Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.2 | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.l.1084.23 |
$q$-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 \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.37097i | − | 1.67653i | −0.545265 | − | 0.838264i | \(-0.683571\pi\) | ||
0.545265 | − | 0.838264i | \(-0.316429\pi\) | |||||||
\(3\) | − | 2.28512i | − | 1.31931i | −0.751567 | − | 0.659656i | \(-0.770702\pi\) | ||
0.751567 | − | 0.659656i | \(-0.229298\pi\) | |||||||
\(4\) | −3.62149 | −1.81075 | ||||||||
\(5\) | 1.17411 | − | 1.90301i | 0.525079 | − | 0.851053i | ||||
\(6\) | −5.41794 | −2.21186 | ||||||||
\(7\) | − | 1.63677i | − | 0.618642i | −0.950958 | − | 0.309321i | \(-0.899898\pi\) | ||
0.950958 | − | 0.309321i | \(-0.100102\pi\) | |||||||
\(8\) | 3.84450i | 1.35924i | ||||||||
\(9\) | −2.22176 | −0.740585 | ||||||||
\(10\) | −4.51198 | − | 2.78378i | −1.42681 | − | 0.880310i | ||||
\(11\) | 2.72748 | 0.822365 | 0.411183 | − | 0.911553i | \(-0.365116\pi\) | ||||
0.411183 | + | 0.911553i | \(0.365116\pi\) | |||||||
\(12\) | 8.27553i | 2.38894i | ||||||||
\(13\) | − | 6.19933i | − | 1.71938i | −0.510812 | − | 0.859692i | \(-0.670655\pi\) | ||
0.510812 | − | 0.859692i | \(-0.329345\pi\) | |||||||
\(14\) | −3.88073 | −1.03717 | ||||||||
\(15\) | −4.34861 | − | 2.68298i | −1.12281 | − | 0.692743i | ||||
\(16\) | 1.87222 | 0.468054 | ||||||||
\(17\) | 3.12451i | 0.757804i | 0.925437 | + | 0.378902i | \(0.123698\pi\) | ||||
−0.925437 | + | 0.378902i | \(0.876302\pi\) | |||||||
\(18\) | 5.26771i | 1.24161i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −4.25204 | + | 6.89175i | −0.950785 | + | 1.54104i | ||||
\(21\) | −3.74021 | −0.816182 | ||||||||
\(22\) | − | 6.46676i | − | 1.37872i | ||||||
\(23\) | 7.29904i | 1.52195i | 0.648779 | + | 0.760977i | \(0.275280\pi\) | ||||
−0.648779 | + | 0.760977i | \(0.724720\pi\) | |||||||
\(24\) | 8.78514 | 1.79326 | ||||||||
\(25\) | −2.24292 | − | 4.46870i | −0.448584 | − | 0.893741i | ||||
\(26\) | −14.6984 | −2.88260 | ||||||||
\(27\) | − | 1.77838i | − | 0.342249i | ||||||
\(28\) | 5.92756i | 1.12020i | ||||||||
\(29\) | 2.22572 | 0.413306 | 0.206653 | − | 0.978414i | \(-0.433743\pi\) | ||||
0.206653 | + | 0.978414i | \(0.433743\pi\) | |||||||
\(30\) | −6.36127 | + | 10.3104i | −1.16140 | + | 1.88241i | ||||
\(31\) | −4.42666 | −0.795051 | −0.397526 | − | 0.917591i | \(-0.630131\pi\) | ||||
−0.397526 | + | 0.917591i | \(0.630131\pi\) | |||||||
\(32\) | 3.25005i | 0.574532i | ||||||||
\(33\) | − | 6.23260i | − | 1.08496i | ||||||
\(34\) | 7.40811 | 1.27048 | ||||||||
\(35\) | −3.11480 | − | 1.92175i | −0.526497 | − | 0.324836i | ||||
\(36\) | 8.04607 | 1.34101 | ||||||||
\(37\) | − | 2.04016i | − | 0.335400i | −0.985838 | − | 0.167700i | \(-0.946366\pi\) | ||
0.985838 | − | 0.167700i | \(-0.0536339\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.1662 | −2.26841 | ||||||||
\(40\) | 7.31614 | + | 4.51388i | 1.15678 | + | 0.713707i | ||||
\(41\) | −3.92482 | −0.612954 | −0.306477 | − | 0.951878i | \(-0.599150\pi\) | ||||
−0.306477 | + | 0.951878i | \(0.599150\pi\) | |||||||
\(42\) | 8.86793i | 1.36835i | ||||||||
\(43\) | 0.472856i | 0.0721099i | 0.999350 | + | 0.0360549i | \(0.0114791\pi\) | ||||
−0.999350 | + | 0.0360549i | \(0.988521\pi\) | |||||||
\(44\) | −9.87754 | −1.48909 | ||||||||
\(45\) | −2.60859 | + | 4.22803i | −0.388866 | + | 0.630278i | ||||
\(46\) | 17.3058 | 2.55160 | ||||||||
\(47\) | − | 2.30160i | − | 0.335723i | −0.985811 | − | 0.167862i | \(-0.946314\pi\) | ||
0.985811 | − | 0.167862i | \(-0.0536862\pi\) | |||||||
\(48\) | − | 4.27823i | − | 0.617509i | ||||||
\(49\) | 4.32098 | 0.617282 | ||||||||
\(50\) | −10.5952 | + | 5.31789i | −1.49838 | + | 0.752063i | ||||
\(51\) | 7.13986 | 0.999781 | ||||||||
\(52\) | 22.4508i | 3.11337i | ||||||||
\(53\) | 6.36387i | 0.874145i | 0.899426 | + | 0.437072i | \(0.143985\pi\) | ||||
−0.899426 | + | 0.437072i | \(0.856015\pi\) | |||||||
\(54\) | −4.21648 | −0.573790 | ||||||||
\(55\) | 3.20237 | − | 5.19043i | 0.431807 | − | 0.699877i | ||||
\(56\) | 6.29258 | 0.840881 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 5.27711i | − | 0.692919i | ||||||
\(59\) | 12.2661 | 1.59691 | 0.798454 | − | 0.602056i | \(-0.205652\pi\) | ||||
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(60\) | 15.7484 | + | 9.71640i | 2.03311 | + | 1.25438i | ||||
\(61\) | −4.79076 | −0.613393 | −0.306697 | − | 0.951807i | \(-0.599224\pi\) | ||||
−0.306697 | + | 0.951807i | \(0.599224\pi\) | |||||||
\(62\) | 10.4955i | 1.33293i | ||||||||
\(63\) | 3.63651i | 0.458157i | ||||||||
\(64\) | 11.4502 | 1.43127 | ||||||||
\(65\) | −11.7974 | − | 7.27871i | −1.46329 | − | 0.902813i | ||||
\(66\) | −14.7773 | −1.81896 | ||||||||
\(67\) | − | 0.670960i | − | 0.0819708i | −0.999160 | − | 0.0409854i | \(-0.986950\pi\) | ||
0.999160 | − | 0.0409854i | \(-0.0130497\pi\) | |||||||
\(68\) | − | 11.3154i | − | 1.37219i | ||||||
\(69\) | 16.6791 | 2.00793 | ||||||||
\(70\) | −4.55642 | + | 7.38509i | −0.544596 | + | 0.882687i | ||||
\(71\) | −2.63494 | −0.312710 | −0.156355 | − | 0.987701i | \(-0.549974\pi\) | ||||
−0.156355 | + | 0.987701i | \(0.549974\pi\) | |||||||
\(72\) | − | 8.54155i | − | 1.00663i | ||||||
\(73\) | − | 6.51298i | − | 0.762287i | −0.924516 | − | 0.381143i | \(-0.875530\pi\) | ||
0.924516 | − | 0.381143i | \(-0.124470\pi\) | |||||||
\(74\) | −4.83714 | −0.562307 | ||||||||
\(75\) | −10.2115 | + | 5.12533i | −1.17912 | + | 0.591822i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.46426i | − | 0.508750i | ||||||
\(78\) | 33.5876i | 3.80305i | ||||||||
\(79\) | 4.12016 | 0.463555 | 0.231777 | − | 0.972769i | \(-0.425546\pi\) | ||||
0.231777 | + | 0.972769i | \(0.425546\pi\) | |||||||
\(80\) | 2.19819 | − | 3.56285i | 0.245765 | − | 0.398339i | ||||
\(81\) | −10.7291 | −1.19212 | ||||||||
\(82\) | 9.30563i | 1.02763i | ||||||||
\(83\) | 6.42396i | 0.705121i | 0.935789 | + | 0.352560i | \(0.114689\pi\) | ||||
−0.935789 | + | 0.352560i | \(0.885311\pi\) | |||||||
\(84\) | 13.5452 | 1.47790 | ||||||||
\(85\) | 5.94598 | + | 3.66852i | 0.644932 | + | 0.397907i | ||||
\(86\) | 1.12113 | 0.120894 | ||||||||
