Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [946,2,Mod(345,946)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(946, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("946.345");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 946 = 2 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 946.f (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.55384803121\) |
Analytic rank: | \(1\) |
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 | 775.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 946.775 |
Dual form | 946.2.f.a.603.1 |
$q$-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 \(\left(\mathbb{Z}/946\mathbb{Z}\right)^\times\).
\(n\) | \(89\) | \(431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | −2.61803 | − | 1.90211i | −1.51152 | − | 1.09819i | −0.965496 | − | 0.260418i | \(-0.916140\pi\) |
−0.546027 | − | 0.837768i | \(-0.683860\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −1.00000 | + | 3.07768i | −0.447214 | + | 1.37638i | 0.432824 | + | 0.901478i | \(0.357517\pi\) |
−0.880038 | + | 0.474904i | \(0.842483\pi\) | |||||||
\(6\) | 1.00000 | − | 3.07768i | 0.408248 | − | 1.25646i | ||||
\(7\) | −3.61803 | + | 2.62866i | −1.36749 | + | 0.993538i | −0.369560 | + | 0.929207i | \(0.620491\pi\) |
−0.997929 | + | 0.0643314i | \(0.979509\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 2.30902 | + | 7.10642i | 0.769672 | + | 2.36881i | ||||
\(10\) | −3.23607 | −1.02333 | ||||||||
\(11\) | −3.23607 | − | 0.726543i | −0.975711 | − | 0.219061i | ||||
\(12\) | 3.23607 | 0.934172 | ||||||||
\(13\) | −0.190983 | − | 0.587785i | −0.0529692 | − | 0.163022i | 0.921073 | − | 0.389391i | \(-0.127315\pi\) |
−0.974042 | + | 0.226369i | \(0.927315\pi\) | |||||||
\(14\) | −3.61803 | − | 2.62866i | −0.966960 | − | 0.702538i | ||||
\(15\) | 8.47214 | − | 6.15537i | 2.18750 | − | 1.58931i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −1.50000 | + | 4.61653i | −0.363803 | + | 1.11967i | 0.586924 | + | 0.809642i | \(0.300339\pi\) |
−0.950727 | + | 0.310029i | \(0.899661\pi\) | |||||||
\(18\) | −6.04508 | + | 4.39201i | −1.42484 | + | 1.03521i | ||||
\(19\) | −1.61803 | − | 1.17557i | −0.371202 | − | 0.269694i | 0.386507 | − | 0.922287i | \(-0.373682\pi\) |
−0.757709 | + | 0.652592i | \(0.773682\pi\) | |||||||
\(20\) | −1.00000 | − | 3.07768i | −0.223607 | − | 0.688191i | ||||
\(21\) | 14.4721 | 3.15808 | ||||||||
\(22\) | −0.309017 | − | 3.30220i | −0.0658826 | − | 0.704031i | ||||
\(23\) | 7.09017 | 1.47840 | 0.739201 | − | 0.673485i | \(-0.235203\pi\) | ||||
0.739201 | + | 0.673485i | \(0.235203\pi\) | |||||||
\(24\) | 1.00000 | + | 3.07768i | 0.204124 | + | 0.628230i | ||||
\(25\) | −4.42705 | − | 3.21644i | −0.885410 | − | 0.643288i | ||||
\(26\) | 0.500000 | − | 0.363271i | 0.0980581 | − | 0.0712434i | ||||
\(27\) | 4.47214 | − | 13.7638i | 0.860663 | − | 2.64885i | ||||
\(28\) | 1.38197 | − | 4.25325i | 0.261167 | − | 0.803789i | ||||
\(29\) | −8.47214 | + | 6.15537i | −1.57324 | + | 1.14302i | −0.649264 | + | 0.760563i | \(0.724923\pi\) |
−0.923972 | + | 0.382460i | \(0.875077\pi\) | |||||||
\(30\) | 8.47214 | + | 6.15537i | 1.54679 | + | 1.12381i | ||||
\(31\) | 0.118034 | + | 0.363271i | 0.0211995 | + | 0.0652454i | 0.961097 | − | 0.276212i | \(-0.0890793\pi\) |
−0.939897 | + | 0.341458i | \(0.889079\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.09017 | + | 8.05748i | 1.23424 | + | 1.40263i | ||||
\(34\) | −4.85410 | −0.832472 | ||||||||
\(35\) | −4.47214 | − | 13.7638i | −0.755929 | − | 2.32651i | ||||
\(36\) | −6.04508 | − | 4.39201i | −1.00751 | − | 0.732002i | ||||
\(37\) | 6.47214 | − | 4.70228i | 1.06401 | − | 0.773050i | 0.0891861 | − | 0.996015i | \(-0.471573\pi\) |
0.974827 | + | 0.222965i | \(0.0715734\pi\) | |||||||
\(38\) | 0.618034 | − | 1.90211i | 0.100258 | − | 0.308563i | ||||
\(39\) | −0.618034 | + | 1.90211i | −0.0989646 | + | 0.304582i | ||||
\(40\) | 2.61803 | − | 1.90211i | 0.413948 | − | 0.300750i | ||||
\(41\) | −0.381966 | − | 0.277515i | −0.0596531 | − | 0.0433405i | 0.557559 | − | 0.830137i | \(-0.311738\pi\) |
−0.617212 | + | 0.786797i | \(0.711738\pi\) | |||||||
\(42\) | 4.47214 | + | 13.7638i | 0.690066 | + | 2.12380i | ||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 3.04508 | − | 1.31433i | 0.459064 | − | 0.198142i | ||||
\(45\) | −24.1803 | −3.60459 | ||||||||
\(46\) | 2.19098 | + | 6.74315i | 0.323043 | + | 0.994224i | ||||
\(47\) | −0.927051 | − | 0.673542i | −0.135224 | − | 0.0982462i | 0.518117 | − | 0.855310i | \(-0.326633\pi\) |
−0.653341 | + | 0.757064i | \(0.726633\pi\) | |||||||
\(48\) | −2.61803 | + | 1.90211i | −0.377881 | + | 0.274546i | ||||
\(49\) | 4.01722 | − | 12.3637i | 0.573889 | − | 1.76625i | ||||
\(50\) | 1.69098 | − | 5.20431i | 0.239141 | − | 0.736001i | ||||
\(51\) | 12.7082 | − | 9.23305i | 1.77950 | − | 1.29289i | ||||
\(52\) | 0.500000 | + | 0.363271i | 0.0693375 | + | 0.0503767i | ||||
\(53\) | −4.26393 | − | 13.1230i | −0.585696 | − | 1.80259i | −0.596457 | − | 0.802645i | \(-0.703425\pi\) |
0.0107607 | − | 0.999942i | \(-0.496575\pi\) | |||||||
\(54\) | 14.4721 | 1.96941 | ||||||||
\(55\) | 5.47214 | − | 9.23305i | 0.737863 | − | 1.24498i | ||||
\(56\) | 4.47214 | 0.597614 | ||||||||
\(57\) | 2.00000 | + | 6.15537i | 0.264906 | + | 0.815298i | ||||
\(58\) | −8.47214 | − | 6.15537i | −1.11245 | − | 0.808239i | ||||
\(59\) | −3.50000 | + | 2.54290i | −0.455661 | + | 0.331057i | −0.791827 | − | 0.610746i | \(-0.790870\pi\) |
0.336166 | + | 0.941803i | \(0.390870\pi\) | |||||||
\(60\) | −3.23607 | + | 9.95959i | −0.417775 | + | 1.28578i | ||||
\(61\) | −2.61803 | + | 8.05748i | −0.335205 | + | 1.03165i | 0.631416 | + | 0.775444i | \(0.282474\pi\) |
−0.966621 | + | 0.256210i | \(0.917526\pi\) | |||||||
\(62\) | −0.309017 | + | 0.224514i | −0.0392452 | + | 0.0285133i | ||||
\(63\) | −27.0344 | − | 19.6417i | −3.40602 | − | 2.47462i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | −5.47214 | + | 9.23305i | −0.673573 | + | 1.13651i | ||||
\(67\) | 4.32624 | 0.528534 | 0.264267 | − | 0.964450i | \(-0.414870\pi\) | ||||
0.264267 | + | 0.964450i | \(0.414870\pi\) | |||||||
\(68\) | −1.50000 | − | 4.61653i | −0.181902 | − | 0.559836i | ||||
\(69\) | −18.5623 | − | 13.4863i | −2.23464 | − | 1.62356i | ||||
\(70\) | 11.7082 | − | 8.50651i | 1.39940 | − | 1.01672i | ||||
\(71\) | −0.763932 | + | 2.35114i | −0.0906621 | + | 0.279029i | −0.986099 | − | 0.166159i | \(-0.946863\pi\) |
0.895437 | + | 0.445189i | \(0.146863\pi\) | |||||||
\(72\) | 2.30902 | − | 7.10642i | 0.272120 | − | 0.837500i | ||||
\(73\) | 1.23607 | − | 0.898056i | 0.144671 | − | 0.105109i | −0.513096 | − | 0.858331i | \(-0.671501\pi\) |
0.657766 | + | 0.753222i | \(0.271501\pi\) | |||||||
\(74\) | 6.47214 | + | 4.70228i | 0.752371 | + | 0.546629i | ||||
\(75\) | 5.47214 | + | 16.8415i | 0.631868 | + | 1.94469i | ||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 13.6180 | − | 5.87785i | 1.55192 | − | 0.669843i | ||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −0.645898 | − | 1.98787i | −0.0726692 | − | 0.223653i | 0.908125 | − | 0.418700i | \(-0.137514\pi\) |
−0.980794 | + | 0.195047i | \(0.937514\pi\) | |||||||
\(80\) | 2.61803 | + | 1.90211i | 0.292705 | + | 0.212663i | ||||
\(81\) | −19.7533 | + | 14.3516i | −2.19481 | + | 1.59462i | ||||
\(82\) | 0.145898 | − | 0.449028i | 0.0161117 | − | 0.0495868i | ||||
\(83\) | 0.118034 | − | 0.363271i | 0.0129559 | − | 0.0398742i | −0.944370 | − | 0.328886i | \(-0.893327\pi\) |
0.957325 | + | 0.289012i | \(0.0933267\pi\) | |||||||
\(84\) | −11.7082 | + | 8.50651i | −1.27747 | + | 0.928136i | ||||
\(85\) | −12.7082 | − | 9.23305i | −1.37840 | − | 1.00146i | ||||
\(86\) | −0.309017 | − | 0.951057i | −0.0333222 | − | 0.102555i | ||||
\(87\) | 33.8885 | 3.63323 | ||||||||
\(88\) | 2.19098 | + | 2.48990i | 0.233560 | + | 0.265424i | ||||
\(89\) | 5.23607 | 0.555022 | 0.277511 | − | 0.960722i | \(-0.410490\pi\) | ||||
0.277511 | + | 0.960722i | \(0.410490\pi\) | |||||||
\(90\) | −7.47214 | − | 22.9969i | −0.787632 | − | 2.42408i | ||||
\(91\) | 2.23607 | + | 1.62460i | 0.234404 | + | 0.170304i | ||||
\(92\) | −5.73607 | + | 4.16750i | −0.598026 | + | 0.434492i | ||||
\(93\) | 0.381966 | − | 1.17557i | 0.0396080 | − | 0.121901i | ||||
\(94\) | 0.354102 | − | 1.08981i | 0.0365228 | − | 0.112406i | ||||
\(95\) | 5.23607 | − | 3.80423i | 0.537209 | − | 0.390305i | ||||
\(96\) | −2.61803 | − | 1.90211i | −0.267202 | − | 0.194134i | ||||
\(97\) | 3.42705 | + | 10.5474i | 0.347964 | + | 1.07092i | 0.959978 | + | 0.280077i | \(0.0903599\pi\) |
−0.612013 | + | 0.790847i | \(0.709640\pi\) | |||||||
\(98\) | 13.0000 | 1.31320 | ||||||||
\(99\) | −2.30902 | − | 24.6745i | −0.232065 | − | 2.47988i | ||||
\(100\) | 5.47214 | 0.547214 | ||||||||
\(101\) | −0.663119 | − | 2.04087i | −0.0659828 | − | 0.203074i | 0.912629 | − | 0.408788i | \(-0.134048\pi\) |
−0.978612 | + | 0.205714i | \(0.934048\pi\) | |||||||
\(102\) | 12.7082 | + | 9.23305i | 1.25830 | + | 0.914208i | ||||
\(103\) | 0.454915 | − | 0.330515i | 0.0448241 | − | 0.0325666i | −0.565148 | − | 0.824990i | \(-0.691181\pi\) |
0.609972 | + | 0.792423i | \(0.291181\pi\) | |||||||
\(104\) | −0.190983 | + | 0.587785i | −0.0187274 | + | 0.0576371i | ||||
\(105\) | −14.4721 | + | 44.5407i | −1.41234 | + | 4.34672i | ||||
\(106\) | 11.1631 | − | 8.11048i | 1.08426 | − | 0.787760i | ||||
\(107\) | 2.50000 | + | 1.81636i | 0.241684 | + | 0.175594i | 0.702033 | − | 0.712144i | \(-0.252276\pi\) |
−0.460349 | + | 0.887738i | \(0.652276\pi\) | |||||||
\(108\) | 4.47214 | + | 13.7638i | 0.430331 | + | 1.32442i | ||||
\(109\) | 4.09017 | 0.391767 | 0.195884 | − | 0.980627i | \(-0.437243\pi\) | ||||
0.195884 | + | 0.980627i | \(0.437243\pi\) | |||||||
\(110\) | 10.4721 | + | 2.35114i | 0.998479 | + | 0.224172i | ||||
\(111\) | −25.8885 | −2.45723 | ||||||||
\(112\) | 1.38197 | + | 4.25325i | 0.130584 | + | 0.401895i | ||||
\(113\) | 9.32624 | + | 6.77591i | 0.877339 | + | 0.637424i | 0.932546 | − | 0.361051i | \(-0.117582\pi\) |
