Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [385,2,Mod(36,385)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(385, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("385.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.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: | \(3.07424047782\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 385.71 |
Dual form | 385.2.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 \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(276\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.690983 | + | 2.12663i | 0.488599 | + | 1.50375i | 0.826700 | + | 0.562643i | \(0.190215\pi\) |
−0.338101 | + | 0.941110i | \(0.609785\pi\) | |||||||
\(3\) | 1.30902 | + | 0.951057i | 0.755761 | + | 0.549093i | 0.897607 | − | 0.440796i | \(-0.145304\pi\) |
−0.141846 | + | 0.989889i | \(0.545304\pi\) | |||||||
\(4\) | −2.42705 | + | 1.76336i | −1.21353 | + | 0.881678i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | −1.11803 | + | 3.44095i | −0.456435 | + | 1.40476i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | −1.80902 | − | 1.31433i | −0.639584 | − | 0.464685i | ||||
\(9\) | −0.118034 | − | 0.363271i | −0.0393447 | − | 0.121090i | ||||
\(10\) | −2.23607 | −0.707107 | ||||||||
\(11\) | −2.54508 | + | 2.12663i | −0.767372 | + | 0.641202i | ||||
\(12\) | −4.85410 | −1.40126 | ||||||||
\(13\) | 0.736068 | + | 2.26538i | 0.204149 | + | 0.628305i | 0.999747 | + | 0.0224806i | \(0.00715641\pi\) |
−0.795599 | + | 0.605824i | \(0.792844\pi\) | |||||||
\(14\) | 1.80902 | + | 1.31433i | 0.483480 | + | 0.351269i | ||||
\(15\) | −1.30902 | + | 0.951057i | −0.337987 | + | 0.245562i | ||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 1.04508 | − | 3.21644i | 0.253470 | − | 0.780101i | −0.740657 | − | 0.671883i | \(-0.765486\pi\) |
0.994127 | − | 0.108218i | \(-0.0345144\pi\) | |||||||
\(18\) | 0.690983 | − | 0.502029i | 0.162866 | − | 0.118329i | ||||
\(19\) | −1.00000 | − | 0.726543i | −0.229416 | − | 0.166680i | 0.467139 | − | 0.884184i | \(-0.345285\pi\) |
−0.696555 | + | 0.717504i | \(0.745285\pi\) | |||||||
\(20\) | −0.927051 | − | 2.85317i | −0.207295 | − | 0.637988i | ||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | −6.28115 | − | 3.94298i | −1.33915 | − | 0.840647i | ||||
\(23\) | 4.47214 | 0.932505 | 0.466252 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466252 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(24\) | −1.11803 | − | 3.44095i | −0.228218 | − | 0.702382i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | −4.30902 | + | 3.13068i | −0.845068 | + | 0.613978i | ||||
\(27\) | 1.69098 | − | 5.20431i | 0.325430 | − | 1.00157i | ||||
\(28\) | −0.927051 | + | 2.85317i | −0.175196 | + | 0.539198i | ||||
\(29\) | 4.73607 | − | 3.44095i | 0.879466 | − | 0.638969i | −0.0536443 | − | 0.998560i | \(-0.517084\pi\) |
0.933110 | + | 0.359591i | \(0.117084\pi\) | |||||||
\(30\) | −2.92705 | − | 2.12663i | −0.534404 | − | 0.388267i | ||||
\(31\) | −0.381966 | − | 1.17557i | −0.0686031 | − | 0.211139i | 0.910878 | − | 0.412677i | \(-0.135406\pi\) |
−0.979481 | + | 0.201538i | \(0.935406\pi\) | |||||||
\(32\) | −6.70820 | −1.18585 | ||||||||
\(33\) | −5.35410 | + | 0.363271i | −0.932030 | + | 0.0632374i | ||||
\(34\) | 7.56231 | 1.29692 | ||||||||
\(35\) | 0.309017 | + | 0.951057i | 0.0522334 | + | 0.160758i | ||||
\(36\) | 0.927051 | + | 0.673542i | 0.154508 | + | 0.112257i | ||||
\(37\) | 2.23607 | − | 1.62460i | 0.367607 | − | 0.267082i | −0.388611 | − | 0.921402i | \(-0.627045\pi\) |
0.756218 | + | 0.654320i | \(0.227045\pi\) | |||||||
\(38\) | 0.854102 | − | 2.62866i | 0.138554 | − | 0.426424i | ||||
\(39\) | −1.19098 | + | 3.66547i | −0.190710 | + | 0.586945i | ||||
\(40\) | 1.80902 | − | 1.31433i | 0.286031 | − | 0.207813i | ||||
\(41\) | 5.23607 | + | 3.80423i | 0.817736 | + | 0.594120i | 0.916063 | − | 0.401034i | \(-0.131349\pi\) |
−0.0983268 | + | 0.995154i | \(0.531349\pi\) | |||||||
\(42\) | 1.11803 | + | 3.44095i | 0.172516 | + | 0.530951i | ||||
\(43\) | −0.763932 | −0.116499 | −0.0582493 | − | 0.998302i | \(-0.518552\pi\) | ||||
−0.0582493 | + | 0.998302i | \(0.518552\pi\) | |||||||
\(44\) | 2.42705 | − | 9.64932i | 0.365892 | − | 1.45469i | ||||
\(45\) | 0.381966 | 0.0569401 | ||||||||
\(46\) | 3.09017 | + | 9.51057i | 0.455621 | + | 1.40226i | ||||
\(47\) | 6.35410 | + | 4.61653i | 0.926841 | + | 0.673389i | 0.945217 | − | 0.326442i | \(-0.105850\pi\) |
−0.0183763 | + | 0.999831i | \(0.505850\pi\) | |||||||
\(48\) | −1.30902 | + | 0.951057i | −0.188940 | + | 0.137273i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 0.690983 | − | 2.12663i | 0.0977198 | − | 0.300750i | ||||
\(51\) | 4.42705 | − | 3.21644i | 0.619911 | − | 0.450392i | ||||
\(52\) | −5.78115 | − | 4.20025i | −0.801702 | − | 0.582470i | ||||
\(53\) | −3.23607 | − | 9.95959i | −0.444508 | − | 1.36806i | −0.883022 | − | 0.469331i | \(-0.844495\pi\) |
0.438514 | − | 0.898724i | \(-0.355505\pi\) | |||||||
\(54\) | 12.2361 | 1.66512 | ||||||||
\(55\) | −1.23607 | − | 3.07768i | −0.166671 | − | 0.414995i | ||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | −0.618034 | − | 1.90211i | −0.0818606 | − | 0.251941i | ||||
\(58\) | 10.5902 | + | 7.69421i | 1.39056 | + | 1.01030i | ||||
\(59\) | 3.85410 | − | 2.80017i | 0.501761 | − | 0.364551i | −0.307928 | − | 0.951410i | \(-0.599636\pi\) |
0.809689 | + | 0.586859i | \(0.199636\pi\) | |||||||
\(60\) | 1.50000 | − | 4.61653i | 0.193649 | − | 0.595991i | ||||
\(61\) | −2.85410 | + | 8.78402i | −0.365430 | + | 1.12468i | 0.584281 | + | 0.811552i | \(0.301377\pi\) |
−0.949711 | + | 0.313127i | \(0.898623\pi\) | |||||||
\(62\) | 2.23607 | − | 1.62460i | 0.283981 | − | 0.206324i | ||||
\(63\) | −0.309017 | − | 0.224514i | −0.0389325 | − | 0.0282861i | ||||
\(64\) | −4.01722 | − | 12.3637i | −0.502153 | − | 1.54547i | ||||
\(65\) | −2.38197 | −0.295447 | ||||||||
\(66\) | −4.47214 | − | 11.1352i | −0.550482 | − | 1.37064i | ||||
\(67\) | −14.1803 | −1.73240 | −0.866202 | − | 0.499694i | \(-0.833446\pi\) | ||||
−0.866202 | + | 0.499694i | \(0.833446\pi\) | |||||||
\(68\) | 3.13525 | + | 9.64932i | 0.380206 | + | 1.17015i | ||||
\(69\) | 5.85410 | + | 4.25325i | 0.704751 | + | 0.512032i | ||||
\(70\) | −1.80902 | + | 1.31433i | −0.216219 | + | 0.157092i | ||||
\(71\) | 0.208204 | − | 0.640786i | 0.0247093 | − | 0.0760473i | −0.937941 | − | 0.346794i | \(-0.887270\pi\) |
0.962651 | + | 0.270746i | \(0.0872704\pi\) | |||||||
\(72\) | −0.263932 | + | 0.812299i | −0.0311047 | + | 0.0957304i | ||||
\(73\) | −6.97214 | + | 5.06555i | −0.816027 | + | 0.592878i | −0.915572 | − | 0.402155i | \(-0.868261\pi\) |
0.0995449 | + | 0.995033i | \(0.468261\pi\) | |||||||
\(74\) | 5.00000 | + | 3.63271i | 0.581238 | + | 0.422294i | ||||
\(75\) | −0.500000 | − | 1.53884i | −0.0577350 | − | 0.177690i | ||||
\(76\) | 3.70820 | 0.425360 | ||||||||
\(77\) | −0.809017 | + | 3.21644i | −0.0921960 | + | 0.366547i | ||||
\(78\) | −8.61803 | −0.975800 | ||||||||
\(79\) | −4.26393 | − | 13.1230i | −0.479730 | − | 1.47646i | −0.839471 | − | 0.543404i | \(-0.817135\pi\) |
0.359741 | − | 0.933052i | \(-0.382865\pi\) | |||||||
\(80\) | −0.809017 | − | 0.587785i | −0.0904508 | − | 0.0657164i | ||||
\(81\) | 6.23607 | − | 4.53077i | 0.692896 | − | 0.503419i | ||||
\(82\) | −4.47214 | + | 13.7638i | −0.493865 | + | 1.51996i | ||||
\(83\) | −3.26393 | + | 10.0453i | −0.358263 | + | 1.10262i | 0.595830 | + | 0.803111i | \(0.296823\pi\) |
−0.954093 | + | 0.299510i | \(0.903177\pi\) | |||||||
\(84\) | −3.92705 | + | 2.85317i | −0.428476 | + | 0.311306i | ||||
\(85\) | 2.73607 | + | 1.98787i | 0.296768 | + | 0.215615i | ||||
\(86\) | −0.527864 | − | 1.62460i | −0.0569210 | − | 0.175185i | ||||
\(87\) | 9.47214 | 1.01552 | ||||||||
\(88\) | 7.39919 | − | 0.502029i | 0.788756 | − | 0.0535164i | ||||
\(89\) | 17.2361 | 1.82702 | 0.913510 | − | 0.406817i | \(-0.133361\pi\) | ||||
0.913510 | + | 0.406817i | \(0.133361\pi\) | |||||||
\(90\) | 0.263932 | + | 0.812299i | 0.0278209 | + | 0.0856239i | ||||
\(91\) | 1.92705 | + | 1.40008i | 0.202010 | + | 0.146769i | ||||
\(92\) | −10.8541 | + | 7.88597i | −1.13162 | + | 0.822169i | ||||
\(93\) | 0.618034 | − | 1.90211i | 0.0640871 | − | 0.197240i | ||||
\(94\) | −5.42705 | + | 16.7027i | −0.559758 | + | 1.72276i | ||||
\(95\) | 1.00000 | − | 0.726543i | 0.102598 | − | 0.0745417i | ||||
\(96\) | −8.78115 | − | 6.37988i | −0.896223 | − | 0.651144i | ||||
\(97\) | 0.100813 | + | 0.310271i | 0.0102360 | + | 0.0315032i | 0.956044 | − | 0.293223i | \(-0.0947278\pi\) |
−0.945808 | + | 0.324726i | \(0.894728\pi\) | |||||||
\(98\) | 2.23607 | 0.225877 | ||||||||
\(99\) | 1.07295 | + | 0.673542i | 0.107835 | + | 0.0676935i | ||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | −0.0901699 | − | 0.277515i | −0.00897224 | − | 0.0276137i | 0.946470 | − | 0.322791i | \(-0.104621\pi\) |
−0.955442 | + | 0.295178i | \(0.904621\pi\) | |||||||
\(102\) | 9.89919 | + | 7.19218i | 0.980166 | + | 0.712132i | ||||
\(103\) | 1.35410 | − | 0.983813i | 0.133424 | − | 0.0969379i | −0.519072 | − | 0.854731i | \(-0.673722\pi\) |
0.652495 | + | 0.757793i | \(0.273722\pi\) | |||||||
\(104\) | 1.64590 | − | 5.06555i | 0.161394 | − | 0.496718i | ||||
\(105\) | −0.500000 | + | 1.53884i | −0.0487950 | + | 0.150176i | ||||
\(106\) | 18.9443 | − | 13.7638i | 1.84003 | − | 1.33686i | ||||
\(107\) | 2.23607 | + | 1.62460i | 0.216169 | + | 0.157056i | 0.690600 | − | 0.723237i | \(-0.257346\pi\) |
−0.474432 | + | 0.880292i | \(0.657346\pi\) | |||||||
\(108\) | 5.07295 | + | 15.6129i | 0.488145 | + | 1.50236i | ||||
\(109\) | −20.4721 | −1.96087 | −0.980437 | − | 0.196831i | \(-0.936935\pi\) | ||||
−0.980437 | + | 0.196831i | \(0.936935\pi\) | |||||||
\(110\) | 5.69098 | − | 4.75528i | 0.542614 | − | 0.453398i | ||||
\(111\) | 4.47214 | 0.424476 | ||||||||
\(112\) | 0.309017 | + | 0.951057i | 0.0291994 | + | 0.0898664i | ||||
\(113\) | −1.23607 | − | 0.898056i | −0.116279 | − | 0.0844820i | 0.528126 | − | 0.849166i | \(-0.322895\pi\) |
