Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.10 | ||
Root | \(-0.537675i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.11 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.537675i | − | 0.268838i | −0.990925 | − | 0.134419i | \(-0.957083\pi\) | ||
0.990925 | − | 0.134419i | \(-0.0429168\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 3.71091 | 0.927726 | ||||||||
\(5\) | −0.803210 | −0.160642 | −0.0803210 | − | 0.996769i | \(-0.525595\pi\) | ||||
−0.0803210 | + | 0.996769i | \(0.525595\pi\) | |||||||
\(6\) | 0.931281i | 0.155214i | ||||||||
\(7\) | 5.11098 | 0.730140 | 0.365070 | − | 0.930980i | \(-0.381045\pi\) | ||||
0.365070 | + | 0.930980i | \(0.381045\pi\) | |||||||
\(8\) | − | 4.14596i | − | 0.518245i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0.431866i | 0.0431866i | ||||||||
\(11\) | 17.7567i | 1.61424i | 0.590386 | + | 0.807121i | \(0.298976\pi\) | ||||
−0.590386 | + | 0.807121i | \(0.701024\pi\) | |||||||
\(12\) | −6.42748 | −0.535623 | ||||||||
\(13\) | − | 24.6407i | − | 1.89544i | −0.319101 | − | 0.947721i | \(-0.603381\pi\) | ||
0.319101 | − | 0.947721i | \(-0.396619\pi\) | |||||||
\(14\) | − | 2.74805i | − | 0.196289i | ||||||
\(15\) | 1.39120 | 0.0927467 | ||||||||
\(16\) | 12.6144 | 0.788402 | ||||||||
\(17\) | 18.2784 | 1.07520 | 0.537600 | − | 0.843200i | \(-0.319331\pi\) | ||||
0.537600 | + | 0.843200i | \(0.319331\pi\) | |||||||
\(18\) | − | 1.61303i | − | 0.0896126i | ||||||
\(19\) | 28.5669 | 1.50352 | 0.751760 | − | 0.659437i | \(-0.229205\pi\) | ||||
0.751760 | + | 0.659437i | \(0.229205\pi\) | |||||||
\(20\) | −2.98064 | −0.149032 | ||||||||
\(21\) | −8.85247 | −0.421546 | ||||||||
\(22\) | 9.54732 | 0.433969 | ||||||||
\(23\) | − | 11.8668i | − | 0.515949i | −0.966152 | − | 0.257974i | \(-0.916945\pi\) | ||
0.966152 | − | 0.257974i | \(-0.0830550\pi\) | |||||||
\(24\) | 7.18102i | 0.299209i | ||||||||
\(25\) | −24.3549 | −0.974194 | ||||||||
\(26\) | −13.2487 | −0.509566 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 18.9664 | 0.677370 | ||||||||
\(29\) | 9.01975 | 0.311026 | 0.155513 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155513 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(30\) | − | 0.748014i | − | 0.0249338i | ||||||
\(31\) | − | 4.94288i | − | 0.159448i | −0.996817 | − | 0.0797239i | \(-0.974596\pi\) | ||
0.996817 | − | 0.0797239i | \(-0.0254039\pi\) | |||||||
\(32\) | − | 23.3663i | − | 0.730198i | ||||||
\(33\) | − | 30.7554i | − | 0.931983i | ||||||
\(34\) | − | 9.82784i | − | 0.289054i | ||||||
\(35\) | −4.10519 | −0.117291 | ||||||||
\(36\) | 11.1327 | 0.309242 | ||||||||
\(37\) | 39.7950i | 1.07554i | 0.843091 | + | 0.537770i | \(0.180733\pi\) | ||||
−0.843091 | + | 0.537770i | \(0.819267\pi\) | |||||||
\(38\) | − | 15.3597i | − | 0.404203i | ||||||
\(39\) | 42.6790i | 1.09433i | ||||||||
\(40\) | 3.33008i | 0.0832520i | ||||||||
\(41\) | −38.0744 | −0.928644 | −0.464322 | − | 0.885667i | \(-0.653702\pi\) | ||||
−0.464322 | + | 0.885667i | \(0.653702\pi\) | |||||||
\(42\) | 4.75976i | 0.113328i | ||||||||
\(43\) | − | 19.2551i | − | 0.447793i | −0.974613 | − | 0.223896i | \(-0.928122\pi\) | ||
0.974613 | − | 0.223896i | \(-0.0718778\pi\) | |||||||
\(44\) | 65.8933i | 1.49758i | ||||||||
\(45\) | −2.40963 | −0.0535473 | ||||||||
\(46\) | −6.38050 | −0.138706 | ||||||||
\(47\) | 65.6973i | 1.39782i | 0.715212 | + | 0.698908i | \(0.246330\pi\) | ||||
−0.715212 | + | 0.698908i | \(0.753670\pi\) | |||||||
\(48\) | −21.8488 | −0.455184 | ||||||||
\(49\) | −22.8779 | −0.466896 | ||||||||
\(50\) | 13.0950i | 0.261900i | ||||||||
\(51\) | −31.6591 | −0.620767 | ||||||||
\(52\) | − | 91.4394i | − | 1.75845i | ||||||
\(53\) | −40.1506 | −0.757559 | −0.378779 | − | 0.925487i | \(-0.623656\pi\) | ||||
−0.378779 | + | 0.925487i | \(0.623656\pi\) | |||||||
\(54\) | 2.79384i | 0.0517378i | ||||||||
\(55\) | − | 14.2623i | − | 0.259315i | ||||||
\(56\) | − | 21.1899i | − | 0.378392i | ||||||
\(57\) | −49.4793 | −0.868058 | ||||||||
\(58\) | − | 4.84970i | − | 0.0836155i | ||||||
\(59\) | −53.3901 | − | 25.1097i | −0.904917 | − | 0.425589i | ||||
\(60\) | 5.16261 | 0.0860435 | ||||||||
\(61\) | 110.438i | 1.81047i | 0.424916 | + | 0.905233i | \(0.360303\pi\) | ||||
−0.424916 | + | 0.905233i | \(0.639697\pi\) | |||||||
\(62\) | −2.65767 | −0.0428656 | ||||||||
\(63\) | 15.3329 | 0.243380 | ||||||||
\(64\) | 37.8943 | 0.592098 | ||||||||
\(65\) | 19.7917i | 0.304487i | ||||||||
\(66\) | −16.5364 | −0.250552 | ||||||||
\(67\) | − | 30.7950i | − | 0.459627i | −0.973235 | − | 0.229814i | \(-0.926188\pi\) | ||
0.973235 | − | 0.229814i | \(-0.0738117\pi\) | |||||||
\(68\) | 67.8294 | 0.997491 | ||||||||
\(69\) | 20.5539i | 0.297883i | ||||||||
\(70\) | 2.20726i | 0.0315323i | ||||||||
\(71\) | −95.0078 | −1.33814 | −0.669069 | − | 0.743200i | \(-0.733307\pi\) | ||||
−0.669069 | + | 0.743200i | \(0.733307\pi\) | |||||||
\(72\) | − | 12.4379i | − | 0.172748i | ||||||
\(73\) | 71.2671i | 0.976262i | 0.872770 | + | 0.488131i | \(0.162321\pi\) | ||||
−0.872770 | + | 0.488131i | \(0.837679\pi\) | |||||||
\(74\) | 21.3968 | 0.289146 | ||||||||
\(75\) | 42.1838 | 0.562451 | ||||||||
\(76\) | 106.009 | 1.39486 | ||||||||
\(77\) | 90.7539i | 1.17862i | ||||||||
\(78\) | 22.9474 | 0.294198 | ||||||||
\(79\) | −13.3580 | −0.169089 | −0.0845446 | − | 0.996420i | \(-0.526944\pi\) | ||||
−0.0845446 | + | 0.996420i | \(0.526944\pi\) | |||||||
\(80\) | −10.1320 | −0.126651 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 20.4717i | 0.249654i | ||||||||
\(83\) | − | 142.514i | − | 1.71704i | −0.512783 | − | 0.858518i | \(-0.671386\pi\) | ||
0.512783 | − | 0.858518i | \(-0.328614\pi\) | |||||||
\(84\) | −32.8507 | −0.391080 | ||||||||
\(85\) | −14.6814 | −0.172722 | ||||||||
\(86\) | −10.3530 | −0.120384 | ||||||||
\(87\) | −15.6227 | −0.179571 | ||||||||
\(88\) | 73.6185 | 0.836574 | ||||||||
\(89\) | − | 128.582i | − | 1.44474i | −0.691506 | − | 0.722371i | \(-0.743052\pi\) | ||
0.691506 | − | 0.722371i | \(-0.256948\pi\) | |||||||
\(90\) | 1.29560i | 0.0143955i | ||||||||
\(91\) | − | 125.938i | − | 1.38394i | ||||||
\(92\) | − | 44.0366i | − | 0.478659i | ||||||
\(93\) | 8.56133i | 0.0920573i | ||||||||
\(94\) | 35.3238 | 0.375786 | ||||||||
\(95\) | −22.9452 | −0.241528 | ||||||||
\(96\) | 40.4717i | 0.421580i | ||||||||
\(97\) | − | 97.1513i | − | 1.00156i | −0.865575 | − | 0.500780i | \(-0.833047\pi\) | ||
0.865575 | − | 0.500780i | \(-0.166953\pi\) | |||||||
\(98\) | 12.3009i | 0.125519i | ||||||||
\(99\) | 53.2700i | 0.538081i | ||||||||
\(100\) | −90.3786 | −0.903786 | ||||||||
\(101\) | 100.698i | 0.997012i | 0.866886 | + | 0.498506i | \(0.166118\pi\) | ||||
−0.866886 | + | 0.498506i | \(0.833882\pi\) | |||||||
\(102\) | 17.0223i | 0.166886i | ||||||||
\(103\) | 118.731i | 1.15273i | 0.817194 | + | 0.576363i | \(0.195528\pi\) | ||||
−0.817194 | + | 0.576363i | \(0.804472\pi\) | |||||||
\(104\) | −102.160 | −0.982304 | ||||||||
\(105\) | 7.11039 | 0.0677180 | ||||||||
\(106\) | 21.5880i | 0.203660i | ||||||||
\(107\) | 158.040 | 1.47701 | 0.738503 | − | 0.674250i | \(-0.235533\pi\) | ||||
0.738503 | + | 0.674250i | \(0.235533\pi\) | |||||||
\(108\) | −19.2824 | −0.178541 | ||||||||
\(109\) | − | 88.9732i | − | 0.816268i | −0.912922 | − | 0.408134i | \(-0.866180\pi\) | ||
0.912922 | − | 0.408134i | \(-0.133820\pi\) | |||||||
\(110\) | −7.66850 | −0.0697137 | ||||||||
\(111\) | − | 68.9270i | − | 0.620964i | ||||||
\(112\) | 64.4721 | 0.575644 | ||||||||
