0.664264\pi\) | ||||
−0.493449 | + | 0.869775i | \(0.664264\pi\) | |||||||
\(420\) | −0.238122 | + | 0.732863i | −0.0116191 | + | 0.0357600i | ||||
\(421\) | 10.2803 | − | 7.46911i | 0.501033 | − | 0.364022i | −0.308378 | − | 0.951264i | \(-0.599786\pi\) |
0.809412 | + | 0.587242i | \(0.199786\pi\) | |||||||
\(422\) | −4.53947 | − | 3.29812i | −0.220978 | − | 0.160550i | ||||
\(423\) | 2.99871 | + | 9.22907i | 0.145802 | + | 0.448733i | ||||
\(424\) | −2.87949 | − | 8.86217i | −0.139841 | − | 0.430385i | ||||
\(425\) | −22.8487 | − | 16.6005i | −1.10832 | − | 0.805244i | ||||
\(426\) | −19.9495 | + | 14.4942i | −0.966556 | + | 0.702244i | ||||
\(427\) | −1.19935 | + | 3.69122i | −0.0580407 | + | 0.178631i | ||||
\(428\) | 8.63080 | 0.417185 | ||||||||
\(429\) | 1.99139 | − | 3.18016i | 0.0961450 | − | 0.153540i | ||||
\(430\) | −4.55693 | −0.219754 | ||||||||
\(431\) | −9.75883 | + | 30.0346i | −0.470066 | + | 1.44672i | 0.382431 | + | 0.923984i | \(0.375087\pi\) |
−0.852497 | + | 0.522731i | \(0.824913\pi\) | |||||||
\(432\) | 2.52935 | − | 1.83768i | 0.121693 | − | 0.0884154i | ||||
\(433\) | −17.1813 | − | 12.4830i | −0.825682 | − | 0.599893i | 0.0926526 | − | 0.995698i | \(-0.470465\pi\) |
−0.918334 | + | 0.395806i | \(0.870465\pi\) | |||||||
\(434\) | 1.45905 | + | 4.49048i | 0.0700365 | + | 0.215550i | ||||
\(435\) | 1.21903 | + | 3.75179i | 0.0584480 | + | 0.179885i | ||||
\(436\) | −6.55595 | − | 4.76318i | −0.313973 | − | 0.228115i | ||||
\(437\) | 5.41666 | − | 3.93543i | 0.259114 | − | 0.188257i | ||||
\(438\) | −8.11735 | + | 24.9826i | −0.387862 | + | 1.19372i | ||||
\(439\) | 23.1919 | 1.10689 | 0.553445 | − | 0.832886i | \(-0.313313\pi\) | ||||
0.553445 | + | 0.832886i | \(0.313313\pi\) | |||||||
\(440\) | 0.101498 | + | 1.47156i | 0.00483871 | + | 0.0701540i | ||||
\(441\) | −9.70444 | −0.462116 | ||||||||
\(442\) | 0.965885 | − | 2.97269i | 0.0459425 | − | 0.141396i | ||||
\(443\) | 13.4663 | − | 9.78387i | 0.639805 | − | 0.464846i | −0.219978 | − | 0.975505i | \(-0.570599\pi\) |
0.859783 | + | 0.510659i | \(0.170599\pi\) | |||||||
\(444\) | −4.09062 | − | 2.97201i | −0.194132 | − | 0.141045i | ||||
\(445\) | −1.01723 | − | 3.13072i | −0.0482215 | − | 0.148411i | ||||
\(446\) | 7.41215 | + | 22.8122i | 0.350975 | + | 1.08019i | ||||
\(447\) | −2.15134 | − | 1.56304i | −0.101755 | − | 0.0739291i | ||||
\(448\) | −0.658492 | + | 0.478423i | −0.0311108 | + | 0.0226034i | ||||
\(449\) | −0.690204 | + | 2.12423i | −0.0325727 | + | 0.100249i | −0.966021 | − | 0.258463i | \(-0.916784\pi\) |
0.933448 | + | 0.358712i | \(0.116784\pi\) | |||||||
\(450\) | 7.35348 | 0.346646 | ||||||||
\(451\) | −33.0001 | − | 8.26113i | −1.55391 | − | 0.389002i | ||||
\(452\) | 4.66260 | 0.219310 | ||||||||
\(453\) | −9.11229 | + | 28.0447i | −0.428133 | + | 1.31766i | ||||
\(454\) | −2.85398 | + | 2.07354i | −0.133944 | + | 0.0973159i | ||||
\(455\) | 0.155648 | + | 0.113085i | 0.00729690 | + | 0.00530151i | ||||
\(456\) | 0.657798 | + | 2.02449i | 0.0308042 | + | 0.0948056i | ||||
\(457\) | 3.84000 | + | 11.8183i | 0.179628 | + | 0.552837i | 0.999815 | − | 0.0192585i | \(-0.00613055\pi\) |
−0.820187 | + | 0.572096i | \(0.806131\pi\) | |||||||
\(458\) | −15.8339 | − | 11.5040i | −0.739868 | − | 0.537546i | ||||
\(459\) | −14.8755 | + | 10.8077i | −0.694330 | + | 0.504460i | ||||
\(460\) | −0.920173 | + | 2.83200i | −0.0429033 | + | 0.132043i | ||||
\(461\) | 31.8148 | 1.48176 | 0.740881 | − | 0.671636i | \(-0.234408\pi\) | ||||
0.740881 | + | 0.671636i | \(0.234408\pi\) | |||||||
\(462\) | 5.33006 | − | 2.14760i | 0.247977 | − | 0.0999153i | ||||
\(463\) | −0.0722953 | −0.00335985 | −0.00167992 | − | 0.999999i | \(-0.500535\pi\) | ||||
−0.00167992 | + | 0.999999i | \(0.500535\pi\) | |||||||
\(464\) | −1.28763 | + | 3.96292i | −0.0597768 | + | 0.183974i | ||||
\(465\) | −4.44298 | + | 3.22801i | −0.206038 | + | 0.149696i | ||||
\(466\) | 15.5347 | + | 11.2866i | 0.719630 | + | 0.522842i | ||||
\(467\) | −10.4480 | − | 32.1557i | −0.483476 | − | 1.48799i | −0.834175 | − | 0.551499i | \(-0.814056\pi\) |
0.350699 | − | 0.936488i | \(-0.385944\pi\) | |||||||
\(468\) | 0.251487 | + | 0.773996i | 0.0116250 | + | 0.0357780i | ||||
\(469\) | 0.810228 | + | 0.588665i | 0.0374129 | + | 0.0271820i | ||||
\(470\) | −2.28018 | + | 1.65665i | −0.105177 | + | 0.0764156i | ||||
\(471\) | 11.3863 | − | 35.0433i | 0.524651 | − | 1.61471i | ||||
\(472\) | −3.37870 | −0.155517 | ||||||||
\(473\) | 21.8188 | + | 26.0528i | 1.00323 | + | 1.19791i | ||||
\(474\) | 7.38643 | 0.339270 | ||||||||
\(475\) | 1.48396 | − | 4.56716i | 0.0680888 | − | 0.209556i | ||||
\(476\) | 3.87270 | − | 2.81368i | 0.177505 | − | 0.128965i | ||||
\(477\) | −11.5437 | − | 8.38696i | −0.528548 | − | 0.384013i | ||||
\(478\) | 5.98871 | + | 18.4314i | 0.273917 | + | 0.843031i | ||||
\(479\) | −2.37442 | − | 7.30771i | −0.108490 | − | 0.333898i | 0.882044 | − | 0.471167i | \(-0.156167\pi\) |
−0.990534 | + | 0.137270i | \(0.956167\pi\) | |||||||
\(480\) | −0.765915 | − | 0.556470i | −0.0349591 | − | 0.0253993i | ||||
\(481\) | −1.02131 | + | 0.742029i | −0.0465679 | + | 0.0338336i | ||||
\(482\) | −1.60987 | + | 4.95466i | −0.0733275 | + | 0.225679i | ||||
\(483\) | 11.6005 | 0.527842 | ||||||||
\(484\) | 7.92723 | − | 7.62620i | 0.360329 | − | 0.346646i | ||||
\(485\) | 6.32854 | 0.287364 | ||||||||
\(486\) | 4.50121 | − | 13.8533i | 0.204179 | − | 0.628398i | ||||
\(487\) | 24.5685 | − | 17.8500i | 1.11330 | − | 0.808862i | 0.130123 | − | 0.991498i | \(-0.458463\pi\) |
0.983181 | + | 0.182636i | \(0.0584628\pi\) | |||||||
\(488\) | −3.85770 | − | 2.80278i | −0.174630 | − | 0.126876i | ||||
\(489\) | −6.56038 | − | 20.1908i | −0.296671 | − | 0.913059i | ||||
