Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 71.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.71 |
Dual form | 770.2.n.b.141.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | −2.11803 | − | 1.53884i | −1.22285 | − | 0.888451i | −0.226514 | − | 0.974008i | \(-0.572733\pi\) |
−0.996333 | + | 0.0855571i | \(0.972733\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | −0.809017 | + | 2.48990i | −0.330280 | + | 1.01650i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | 1.19098 | + | 3.66547i | 0.396994 | + | 1.22182i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.809017 | + | 3.21644i | −0.243928 | + | 0.969793i | ||||
\(12\) | 2.61803 | 0.755761 | ||||||||
\(13\) | −0.618034 | − | 1.90211i | −0.171412 | − | 0.527551i | 0.828040 | − | 0.560670i | \(-0.189456\pi\) |
−0.999451 | + | 0.0331183i | \(0.989456\pi\) | |||||||
\(14\) | −0.809017 | − | 0.587785i | −0.216219 | − | 0.157092i | ||||
\(15\) | 2.11803 | − | 1.53884i | 0.546874 | − | 0.397327i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 0.500000 | − | 1.53884i | 0.121268 | − | 0.373224i | −0.871935 | − | 0.489622i | \(-0.837135\pi\) |
0.993203 | + | 0.116398i | \(0.0371348\pi\) | |||||||
\(18\) | 3.11803 | − | 2.26538i | 0.734928 | − | 0.533956i | ||||
\(19\) | 5.54508 | + | 4.02874i | 1.27213 | + | 0.924256i | 0.999285 | − | 0.0378018i | \(-0.0120356\pi\) |
0.272844 | + | 0.962058i | \(0.412036\pi\) | |||||||
\(20\) | −0.309017 | − | 0.951057i | −0.0690983 | − | 0.212663i | ||||
\(21\) | −2.61803 | −0.571302 | ||||||||
\(22\) | 3.30902 | − | 0.224514i | 0.705485 | − | 0.0478665i | ||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | −0.809017 | − | 2.48990i | −0.165140 | − | 0.508248i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | −1.61803 | + | 1.17557i | −0.317323 | + | 0.230548i | ||||
\(27\) | 0.690983 | − | 2.12663i | 0.132980 | − | 0.409270i | ||||
\(28\) | −0.309017 | + | 0.951057i | −0.0583987 | + | 0.179733i | ||||
\(29\) | 2.61803 | − | 1.90211i | 0.486157 | − | 0.353214i | −0.317548 | − | 0.948242i | \(-0.602859\pi\) |
0.803704 | + | 0.595029i | \(0.202859\pi\) | |||||||
\(30\) | −2.11803 | − | 1.53884i | −0.386698 | − | 0.280953i | ||||
\(31\) | −0.381966 | − | 1.17557i | −0.0686031 | − | 0.211139i | 0.910878 | − | 0.412677i | \(-0.135406\pi\) |
−0.979481 | + | 0.201538i | \(0.935406\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.66312 | − | 5.56758i | 1.15990 | − | 0.969192i | ||||
\(34\) | −1.61803 | −0.277491 | ||||||||
\(35\) | 0.309017 | + | 0.951057i | 0.0522334 | + | 0.160758i | ||||
\(36\) | −3.11803 | − | 2.26538i | −0.519672 | − | 0.377564i | ||||
\(37\) | 5.23607 | − | 3.80423i | 0.860804 | − | 0.625411i | −0.0672994 | − | 0.997733i | \(-0.521438\pi\) |
0.928104 | + | 0.372322i | \(0.121438\pi\) | |||||||
\(38\) | 2.11803 | − | 6.51864i | 0.343590 | − | 1.05746i | ||||
\(39\) | −1.61803 | + | 4.97980i | −0.259093 | + | 0.797406i | ||||
\(40\) | −0.809017 | + | 0.587785i | −0.127917 | + | 0.0929370i | ||||
\(41\) | −8.35410 | − | 6.06961i | −1.30469 | − | 0.947914i | −0.304702 | − | 0.952448i | \(-0.598557\pi\) |
−0.999990 | + | 0.00453391i | \(0.998557\pi\) | |||||||
\(42\) | 0.809017 | + | 2.48990i | 0.124834 | + | 0.384200i | ||||
\(43\) | −1.85410 | −0.282748 | −0.141374 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141374 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(44\) | −1.23607 | − | 3.07768i | −0.186344 | − | 0.463978i | ||||
\(45\) | −3.85410 | −0.574536 | ||||||||
\(46\) | −1.85410 | − | 5.70634i | −0.273372 | − | 0.841354i | ||||
\(47\) | −7.47214 | − | 5.42882i | −1.08992 | − | 0.791875i | −0.110537 | − | 0.993872i | \(-0.535257\pi\) |
−0.979386 | + | 0.201997i | \(0.935257\pi\) | |||||||
\(48\) | −2.11803 | + | 1.53884i | −0.305712 | + | 0.222113i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | −0.309017 | + | 0.951057i | −0.0437016 | + | 0.134500i | ||||
\(51\) | −3.42705 | + | 2.48990i | −0.479883 | + | 0.348655i | ||||
\(52\) | 1.61803 | + | 1.17557i | 0.224381 | + | 0.163022i | ||||
\(53\) | 0.381966 | + | 1.17557i | 0.0524671 | + | 0.161477i | 0.973857 | − | 0.227163i | \(-0.0729450\pi\) |
−0.921390 | + | 0.388640i | \(0.872945\pi\) | |||||||
\(54\) | −2.23607 | −0.304290 | ||||||||
\(55\) | −2.80902 | − | 1.76336i | −0.378768 | − | 0.237771i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −5.54508 | − | 17.0660i | −0.734464 | − | 2.26045i | ||||
\(58\) | −2.61803 | − | 1.90211i | −0.343765 | − | 0.249760i | ||||
\(59\) | 6.16312 | − | 4.47777i | 0.802370 | − | 0.582956i | −0.109239 | − | 0.994016i | \(-0.534841\pi\) |
0.911608 | + | 0.411060i | \(0.134841\pi\) | |||||||
\(60\) | −0.809017 | + | 2.48990i | −0.104444 | + | 0.321444i | ||||
\(61\) | 1.09017 | − | 3.35520i | 0.139582 | − | 0.429589i | −0.856693 | − | 0.515827i | \(-0.827485\pi\) |
0.996275 | + | 0.0862382i | \(0.0274846\pi\) | |||||||
\(62\) | −1.00000 | + | 0.726543i | −0.127000 | + | 0.0922710i | ||||
\(63\) | 3.11803 | + | 2.26538i | 0.392835 | + | 0.285412i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | −7.35410 | − | 4.61653i | −0.905227 | − | 0.568255i | ||||
\(67\) | 6.09017 | 0.744033 | 0.372016 | − | 0.928226i | \(-0.378667\pi\) | ||||
0.372016 | + | 0.928226i | \(0.378667\pi\) | |||||||
\(68\) | 0.500000 | + | 1.53884i | 0.0606339 | + | 0.186612i | ||||
\(69\) | −12.7082 | − | 9.23305i | −1.52989 | − | 1.11153i | ||||
\(70\) | 0.809017 | − | 0.587785i | 0.0966960 | − | 0.0702538i | ||||
\(71\) | −3.00000 | + | 9.23305i | −0.356034 | + | 1.09576i | 0.599373 | + | 0.800470i | \(0.295417\pi\) |
−0.955407 | + | 0.295291i | \(0.904583\pi\) | |||||||
\(72\) | −1.19098 | + | 3.66547i | −0.140359 | + | 0.431980i | ||||
\(73\) | 11.2082 | − | 8.14324i | 1.31182 | − | 0.953094i | 0.311825 | − | 0.950139i | \(-0.399060\pi\) |
0.999996 | − | 0.00295436i | \(-0.000940404\pi\) | |||||||
\(74\) | −5.23607 | − | 3.80423i | −0.608681 | − | 0.442232i | ||||
\(75\) | 0.809017 | + | 2.48990i | 0.0934172 | + | 0.287509i | ||||
\(76\) | −6.85410 | −0.786219 | ||||||||
\(77\) | 1.23607 | + | 3.07768i | 0.140863 | + | 0.350735i | ||||
\(78\) | 5.23607 | 0.592868 | ||||||||
\(79\) | 2.61803 | + | 8.05748i | 0.294552 | + | 0.906537i | 0.983372 | + | 0.181605i | \(0.0581291\pi\) |
−0.688820 | + | 0.724933i | \(0.741871\pi\) | |||||||
\(80\) | 0.809017 | + | 0.587785i | 0.0904508 | + | 0.0657164i | ||||
\(81\) | 4.61803 | − | 3.35520i | 0.513115 | − | 0.372800i | ||||
\(82\) | −3.19098 | + | 9.82084i | −0.352385 | + | 1.08453i | ||||
\(83\) | −3.19098 | + | 9.82084i | −0.350256 | + | 1.07798i | 0.608454 | + | 0.793589i | \(0.291790\pi\) |
−0.958709 | + | 0.284387i | \(0.908210\pi\) | |||||||
\(84\) | 2.11803 | − | 1.53884i | 0.231096 | − | 0.167901i | ||||
\(85\) | 1.30902 | + | 0.951057i | 0.141983 | + | 0.103157i | ||||
\(86\) | 0.572949 | + | 1.76336i | 0.0617827 | + | 0.190148i | ||||
\(87\) | −8.47214 | −0.908308 | ||||||||
\(88\) | −2.54508 | + | 2.12663i | −0.271307 | + | 0.226699i | ||||
\(89\) | 13.0902 | 1.38756 | 0.693778 | − | 0.720189i | \(-0.255945\pi\) | ||||
0.693778 | + | 0.720189i | \(0.255945\pi\) | |||||||
\(90\) | 1.19098 | + | 3.66547i | 0.125541 | + | 0.386374i | ||||
\(91\) | −1.61803 | − | 1.17557i | −0.169616 | − | 0.123233i | ||||
\(92\) | −4.85410 | + | 3.52671i | −0.506075 | + | 0.367685i | ||||
\(93\) | −1.00000 | + | 3.07768i | −0.103695 | + | 0.319141i | ||||
\(94\) | −2.85410 | + | 8.78402i | −0.294378 | + | 0.906003i | ||||
\(95\) | −5.54508 | + | 4.02874i | −0.568914 | + | 0.413340i | ||||
\(96\) | 2.11803 | + | 1.53884i | 0.216171 | + | 0.157057i | ||||
\(97\) | −2.95492 | − | 9.09429i | −0.300026 | − | 0.923386i | −0.981487 | − | 0.191531i | \(-0.938655\pi\) |
0.681460 | − | 0.731855i | \(-0.261345\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −12.7533 | + | 0.865300i | −1.28175 | + | 0.0869659i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.76393 | − | 8.50651i | −0.275022 | − | 0.846429i | −0.989214 | − | 0.146480i | \(-0.953206\pi\) |
0.714192 | − | 0.699950i | \(-0.246794\pi\) | |||||||
\(102\) | 3.42705 | + | 2.48990i | 0.339329 | + | 0.246537i | ||||
\(103\) | 13.7082 | − | 9.95959i | 1.35071 | − | 0.981348i | 0.351734 | − | 0.936100i | \(-0.385592\pi\) |
0.998976 | − | 0.0452478i | \(-0.0144077\pi\) | |||||||
\(104\) | 0.618034 | − | 1.90211i | 0.0606032 | − | 0.186518i | ||||
\(105\) | 0.809017 | − | 2.48990i | 0.0789520 | − | 0.242989i | ||||
\(106\) | 1.00000 | − | 0.726543i | 0.0971286 | − | 0.0705680i | ||||
\(107\) | 12.4443 | + | 9.04129i | 1.20303 | + | 0.874055i | 0.994580 | − | 0.103978i | \(-0.0331570\pi\) |
0.208454 | + | 0.978032i | \(0.433157\pi\) | |||||||
\(108\) | 0.690983 | + | 2.12663i | 0.0664899 | + | 0.204635i | ||||
\(109\) | 0.472136 | 0.0452224 | 0.0226112 | − | 0.999744i | \(-0.492802\pi\) | ||||
0.0226112 | + | 0.999744i | \(0.492802\pi\) | |||||||
\(110\) | −0.809017 | + | 3.21644i | −0.0771367 | + | 0.306676i | ||||
\(111\) | −16.9443 | −1.60828 | ||||||||
\(112\) | −0.309017 | − | 0.951057i | −0.0291994 | − | 0.0898664i | ||||
\(113\) | 7.54508 | + | 5.48183i | 0.709782 | + | 0.515687i | 0.883103 | − | 0.469179i | \(-0.155450\pi\) |
−0.173321 | + | 0.984865i | \(0.555450\pi\) | |||||||
\(114\) | −14.5172 | + | 10.5474i | −1.35966 | + | 0.987852i | ||||
\(115\) | −1.85410 | + | 5.70634i | −0.172896 | + | 0.532119i | ||||
\(116\) | −1.00000 | + | 3.07768i | −0.0928477 | + | 0.285756i | ||||
\(117\) | 6.23607 | − | 4.53077i | 0.576525 | − | 0.418870i | ||||
\(118\) | −6.16312 | − | 4.47777i | −0.567361 | − | 0.412212i | ||||
\(119\) | −0.500000 | − | 1.53884i | −0.0458349 | − | 0.141065i | ||||
\(120\) | 2.61803 | 0.238993 | ||||||||
\(121\) | −9.69098 | − | 5.20431i | −0.880998 | − | 0.473119i | ||||
\(122\) | −3.52786 | −0.319398 | ||||||||
\(123\) | 8.35410 | + | 25.7113i | 0.753264 | + | 2.31831i | ||||