\(113\) | 158.257i | 1.40050i | 0.713895 | + | 0.700252i | \(0.246929\pi\) | ||||
−0.713895 | + | 0.700252i | \(0.753071\pi\) | |||||||
\(114\) | 26.6038i | 0.233367i | ||||||||
\(115\) | 9.53155i | 0.0828830i | ||||||||
\(116\) | 33.4714 | 0.288547 | ||||||||
\(117\) | − | 73.9222i | − | 0.631814i | ||||||
\(118\) | −13.5009 | + | 28.7065i | −0.114414 | + | 0.243276i | ||||
\(119\) | 93.4205 | 0.785046 | ||||||||
\(120\) | − | 5.76787i | − | 0.0480655i | ||||||
\(121\) | −194.299 | −1.60578 | ||||||||
\(122\) | 59.3800 | 0.486721 | ||||||||
\(123\) | 65.9468 | 0.536153 | ||||||||
\(124\) | − | 18.3426i | − | 0.147924i | ||||||
\(125\) | 39.6423 | 0.317138 | ||||||||
\(126\) | − | 8.24414i | − | 0.0654297i | ||||||
\(127\) | −101.633 | −0.800259 | −0.400129 | − | 0.916459i | \(-0.631035\pi\) | ||||
−0.400129 | + | 0.916459i | \(0.631035\pi\) | |||||||
\(128\) | − | 113.840i | − | 0.889376i | ||||||
\(129\) | 33.3508i | 0.258533i | ||||||||
\(130\) | 10.6415 | 0.0818577 | ||||||||
\(131\) | − | 86.1937i | − | 0.657967i | −0.944336 | − | 0.328984i | \(-0.893294\pi\) | ||
0.944336 | − | 0.328984i | \(-0.106706\pi\) | |||||||
\(132\) | − | 114.131i | − | 0.864625i | ||||||
\(133\) | 146.005 | 1.09778 | ||||||||
\(134\) | −16.5577 | −0.123565 | ||||||||
\(135\) | 4.17360 | 0.0309156 | ||||||||
\(136\) | − | 75.7816i | − | 0.557217i | ||||||
\(137\) | −174.098 | −1.27079 | −0.635395 | − | 0.772188i | \(-0.719163\pi\) | ||||
−0.635395 | + | 0.772188i | \(0.719163\pi\) | |||||||
\(138\) | 11.0513 | 0.0800822 | ||||||||
\(139\) | 166.414 | 1.19722 | 0.598612 | − | 0.801039i | \(-0.295719\pi\) | ||||
0.598612 | + | 0.801039i | \(0.295719\pi\) | |||||||
\(140\) | −15.2340 | −0.108814 | ||||||||
\(141\) | − | 113.791i | − | 0.807029i | ||||||
\(142\) | 51.0834i | 0.359742i | ||||||||
\(143\) | 437.537 | 3.05970 | ||||||||
\(144\) | 37.8433 | 0.262801 | ||||||||
\(145\) | −7.24475 | −0.0499638 | ||||||||
\(146\) | 38.3186 | 0.262456 | ||||||||
\(147\) | 39.6257 | 0.269563 | ||||||||
\(148\) | 147.676i | 0.997808i | ||||||||
\(149\) | 27.1832i | 0.182438i | 0.995831 | + | 0.0912188i | \(0.0290763\pi\) | ||||
−0.995831 | + | 0.0912188i | \(0.970924\pi\) | |||||||
\(150\) | − | 22.6812i | − | 0.151208i | ||||||
\(151\) | 94.4601i | 0.625563i | 0.949825 | + | 0.312782i | \(0.101261\pi\) | ||||
−0.949825 | + | 0.312782i | \(0.898739\pi\) | |||||||
\(152\) | − | 118.437i | − | 0.779192i | ||||||
\(153\) | 54.8352 | 0.358400 | ||||||||
\(154\) | 48.7961 | 0.316858 | ||||||||
\(155\) | 3.97017i | 0.0256140i | ||||||||
\(156\) | 158.378i | 1.01524i | ||||||||
\(157\) | 13.0757i | 0.0832847i | 0.999133 | + | 0.0416424i | \(0.0132590\pi\) | ||||
−0.999133 | + | 0.0416424i | \(0.986741\pi\) | |||||||
\(158\) | 7.18229i | 0.0454575i | ||||||||
\(159\) | 69.5429 | 0.437377 | ||||||||
\(160\) | 18.7681i | 0.117300i | ||||||||
\(161\) | − | 60.6511i | − | 0.376715i | ||||||
\(162\) | − | 4.83908i | − | 0.0298709i | ||||||
\(163\) | −31.6216 | −0.193998 | −0.0969989 | − | 0.995284i | \(-0.530924\pi\) | ||||
−0.0969989 | + | 0.995284i | \(0.530924\pi\) | |||||||
\(164\) | −141.290 | −0.861527 | ||||||||
\(165\) | 24.7031i | 0.149716i | ||||||||
\(166\) | −76.6263 | −0.461604 | ||||||||
\(167\) | 142.242 | 0.851751 | 0.425875 | − | 0.904782i | \(-0.359966\pi\) | ||||
0.425875 | + | 0.904782i | \(0.359966\pi\) | |||||||
\(168\) | 36.7020i | 0.218464i | ||||||||
\(169\) | −438.166 | −2.59270 | ||||||||
\(170\) | 7.89382i | 0.0464342i | ||||||||
\(171\) | 85.7006 | 0.501173 | ||||||||
\(172\) | − | 71.4538i | − | 0.415429i | ||||||
\(173\) | − | 202.500i | − | 1.17052i | −0.810845 | − | 0.585261i | \(-0.800992\pi\) | ||
0.810845 | − | 0.585261i | \(-0.199008\pi\) | |||||||
\(174\) | 8.39992i | 0.0482754i | ||||||||
\(175\) | −124.477 | −0.711298 | ||||||||
\(176\) | 223.990i | 1.27267i | ||||||||
\(177\) | 92.4743 | + | 43.4913i | 0.522454 | + | 0.245714i | ||||
\(178\) | −69.1354 | −0.388401 | ||||||||
\(179\) | − | 190.907i | − | 1.06652i | −0.845952 | − | 0.533259i | \(-0.820967\pi\) | ||
0.845952 | − | 0.533259i | \(-0.179033\pi\) | |||||||
\(180\) | −8.94191 | −0.0496773 | ||||||||
\(181\) | −123.971 | −0.684922 | −0.342461 | − | 0.939532i | \(-0.611261\pi\) | ||||
−0.342461 | + | 0.939532i | \(0.611261\pi\) | |||||||
\(182\) | −67.7139 | −0.372054 | ||||||||
\(183\) | − | 191.285i | − | 1.04527i | ||||||
\(184\) | −49.1994 | −0.267388 | ||||||||
\(185\) | − | 31.9637i | − | 0.172777i | ||||||
\(186\) | 4.60321 | 0.0247485 | ||||||||
\(187\) | 324.563i | 1.73563i | ||||||||
\(188\) | 243.797i | 1.29679i | ||||||||
\(189\) | −26.5574 | −0.140515 | ||||||||
\(190\) | 12.3371i | 0.0649319i | ||||||||
\(191\) | 125.336i | 0.656211i | 0.944641 | + | 0.328105i | \(0.106410\pi\) | ||||
−0.944641 | + | 0.328105i | \(0.893590\pi\) | |||||||
\(192\) | −65.6348 | −0.341848 | ||||||||
\(193\) | −108.008 | −0.559626 | −0.279813 | − | 0.960055i | \(-0.590272\pi\) | ||||
−0.279813 | + | 0.960055i | \(0.590272\pi\) | |||||||
\(194\) | −52.2358 | −0.269257 | ||||||||
\(195\) | − | 34.2802i | − | 0.175796i | ||||||
\(196\) | −84.8978 | −0.433152 | ||||||||
\(197\) | −132.587 | −0.673031 | −0.336516 | − | 0.941678i | \(-0.609248\pi\) | ||||
−0.336516 | + | 0.941678i | \(0.609248\pi\) | |||||||
\(198\) | 28.6420 | 0.144656 | ||||||||
\(199\) | −229.429 | −1.15291 | −0.576455 | − | 0.817129i | \(-0.695564\pi\) | ||||
−0.576455 | + | 0.817129i | \(0.695564\pi\) | |||||||
\(200\) | 100.974i | 0.504872i | ||||||||
\(201\) | 53.3386i | 0.265366i | ||||||||
\(202\) | 54.1429 | 0.268034 | ||||||||
\(203\) | 46.0997 | 0.227092 | ||||||||
\(204\) | −117.484 | −0.575902 | ||||||||
\(205\) | 30.5817 | 0.149179 | ||||||||
\(206\) | 63.8386 | 0.309896 | ||||||||
\(207\) | − | 35.6005i | − | 0.171983i | ||||||
\(208\) | − | 310.829i | − | 1.49437i | ||||||
\(209\) | 507.253i | 2.42705i | ||||||||
\(210\) | − | 3.82308i | − | 0.0182052i | ||||||
\(211\) | 270.274i | 1.28092i | 0.767991 | + | 0.640461i | \(0.221257\pi\) | ||||
−0.767991 | + | 0.640461i | \(0.778743\pi\) | |||||||
\(212\) | −148.995 | −0.702807 | ||||||||
\(213\) | 164.558 | 0.772575 | ||||||||
\(214\) | − | 84.9741i | − | 0.397075i | ||||||
\(215\) | 15.4659i | 0.0719343i | ||||||||
\(216\) | 21.5431i | 0.0997364i | ||||||||
\(217\) | − | 25.2630i | − | 0.116419i | ||||||
\(218\) | −47.8387 | −0.219444 | ||||||||
\(219\) | − | 123.438i | − | 0.563645i | ||||||
\(220\) | − | 52.9261i | − | 0.240573i | ||||||
\(221\) | − | 450.393i | − | 2.03798i | ||||||
\(222\) | −37.0603 | −0.166938 | ||||||||
\(223\) | 37.2371 | 0.166982 | 0.0834912 | − | 0.996509i | \(-0.473393\pi\) | ||||
0.0834912 | + | 0.996509i | \(0.473393\pi\) | |||||||
\(224\) | − | 119.425i | − | 0.533146i | ||||||
\(225\) | −73.0646 | −0.324731 | ||||||||
\(226\) | 85.0909 | 0.376508 | ||||||||
\(227\) | 157.805i | 0.695175i | 0.937648 | + | 0.347587i | \(0.112999\pi\) | ||||
−0.937648 | + | 0.347587i | \(0.887001\pi\) | |||||||
\(228\) | −183.613 | −0.805320 | ||||||||
\(229\) | 304.839i | 1.33118i | 0.746319 | + | 0.665588i | \(0.231819\pi\) | ||||
−0.746319 | + | 0.665588i | \(0.768181\pi\) | |||||||
\(230\) | 5.12488 | 0.0222821 | ||||||||
\(231\) | − | 157.190i | − | 0.680478i | ||||||
\(232\) | − | 37.3956i | − | 0.161188i | ||||||
\(233\) | − | 163.385i | − | 0.701221i | −0.936521 | − | 0.350611i | \(-0.885974\pi\) | ||
0.936521 | − | 0.350611i | \(-0.114026\pi\) | |||||||
\(234\) | −39.7461 | −0.169855 | ||||||||
\(235\) | − | 52.7687i | − | 0.224548i | ||||||
\(236\) | −198.126 | − | 93.1798i | −0.839515 | − | 0.394830i | ||||