\(87\) | − | 5.08603i | − | 0.545280i | ||||||
\(88\) | 10.4858i | 1.11779i | ||||||||
\(89\) | 17.3044 | 1.83426 | 0.917130 | − | 0.398589i | \(-0.130500\pi\) | ||||
0.917130 | + | 0.398589i | \(0.130500\pi\) | |||||||
\(90\) | 10.0245 | + | 6.18489i | 1.05668 | + | 0.651945i | ||||
\(91\) | −10.1469 | −1.06368 | ||||||||
\(92\) | − | 26.4334i | − | 2.75587i | ||||||
\(93\) | 10.1154i | 1.04892i | ||||||||
\(94\) | −5.45702 | −0.562849 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.42673 | 0.757988 | ||||||||
\(97\) | − | 0.129944i | − | 0.0131938i | −0.999978 | − | 0.00659689i | \(-0.997900\pi\) | ||
0.999978 | − | 0.00659689i | \(-0.00209987\pi\) | |||||||
\(98\) | − | 10.2449i | − | 1.03489i | ||||||
\(99\) | −6.05979 | −0.609032 | ||||||||
\(100\) | 8.12271 | + | 16.1834i | 0.812271 | + | 1.61834i | ||||
\(101\) | 3.73547 | 0.371693 | 0.185846 | − | 0.982579i | \(-0.440497\pi\) | ||||
0.185846 | + | 0.982579i | \(0.440497\pi\) | |||||||
\(102\) | − | 16.9284i | − | 1.67616i | ||||||
\(103\) | 6.59954i | 0.650272i | 0.945667 | + | 0.325136i | \(0.105410\pi\) | ||||
−0.945667 | + | 0.325136i | \(0.894590\pi\) | |||||||
\(104\) | 23.8333 | 2.33705 | ||||||||
\(105\) | −4.39143 | + | 7.11768i | −0.428560 | + | 0.694614i | ||||
\(106\) | 15.0885 | 1.46553 | ||||||||
\(107\) | − | 11.7953i | − | 1.14029i | −0.821543 | − | 0.570146i | \(-0.806886\pi\) | ||
0.821543 | − | 0.570146i | \(-0.193114\pi\) | |||||||
\(108\) | 6.44038i | 0.619726i | ||||||||
\(109\) | 7.23806 | 0.693281 | 0.346640 | − | 0.937998i | \(-0.387322\pi\) | ||||
0.346640 | + | 0.937998i | \(0.387322\pi\) | |||||||
\(110\) | −12.3063 | − | 7.59271i | −1.17336 | − | 0.723936i | ||||
\(111\) | −4.66199 | −0.442497 | ||||||||
\(112\) | − | 3.06439i | − | 0.289558i | ||||||
\(113\) | − | 13.2879i | − | 1.25002i | −0.780616 | − | 0.625010i | \(-0.785095\pi\) | ||
0.780616 | − | 0.625010i | \(-0.214905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8902 | + | 8.56989i | 1.29526 | + | 0.799146i | ||||
\(116\) | −8.06043 | −0.748392 | ||||||||
\(117\) | 13.7734i | 1.27335i | ||||||||
\(118\) | − | 29.0825i | − | 2.67726i | ||||||
\(119\) | 5.11411 | 0.468809 | ||||||||
\(120\) | 10.3147 | − | 16.7182i | 0.941603 | − | 1.52616i | ||||
\(121\) | −3.56087 | −0.323715 | ||||||||
\(122\) | 11.3587i | 1.02837i | ||||||||
\(123\) | 8.96867i | 0.808678i | ||||||||
\(124\) | 16.0311 | 1.43964 | ||||||||
\(125\) | −11.1374 | − | 0.978456i | −0.996163 | − | 0.0875158i | ||||
\(126\) | 8.62205 | 0.768113 | ||||||||
\(127\) | − | 8.69369i | − | 0.771440i | −0.922616 | − | 0.385720i | \(-0.873953\pi\) | ||
0.922616 | − | 0.385720i | \(-0.126047\pi\) | |||||||
\(128\) | − | 20.6479i | − | 1.82504i | ||||||
\(129\) | 1.08053 | 0.0951355 | ||||||||
\(130\) | −17.2576 | + | 27.9713i | −1.51359 | + | 2.45324i | ||||
\(131\) | 10.5459 | 0.921402 | 0.460701 | − | 0.887555i | \(-0.347598\pi\) | ||||
0.460701 | + | 0.887555i | \(0.347598\pi\) | |||||||
\(132\) | 22.5713i | 1.96458i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.59083 | −0.137426 | ||||||||
\(135\) | −3.38428 | − | 2.08801i | −0.291272 | − | 0.179708i | ||||
\(136\) | −12.0122 | −1.03004 | ||||||||
\(137\) | − | 0.397219i | − | 0.0339367i | −0.999856 | − | 0.0169683i | \(-0.994599\pi\) | ||
0.999856 | − | 0.0169683i | \(-0.00540145\pi\) | |||||||
\(138\) | − | 39.5457i | − | 3.36636i | ||||||
\(139\) | 7.50543 | 0.636602 | 0.318301 | − | 0.947990i | \(-0.396888\pi\) | ||||
0.318301 | + | 0.947990i | \(0.396888\pi\) | |||||||
\(140\) | 11.2802 | + | 6.95962i | 0.953352 | + | 0.588195i | ||||
\(141\) | −5.25943 | −0.442924 | ||||||||
\(142\) | 6.24735i | 0.524266i | ||||||||
\(143\) | − | 16.9085i | − | 1.41396i | ||||||
\(144\) | −4.15961 | −0.346634 | ||||||||
\(145\) | 2.61325 | − | 4.23558i | 0.217018 | − | 0.351745i | ||||
\(146\) | −15.4421 | −1.27800 | ||||||||
\(147\) | − | 9.87393i | − | 0.814388i | ||||||
\(148\) | 7.38841i | 0.607323i | ||||||||
\(149\) | 3.68581 | 0.301953 | 0.150977 | − | 0.988537i | \(-0.451758\pi\) | ||||
0.150977 | + | 0.988537i | \(0.451758\pi\) | |||||||
\(150\) | 12.1520 | + | 24.2112i | 0.992207 | + | 1.97683i | ||||
\(151\) | 4.49051 | 0.365433 | 0.182716 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182716 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.94189i | − | 0.561219i | ||||||
\(154\) | −10.5846 | −0.852933 | ||||||||
\(155\) | −5.19740 | + | 8.42399i | −0.417465 | + | 0.676631i | ||||
\(156\) | 51.3027 | 4.10751 | ||||||||
\(157\) | 20.2651i | 1.61733i | 0.588266 | + | 0.808667i | \(0.299811\pi\) | ||||
−0.588266 | + | 0.808667i | \(0.700189\pi\) | |||||||
\(158\) | − | 9.76878i | − | 0.777162i | ||||||
\(159\) | 14.5422 | 1.15327 | ||||||||
\(160\) | 6.18488 | + | 3.81592i | 0.488958 | + | 0.301675i | ||||
\(161\) | 11.9469 | 0.941544 | ||||||||
\(162\) | 25.4383i | 1.99862i | ||||||||
\(163\) | − | 15.6590i | − | 1.22651i | −0.789887 | − | 0.613253i | \(-0.789861\pi\) | ||
0.789887 | − | 0.613253i | \(-0.210139\pi\) | |||||||
\(164\) | 14.2137 | 1.10990 | ||||||||
\(165\) | −11.8607 | − | 7.31778i | −0.923356 | − | 0.569688i | ||||
\(166\) | 15.2310 | 1.18215 | ||||||||
\(167\) | − | 6.04571i | − | 0.467831i | −0.972257 | − | 0.233915i | \(-0.924846\pi\) | ||
0.972257 | − | 0.233915i | \(-0.0751539\pi\) | |||||||
\(168\) | − | 14.3793i | − | 1.10938i | ||||||
\(169\) | −25.4317 | −1.95628 | ||||||||
\(170\) | 8.69795 | − | 14.0977i | 0.667103 | − | 1.08125i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.71244i | − | 0.130573i | ||||||
\(173\) | 1.64040i | 0.124717i | 0.998054 | + | 0.0623586i | \(0.0198623\pi\) | ||||
−0.998054 | + | 0.0623586i | \(0.980138\pi\) | |||||||
\(174\) | −12.0588 | −0.914177 | ||||||||
\(175\) | −7.31425 | + | 3.67115i | −0.552905 | + | 0.277513i | ||||
\(176\) | 5.10642 | 0.384911 | ||||||||
\(177\) | − | 28.0294i | − | 2.10682i | ||||||
\(178\) | − | 41.0281i | − | 3.07519i | ||||||
\(179\) | −14.1885 | −1.06050 | −0.530248 | − | 0.847842i | \(-0.677901\pi\) | ||||
−0.530248 | + | 0.847842i | \(0.677901\pi\) | |||||||
\(180\) | 9.44699 | − | 15.3118i | 0.704137 | − | 1.14127i | ||||
