Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(461,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.461");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.f (of order \(2\), degree \(1\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.15 | ||
Character | \(\chi\) | \(=\) | 966.461 |
Dual form | 966.2.f.c.461.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.64221 | + | 0.550576i | −0.948132 | + | 0.317875i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.99217 | −0.890925 | −0.445462 | − | 0.895301i | \(-0.646961\pi\) | ||||
−0.445462 | + | 0.895301i | \(0.646961\pi\) | |||||||
\(6\) | −0.550576 | − | 1.64221i | −0.224772 | − | 0.670431i | ||||
\(7\) | 2.64482 | + | 0.0703415i | 0.999647 | + | 0.0265866i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.39373 | − | 1.80833i | 0.797910 | − | 0.602776i | ||||
\(10\) | − | 1.99217i | − | 0.629979i | ||||||
\(11\) | 1.51113i | 0.455623i | 0.973705 | + | 0.227811i | \(0.0731570\pi\) | ||||
−0.973705 | + | 0.227811i | \(0.926843\pi\) | |||||||
\(12\) | 1.64221 | − | 0.550576i | 0.474066 | − | 0.158938i | ||||
\(13\) | 5.17124i | 1.43424i | 0.696948 | + | 0.717121i | \(0.254541\pi\) | ||||
−0.696948 | + | 0.717121i | \(0.745459\pi\) | |||||||
\(14\) | −0.0703415 | + | 2.64482i | −0.0187995 | + | 0.706857i | ||||
\(15\) | 3.27157 | − | 1.09684i | 0.844715 | − | 0.283203i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.10115 | 0.267069 | 0.133534 | − | 0.991044i | \(-0.457367\pi\) | ||||
0.133534 | + | 0.991044i | \(0.457367\pi\) | |||||||
\(18\) | 1.80833 | + | 2.39373i | 0.426227 | + | 0.564208i | ||||
\(19\) | 0.372080i | 0.0853611i | 0.999089 | + | 0.0426806i | \(0.0135898\pi\) | ||||
−0.999089 | + | 0.0426806i | \(0.986410\pi\) | |||||||
\(20\) | 1.99217 | 0.445462 | ||||||||
\(21\) | −4.38208 | + | 1.34066i | −0.956249 | + | 0.292555i | ||||
\(22\) | −1.51113 | −0.322174 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0.550576 | + | 1.64221i | 0.112386 | + | 0.335215i | ||||
\(25\) | −1.03127 | −0.206253 | ||||||||
\(26\) | −5.17124 | −1.01416 | ||||||||
\(27\) | −2.93540 | + | 4.28759i | −0.564917 | + | 0.825148i | ||||
\(28\) | −2.64482 | − | 0.0703415i | −0.499823 | − | 0.0132933i | ||||
\(29\) | 1.32252i | 0.245586i | 0.992432 | + | 0.122793i | \(0.0391852\pi\) | ||||
−0.992432 | + | 0.122793i | \(0.960815\pi\) | |||||||
\(30\) | 1.09684 | + | 3.27157i | 0.200255 | + | 0.597303i | ||||
\(31\) | − | 2.16237i | − | 0.388373i | −0.980965 | − | 0.194186i | \(-0.937793\pi\) | ||
0.980965 | − | 0.194186i | \(-0.0622067\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −0.831993 | − | 2.48160i | −0.144831 | − | 0.431991i | ||||
\(34\) | 1.10115i | 0.188846i | ||||||||
\(35\) | −5.26892 | − | 0.140132i | −0.890610 | − | 0.0236866i | ||||
\(36\) | −2.39373 | + | 1.80833i | −0.398955 | + | 0.301388i | ||||
\(37\) | −10.7679 | −1.77023 | −0.885114 | − | 0.465375i | \(-0.845919\pi\) | ||||
−0.885114 | + | 0.465375i | \(0.845919\pi\) | |||||||
\(38\) | −0.372080 | −0.0603594 | ||||||||
\(39\) | −2.84716 | − | 8.49227i | −0.455911 | − | 1.35985i | ||||
\(40\) | 1.99217i | 0.314989i | ||||||||
\(41\) | 5.04520 | 0.787928 | 0.393964 | − | 0.919126i | \(-0.371104\pi\) | ||||
0.393964 | + | 0.919126i | \(0.371104\pi\) | |||||||
\(42\) | −1.34066 | − | 4.38208i | −0.206868 | − | 0.676170i | ||||
\(43\) | −1.65782 | −0.252815 | −0.126407 | − | 0.991978i | \(-0.540345\pi\) | ||||
−0.126407 | + | 0.991978i | \(0.540345\pi\) | |||||||
\(44\) | − | 1.51113i | − | 0.227811i | ||||||
\(45\) | −4.76872 | + | 3.60249i | −0.710878 | + | 0.537028i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −6.00567 | −0.876017 | −0.438008 | − | 0.898971i | \(-0.644316\pi\) | ||||
−0.438008 | + | 0.898971i | \(0.644316\pi\) | |||||||
\(48\) | −1.64221 | + | 0.550576i | −0.237033 | + | 0.0794689i | ||||
\(49\) | 6.99010 | + | 0.372080i | 0.998586 | + | 0.0531544i | ||||
\(50\) | − | 1.03127i | − | 0.145843i | ||||||
\(51\) | −1.80833 | + | 0.606269i | −0.253217 | + | 0.0848946i | ||||
\(52\) | − | 5.17124i | − | 0.717121i | ||||||
\(53\) | 3.58482i | 0.492413i | 0.969217 | + | 0.246206i | \(0.0791841\pi\) | ||||
−0.969217 | + | 0.246206i | \(0.920816\pi\) | |||||||
\(54\) | −4.28759 | − | 2.93540i | −0.583468 | − | 0.399457i | ||||
\(55\) | − | 3.01042i | − | 0.405926i | ||||||
\(56\) | 0.0703415 | − | 2.64482i | 0.00939977 | − | 0.353428i | ||||
\(57\) | −0.204859 | − | 0.611036i | −0.0271342 | − | 0.0809336i | ||||
\(58\) | −1.32252 | −0.173656 | ||||||||
\(59\) | −11.6790 | −1.52048 | −0.760238 | − | 0.649645i | \(-0.774918\pi\) | ||||
−0.760238 | + | 0.649645i | \(0.774918\pi\) | |||||||
\(60\) | −3.27157 | + | 1.09684i | −0.422357 | + | 0.141602i | ||||
\(61\) | − | 5.71197i | − | 0.731343i | −0.930744 | − | 0.365671i | \(-0.880839\pi\) | ||
0.930744 | − | 0.365671i | \(-0.119161\pi\) | |||||||
\(62\) | 2.16237 | 0.274621 | ||||||||
\(63\) | 6.45818 | − | 4.61432i | 0.813654 | − | 0.581349i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 10.3020i | − | 1.27780i | ||||||
\(66\) | 2.48160 | − | 0.831993i | 0.305464 | − | 0.102411i | ||||
\(67\) | −6.62562 | −0.809448 | −0.404724 | − | 0.914439i | \(-0.632632\pi\) | ||||
−0.404724 | + | 0.914439i | \(0.632632\pi\) | |||||||
\(68\) | −1.10115 | −0.133534 | ||||||||
\(69\) | −0.550576 | − | 1.64221i | −0.0662816 | − | 0.197699i | ||||
\(70\) | 0.140132 | − | 5.26892i | 0.0167490 | − | 0.629756i | ||||
\(71\) | 13.6887i | 1.62455i | 0.583273 | + | 0.812276i | \(0.301772\pi\) | ||||
−0.583273 | + | 0.812276i | \(0.698228\pi\) | |||||||
\(72\) | −1.80833 | − | 2.39373i | −0.213114 | − | 0.282104i | ||||
\(73\) | − | 9.75254i | − | 1.14145i | −0.821142 | − | 0.570724i | \(-0.806663\pi\) | ||
0.821142 | − | 0.570724i | \(-0.193337\pi\) | |||||||
\(74\) | − | 10.7679i | − | 1.25174i | ||||||
\(75\) | 1.69356 | − | 0.567791i | 0.195555 | − | 0.0655628i | ||||
\(76\) | − | 0.372080i | − | 0.0426806i | ||||||
\(77\) | −0.106295 | + | 3.99666i | −0.0121135 | + | 0.455462i | ||||
\(78\) | 8.49227 | − | 2.84716i | 0.961561 | − | 0.322377i | ||||
\(79\) | −3.85596 | −0.433829 | −0.216915 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216915 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(80\) | −1.99217 | −0.222731 | ||||||||
\(81\) | 2.45990 | − | 8.65730i | 0.273322 | − | 0.961923i | ||||
\(82\) | 5.04520i | 0.557149i | ||||||||
\(83\) | 0.708838 | 0.0778050 | 0.0389025 | − | 0.999243i | \(-0.487614\pi\) | ||||
0.0389025 | + | 0.999243i | \(0.487614\pi\) | |||||||
\(84\) | 4.38208 | − | 1.34066i | 0.478124 | − | 0.146278i | ||||
\(85\) | −2.19368 | −0.237938 | ||||||||
\(86\) | − | 1.65782i | − | 0.178767i | ||||||
\(87\) | −0.728150 | − | 2.17187i | −0.0780659 | − | 0.232848i | ||||
\(88\) | 1.51113 | 0.161087 | ||||||||
\(89\) | −9.89948 | −1.04934 | −0.524671 | − | 0.851305i | \(-0.675812\pi\) | ||||
−0.524671 | + | 0.851305i | \(0.675812\pi\) | |||||||
\(90\) | −3.60249 | − | 4.76872i | −0.379736 | − | 0.502667i | ||||
\(91\) | −0.363752 | + | 13.6770i | −0.0381316 | + | 1.43374i | ||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | 1.19055 | + | 3.55107i | 0.123454 | + | 0.368229i | ||||
\(94\) | − | 6.00567i | − | 0.619437i | ||||||
\(95\) | − | 0.741247i | − | 0.0760503i | ||||||
\(96\) | −0.550576 | − | 1.64221i | −0.0561930 | − | 0.167608i | ||||
\(97\) | − | 1.06712i | − | 0.108350i | −0.998531 | − | 0.0541749i | \(-0.982747\pi\) | ||
0.998531 | − | 0.0541749i | \(-0.0172529\pi\) | |||||||
\(98\) | −0.372080 | + | 6.99010i | −0.0375858 | + | 0.706107i | ||||
\(99\) | 2.73262 | + | 3.61724i | 0.274639 | + | 0.363546i | ||||
\(100\) | 1.03127 | 0.103127 | ||||||||
\(101\) | −4.85686 | −0.483276 | −0.241638 | − | 0.970367i | \(-0.577685\pi\) | ||||
−0.241638 | + | 0.970367i | \(0.577685\pi\) | |||||||
\(102\) | −0.606269 | − | 1.80833i | −0.0600296 | − | 0.179051i | ||||
\(103\) | 16.7641i | 1.65182i | 0.563803 | + | 0.825909i | \(0.309338\pi\) | ||||
−0.563803 | + | 0.825909i | \(0.690662\pi\) | |||||||
\(104\) | 5.17124 | 0.507081 | ||||||||
\(105\) | 8.72984 | − | 2.67082i | 0.851945 | − | 0.260645i | ||||
\(106\) | −3.58482 | −0.348189 | ||||||||
\(107\) | 6.16806i | 0.596289i | 0.954521 | + | 0.298144i | \(0.0963677\pi\) | ||||
−0.954521 | + | 0.298144i | \(0.903632\pi\) | |||||||
\(108\) | 2.93540 | − | 4.28759i | 0.282459 | − | 0.412574i | ||||
\(109\) | −5.38632 | −0.515916 | −0.257958 | − | 0.966156i | \(-0.583050\pi\) | ||||
−0.257958 | + | 0.966156i | \(0.583050\pi\) | |||||||
\(110\) | 3.01042 | 0.287033 | ||||||||
\(111\) | 17.6831 | − | 5.92854i | 1.67841 | − | 0.562712i | ||||
\(112\) | 2.64482 | + | 0.0703415i | 0.249912 | + | 0.00664664i | ||||
\(113\) | 16.8518i | 1.58529i | 0.609686 | + | 0.792643i | \(0.291296\pi\) | ||||
−0.609686 | + | 0.792643i | \(0.708704\pi\) | |||||||