\(490\) | −0.870990 | − | 2.68063i | −0.0393473 | − | 0.121099i | ||||
\(491\) | −8.18301 | − | 5.94531i | −0.369294 | − | 0.268308i | 0.387624 | − | 0.921818i | \(-0.373296\pi\) |
−0.756918 | + | 0.653510i | \(0.773296\pi\) | |||||||
\(492\) | 17.6638 | − | 12.8335i | 0.796348 | − | 0.578580i | ||||
\(493\) | 7.57277 | − | 23.3066i | 0.341060 | − | 1.04968i | ||||
\(494\) | 0.531472 | 0.0239120 | ||||||||
\(495\) | 1.45023 | + | 1.73166i | 0.0651831 | + | 0.0778321i | ||||
\(496\) | −5.80088 | −0.260467 | ||||||||
\(497\) | −2.91366 | + | 8.96734i | −0.130696 | + | 0.402240i | ||||
\(498\) | −22.1569 | + | 16.0979i | −0.992874 | + | 0.721365i | ||||
\(499\) | 15.0982 | + | 10.9695i | 0.675890 | + | 0.491063i | 0.871992 | − | 0.489521i | \(-0.162828\pi\) |
−0.196102 | + | 0.980584i | \(0.562828\pi\) | |||||||
\(500\) | 1.34716 | + | 4.14613i | 0.0602468 | + | 0.185421i | ||||
\(501\) | 15.0624 | + | 46.3572i | 0.672937 | + | 2.07109i | ||||
\(502\) | 11.0021 | + | 7.99349i | 0.491047 | + | 0.356767i | ||||
\(503\) | 10.7921 | − | 7.84090i | 0.481195 | − | 0.349609i | −0.320593 | − | 0.947217i | \(-0.603882\pi\) |
0.801788 | + | 0.597608i | \(0.203882\pi\) | |||||||
\(504\) | −0.385148 | + | 1.18536i | −0.0171559 | + | 0.0528003i | ||||
\(505\) | −1.55887 | −0.0693688 | ||||||||
\(506\) | 20.5969 | − | 8.29896i | 0.915646 | − | 0.368934i | ||||
\(507\) | −27.0716 | −1.20229 | ||||||||
\(508\) | 1.77843 | − | 5.47344i | 0.0789050 | − | 0.242845i | ||||
\(509\) | −28.4656 | + | 20.6815i | −1.26172 | + | 0.916691i | −0.998841 | − | 0.0481379i | \(-0.984671\pi\) |
−0.262877 | + | 0.964829i | \(0.584671\pi\) | |||||||
\(510\) | 4.50447 | + | 3.27269i | 0.199461 | + | 0.144917i | ||||
\(511\) | 3.10383 | + | 9.55260i | 0.137305 | + | 0.422582i | ||||
\(512\) | −0.309017 | − | 0.951057i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | −2.52935 | − | 1.83768i | −0.111674 | − | 0.0811356i | ||||
\(514\) | −8.86110 | + | 6.43797i | −0.390846 | + | 0.283966i | ||||
\(515\) | −0.0953963 | + | 0.293600i | −0.00420366 | + | 0.0129375i | ||||
\(516\) | −21.8107 | −0.960161 | ||||||||
\(517\) | 20.3890 | + | 5.10412i | 0.896708 | + | 0.224479i | ||||
\(518\) | −1.93337 | −0.0849474 | ||||||||
\(519\) | −5.09742 | + | 15.6883i | −0.223752 | + | 0.688638i | ||||
\(520\) | −0.191228 | + | 0.138935i | −0.00838589 | + | 0.00609270i | ||||
\(521\) | 21.9260 | + | 15.9301i | 0.960593 | + | 0.697912i | 0.953289 | − | 0.302061i | \(-0.0976747\pi\) |
0.00730498 | + | 0.999973i | \(0.497675\pi\) | |||||||
\(522\) | 1.97171 | + | 6.06831i | 0.0862996 | + | 0.265603i | ||||
\(523\) | 3.78202 | + | 11.6399i | 0.165376 | + | 0.508976i | 0.999064 | − | 0.0432606i | \(-0.0137746\pi\) |
−0.833688 | + | 0.552236i | \(0.813775\pi\) | |||||||
\(524\) | 0.784990 | + | 0.570329i | 0.0342925 | + | 0.0249149i | ||||
\(525\) | 6.73133 | − | 4.89060i | 0.293780 | − | 0.213443i | ||||
\(526\) | −8.60927 | + | 26.4966i | −0.375382 | + | 1.15531i | ||||
\(527\) | 34.1159 | 1.48611 | ||||||||
\(528\) | 0.485795 | + | 7.04329i | 0.0211415 | + | 0.306520i | ||||
\(529\) | 21.8279 | 0.949038 | ||||||||
\(530\) | 1.28065 | − | 3.94142i | 0.0556277 | − | 0.171204i | ||||
\(531\) | −4.18562 | + | 3.04103i | −0.181640 | + | 0.131969i | ||||
\(532\) | 0.658492 | + | 0.478423i | 0.0285493 | + | 0.0207423i | ||||
\(533\) | −1.68453 | − | 5.18447i | −0.0729653 | − | 0.224564i | ||||
\(534\) | −4.86875 | − | 14.9845i | −0.210692 | − | 0.648442i | ||||
\(535\) | 3.10543 | + | 2.25623i | 0.134259 | + | 0.0975452i | ||||
\(536\) | −0.995438 | + | 0.723228i | −0.0429964 | + | 0.0312387i | ||||
\(537\) | 8.66901 | − | 26.6805i | 0.374095 | − | 1.15135i | ||||
\(538\) | −12.9191 | −0.556983 | ||||||||
\(539\) | −11.1554 | + | 17.8146i | −0.480495 | + | 0.767330i | ||||
\(540\) | 1.39048 | 0.0598367 | ||||||||
\(541\) | 13.8116 | − | 42.5078i | 0.593808 | − | 1.82755i | 0.0332353 | − | 0.999448i | \(-0.489419\pi\) |
0.560573 | − | 0.828105i | \(-0.310581\pi\) | |||||||
\(542\) | 6.55792 | − | 4.76461i | 0.281687 | − | 0.204657i | ||||
\(543\) | 15.7777 | + | 11.4632i | 0.677088 | + | 0.491933i | ||||
\(544\) | 1.81738 | + | 5.59332i | 0.0779195 | + | 0.239811i | ||||
\(545\) | −1.11371 | − | 3.42766i | −0.0477063 | − | 0.146825i | ||||
\(546\) | 0.744974 | + | 0.541255i | 0.0318819 | + | 0.0231636i | ||||
\(547\) | 2.29936 | − | 1.67058i | 0.0983133 | − | 0.0714288i | −0.537543 | − | 0.843237i | \(-0.680647\pi\) |
0.635856 | + | 0.771808i | \(0.280647\pi\) | |||||||
\(548\) | 0.663405 | − | 2.04175i | 0.0283392 | − | 0.0872192i | ||||
\(549\) | −7.30169 | −0.311629 | ||||||||
\(550\) | 8.45290 | − | 13.4989i | 0.360433 | − | 0.575596i | ||||
\(551\) | 4.16686 | 0.177514 | ||||||||
\(552\) | −4.40419 | + | 13.5547i | −0.187455 | + | 0.576927i | ||||
\(553\) | 2.28494 | − | 1.66011i | 0.0971656 | − | 0.0705949i | ||||
\(554\) | 18.9824 | + | 13.7915i | 0.806485 | + | 0.585945i | ||||
\(555\) | −0.694908 | − | 2.13871i | −0.0294972 | − | 0.0907831i | ||||
\(556\) | −3.02471 | − | 9.30909i | −0.128276 | − | 0.394793i | ||||
\(557\) | 25.5925 | + | 18.5940i | 1.08439 | + | 0.787855i | 0.978443 | − | 0.206517i | \(-0.0662129\pi\) |
0.105946 | + | 0.994372i | \(0.466213\pi\) | |||||||
\(558\) | −7.18627 | + | 5.22113i | −0.304219 | + | 0.221028i | ||||
\(559\) | −1.68276 | + | 5.17899i | −0.0711730 | + | 0.219048i | ||||
\(560\) | −0.361998 | −0.0152972 | ||||||||
\(561\) | −2.85704 | − | 41.4228i | −0.120624 | − | 1.74887i | ||||
\(562\) | 14.3704 | 0.606180 | ||||||||
\(563\) | −1.35629 | + | 4.17422i | −0.0571606 | + | 0.175922i | −0.975560 | − | 0.219731i | \(-0.929482\pi\) |
0.918400 | + | 0.395654i | \(0.129482\pi\) | |||||||
\(564\) | −10.9136 | + | 7.92917i | −0.459544 | + | 0.333878i | ||||