\(237\) | 23.1368 | 0.0976237 | ||||||||
\(238\) | − | 50.2299i | − | 0.211050i | ||||||
\(239\) | −235.307 | −0.984549 | −0.492275 | − | 0.870440i | \(-0.663834\pi\) | ||||
−0.492275 | + | 0.870440i | \(0.663834\pi\) | |||||||
\(240\) | 17.5492 | 0.0731217 | ||||||||
\(241\) | 71.2458 | 0.295626 | 0.147813 | − | 0.989015i | \(-0.452777\pi\) | ||||
0.147813 | + | 0.989015i | \(0.452777\pi\) | |||||||
\(242\) | 104.470i | 0.431694i | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 409.826i | 1.67962i | ||||||||
\(245\) | 18.3758 | 0.0750031 | ||||||||
\(246\) | − | 35.4580i | − | 0.144138i | ||||||
\(247\) | − | 703.909i | − | 2.84983i | ||||||
\(248\) | −20.4930 | −0.0826331 | ||||||||
\(249\) | 246.842i | 0.991331i | ||||||||
\(250\) | − | 21.3147i | − | 0.0852587i | ||||||
\(251\) | 415.223 | 1.65427 | 0.827137 | − | 0.562001i | \(-0.189968\pi\) | ||||
0.827137 | + | 0.562001i | \(0.189968\pi\) | |||||||
\(252\) | 56.8991 | 0.225790 | ||||||||
\(253\) | 210.715 | 0.832866 | ||||||||
\(254\) | 54.6455i | 0.215140i | ||||||||
\(255\) | 25.4289 | 0.0997212 | ||||||||
\(256\) | 90.3680 | 0.353000 | ||||||||
\(257\) | 383.556 | 1.49244 | 0.746218 | − | 0.665701i | \(-0.231868\pi\) | ||||
0.746218 | + | 0.665701i | \(0.231868\pi\) | |||||||
\(258\) | 17.9319 | 0.0695035 | ||||||||
\(259\) | 203.391i | 0.785295i | ||||||||
\(260\) | 73.4450i | 0.282481i | ||||||||
\(261\) | 27.0593 | 0.103675 | ||||||||
\(262\) | −46.3442 | −0.176886 | ||||||||
\(263\) | −176.978 | −0.672921 | −0.336460 | − | 0.941698i | \(-0.609230\pi\) | ||||
−0.336460 | + | 0.941698i | \(0.609230\pi\) | |||||||
\(264\) | −127.511 | −0.482996 | ||||||||
\(265\) | 32.2494 | 0.121696 | ||||||||
\(266\) | − | 78.5031i | − | 0.295124i | ||||||
\(267\) | 222.711i | 0.834122i | ||||||||
\(268\) | − | 114.277i | − | 0.426408i | ||||||
\(269\) | 151.733i | 0.564063i | 0.959405 | + | 0.282031i | \(0.0910082\pi\) | ||||
−0.959405 | + | 0.282031i | \(0.908992\pi\) | |||||||
\(270\) | − | 2.24404i | − | 0.00831127i | ||||||
\(271\) | 316.355 | 1.16736 | 0.583680 | − | 0.811984i | \(-0.301612\pi\) | ||||
0.583680 | + | 0.811984i | \(0.301612\pi\) | |||||||
\(272\) | 230.572 | 0.847690 | ||||||||
\(273\) | 218.131i | 0.799016i | ||||||||
\(274\) | 93.6083i | 0.341636i | ||||||||
\(275\) | − | 432.461i | − | 1.57259i | ||||||
\(276\) | 76.2737i | 0.276354i | ||||||||
\(277\) | 122.572 | 0.442499 | 0.221250 | − | 0.975217i | \(-0.428986\pi\) | ||||
0.221250 | + | 0.975217i | \(0.428986\pi\) | |||||||
\(278\) | − | 89.4768i | − | 0.321859i | ||||||
\(279\) | − | 14.8287i | − | 0.0531493i | ||||||
\(280\) | 17.0200i | 0.0607856i | ||||||||
\(281\) | −188.817 | −0.671945 | −0.335973 | − | 0.941872i | \(-0.609065\pi\) | ||||
−0.335973 | + | 0.941872i | \(0.609065\pi\) | |||||||
\(282\) | −61.1827 | −0.216960 | ||||||||
\(283\) | − | 326.692i | − | 1.15439i | −0.816606 | − | 0.577195i | \(-0.804147\pi\) | ||
0.816606 | − | 0.577195i | \(-0.195853\pi\) | |||||||
\(284\) | −352.565 | −1.24143 | ||||||||
\(285\) | 39.7422 | 0.139446 | ||||||||
\(286\) | − | 235.253i | − | 0.822563i | ||||||
\(287\) | −194.597 | −0.678039 | ||||||||
\(288\) | − | 70.0990i | − | 0.243399i | ||||||
\(289\) | 45.0999 | 0.156055 | ||||||||
\(290\) | 3.89532i | 0.0134322i | ||||||||
\(291\) | 168.271i | 0.578251i | ||||||||
\(292\) | 264.466i | 0.905704i | ||||||||
\(293\) | 61.3922 | 0.209530 | 0.104765 | − | 0.994497i | \(-0.466591\pi\) | ||||
0.104765 | + | 0.994497i | \(0.466591\pi\) | |||||||
\(294\) | − | 21.3058i | − | 0.0724686i | ||||||
\(295\) | 42.8834 | + | 20.1684i | 0.145368 | + | 0.0683674i | ||||
\(296\) | 164.989 | 0.557394 | ||||||||
\(297\) | − | 92.2663i | − | 0.310661i | ||||||
\(298\) | 14.6157 | 0.0490461 | ||||||||
\(299\) | −292.407 | −0.977950 | ||||||||
\(300\) | 156.540 | 0.521801 | ||||||||
\(301\) | − | 98.4124i | − | 0.326951i | ||||||
\(302\) | 50.7888 | 0.168175 | ||||||||
\(303\) | − | 174.414i | − | 0.575625i | ||||||
\(304\) | 360.355 | 1.18538 | ||||||||
\(305\) | − | 88.7052i | − | 0.290837i | ||||||
\(306\) | − | 29.4835i | − | 0.0963514i | ||||||
\(307\) | −274.766 | −0.895003 | −0.447501 | − | 0.894283i | \(-0.647686\pi\) | ||||
−0.447501 | + | 0.894283i | \(0.647686\pi\) | |||||||
\(308\) | 336.779i | 1.09344i | ||||||||
\(309\) | − | 205.648i | − | 0.665526i | ||||||
\(310\) | 2.13466 | 0.00688601 | ||||||||
\(311\) | 488.255 | 1.56995 | 0.784976 | − | 0.619526i | \(-0.212675\pi\) | ||||
0.784976 | + | 0.619526i | \(0.212675\pi\) | |||||||
\(312\) | 176.946 | 0.567133 | ||||||||
\(313\) | − | 244.585i | − | 0.781421i | −0.920514 | − | 0.390711i | \(-0.872229\pi\) | ||
0.920514 | − | 0.390711i | \(-0.127771\pi\) | |||||||
\(314\) | 7.03048 | 0.0223901 | ||||||||
\(315\) | −12.3156 | −0.0390970 | ||||||||
\(316\) | −49.5704 | −0.156868 | ||||||||
\(317\) | −329.194 | −1.03847 | −0.519234 | − | 0.854632i | \(-0.673783\pi\) | ||||
−0.519234 | + | 0.854632i | \(0.673783\pi\) | |||||||
\(318\) | − | 37.3915i | − | 0.117583i | ||||||
\(319\) | 160.161i | 0.502071i | ||||||||
\(320\) | −30.4370 | −0.0951157 | ||||||||
\(321\) | −273.733 | −0.852750 | ||||||||
\(322\) | −32.6106 | −0.101275 | ||||||||
\(323\) | 522.157 | 1.61658 | ||||||||
\(324\) | 33.3981 | 0.103081 | ||||||||
\(325\) | 600.121i | 1.84653i | ||||||||
\(326\) | 17.0022i | 0.0521539i | ||||||||
\(327\) | 154.106i | 0.471272i | ||||||||
\(328\) | 157.855i | 0.481265i | ||||||||
\(329\) | 335.778i | 1.02060i | ||||||||
\(330\) | 13.2822 | 0.0402492 | ||||||||
\(331\) | 397.945 | 1.20225 | 0.601126 | − | 0.799154i | \(-0.294719\pi\) | ||||
0.601126 | + | 0.799154i | \(0.294719\pi\) | |||||||
\(332\) | − | 528.856i | − | 1.59294i | ||||||
\(333\) | 119.385i | 0.358514i | ||||||||
\(334\) | − | 76.4802i | − | 0.228983i | ||||||
\(335\) | 24.7349i | 0.0738354i | ||||||||
\(336\) | −111.669 | −0.332348 | ||||||||
\(337\) | − | 120.588i | − | 0.357829i | −0.983865 | − | 0.178915i | \(-0.942741\pi\) | ||
0.983865 | − | 0.178915i | \(-0.0572586\pi\) | |||||||
\(338\) | 235.591i | 0.697015i | ||||||||
\(339\) | − | 274.109i | − | 0.808582i | ||||||
\(340\) | −54.4812 | −0.160239 | ||||||||
\(341\) | 87.7692 | 0.257388 | ||||||||
\(342\) | − | 46.0791i | − | 0.134734i | ||||||
\(343\) | −367.366 | −1.07104 | ||||||||
\(344\) | −79.8309 | −0.232067 | ||||||||
\(345\) | − | 16.5091i | − | 0.0478525i | ||||||
\(346\) | −108.879 | −0.314680 | ||||||||
\(347\) | 170.990i | 0.492767i | 0.969172 | + | 0.246384i | \(0.0792423\pi\) | ||||
−0.969172 | + | 0.246384i | \(0.920758\pi\) | |||||||
\(348\) | −57.9742 | −0.166593 | ||||||||
\(349\) | − | 294.342i | − | 0.843388i | −0.906738 | − | 0.421694i | \(-0.861436\pi\) | ||
0.906738 | − | 0.421694i | \(-0.138564\pi\) | |||||||
\(350\) | 66.9283i | 0.191224i | ||||||||
\(351\) | 128.037i | 0.364778i | ||||||||
\(352\) | 414.908 | 1.17872 | ||||||||
\(353\) | − | 165.480i | − | 0.468783i | −0.972142 | − | 0.234391i | \(-0.924690\pi\) | ||
0.972142 | − | 0.234391i | \(-0.0753098\pi\) | |||||||
\(354\) | 23.3842 | − | 49.7212i | 0.0660571 | − | 0.140455i | ||||
\(355\) | 76.3112 | 0.214961 | ||||||||
\(356\) | − | 477.156i | − | 1.34032i | ||||||
\(357\) | −161.809 | −0.453247 | ||||||||
\(358\) | −102.646 | −0.286720 | ||||||||
\(359\) | 231.500 | 0.644845 | 0.322423 | − | 0.946596i | \(-0.395503\pi\) | ||||
0.322423 | + | 0.946596i | \(0.395503\pi\) | |||||||
\(360\) | 9.99024i | 0.0277507i | ||||||||
\(361\) | 455.067 | 1.26057 | ||||||||
\(362\) | 66.6561i | 0.184133i | ||||||||