\(114\) | 0.611036 | − | 0.204859i | 0.0572287 | − | 0.0191868i | ||||
\(115\) | − | 1.99217i | − | 0.185771i | ||||||
\(116\) | − | 1.32252i | − | 0.122793i | ||||||
\(117\) | 9.35129 | + | 12.3785i | 0.864527 | + | 1.14440i | ||||
\(118\) | − | 11.6790i | − | 1.07514i | ||||||
\(119\) | 2.91235 | + | 0.0774567i | 0.266974 | + | 0.00710044i | ||||
\(120\) | −1.09684 | − | 3.27157i | −0.100127 | − | 0.298652i | ||||
\(121\) | 8.71649 | 0.792408 | ||||||||
\(122\) | 5.71197 | 0.517138 | ||||||||
\(123\) | −8.28529 | + | 2.77777i | −0.747060 | + | 0.250463i | ||||
\(124\) | 2.16237i | 0.194186i | ||||||||
\(125\) | 12.0153 | 1.07468 | ||||||||
\(126\) | 4.61432 | + | 6.45818i | 0.411076 | + | 0.575340i | ||||
\(127\) | −13.2753 | −1.17799 | −0.588995 | − | 0.808137i | \(-0.700476\pi\) | ||||
−0.588995 | + | 0.808137i | \(0.700476\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 2.72249 | − | 0.912756i | 0.239702 | − | 0.0803637i | ||||
\(130\) | 10.3020 | 0.903543 | ||||||||
\(131\) | 13.7049 | 1.19741 | 0.598703 | − | 0.800971i | \(-0.295683\pi\) | ||||
0.598703 | + | 0.800971i | \(0.295683\pi\) | |||||||
\(132\) | 0.831993 | + | 2.48160i | 0.0724157 | + | 0.215995i | ||||
\(133\) | −0.0261727 | + | 0.984084i | −0.00226946 | + | 0.0853309i | ||||
\(134\) | − | 6.62562i | − | 0.572366i | ||||||
\(135\) | 5.84780 | − | 8.54161i | 0.503299 | − | 0.735144i | ||||
\(136\) | − | 1.10115i | − | 0.0944231i | ||||||
\(137\) | 7.71208i | 0.658887i | 0.944175 | + | 0.329444i | \(0.106861\pi\) | ||||
−0.944175 | + | 0.329444i | \(0.893139\pi\) | |||||||
\(138\) | 1.64221 | − | 0.550576i | 0.139795 | − | 0.0468682i | ||||
\(139\) | 14.9440i | 1.26753i | 0.773524 | + | 0.633767i | \(0.218492\pi\) | ||||
−0.773524 | + | 0.633767i | \(0.781508\pi\) | |||||||
\(140\) | 5.26892 | + | 0.140132i | 0.445305 | + | 0.0118433i | ||||
\(141\) | 9.86259 | − | 3.30658i | 0.830580 | − | 0.278464i | ||||
\(142\) | −13.6887 | −1.14873 | ||||||||
\(143\) | −7.81441 | −0.653474 | ||||||||
\(144\) | 2.39373 | − | 1.80833i | 0.199478 | − | 0.150694i | ||||
\(145\) | − | 2.63469i | − | 0.218799i | ||||||
\(146\) | 9.75254 | 0.807126 | ||||||||
\(147\) | −11.6841 | + | 3.23755i | −0.963689 | + | 0.267029i | ||||
\(148\) | 10.7679 | 0.885114 | ||||||||
\(149\) | − | 10.9768i | − | 0.899251i | −0.893217 | − | 0.449626i | \(-0.851557\pi\) | ||
0.893217 | − | 0.449626i | \(-0.148443\pi\) | |||||||
\(150\) | 0.567791 | + | 1.69356i | 0.0463599 | + | 0.138279i | ||||
\(151\) | −2.93475 | −0.238826 | −0.119413 | − | 0.992845i | \(-0.538101\pi\) | ||||
−0.119413 | + | 0.992845i | \(0.538101\pi\) | |||||||
\(152\) | 0.372080 | 0.0301797 | ||||||||
\(153\) | 2.63586 | − | 1.99125i | 0.213097 | − | 0.160983i | ||||
\(154\) | −3.99666 | − | 0.106295i | −0.322060 | − | 0.00856550i | ||||
\(155\) | 4.30780i | 0.346011i | ||||||||
\(156\) | 2.84716 | + | 8.49227i | 0.227955 | + | 0.679926i | ||||
\(157\) | − | 13.1983i | − | 1.05334i | −0.850070 | − | 0.526670i | \(-0.823440\pi\) | ||
0.850070 | − | 0.526670i | \(-0.176560\pi\) | |||||||
\(158\) | − | 3.85596i | − | 0.306764i | ||||||
\(159\) | −1.97372 | − | 5.88704i | −0.156526 | − | 0.466873i | ||||
\(160\) | − | 1.99217i | − | 0.157495i | ||||||
\(161\) | −0.0703415 | + | 2.64482i | −0.00554368 | + | 0.208441i | ||||
\(162\) | 8.65730 | + | 2.45990i | 0.680182 | + | 0.193268i | ||||
\(163\) | −13.9521 | −1.09282 | −0.546408 | − | 0.837519i | \(-0.684005\pi\) | ||||
−0.546408 | + | 0.837519i | \(0.684005\pi\) | |||||||
\(164\) | −5.04520 | −0.393964 | ||||||||
\(165\) | 1.65747 | + | 4.94376i | 0.129034 | + | 0.384871i | ||||
\(166\) | 0.708838i | 0.0550165i | ||||||||
\(167\) | 5.28517 | 0.408979 | 0.204489 | − | 0.978869i | \(-0.434447\pi\) | ||||
0.204489 | + | 0.978869i | \(0.434447\pi\) | |||||||
\(168\) | 1.34066 | + | 4.38208i | 0.103434 | + | 0.338085i | ||||
\(169\) | −13.7417 | −1.05705 | ||||||||
\(170\) | − | 2.19368i | − | 0.168248i | ||||||
\(171\) | 0.672844 | + | 0.890661i | 0.0514536 | + | 0.0681105i | ||||
\(172\) | 1.65782 | 0.126407 | ||||||||
\(173\) | −5.96305 | −0.453362 | −0.226681 | − | 0.973969i | \(-0.572788\pi\) | ||||
−0.226681 | + | 0.973969i | \(0.572788\pi\) | |||||||
\(174\) | 2.17187 | − | 0.728150i | 0.164649 | − | 0.0552009i | ||||
\(175\) | −2.72751 | − | 0.0725408i | −0.206180 | − | 0.00548357i | ||||
\(176\) | 1.51113i | 0.113906i | ||||||||
\(177\) | 19.1794 | − | 6.43018i | 1.44161 | − | 0.483322i | ||||
\(178\) | − | 9.89948i | − | 0.741997i | ||||||
\(179\) | − | 5.06422i | − | 0.378518i | −0.981927 | − | 0.189259i | \(-0.939391\pi\) | ||
0.981927 | − | 0.189259i | \(-0.0606086\pi\) | |||||||
\(180\) | 4.76872 | − | 3.60249i | 0.355439 | − | 0.268514i | ||||
\(181\) | − | 2.03182i | − | 0.151024i | −0.997145 | − | 0.0755119i | \(-0.975941\pi\) | ||
0.997145 | − | 0.0755119i | \(-0.0240591\pi\) | |||||||
\(182\) | −13.6770 | − | 0.363752i | −1.01380 | − | 0.0269631i | ||||
\(183\) | 3.14488 | + | 9.38028i | 0.232476 | + | 0.693410i | ||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 21.4514 | 1.57714 | ||||||||
\(186\) | −3.55107 | + | 1.19055i | −0.260377 | + | 0.0872953i | ||||
\(187\) | 1.66399i | 0.121683i | ||||||||
\(188\) | 6.00567 | 0.438008 | ||||||||
\(189\) | −8.06518 | + | 11.1334i | −0.586655 | + | 0.809837i | ||||
\(190\) | 0.741247 | 0.0537757 | ||||||||
\(191\) | 2.46441i | 0.178319i | 0.996017 | + | 0.0891593i | \(0.0284180\pi\) | ||||
−0.996017 | + | 0.0891593i | \(0.971582\pi\) | |||||||
\(192\) | 1.64221 | − | 0.550576i | 0.118517 | − | 0.0397344i | ||||
\(193\) | −1.23713 | −0.0890502 | −0.0445251 | − | 0.999008i | \(-0.514177\pi\) | ||||
−0.0445251 | + | 0.999008i | \(0.514177\pi\) | |||||||
\(194\) | 1.06712 | 0.0766149 | ||||||||
\(195\) | 5.67202 | + | 16.9180i | 0.406182 | + | 1.21153i | ||||
\(196\) | −6.99010 | − | 0.372080i | −0.499293 | − | 0.0265772i | ||||
\(197\) | 4.06740i | 0.289790i | 0.989447 | + | 0.144895i | \(0.0462845\pi\) | ||||
−0.989447 | + | 0.144895i | \(0.953716\pi\) | |||||||
\(198\) | −3.61724 | + | 2.73262i | −0.257066 | + | 0.194199i | ||||
\(199\) | 3.97727i | 0.281941i | 0.990014 | + | 0.140971i | \(0.0450223\pi\) | ||||
−0.990014 | + | 0.140971i | \(0.954978\pi\) | |||||||
\(200\) | 1.03127i | 0.0729215i | ||||||||
\(201\) | 10.8807 | − | 3.64791i | 0.767464 | − | 0.257304i | ||||
\(202\) | − | 4.85686i | − | 0.341727i | ||||||
\(203\) | −0.0930282 | + | 3.49783i | −0.00652930 | + | 0.245500i | ||||
\(204\) | 1.80833 | − | 0.606269i | 0.126608 | − | 0.0424473i | ||||
\(205\) | −10.0509 | −0.701984 | ||||||||
\(206\) | −16.7641 | −1.16801 | ||||||||
\(207\) | 1.80833 | + | 2.39373i | 0.125687 | + | 0.166376i | ||||
\(208\) | 5.17124i | 0.358561i | ||||||||
\(209\) | −0.562262 | −0.0388925 | ||||||||
\(210\) | 2.67082 | + | 8.72984i | 0.184304 | + | 0.602416i | ||||
\(211\) | 19.5402 | 1.34520 | 0.672601 | − | 0.740006i | \(-0.265177\pi\) | ||||
0.672601 | + | 0.740006i | \(0.265177\pi\) | |||||||
\(212\) | − | 3.58482i | − | 0.246206i | ||||||
\(213\) | −7.53669 | − | 22.4798i | −0.516405 | − | 1.54029i | ||||
\(214\) | −6.16806 | −0.421640 | ||||||||
\(215\) | 3.30265 | 0.225239 | ||||||||
\(216\) | 4.28759 | + | 2.93540i | 0.291734 | + | 0.199728i | ||||
\(217\) | 0.152104 | − | 5.71907i | 0.0103255 | − | 0.388236i | ||||
\(218\) | − | 5.38632i | − | 0.364807i | ||||||
\(219\) | 5.36952 | + | 16.0157i | 0.362838 | + | 1.08224i | ||||
\(220\) | 3.01042i | 0.202963i | ||||||||
\(221\) | 5.69432i | 0.383041i | ||||||||
\(222\) | 5.92854 | + | 17.6831i | 0.397897 | + | 1.18681i | ||||
\(223\) | 26.3878i | 1.76706i | 0.468374 | + | 0.883530i | \(0.344840\pi\) | ||||
−0.468374 | + | 0.883530i | \(0.655160\pi\) | |||||||
\(224\) | −0.0703415 | + | 2.64482i | −0.00469989 | + | 0.176714i | ||||
\(225\) | −2.46857 | + | 1.86487i | −0.164572 | + | 0.124325i | ||||
\(226\) | −16.8518 | −1.12097 | ||||||||
\(227\) | −5.16418 | −0.342759 | −0.171379 | − | 0.985205i | \(-0.554822\pi\) | ||||
−0.171379 | + | 0.985205i | \(0.554822\pi\) | |||||||
\(228\) | 0.204859 | + | 0.611036i | 0.0135671 | + | 0.0404668i | ||||
\(229\) | 13.1393i | 0.868269i | 0.900848 | + | 0.434134i | \(0.142946\pi\) | ||||
−0.900848 | + | 0.434134i | \(0.857054\pi\) | |||||||
\(230\) | 1.99217 | 0.131360 | ||||||||
\(231\) | −2.02591 | − | 6.62189i | −0.133295 | − | 0.435689i | ||||
\(232\) | 1.32252 | 0.0868279 | ||||||||
\(233\) | − | 21.2452i | − | 1.39182i | −0.718129 | − | 0.695910i | \(-0.755001\pi\) | ||
0.718129 | − | 0.695910i | \(-0.244999\pi\) | |||||||
\(234\) | −12.3785 | + | 9.35129i | −0.809211 | + | 0.611313i | ||||
\(235\) | 11.9643 | 0.780465 | ||||||||
\(236\) | 11.6790 | 0.760238 | ||||||||
\(237\) | 6.33231 | − | 2.12300i | 0.411328 | − | 0.137904i | ||||
\(238\) | −0.0774567 | + | 2.91235i | −0.00502077 | + | 0.188779i | ||||
\(239\) | − | 30.1168i | − | 1.94809i | −0.226346 | − | 0.974047i | \(-0.572678\pi\) | ||