\(565\) | 1.67764 | + | 1.21888i | 0.0705788 | + | 0.0512785i | ||||
\(566\) | 3.61207 | + | 11.1168i | 0.151827 | + | 0.467274i | ||||
\(567\) | −2.82937 | − | 8.70792i | −0.118823 | − | 0.365698i | ||||
\(568\) | −9.37177 | − | 6.80899i | −0.393231 | − | 0.285699i | ||||
\(569\) | 31.3993 | − | 22.8129i | 1.31633 | − | 0.956367i | 0.316356 | − | 0.948641i | \(-0.397541\pi\) |
0.999970 | − | 0.00772642i | \(-0.00245942\pi\) | |||||||
\(570\) | −0.292554 | + | 0.900388i | −0.0122537 | + | 0.0377131i | ||||
\(571\) | −22.3077 | −0.933547 | −0.466774 | − | 0.884377i | \(-0.654584\pi\) | ||||
−0.466774 | + | 0.884377i | \(0.654584\pi\) | |||||||
\(572\) | 1.70993 | + | 0.428058i | 0.0714956 | + | 0.0178980i | ||||
\(573\) | −30.9996 | −1.29503 | ||||||||
\(574\) | 2.57984 | − | 7.93994i | 0.107681 | − | 0.331407i | ||||
\(575\) | 26.0119 | − | 18.8987i | 1.08477 | − | 0.788132i | ||||
\(576\) | −1.23883 | − | 0.900059i | −0.0516177 | − | 0.0375025i | ||||
\(577\) | 6.07195 | + | 18.6875i | 0.252779 | + | 0.777973i | 0.994259 | + | 0.106998i | \(0.0341240\pi\) |
−0.741481 | + | 0.670974i | \(0.765876\pi\) | |||||||
\(578\) | −5.43501 | − | 16.7272i | −0.226067 | − | 0.695761i | ||||
\(579\) | 4.18581 | + | 3.04117i | 0.173956 | + | 0.126387i | ||||
\(580\) | −1.49927 | + | 1.08928i | −0.0622538 | + | 0.0452300i | ||||
\(581\) | −3.23606 | + | 9.95957i | −0.134254 | + | 0.413193i | ||||
\(582\) | 30.2901 | 1.25556 | ||||||||
\(583\) | −28.6657 | + | 11.5500i | −1.18721 | + | 0.478354i | ||||
\(584\) | −12.3402 | −0.510641 | ||||||||
\(585\) | −0.111848 | + | 0.344233i | −0.00462434 | + | 0.0142323i | ||||
\(586\) | 19.9706 | − | 14.5095i | 0.824980 | − | 0.599383i | ||||
\(587\) | −32.7802 | − | 23.8162i | −1.35298 | − | 0.983001i | −0.998857 | − | 0.0478041i | \(-0.984778\pi\) |
−0.354128 | − | 0.935197i | \(-0.615222\pi\) | |||||||
\(588\) | −4.16879 | − | 12.8302i | −0.171918 | − | 0.529110i | ||||
\(589\) | 1.79257 | + | 5.51696i | 0.0738615 | + | 0.227322i | ||||
\(590\) | −1.21568 | − | 0.883245i | −0.0500489 | − | 0.0363626i | ||||
\(591\) | 18.7794 | − | 13.6440i | 0.772481 | − | 0.561241i | ||||
\(592\) | 0.734014 | − | 2.25906i | 0.0301678 | − | 0.0928469i | ||||
\(593\) | −11.8720 | −0.487525 | −0.243762 | − | 0.969835i | \(-0.578382\pi\) | ||||
−0.243762 | + | 0.969835i | \(0.578382\pi\) | |||||||
\(594\) | −6.65768 | − | 7.94964i | −0.273168 | − | 0.326178i | ||||
\(595\) | 2.12897 | 0.0872792 | ||||||||
\(596\) | 0.386032 | − | 1.18808i | 0.0158125 | − | 0.0486658i | ||||
\(597\) | 26.3493 | − | 19.1439i | 1.07841 | − | 0.783508i | ||||
\(598\) | 2.87880 | + | 2.09157i | 0.117723 | + | 0.0855307i | ||||
\(599\) | −11.4996 | − | 35.3921i | −0.469861 | − | 1.44608i | −0.852765 | − | 0.522294i | \(-0.825076\pi\) |
0.382905 | − | 0.923788i | \(-0.374924\pi\) | |||||||
\(600\) | 3.15888 | + | 9.72202i | 0.128961 | + | 0.396900i | ||||
\(601\) | 14.0134 | + | 10.1813i | 0.571619 | + | 0.415305i | 0.835693 | − | 0.549197i | \(-0.185066\pi\) |
−0.264074 | + | 0.964502i | \(0.585066\pi\) | |||||||
\(602\) | −6.74698 | + | 4.90197i | −0.274987 | + | 0.199789i | ||||
\(603\) | −0.582226 | + | 1.79191i | −0.0237101 | + | 0.0729721i | ||||
\(604\) | −13.8527 | −0.563659 | ||||||||
\(605\) | 4.84589 | − | 0.671664i | 0.197013 | − | 0.0273070i | ||||
\(606\) | −7.46117 | −0.303089 | ||||||||
\(607\) | 0.291352 | − | 0.896689i | 0.0118256 | − | 0.0363955i | −0.944970 | − | 0.327158i | \(-0.893909\pi\) |
0.956795 | + | 0.290763i | \(0.0939090\pi\) | |||||||
\(608\) | −0.809017 | + | 0.587785i | −0.0328100 | + | 0.0238378i | ||||
\(609\) | 5.84077 | + | 4.24357i | 0.236680 | + | 0.171958i | ||||
\(610\) | −0.655339 | − | 2.01693i | −0.0265339 | − | 0.0816630i | ||||
\(611\) | 1.04079 | + | 3.20321i | 0.0421057 | + | 0.129588i | ||||
\(612\) | 7.28573 | + | 5.29339i | 0.294508 | + | 0.213973i | ||||
\(613\) | 27.5265 | − | 19.9992i | 1.11178 | − | 0.807759i | 0.128841 | − | 0.991665i | \(-0.458874\pi\) |
0.982944 | + | 0.183906i | \(0.0588743\pi\) | |||||||
\(614\) | 3.47728 | − | 10.7020i | 0.140331 | − | 0.431896i | ||||
\(615\) | 9.71048 | 0.391564 | ||||||||
\(616\) | 1.73327 | + | 2.06961i | 0.0698353 | + | 0.0833871i | ||||
\(617\) | −12.4983 | −0.503162 | −0.251581 | − | 0.967836i | \(-0.580950\pi\) | ||||
−0.251581 | + | 0.967836i | \(0.580950\pi\) | |||||||
\(618\) | −0.456592 | + | 1.40525i | −0.0183668 | + | 0.0565273i | ||||
\(619\) | 23.8010 | − | 17.2924i | 0.956642 | − | 0.695041i | 0.00427361 | − | 0.999991i | \(-0.498640\pi\) |
0.952368 | + | 0.304950i | \(0.0986397\pi\) | |||||||
\(620\) | −2.08720 | − | 1.51644i | −0.0838240 | − | 0.0609017i | ||||
\(621\) | −6.46856 | − | 19.9082i | −0.259574 | − | 0.798888i | ||||
\(622\) | −1.05285 | − | 3.24035i | −0.0422156 | − | 0.129926i | ||||
\(623\) | −4.87390 | − | 3.54109i | −0.195269 | − | 0.141871i | ||||
\(624\) | −0.915267 | + | 0.664980i | −0.0366400 | + | 0.0266205i | ||||
\(625\) | 6.82066 | − | 20.9918i | 0.272826 | − | 0.839674i | ||||
\(626\) | −20.6424 | −0.825035 | ||||||||
\(627\) | 6.54845 | − | 2.63852i | 0.261520 | − | 0.105372i | ||||
\(628\) | 17.3097 | 0.690731 | ||||||||
\(629\) | −4.31685 | + | 13.2859i | −0.172124 | + | 0.529744i | ||||
\(630\) | −0.448452 | + | 0.325820i | −0.0178668 | + | 0.0129810i | ||||
\(631\) | −6.27948 | − | 4.56231i | −0.249982 | − | 0.181623i | 0.455737 | − | 0.890115i | \(-0.349376\pi\) |
−0.705719 | + | 0.708492i | \(0.749376\pi\) | |||||||
\(632\) | 1.07228 | + | 3.30013i | 0.0426529 | + | 0.131272i | ||||
\(633\) | −3.69097 | − | 11.3596i | −0.146703 | − | 0.451505i | ||||
\(634\) | −21.1980 | − | 15.4013i | −0.841882 | − | 0.611663i | ||||
\(635\) | 2.07074 | − | 1.50448i | 0.0821747 | − | 0.0597034i | ||||
\(636\) | 6.12951 | − | 18.8647i | 0.243051 | − | 0.748034i | ||||