−0.0552074 | + | 0.998475i | \(0.517582\pi\) | |||||||
\(114\) | −5.23607 | + | 3.80423i | −0.490403 | + | 0.356298i | ||||
\(115\) | −7.09017 | + | 21.8213i | −0.661162 | + | 2.03485i | ||||
\(116\) | 3.23607 | − | 9.95959i | 0.300461 | − | 0.924725i | ||||
\(117\) | 3.73607 | − | 2.71441i | 0.345400 | − | 0.250948i | ||||
\(118\) | −3.50000 | − | 2.54290i | −0.322201 | − | 0.234093i | ||||
\(119\) | −6.70820 | − | 20.6457i | −0.614940 | − | 1.89259i | ||||
\(120\) | −10.4721 | −0.955971 | ||||||||
\(121\) | 9.94427 | + | 4.70228i | 0.904025 | + | 0.427480i | ||||
\(122\) | −8.47214 | −0.767031 | ||||||||
\(123\) | 0.472136 | + | 1.45309i | 0.0425711 | + | 0.131020i | ||||
\(124\) | −0.309017 | − | 0.224514i | −0.0277505 | − | 0.0201620i | ||||
\(125\) | 1.23607 | − | 0.898056i | 0.110557 | − | 0.0803246i | ||||
\(126\) | 10.3262 | − | 31.7809i | 0.919934 | − | 2.83127i | ||||
\(127\) | 3.70820 | − | 11.4127i | 0.329050 | − | 1.01271i | −0.640529 | − | 0.767934i | \(-0.721285\pi\) |
0.969579 | − | 0.244778i | \(-0.0787150\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | 2.61803 | + | 1.90211i | 0.230505 | + | 0.167472i | ||||
\(130\) | 0.618034 | + | 1.90211i | 0.0542052 | + | 0.166826i | ||||
\(131\) | 1.05573 | 0.0922394 | 0.0461197 | − | 0.998936i | \(-0.485314\pi\) | ||||
0.0461197 | + | 0.998936i | \(0.485314\pi\) | |||||||
\(132\) | −10.4721 | − | 2.35114i | −0.911482 | − | 0.204641i | ||||
\(133\) | 8.94427 | 0.775567 | ||||||||
\(134\) | 1.33688 | + | 4.11450i | 0.115489 | + | 0.355438i | ||||
\(135\) | 37.8885 | + | 27.5276i | 3.26093 | + | 2.36920i | ||||
\(136\) | 3.92705 | − | 2.85317i | 0.336742 | − | 0.244657i | ||||
\(137\) | −7.00000 | + | 21.5438i | −0.598050 | + | 1.84061i | −0.0591347 | + | 0.998250i | \(0.518834\pi\) |
−0.538916 | + | 0.842360i | \(0.681166\pi\) | |||||||
\(138\) | 7.09017 | − | 21.8213i | 0.603555 | − | 1.85755i | ||||
\(139\) | −16.4443 | + | 11.9475i | −1.39478 | + | 1.01337i | −0.399464 | + | 0.916749i | \(0.630804\pi\) |
−0.995321 | + | 0.0966216i | \(0.969196\pi\) | |||||||
\(140\) | 11.7082 | + | 8.50651i | 0.989524 | + | 0.718931i | ||||
\(141\) | 1.14590 | + | 3.52671i | 0.0965020 | + | 0.297003i | ||||
\(142\) | −2.47214 | −0.207457 | ||||||||
\(143\) | 0.190983 | + | 2.04087i | 0.0159708 | + | 0.170666i | ||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | −10.4721 | − | 32.2299i | −0.869664 | − | 2.67655i | ||||
\(146\) | 1.23607 | + | 0.898056i | 0.102298 | + | 0.0743236i | ||||
\(147\) | −34.0344 | + | 24.7275i | −2.80711 | + | 2.03949i | ||||
\(148\) | −2.47214 | + | 7.60845i | −0.203208 | + | 0.625411i | ||||
\(149\) | −3.52786 | + | 10.8576i | −0.289014 | + | 0.889493i | 0.696153 | + | 0.717894i | \(0.254894\pi\) |
−0.985167 | + | 0.171600i | \(0.945106\pi\) | |||||||
\(150\) | −14.3262 | + | 10.4086i | −1.16973 | + | 0.849860i | ||||
\(151\) | −8.32624 | − | 6.04937i | −0.677580 | − | 0.492290i | 0.194974 | − | 0.980808i | \(-0.437538\pi\) |
−0.872554 | + | 0.488518i | \(0.837538\pi\) | |||||||
\(152\) | 0.618034 | + | 1.90211i | 0.0501292 | + | 0.154282i | ||||
\(153\) | −36.2705 | −2.93230 | ||||||||
\(154\) | 9.79837 | + | 11.1352i | 0.789575 | + | 0.897297i | ||||
\(155\) | −1.23607 | −0.0992834 | ||||||||
\(156\) | −0.618034 | − | 1.90211i | −0.0494823 | − | 0.152291i | ||||
\(157\) | −4.00000 | − | 2.90617i | −0.319235 | − | 0.231938i | 0.416614 | − | 0.909083i | \(-0.363217\pi\) |
−0.735849 | + | 0.677146i | \(0.763217\pi\) | |||||||
\(158\) | 1.69098 | − | 1.22857i | 0.134527 | − | 0.0977399i | ||||
\(159\) | −13.7984 | + | 42.4670i | −1.09428 | + | 3.36785i | ||||
\(160\) | −1.00000 | + | 3.07768i | −0.0790569 | + | 0.243312i | ||||
\(161\) | −25.6525 | + | 18.6376i | −2.02170 | + | 1.46885i | ||||
\(162\) | −19.7533 | − | 14.3516i | −1.55196 | − | 1.12757i | ||||
\(163\) | −3.23607 | − | 9.95959i | −0.253468 | − | 0.780096i | −0.994128 | − | 0.108215i | \(-0.965487\pi\) |
0.740659 | − | 0.671881i | \(-0.234513\pi\) | |||||||
\(164\) | 0.472136 | 0.0368676 | ||||||||
\(165\) | −31.8885 | + | 13.7638i | −2.48252 | + | 1.07151i | ||||
\(166\) | 0.381966 | 0.0296463 | ||||||||
\(167\) | 3.71885 | + | 11.4454i | 0.287773 | + | 0.885674i | 0.985554 | + | 0.169363i | \(0.0541710\pi\) |
−0.697781 | + | 0.716311i | \(0.745829\pi\) | |||||||
\(168\) | −11.7082 | − | 8.50651i | −0.903308 | − | 0.656291i | ||||
\(169\) | 10.2082 | − | 7.41669i | 0.785246 | − | 0.570515i | ||||
\(170\) | 4.85410 | − | 14.9394i | 0.372293 | − | 1.14580i | ||||
\(171\) | 4.61803 | − | 14.2128i | 0.353150 | − | 1.08688i | ||||
\(172\) | 0.809017 | − | 0.587785i | 0.0616870 | − | 0.0448182i | ||||
\(173\) | 5.30902 | + | 3.85723i | 0.403637 | + | 0.293260i | 0.771021 | − | 0.636810i | \(-0.219746\pi\) |
−0.367384 | + | 0.930069i | \(0.619746\pi\) | |||||||
\(174\) | 10.4721 | + | 32.2299i | 0.793891 | + | 2.44334i | ||||
\(175\) | 24.4721 | 1.84992 | ||||||||
\(176\) | −1.69098 | + | 2.85317i | −0.127463 | + | 0.215066i | ||||
\(177\) | 14.0000 | 1.05230 | ||||||||
\(178\) | 1.61803 | + | 4.97980i | 0.121277 | + | 0.373252i | ||||
\(179\) | 1.76393 | + | 1.28157i | 0.131842 | + | 0.0957892i | 0.651752 | − | 0.758432i | \(-0.274034\pi\) |
−0.519909 | + | 0.854221i | \(0.674034\pi\) | |||||||
\(180\) | 19.5623 | − | 14.2128i | 1.45809 | − | 1.05936i | ||||
\(181\) | 6.66312 | − | 20.5070i | 0.495266 | − | 1.52427i | −0.321276 | − | 0.946985i | \(-0.604112\pi\) |
0.816542 | − | 0.577286i | \(-0.195888\pi\) | |||||||
\(182\) | −0.854102 | + | 2.62866i | −0.0633102 | + | 0.194849i | ||||
\(183\) | 22.1803 | − | 16.1150i | 1.63962 | − | 1.19125i | ||||
\(184\) | −5.73607 | − | 4.16750i | −0.422869 | − | 0.307232i | ||||
\(185\) | 8.00000 | + | 24.6215i | 0.588172 | + | 1.81021i | ||||
\(186\) | 1.23607 | 0.0906329 | ||||||||
\(187\) | 8.20820 | − | 13.8496i | 0.600243 | − | 1.01278i | ||||
\(188\) | 1.14590 | 0.0835732 | ||||||||
\(189\) | 20.0000 | + | 61.5537i | 1.45479 | + | 4.47737i | ||||
\(190\) | 5.23607 | + | 3.80423i | 0.379864 | + | 0.275988i | ||||
\(191\) | 10.8541 | − | 7.88597i | 0.785375 | − | 0.570609i | −0.121212 | − | 0.992627i | \(-0.538678\pi\) |
0.906587 | + | 0.422018i | \(0.138678\pi\) | |||||||
\(192\) | 1.00000 | − | 3.07768i | 0.0721688 | − | 0.222113i | ||||
\(193\) | 5.20820 | − | 16.0292i | 0.374895 | − | 1.15381i | −0.568655 | − | 0.822576i | \(-0.692536\pi\) |
0.943550 | − | 0.331231i | \(-0.107464\pi\) | |||||||
\(194\) | −8.97214 | + | 6.51864i | −0.644162 | + | 0.468011i | ||||
\(195\) | −5.23607 | − | 3.80423i | −0.374963 | − | 0.272426i | ||||
\(196\) | 4.01722 | + | 12.3637i | 0.286944 | + | 0.883124i | ||||
\(197\) | 17.8541 | 1.27205 | 0.636026 | − | 0.771668i | \(-0.280577\pi\) | ||||
0.636026 | + | 0.771668i | \(0.280577\pi\) | |||||||
\(198\) | 22.7533 | − | 9.82084i | 1.61701 | − | 0.697936i | ||||
\(199\) | −19.4164 | −1.37639 | −0.688196 | − | 0.725525i | \(-0.741597\pi\) | ||||
−0.688196 | + | 0.725525i | \(0.741597\pi\) | |||||||
\(200\) | 1.69098 | + | 5.20431i | 0.119571 | + | 0.368000i | ||||
\(201\) | −11.3262 | − | 8.22899i | −0.798891 | − | 0.580428i | ||||
\(202\) | 1.73607 | − | 1.26133i | 0.122149 | − | 0.0887467i | ||||
\(203\) | 14.4721 | − | 44.5407i | 1.01574 | − | 3.12614i | ||||
\(204\) | −4.85410 | + | 14.9394i | −0.339855 | + | 1.04597i | ||||
\(205\) | 1.23607 | − | 0.898056i | 0.0863307 | − | 0.0627229i | ||||
\(206\) | 0.454915 | + | 0.330515i | 0.0316954 | + | 0.0230281i | ||||
\(207\) | 16.3713 | + | 50.3858i | 1.13789 | + | 3.50205i | ||||
\(208\) | −0.618034 | −0.0428529 | ||||||||
\(209\) | 4.38197 | + | 4.97980i | 0.303107 | + | 0.344460i | ||||
\(210\) | −46.8328 | −3.23177 | ||||||||
\(211\) | 6.09017 | + | 18.7436i | 0.419265 | + | 1.29036i | 0.908380 | + | 0.418145i | \(0.137320\pi\) |
−0.489116 | + | 0.872219i | \(0.662680\pi\) | |||||||
\(212\) | 11.1631 | + | 8.11048i | 0.766686 | + | 0.557030i | ||||
\(213\) | 6.47214 | − | 4.70228i | 0.443463 | − | 0.322195i | ||||
\(214\) | −0.954915 | + | 2.93893i | −0.0652766 | + | 0.200901i | ||||
\(215\) | 1.00000 | − | 3.07768i | 0.0681994 | − | 0.209896i | ||||
\(216\) | −11.7082 | + | 8.50651i | −0.796642 | + | 0.578795i | ||||
\(217\) | −1.38197 | − | 1.00406i | −0.0938140 | − | 0.0681598i | ||||
\(218\) | 1.26393 | + | 3.88998i | 0.0856043 | + | 0.263463i | ||||
\(219\) | −4.94427 | −0.334103 | ||||||||
\(220\) | 1.00000 | + | 10.6861i | 0.0674200 | + | 0.720459i | ||||
\(221\) | 3.00000 | 0.201802 | ||||||||
\(222\) | −8.00000 | − | 24.6215i | −0.536925 | − | 1.65248i | ||||
\(223\) | −11.4721 | − | 8.33499i | −0.768231 | − | 0.558153i | 0.133193 | − | 0.991090i | \(-0.457477\pi\) |
−0.901424 | + | 0.432938i | \(0.857477\pi\) | |||||||
\(224\) | −3.61803 | + | 2.62866i | −0.241740 | + | 0.175634i | ||||
\(225\) | 12.6353 | − | 38.8873i | 0.842350 | − | 2.59249i | ||||
\(226\) | −3.56231 | + | 10.9637i | −0.236961 | + | 0.729291i | ||||
\(227\) | 6.09017 | − | 4.42477i | 0.404219 | − | 0.293682i | −0.367038 | − | 0.930206i | \(-0.619628\pi\) |
0.771257 | + | 0.636524i | \(0.219628\pi\) | |||||||
\(228\) | −5.23607 | − | 3.80423i | −0.346767 | − | 0.251941i | ||||
\(229\) | −6.57295 | − | 20.2295i | −0.434353 | − | 1.33680i | −0.893748 | − | 0.448568i | \(-0.851934\pi\) |
0.459396 | − | 0.888232i | \(-0.348066\pi\) | |||||||
\(230\) | −22.9443 | −1.51290 | ||||||||
\(231\) | −46.8328 | − | 10.5146i | −3.08137 | − | 0.691811i | ||||
\(232\) | 10.4721 | 0.687529 | ||||||||
\(233\) | −1.94427 | − | 5.98385i | −0.127373 | − | 0.392015i | 0.866953 | − | 0.498391i | \(-0.166075\pi\) |
−0.994326 | + | 0.106375i | \(0.966075\pi\) | |||||||
\(234\) | 3.73607 | + | 2.71441i | 0.244234 | + | 0.177447i | ||||
\(235\) | 3.00000 | − | 2.17963i | 0.195698 | − | 0.142183i | ||||
\(236\) | 1.33688 | − | 4.11450i | 0.0870235 | − | 0.267831i | ||||
\(237\) | −2.09017 | + | 6.43288i | −0.135771 | + | 0.417861i | ||||
\(238\) | 17.5623 | − | 12.7598i | 1.13840 | − | 0.827093i | ||||