0.226346 | − | 0.974047i | \(-0.427322\pi\) | |||||||
\(240\) | 3.27157 | − | 1.09684i | 0.211179 | − | 0.0708008i | ||||
\(241\) | − | 3.61167i | − | 0.232648i | −0.993211 | − | 0.116324i | \(-0.962889\pi\) | ||
0.993211 | − | 0.116324i | \(-0.0371112\pi\) | |||||||
\(242\) | 8.71649i | 0.560317i | ||||||||
\(243\) | 0.726829 | + | 15.5715i | 0.0466261 | + | 0.998912i | ||||
\(244\) | 5.71197i | 0.365671i | ||||||||
\(245\) | −13.9255 | − | 0.741247i | −0.889665 | − | 0.0473565i | ||||
\(246\) | −2.77777 | − | 8.28529i | −0.177104 | − | 0.528251i | ||||
\(247\) | −1.92412 | −0.122429 | ||||||||
\(248\) | −2.16237 | −0.137311 | ||||||||
\(249\) | −1.16406 | + | 0.390269i | −0.0737695 | + | 0.0247323i | ||||
\(250\) | 12.0153i | 0.759914i | ||||||||
\(251\) | 26.3289 | 1.66186 | 0.830932 | − | 0.556373i | \(-0.187808\pi\) | ||||
0.830932 | + | 0.556373i | \(0.187808\pi\) | |||||||
\(252\) | −6.45818 | + | 4.61432i | −0.406827 | + | 0.290675i | ||||
\(253\) | −1.51113 | −0.0950039 | ||||||||
\(254\) | − | 13.2753i | − | 0.832965i | ||||||
\(255\) | 3.60249 | − | 1.20779i | 0.225597 | − | 0.0756347i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.5168 | 1.52932 | 0.764659 | − | 0.644435i | \(-0.222907\pi\) | ||||
0.764659 | + | 0.644435i | \(0.222907\pi\) | |||||||
\(258\) | 0.912756 | + | 2.72249i | 0.0568257 | + | 0.169495i | ||||
\(259\) | −28.4790 | − | 0.757428i | −1.76960 | − | 0.0470643i | ||||
\(260\) | 10.3020i | 0.638901i | ||||||||
\(261\) | 2.39156 | + | 3.16576i | 0.148034 | + | 0.195956i | ||||
\(262\) | 13.7049i | 0.846693i | ||||||||
\(263\) | 10.1241i | 0.624278i | 0.950036 | + | 0.312139i | \(0.101045\pi\) | ||||
−0.950036 | + | 0.312139i | \(0.898955\pi\) | |||||||
\(264\) | −2.48160 | + | 0.831993i | −0.152732 | + | 0.0512056i | ||||
\(265\) | − | 7.14157i | − | 0.438703i | ||||||
\(266\) | −0.984084 | − | 0.0261727i | −0.0603381 | − | 0.00160475i | ||||
\(267\) | 16.2571 | − | 5.45042i | 0.994916 | − | 0.333560i | ||||
\(268\) | 6.62562 | 0.404724 | ||||||||
\(269\) | −0.339791 | −0.0207174 | −0.0103587 | − | 0.999946i | \(-0.503297\pi\) | ||||
−0.0103587 | + | 0.999946i | \(0.503297\pi\) | |||||||
\(270\) | 8.54161 | + | 5.84780i | 0.519826 | + | 0.355886i | ||||
\(271\) | − | 15.1379i | − | 0.919561i | −0.888033 | − | 0.459780i | \(-0.847928\pi\) | ||
0.888033 | − | 0.459780i | \(-0.152072\pi\) | |||||||
\(272\) | 1.10115 | 0.0667672 | ||||||||
\(273\) | −6.93286 | − | 22.6608i | −0.419596 | − | 1.37149i | ||||
\(274\) | −7.71208 | −0.465904 | ||||||||
\(275\) | − | 1.55838i | − | 0.0939737i | ||||||
\(276\) | 0.550576 | + | 1.64221i | 0.0331408 | + | 0.0988496i | ||||
\(277\) | 25.5666 | 1.53615 | 0.768073 | − | 0.640362i | \(-0.221216\pi\) | ||||
0.768073 | + | 0.640362i | \(0.221216\pi\) | |||||||
\(278\) | −14.9440 | −0.896282 | ||||||||
\(279\) | −3.91027 | − | 5.17613i | −0.234102 | − | 0.309887i | ||||
\(280\) | −0.140132 | + | 5.26892i | −0.00837449 | + | 0.314878i | ||||
\(281\) | − | 16.9275i | − | 1.00981i | −0.863175 | − | 0.504904i | \(-0.831528\pi\) | ||
0.863175 | − | 0.504904i | \(-0.168472\pi\) | |||||||
\(282\) | 3.30658 | + | 9.86259i | 0.196904 | + | 0.587309i | ||||
\(283\) | 20.4813i | 1.21748i | 0.793368 | + | 0.608742i | \(0.208326\pi\) | ||||
−0.793368 | + | 0.608742i | \(0.791674\pi\) | |||||||
\(284\) | − | 13.6887i | − | 0.812276i | ||||||
\(285\) | 0.408113 | + | 1.21729i | 0.0241745 | + | 0.0721058i | ||||
\(286\) | − | 7.81441i | − | 0.462076i | ||||||
\(287\) | 13.3436 | + | 0.354887i | 0.787649 | + | 0.0209483i | ||||
\(288\) | 1.80833 | + | 2.39373i | 0.106557 | + | 0.141052i | ||||
\(289\) | −15.7875 | −0.928674 | ||||||||
\(290\) | 2.63469 | 0.154714 | ||||||||
\(291\) | 0.587532 | + | 1.75244i | 0.0344417 | + | 0.102730i | ||||
\(292\) | 9.75254i | 0.570724i | ||||||||
\(293\) | 18.9978 | 1.10986 | 0.554932 | − | 0.831895i | \(-0.312744\pi\) | ||||
0.554932 | + | 0.831895i | \(0.312744\pi\) | |||||||
\(294\) | −3.23755 | − | 11.6841i | −0.188818 | − | 0.681431i | ||||
\(295\) | 23.2665 | 1.35463 | ||||||||
\(296\) | 10.7679i | 0.625870i | ||||||||
\(297\) | −6.47911 | − | 4.43576i | −0.375956 | − | 0.257389i | ||||
\(298\) | 10.9768 | 0.635867 | ||||||||
\(299\) | −5.17124 | −0.299060 | ||||||||
\(300\) | −1.69356 | + | 0.567791i | −0.0977777 | + | 0.0327814i | ||||
\(301\) | −4.38462 | − | 0.116613i | −0.252726 | − | 0.00672148i | ||||
\(302\) | − | 2.93475i | − | 0.168876i | ||||||
\(303\) | 7.97600 | − | 2.67407i | 0.458209 | − | 0.153621i | ||||
\(304\) | 0.372080i | 0.0213403i | ||||||||
\(305\) | 11.3792i | 0.651571i | ||||||||
\(306\) | 1.99125 | + | 2.63586i | 0.113832 | + | 0.150682i | ||||
\(307\) | 17.1863i | 0.980873i | 0.871477 | + | 0.490436i | \(0.163163\pi\) | ||||
−0.871477 | + | 0.490436i | \(0.836837\pi\) | |||||||
\(308\) | 0.106295 | − | 3.99666i | 0.00605673 | − | 0.227731i | ||||
\(309\) | −9.22993 | − | 27.5303i | −0.525073 | − | 1.56614i | ||||
\(310\) | −4.30780 | −0.244667 | ||||||||
\(311\) | −19.2329 | −1.09060 | −0.545298 | − | 0.838242i | \(-0.683583\pi\) | ||||
−0.545298 | + | 0.838242i | \(0.683583\pi\) | |||||||
\(312\) | −8.49227 | + | 2.84716i | −0.480780 | + | 0.161189i | ||||
\(313\) | − | 22.8922i | − | 1.29394i | −0.762515 | − | 0.646971i | \(-0.776036\pi\) | ||
0.762515 | − | 0.646971i | \(-0.223964\pi\) | |||||||
\(314\) | 13.1983 | 0.744825 | ||||||||
\(315\) | −12.8658 | + | 9.19250i | −0.724905 | + | 0.517938i | ||||
\(316\) | 3.85596 | 0.216915 | ||||||||
\(317\) | − | 14.7130i | − | 0.826364i | −0.910648 | − | 0.413182i | \(-0.864417\pi\) | ||
0.910648 | − | 0.413182i | \(-0.135583\pi\) | |||||||
\(318\) | 5.88704 | − | 1.97372i | 0.330129 | − | 0.110681i | ||||
\(319\) | −1.99850 | −0.111895 | ||||||||
\(320\) | 1.99217 | 0.111366 | ||||||||
\(321\) | −3.39599 | − | 10.1293i | −0.189546 | − | 0.565361i | ||||
\(322\) | −2.64482 | − | 0.0703415i | −0.147390 | − | 0.00391998i | ||||
\(323\) | 0.409717i | 0.0227973i | ||||||||
\(324\) | −2.45990 | + | 8.65730i | −0.136661 | + | 0.480961i | ||||
\(325\) | − | 5.33292i | − | 0.295817i | ||||||
\(326\) | − | 13.9521i | − | 0.772737i | ||||||
\(327\) | 8.84548 | − | 2.96558i | 0.489156 | − | 0.163997i | ||||
\(328\) | − | 5.04520i | − | 0.278574i | ||||||
\(329\) | −15.8839 | − | 0.422447i | −0.875707 | − | 0.0232903i | ||||
\(330\) | −4.94376 | + | 1.65747i | −0.272145 | + | 0.0912407i | ||||
\(331\) | −20.0559 | −1.10237 | −0.551185 | − | 0.834383i | \(-0.685824\pi\) | ||||
−0.551185 | + | 0.834383i | \(0.685824\pi\) | |||||||
\(332\) | −0.708838 | −0.0389025 | ||||||||
\(333\) | −25.7754 | + | 19.4718i | −1.41248 | + | 1.06705i | ||||
\(334\) | 5.28517i | 0.289192i | ||||||||
\(335\) | 13.1993 | 0.721157 | ||||||||
\(336\) | −4.38208 | + | 1.34066i | −0.239062 | + | 0.0731389i | ||||
\(337\) | −10.7491 | −0.585543 | −0.292771 | − | 0.956182i | \(-0.594577\pi\) | ||||
−0.292771 | + | 0.956182i | \(0.594577\pi\) | |||||||
\(338\) | − | 13.7417i | − | 0.747449i | ||||||
\(339\) | −9.27822 | − | 27.6743i | −0.503924 | − | 1.50306i | ||||
\(340\) | 2.19368 | 0.118969 | ||||||||
\(341\) | 3.26762 | 0.176952 | ||||||||
\(342\) | −0.890661 | + | 0.672844i | −0.0481614 | + | 0.0363832i | ||||
\(343\) | 18.4614 | + | 1.47578i | 0.996820 | + | 0.0796846i | ||||
\(344\) | 1.65782i | 0.0893836i | ||||||||
\(345\) | 1.09684 | + | 3.27157i | 0.0590519 | + | 0.176135i | ||||
\(346\) | − | 5.96305i | − | 0.320576i | ||||||
\(347\) | 21.6678i | 1.16319i | 0.813478 | + | 0.581595i | \(0.197571\pi\) | ||||
−0.813478 | + | 0.581595i | \(0.802429\pi\) | |||||||
\(348\) | 0.728150 | + | 2.17187i | 0.0390329 | + | 0.116424i | ||||
\(349\) | 15.5372i | 0.831687i | 0.909436 | + | 0.415843i | \(0.136514\pi\) | ||||
−0.909436 | + | 0.415843i | \(0.863486\pi\) | |||||||
\(350\) | 0.0725408 | − | 2.72751i | 0.00387747 | − | 0.145792i | ||||
\(351\) | −22.1722 | − | 15.1796i | −1.18346 | − | 0.810228i | ||||
\(352\) | −1.51113 | −0.0805435 | ||||||||
\(353\) | 14.7290 | 0.783943 | 0.391972 | − | 0.919977i | \(-0.371793\pi\) | ||||
0.391972 | + | 0.919977i | \(0.371793\pi\) | |||||||
\(354\) | 6.43018 | + | 19.1794i | 0.341760 | + | 1.01937i | ||||
\(355\) | − | 27.2702i | − | 1.44735i | ||||||
\(356\) | 9.89948 | 0.524671 | ||||||||
\(357\) | −4.82534 | + | 1.47627i | −0.255384 | + | 0.0781324i | ||||
\(358\) | 5.06422 | 0.267653 | ||||||||
\(359\) | 29.7728i | 1.57135i | 0.618641 | + | 0.785674i | \(0.287684\pi\) | ||||
−0.618641 | + | 0.785674i | \(0.712316\pi\) | |||||||
\(360\) | 3.60249 | + | 4.76872i | 0.189868 | + | 0.251333i | ||||
\(361\) | 18.8616 | 0.992713 | ||||||||
\(362\) | 2.03182 | 0.106790 | ||||||||
\(363\) | −14.3143 | + | 4.79909i | −0.751308 | + | 0.251887i | ||||
\(364\) | 0.363752 | − | 13.6770i | 0.0190658 | − | 0.716868i | ||||
\(365\) | 19.4287i | 1.01694i | ||||||||