\(181\) | −22.9459 | −1.70555 | −0.852776 | − | 0.522277i | \(-0.825083\pi\) | ||||
−0.852776 | + | 0.522277i | \(0.825083\pi\) | |||||||
\(182\) | 24.0580i | 1.78329i | ||||||||
\(183\) | 10.9474i | 0.809258i | ||||||||
\(184\) | −28.0612 | −2.06870 | ||||||||
\(185\) | −3.88244 | − | 2.39537i | −0.285443 | − | 0.176111i | ||||
\(186\) | 23.9834 | 1.75855 | ||||||||
\(187\) | 8.52202i | 0.623192i | ||||||||
\(188\) | 8.33523i | 0.607909i | ||||||||
\(189\) | −2.91080 | −0.211729 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.2099 | 0.738762 | 0.369381 | − | 0.929278i | \(-0.379570\pi\) | ||||
0.369381 | + | 0.929278i | \(0.379570\pi\) | |||||||
\(192\) | − | 26.1650i | − | 1.88830i | ||||||
\(193\) | − | 11.8312i | − | 0.851631i | −0.904810 | − | 0.425816i | \(-0.859987\pi\) | ||
0.904810 | − | 0.425816i | \(-0.140013\pi\) | |||||||
\(194\) | −0.308092 | −0.0221197 | ||||||||
\(195\) | −16.6327 | + | 26.9584i | −1.19109 | + | 1.93053i | ||||
\(196\) | −15.6484 | −1.11774 | ||||||||
\(197\) | 2.72674i | 0.194273i | 0.995271 | + | 0.0971363i | \(0.0309683\pi\) | ||||
−0.995271 | + | 0.0971363i | \(0.969032\pi\) | |||||||
\(198\) | 14.3676i | 1.02106i | ||||||||
\(199\) | −4.47838 | −0.317464 | −0.158732 | − | 0.987322i | \(-0.550741\pi\) | ||||
−0.158732 | + | 0.987322i | \(0.550741\pi\) | |||||||
\(200\) | 17.1799 | − | 8.62291i | 1.21481 | − | 0.609732i | ||||
\(201\) | −1.53322 | −0.108145 | ||||||||
\(202\) | − | 8.85667i | − | 0.623153i | ||||||
\(203\) | − | 3.64300i | − | 0.255688i | ||||||
\(204\) | −25.8569 | −1.81035 | ||||||||
\(205\) | −4.60818 | + | 7.46899i | −0.321849 | + | 0.521657i | ||||
\(206\) | 15.6473 | 1.09020 | ||||||||
\(207\) | − | 16.2167i | − | 1.12714i | ||||||
\(208\) | − | 11.6065i | − | 0.804764i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 16.8758 | + | 10.4119i | 1.16454 | + | 0.718493i | ||||
\(211\) | 7.34023 | 0.505322 | 0.252661 | − | 0.967555i | \(-0.418694\pi\) | ||||
0.252661 | + | 0.967555i | \(0.418694\pi\) | |||||||
\(212\) | − | 23.0467i | − | 1.58285i | ||||||
\(213\) | 6.02114i | 0.412562i | ||||||||
\(214\) | −27.9662 | −1.91173 | ||||||||
\(215\) | 0.899852 | + | 0.555186i | 0.0613694 | + | 0.0378634i | ||||
\(216\) | 6.83698 | 0.465197 | ||||||||
\(217\) | 7.24543i | 0.491852i | ||||||||
\(218\) | − | 17.1612i | − | 1.16230i | ||||||
\(219\) | −14.8829 | −1.00569 | ||||||||
\(220\) | −11.5973 | + | 18.7971i | −0.781892 | + | 1.26730i | ||||
\(221\) | 19.3699 | 1.30296 | ||||||||
\(222\) | 11.0534i | 0.741858i | ||||||||
\(223\) | 16.5811i | 1.11035i | 0.831733 | + | 0.555176i | \(0.187349\pi\) | ||||
−0.831733 | + | 0.555176i | \(0.812651\pi\) | |||||||
\(224\) | 5.31958 | 0.355430 | ||||||||
\(225\) | 4.98322 | + | 9.92837i | 0.332215 | + | 0.661891i | ||||
\(226\) | −31.5052 | −2.09569 | ||||||||
\(227\) | 11.7828i | 0.782052i | 0.920380 | + | 0.391026i | \(0.127880\pi\) | ||||
−0.920380 | + | 0.391026i | \(0.872120\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.82331 | 0.516979 | 0.258490 | − | 0.966014i | \(-0.416775\pi\) | ||||
0.258490 | + | 0.966014i | \(0.416775\pi\) | |||||||
\(230\) | 20.3189 | − | 32.9331i | 1.33979 | − | 2.17155i | ||||
\(231\) | −10.2014 | −0.671200 | ||||||||
\(232\) | 8.55679i | 0.561781i | ||||||||
\(233\) | − | 6.71975i | − | 0.440225i | −0.975474 | − | 0.220113i | \(-0.929358\pi\) | ||
0.975474 | − | 0.220113i | \(-0.0706425\pi\) | |||||||
\(234\) | 32.6563 | 2.13481 | ||||||||
\(235\) | −4.37998 | − | 2.70234i | −0.285718 | − | 0.176281i | ||||
\(236\) | −44.4215 | −2.89159 | ||||||||
\(237\) | − | 9.41505i | − | 0.611573i | ||||||
\(238\) | − | 12.1254i | − | 0.785972i | ||||||
\(239\) | 15.9746 | 1.03331 | 0.516654 | − | 0.856194i | \(-0.327177\pi\) | ||||
0.516654 | + | 0.856194i | \(0.327177\pi\) | |||||||
\(240\) | −8.14153 | − | 5.02312i | −0.525533 | − | 0.324241i | ||||
\(241\) | −10.4554 | −0.673493 | −0.336747 | − | 0.941595i | \(-0.609327\pi\) | ||||
−0.336747 | + | 0.941595i | \(0.609327\pi\) | |||||||
\(242\) | 8.44270i | 0.542717i | ||||||||
\(243\) | 19.1820i | 1.23053i | ||||||||
\(244\) | 17.3497 | 1.11070 | ||||||||
\(245\) | 5.07331 | − | 8.22288i | 0.324122 | − | 0.525340i | ||||
\(246\) | 21.2644 | 1.35577 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 17.0183i | − | 1.08066i | ||||||
\(249\) | 14.6795 | 0.930275 | ||||||||
\(250\) | −2.31989 | + | 26.4065i | −0.146723 | + | 1.67010i | ||||
\(251\) | −11.8661 | −0.748984 | −0.374492 | − | 0.927230i | \(-0.622183\pi\) | ||||
−0.374492 | + | 0.927230i | \(0.622183\pi\) | |||||||
\(252\) | − | 13.1696i | − | 0.829606i | ||||||
\(253\) | 19.9080i | 1.25160i | ||||||||
\(254\) | −20.6125 | −1.29334 | ||||||||
\(255\) | 8.38300 | − | 13.5873i | 0.524964 | − | 0.850867i | ||||
\(256\) | −26.0552 | −1.62845 | ||||||||
\(257\) | 3.81629i | 0.238053i | 0.992891 | + | 0.119027i | \(0.0379774\pi\) | ||||
−0.992891 | + | 0.119027i | \(0.962023\pi\) | |||||||
\(258\) | − | 2.56191i | − | 0.159497i | ||||||
\(259\) | −3.33927 | −0.207492 | ||||||||
\(260\) | 42.7242 | + | 26.3598i | 2.64964 | + | 1.63476i | ||||
\(261\) | −4.94501 | −0.306088 | ||||||||
\(262\) | − | 25.0041i | − | 1.54476i | ||||||
\(263\) | 2.11957i | 0.130699i | 0.997862 | + | 0.0653493i | \(0.0208161\pi\) | ||||
−0.997862 | + | 0.0653493i | \(0.979184\pi\) | |||||||
\(264\) | 23.9613 | 1.47471 | ||||||||
\(265\) | 12.1105 | + | 7.47190i | 0.743944 | + | 0.458995i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 39.5425i | − | 2.41996i | ||||||
\(268\) | 2.42988i | 0.148428i | ||||||||
\(269\) | −3.92827 | −0.239511 | −0.119755 | − | 0.992803i | \(-0.538211\pi\) | ||||
−0.119755 | + | 0.992803i | \(0.538211\pi\) | |||||||
\(270\) | −4.95062 | + | 8.02401i | −0.301285 | + | 0.488326i | ||||
\(271\) | 18.9358 | 1.15027 | 0.575135 | − | 0.818058i | \(-0.304949\pi\) | ||||
0.575135 | + | 0.818058i | \(0.304949\pi\) | |||||||
\(272\) | 5.84975i | 0.354693i | ||||||||
\(273\) | 23.1868i | 1.40333i | ||||||||
\(274\) | −0.941793 | −0.0568958 | ||||||||
\(275\) | −6.11751 | − | 12.1883i | −0.368900 | − | 0.734982i | ||||
\(276\) | −60.4034 | −3.63586 | ||||||||
\(277\) | 15.0274i | 0.902909i | 0.892294 | + | 0.451454i | \(0.149095\pi\) | ||||