\(239\) | −13.6803 | − | 9.93935i | −0.884908 | − | 0.642923i | 0.0496376 | − | 0.998767i | \(-0.484193\pi\) |
−0.934545 | + | 0.355844i | \(0.884193\pi\) | |||||||
\(240\) | −3.23607 | − | 9.95959i | −0.208887 | − | 0.642889i | ||||
\(241\) | −17.7082 | −1.14069 | −0.570343 | − | 0.821407i | \(-0.693190\pi\) | ||||
−0.570343 | + | 0.821407i | \(0.693190\pi\) | |||||||
\(242\) | −1.39919 | + | 10.9106i | −0.0899431 | + | 0.701363i | ||||
\(243\) | 35.5967 | 2.28353 | ||||||||
\(244\) | −2.61803 | − | 8.05748i | −0.167602 | − | 0.515827i | ||||
\(245\) | 34.0344 | + | 24.7275i | 2.17438 | + | 1.57978i | ||||
\(246\) | −1.23607 | + | 0.898056i | −0.0788088 | + | 0.0572580i | ||||
\(247\) | −0.381966 | + | 1.17557i | −0.0243039 | + | 0.0747998i | ||||
\(248\) | 0.118034 | − | 0.363271i | 0.00749517 | − | 0.0230677i | ||||
\(249\) | −1.00000 | + | 0.726543i | −0.0633724 | + | 0.0460428i | ||||
\(250\) | 1.23607 | + | 0.898056i | 0.0781758 | + | 0.0567980i | ||||
\(251\) | 4.64590 | + | 14.2986i | 0.293246 | + | 0.902520i | 0.983805 | + | 0.179243i | \(0.0573649\pi\) |
−0.690558 | + | 0.723277i | \(0.742635\pi\) | |||||||
\(252\) | 33.4164 | 2.10504 | ||||||||
\(253\) | −22.9443 | − | 5.15131i | −1.44249 | − | 0.323860i | ||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 15.7082 | + | 48.3449i | 0.983686 | + | 3.02747i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 12.4721 | − | 9.06154i | 0.777990 | − | 0.565243i | −0.126385 | − | 0.991981i | \(-0.540337\pi\) |
0.904375 | + | 0.426738i | \(0.140337\pi\) | |||||||
\(258\) | −1.00000 | + | 3.07768i | −0.0622573 | + | 0.191608i | ||||
\(259\) | −11.0557 | + | 34.0260i | −0.686970 | + | 2.11427i | ||||
\(260\) | −1.61803 | + | 1.17557i | −0.100346 | + | 0.0729058i | ||||
\(261\) | −63.3050 | − | 45.9937i | −3.91848 | − | 2.84694i | ||||
\(262\) | 0.326238 | + | 1.00406i | 0.0201550 | + | 0.0620309i | ||||
\(263\) | −23.8885 | −1.47303 | −0.736515 | − | 0.676421i | \(-0.763530\pi\) | ||||
−0.736515 | + | 0.676421i | \(0.763530\pi\) | |||||||
\(264\) | −1.00000 | − | 10.6861i | −0.0615457 | − | 0.657686i | ||||
\(265\) | 44.6525 | 2.74298 | ||||||||
\(266\) | 2.76393 | + | 8.50651i | 0.169468 | + | 0.521567i | ||||
\(267\) | −13.7082 | − | 9.95959i | −0.838928 | − | 0.609517i | ||||
\(268\) | −3.50000 | + | 2.54290i | −0.213797 | + | 0.155332i | ||||
\(269\) | −3.79180 | + | 11.6699i | −0.231190 | + | 0.711529i | 0.766414 | + | 0.642347i | \(0.222039\pi\) |
−0.997604 | + | 0.0691825i | \(0.977961\pi\) | |||||||
\(270\) | −14.4721 | + | 44.5407i | −0.880746 | + | 2.71066i | ||||
\(271\) | −13.8713 | + | 10.0781i | −0.842623 | + | 0.612201i | −0.923102 | − | 0.384555i | \(-0.874355\pi\) |
0.0804792 | + | 0.996756i | \(0.474355\pi\) | |||||||
\(272\) | 3.92705 | + | 2.85317i | 0.238112 | + | 0.172999i | ||||
\(273\) | −2.76393 | − | 8.50651i | −0.167281 | − | 0.514837i | ||||
\(274\) | −22.6525 | −1.36849 | ||||||||
\(275\) | 11.9894 | + | 13.6251i | 0.722985 | + | 0.821622i | ||||
\(276\) | 22.9443 | 1.38108 | ||||||||
\(277\) | −7.14590 | − | 21.9928i | −0.429355 | − | 1.32142i | −0.898762 | − | 0.438438i | \(-0.855532\pi\) |
0.469406 | − | 0.882982i | \(-0.344468\pi\) | |||||||
\(278\) | −16.4443 | − | 11.9475i | −0.986262 | − | 0.716561i | ||||
\(279\) | −2.30902 | + | 1.67760i | −0.138237 | + | 0.100435i | ||||
\(280\) | −4.47214 | + | 13.7638i | −0.267261 | + | 0.822546i | ||||
\(281\) | 0.663119 | − | 2.04087i | 0.0395584 | − | 0.121748i | −0.929327 | − | 0.369257i | \(-0.879612\pi\) |
0.968886 | + | 0.247509i | \(0.0796121\pi\) | |||||||
\(282\) | −3.00000 | + | 2.17963i | −0.178647 | + | 0.129795i | ||||
\(283\) | −16.1803 | − | 11.7557i | −0.961821 | − | 0.698804i | −0.00824833 | − | 0.999966i | \(-0.502626\pi\) |
−0.953573 | + | 0.301162i | \(0.902626\pi\) | |||||||
\(284\) | −0.763932 | − | 2.35114i | −0.0453310 | − | 0.139515i | ||||
\(285\) | −20.9443 | −1.24063 | ||||||||
\(286\) | −1.88197 | + | 0.812299i | −0.111283 | + | 0.0480323i | ||||
\(287\) | 2.11146 | 0.124635 | ||||||||
\(288\) | 2.30902 | + | 7.10642i | 0.136060 | + | 0.418750i | ||||
\(289\) | −5.30902 | − | 3.85723i | −0.312295 | − | 0.226896i | ||||
\(290\) | 27.4164 | − | 19.9192i | 1.60995 | − | 1.16969i | ||||
\(291\) | 11.0902 | − | 34.1320i | 0.650117 | − | 2.00086i | ||||
\(292\) | −0.472136 | + | 1.45309i | −0.0276297 | + | 0.0850354i | ||||
\(293\) | 14.8541 | − | 10.7921i | 0.867786 | − | 0.630483i | −0.0622060 | − | 0.998063i | \(-0.519814\pi\) |
0.929992 | + | 0.367580i | \(0.119814\pi\) | |||||||
\(294\) | −34.0344 | − | 24.7275i | −1.98493 | − | 1.44214i | ||||
\(295\) | −4.32624 | − | 13.3148i | −0.251883 | − | 0.775217i | ||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | −24.4721 | + | 41.2915i | −1.42002 | + | 2.39597i | ||||
\(298\) | −11.4164 | −0.661335 | ||||||||
\(299\) | −1.35410 | − | 4.16750i | −0.0783097 | − | 0.241013i | ||||
\(300\) | −14.3262 | − | 10.4086i | −0.827126 | − | 0.600942i | ||||
\(301\) | 3.61803 | − | 2.62866i | 0.208540 | − | 0.151513i | ||||
\(302\) | 3.18034 | − | 9.78808i | 0.183008 | − | 0.563241i | ||||
\(303\) | −2.14590 | + | 6.60440i | −0.123279 | + | 0.379413i | ||||
\(304\) | −1.61803 | + | 1.17557i | −0.0928006 | + | 0.0674236i | ||||
\(305\) | −22.1803 | − | 16.1150i | −1.27004 | − | 0.922740i | ||||
\(306\) | −11.2082 | − | 34.4953i | −0.640730 | − | 1.97197i | ||||
\(307\) | 10.8541 | 0.619476 | 0.309738 | − | 0.950822i | \(-0.399759\pi\) | ||||
0.309738 | + | 0.950822i | \(0.399759\pi\) | |||||||
\(308\) | −7.56231 | + | 12.7598i | −0.430902 | + | 0.727055i | ||||
\(309\) | −1.81966 | −0.103517 | ||||||||
\(310\) | −0.381966 | − | 1.17557i | −0.0216942 | − | 0.0667679i | ||||
\(311\) | −11.9721 | − | 8.69827i | −0.678878 | − | 0.493233i | 0.194108 | − | 0.980980i | \(-0.437819\pi\) |
−0.872985 | + | 0.487747i | \(0.837819\pi\) | |||||||
\(312\) | 1.61803 | − | 1.17557i | 0.0916031 | − | 0.0665536i | ||||
\(313\) | −1.23607 | + | 3.80423i | −0.0698667 | + | 0.215028i | −0.979893 | − | 0.199522i | \(-0.936061\pi\) |
0.910027 | + | 0.414550i | \(0.136061\pi\) | |||||||
\(314\) | 1.52786 | − | 4.70228i | 0.0862224 | − | 0.265365i | ||||
\(315\) | 87.4853 | − | 63.5618i | 4.92924 | − | 3.58130i | ||||
\(316\) | 1.69098 | + | 1.22857i | 0.0951252 | + | 0.0691125i | ||||
\(317\) | −3.26393 | − | 10.0453i | −0.183321 | − | 0.564203i | 0.816595 | − | 0.577211i | \(-0.195859\pi\) |
−0.999915 | + | 0.0130084i | \(0.995859\pi\) | |||||||
\(318\) | −44.6525 | −2.50399 | ||||||||
\(319\) | 31.8885 | − | 13.7638i | 1.78542 | − | 0.770626i | ||||
\(320\) | −3.23607 | −0.180902 | ||||||||
\(321\) | −3.09017 | − | 9.51057i | −0.172476 | − | 0.530828i | ||||
\(322\) | −25.6525 | − | 18.6376i | −1.42956 | − | 1.03863i | ||||
\(323\) | 7.85410 | − | 5.70634i | 0.437014 | − | 0.317509i | ||||
\(324\) | 7.54508 | − | 23.2214i | 0.419171 | − | 1.29008i | ||||
\(325\) | −1.04508 | + | 3.21644i | −0.0579709 | + | 0.178416i | ||||
\(326\) | 8.47214 | − | 6.15537i | 0.469228 | − | 0.340914i | ||||
\(327\) | −10.7082 | − | 7.77997i | −0.592165 | − | 0.430233i | ||||
\(328\) | 0.145898 | + | 0.449028i | 0.00805587 | + | 0.0247934i | ||||
\(329\) | 5.12461 | 0.282529 | ||||||||
\(330\) | −22.9443 | − | 26.0746i | −1.26304 | − | 1.43536i | ||||
\(331\) | −21.8885 | −1.20310 | −0.601552 | − | 0.798834i | \(-0.705451\pi\) | ||||
−0.601552 | + | 0.798834i | \(0.705451\pi\) | |||||||
\(332\) | 0.118034 | + | 0.363271i | 0.00647796 | + | 0.0199371i | ||||
\(333\) | 48.3607 | + | 35.1361i | 2.65015 | + | 1.92545i | ||||
\(334\) | −9.73607 | + | 7.07367i | −0.532734 | + | 0.387054i | ||||
\(335\) | −4.32624 | + | 13.3148i | −0.236368 | + | 0.727465i | ||||
\(336\) | 4.47214 | − | 13.7638i | 0.243975 | − | 0.750878i | ||||
\(337\) | −19.6803 | + | 14.2986i | −1.07206 | + | 0.778895i | −0.976281 | − | 0.216508i | \(-0.930533\pi\) |
−0.0957757 | + | 0.995403i | \(0.530533\pi\) | |||||||
\(338\) | 10.2082 | + | 7.41669i | 0.555253 | + | 0.403415i | ||||
\(339\) | −11.5279 | − | 35.4791i | −0.626108 | − | 1.92696i | ||||
\(340\) | 15.7082 | 0.851897 | ||||||||
\(341\) | −0.118034 | − | 1.26133i | −0.00639190 | − | 0.0683047i | ||||
\(342\) | 14.9443 | 0.808094 | ||||||||
\(343\) | 8.29180 | + | 25.5195i | 0.447715 | + | 1.37792i | ||||
\(344\) | 0.809017 | + | 0.587785i | 0.0436193 | + | 0.0316913i | ||||
\(345\) | 60.0689 | − | 43.6426i | 3.23400 | − | 2.34964i | ||||
\(346\) | −2.02786 | + | 6.24112i | −0.109019 | + | 0.335525i | ||||
\(347\) | 10.2705 | − | 31.6094i | 0.551350 | − | 1.69688i | −0.154043 | − | 0.988064i | \(-0.549230\pi\) |
0.705393 | − | 0.708816i | \(-0.250770\pi\) | |||||||
\(348\) | −27.4164 | + | 19.9192i | −1.46967 | + | 1.06778i | ||||
\(349\) | 0.145898 | + | 0.106001i | 0.00780974 | + | 0.00567411i | 0.591683 | − | 0.806171i | \(-0.298464\pi\) |
−0.583874 | + | 0.811845i | \(0.698464\pi\) | |||||||
\(350\) | 7.56231 | + | 23.2744i | 0.404222 | + | 1.24407i | ||||
\(351\) | −8.94427 | −0.477410 | ||||||||
\(352\) | −3.23607 | − | 0.726543i | −0.172483 | − | 0.0387248i | ||||
\(353\) | −8.03444 | −0.427630 | −0.213815 | − | 0.976874i | \(-0.568589\pi\) | ||||
−0.213815 | + | 0.976874i | \(0.568589\pi\) | |||||||
\(354\) | 4.32624 | + | 13.3148i | 0.229937 | + | 0.707673i | ||||
\(355\) | −6.47214 | − | 4.70228i | −0.343505 | − | 0.249571i | ||||
\(356\) | −4.23607 | + | 3.07768i | −0.224511 | + | 0.163117i | ||||
\(357\) | −21.7082 | + | 66.8110i | −1.14892 | + | 3.53601i | ||||
\(358\) | −0.673762 | + | 2.07363i | −0.0356094 | + | 0.109595i | ||||
\(359\) | 17.1074 | − | 12.4292i | 0.902894 | − | 0.655991i | −0.0363140 | − | 0.999340i | \(-0.511562\pi\) |
0.939208 | + | 0.343350i | \(0.111562\pi\) | |||||||
\(360\) | 19.5623 | + | 14.2128i | 1.03102 | + | 0.749083i | ||||
\(361\) | −4.63525 | − | 14.2658i | −0.243961 | − | 0.750834i | ||||
\(362\) | 21.5623 | 1.13329 | ||||||||
\(363\) | −17.0902 | − | 31.2259i | −0.897001 | − | 1.63893i | ||||