\(366\) | −9.38028 | + | 3.14488i | −0.490315 | + | 0.164385i | ||||
\(367\) | 20.2090i | 1.05490i | 0.849586 | + | 0.527449i | \(0.176852\pi\) | ||||
−0.849586 | + | 0.527449i | \(0.823148\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 12.0768 | − | 9.12337i | 0.628696 | − | 0.474944i | ||||
\(370\) | 21.4514i | 1.11521i | ||||||||
\(371\) | −0.252162 | + | 9.48119i | −0.0130916 | + | 0.492239i | ||||
\(372\) | −1.19055 | − | 3.55107i | −0.0617271 | − | 0.184115i | ||||
\(373\) | 36.6965 | 1.90007 | 0.950036 | − | 0.312141i | \(-0.101046\pi\) | ||||
0.950036 | + | 0.312141i | \(0.101046\pi\) | |||||||
\(374\) | −1.66399 | −0.0860426 | ||||||||
\(375\) | −19.7317 | + | 6.61534i | −1.01894 | + | 0.341615i | ||||
\(376\) | 6.00567i | 0.309719i | ||||||||
\(377\) | −6.83908 | −0.352230 | ||||||||
\(378\) | −11.1334 | − | 8.06518i | −0.572641 | − | 0.414828i | ||||
\(379\) | −4.31615 | −0.221706 | −0.110853 | − | 0.993837i | \(-0.535358\pi\) | ||||
−0.110853 | + | 0.993837i | \(0.535358\pi\) | |||||||
\(380\) | 0.741247i | 0.0380252i | ||||||||
\(381\) | 21.8008 | − | 7.30905i | 1.11689 | − | 0.374454i | ||||
\(382\) | −2.46441 | −0.126090 | ||||||||
\(383\) | −10.0077 | −0.511369 | −0.255685 | − | 0.966760i | \(-0.582301\pi\) | ||||
−0.255685 | + | 0.966760i | \(0.582301\pi\) | |||||||
\(384\) | 0.550576 | + | 1.64221i | 0.0280965 | + | 0.0838039i | ||||
\(385\) | 0.211758 | − | 7.96202i | 0.0107922 | − | 0.405782i | ||||
\(386\) | − | 1.23713i | − | 0.0629680i | ||||||
\(387\) | −3.96837 | + | 2.99788i | −0.201724 | + | 0.152391i | ||||
\(388\) | 1.06712i | 0.0541749i | ||||||||
\(389\) | 3.27499i | 0.166049i | 0.996548 | + | 0.0830244i | \(0.0264579\pi\) | ||||
−0.996548 | + | 0.0830244i | \(0.973542\pi\) | |||||||
\(390\) | −16.9180 | + | 5.67202i | −0.856678 | + | 0.287214i | ||||
\(391\) | 1.10115i | 0.0556877i | ||||||||
\(392\) | 0.372080 | − | 6.99010i | 0.0187929 | − | 0.353054i | ||||
\(393\) | −22.5064 | + | 7.54561i | −1.13530 | + | 0.380626i | ||||
\(394\) | −4.06740 | −0.204913 | ||||||||
\(395\) | 7.68172 | 0.386509 | ||||||||
\(396\) | −2.73262 | − | 3.61724i | −0.137319 | − | 0.181773i | ||||
\(397\) | − | 5.59615i | − | 0.280863i | −0.990090 | − | 0.140431i | \(-0.955151\pi\) | ||
0.990090 | − | 0.140431i | \(-0.0448490\pi\) | |||||||
\(398\) | −3.97727 | −0.199363 | ||||||||
\(399\) | −0.498833 | − | 1.63049i | −0.0249729 | − | 0.0816264i | ||||
\(400\) | −1.03127 | −0.0515633 | ||||||||
\(401\) | − | 1.91564i | − | 0.0956623i | −0.998855 | − | 0.0478312i | \(-0.984769\pi\) | ||
0.998855 | − | 0.0478312i | \(-0.0152309\pi\) | |||||||
\(402\) | 3.64791 | + | 10.8807i | 0.181941 | + | 0.542679i | ||||
\(403\) | 11.1821 | 0.557021 | ||||||||
\(404\) | 4.85686 | 0.241638 | ||||||||
\(405\) | −4.90053 | + | 17.2468i | −0.243509 | + | 0.857001i | ||||
\(406\) | −3.49783 | − | 0.0930282i | −0.173594 | − | 0.00461691i | ||||
\(407\) | − | 16.2717i | − | 0.806556i | ||||||
\(408\) | 0.606269 | + | 1.80833i | 0.0300148 | + | 0.0895256i | ||||
\(409\) | − | 28.2363i | − | 1.39619i | −0.716003 | − | 0.698097i | \(-0.754030\pi\) | ||
0.716003 | − | 0.698097i | \(-0.245970\pi\) | |||||||
\(410\) | − | 10.0509i | − | 0.496378i | ||||||
\(411\) | −4.24609 | − | 12.6649i | −0.209444 | − | 0.624713i | ||||
\(412\) | − | 16.7641i | − | 0.825909i | ||||||
\(413\) | −30.8888 | − | 0.821518i | −1.51994 | − | 0.0404242i | ||||
\(414\) | −2.39373 | + | 1.80833i | −0.117645 | + | 0.0888745i | ||||
\(415\) | −1.41212 | −0.0693184 | ||||||||
\(416\) | −5.17124 | −0.253541 | ||||||||
\(417\) | −8.22782 | − | 24.5413i | −0.402918 | − | 1.20179i | ||||
\(418\) | − | 0.562262i | − | 0.0275011i | ||||||
\(419\) | −37.2658 | −1.82055 | −0.910277 | − | 0.413999i | \(-0.864132\pi\) | ||||
−0.910277 | + | 0.413999i | \(0.864132\pi\) | |||||||
\(420\) | −8.72984 | + | 2.67082i | −0.425973 | + | 0.130322i | ||||
\(421\) | −20.6006 | −1.00401 | −0.502005 | − | 0.864865i | \(-0.667404\pi\) | ||||
−0.502005 | + | 0.864865i | \(0.667404\pi\) | |||||||
\(422\) | 19.5402i | 0.951201i | ||||||||
\(423\) | −14.3760 | + | 10.8602i | −0.698983 | + | 0.528042i | ||||
\(424\) | 3.58482 | 0.174094 | ||||||||
\(425\) | −1.13558 | −0.0550838 | ||||||||
\(426\) | 22.4798 | − | 7.53669i | 1.08915 | − | 0.365154i | ||||
\(427\) | 0.401788 | − | 15.1071i | 0.0194439 | − | 0.731084i | ||||
\(428\) | − | 6.16806i | − | 0.298144i | ||||||
\(429\) | 12.8329 | − | 4.30243i | 0.619580 | − | 0.207723i | ||||
\(430\) | 3.30265i | 0.159268i | ||||||||
\(431\) | − | 37.1134i | − | 1.78769i | −0.448377 | − | 0.893845i | \(-0.647998\pi\) | ||
0.448377 | − | 0.893845i | \(-0.352002\pi\) | |||||||
\(432\) | −2.93540 | + | 4.28759i | −0.141229 | + | 0.206287i | ||||
\(433\) | − | 40.1533i | − | 1.92965i | −0.262901 | − | 0.964823i | \(-0.584679\pi\) | ||
0.262901 | − | 0.964823i | \(-0.415321\pi\) | |||||||
\(434\) | 5.71907 | + | 0.152104i | 0.274524 | + | 0.00730124i | ||||
\(435\) | 1.45060 | + | 4.32672i | 0.0695508 | + | 0.207450i | ||||
\(436\) | 5.38632 | 0.257958 | ||||||||
\(437\) | −0.372080 | −0.0177990 | ||||||||
\(438\) | −16.0157 | + | 5.36952i | −0.765262 | + | 0.256565i | ||||
\(439\) | 17.1510i | 0.818573i | 0.912406 | + | 0.409287i | \(0.134222\pi\) | ||||
−0.912406 | + | 0.409287i | \(0.865778\pi\) | |||||||
\(440\) | −3.01042 | −0.143516 | ||||||||
\(441\) | 17.4053 | − | 11.7497i | 0.828823 | − | 0.559512i | ||||
\(442\) | −5.69432 | −0.270851 | ||||||||
\(443\) | 1.89816i | 0.0901842i | 0.998983 | + | 0.0450921i | \(0.0143581\pi\) | ||||
−0.998983 | + | 0.0450921i | \(0.985642\pi\) | |||||||
\(444\) | −17.6831 | + | 5.92854i | −0.839205 | + | 0.281356i | ||||
\(445\) | 19.7214 | 0.934885 | ||||||||
\(446\) | −26.3878 | −1.24950 | ||||||||
\(447\) | 6.04355 | + | 18.0262i | 0.285850 | + | 0.852609i | ||||
\(448\) | −2.64482 | − | 0.0703415i | −0.124956 | − | 0.00332332i | ||||
\(449\) | 19.3704i | 0.914148i | 0.889429 | + | 0.457074i | \(0.151102\pi\) | ||||
−0.889429 | + | 0.457074i | \(0.848898\pi\) | |||||||
\(450\) | −1.86487 | − | 2.46857i | −0.0879107 | − | 0.116370i | ||||
\(451\) | 7.62395i | 0.358998i | ||||||||
\(452\) | − | 16.8518i | − | 0.792643i | ||||||
\(453\) | 4.81948 | − | 1.61580i | 0.226439 | − | 0.0759170i | ||||
\(454\) | − | 5.16418i | − | 0.242367i | ||||||
\(455\) | 0.724656 | − | 27.2468i | 0.0339724 | − | 1.27735i | ||||
\(456\) | −0.611036 | + | 0.204859i | −0.0286144 | + | 0.00959339i | ||||
\(457\) | −2.69634 | −0.126129 | −0.0630647 | − | 0.998009i | \(-0.520087\pi\) | ||||
−0.0630647 | + | 0.998009i | \(0.520087\pi\) | |||||||
\(458\) | −13.1393 | −0.613959 | ||||||||
\(459\) | −3.23232 | + | 4.72130i | −0.150872 | + | 0.220371i | ||||
\(460\) | 1.99217i | 0.0928853i | ||||||||
\(461\) | 22.6634 | 1.05554 | 0.527770 | − | 0.849387i | \(-0.323028\pi\) | ||||
0.527770 | + | 0.849387i | \(0.323028\pi\) | |||||||
\(462\) | 6.62189 | − | 2.02591i | 0.308078 | − | 0.0942538i | ||||
\(463\) | 38.9153 | 1.80855 | 0.904273 | − | 0.426955i | \(-0.140414\pi\) | ||||
0.904273 | + | 0.426955i | \(0.140414\pi\) | |||||||
\(464\) | 1.32252i | 0.0613966i | ||||||||
\(465\) | −2.37177 | − | 7.07433i | −0.109988 | − | 0.328064i | ||||
\(466\) | 21.2452 | 0.984165 | ||||||||
\(467\) | 13.0789 | 0.605219 | 0.302610 | − | 0.953115i | \(-0.402142\pi\) | ||||
0.302610 | + | 0.953115i | \(0.402142\pi\) | |||||||
\(468\) | −9.35129 | − | 12.3785i | −0.432264 | − | 0.572199i | ||||
\(469\) | −17.5235 | − | 0.466056i | −0.809162 | − | 0.0215204i | ||||
\(470\) | 11.9643i | 0.551872i | ||||||||
\(471\) | 7.26669 | + | 21.6745i | 0.334831 | + | 0.998707i | ||||
\(472\) | 11.6790i | 0.537569i | ||||||||
\(473\) | − | 2.50518i | − | 0.115188i | ||||||
\(474\) | 2.12300 | + | 6.33231i | 0.0975126 | + | 0.290853i | ||||
\(475\) | − | 0.383714i | − | 0.0176060i | ||||||
\(476\) | −2.91235 | − | 0.0774567i | −0.133487 | − | 0.00355022i | ||||
\(477\) | 6.48253 | + | 8.58110i | 0.296815 | + | 0.392901i | ||||
\(478\) | 30.1168 | 1.37751 | ||||||||
\(479\) | −20.6284 | −0.942536 | −0.471268 | − | 0.881990i | \(-0.656204\pi\) | ||||
−0.471268 | + | 0.881990i | \(0.656204\pi\) | |||||||
\(480\) | 1.09684 | + | 3.27157i | 0.0500637 | + | 0.149326i | ||||
\(481\) | − | 55.6832i | − | 2.53894i | ||||||
\(482\) | 3.61167 | 0.164507 | ||||||||
\(483\) | −1.34066 | − | 4.38208i | −0.0610020 | − | 0.199392i | ||||
\(484\) | −8.71649 | −0.396204 | ||||||||
\(485\) | 2.12589i | 0.0965315i | ||||||||
\(486\) | −15.5715 | + | 0.726829i | −0.706338 | + | 0.0329696i | ||||
\(487\) | 15.9670 | 0.723536 | 0.361768 | − | 0.932268i | \(-0.382173\pi\) | ||||
0.361768 | + | 0.932268i | \(0.382173\pi\) | |||||||
\(488\) | −5.71197 | −0.258569 | ||||||||
\(489\) | 22.9124 | − | 7.68172i | 1.03613 | − | 0.347379i | ||||
\(490\) | 0.741247 | − | 13.9255i | 0.0334861 | − | 0.629088i | ||||