\(124\) | 1.00000 | + | 0.726543i | 0.0898027 | + | 0.0652454i | ||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | 1.19098 | − | 3.66547i | 0.106101 | − | 0.326546i | ||||
\(127\) | 3.52786 | − | 10.8576i | 0.313047 | − | 0.963461i | −0.663503 | − | 0.748173i | \(-0.730931\pi\) |
0.976551 | − | 0.215287i | \(-0.0690688\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | 3.92705 | + | 2.85317i | 0.345758 | + | 0.251208i | ||||
\(130\) | −0.618034 | − | 1.90211i | −0.0542052 | − | 0.166826i | ||||
\(131\) | 7.79837 | 0.681347 | 0.340674 | − | 0.940182i | \(-0.389345\pi\) | ||||
0.340674 | + | 0.940182i | \(0.389345\pi\) | |||||||
\(132\) | −2.11803 | + | 8.42075i | −0.184351 | + | 0.732932i | ||||
\(133\) | 6.85410 | 0.594326 | ||||||||
\(134\) | −1.88197 | − | 5.79210i | −0.162577 | − | 0.500361i | ||||
\(135\) | 1.80902 | + | 1.31433i | 0.155695 | + | 0.113119i | ||||
\(136\) | 1.30902 | − | 0.951057i | 0.112247 | − | 0.0815524i | ||||
\(137\) | −0.336881 | + | 1.03681i | −0.0287817 | + | 0.0885809i | −0.964416 | − | 0.264391i | \(-0.914829\pi\) |
0.935634 | + | 0.352972i | \(0.114829\pi\) | |||||||
\(138\) | −4.85410 | + | 14.9394i | −0.413209 | + | 1.27173i | ||||
\(139\) | 14.9443 | − | 10.8576i | 1.26756 | − | 0.920934i | 0.268454 | − | 0.963292i | \(-0.413487\pi\) |
0.999102 | + | 0.0423587i | \(0.0134872\pi\) | |||||||
\(140\) | −0.809017 | − | 0.587785i | −0.0683744 | − | 0.0496769i | ||||
\(141\) | 7.47214 | + | 22.9969i | 0.629267 | + | 1.93669i | ||||
\(142\) | 9.70820 | 0.814694 | ||||||||
\(143\) | 6.61803 | − | 0.449028i | 0.553428 | − | 0.0375496i | ||||
\(144\) | 3.85410 | 0.321175 | ||||||||
\(145\) | 1.00000 | + | 3.07768i | 0.0830455 | + | 0.255588i | ||||
\(146\) | −11.2082 | − | 8.14324i | −0.927598 | − | 0.673939i | ||||
\(147\) | −2.11803 | + | 1.53884i | −0.174692 | + | 0.126922i | ||||
\(148\) | −2.00000 | + | 6.15537i | −0.164399 | + | 0.505968i | ||||
\(149\) | −7.47214 | + | 22.9969i | −0.612141 | + | 1.88398i | −0.175051 | + | 0.984559i | \(0.556009\pi\) |
−0.437090 | + | 0.899418i | \(0.643991\pi\) | |||||||
\(150\) | 2.11803 | − | 1.53884i | 0.172937 | − | 0.125646i | ||||
\(151\) | 1.85410 | + | 1.34708i | 0.150885 | + | 0.109624i | 0.660666 | − | 0.750680i | \(-0.270274\pi\) |
−0.509782 | + | 0.860304i | \(0.670274\pi\) | |||||||
\(152\) | 2.11803 | + | 6.51864i | 0.171795 | + | 0.528731i | ||||
\(153\) | 6.23607 | 0.504156 | ||||||||
\(154\) | 2.54508 | − | 2.12663i | 0.205089 | − | 0.171368i | ||||
\(155\) | 1.23607 | 0.0992834 | ||||||||
\(156\) | −1.61803 | − | 4.97980i | −0.129546 | − | 0.398703i | ||||
\(157\) | −0.236068 | − | 0.171513i | −0.0188403 | − | 0.0136883i | 0.578325 | − | 0.815806i | \(-0.303706\pi\) |
−0.597166 | + | 0.802118i | \(0.703706\pi\) | |||||||
\(158\) | 6.85410 | − | 4.97980i | 0.545283 | − | 0.396171i | ||||
\(159\) | 1.00000 | − | 3.07768i | 0.0793052 | − | 0.244076i | ||||
\(160\) | 0.309017 | − | 0.951057i | 0.0244299 | − | 0.0751876i | ||||
\(161\) | 4.85410 | − | 3.52671i | 0.382557 | − | 0.277944i | ||||
\(162\) | −4.61803 | − | 3.35520i | −0.362827 | − | 0.263609i | ||||
\(163\) | 0.881966 | + | 2.71441i | 0.0690809 | + | 0.212609i | 0.979637 | − | 0.200776i | \(-0.0643463\pi\) |
−0.910556 | + | 0.413385i | \(0.864346\pi\) | |||||||
\(164\) | 10.3262 | 0.806344 | ||||||||
\(165\) | 3.23607 | + | 8.05748i | 0.251928 | + | 0.627274i | ||||
\(166\) | 10.3262 | 0.801471 | ||||||||
\(167\) | −2.00000 | − | 6.15537i | −0.154765 | − | 0.476317i | 0.843372 | − | 0.537330i | \(-0.180567\pi\) |
−0.998137 | + | 0.0610130i | \(0.980567\pi\) | |||||||
\(168\) | −2.11803 | − | 1.53884i | −0.163410 | − | 0.118724i | ||||
\(169\) | 7.28115 | − | 5.29007i | 0.560089 | − | 0.406928i | ||||
\(170\) | 0.500000 | − | 1.53884i | 0.0383482 | − | 0.118024i | ||||
\(171\) | −8.16312 | + | 25.1235i | −0.624249 | + | 1.92124i | ||||
\(172\) | 1.50000 | − | 1.08981i | 0.114374 | − | 0.0830975i | ||||
\(173\) | 9.70820 | + | 7.05342i | 0.738101 | + | 0.536262i | 0.892116 | − | 0.451807i | \(-0.149220\pi\) |
−0.154015 | + | 0.988069i | \(0.549220\pi\) | |||||||
\(174\) | 2.61803 | + | 8.05748i | 0.198473 | + | 0.610836i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 2.80902 | + | 1.76336i | 0.211738 | + | 0.132918i | ||||
\(177\) | −19.9443 | −1.49910 | ||||||||
\(178\) | −4.04508 | − | 12.4495i | −0.303192 | − | 0.933129i | ||||
\(179\) | 5.16312 | + | 3.75123i | 0.385910 | + | 0.280380i | 0.763777 | − | 0.645480i | \(-0.223343\pi\) |
−0.377868 | + | 0.925860i | \(0.623343\pi\) | |||||||
\(180\) | 3.11803 | − | 2.26538i | 0.232405 | − | 0.168852i | ||||
\(181\) | 1.09017 | − | 3.35520i | 0.0810317 | − | 0.249390i | −0.902331 | − | 0.431044i | \(-0.858145\pi\) |
0.983362 | + | 0.181654i | \(0.0581452\pi\) | |||||||
\(182\) | −0.618034 | + | 1.90211i | −0.0458117 | + | 0.140994i | ||||
\(183\) | −7.47214 | + | 5.42882i | −0.552356 | + | 0.401310i | ||||
\(184\) | 4.85410 | + | 3.52671i | 0.357849 | + | 0.259993i | ||||
\(185\) | 2.00000 | + | 6.15537i | 0.147043 | + | 0.452552i | ||||
\(186\) | 3.23607 | 0.237280 | ||||||||
\(187\) | 4.54508 | + | 2.85317i | 0.332370 | + | 0.208644i | ||||
\(188\) | 9.23607 | 0.673609 | ||||||||
\(189\) | −0.690983 | − | 2.12663i | −0.0502616 | − | 0.154689i | ||||
\(190\) | 5.54508 | + | 4.02874i | 0.402283 | + | 0.292276i | ||||
\(191\) | 1.23607 | − | 0.898056i | 0.0894387 | − | 0.0649810i | −0.542167 | − | 0.840271i | \(-0.682396\pi\) |
0.631606 | + | 0.775290i | \(0.282396\pi\) | |||||||
\(192\) | 0.809017 | − | 2.48990i | 0.0583858 | − | 0.179693i | ||||
\(193\) | 0.618034 | − | 1.90211i | 0.0444871 | − | 0.136917i | −0.926346 | − | 0.376674i | \(-0.877068\pi\) |
0.970833 | + | 0.239757i | \(0.0770677\pi\) | |||||||
\(194\) | −7.73607 | + | 5.62058i | −0.555417 | + | 0.403534i | ||||
\(195\) | −4.23607 | − | 3.07768i | −0.303351 | − | 0.220397i | ||||
\(196\) | 0.309017 | + | 0.951057i | 0.0220726 | + | 0.0679326i | ||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 4.76393 | + | 11.8617i | 0.338558 | + | 0.842975i | ||||
\(199\) | −19.4164 | −1.37639 | −0.688196 | − | 0.725525i | \(-0.741597\pi\) | ||||
−0.688196 | + | 0.725525i | \(0.741597\pi\) | |||||||
\(200\) | −0.309017 | − | 0.951057i | −0.0218508 | − | 0.0672499i | ||||
\(201\) | −12.8992 | − | 9.37181i | −0.909838 | − | 0.661036i | ||||
\(202\) | −7.23607 | + | 5.25731i | −0.509128 | + | 0.369903i | ||||
\(203\) | 1.00000 | − | 3.07768i | 0.0701862 | − | 0.216011i | ||||
\(204\) | 1.30902 | − | 4.02874i | 0.0916495 | − | 0.282068i | ||||
\(205\) | 8.35410 | − | 6.06961i | 0.583476 | − | 0.423920i | ||||
\(206\) | −13.7082 | − | 9.95959i | −0.955096 | − | 0.693918i | ||||
\(207\) | 7.14590 | + | 21.9928i | 0.496674 | + | 1.52861i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | −17.4443 | + | 14.5761i | −1.20665 | + | 1.00825i | ||||
\(210\) | −2.61803 | −0.180662 | ||||||||
\(211\) | −3.48278 | − | 10.7189i | −0.239764 | − | 0.737919i | −0.996454 | − | 0.0841442i | \(-0.973184\pi\) |
0.756689 | − | 0.653775i | \(-0.226816\pi\) | |||||||
\(212\) | −1.00000 | − | 0.726543i | −0.0686803 | − | 0.0498991i | ||||
\(213\) | 20.5623 | − | 14.9394i | 1.40891 | − | 1.02363i | ||||
\(214\) | 4.75329 | − | 14.6291i | 0.324928 | − | 1.00003i | ||||
\(215\) | 0.572949 | − | 1.76336i | 0.0390748 | − | 0.120260i | ||||
\(216\) | 1.80902 | − | 1.31433i | 0.123088 | − | 0.0894287i | ||||
\(217\) | −1.00000 | − | 0.726543i | −0.0678844 | − | 0.0493209i | ||||
\(218\) | −0.145898 | − | 0.449028i | −0.00988146 | − | 0.0304120i | ||||
\(219\) | −36.2705 | −2.45093 | ||||||||
\(220\) | 3.30902 | − | 0.224514i | 0.223094 | − | 0.0151367i | ||||
\(221\) | −3.23607 | −0.217681 | ||||||||
\(222\) | 5.23607 | + | 16.1150i | 0.351422 | + | 1.08157i | ||||
\(223\) | −5.09017 | − | 3.69822i | −0.340863 | − | 0.247651i | 0.404163 | − | 0.914687i | \(-0.367563\pi\) |
−0.745026 | + | 0.667036i | \(0.767563\pi\) | |||||||
\(224\) | −0.809017 | + | 0.587785i | −0.0540547 | + | 0.0392731i | ||||
\(225\) | 1.19098 | − | 3.66547i | 0.0793989 | − | 0.244365i | ||||
\(226\) | 2.88197 | − | 8.86978i | 0.191706 | − | 0.590009i | ||||
\(227\) | −19.6353 | + | 14.2658i | −1.30324 | + | 0.946858i | −0.999982 | − | 0.00605157i | \(-0.998074\pi\) |
−0.303256 | + | 0.952909i | \(0.598074\pi\) | |||||||
\(228\) | 14.5172 | + | 10.5474i | 0.961426 | + | 0.698517i | ||||
\(229\) | 3.43769 | + | 10.5801i | 0.227169 | + | 0.699155i | 0.998064 | + | 0.0621927i | \(0.0198093\pi\) |
−0.770895 | + | 0.636962i | \(0.780191\pi\) | |||||||
\(230\) | 6.00000 | 0.395628 | ||||||||
\(231\) | 2.11803 | − | 8.42075i | 0.139356 | − | 0.554045i | ||||
\(232\) | 3.23607 | 0.212458 | ||||||||
\(233\) | −3.37132 | − | 10.3759i | −0.220863 | − | 0.679746i | −0.998685 | − | 0.0512616i | \(-0.983676\pi\) |
0.777823 | − | 0.628484i | \(-0.216324\pi\) | |||||||
\(234\) | −6.23607 | − | 4.53077i | −0.407665 | − | 0.296186i | ||||
\(235\) | 7.47214 | − | 5.42882i | 0.487428 | − | 0.354137i | ||||
\(236\) | −2.35410 | + | 7.24518i | −0.153239 | + | 0.471621i | ||||
\(237\) | 6.85410 | − | 21.0948i | 0.445222 | − | 1.37025i | ||||
\(238\) | −1.30902 | + | 0.951057i | −0.0848510 | + | 0.0616478i | ||||
\(239\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(240\) | −0.809017 | − | 2.48990i | −0.0522218 | − | 0.160722i | ||||
\(241\) | 6.27051 | 0.403919 | 0.201960 | − | 0.979394i | \(-0.435269\pi\) | ||||
0.201960 | + | 0.979394i | \(0.435269\pi\) | |||||||
\(242\) | −1.95492 | + | 10.8249i | −0.125667 | + | 0.695850i | ||||
\(243\) | −21.6525 | −1.38901 | ||||||||
\(244\) | 1.09017 | + | 3.35520i | 0.0697910 | + | 0.214795i | ||||
\(245\) | 0.809017 | + | 0.587785i | 0.0516862 | + | 0.0375522i | ||||
\(246\) | 21.8713 | − | 15.8904i | 1.39446 | − | 1.01314i | ||||
\(247\) | 4.23607 | − | 13.0373i | 0.269535 | − | 0.829542i | ||||