\(364\) | −2.76393 | −0.144869 | ||||||||
\(365\) | 1.52786 | + | 4.70228i | 0.0799721 | + | 0.246129i | ||||
\(366\) | 22.1803 | + | 16.1150i | 1.15938 | + | 0.842342i | ||||
\(367\) | −11.9721 | + | 8.69827i | −0.624940 | + | 0.454046i | −0.854644 | − | 0.519215i | \(-0.826224\pi\) |
0.229703 | + | 0.973261i | \(0.426224\pi\) | |||||||
\(368\) | 2.19098 | − | 6.74315i | 0.114213 | − | 0.351511i | ||||
\(369\) | 1.09017 | − | 3.35520i | 0.0567520 | − | 0.174665i | ||||
\(370\) | −20.9443 | + | 15.2169i | −1.08884 | + | 0.791089i | ||||
\(371\) | 49.9230 | + | 36.2712i | 2.59187 | + | 1.88311i | ||||
\(372\) | 0.381966 | + | 1.17557i | 0.0198040 | + | 0.0609505i | ||||
\(373\) | −20.1803 | −1.04490 | −0.522449 | − | 0.852670i | \(-0.674982\pi\) | ||||
−0.522449 | + | 0.852670i | \(0.674982\pi\) | |||||||
\(374\) | 15.7082 | + | 3.52671i | 0.812252 | + | 0.182362i | ||||
\(375\) | −4.94427 | −0.255321 | ||||||||
\(376\) | 0.354102 | + | 1.08981i | 0.0182614 | + | 0.0562029i | ||||
\(377\) | 5.23607 | + | 3.80423i | 0.269671 | + | 0.195928i | ||||
\(378\) | −52.3607 | + | 38.0423i | −2.69314 | + | 1.95668i | ||||
\(379\) | 2.40983 | − | 7.41669i | 0.123785 | − | 0.380970i | −0.869893 | − | 0.493240i | \(-0.835812\pi\) |
0.993678 | + | 0.112270i | \(0.0358123\pi\) | |||||||
\(380\) | −2.00000 | + | 6.15537i | −0.102598 | + | 0.315764i | ||||
\(381\) | −31.4164 | + | 22.8254i | −1.60951 | + | 1.16938i | ||||
\(382\) | 10.8541 | + | 7.88597i | 0.555344 | + | 0.403481i | ||||
\(383\) | 4.94427 | + | 15.2169i | 0.252640 | + | 0.777547i | 0.994285 | + | 0.106755i | \(0.0340460\pi\) |
−0.741645 | + | 0.670793i | \(0.765954\pi\) | |||||||
\(384\) | 3.23607 | 0.165140 | ||||||||
\(385\) | 4.47214 | + | 47.7899i | 0.227921 | + | 2.43560i | ||||
\(386\) | 16.8541 | 0.857851 | ||||||||
\(387\) | −2.30902 | − | 7.10642i | −0.117374 | − | 0.361240i | ||||
\(388\) | −8.97214 | − | 6.51864i | −0.455491 | − | 0.330934i | ||||
\(389\) | 12.0902 | − | 8.78402i | 0.612996 | − | 0.445368i | −0.237472 | − | 0.971394i | \(-0.576319\pi\) |
0.850468 | + | 0.526027i | \(0.176319\pi\) | |||||||
\(390\) | 2.00000 | − | 6.15537i | 0.101274 | − | 0.311689i | ||||
\(391\) | −10.6353 | + | 32.7319i | −0.537848 | + | 1.65533i | ||||
\(392\) | −10.5172 | + | 7.64121i | −0.531200 | + | 0.385939i | ||||
\(393\) | −2.76393 | − | 2.00811i | −0.139422 | − | 0.101296i | ||||
\(394\) | 5.51722 | + | 16.9803i | 0.277954 | + | 0.855453i | ||||
\(395\) | 6.76393 | 0.340330 | ||||||||
\(396\) | 16.3713 | + | 18.6049i | 0.822690 | + | 0.934929i | ||||
\(397\) | −1.79837 | −0.0902578 | −0.0451289 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451289 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(398\) | −6.00000 | − | 18.4661i | −0.300753 | − | 0.925622i | ||||
\(399\) | −23.4164 | − | 17.0130i | −1.17229 | − | 0.851716i | ||||
\(400\) | −4.42705 | + | 3.21644i | −0.221353 | + | 0.160822i | ||||
\(401\) | −5.68034 | + | 17.4823i | −0.283663 | + | 0.873024i | 0.703134 | + | 0.711058i | \(0.251784\pi\) |
−0.986796 | + | 0.161966i | \(0.948216\pi\) | |||||||
\(402\) | 4.32624 | − | 13.3148i | 0.215773 | − | 0.664081i | ||||
\(403\) | 0.190983 | − | 0.138757i | 0.00951354 | − | 0.00691199i | ||||
\(404\) | 1.73607 | + | 1.26133i | 0.0863726 | + | 0.0627534i | ||||
\(405\) | −24.4164 | − | 75.1460i | −1.21326 | − | 3.73403i | ||||
\(406\) | 46.8328 | 2.32427 | ||||||||
\(407\) | −24.3607 | + | 10.5146i | −1.20751 | + | 0.521190i | ||||
\(408\) | −15.7082 | −0.777672 | ||||||||
\(409\) | 4.14590 | + | 12.7598i | 0.205001 | + | 0.630930i | 0.999713 | + | 0.0239428i | \(0.00762195\pi\) |
−0.794712 | + | 0.606987i | \(0.792378\pi\) | |||||||
\(410\) | 1.23607 | + | 0.898056i | 0.0610450 | + | 0.0443518i | ||||
\(411\) | 59.3050 | − | 43.0876i | 2.92530 | − | 2.12535i | ||||
\(412\) | −0.173762 | + | 0.534785i | −0.00856064 | + | 0.0263470i | ||||
\(413\) | 5.97871 | − | 18.4006i | 0.294193 | − | 0.905434i | ||||
\(414\) | −42.8607 | + | 31.1401i | −2.10649 | + | 1.53045i | ||||
\(415\) | 1.00000 | + | 0.726543i | 0.0490881 | + | 0.0356646i | ||||
\(416\) | −0.190983 | − | 0.587785i | −0.00936371 | − | 0.0288185i | ||||
\(417\) | 65.7771 | 3.22112 | ||||||||
\(418\) | −3.38197 | + | 5.70634i | −0.165417 | + | 0.279106i | ||||
\(419\) | −37.8885 | −1.85098 | −0.925488 | − | 0.378776i | \(-0.876345\pi\) | ||||
−0.925488 | + | 0.378776i | \(0.876345\pi\) | |||||||
\(420\) | −14.4721 | − | 44.5407i | −0.706168 | − | 2.17336i | ||||
\(421\) | −5.85410 | − | 4.25325i | −0.285311 | − | 0.207291i | 0.435919 | − | 0.899986i | \(-0.356423\pi\) |
−0.721231 | + | 0.692695i | \(0.756423\pi\) | |||||||
\(422\) | −15.9443 | + | 11.5842i | −0.776155 | + | 0.563910i | ||||
\(423\) | 2.64590 | − | 8.14324i | 0.128648 | − | 0.395938i | ||||
\(424\) | −4.26393 | + | 13.1230i | −0.207075 | + | 0.637311i | ||||
\(425\) | 21.4894 | − | 15.6129i | 1.04239 | − | 0.757338i | ||||
\(426\) | 6.47214 | + | 4.70228i | 0.313576 | + | 0.227826i | ||||
\(427\) | −11.7082 | − | 36.0341i | −0.566600 | − | 1.74381i | ||||
\(428\) | −3.09017 | −0.149369 | ||||||||
\(429\) | 3.38197 | − | 5.70634i | 0.163283 | − | 0.275505i | ||||
\(430\) | 3.23607 | 0.156057 | ||||||||
\(431\) | 4.28115 | + | 13.1760i | 0.206216 | + | 0.634667i | 0.999661 | + | 0.0260258i | \(0.00828520\pi\) |
−0.793445 | + | 0.608641i | \(0.791715\pi\) | |||||||
\(432\) | −11.7082 | − | 8.50651i | −0.563311 | − | 0.409270i | ||||
\(433\) | 3.47214 | − | 2.52265i | 0.166860 | − | 0.121231i | −0.501221 | − | 0.865319i | \(-0.667116\pi\) |
0.668082 | + | 0.744088i | \(0.267116\pi\) | |||||||
\(434\) | 0.527864 | − | 1.62460i | 0.0253383 | − | 0.0779832i | ||||
\(435\) | −33.8885 | + | 104.298i | −1.62483 | + | 5.00072i | ||||
\(436\) | −3.30902 | + | 2.40414i | −0.158473 | + | 0.115137i | ||||
\(437\) | −11.4721 | − | 8.33499i | −0.548787 | − | 0.398717i | ||||
\(438\) | −1.52786 | − | 4.70228i | −0.0730042 | − | 0.224684i | ||||
\(439\) | 23.2148 | 1.10798 | 0.553991 | − | 0.832523i | \(-0.313104\pi\) | ||||
0.553991 | + | 0.832523i | \(0.313104\pi\) | |||||||
\(440\) | −9.85410 | + | 4.25325i | −0.469776 | + | 0.202766i | ||||
\(441\) | 97.1378 | 4.62561 | ||||||||
\(442\) | 0.927051 | + | 2.85317i | 0.0440953 | + | 0.135711i | ||||
\(443\) | 18.6353 | + | 13.5393i | 0.885388 | + | 0.643272i | 0.934671 | − | 0.355513i | \(-0.115694\pi\) |
−0.0492836 | + | 0.998785i | \(0.515694\pi\) | |||||||
\(444\) | 20.9443 | − | 15.2169i | 0.993971 | − | 0.722162i | ||||
\(445\) | −5.23607 | + | 16.1150i | −0.248213 | + | 0.763922i | ||||
\(446\) | 4.38197 | − | 13.4863i | 0.207492 | − | 0.638595i | ||||
\(447\) | 29.8885 | − | 21.7153i | 1.41368 | − | 1.02710i | ||||
\(448\) | −3.61803 | − | 2.62866i | −0.170936 | − | 0.124192i | ||||
\(449\) | 3.70820 | + | 11.4127i | 0.175001 | + | 0.538598i | 0.999634 | − | 0.0270712i | \(-0.00861808\pi\) |
−0.824633 | + | 0.565669i | \(0.808618\pi\) | |||||||
\(450\) | 40.8885 | 1.92750 | ||||||||
\(451\) | 1.03444 | + | 1.17557i | 0.0487100 | + | 0.0553555i | ||||
\(452\) | −11.5279 | −0.542225 | ||||||||
\(453\) | 10.2918 | + | 31.6749i | 0.483551 | + | 1.48822i | ||||
\(454\) | 6.09017 | + | 4.42477i | 0.285826 | + | 0.207665i | ||||
\(455\) | −7.23607 | + | 5.25731i | −0.339232 | + | 0.246467i | ||||
\(456\) | 2.00000 | − | 6.15537i | 0.0936586 | − | 0.288251i | ||||
\(457\) | 7.23607 | − | 22.2703i | 0.338489 | − | 1.04176i | −0.626489 | − | 0.779430i | \(-0.715509\pi\) |
0.964978 | − | 0.262332i | \(-0.0844914\pi\) | |||||||
\(458\) | 17.2082 | − | 12.5025i | 0.804087 | − | 0.584203i | ||||
\(459\) | 56.8328 | + | 41.2915i | 2.65273 | + | 1.92732i | ||||
\(460\) | −7.09017 | − | 21.8213i | −0.330581 | − | 1.01742i | ||||
\(461\) | −33.8541 | −1.57674 | −0.788371 | − | 0.615200i | \(-0.789075\pi\) | ||||
−0.788371 | + | 0.615200i | \(0.789075\pi\) | |||||||
\(462\) | −4.47214 | − | 47.7899i | −0.208063 | − | 2.22339i | ||||
\(463\) | −27.4164 | −1.27415 | −0.637074 | − | 0.770802i | \(-0.719856\pi\) | ||||
−0.637074 | + | 0.770802i | \(0.719856\pi\) | |||||||
\(464\) | 3.23607 | + | 9.95959i | 0.150231 | + | 0.462363i | ||||
\(465\) | 3.23607 | + | 2.35114i | 0.150069 | + | 0.109032i | ||||
\(466\) | 5.09017 | − | 3.69822i | 0.235798 | − | 0.171317i | ||||
\(467\) | −11.0902 | + | 34.1320i | −0.513192 | + | 1.57944i | 0.273356 | + | 0.961913i | \(0.411866\pi\) |
−0.786548 | + | 0.617529i | \(0.788134\pi\) | |||||||
\(468\) | −1.42705 | + | 4.39201i | −0.0659655 | + | 0.203021i | ||||
\(469\) | −15.6525 | + | 11.3722i | −0.722764 | + | 0.525119i | ||||
\(470\) | 3.00000 | + | 2.17963i | 0.138380 | + | 0.100539i | ||||
\(471\) | 4.94427 | + | 15.2169i | 0.227820 | + | 0.701158i | ||||
\(472\) | 4.32624 | 0.199131 | ||||||||
\(473\) | 3.23607 | + | 0.726543i | 0.148795 | + | 0.0334065i | ||||
\(474\) | −6.76393 | −0.310678 | ||||||||
\(475\) | 3.38197 | + | 10.4086i | 0.155175 | + | 0.477580i | ||||
\(476\) | 17.5623 | + | 12.7598i | 0.804967 | + | 0.584843i | ||||
\(477\) | 83.4123 | − | 60.6026i | 3.81919 | − | 2.77480i | ||||
\(478\) | 5.22542 | − | 16.0822i | 0.239005 | − | 0.735583i | ||||
\(479\) | 5.60739 | − | 17.2578i | 0.256208 | − | 0.788528i | −0.737381 | − | 0.675477i | \(-0.763938\pi\) |
0.993589 | − | 0.113051i | \(-0.0360623\pi\) | |||||||
\(480\) | 8.47214 | − | 6.15537i | 0.386698 | − | 0.280953i | ||||
\(481\) | −4.00000 | − | 2.90617i | −0.182384 | − | 0.132510i | ||||
\(482\) | −5.47214 | − | 16.8415i | −0.249249 | − | 0.767109i | ||||
\(483\) | 102.610 | 4.66891 | ||||||||
\(484\) | −10.8090 | + | 2.04087i | −0.491319 | + | 0.0927668i | ||||
\(485\) | −35.8885 | −1.62961 | ||||||||
\(486\) | 11.0000 | + | 33.8545i | 0.498970 | + | 1.53567i | ||||
\(487\) | 17.9164 | + | 13.0170i | 0.811870 | + | 0.589858i | 0.914372 | − | 0.404875i | \(-0.132685\pi\) |
−0.102502 | + | 0.994733i | \(0.532685\pi\) | |||||||
\(488\) | 6.85410 | − | 4.97980i | 0.310271 | − | 0.225425i | ||||