\(363\) | 336.536 | 0.927097 | ||||||||
\(364\) | − | 467.345i | − | 1.28391i | ||||||
\(365\) | − | 57.2425i | − | 0.156829i | ||||||
\(366\) | −102.849 | −0.281009 | ||||||||
\(367\) | 23.9385i | 0.0652276i | 0.999468 | + | 0.0326138i | \(0.0103831\pi\) | ||||
−0.999468 | + | 0.0326138i | \(0.989617\pi\) | |||||||
\(368\) | − | 149.693i | − | 0.406775i | ||||||
\(369\) | −114.223 | −0.309548 | ||||||||
\(370\) | −17.1861 | −0.0464490 | ||||||||
\(371\) | −205.209 | −0.553124 | ||||||||
\(372\) | 31.7703i | 0.0854040i | ||||||||
\(373\) | 279.182 | 0.748476 | 0.374238 | − | 0.927333i | \(-0.377904\pi\) | ||||
0.374238 | + | 0.927333i | \(0.377904\pi\) | |||||||
\(374\) | 174.510 | 0.466604 | ||||||||
\(375\) | −68.6625 | −0.183100 | ||||||||
\(376\) | 272.379 | 0.724412 | ||||||||
\(377\) | − | 222.253i | − | 0.589531i | ||||||
\(378\) | 14.2793i | 0.0377758i | ||||||||
\(379\) | 89.9356 | 0.237297 | 0.118649 | − | 0.992936i | \(-0.462144\pi\) | ||||
0.118649 | + | 0.992936i | \(0.462144\pi\) | |||||||
\(380\) | −85.1475 | −0.224072 | ||||||||
\(381\) | 176.033 | 0.462030 | ||||||||
\(382\) | 67.3902 | 0.176414 | ||||||||
\(383\) | −143.916 | −0.375761 | −0.187880 | − | 0.982192i | \(-0.560162\pi\) | ||||
−0.187880 | + | 0.982192i | \(0.560162\pi\) | |||||||
\(384\) | 197.177i | 0.513481i | ||||||||
\(385\) | − | 72.8944i | − | 0.189336i | ||||||
\(386\) | 58.0731i | 0.150448i | ||||||||
\(387\) | − | 57.7653i | − | 0.149264i | ||||||
\(388\) | − | 360.519i | − | 0.929173i | ||||||
\(389\) | −182.927 | −0.470250 | −0.235125 | − | 0.971965i | \(-0.575550\pi\) | ||||
−0.235125 | + | 0.971965i | \(0.575550\pi\) | |||||||
\(390\) | −18.4316 | −0.0472605 | ||||||||
\(391\) | − | 216.907i | − | 0.554748i | ||||||
\(392\) | 94.8510i | 0.241967i | ||||||||
\(393\) | 149.292i | 0.379877i | ||||||||
\(394\) | 71.2888i | 0.180936i | ||||||||
\(395\) | 10.7293 | 0.0271628 | ||||||||
\(396\) | 197.680i | 0.499192i | ||||||||
\(397\) | − | 170.243i | − | 0.428823i | −0.976743 | − | 0.214412i | \(-0.931217\pi\) | ||
0.976743 | − | 0.214412i | \(-0.0687834\pi\) | |||||||
\(398\) | 123.358i | 0.309945i | ||||||||
\(399\) | −252.888 | −0.633803 | ||||||||
\(400\) | −307.223 | −0.768057 | ||||||||
\(401\) | 512.169i | 1.27723i | 0.769527 | + | 0.638614i | \(0.220492\pi\) | ||||
−0.769527 | + | 0.638614i | \(0.779508\pi\) | |||||||
\(402\) | 28.6788 | 0.0713404 | ||||||||
\(403\) | −121.796 | −0.302224 | ||||||||
\(404\) | 373.682i | 0.924954i | ||||||||
\(405\) | −7.22889 | −0.0178491 | ||||||||
\(406\) | − | 24.7867i | − | 0.0610510i | ||||||
\(407\) | −706.627 | −1.73618 | ||||||||
\(408\) | 131.258i | 0.321710i | ||||||||
\(409\) | 91.1229i | 0.222794i | 0.993776 | + | 0.111397i | \(0.0355326\pi\) | ||||
−0.993776 | + | 0.111397i | \(0.964467\pi\) | |||||||
\(410\) | − | 16.4430i | − | 0.0401050i | ||||||
\(411\) | 301.547 | 0.733690 | ||||||||
\(412\) | 440.598i | 1.06941i | ||||||||
\(413\) | −272.875 | − | 128.335i | −0.660715 | − | 0.310739i | ||||
\(414\) | −19.1415 | −0.0462355 | ||||||||
\(415\) | 114.469i | 0.275828i | ||||||||
\(416\) | −575.763 | −1.38405 | ||||||||
\(417\) | −288.238 | −0.691218 | ||||||||
\(418\) | 272.737 | 0.652481 | ||||||||
\(419\) | − | 90.7750i | − | 0.216647i | −0.994116 | − | 0.108323i | \(-0.965452\pi\) | ||
0.994116 | − | 0.108323i | \(-0.0345482\pi\) | |||||||
\(420\) | 26.3860 | 0.0628238 | ||||||||
\(421\) | − | 504.157i | − | 1.19752i | −0.800927 | − | 0.598762i | \(-0.795660\pi\) | ||
0.800927 | − | 0.598762i | \(-0.204340\pi\) | |||||||
\(422\) | 145.320 | 0.344360 | ||||||||
\(423\) | 197.092i | 0.465939i | ||||||||
\(424\) | 166.463i | 0.392601i | ||||||||
\(425\) | −445.168 | −1.04745 | ||||||||
\(426\) | − | 88.4790i | − | 0.207697i | ||||||
\(427\) | 564.448i | 1.32189i | ||||||||
\(428\) | 586.470 | 1.37026 | ||||||||
\(429\) | −757.837 | −1.76652 | ||||||||
\(430\) | 8.31562 | 0.0193387 | ||||||||
\(431\) | 335.908i | 0.779369i | 0.920948 | + | 0.389685i | \(0.127416\pi\) | ||||
−0.920948 | + | 0.389685i | \(0.872584\pi\) | |||||||
\(432\) | −65.5465 | −0.151728 | ||||||||
\(433\) | 165.667 | 0.382603 | 0.191302 | − | 0.981531i | \(-0.438729\pi\) | ||||
0.191302 | + | 0.981531i | \(0.438729\pi\) | |||||||
\(434\) | −13.5833 | −0.0312979 | ||||||||
\(435\) | 12.5483 | 0.0288466 | ||||||||
\(436\) | − | 330.171i | − | 0.757273i | ||||||
\(437\) | − | 338.998i | − | 0.775739i | ||||||
\(438\) | −66.3697 | −0.151529 | ||||||||
\(439\) | −159.958 | −0.364369 | −0.182185 | − | 0.983264i | \(-0.558317\pi\) | ||||
−0.182185 | + | 0.983264i | \(0.558317\pi\) | |||||||
\(440\) | −59.1311 | −0.134389 | ||||||||
\(441\) | −68.6337 | −0.155632 | ||||||||
\(442\) | −242.165 | −0.547885 | ||||||||
\(443\) | 65.1418i | 0.147047i | 0.997293 | + | 0.0735235i | \(0.0234244\pi\) | ||||
−0.997293 | + | 0.0735235i | \(0.976576\pi\) | |||||||
\(444\) | − | 255.781i | − | 0.576084i | ||||||
\(445\) | 103.278i | 0.232086i | ||||||||
\(446\) | − | 20.0215i | − | 0.0448912i | ||||||
\(447\) | − | 47.0827i | − | 0.105330i | ||||||
\(448\) | 193.677 | 0.432314 | ||||||||
\(449\) | −371.170 | −0.826658 | −0.413329 | − | 0.910582i | \(-0.635634\pi\) | ||||
−0.413329 | + | 0.910582i | \(0.635634\pi\) | |||||||
\(450\) | 39.2850i | 0.0873000i | ||||||||
\(451\) | − | 676.074i | − | 1.49906i | ||||||
\(452\) | 587.277i | 1.29929i | ||||||||
\(453\) | − | 163.610i | − | 0.361169i | ||||||
\(454\) | 84.8477 | 0.186889 | ||||||||
\(455\) | 101.155i | 0.222318i | ||||||||
\(456\) | 205.139i | 0.449867i | ||||||||
\(457\) | 169.801i | 0.371555i | 0.982592 | + | 0.185777i | \(0.0594803\pi\) | ||||
−0.982592 | + | 0.185777i | \(0.940520\pi\) | |||||||
\(458\) | 163.905 | 0.357870 | ||||||||
\(459\) | −94.9774 | −0.206922 | ||||||||
\(460\) | 35.3707i | 0.0768928i | ||||||||
\(461\) | −657.621 | −1.42651 | −0.713255 | − | 0.700905i | \(-0.752780\pi\) | ||||
−0.713255 | + | 0.700905i | \(0.752780\pi\) | |||||||
\(462\) | −84.5174 | −0.182938 | ||||||||
\(463\) | 729.046i | 1.57461i | 0.616562 | + | 0.787306i | \(0.288525\pi\) | ||||
−0.616562 | + | 0.787306i | \(0.711475\pi\) | |||||||
\(464\) | 113.779 | 0.245214 | ||||||||
\(465\) | − | 6.87654i | − | 0.0147883i | ||||||
\(466\) | −87.8478 | −0.188515 | ||||||||
\(467\) | − | 144.936i | − | 0.310355i | −0.987887 | − | 0.155178i | \(-0.950405\pi\) | ||
0.987887 | − | 0.155178i | \(-0.0495950\pi\) | |||||||
\(468\) | − | 274.318i | − | 0.586150i | ||||||
\(469\) | − | 157.393i | − | 0.335592i | ||||||
\(470\) | −28.3725 | −0.0603669 | ||||||||
\(471\) | − | 22.6478i | − | 0.0480844i | ||||||
\(472\) | −104.104 | + | 221.353i | −0.220559 | + | 0.468969i | ||||
\(473\) | 341.906 | 0.722846 | ||||||||
\(474\) | − | 12.4401i | − | 0.0262449i | ||||||
\(475\) | −695.742 | −1.46472 | ||||||||
\(476\) | 346.675 | 0.728308 | ||||||||
\(477\) | −120.452 | −0.252520 | ||||||||
\(478\) | 126.519i | 0.264684i | ||||||||
\(479\) | −73.1977 | −0.152814 | −0.0764068 | − | 0.997077i | \(-0.524345\pi\) | ||||
−0.0764068 | + | 0.997077i | \(0.524345\pi\) | |||||||
\(480\) | − | 32.5072i | − | 0.0677234i | ||||||
\(481\) | 980.578 | 2.03862 | ||||||||
\(482\) | − | 38.3071i | − | 0.0794753i | ||||||
\(483\) | 105.051i | 0.217496i | ||||||||
\(484\) | −721.026 | −1.48972 | ||||||||
\(485\) | 78.0328i | 0.160892i | ||||||||
\(486\) | 8.38153i | 0.0172459i | ||||||||
\(487\) | −54.7261 | −0.112374 | −0.0561869 | − | 0.998420i | \(-0.517894\pi\) | ||||
−0.0561869 | + | 0.998420i | \(0.517894\pi\) | |||||||
\(488\) | 457.873 | 0.938265 | ||||||||