\(491\) | 6.00786i | 0.271131i | 0.990768 | + | 0.135566i | \(0.0432851\pi\) | ||||
−0.990768 | + | 0.135566i | \(0.956715\pi\) | |||||||
\(492\) | 8.28529 | − | 2.77777i | 0.373530 | − | 0.125231i | ||||
\(493\) | 1.45630i | 0.0655885i | ||||||||
\(494\) | − | 1.92412i | − | 0.0865701i | ||||||
\(495\) | −5.44384 | − | 7.20615i | −0.244682 | − | 0.323892i | ||||
\(496\) | − | 2.16237i | − | 0.0970932i | ||||||
\(497\) | −0.962885 | + | 36.2042i | −0.0431913 | + | 1.62398i | ||||
\(498\) | −0.390269 | − | 1.16406i | −0.0174884 | − | 0.0521629i | ||||
\(499\) | 26.5494 | 1.18852 | 0.594258 | − | 0.804275i | \(-0.297446\pi\) | ||||
0.594258 | + | 0.804275i | \(0.297446\pi\) | |||||||
\(500\) | −12.0153 | −0.537340 | ||||||||
\(501\) | −8.67938 | + | 2.90989i | −0.387766 | + | 0.130004i | ||||
\(502\) | 26.3289i | 1.17512i | ||||||||
\(503\) | −41.9026 | −1.86834 | −0.934171 | − | 0.356825i | \(-0.883859\pi\) | ||||
−0.934171 | + | 0.356825i | \(0.883859\pi\) | |||||||
\(504\) | −4.61432 | − | 6.45818i | −0.205538 | − | 0.287670i | ||||
\(505\) | 9.67568 | 0.430562 | ||||||||
\(506\) | − | 1.51113i | − | 0.0671779i | ||||||
\(507\) | 22.5668 | − | 7.56584i | 1.00223 | − | 0.336011i | ||||
\(508\) | 13.2753 | 0.588995 | ||||||||
\(509\) | −8.32516 | −0.369006 | −0.184503 | − | 0.982832i | \(-0.559068\pi\) | ||||
−0.184503 | + | 0.982832i | \(0.559068\pi\) | |||||||
\(510\) | 1.20779 | + | 3.60249i | 0.0534818 | + | 0.159521i | ||||
\(511\) | 0.686008 | − | 25.7937i | 0.0303472 | − | 1.14104i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.59533 | − | 1.09220i | −0.0704355 | − | 0.0482220i | ||||
\(514\) | 24.5168i | 1.08139i | ||||||||
\(515\) | − | 33.3970i | − | 1.47165i | ||||||
\(516\) | −2.72249 | + | 0.912756i | −0.119851 | + | 0.0401818i | ||||
\(517\) | − | 9.07534i | − | 0.399133i | ||||||
\(518\) | 0.757428 | − | 28.4790i | 0.0332795 | − | 1.25130i | ||||
\(519\) | 9.79260 | − | 3.28312i | 0.429848 | − | 0.144113i | ||||
\(520\) | −10.3020 | −0.451771 | ||||||||
\(521\) | −27.3282 | −1.19727 | −0.598634 | − | 0.801023i | \(-0.704290\pi\) | ||||
−0.598634 | + | 0.801023i | \(0.704290\pi\) | |||||||
\(522\) | −3.16576 | + | 2.39156i | −0.138562 | + | 0.104676i | ||||
\(523\) | − | 22.3056i | − | 0.975356i | −0.873023 | − | 0.487678i | \(-0.837844\pi\) | ||
0.873023 | − | 0.487678i | \(-0.162156\pi\) | |||||||
\(524\) | −13.7049 | −0.598703 | ||||||||
\(525\) | 4.51909 | − | 1.38257i | 0.197229 | − | 0.0603405i | ||||
\(526\) | −10.1241 | −0.441431 | ||||||||
\(527\) | − | 2.38110i | − | 0.103722i | ||||||
\(528\) | −0.831993 | − | 2.48160i | −0.0362078 | − | 0.107998i | ||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 7.14157 | 0.310210 | ||||||||
\(531\) | −27.9564 | + | 21.1195i | −1.21320 | + | 0.916506i | ||||
\(532\) | 0.0261727 | − | 0.984084i | 0.00113473 | − | 0.0426655i | ||||
\(533\) | 26.0899i | 1.13008i | ||||||||
\(534\) | 5.45042 | + | 16.2571i | 0.235863 | + | 0.703512i | ||||
\(535\) | − | 12.2878i | − | 0.531248i | ||||||
\(536\) | 6.62562i | 0.286183i | ||||||||
\(537\) | 2.78824 | + | 8.31654i | 0.120322 | + | 0.358885i | ||||
\(538\) | − | 0.339791i | − | 0.0146494i | ||||||
\(539\) | −0.562262 | + | 10.5630i | −0.0242183 | + | 0.454979i | ||||
\(540\) | −5.84780 | + | 8.54161i | −0.251649 | + | 0.367572i | ||||
\(541\) | 29.2687 | 1.25836 | 0.629180 | − | 0.777259i | \(-0.283391\pi\) | ||||
0.629180 | + | 0.777259i | \(0.283391\pi\) | |||||||
\(542\) | 15.1379 | 0.650228 | ||||||||
\(543\) | 1.11867 | + | 3.33668i | 0.0480068 | + | 0.143191i | ||||
\(544\) | 1.10115i | 0.0472115i | ||||||||
\(545\) | 10.7305 | 0.459642 | ||||||||
\(546\) | 22.6608 | − | 6.93286i | 0.969792 | − | 0.296699i | ||||
\(547\) | −43.0965 | −1.84267 | −0.921336 | − | 0.388768i | \(-0.872901\pi\) | ||||
−0.921336 | + | 0.388768i | \(0.872901\pi\) | |||||||
\(548\) | − | 7.71208i | − | 0.329444i | ||||||
\(549\) | −10.3291 | − | 13.6729i | −0.440836 | − | 0.583546i | ||||
\(550\) | 1.55838 | 0.0664494 | ||||||||
\(551\) | −0.492085 | −0.0209635 | ||||||||
\(552\) | −1.64221 | + | 0.550576i | −0.0698973 | + | 0.0234341i | ||||
\(553\) | −10.1983 | − | 0.271234i | −0.433676 | − | 0.0115340i | ||||
\(554\) | 25.5666i | 1.08622i | ||||||||
\(555\) | −35.2278 | + | 11.8106i | −1.49534 | + | 0.501334i | ||||
\(556\) | − | 14.9440i | − | 0.633767i | ||||||
\(557\) | 35.2668i | 1.49430i | 0.664654 | + | 0.747151i | \(0.268579\pi\) | ||||
−0.664654 | + | 0.747151i | \(0.731421\pi\) | |||||||
\(558\) | 5.17613 | − | 3.91027i | 0.219123 | − | 0.165535i | ||||
\(559\) | − | 8.57297i | − | 0.362598i | ||||||
\(560\) | −5.26892 | − | 0.140132i | −0.222652 | − | 0.00592166i | ||||
\(561\) | −0.916151 | − | 2.73262i | −0.0386799 | − | 0.115371i | ||||
\(562\) | 16.9275 | 0.714042 | ||||||||
\(563\) | 0.979062 | 0.0412625 | 0.0206313 | − | 0.999787i | \(-0.493432\pi\) | ||||
0.0206313 | + | 0.999787i | \(0.493432\pi\) | |||||||
\(564\) | −9.86259 | + | 3.30658i | −0.415290 | + | 0.139232i | ||||
\(565\) | − | 33.5717i | − | 1.41237i | ||||||
\(566\) | −20.4813 | −0.860892 | ||||||||
\(567\) | 7.11495 | − | 22.7239i | 0.298800 | − | 0.954316i | ||||
\(568\) | 13.6887 | 0.574366 | ||||||||
\(569\) | 16.0706i | 0.673715i | 0.941556 | + | 0.336857i | \(0.109364\pi\) | ||||
−0.941556 | + | 0.336857i | \(0.890636\pi\) | |||||||
\(570\) | −1.21729 | + | 0.408113i | −0.0509865 | + | 0.0170940i | ||||
\(571\) | 12.1219 | 0.507285 | 0.253643 | − | 0.967298i | \(-0.418371\pi\) | ||||
0.253643 | + | 0.967298i | \(0.418371\pi\) | |||||||
\(572\) | 7.81441 | 0.326737 | ||||||||
\(573\) | −1.35685 | − | 4.04709i | −0.0566831 | − | 0.169070i | ||||
\(574\) | −0.354887 | + | 13.3436i | −0.0148127 | + | 0.556952i | ||||
\(575\) | − | 1.03127i | − | 0.0430068i | ||||||
\(576\) | −2.39373 | + | 1.80833i | −0.0997388 | + | 0.0753470i | ||||
\(577\) | 36.3260i | 1.51227i | 0.654414 | + | 0.756136i | \(0.272915\pi\) | ||||
−0.654414 | + | 0.756136i | \(0.727085\pi\) | |||||||
\(578\) | − | 15.7875i | − | 0.656672i | ||||||
\(579\) | 2.03162 | − | 0.681132i | 0.0844314 | − | 0.0283069i | ||||
\(580\) | 2.63469i | 0.109399i | ||||||||
\(581\) | 1.87475 | + | 0.0498607i | 0.0777775 | + | 0.00206857i | ||||
\(582\) | −1.75244 | + | 0.587532i | −0.0726411 | + | 0.0243540i | ||||
\(583\) | −5.41713 | −0.224355 | ||||||||
\(584\) | −9.75254 | −0.403563 | ||||||||
\(585\) | −18.6293 | − | 24.6601i | −0.770229 | − | 1.01957i | ||||
\(586\) | 18.9978i | 0.784793i | ||||||||
\(587\) | 33.4043 | 1.37874 | 0.689372 | − | 0.724408i | \(-0.257887\pi\) | ||||
0.689372 | + | 0.724408i | \(0.257887\pi\) | |||||||
\(588\) | 11.6841 | − | 3.23755i | 0.481844 | − | 0.133514i | ||||
\(589\) | 0.804575 | 0.0331519 | ||||||||
\(590\) | 23.2665i | 0.957867i | ||||||||
\(591\) | −2.23941 | − | 6.67954i | −0.0921172 | − | 0.274759i | ||||
\(592\) | −10.7679 | −0.442557 | ||||||||
\(593\) | 13.6187 | 0.559253 | 0.279626 | − | 0.960109i | \(-0.409789\pi\) | ||||
0.279626 | + | 0.960109i | \(0.409789\pi\) | |||||||
\(594\) | 4.43576 | − | 6.47911i | 0.182002 | − | 0.265841i | ||||
\(595\) | −5.80188 | − | 0.154307i | −0.237854 | − | 0.00632596i | ||||
\(596\) | 10.9768i | 0.449626i | ||||||||
\(597\) | −2.18979 | − | 6.53153i | −0.0896222 | − | 0.267318i | ||||
\(598\) | − | 5.17124i | − | 0.211468i | ||||||
\(599\) | − | 11.6957i | − | 0.477873i | −0.971035 | − | 0.238937i | \(-0.923201\pi\) | ||
0.971035 | − | 0.238937i | \(-0.0767988\pi\) | |||||||
\(600\) | −0.567791 | − | 1.69356i | −0.0231800 | − | 0.0691393i | ||||
\(601\) | 46.6845i | 1.90430i | 0.305629 | + | 0.952151i | \(0.401133\pi\) | ||||
−0.305629 | + | 0.952151i | \(0.598867\pi\) | |||||||
\(602\) | 0.116613 | − | 4.38462i | 0.00475281 | − | 0.178704i | ||||
\(603\) | −15.8599 | + | 11.9813i | −0.645867 | + | 0.487916i | ||||
\(604\) | 2.93475 | 0.119413 | ||||||||
\(605\) | −17.3647 | −0.705976 | ||||||||
\(606\) | 2.67407 | + | 7.97600i | 0.108627 | + | 0.324003i | ||||
\(607\) | 34.3837i | 1.39559i | 0.716297 | + | 0.697796i | \(0.245836\pi\) | ||||
−0.716297 | + | 0.697796i | \(0.754164\pi\) | |||||||
\(608\) | −0.372080 | −0.0150899 | ||||||||
\(609\) | −1.77305 | − | 5.79540i | −0.0718476 | − | 0.234842i | ||||
\(610\) | −11.3792 | −0.460731 | ||||||||
\(611\) | − | 31.0567i | − | 1.25642i | ||||||
\(612\) | −2.63586 | + | 1.99125i | −0.106548 | + | 0.0804913i | ||||
\(613\) | 4.03328 | 0.162903 | 0.0814513 | − | 0.996677i | \(-0.474045\pi\) | ||||
0.0814513 | + | 0.996677i | \(0.474045\pi\) | |||||||
\(614\) | −17.1863 | −0.693582 | ||||||||
\(615\) | 16.5057 | − | 5.53378i | 0.665574 | − | 0.223144i | ||||
\(616\) | 3.99666 | + | 0.106295i | 0.161030 | + | 0.00428275i | ||||
\(617\) | 3.14403i | 0.126574i | 0.997995 | + | 0.0632869i | \(0.0201583\pi\) | ||||
−0.997995 | + | 0.0632869i | \(0.979842\pi\) | |||||||
\(618\) | 27.5303 | − | 9.22993i | 1.10743 | − | 0.371282i | ||||