\(489\) | −10.4721 | + | 32.2299i | −0.473566 | + | 1.45749i | ||||
\(490\) | −13.0000 | + | 40.0099i | −0.587280 | + | 1.80746i | ||||
\(491\) | 9.56231 | − | 6.94742i | 0.431541 | − | 0.313533i | −0.350724 | − | 0.936479i | \(-0.614064\pi\) |
0.782265 | + | 0.622946i | \(0.214064\pi\) | |||||||
\(492\) | −1.23607 | − | 0.898056i | −0.0557262 | − | 0.0404875i | ||||
\(493\) | −15.7082 | − | 48.3449i | −0.707462 | − | 2.17734i | ||||
\(494\) | −1.23607 | −0.0556133 | ||||||||
\(495\) | 78.2492 | + | 17.5680i | 3.51704 | + | 0.789625i | ||||
\(496\) | 0.381966 | 0.0171508 | ||||||||
\(497\) | −3.41641 | − | 10.5146i | −0.153247 | − | 0.471645i | ||||
\(498\) | −1.00000 | − | 0.726543i | −0.0448111 | − | 0.0325571i | ||||
\(499\) | 26.5623 | − | 19.2986i | 1.18909 | − | 0.863926i | 0.195924 | − | 0.980619i | \(-0.437229\pi\) |
0.993168 | + | 0.116693i | \(0.0372294\pi\) | |||||||
\(500\) | −0.472136 | + | 1.45309i | −0.0211146 | + | 0.0649839i | ||||
\(501\) | 12.0344 | − | 37.0382i | 0.537659 | − | 1.65474i | ||||
\(502\) | −12.1631 | + | 8.83702i | −0.542867 | + | 0.394416i | ||||
\(503\) | 32.5066 | + | 23.6174i | 1.44940 | + | 1.05305i | 0.985972 | + | 0.166912i | \(0.0533796\pi\) |
0.463425 | + | 0.886136i | \(0.346620\pi\) | |||||||
\(504\) | 10.3262 | + | 31.7809i | 0.459967 | + | 1.41563i | ||||
\(505\) | 6.94427 | 0.309016 | ||||||||
\(506\) | −2.19098 | − | 23.4131i | −0.0974011 | − | 1.04084i | ||||
\(507\) | −40.8328 | −1.81345 | ||||||||
\(508\) | 3.70820 | + | 11.4127i | 0.164525 | + | 0.506356i | ||||
\(509\) | −24.6803 | − | 17.9313i | −1.09394 | − | 0.794792i | −0.113877 | − | 0.993495i | \(-0.536327\pi\) |
−0.980060 | + | 0.198703i | \(0.936327\pi\) | |||||||
\(510\) | −41.1246 | + | 29.8788i | −1.82103 | + | 1.32305i | ||||
\(511\) | −2.11146 | + | 6.49839i | −0.0934053 | + | 0.287472i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | −23.4164 | + | 17.0130i | −1.03386 | + | 0.751143i | ||||
\(514\) | 12.4721 | + | 9.06154i | 0.550122 | + | 0.399687i | ||||
\(515\) | 0.562306 | + | 1.73060i | 0.0247782 | + | 0.0762593i | ||||
\(516\) | −3.23607 | −0.142460 | ||||||||
\(517\) | 2.51064 | + | 2.85317i | 0.110418 | + | 0.125482i | ||||
\(518\) | −35.7771 | −1.57195 | ||||||||
\(519\) | −6.56231 | − | 20.1967i | −0.288053 | − | 0.886537i | ||||
\(520\) | −1.61803 | − | 1.17557i | −0.0709555 | − | 0.0515522i | ||||
\(521\) | −11.7984 | + | 8.57202i | −0.516896 | + | 0.375547i | −0.815433 | − | 0.578851i | \(-0.803501\pi\) |
0.298537 | + | 0.954398i | \(0.403501\pi\) | |||||||
\(522\) | 24.1803 | − | 74.4194i | 1.05834 | − | 3.25725i | ||||
\(523\) | 0.201626 | − | 0.620541i | 0.00881649 | − | 0.0271344i | −0.946551 | − | 0.322553i | \(-0.895459\pi\) |
0.955368 | + | 0.295418i | \(0.0954590\pi\) | |||||||
\(524\) | −0.854102 | + | 0.620541i | −0.0373116 | + | 0.0271085i | ||||
\(525\) | −64.0689 | − | 46.5488i | −2.79620 | − | 2.03155i | ||||
\(526\) | −7.38197 | − | 22.7194i | −0.321869 | − | 0.990611i | ||||
\(527\) | −1.85410 | −0.0807660 | ||||||||
\(528\) | 9.85410 | − | 4.25325i | 0.428845 | − | 0.185099i | ||||
\(529\) | 27.2705 | 1.18567 | ||||||||
\(530\) | 13.7984 | + | 42.4670i | 0.599363 | + | 1.84465i | ||||
\(531\) | −26.1525 | − | 19.0009i | −1.13492 | − | 0.824568i | ||||
\(532\) | −7.23607 | + | 5.25731i | −0.313723 | + | 0.227933i | ||||
\(533\) | −0.0901699 | + | 0.277515i | −0.00390569 | + | 0.0120205i | ||||
\(534\) | 5.23607 | − | 16.1150i | 0.226587 | − | 0.697363i | ||||
\(535\) | −8.09017 | + | 5.87785i | −0.349769 | + | 0.254122i | ||||
\(536\) | −3.50000 | − | 2.54290i | −0.151177 | − | 0.109837i | ||||
\(537\) | −2.18034 | − | 6.71040i | −0.0940886 | − | 0.289575i | ||||
\(538\) | −12.2705 | −0.529019 | ||||||||
\(539\) | −21.9828 | + | 37.0912i | −0.946865 | + | 1.59763i | ||||
\(540\) | −46.8328 | −2.01536 | ||||||||
\(541\) | 9.27051 | + | 28.5317i | 0.398570 | + | 1.22667i | 0.926146 | + | 0.377165i | \(0.123101\pi\) |
−0.527576 | + | 0.849508i | \(0.676899\pi\) | |||||||
\(542\) | −13.8713 | − | 10.0781i | −0.595824 | − | 0.432892i | ||||
\(543\) | −56.4508 | + | 41.0139i | −2.42254 | + | 1.76008i | ||||
\(544\) | −1.50000 | + | 4.61653i | −0.0643120 | + | 0.197932i | ||||
\(545\) | −4.09017 | + | 12.5882i | −0.175204 | + | 0.539221i | ||||
\(546\) | 7.23607 | − | 5.25731i | 0.309675 | − | 0.224992i | ||||
\(547\) | −3.39919 | − | 2.46965i | −0.145339 | − | 0.105595i | 0.512740 | − | 0.858544i | \(-0.328631\pi\) |
−0.658079 | + | 0.752949i | \(0.728631\pi\) | |||||||
\(548\) | −7.00000 | − | 21.5438i | −0.299025 | − | 0.920305i | ||||
\(549\) | −63.3050 | −2.70179 | ||||||||
\(550\) | −9.25329 | + | 15.6129i | −0.394562 | + | 0.665738i | ||||
\(551\) | 20.9443 | 0.892256 | ||||||||
\(552\) | 7.09017 | + | 21.8213i | 0.301778 | + | 0.928776i | ||||
\(553\) | 7.56231 | + | 5.49434i | 0.321582 | + | 0.233643i | ||||
\(554\) | 18.7082 | − | 13.5923i | 0.794835 | − | 0.577482i | ||||
\(555\) | 25.8885 | − | 79.6767i | 1.09891 | − | 3.38209i | ||||
\(556\) | 6.28115 | − | 19.3314i | 0.266380 | − | 0.819834i | ||||
\(557\) | 28.5623 | − | 20.7517i | 1.21022 | − | 0.879279i | 0.214973 | − | 0.976620i | \(-0.431034\pi\) |
0.995251 | + | 0.0973411i | \(0.0310338\pi\) | |||||||
\(558\) | −2.30902 | − | 1.67760i | −0.0977485 | − | 0.0710184i | ||||
\(559\) | 0.190983 | + | 0.587785i | 0.00807772 | + | 0.0248607i | ||||
\(560\) | −14.4721 | −0.611559 | ||||||||
\(561\) | −47.8328 | + | 20.6457i | −2.01950 | + | 0.871663i | ||||
\(562\) | 2.14590 | 0.0905192 | ||||||||
\(563\) | −3.71885 | − | 11.4454i | −0.156731 | − | 0.482368i | 0.841601 | − | 0.540099i | \(-0.181613\pi\) |
−0.998332 | + | 0.0577316i | \(0.981613\pi\) | |||||||
\(564\) | −3.00000 | − | 2.17963i | −0.126323 | − | 0.0917789i | ||||
\(565\) | −30.1803 | + | 21.9273i | −1.26970 | + | 0.922488i | ||||
\(566\) | 6.18034 | − | 19.0211i | 0.259779 | − | 0.799518i | ||||
\(567\) | 33.7426 | − | 103.849i | 1.41706 | − | 4.36126i | ||||
\(568\) | 2.00000 | − | 1.45309i | 0.0839181 | − | 0.0609701i | ||||
\(569\) | −0.690983 | − | 0.502029i | −0.0289675 | − | 0.0210461i | 0.573207 | − | 0.819410i | \(-0.305699\pi\) |
−0.602175 | + | 0.798364i | \(0.705699\pi\) | |||||||
\(570\) | −6.47214 | − | 19.9192i | −0.271088 | − | 0.834323i | ||||
\(571\) | 5.52786 | 0.231334 | 0.115667 | − | 0.993288i | \(-0.463099\pi\) | ||||
0.115667 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(572\) | −1.35410 | − | 1.53884i | −0.0566178 | − | 0.0643422i | ||||
\(573\) | −43.4164 | −1.81375 | ||||||||
\(574\) | 0.652476 | + | 2.00811i | 0.0272338 | + | 0.0838171i | ||||
\(575\) | −31.3885 | − | 22.8051i | −1.30899 | − | 0.951039i | ||||
\(576\) | −6.04508 | + | 4.39201i | −0.251879 | + | 0.183000i | ||||
\(577\) | −3.50658 | + | 10.7921i | −0.145981 | + | 0.449283i | −0.997136 | − | 0.0756318i | \(-0.975903\pi\) |
0.851155 | + | 0.524914i | \(0.175903\pi\) | |||||||
\(578\) | 2.02786 | − | 6.24112i | 0.0843480 | − | 0.259597i | ||||
\(579\) | −44.1246 | + | 32.0584i | −1.83376 | + | 1.33230i | ||||
\(580\) | 27.4164 | + | 19.9192i | 1.13840 | + | 0.827099i | ||||
\(581\) | 0.527864 | + | 1.62460i | 0.0218995 | + | 0.0673997i | ||||
\(582\) | 35.8885 | 1.48763 | ||||||||
\(583\) | 4.26393 | + | 45.5650i | 0.176594 | + | 1.88711i | ||||
\(584\) | −1.52786 | −0.0632235 | ||||||||
\(585\) | 4.61803 | + | 14.2128i | 0.190932 | + | 0.587629i | ||||
\(586\) | 14.8541 | + | 10.7921i | 0.613617 | + | 0.445819i | ||||
\(587\) | −6.32624 | + | 4.59628i | −0.261112 | + | 0.189709i | −0.710637 | − | 0.703559i | \(-0.751593\pi\) |
0.449525 | + | 0.893268i | \(0.351593\pi\) | |||||||
\(588\) | 13.0000 | − | 40.0099i | 0.536111 | − | 1.64998i | ||||
\(589\) | 0.236068 | − | 0.726543i | 0.00972701 | − | 0.0299367i | ||||
\(590\) | 11.3262 | − | 8.22899i | 0.466294 | − | 0.338782i | ||||
\(591\) | −46.7426 | − | 33.9605i | −1.92274 | − | 1.39695i | ||||
\(592\) | −2.47214 | − | 7.60845i | −0.101604 | − | 0.312705i | ||||
\(593\) | 8.76393 | 0.359892 | 0.179946 | − | 0.983677i | \(-0.442408\pi\) | ||||
0.179946 | + | 0.983677i | \(0.442408\pi\) | |||||||
\(594\) | −46.8328 | − | 10.5146i | −1.92157 | − | 0.431420i | ||||
\(595\) | 70.2492 | 2.87994 | ||||||||
\(596\) | −3.52786 | − | 10.8576i | −0.144507 | − | 0.444747i | ||||
\(597\) | 50.8328 | + | 36.9322i | 2.08045 | + | 1.51153i | ||||
\(598\) | 3.54508 | − | 2.57565i | 0.144969 | − | 0.105326i | ||||
\(599\) | −4.66312 | + | 14.3516i | −0.190530 | + | 0.586391i | −1.00000 | 0.000770814i | \(-0.999755\pi\) | |
0.809470 | + | 0.587161i | \(0.199755\pi\) | |||||||
\(600\) | 5.47214 | − | 16.8415i | 0.223399 | − | 0.687551i | ||||
\(601\) | −1.38197 | + | 1.00406i | −0.0563716 | + | 0.0409563i | −0.615614 | − | 0.788048i | \(-0.711092\pi\) |
0.559243 | + | 0.829004i | \(0.311092\pi\) | |||||||
\(602\) | 3.61803 | + | 2.62866i | 0.147460 | + | 0.107136i | ||||
\(603\) | 9.98936 | + | 30.7441i | 0.406798 | + | 1.25200i | ||||
\(604\) | 10.2918 | 0.418767 | ||||||||
\(605\) | −24.4164 | + | 25.9030i | −0.992668 | + | 1.05311i | ||||
\(606\) | −6.94427 | −0.282092 | ||||||||
\(607\) | −13.1803 | − | 40.5649i | −0.534973 | − | 1.64648i | −0.743706 | − | 0.668506i | \(-0.766934\pi\) |
0.208733 | − | 0.977973i | \(-0.433066\pi\) | |||||||
\(608\) | −1.61803 | − | 1.17557i | −0.0656199 | − | 0.0476757i | ||||
\(609\) | −122.610 | + | 89.0813i | −4.96840 | + | 3.60976i | ||||
\(610\) | 8.47214 | − | 26.0746i | 0.343027 | − | 1.05573i | ||||
\(611\) | −0.218847 | + | 0.673542i | −0.00885360 | + | 0.0272486i | ||||
\(612\) | 29.3435 | − | 21.3193i | 1.18614 | − | 0.861780i | ||||
\(613\) | −5.92705 | − | 4.30625i | −0.239391 | − | 0.173928i | 0.461621 | − | 0.887077i | \(-0.347268\pi\) |
−0.701012 | + | 0.713149i | \(0.747268\pi\) | |||||||
\(614\) | 3.35410 | + | 10.3229i | 0.135361 | + | 0.416597i | ||||
\(615\) | −4.94427 | −0.199372 | ||||||||
\(616\) | −14.4721 | − | 3.24920i | −0.583099 | − | 0.130914i | ||||
\(617\) | 39.1033 | 1.57424 | 0.787120 | − | 0.616800i | \(-0.211571\pi\) | ||||