−0.892294 | + | 0.451454i | \(0.850905\pi\) | |||||||
\(278\) | − | 17.7951i | − | 1.06728i | ||||||
\(279\) | 9.83496 | 0.588803 | ||||||||
\(280\) | 7.38819 | − | 11.9749i | 0.441529 | − | 0.715635i | ||||
\(281\) | −27.4830 | −1.63950 | −0.819750 | − | 0.572722i | \(-0.805888\pi\) | ||||
−0.819750 | + | 0.572722i | \(0.805888\pi\) | |||||||
\(282\) | 12.4699i | 0.742574i | ||||||||
\(283\) | − | 20.3357i | − | 1.20883i | −0.796669 | − | 0.604415i | \(-0.793407\pi\) | ||
0.796669 | − | 0.604415i | \(-0.206593\pi\) | |||||||
\(284\) | 9.54240 | 0.566237 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −40.0896 | −2.37055 | ||||||||
\(287\) | 6.42404i | 0.379199i | ||||||||
\(288\) | − | 7.22081i | − | 0.425490i | ||||||
\(289\) | 7.23745 | 0.425732 | ||||||||
\(290\) | −10.0424 | − | 6.19593i | −0.589711 | − | 0.363837i | ||||
\(291\) | −0.296936 | −0.0174067 | ||||||||
\(292\) | 23.5867i | 1.38031i | ||||||||
\(293\) | 4.58659i | 0.267951i | 0.990985 | + | 0.133976i | \(0.0427744\pi\) | ||||
−0.990985 | + | 0.133976i | \(0.957226\pi\) | |||||||
\(294\) | −23.4108 | −1.36534 | ||||||||
\(295\) | 14.4018 | − | 23.3425i | 0.838503 | − | 1.35905i | ||||
\(296\) | 7.84339 | 0.455888 | ||||||||
\(297\) | − | 4.85048i | − | 0.281454i | ||||||
\(298\) | − | 8.73893i | − | 0.506233i | ||||||
\(299\) | 45.2491 | 2.61682 | ||||||||
\(300\) | 36.9809 | − | 18.5613i | 2.13509 | − | 1.07164i | ||||
\(301\) | 0.773958 | 0.0446102 | ||||||||
\(302\) | − | 10.6469i | − | 0.612658i | ||||||
\(303\) | − | 8.53597i | − | 0.490379i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.62489 | + | 9.11687i | −0.322080 | + | 0.522031i | ||||
\(306\) | −16.4590 | −0.940899 | ||||||||
\(307\) | 24.3228i | 1.38818i | 0.719890 | + | 0.694088i | \(0.244192\pi\) | ||||
−0.719890 | + | 0.694088i | \(0.755808\pi\) | |||||||
\(308\) | 16.1673i | 0.921216i | ||||||||
\(309\) | 15.0807 | 0.857911 | ||||||||
\(310\) | 19.9730 | + | 12.3229i | 1.13439 | + | 0.699891i | ||||
\(311\) | 22.0205 | 1.24867 | 0.624334 | − | 0.781157i | \(-0.285370\pi\) | ||||
0.624334 | + | 0.781157i | \(0.285370\pi\) | |||||||
\(312\) | − | 54.4620i | − | 3.08330i | ||||||
\(313\) | 29.4817i | 1.66640i | 0.552969 | + | 0.833202i | \(0.313495\pi\) | ||||
−0.552969 | + | 0.833202i | \(0.686505\pi\) | |||||||
\(314\) | 48.0480 | 2.71151 | ||||||||
\(315\) | 6.92032 | + | 4.26967i | 0.389916 | + | 0.240569i | ||||
\(316\) | −14.9211 | −0.839379 | ||||||||
\(317\) | − | 8.04314i | − | 0.451748i | −0.974157 | − | 0.225874i | \(-0.927476\pi\) | ||
0.974157 | − | 0.225874i | \(-0.0725237\pi\) | |||||||
\(318\) | − | 34.4791i | − | 1.93349i | ||||||
\(319\) | 6.07060 | 0.339889 | ||||||||
\(320\) | 13.4438 | − | 21.7899i | 0.751532 | − | 1.21809i | ||||
\(321\) | −26.9536 | −1.50440 | ||||||||
\(322\) | − | 28.3256i | − | 1.57853i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 38.8552 | 2.15862 | ||||||||
\(325\) | −27.7030 | + | 13.9046i | −1.53668 | + | 0.771288i | ||||
\(326\) | −37.1269 | −2.05627 | ||||||||
\(327\) | − | 16.5398i | − | 0.914654i | ||||||
\(328\) | − | 15.0890i | − | 0.833150i | ||||||
\(329\) | −3.76720 | −0.207692 | ||||||||
\(330\) | −17.3502 | + | 28.1214i | −0.955098 | + | 1.54803i | ||||
\(331\) | −18.2183 | −1.00137 | −0.500685 | − | 0.865630i | \(-0.666918\pi\) | ||||
−0.500685 | + | 0.865630i | \(0.666918\pi\) | |||||||
\(332\) | − | 23.2643i | − | 1.27679i | ||||||
\(333\) | 4.53273i | 0.248392i | ||||||||
\(334\) | −14.3342 | −0.784331 | ||||||||
\(335\) | −1.27685 | − | 0.787783i | −0.0697615 | − | 0.0430412i | ||||
\(336\) | −7.00249 | −0.382017 | ||||||||
\(337\) | 9.60328i | 0.523124i | 0.965187 | + | 0.261562i | \(0.0842376\pi\) | ||||
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(338\) | 60.2977i | 3.27976i | ||||||||
\(339\) | −30.3644 | −1.64917 | ||||||||
\(340\) | −21.5333 | − | 13.2855i | −1.16781 | − | 0.720509i | ||||
\(341\) | −12.0736 | −0.653823 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5299i | − | 1.00052i | ||||||
\(344\) | −1.81790 | −0.0980144 | ||||||||
\(345\) | 19.5832 | − | 31.7406i | 1.05432 | − | 1.70886i | ||||
\(346\) | 3.88934 | 0.209092 | ||||||||
\(347\) | − | 1.26627i | − | 0.0679771i | −0.999422 | − | 0.0339885i | \(-0.989179\pi\) | ||
0.999422 | − | 0.0339885i | \(-0.0108210\pi\) | |||||||
\(348\) | 18.4190i | 0.987363i | ||||||||
\(349\) | −26.6148 | −1.42466 | −0.712330 | − | 0.701845i | \(-0.752360\pi\) | ||||
−0.712330 | + | 0.701845i | \(0.752360\pi\) | |||||||
\(350\) | 8.70418 | + | 17.3419i | 0.465258 | + | 0.926961i | ||||
\(351\) | −11.0247 | −0.588457 | ||||||||
\(352\) | 8.86443i | 0.472475i | ||||||||
\(353\) | − | 26.8743i | − | 1.43037i | −0.698934 | − | 0.715187i | \(-0.746342\pi\) | ||
0.698934 | − | 0.715187i | \(-0.253658\pi\) | |||||||
\(354\) | −66.4568 | −3.53214 | ||||||||
\(355\) | −3.09371 | + | 5.01432i | −0.164197 | + | 0.266133i | ||||
\(356\) | −62.6676 | −3.32138 | ||||||||
\(357\) | − | 11.6863i | − | 0.618506i | ||||||
\(358\) | 33.6404i | 1.77795i | ||||||||
\(359\) | 21.0567 | 1.11133 | 0.555664 | − | 0.831407i | \(-0.312464\pi\) | ||||
0.555664 | + | 0.831407i | \(0.312464\pi\) | |||||||
\(360\) | −16.2547 | − | 10.0287i | −0.856697 | − | 0.528561i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 54.4039i | 2.85940i | ||||||||
\(363\) | 8.13699i | 0.427081i | ||||||||
\(364\) | 36.7469 | 1.92606 | ||||||||
\(365\) | −12.3943 | − | 7.64697i | −0.648747 | − | 0.400261i | ||||
\(366\) | 25.9560 | 1.35674 | ||||||||
\(367\) | 11.0177i | 0.575118i | 0.957763 | + | 0.287559i | \(0.0928437\pi\) | ||||
−0.957763 | + | 0.287559i | \(0.907156\pi\) | |||||||
\(368\) | 13.6654i | 0.712356i | ||||||||
\(369\) | 8.72000 | 0.453945 | ||||||||
\(370\) | −5.67935 | + | 9.20515i | −0.295255 | + | 0.478553i | ||||
\(371\) | 10.4162 | 0.540782 | ||||||||
\(372\) | − | 36.6329i | − | 1.89933i | ||||||
\(373\) | − | 4.83309i | − | 0.250248i | −0.992141 | − | 0.125124i | \(-0.960067\pi\) | ||
0.992141 | − | 0.125124i | \(-0.0399328\pi\) | |||||||
\(374\) | 20.2055 | 1.04480 | ||||||||
\(375\) | −2.23589 | + | 25.4504i | −0.115461 | + | 1.31425i | ||||
\(376\) | 8.84852 | 0.456327 | ||||||||