\(489\) | 54.7703 | 0.112005 | ||||||||
\(490\) | − | 9.88020i | − | 0.0201637i | ||||||
\(491\) | 588.790 | 1.19916 | 0.599582 | − | 0.800313i | \(-0.295333\pi\) | ||||
0.599582 | + | 0.800313i | \(0.295333\pi\) | |||||||
\(492\) | 244.722 | 0.497403 | ||||||||
\(493\) | 164.867 | 0.334415 | ||||||||
\(494\) | −378.474 | −0.766143 | ||||||||
\(495\) | − | 42.7870i | − | 0.0864384i | ||||||
\(496\) | − | 62.3517i | − | 0.125709i | ||||||
\(497\) | −485.583 | −0.977028 | ||||||||
\(498\) | 132.721 | 0.266507 | ||||||||
\(499\) | 368.842 | 0.739162 | 0.369581 | − | 0.929199i | \(-0.379501\pi\) | ||||
0.369581 | + | 0.929199i | \(0.379501\pi\) | |||||||
\(500\) | 147.109 | 0.294218 | ||||||||
\(501\) | −246.371 | −0.491758 | ||||||||
\(502\) | − | 223.255i | − | 0.444731i | ||||||
\(503\) | 74.8276i | 0.148763i | 0.997230 | + | 0.0743813i | \(0.0236982\pi\) | ||||
−0.997230 | + | 0.0743813i | \(0.976302\pi\) | |||||||
\(504\) | − | 63.5698i | − | 0.126131i | ||||||
\(505\) | − | 80.8818i | − | 0.160162i | ||||||
\(506\) | − | 113.296i | − | 0.223906i | ||||||
\(507\) | 758.925 | 1.49689 | ||||||||
\(508\) | −377.150 | −0.742421 | ||||||||
\(509\) | 853.153i | 1.67614i | 0.545566 | + | 0.838068i | \(0.316315\pi\) | ||||
−0.545566 | + | 0.838068i | \(0.683685\pi\) | |||||||
\(510\) | − | 13.6725i | − | 0.0268088i | ||||||
\(511\) | 364.245i | 0.712808i | ||||||||
\(512\) | − | 503.949i | − | 0.984276i | ||||||
\(513\) | −148.438 | −0.289353 | ||||||||
\(514\) | − | 206.229i | − | 0.401223i | ||||||
\(515\) | − | 95.3657i | − | 0.185176i | ||||||
\(516\) | 123.762i | 0.239848i | ||||||||
\(517\) | −1166.57 | −2.25641 | ||||||||
\(518\) | 109.359 | 0.211117 | ||||||||
\(519\) | 350.741i | 0.675801i | ||||||||
\(520\) | 82.0556 | 0.157799 | ||||||||
\(521\) | 168.377 | 0.323180 | 0.161590 | − | 0.986858i | \(-0.448338\pi\) | ||||
0.161590 | + | 0.986858i | \(0.448338\pi\) | |||||||
\(522\) | − | 14.5491i | − | 0.0278718i | ||||||
\(523\) | −213.899 | −0.408986 | −0.204493 | − | 0.978868i | \(-0.565554\pi\) | ||||
−0.204493 | + | 0.978868i | \(0.565554\pi\) | |||||||
\(524\) | − | 319.857i | − | 0.610413i | ||||||
\(525\) | 215.601 | 0.410668 | ||||||||
\(526\) | 95.1568i | 0.180906i | ||||||||
\(527\) | − | 90.3480i | − | 0.171438i | ||||||
\(528\) | − | 387.963i | − | 0.734778i | ||||||
\(529\) | 388.179 | 0.733797 | ||||||||
\(530\) | − | 17.3397i | − | 0.0327164i | ||||||
\(531\) | −160.170 | − | 75.3292i | −0.301639 | − | 0.141863i | ||||
\(532\) | 541.810 | 1.01844 | ||||||||
\(533\) | 938.181i | 1.76019i | ||||||||
\(534\) | 119.746 | 0.224243 | ||||||||
\(535\) | −126.939 | −0.237269 | ||||||||
\(536\) | −127.675 | −0.238200 | ||||||||
\(537\) | 330.660i | 0.615754i | ||||||||
\(538\) | 81.5830 | 0.151641 | ||||||||
\(539\) | − | 406.235i | − | 0.753684i | ||||||
\(540\) | 15.4878 | 0.0286812 | ||||||||
\(541\) | 236.317i | 0.436816i | 0.975858 | + | 0.218408i | \(0.0700863\pi\) | ||||
−0.975858 | + | 0.218408i | \(0.929914\pi\) | |||||||
\(542\) | − | 170.096i | − | 0.313831i | ||||||
\(543\) | 214.724 | 0.395440 | ||||||||
\(544\) | − | 427.099i | − | 0.785109i | ||||||
\(545\) | 71.4641i | 0.131127i | ||||||||
\(546\) | 117.284 | 0.214806 | ||||||||
\(547\) | −466.310 | −0.852487 | −0.426243 | − | 0.904609i | \(-0.640163\pi\) | ||||
−0.426243 | + | 0.904609i | \(0.640163\pi\) | |||||||
\(548\) | −646.062 | −1.17894 | ||||||||
\(549\) | 331.315i | 0.603488i | ||||||||
\(550\) | −232.524 | −0.422770 | ||||||||
\(551\) | 257.666 | 0.467634 | ||||||||
\(552\) | 85.2159 | 0.154377 | ||||||||
\(553\) | −68.2726 | −0.123459 | ||||||||
\(554\) | − | 65.9041i | − | 0.118960i | ||||||
\(555\) | 55.3628i | 0.0997528i | ||||||||
\(556\) | 617.547 | 1.11070 | ||||||||
\(557\) | 1045.31 | 1.87668 | 0.938339 | − | 0.345717i | \(-0.112364\pi\) | ||||
0.938339 | + | 0.345717i | \(0.112364\pi\) | |||||||
\(558\) | −7.97300 | −0.0142885 | ||||||||
\(559\) | −474.460 | −0.848765 | ||||||||
\(560\) | −51.7846 | −0.0924725 | ||||||||
\(561\) | − | 562.160i | − | 1.00207i | ||||||
\(562\) | 101.522i | 0.180644i | ||||||||
\(563\) | − | 1039.19i | − | 1.84581i | −0.385026 | − | 0.922906i | \(-0.625808\pi\) | ||
0.385026 | − | 0.922906i | \(-0.374192\pi\) | |||||||
\(564\) | − | 422.268i | − | 0.748702i | ||||||
\(565\) | − | 127.114i | − | 0.224980i | ||||||
\(566\) | −175.654 | −0.310343 | ||||||||
\(567\) | 45.9988 | 0.0811266 | ||||||||
\(568\) | 393.899i | 0.693484i | ||||||||
\(569\) | − | 206.318i | − | 0.362597i | −0.983428 | − | 0.181298i | \(-0.941970\pi\) | ||
0.983428 | − | 0.181298i | \(-0.0580300\pi\) | |||||||
\(570\) | − | 21.3684i | − | 0.0374885i | ||||||
\(571\) | − | 144.089i | − | 0.252345i | −0.992008 | − | 0.126173i | \(-0.959731\pi\) | ||
0.992008 | − | 0.126173i | \(-0.0402693\pi\) | |||||||
\(572\) | 1623.66 | 2.83857 | ||||||||
\(573\) | − | 217.089i | − | 0.378863i | ||||||
\(574\) | 104.630i | 0.182283i | ||||||||
\(575\) | 289.015i | 0.502634i | ||||||||
\(576\) | 113.683 | 0.197366 | ||||||||
\(577\) | −596.647 | −1.03405 | −0.517025 | − | 0.855970i | \(-0.672961\pi\) | ||||
−0.517025 | + | 0.855970i | \(0.672961\pi\) | |||||||
\(578\) | − | 24.2491i | − | 0.0419535i | ||||||
\(579\) | 187.075 | 0.323100 | ||||||||
\(580\) | −26.8846 | −0.0463527 | ||||||||
\(581\) | − | 728.386i | − | 1.25368i | ||||||
\(582\) | 90.4751 | 0.155456 | ||||||||
\(583\) | − | 712.941i | − | 1.22288i | ||||||
\(584\) | 295.471 | 0.505943 | ||||||||
\(585\) | 59.3750i | 0.101496i | ||||||||
\(586\) | − | 33.0091i | − | 0.0563295i | ||||||
\(587\) | 177.665i | 0.302666i | 0.988483 | + | 0.151333i | \(0.0483566\pi\) | ||||
−0.988483 | + | 0.151333i | \(0.951643\pi\) | |||||||
\(588\) | 147.047 | 0.250080 | ||||||||
\(589\) | − | 141.203i | − | 0.239733i | ||||||
\(590\) | 10.8440 | − | 23.0574i | 0.0183797 | − | 0.0390803i | ||||
\(591\) | 229.648 | 0.388575 | ||||||||
\(592\) | 501.992i | 0.847959i | ||||||||
\(593\) | −297.828 | −0.502240 | −0.251120 | − | 0.967956i | \(-0.580799\pi\) | ||||
−0.251120 | + | 0.967956i | \(0.580799\pi\) | |||||||
\(594\) | −49.6093 | −0.0835174 | ||||||||
\(595\) | −75.0362 | −0.126111 | ||||||||
\(596\) | 100.874i | 0.169252i | ||||||||
\(597\) | 397.383 | 0.665632 | ||||||||
\(598\) | 157.220i | 0.262910i | ||||||||
\(599\) | −665.978 | −1.11182 | −0.555908 | − | 0.831244i | \(-0.687629\pi\) | ||||
−0.555908 | + | 0.831244i | \(0.687629\pi\) | |||||||
\(600\) | − | 174.893i | − | 0.291488i | ||||||
\(601\) | 892.749i | 1.48544i | 0.669603 | + | 0.742720i | \(0.266464\pi\) | ||||
−0.669603 | + | 0.742720i | \(0.733536\pi\) | |||||||
\(602\) | −52.9139 | −0.0878968 | ||||||||
\(603\) | − | 92.3851i | − | 0.153209i | ||||||
\(604\) | 350.532i | 0.580351i | ||||||||
\(605\) | 156.063 | 0.257955 | ||||||||
\(606\) | −93.7783 | −0.154750 | ||||||||
\(607\) | −507.085 | −0.835395 | −0.417697 | − | 0.908586i | \(-0.637163\pi\) | ||||
−0.417697 | + | 0.908586i | \(0.637163\pi\) | |||||||
\(608\) | − | 667.503i | − | 1.09787i | ||||||
\(609\) | −79.8471 | −0.131112 | ||||||||
\(610\) | −47.6946 | −0.0781879 | ||||||||
\(611\) | 1618.83 | 2.64948 | ||||||||
\(612\) | 203.488 | 0.332497 | ||||||||
\(613\) | 16.5526i | 0.0270026i | 0.999909 | + | 0.0135013i | \(0.00429774\pi\) | ||||
−0.999909 | + | 0.0135013i | \(0.995702\pi\) | |||||||
\(614\) | 147.735i | 0.240610i | ||||||||
\(615\) | −52.9691 | −0.0861286 | ||||||||
\(616\) | 376.262 | 0.610816 | ||||||||
\(617\) | −357.976 | −0.580188 | −0.290094 | − | 0.956998i | \(-0.593687\pi\) | ||||