\(248\) | 0.381966 | − | 1.17557i | 0.0242549 | − | 0.0746488i | ||||
\(249\) | 21.8713 | − | 15.8904i | 1.38604 | − | 1.00702i | ||||
\(250\) | −0.809017 | − | 0.587785i | −0.0511667 | − | 0.0371748i | ||||
\(251\) | 8.29180 | + | 25.5195i | 0.523374 | + | 1.61078i | 0.767510 | + | 0.641037i | \(0.221496\pi\) |
−0.244136 | + | 0.969741i | \(0.578504\pi\) | |||||||
\(252\) | −3.85410 | −0.242786 | ||||||||
\(253\) | −4.85410 | + | 19.2986i | −0.305175 | + | 1.21330i | ||||
\(254\) | −11.4164 | −0.716329 | ||||||||
\(255\) | −1.30902 | − | 4.02874i | −0.0819738 | − | 0.252289i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −23.9164 | + | 17.3763i | −1.49186 | + | 1.08390i | −0.518380 | + | 0.855150i | \(0.673465\pi\) |
−0.973485 | + | 0.228753i | \(0.926535\pi\) | |||||||
\(258\) | 1.50000 | − | 4.61653i | 0.0933859 | − | 0.287412i | ||||
\(259\) | 2.00000 | − | 6.15537i | 0.124274 | − | 0.382476i | ||||
\(260\) | −1.61803 | + | 1.17557i | −0.100346 | + | 0.0729058i | ||||
\(261\) | 10.0902 | + | 7.33094i | 0.624566 | + | 0.453774i | ||||
\(262\) | −2.40983 | − | 7.41669i | −0.148880 | − | 0.458205i | ||||
\(263\) | −20.1803 | −1.24437 | −0.622187 | − | 0.782869i | \(-0.713755\pi\) | ||||
−0.622187 | + | 0.782869i | \(0.713755\pi\) | |||||||
\(264\) | 8.66312 | − | 0.587785i | 0.533178 | − | 0.0361757i | ||||
\(265\) | −1.23607 | −0.0759311 | ||||||||
\(266\) | −2.11803 | − | 6.51864i | −0.129865 | − | 0.399683i | ||||
\(267\) | −27.7254 | − | 20.1437i | −1.69677 | − | 1.23277i | ||||
\(268\) | −4.92705 | + | 3.57971i | −0.300968 | + | 0.218666i | ||||
\(269\) | −3.76393 | + | 11.5842i | −0.229491 | + | 0.706301i | 0.768314 | + | 0.640074i | \(0.221096\pi\) |
−0.997805 | + | 0.0662270i | \(0.978904\pi\) | |||||||
\(270\) | 0.690983 | − | 2.12663i | 0.0420519 | − | 0.129422i | ||||
\(271\) | −7.61803 | + | 5.53483i | −0.462763 | + | 0.336217i | −0.794614 | − | 0.607115i | \(-0.792327\pi\) |
0.331851 | + | 0.943332i | \(0.392327\pi\) | |||||||
\(272\) | −1.30902 | − | 0.951057i | −0.0793708 | − | 0.0576663i | ||||
\(273\) | 1.61803 | + | 4.97980i | 0.0979279 | + | 0.301391i | ||||
\(274\) | 1.09017 | 0.0658596 | ||||||||
\(275\) | 2.54508 | − | 2.12663i | 0.153474 | − | 0.128240i | ||||
\(276\) | 15.7082 | 0.945523 | ||||||||
\(277\) | −1.94427 | − | 5.98385i | −0.116820 | − | 0.359535i | 0.875502 | − | 0.483214i | \(-0.160531\pi\) |
−0.992322 | + | 0.123679i | \(0.960531\pi\) | |||||||
\(278\) | −14.9443 | − | 10.8576i | −0.896298 | − | 0.651199i | ||||
\(279\) | 3.85410 | − | 2.80017i | 0.230739 | − | 0.167642i | ||||
\(280\) | −0.309017 | + | 0.951057i | −0.0184673 | + | 0.0568365i | ||||
\(281\) | 7.42705 | − | 22.8581i | 0.443061 | − | 1.36360i | −0.441536 | − | 0.897244i | \(-0.645566\pi\) |
0.884597 | − | 0.466357i | \(-0.154434\pi\) | |||||||
\(282\) | 19.5623 | − | 14.2128i | 1.16492 | − | 0.846363i | ||||
\(283\) | −9.70820 | − | 7.05342i | −0.577093 | − | 0.419282i | 0.260582 | − | 0.965452i | \(-0.416086\pi\) |
−0.837675 | + | 0.546169i | \(0.816086\pi\) | |||||||
\(284\) | −3.00000 | − | 9.23305i | −0.178017 | − | 0.547881i | ||||
\(285\) | 17.9443 | 1.06293 | ||||||||
\(286\) | −2.47214 | − | 6.15537i | −0.146180 | − | 0.363974i | ||||
\(287\) | −10.3262 | −0.609539 | ||||||||
\(288\) | −1.19098 | − | 3.66547i | −0.0701793 | − | 0.215990i | ||||
\(289\) | 11.6353 | + | 8.45351i | 0.684427 | + | 0.497265i | ||||
\(290\) | 2.61803 | − | 1.90211i | 0.153736 | − | 0.111696i | ||||
\(291\) | −7.73607 | + | 23.8092i | −0.453496 | + | 1.39572i | ||||
\(292\) | −4.28115 | + | 13.1760i | −0.250536 | + | 0.771069i | ||||
\(293\) | 13.3262 | − | 9.68208i | 0.778527 | − | 0.565633i | −0.126009 | − | 0.992029i | \(-0.540217\pi\) |
0.904537 | + | 0.426396i | \(0.140217\pi\) | |||||||
\(294\) | 2.11803 | + | 1.53884i | 0.123526 | + | 0.0897471i | ||||
\(295\) | 2.35410 | + | 7.24518i | 0.137061 | + | 0.421831i | ||||
\(296\) | 6.47214 | 0.376185 | ||||||||
\(297\) | 6.28115 | + | 3.94298i | 0.364469 | + | 0.228795i | ||||
\(298\) | 24.1803 | 1.40073 | ||||||||
\(299\) | −3.70820 | − | 11.4127i | −0.214451 | − | 0.660012i | ||||
\(300\) | −2.11803 | − | 1.53884i | −0.122285 | − | 0.0888451i | ||||
\(301\) | −1.50000 | + | 1.08981i | −0.0864586 | + | 0.0628158i | ||||
\(302\) | 0.708204 | − | 2.17963i | 0.0407526 | − | 0.125423i | ||||
\(303\) | −7.23607 | + | 22.2703i | −0.415701 | + | 1.27940i | ||||
\(304\) | 5.54508 | − | 4.02874i | 0.318032 | − | 0.231064i | ||||
\(305\) | 2.85410 | + | 2.07363i | 0.163425 | + | 0.118736i | ||||
\(306\) | −1.92705 | − | 5.93085i | −0.110162 | − | 0.339044i | ||||
\(307\) | 27.5623 | 1.57306 | 0.786532 | − | 0.617550i | \(-0.211875\pi\) | ||||
0.786532 | + | 0.617550i | \(0.211875\pi\) | |||||||
\(308\) | −2.80902 | − | 1.76336i | −0.160059 | − | 0.100477i | ||||
\(309\) | −44.3607 | −2.52359 | ||||||||
\(310\) | −0.381966 | − | 1.17557i | −0.0216942 | − | 0.0667679i | ||||
\(311\) | 23.5623 | + | 17.1190i | 1.33610 | + | 0.970730i | 0.999578 | + | 0.0290534i | \(0.00924927\pi\) |
0.336518 | + | 0.941677i | \(0.390751\pi\) | |||||||
\(312\) | −4.23607 | + | 3.07768i | −0.239820 | + | 0.174240i | ||||
\(313\) | −0.263932 | + | 0.812299i | −0.0149183 | + | 0.0459139i | −0.958239 | − | 0.285970i | \(-0.907684\pi\) |
0.943320 | + | 0.331884i | \(0.107684\pi\) | |||||||
\(314\) | −0.0901699 | + | 0.277515i | −0.00508858 | + | 0.0156611i | ||||
\(315\) | −3.11803 | + | 2.26538i | −0.175681 | + | 0.127640i | ||||
\(316\) | −6.85410 | − | 4.97980i | −0.385573 | − | 0.280135i | ||||
\(317\) | −6.41641 | − | 19.7477i | −0.360381 | − | 1.10914i | −0.952823 | − | 0.303526i | \(-0.901836\pi\) |
0.592442 | − | 0.805613i | \(-0.298164\pi\) | |||||||
\(318\) | −3.23607 | −0.181470 | ||||||||
\(319\) | 4.00000 | + | 9.95959i | 0.223957 | + | 0.557630i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −12.4443 | − | 38.2995i | −0.694572 | − | 2.13767i | ||||
\(322\) | −4.85410 | − | 3.52671i | −0.270509 | − | 0.196536i | ||||
\(323\) | 8.97214 | − | 6.51864i | 0.499223 | − | 0.362707i | ||||
\(324\) | −1.76393 | + | 5.42882i | −0.0979962 | + | 0.301601i | ||||
\(325\) | −0.618034 | + | 1.90211i | −0.0342824 | + | 0.105510i | ||||
\(326\) | 2.30902 | − | 1.67760i | 0.127885 | − | 0.0929136i | ||||
\(327\) | −1.00000 | − | 0.726543i | −0.0553001 | − | 0.0401779i | ||||
\(328\) | −3.19098 | − | 9.82084i | −0.176193 | − | 0.542265i | ||||
\(329\) | −9.23607 | −0.509201 | ||||||||
\(330\) | 6.66312 | − | 5.56758i | 0.366793 | − | 0.306485i | ||||
\(331\) | 6.03444 | 0.331683 | 0.165841 | − | 0.986152i | \(-0.446966\pi\) | ||||
0.165841 | + | 0.986152i | \(0.446966\pi\) | |||||||
\(332\) | −3.19098 | − | 9.82084i | −0.175128 | − | 0.538988i | ||||
\(333\) | 20.1803 | + | 14.6619i | 1.10588 | + | 0.803466i | ||||
\(334\) | −5.23607 | + | 3.80423i | −0.286505 | + | 0.208158i | ||||
\(335\) | −1.88197 | + | 5.79210i | −0.102823 | + | 0.316456i | ||||
\(336\) | −0.809017 | + | 2.48990i | −0.0441355 | + | 0.135835i | ||||
\(337\) | −12.6353 | + | 9.18005i | −0.688286 | + | 0.500069i | −0.876096 | − | 0.482136i | \(-0.839861\pi\) |
0.187810 | + | 0.982205i | \(0.439861\pi\) | |||||||
\(338\) | −7.28115 | − | 5.29007i | −0.396043 | − | 0.287742i | ||||
\(339\) | −7.54508 | − | 23.2214i | −0.409793 | − | 1.26121i | ||||
\(340\) | −1.61803 | −0.0877502 | ||||||||
\(341\) | 4.09017 | − | 0.277515i | 0.221495 | − | 0.0150283i | ||||
\(342\) | 26.4164 | 1.42844 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | −1.50000 | − | 1.08981i | −0.0808746 | − | 0.0587588i | ||||
\(345\) | 12.7082 | − | 9.23305i | 0.684187 | − | 0.497091i | ||||
\(346\) | 3.70820 | − | 11.4127i | 0.199354 | − | 0.613549i | ||||
\(347\) | −1.64590 | + | 5.06555i | −0.0883564 | + | 0.271933i | −0.985465 | − | 0.169876i | \(-0.945663\pi\) |
0.897109 | + | 0.441809i | \(0.145663\pi\) | |||||||
\(348\) | 6.85410 | − | 4.97980i | 0.367418 | − | 0.266945i | ||||
\(349\) | 4.47214 | + | 3.24920i | 0.239388 | + | 0.173926i | 0.701011 | − | 0.713151i | \(-0.252733\pi\) |
−0.461623 | + | 0.887076i | \(0.652733\pi\) | |||||||
\(350\) | 0.309017 | + | 0.951057i | 0.0165177 | + | 0.0508361i | ||||
\(351\) | −4.47214 | −0.238705 | ||||||||
\(352\) | 0.809017 | − | 3.21644i | 0.0431208 | − | 0.171437i | ||||
\(353\) | −28.4508 | −1.51429 | −0.757143 | − | 0.653249i | \(-0.773405\pi\) | ||||
−0.757143 | + | 0.653249i | \(0.773405\pi\) | |||||||
\(354\) | 6.16312 | + | 18.9681i | 0.327566 | + | 1.00814i | ||||
\(355\) | −7.85410 | − | 5.70634i | −0.416852 | − | 0.302861i | ||||
\(356\) | −10.5902 | + | 7.69421i | −0.561278 | + | 0.407792i | ||||
\(357\) | −1.30902 | + | 4.02874i | −0.0692805 | + | 0.213224i | ||||
\(358\) | 1.97214 | − | 6.06961i | 0.104231 | − | 0.320789i | ||||
\(359\) | 15.0902 | − | 10.9637i | 0.796429 | − | 0.578639i | −0.113436 | − | 0.993545i | \(-0.536186\pi\) |
0.909864 | + | 0.414906i | \(0.136186\pi\) | |||||||
\(360\) | −3.11803 | − | 2.26538i | −0.164335 | − | 0.119396i | ||||
\(361\) | 8.64590 | + | 26.6093i | 0.455047 | + | 1.40049i | ||||
\(362\) | −3.52786 | −0.185420 | ||||||||
\(363\) | 12.5172 | + | 25.9358i | 0.656984 | + | 1.36128i | ||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 4.28115 | + | 13.1760i | 0.224086 | + | 0.689665i | ||||
\(366\) | 7.47214 | + | 5.42882i | 0.390575 | + | 0.283769i | ||||
\(367\) | −22.7984 | + | 16.5640i | −1.19007 | + | 0.864633i | −0.993271 | − | 0.115812i | \(-0.963053\pi\) |
−0.196794 | + | 0.980445i | \(0.563053\pi\) | |||||||
\(368\) | 1.85410 | − | 5.70634i | 0.0966517 | − | 0.297463i | ||||
\(369\) | 12.2984 | − | 37.8505i | 0.640228 | − | 1.97042i | ||||
\(370\) | 5.23607 | − | 3.80423i | 0.272210 | − | 0.197772i | ||||
\(371\) | 1.00000 | + | 0.726543i | 0.0519174 | + | 0.0377202i | ||||
\(372\) | −1.00000 | − | 3.07768i | −0.0518476 | − | 0.159570i | ||||
\(373\) | 24.4721 | 1.26712 | 0.633560 | − | 0.773694i | \(-0.281593\pi\) | ||||