0.787120 | + | 0.616800i | \(0.211571\pi\) | |||||||
\(618\) | −0.562306 | − | 1.73060i | −0.0226193 | − | 0.0696149i | ||||
\(619\) | 8.63525 | + | 6.27388i | 0.347080 | + | 0.252169i | 0.747643 | − | 0.664101i | \(-0.231185\pi\) |
−0.400563 | + | 0.916269i | \(0.631185\pi\) | |||||||
\(620\) | 1.00000 | − | 0.726543i | 0.0401610 | − | 0.0291787i | ||||
\(621\) | 31.7082 | − | 97.5878i | 1.27241 | − | 3.91606i | ||||
\(622\) | 4.57295 | − | 14.0741i | 0.183359 | − | 0.564320i | ||||
\(623\) | −18.9443 | + | 13.7638i | −0.758986 | + | 0.551436i | ||||
\(624\) | 1.61803 | + | 1.17557i | 0.0647732 | + | 0.0470605i | ||||
\(625\) | −6.92705 | − | 21.3193i | −0.277082 | − | 0.852771i | ||||
\(626\) | −4.00000 | −0.159872 | ||||||||
\(627\) | −2.00000 | − | 21.3723i | −0.0798723 | − | 0.853526i | ||||
\(628\) | 4.94427 | 0.197298 | ||||||||
\(629\) | 12.0000 | + | 36.9322i | 0.478471 | + | 1.47258i | ||||
\(630\) | 87.4853 | + | 63.5618i | 3.48550 | + | 2.53236i | ||||
\(631\) | 19.7984 | − | 14.3844i | 0.788161 | − | 0.572632i | −0.119256 | − | 0.992864i | \(-0.538051\pi\) |
0.907417 | + | 0.420231i | \(0.138051\pi\) | |||||||
\(632\) | −0.645898 | + | 1.98787i | −0.0256924 | + | 0.0790732i | ||||
\(633\) | 19.7082 | − | 60.6556i | 0.783331 | − | 2.41084i | ||||
\(634\) | 8.54508 | − | 6.20837i | 0.339369 | − | 0.246566i | ||||
\(635\) | 31.4164 | + | 22.8254i | 1.24672 | + | 0.905797i | ||||
\(636\) | −13.7984 | − | 42.4670i | −0.547141 | − | 1.68393i | ||||
\(637\) | −8.03444 | −0.318336 | ||||||||
\(638\) | 22.9443 | + | 26.0746i | 0.908372 | + | 1.03230i | ||||
\(639\) | −18.4721 | −0.730746 | ||||||||
\(640\) | −1.00000 | − | 3.07768i | −0.0395285 | − | 0.121656i | ||||
\(641\) | −36.6525 | − | 26.6296i | −1.44769 | − | 1.05181i | −0.986365 | − | 0.164572i | \(-0.947376\pi\) |
−0.461321 | − | 0.887233i | \(-0.652624\pi\) | |||||||
\(642\) | 8.09017 | − | 5.87785i | 0.319294 | − | 0.231980i | ||||
\(643\) | 4.11803 | − | 12.6740i | 0.162399 | − | 0.499814i | −0.836436 | − | 0.548065i | \(-0.815365\pi\) |
0.998835 | + | 0.0482509i | \(0.0153647\pi\) | |||||||
\(644\) | 9.79837 | − | 30.1563i | 0.386110 | − | 1.18832i | ||||
\(645\) | −8.47214 | + | 6.15537i | −0.333590 | + | 0.242367i | ||||
\(646\) | 7.85410 | + | 5.70634i | 0.309016 | + | 0.224513i | ||||
\(647\) | −11.2361 | − | 34.5811i | −0.441735 | − | 1.35952i | −0.886025 | − | 0.463638i | \(-0.846544\pi\) |
0.444289 | − | 0.895883i | \(-0.353456\pi\) | |||||||
\(648\) | 24.4164 | 0.959167 | ||||||||
\(649\) | 13.1738 | − | 5.68609i | 0.517115 | − | 0.223199i | ||||
\(650\) | −3.38197 | −0.132652 | ||||||||
\(651\) | 1.70820 | + | 5.25731i | 0.0669498 | + | 0.206050i | ||||
\(652\) | 8.47214 | + | 6.15537i | 0.331794 | + | 0.241063i | ||||
\(653\) | 15.5623 | − | 11.3067i | 0.609000 | − | 0.442464i | −0.240062 | − | 0.970758i | \(-0.577168\pi\) |
0.849062 | + | 0.528293i | \(0.177168\pi\) | |||||||
\(654\) | 4.09017 | − | 12.5882i | 0.159938 | − | 0.492239i | ||||
\(655\) | −1.05573 | + | 3.24920i | −0.0412507 | + | 0.126957i | ||||
\(656\) | −0.381966 | + | 0.277515i | −0.0149133 | + | 0.0108351i | ||||
\(657\) | 9.23607 | + | 6.71040i | 0.360333 | + | 0.261797i | ||||
\(658\) | 1.58359 | + | 4.87380i | 0.0617348 | + | 0.190000i | ||||
\(659\) | 7.96556 | 0.310294 | 0.155147 | − | 0.987891i | \(-0.450415\pi\) | ||||
0.155147 | + | 0.987891i | \(0.450415\pi\) | |||||||
\(660\) | 17.7082 | − | 29.8788i | 0.689291 | − | 1.16303i | ||||
\(661\) | −32.0344 | −1.24600 | −0.622998 | − | 0.782224i | \(-0.714085\pi\) | ||||
−0.622998 | + | 0.782224i | \(0.714085\pi\) | |||||||
\(662\) | −6.76393 | − | 20.8172i | −0.262888 | − | 0.809085i | ||||
\(663\) | −7.85410 | − | 5.70634i | −0.305028 | − | 0.221616i | ||||
\(664\) | −0.309017 | + | 0.224514i | −0.0119922 | + | 0.00871283i | ||||
\(665\) | −8.94427 | + | 27.5276i | −0.346844 | + | 1.06748i | ||||
\(666\) | −18.4721 | + | 56.8514i | −0.715781 | + | 2.20295i | ||||
\(667\) | −60.0689 | + | 43.6426i | −2.32588 | + | 1.68985i | ||||
\(668\) | −9.73607 | − | 7.07367i | −0.376700 | − | 0.273688i | ||||
\(669\) | 14.1803 | + | 43.6426i | 0.548244 | + | 1.68732i | ||||
\(670\) | −14.0000 | −0.540867 | ||||||||
\(671\) | 14.3262 | − | 24.1724i | 0.553058 | − | 0.933167i | ||||
\(672\) | 14.4721 | 0.558275 | ||||||||
\(673\) | −1.81966 | − | 5.60034i | −0.0701427 | − | 0.215877i | 0.909840 | − | 0.414959i | \(-0.136204\pi\) |
−0.979983 | + | 0.199082i | \(0.936204\pi\) | |||||||
\(674\) | −19.6803 | − | 14.2986i | −0.758058 | − | 0.550762i | ||||
\(675\) | −64.0689 | + | 46.5488i | −2.46601 | + | 1.79166i | ||||
\(676\) | −3.89919 | + | 12.0005i | −0.149969 | + | 0.461556i | ||||
\(677\) | 8.52786 | − | 26.2461i | 0.327752 | − | 1.00872i | −0.642430 | − | 0.766344i | \(-0.722074\pi\) |
0.970183 | − | 0.242374i | \(-0.0779262\pi\) | |||||||
\(678\) | 30.1803 | − | 21.9273i | 1.15907 | − | 0.842113i | ||||
\(679\) | −40.1246 | − | 29.1522i | −1.53984 | − | 1.11876i | ||||
\(680\) | 4.85410 | + | 14.9394i | 0.186146 | + | 0.572899i | ||||
\(681\) | −24.3607 | −0.933503 | ||||||||
\(682\) | 1.16312 | − | 0.502029i | 0.0445381 | − | 0.0192237i | ||||
\(683\) | −11.7984 | −0.451452 | −0.225726 | − | 0.974191i | \(-0.572475\pi\) | ||||
−0.225726 | + | 0.974191i | \(0.572475\pi\) | |||||||
\(684\) | 4.61803 | + | 14.2128i | 0.176575 | + | 0.543442i | ||||
\(685\) | −59.3050 | − | 43.0876i | −2.26593 | − | 1.64629i | ||||
\(686\) | −21.7082 | + | 15.7719i | −0.828823 | + | 0.602175i | ||||
\(687\) | −21.2705 | + | 65.4639i | −0.811521 | + | 2.49760i | ||||
\(688\) | −0.309017 | + | 0.951057i | −0.0117812 | + | 0.0362587i | ||||
\(689\) | −6.89919 | + | 5.01255i | −0.262838 | + | 0.190963i | ||||
\(690\) | 60.0689 | + | 43.6426i | 2.28678 | + | 1.66145i | ||||
\(691\) | 12.8885 | + | 39.6669i | 0.490303 | + | 1.50900i | 0.824150 | + | 0.566371i | \(0.191653\pi\) |
−0.333847 | + | 0.942627i | \(0.608347\pi\) | |||||||
\(692\) | −6.56231 | −0.249461 | ||||||||
\(693\) | 73.2148 | + | 83.2035i | 2.78120 | + | 3.16064i | ||||
\(694\) | 33.2361 | 1.26162 | ||||||||
\(695\) | −20.3262 | − | 62.5577i | −0.771018 | − | 2.37295i | ||||
\(696\) | −27.4164 | − | 19.9192i | −1.03922 | − | 0.755035i | ||||
\(697\) | 1.85410 | − | 1.34708i | 0.0702291 | − | 0.0510244i | ||||
\(698\) | −0.0557281 | + | 0.171513i | −0.00210934 | + | 0.00649188i | ||||
\(699\) | −6.29180 | + | 19.3642i | −0.237978 | + | 0.732420i | ||||
\(700\) | −19.7984 | + | 14.3844i | −0.748308 | + | 0.543678i | ||||
\(701\) | 7.16312 | + | 5.20431i | 0.270547 | + | 0.196564i | 0.714784 | − | 0.699345i | \(-0.246525\pi\) |
−0.444237 | + | 0.895909i | \(0.646525\pi\) | |||||||
\(702\) | −2.76393 | − | 8.50651i | −0.104318 | − | 0.321057i | ||||
\(703\) | −16.0000 | −0.603451 | ||||||||
\(704\) | −0.309017 | − | 3.30220i | −0.0116465 | − | 0.124456i | ||||
\(705\) | −12.0000 | −0.451946 | ||||||||
\(706\) | −2.48278 | − | 7.64121i | −0.0934406 | − | 0.287581i | ||||
\(707\) | 7.76393 | + | 5.64083i | 0.291993 | + | 0.212145i | ||||
\(708\) | −11.3262 | + | 8.22899i | −0.425666 | + | 0.309265i | ||||
\(709\) | 1.33688 | − | 4.11450i | 0.0502076 | − | 0.154523i | −0.922809 | − | 0.385257i | \(-0.874113\pi\) |
0.973017 | + | 0.230734i | \(0.0741127\pi\) | |||||||
\(710\) | 2.47214 | − | 7.60845i | 0.0927776 | − | 0.285540i | ||||
\(711\) | 12.6353 | − | 9.18005i | 0.473859 | − | 0.344279i | ||||
\(712\) | −4.23607 | − | 3.07768i | −0.158753 | − | 0.115341i | ||||
\(713\) | 0.836881 | + | 2.57565i | 0.0313414 | + | 0.0964590i | ||||
\(714\) | −70.2492 | −2.62901 | ||||||||
\(715\) | −6.47214 | − | 1.45309i | −0.242044 | − | 0.0543423i | ||||
\(716\) | −2.18034 | −0.0814831 | ||||||||
\(717\) | 16.9098 | + | 52.0431i | 0.631509 | + | 1.94359i | ||||
\(718\) | 17.1074 | + | 12.4292i | 0.638442 | + | 0.463855i | ||||
\(719\) | −29.1525 | + | 21.1805i | −1.08720 | + | 0.789900i | −0.978925 | − | 0.204221i | \(-0.934534\pi\) |
−0.108279 | + | 0.994121i | \(0.534534\pi\) | |||||||
\(720\) | −7.47214 | + | 22.9969i | −0.278470 | + | 0.857043i | ||||
\(721\) | −0.777088 | + | 2.39163i | −0.0289403 | + | 0.0890689i | ||||
\(722\) | 12.1353 | − | 8.81678i | 0.451627 | − | 0.328127i | ||||
\(723\) | 46.3607 | + | 33.6830i | 1.72417 | + | 1.25268i | ||||
\(724\) | 6.66312 | + | 20.5070i | 0.247633 | + | 0.762136i | ||||
\(725\) | 57.3050 | 2.12825 | ||||||||
\(726\) | 24.4164 | − | 25.9030i | 0.906178 | − | 0.961352i | ||||
\(727\) | −15.5279 | −0.575897 | −0.287948 | − | 0.957646i | \(-0.592973\pi\) | ||||
−0.287948 | + | 0.957646i | \(0.592973\pi\) | |||||||
\(728\) | −0.854102 | − | 2.62866i | −0.0316551 | − | 0.0974245i | ||||
\(729\) | −33.9336 | − | 24.6542i | −1.25680 | − | 0.913119i | ||||
\(730\) | −4.00000 | + | 2.90617i | −0.148047 | + | 0.107562i | ||||
\(731\) | 1.50000 | − | 4.61653i | 0.0554795 | − | 0.170748i | ||||
\(732\) | −8.47214 | + | 26.0746i | −0.313139 | + | 0.963743i | ||||
\(733\) | 2.14590 | − | 1.55909i | 0.0792606 | − | 0.0575862i | −0.547449 | − | 0.836839i | \(-0.684401\pi\) |
0.626710 | + | 0.779253i | \(0.284401\pi\) | |||||||
\(734\) | −11.9721 | − | 8.69827i | −0.441900 | − | 0.321059i | ||||
\(735\) | −42.0689 | − | 129.475i | −1.55173 | − | 4.77575i | ||||
\(736\) | 7.09017 | 0.261347 | ||||||||
\(737\) | −14.0000 | − | 3.14320i | −0.515697 | − | 0.115781i | ||||
\(738\) | 3.52786 | 0.129862 | ||||||||
\(739\) | −13.4377 | − | 41.3570i | −0.494314 | − | 1.52134i | −0.818024 | − | 0.575184i | \(-0.804930\pi\) |
0.323710 | − | 0.946156i | \(-0.395070\pi\) | |||||||
\(740\) | −20.9443 | − | 15.2169i | −0.769927 | − | 0.559385i | ||||
\(741\) | 3.23607 | − | 2.35114i | 0.118880 | − | 0.0863713i | ||||
\(742\) | −19.0689 | + | 58.6880i | −0.700041 | + | 2.15450i | ||||
\(743\) | −9.61803 | + | 29.6013i | −0.352851 | + | 1.08597i | 0.604393 | + | 0.796686i | \(0.293416\pi\) |
−0.957245 | + | 0.289279i | \(0.906584\pi\) | |||||||
\(744\) | −1.00000 | + | 0.726543i | −0.0366618 | + | 0.0266363i | ||||