\(637\) | −3.36820 | −0.133453 | ||||||||
\(638\) | 13.4062 | + | 3.35607i | 0.530758 | + | 0.132868i | ||||
\(639\) | −17.7385 | −0.701724 | ||||||||
\(640\) | 0.137434 | − | 0.422980i | 0.00543257 | − | 0.0167197i | ||||
\(641\) | −15.7958 | + | 11.4763i | −0.623898 | + | 0.453288i | −0.854281 | − | 0.519812i | \(-0.826002\pi\) |
0.230383 | + | 0.973100i | \(0.426002\pi\) | |||||||
\(642\) | 14.8634 | + | 10.7989i | 0.586612 | + | 0.426199i | ||||
\(643\) | −14.9691 | − | 46.0701i | −0.590323 | − | 1.81683i | −0.576753 | − | 0.816919i | \(-0.695681\pi\) |
−0.0135697 | − | 0.999908i | \(-0.504319\pi\) | |||||||
\(644\) | 1.68403 | + | 5.18291i | 0.0663600 | + | 0.204235i | ||||
\(645\) | −7.84765 | − | 5.70165i | −0.309001 | − | 0.224502i | ||||
\(646\) | 4.75796 | − | 3.45686i | 0.187199 | − | 0.136008i | ||||
\(647\) | 9.90054 | − | 30.4707i | 0.389230 | − | 1.19793i | −0.544134 | − | 0.838998i | \(-0.683142\pi\) |
0.933364 | − | 0.358930i | \(-0.116858\pi\) | |||||||
\(648\) | 11.2490 | 0.441903 | ||||||||
\(649\) | 0.771068 | + | 11.1793i | 0.0302671 | + | 0.438827i | ||||
\(650\) | 2.55223 | 0.100107 | ||||||||
\(651\) | −3.10584 | + | 9.55880i | −0.121728 | + | 0.374639i | ||||
\(652\) | 8.06853 | − | 5.86213i | 0.315988 | − | 0.229579i | ||||
\(653\) | 29.7434 | + | 21.6098i | 1.16395 | + | 0.845658i | 0.990272 | − | 0.139145i | \(-0.0444355\pi\) |
0.173676 | + | 0.984803i | \(0.444435\pi\) | |||||||
\(654\) | −5.33053 | − | 16.4057i | −0.208440 | − | 0.641513i | ||||
\(655\) | 0.133353 | + | 0.410418i | 0.00521053 | + | 0.0160363i | ||||
\(656\) | 8.29803 | + | 6.02887i | 0.323984 | + | 0.235388i | ||||
\(657\) | −15.2873 | + | 11.1069i | −0.596416 | + | 0.433322i | ||||
\(658\) | −1.59395 | + | 4.90567i | −0.0621386 | + | 0.191243i | ||||
\(659\) | −1.92517 | −0.0749940 | −0.0374970 | − | 0.999297i | \(-0.511938\pi\) | ||||
−0.0374970 | + | 0.999297i | \(0.511938\pi\) | |||||||
\(660\) | −1.66644 | + | 2.66123i | −0.0648659 | + | 0.103588i | ||||
\(661\) | −0.375942 | −0.0146225 | −0.00731123 | − | 0.999973i | \(-0.502327\pi\) | ||||
−0.00731123 | + | 0.999973i | \(0.502327\pi\) | |||||||
\(662\) | −7.04037 | + | 21.6680i | −0.273632 | + | 0.842152i | ||||
\(663\) | 5.38283 | − | 3.91086i | 0.209052 | − | 0.151885i | ||||
\(664\) | −10.4088 | − | 7.56240i | −0.403938 | − | 0.293478i | ||||
\(665\) | 0.111864 | + | 0.344281i | 0.00433788 | + | 0.0133506i | ||||
\(666\) | −1.12398 | − | 3.45924i | −0.0435531 | − | 0.134043i | ||||
\(667\) | 22.5705 | + | 16.3984i | 0.873932 | + | 0.634949i | ||||
\(668\) | −18.5250 | + | 13.4592i | −0.716754 | + | 0.520752i | ||||
\(669\) | −15.7781 | + | 48.5599i | −0.610016 | + | 1.87744i | ||||
\(670\) | −0.547230 | −0.0211413 | ||||||||
\(671\) | −8.39337 | + | 13.4039i | −0.324022 | + | 0.517450i | ||||
\(672\) | −1.73262 | −0.0668373 | ||||||||
\(673\) | −4.19012 | + | 12.8959i | −0.161517 | + | 0.497099i | −0.998763 | − | 0.0497281i | \(-0.984165\pi\) |
0.837245 | + | 0.546827i | \(0.184165\pi\) | |||||||
\(674\) | −13.4952 | + | 9.80482i | −0.519815 | + | 0.377668i | ||||
\(675\) | −12.1464 | − | 8.82491i | −0.467517 | − | 0.339671i | ||||
\(676\) | −3.92994 | − | 12.0951i | −0.151151 | − | 0.465196i | ||||
\(677\) | 14.2656 | + | 43.9051i | 0.548273 | + | 1.68741i | 0.713077 | + | 0.701085i | \(0.247301\pi\) |
−0.164804 | + | 0.986326i | \(0.552699\pi\) | |||||||
\(678\) | 8.02963 | + | 5.83387i | 0.308376 | + | 0.224048i | ||||
\(679\) | 9.37003 | − | 6.80773i | 0.359589 | − | 0.261257i | ||||
\(680\) | −0.808274 | + | 2.48761i | −0.0309959 | + | 0.0953955i | ||||
\(681\) | −7.50937 | −0.287759 | ||||||||
\(682\) | 1.32384 | + | 19.1937i | 0.0506926 | + | 0.734966i | ||||
\(683\) | 13.2284 | 0.506170 | 0.253085 | − | 0.967444i | \(-0.418555\pi\) | ||||
0.253085 | + | 0.967444i | \(0.418555\pi\) | |||||||
\(684\) | −0.473189 | + | 1.45633i | −0.0180928 | + | 0.0556840i | ||||
\(685\) | 0.772444 | − | 0.561213i | 0.0295136 | − | 0.0214429i | ||||
\(686\) | −8.78264 | − | 6.38096i | −0.335323 | − | 0.243626i | ||||
\(687\) | −12.8742 | − | 39.6229i | −0.491183 | − | 1.51171i | ||||
\(688\) | −3.16622 | − | 9.74463i | −0.120711 | − | 0.371510i | ||||
\(689\) | −4.00656 | − | 2.91093i | −0.152638 | − | 0.110898i | ||||
\(690\) | −5.12808 | + | 3.72577i | −0.195223 | + | 0.141838i | ||||
\(691\) | 9.53953 | − | 29.3597i | 0.362901 | − | 1.11689i | −0.588384 | − | 0.808581i | \(-0.700236\pi\) |
0.951285 | − | 0.308312i | \(-0.0997642\pi\) | |||||||
\(692\) | −7.74923 | −0.294581 | ||||||||
\(693\) | 4.00999 | + | 1.00385i | 0.152327 | + | 0.0381330i | ||||
\(694\) | −24.8615 | −0.943728 | ||||||||
\(695\) | 1.34523 | − | 4.14019i | 0.0510275 | − | 0.157046i | ||||
\(696\) | −7.17591 | + | 5.21360i | −0.272002 | + | 0.197621i | ||||
\(697\) | −48.8021 | − | 35.4568i | −1.84851 | − | 1.34302i | ||||
\(698\) | −6.04386 | − | 18.6011i | −0.228763 | − | 0.704061i | ||||
\(699\) | 12.6310 | + | 38.8741i | 0.477747 | + | 1.47036i | ||||
\(700\) | 3.16221 | + | 2.29748i | 0.119520 | + | 0.0868367i | ||||
\(701\) | 39.3647 | − | 28.6001i | 1.48678 | − | 1.08021i | 0.511493 | − | 0.859287i | \(-0.329093\pi\) |
0.975291 | − | 0.220925i | \(-0.0709074\pi\) | |||||||
\(702\) | 0.513468 | − | 1.58029i | 0.0193796 | − | 0.0596443i | ||||
\(703\) | −2.37532 | −0.0895868 | ||||||||
\(704\) | −3.07630 | + | 1.23951i | −0.115942 | + | 0.0467158i | ||||
\(705\) | −5.99960 | −0.225958 | ||||||||
\(706\) | 5.30869 | − | 16.3385i | 0.199795 | − | 0.614906i | ||||
\(707\) | −2.30806 | + | 1.67691i | −0.0868036 | + | 0.0630665i | ||||
\(708\) | −5.81858 | − | 4.22745i | −0.218676 | − | 0.158877i | ||||
\(709\) | −1.31869 | − | 4.05852i | −0.0495246 | − | 0.152421i | 0.923236 | − | 0.384234i | \(-0.125534\pi\) |