0.633560 | + | 0.773694i | \(0.281593\pi\) | |||||||
\(374\) | 1.30902 | − | 5.20431i | 0.0676877 | − | 0.269108i | ||||
\(375\) | −2.61803 | −0.135195 | ||||||||
\(376\) | −2.85410 | − | 8.78402i | −0.147189 | − | 0.453001i | ||||
\(377\) | −5.23607 | − | 3.80423i | −0.269671 | − | 0.195928i | ||||
\(378\) | −1.80902 | + | 1.31433i | −0.0930458 | + | 0.0676017i | ||||
\(379\) | −8.60739 | + | 26.4908i | −0.442132 | + | 1.36074i | 0.443467 | + | 0.896291i | \(0.353748\pi\) |
−0.885599 | + | 0.464451i | \(0.846252\pi\) | |||||||
\(380\) | 2.11803 | − | 6.51864i | 0.108653 | − | 0.334399i | ||||
\(381\) | −24.1803 | + | 17.5680i | −1.23880 | + | 0.900038i | ||||
\(382\) | −1.23607 | − | 0.898056i | −0.0632427 | − | 0.0459485i | ||||
\(383\) | −7.41641 | − | 22.8254i | −0.378961 | − | 1.16632i | −0.940767 | − | 0.339053i | \(-0.889894\pi\) |
0.561807 | − | 0.827269i | \(-0.310106\pi\) | |||||||
\(384\) | −2.61803 | −0.133601 | ||||||||
\(385\) | −3.30902 | + | 0.224514i | −0.168643 | + | 0.0114423i | ||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | −2.20820 | − | 6.79615i | −0.112249 | − | 0.345468i | ||||
\(388\) | 7.73607 | + | 5.62058i | 0.392739 | + | 0.285342i | ||||
\(389\) | 26.5623 | − | 19.2986i | 1.34676 | − | 0.978480i | 0.347597 | − | 0.937644i | \(-0.386998\pi\) |
0.999166 | − | 0.0408359i | \(-0.0130021\pi\) | |||||||
\(390\) | −1.61803 | + | 4.97980i | −0.0819323 | + | 0.252162i | ||||
\(391\) | 3.00000 | − | 9.23305i | 0.151717 | − | 0.466935i | ||||
\(392\) | 0.809017 | − | 0.587785i | 0.0408615 | − | 0.0296876i | ||||
\(393\) | −16.5172 | − | 12.0005i | −0.833184 | − | 0.605343i | ||||
\(394\) | 1.85410 | + | 5.70634i | 0.0934083 | + | 0.287481i | ||||
\(395\) | −8.47214 | −0.426279 | ||||||||
\(396\) | 9.80902 | − | 8.19624i | 0.492922 | − | 0.411876i | ||||
\(397\) | −16.9443 | −0.850409 | −0.425204 | − | 0.905097i | \(-0.639798\pi\) | ||||
−0.425204 | + | 0.905097i | \(0.639798\pi\) | |||||||
\(398\) | 6.00000 | + | 18.4661i | 0.300753 | + | 0.925622i | ||||
\(399\) | −14.5172 | − | 10.5474i | −0.726770 | − | 0.528029i | ||||
\(400\) | −0.809017 | + | 0.587785i | −0.0404508 | + | 0.0293893i | ||||
\(401\) | −8.19098 | + | 25.2093i | −0.409038 | + | 1.25889i | 0.508438 | + | 0.861099i | \(0.330223\pi\) |
−0.917476 | + | 0.397791i | \(0.869777\pi\) | |||||||
\(402\) | −4.92705 | + | 15.1639i | −0.245739 | + | 0.756307i | ||||
\(403\) | −2.00000 | + | 1.45309i | −0.0996271 | + | 0.0723833i | ||||
\(404\) | 7.23607 | + | 5.25731i | 0.360008 | + | 0.261561i | ||||
\(405\) | 1.76393 | + | 5.42882i | 0.0876505 | + | 0.269760i | ||||
\(406\) | −3.23607 | −0.160603 | ||||||||
\(407\) | 8.00000 | + | 19.9192i | 0.396545 | + | 0.987357i | ||||
\(408\) | −4.23607 | −0.209717 | ||||||||
\(409\) | −8.61803 | − | 26.5236i | −0.426134 | − | 1.31151i | −0.901904 | − | 0.431937i | \(-0.857830\pi\) |
0.475770 | − | 0.879570i | \(-0.342170\pi\) | |||||||
\(410\) | −8.35410 | − | 6.06961i | −0.412580 | − | 0.299757i | ||||
\(411\) | 2.30902 | − | 1.67760i | 0.113895 | − | 0.0827499i | ||||
\(412\) | −5.23607 | + | 16.1150i | −0.257963 | + | 0.793927i | ||||
\(413\) | 2.35410 | − | 7.24518i | 0.115838 | − | 0.356512i | ||||
\(414\) | 18.7082 | − | 13.5923i | 0.919458 | − | 0.668025i | ||||
\(415\) | −8.35410 | − | 6.06961i | −0.410087 | − | 0.297945i | ||||
\(416\) | 0.618034 | + | 1.90211i | 0.0303016 | + | 0.0932588i | ||||
\(417\) | −48.3607 | −2.36823 | ||||||||
\(418\) | 19.2533 | + | 12.0862i | 0.941709 | + | 0.591156i | ||||
\(419\) | 12.3262 | 0.602176 | 0.301088 | − | 0.953596i | \(-0.402650\pi\) | ||||
0.301088 | + | 0.953596i | \(0.402650\pi\) | |||||||
\(420\) | 0.809017 | + | 2.48990i | 0.0394760 | + | 0.121495i | ||||
\(421\) | 5.14590 | + | 3.73871i | 0.250796 | + | 0.182214i | 0.706079 | − | 0.708133i | \(-0.250462\pi\) |
−0.455284 | + | 0.890346i | \(0.650462\pi\) | |||||||
\(422\) | −9.11803 | + | 6.62464i | −0.443859 | + | 0.322482i | ||||
\(423\) | 11.0000 | − | 33.8545i | 0.534838 | − | 1.64606i | ||||
\(424\) | −0.381966 | + | 1.17557i | −0.0185499 | + | 0.0570908i | ||||
\(425\) | −1.30902 | + | 0.951057i | −0.0634967 | + | 0.0461330i | ||||
\(426\) | −20.5623 | − | 14.9394i | −0.996247 | − | 0.723816i | ||||
\(427\) | −1.09017 | − | 3.35520i | −0.0527570 | − | 0.162369i | ||||
\(428\) | −15.3820 | −0.743515 | ||||||||
\(429\) | −14.7082 | − | 9.23305i | −0.710119 | − | 0.445776i | ||||
\(430\) | −1.85410 | −0.0894127 | ||||||||
\(431\) | −9.65248 | − | 29.7073i | −0.464943 | − | 1.43095i | −0.859054 | − | 0.511885i | \(-0.828947\pi\) |
0.394110 | − | 0.919063i | \(-0.371053\pi\) | |||||||
\(432\) | −1.80902 | − | 1.31433i | −0.0870364 | − | 0.0632356i | ||||
\(433\) | −13.3090 | + | 9.66957i | −0.639591 | + | 0.464690i | −0.859709 | − | 0.510783i | \(-0.829355\pi\) |
0.220119 | + | 0.975473i | \(0.429355\pi\) | |||||||
\(434\) | −0.381966 | + | 1.17557i | −0.0183350 | + | 0.0564292i | ||||
\(435\) | 2.61803 | − | 8.05748i | 0.125525 | − | 0.386327i | ||||
\(436\) | −0.381966 | + | 0.277515i | −0.0182929 | + | 0.0132905i | ||||
\(437\) | 33.2705 | + | 24.1724i | 1.59154 | + | 1.15632i | ||||
\(438\) | 11.2082 | + | 34.4953i | 0.535549 | + | 1.64825i | ||||
\(439\) | 28.6525 | 1.36751 | 0.683754 | − | 0.729713i | \(-0.260346\pi\) | ||||
0.683754 | + | 0.729713i | \(0.260346\pi\) | |||||||
\(440\) | −1.23607 | − | 3.07768i | −0.0589272 | − | 0.146723i | ||||
\(441\) | 3.85410 | 0.183529 | ||||||||
\(442\) | 1.00000 | + | 3.07768i | 0.0475651 | + | 0.146390i | ||||
\(443\) | −22.6803 | − | 16.4782i | −1.07758 | − | 0.782904i | −0.100317 | − | 0.994956i | \(-0.531986\pi\) |
−0.977259 | + | 0.212051i | \(0.931986\pi\) | |||||||
\(444\) | 13.7082 | − | 9.95959i | 0.650563 | − | 0.472661i | ||||
\(445\) | −4.04508 | + | 12.4495i | −0.191755 | + | 0.590162i | ||||
\(446\) | −1.94427 | + | 5.98385i | −0.0920639 | + | 0.283344i | ||||
\(447\) | 51.2148 | − | 37.2097i | 2.42238 | − | 1.75996i | ||||
\(448\) | 0.809017 | + | 0.587785i | 0.0382225 | + | 0.0277702i | ||||
\(449\) | 7.55573 | + | 23.2541i | 0.356577 | + | 1.09743i | 0.955090 | + | 0.296317i | \(0.0957586\pi\) |
−0.598513 | + | 0.801113i | \(0.704241\pi\) | |||||||
\(450\) | −3.85410 | −0.181684 | ||||||||
\(451\) | 26.2812 | − | 21.9601i | 1.23753 | − | 1.03406i | ||||
\(452\) | −9.32624 | −0.438669 | ||||||||
\(453\) | −1.85410 | − | 5.70634i | −0.0871133 | − | 0.268107i | ||||
\(454\) | 19.6353 | + | 14.2658i | 0.921528 | + | 0.669529i | ||||
\(455\) | 1.61803 | − | 1.17557i | 0.0758546 | − | 0.0551116i | ||||
\(456\) | 5.54508 | − | 17.0660i | 0.259672 | − | 0.799189i | ||||
\(457\) | 9.66312 | − | 29.7400i | 0.452022 | − | 1.39118i | −0.422575 | − | 0.906328i | \(-0.638874\pi\) |
0.874596 | − | 0.484852i | \(-0.161126\pi\) | |||||||
\(458\) | 9.00000 | − | 6.53888i | 0.420542 | − | 0.305542i | ||||
\(459\) | −2.92705 | − | 2.12663i | −0.136623 | − | 0.0992624i | ||||
\(460\) | −1.85410 | − | 5.70634i | −0.0864479 | − | 0.266059i | ||||
\(461\) | −6.94427 | −0.323427 | −0.161713 | − | 0.986838i | \(-0.551702\pi\) | ||||
−0.161713 | + | 0.986838i | \(0.551702\pi\) | |||||||
\(462\) | −8.66312 | + | 0.587785i | −0.403045 | + | 0.0273462i | ||||
\(463\) | −7.41641 | −0.344670 | −0.172335 | − | 0.985038i | \(-0.555131\pi\) | ||||
−0.172335 | + | 0.985038i | \(0.555131\pi\) | |||||||
\(464\) | −1.00000 | − | 3.07768i | −0.0464238 | − | 0.142878i | ||||
\(465\) | −2.61803 | − | 1.90211i | −0.121408 | − | 0.0882084i | ||||
\(466\) | −8.82624 | + | 6.41264i | −0.408868 | + | 0.297060i | ||||
\(467\) | −5.52786 | + | 17.0130i | −0.255799 | + | 0.787268i | 0.737872 | + | 0.674941i | \(0.235831\pi\) |
−0.993671 | + | 0.112328i | \(0.964169\pi\) | |||||||
\(468\) | −2.38197 | + | 7.33094i | −0.110106 | + | 0.338873i | ||||
\(469\) | 4.92705 | − | 3.57971i | 0.227510 | − | 0.165296i | ||||
\(470\) | −7.47214 | − | 5.42882i | −0.344664 | − | 0.250413i | ||||
\(471\) | 0.236068 | + | 0.726543i | 0.0108774 | + | 0.0334773i | ||||
\(472\) | 7.61803 | 0.350648 | ||||||||
\(473\) | 1.50000 | − | 5.96361i | 0.0689701 | − | 0.274207i | ||||
\(474\) | −22.1803 | −1.01878 | ||||||||
\(475\) | −2.11803 | − | 6.51864i | −0.0971821 | − | 0.299096i | ||||
\(476\) | 1.30902 | + | 0.951057i | 0.0599987 | + | 0.0435916i | ||||
\(477\) | −3.85410 | + | 2.80017i | −0.176467 | + | 0.128211i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.7082 | − | 36.0341i | 0.534961 | − | 1.64644i | −0.208771 | − | 0.977965i | \(-0.566946\pi\) |
0.743732 | − | 0.668478i | \(-0.233054\pi\) | |||||||
\(480\) | −2.11803 | + | 1.53884i | −0.0966746 | + | 0.0702382i | ||||
\(481\) | −10.4721 | − | 7.60845i | −0.477488 | − | 0.346916i | ||||
\(482\) | −1.93769 | − | 5.96361i | −0.0882595 | − | 0.271635i | ||||
\(483\) | −15.7082 | −0.714748 | ||||||||
\(484\) | 10.8992 | − | 1.48584i | 0.495418 | − | 0.0675382i | ||||
\(485\) | 9.56231 | 0.434202 | ||||||||
\(486\) | 6.69098 | + | 20.5927i | 0.303509 | + | 0.934105i | ||||
\(487\) | 21.7082 | + | 15.7719i | 0.983693 | + | 0.714695i | 0.958531 | − | 0.284989i | \(-0.0919899\pi\) |
0.0251618 | + | 0.999683i | \(0.491990\pi\) | |||||||
\(488\) | 2.85410 | − | 2.07363i | 0.129199 | − | 0.0938687i | ||||
\(489\) | 2.30902 | − | 7.10642i | 0.104417 | − | 0.321364i | ||||
\(490\) | 0.309017 | − | 0.951057i | 0.0139600 | − | 0.0429644i | ||||
\(491\) | −26.2984 | + | 19.1069i | −1.18683 | + | 0.862282i | −0.992926 | − | 0.118739i | \(-0.962115\pi\) |
−0.193903 | + | 0.981021i | \(0.562115\pi\) | |||||||
\(492\) | −21.8713 | − | 15.8904i | −0.986035 | − | 0.716397i | ||||
\(493\) | −1.61803 | − | 4.97980i | −0.0728726 | − | 0.224279i | ||||
\(494\) | −13.7082 | −0.616761 | ||||||||
\(495\) | 3.11803 | − | 12.3965i | 0.140145 | − | 0.557181i | ||||
\(496\) | −1.23607 | −0.0555011 | ||||||||
\(497\) | 3.00000 | + | 9.23305i | 0.134568 | + | 0.414159i | ||||