\(377\) | − | 13.7980i | − | 0.710632i | ||||||
\(378\) | 6.90141i | 0.354970i | ||||||||
\(379\) | 2.03721 | 0.104644 | 0.0523221 | − | 0.998630i | \(-0.483338\pi\) | ||||
0.0523221 | + | 0.998630i | \(0.483338\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.8661 | −1.01777 | ||||||||
\(382\) | − | 24.2073i | − | 1.23856i | ||||||
\(383\) | 34.5805i | 1.76698i | 0.468451 | + | 0.883489i | \(0.344812\pi\) | ||||
−0.468451 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(384\) | −47.1829 | −2.40779 | ||||||||
\(385\) | −8.49554 | − | 5.24154i | −0.432973 | − | 0.267134i | ||||
\(386\) | −28.0515 | −1.42778 | ||||||||
\(387\) | − | 1.05057i | − | 0.0534035i | ||||||
\(388\) | 0.470590i | 0.0238906i | ||||||||
\(389\) | 4.53021 | 0.229691 | 0.114845 | − | 0.993383i | \(-0.463363\pi\) | ||||
0.114845 | + | 0.993383i | \(0.463363\pi\) | |||||||
\(390\) | 63.9176 | + | 39.4356i | 3.23659 | + | 1.99690i | ||||
\(391\) | −22.8059 | −1.15334 | ||||||||
\(392\) | 16.6120i | 0.839033i | ||||||||
\(393\) | − | 24.0987i | − | 1.21562i | ||||||
\(394\) | 6.46503 | 0.325703 | ||||||||
\(395\) | 4.83754 | − | 7.84073i | 0.243403 | − | 0.394510i | ||||
\(396\) | 21.9455 | 1.10280 | ||||||||
\(397\) | 25.1348i | 1.26148i | 0.775995 | + | 0.630739i | \(0.217248\pi\) | ||||
−0.775995 | + | 0.630739i | \(0.782752\pi\) | |||||||
\(398\) | 10.6181i | 0.532237i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.19923 | − | 8.36637i | −0.209961 | − | 0.418319i | ||||
\(401\) | −28.9116 | −1.44378 | −0.721888 | − | 0.692010i | \(-0.756725\pi\) | ||||
−0.721888 | + | 0.692010i | \(0.756725\pi\) | |||||||
\(402\) | 3.63522i | 0.181308i | ||||||||
\(403\) | 27.4423i | 1.36700i | ||||||||
\(404\) | −13.5280 | −0.673041 | ||||||||
\(405\) | −12.5971 | + | 20.4176i | −0.625957 | + | 1.01456i | ||||
\(406\) | −8.63743 | −0.428669 | ||||||||
\(407\) | − | 5.56448i | − | 0.275821i | ||||||
\(408\) | 27.4492i | 1.35894i | ||||||||
\(409\) | −22.9616 | −1.13538 | −0.567689 | − | 0.823243i | \(-0.692163\pi\) | ||||
−0.567689 | + | 0.823243i | \(0.692163\pi\) | |||||||
\(410\) | 17.7087 | + | 10.9259i | 0.874572 | + | 0.539589i | ||||
\(411\) | −0.907691 | −0.0447731 | ||||||||
\(412\) | − | 23.9002i | − | 1.17748i | ||||||
\(413\) | − | 20.0768i | − | 0.987913i | ||||||
\(414\) | −38.4492 | −1.88968 | ||||||||
\(415\) | 12.2249 | + | 7.54245i | 0.600096 | + | 0.370244i | ||||
\(416\) | 20.1481 | 0.987842 | ||||||||
\(417\) | − | 17.1508i | − | 0.839877i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.98058 | −0.438730 | −0.219365 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219365 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(420\) | 15.9035 | − | 25.7766i | 0.776013 | − | 1.25777i | ||||
\(421\) | 34.0406 | 1.65904 | 0.829519 | − | 0.558478i | \(-0.188615\pi\) | ||||
0.829519 | + | 0.558478i | \(0.188615\pi\) | |||||||
\(422\) | − | 17.4034i | − | 0.847187i | ||||||
\(423\) | 5.11360i | 0.248632i | ||||||||
\(424\) | −24.4659 | −1.18817 | ||||||||
\(425\) | 13.9625 | − | 7.00802i | 0.677281 | − | 0.339939i | ||||
\(426\) | 14.2759 | 0.691671 | ||||||||
\(427\) | 7.84138i | 0.379471i | ||||||||
\(428\) | 42.7165i | 2.06478i | ||||||||
\(429\) | −38.6380 | −1.86546 | ||||||||
\(430\) | 1.31633 | − | 2.13352i | 0.0634790 | − | 0.102887i | ||||
\(431\) | −37.9730 | −1.82909 | −0.914547 | − | 0.404480i | \(-0.867453\pi\) | ||||
−0.914547 | + | 0.404480i | \(0.867453\pi\) | |||||||
\(432\) | − | 3.32950i | − | 0.160191i | ||||||
\(433\) | − | 36.9800i | − | 1.77714i | −0.458738 | − | 0.888572i | \(-0.651698\pi\) | ||
0.458738 | − | 0.888572i | \(-0.348302\pi\) | |||||||
\(434\) | 17.1787 | 0.824603 | ||||||||
\(435\) | −9.67878 | − | 5.97157i | −0.464062 | − | 0.286315i | ||||
\(436\) | −26.2126 | −1.25535 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 35.2869i | 1.68607i | ||||||||
\(439\) | 22.1830 | 1.05874 | 0.529369 | − | 0.848392i | \(-0.322429\pi\) | ||||
0.529369 | + | 0.848392i | \(0.322429\pi\) | |||||||
\(440\) | 19.9546 | + | 12.3115i | 0.951299 | + | 0.586928i | ||||
\(441\) | −9.60016 | −0.457150 | ||||||||
\(442\) | − | 45.9253i | − | 2.18444i | ||||||
\(443\) | 9.84880i | 0.467931i | 0.972245 | + | 0.233965i | \(0.0751702\pi\) | ||||
−0.972245 | + | 0.233965i | \(0.924830\pi\) | |||||||
\(444\) | 16.8834 | 0.801249 | ||||||||
\(445\) | 20.3173 | − | 32.9304i | 0.963131 | − | 1.56105i | ||||
\(446\) | 39.3133 | 1.86154 | ||||||||
\(447\) | − | 8.42250i | − | 0.398370i | ||||||
\(448\) | − | 18.7413i | − | 0.885445i | ||||||
\(449\) | −37.3039 | −1.76048 | −0.880240 | − | 0.474528i | \(-0.842619\pi\) | ||||
−0.880240 | + | 0.474528i | \(0.842619\pi\) | |||||||
\(450\) | 23.5399 | − | 11.8151i | 1.10968 | − | 0.556967i | ||||
\(451\) | −10.7049 | −0.504072 | ||||||||
\(452\) | 48.1220i | 2.26347i | ||||||||
\(453\) | − | 10.2613i | − | 0.482120i | ||||||
\(454\) | 27.9367 | 1.31113 | ||||||||
\(455\) | −11.9136 | + | 19.3097i | −0.558518 | + | 0.905251i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0343i | 0.656498i | 0.944591 | + | 0.328249i | \(0.106458\pi\) | ||||
−0.944591 | + | 0.328249i | \(0.893542\pi\) | |||||||
\(458\) | − | 18.5488i | − | 0.866730i | ||||||
\(459\) | 5.55655 | 0.259358 | ||||||||
\(460\) | −50.3031 | − | 31.0358i | −2.34539 | − | 1.44705i | ||||
\(461\) | −10.1359 | −0.472077 | −0.236039 | − | 0.971744i | \(-0.575849\pi\) | ||||
−0.236039 | + | 0.971744i | \(0.575849\pi\) | |||||||
\(462\) | 24.1871i | 1.12528i | ||||||||
\(463\) | 0.722130i | 0.0335602i | 0.999859 | + | 0.0167801i | \(0.00534153\pi\) | ||||
−0.999859 | + | 0.0167801i | \(0.994658\pi\) | |||||||
\(464\) | 4.16703 | 0.193449 | ||||||||
\(465\) | 19.2498 | + | 11.8767i | 0.892688 | + | 0.550767i | ||||
\(466\) | −15.9323 | −0.738050 | ||||||||
\(467\) | − | 35.0172i | − | 1.62040i | −0.586152 | − | 0.810201i | \(-0.699358\pi\) | ||
0.586152 | − | 0.810201i | \(-0.300642\pi\) | |||||||
\(468\) | − | 49.8802i | − | 2.30572i | ||||||
\(469\) | −1.09821 | −0.0507106 | ||||||||
\(470\) | −6.40716 | + | 10.3848i | −0.295540 | + | 0.479015i | ||||
\(471\) | 46.3082 | 2.13377 | ||||||||
\(472\) | 47.1570i | 2.17058i | ||||||||