−0.644405 | + | 0.764684i | \(0.722895\pi\) | |||||||
\(114\) | 3.61803 | − | 2.62866i | 0.338860 | − | 0.246196i | ||||
\(115\) | −1.38197 | + | 4.25325i | −0.128869 | + | 0.396618i | ||||
\(116\) | −5.42705 | + | 16.7027i | −0.503889 | + | 1.55081i | ||||
\(117\) | 0.736068 | − | 0.534785i | 0.0680495 | − | 0.0494409i | ||||
\(118\) | 8.61803 | + | 6.26137i | 0.793354 | + | 0.576406i | ||||
\(119\) | −1.04508 | − | 3.21644i | −0.0958028 | − | 0.294851i | ||||
\(120\) | 3.61803 | 0.330280 | ||||||||
\(121\) | 1.95492 | − | 10.8249i | 0.177720 | − | 0.984081i | ||||
\(122\) | −20.6525 | −1.86979 | ||||||||
\(123\) | 3.23607 | + | 9.95959i | 0.291786 | + | 0.898026i | ||||
\(124\) | 3.00000 | + | 2.17963i | 0.269408 | + | 0.195736i | ||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | 0.263932 | − | 0.812299i | 0.0235129 | − | 0.0723654i | ||||
\(127\) | 1.47214 | − | 4.53077i | 0.130631 | − | 0.402041i | −0.864254 | − | 0.503056i | \(-0.832209\pi\) |
0.994885 | + | 0.101015i | \(0.0322090\pi\) | |||||||
\(128\) | 12.6631 | − | 9.20029i | 1.11927 | − | 0.813199i | ||||
\(129\) | −1.00000 | − | 0.726543i | −0.0880451 | − | 0.0639685i | ||||
\(130\) | −1.64590 | − | 5.06555i | −0.144355 | − | 0.444278i | ||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 12.3541 | − | 10.3229i | 1.07529 | − | 0.898490i | ||||
\(133\) | −1.23607 | −0.107181 | ||||||||
\(134\) | −9.79837 | − | 30.1563i | −0.846451 | − | 2.60511i | ||||
\(135\) | 4.42705 | + | 3.21644i | 0.381020 | + | 0.276827i | ||||
\(136\) | −6.11803 | + | 4.44501i | −0.524617 | + | 0.381157i | ||||
\(137\) | 4.76393 | − | 14.6619i | 0.407010 | − | 1.25265i | −0.512195 | − | 0.858869i | \(-0.671167\pi\) |
0.919205 | − | 0.393779i | \(-0.128833\pi\) | |||||||
\(138\) | −5.00000 | + | 15.3884i | −0.425628 | + | 1.30995i | ||||
\(139\) | −11.7082 | + | 8.50651i | −0.993077 | + | 0.721513i | −0.960593 | − | 0.277960i | \(-0.910342\pi\) |
−0.0324841 | + | 0.999472i | \(0.510342\pi\) | |||||||
\(140\) | −2.42705 | − | 1.76336i | −0.205123 | − | 0.149031i | ||||
\(141\) | 3.92705 | + | 12.0862i | 0.330717 | + | 1.01784i | ||||
\(142\) | 1.50658 | 0.126429 | ||||||||
\(143\) | −6.69098 | − | 4.20025i | −0.559528 | − | 0.351243i | ||||
\(144\) | 0.381966 | 0.0318305 | ||||||||
\(145\) | 1.80902 | + | 5.56758i | 0.150231 | + | 0.462363i | ||||
\(146\) | −15.5902 | − | 11.3269i | −1.29025 | − | 0.937423i | ||||
\(147\) | 1.30902 | − | 0.951057i | 0.107966 | − | 0.0784418i | ||||
\(148\) | −2.56231 | + | 7.88597i | −0.210620 | + | 0.648222i | ||||
\(149\) | −3.44427 | + | 10.6004i | −0.282166 | + | 0.868417i | 0.705068 | + | 0.709140i | \(0.250916\pi\) |
−0.987234 | + | 0.159277i | \(0.949084\pi\) | |||||||
\(150\) | 2.92705 | − | 2.12663i | 0.238993 | − | 0.173638i | ||||
\(151\) | 2.11803 | + | 1.53884i | 0.172363 | + | 0.125229i | 0.670622 | − | 0.741799i | \(-0.266027\pi\) |
−0.498259 | + | 0.867028i | \(0.666027\pi\) | |||||||
\(152\) | 0.854102 | + | 2.62866i | 0.0692768 | + | 0.213212i | ||||
\(153\) | −1.29180 | −0.104436 | ||||||||
\(154\) | −7.39919 | + | 0.502029i | −0.596243 | + | 0.0404546i | ||||
\(155\) | 1.23607 | 0.0992834 | ||||||||
\(156\) | −3.57295 | − | 10.9964i | −0.286065 | − | 0.880417i | ||||
\(157\) | 3.97214 | + | 2.88593i | 0.317011 | + | 0.230322i | 0.734899 | − | 0.678177i | \(-0.237230\pi\) |
−0.417888 | + | 0.908499i | \(0.637230\pi\) | |||||||
\(158\) | 24.9615 | − | 18.1356i | 1.98583 | − | 1.44279i | ||||
\(159\) | 5.23607 | − | 16.1150i | 0.415247 | − | 1.27800i | ||||
\(160\) | 2.07295 | − | 6.37988i | 0.163881 | − | 0.504374i | ||||
\(161\) | 3.61803 | − | 2.62866i | 0.285141 | − | 0.207167i | ||||
\(162\) | 13.9443 | + | 10.1311i | 1.09557 | + | 0.795975i | ||||
\(163\) | 0.0557281 | + | 0.171513i | 0.00436496 | + | 0.0134340i | 0.953215 | − | 0.302292i | \(-0.0977519\pi\) |
−0.948850 | + | 0.315726i | \(0.897752\pi\) | |||||||
\(164\) | −19.4164 | −1.51617 | ||||||||
\(165\) | 1.30902 | − | 5.20431i | 0.101907 | − | 0.405155i | ||||
\(166\) | −23.6180 | −1.83311 | ||||||||
\(167\) | −3.70820 | − | 11.4127i | −0.286949 | − | 0.883140i | −0.985808 | − | 0.167879i | \(-0.946308\pi\) |
0.698858 | − | 0.715260i | \(-0.253692\pi\) | |||||||
\(168\) | −2.92705 | − | 2.12663i | −0.225827 | − | 0.164073i | ||||
\(169\) | 5.92705 | − | 4.30625i | 0.455927 | − | 0.331250i | ||||
\(170\) | −2.33688 | + | 7.19218i | −0.179231 | + | 0.551615i | ||||
\(171\) | −0.145898 | + | 0.449028i | −0.0111571 | + | 0.0343380i | ||||
\(172\) | 1.85410 | − | 1.34708i | 0.141374 | − | 0.102714i | ||||
\(173\) | −15.0172 | − | 10.9106i | −1.14174 | − | 0.829521i | −0.154378 | − | 0.988012i | \(-0.549337\pi\) |
−0.987360 | + | 0.158491i | \(0.949337\pi\) | |||||||
\(174\) | 6.54508 | + | 20.1437i | 0.496182 | + | 1.52709i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −1.23607 | − | 3.07768i | −0.0931721 | − | 0.231989i | ||||
\(177\) | 7.70820 | 0.579384 | ||||||||
\(178\) | 11.9098 | + | 36.6547i | 0.892680 | + | 2.74739i | ||||
\(179\) | −14.0623 | − | 10.2169i | −1.05107 | − | 0.763644i | −0.0786512 | − | 0.996902i | \(-0.525061\pi\) |
−0.972415 | + | 0.233258i | \(0.925061\pi\) | |||||||
\(180\) | −0.927051 | + | 0.673542i | −0.0690983 | + | 0.0502029i | ||||
\(181\) | 4.47214 | − | 13.7638i | 0.332411 | − | 1.02306i | −0.635572 | − | 0.772042i | \(-0.719236\pi\) |
0.967983 | − | 0.251015i | \(-0.0807643\pi\) | |||||||
\(182\) | −1.64590 | + | 5.06555i | −0.122002 | + | 0.375484i | ||||
\(183\) | −12.0902 | + | 8.78402i | −0.893731 | + | 0.649334i | ||||
\(184\) | −8.09017 | − | 5.87785i | −0.596415 | − | 0.433321i | ||||
\(185\) | 0.854102 | + | 2.62866i | 0.0627948 | + | 0.193263i | ||||
\(186\) | 4.47214 | 0.327913 | ||||||||
\(187\) | 4.18034 | + | 10.4086i | 0.305697 | + | 0.761154i | ||||
\(188\) | −23.5623 | −1.71846 | ||||||||
\(189\) | −1.69098 | − | 5.20431i | −0.123001 | − | 0.378558i | ||||
\(190\) | 2.23607 | + | 1.62460i | 0.162221 | + | 0.117861i | ||||
\(191\) | −9.63525 | + | 7.00042i | −0.697183 | + | 0.506533i | −0.879013 | − | 0.476797i | \(-0.841798\pi\) |
0.181831 | + | 0.983330i | \(0.441798\pi\) | |||||||
\(192\) | 6.50000 | − | 20.0049i | 0.469097 | − | 1.44373i | ||||
\(193\) | 1.23607 | − | 3.80423i | 0.0889741 | − | 0.273834i | −0.896662 | − | 0.442715i | \(-0.854015\pi\) |
0.985636 | + | 0.168881i | \(0.0540153\pi\) | |||||||
\(194\) | −0.590170 | + | 0.428784i | −0.0423717 | + | 0.0307849i | ||||
\(195\) | −3.11803 | − | 2.26538i | −0.223287 | − | 0.162228i | ||||
\(196\) | 0.927051 | + | 2.85317i | 0.0662179 | + | 0.203798i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | −0.690983 | + | 2.74717i | −0.0491060 | + | 0.195233i | ||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 0.690983 | + | 2.12663i | 0.0488599 | + | 0.150375i | ||||
\(201\) | −18.5623 | − | 13.4863i | −1.30928 | − | 0.951251i | ||||
\(202\) | 0.527864 | − | 0.383516i | 0.0371404 | − | 0.0269841i | ||||
\(203\) | 1.80902 | − | 5.56758i | 0.126968 | − | 0.390768i | ||||
\(204\) | −5.07295 | + | 15.6129i | −0.355177 | + | 1.09312i | ||||
\(205\) | −5.23607 | + | 3.80423i | −0.365703 | + | 0.265699i | ||||
\(206\) | 3.02786 | + | 2.19987i | 0.210961 | + | 0.153272i | ||||
\(207\) | −0.527864 | − | 1.62460i | −0.0366891 | − | 0.112917i | ||||
\(208\) | −2.38197 | −0.165160 | ||||||||
\(209\) | 4.09017 | − | 0.277515i | 0.282923 | − | 0.0191961i | ||||
\(210\) | −3.61803 | −0.249668 | ||||||||
\(211\) | 7.20820 | + | 22.1846i | 0.496233 | + | 1.52725i | 0.815026 | + | 0.579424i | \(0.196723\pi\) |
−0.318793 | + | 0.947824i | \(0.603277\pi\) | |||||||
\(212\) | 25.4164 | + | 18.4661i | 1.74561 | + | 1.26826i | ||||
\(213\) | 0.881966 | − | 0.640786i | 0.0604313 | − | 0.0439059i | ||||
\(214\) | −1.90983 | + | 5.87785i | −0.130553 | + | 0.401802i | ||||
\(215\) | 0.236068 | − | 0.726543i | 0.0160997 | − | 0.0495498i | ||||
\(216\) | −9.89919 | + | 7.19218i | −0.673554 | + | 0.489366i | ||||
\(217\) | −1.00000 | − | 0.726543i | −0.0678844 | − | 0.0493209i | ||||
\(218\) | −14.1459 | − | 43.5366i | −0.958081 | − | 2.94867i | ||||
\(219\) | −13.9443 | −0.942267 | ||||||||
\(220\) | 8.42705 | + | 5.29007i | 0.568152 | + | 0.356656i | ||||
\(221\) | 8.05573 | 0.541887 | ||||||||
\(222\) | 3.09017 | + | 9.51057i | 0.207399 | + | 0.638307i | ||||
\(223\) | −8.47214 | − | 6.15537i | −0.567336 | − | 0.412194i | 0.266800 | − | 0.963752i | \(-0.414034\pi\) |
−0.834137 | + | 0.551558i | \(0.814034\pi\) | |||||||
\(224\) | −5.42705 | + | 3.94298i | −0.362610 | + | 0.263452i | ||||
\(225\) | −0.118034 | + | 0.363271i | −0.00786893 | + | 0.0242181i | ||||
\(226\) | 1.05573 | − | 3.24920i | 0.0702260 | − | 0.216133i | ||||
\(227\) | −11.1631 | + | 8.11048i | −0.740922 | + | 0.538312i | −0.893000 | − | 0.450057i | \(-0.851404\pi\) |
0.152078 | + | 0.988369i | \(0.451404\pi\) | |||||||
\(228\) | 4.85410 | + | 3.52671i | 0.321471 | + | 0.233562i | ||||
\(229\) | −9.03444 | − | 27.8052i | −0.597013 | − | 1.83742i | −0.544441 | − | 0.838799i | \(-0.683258\pi\) |
−0.0525716 | − | 0.998617i | \(-0.516742\pi\) | |||||||
\(230\) | −10.0000 | −0.659380 | ||||||||
\(231\) | −4.11803 | + | 3.44095i | −0.270947 | + | 0.226398i | ||||
\(232\) | −13.0902 | −0.859412 | ||||||||
\(233\) | −7.61803 | − | 23.4459i | −0.499074 | − | 1.53599i | −0.810510 | − | 0.585725i | \(-0.800810\pi\) |
0.311436 | − | 0.950267i | \(-0.399190\pi\) | |||||||
\(234\) | 1.64590 | + | 1.19581i | 0.107596 | + | 0.0781729i | ||||
\(235\) | −6.35410 | + | 4.61653i | −0.414496 | + | 0.301149i | ||||
\(236\) | −4.41641 | + | 13.5923i | −0.287484 | + | 0.884784i | ||||
\(237\) | 6.89919 | − | 21.2335i | 0.448150 | − | 1.37926i | ||||
\(238\) | 6.11803 | − | 4.44501i | 0.396573 | − | 0.288127i | ||||
\(239\) | 17.7812 | + | 12.9188i | 1.15017 | + | 0.835645i | 0.988503 | − | 0.151200i | \(-0.0483139\pi\) |
0.161664 | + | 0.986846i | \(0.448314\pi\) | |||||||
\(240\) | −0.500000 | − | 1.53884i | −0.0322749 | − | 0.0993318i | ||||