\(498\) | −21.8713 | − | 15.8904i | −0.980077 | − | 0.712068i | ||||
\(499\) | 12.2984 | − | 8.93529i | 0.550551 | − | 0.399999i | −0.277438 | − | 0.960744i | \(-0.589485\pi\) |
0.827989 | + | 0.560745i | \(0.189485\pi\) | |||||||
\(500\) | −0.309017 | + | 0.951057i | −0.0138197 | + | 0.0425325i | ||||
\(501\) | −5.23607 | + | 16.1150i | −0.233930 | + | 0.719963i | ||||
\(502\) | 21.7082 | − | 15.7719i | 0.968885 | − | 0.703936i | ||||
\(503\) | −13.8541 | − | 10.0656i | −0.617724 | − | 0.448803i | 0.234402 | − | 0.972140i | \(-0.424687\pi\) |
−0.852126 | + | 0.523337i | \(0.824687\pi\) | |||||||
\(504\) | 1.19098 | + | 3.66547i | 0.0530506 | + | 0.163273i | ||||
\(505\) | 8.94427 | 0.398015 | ||||||||
\(506\) | 19.8541 | − | 1.34708i | 0.882622 | − | 0.0598852i | ||||
\(507\) | −23.5623 | −1.04644 | ||||||||
\(508\) | 3.52786 | + | 10.8576i | 0.156524 | + | 0.481730i | ||||
\(509\) | 20.6525 | + | 15.0049i | 0.915405 | + | 0.665081i | 0.942376 | − | 0.334556i | \(-0.108586\pi\) |
−0.0269711 | + | 0.999636i | \(0.508586\pi\) | |||||||
\(510\) | −3.42705 | + | 2.48990i | −0.151752 | + | 0.110255i | ||||
\(511\) | 4.28115 | − | 13.1760i | 0.189387 | − | 0.582873i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | 12.3992 | − | 9.00854i | 0.547437 | − | 0.397737i | ||||
\(514\) | 23.9164 | + | 17.3763i | 1.05491 | + | 0.766435i | ||||
\(515\) | 5.23607 | + | 16.1150i | 0.230729 | + | 0.710110i | ||||
\(516\) | −4.85410 | −0.213690 | ||||||||
\(517\) | 23.5066 | − | 19.6417i | 1.03382 | − | 0.863840i | ||||
\(518\) | −6.47214 | −0.284369 | ||||||||
\(519\) | −9.70820 | − | 29.8788i | −0.426143 | − | 1.31153i | ||||
\(520\) | 1.61803 | + | 1.17557i | 0.0709555 | + | 0.0515522i | ||||
\(521\) | −28.9615 | + | 21.0418i | −1.26883 | + | 0.921856i | −0.999155 | − | 0.0410965i | \(-0.986915\pi\) |
−0.269671 | + | 0.962953i | \(0.586915\pi\) | |||||||
\(522\) | 3.85410 | − | 11.8617i | 0.168689 | − | 0.519173i | ||||
\(523\) | −1.84752 | + | 5.68609i | −0.0807866 | + | 0.248636i | −0.983290 | − | 0.182048i | \(-0.941727\pi\) |
0.902503 | + | 0.430683i | \(0.141727\pi\) | |||||||
\(524\) | −6.30902 | + | 4.58377i | −0.275611 | + | 0.200243i | ||||
\(525\) | 2.11803 | + | 1.53884i | 0.0924386 | + | 0.0671606i | ||||
\(526\) | 6.23607 | + | 19.1926i | 0.271905 | + | 0.836839i | ||||
\(527\) | −2.00000 | −0.0871214 | ||||||||
\(528\) | −3.23607 | − | 8.05748i | −0.140832 | − | 0.350657i | ||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0.381966 | + | 1.17557i | 0.0165915 | + | 0.0510635i | ||||
\(531\) | 23.7533 | + | 17.2578i | 1.03080 | + | 0.748924i | ||||
\(532\) | −5.54508 | + | 4.02874i | −0.240410 | + | 0.174668i | ||||
\(533\) | −6.38197 | + | 19.6417i | −0.276434 | + | 0.850775i | ||||
\(534\) | −10.5902 | + | 32.5932i | −0.458281 | + | 1.41045i | ||||
\(535\) | −12.4443 | + | 9.04129i | −0.538013 | + | 0.390889i | ||||
\(536\) | 4.92705 | + | 3.57971i | 0.212816 | + | 0.154620i | ||||
\(537\) | −5.16312 | − | 15.8904i | −0.222805 | − | 0.685723i | ||||
\(538\) | 12.1803 | 0.525132 | ||||||||
\(539\) | 2.80902 | + | 1.76336i | 0.120993 | + | 0.0759531i | ||||
\(540\) | −2.23607 | −0.0962250 | ||||||||
\(541\) | −4.58359 | − | 14.1068i | −0.197064 | − | 0.606501i | −0.999946 | − | 0.0103631i | \(-0.996701\pi\) |
0.802882 | − | 0.596138i | \(-0.203299\pi\) | |||||||
\(542\) | 7.61803 | + | 5.53483i | 0.327223 | + | 0.237741i | ||||
\(543\) | −7.47214 | + | 5.42882i | −0.320660 | + | 0.232973i | ||||
\(544\) | −0.500000 | + | 1.53884i | −0.0214373 | + | 0.0659773i | ||||
\(545\) | −0.145898 | + | 0.449028i | −0.00624959 | + | 0.0192342i | ||||
\(546\) | 4.23607 | − | 3.07768i | 0.181287 | − | 0.131713i | ||||
\(547\) | −14.4894 | − | 10.5271i | −0.619520 | − | 0.450108i | 0.233234 | − | 0.972421i | \(-0.425069\pi\) |
−0.852754 | + | 0.522313i | \(0.825069\pi\) | |||||||
\(548\) | −0.336881 | − | 1.03681i | −0.0143908 | − | 0.0442905i | ||||
\(549\) | 13.5967 | 0.580295 | ||||||||
\(550\) | −2.80902 | − | 1.76336i | −0.119777 | − | 0.0751897i | ||||
\(551\) | 22.1803 | 0.944914 | ||||||||
\(552\) | −4.85410 | − | 14.9394i | −0.206604 | − | 0.635863i | ||||
\(553\) | 6.85410 | + | 4.97980i | 0.291466 | + | 0.211762i | ||||
\(554\) | −5.09017 | + | 3.69822i | −0.216261 | + | 0.157123i | ||||
\(555\) | 5.23607 | − | 16.1150i | 0.222259 | − | 0.684042i | ||||
\(556\) | −5.70820 | + | 17.5680i | −0.242082 | + | 0.745051i | ||||
\(557\) | 30.8885 | − | 22.4418i | 1.30879 | − | 0.950891i | 0.308790 | − | 0.951130i | \(-0.400076\pi\) |
1.00000 | 0.000239051i | \(7.60924e-5\pi\) | ||||||||
\(558\) | −3.85410 | − | 2.80017i | −0.163157 | − | 0.118541i | ||||
\(559\) | 1.14590 | + | 3.52671i | 0.0484663 | + | 0.149164i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −5.23607 | − | 13.0373i | −0.221067 | − | 0.550434i | ||||
\(562\) | −24.0344 | −1.01383 | ||||||||
\(563\) | −1.07953 | − | 3.32244i | −0.0454966 | − | 0.140024i | 0.925728 | − | 0.378191i | \(-0.123454\pi\) |
−0.971224 | + | 0.238166i | \(0.923454\pi\) | |||||||
\(564\) | −19.5623 | − | 14.2128i | −0.823722 | − | 0.598469i | ||||
\(565\) | −7.54508 | + | 5.48183i | −0.317424 | + | 0.230622i | ||||
\(566\) | −3.70820 | + | 11.4127i | −0.155867 | + | 0.479711i | ||||
\(567\) | 1.76393 | − | 5.42882i | 0.0740782 | − | 0.227989i | ||||
\(568\) | −7.85410 | + | 5.70634i | −0.329551 | + | 0.239433i | ||||
\(569\) | −6.54508 | − | 4.75528i | −0.274384 | − | 0.199352i | 0.442080 | − | 0.896976i | \(-0.354241\pi\) |
−0.716464 | + | 0.697624i | \(0.754241\pi\) | |||||||
\(570\) | −5.54508 | − | 17.0660i | −0.232258 | − | 0.714817i | ||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | −5.09017 | + | 4.25325i | −0.212831 | + | 0.177837i | ||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 3.19098 | + | 9.82084i | 0.133189 | + | 0.409914i | ||||
\(575\) | −4.85410 | − | 3.52671i | −0.202430 | − | 0.147074i | ||||
\(576\) | −3.11803 | + | 2.26538i | −0.129918 | + | 0.0943910i | ||||
\(577\) | 7.79180 | − | 23.9807i | 0.324377 | − | 0.998329i | −0.647344 | − | 0.762198i | \(-0.724120\pi\) |
0.971721 | − | 0.236131i | \(-0.0758795\pi\) | |||||||
\(578\) | 4.44427 | − | 13.6781i | 0.184857 | − | 0.568932i | ||||
\(579\) | −4.23607 | + | 3.07768i | −0.176045 | + | 0.127904i | ||||
\(580\) | −2.61803 | − | 1.90211i | −0.108708 | − | 0.0789809i | ||||
\(581\) | 3.19098 | + | 9.82084i | 0.132384 | + | 0.407437i | ||||
\(582\) | 25.0344 | 1.03771 | ||||||||
\(583\) | −4.09017 | + | 0.277515i | −0.169398 | + | 0.0114935i | ||||
\(584\) | 13.8541 | 0.573287 | ||||||||
\(585\) | 2.38197 | + | 7.33094i | 0.0984822 | + | 0.303097i | ||||
\(586\) | −13.3262 | − | 9.68208i | −0.550502 | − | 0.399963i | ||||
\(587\) | −2.21885 | + | 1.61209i | −0.0915816 | + | 0.0665379i | −0.632634 | − | 0.774451i | \(-0.718026\pi\) |
0.541052 | + | 0.840989i | \(0.318026\pi\) | |||||||
\(588\) | 0.809017 | − | 2.48990i | 0.0333633 | − | 0.102682i | ||||
\(589\) | 2.61803 | − | 8.05748i | 0.107874 | − | 0.332003i | ||||
\(590\) | 6.16312 | − | 4.47777i | 0.253732 | − | 0.184347i | ||||
\(591\) | 12.7082 | + | 9.23305i | 0.522746 | + | 0.379797i | ||||
\(592\) | −2.00000 | − | 6.15537i | −0.0821995 | − | 0.252984i | ||||
\(593\) | −12.0902 | −0.496484 | −0.248242 | − | 0.968698i | \(-0.579853\pi\) | ||||
−0.248242 | + | 0.968698i | \(0.579853\pi\) | |||||||
\(594\) | 1.80902 | − | 7.19218i | 0.0742249 | − | 0.295099i | ||||
\(595\) | 1.61803 | 0.0663329 | ||||||||
\(596\) | −7.47214 | − | 22.9969i | −0.306071 | − | 0.941988i | ||||
\(597\) | 41.1246 | + | 29.8788i | 1.68312 | + | 1.22286i | ||||
\(598\) | −9.70820 | + | 7.05342i | −0.396998 | + | 0.288436i | ||||
\(599\) | −7.79837 | + | 24.0009i | −0.318633 | + | 0.980651i | 0.655600 | + | 0.755108i | \(0.272416\pi\) |
−0.974233 | + | 0.225543i | \(0.927584\pi\) | |||||||
\(600\) | −0.809017 | + | 2.48990i | −0.0330280 | + | 0.101650i | ||||
\(601\) | −23.5344 | + | 17.0988i | −0.959990 | + | 0.697473i | −0.953148 | − | 0.302503i | \(-0.902178\pi\) |
−0.00684151 | + | 0.999977i | \(0.502178\pi\) | |||||||
\(602\) | 1.50000 | + | 1.08981i | 0.0611354 | + | 0.0444175i | ||||
\(603\) | 7.25329 | + | 22.3233i | 0.295377 | + | 0.909076i | ||||
\(604\) | −2.29180 | −0.0932519 | ||||||||
\(605\) | 7.94427 | − | 7.60845i | 0.322981 | − | 0.309328i | ||||
\(606\) | 23.4164 | 0.951227 | ||||||||
\(607\) | 9.14590 | + | 28.1482i | 0.371221 | + | 1.14250i | 0.945993 | + | 0.324186i | \(0.105090\pi\) |
−0.574773 | + | 0.818313i | \(0.694910\pi\) | |||||||
\(608\) | −5.54508 | − | 4.02874i | −0.224883 | − | 0.163387i | ||||
\(609\) | −6.85410 | + | 4.97980i | −0.277742 | + | 0.201792i | ||||
\(610\) | 1.09017 | − | 3.35520i | 0.0441397 | − | 0.135848i | ||||
\(611\) | −5.70820 | + | 17.5680i | −0.230929 | + | 0.710727i | ||||
\(612\) | −5.04508 | + | 3.66547i | −0.203935 | + | 0.148168i | ||||
\(613\) | −30.2705 | − | 21.9928i | −1.22261 | − | 0.888281i | −0.226300 | − | 0.974058i | \(-0.572663\pi\) |
−0.996314 | + | 0.0857763i | \(0.972663\pi\) | |||||||
\(614\) | −8.51722 | − | 26.2133i | −0.343727 | − | 1.05788i | ||||
\(615\) | −27.0344 | −1.09013 | ||||||||
\(616\) | −0.809017 | + | 3.21644i | −0.0325962 | + | 0.129594i | ||||
\(617\) | 23.0344 | 0.927332 | 0.463666 | − | 0.886010i | \(-0.346534\pi\) | ||||
0.463666 | + | 0.886010i | \(0.346534\pi\) | |||||||
\(618\) | 13.7082 | + | 42.1895i | 0.551425 | + | 1.69711i | ||||
\(619\) | −15.1074 | − | 10.9762i | −0.607217 | − | 0.441169i | 0.241216 | − | 0.970471i | \(-0.422454\pi\) |
−0.848433 | + | 0.529302i | \(0.822454\pi\) | |||||||
\(620\) | −1.00000 | + | 0.726543i | −0.0401610 | + | 0.0291787i | ||||
\(621\) | 4.14590 | − | 12.7598i | 0.166369 | − | 0.512032i | ||||
\(622\) | 9.00000 | − | 27.6992i | 0.360867 | − | 1.11063i | ||||
\(623\) | 10.5902 | − | 7.69421i | 0.424286 | − | 0.308262i | ||||