\(473\) | 1.28970i | 0.0593007i | ||||||||
\(474\) | −22.3228 | −1.02532 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −18.5207 | −0.848895 | ||||||||
\(477\) | − | 14.1390i | − | 0.647379i | ||||||
\(478\) | − | 37.8752i | − | 1.73237i | ||||||
\(479\) | 26.9601 | 1.23184 | 0.615920 | − | 0.787809i | \(-0.288784\pi\) | ||||
0.615920 | + | 0.787809i | \(0.288784\pi\) | |||||||
\(480\) | 8.71982 | − | 14.1332i | 0.398003 | − | 0.645088i | ||||
\(481\) | −12.6476 | −0.576681 | ||||||||
\(482\) | 24.7895i | 1.12913i | ||||||||
\(483\) | − | 27.3000i | − | 1.24219i | ||||||
\(484\) | 12.8956 | 0.586166 | ||||||||
\(485\) | −0.247285 | − | 0.152569i | −0.0112286 | − | 0.00692778i | ||||
\(486\) | 45.4800 | 2.06301 | ||||||||
\(487\) | − | 3.06758i | − | 0.139005i | −0.997582 | − | 0.0695026i | \(-0.977859\pi\) | ||
0.997582 | − | 0.0695026i | \(-0.0221412\pi\) | |||||||
\(488\) | − | 18.4181i | − | 0.833747i | ||||||
\(489\) | −35.7826 | −1.61814 | ||||||||
\(490\) | −19.4962 | − | 12.0287i | −0.880748 | − | 0.543400i | ||||
\(491\) | 1.24888 | 0.0563613 | 0.0281806 | − | 0.999603i | \(-0.491029\pi\) | ||||
0.0281806 | + | 0.999603i | \(0.491029\pi\) | |||||||
\(492\) | − | 32.4800i | − | 1.46431i | ||||||
\(493\) | 6.95428i | 0.313205i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.11488 | + | 11.5319i | −0.319790 | + | 0.518319i | ||||
\(496\) | −8.28766 | −0.372127 | ||||||||
\(497\) | 4.31279i | 0.193455i | ||||||||
\(498\) | − | 34.8046i | − | 1.55963i | ||||||
\(499\) | −19.5720 | −0.876165 | −0.438083 | − | 0.898935i | \(-0.644342\pi\) | ||||
−0.438083 | + | 0.898935i | \(0.644342\pi\) | |||||||
\(500\) | 40.3341 | + | 3.54347i | 1.80380 | + | 0.158469i | ||||
\(501\) | −13.8151 | −0.617215 | ||||||||
\(502\) | 28.1342i | 1.25569i | ||||||||
\(503\) | 5.11859i | 0.228227i | 0.993468 | + | 0.114113i | \(0.0364027\pi\) | ||||
−0.993468 | + | 0.114113i | \(0.963597\pi\) | |||||||
\(504\) | −13.9806 | −0.622744 | ||||||||
\(505\) | 4.38586 | − | 7.10864i | 0.195168 | − | 0.316330i | ||||
\(506\) | 47.2011 | 2.09835 | ||||||||
\(507\) | 58.1144i | 2.58095i | ||||||||
\(508\) | 31.4841i | 1.39688i | ||||||||
\(509\) | −15.8349 | −0.701871 | −0.350935 | − | 0.936400i | \(-0.614136\pi\) | ||||
−0.350935 | + | 0.936400i | \(0.614136\pi\) | |||||||
\(510\) | −32.2150 | − | 19.8758i | −1.42650 | − | 0.880117i | ||||
\(511\) | −10.6603 | −0.471582 | ||||||||
\(512\) | 20.4803i | 0.905108i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.04830 | 0.399103 | ||||||||
\(515\) | 12.5590 | + | 7.74860i | 0.553416 | + | 0.341444i | ||||
\(516\) | −3.91313 | −0.172266 | ||||||||
\(517\) | − | 6.27757i | − | 0.276087i | ||||||
\(518\) | 7.91730i | 0.347866i | ||||||||
\(519\) | 3.74850 | 0.164541 | ||||||||
\(520\) | 27.9830 | − | 45.3552i | 1.22714 | − | 1.98896i | ||||
\(521\) | 29.9732 | 1.31315 | 0.656575 | − | 0.754261i | \(-0.272004\pi\) | ||||
0.656575 | + | 0.754261i | \(0.272004\pi\) | |||||||
\(522\) | 11.7245i | 0.513166i | ||||||||
\(523\) | 30.3765i | 1.32827i | 0.747611 | + | 0.664136i | \(0.231201\pi\) | ||||
−0.747611 | + | 0.664136i | \(0.768799\pi\) | |||||||
\(524\) | −38.1920 | −1.66843 | ||||||||
\(525\) | 8.38900 | + | 16.7139i | 0.366126 | + | 0.729455i | ||||
\(526\) | 5.02544 | 0.219120 | ||||||||
\(527\) | − | 13.8311i | − | 0.602493i | ||||||
\(528\) | − | 11.6688i | − | 0.507818i | ||||||
\(529\) | −30.2759 | −1.31635 | ||||||||
\(530\) | 17.7156 | − | 28.7137i | 0.769518 | − | 1.24724i | ||||
\(531\) | −27.2522 | −1.18265 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.3313i | 1.05390i | ||||||||
\(534\) | −93.7540 | −4.05713 | ||||||||
\(535\) | −22.4466 | − | 13.8490i | −0.970450 | − | 0.598744i | ||||
\(536\) | 2.57951 | 0.111418 | ||||||||
\(537\) | 32.4223i | 1.39913i | ||||||||
\(538\) | 9.31380i | 0.401546i | ||||||||
\(539\) | 11.7854 | 0.507632 | ||||||||
\(540\) | 12.2561 | + | 7.56173i | 0.527420 | + | 0.325405i | ||||
\(541\) | −23.8593 | −1.02579 | −0.512895 | − | 0.858451i | \(-0.671427\pi\) | ||||
−0.512895 | + | 0.858451i | \(0.671427\pi\) | |||||||
\(542\) | − | 44.8963i | − | 1.92846i | ||||||
\(543\) | 52.4339i | 2.25016i | ||||||||
\(544\) | −10.1548 | −0.435383 | ||||||||
\(545\) | 8.49830 | − | 13.7741i | 0.364027 | − | 0.590019i | ||||
\(546\) | 54.9752 | 2.35272 | ||||||||
\(547\) | 13.7402i | 0.587489i | 0.955884 | + | 0.293745i | \(0.0949015\pi\) | ||||
−0.955884 | + | 0.293745i | \(0.905098\pi\) | |||||||
\(548\) | 1.43852i | 0.0614507i | ||||||||
\(549\) | 10.6439 | 0.454270 | ||||||||
\(550\) | −28.8980 | + | 14.5044i | −1.23222 | + | 0.618471i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 64.1230i | 2.72926i | ||||||||
\(553\) | − | 6.74377i | − | 0.286774i | ||||||
\(554\) | 35.6295 | 1.51375 | ||||||||
\(555\) | −5.47370 | + | 8.87183i | −0.232346 | + | 0.376588i | ||||
\(556\) | −27.1808 | −1.15272 | ||||||||
\(557\) | − | 27.0314i | − | 1.14536i | −0.819780 | − | 0.572679i | \(-0.805904\pi\) | ||
0.819780 | − | 0.572679i | \(-0.194096\pi\) | |||||||
\(558\) | − | 23.3184i | − | 0.987145i | ||||||
\(559\) | 2.93139 | 0.123985 | ||||||||
\(560\) | −5.83157 | − | 3.59794i | −0.246429 | − | 0.152041i | ||||
\(561\) | 19.4738 | 0.822185 | ||||||||
\(562\) | 65.1614i | 2.74867i | ||||||||
\(563\) | 38.1678i | 1.60858i | 0.594237 | + | 0.804290i | \(0.297454\pi\) | ||||
−0.594237 | + | 0.804290i | \(0.702546\pi\) | |||||||
\(564\) | 19.0470 | 0.802022 | ||||||||
\(565\) | −25.2871 | − | 15.6015i | −1.06383 | − | 0.656360i | ||||
\(566\) | −48.2153 | −2.02664 | ||||||||
\(567\) | 17.5610i | 0.737494i | ||||||||
\(568\) | − | 10.1300i | − | 0.425046i | ||||||
\(569\) | 2.28061 | 0.0956082 | 0.0478041 | − | 0.998857i | \(-0.484778\pi\) | ||||
0.0478041 | + | 0.998857i | \(0.484778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.4656 | −0.605367 | −0.302683 | − | 0.953091i | \(-0.597883\pi\) | ||||
−0.302683 | + | 0.953091i | \(0.597883\pi\) | |||||||
\(572\) | 61.2341i | 2.56033i | ||||||||
\(573\) | − | 23.3308i | − | 0.974658i | ||||||
\(574\) | 15.2312 | 0.635738 | ||||||||
\(575\) | 32.6172 | − | 16.3712i | 1.36023 | − | 0.682724i | ||||
\(576\) | −25.4395 | −1.05998 | ||||||||