−0.290094 | + | 0.956998i | \(0.593687\pi\) | |||||||
\(618\) | −110.572 | −0.178919 | ||||||||
\(619\) | −484.085 | −0.782044 | −0.391022 | − | 0.920381i | \(-0.627878\pi\) | ||||
−0.391022 | + | 0.920381i | \(0.627878\pi\) | |||||||
\(620\) | 14.7329i | 0.0237628i | ||||||||
\(621\) | 61.6618i | 0.0992944i | ||||||||
\(622\) | − | 262.523i | − | 0.422062i | ||||||
\(623\) | − | 657.180i | − | 1.05486i | ||||||
\(624\) | 538.372i | 0.862775i | ||||||||
\(625\) | 577.030 | 0.923248 | ||||||||
\(626\) | −131.507 | −0.210076 | ||||||||
\(627\) | − | 878.587i | − | 1.40126i | ||||||
\(628\) | 48.5227i | 0.0772654i | ||||||||
\(629\) | 727.389i | 1.15642i | ||||||||
\(630\) | 6.62177i | 0.0105108i | ||||||||
\(631\) | 517.329 | 0.819856 | 0.409928 | − | 0.912118i | \(-0.365554\pi\) | ||||
0.409928 | + | 0.912118i | \(0.365554\pi\) | |||||||
\(632\) | 55.3820i | 0.0876297i | ||||||||
\(633\) | − | 468.129i | − | 0.739540i | ||||||
\(634\) | 177.000i | 0.279179i | ||||||||
\(635\) | 81.6325 | 0.128555 | ||||||||
\(636\) | 258.067 | 0.405766 | ||||||||
\(637\) | 563.729i | 0.884974i | ||||||||
\(638\) | 86.1145 | 0.134976 | ||||||||
\(639\) | −285.023 | −0.446046 | ||||||||
\(640\) | 91.4375i | 0.142871i | ||||||||
\(641\) | −412.313 | −0.643234 | −0.321617 | − | 0.946870i | \(-0.604226\pi\) | ||||
−0.321617 | + | 0.946870i | \(0.604226\pi\) | |||||||
\(642\) | 147.179i | 0.229251i | ||||||||
\(643\) | 77.3753 | 0.120335 | 0.0601674 | − | 0.998188i | \(-0.480837\pi\) | ||||
0.0601674 | + | 0.998188i | \(0.480837\pi\) | |||||||
\(644\) | − | 225.070i | − | 0.349488i | ||||||
\(645\) | − | 26.7877i | − | 0.0415313i | ||||||
\(646\) | − | 280.751i | − | 0.434599i | ||||||
\(647\) | 1058.14 | 1.63546 | 0.817728 | − | 0.575605i | \(-0.195233\pi\) | ||||
0.817728 | + | 0.575605i | \(0.195233\pi\) | |||||||
\(648\) | − | 37.3137i | − | 0.0575828i | ||||||
\(649\) | 445.865 | − | 948.030i | 0.687003 | − | 1.46075i | ||||
\(650\) | 322.671 | 0.496416 | ||||||||
\(651\) | 43.7567i | 0.0672147i | ||||||||
\(652\) | −117.345 | −0.179977 | ||||||||
\(653\) | −399.017 | −0.611052 | −0.305526 | − | 0.952184i | \(-0.598832\pi\) | ||||
−0.305526 | + | 0.952184i | \(0.598832\pi\) | |||||||
\(654\) | 82.8591 | 0.126696 | ||||||||
\(655\) | 69.2316i | 0.105697i | ||||||||
\(656\) | −480.287 | −0.732145 | ||||||||
\(657\) | 213.801i | 0.325421i | ||||||||
\(658\) | 180.539 | 0.274376 | ||||||||
\(659\) | 309.391i | 0.469486i | 0.972057 | + | 0.234743i | \(0.0754249\pi\) | ||||
−0.972057 | + | 0.234743i | \(0.924575\pi\) | |||||||
\(660\) | 91.6708i | 0.138895i | ||||||||
\(661\) | 646.215 | 0.977633 | 0.488816 | − | 0.872387i | \(-0.337429\pi\) | ||||
0.488816 | + | 0.872387i | \(0.337429\pi\) | |||||||
\(662\) | − | 213.965i | − | 0.323210i | ||||||
\(663\) | 780.104i | 1.17663i | ||||||||
\(664\) | −590.858 | −0.889846 | ||||||||
\(665\) | −117.272 | −0.176349 | ||||||||
\(666\) | 64.1904 | 0.0963820 | ||||||||
\(667\) | − | 107.036i | − | 0.160473i | ||||||
\(668\) | 527.848 | 0.790191 | ||||||||
\(669\) | −64.4965 | −0.0964073 | ||||||||
\(670\) | 13.2993 | 0.0198497 | ||||||||
\(671\) | −1961.02 | −2.92253 | ||||||||
\(672\) | 206.850i | 0.307812i | ||||||||
\(673\) | − | 940.573i | − | 1.39758i | −0.715326 | − | 0.698791i | \(-0.753722\pi\) | ||
0.715326 | − | 0.698791i | \(-0.246278\pi\) | |||||||
\(674\) | −64.8374 | −0.0961979 | ||||||||
\(675\) | 126.552 | 0.187484 | ||||||||
\(676\) | −1625.99 | −2.40531 | ||||||||
\(677\) | 1185.19 | 1.75065 | 0.875327 | − | 0.483531i | \(-0.160646\pi\) | ||||
0.875327 | + | 0.483531i | \(0.160646\pi\) | |||||||
\(678\) | −147.382 | −0.217377 | ||||||||
\(679\) | − | 496.538i | − | 0.731278i | ||||||
\(680\) | 60.8685i | 0.0895125i | ||||||||
\(681\) | − | 273.326i | − | 0.401359i | ||||||
\(682\) | − | 47.1913i | − | 0.0691955i | ||||||
\(683\) | − | 126.072i | − | 0.184586i | −0.995732 | − | 0.0922928i | \(-0.970580\pi\) | ||
0.995732 | − | 0.0922928i | \(-0.0294196\pi\) | |||||||
\(684\) | 318.027 | 0.464952 | ||||||||
\(685\) | 139.837 | 0.204142 | ||||||||
\(686\) | 197.524i | 0.287936i | ||||||||
\(687\) | − | 527.997i | − | 0.768555i | ||||||
\(688\) | − | 242.892i | − | 0.353041i | ||||||
\(689\) | 989.341i | 1.43591i | ||||||||
\(690\) | −8.87655 | −0.0128646 | ||||||||
\(691\) | 1168.97i | 1.69171i | 0.533410 | + | 0.845857i | \(0.320910\pi\) | ||||
−0.533410 | + | 0.845857i | \(0.679090\pi\) | |||||||
\(692\) | − | 751.459i | − | 1.08592i | ||||||
\(693\) | 272.262i | 0.392874i | ||||||||
\(694\) | 91.9372 | 0.132474 | ||||||||
\(695\) | −133.665 | −0.192324 | ||||||||
\(696\) | 64.7710i | 0.0930618i | ||||||||
\(697\) | −695.939 | −0.998478 | ||||||||
\(698\) | −158.261 | −0.226734 | ||||||||
\(699\) | 282.990i | 0.404850i | ||||||||
\(700\) | −461.923 | −0.659890 | ||||||||
\(701\) | − | 747.168i | − | 1.06586i | −0.846159 | − | 0.532930i | \(-0.821091\pi\) | ||
0.846159 | − | 0.532930i | \(-0.178909\pi\) | |||||||
\(702\) | 68.8423 | 0.0980660 | ||||||||
\(703\) | 1136.82i | 1.61710i | ||||||||
\(704\) | 672.876i | 0.955789i | ||||||||
\(705\) | 91.3981i | 0.129643i | ||||||||
\(706\) | −88.9747 | −0.126027 | ||||||||
\(707\) | 514.666i | 0.727958i | ||||||||
\(708\) | 343.164 | + | 161.392i | 0.484694 | + | 0.227955i | ||||
\(709\) | 1148.98 | 1.62056 | 0.810282 | − | 0.586040i | \(-0.199314\pi\) | ||||
0.810282 | + | 0.586040i | \(0.199314\pi\) | |||||||
\(710\) | − | 41.0307i | − | 0.0577897i | ||||||
\(711\) | −40.0741 | −0.0563630 | ||||||||
\(712\) | −533.096 | −0.748731 | ||||||||
\(713\) | −58.6563 | −0.0822669 | ||||||||
\(714\) | 87.0007i | 0.121850i | ||||||||
\(715\) | −351.434 | −0.491516 | ||||||||
\(716\) | − | 708.437i | − | 0.989437i | ||||||
\(717\) | 407.564 | 0.568430 | ||||||||
\(718\) | − | 124.472i | − | 0.173359i | ||||||
\(719\) | − | 392.721i | − | 0.546204i | −0.961985 | − | 0.273102i | \(-0.911950\pi\) | ||
0.961985 | − | 0.273102i | \(-0.0880496\pi\) | |||||||
\(720\) | −30.3961 | −0.0422168 | ||||||||
\(721\) | 606.830i | 0.841650i | ||||||||
\(722\) | − | 244.678i | − | 0.338889i | ||||||
\(723\) | −123.401 | −0.170680 | ||||||||
\(724\) | −460.044 | −0.635421 | ||||||||
\(725\) | −219.675 | −0.303000 | ||||||||
\(726\) | − | 180.947i | − | 0.249239i | ||||||
\(727\) | 1029.86 | 1.41658 | 0.708292 | − | 0.705920i | \(-0.249466\pi\) | ||||
0.708292 | + | 0.705920i | \(0.249466\pi\) | |||||||
\(728\) | −522.135 | −0.717219 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −30.7779 | −0.0421615 | ||||||||
\(731\) | − | 351.952i | − | 0.481467i | ||||||
\(732\) | − | 709.840i | − | 0.969727i | ||||||
\(733\) | −679.097 | −0.926462 | −0.463231 | − | 0.886238i | \(-0.653310\pi\) | ||||
−0.463231 | + | 0.886238i | \(0.653310\pi\) | |||||||
\(734\) | 12.8712 | 0.0175356 | ||||||||
\(735\) | −31.8278 | −0.0433031 | ||||||||
\(736\) | −277.284 | −0.376745 | ||||||||
\(737\) | 546.817 | 0.741950 | ||||||||
\(738\) | 61.4150i | 0.0832181i | ||||||||
\(739\) | 297.353i | 0.402372i | 0.979553 | + | 0.201186i | \(0.0644795\pi\) | ||||
−0.979553 | + | 0.201186i | \(0.935521\pi\) | |||||||
\(740\) | − | 118.614i | − | 0.160290i | ||||||
\(741\) | 1219.21i | 1.64535i | ||||||||
\(742\) | 110.336i | 0.148701i | ||||||||
\(743\) | 592.272 | 0.797136 | 0.398568 | − | 0.917139i | \(-0.369507\pi\) | ||||
0.398568 | + | 0.917139i | \(0.369507\pi\) | |||||||
\(744\) | 35.4950 | 0.0477083 | ||||||||
\(745\) | − | 21.8338i | − | 0.0293071i | ||||||
\(746\) | − | 150.109i | − | 0.201219i | ||||||
\(747\) | − | 427.542i | − | 0.572345i | ||||||