\(624\) | 4.23607 | + | 3.07768i | 0.169578 | + | 0.123206i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 0.854102 | 0.0341368 | ||||||||
\(627\) | 59.3779 | − | 4.02874i | 2.37132 | − | 0.160892i | ||||
\(628\) | 0.291796 | 0.0116439 | ||||||||
\(629\) | −3.23607 | − | 9.95959i | −0.129030 | − | 0.397115i | ||||
\(630\) | 3.11803 | + | 2.26538i | 0.124225 | + | 0.0902551i | ||||
\(631\) | 19.1803 | − | 13.9353i | 0.763557 | − | 0.554757i | −0.136442 | − | 0.990648i | \(-0.543567\pi\) |
0.899999 | + | 0.435891i | \(0.143567\pi\) | |||||||
\(632\) | −2.61803 | + | 8.05748i | −0.104140 | + | 0.320509i | ||||
\(633\) | −9.11803 | + | 28.0624i | −0.362409 | + | 1.11538i | ||||
\(634\) | −16.7984 | + | 12.2047i | −0.667149 | + | 0.484712i | ||||
\(635\) | 9.23607 | + | 6.71040i | 0.366522 | + | 0.266294i | ||||
\(636\) | 1.00000 | + | 3.07768i | 0.0396526 | + | 0.122038i | ||||
\(637\) | −2.00000 | −0.0792429 | ||||||||
\(638\) | 8.23607 | − | 6.88191i | 0.326069 | − | 0.272457i | ||||
\(639\) | −37.4164 | −1.48017 | ||||||||
\(640\) | 0.309017 | + | 0.951057i | 0.0122150 | + | 0.0375938i | ||||
\(641\) | −32.6246 | − | 23.7032i | −1.28859 | − | 0.936219i | −0.288819 | − | 0.957384i | \(-0.593262\pi\) |
−0.999776 | + | 0.0211650i | \(0.993262\pi\) | |||||||
\(642\) | −32.5795 | + | 23.6704i | −1.28581 | + | 0.934197i | ||||
\(643\) | −4.62868 | + | 14.2456i | −0.182537 | + | 0.561792i | −0.999897 | − | 0.0143355i | \(-0.995437\pi\) |
0.817360 | + | 0.576127i | \(0.195437\pi\) | |||||||
\(644\) | −1.85410 | + | 5.70634i | −0.0730619 | + | 0.224861i | ||||
\(645\) | −3.92705 | + | 2.85317i | −0.154627 | + | 0.112343i | ||||
\(646\) | −8.97214 | − | 6.51864i | −0.353004 | − | 0.256472i | ||||
\(647\) | 0.0557281 | + | 0.171513i | 0.00219090 | + | 0.00674289i | 0.952146 | − | 0.305644i | \(-0.0988716\pi\) |
−0.949955 | + | 0.312386i | \(0.898872\pi\) | |||||||
\(648\) | 5.70820 | 0.224239 | ||||||||
\(649\) | 9.41641 | + | 23.4459i | 0.369626 | + | 0.920332i | ||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 1.00000 | + | 3.07768i | 0.0391931 | + | 0.120624i | ||||
\(652\) | −2.30902 | − | 1.67760i | −0.0904281 | − | 0.0656998i | ||||
\(653\) | −21.7082 | + | 15.7719i | −0.849508 | + | 0.617203i | −0.925010 | − | 0.379942i | \(-0.875944\pi\) |
0.0755026 | + | 0.997146i | \(0.475944\pi\) | |||||||
\(654\) | −0.381966 | + | 1.17557i | −0.0149361 | + | 0.0459684i | ||||
\(655\) | −2.40983 | + | 7.41669i | −0.0941599 | + | 0.289794i | ||||
\(656\) | −8.35410 | + | 6.06961i | −0.326173 | + | 0.236978i | ||||
\(657\) | 43.1976 | + | 31.3849i | 1.68530 | + | 1.22444i | ||||
\(658\) | 2.85410 | + | 8.78402i | 0.111264 | + | 0.342437i | ||||
\(659\) | −4.09017 | −0.159330 | −0.0796652 | − | 0.996822i | \(-0.525385\pi\) | ||||
−0.0796652 | + | 0.996822i | \(0.525385\pi\) | |||||||
\(660\) | −7.35410 | − | 4.61653i | −0.286258 | − | 0.179698i | ||||
\(661\) | −45.8885 | −1.78486 | −0.892429 | − | 0.451188i | \(-0.851000\pi\) | ||||
−0.892429 | + | 0.451188i | \(0.851000\pi\) | |||||||
\(662\) | −1.86475 | − | 5.73910i | −0.0724754 | − | 0.223056i | ||||
\(663\) | 6.85410 | + | 4.97980i | 0.266191 | + | 0.193399i | ||||
\(664\) | −8.35410 | + | 6.06961i | −0.324202 | + | 0.235547i | ||||
\(665\) | −2.11803 | + | 6.51864i | −0.0821338 | + | 0.252782i | ||||
\(666\) | 7.70820 | − | 23.7234i | 0.298687 | − | 0.919264i | ||||
\(667\) | 15.7082 | − | 11.4127i | 0.608224 | − | 0.441901i | ||||
\(668\) | 5.23607 | + | 3.80423i | 0.202590 | + | 0.147190i | ||||
\(669\) | 5.09017 | + | 15.6659i | 0.196797 | + | 0.605680i | ||||
\(670\) | 6.09017 | 0.235284 | ||||||||
\(671\) | 9.90983 | + | 6.22088i | 0.382565 | + | 0.240154i | ||||
\(672\) | 2.61803 | 0.100993 | ||||||||
\(673\) | 12.0066 | + | 36.9524i | 0.462820 | + | 1.42441i | 0.861704 | + | 0.507411i | \(0.169397\pi\) |
−0.398885 | + | 0.917001i | \(0.630603\pi\) | |||||||
\(674\) | 12.6353 | + | 9.18005i | 0.486692 | + | 0.353602i | ||||
\(675\) | −1.80902 | + | 1.31433i | −0.0696291 | + | 0.0505885i | ||||
\(676\) | −2.78115 | + | 8.55951i | −0.106967 | + | 0.329212i | ||||
\(677\) | 4.20163 | − | 12.9313i | 0.161482 | − | 0.496989i | −0.837278 | − | 0.546777i | \(-0.815855\pi\) |
0.998760 | + | 0.0497878i | \(0.0158545\pi\) | |||||||
\(678\) | −19.7533 | + | 14.3516i | −0.758620 | + | 0.551170i | ||||
\(679\) | −7.73607 | − | 5.62058i | −0.296883 | − | 0.215698i | ||||
\(680\) | 0.500000 | + | 1.53884i | 0.0191741 | + | 0.0590119i | ||||
\(681\) | 63.5410 | 2.43490 | ||||||||
\(682\) | −1.52786 | − | 3.80423i | −0.0585049 | − | 0.145671i | ||||
\(683\) | −31.0557 | −1.18831 | −0.594157 | − | 0.804349i | \(-0.702514\pi\) | ||||
−0.594157 | + | 0.804349i | \(0.702514\pi\) | |||||||
\(684\) | −8.16312 | − | 25.1235i | −0.312125 | − | 0.960621i | ||||
\(685\) | −0.881966 | − | 0.640786i | −0.0336982 | − | 0.0244832i | ||||
\(686\) | −0.809017 | + | 0.587785i | −0.0308884 | + | 0.0224417i | ||||
\(687\) | 9.00000 | − | 27.6992i | 0.343371 | − | 1.05679i | ||||
\(688\) | −0.572949 | + | 1.76336i | −0.0218435 | + | 0.0672273i | ||||
\(689\) | 2.00000 | − | 1.45309i | 0.0761939 | − | 0.0553581i | ||||
\(690\) | −12.7082 | − | 9.23305i | −0.483793 | − | 0.351496i | ||||
\(691\) | 6.53444 | + | 20.1109i | 0.248582 | + | 0.765056i | 0.995027 | + | 0.0996090i | \(0.0317592\pi\) |
−0.746445 | + | 0.665447i | \(0.768241\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | −9.80902 | + | 8.19624i | −0.372614 | + | 0.311349i | ||||
\(694\) | 5.32624 | 0.202181 | ||||||||
\(695\) | 5.70820 | + | 17.5680i | 0.216525 | + | 0.666394i | ||||
\(696\) | −6.85410 | − | 4.97980i | −0.259804 | − | 0.188759i | ||||
\(697\) | −13.5172 | + | 9.82084i | −0.512001 | + | 0.371991i | ||||
\(698\) | 1.70820 | − | 5.25731i | 0.0646565 | − | 0.198992i | ||||
\(699\) | −8.82624 | + | 27.1644i | −0.333839 | + | 1.02745i | ||||
\(700\) | 0.809017 | − | 0.587785i | 0.0305780 | − | 0.0222162i | ||||
\(701\) | −9.85410 | − | 7.15942i | −0.372184 | − | 0.270408i | 0.385932 | − | 0.922527i | \(-0.373880\pi\) |
−0.758116 | + | 0.652120i | \(0.773880\pi\) | |||||||
\(702\) | 1.38197 | + | 4.25325i | 0.0521589 | + | 0.160529i | ||||
\(703\) | 44.3607 | 1.67309 | ||||||||
\(704\) | −3.30902 | + | 0.224514i | −0.124713 | + | 0.00846169i | ||||
\(705\) | −24.1803 | −0.910684 | ||||||||
\(706\) | 8.79180 | + | 27.0584i | 0.330884 | + | 1.01836i | ||||
\(707\) | −7.23607 | − | 5.25731i | −0.272140 | − | 0.197722i | ||||
\(708\) | 16.1353 | − | 11.7229i | 0.606400 | − | 0.440575i | ||||
\(709\) | −7.70820 | + | 23.7234i | −0.289488 | + | 0.890951i | 0.695530 | + | 0.718497i | \(0.255170\pi\) |
−0.985018 | + | 0.172454i | \(0.944830\pi\) | |||||||
\(710\) | −3.00000 | + | 9.23305i | −0.112588 | + | 0.346510i | ||||
\(711\) | −26.4164 | + | 19.1926i | −0.990693 | + | 0.719780i | ||||
\(712\) | 10.5902 | + | 7.69421i | 0.396883 | + | 0.288353i | ||||
\(713\) | −2.29180 | − | 7.05342i | −0.0858284 | − | 0.264153i | ||||
\(714\) | 4.23607 | 0.158531 | ||||||||
\(715\) | −1.61803 | + | 6.43288i | −0.0605110 | + | 0.240576i | ||||
\(716\) | −6.38197 | −0.238505 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.0902 | − | 10.9637i | −0.563160 | − | 0.409160i | ||||
\(719\) | −26.1803 | + | 19.0211i | −0.976362 | + | 0.709368i | −0.956893 | − | 0.290442i | \(-0.906198\pi\) |
−0.0194693 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(720\) | −1.19098 | + | 3.66547i | −0.0443853 | + | 0.136604i | ||||
\(721\) | 5.23607 | − | 16.1150i | 0.195001 | − | 0.600152i | ||||
\(722\) | 22.6353 | − | 16.4455i | 0.842397 | − | 0.612037i | ||||
\(723\) | −13.2812 | − | 9.64932i | −0.493931 | − | 0.358862i | ||||
\(724\) | 1.09017 | + | 3.35520i | 0.0405158 | + | 0.124695i | ||||
\(725\) | −3.23607 | −0.120185 | ||||||||
\(726\) | 20.7984 | − | 19.9192i | 0.771900 | − | 0.739270i | ||||
\(727\) | 38.8328 | 1.44023 | 0.720115 | − | 0.693855i | \(-0.244089\pi\) | ||||
0.720115 | + | 0.693855i | \(0.244089\pi\) | |||||||
\(728\) | −0.618034 | − | 1.90211i | −0.0229059 | − | 0.0704970i | ||||
\(729\) | 32.0066 | + | 23.2541i | 1.18543 | + | 0.861264i | ||||
\(730\) | 11.2082 | − | 8.14324i | 0.414834 | − | 0.301395i | ||||
\(731\) | −0.927051 | + | 2.85317i | −0.0342882 | + | 0.105528i | ||||
\(732\) | 2.85410 | − | 8.78402i | 0.105491 | − | 0.324667i | ||||
\(733\) | −10.7082 | + | 7.77997i | −0.395517 | + | 0.287360i | −0.767712 | − | 0.640795i | \(-0.778605\pi\) |
0.372196 | + | 0.928154i | \(0.378605\pi\) | |||||||
\(734\) | 22.7984 | + | 16.5640i | 0.841503 | + | 0.611388i | ||||
\(735\) | −0.809017 | − | 2.48990i | −0.0298410 | − | 0.0918413i | ||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | −4.92705 | + | 19.5887i | −0.181490 | + | 0.721558i | ||||
\(738\) | −39.7984 | −1.46500 | ||||||||
\(739\) | 7.62461 | + | 23.4661i | 0.280476 | + | 0.863216i | 0.987718 | + | 0.156245i | \(0.0499389\pi\) |
−0.707242 | + | 0.706971i | \(0.750061\pi\) | |||||||
\(740\) | −5.23607 | − | 3.80423i | −0.192482 | − | 0.139846i | ||||
\(741\) | −29.0344 | + | 21.0948i | −1.06661 | + | 0.774935i | ||||
\(742\) | 0.381966 | − | 1.17557i | 0.0140224 | − | 0.0431566i | ||||
\(743\) | 3.74265 | − | 11.5187i | 0.137304 | − | 0.422579i | −0.858637 | − | 0.512584i | \(-0.828688\pi\) |
0.995941 | + | 0.0900048i | \(0.0286882\pi\) | |||||||
\(744\) | −2.61803 | + | 1.90211i | −0.0959818 | + | 0.0697348i | ||||
\(745\) | −19.5623 | − | 14.2128i | −0.716707 | − | 0.520718i | ||||
\(746\) | −7.56231 | − | 23.2744i | −0.276876 | − | 0.852136i | ||||
\(747\) | −39.7984 | −1.45615 | ||||||||
\(748\) | −5.35410 | + | 0.363271i | −0.195765 | + | 0.0132825i | ||||
\(749\) | 15.3820 | 0.562045 | ||||||||
\(750\) | 0.809017 | + | 2.48990i | 0.0295411 | + | 0.0909182i | ||||
\(751\) | 26.4164 | + | 19.1926i | 0.963948 | + | 0.700350i | 0.954064 | − | 0.299602i | \(-0.0968538\pi\) |