\(619\) | − | 46.9319i | − | 1.88635i | −0.332295 | − | 0.943175i | \(-0.607823\pi\) | ||
0.332295 | − | 0.943175i | \(-0.392177\pi\) | |||||||
\(620\) | − | 4.30780i | − | 0.173006i | ||||||
\(621\) | −4.28759 | − | 2.93540i | −0.172055 | − | 0.117793i | ||||
\(622\) | − | 19.2329i | − | 0.771168i | ||||||
\(623\) | −26.1823 | − | 0.696344i | −1.04897 | − | 0.0278984i | ||||
\(624\) | −2.84716 | − | 8.49227i | −0.113978 | − | 0.339963i | ||||
\(625\) | −18.7802 | −0.751206 | ||||||||
\(626\) | 22.8922 | 0.914955 | ||||||||
\(627\) | 0.923354 | − | 0.309568i | 0.0368752 | − | 0.0123630i | ||||
\(628\) | 13.1983i | 0.526670i | ||||||||
\(629\) | −11.8571 | −0.472772 | ||||||||
\(630\) | −9.19250 | − | 12.8658i | −0.366238 | − | 0.512585i | ||||
\(631\) | 6.79460 | 0.270489 | 0.135244 | − | 0.990812i | \(-0.456818\pi\) | ||||
0.135244 | + | 0.990812i | \(0.456818\pi\) | |||||||
\(632\) | 3.85596i | 0.153382i | ||||||||
\(633\) | −32.0891 | + | 10.7584i | −1.27543 | + | 0.427606i | ||||
\(634\) | 14.7130 | 0.584328 | ||||||||
\(635\) | 26.4466 | 1.04950 | ||||||||
\(636\) | 1.97372 | + | 5.88704i | 0.0782630 | + | 0.233436i | ||||
\(637\) | −1.92412 | + | 36.1475i | −0.0762362 | + | 1.43222i | ||||
\(638\) | − | 1.99850i | − | 0.0791215i | ||||||
\(639\) | 24.7537 | + | 32.7671i | 0.979241 | + | 1.29625i | ||||
\(640\) | 1.99217i | 0.0787474i | ||||||||
\(641\) | 41.1142i | 1.62391i | 0.583717 | + | 0.811957i | \(0.301598\pi\) | ||||
−0.583717 | + | 0.811957i | \(0.698402\pi\) | |||||||
\(642\) | 10.1293 | − | 3.39599i | 0.399770 | − | 0.134029i | ||||
\(643\) | 30.5897i | 1.20634i | 0.797613 | + | 0.603170i | \(0.206096\pi\) | ||||
−0.797613 | + | 0.603170i | \(0.793904\pi\) | |||||||
\(644\) | 0.0703415 | − | 2.64482i | 0.00277184 | − | 0.104220i | ||||
\(645\) | −5.42366 | + | 1.81836i | −0.213556 | + | 0.0715980i | ||||
\(646\) | −0.409717 | −0.0161201 | ||||||||
\(647\) | −19.7951 | −0.778224 | −0.389112 | − | 0.921190i | \(-0.627218\pi\) | ||||
−0.389112 | + | 0.921190i | \(0.627218\pi\) | |||||||
\(648\) | −8.65730 | − | 2.45990i | −0.340091 | − | 0.0966339i | ||||
\(649\) | − | 17.6485i | − | 0.692763i | ||||||
\(650\) | 5.33292 | 0.209174 | ||||||||
\(651\) | 2.89900 | + | 9.47568i | 0.113621 | + | 0.371381i | ||||
\(652\) | 13.9521 | 0.546408 | ||||||||
\(653\) | 24.0068i | 0.939459i | 0.882810 | + | 0.469730i | \(0.155649\pi\) | ||||
−0.882810 | + | 0.469730i | \(0.844351\pi\) | |||||||
\(654\) | 2.96558 | + | 8.84548i | 0.115963 | + | 0.345886i | ||||
\(655\) | −27.3025 | −1.06680 | ||||||||
\(656\) | 5.04520 | 0.196982 | ||||||||
\(657\) | −17.6358 | − | 23.3449i | −0.688038 | − | 0.910773i | ||||
\(658\) | 0.422447 | − | 15.8839i | 0.0164687 | − | 0.619218i | ||||
\(659\) | − | 40.1169i | − | 1.56273i | −0.624072 | − | 0.781367i | \(-0.714523\pi\) | ||
0.624072 | − | 0.781367i | \(-0.285477\pi\) | |||||||
\(660\) | −1.65747 | − | 4.94376i | −0.0645169 | − | 0.192436i | ||||
\(661\) | 19.0674i | 0.741635i | 0.928706 | + | 0.370818i | \(0.120923\pi\) | ||||
−0.928706 | + | 0.370818i | \(0.879077\pi\) | |||||||
\(662\) | − | 20.0559i | − | 0.779493i | ||||||
\(663\) | −3.13516 | − | 9.35129i | −0.121759 | − | 0.363174i | ||||
\(664\) | − | 0.708838i | − | 0.0275082i | ||||||
\(665\) | 0.0521404 | − | 1.96046i | 0.00202192 | − | 0.0760234i | ||||
\(666\) | −19.4718 | − | 25.7754i | −0.754519 | − | 0.998776i | ||||
\(667\) | −1.32252 | −0.0512083 | ||||||||
\(668\) | −5.28517 | −0.204489 | ||||||||
\(669\) | −14.5285 | − | 43.3345i | −0.561705 | − | 1.67541i | ||||
\(670\) | 13.1993i | 0.509935i | ||||||||
\(671\) | 8.63153 | 0.333216 | ||||||||
\(672\) | −1.34066 | − | 4.38208i | −0.0517170 | − | 0.169042i | ||||
\(673\) | −13.5361 | −0.521779 | −0.260890 | − | 0.965369i | \(-0.584016\pi\) | ||||
−0.260890 | + | 0.965369i | \(0.584016\pi\) | |||||||
\(674\) | − | 10.7491i | − | 0.414041i | ||||||
\(675\) | 3.02717 | − | 4.42165i | 0.116516 | − | 0.170189i | ||||
\(676\) | 13.7417 | 0.528526 | ||||||||
\(677\) | −11.7065 | −0.449917 | −0.224959 | − | 0.974368i | \(-0.572225\pi\) | ||||
−0.224959 | + | 0.974368i | \(0.572225\pi\) | |||||||
\(678\) | 27.6743 | − | 9.27822i | 1.06283 | − | 0.356328i | ||||
\(679\) | 0.0750629 | − | 2.82234i | 0.00288065 | − | 0.108312i | ||||
\(680\) | 2.19368i | 0.0841238i | ||||||||
\(681\) | 8.48069 | − | 2.84328i | 0.324981 | − | 0.108955i | ||||
\(682\) | 3.26762i | 0.125124i | ||||||||
\(683\) | 33.6577i | 1.28788i | 0.765078 | + | 0.643938i | \(0.222701\pi\) | ||||
−0.765078 | + | 0.643938i | \(0.777299\pi\) | |||||||
\(684\) | −0.672844 | − | 0.890661i | −0.0257268 | − | 0.0340553i | ||||
\(685\) | − | 15.3638i | − | 0.587019i | ||||||
\(686\) | −1.47578 | + | 18.4614i | −0.0563455 | + | 0.704858i | ||||
\(687\) | −7.23418 | − | 21.5775i | −0.276001 | − | 0.823234i | ||||
\(688\) | −1.65782 | −0.0632037 | ||||||||
\(689\) | −18.5380 | −0.706240 | ||||||||
\(690\) | −3.27157 | + | 1.09684i | −0.124546 | + | 0.0417560i | ||||
\(691\) | 1.22804i | 0.0467168i | 0.999727 | + | 0.0233584i | \(0.00743588\pi\) | ||||
−0.999727 | + | 0.0233584i | \(0.992564\pi\) | |||||||
\(692\) | 5.96305 | 0.226681 | ||||||||
\(693\) | 6.97283 | + | 9.75915i | 0.264876 | + | 0.370719i | ||||
\(694\) | −21.6678 | −0.822500 | ||||||||
\(695\) | − | 29.7710i | − | 1.12928i | ||||||
\(696\) | −2.17187 | + | 0.728150i | −0.0823243 | + | 0.0276005i | ||||
\(697\) | 5.55553 | 0.210431 | ||||||||
\(698\) | −15.5372 | −0.588091 | ||||||||
\(699\) | 11.6971 | + | 34.8891i | 0.442425 | + | 1.31963i | ||||
\(700\) | 2.72751 | + | 0.0725408i | 0.103090 | + | 0.00274178i | ||||
\(701\) | − | 28.8736i | − | 1.09054i | −0.838260 | − | 0.545270i | \(-0.816427\pi\) | ||
0.838260 | − | 0.545270i | \(-0.183573\pi\) | |||||||
\(702\) | 15.1796 | − | 22.1722i | 0.572918 | − | 0.836834i | ||||
\(703\) | − | 4.00651i | − | 0.151109i | ||||||
\(704\) | − | 1.51113i | − | 0.0569529i | ||||||
\(705\) | −19.6479 | + | 6.58726i | −0.739984 | + | 0.248091i | ||||
\(706\) | 14.7290i | 0.554332i | ||||||||
\(707\) | −12.8455 | − | 0.341639i | −0.483105 | − | 0.0128486i | ||||
\(708\) | −19.1794 | + | 6.43018i | −0.720806 | + | 0.241661i | ||||
\(709\) | −23.0384 | −0.865225 | −0.432613 | − | 0.901580i | \(-0.642408\pi\) | ||||
−0.432613 | + | 0.901580i | \(0.642408\pi\) | |||||||
\(710\) | 27.2702 | 1.02343 | ||||||||
\(711\) | −9.23013 | + | 6.97284i | −0.346157 | + | 0.261502i | ||||
\(712\) | 9.89948i | 0.370999i | ||||||||
\(713\) | 2.16237 | 0.0809814 | ||||||||
\(714\) | −1.47627 | − | 4.82534i | −0.0552480 | − | 0.180584i | ||||
\(715\) | 15.5676 | 0.582196 | ||||||||
\(716\) | 5.06422i | 0.189259i | ||||||||
\(717\) | 16.5816 | + | 49.4582i | 0.619251 | + | 1.84705i | ||||
\(718\) | −29.7728 | −1.11111 | ||||||||
\(719\) | 31.1227 | 1.16068 | 0.580340 | − | 0.814374i | \(-0.302920\pi\) | ||||
0.580340 | + | 0.814374i | \(0.302920\pi\) | |||||||
\(720\) | −4.76872 | + | 3.60249i | −0.177720 | + | 0.134257i | ||||
\(721\) | −1.17921 | + | 44.3380i | −0.0439162 | + | 1.65123i | ||||
\(722\) | 18.8616i | 0.701954i | ||||||||
\(723\) | 1.98850 | + | 5.93114i | 0.0739532 | + | 0.220581i | ||||
\(724\) | 2.03182i | 0.0755119i | ||||||||
\(725\) | − | 1.36387i | − | 0.0506530i | ||||||
\(726\) | −4.79909 | − | 14.3143i | −0.178111 | − | 0.531255i | ||||
\(727\) | 33.9221i | 1.25810i | 0.777365 | + | 0.629050i | \(0.216556\pi\) | ||||
−0.777365 | + | 0.629050i | \(0.783444\pi\) | |||||||
\(728\) | 13.6770 | + | 0.363752i | 0.506902 | + | 0.0134816i | ||||
\(729\) | −9.76691 | − | 25.1716i | −0.361737 | − | 0.932280i | ||||
\(730\) | −19.4287 | −0.719088 | ||||||||
\(731\) | −1.82551 | −0.0675190 | ||||||||
\(732\) | −3.14488 | − | 9.38028i | −0.116238 | − | 0.346705i | ||||
\(733\) | 13.5652i | 0.501040i | 0.968111 | + | 0.250520i | \(0.0806017\pi\) | ||||
−0.968111 | + | 0.250520i | \(0.919398\pi\) | |||||||
\(734\) | −20.2090 | −0.745926 | ||||||||
\(735\) | 23.2767 | − | 6.44975i | 0.858574 | − | 0.237902i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | − | 10.0122i | − | 0.368803i | ||||||
\(738\) | 9.12337 | + | 12.0768i | 0.335836 | + | 0.444555i | ||||
\(739\) | 26.2623 | 0.966076 | 0.483038 | − | 0.875599i | \(-0.339533\pi\) | ||||
0.483038 | + | 0.875599i | \(0.339533\pi\) | |||||||
\(740\) | −21.4514 | −0.788570 | ||||||||
\(741\) | 3.15981 | − | 1.05937i | 0.116078 | − | 0.0389170i | ||||
\(742\) | −9.48119 | − | 0.252162i | −0.348065 | − | 0.00925714i | ||||
\(743\) | − | 13.8311i | − | 0.507415i | −0.967281 | − | 0.253707i | \(-0.918350\pi\) | ||
0.967281 | − | 0.253707i | \(-0.0816500\pi\) | |||||||
\(744\) | 3.55107 | − | 1.19055i | 0.130189 | − | 0.0436477i | ||||
\(745\) | 21.8676i | 0.801165i | ||||||||
\(746\) | 36.6965i | 1.34355i | ||||||||
\(747\) | 1.69677 | − | 1.28181i | 0.0620814 | − | 0.0468990i | ||||