\(241\) | 23.1246 | 1.48959 | 0.744794 | − | 0.667295i | \(-0.232548\pi\) | ||||
0.744794 | + | 0.667295i | \(0.232548\pi\) | |||||||
\(242\) | 24.3713 | − | 3.32244i | 1.56665 | − | 0.213575i | ||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | −8.56231 | − | 26.3521i | −0.548145 | − | 1.68702i | ||||
\(245\) | 0.809017 | + | 0.587785i | 0.0516862 | + | 0.0375522i | ||||
\(246\) | −18.9443 | + | 13.7638i | −1.20784 | + | 0.877549i | ||||
\(247\) | 0.909830 | − | 2.80017i | 0.0578911 | − | 0.178170i | ||||
\(248\) | −0.854102 | + | 2.62866i | −0.0542355 | + | 0.166920i | ||||
\(249\) | −13.8262 | + | 10.0453i | −0.876202 | + | 0.636598i | ||||
\(250\) | 1.80902 | + | 1.31433i | 0.114412 | + | 0.0831254i | ||||
\(251\) | 1.76393 | + | 5.42882i | 0.111338 | + | 0.342664i | 0.991166 | − | 0.132629i | \(-0.0423419\pi\) |
−0.879827 | + | 0.475293i | \(0.842342\pi\) | |||||||
\(252\) | 1.14590 | 0.0721848 | ||||||||
\(253\) | −11.3820 | + | 9.51057i | −0.715578 | + | 0.597924i | ||||
\(254\) | 10.6525 | 0.668396 | ||||||||
\(255\) | 1.69098 | + | 5.20431i | 0.105893 | + | 0.325907i | ||||
\(256\) | 7.28115 | + | 5.29007i | 0.455072 | + | 0.330629i | ||||
\(257\) | 3.73607 | − | 2.71441i | 0.233050 | − | 0.169320i | −0.465132 | − | 0.885242i | \(-0.653993\pi\) |
0.698181 | + | 0.715921i | \(0.253993\pi\) | |||||||
\(258\) | 0.854102 | − | 2.62866i | 0.0531741 | − | 0.163653i | ||||
\(259\) | 0.854102 | − | 2.62866i | 0.0530713 | − | 0.163337i | ||||
\(260\) | 5.78115 | − | 4.20025i | 0.358532 | − | 0.260489i | ||||
\(261\) | −1.80902 | − | 1.31433i | −0.111975 | − | 0.0813548i | ||||
\(262\) | 5.52786 | + | 17.0130i | 0.341513 | + | 1.05107i | ||||
\(263\) | −8.18034 | −0.504421 | −0.252211 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252211 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(264\) | 10.1631 | + | 6.37988i | 0.625497 | + | 0.392655i | ||||
\(265\) | 10.4721 | 0.643298 | ||||||||
\(266\) | −0.854102 | − | 2.62866i | −0.0523684 | − | 0.161173i | ||||
\(267\) | 22.5623 | + | 16.3925i | 1.38079 | + | 1.00320i | ||||
\(268\) | 34.4164 | − | 25.0050i | 2.10232 | − | 1.52742i | ||||
\(269\) | 3.90983 | − | 12.0332i | 0.238387 | − | 0.733678i | −0.758268 | − | 0.651943i | \(-0.773954\pi\) |
0.996654 | − | 0.0817349i | \(-0.0260461\pi\) | |||||||
\(270\) | −3.78115 | + | 11.6372i | −0.230114 | + | 0.708217i | ||||
\(271\) | −15.1803 | + | 11.0292i | −0.922140 | + | 0.669974i | −0.944056 | − | 0.329786i | \(-0.893023\pi\) |
0.0219158 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(272\) | 2.73607 | + | 1.98787i | 0.165898 | + | 0.120532i | ||||
\(273\) | 1.19098 | + | 3.66547i | 0.0720816 | + | 0.221844i | ||||
\(274\) | 34.4721 | 2.08254 | ||||||||
\(275\) | 3.30902 | − | 0.224514i | 0.199541 | − | 0.0135387i | ||||
\(276\) | −21.7082 | −1.30668 | ||||||||
\(277\) | 5.38197 | + | 16.5640i | 0.323371 | + | 0.995234i | 0.972171 | + | 0.234274i | \(0.0752714\pi\) |
−0.648800 | + | 0.760959i | \(0.724729\pi\) | |||||||
\(278\) | −26.1803 | − | 19.0211i | −1.57019 | − | 1.14081i | ||||
\(279\) | −0.381966 | + | 0.277515i | −0.0228677 | + | 0.0166144i | ||||
\(280\) | 0.690983 | − | 2.12663i | 0.0412941 | − | 0.127090i | ||||
\(281\) | 0.145898 | − | 0.449028i | 0.00870355 | − | 0.0267868i | −0.946610 | − | 0.322380i | \(-0.895517\pi\) |
0.955314 | + | 0.295593i | \(0.0955172\pi\) | |||||||
\(282\) | −22.9894 | + | 16.7027i | −1.36900 | + | 0.994634i | ||||
\(283\) | 22.2984 | + | 16.2007i | 1.32550 | + | 0.963033i | 0.999846 | + | 0.0175439i | \(0.00558467\pi\) |
0.325655 | + | 0.945489i | \(0.394415\pi\) | |||||||
\(284\) | 0.624612 | + | 1.92236i | 0.0370639 | + | 0.114071i | ||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 4.30902 | − | 17.1315i | 0.254798 | − | 1.01301i | ||||
\(287\) | 6.47214 | 0.382038 | ||||||||
\(288\) | 0.791796 | + | 2.43690i | 0.0466570 | + | 0.143596i | ||||
\(289\) | 4.50000 | + | 3.26944i | 0.264706 | + | 0.192320i | ||||
\(290\) | −10.5902 | + | 7.69421i | −0.621876 | + | 0.451820i | ||||
\(291\) | −0.163119 | + | 0.502029i | −0.00956220 | + | 0.0294294i | ||||
\(292\) | 7.98936 | − | 24.5887i | 0.467542 | − | 1.43895i | ||||
\(293\) | −14.0902 | + | 10.2371i | −0.823157 | + | 0.598058i | −0.917615 | − | 0.397471i | \(-0.869888\pi\) |
0.0944584 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(294\) | 2.92705 | + | 2.12663i | 0.170709 | + | 0.124027i | ||||
\(295\) | 1.47214 | + | 4.53077i | 0.0857111 | + | 0.263792i | ||||
\(296\) | −6.18034 | −0.359225 | ||||||||
\(297\) | 6.76393 | + | 16.8415i | 0.392483 | + | 0.977243i | ||||
\(298\) | −24.9230 | −1.44375 | ||||||||
\(299\) | 3.29180 | + | 10.1311i | 0.190369 | + | 0.585897i | ||||
\(300\) | 3.92705 | + | 2.85317i | 0.226728 | + | 0.164728i | ||||
\(301\) | −0.618034 | + | 0.449028i | −0.0356229 | + | 0.0258815i | ||||
\(302\) | −1.80902 | + | 5.56758i | −0.104097 | + | 0.320378i | ||||
\(303\) | 0.145898 | − | 0.449028i | 0.00838162 | − | 0.0257960i | ||||
\(304\) | 1.00000 | − | 0.726543i | 0.0573539 | − | 0.0416701i | ||||
\(305\) | −7.47214 | − | 5.42882i | −0.427853 | − | 0.310854i | ||||
\(306\) | −0.892609 | − | 2.74717i | −0.0510271 | − | 0.157045i | ||||
\(307\) | −0.437694 | −0.0249805 | −0.0124903 | − | 0.999922i | \(-0.503976\pi\) | ||||
−0.0124903 | + | 0.999922i | \(0.503976\pi\) | |||||||
\(308\) | −3.70820 | − | 9.23305i | −0.211295 | − | 0.526102i | ||||
\(309\) | 2.70820 | 0.154064 | ||||||||
\(310\) | 0.854102 | + | 2.62866i | 0.0485097 | + | 0.149298i | ||||
\(311\) | 21.9443 | + | 15.9434i | 1.24435 | + | 0.904070i | 0.997880 | − | 0.0650816i | \(-0.0207308\pi\) |
0.246466 | + | 0.969152i | \(0.420731\pi\) | |||||||
\(312\) | 6.97214 | − | 5.06555i | 0.394719 | − | 0.286780i | ||||
\(313\) | −5.56231 | + | 17.1190i | −0.314400 | + | 0.967624i | 0.661601 | + | 0.749856i | \(0.269877\pi\) |
−0.976001 | + | 0.217768i | \(0.930123\pi\) | |||||||
\(314\) | −3.39261 | + | 10.4414i | −0.191456 | + | 0.589241i | ||||
\(315\) | 0.309017 | − | 0.224514i | 0.0174111 | − | 0.0126499i | ||||
\(316\) | 33.4894 | + | 24.3314i | 1.88392 | + | 1.36875i | ||||
\(317\) | −9.41641 | − | 28.9807i | −0.528878 | − | 1.62772i | −0.756517 | − | 0.653974i | \(-0.773101\pi\) |
0.227639 | − | 0.973746i | \(-0.426899\pi\) | |||||||
\(318\) | 37.8885 | 2.12468 | ||||||||
\(319\) | −4.73607 | + | 18.8294i | −0.265169 | + | 1.05424i | ||||
\(320\) | 13.0000 | 0.726722 | ||||||||
\(321\) | 1.38197 | + | 4.25325i | 0.0771338 | + | 0.237393i | ||||
\(322\) | 8.09017 | + | 5.87785i | 0.450848 | + | 0.327560i | ||||
\(323\) | −3.38197 | + | 2.45714i | −0.188178 | + | 0.136719i | ||||
\(324\) | −7.14590 | + | 21.9928i | −0.396994 | + | 1.22182i | ||||
\(325\) | 0.736068 | − | 2.26538i | 0.0408297 | − | 0.125661i | ||||
\(326\) | −0.326238 | + | 0.237026i | −0.0180686 | + | 0.0131276i | ||||
\(327\) | −26.7984 | − | 19.4702i | −1.48195 | − | 1.07670i | ||||
\(328\) | −4.47214 | − | 13.7638i | −0.246932 | − | 0.759980i | ||||
\(329\) | 7.85410 | 0.433011 | ||||||||
\(330\) | 11.9721 | − | 0.812299i | 0.659044 | − | 0.0447156i | ||||
\(331\) | 19.5066 | 1.07218 | 0.536089 | − | 0.844161i | \(-0.319901\pi\) | ||||
0.536089 | + | 0.844161i | \(0.319901\pi\) | |||||||
\(332\) | −9.79180 | − | 30.1360i | −0.537395 | − | 1.65393i | ||||
\(333\) | −0.854102 | − | 0.620541i | −0.0468045 | − | 0.0340055i | ||||
\(334\) | 21.7082 | − | 15.7719i | 1.18782 | − | 0.863002i | ||||
\(335\) | 4.38197 | − | 13.4863i | 0.239412 | − | 0.736836i | ||||
\(336\) | −0.500000 | + | 1.53884i | −0.0272772 | + | 0.0839507i | ||||
\(337\) | 3.70820 | − | 2.69417i | 0.201999 | − | 0.146761i | −0.482187 | − | 0.876068i | \(-0.660158\pi\) |
0.684186 | + | 0.729307i | \(0.260158\pi\) | |||||||
\(338\) | 13.2533 | + | 9.62908i | 0.720884 | + | 0.523753i | ||||
\(339\) | −0.763932 | − | 2.35114i | −0.0414911 | − | 0.127696i | ||||
\(340\) | −10.1459 | −0.550239 | ||||||||
\(341\) | 3.47214 | + | 2.17963i | 0.188027 | + | 0.118033i | ||||
\(342\) | −1.05573 | −0.0570872 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | 1.38197 | + | 1.00406i | 0.0745106 | + | 0.0541351i | ||||
\(345\) | −5.85410 | + | 4.25325i | −0.315174 | + | 0.228988i | ||||
\(346\) | 12.8262 | − | 39.4751i | 0.689543 | − | 2.12219i | ||||
\(347\) | −3.23607 | + | 9.95959i | −0.173721 | + | 0.534659i | −0.999573 | − | 0.0292287i | \(-0.990695\pi\) |
0.825852 | + | 0.563888i | \(0.190695\pi\) | |||||||
\(348\) | −22.9894 | + | 16.7027i | −1.23236 | + | 0.895361i | ||||
\(349\) | 25.7984 | + | 18.7436i | 1.38096 | + | 1.00332i | 0.996790 | + | 0.0800583i | \(0.0255107\pi\) |
0.384165 | + | 0.923264i | \(0.374489\pi\) | |||||||
\(350\) | −0.690983 | − | 2.12663i | −0.0369346 | − | 0.113673i | ||||
\(351\) | 13.0344 | 0.695727 | ||||||||
\(352\) | 17.0729 | − | 14.2658i | 0.909991 | − | 0.760372i | ||||
\(353\) | 6.56231 | 0.349276 | 0.174638 | − | 0.984633i | \(-0.444124\pi\) | ||||
0.174638 | + | 0.984633i | \(0.444124\pi\) | |||||||
\(354\) | 5.32624 | + | 16.3925i | 0.283086 | + | 0.871250i | ||||
\(355\) | 0.545085 | + | 0.396027i | 0.0289301 | + | 0.0210190i | ||||
\(356\) | −41.8328 | + | 30.3933i | −2.21713 | + | 1.61084i | ||||
\(357\) | 1.69098 | − | 5.20431i | 0.0894963 | − | 0.275441i | ||||
\(358\) | 12.0106 | − | 36.9650i | 0.634782 | − | 1.95366i | ||||
\(359\) | −27.4894 | + | 19.9722i | −1.45083 | + | 1.05409i | −0.465197 | + | 0.885207i | \(0.654016\pi\) |
−0.985636 | + | 0.168884i | \(0.945984\pi\) | |||||||
\(360\) | −0.690983 | − | 0.502029i | −0.0364180 | − | 0.0264592i | ||||
\(361\) | −5.39919 | − | 16.6170i | −0.284168 | − | 0.874578i | ||||
\(362\) | 32.3607 | 1.70084 | ||||||||
\(363\) | 12.8541 | − | 12.3107i | 0.674665 | − | 0.646146i | ||||
\(364\) | −7.14590 | −0.374547 | ||||||||
\(365\) | −2.66312 | − | 8.19624i | −0.139394 | − | 0.429011i | ||||
\(366\) | −27.0344 | − | 19.6417i | −1.41311 | − | 1.02669i | ||||
\(367\) | −19.7812 | + | 14.3718i | −1.03257 | + | 0.750204i | −0.968821 | − | 0.247762i | \(-0.920305\pi\) |