0.00988402 | + | 0.999951i | \(0.496854\pi\) | |||||||
\(752\) | −7.47214 | + | 5.42882i | −0.272481 | + | 0.197969i | ||||
\(753\) | 21.7082 | − | 66.8110i | 0.791091 | − | 2.43473i | ||||
\(754\) | −2.00000 | + | 6.15537i | −0.0728357 | + | 0.224165i | ||||
\(755\) | −1.85410 | + | 1.34708i | −0.0674777 | + | 0.0490254i | ||||
\(756\) | 1.80902 | + | 1.31433i | 0.0657933 | + | 0.0478016i | ||||
\(757\) | 6.14590 | + | 18.9151i | 0.223376 | + | 0.687482i | 0.998452 | + | 0.0556139i | \(0.0177116\pi\) |
−0.775076 | + | 0.631868i | \(0.782288\pi\) | |||||||
\(758\) | 27.8541 | 1.01171 | ||||||||
\(759\) | 39.9787 | − | 33.4055i | 1.45114 | − | 1.21254i | ||||
\(760\) | −6.85410 | −0.248624 | ||||||||
\(761\) | 9.82624 | + | 30.2421i | 0.356201 | + | 1.09627i | 0.955310 | + | 0.295606i | \(0.0955216\pi\) |
−0.599109 | + | 0.800667i | \(0.704478\pi\) | |||||||
\(762\) | 24.1803 | + | 17.5680i | 0.875961 | + | 0.636423i | ||||
\(763\) | 0.381966 | − | 0.277515i | 0.0138281 | − | 0.0100467i | ||||
\(764\) | −0.472136 | + | 1.45309i | −0.0170813 | + | 0.0525708i | ||||
\(765\) | −1.92705 | + | 5.93085i | −0.0696727 | + | 0.214430i | ||||
\(766\) | −19.4164 | + | 14.1068i | −0.701543 | + | 0.509701i | ||||
\(767\) | −12.3262 | − | 8.95554i | −0.445075 | − | 0.323366i | ||||
\(768\) | 0.809017 | + | 2.48990i | 0.0291929 | + | 0.0898465i | ||||
\(769\) | 7.88854 | 0.284468 | 0.142234 | − | 0.989833i | \(-0.454571\pi\) | ||||
0.142234 | + | 0.989833i | \(0.454571\pi\) | |||||||
\(770\) | 1.23607 | + | 3.07768i | 0.0445448 | + | 0.110912i | ||||
\(771\) | 77.3951 | 2.78732 | ||||||||
\(772\) | 0.618034 | + | 1.90211i | 0.0222435 | + | 0.0684585i | ||||
\(773\) | 19.9443 | + | 14.4904i | 0.717346 | + | 0.521182i | 0.885535 | − | 0.464573i | \(-0.153792\pi\) |
−0.168189 | + | 0.985755i | \(0.553792\pi\) | |||||||
\(774\) | −5.78115 | + | 4.20025i | −0.207799 | + | 0.150975i | ||||
\(775\) | −0.381966 | + | 1.17557i | −0.0137206 | + | 0.0422277i | ||||
\(776\) | 2.95492 | − | 9.09429i | 0.106075 | − | 0.326466i | ||||
\(777\) | −13.7082 | + | 9.95959i | −0.491779 | + | 0.357298i | ||||
\(778\) | −26.5623 | − | 19.2986i | −0.952305 | − | 0.691890i | ||||
\(779\) | −21.8713 | − | 67.3130i | −0.783621 | − | 2.41174i | ||||
\(780\) | 5.23607 | 0.187481 | ||||||||
\(781\) | −27.2705 | − | 17.1190i | −0.975816 | − | 0.612567i | ||||
\(782\) | −9.70820 | −0.347165 | ||||||||
\(783\) | −2.23607 | − | 6.88191i | −0.0799106 | − | 0.245939i | ||||
\(784\) | −0.809017 | − | 0.587785i | −0.0288935 | − | 0.0209923i | ||||
\(785\) | 0.236068 | − | 0.171513i | 0.00842563 | − | 0.00612158i | ||||
\(786\) | −6.30902 | + | 19.4172i | −0.225035 | + | 0.692587i | ||||
\(787\) | −15.7918 | + | 48.6022i | −0.562917 | + | 1.73248i | 0.111145 | + | 0.993804i | \(0.464548\pi\) |
−0.674061 | + | 0.738675i | \(0.735452\pi\) | |||||||
\(788\) | 4.85410 | − | 3.52671i | 0.172920 | − | 0.125634i | ||||
\(789\) | 42.7426 | + | 31.0543i | 1.52168 | + | 1.10556i | ||||
\(790\) | 2.61803 | + | 8.05748i | 0.0931455 | + | 0.286672i | ||||
\(791\) | 9.32624 | 0.331603 | ||||||||
\(792\) | −10.8262 | − | 6.79615i | −0.384694 | − | 0.241491i | ||||
\(793\) | −7.05573 | −0.250556 | ||||||||
\(794\) | 5.23607 | + | 16.1150i | 0.185821 | + | 0.571899i | ||||
\(795\) | 2.61803 | + | 1.90211i | 0.0928521 | + | 0.0674610i | ||||
\(796\) | 15.7082 | − | 11.4127i | 0.556763 | − | 0.404512i | ||||
\(797\) | −1.96556 | + | 6.04937i | −0.0696236 | + | 0.214280i | −0.979814 | − | 0.199910i | \(-0.935935\pi\) |
0.910191 | + | 0.414190i | \(0.135935\pi\) | |||||||
\(798\) | −5.54508 | + | 17.0660i | −0.196294 | + | 0.604130i | ||||
\(799\) | −12.0902 | + | 8.78402i | −0.427719 | + | 0.310756i | ||||
\(800\) | 0.809017 | + | 0.587785i | 0.0286031 | + | 0.0207813i | ||||
\(801\) | 15.5902 | + | 47.9816i | 0.550852 | + | 1.69535i | ||||
\(802\) | 26.5066 | 0.935980 | ||||||||
\(803\) | 17.1246 | + | 42.6385i | 0.604314 | + | 1.50468i | ||||
\(804\) | 15.9443 | 0.562311 | ||||||||
\(805\) | 1.85410 | + | 5.70634i | 0.0653485 | + | 0.201122i | ||||
\(806\) | 2.00000 | + | 1.45309i | 0.0704470 | + | 0.0511827i | ||||
\(807\) | 25.7984 | − | 18.7436i | 0.908146 | − | 0.659807i | ||||
\(808\) | 2.76393 | − | 8.50651i | 0.0972348 | − | 0.299258i | ||||
\(809\) | 15.0836 | − | 46.4225i | 0.530311 | − | 1.63213i | −0.223258 | − | 0.974759i | \(-0.571669\pi\) |
0.753568 | − | 0.657370i | \(-0.228331\pi\) | |||||||
\(810\) | 4.61803 | − | 3.35520i | 0.162261 | − | 0.117890i | ||||
\(811\) | −24.2082 | − | 17.5883i | −0.850065 | − | 0.617608i | 0.0750989 | − | 0.997176i | \(-0.476073\pi\) |
−0.925164 | + | 0.379568i | \(0.876073\pi\) | |||||||
\(812\) | 1.00000 | + | 3.07768i | 0.0350931 | + | 0.108006i | ||||
\(813\) | 24.6525 | 0.864600 | ||||||||
\(814\) | 16.4721 | − | 13.7638i | 0.577348 | − | 0.482422i | ||||
\(815\) | −2.85410 | −0.0999748 | ||||||||
\(816\) | 1.30902 | + | 4.02874i | 0.0458248 | + | 0.141034i | ||||
\(817\) | −10.2812 | − | 7.46969i | −0.359692 | − | 0.261332i | ||||
\(818\) | −22.5623 | + | 16.3925i | −0.788873 | + | 0.573149i | ||||
\(819\) | 2.38197 | − | 7.33094i | 0.0832326 | − | 0.256164i | ||||
\(820\) | −3.19098 | + | 9.82084i | −0.111434 | + | 0.342958i | ||||
\(821\) | 25.1246 | − | 18.2541i | 0.876855 | − | 0.637072i | −0.0555626 | − | 0.998455i | \(-0.517695\pi\) |
0.932418 | + | 0.361383i | \(0.117695\pi\) | |||||||
\(822\) | −2.30902 | − | 1.67760i | −0.0805362 | − | 0.0585130i | ||||
\(823\) | −0.875388 | − | 2.69417i | −0.0305141 | − | 0.0939128i | 0.934640 | − | 0.355597i | \(-0.115722\pi\) |
−0.965154 | + | 0.261684i | \(0.915722\pi\) | |||||||
\(824\) | 16.9443 | 0.590282 | ||||||||
\(825\) | −8.66312 | + | 0.587785i | −0.301611 | + | 0.0204641i | ||||
\(826\) | −7.61803 | −0.265065 | ||||||||
\(827\) | 12.5902 | + | 38.7486i | 0.437803 | + | 1.34742i | 0.890187 | + | 0.455596i | \(0.150574\pi\) |
−0.452384 | + | 0.891823i | \(0.649426\pi\) | |||||||
\(828\) | −18.7082 | − | 13.5923i | −0.650155 | − | 0.472365i | ||||
\(829\) | −27.6525 | + | 20.0907i | −0.960410 | + | 0.697779i | −0.953246 | − | 0.302195i | \(-0.902280\pi\) |
−0.00716421 | + | 0.999974i | \(0.502280\pi\) | |||||||
\(830\) | −3.19098 | + | 9.82084i | −0.110761 | + | 0.340886i | ||||
\(831\) | −5.09017 | + | 15.6659i | −0.176576 | + | 0.543445i | ||||
\(832\) | 1.61803 | − | 1.17557i | 0.0560952 | − | 0.0407556i | ||||
\(833\) | −1.30902 | − | 0.951057i | −0.0453548 | − | 0.0329522i | ||||
\(834\) | 14.9443 | + | 45.9937i | 0.517478 | + | 1.59263i | ||||
\(835\) | 6.47214 | 0.223978 | ||||||||
\(836\) | 5.54508 | − | 22.0458i | 0.191781 | − | 0.762470i | ||||
\(837\) | −2.76393 | −0.0955355 | ||||||||
\(838\) | −3.80902 | − | 11.7229i | −0.131580 | − | 0.404963i | ||||
\(839\) | −3.61803 | − | 2.62866i | −0.124908 | − | 0.0907513i | 0.523577 | − | 0.851978i | \(-0.324597\pi\) |
−0.648485 | + | 0.761227i | \(0.724597\pi\) | |||||||
\(840\) | 2.11803 | − | 1.53884i | 0.0730791 | − | 0.0530951i | ||||
\(841\) | −5.72542 | + | 17.6210i | −0.197428 | + | 0.607622i | ||||
\(842\) | 1.96556 | − | 6.04937i | 0.0677376 | − | 0.208475i | ||||
\(843\) | −50.9058 | + | 36.9852i | −1.75329 | + | 1.27384i | ||||
\(844\) | 9.11803 | + | 6.62464i | 0.313856 | + | 0.228029i | ||||
\(845\) | 2.78115 | + | 8.55951i | 0.0956746 | + | 0.294456i | ||||
\(846\) | −35.5967 | −1.22384 | ||||||||
\(847\) | −10.8992 | + | 1.48584i | −0.374500 | + | 0.0510541i | ||||
\(848\) | 1.23607 | 0.0424467 | ||||||||
\(849\) | 9.70820 | + | 29.8788i | 0.333185 | + | 1.02544i | ||||
\(850\) | 1.30902 | + | 0.951057i | 0.0448989 | + | 0.0326210i | ||||
\(851\) | 31.4164 | − | 22.8254i | 1.07694 | − | 0.782443i | ||||
\(852\) | −7.85410 | + | 24.1724i | −0.269077 | + | 0.828134i | ||||
\(853\) | 1.32624 | − | 4.08174i | 0.0454095 | − | 0.139756i | −0.925781 | − | 0.378060i | \(-0.876591\pi\) |
0.971191 | + | 0.238304i | \(0.0765914\pi\) | |||||||
\(854\) | −2.85410 | + | 2.07363i | −0.0976654 | + | 0.0709580i | ||||
\(855\) | −21.3713 | − | 15.5272i | −0.730884 | − | 0.531018i | ||||
\(856\) | 4.75329 | + | 14.6291i | 0.162464 | + | 0.500013i | ||||
\(857\) | 9.27051 | 0.316675 | 0.158337 | − | 0.987385i | \(-0.449387\pi\) | ||||
0.158337 | + | 0.987385i | \(0.449387\pi\) | |||||||
\(858\) | −4.23607 | + | 16.8415i | −0.144617 | + | 0.574959i | ||||
\(859\) | −7.43769 | −0.253771 | −0.126885 | − | 0.991917i | \(-0.540498\pi\) | ||||
−0.126885 | + | 0.991917i | \(0.540498\pi\) | |||||||
\(860\) | 0.572949 | + | 1.76336i | 0.0195374 | + | 0.0601299i | ||||
\(861\) | 21.8713 | + | 15.8904i | 0.745373 | + | 0.541545i | ||||
\(862\) | −25.2705 | + | 18.3601i | −0.860717 | + | 0.625347i | ||||
\(863\) | 2.09017 | − | 6.43288i | 0.0711502 | − | 0.218978i | −0.909158 | − | 0.416451i | \(-0.863274\pi\) |
0.980308 | + | 0.197473i | \(0.0632736\pi\) | |||||||
\(864\) | −0.690983 | + | 2.12663i | −0.0235077 | + | 0.0723493i | ||||
\(865\) | −9.70820 | + | 7.05342i | −0.330089 | + | 0.239824i | ||||
\(866\) | 13.3090 | + | 9.66957i | 0.452259 | + | 0.328585i | ||||
\(867\) | −11.6353 | − | 35.8096i | −0.395154 | − | 1.21616i | ||||
\(868\) | 1.23607 | 0.0419549 | ||||||||
\(869\) | −28.0344 | + | 1.90211i | −0.951003 | + | 0.0645248i | ||||
\(870\) | −8.47214 | −0.287232 | ||||||||
\(871\) | −3.76393 | − | 11.5842i | −0.127536 | − | 0.392515i | ||||
\(872\) | 0.381966 | + | 0.277515i | 0.0129350 | + | 0.00939783i | ||||
\(873\) | 29.8156 | − | 21.6623i | 1.00910 | − | 0.733158i | ||||
\(874\) | 12.7082 | − | 39.1118i | 0.429861 | − | 1.32298i | ||||
\(875\) | 0.309017 | − | 0.951057i | 0.0104467 | − | 0.0321516i | ||||
\(876\) | 29.3435 | − | 21.3193i | 0.991424 | − | 0.720311i | ||||
\(877\) | 14.5623 | + | 10.5801i | 0.491734 | + | 0.357266i | 0.805851 | − | 0.592119i | \(-0.201708\pi\) |
−0.314117 | + | 0.949384i | \(0.601708\pi\) | |||||||