\(577\) | 8.17830i | 0.340467i | 0.985404 | + | 0.170234i | \(0.0544522\pi\) | ||||
−0.985404 | + | 0.170234i | \(0.945548\pi\) | |||||||
\(578\) | − | 17.1598i | − | 0.713752i | ||||||
\(579\) | −27.0358 | −1.12357 | ||||||||
\(580\) | −9.46385 | + | 15.3391i | −0.392965 | + | 0.636922i | ||||
\(581\) | 10.5146 | 0.436217 | ||||||||
\(582\) | 0.704027i | 0.0291829i | ||||||||
\(583\) | 17.3573i | 0.718867i | ||||||||
\(584\) | 25.0392 | 1.03613 | ||||||||
\(585\) | 26.2110 | + | 16.1715i | 1.08369 | + | 0.668610i | ||||
\(586\) | 10.8746 | 0.449228 | ||||||||
\(587\) | 34.4354i | 1.42130i | 0.703544 | + | 0.710651i | \(0.251600\pi\) | ||||
−0.703544 | + | 0.710651i | \(0.748400\pi\) | |||||||
\(588\) | 35.7584i | 1.47465i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −55.3443 | − | 34.1461i | −2.27849 | − | 1.40577i | ||||
\(591\) | 6.23093 | 0.256306 | ||||||||
\(592\) | − | 3.81961i | − | 0.156985i | ||||||
\(593\) | 2.65119i | 0.108871i | 0.998517 | + | 0.0544357i | \(0.0173360\pi\) | ||||
−0.998517 | + | 0.0544357i | \(0.982664\pi\) | |||||||
\(594\) | −11.5003 | −0.471865 | ||||||||
\(595\) | 6.00454 | − | 9.73221i | 0.246162 | − | 0.398982i | ||||
\(596\) | −13.3481 | −0.546760 | ||||||||
\(597\) | 10.2336i | 0.418834i | ||||||||
\(598\) | − | 107.284i | − | 4.38718i | ||||||
\(599\) | −2.45464 | −0.100294 | −0.0501469 | − | 0.998742i | \(-0.515969\pi\) | ||||
−0.0501469 | + | 0.998742i | \(0.515969\pi\) | |||||||
\(600\) | −19.7044 | − | 39.2582i | −0.804427 | − | 1.60271i | ||||
\(601\) | −14.9631 | −0.610356 | −0.305178 | − | 0.952295i | \(-0.598716\pi\) | ||||
−0.305178 | + | 0.952295i | \(0.598716\pi\) | |||||||
\(602\) | − | 1.83503i | − | 0.0747902i | ||||||
\(603\) | 1.49071i | 0.0607064i | ||||||||
\(604\) | −16.2623 | −0.661705 | ||||||||
\(605\) | −4.18086 | + | 6.77638i | −0.169976 | + | 0.275499i | ||||
\(606\) | −20.2385 | −0.822134 | ||||||||
\(607\) | − | 43.0431i | − | 1.74706i | −0.486767 | − | 0.873532i | \(-0.661824\pi\) | ||
0.486767 | − | 0.873532i | \(-0.338176\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.32467 | −0.337333 | ||||||||
\(610\) | 21.6158 | + | 13.3364i | 0.875199 | + | 0.539976i | ||||
\(611\) | −14.2684 | −0.577237 | ||||||||
\(612\) | 25.1400i | 1.01622i | ||||||||
\(613\) | − | 39.1922i | − | 1.58296i | −0.611198 | − | 0.791478i | \(-0.709312\pi\) | ||
0.611198 | − | 0.791478i | \(-0.290688\pi\) | |||||||
\(614\) | 57.6686 | 2.32732 | ||||||||
\(615\) | 17.0675 | + | 10.5302i | 0.688228 | + | 0.424620i | ||||
\(616\) | 17.1629 | 0.691511 | ||||||||
\(617\) | − | 27.9028i | − | 1.12332i | −0.827367 | − | 0.561662i | \(-0.810162\pi\) | ||
0.827367 | − | 0.561662i | \(-0.189838\pi\) | |||||||
\(618\) | − | 35.7559i | − | 1.43831i | ||||||
\(619\) | 24.8596 | 0.999193 | 0.499597 | − | 0.866258i | \(-0.333482\pi\) | ||||
0.499597 | + | 0.866258i | \(0.333482\pi\) | |||||||
\(620\) | 18.8223 | − | 30.5074i | 0.755923 | − | 1.22521i | ||||
\(621\) | 12.9804 | 0.520887 | ||||||||
\(622\) | − | 52.2099i | − | 2.09343i | ||||||
\(623\) | − | 28.3233i | − | 1.13475i | ||||||
\(624\) | −26.5222 | −1.06174 | ||||||||
\(625\) | −14.9386 | + | 20.0459i | −0.597545 | + | 0.801835i | ||||
\(626\) | 69.9001 | 2.79377 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 73.3901i | − | 2.92858i | ||||||
\(629\) | 6.37448 | 0.254167 | ||||||||
\(630\) | 10.1233 | − | 16.4079i | 0.403320 | − | 0.653705i | ||||
\(631\) | 44.2670 | 1.76224 | 0.881120 | − | 0.472893i | \(-0.156790\pi\) | ||||
0.881120 | + | 0.472893i | \(0.156790\pi\) | |||||||
\(632\) | 15.8400i | 0.630081i | ||||||||
\(633\) | − | 16.7733i | − | 0.666678i | ||||||
\(634\) | −19.0700 | −0.757368 | ||||||||
\(635\) | −16.5442 | − | 10.2074i | −0.656537 | − | 0.405067i | ||||
\(636\) | −52.6644 | −2.08828 | ||||||||
\(637\) | − | 26.7872i | − | 1.06135i | ||||||
\(638\) | − | 14.3932i | − | 0.569833i | ||||||
\(639\) | 5.85419 | 0.231588 | ||||||||
\(640\) | −39.2933 | − | 24.2430i | −1.55320 | − | 0.958289i | ||||
\(641\) | −20.3402 | −0.803389 | −0.401695 | − | 0.915774i | \(-0.631579\pi\) | ||||
−0.401695 | + | 0.915774i | \(0.631579\pi\) | |||||||
\(642\) | 63.9061i | 2.52217i | ||||||||
\(643\) | − | 30.3707i | − | 1.19770i | −0.800860 | − | 0.598852i | \(-0.795624\pi\) | ||
0.800860 | − | 0.598852i | \(-0.204376\pi\) | |||||||
\(644\) | −43.2654 | −1.70490 | ||||||||
\(645\) | 1.26867 | − | 2.05627i | 0.0499536 | − | 0.0809654i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 48.5913i | − | 1.91032i | −0.296087 | − | 0.955161i | \(-0.595682\pi\) | ||
0.296087 | − | 0.955161i | \(-0.404318\pi\) | |||||||
\(648\) | − | 41.2479i | − | 1.62037i | ||||||
\(649\) | 33.4554 | 1.31324 | ||||||||
\(650\) | 32.9674 | + | 65.6829i | 1.29309 | + | 2.57629i | ||||
\(651\) | 16.5567 | 0.648906 | ||||||||
\(652\) | 56.7088i | 2.22089i | ||||||||
\(653\) | 19.9555i | 0.780918i | 0.920620 | + | 0.390459i | \(0.127684\pi\) | ||||
−0.920620 | + | 0.390459i | \(0.872316\pi\) | |||||||
\(654\) | −39.2154 | −1.53344 | ||||||||
\(655\) | 12.3821 | − | 20.0690i | 0.483809 | − | 0.784163i | ||||
\(656\) | −7.34811 | −0.286895 | ||||||||
\(657\) | 14.4703i | 0.564539i | ||||||||
\(658\) | 8.93191i | 0.348202i | ||||||||
\(659\) | −17.0285 | −0.663335 | −0.331667 | − | 0.943396i | \(-0.607611\pi\) | ||||
−0.331667 | + | 0.943396i | \(0.607611\pi\) | |||||||
\(660\) | 42.9535 | + | 26.5013i | 1.67196 | + | 1.03156i | ||||
\(661\) | 27.5335 | 1.07093 | 0.535464 | − | 0.844558i | \(-0.320137\pi\) | ||||
0.535464 | + | 0.844558i | \(0.320137\pi\) | |||||||
\(662\) | 43.1951i | 1.67882i | ||||||||
\(663\) | − | 44.2624i | − | 1.71901i | ||||||
\(664\) | −24.6969 | −0.958427 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.7470 | 0.416436 | ||||||||
\(667\) | 16.2456i | 0.629033i | ||||||||
\(668\) | 21.8945i | 0.847122i | ||||||||
\(669\) | 37.8897 | 1.46490 | ||||||||
\(670\) | −1.86781 | + | 3.02736i | −0.0721597 | + | 0.116957i | ||||
\(671\) | −13.0667 | −0.504434 | ||||||||
\(672\) | − | 12.1559i | − | 0.468923i | ||||||
\(673\) | − | 37.2560i | − | 1.43611i | −0.695984 | − | 0.718057i | \(-0.745032\pi\) | ||
0.695984 | − | 0.718057i | \(-0.254968\pi\) | |||||||