−0.0637468 | + | 0.997966i | \(0.520305\pi\) | |||||||
\(368\) | −1.38197 | + | 4.25325i | −0.0720400 | + | 0.221716i | ||||
\(369\) | 0.763932 | − | 2.35114i | 0.0397687 | − | 0.122396i | ||||
\(370\) | −5.00000 | + | 3.63271i | −0.259938 | + | 0.188856i | ||||
\(371\) | −8.47214 | − | 6.15537i | −0.439851 | − | 0.319571i | ||||
\(372\) | 1.85410 | + | 5.70634i | 0.0961307 | + | 0.295860i | ||||
\(373\) | −29.1246 | −1.50802 | −0.754008 | − | 0.656866i | \(-0.771882\pi\) | ||||
−0.754008 | + | 0.656866i | \(0.771882\pi\) | |||||||
\(374\) | −19.2467 | + | 16.0822i | −0.995224 | + | 0.831591i | ||||
\(375\) | 1.61803 | 0.0835549 | ||||||||
\(376\) | −5.42705 | − | 16.7027i | −0.279879 | − | 0.861378i | ||||
\(377\) | 11.2812 | + | 8.19624i | 0.581009 | + | 0.422128i | ||||
\(378\) | 9.89919 | − | 7.19218i | 0.509159 | − | 0.369926i | ||||
\(379\) | −5.48278 | + | 16.8743i | −0.281631 | + | 0.866772i | 0.705757 | + | 0.708454i | \(0.250607\pi\) |
−0.987388 | + | 0.158318i | \(0.949393\pi\) | |||||||
\(380\) | −1.14590 | + | 3.52671i | −0.0587833 | + | 0.180916i | ||||
\(381\) | 6.23607 | − | 4.53077i | 0.319483 | − | 0.232118i | ||||
\(382\) | −21.5451 | − | 15.6534i | −1.10234 | − | 0.800899i | ||||
\(383\) | 0.680340 | + | 2.09387i | 0.0347637 | + | 0.106992i | 0.966933 | − | 0.255032i | \(-0.0820860\pi\) |
−0.932169 | + | 0.362024i | \(0.882086\pi\) | |||||||
\(384\) | 25.3262 | 1.29242 | ||||||||
\(385\) | −2.80902 | − | 1.76336i | −0.143161 | − | 0.0898689i | ||||
\(386\) | 8.94427 | 0.455251 | ||||||||
\(387\) | 0.0901699 | + | 0.277515i | 0.00458360 | + | 0.0141069i | ||||
\(388\) | −0.791796 | − | 0.575274i | −0.0401974 | − | 0.0292051i | ||||
\(389\) | 10.8713 | − | 7.89848i | 0.551198 | − | 0.400469i | −0.277029 | − | 0.960862i | \(-0.589350\pi\) |
0.828227 | + | 0.560393i | \(0.189350\pi\) | |||||||
\(390\) | 2.66312 | − | 8.19624i | 0.134852 | − | 0.415033i | ||||
\(391\) | 4.67376 | − | 14.3844i | 0.236362 | − | 0.727448i | ||||
\(392\) | −1.80902 | + | 1.31433i | −0.0913692 | + | 0.0663836i | ||||
\(393\) | 10.4721 | + | 7.60845i | 0.528249 | + | 0.383796i | ||||
\(394\) | −8.29180 | − | 25.5195i | −0.417735 | − | 1.28566i | ||||
\(395\) | 13.7984 | 0.694272 | ||||||||
\(396\) | −3.79180 | + | 0.257270i | −0.190545 | + | 0.0129283i | ||||
\(397\) | −34.1591 | −1.71439 | −0.857197 | − | 0.514989i | \(-0.827796\pi\) | ||||
−0.857197 | + | 0.514989i | \(0.827796\pi\) | |||||||
\(398\) | −12.4377 | − | 38.2793i | −0.623445 | − | 1.91877i | ||||
\(399\) | −1.61803 | − | 1.17557i | −0.0810030 | − | 0.0588521i | ||||
\(400\) | 0.809017 | − | 0.587785i | 0.0404508 | − | 0.0293893i | ||||
\(401\) | −6.95492 | + | 21.4050i | −0.347312 | + | 1.06892i | 0.613023 | + | 0.790065i | \(0.289953\pi\) |
−0.960334 | + | 0.278851i | \(0.910047\pi\) | |||||||
\(402\) | 15.8541 | − | 48.7939i | 0.790731 | − | 2.43362i | ||||
\(403\) | 2.38197 | − | 1.73060i | 0.118654 | − | 0.0862073i | ||||
\(404\) | 0.708204 | + | 0.514540i | 0.0352345 | + | 0.0255993i | ||||
\(405\) | 2.38197 | + | 7.33094i | 0.118361 | + | 0.364277i | ||||
\(406\) | 13.0902 | 0.649654 | ||||||||
\(407\) | −2.23607 | + | 8.89002i | −0.110838 | + | 0.440662i | ||||
\(408\) | −12.2361 | −0.605776 | ||||||||
\(409\) | 0.381966 | + | 1.17557i | 0.0188870 | + | 0.0581282i | 0.960056 | − | 0.279809i | \(-0.0902710\pi\) |
−0.941169 | + | 0.337937i | \(0.890271\pi\) | |||||||
\(410\) | −11.7082 | − | 8.50651i | −0.578227 | − | 0.420106i | ||||
\(411\) | 20.1803 | − | 14.6619i | 0.995423 | − | 0.723217i | ||||
\(412\) | −1.55166 | + | 4.77553i | −0.0764449 | + | 0.235273i | ||||
\(413\) | 1.47214 | − | 4.53077i | 0.0724391 | − | 0.222945i | ||||
\(414\) | 3.09017 | − | 2.24514i | 0.151874 | − | 0.110343i | ||||
\(415\) | −8.54508 | − | 6.20837i | −0.419462 | − | 0.304757i | ||||
\(416\) | −4.93769 | − | 15.1967i | −0.242090 | − | 0.745078i | ||||
\(417\) | −23.4164 | −1.14671 | ||||||||
\(418\) | 3.41641 | + | 8.50651i | 0.167102 | + | 0.416067i | ||||
\(419\) | 27.3050 | 1.33393 | 0.666967 | − | 0.745087i | \(-0.267592\pi\) | ||||
0.666967 | + | 0.745087i | \(0.267592\pi\) | |||||||
\(420\) | −1.50000 | − | 4.61653i | −0.0731925 | − | 0.225263i | ||||
\(421\) | −2.83688 | − | 2.06111i | −0.138261 | − | 0.100453i | 0.516505 | − | 0.856284i | \(-0.327233\pi\) |
−0.654766 | + | 0.755832i | \(0.727233\pi\) | |||||||
\(422\) | −42.1976 | + | 30.6583i | −2.05415 | + | 1.49242i | ||||
\(423\) | 0.927051 | − | 2.85317i | 0.0450748 | − | 0.138726i | ||||
\(424\) | −7.23607 | + | 22.2703i | −0.351415 | + | 1.08154i | ||||
\(425\) | −2.73607 | + | 1.98787i | −0.132719 | + | 0.0964258i | ||||
\(426\) | 1.97214 | + | 1.43284i | 0.0955503 | + | 0.0694214i | ||||
\(427\) | 2.85410 | + | 8.78402i | 0.138120 | + | 0.425089i | ||||
\(428\) | −8.29180 | −0.400799 | ||||||||
\(429\) | −4.76393 | − | 11.8617i | −0.230005 | − | 0.572689i | ||||
\(430\) | 1.70820 | 0.0823769 | ||||||||
\(431\) | 3.19098 | + | 9.82084i | 0.153704 | + | 0.473053i | 0.998027 | − | 0.0627814i | \(-0.0199971\pi\) |
−0.844323 | + | 0.535834i | \(0.819997\pi\) | |||||||
\(432\) | 4.42705 | + | 3.21644i | 0.212997 | + | 0.154751i | ||||
\(433\) | 13.7812 | − | 10.0126i | 0.662280 | − | 0.481175i | −0.205152 | − | 0.978730i | \(-0.565769\pi\) |
0.867432 | + | 0.497556i | \(0.165769\pi\) | |||||||
\(434\) | 0.854102 | − | 2.62866i | 0.0409982 | − | 0.126180i | ||||
\(435\) | −2.92705 | + | 9.00854i | −0.140341 | + | 0.431926i | ||||
\(436\) | 49.6869 | − | 36.0997i | 2.37957 | − | 1.72886i | ||||
\(437\) | −4.47214 | − | 3.24920i | −0.213931 | − | 0.155430i | ||||
\(438\) | −9.63525 | − | 29.6543i | −0.460390 | − | 1.41694i | ||||
\(439\) | 17.7082 | 0.845166 | 0.422583 | − | 0.906324i | \(-0.361123\pi\) | ||||
0.422583 | + | 0.906324i | \(0.361123\pi\) | |||||||
\(440\) | −1.80902 | + | 7.19218i | −0.0862415 | + | 0.342874i | ||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 5.56637 | + | 17.1315i | 0.264765 | + | 0.814864i | ||||
\(443\) | 28.0344 | + | 20.3682i | 1.33196 | + | 0.967723i | 0.999699 | + | 0.0245344i | \(0.00781031\pi\) |
0.332258 | + | 0.943189i | \(0.392190\pi\) | |||||||
\(444\) | −10.8541 | + | 7.88597i | −0.515113 | + | 0.374251i | ||||
\(445\) | −5.32624 | + | 16.3925i | −0.252488 | + | 0.777078i | ||||
\(446\) | 7.23607 | − | 22.2703i | 0.342638 | − | 1.05453i | ||||
\(447\) | −14.5902 | + | 10.6004i | −0.690091 | + | 0.501381i | ||||
\(448\) | −10.5172 | − | 7.64121i | −0.496892 | − | 0.361013i | ||||
\(449\) | 7.50000 | + | 23.0826i | 0.353947 | + | 1.08934i | 0.956618 | + | 0.291347i | \(0.0941033\pi\) |
−0.602671 | + | 0.797990i | \(0.705897\pi\) | |||||||
\(450\) | −0.854102 | −0.0402628 | ||||||||
\(451\) | −21.4164 | + | 1.45309i | −1.00846 | + | 0.0684231i | ||||
\(452\) | 4.58359 | 0.215594 | ||||||||
\(453\) | 1.30902 | + | 4.02874i | 0.0615030 | + | 0.189287i | ||||
\(454\) | −24.9615 | − | 18.1356i | −1.17150 | − | 0.851145i | ||||
\(455\) | −1.92705 | + | 1.40008i | −0.0903415 | + | 0.0656370i | ||||
\(456\) | −1.38197 | + | 4.25325i | −0.0647165 | + | 0.199177i | ||||
\(457\) | 10.4377 | − | 32.1239i | 0.488255 | − | 1.50269i | −0.338956 | − | 0.940802i | \(-0.610074\pi\) |
0.827211 | − | 0.561891i | \(-0.189926\pi\) | |||||||
\(458\) | 52.8885 | − | 38.4258i | 2.47132 | − | 1.79552i | ||||
\(459\) | −14.9721 | − | 10.8779i | −0.698839 | − | 0.507737i | ||||
\(460\) | −4.14590 | − | 12.7598i | −0.193303 | − | 0.594927i | ||||
\(461\) | 29.7082 | 1.38365 | 0.691825 | − | 0.722066i | \(-0.256807\pi\) | ||||
0.691825 | + | 0.722066i | \(0.256807\pi\) | |||||||
\(462\) | −10.1631 | − | 6.37988i | −0.472831 | − | 0.296819i | ||||
\(463\) | 23.1246 | 1.07469 | 0.537346 | − | 0.843362i | \(-0.319427\pi\) | ||||
0.537346 | + | 0.843362i | \(0.319427\pi\) | |||||||
\(464\) | 1.80902 | + | 5.56758i | 0.0839815 | + | 0.258468i | ||||
\(465\) | 1.61803 | + | 1.17557i | 0.0750345 | + | 0.0545158i | ||||
\(466\) | 44.5967 | − | 32.4014i | 2.06590 | − | 1.50097i | ||||
\(467\) | −5.15248 | + | 15.8577i | −0.238428 | + | 0.733806i | 0.758220 | + | 0.651999i | \(0.226069\pi\) |
−0.996648 | + | 0.0818076i | \(0.973931\pi\) | |||||||
\(468\) | −0.843459 | + | 2.59590i | −0.0389889 | + | 0.119995i | ||||
\(469\) | −11.4721 | + | 8.33499i | −0.529734 | + | 0.384874i | ||||
\(470\) | −14.2082 | − | 10.3229i | −0.655376 | − | 0.476158i | ||||
\(471\) | 2.45492 | + | 7.55545i | 0.113117 | + | 0.348137i | ||||
\(472\) | −10.6525 | −0.490320 | ||||||||
\(473\) | 1.94427 | − | 1.62460i | 0.0893977 | − | 0.0746991i | ||||
\(474\) | 49.9230 | 2.29304 | ||||||||
\(475\) | 0.381966 | + | 1.17557i | 0.0175258 | + | 0.0539389i | ||||
\(476\) | 8.20820 | + | 5.96361i | 0.376222 | + | 0.273342i | ||||
\(477\) | −3.23607 | + | 2.35114i | −0.148169 | + | 0.107651i | ||||
\(478\) | −15.1869 | + | 46.7405i | −0.694633 | + | 2.13786i | ||||
\(479\) | −2.67376 | + | 8.22899i | −0.122167 | + | 0.375992i | −0.993374 | − | 0.114923i | \(-0.963338\pi\) |
0.871207 | + | 0.490916i | \(0.163338\pi\) | |||||||
\(480\) | 8.78115 | − | 6.37988i | 0.400803 | − | 0.291200i | ||||
\(481\) | 5.32624 | + | 3.86974i | 0.242856 | + | 0.176445i | ||||
\(482\) | 15.9787 | + | 49.1774i | 0.727810 | + | 2.23997i | ||||
\(483\) | 7.23607 | 0.329252 | ||||||||
\(484\) | 14.3435 | + | 29.7198i | 0.651975 | + | 1.35090i | ||||
\(485\) | −0.326238 | −0.0148137 | ||||||||
\(486\) | −2.72542 | − | 8.38800i | −0.123628 | − | 0.380487i | ||||
\(487\) | 19.5623 | + | 14.2128i | 0.886453 | + | 0.644046i | 0.934951 | − | 0.354778i | \(-0.115443\pi\) |
−0.0484980 | + | 0.998823i | \(0.515443\pi\) | |||||||
\(488\) | 16.7082 | − | 12.1392i | 0.756345 | − | 0.549517i | ||||
\(489\) | −0.0901699 | + | 0.277515i | −0.00407763 | + | 0.0125496i | ||||
\(490\) | −0.690983 | + | 2.12663i | −0.0312154 | + | 0.0960712i | ||||
\(491\) | −30.6525 | + | 22.2703i | −1.38333 | + | 1.00505i | −0.386766 | + | 0.922178i | \(0.626408\pi\) |