\(748\) | 1204.42i | 1.61019i | ||||||||
\(749\) | 807.737 | 1.07842 | ||||||||
\(750\) | 36.9181i | 0.0492242i | ||||||||
\(751\) | 546.455i | 0.727637i | 0.931470 | + | 0.363818i | \(0.118527\pi\) | ||||
−0.931470 | + | 0.363818i | \(0.881473\pi\) | |||||||
\(752\) | 828.735i | 1.10204i | ||||||||
\(753\) | −719.187 | −0.955095 | ||||||||
\(754\) | −119.500 | −0.158488 | ||||||||
\(755\) | − | 75.8712i | − | 0.100492i | ||||||
\(756\) | −98.5521 | −0.130360 | ||||||||
\(757\) | −392.628 | −0.518663 | −0.259331 | − | 0.965788i | \(-0.583502\pi\) | ||||
−0.259331 | + | 0.965788i | \(0.583502\pi\) | |||||||
\(758\) | − | 48.3561i | − | 0.0637944i | ||||||
\(759\) | −364.969 | −0.480856 | ||||||||
\(760\) | 95.1300i | 0.125171i | ||||||||
\(761\) | −526.584 | −0.691963 | −0.345982 | − | 0.938241i | \(-0.612454\pi\) | ||||
−0.345982 | + | 0.938241i | \(0.612454\pi\) | |||||||
\(762\) | − | 94.6488i | − | 0.124211i | ||||||
\(763\) | − | 454.740i | − | 0.595989i | ||||||
\(764\) | 465.111i | 0.608784i | ||||||||
\(765\) | −44.0442 | −0.0575741 | ||||||||
\(766\) | 77.3803i | 0.101019i | ||||||||
\(767\) | −618.722 | + | 1315.57i | −0.806678 | + | 1.71522i | ||||
\(768\) | −156.522 | −0.203805 | ||||||||
\(769\) | − | 1298.20i | − | 1.68817i | −0.536212 | − | 0.844084i | \(-0.680145\pi\) | ||
0.536212 | − | 0.844084i | \(-0.319855\pi\) | |||||||
\(770\) | −39.1935 | −0.0509007 | ||||||||
\(771\) | −664.339 | −0.861659 | ||||||||
\(772\) | −400.807 | −0.519179 | ||||||||
\(773\) | − | 1105.65i | − | 1.43034i | −0.698951 | − | 0.715170i | \(-0.746349\pi\) | ||
0.698951 | − | 0.715170i | \(-0.253651\pi\) | |||||||
\(774\) | −31.0590 | −0.0401279 | ||||||||
\(775\) | 120.383i | 0.155333i | ||||||||
\(776\) | −402.786 | −0.519054 | ||||||||
\(777\) | − | 352.284i | − | 0.453390i | ||||||
\(778\) | 98.3554i | 0.126421i | ||||||||
\(779\) | −1087.67 | −1.39623 | ||||||||
\(780\) | − | 127.211i | − | 0.163090i | ||||||
\(781\) | − | 1687.02i | − | 2.16008i | ||||||
\(782\) | −116.625 | −0.149137 | ||||||||
\(783\) | −46.8680 | −0.0598570 | ||||||||
\(784\) | −288.592 | −0.368102 | ||||||||
\(785\) | − | 10.5025i | − | 0.0133790i | ||||||
\(786\) | 80.2705 | 0.102125 | ||||||||
\(787\) | 597.635 | 0.759384 | 0.379692 | − | 0.925113i | \(-0.376030\pi\) | ||||
0.379692 | + | 0.925113i | \(0.376030\pi\) | |||||||
\(788\) | −492.018 | −0.624389 | ||||||||
\(789\) | 306.535 | 0.388511 | ||||||||
\(790\) | − | 5.76889i | − | 0.00730239i | ||||||
\(791\) | 808.848i | 1.02256i | ||||||||
\(792\) | 220.855 | 0.278858 | ||||||||
\(793\) | 2721.28 | 3.43163 | ||||||||
\(794\) | −91.5354 | −0.115284 | ||||||||
\(795\) | −55.8576 | −0.0702611 | ||||||||
\(796\) | −851.389 | −1.06958 | ||||||||
\(797\) | 974.030i | 1.22212i | 0.791584 | + | 0.611060i | \(0.209257\pi\) | ||||
−0.791584 | + | 0.611060i | \(0.790743\pi\) | |||||||
\(798\) | 135.971i | 0.170390i | ||||||||
\(799\) | 1200.84i | 1.50293i | ||||||||
\(800\) | 569.083i | 0.711354i | ||||||||
\(801\) | − | 385.746i | − | 0.481580i | ||||||
\(802\) | 275.380 | 0.343367 | ||||||||
\(803\) | −1265.47 | −1.57592 | ||||||||
\(804\) | 197.934i | 0.246187i | ||||||||
\(805\) | 48.7155i | 0.0605162i | ||||||||
\(806\) | 65.4869i | 0.0812492i | ||||||||
\(807\) | − | 262.809i | − | 0.325662i | ||||||
\(808\) | 417.491 | 0.516697 | ||||||||
\(809\) | − | 971.146i | − | 1.20043i | −0.799840 | − | 0.600214i | \(-0.795082\pi\) | ||
0.799840 | − | 0.600214i | \(-0.204918\pi\) | |||||||
\(810\) | 3.88679i | 0.00479851i | ||||||||
\(811\) | − | 66.0398i | − | 0.0814301i | −0.999171 | − | 0.0407151i | \(-0.987036\pi\) | ||
0.999171 | − | 0.0407151i | \(-0.0129636\pi\) | |||||||
\(812\) | 171.072 | 0.210680 | ||||||||
\(813\) | −547.942 | −0.673976 | ||||||||
\(814\) | 379.936i | 0.466752i | ||||||||
\(815\) | 25.3988 | 0.0311642 | ||||||||
\(816\) | −399.362 | −0.489414 | ||||||||
\(817\) | − | 550.058i | − | 0.673266i | ||||||
\(818\) | 48.9945 | 0.0598955 | ||||||||
\(819\) | − | 377.815i | − | 0.461312i | ||||||
\(820\) | 113.486 | 0.138397 | ||||||||
\(821\) | − | 420.533i | − | 0.512220i | −0.966648 | − | 0.256110i | \(-0.917559\pi\) | ||
0.966648 | − | 0.256110i | \(-0.0824410\pi\) | |||||||
\(822\) | − | 162.134i | − | 0.197244i | ||||||
\(823\) | − | 490.370i | − | 0.595832i | −0.954592 | − | 0.297916i | \(-0.903708\pi\) | ||
0.954592 | − | 0.297916i | \(-0.0962916\pi\) | |||||||
\(824\) | 492.253 | 0.597395 | ||||||||
\(825\) | 749.044i | 0.907933i | ||||||||
\(826\) | −69.0027 | + | 146.718i | −0.0835384 | + | 0.177625i | ||||
\(827\) | 884.674 | 1.06974 | 0.534870 | − | 0.844935i | \(-0.320361\pi\) | ||||
0.534870 | + | 0.844935i | \(0.320361\pi\) | |||||||
\(828\) | − | 132.110i | − | 0.159553i | ||||||
\(829\) | 379.340 | 0.457587 | 0.228794 | − | 0.973475i | \(-0.426522\pi\) | ||||
0.228794 | + | 0.973475i | \(0.426522\pi\) | |||||||
\(830\) | 61.5470 | 0.0741530 | ||||||||
\(831\) | −212.301 | −0.255477 | ||||||||
\(832\) | − | 933.742i | − | 1.12229i | ||||||
\(833\) | −418.172 | −0.502007 | ||||||||
\(834\) | 154.978i | 0.185825i | ||||||||
\(835\) | −114.250 | −0.136827 | ||||||||
\(836\) | 1882.37i | 2.25163i | ||||||||
\(837\) | 25.6840i | 0.0306858i | ||||||||
\(838\) | −48.8075 | −0.0582428 | ||||||||
\(839\) | 59.4763i | 0.0708896i | 0.999372 | + | 0.0354448i | \(0.0112848\pi\) | ||||
−0.999372 | + | 0.0354448i | \(0.988715\pi\) | |||||||
\(840\) | − | 29.4794i | − | 0.0350946i | ||||||
\(841\) | −759.644 | −0.903263 | ||||||||
\(842\) | −271.073 | −0.321939 | ||||||||
\(843\) | 327.040 | 0.387948 | ||||||||
\(844\) | 1002.96i | 1.18834i | ||||||||
\(845\) | 351.939 | 0.416496 | ||||||||
\(846\) | 105.972 | 0.125262 | ||||||||
\(847\) | −993.059 | −1.17244 | ||||||||
\(848\) | −506.478 | −0.597261 | ||||||||
\(849\) | 565.848i | 0.666487i | ||||||||
\(850\) | 239.356i | 0.281595i | ||||||||
\(851\) | 472.240 | 0.554924 | ||||||||
\(852\) | 610.661 | 0.716738 | ||||||||
\(853\) | 18.7626 | 0.0219960 | 0.0109980 | − | 0.999940i | \(-0.496499\pi\) | ||||
0.0109980 | + | 0.999940i | \(0.496499\pi\) | |||||||
\(854\) | 303.490 | 0.355374 | ||||||||
\(855\) | −68.8356 | −0.0805095 | ||||||||
\(856\) | − | 655.227i | − | 0.765452i | ||||||
\(857\) | − | 1345.88i | − | 1.57046i | −0.619204 | − | 0.785230i | \(-0.712544\pi\) | ||
0.619204 | − | 0.785230i | \(-0.287456\pi\) | |||||||
\(858\) | 407.470i | 0.474907i | ||||||||
\(859\) | − | 1534.35i | − | 1.78620i | −0.449854 | − | 0.893102i | \(-0.648524\pi\) | ||
0.449854 | − | 0.893102i | \(-0.351476\pi\) | |||||||
\(860\) | 57.3924i | 0.0667354i | ||||||||
\(861\) | 337.052 | 0.391466 | ||||||||
\(862\) | 180.610 | 0.209524 | ||||||||
\(863\) | − | 301.276i | − | 0.349103i | −0.984648 | − | 0.174551i | \(-0.944152\pi\) | ||
0.984648 | − | 0.174551i | \(-0.0558475\pi\) | |||||||
\(864\) | 121.415i | 0.140527i | ||||||||
\(865\) | 162.650i | 0.188035i | ||||||||
\(866\) | − | 89.0751i | − | 0.102858i | ||||||
\(867\) | −78.1153 | −0.0900984 | ||||||||
\(868\) | − | 93.7485i | − | 0.108005i | ||||||
\(869\) | − | 237.194i | − | 0.272951i | ||||||
\(870\) | − | 6.74690i | − | 0.00775506i | ||||||
\(871\) | −758.812 | −0.871197 | ||||||||
\(872\) | −368.880 | −0.423027 | ||||||||
\(873\) | − | 291.454i | − | 0.333853i | ||||||
\(874\) | −182.271 | −0.208548 | ||||||||
\(875\) | 202.611 | 0.231555 | ||||||||
\(876\) | − | 458.068i | − | 0.522909i | ||||||
\(877\) | −88.0368 | −0.100384 | −0.0501920 | − | 0.998740i | \(-0.515983\pi\) | ||||