−0.972760 | + | 0.231813i | \(0.925534\pi\) | |||||||
\(710\) | −1.59206 | − | 4.89986i | −0.0597490 | − | 0.183888i | ||||
\(711\) | 4.29867 | + | 3.12317i | 0.161213 | + | 0.117128i | ||||
\(712\) | 5.98802 | − | 4.35055i | 0.224410 | − | 0.163044i | ||||
\(713\) | −12.0019 | + | 36.9381i | −0.449475 | + | 1.38334i | ||||
\(714\) | 10.1898 | 0.381344 | ||||||||
\(715\) | 0.503344 | + | 0.601020i | 0.0188240 | + | 0.0224769i | ||||
\(716\) | 13.1788 | 0.492516 | ||||||||
\(717\) | −12.7480 | + | 39.2344i | −0.476084 | + | 1.46524i | ||||
\(718\) | 15.3867 | − | 11.1791i | 0.574227 | − | 0.417200i | ||||
\(719\) | −24.7032 | − | 17.9479i | −0.921275 | − | 0.669345i | 0.0225663 | − | 0.999745i | \(-0.492816\pi\) |
−0.943841 | + | 0.330400i | \(0.892816\pi\) | |||||||
\(720\) | −0.210449 | − | 0.647697i | −0.00784299 | − | 0.0241382i | ||||
\(721\) | 0.174587 | + | 0.537323i | 0.00650196 | + | 0.0200110i | ||||
\(722\) | 0.809017 | + | 0.587785i | 0.0301085 | + | 0.0218751i | ||||
\(723\) | −8.97172 | + | 6.51833i | −0.333662 | + | 0.242419i | ||||
\(724\) | −2.83113 | + | 8.71331i | −0.105218 | + | 0.323828i | ||||
\(725\) | 20.0101 | 0.743157 | ||||||||
\(726\) | 23.1937 | − | 3.21476i | 0.860800 | − | 0.119311i | ||||
\(727\) | −3.87417 | −0.143685 | −0.0718425 | − | 0.997416i | \(-0.522888\pi\) | ||||
−0.0718425 | + | 0.997416i | \(0.522888\pi\) | |||||||
\(728\) | −0.133677 | + | 0.411414i | −0.00495439 | + | 0.0152480i | ||||
\(729\) | −2.21695 | + | 1.61071i | −0.0821091 | + | 0.0596558i | ||||
\(730\) | −4.44010 | − | 3.22592i | −0.164335 | − | 0.119397i | ||||
\(731\) | 18.6211 | + | 57.3097i | 0.688725 | + | 2.11968i | ||||
\(732\) | −3.13663 | − | 9.65356i | −0.115933 | − | 0.356806i | ||||
\(733\) | −18.6740 | − | 13.5675i | −0.689740 | − | 0.501125i | 0.186835 | − | 0.982391i | \(-0.440177\pi\) |
−0.876575 | + | 0.481266i | \(0.840177\pi\) | |||||||
\(734\) | 3.39444 | − | 2.46621i | 0.125291 | − | 0.0910294i | ||||
\(735\) | 1.85406 | − | 5.70621i | 0.0683880 | − | 0.210477i | ||||
\(736\) | −6.69536 | −0.246794 | ||||||||
\(737\) | 2.62016 | + | 3.12862i | 0.0965150 | + | 0.115244i | ||||
\(738\) | 15.7062 | 0.578152 | ||||||||
\(739\) | −9.21373 | + | 28.3570i | −0.338933 | + | 1.04313i | 0.625820 | + | 0.779968i | \(0.284765\pi\) |
−0.964752 | + | 0.263160i | \(0.915235\pi\) | |||||||
\(740\) | 0.854658 | − | 0.620946i | 0.0314179 | − | 0.0228264i | ||||
\(741\) | 0.915267 | + | 0.664980i | 0.0336232 | + | 0.0244287i | ||||
\(742\) | −2.34374 | − | 7.21329i | −0.0860413 | − | 0.264808i | ||||
\(743\) | 0.884905 | + | 2.72346i | 0.0324640 | + | 0.0999140i | 0.965976 | − | 0.258633i | \(-0.0832722\pi\) |
−0.933512 | + | 0.358547i | \(0.883272\pi\) | |||||||
\(744\) | −9.98991 | − | 7.25809i | −0.366248 | − | 0.266095i | ||||
\(745\) | 0.449481 | − | 0.326567i | 0.0164677 | − | 0.0119645i | ||||
\(746\) | 9.44828 | − | 29.0788i | 0.345926 | − | 1.06465i | ||||
\(747\) | −19.7012 | −0.720831 | ||||||||
\(748\) | 18.0922 | − | 7.28975i | 0.661517 | − | 0.266540i | ||||
\(749\) | 7.02496 | 0.256687 | ||||||||
\(750\) | −2.86767 | + | 8.82578i | −0.104712 | + | 0.322272i | ||||
\(751\) | 39.1192 | − | 28.4218i | 1.42748 | − | 1.03713i | 0.437002 | − | 0.899460i | \(-0.356040\pi\) |
0.990479 | − | 0.137665i | \(-0.0439598\pi\) | |||||||
\(752\) | −5.12692 | − | 3.72493i | −0.186960 | − | 0.135834i | ||||
\(753\) | 8.94561 | + | 27.5318i | 0.325996 | + | 1.00331i | ||||
\(754\) | 0.684339 | + | 2.10618i | 0.0249222 | + | 0.0767026i | ||||
\(755\) | −4.98432 | − | 3.62132i | −0.181398 | − | 0.131793i | ||||
\(756\) | 2.05874 | − | 1.49576i | 0.0748758 | − | 0.0544004i | ||||
\(757\) | 7.05841 | − | 21.7236i | 0.256542 | − | 0.789556i | −0.736980 | − | 0.675915i | \(-0.763749\pi\) |
0.993522 | − | 0.113641i | \(-0.0362514\pi\) | |||||||
\(758\) | −27.9152 | −1.01393 | ||||||||
\(759\) | 45.8545 | + | 11.4791i | 1.66441 | + | 0.416663i | ||||
\(760\) | −0.444747 | −0.0161327 | ||||||||
\(761\) | 7.31760 | − | 22.5213i | 0.265263 | − | 0.816395i | −0.726370 | − | 0.687304i | \(-0.758794\pi\) |
0.991633 | − | 0.129091i | \(-0.0412059\pi\) | |||||||
\(762\) | 9.91110 | − | 7.20084i | 0.359041 | − | 0.260859i | ||||
\(763\) | −5.33616 | − | 3.87695i | −0.193182 | − | 0.140355i | ||||
\(764\) | −4.50017 | − | 13.8501i | −0.162810 | − | 0.501079i | ||||
\(765\) | 1.23769 | + | 3.80921i | 0.0447487 | + | 0.137722i | ||||
\(766\) | −10.7869 | − | 7.83717i | −0.389748 | − | 0.283168i | ||||
\(767\) | −1.45274 | + | 1.05548i | −0.0524553 | + | 0.0381110i | ||||
\(768\) | 0.657798 | − | 2.02449i | 0.0237362 | − | 0.0730526i | ||||
\(769\) | −49.9760 | −1.80218 | −0.901090 | − | 0.433633i | \(-0.857231\pi\) | ||||
−0.901090 | + | 0.433633i | \(0.857231\pi\) | |||||||
\(770\) | 0.0826132 | + | 1.19777i | 0.00297717 | + | 0.0431645i | ||||
\(771\) | −23.3152 | −0.839678 | ||||||||
\(772\) | −0.751094 | + | 2.31163i | −0.0270325 | + | 0.0831974i | ||||
\(773\) | 27.0838 | − | 19.6775i | 0.974135 | − | 0.707751i | 0.0177449 | − | 0.999843i | \(-0.494351\pi\) |
0.956390 | + | 0.292092i | \(0.0943513\pi\) | |||||||
\(774\) | −12.6931 | − | 9.22210i | −0.456245 | − | 0.331482i | ||||
\(775\) | 8.60828 | + | 26.4936i | 0.309218 | + | 0.951677i | ||||
\(776\) | 4.39716 | + | 13.5331i | 0.157849 | + | 0.485809i | ||||
\(777\) | −3.32953 | − | 2.41904i | −0.119446 | − | 0.0867827i | ||||
\(778\) | −4.85839 | + | 3.52983i | −0.174182 | + | 0.126551i | ||||
\(779\) | 3.16957 | − | 9.75492i | 0.113562 | − | 0.349506i | ||||
\(780\) | −0.503157 | −0.0180159 | ||||||||
\(781\) | −20.3906 | + | 32.5629i | −0.729632 | + | 1.16519i | ||||
\(782\) | 39.3765 | 1.40810 | ||||||||
\(783\) | 4.02571 | − | 12.3899i | 0.143867 | − | 0.442778i | ||||