−0.996561 | + | 0.0828681i | \(0.973592\pi\) | |||||||
\(492\) | −25.4164 | − | 18.4661i | −1.14586 | − | 0.832516i | ||||
\(493\) | −6.11803 | − | 18.8294i | −0.275542 | − | 0.848032i | ||||
\(494\) | 6.58359 | 0.296210 | ||||||||
\(495\) | −0.972136 | + | 0.812299i | −0.0436943 | + | 0.0365101i | ||||
\(496\) | 1.23607 | 0.0555011 | ||||||||
\(497\) | −0.208204 | − | 0.640786i | −0.00933922 | − | 0.0287432i | ||||
\(498\) | −30.9164 | − | 22.4621i | −1.38540 | − | 1.00655i | ||||
\(499\) | −4.88197 | + | 3.54696i | −0.218547 | + | 0.158784i | −0.691672 | − | 0.722212i | \(-0.743126\pi\) |
0.473125 | + | 0.880995i | \(0.343126\pi\) | |||||||
\(500\) | −0.927051 | + | 2.85317i | −0.0414590 | + | 0.127598i | ||||
\(501\) | 6.00000 | − | 18.4661i | 0.268060 | − | 0.825005i | ||||
\(502\) | −10.3262 | + | 7.50245i | −0.460883 | + | 0.334851i | ||||
\(503\) | 6.54508 | + | 4.75528i | 0.291831 | + | 0.212028i | 0.724061 | − | 0.689736i | \(-0.242273\pi\) |
−0.432230 | + | 0.901763i | \(0.642273\pi\) | |||||||
\(504\) | 0.263932 | + | 0.812299i | 0.0117565 | + | 0.0361827i | ||||
\(505\) | 0.291796 | 0.0129848 | ||||||||
\(506\) | −28.0902 | − | 17.6336i | −1.24876 | − | 0.783907i | ||||
\(507\) | 11.8541 | 0.526459 | ||||||||
\(508\) | 4.41641 | + | 13.5923i | 0.195946 | + | 0.603061i | ||||
\(509\) | 14.8541 | + | 10.7921i | 0.658396 | + | 0.478353i | 0.866121 | − | 0.499834i | \(-0.166606\pi\) |
−0.207725 | + | 0.978187i | \(0.566606\pi\) | |||||||
\(510\) | −9.89919 | + | 7.19218i | −0.438343 | + | 0.318475i | ||||
\(511\) | −2.66312 | + | 8.19624i | −0.117809 | + | 0.362580i | ||||
\(512\) | 3.45492 | − | 10.6331i | 0.152687 | − | 0.469923i | ||||
\(513\) | −5.47214 | + | 3.97574i | −0.241601 | + | 0.175533i | ||||
\(514\) | 8.35410 | + | 6.06961i | 0.368484 | + | 0.267719i | ||||
\(515\) | 0.517221 | + | 1.59184i | 0.0227915 | + | 0.0701450i | ||||
\(516\) | 3.70820 | 0.163245 | ||||||||
\(517\) | −25.9894 | + | 1.76336i | −1.14301 | + | 0.0775523i | ||||
\(518\) | 6.18034 | 0.271549 | ||||||||
\(519\) | −9.28115 | − | 28.5645i | −0.407397 | − | 1.25384i | ||||
\(520\) | 4.30902 | + | 3.13068i | 0.188963 | + | 0.137290i | ||||
\(521\) | −6.61803 | + | 4.80828i | −0.289941 | + | 0.210655i | −0.723242 | − | 0.690595i | \(-0.757349\pi\) |
0.433301 | + | 0.901249i | \(0.357349\pi\) | |||||||
\(522\) | 1.54508 | − | 4.75528i | 0.0676265 | − | 0.208133i | ||||
\(523\) | 2.42705 | − | 7.46969i | 0.106128 | − | 0.326627i | −0.883866 | − | 0.467740i | \(-0.845068\pi\) |
0.989993 | + | 0.141113i | \(0.0450682\pi\) | |||||||
\(524\) | −19.4164 | + | 14.1068i | −0.848210 | + | 0.616260i | ||||
\(525\) | −1.30902 | − | 0.951057i | −0.0571302 | − | 0.0415075i | ||||
\(526\) | −5.65248 | − | 17.3965i | −0.246460 | − | 0.758525i | ||||
\(527\) | −4.18034 | −0.182098 | ||||||||
\(528\) | 1.30902 | − | 5.20431i | 0.0569677 | − | 0.226489i | ||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 7.23607 | + | 22.2703i | 0.314315 | + | 0.967361i | ||||
\(531\) | −1.47214 | − | 1.06957i | −0.0638853 | − | 0.0464154i | ||||
\(532\) | 3.00000 | − | 2.17963i | 0.130066 | − | 0.0944988i | ||||
\(533\) | −4.76393 | + | 14.6619i | −0.206349 | + | 0.635076i | ||||
\(534\) | −19.2705 | + | 59.3085i | −0.833917 | + | 2.56653i | ||||
\(535\) | −2.23607 | + | 1.62460i | −0.0966736 | + | 0.0702375i | ||||
\(536\) | 25.6525 | + | 18.6376i | 1.10802 | + | 0.805022i | ||||
\(537\) | −8.69098 | − | 26.7481i | −0.375044 | − | 1.15427i | ||||
\(538\) | 28.2918 | 1.21975 | ||||||||
\(539\) | 1.23607 | + | 3.07768i | 0.0532412 | + | 0.132565i | ||||
\(540\) | −16.4164 | −0.706450 | ||||||||
\(541\) | 3.97214 | + | 12.2250i | 0.170775 | + | 0.525593i | 0.999415 | − | 0.0341892i | \(-0.0108849\pi\) |
−0.828640 | + | 0.559782i | \(0.810885\pi\) | |||||||
\(542\) | −33.9443 | − | 24.6620i | −1.45803 | − | 1.05932i | ||||
\(543\) | 18.9443 | − | 13.7638i | 0.812977 | − | 0.590662i | ||||
\(544\) | −7.01064 | + | 21.5765i | −0.300579 | + | 0.925087i | ||||
\(545\) | 6.32624 | − | 19.4702i | 0.270986 | − | 0.834010i | ||||
\(546\) | −6.97214 | + | 5.06555i | −0.298380 | + | 0.216786i | ||||
\(547\) | −32.4164 | − | 23.5519i | −1.38603 | − | 1.00701i | −0.996288 | − | 0.0860804i | \(-0.972566\pi\) |
−0.389737 | − | 0.920926i | \(-0.627434\pi\) | |||||||
\(548\) | 14.2918 | + | 43.9856i | 0.610515 | + | 1.87897i | ||||
\(549\) | 3.52786 | 0.150566 | ||||||||
\(550\) | 2.76393 | + | 6.88191i | 0.117854 | + | 0.293446i | ||||
\(551\) | −7.23607 | −0.308267 | ||||||||
\(552\) | −5.00000 | − | 15.3884i | −0.212814 | − | 0.654975i | ||||
\(553\) | −11.1631 | − | 8.11048i | −0.474704 | − | 0.344893i | ||||
\(554\) | −31.5066 | + | 22.8909i | −1.33859 | + | 0.972540i | ||||
\(555\) | −1.38197 | + | 4.25325i | −0.0586612 | + | 0.180541i | ||||
\(556\) | 13.4164 | − | 41.2915i | 0.568982 | − | 1.75115i | ||||
\(557\) | 3.47214 | − | 2.52265i | 0.147119 | − | 0.106888i | −0.511791 | − | 0.859110i | \(-0.671018\pi\) |
0.658910 | + | 0.752222i | \(0.271018\pi\) | |||||||
\(558\) | −0.854102 | − | 0.620541i | −0.0361570 | − | 0.0262696i | ||||
\(559\) | −0.562306 | − | 1.73060i | −0.0237830 | − | 0.0731966i | ||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | −4.42705 | + | 17.6008i | −0.186910 | + | 0.743106i | ||||
\(562\) | 1.05573 | 0.0445332 | ||||||||
\(563\) | −6.60739 | − | 20.3355i | −0.278468 | − | 0.857037i | −0.988281 | − | 0.152647i | \(-0.951220\pi\) |
0.709812 | − | 0.704391i | \(-0.248780\pi\) | |||||||
\(564\) | −30.8435 | − | 22.4091i | −1.29874 | − | 0.943593i | ||||
\(565\) | 1.23607 | − | 0.898056i | 0.0520018 | − | 0.0377815i | ||||
\(566\) | −19.0451 | + | 58.6147i | −0.800525 | + | 2.46376i | ||||
\(567\) | 2.38197 | − | 7.33094i | 0.100033 | − | 0.307870i | ||||
\(568\) | −1.21885 | + | 0.885544i | −0.0511417 | + | 0.0371566i | ||||
\(569\) | 10.6803 | + | 7.75972i | 0.447743 | + | 0.325304i | 0.788704 | − | 0.614773i | \(-0.210752\pi\) |
−0.340961 | + | 0.940077i | \(0.610752\pi\) | |||||||
\(570\) | 1.38197 | + | 4.25325i | 0.0578842 | + | 0.178149i | ||||
\(571\) | 10.9787 | 0.459445 | 0.229722 | − | 0.973256i | \(-0.426218\pi\) | ||||
0.229722 | + | 0.973256i | \(0.426218\pi\) | |||||||
\(572\) | 23.6459 | − | 1.60435i | 0.988685 | − | 0.0670814i | ||||
\(573\) | −19.2705 | −0.805037 | ||||||||
\(574\) | 4.47214 | + | 13.7638i | 0.186663 | + | 0.574491i | ||||
\(575\) | −3.61803 | − | 2.62866i | −0.150882 | − | 0.109623i | ||||
\(576\) | −4.01722 | + | 2.91868i | −0.167384 | + | 0.121612i | ||||
\(577\) | −5.62868 | + | 17.3233i | −0.234325 | + | 0.721178i | 0.762885 | + | 0.646534i | \(0.223782\pi\) |
−0.997210 | + | 0.0746441i | \(0.976218\pi\) | |||||||
\(578\) | −3.84346 | + | 11.8290i | −0.159867 | + | 0.492019i | ||||
\(579\) | 5.23607 | − | 3.80423i | 0.217604 | − | 0.158098i | ||||
\(580\) | −14.2082 | − | 10.3229i | −0.589964 | − | 0.428634i | ||||
\(581\) | 3.26393 | + | 10.0453i | 0.135411 | + | 0.416751i | ||||
\(582\) | −1.18034 | −0.0489267 | ||||||||
\(583\) | 29.4164 | + | 18.4661i | 1.21830 | + | 0.764788i | ||||
\(584\) | 19.2705 | 0.797419 | ||||||||
\(585\) | 0.281153 | + | 0.865300i | 0.0116242 | + | 0.0357757i | ||||
\(586\) | −31.5066 | − | 22.8909i | −1.30152 | − | 0.945613i | ||||
\(587\) | −32.5795 | + | 23.6704i | −1.34470 | + | 0.976982i | −0.345444 | + | 0.938439i | \(0.612272\pi\) |
−0.999257 | + | 0.0385431i | \(0.987728\pi\) | |||||||
\(588\) | −1.50000 | + | 4.61653i | −0.0618590 | + | 0.190382i | ||||
\(589\) | −0.472136 | + | 1.45309i | −0.0194540 | + | 0.0598733i | ||||
\(590\) | −8.61803 | + | 6.26137i | −0.354799 | + | 0.257776i | ||||
\(591\) | −15.7082 | − | 11.4127i | −0.646149 | − | 0.469455i | ||||
\(592\) | 0.854102 | + | 2.62866i | 0.0351034 | + | 0.108037i | ||||
\(593\) | −14.7984 | −0.607696 | −0.303848 | − | 0.952720i | \(-0.598272\pi\) | ||||
−0.303848 | + | 0.952720i | \(0.598272\pi\) | |||||||
\(594\) | −31.1418 | + | 26.0216i | −1.27776 | + | 1.06768i | ||||
\(595\) | 3.38197 | 0.138647 | ||||||||
\(596\) | −10.3328 | − | 31.8011i | −0.423249 | − | 1.30263i | ||||
\(597\) | −23.5623 | − | 17.1190i | −0.964341 | − | 0.700635i | ||||
\(598\) | −19.2705 | + | 14.0008i | −0.788030 | + | 0.572537i | ||||
\(599\) | −2.24671 | + | 6.91467i | −0.0917981 | + | 0.282526i | −0.986406 | − | 0.164326i | \(-0.947455\pi\) |
0.894608 | + | 0.446852i | \(0.147455\pi\) | |||||||
\(600\) | −1.11803 | + | 3.44095i | −0.0456435 | + | 0.140476i | ||||
\(601\) | −9.23607 | + | 6.71040i | −0.376747 | + | 0.273723i | −0.760003 | − | 0.649919i | \(-0.774803\pi\) |
0.383256 | + | 0.923642i | \(0.374803\pi\) | |||||||
\(602\) | −1.38197 | − | 1.00406i | −0.0563247 | − | 0.0409223i | ||||
\(603\) | 1.67376 | + | 5.15131i | 0.0681609 | + | 0.209778i | ||||
\(604\) | −7.85410 | −0.319579 | ||||||||
\(605\) | 9.69098 | + | 5.20431i | 0.393994 | + | 0.211585i | ||||
\(606\) | 1.05573 | 0.0428860 | ||||||||
\(607\) | −4.04508 | − | 12.4495i | −0.164185 | − | 0.505309i | 0.834790 | − | 0.550568i | \(-0.185589\pi\) |
−0.998975 | + | 0.0452587i | \(0.985589\pi\) | |||||||
\(608\) | 6.70820 | + | 4.87380i | 0.272054 | + | 0.197659i | ||||
\(609\) | 7.66312 | − | 5.56758i | 0.310525 | − | 0.225610i | ||||
\(610\) | 6.38197 | − | 19.6417i | 0.258398 | − | 0.795268i | ||||
\(611\) | −5.78115 | + | 17.7926i | −0.233880 | + | 0.719810i | ||||
\(612\) | 3.13525 | − | 2.27790i | 0.126735 | − | 0.0920785i | ||||
\(613\) | −10.3820 | − | 7.54294i | −0.419324 | − | 0.304656i | 0.358042 | − | 0.933705i | \(-0.383444\pi\) |
−0.777366 | + | 0.629049i | \(0.783444\pi\) | |||||||
\(614\) | −0.302439 | − | 0.930812i | −0.0122055 | − | 0.0375645i | ||||
\(615\) | −10.4721 | −0.422277 | ||||||||
\(616\) | 5.69098 | − | 4.75528i | 0.229296 | − | 0.191596i | ||||
\(617\) | −7.23607 | −0.291313 | −0.145657 | − | 0.989335i | \(-0.546529\pi\) | ||||
−0.145657 | + | 0.989335i | \(0.546529\pi\) | |||||||
\(618\) | 1.87132 | + | 5.75934i | 0.0752756 | + | 0.231675i | ||||