\(878\) | −8.85410 | − | 27.2501i | −0.298811 | − | 0.919647i | ||||
\(879\) | −43.1246 | −1.45456 | ||||||||
\(880\) | −2.54508 | + | 2.12663i | −0.0857948 | + | 0.0716886i | ||||
\(881\) | 4.14590 | 0.139679 | 0.0698394 | − | 0.997558i | \(-0.477751\pi\) | ||||
0.0698394 | + | 0.997558i | \(0.477751\pi\) | |||||||
\(882\) | −1.19098 | − | 3.66547i | −0.0401025 | − | 0.123423i | ||||
\(883\) | −1.97214 | − | 1.43284i | −0.0663677 | − | 0.0482189i | 0.554107 | − | 0.832446i | \(-0.313060\pi\) |
−0.620474 | + | 0.784227i | \(0.713060\pi\) | |||||||
\(884\) | 2.61803 | − | 1.90211i | 0.0880540 | − | 0.0639750i | ||||
\(885\) | 6.16312 | − | 18.9681i | 0.207171 | − | 0.637607i | ||||
\(886\) | −8.66312 | + | 26.6623i | −0.291043 | + | 0.895739i | ||||
\(887\) | −3.52786 | + | 2.56314i | −0.118454 | + | 0.0860619i | −0.645435 | − | 0.763815i | \(-0.723324\pi\) |
0.526981 | + | 0.849877i | \(0.323324\pi\) | |||||||
\(888\) | −13.7082 | − | 9.95959i | −0.460017 | − | 0.334222i | ||||
\(889\) | −3.52786 | − | 10.8576i | −0.118321 | − | 0.364154i | ||||
\(890\) | 13.0902 | 0.438783 | ||||||||
\(891\) | 7.05573 | + | 17.5680i | 0.236376 | + | 0.588552i | ||||
\(892\) | 6.29180 | 0.210665 | ||||||||
\(893\) | −19.5623 | − | 60.2066i | −0.654628 | − | 2.01474i | ||||
\(894\) | −51.2148 | − | 37.2097i | −1.71288 | − | 1.24448i | ||||
\(895\) | −5.16312 | + | 3.75123i | −0.172584 | + | 0.125390i | ||||
\(896\) | 0.309017 | − | 0.951057i | 0.0103235 | − | 0.0317726i | ||||
\(897\) | −9.70820 | + | 29.8788i | −0.324147 | + | 0.997623i | ||||
\(898\) | 19.7812 | − | 14.3718i | 0.660106 | − | 0.479595i | ||||
\(899\) | −3.23607 | − | 2.35114i | −0.107929 | − | 0.0784149i | ||||
\(900\) | 1.19098 | + | 3.66547i | 0.0396994 | + | 0.122182i | ||||
\(901\) | 2.00000 | 0.0666297 | ||||||||
\(902\) | −29.0066 | − | 18.2088i | −0.965813 | − | 0.606288i | ||||
\(903\) | 4.85410 | 0.161534 | ||||||||
\(904\) | 2.88197 | + | 8.86978i | 0.0958528 | + | 0.295004i | ||||
\(905\) | 2.85410 | + | 2.07363i | 0.0948736 | + | 0.0689297i | ||||
\(906\) | −4.85410 | + | 3.52671i | −0.161267 | + | 0.117167i | ||||
\(907\) | 6.88197 | − | 21.1805i | 0.228512 | − | 0.703287i | −0.769404 | − | 0.638762i | \(-0.779447\pi\) |
0.997916 | − | 0.0645251i | \(-0.0205533\pi\) | |||||||
\(908\) | 7.50000 | − | 23.0826i | 0.248896 | − | 0.766024i | ||||
\(909\) | 27.8885 | − | 20.2622i | 0.925005 | − | 0.672055i | ||||
\(910\) | −1.61803 | − | 1.17557i | −0.0536373 | − | 0.0389698i | ||||
\(911\) | −15.9443 | − | 49.0714i | −0.528257 | − | 1.62581i | −0.757783 | − | 0.652506i | \(-0.773718\pi\) |
0.229526 | − | 0.973303i | \(-0.426282\pi\) | |||||||
\(912\) | −17.9443 | −0.594194 | ||||||||
\(913\) | −29.0066 | − | 18.2088i | −0.959978 | − | 0.602624i | ||||
\(914\) | −31.2705 | −1.03434 | ||||||||
\(915\) | −2.85410 | − | 8.78402i | −0.0943537 | − | 0.290391i | ||||
\(916\) | −9.00000 | − | 6.53888i | −0.297368 | − | 0.216051i | ||||
\(917\) | 6.30902 | − | 4.58377i | 0.208342 | − | 0.151369i | ||||
\(918\) | −1.11803 | + | 3.44095i | −0.0369006 | + | 0.113568i | ||||
\(919\) | 2.72949 | − | 8.40051i | 0.0900376 | − | 0.277107i | −0.895891 | − | 0.444274i | \(-0.853462\pi\) |
0.985929 | + | 0.167167i | \(0.0534618\pi\) | |||||||
\(920\) | −4.85410 | + | 3.52671i | −0.160035 | + | 0.116272i | ||||
\(921\) | −58.3779 | − | 42.4140i | −1.92362 | − | 1.39759i | ||||
\(922\) | 2.14590 | + | 6.60440i | 0.0706714 | + | 0.217504i | ||||
\(923\) | 19.4164 | 0.639099 | ||||||||
\(924\) | 3.23607 | + | 8.05748i | 0.106459 | + | 0.265072i | ||||
\(925\) | −6.47214 | −0.212803 | ||||||||
\(926\) | 2.29180 | + | 7.05342i | 0.0753131 | + | 0.231790i | ||||
\(927\) | 52.8328 | + | 38.3853i | 1.73526 | + | 1.26074i | ||||
\(928\) | −2.61803 | + | 1.90211i | −0.0859412 | + | 0.0624399i | ||||
\(929\) | −1.00658 | + | 3.09793i | −0.0330247 | + | 0.101640i | −0.966210 | − | 0.257756i | \(-0.917017\pi\) |
0.933185 | + | 0.359395i | \(0.117017\pi\) | |||||||
\(930\) | −1.00000 | + | 3.07768i | −0.0327913 | + | 0.100921i | ||||
\(931\) | 5.54508 | − | 4.02874i | 0.181733 | − | 0.132037i | ||||
\(932\) | 8.82624 | + | 6.41264i | 0.289113 | + | 0.210053i | ||||
\(933\) | −23.5623 | − | 72.5173i | −0.771395 | − | 2.37411i | ||||
\(934\) | 17.8885 | 0.585331 | ||||||||
\(935\) | −4.11803 | + | 3.44095i | −0.134674 | + | 0.112531i | ||||
\(936\) | 7.70820 | 0.251951 | ||||||||
\(937\) | −10.3197 | − | 31.7606i | −0.337129 | − | 1.03758i | −0.965664 | − | 0.259794i | \(-0.916345\pi\) |
0.628535 | − | 0.777781i | \(-0.283655\pi\) | |||||||
\(938\) | −4.92705 | − | 3.57971i | −0.160874 | − | 0.116882i | ||||
\(939\) | 1.80902 | − | 1.31433i | 0.0590350 | − | 0.0428915i | ||||
\(940\) | −2.85410 | + | 8.78402i | −0.0930905 | + | 0.286503i | ||||
\(941\) | −10.5623 | + | 32.5074i | −0.344321 | + | 1.05971i | 0.617625 | + | 0.786473i | \(0.288095\pi\) |
−0.961946 | + | 0.273239i | \(0.911905\pi\) | |||||||
\(942\) | 0.618034 | − | 0.449028i | 0.0201366 | − | 0.0146301i | ||||
\(943\) | −50.1246 | − | 36.4177i | −1.63228 | − | 1.18592i | ||||
\(944\) | −2.35410 | − | 7.24518i | −0.0766195 | − | 0.235811i | ||||
\(945\) | 2.23607 | 0.0727393 | ||||||||
\(946\) | −6.13525 | + | 0.416272i | −0.199474 | + | 0.0135342i | ||||
\(947\) | −41.9098 | −1.36189 | −0.680943 | − | 0.732336i | \(-0.738430\pi\) | ||||
−0.680943 | + | 0.732336i | \(0.738430\pi\) | |||||||
\(948\) | 6.85410 | + | 21.0948i | 0.222611 | + | 0.685126i | ||||
\(949\) | −22.4164 | − | 16.2865i | −0.727667 | − | 0.528681i | ||||
\(950\) | −5.54508 | + | 4.02874i | −0.179906 | + | 0.130710i | ||||
\(951\) | −16.7984 | + | 51.7001i | −0.544725 | + | 1.67649i | ||||
\(952\) | 0.500000 | − | 1.53884i | 0.0162051 | − | 0.0498741i | ||||
\(953\) | 23.8262 | − | 17.3108i | 0.771808 | − | 0.560751i | −0.130702 | − | 0.991422i | \(-0.541723\pi\) |
0.902509 | + | 0.430671i | \(0.141723\pi\) | |||||||
\(954\) | 3.85410 | + | 2.80017i | 0.124781 | + | 0.0906588i | ||||
\(955\) | 0.472136 | + | 1.45309i | 0.0152780 | + | 0.0470207i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.85410 | − | 27.2501i | 0.221562 | − | 0.880871i | ||||
\(958\) | −37.8885 | −1.22412 | ||||||||
\(959\) | 0.336881 | + | 1.03681i | 0.0108785 | + | 0.0334804i | ||||
\(960\) | 2.11803 | + | 1.53884i | 0.0683593 | + | 0.0496659i | ||||
\(961\) | 23.8435 | − | 17.3233i | 0.769144 | − | 0.558816i | ||||
\(962\) | −4.00000 | + | 12.3107i | −0.128965 | + | 0.396914i | ||||
\(963\) | −18.3197 | + | 56.3821i | −0.590343 | + | 1.81689i | ||||
\(964\) | −5.07295 | + | 3.68571i | −0.163389 | + | 0.118709i | ||||
\(965\) | 1.61803 | + | 1.17557i | 0.0520864 | + | 0.0378430i | ||||
\(966\) | 4.85410 | + | 14.9394i | 0.156178 | + | 0.480667i | ||||
\(967\) | −27.0132 | −0.868685 | −0.434342 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434342 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(968\) | −4.78115 | − | 9.90659i | −0.153672 | − | 0.318410i | ||||
\(969\) | −29.0344 | −0.932721 | ||||||||
\(970\) | −2.95492 | − | 9.09429i | −0.0948766 | − | 0.292000i | ||||
\(971\) | 21.7082 | + | 15.7719i | 0.696649 | + | 0.506145i | 0.878839 | − | 0.477118i | \(-0.158319\pi\) |
−0.182190 | + | 0.983263i | \(0.558319\pi\) | |||||||
\(972\) | 17.5172 | − | 12.7270i | 0.561865 | − | 0.408219i | ||||
\(973\) | 5.70820 | − | 17.5680i | 0.182997 | − | 0.563206i | ||||
\(974\) | 8.29180 | − | 25.5195i | 0.265686 | − | 0.817698i | ||||
\(975\) | 4.23607 | − | 3.07768i | 0.135663 | − | 0.0985648i | ||||
\(976\) | −2.85410 | − | 2.07363i | −0.0913576 | − | 0.0663752i | ||||
\(977\) | 13.3820 | + | 41.1855i | 0.428127 | + | 1.31764i | 0.899968 | + | 0.435956i | \(0.143590\pi\) |
−0.471841 | + | 0.881684i | \(0.656410\pi\) | |||||||
\(978\) | −7.47214 | −0.238933 | ||||||||
\(979\) | −10.5902 | + | 42.1038i | −0.338463 | + | 1.34564i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 0.562306 | + | 1.73060i | 0.0179530 | + | 0.0552538i | ||||
\(982\) | 26.2984 | + | 19.1069i | 0.839215 | + | 0.609725i | ||||
\(983\) | 11.8541 | − | 8.61251i | 0.378087 | − | 0.274696i | −0.382469 | − | 0.923968i | \(-0.624926\pi\) |
0.760556 | + | 0.649272i | \(0.224926\pi\) | |||||||
\(984\) | −8.35410 | + | 25.7113i | −0.266319 | + | 0.819646i | ||||
\(985\) | 1.85410 | − | 5.70634i | 0.0590766 | − | 0.181819i | ||||
\(986\) | −4.23607 | + | 3.07768i | −0.134904 | + | 0.0980134i | ||||
\(987\) | 19.5623 | + | 14.2128i | 0.622675 | + | 0.452400i | ||||
\(988\) | 4.23607 | + | 13.0373i | 0.134767 | + | 0.414771i | ||||
\(989\) | −11.1246 | −0.353742 | ||||||||
\(990\) | −12.7533 | + | 0.865300i | −0.405326 | + | 0.0275010i | ||||
\(991\) | 20.6525 | 0.656048 | 0.328024 | − | 0.944669i | \(-0.393617\pi\) | ||||
0.328024 | + | 0.944669i | \(0.393617\pi\) | |||||||
\(992\) | 0.381966 | + | 1.17557i | 0.0121274 | + | 0.0373244i | ||||
\(993\) | −12.7812 | − | 9.28605i | −0.405598 | − | 0.294684i | ||||
\(994\) | 7.85410 | − | 5.70634i | 0.249117 | − | 0.180994i | ||||
\(995\) | 6.00000 | − | 18.4661i | 0.190213 | − | 0.585415i | ||||
\(996\) | −8.35410 | + | 25.7113i | −0.264710 | + | 0.814693i | ||||
\(997\) | −18.7082 | + | 13.5923i | −0.592495 | + | 0.430473i | −0.843207 | − | 0.537589i | \(-0.819335\pi\) |
0.250712 | + | 0.968062i | \(0.419335\pi\) | |||||||
\(998\) | −12.2984 | − | 8.93529i | −0.389298 | − | 0.282842i | ||||
\(999\) | −4.47214 | − | 13.7638i | −0.141492 | − | 0.435468i |
(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 | 770.2.n.b.71.1 | ✓ | 4 | |
11.3 | even | 5 | 8470.2.a.bt.1.2 | 2 | |||
11.8 | odd | 10 | 8470.2.a.cf.1.2 | 2 | |||
11.9 | even | 5 | inner | 770.2.n.b.141.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.b.71.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
770.2.n.b.141.1 | yes | 4 | 11.9 | even | 5 | inner | |
8470.2.a.bt.1.2 | 2 | 11.3 | even | 5 | |||
8470.2.a.cf.1.2 | 2 | 11.8 | odd | 10 |