−0.0501920 | + | 0.998740i | \(0.515983\pi\) | |||||||
\(878\) | 86.0055i | 0.0979561i | ||||||||
\(879\) | −106.334 | −0.120972 | ||||||||
\(880\) | − | 179.911i | − | 0.204445i | ||||||
\(881\) | − | 282.027i | − | 0.320121i | −0.987107 | − | 0.160060i | \(-0.948831\pi\) | ||
0.987107 | − | 0.160060i | \(-0.0511689\pi\) | |||||||
\(882\) | 36.9027i | 0.0418398i | ||||||||
\(883\) | 1417.42 | 1.60524 | 0.802619 | − | 0.596493i | \(-0.203440\pi\) | ||||
0.802619 | + | 0.596493i | \(0.203440\pi\) | |||||||
\(884\) | − | 1671.37i | − | 1.89069i | ||||||
\(885\) | −74.2763 | − | 34.9327i | −0.0839280 | − | 0.0394719i | ||||
\(886\) | 35.0252 | 0.0395318 | ||||||||
\(887\) | − | 9.10283i | − | 0.0102625i | −0.999987 | − | 0.00513125i | \(-0.998367\pi\) | ||
0.999987 | − | 0.00513125i | \(-0.00163333\pi\) | |||||||
\(888\) | −285.769 | −0.321812 | ||||||||
\(889\) | −519.443 | −0.584301 | ||||||||
\(890\) | 55.5302 | 0.0623935 | ||||||||
\(891\) | 159.810i | 0.179360i | ||||||||
\(892\) | 138.183 | 0.154914 | ||||||||
\(893\) | 1876.77i | 2.10164i | ||||||||
\(894\) | −25.3152 | −0.0283168 | ||||||||
\(895\) | 153.338i | 0.171328i | ||||||||
\(896\) | − | 581.834i | − | 0.649369i | ||||||
\(897\) | 506.464 | 0.564620 | ||||||||
\(898\) | 199.569i | 0.222237i | ||||||||
\(899\) | − | 44.5836i | − | 0.0495924i | ||||||
\(900\) | −271.136 | −0.301262 | ||||||||
\(901\) | −733.889 | −0.814527 | ||||||||
\(902\) | −363.508 | −0.403003 | ||||||||
\(903\) | 170.455i | 0.188765i | ||||||||
\(904\) | 656.128 | 0.725805 | ||||||||
\(905\) | 99.5747 | 0.110027 | ||||||||
\(906\) | −87.9689 | −0.0970959 | ||||||||
\(907\) | −443.496 | −0.488970 | −0.244485 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244485 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(908\) | 585.598i | 0.644932i | ||||||||
\(909\) | 302.095i | 0.332337i | ||||||||
\(910\) | 54.3884 | 0.0597675 | ||||||||
\(911\) | 114.969 | 0.126201 | 0.0631003 | − | 0.998007i | \(-0.479901\pi\) | ||||
0.0631003 | + | 0.998007i | \(0.479901\pi\) | |||||||
\(912\) | −624.153 | −0.684379 | ||||||||
\(913\) | 2530.57 | 2.77171 | ||||||||
\(914\) | 91.2976 | 0.0998880 | ||||||||
\(915\) | 153.642i | 0.167915i | ||||||||
\(916\) | 1131.23i | 1.23497i | ||||||||
\(917\) | − | 440.534i | − | 0.480408i | ||||||
\(918\) | 51.0670i | 0.0556285i | ||||||||
\(919\) | − | 1066.64i | − | 1.16066i | −0.814383 | − | 0.580328i | \(-0.802924\pi\) | ||
0.814383 | − | 0.580328i | \(-0.197076\pi\) | |||||||
\(920\) | 39.5174 | 0.0429537 | ||||||||
\(921\) | 475.908 | 0.516730 | ||||||||
\(922\) | 353.586i | 0.383499i | ||||||||
\(923\) | 2341.06i | 2.53636i | ||||||||
\(924\) | − | 583.319i | − | 0.631297i | ||||||
\(925\) | − | 969.202i | − | 1.04779i | ||||||
\(926\) | 391.990 | 0.423315 | ||||||||
\(927\) | 356.192i | 0.384242i | ||||||||
\(928\) | − | 210.758i | − | 0.227110i | ||||||
\(929\) | − | 842.876i | − | 0.907294i | −0.891182 | − | 0.453647i | \(-0.850123\pi\) | ||
0.891182 | − | 0.453647i | \(-0.149877\pi\) | |||||||
\(930\) | −3.69735 | −0.00397564 | ||||||||
\(931\) | −653.551 | −0.701988 | ||||||||
\(932\) | − | 606.305i | − | 0.650541i | ||||||
\(933\) | −845.683 | −0.906412 | ||||||||
\(934\) | −77.9285 | −0.0834352 | ||||||||
\(935\) | − | 260.693i | − | 0.278816i | ||||||
\(936\) | −306.479 | −0.327435 | ||||||||
\(937\) | 1628.55i | 1.73805i | 0.494772 | + | 0.869023i | \(0.335252\pi\) | ||||
−0.494772 | + | 0.869023i | \(0.664748\pi\) | |||||||
\(938\) | −84.6262 | −0.0902198 | ||||||||
\(939\) | 423.633i | 0.451154i | ||||||||
\(940\) | − | 195.820i | − | 0.208319i | ||||||
\(941\) | − | 216.768i | − | 0.230359i | −0.993345 | − | 0.115179i | \(-0.963256\pi\) | ||
0.993345 | − | 0.115179i | \(-0.0367443\pi\) | |||||||
\(942\) | −12.1771 | −0.0129269 | ||||||||
\(943\) | 451.822i | 0.479132i | ||||||||
\(944\) | −673.486 | − | 316.745i | −0.713439 | − | 0.335535i | ||||
\(945\) | 21.3312 | 0.0225727 | ||||||||
\(946\) | − | 183.835i | − | 0.194328i | ||||||
\(947\) | 945.701 | 0.998629 | 0.499314 | − | 0.866421i | \(-0.333585\pi\) | ||||
0.499314 | + | 0.866421i | \(0.333585\pi\) | |||||||
\(948\) | 85.8585 | 0.0905680 | ||||||||
\(949\) | 1756.07 | 1.85045 | ||||||||
\(950\) | 374.083i | 0.393772i | ||||||||
\(951\) | 570.181 | 0.599560 | ||||||||
\(952\) | − | 387.318i | − | 0.406847i | ||||||
\(953\) | 106.234 | 0.111473 | 0.0557365 | − | 0.998446i | \(-0.482249\pi\) | ||||
0.0557365 | + | 0.998446i | \(0.482249\pi\) | |||||||
\(954\) | 64.7640i | 0.0678868i | ||||||||
\(955\) | − | 100.671i | − | 0.105415i | ||||||
\(956\) | −873.203 | −0.913392 | ||||||||
\(957\) | − | 277.406i | − | 0.289871i | ||||||
\(958\) | 39.3566i | 0.0410821i | ||||||||
\(959\) | −889.811 | −0.927853 | ||||||||
\(960\) | 52.7185 | 0.0549151 | ||||||||
\(961\) | 936.568 | 0.974576 | ||||||||
\(962\) | − | 527.233i | − | 0.548059i | ||||||
\(963\) | 474.119 | 0.492336 | ||||||||
\(964\) | 264.386 | 0.274260 | ||||||||
\(965\) | 86.7529 | 0.0898994 | ||||||||
\(966\) | 56.4832 | 0.0584712 | ||||||||
\(967\) | 898.516i | 0.929179i | 0.885526 | + | 0.464590i | \(0.153798\pi\) | ||||
−0.885526 | + | 0.464590i | \(0.846202\pi\) | |||||||
\(968\) | 805.557i | 0.832187i | ||||||||
\(969\) | −904.402 | −0.933336 | ||||||||
\(970\) | 41.9563 | 0.0432540 | ||||||||
\(971\) | 96.7025 | 0.0995907 | 0.0497953 | − | 0.998759i | \(-0.484143\pi\) | ||||
0.0497953 | + | 0.998759i | \(0.484143\pi\) | |||||||
\(972\) | −57.8473 | −0.0595137 | ||||||||
\(973\) | 850.539 | 0.874141 | ||||||||
\(974\) | 29.4249i | 0.0302103i | ||||||||
\(975\) | − | 1039.44i | − | 1.06609i | ||||||
\(976\) | 1393.12i | 1.42738i | ||||||||
\(977\) | 1230.50i | 1.25946i | 0.776812 | + | 0.629732i | \(0.216835\pi\) | ||||
−0.776812 | + | 0.629732i | \(0.783165\pi\) | |||||||
\(978\) | − | 29.4486i | − | 0.0301111i | ||||||
\(979\) | 2283.19 | 2.33216 | ||||||||
\(980\) | 68.1907 | 0.0695824 | ||||||||
\(981\) | − | 266.920i | − | 0.272089i | ||||||
\(982\) | − | 316.578i | − | 0.322381i | ||||||
\(983\) | − | 1521.39i | − | 1.54770i | −0.633368 | − | 0.773851i | \(-0.718328\pi\) | ||
0.633368 | − | 0.773851i | \(-0.281672\pi\) | |||||||
\(984\) | − | 273.413i | − | 0.277859i | ||||||
\(985\) | 106.495 | 0.108117 | ||||||||
\(986\) | − | 88.6447i | − | 0.0899034i | ||||||
\(987\) | − | 581.584i | − | 0.589244i | ||||||
\(988\) | − | 2612.14i | − | 2.64387i | ||||||
\(989\) | −228.497 | −0.231038 | ||||||||
\(990\) | −23.0055 | −0.0232379 | ||||||||
\(991\) | − | 1725.31i | − | 1.74098i | −0.492186 | − | 0.870490i | \(-0.663802\pi\) | ||
0.492186 | − | 0.870490i | \(-0.336198\pi\) | |||||||
\(992\) | −115.497 | −0.116428 | ||||||||
\(993\) | −689.261 | −0.694120 | ||||||||
\(994\) | 261.086i | 0.262662i | ||||||||
\(995\) | 184.280 | 0.185206 | ||||||||
\(996\) | 916.005i | 0.919684i | ||||||||
\(997\) | −1404.90 | −1.40912 | −0.704561 | − | 0.709643i | \(-0.748856\pi\) | ||||
−0.704561 | + | 0.709643i | \(0.748856\pi\) | |||||||
\(998\) | − | 198.317i | − | 0.198715i | ||||||
\(999\) | − | 206.781i | − | 0.206988i |
(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 | 177.3.c.a.58.10 | ✓ | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.11 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.11 | yes | 20 | |
177.176 | even | 2 | 531.3.c.c.235.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.10 | ✓ | 20 | 1.1 | even | 1 | trivial | |
177.3.c.a.58.11 | yes | 20 | 59.58 | odd | 2 | inner | |
531.3.c.c.235.10 | 20 | 177.176 | even | 2 | |||
531.3.c.c.235.11 | 20 | 3.2 | odd | 2 |