\(784\) | 5.12714 | − | 3.72509i | 0.183112 | − | 0.133039i | ||||
\(785\) | 6.22815 | + | 4.52502i | 0.222292 | + | 0.161505i | ||||
\(786\) | 0.638262 | + | 1.96437i | 0.0227661 | + | 0.0700667i | ||||
\(787\) | 5.18358 | + | 15.9534i | 0.184775 | + | 0.568678i | 0.999944 | − | 0.0105440i | \(-0.00335633\pi\) |
−0.815170 | + | 0.579222i | \(0.803356\pi\) | |||||||
\(788\) | 8.82209 | + | 6.40963i | 0.314274 | + | 0.228334i | ||||
\(789\) | −47.9791 | + | 34.8588i | −1.70810 | + | 1.24101i | ||||
\(790\) | −0.476892 | + | 1.46772i | −0.0169670 | + | 0.0522192i | ||||
\(791\) | 3.79508 | 0.134938 | ||||||||
\(792\) | −2.69537 | + | 4.30439i | −0.0957757 | + | 0.152950i | ||||
\(793\) | −2.53426 | −0.0899942 | ||||||||
\(794\) | 8.56666 | − | 26.3655i | 0.304019 | − | 0.935676i | ||||
\(795\) | 7.13698 | − | 5.18532i | 0.253123 | − | 0.183904i | ||||
\(796\) | 12.3783 | + | 8.99333i | 0.438736 | + | 0.318760i | ||||
\(797\) | 6.82448 | + | 21.0036i | 0.241736 | + | 0.743985i | 0.996156 | + | 0.0875942i | \(0.0279179\pi\) |
−0.754421 | + | 0.656391i | \(0.772082\pi\) | |||||||
\(798\) | 0.535409 | + | 1.64782i | 0.0189533 | + | 0.0583322i | ||||
\(799\) | 30.1522 | + | 21.9069i | 1.06671 | + | 0.775010i | ||||
\(800\) | −3.88506 | + | 2.82266i | −0.137358 | + | 0.0997962i | ||||
\(801\) | 3.50236 | − | 10.7791i | 0.123750 | − | 0.380862i | ||||
\(802\) | −29.1632 | −1.02979 | ||||||||
\(803\) | 2.81621 | + | 40.8308i | 0.0993819 | + | 1.44089i | ||||
\(804\) | −2.61919 | −0.0923716 | ||||||||
\(805\) | −0.748967 | + | 2.30508i | −0.0263976 | + | 0.0812435i | ||||
\(806\) | −2.49420 | + | 1.81214i | −0.0878545 | + | 0.0638300i | ||||
\(807\) | −22.2485 | − | 16.1645i | −0.783185 | − | 0.569017i | ||||
\(808\) | −1.08313 | − | 3.33352i | −0.0381042 | − | 0.117273i | ||||
\(809\) | 9.00008 | + | 27.6994i | 0.316426 | + | 0.973859i | 0.975164 | + | 0.221486i | \(0.0710907\pi\) |
−0.658738 | + | 0.752373i | \(0.728909\pi\) | |||||||
\(810\) | 4.04749 | + | 2.94067i | 0.142214 | + | 0.103325i | ||||
\(811\) | −24.5497 | + | 17.8364i | −0.862056 | + | 0.626320i | −0.928444 | − | 0.371473i | \(-0.878853\pi\) |
0.0663874 | + | 0.997794i | \(0.478853\pi\) | |||||||
\(812\) | −1.04806 | + | 3.22559i | −0.0367796 | + | 0.113196i | ||||
\(813\) | 17.2551 | 0.605164 | ||||||||
\(814\) | −7.64222 | − | 1.91313i | −0.267860 | − | 0.0670551i | ||||
\(815\) | 4.43557 | 0.155371 | ||||||||
\(816\) | −3.86862 | + | 11.9064i | −0.135429 | + | 0.416806i | ||||
\(817\) | −8.28927 | + | 6.02251i | −0.290005 | + | 0.210701i | ||||
\(818\) | 9.08735 | + | 6.60235i | 0.317732 | + | 0.230846i | ||||
\(819\) | 0.204695 | + | 0.629988i | 0.00715264 | + | 0.0220136i | ||||
\(820\) | 1.40966 | + | 4.33847i | 0.0492273 | + | 0.151506i | ||||
\(821\) | −5.72340 | − | 4.15829i | −0.199748 | − | 0.145125i | 0.483415 | − | 0.875391i | \(-0.339396\pi\) |
−0.683163 | + | 0.730266i | \(0.739396\pi\) | |||||||
\(822\) | 3.69712 | − | 2.68612i | 0.128952 | − | 0.0936891i | ||||
\(823\) | −9.21619 | + | 28.3645i | −0.321256 | + | 0.988725i | 0.651846 | + | 0.758351i | \(0.273995\pi\) |
−0.973102 | + | 0.230374i | \(0.926005\pi\) | |||||||
\(824\) | −0.694123 | −0.0241809 | ||||||||
\(825\) | 31.4470 | − | 12.6707i | 1.09484 | − | 0.441137i | ||||
\(826\) | −2.75006 | −0.0956869 | ||||||||
\(827\) | 12.5743 | − | 38.6999i | 0.437253 | − | 1.34573i | −0.453507 | − | 0.891253i | \(-0.649827\pi\) |
0.890760 | − | 0.454473i | \(-0.150173\pi\) | |||||||
\(828\) | −8.29438 | + | 6.02622i | −0.288250 | + | 0.209426i | ||||
\(829\) | −11.3922 | − | 8.27694i | −0.395668 | − | 0.287470i | 0.372106 | − | 0.928190i | \(-0.378636\pi\) |
−0.767774 | + | 0.640720i | \(0.778636\pi\) | |||||||
\(830\) | −1.76822 | − | 5.44203i | −0.0613759 | − | 0.188895i | ||||
\(831\) | 15.4343 | + | 47.5018i | 0.535408 | + | 1.64782i | ||||
\(832\) | −0.429970 | − | 0.312391i | −0.0149065 | − | 0.0108302i | ||||
\(833\) | −30.1536 | + | 21.9078i | −1.04476 | + | 0.759062i | ||||
\(834\) | 6.43863 | − | 19.8161i | 0.222951 | − | 0.686174i | ||||
\(835\) | −10.1839 | −0.352428 | ||||||||
\(836\) | 2.12947 | + | 2.54271i | 0.0736493 | + | 0.0879413i | ||||
\(837\) | 18.1361 | 0.626877 | ||||||||
\(838\) | 6.24254 | − | 19.2126i | 0.215645 | − | 0.663687i | ||||
\(839\) | −40.0321 | + | 29.0850i | −1.38206 | + | 1.00413i | −0.385379 | + | 0.922759i | \(0.625929\pi\) |
−0.996684 | + | 0.0813688i | \(0.974071\pi\) | |||||||
\(840\) | −0.623410 | − | 0.452934i | −0.0215097 | − | 0.0156277i | ||||
\(841\) | −3.59611 | − | 11.0677i | −0.124004 | − | 0.381645i | ||||
\(842\) | 3.92674 | + | 12.0853i | 0.135325 | + | 0.416486i | ||||
\(843\) | 24.7479 | + | 17.9804i | 0.852362 | + | 0.619277i | ||||
\(844\) | 4.53947 | − | 3.29812i | 0.156255 | − | 0.113526i | ||||
\(845\) | 1.74783 | − | 5.37926i | 0.0601271 | − | 0.185052i | ||||
\(846\) | −9.70401 | −0.333631 | ||||||||
\(847\) | 6.45231 | − | 6.20728i | 0.221704 | − | 0.213285i | ||||
\(848\) | 9.31823 | 0.319989 | ||||||||
\(849\) | −7.68893 | + | 23.6641i | −0.263883 | + | 0.812150i | ||||
\(850\) | 22.8487 | − | 16.6005i | 0.783703 | − | 0.569394i | ||||
\(851\) | −12.8663 | − | 9.34791i | −0.441051 | − | 0.320442i | ||||
\(852\) | −7.62003 | − | 23.4520i | −0.261058 | − | 0.803453i | ||||
\(853\) | 7.31294 | + | 22.5069i | 0.250390 | + | 0.770622i | 0.994703 | + | 0.102791i | \(0.0327773\pi\) |
−0.744313 | + | 0.667831i | \(0.767223\pi\) | |||||||
\(854\) | −3.13994 | − | 2.28130i | −0.107447 | − | 0.0780645i | ||||
\(855\) | −0.550964 | + | 0.400299i | −0.0188426 | + | 0.0136899i | ||||
\(856\) | −2.66706 | + | 8.20838i | −0.0911583 | + | 0.280557i | ||||
\(857\) | −17.6097 | −0.601535 | −0.300768 | − | 0.953697i | \(-0.597243\pi\) | ||||