\(619\) | 10.9443 | + | 7.95148i | 0.439887 | + | 0.319597i | 0.785590 | − | 0.618747i | \(-0.212359\pi\) |
−0.345703 | + | 0.938344i | \(0.612359\pi\) | |||||||
\(620\) | −3.00000 | + | 2.17963i | −0.120483 | + | 0.0875360i | ||||
\(621\) | 7.56231 | − | 23.2744i | 0.303465 | − | 0.933969i | ||||
\(622\) | −18.7426 | + | 57.6839i | −0.751512 | + | 2.31291i | ||||
\(623\) | 13.9443 | − | 10.1311i | 0.558665 | − | 0.405894i | ||||
\(624\) | −3.11803 | − | 2.26538i | −0.124821 | − | 0.0906880i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | −40.2492 | −1.60868 | ||||||||
\(627\) | 5.61803 | + | 3.52671i | 0.224363 | + | 0.140843i | ||||
\(628\) | −14.7295 | −0.587771 | ||||||||
\(629\) | −2.88854 | − | 8.89002i | −0.115174 | − | 0.354468i | ||||
\(630\) | 0.690983 | + | 0.502029i | 0.0275294 | + | 0.0200013i | ||||
\(631\) | −23.0623 | + | 16.7557i | −0.918096 | + | 0.667036i | −0.943049 | − | 0.332653i | \(-0.892056\pi\) |
0.0249534 | + | 0.999689i | \(0.492056\pi\) | |||||||
\(632\) | −9.53444 | + | 29.3440i | −0.379260 | + | 1.16724i | ||||
\(633\) | −11.6631 | + | 35.8954i | −0.463567 | + | 1.42671i | ||||
\(634\) | 55.1246 | − | 40.0504i | 2.18928 | − | 1.59060i | ||||
\(635\) | 3.85410 | + | 2.80017i | 0.152945 | + | 0.111121i | ||||
\(636\) | 15.7082 | + | 48.3449i | 0.622871 | + | 1.91700i | ||||
\(637\) | 2.38197 | 0.0943769 | ||||||||
\(638\) | −43.3156 | + | 2.93893i | −1.71488 | + | 0.116353i | ||||
\(639\) | −0.257354 | −0.0101808 | ||||||||
\(640\) | 4.83688 | + | 14.8864i | 0.191195 | + | 0.588436i | ||||
\(641\) | 21.0172 | + | 15.2699i | 0.830130 | + | 0.603125i | 0.919596 | − | 0.392865i | \(-0.128516\pi\) |
−0.0894659 | + | 0.995990i | \(0.528516\pi\) | |||||||
\(642\) | −8.09017 | + | 5.87785i | −0.319294 | + | 0.231980i | ||||
\(643\) | −4.26393 | + | 13.1230i | −0.168153 | + | 0.517522i | −0.999255 | − | 0.0385985i | \(-0.987711\pi\) |
0.831102 | + | 0.556120i | \(0.187711\pi\) | |||||||
\(644\) | −4.14590 | + | 12.7598i | −0.163371 | + | 0.502805i | ||||
\(645\) | 1.00000 | − | 0.726543i | 0.0393750 | − | 0.0286076i | ||||
\(646\) | −7.56231 | − | 5.49434i | −0.297535 | − | 0.216172i | ||||
\(647\) | −12.4058 | − | 38.1810i | −0.487721 | − | 1.50105i | −0.828001 | − | 0.560727i | \(-0.810522\pi\) |
0.340280 | − | 0.940324i | \(-0.389478\pi\) | |||||||
\(648\) | −17.2361 | −0.677097 | ||||||||
\(649\) | −3.85410 | + | 15.3229i | −0.151287 | + | 0.601477i | ||||
\(650\) | 5.32624 | 0.208912 | ||||||||
\(651\) | −0.618034 | − | 1.90211i | −0.0242227 | − | 0.0745497i | ||||
\(652\) | −0.437694 | − | 0.318003i | −0.0171414 | − | 0.0124540i | ||||
\(653\) | 12.7984 | − | 9.29856i | 0.500839 | − | 0.363881i | −0.308498 | − | 0.951225i | \(-0.599826\pi\) |
0.809337 | + | 0.587344i | \(0.199826\pi\) | |||||||
\(654\) | 22.8885 | − | 70.4437i | 0.895013 | − | 2.75457i | ||||
\(655\) | −2.47214 | + | 7.60845i | −0.0965943 | + | 0.297287i | ||||
\(656\) | −5.23607 | + | 3.80423i | −0.204434 | + | 0.148530i | ||||
\(657\) | 2.66312 | + | 1.93487i | 0.103898 | + | 0.0754864i | ||||
\(658\) | 5.42705 | + | 16.7027i | 0.211568 | + | 0.651141i | ||||
\(659\) | 25.0344 | 0.975203 | 0.487602 | − | 0.873066i | \(-0.337872\pi\) | ||||
0.487602 | + | 0.873066i | \(0.337872\pi\) | |||||||
\(660\) | 6.00000 | + | 14.9394i | 0.233550 | + | 0.581515i | ||||
\(661\) | −33.4164 | −1.29975 | −0.649874 | − | 0.760042i | \(-0.725178\pi\) | ||||
−0.649874 | + | 0.760042i | \(0.725178\pi\) | |||||||
\(662\) | 13.4787 | + | 41.4832i | 0.523865 | + | 1.61229i | ||||
\(663\) | 10.5451 | + | 7.66145i | 0.409537 | + | 0.297546i | ||||
\(664\) | 19.1074 | − | 13.8823i | 0.741511 | − | 0.538739i | ||||
\(665\) | 0.381966 | − | 1.17557i | 0.0148120 | − | 0.0455867i | ||||
\(666\) | 0.729490 | − | 2.24514i | 0.0282672 | − | 0.0869974i | ||||
\(667\) | 21.1803 | − | 15.3884i | 0.820106 | − | 0.595842i | ||||
\(668\) | 29.1246 | + | 21.1603i | 1.12687 | + | 0.818715i | ||||
\(669\) | −5.23607 | − | 16.1150i | −0.202438 | − | 0.623040i | ||||
\(670\) | 31.7082 | 1.22499 | ||||||||
\(671\) | −11.4164 | − | 28.4257i | −0.440726 | − | 1.09736i | ||||
\(672\) | −10.8541 | −0.418706 | ||||||||
\(673\) | −4.29180 | − | 13.2088i | −0.165437 | − | 0.509161i | 0.833632 | − | 0.552321i | \(-0.186258\pi\) |
−0.999068 | + | 0.0431594i | \(0.986258\pi\) | |||||||
\(674\) | 8.29180 | + | 6.02434i | 0.319388 | + | 0.232049i | ||||
\(675\) | −4.42705 | + | 3.21644i | −0.170397 | + | 0.123801i | ||||
\(676\) | −6.79180 | + | 20.9030i | −0.261223 | + | 0.803961i | ||||
\(677\) | 13.0238 | − | 40.0831i | 0.500545 | − | 1.54052i | −0.307588 | − | 0.951520i | \(-0.599522\pi\) |
0.808133 | − | 0.589000i | \(-0.200478\pi\) | |||||||
\(678\) | 4.47214 | − | 3.24920i | 0.171751 | − | 0.124785i | ||||
\(679\) | 0.263932 | + | 0.191758i | 0.0101288 | + | 0.00735899i | ||||
\(680\) | −2.33688 | − | 7.19218i | −0.0896153 | − | 0.275808i | ||||
\(681\) | −22.3262 | −0.855543 | ||||||||
\(682\) | −2.23607 | + | 8.89002i | −0.0856235 | + | 0.340417i | ||||
\(683\) | 39.2361 | 1.50133 | 0.750663 | − | 0.660685i | \(-0.229734\pi\) | ||||
0.750663 | + | 0.660685i | \(0.229734\pi\) | |||||||
\(684\) | −0.437694 | − | 1.34708i | −0.0167357 | − | 0.0515070i | ||||
\(685\) | 12.4721 | + | 9.06154i | 0.476536 | + | 0.346224i | ||||
\(686\) | 1.80902 | − | 1.31433i | 0.0690686 | − | 0.0501813i | ||||
\(687\) | 14.6180 | − | 44.9897i | 0.557713 | − | 1.71646i | ||||
\(688\) | 0.236068 | − | 0.726543i | 0.00900001 | − | 0.0276992i | ||||
\(689\) | 20.1803 | − | 14.6619i | 0.768810 | − | 0.558573i | ||||
\(690\) | −13.0902 | − | 9.51057i | −0.498334 | − | 0.362061i | ||||
\(691\) | 8.29180 | + | 25.5195i | 0.315435 | + | 0.970808i | 0.975575 | + | 0.219666i | \(0.0704968\pi\) |
−0.660140 | + | 0.751142i | \(0.729503\pi\) | |||||||
\(692\) | 55.6869 | 2.11690 | ||||||||
\(693\) | 1.26393 | − | 0.0857567i | 0.0480128 | − | 0.00325763i | ||||
\(694\) | −23.4164 | −0.888875 | ||||||||
\(695\) | −4.47214 | − | 13.7638i | −0.169638 | − | 0.522091i | ||||
\(696\) | −17.1353 | − | 12.4495i | −0.649510 | − | 0.471897i | ||||
\(697\) | 17.7082 | − | 12.8658i | 0.670746 | − | 0.487326i | ||||
\(698\) | −22.0344 | + | 67.8150i | −0.834016 | + | 2.56684i | ||||
\(699\) | 12.3262 | − | 37.9363i | 0.466221 | − | 1.43488i | ||||
\(700\) | 2.42705 | − | 1.76336i | 0.0917339 | − | 0.0666486i | ||||
\(701\) | −9.14590 | − | 6.64488i | −0.345436 | − | 0.250974i | 0.401516 | − | 0.915852i | \(-0.368483\pi\) |
−0.746952 | + | 0.664878i | \(0.768483\pi\) | |||||||
\(702\) | 9.00658 | + | 27.7194i | 0.339931 | + | 1.04620i | ||||
\(703\) | −3.41641 | −0.128852 | ||||||||
\(704\) | 36.5172 | + | 22.9236i | 1.37629 | + | 0.863967i | ||||
\(705\) | −12.7082 | −0.478619 | ||||||||
\(706\) | 4.53444 | + | 13.9556i | 0.170656 | + | 0.525225i | ||||
\(707\) | −0.236068 | − | 0.171513i | −0.00887825 | − | 0.00645043i | ||||
\(708\) | −18.7082 | + | 13.5923i | −0.703097 | + | 0.510830i | ||||
\(709\) | 13.2082 | − | 40.6507i | 0.496045 | − | 1.52667i | −0.319278 | − | 0.947661i | \(-0.603440\pi\) |
0.815323 | − | 0.579007i | \(-0.196560\pi\) | |||||||
\(710\) | −0.465558 | + | 1.43284i | −0.0174721 | + | 0.0537736i | ||||
\(711\) | −4.26393 | + | 3.09793i | −0.159910 | + | 0.116181i | ||||
\(712\) | −31.1803 | − | 22.6538i | −1.16853 | − | 0.848989i | ||||
\(713\) | −1.70820 | − | 5.25731i | −0.0639727 | − | 0.196888i | ||||
\(714\) | 12.2361 | 0.457923 | ||||||||
\(715\) | 6.06231 | − | 5.06555i | 0.226717 | − | 0.189441i | ||||
\(716\) | 52.1459 | 1.94878 | ||||||||
\(717\) | 10.9894 | + | 33.8218i | 0.410405 | + | 1.26310i | ||||
\(718\) | −61.4681 | − | 44.6592i | −2.29397 | − | 1.66667i | ||||
\(719\) | 11.2361 | − | 8.16348i | 0.419035 | − | 0.304446i | −0.358215 | − | 0.933639i | \(-0.616614\pi\) |
0.777249 | + | 0.629193i | \(0.216614\pi\) | |||||||
\(720\) | −0.118034 | + | 0.363271i | −0.00439887 | + | 0.0135383i | ||||
\(721\) | 0.517221 | − | 1.59184i | 0.0192623 | − | 0.0592833i | ||||
\(722\) | 31.6074 | − | 22.9641i | 1.17631 | − | 0.854636i | ||||
\(723\) | 30.2705 | + | 21.9928i | 1.12577 | + | 0.817922i | ||||
\(724\) | 13.4164 | + | 41.2915i | 0.498617 | + | 1.53458i | ||||
\(725\) | −5.85410 | −0.217416 | ||||||||
\(726\) | 35.0623 | + | 18.8294i | 1.30128 | + | 0.698824i | ||||
\(727\) | −21.4377 | −0.795080 | −0.397540 | − | 0.917585i | \(-0.630136\pi\) | ||||
−0.397540 | + | 0.917585i | \(0.630136\pi\) | |||||||
\(728\) | −1.64590 | − | 5.06555i | −0.0610010 | − | 0.187742i | ||||
\(729\) | −23.8713 | − | 17.3435i | −0.884123 | − | 0.642353i | ||||
\(730\) | 15.5902 | − | 11.3269i | 0.577018 | − | 0.419228i | ||||
\(731\) | −0.798374 | + | 2.45714i | −0.0295289 | + | 0.0908807i | ||||
\(732\) | 13.8541 | − | 42.6385i | 0.512062 | − | 1.57597i | ||||
\(733\) | 38.7254 | − | 28.1357i | 1.43036 | − | 1.03921i | 0.440406 | − | 0.897799i | \(-0.354835\pi\) |
0.989950 | − | 0.141416i | \(-0.0451655\pi\) | |||||||
\(734\) | −44.2320 | − | 32.1364i | −1.63263 | − | 1.18618i | ||||
\(735\) | 0.500000 | + | 1.53884i | 0.0184428 | + | 0.0567610i | ||||
\(736\) | −30.0000 | −1.10581 | ||||||||
\(737\) | 36.0902 | − | 30.1563i | 1.32940 | − | 1.11082i | ||||
\(738\) | 5.52786 | 0.203483 | ||||||||
\(739\) | 3.70820 | + | 11.4127i | 0.136408 | + | 0.419822i | 0.995806 | − | 0.0914851i | \(-0.0291614\pi\) |
−0.859398 | + | 0.511307i | \(0.829161\pi\) | |||||||
\(740\) | −6.70820 | − | 4.87380i | −0.246598 | − | 0.179164i | ||||
\(741\) | 3.85410 | − | 2.80017i | 0.141584 | − | 0.102867i | ||||
\(742\) | 7.23607 | − | 22.2703i | 0.265644 | − | 0.817569i | ||||
\(743\) | 11.3262 | − | 34.8586i | 0.415519 | − | 1.27884i | −0.496266 | − | 0.868170i | \(-0.665296\pi\) |
0.911786 | − | 0.410667i | \(-0.134704\pi\) | |||||||
\(744\) | −3.61803 | + | 2.62866i | −0.132644 | + | 0.0963712i | ||||
\(745\) | −9.01722 | − | 6.55139i | −0.330365 | − | 0.240025i | ||||
\(746\) | −20.1246 | − | 61.9372i | −0.736814 | − | 2.26768i | ||||
\(747\) | 4.03444 | 0.147613 | ||||||||