\(745\) | −29.8885 | − | 21.7153i | −1.09503 | − | 0.795587i | ||||
\(746\) | −6.23607 | − | 19.1926i | −0.228319 | − | 0.702693i | ||||
\(747\) | 2.85410 | 0.104426 | ||||||||
\(748\) | 1.50000 | + | 16.0292i | 0.0548454 | + | 0.586086i | ||||
\(749\) | −13.8197 | −0.504959 | ||||||||
\(750\) | −1.52786 | − | 4.70228i | −0.0557897 | − | 0.171703i | ||||
\(751\) | 4.47214 | + | 3.24920i | 0.163191 | + | 0.118565i | 0.666383 | − | 0.745609i | \(-0.267841\pi\) |
−0.503193 | + | 0.864174i | \(0.667841\pi\) | |||||||
\(752\) | −0.927051 | + | 0.673542i | −0.0338061 | + | 0.0245615i | ||||
\(753\) | 15.0344 | − | 46.2713i | 0.547886 | − | 1.68622i | ||||
\(754\) | −2.00000 | + | 6.15537i | −0.0728357 | + | 0.224165i | ||||
\(755\) | 26.9443 | − | 19.5762i | 0.980602 | − | 0.712449i | ||||
\(756\) | −52.3607 | − | 38.0423i | −1.90434 | − | 1.38358i | ||||
\(757\) | −0.888544 | − | 2.73466i | −0.0322947 | − | 0.0993928i | 0.933610 | − | 0.358291i | \(-0.116641\pi\) |
−0.965905 | + | 0.258898i | \(0.916641\pi\) | |||||||
\(758\) | 7.79837 | 0.283250 | ||||||||
\(759\) | 50.2705 | + | 57.1289i | 1.82470 | + | 2.07365i | ||||
\(760\) | −6.47214 | −0.234769 | ||||||||
\(761\) | −5.52786 | − | 17.0130i | −0.200385 | − | 0.616721i | −0.999871 | − | 0.0160373i | \(-0.994895\pi\) |
0.799486 | − | 0.600684i | \(-0.205105\pi\) | |||||||
\(762\) | −31.4164 | − | 22.8254i | −1.13810 | − | 0.826875i | ||||
\(763\) | −14.7984 | + | 10.7516i | −0.535737 | + | 0.389236i | ||||
\(764\) | −4.14590 | + | 12.7598i | −0.149993 | + | 0.461632i | ||||
\(765\) | 36.2705 | − | 111.629i | 1.31136 | − | 4.03596i | ||||
\(766\) | −12.9443 | + | 9.40456i | −0.467696 | + | 0.339801i | ||||
\(767\) | 2.16312 | + | 1.57160i | 0.0781057 | + | 0.0567471i | ||||
\(768\) | 1.00000 | + | 3.07768i | 0.0360844 | + | 0.111056i | ||||
\(769\) | 39.3262 | 1.41814 | 0.709070 | − | 0.705138i | \(-0.249115\pi\) | ||||
0.709070 | + | 0.705138i | \(0.249115\pi\) | |||||||
\(770\) | −44.0689 | + | 19.0211i | −1.58813 | + | 0.685474i | ||||
\(771\) | −49.8885 | −1.79669 | ||||||||
\(772\) | 5.20820 | + | 16.0292i | 0.187447 | + | 0.576904i | ||||
\(773\) | 36.9787 | + | 26.8666i | 1.33003 | + | 0.966325i | 0.999748 | + | 0.0224430i | \(0.00714444\pi\) |
0.330284 | + | 0.943882i | \(0.392856\pi\) | |||||||
\(774\) | 6.04508 | − | 4.39201i | 0.217286 | − | 0.157868i | ||||
\(775\) | 0.645898 | − | 1.98787i | 0.0232013 | − | 0.0714064i | ||||
\(776\) | 3.42705 | − | 10.5474i | 0.123024 | − | 0.378629i | ||||
\(777\) | 93.6656 | − | 68.0521i | 3.36024 | − | 2.44135i | ||||
\(778\) | 12.0902 | + | 8.78402i | 0.433454 | + | 0.314922i | ||||
\(779\) | 0.291796 | + | 0.898056i | 0.0104547 | + | 0.0321762i | ||||
\(780\) | 6.47214 | 0.231740 | ||||||||
\(781\) | 4.18034 | − | 7.05342i | 0.149584 | − | 0.252391i | ||||
\(782\) | −34.4164 | −1.23073 | ||||||||
\(783\) | 46.8328 | + | 144.137i | 1.67367 | + | 5.15102i | ||||
\(784\) | −10.5172 | − | 7.64121i | −0.375615 | − | 0.272900i | ||||
\(785\) | 12.9443 | − | 9.40456i | 0.462001 | − | 0.335663i | ||||
\(786\) | 1.05573 | − | 3.24920i | 0.0376566 | − | 0.115895i | ||||
\(787\) | −4.07953 | + | 12.5555i | −0.145419 | + | 0.447555i | −0.997065 | − | 0.0765637i | \(-0.975605\pi\) |
0.851645 | + | 0.524119i | \(0.175605\pi\) | |||||||
\(788\) | −14.4443 | + | 10.4944i | −0.514556 | + | 0.373847i | ||||
\(789\) | 62.5410 | + | 45.4387i | 2.22652 | + | 1.61766i | ||||
\(790\) | 2.09017 | + | 6.43288i | 0.0743649 | + | 0.228872i | ||||
\(791\) | −51.5542 | −1.83306 | ||||||||
\(792\) | −12.6353 | + | 21.3193i | −0.448974 | + | 0.757547i | ||||
\(793\) | 5.23607 | 0.185938 | ||||||||
\(794\) | −0.555728 | − | 1.71036i | −0.0197221 | − | 0.0606982i | ||||
\(795\) | −116.902 | − | 84.9341i | −4.14608 | − | 3.01230i | ||||
\(796\) | 15.7082 | − | 11.4127i | 0.556763 | − | 0.404512i | ||||
\(797\) | 14.8435 | − | 45.6835i | 0.525782 | − | 1.61819i | −0.236981 | − | 0.971514i | \(-0.576158\pi\) |
0.762764 | − | 0.646677i | \(-0.223842\pi\) | |||||||
\(798\) | 8.94427 | − | 27.5276i | 0.316624 | − | 0.974468i | ||||
\(799\) | 4.50000 | − | 3.26944i | 0.159199 | − | 0.115665i | ||||
\(800\) | −4.42705 | − | 3.21644i | −0.156520 | − | 0.113718i | ||||
\(801\) | 12.0902 | + | 37.2097i | 0.427185 | + | 1.31474i | ||||
\(802\) | −18.3820 | −0.649090 | ||||||||
\(803\) | −4.65248 | + | 2.00811i | −0.164182 | + | 0.0708648i | ||||
\(804\) | 14.0000 | 0.493742 | ||||||||
\(805\) | −31.7082 | − | 97.5878i | −1.11757 | − | 3.43952i | ||||
\(806\) | 0.190983 | + | 0.138757i | 0.00672709 | + | 0.00488752i | ||||
\(807\) | 32.1246 | − | 23.3399i | 1.13084 | − | 0.821603i | ||||
\(808\) | −0.663119 | + | 2.04087i | −0.0233284 | + | 0.0717976i | ||||
\(809\) | −1.38197 | + | 4.25325i | −0.0485873 | + | 0.149536i | −0.972407 | − | 0.233292i | \(-0.925050\pi\) |
0.923819 | + | 0.382829i | \(0.125050\pi\) | |||||||
\(810\) | 63.9230 | − | 46.4428i | 2.24602 | − | 1.63183i | ||||
\(811\) | 17.2705 | + | 12.5478i | 0.606450 | + | 0.440611i | 0.848162 | − | 0.529736i | \(-0.177709\pi\) |
−0.241713 | + | 0.970348i | \(0.577709\pi\) | |||||||
\(812\) | 14.4721 | + | 44.5407i | 0.507872 | + | 1.56307i | ||||
\(813\) | 55.4853 | 1.94595 | ||||||||
\(814\) | −17.5279 | − | 19.9192i | −0.614351 | − | 0.698167i | ||||
\(815\) | 33.8885 | 1.18706 | ||||||||
\(816\) | −4.85410 | − | 14.9394i | −0.169928 | − | 0.522983i | ||||
\(817\) | 1.61803 | + | 1.17557i | 0.0566078 | + | 0.0411280i | ||||
\(818\) | −10.8541 | + | 7.88597i | −0.379505 | + | 0.275726i | ||||
\(819\) | −6.38197 | + | 19.6417i | −0.223004 | + | 0.686336i | ||||
\(820\) | −0.472136 | + | 1.45309i | −0.0164877 | + | 0.0507439i | ||||
\(821\) | 28.7254 | − | 20.8702i | 1.00252 | − | 0.728376i | 0.0398963 | − | 0.999204i | \(-0.487297\pi\) |
0.962628 | + | 0.270827i | \(0.0872972\pi\) | |||||||
\(822\) | 59.3050 | + | 43.0876i | 2.06850 | + | 1.50285i | ||||
\(823\) | −9.46556 | − | 29.1320i | −0.329949 | − | 1.01548i | −0.969157 | − | 0.246444i | \(-0.920738\pi\) |
0.639208 | − | 0.769034i | \(-0.279262\pi\) | |||||||
\(824\) | −0.562306 | −0.0195889 | ||||||||
\(825\) | −5.47214 | − | 58.4760i | −0.190515 | − | 2.03587i | ||||
\(826\) | 19.3475 | 0.673186 | ||||||||
\(827\) | 6.35410 | + | 19.5559i | 0.220954 | + | 0.680026i | 0.998677 | + | 0.0514191i | \(0.0163744\pi\) |
−0.777723 | + | 0.628607i | \(0.783626\pi\) | |||||||
\(828\) | −42.8607 | − | 31.1401i | −1.48951 | − | 1.08219i | ||||
\(829\) | 26.1803 | − | 19.0211i | 0.909281 | − | 0.660631i | −0.0315521 | − | 0.999502i | \(-0.510045\pi\) |
0.940833 | + | 0.338871i | \(0.110045\pi\) | |||||||
\(830\) | −0.381966 | + | 1.17557i | −0.0132582 | + | 0.0408046i | ||||
\(831\) | −23.1246 | + | 71.1702i | −0.802184 | + | 2.46887i | ||||
\(832\) | 0.500000 | − | 0.363271i | 0.0173344 | − | 0.0125942i | ||||
\(833\) | 51.0517 | + | 37.0912i | 1.76884 | + | 1.28513i | ||||
\(834\) | 20.3262 | + | 62.5577i | 0.703840 | + | 2.16620i | ||||
\(835\) | −38.9443 | −1.34772 | ||||||||
\(836\) | −6.47214 | − | 1.45309i | −0.223844 | − | 0.0502560i | ||||
\(837\) | 5.52786 | 0.191071 | ||||||||
\(838\) | −11.7082 | − | 36.0341i | −0.404453 | − | 1.24478i | ||||
\(839\) | −29.1803 | − | 21.2008i | −1.00742 | − | 0.731931i | −0.0437514 | − | 0.999042i | \(-0.513931\pi\) |
−0.963666 | + | 0.267111i | \(0.913931\pi\) | |||||||
\(840\) | 37.8885 | − | 27.5276i | 1.30728 | − | 0.949794i | ||||
\(841\) | 24.9271 | − | 76.7176i | 0.859553 | − | 2.64543i | ||||
\(842\) | 2.23607 | − | 6.88191i | 0.0770600 | − | 0.237166i | ||||
\(843\) | −5.61803 | + | 4.08174i | −0.193495 | + | 0.140583i | ||||
\(844\) | −15.9443 | − | 11.5842i | −0.548824 | − | 0.398744i | ||||
\(845\) | 12.6180 | + | 38.8343i | 0.434074 | + | 1.33594i | ||||
\(846\) | 8.56231 | 0.294378 | ||||||||
\(847\) | −48.3394 | + | 9.12705i | −1.66096 | + | 0.313609i | ||||
\(848\) | −13.7984 | −0.473838 | ||||||||
\(849\) | 20.0000 | + | 61.5537i | 0.686398 | + | 2.11252i | ||||
\(850\) | 21.4894 | + | 15.6129i | 0.737079 | + | 0.535519i | ||||
\(851\) | 45.8885 | − | 33.3400i | 1.57304 | − | 1.14288i | ||||
\(852\) | −2.47214 | + | 7.60845i | −0.0846940 | + | 0.260661i | ||||
\(853\) | −4.43769 | + | 13.6578i | −0.151944 | + | 0.467635i | −0.997838 | − | 0.0657152i | \(-0.979067\pi\) |
0.845895 | + | 0.533350i | \(0.179067\pi\) | |||||||
\(854\) | 30.6525 | − | 22.2703i | 1.04891 | − | 0.762075i | ||||
\(855\) | 39.1246 | + | 28.4257i | 1.33803 | + | 0.972138i | ||||
\(856\) | −0.954915 | − | 2.93893i | −0.0326383 | − | 0.100450i | ||||
\(857\) | −49.9787 | −1.70724 | −0.853620 | − | 0.520896i | \(-0.825598\pi\) | ||||
−0.853620 | + | 0.520896i | \(0.825598\pi\) | |||||||
\(858\) | 6.47214 | + | 1.45309i | 0.220955 | + | 0.0496075i | ||||
\(859\) | 9.81966 | 0.335042 | 0.167521 | − | 0.985868i | \(-0.446424\pi\) | ||||
0.167521 | + | 0.985868i | \(0.446424\pi\) | |||||||
\(860\) | 1.00000 | + | 3.07768i | 0.0340997 | + | 0.104948i | ||||
\(861\) | −5.52786 | − | 4.01623i | −0.188389 | − | 0.136873i | ||||
\(862\) | −11.2082 | + | 8.14324i | −0.381753 | + | 0.277360i | ||||
\(863\) | 1.52786 | − | 4.70228i | 0.0520091 | − | 0.160068i | −0.921678 | − | 0.387955i | \(-0.873182\pi\) |
0.973688 | + | 0.227887i | \(0.0731817\pi\) | |||||||
\(864\) | 4.47214 | − | 13.7638i | 0.152145 | − | 0.468255i | ||||
\(865\) | −17.1803 | + | 12.4822i | −0.584149 | + | 0.424409i | ||||
\(866\) | 3.47214 | + | 2.52265i | 0.117988 | + | 0.0857233i | ||||
\(867\) | 6.56231 | + | 20.1967i | 0.222868 | + | 0.685916i | ||||
\(868\) | 1.70820 | 0.0579802 | ||||||||
\(869\) | 0.645898 | + | 6.90215i | 0.0219106 | + | 0.234140i | ||||
\(870\) | −109.666 | −3.71801 | ||||||||
\(871\) | −0.826238 | − | 2.54290i | −0.0279960 | − | 0.0861628i | ||||
\(872\) | −3.30902 | − | 2.40414i | −0.112057 | − | 0.0814145i | ||||
\(873\) | −67.0410 | + | 48.7082i | −2.26899 | + | 1.64852i | ||||
\(874\) | 4.38197 | − | 13.4863i | 0.148222 | − | 0.456181i | ||||