−0.300768 | + | 0.953697i | \(0.597243\pi\) | |||||||
\(858\) | 2.40914 | + | 2.87664i | 0.0822467 | + | 0.0982070i | ||||
\(859\) | 35.6398 | 1.21602 | 0.608008 | − | 0.793931i | \(-0.291969\pi\) | ||||
0.608008 | + | 0.793931i | \(0.291969\pi\) | |||||||
\(860\) | 1.40817 | − | 4.33389i | 0.0480181 | − | 0.147785i | ||||
\(861\) | 14.3773 | − | 10.4457i | 0.489978 | − | 0.355990i | ||||
\(862\) | −25.5490 | − | 18.5624i | −0.870201 | − | 0.632238i | ||||
\(863\) | 9.94672 | + | 30.6128i | 0.338590 | + | 1.04207i | 0.964926 | + | 0.262520i | \(0.0845537\pi\) |
−0.626336 | + | 0.779553i | \(0.715446\pi\) | |||||||
\(864\) | 0.966126 | + | 2.97343i | 0.0328683 | + | 0.101158i | ||||
\(865\) | −2.78823 | − | 2.02577i | −0.0948028 | − | 0.0688782i | ||||
\(866\) | 17.1813 | − | 12.4830i | 0.583845 | − | 0.424188i | ||||
\(867\) | 11.5694 | − | 35.6069i | 0.392917 | − | 1.20927i | ||||
\(868\) | −4.72157 | −0.160261 | ||||||||
\(869\) | 10.6746 | − | 4.30104i | 0.362112 | − | 0.145903i | ||||
\(870\) | −3.94487 | −0.133743 | ||||||||
\(871\) | −0.202078 | + | 0.621932i | −0.00684715 | + | 0.0210734i | ||||
\(872\) | 6.55595 | − | 4.76318i | 0.222013 | − | 0.161302i | ||||
\(873\) | 17.6279 | + | 12.8074i | 0.596614 | + | 0.433465i | ||||
\(874\) | 2.06898 | + | 6.36767i | 0.0699843 | + | 0.215390i | ||||
\(875\) | 1.09651 | + | 3.37471i | 0.0370688 | + | 0.114086i | ||||
\(876\) | −21.2515 | − | 15.4401i | −0.718022 | − | 0.521674i | ||||
\(877\) | −23.5808 | + | 17.1324i | −0.796265 | + | 0.578521i | −0.909816 | − | 0.415012i | \(-0.863778\pi\) |
0.113551 | + | 0.993532i | \(0.463778\pi\) | |||||||
\(878\) | −7.16670 | + | 22.0568i | −0.241864 | + | 0.744382i | ||||
\(879\) | 52.5466 | 1.77235 | ||||||||
\(880\) | −1.43090 | − | 0.358208i | −0.0482358 | − | 0.0120752i | ||||
\(881\) | −17.4611 | −0.588279 | −0.294139 | − | 0.955763i | \(-0.595033\pi\) | ||||
−0.294139 | + | 0.955763i | \(0.595033\pi\) | |||||||
\(882\) | 2.99884 | − | 9.22947i | 0.100976 | − | 0.310772i | ||||
\(883\) | −8.27556 | + | 6.01255i | −0.278495 | + | 0.202338i | −0.718261 | − | 0.695774i | \(-0.755061\pi\) |
0.439766 | + | 0.898113i | \(0.355061\pi\) | |||||||
\(884\) | 2.52872 | + | 1.83722i | 0.0850501 | + | 0.0617925i | ||||
\(885\) | −0.988451 | − | 3.04214i | −0.0332264 | − | 0.102260i | ||||
\(886\) | 5.14368 | + | 15.8306i | 0.172805 | + | 0.531841i | ||||
\(887\) | 23.9251 | + | 17.3826i | 0.803326 | + | 0.583651i | 0.911888 | − | 0.410439i | \(-0.134625\pi\) |
−0.108562 | + | 0.994090i | \(0.534625\pi\) | |||||||
\(888\) | 4.09062 | − | 2.97201i | 0.137272 | − | 0.0997342i | ||||
\(889\) | 1.44754 | − | 4.45506i | 0.0485488 | − | 0.149418i | ||||
\(890\) | 3.29184 | 0.110343 | ||||||||
\(891\) | −2.56719 | − | 37.2204i | −0.0860040 | − | 1.24693i | ||||
\(892\) | −23.9862 | −0.803118 | ||||||||
\(893\) | −1.95831 | + | 6.02706i | −0.0655323 | + | 0.201688i | ||||
\(894\) | 2.15134 | − | 1.56304i | 0.0719515 | − | 0.0522758i | ||||
\(895\) | 4.74185 | + | 3.44515i | 0.158502 | + | 0.115159i | ||||
\(896\) | −0.251522 | − | 0.774104i | −0.00840275 | − | 0.0258610i | ||||
\(897\) | 2.34070 | + | 7.20395i | 0.0781538 | + | 0.240533i | ||||
\(898\) | −1.80698 | − | 1.31285i | −0.0602996 | − | 0.0438102i | ||||
\(899\) | −19.5551 | + | 14.2076i | −0.652200 | + | 0.473851i | ||||
\(900\) | −2.27235 | + | 6.99357i | −0.0757450 | + | 0.233119i | ||||
\(901\) | −54.8020 | −1.82572 | ||||||||
\(902\) | 18.0544 | − | 28.8321i | 0.601145 | − | 0.960004i | ||||
\(903\) | −17.7526 | −0.590770 | ||||||||
\(904\) | −1.44082 | + | 4.43439i | −0.0479210 | + | 0.147486i | ||||
\(905\) | −3.29646 | + | 2.39502i | −0.109578 | + | 0.0796131i | ||||
\(906\) | −23.8563 | − | 17.3326i | −0.792572 | − | 0.575837i | ||||
\(907\) | −3.64126 | − | 11.2066i | −0.120906 | − | 0.372110i | 0.872227 | − | 0.489101i | \(-0.162675\pi\) |
−0.993133 | + | 0.116991i | \(0.962675\pi\) | |||||||
\(908\) | −1.09012 | − | 3.35505i | −0.0361770 | − | 0.111341i | ||||
\(909\) | −4.34217 | − | 3.15477i | −0.144021 | − | 0.104637i | ||||
\(910\) | −0.155648 | + | 0.113085i | −0.00515969 | + | 0.00374873i | ||||
\(911\) | −15.0388 | + | 46.2847i | −0.498258 | + | 1.53348i | 0.313560 | + | 0.949568i | \(0.398478\pi\) |
−0.811818 | + | 0.583911i | \(0.801522\pi\) | |||||||
\(912\) | −2.12868 | −0.0704876 | ||||||||
\(913\) | −22.6468 | + | 36.1660i | −0.749499 | + | 1.19692i | ||||
\(914\) | −12.4265 | −0.411032 | ||||||||
\(915\) | 1.39501 | − | 4.29339i | 0.0461175 | − | 0.141935i | ||||
\(916\) | 15.8339 | − | 11.5040i | 0.523166 | − | 0.380102i | ||||
\(917\) | 0.638936 | + | 0.464214i | 0.0210995 | + | 0.0153297i | ||||
\(918\) | −5.68194 | − | 17.4872i | −0.187532 | − | 0.577164i | ||||
\(919\) | −13.8401 | − | 42.5953i | −0.456542 | − | 1.40509i | −0.869316 | − | 0.494257i | \(-0.835440\pi\) |
0.412774 | − | 0.910833i | \(-0.364560\pi\) | |||||||
\(920\) | −2.40904 | − | 1.75027i | −0.0794238 | − | 0.0577048i | ||||
\(921\) | 19.3787 | − | 14.0794i | 0.638550 | − | 0.463933i | ||||
\(922\) | −9.83131 | + | 30.2577i | −0.323777 | + | 0.996483i | ||||
\(923\) | −6.15665 | −0.202648 | ||||||||
\(924\) | 0.395409 | + | 5.73283i | 0.0130080 | + | 0.188596i | ||||
\(925\) | −11.4068 | −0.375052 | ||||||||
\(926\) | 0.0223405 | − | 0.0687569i | 0.000734153 | − | 0.00225949i | ||||
\(927\) | −0.859897 | + | 0.624752i | −0.0282427 | + | 0.0205195i | ||||
\(928\) | −3.37106 | − | 2.44922i | −0.110661 | − | 0.0803996i | ||||
\(929\) | 12.6548 | + | 38.9475i | 0.415191 | + | 1.27783i | 0.912080 | + | 0.410012i | \(0.134476\pi\) |
−0.496889 | + | 0.867814i | \(0.665524\pi\) | |||||||
\(930\) | −1.69707 | − | 5.22304i | −0.0556490 | − | 0.171270i | ||||
\(931\) | −5.12714 | − | 3.72509i | −0.168035 | − | 0.122085i | ||||