\(748\) | −28.5000 | − | 17.8908i | −1.04206 | − | 0.654153i | ||||
\(749\) | 2.76393 | 0.100992 | ||||||||
\(750\) | 1.11803 | + | 3.44095i | 0.0408248 | + | 0.125646i | ||||
\(751\) | −17.5344 | − | 12.7395i | −0.639841 | − | 0.464872i | 0.219955 | − | 0.975510i | \(-0.429409\pi\) |
−0.859796 | + | 0.510638i | \(0.829409\pi\) | |||||||
\(752\) | −6.35410 | + | 4.61653i | −0.231710 | + | 0.168347i | ||||
\(753\) | −2.85410 | + | 8.78402i | −0.104009 | + | 0.320108i | ||||
\(754\) | −9.63525 | + | 29.6543i | −0.350895 | + | 1.07994i | ||||
\(755\) | −2.11803 | + | 1.53884i | −0.0770831 | + | 0.0560042i | ||||
\(756\) | 13.2812 | + | 9.64932i | 0.483031 | + | 0.350942i | ||||
\(757\) | −5.61803 | − | 17.2905i | −0.204191 | − | 0.628435i | −0.999746 | − | 0.0225533i | \(-0.992820\pi\) |
0.795555 | − | 0.605882i | \(-0.207180\pi\) | |||||||
\(758\) | −39.6738 | −1.44102 | ||||||||
\(759\) | −23.9443 | + | 1.62460i | −0.869122 | + | 0.0589692i | ||||
\(760\) | −2.76393 | −0.100258 | ||||||||
\(761\) | −1.49342 | − | 4.59628i | −0.0541365 | − | 0.166615i | 0.920333 | − | 0.391137i | \(-0.127918\pi\) |
−0.974469 | + | 0.224522i | \(0.927918\pi\) | |||||||
\(762\) | 13.9443 | + | 10.1311i | 0.505148 | + | 0.367011i | ||||
\(763\) | −16.5623 | + | 12.0332i | −0.599596 | + | 0.435632i | ||||
\(764\) | 11.0410 | − | 33.9808i | 0.399450 | − | 1.22938i | ||||
\(765\) | 0.399187 | − | 1.22857i | 0.0144326 | − | 0.0444191i | ||||
\(766\) | −3.98278 | + | 2.89366i | −0.143904 | + | 0.104552i | ||||
\(767\) | 9.18034 | + | 6.66991i | 0.331483 | + | 0.240836i | ||||
\(768\) | 4.50000 | + | 13.8496i | 0.162380 | + | 0.499754i | ||||
\(769\) | −1.70820 | −0.0615994 | −0.0307997 | − | 0.999526i | \(-0.509805\pi\) | ||||
−0.0307997 | + | 0.999526i | \(0.509805\pi\) | |||||||
\(770\) | 1.80902 | − | 7.19218i | 0.0651924 | − | 0.259188i | ||||
\(771\) | 7.47214 | 0.269102 | ||||||||
\(772\) | 3.70820 | + | 11.4127i | 0.133461 | + | 0.410751i | ||||
\(773\) | 23.9615 | + | 17.4090i | 0.861835 | + | 0.626160i | 0.928384 | − | 0.371623i | \(-0.121199\pi\) |
−0.0665486 | + | 0.997783i | \(0.521199\pi\) | |||||||
\(774\) | −0.527864 | + | 0.383516i | −0.0189737 | + | 0.0137852i | ||||
\(775\) | −0.381966 | + | 1.17557i | −0.0137206 | + | 0.0422277i | ||||
\(776\) | 0.225425 | − | 0.693786i | 0.00809228 | − | 0.0249055i | ||||
\(777\) | 3.61803 | − | 2.62866i | 0.129796 | − | 0.0943025i | ||||
\(778\) | 24.3090 | + | 17.6615i | 0.871520 | + | 0.633197i | ||||
\(779\) | −2.47214 | − | 7.60845i | −0.0885735 | − | 0.272601i | ||||
\(780\) | 11.5623 | 0.413997 | ||||||||
\(781\) | 0.832816 | + | 2.07363i | 0.0298005 | + | 0.0742002i | ||||
\(782\) | 33.8197 | 1.20939 | ||||||||
\(783\) | −9.89919 | − | 30.4666i | −0.353768 | − | 1.08879i | ||||
\(784\) | 0.809017 | + | 0.587785i | 0.0288935 | + | 0.0209923i | ||||
\(785\) | −3.97214 | + | 2.88593i | −0.141772 | + | 0.103003i | ||||
\(786\) | −8.94427 | + | 27.5276i | −0.319032 | + | 0.981878i | ||||
\(787\) | 3.38854 | − | 10.4289i | 0.120789 | − | 0.371749i | −0.872322 | − | 0.488932i | \(-0.837387\pi\) |
0.993110 | + | 0.117183i | \(0.0373865\pi\) | |||||||
\(788\) | 29.1246 | − | 21.1603i | 1.03752 | − | 0.753803i | ||||
\(789\) | −10.7082 | − | 7.77997i | −0.381222 | − | 0.276974i | ||||
\(790\) | 9.53444 | + | 29.3440i | 0.339220 | + | 1.04401i | ||||
\(791\) | −1.52786 | −0.0543246 | ||||||||
\(792\) | −1.05573 | − | 2.62866i | −0.0375137 | − | 0.0934052i | ||||
\(793\) | −22.0000 | −0.781243 | ||||||||
\(794\) | −23.6033 | − | 72.6436i | −0.837651 | − | 2.57802i | ||||
\(795\) | 13.7082 | + | 9.95959i | 0.486180 | + | 0.353230i | ||||
\(796\) | 43.6869 | − | 31.7404i | 1.54844 | − | 1.12501i | ||||
\(797\) | −13.3197 | + | 40.9937i | −0.471807 | + | 1.45207i | 0.378410 | + | 0.925638i | \(0.376471\pi\) |
−0.850217 | + | 0.526433i | \(0.823529\pi\) | |||||||
\(798\) | 1.38197 | − | 4.25325i | 0.0489211 | − | 0.150564i | ||||
\(799\) | 21.4894 | − | 15.6129i | 0.760239 | − | 0.552346i | ||||
\(800\) | 5.42705 | + | 3.94298i | 0.191875 | + | 0.139406i | ||||
\(801\) | −2.03444 | − | 6.26137i | −0.0718835 | − | 0.221235i | ||||
\(802\) | −50.3262 | −1.77708 | ||||||||
\(803\) | 6.97214 | − | 27.7194i | 0.246041 | − | 0.978196i | ||||
\(804\) | 68.8328 | 2.42755 | ||||||||
\(805\) | 1.38197 | + | 4.25325i | 0.0487079 | + | 0.149908i | ||||
\(806\) | 5.32624 | + | 3.86974i | 0.187609 | + | 0.136306i | ||||
\(807\) | 16.5623 | − | 12.0332i | 0.583021 | − | 0.423589i | ||||
\(808\) | −0.201626 | + | 0.620541i | −0.00709318 | + | 0.0218306i | ||||
\(809\) | 2.50000 | − | 7.69421i | 0.0878953 | − | 0.270514i | −0.897442 | − | 0.441133i | \(-0.854577\pi\) |
0.985337 | + | 0.170619i | \(0.0545767\pi\) | |||||||
\(810\) | −13.9443 | + | 10.1311i | −0.489952 | + | 0.355971i | ||||
\(811\) | −3.70820 | − | 2.69417i | −0.130213 | − | 0.0946050i | 0.520772 | − | 0.853696i | \(-0.325644\pi\) |
−0.650985 | + | 0.759090i | \(0.725644\pi\) | |||||||
\(812\) | 5.42705 | + | 16.7027i | 0.190452 | + | 0.586151i | ||||
\(813\) | −30.3607 | −1.06480 | ||||||||
\(814\) | −20.4508 | + | 1.38757i | −0.716802 | + | 0.0486344i | ||||
\(815\) | −0.180340 | −0.00631703 | ||||||||
\(816\) | 1.69098 | + | 5.20431i | 0.0591962 | + | 0.182187i | ||||
\(817\) | 0.763932 | + | 0.555029i | 0.0267266 | + | 0.0194180i | ||||
\(818\) | −2.23607 | + | 1.62460i | −0.0781823 | + | 0.0568028i | ||||
\(819\) | 0.281153 | − | 0.865300i | 0.00982428 | − | 0.0302360i | ||||
\(820\) | 6.00000 | − | 18.4661i | 0.209529 | − | 0.644864i | ||||
\(821\) | −22.9164 | + | 16.6497i | −0.799788 | + | 0.581080i | −0.910852 | − | 0.412733i | \(-0.864574\pi\) |
0.111064 | + | 0.993813i | \(0.464574\pi\) | |||||||
\(822\) | 45.1246 | + | 32.7849i | 1.57390 | + | 1.14351i | ||||
\(823\) | −6.18034 | − | 19.0211i | −0.215433 | − | 0.663035i | −0.999123 | − | 0.0418821i | \(-0.986665\pi\) |
0.783689 | − | 0.621153i | \(-0.213335\pi\) | |||||||
\(824\) | −3.74265 | −0.130381 | ||||||||
\(825\) | 4.54508 | + | 2.85317i | 0.158240 | + | 0.0993346i | ||||
\(826\) | 10.6525 | 0.370647 | ||||||||
\(827\) | −0.652476 | − | 2.00811i | −0.0226888 | − | 0.0698290i | 0.939071 | − | 0.343723i | \(-0.111688\pi\) |
−0.961760 | + | 0.273894i | \(0.911688\pi\) | |||||||
\(828\) | 4.14590 | + | 3.01217i | 0.144080 | + | 0.104680i | ||||
\(829\) | 1.52786 | − | 1.11006i | 0.0530649 | − | 0.0385539i | −0.560937 | − | 0.827859i | \(-0.689559\pi\) |
0.614002 | + | 0.789305i | \(0.289559\pi\) | |||||||
\(830\) | 7.29837 | − | 22.4621i | 0.253330 | − | 0.779670i | ||||
\(831\) | −8.70820 | + | 26.8011i | −0.302084 | + | 0.929720i | ||||
\(832\) | 25.0517 | − | 18.2011i | 0.868510 | − | 0.631010i | ||||
\(833\) | −2.73607 | − | 1.98787i | −0.0947991 | − | 0.0688756i | ||||
\(834\) | −16.1803 | − | 49.7980i | −0.560279 | − | 1.72436i | ||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | −9.43769 | + | 7.88597i | −0.326409 | + | 0.272742i | ||||
\(837\) | −6.76393 | −0.233796 | ||||||||
\(838\) | 18.8673 | + | 58.0674i | 0.651759 | + | 2.00591i | ||||
\(839\) | −42.3607 | − | 30.7768i | −1.46245 | − | 1.06253i | −0.982715 | − | 0.185122i | \(-0.940732\pi\) |
−0.479738 | − | 0.877412i | \(-0.659268\pi\) | |||||||
\(840\) | 2.92705 | − | 2.12663i | 0.100993 | − | 0.0733756i | ||||
\(841\) | 1.62868 | − | 5.01255i | 0.0561613 | − | 0.172847i | ||||
\(842\) | 2.42299 | − | 7.45718i | 0.0835016 | − | 0.256992i | ||||
\(843\) | 0.618034 | − | 0.449028i | 0.0212862 | − | 0.0154653i | ||||
\(844\) | −56.6140 | − | 41.1325i | −1.94873 | − | 1.41584i | ||||
\(845\) | 2.26393 | + | 6.96767i | 0.0778816 | + | 0.239695i | ||||
\(846\) | 6.70820 | 0.230633 | ||||||||
\(847\) | −4.78115 | − | 9.90659i | −0.164282 | − | 0.340395i | ||||
\(848\) | 10.4721 | 0.359615 | ||||||||
\(849\) | 13.7812 | + | 42.4140i | 0.472968 | + | 1.45565i | ||||
\(850\) | −6.11803 | − | 4.44501i | −0.209847 | − | 0.152463i | ||||
\(851\) | 10.0000 | − | 7.26543i | 0.342796 | − | 0.249056i | ||||
\(852\) | −1.01064 | + | 3.11044i | −0.0346241 | + | 0.106562i | ||||
\(853\) | 11.9164 | − | 36.6749i | 0.408010 | − | 1.25573i | −0.510346 | − | 0.859969i | \(-0.670482\pi\) |
0.918356 | − | 0.395756i | \(-0.129518\pi\) | |||||||
\(854\) | −16.7082 | + | 12.1392i | −0.571743 | + | 0.415396i | ||||
\(855\) | −0.381966 | − | 0.277515i | −0.0130630 | − | 0.00949080i | ||||
\(856\) | −1.90983 | − | 5.87785i | −0.0652766 | − | 0.200901i | ||||
\(857\) | 41.1935 | 1.40714 | 0.703572 | − | 0.710624i | \(-0.251587\pi\) | ||||
0.703572 | + | 0.710624i | \(0.251587\pi\) | |||||||
\(858\) | 21.9336 | − | 18.3273i | 0.748802 | − | 0.625685i | ||||
\(859\) | −28.9443 | −0.987566 | −0.493783 | − | 0.869585i | \(-0.664386\pi\) | ||||
−0.493783 | + | 0.869585i | \(0.664386\pi\) | |||||||
\(860\) | 0.708204 | + | 2.17963i | 0.0241496 | + | 0.0743247i | ||||
\(861\) | 8.47214 | + | 6.15537i | 0.288730 | + | 0.209774i | ||||
\(862\) | −18.6803 | + | 13.5721i | −0.636255 | + | 0.462266i | ||||
\(863\) | 6.47214 | − | 19.9192i | 0.220314 | − | 0.678057i | −0.778419 | − | 0.627744i | \(-0.783978\pi\) |
0.998734 | − | 0.0503125i | \(-0.0160217\pi\) | |||||||
\(864\) | −11.3435 | + | 34.9116i | −0.385912 | + | 1.18772i | ||||
\(865\) | 15.0172 | − | 10.9106i | 0.510601 | − | 0.370973i | ||||
\(866\) | 30.8156 | + | 22.3888i | 1.04716 | + | 0.760804i | ||||
\(867\) | 2.78115 | + | 8.55951i | 0.0944529 | + | 0.290696i | ||||
\(868\) | 3.70820 | 0.125865 | ||||||||
\(869\) | 38.7599 | + | 24.3314i | 1.31484 | + | 0.825388i | ||||
\(870\) | −21.1803 | −0.718081 | ||||||||
\(871\) | −10.4377 | − | 32.1239i | −0.353668 | − | 1.08848i | ||||
\(872\) | 37.0344 | + | 26.9071i | 1.25414 | + | 0.911189i | ||||
\(873\) | 0.100813 | − | 0.0732450i | 0.00341201 | − | 0.00247897i | ||||
\(874\) | 3.81966 | − | 11.7557i | 0.129202 | − | 0.397643i | ||||
\(875\) | 0.309017 | − | 0.951057i | 0.0104467 | − | 0.0321516i | ||||
\(876\) | 33.8435 | − | 24.5887i | 1.14346 | − | 0.830776i | ||||