\(875\) | −2.11146 | + | 6.49839i | −0.0713802 | + | 0.219686i | ||||
\(876\) | 4.00000 | − | 2.90617i | 0.135147 | − | 0.0981904i | ||||
\(877\) | −12.9721 | − | 9.42481i | −0.438038 | − | 0.318253i | 0.346817 | − | 0.937933i | \(-0.387263\pi\) |
−0.784855 | + | 0.619680i | \(0.787263\pi\) | |||||||
\(878\) | 7.17376 | + | 22.0786i | 0.242103 | + | 0.745116i | ||||
\(879\) | −59.4164 | −2.00407 | ||||||||
\(880\) | −7.09017 | − | 8.05748i | −0.239010 | − | 0.271618i | ||||
\(881\) | 23.3820 | 0.787758 | 0.393879 | − | 0.919162i | \(-0.371133\pi\) | ||||
0.393879 | + | 0.919162i | \(0.371133\pi\) | |||||||
\(882\) | 30.0172 | + | 92.3835i | 1.01073 | + | 3.11071i | ||||
\(883\) | −26.3435 | − | 19.1396i | −0.886528 | − | 0.644100i | 0.0484424 | − | 0.998826i | \(-0.484574\pi\) |
−0.934970 | + | 0.354726i | \(0.884574\pi\) | |||||||
\(884\) | −2.42705 | + | 1.76336i | −0.0816306 | + | 0.0593081i | ||||
\(885\) | −14.0000 | + | 43.0876i | −0.470605 | + | 1.44837i | ||||
\(886\) | −7.11803 | + | 21.9071i | −0.239135 | + | 0.735982i | ||||
\(887\) | 22.6525 | − | 16.4580i | 0.760596 | − | 0.552605i | −0.138497 | − | 0.990363i | \(-0.544227\pi\) |
0.899093 | + | 0.437758i | \(0.144227\pi\) | |||||||
\(888\) | 20.9443 | + | 15.2169i | 0.702844 | + | 0.510646i | ||||
\(889\) | 16.5836 | + | 51.0390i | 0.556196 | + | 1.71179i | ||||
\(890\) | −16.9443 | −0.567973 | ||||||||
\(891\) | 74.3500 | − | 32.0912i | 2.49082 | − | 1.07509i | ||||
\(892\) | 14.1803 | 0.474793 | ||||||||
\(893\) | 0.708204 | + | 2.17963i | 0.0236991 | + | 0.0729385i | ||||
\(894\) | 29.8885 | + | 21.7153i | 0.999622 | + | 0.726268i | ||||
\(895\) | −5.70820 | + | 4.14725i | −0.190804 | + | 0.138627i | ||||
\(896\) | 1.38197 | − | 4.25325i | 0.0461682 | − | 0.142091i | ||||
\(897\) | −4.38197 | + | 13.4863i | −0.146310 | + | 0.450295i | ||||
\(898\) | −9.70820 | + | 7.05342i | −0.323967 | + | 0.235376i | ||||
\(899\) | −3.23607 | − | 2.35114i | −0.107929 | − | 0.0784149i | ||||
\(900\) | 12.6353 | + | 38.8873i | 0.421175 | + | 1.29624i | ||||
\(901\) | 66.9787 | 2.23138 | ||||||||
\(902\) | −0.798374 | + | 1.34708i | −0.0265829 | + | 0.0448530i | ||||
\(903\) | −14.4721 | −0.481603 | ||||||||
\(904\) | −3.56231 | − | 10.9637i | −0.118481 | − | 0.364646i | ||||
\(905\) | 56.4508 | + | 41.0139i | 1.87649 | + | 1.36335i | ||||
\(906\) | −26.9443 | + | 19.5762i | −0.895163 | + | 0.650374i | ||||
\(907\) | −1.71885 | + | 5.29007i | −0.0570734 | + | 0.175654i | −0.975529 | − | 0.219870i | \(-0.929437\pi\) |
0.918456 | + | 0.395523i | \(0.129437\pi\) | |||||||
\(908\) | −2.32624 | + | 7.15942i | −0.0771989 | + | 0.237594i | ||||
\(909\) | 12.9721 | − | 9.42481i | 0.430259 | − | 0.312601i | ||||
\(910\) | −7.23607 | − | 5.25731i | −0.239873 | − | 0.174278i | ||||
\(911\) | 12.5967 | + | 38.7688i | 0.417349 | + | 1.28447i | 0.910133 | + | 0.414316i | \(0.135979\pi\) |
−0.492784 | + | 0.870152i | \(0.664021\pi\) | |||||||
\(912\) | 6.47214 | 0.214314 | ||||||||
\(913\) | −0.645898 | + | 1.08981i | −0.0213761 | + | 0.0360676i | ||||
\(914\) | 23.4164 | 0.774546 | ||||||||
\(915\) | 27.4164 | + | 84.3790i | 0.906358 | + | 2.78948i | ||||
\(916\) | 17.2082 | + | 12.5025i | 0.568575 | + | 0.413094i | ||||
\(917\) | −3.81966 | + | 2.77515i | −0.126136 | + | 0.0916434i | ||||
\(918\) | −21.7082 | + | 66.8110i | −0.716477 | + | 2.20509i | ||||
\(919\) | −9.69756 | + | 29.8460i | −0.319893 | + | 0.984529i | 0.653800 | + | 0.756667i | \(0.273174\pi\) |
−0.973693 | + | 0.227862i | \(0.926826\pi\) | |||||||
\(920\) | 18.5623 | − | 13.4863i | 0.611981 | − | 0.444630i | ||||
\(921\) | −28.4164 | − | 20.6457i | −0.936352 | − | 0.680300i | ||||
\(922\) | −10.4615 | − | 32.1972i | −0.344531 | − | 1.06036i | ||||
\(923\) | 1.52786 | 0.0502903 | ||||||||
\(924\) | 44.0689 | − | 19.0211i | 1.44976 | − | 0.625749i | ||||
\(925\) | −43.7771 | −1.43938 | ||||||||
\(926\) | −8.47214 | − | 26.0746i | −0.278412 | − | 0.856863i | ||||
\(927\) | 3.39919 | + | 2.46965i | 0.111644 | + | 0.0811141i | ||||
\(928\) | −8.47214 | + | 6.15537i | −0.278111 | + | 0.202060i | ||||
\(929\) | 2.67376 | − | 8.22899i | 0.0877233 | − | 0.269985i | −0.897566 | − | 0.440881i | \(-0.854666\pi\) |
0.985289 | + | 0.170896i | \(0.0546662\pi\) | |||||||
\(930\) | −1.23607 | + | 3.80423i | −0.0405323 | + | 0.124745i | ||||
\(931\) | −21.0344 | + | 15.2824i | −0.689376 | + | 0.500861i | ||||
\(932\) | 5.09017 | + | 3.69822i | 0.166734 | + | 0.121139i | ||||
\(933\) | 14.7984 | + | 45.5447i | 0.484477 | + | 1.49107i | ||||
\(934\) | −35.8885 | −1.17431 | ||||||||
\(935\) | 34.4164 | + | 39.1118i | 1.12554 | + | 1.27909i | ||||
\(936\) | −4.61803 | −0.150945 | ||||||||
\(937\) | 3.61803 | + | 11.1352i | 0.118196 | + | 0.363770i | 0.992600 | − | 0.121428i | \(-0.0387474\pi\) |
−0.874404 | + | 0.485198i | \(0.838747\pi\) | |||||||
\(938\) | −15.6525 | − | 11.3722i | −0.511071 | − | 0.371315i | ||||
\(939\) | 10.4721 | − | 7.60845i | 0.341745 | − | 0.248292i | ||||
\(940\) | −1.14590 | + | 3.52671i | −0.0373751 | + | 0.115029i | ||||
\(941\) | −6.50000 | + | 20.0049i | −0.211894 | + | 0.652143i | 0.787466 | + | 0.616359i | \(0.211393\pi\) |
−0.999360 | + | 0.0357839i | \(0.988607\pi\) | |||||||
\(942\) | −12.9443 | + | 9.40456i | −0.421747 | + | 0.306417i | ||||
\(943\) | −2.70820 | − | 1.96763i | −0.0881913 | − | 0.0640747i | ||||
\(944\) | 1.33688 | + | 4.11450i | 0.0435118 | + | 0.133915i | ||||
\(945\) | −209.443 | −6.81317 | ||||||||
\(946\) | 0.309017 | + | 3.30220i | 0.0100470 | + | 0.107364i | ||||
\(947\) | −51.0344 | −1.65840 | −0.829198 | − | 0.558955i | \(-0.811203\pi\) | ||||
−0.829198 | + | 0.558955i | \(0.811203\pi\) | |||||||
\(948\) | −2.09017 | − | 6.43288i | −0.0678856 | − | 0.208930i | ||||
\(949\) | −0.763932 | − | 0.555029i | −0.0247983 | − | 0.0180170i | ||||
\(950\) | −8.85410 | + | 6.43288i | −0.287265 | + | 0.208710i | ||||
\(951\) | −10.5623 | + | 32.5074i | −0.342506 | + | 1.05413i | ||||
\(952\) | −6.70820 | + | 20.6457i | −0.217414 | + | 0.669132i | ||||
\(953\) | −8.79837 | + | 6.39239i | −0.285007 | + | 0.207070i | −0.721099 | − | 0.692833i | \(-0.756362\pi\) |
0.436091 | + | 0.899902i | \(0.356362\pi\) | |||||||
\(954\) | 83.4123 | + | 60.6026i | 2.70057 | + | 1.96208i | ||||
\(955\) | 13.4164 | + | 41.2915i | 0.434145 | + | 1.33616i | ||||
\(956\) | 16.9098 | 0.546903 | ||||||||
\(957\) | −109.666 | − | 24.6215i | −3.54499 | − | 0.795899i | ||||
\(958\) | 18.1459 | 0.586267 | ||||||||
\(959\) | −31.3050 | − | 96.3467i | −1.01089 | − | 3.11120i | ||||
\(960\) | 8.47214 | + | 6.15537i | 0.273437 | + | 0.198664i | ||||
\(961\) | 24.9615 | − | 18.1356i | 0.805209 | − | 0.585019i | ||||
\(962\) | 1.52786 | − | 4.70228i | 0.0492603 | − | 0.151608i | ||||
\(963\) | −7.13525 | + | 21.9601i | −0.229930 | + | 0.707653i | ||||
\(964\) | 14.3262 | − | 10.4086i | 0.461417 | − | 0.335239i | ||||
\(965\) | 44.1246 | + | 32.0584i | 1.42042 | + | 1.03200i | ||||
\(966\) | 31.7082 | + | 97.5878i | 1.02019 | + | 3.13984i | ||||
\(967\) | −15.2148 | −0.489274 | −0.244637 | − | 0.969615i | \(-0.578669\pi\) | ||||
−0.244637 | + | 0.969615i | \(0.578669\pi\) | |||||||
\(968\) | −5.28115 | − | 9.64932i | −0.169743 | − | 0.310141i | ||||
\(969\) | −31.4164 | −1.00924 | ||||||||
\(970\) | −11.0902 | − | 34.1320i | −0.356084 | − | 1.09591i | ||||
\(971\) | 19.9164 | + | 14.4701i | 0.639148 | + | 0.464368i | 0.859557 | − | 0.511039i | \(-0.170739\pi\) |
−0.220409 | + | 0.975407i | \(0.570739\pi\) | |||||||
\(972\) | −28.7984 | + | 20.9232i | −0.923708 | + | 0.671113i | ||||
\(973\) | 28.0902 | − | 86.4527i | 0.900530 | − | 2.77154i | ||||
\(974\) | −6.84346 | + | 21.0620i | −0.219279 | + | 0.674870i | ||||
\(975\) | 8.85410 | − | 6.43288i | 0.283558 | − | 0.206017i | ||||
\(976\) | 6.85410 | + | 4.97980i | 0.219394 | + | 0.159399i | ||||
\(977\) | 2.55166 | + | 7.85321i | 0.0816349 | + | 0.251246i | 0.983541 | − | 0.180686i | \(-0.0578318\pi\) |
−0.901906 | + | 0.431933i | \(0.857832\pi\) | |||||||
\(978\) | −33.8885 | −1.08364 | ||||||||
\(979\) | −16.9443 | − | 3.80423i | −0.541541 | − | 0.121584i | ||||
\(980\) | −42.0689 | −1.34384 | ||||||||
\(981\) | 9.44427 | + | 29.0665i | 0.301532 | + | 0.928021i | ||||
\(982\) | 9.56231 | + | 6.94742i | 0.305145 | + | 0.221701i | ||||
\(983\) | −14.1803 | + | 10.3026i | −0.452283 | + | 0.328603i | −0.790496 | − | 0.612467i | \(-0.790177\pi\) |
0.338214 | + | 0.941069i | \(0.390177\pi\) | |||||||
\(984\) | 0.472136 | − | 1.45309i | 0.0150511 | − | 0.0463227i | ||||
\(985\) | −17.8541 | + | 54.9493i | −0.568879 | + | 1.75083i | ||||
\(986\) | 41.1246 | − | 29.8788i | 1.30967 | − | 0.951534i | ||||
\(987\) | −13.4164 | − | 9.74759i | −0.427049 | − | 0.310269i | ||||
\(988\) | −0.381966 | − | 1.17557i | −0.0121520 | − | 0.0373999i | ||||
\(989\) | −7.09017 | −0.225454 | ||||||||
\(990\) | 7.47214 | + | 79.8483i | 0.237480 | + | 2.53774i | ||||
\(991\) | −6.29180 | −0.199865 | −0.0999327 | − | 0.994994i | \(-0.531863\pi\) | ||||
−0.0999327 | + | 0.994994i | \(0.531863\pi\) | |||||||
\(992\) | 0.118034 | + | 0.363271i | 0.00374758 | + | 0.0115339i | ||||
\(993\) | 57.3050 | + | 41.6345i | 1.81852 | + | 1.32123i | ||||
\(994\) | 8.94427 | − | 6.49839i | 0.283695 | − | 0.206117i | ||||
\(995\) | 19.4164 | − | 59.7576i | 0.615542 | − | 1.89444i | ||||
\(996\) | 0.381966 | − | 1.17557i | 0.0121031 | − | 0.0372494i | ||||
\(997\) | −43.5066 | + | 31.6094i | −1.37787 | + | 1.00108i | −0.380791 | + | 0.924661i | \(0.624348\pi\) |
−0.997076 | + | 0.0764181i | \(0.975652\pi\) | |||||||
\(998\) | 26.5623 | + | 19.2986i | 0.840815 | + | 0.610888i | ||||
\(999\) | −35.7771 | − | 110.111i | −1.13194 | − | 3.48374i |
(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 | 946.2.f.a.775.1 | yes | 4 | |
11.9 | even | 5 | inner | 946.2.f.a.603.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
946.2.f.a.603.1 | ✓ | 4 | 11.9 | even | 5 | inner | |
946.2.f.a.775.1 | yes | 4 | 1.1 | even | 1 | trivial |