\(748\) | − | 1.66399i | − | 0.0608413i | ||||||
\(749\) | −0.433870 | + | 16.3134i | −0.0158533 | + | 0.596078i | ||||
\(750\) | −6.61534 | − | 19.7317i | −0.241558 | − | 0.720499i | ||||
\(751\) | 5.93861 | 0.216703 | 0.108351 | − | 0.994113i | \(-0.465443\pi\) | ||||
0.108351 | + | 0.994113i | \(0.465443\pi\) | |||||||
\(752\) | −6.00567 | −0.219004 | ||||||||
\(753\) | −43.2377 | + | 14.4961i | −1.57567 | + | 0.528266i | ||||
\(754\) | − | 6.83908i | − | 0.249065i | ||||||
\(755\) | 5.84651 | 0.212776 | ||||||||
\(756\) | 8.06518 | − | 11.1334i | 0.293328 | − | 0.404918i | ||||
\(757\) | 30.3634 | 1.10358 | 0.551788 | − | 0.833985i | \(-0.313946\pi\) | ||||
0.551788 | + | 0.833985i | \(0.313946\pi\) | |||||||
\(758\) | − | 4.31615i | − | 0.156770i | ||||||
\(759\) | 2.48160 | − | 0.831993i | 0.0900763 | − | 0.0301994i | ||||
\(760\) | −0.741247 | −0.0268879 | ||||||||
\(761\) | 7.92613 | 0.287322 | 0.143661 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143661 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(762\) | 7.30905 | + | 21.8008i | 0.264779 | + | 0.789761i | ||||
\(763\) | −14.2458 | − | 0.378882i | −0.515733 | − | 0.0137164i | ||||
\(764\) | − | 2.46441i | − | 0.0891593i | ||||||
\(765\) | −5.25108 | + | 3.96690i | −0.189853 | + | 0.143423i | ||||
\(766\) | − | 10.0077i | − | 0.361593i | ||||||
\(767\) | − | 60.3948i | − | 2.18073i | ||||||
\(768\) | −1.64221 | + | 0.550576i | −0.0592583 | + | 0.0198672i | ||||
\(769\) | − | 40.0002i | − | 1.44244i | −0.692704 | − | 0.721222i | \(-0.743581\pi\) | ||
0.692704 | − | 0.721222i | \(-0.256419\pi\) | |||||||
\(770\) | 7.96202 | + | 0.211758i | 0.286931 | + | 0.00763122i | ||||
\(771\) | −40.2619 | + | 13.4984i | −1.45000 | + | 0.486133i | ||||
\(772\) | 1.23713 | 0.0445251 | ||||||||
\(773\) | 0.612052 | 0.0220140 | 0.0110070 | − | 0.999939i | \(-0.496496\pi\) | ||||
0.0110070 | + | 0.999939i | \(0.496496\pi\) | |||||||
\(774\) | −2.99788 | − | 3.96837i | −0.107757 | − | 0.142640i | ||||
\(775\) | 2.22998i | 0.0801032i | ||||||||
\(776\) | −1.06712 | −0.0383074 | ||||||||
\(777\) | 47.1857 | − | 14.4360i | 1.69278 | − | 0.517890i | ||||
\(778\) | −3.27499 | −0.117414 | ||||||||
\(779\) | 1.87722i | 0.0672584i | ||||||||
\(780\) | −5.67202 | − | 16.9180i | −0.203091 | − | 0.605763i | ||||
\(781\) | −20.6854 | −0.740183 | ||||||||
\(782\) | −1.10115 | −0.0393771 | ||||||||
\(783\) | −5.67044 | − | 3.88213i | −0.202645 | − | 0.138736i | ||||
\(784\) | 6.99010 | + | 0.372080i | 0.249647 | + | 0.0132886i | ||||
\(785\) | 26.2933i | 0.938447i | ||||||||
\(786\) | −7.54561 | − | 22.5064i | −0.269143 | − | 0.802777i | ||||
\(787\) | 6.88190i | 0.245313i | 0.992449 | + | 0.122657i | \(0.0391414\pi\) | ||||
−0.992449 | + | 0.122657i | \(0.960859\pi\) | |||||||
\(788\) | − | 4.06740i | − | 0.144895i | ||||||
\(789\) | −5.57408 | − | 16.6259i | −0.198443 | − | 0.591898i | ||||
\(790\) | 7.68172i | 0.273303i | ||||||||
\(791\) | −1.18538 | + | 44.5700i | −0.0421473 | + | 1.58473i | ||||
\(792\) | 3.61724 | − | 2.73262i | 0.128533 | − | 0.0970994i | ||||
\(793\) | 29.5379 | 1.04892 | ||||||||
\(794\) | 5.59615 | 0.198600 | ||||||||
\(795\) | 3.93198 | + | 11.7280i | 0.139453 | + | 0.415948i | ||||
\(796\) | − | 3.97727i | − | 0.140971i | ||||||
\(797\) | 40.2239 | 1.42480 | 0.712401 | − | 0.701772i | \(-0.247608\pi\) | ||||
0.712401 | + | 0.701772i | \(0.247608\pi\) | |||||||
\(798\) | 1.63049 | − | 0.498833i | 0.0577186 | − | 0.0176585i | ||||
\(799\) | −6.61316 | −0.233957 | ||||||||
\(800\) | − | 1.03127i | − | 0.0364608i | ||||||
\(801\) | −23.6967 | + | 17.9015i | −0.837281 | + | 0.632519i | ||||
\(802\) | 1.91564 | 0.0676435 | ||||||||
\(803\) | 14.7373 | 0.520070 | ||||||||
\(804\) | −10.8807 | + | 3.64791i | −0.383732 | + | 0.128652i | ||||
\(805\) | 0.140132 | − | 5.26892i | 0.00493901 | − | 0.185705i | ||||
\(806\) | 11.1821i | 0.393873i | ||||||||
\(807\) | 0.558010 | − | 0.187081i | 0.0196429 | − | 0.00658557i | ||||
\(808\) | 4.85686i | 0.170864i | ||||||||
\(809\) | 16.9551i | 0.596109i | 0.954549 | + | 0.298054i | \(0.0963377\pi\) | ||||
−0.954549 | + | 0.298054i | \(0.903662\pi\) | |||||||
\(810\) | −17.2468 | − | 4.90053i | −0.605991 | − | 0.172187i | ||||
\(811\) | − | 30.8341i | − | 1.08273i | −0.840787 | − | 0.541366i | \(-0.817907\pi\) | ||
0.840787 | − | 0.541366i | \(-0.182093\pi\) | |||||||
\(812\) | 0.0930282 | − | 3.49783i | 0.00326465 | − | 0.122750i | ||||
\(813\) | 8.33456 | + | 24.8596i | 0.292306 | + | 0.871865i | ||||
\(814\) | 16.2717 | 0.570321 | ||||||||
\(815\) | 27.7950 | 0.973617 | ||||||||
\(816\) | −1.80833 | + | 0.606269i | −0.0633041 | + | 0.0212237i | ||||
\(817\) | − | 0.616842i | − | 0.0215806i | ||||||
\(818\) | 28.2363 | 0.987259 | ||||||||
\(819\) | 23.8617 | + | 33.3968i | 0.833796 | + | 1.16698i | ||||
\(820\) | 10.0509 | 0.350992 | ||||||||
\(821\) | 3.15438i | 0.110089i | 0.998484 | + | 0.0550443i | \(0.0175300\pi\) | ||||
−0.998484 | + | 0.0550443i | \(0.982470\pi\) | |||||||
\(822\) | 12.6649 | − | 4.24609i | 0.441738 | − | 0.148099i | ||||
\(823\) | 13.0983 | 0.456579 | 0.228290 | − | 0.973593i | \(-0.426687\pi\) | ||||
0.228290 | + | 0.973593i | \(0.426687\pi\) | |||||||
\(824\) | 16.7641 | 0.584006 | ||||||||
\(825\) | 0.858006 | + | 2.55919i | 0.0298719 | + | 0.0890995i | ||||
\(826\) | 0.821518 | − | 30.8888i | 0.0285843 | − | 1.07476i | ||||
\(827\) | − | 26.0225i | − | 0.904889i | −0.891792 | − | 0.452445i | \(-0.850552\pi\) | ||
0.891792 | − | 0.452445i | \(-0.149448\pi\) | |||||||
\(828\) | −1.80833 | − | 2.39373i | −0.0628437 | − | 0.0831879i | ||||
\(829\) | 14.1499i | 0.491446i | 0.969340 | + | 0.245723i | \(0.0790254\pi\) | ||||
−0.969340 | + | 0.245723i | \(0.920975\pi\) | |||||||
\(830\) | − | 1.41212i | − | 0.0490155i | ||||||
\(831\) | −41.9858 | + | 14.0764i | −1.45647 | + | 0.488303i | ||||
\(832\) | − | 5.17124i | − | 0.179280i | ||||||
\(833\) | 7.69717 | + | 0.409717i | 0.266691 | + | 0.0141959i | ||||
\(834\) | 24.5413 | − | 8.22782i | 0.849794 | − | 0.284906i | ||||
\(835\) | −10.5289 | −0.364369 | ||||||||
\(836\) | 0.562262 | 0.0194462 | ||||||||
\(837\) | 9.27136 | + | 6.34741i | 0.320465 | + | 0.219398i | ||||
\(838\) | − | 37.2658i | − | 1.28733i | ||||||
\(839\) | 2.73390 | 0.0943847 | 0.0471923 | − | 0.998886i | \(-0.484973\pi\) | ||||
0.0471923 | + | 0.998886i | \(0.484973\pi\) | |||||||
\(840\) | −2.67082 | − | 8.72984i | −0.0921519 | − | 0.301208i | ||||
\(841\) | 27.2509 | 0.939687 | ||||||||
\(842\) | − | 20.6006i | − | 0.709942i | ||||||
\(843\) | 9.31987 | + | 27.7985i | 0.320993 | + | 0.957432i | ||||
\(844\) | −19.5402 | −0.672601 | ||||||||
\(845\) | 27.3757 | 0.941754 | ||||||||
\(846\) | −10.8602 | − | 14.3760i | −0.373382 | − | 0.494255i | ||||
\(847\) | 23.0535 | + | 0.613130i | 0.792128 | + | 0.0210674i | ||||
\(848\) | 3.58482i | 0.123103i | ||||||||
\(849\) | −11.2765 | − | 33.6346i | −0.387008 | − | 1.15434i | ||||
\(850\) | − | 1.13558i | − | 0.0389501i | ||||||
\(851\) | − | 10.7679i | − | 0.369118i | ||||||
\(852\) | 7.53669 | + | 22.4798i | 0.258203 | + | 0.770145i | ||||
\(853\) | 32.3900i | 1.10901i | 0.832179 | + | 0.554507i | \(0.187093\pi\) | ||||
−0.832179 | + | 0.554507i | \(0.812907\pi\) | |||||||
\(854\) | 15.1071 | + | 0.401788i | 0.516955 | + | 0.0137489i | ||||
\(855\) | −1.34042 | − | 1.77435i | −0.0458413 | − | 0.0606813i | ||||
\(856\) | 6.16806 | 0.210820 | ||||||||
\(857\) | 28.3268 | 0.967624 | 0.483812 | − | 0.875172i | \(-0.339252\pi\) | ||||
0.483812 | + | 0.875172i | \(0.339252\pi\) | |||||||
\(858\) | 4.30243 | + | 12.8329i | 0.146883 | + | 0.438109i | ||||
\(859\) | 18.2415i | 0.622393i | 0.950346 | + | 0.311196i | \(0.100730\pi\) | ||||
−0.950346 | + | 0.311196i | \(0.899270\pi\) | |||||||
\(860\) | −3.30265 | −0.112620 | ||||||||
\(861\) | −22.1085 | + | 6.76388i | −0.753455 | + | 0.230513i | ||||
\(862\) | 37.1134 | 1.26409 | ||||||||
\(863\) | 17.4332i | 0.593432i | 0.954966 | + | 0.296716i | \(0.0958914\pi\) | ||||
−0.954966 | + | 0.296716i | \(0.904109\pi\) | |||||||
\(864\) | −4.28759 | − | 2.93540i | −0.145867 | − | 0.0998642i | ||||
\(865\) | 11.8794 | 0.403912 | ||||||||
\(866\) | 40.1533 | 1.36447 | ||||||||
\(867\) | 25.9264 | − | 8.69220i | 0.880506 | − | 0.295203i | ||||
\(868\) | −0.152104 | + | 5.71907i | −0.00516275 | + | 0.194118i | ||||
\(869\) | − | 5.82685i | − | 0.197663i | ||||||
\(870\) | −4.32672 | + | 1.45060i | −0.146690 | + | 0.0491799i | ||||
\(871\) | − | 34.2626i | − | 1.16094i | ||||||
\(872\) | 5.38632i | 0.182404i | ||||||||
\(873\) | −1.92971 | − | 2.55440i | −0.0653107 | − | 0.0864534i | ||||
\(874\) | − | 0.372080i | − | 0.0125858i | ||||||
\(875\) | 31.7782 | + | 0.845174i | 1.07430 | + | 0.0285721i | ||||
\(876\) | −5.36952 | − | 16.0157i | −0.181419 | − | 0.541122i | ||||
\(877\) | −47.3073 | −1.59745 | −0.798727 | − | 0.601694i | \(-0.794493\pi\) | ||||