\(877\) | 17.0000 | + | 12.3512i | 0.574049 | + | 0.417071i | 0.836574 | − | 0.547854i | \(-0.184555\pi\) |
−0.262525 | + | 0.964925i | \(0.584555\pi\) | |||||||
\(878\) | 12.2361 | + | 37.6587i | 0.412947 | + | 1.27092i | ||||
\(879\) | −28.1803 | −0.950499 | ||||||||
\(880\) | 3.30902 | − | 0.224514i | 0.111547 | − | 0.00756837i | ||||
\(881\) | −0.763932 | −0.0257375 | −0.0128688 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128688 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(882\) | −0.263932 | − | 0.812299i | −0.00888705 | − | 0.0273515i | ||||
\(883\) | −9.85410 | − | 7.15942i | −0.331617 | − | 0.240934i | 0.409499 | − | 0.912310i | \(-0.365703\pi\) |
−0.741116 | + | 0.671377i | \(0.765703\pi\) | |||||||
\(884\) | −19.5517 | + | 14.2051i | −0.657594 | + | 0.477770i | ||||
\(885\) | −2.38197 | + | 7.33094i | −0.0800689 | + | 0.246427i | ||||
\(886\) | −23.9443 | + | 73.6929i | −0.804424 | + | 2.47576i | ||||
\(887\) | 22.5344 | − | 16.3722i | 0.756633 | − | 0.549726i | −0.141243 | − | 0.989975i | \(-0.545110\pi\) |
0.897876 | + | 0.440249i | \(0.145110\pi\) | |||||||
\(888\) | −8.09017 | − | 5.87785i | −0.271488 | − | 0.197248i | ||||
\(889\) | −1.47214 | − | 4.53077i | −0.0493739 | − | 0.151957i | ||||
\(890\) | −38.5410 | −1.29190 | ||||||||
\(891\) | −6.23607 | + | 24.7930i | −0.208916 | + | 0.830596i | ||||
\(892\) | 31.4164 | 1.05190 | ||||||||
\(893\) | −3.00000 | − | 9.23305i | −0.100391 | − | 0.308972i | ||||
\(894\) | −32.6246 | − | 23.7032i | −1.09113 | − | 0.792753i | ||||
\(895\) | 14.0623 | − | 10.2169i | 0.470051 | − | 0.341512i | ||||
\(896\) | 4.83688 | − | 14.8864i | 0.161589 | − | 0.497319i | ||||
\(897\) | −5.32624 | + | 16.3925i | −0.177838 | + | 0.547329i | ||||
\(898\) | −43.9058 | + | 31.8994i | −1.46515 | + | 1.06450i | ||||
\(899\) | −5.85410 | − | 4.25325i | −0.195245 | − | 0.141854i | ||||
\(900\) | −0.354102 | − | 1.08981i | −0.0118034 | − | 0.0363271i | ||||
\(901\) | −35.4164 | −1.17989 | ||||||||
\(902\) | −17.8885 | − | 44.5407i | −0.595623 | − | 1.48304i | ||||
\(903\) | −1.23607 | −0.0411338 | ||||||||
\(904\) | 1.05573 | + | 3.24920i | 0.0351130 | + | 0.108067i | ||||
\(905\) | 11.7082 | + | 8.50651i | 0.389194 | + | 0.282766i | ||||
\(906\) | −7.66312 | + | 5.56758i | −0.254590 | + | 0.184971i | ||||
\(907\) | −2.43769 | + | 7.50245i | −0.0809423 | + | 0.249115i | −0.983336 | − | 0.181798i | \(-0.941808\pi\) |
0.902394 | + | 0.430913i | \(0.141808\pi\) | |||||||
\(908\) | 12.7918 | − | 39.3691i | 0.424511 | − | 1.30651i | ||||
\(909\) | −0.0901699 | + | 0.0655123i | −0.00299075 | + | 0.00217291i | ||||
\(910\) | −4.30902 | − | 3.13068i | −0.142843 | − | 0.103781i | ||||
\(911\) | 11.2812 | + | 34.7198i | 0.373761 | + | 1.15032i | 0.944311 | + | 0.329056i | \(0.106730\pi\) |
−0.570549 | + | 0.821263i | \(0.693270\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | −13.0557 | − | 32.5074i | −0.432082 | − | 1.07584i | ||||
\(914\) | 75.5279 | 2.49824 | ||||||||
\(915\) | −4.61803 | − | 14.2128i | −0.152667 | − | 0.469862i | ||||
\(916\) | 70.9574 | + | 51.5536i | 2.34450 | + | 1.70338i | ||||
\(917\) | 6.47214 | − | 4.70228i | 0.213729 | − | 0.155283i | ||||
\(918\) | 12.7877 | − | 39.3566i | 0.422058 | − | 1.29896i | ||||
\(919\) | −9.66312 | + | 29.7400i | −0.318757 | + | 0.981033i | 0.655423 | + | 0.755262i | \(0.272490\pi\) |
−0.974180 | + | 0.225771i | \(0.927510\pi\) | |||||||
\(920\) | 8.09017 | − | 5.87785i | 0.266725 | − | 0.193787i | ||||
\(921\) | −0.572949 | − | 0.416272i | −0.0188793 | − | 0.0137166i | ||||
\(922\) | 20.5279 | + | 63.1783i | 0.676049 | + | 2.08067i | ||||
\(923\) | 1.60488 | 0.0528252 | ||||||||
\(924\) | 3.92705 | − | 15.6129i | 0.129190 | − | 0.513628i | ||||
\(925\) | −2.76393 | −0.0908775 | ||||||||
\(926\) | 15.9787 | + | 49.1774i | 0.525093 | + | 1.61607i | ||||
\(927\) | −0.517221 | − | 0.375783i | −0.0169878 | − | 0.0123423i | ||||
\(928\) | −31.7705 | + | 23.0826i | −1.04292 | + | 0.757724i | ||||
\(929\) | 5.52786 | − | 17.0130i | 0.181363 | − | 0.558179i | −0.818503 | − | 0.574502i | \(-0.805196\pi\) |
0.999867 | + | 0.0163227i | \(0.00519590\pi\) | |||||||
\(930\) | −1.38197 | + | 4.25325i | −0.0453165 | + | 0.139470i | ||||
\(931\) | −1.00000 | + | 0.726543i | −0.0327737 | + | 0.0238115i | ||||
\(932\) | 59.8328 | + | 43.4711i | 1.95989 | + | 1.42394i | ||||
\(933\) | 13.5623 | + | 41.7405i | 0.444010 | + | 1.36652i | ||||
\(934\) | −37.2837 | −1.21996 | ||||||||
\(935\) | −11.1910 | + | 0.759299i | −0.365984 | + | 0.0248317i | ||||
\(936\) | −2.03444 | −0.0664978 | ||||||||
\(937\) | 17.4443 | + | 53.6879i | 0.569880 | + | 1.75391i | 0.652988 | + | 0.757368i | \(0.273515\pi\) |
−0.0831084 | + | 0.996541i | \(0.526485\pi\) | |||||||
\(938\) | −25.6525 | − | 18.6376i | −0.837583 | − | 0.608540i | ||||
\(939\) | −23.5623 | + | 17.1190i | −0.768927 | + | 0.558658i | ||||
\(940\) | 7.28115 | − | 22.4091i | 0.237485 | − | 0.730904i | ||||
\(941\) | 11.2918 | − | 34.7526i | 0.368102 | − | 1.13290i | −0.579914 | − | 0.814678i | \(-0.696914\pi\) |
0.948016 | − | 0.318224i | \(-0.103086\pi\) | |||||||
\(942\) | −14.3713 | + | 10.4414i | −0.468243 | + | 0.340198i | ||||
\(943\) | 23.4164 | + | 17.0130i | 0.762543 | + | 0.554020i | ||||
\(944\) | 1.47214 | + | 4.53077i | 0.0479139 | + | 0.147464i | ||||
\(945\) | 5.47214 | 0.178009 | ||||||||
\(946\) | 4.79837 | + | 3.01217i | 0.156009 | + | 0.0979341i | ||||
\(947\) | −24.0689 | −0.782134 | −0.391067 | − | 0.920362i | \(-0.627894\pi\) | ||||
−0.391067 | + | 0.920362i | \(0.627894\pi\) | |||||||
\(948\) | 20.6976 | + | 63.7005i | 0.672226 | + | 2.06890i | ||||
\(949\) | −16.6074 | − | 12.0660i | −0.539099 | − | 0.391678i | ||||
\(950\) | −2.23607 | + | 1.62460i | −0.0725476 | + | 0.0527089i | ||||
\(951\) | 15.2361 | − | 46.8918i | 0.494063 | − | 1.52057i | ||||
\(952\) | −2.33688 | + | 7.19218i | −0.0757387 | + | 0.233100i | ||||
\(953\) | −20.2705 | + | 14.7274i | −0.656626 | + | 0.477067i | −0.865522 | − | 0.500871i | \(-0.833013\pi\) |
0.208896 | + | 0.977938i | \(0.433013\pi\) | |||||||
\(954\) | −7.23607 | − | 5.25731i | −0.234276 | − | 0.170212i | ||||
\(955\) | −3.68034 | − | 11.3269i | −0.119093 | − | 0.366531i | ||||
\(956\) | −65.9361 | −2.13253 | ||||||||
\(957\) | −24.1074 | + | 20.1437i | −0.779281 | + | 0.651153i | ||||
\(958\) | −19.3475 | −0.625090 | ||||||||
\(959\) | −4.76393 | − | 14.6619i | −0.153835 | − | 0.473457i | ||||
\(960\) | 17.0172 | + | 12.3637i | 0.549228 | + | 0.399038i | ||||
\(961\) | 23.8435 | − | 17.3233i | 0.769144 | − | 0.558816i | ||||
\(962\) | −4.54915 | + | 14.0008i | −0.146670 | + | 0.451405i | ||||
\(963\) | 0.326238 | − | 1.00406i | 0.0105129 | − | 0.0323553i | ||||
\(964\) | −56.1246 | + | 40.7769i | −1.80765 | + | 1.31334i | ||||
\(965\) | 3.23607 | + | 2.35114i | 0.104173 | + | 0.0756859i | ||||
\(966\) | 5.00000 | + | 15.3884i | 0.160872 | + | 0.495114i | ||||
\(967\) | −21.2361 | −0.682906 | −0.341453 | − | 0.939899i | \(-0.610919\pi\) | ||||
−0.341453 | + | 0.939899i | \(0.610919\pi\) | |||||||
\(968\) | −17.7639 | + | 17.0130i | −0.570954 | + | 0.546819i | ||||
\(969\) | −6.76393 | −0.217289 | ||||||||
\(970\) | −0.225425 | − | 0.693786i | −0.00723796 | − | 0.0222761i | ||||
\(971\) | 23.7984 | + | 17.2905i | 0.763726 | + | 0.554880i | 0.900051 | − | 0.435785i | \(-0.143529\pi\) |
−0.136325 | + | 0.990664i | \(0.543529\pi\) | |||||||
\(972\) | 9.57295 | − | 6.95515i | 0.307052 | − | 0.223087i | ||||
\(973\) | −4.47214 | + | 13.7638i | −0.143370 | + | 0.441248i | ||||
\(974\) | −16.7082 | + | 51.4226i | −0.535365 | + | 1.64769i | ||||
\(975\) | 3.11803 | − | 2.26538i | 0.0998570 | − | 0.0725504i | ||||
\(976\) | −7.47214 | − | 5.42882i | −0.239177 | − | 0.173772i | ||||
\(977\) | 11.3607 | + | 34.9646i | 0.363460 | + | 1.11862i | 0.950940 | + | 0.309377i | \(0.100120\pi\) |
−0.587479 | + | 0.809239i | \(0.699880\pi\) | |||||||
\(978\) | −0.652476 | −0.0208639 | ||||||||
\(979\) | −43.8673 | + | 36.6547i | −1.40200 | + | 1.17149i | ||||
\(980\) | −3.00000 | −0.0958315 | ||||||||
\(981\) | 2.41641 | + | 7.43694i | 0.0771500 | + | 0.237443i | ||||
\(982\) | −68.5410 | − | 49.7980i | −2.18723 | − | 1.58912i | ||||
\(983\) | −15.3541 | + | 11.1554i | −0.489720 | + | 0.355802i | −0.805077 | − | 0.593171i | \(-0.797876\pi\) |
0.315357 | + | 0.948973i | \(0.397876\pi\) | |||||||
\(984\) | 7.23607 | − | 22.2703i | 0.230677 | − | 0.709952i | ||||
\(985\) | 3.70820 | − | 11.4127i | 0.118153 | − | 0.363638i | ||||
\(986\) | 35.8156 | − | 26.0216i | 1.14060 | − | 0.828695i | ||||
\(987\) | 10.2812 | + | 7.46969i | 0.327253 | + | 0.237763i | ||||
\(988\) | 2.72949 | + | 8.40051i | 0.0868367 | + | 0.267256i | ||||
\(989\) | −3.41641 | −0.108635 | ||||||||
\(990\) | −2.39919 | − | 1.50609i | −0.0762512 | − | 0.0478665i | ||||
\(991\) | 7.14590 | 0.226997 | 0.113498 | − | 0.993538i | \(-0.463794\pi\) | ||||
0.113498 | + | 0.993538i | \(0.463794\pi\) | |||||||
\(992\) | 2.56231 | + | 7.88597i | 0.0813533 | + | 0.250380i | ||||
\(993\) | 25.5344 | + | 18.5519i | 0.810311 | + | 0.588725i | ||||
\(994\) | 1.21885 | − | 0.885544i | 0.0386595 | − | 0.0280878i | ||||
\(995\) | 5.56231 | − | 17.1190i | 0.176337 | − | 0.542709i | ||||
\(996\) | 15.8435 | − | 48.7612i | 0.502019 | − | 1.54506i | ||||
\(997\) | −21.2082 | + | 15.4087i | −0.671671 | + | 0.487997i | −0.870584 | − | 0.492020i | \(-0.836259\pi\) |
0.198913 | + | 0.980017i | \(0.436259\pi\) | |||||||
\(998\) | −10.9164 | − | 7.93123i | −0.345553 | − | 0.251059i | ||||
\(999\) | −4.67376 | − | 14.3844i | −0.147871 | − | 0.455101i |
(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 | 385.2.n.b.71.1 | ✓ | 4 | |
11.3 | even | 5 | 4235.2.a.j.1.2 | 2 | |||
11.8 | odd | 10 | 4235.2.a.k.1.1 | 2 | |||
11.9 | even | 5 | inner | 385.2.n.b.141.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.n.b.71.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
385.2.n.b.141.1 | yes | 4 | 11.9 | even | 5 | inner | |
4235.2.a.j.1.2 | 2 | 11.3 | even | 5 | |||
4235.2.a.k.1.1 | 2 | 11.8 | odd | 10 |