\(932\) | −15.5347 | + | 11.2866i | −0.508855 | + | 0.369705i | ||||
\(933\) | 2.24119 | − | 6.89767i | 0.0733732 | − | 0.225819i | ||||
\(934\) | 33.8105 | 1.10631 | ||||||||
\(935\) | 8.41538 | + | 2.10668i | 0.275212 | + | 0.0688958i | ||||
\(936\) | −0.813828 | −0.0266008 | ||||||||
\(937\) | 1.74918 | − | 5.38343i | 0.0571433 | − | 0.175869i | −0.918411 | − | 0.395628i | \(-0.870527\pi\) |
0.975554 | + | 0.219759i | \(0.0705270\pi\) | |||||||
\(938\) | −0.810228 | + | 0.588665i | −0.0264549 | + | 0.0192206i | ||||
\(939\) | −35.5490 | − | 25.8279i | −1.16010 | − | 0.842860i | ||||
\(940\) | −0.870952 | − | 2.68052i | −0.0284073 | − | 0.0874288i | ||||
\(941\) | −4.46157 | − | 13.7313i | −0.145443 | − | 0.447628i | 0.851625 | − | 0.524152i | \(-0.175618\pi\) |
−0.997068 | + | 0.0765243i | \(0.975618\pi\) | |||||||
\(942\) | 29.8096 | + | 21.6579i | 0.971249 | + | 0.705654i | ||||
\(943\) | 55.5583 | − | 40.3655i | 1.80923 | − | 1.31448i | ||||
\(944\) | 1.04408 | − | 3.21333i | 0.0339818 | − | 0.104585i | ||||
\(945\) | 1.13177 | 0.0368164 | ||||||||
\(946\) | −31.5201 | + | 12.7001i | −1.02481 | + | 0.412917i | ||||
\(947\) | 6.99025 | 0.227153 | 0.113576 | − | 0.993529i | \(-0.463769\pi\) | ||||
0.113576 | + | 0.993529i | \(0.463769\pi\) | |||||||
\(948\) | −2.28253 | + | 7.02491i | −0.0741332 | + | 0.228158i | ||||
\(949\) | −5.30591 | + | 3.85497i | −0.172237 | + | 0.125138i | ||||
\(950\) | 3.88506 | + | 2.82266i | 0.126048 | + | 0.0915793i | ||||
\(951\) | −17.2358 | − | 53.0462i | −0.558908 | − | 1.72014i | ||||
\(952\) | 1.47924 | + | 4.55263i | 0.0479424 | + | 0.147552i | ||||
\(953\) | −13.4794 | − | 9.79336i | −0.436641 | − | 0.317238i | 0.347658 | − | 0.937621i | \(-0.386977\pi\) |
−0.784299 | + | 0.620383i | \(0.786977\pi\) | |||||||
\(954\) | 11.5437 | − | 8.38696i | 0.373740 | − | 0.271538i | ||||
\(955\) | 2.00144 | − | 6.15979i | 0.0647650 | − | 0.199326i | ||||
\(956\) | −19.3799 | −0.626790 | ||||||||
\(957\) | 18.8882 | + | 22.5536i | 0.610570 | + | 0.729053i | ||||
\(958\) | 7.68378 | 0.248252 | ||||||||
\(959\) | 0.539973 | − | 1.66187i | 0.0174366 | − | 0.0536644i | ||||
\(960\) | 0.765915 | − | 0.556470i | 0.0247198 | − | 0.0179600i | ||||
\(961\) | −2.14404 | − | 1.55774i | −0.0691626 | − | 0.0502496i | ||||
\(962\) | −0.390107 | − | 1.20063i | −0.0125776 | − | 0.0387098i | ||||
\(963\) | 4.08400 | + | 12.5693i | 0.131605 | + | 0.405039i | ||||
\(964\) | −4.21469 | − | 3.06215i | −0.135746 | − | 0.0986252i | ||||
\(965\) | −0.874546 | + | 0.635395i | −0.0281526 | + | 0.0204541i | ||||
\(966\) | −3.58476 | + | 11.0327i | −0.115338 | + | 0.354973i | ||||
\(967\) | 8.50933 | 0.273642 | 0.136821 | − | 0.990596i | \(-0.456312\pi\) | ||||
0.136821 | + | 0.990596i | \(0.456312\pi\) | |||||||
\(968\) | 4.80330 | + | 9.89587i | 0.154384 | + | 0.318065i | ||||
\(969\) | 12.5191 | 0.402172 | ||||||||
\(970\) | −1.95563 | + | 6.01880i | −0.0627914 | + | 0.193252i | ||||
\(971\) | 15.1071 | − | 10.9759i | 0.484809 | − | 0.352234i | −0.318376 | − | 0.947965i | \(-0.603137\pi\) |
0.803185 | + | 0.595730i | \(0.203137\pi\) | |||||||
\(972\) | 11.7843 | + | 8.56180i | 0.377982 | + | 0.274620i | ||||
\(973\) | −2.46193 | − | 7.57705i | −0.0789260 | − | 0.242909i | ||||
\(974\) | 9.38432 | + | 28.8820i | 0.300693 | + | 0.925438i | ||||
\(975\) | 4.39530 | + | 3.19337i | 0.140762 | + | 0.102270i | ||||
\(976\) | 3.85770 | − | 2.80278i | 0.123482 | − | 0.0897149i | ||||
\(977\) | −0.0938749 | + | 0.288917i | −0.00300333 | + | 0.00924329i | −0.952547 | − | 0.304392i | \(-0.901547\pi\) |
0.949544 | + | 0.313635i | \(0.101547\pi\) | |||||||
\(978\) | 21.2298 | 0.678856 | ||||||||
\(979\) | −15.7615 | − | 18.8201i | −0.503739 | − | 0.601492i | ||||
\(980\) | 2.81858 | 0.0900364 | ||||||||
\(981\) | 3.83454 | − | 11.8015i | 0.122427 | − | 0.376793i | ||||
\(982\) | 8.18301 | − | 5.94531i | 0.261130 | − | 0.189722i | ||||
\(983\) | −37.1995 | − | 27.0270i | −1.18648 | − | 0.862028i | −0.193592 | − | 0.981082i | \(-0.562014\pi\) |
−0.992888 | + | 0.119054i | \(0.962014\pi\) | |||||||
\(984\) | 6.74699 | + | 20.7651i | 0.215086 | + | 0.661967i | ||||
\(985\) | 1.49868 | + | 4.61247i | 0.0477520 | + | 0.146965i | ||||
\(986\) | 19.8258 | + | 14.4043i | 0.631381 | + | 0.458725i | ||||
\(987\) | −8.88300 | + | 6.45388i | −0.282749 | + | 0.205429i | ||||
\(988\) | −0.164234 | + | 0.505460i | −0.00522497 | + | 0.0160808i | ||||
\(989\) | −68.6014 | −2.18140 | ||||||||
\(990\) | −2.09505 | + | 0.844141i | −0.0665850 | + | 0.0268286i | ||||
\(991\) | 19.4299 | 0.617210 | 0.308605 | − | 0.951190i | \(-0.400138\pi\) | ||||
0.308605 | + | 0.951190i | \(0.400138\pi\) | |||||||
\(992\) | 1.79257 | − | 5.51696i | 0.0569141 | − | 0.175164i | ||||
\(993\) | −39.2356 | + | 28.5064i | −1.24511 | + | 0.904622i | ||||
\(994\) | −7.62807 | − | 5.54212i | −0.241948 | − | 0.175785i | ||||
\(995\) | 2.10280 | + | 6.47174i | 0.0666631 | + | 0.205168i | ||||
\(996\) | −8.46318 | − | 26.0470i | −0.268166 | − | 0.825331i | ||||
\(997\) | 18.2400 | + | 13.2521i | 0.577667 | + | 0.419699i | 0.837882 | − | 0.545851i | \(-0.183794\pi\) |
−0.260215 | + | 0.965551i | \(0.583794\pi\) | |||||||
\(998\) | −15.0982 | + | 10.9695i | −0.477926 | + | 0.347234i | ||||
\(999\) | −2.29486 | + | 7.06284i | −0.0726060 | + | 0.223458i |
(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 | 418.2.f.h.229.1 | yes | 20 | |
11.4 | even | 5 | 4598.2.a.cc.1.9 | 10 | |||
11.5 | even | 5 | inner | 418.2.f.h.115.1 | ✓ | 20 | |
11.7 | odd | 10 | 4598.2.a.cd.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.h.115.1 | ✓ | 20 | 11.5 | even | 5 | inner | |
418.2.f.h.229.1 | yes | 20 | 1.1 | even | 1 | trivial | |
4598.2.a.cc.1.9 | 10 | 11.4 | even | 5 | |||
4598.2.a.cd.1.9 | 10 | 11.7 | odd | 10 |