−0.798727 | + | 0.601694i | \(0.794493\pi\) | |||||||
\(878\) | −17.1510 | −0.578819 | ||||||||
\(879\) | −31.1985 | + | 10.4598i | −1.05230 | + | 0.352799i | ||||
\(880\) | − | 3.01042i | − | 0.101481i | ||||||
\(881\) | −8.43256 | −0.284100 | −0.142050 | − | 0.989859i | \(-0.545369\pi\) | ||||
−0.142050 | + | 0.989859i | \(0.545369\pi\) | |||||||
\(882\) | 11.7497 | + | 17.4053i | 0.395634 | + | 0.586066i | ||||
\(883\) | 27.2561 | 0.917240 | 0.458620 | − | 0.888632i | \(-0.348344\pi\) | ||||
0.458620 | + | 0.888632i | \(0.348344\pi\) | |||||||
\(884\) | − | 5.69432i | − | 0.191521i | ||||||
\(885\) | −38.2086 | + | 12.8100i | −1.28437 | + | 0.430603i | ||||
\(886\) | −1.89816 | −0.0637699 | ||||||||
\(887\) | 11.6157 | 0.390016 | 0.195008 | − | 0.980802i | \(-0.437527\pi\) | ||||
0.195008 | + | 0.980802i | \(0.437527\pi\) | |||||||
\(888\) | −5.92854 | − | 17.6831i | −0.198949 | − | 0.593407i | ||||
\(889\) | −35.1107 | − | 0.933802i | −1.17757 | − | 0.0313187i | ||||
\(890\) | 19.7214i | 0.661064i | ||||||||
\(891\) | 13.0823 | + | 3.71723i | 0.438274 | + | 0.124532i | ||||
\(892\) | − | 26.3878i | − | 0.883530i | ||||||
\(893\) | − | 2.23459i | − | 0.0747778i | ||||||
\(894\) | −18.0262 | + | 6.04355i | −0.602886 | + | 0.202126i | ||||
\(895\) | 10.0888i | 0.337231i | ||||||||
\(896\) | 0.0703415 | − | 2.64482i | 0.00234994 | − | 0.0883571i | ||||
\(897\) | 8.49227 | − | 2.84716i | 0.283549 | − | 0.0950639i | ||||
\(898\) | −19.3704 | −0.646400 | ||||||||
\(899\) | 2.85978 | 0.0953791 | ||||||||
\(900\) | 2.46857 | − | 1.86487i | 0.0822858 | − | 0.0621623i | ||||
\(901\) | 3.94744i | 0.131508i | ||||||||
\(902\) | −7.62395 | −0.253850 | ||||||||
\(903\) | 7.26470 | − | 2.22257i | 0.241754 | − | 0.0739624i | ||||
\(904\) | 16.8518 | 0.560483 | ||||||||
\(905\) | 4.04772i | 0.134551i | ||||||||
\(906\) | 1.61580 | + | 4.81948i | 0.0536814 | + | 0.160116i | ||||
\(907\) | 42.8792 | 1.42378 | 0.711890 | − | 0.702291i | \(-0.247840\pi\) | ||||
0.711890 | + | 0.702291i | \(0.247840\pi\) | |||||||
\(908\) | 5.16418 | 0.171379 | ||||||||
\(909\) | −11.6260 | + | 8.78280i | −0.385611 | + | 0.291307i | ||||
\(910\) | 27.2468 | + | 0.724656i | 0.903223 | + | 0.0240221i | ||||
\(911\) | − | 27.3966i | − | 0.907691i | −0.891080 | − | 0.453845i | \(-0.850052\pi\) | ||
0.891080 | − | 0.453845i | \(-0.149948\pi\) | |||||||
\(912\) | −0.204859 | − | 0.611036i | −0.00678355 | − | 0.0202334i | ||||
\(913\) | 1.07115i | 0.0354497i | ||||||||
\(914\) | − | 2.69634i | − | 0.0891869i | ||||||
\(915\) | −6.26512 | − | 18.6871i | −0.207119 | − | 0.617776i | ||||
\(916\) | − | 13.1393i | − | 0.434134i | ||||||
\(917\) | 36.2470 | + | 0.964025i | 1.19698 | + | 0.0318349i | ||||
\(918\) | −4.72130 | − | 3.23232i | −0.155826 | − | 0.106682i | ||||
\(919\) | −12.2243 | −0.403241 | −0.201620 | − | 0.979464i | \(-0.564621\pi\) | ||||
−0.201620 | + | 0.979464i | \(0.564621\pi\) | |||||||
\(920\) | −1.99217 | −0.0656798 | ||||||||
\(921\) | −9.46236 | − | 28.2235i | −0.311795 | − | 0.929997i | ||||
\(922\) | 22.6634i | 0.746379i | ||||||||
\(923\) | −70.7876 | −2.33000 | ||||||||
\(924\) | 2.02591 | + | 6.62189i | 0.0666475 | + | 0.217844i | ||||
\(925\) | 11.1045 | 0.365115 | ||||||||
\(926\) | 38.9153i | 1.27883i | ||||||||
\(927\) | 30.3150 | + | 40.1288i | 0.995677 | + | 1.31800i | ||||
\(928\) | −1.32252 | −0.0434139 | ||||||||
\(929\) | 3.01871 | 0.0990406 | 0.0495203 | − | 0.998773i | \(-0.484231\pi\) | ||||
0.0495203 | + | 0.998773i | \(0.484231\pi\) | |||||||
\(930\) | 7.07433 | − | 2.37177i | 0.231976 | − | 0.0777736i | ||||
\(931\) | −0.138444 | + | 2.60088i | −0.00453732 | + | 0.0852404i | ||||
\(932\) | 21.2452i | 0.695910i | ||||||||
\(933\) | 31.5845 | − | 10.5892i | 1.03403 | − | 0.346674i | ||||
\(934\) | 13.0789i | 0.427955i | ||||||||
\(935\) | − | 3.31494i | − | 0.108410i | ||||||
\(936\) | 12.3785 | − | 9.35129i | 0.404606 | − | 0.305657i | ||||
\(937\) | 1.21195i | 0.0395928i | 0.999804 | + | 0.0197964i | \(0.00630181\pi\) | ||||
−0.999804 | + | 0.0197964i | \(0.993698\pi\) | |||||||
\(938\) | 0.466056 | − | 17.5235i | 0.0152173 | − | 0.572164i | ||||
\(939\) | 12.6039 | + | 37.5938i | 0.411312 | + | 1.22683i | ||||
\(940\) | −11.9643 | −0.390232 | ||||||||
\(941\) | −12.7187 | −0.414618 | −0.207309 | − | 0.978276i | \(-0.566470\pi\) | ||||
−0.207309 | + | 0.978276i | \(0.566470\pi\) | |||||||
\(942\) | −21.6745 | + | 7.26669i | −0.706192 | + | 0.236761i | ||||
\(943\) | 5.04520i | 0.164294i | ||||||||
\(944\) | −11.6790 | −0.380119 | ||||||||
\(945\) | 16.0672 | − | 22.1796i | 0.522666 | − | 0.721504i | ||||
\(946\) | 2.50518 | 0.0814504 | ||||||||
\(947\) | 1.64646i | 0.0535027i | 0.999642 | + | 0.0267513i | \(0.00851623\pi\) | ||||
−0.999642 | + | 0.0267513i | \(0.991484\pi\) | |||||||
\(948\) | −6.33231 | + | 2.12300i | −0.205664 | + | 0.0689518i | ||||
\(949\) | 50.4327 | 1.63711 | ||||||||
\(950\) | 0.383714 | 0.0124493 | ||||||||
\(951\) | 8.10063 | + | 24.1619i | 0.262681 | + | 0.783503i | ||||
\(952\) | 0.0774567 | − | 2.91235i | 0.00251039 | − | 0.0943897i | ||||
\(953\) | − | 11.8018i | − | 0.382298i | −0.981561 | − | 0.191149i | \(-0.938779\pi\) | ||
0.981561 | − | 0.191149i | \(-0.0612214\pi\) | |||||||
\(954\) | −8.58110 | + | 6.48253i | −0.277823 | + | 0.209880i | ||||
\(955\) | − | 4.90952i | − | 0.158868i | ||||||
\(956\) | 30.1168i | 0.974047i | ||||||||
\(957\) | 3.28197 | − | 1.10033i | 0.106091 | − | 0.0355686i | ||||
\(958\) | − | 20.6284i | − | 0.666474i | ||||||
\(959\) | −0.542479 | + | 20.3970i | −0.0175176 | + | 0.658655i | ||||
\(960\) | −3.27157 | + | 1.09684i | −0.105589 | + | 0.0354004i | ||||
\(961\) | 26.3242 | 0.849166 | ||||||||
\(962\) | 55.6832 | 1.79530 | ||||||||
\(963\) | 11.1539 | + | 14.7647i | 0.359429 | + | 0.475785i | ||||
\(964\) | 3.61167i | 0.116324i | ||||||||
\(965\) | 2.46456 | 0.0793370 | ||||||||
\(966\) | 4.38208 | − | 1.34066i | 0.140991 | − | 0.0431350i | ||||
\(967\) | 12.6572 | 0.407027 | 0.203514 | − | 0.979072i | \(-0.434764\pi\) | ||||
0.203514 | + | 0.979072i | \(0.434764\pi\) | |||||||
\(968\) | − | 8.71649i | − | 0.280158i | ||||||
\(969\) | −0.225581 | − | 0.672844i | −0.00724670 | − | 0.0216149i | ||||
\(970\) | −2.12589 | −0.0682581 | ||||||||
\(971\) | −23.2660 | −0.746642 | −0.373321 | − | 0.927702i | \(-0.621781\pi\) | ||||
−0.373321 | + | 0.927702i | \(0.621781\pi\) | |||||||
\(972\) | −0.726829 | − | 15.5715i | −0.0233131 | − | 0.499456i | ||||
\(973\) | −1.05118 | + | 39.5241i | −0.0336994 | + | 1.26709i | ||||
\(974\) | 15.9670i | 0.511617i | ||||||||
\(975\) | 2.93618 | + | 8.75779i | 0.0940330 | + | 0.280474i | ||||
\(976\) | − | 5.71197i | − | 0.182836i | ||||||
\(977\) | 39.8202i | 1.27396i | 0.770880 | + | 0.636981i | \(0.219817\pi\) | ||||
−0.770880 | + | 0.636981i | \(0.780183\pi\) | |||||||
\(978\) | 7.68172 | + | 22.9124i | 0.245634 | + | 0.732658i | ||||
\(979\) | − | 14.9594i | − | 0.478104i | ||||||
\(980\) | 13.9255 | + | 0.741247i | 0.444833 | + | 0.0236783i | ||||
\(981\) | −12.8934 | + | 9.74023i | −0.411654 | + | 0.310982i | ||||
\(982\) | −6.00786 | −0.191719 | ||||||||
\(983\) | 44.6488 | 1.42407 | 0.712037 | − | 0.702141i | \(-0.247773\pi\) | ||||
0.712037 | + | 0.702141i | \(0.247773\pi\) | |||||||
\(984\) | 2.77777 | + | 8.28529i | 0.0885520 | + | 0.264125i | ||||
\(985\) | − | 8.10294i | − | 0.258181i | ||||||
\(986\) | −1.45630 | −0.0463780 | ||||||||
\(987\) | 26.3173 | − | 8.05154i | 0.837690 | − | 0.256283i | ||||
\(988\) | 1.92412 | 0.0612143 | ||||||||
\(989\) | − | 1.65782i | − | 0.0527156i | ||||||
\(990\) | 7.20615 | − | 5.44384i | 0.229026 | − | 0.173016i | ||||
\(991\) | 49.9489 | 1.58668 | 0.793339 | − | 0.608780i | \(-0.208341\pi\) | ||||
0.793339 | + | 0.608780i | \(0.208341\pi\) | |||||||
\(992\) | 2.16237 | 0.0686553 | ||||||||
\(993\) | 32.9360 | − | 11.0423i | 1.04519 | − | 0.350416i | ||||
\(994\) | −36.2042 | − | 0.962885i | −1.14833 | − | 0.0305409i | ||||
\(995\) | − | 7.92339i | − | 0.251188i | ||||||
\(996\) | 1.16406 | − | 0.390269i | 0.0368847 | − | 0.0123662i | ||||
\(997\) | 32.2007i | 1.01981i | 0.860232 | + | 0.509903i | \(0.170319\pi\) | ||||
−0.860232 | + | 0.509903i | \(0.829681\pi\) | |||||||
\(998\) | 26.5494i | 0.840407i | ||||||||
\(999\) | 31.6080 | − | 46.1683i | 1.00003 | − | 1.46070i |
(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 | 966.2.f.c.461.15 | yes | 28 | |
3.2 | odd | 2 | inner | 966.2.f.c.461.14 | yes | 28 | |
7.6 | odd | 2 | inner | 966.2.f.c.461.28 | yes | 28 | |
21.20 | even | 2 | inner | 966.2.f.c.461.1 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.f.c.461.1 | ✓ | 28 | 21.20 | even | 2 | inner | |
966.2.f.c.461.14 | yes | 28 | 3.2 | odd | 2 | inner | |
966.2.f.c.461.15 | yes | 28 | 1.1 | even | 1 | trivial | |
966.2.f.c.461.28 | yes | 28 | 7.6 | odd | 2 | inner |