\(674\) | 22.7691 | 0.877032 | ||||||||
\(675\) | −7.94704 | + | 3.98876i | −0.305882 | + | 0.153527i | ||||
\(676\) | 92.1006 | 3.54233 | ||||||||
\(677\) | − | 22.7880i | − | 0.875815i | −0.899020 | − | 0.437907i | \(-0.855720\pi\) | ||
0.899020 | − | 0.437907i | \(-0.144280\pi\) | |||||||
\(678\) | 71.9930i | 2.76488i | ||||||||
\(679\) | −0.212688 | −0.00816223 | ||||||||
\(680\) | −14.1037 | + | 22.8593i | −0.540850 | + | 0.876616i | ||||
\(681\) | 26.9251 | 1.03177 | ||||||||
\(682\) | 28.6262i | 1.09615i | ||||||||
\(683\) | − | 4.61408i | − | 0.176553i | −0.996096 | − | 0.0882764i | \(-0.971864\pi\) | ||
0.996096 | − | 0.0882764i | \(-0.0281359\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.755912 | − | 0.466379i | −0.0288819 | − | 0.0178194i | ||||
\(686\) | −43.9337 | −1.67740 | ||||||||
\(687\) | − | 17.8772i | − | 0.682057i | ||||||
\(688\) | 0.885288i | 0.0337513i | ||||||||
\(689\) | 39.4517 | 1.50299 | ||||||||
\(690\) | −75.2561 | − | 46.4311i | −2.86495 | − | 1.76760i | ||||
\(691\) | 35.7599 | 1.36037 | 0.680186 | − | 0.733040i | \(-0.261899\pi\) | ||||
0.680186 | + | 0.733040i | \(0.261899\pi\) | |||||||
\(692\) | − | 5.94069i | − | 0.225831i | ||||||
\(693\) | 9.91850i | 0.376773i | ||||||||
\(694\) | −3.00229 | −0.113965 | ||||||||
\(695\) | 8.81222 | − | 14.2829i | 0.334267 | − | 0.541783i | ||||
\(696\) | 19.5533 | 0.741165 | ||||||||
\(697\) | − | 12.2631i | − | 0.464499i | ||||||
\(698\) | 63.1030i | 2.38848i | ||||||||
\(699\) | −15.3554 | −0.580795 | ||||||||
\(700\) | 26.4885 | − | 13.2950i | 1.00117 | − | 0.502505i | ||||
\(701\) | 32.8766 | 1.24173 | 0.620865 | − | 0.783917i | \(-0.286781\pi\) | ||||
0.620865 | + | 0.783917i | \(0.286781\pi\) | |||||||
\(702\) | 26.1393i | 0.986565i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 31.2301 | 1.17703 | ||||||||
\(705\) | −6.17516 | + | 10.0088i | −0.232570 | + | 0.376952i | ||||
\(706\) | −63.7180 | −2.39806 | ||||||||
\(707\) | − | 6.11411i | − | 0.229945i | ||||||
\(708\) | 101.508i | 3.81491i | ||||||||
\(709\) | −44.4229 | −1.66834 | −0.834169 | − | 0.551510i | \(-0.814052\pi\) | ||||
−0.834169 | + | 0.551510i | \(0.814052\pi\) | |||||||
\(710\) | 11.8888 | + | 7.33510i | 0.446179 | + | 0.275281i | ||||
\(711\) | −9.15400 | −0.343302 | ||||||||
\(712\) | 66.5267i | 2.49319i | ||||||||
\(713\) | − | 32.3103i | − | 1.21003i | ||||||
\(714\) | −27.7079 | −1.03694 | ||||||||
\(715\) | −32.1772 | − | 19.8525i | −1.20336 | − | 0.742442i | ||||
\(716\) | 51.3834 | 1.92029 | ||||||||
\(717\) | − | 36.5037i | − | 1.36326i | ||||||
\(718\) | − | 49.9247i | − | 1.86317i | ||||||
\(719\) | 20.0859 | 0.749079 | 0.374540 | − | 0.927211i | \(-0.377801\pi\) | ||||
0.374540 | + | 0.927211i | \(0.377801\pi\) | |||||||
\(720\) | −4.88385 | + | 7.91579i | −0.182010 | + | 0.295004i | ||||
\(721\) | 10.8019 | 0.402285 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.8919i | 0.888548i | ||||||||
\(724\) | 83.0982 | 3.08832 | ||||||||
\(725\) | −4.99211 | − | 9.94609i | −0.185402 | − | 0.369388i | ||||
\(726\) | 19.2926 | 0.716014 | ||||||||
\(727\) | − | 0.729793i | − | 0.0270665i | −0.999908 | − | 0.0135333i | \(-0.995692\pi\) | ||
0.999908 | − | 0.0135333i | \(-0.00430790\pi\) | |||||||
\(728\) | − | 39.0098i | − | 1.44580i | ||||||
\(729\) | 11.6460 | 0.431333 | ||||||||
\(730\) | −18.1307 | + | 29.3865i | −0.671049 | + | 1.08764i | ||||
\(731\) | −1.47744 | −0.0546452 | ||||||||
\(732\) | − | 39.6460i | − | 1.46536i | ||||||
\(733\) | 29.4948i | 1.08941i | 0.838626 | + | 0.544707i | \(0.183359\pi\) | ||||
−0.838626 | + | 0.544707i | \(0.816641\pi\) | |||||||
\(734\) | 26.1226 | 0.964201 | ||||||||
\(735\) | −18.7902 | − | 11.5931i | −0.693088 | − | 0.427618i | ||||
\(736\) | −23.7222 | −0.874412 | ||||||||
\(737\) | − | 1.83003i | − | 0.0674100i | ||||||
\(738\) | − | 20.6748i | − | 0.761051i | ||||||
\(739\) | 40.4996 | 1.48980 | 0.744901 | − | 0.667175i | \(-0.232497\pi\) | ||||
0.744901 | + | 0.667175i | \(0.232497\pi\) | |||||||
\(740\) | 14.0602 | + | 8.67482i | 0.516864 | + | 0.318893i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 24.6965i | − | 0.906637i | ||||||
\(743\) | − | 19.4337i | − | 0.712955i | −0.934304 | − | 0.356477i | \(-0.883978\pi\) | ||
0.934304 | − | 0.356477i | \(-0.116022\pi\) | |||||||
\(744\) | −38.8888 | −1.42573 | ||||||||
\(745\) | 4.32755 | − | 7.01414i | 0.158549 | − | 0.256978i | ||||
\(746\) | −11.4591 | −0.419547 | ||||||||
\(747\) | − | 14.2725i | − | 0.522202i | ||||||
\(748\) | − | 30.8624i | − | 1.12844i | ||||||
\(749\) | −19.3062 | −0.705433 | ||||||||
\(750\) | 60.3420 | + | 5.30122i | 2.20338 | + | 0.193573i | ||||
\(751\) | −5.66378 | −0.206674 | −0.103337 | − | 0.994646i | \(-0.532952\pi\) | ||||
−0.103337 | + | 0.994646i | \(0.532952\pi\) | |||||||
\(752\) | − | 4.30909i | − | 0.157136i | ||||||
\(753\) | 27.1155i | 0.988144i | ||||||||
\(754\) | −32.7146 | −1.19139 | ||||||||
\(755\) | 5.27236 | − | 8.54550i | 0.191881 | − | 0.311003i | ||||
\(756\) | 10.5414 | 0.383388 | ||||||||
\(757\) | − | 12.5786i | − | 0.457176i | −0.973523 | − | 0.228588i | \(-0.926589\pi\) | ||
0.973523 | − | 0.228588i | \(-0.0734109\pi\) | |||||||
\(758\) | − | 4.83015i | − | 0.175439i | ||||||
\(759\) | 45.4920 | 1.65126 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.0335 | 1.81371 | 0.906857 | − | 0.421439i | \(-0.138475\pi\) | ||||
0.906857 | + | 0.421439i | \(0.138475\pi\) | |||||||
\(762\) | 47.1019i | 1.70632i | ||||||||
\(763\) | − | 11.8471i | − | 0.428892i | ||||||
\(764\) | −36.9750 | −1.33771 | ||||||||
\(765\) | −13.2105 | − | 8.15057i | −0.477627 | − | 0.294684i | ||||
\(766\) | 81.9892 | 2.96239 | ||||||||
\(767\) | − | 76.0414i | − | 2.74570i | ||||||
\(768\) | 59.5392i | 2.14844i | ||||||||
\(769\) | 31.7447 | 1.14474 | 0.572371 | − | 0.819994i | \(-0.306024\pi\) | ||||
0.572371 | + | 0.819994i | \(0.306024\pi\) | |||||||
\(770\) | −12.4275 | + | 20.1427i | −0.447857 | + | 0.725891i | ||||
\(771\) | 8.72066 | 0.314067 | ||||||||
\(772\) | 42.8467i | 1.54209i | ||||||||
\(773\) | − | 11.4374i | − | 0.411373i | −0.978618 | − | 0.205687i | \(-0.934057\pi\) | ||
0.978618 | − | 0.205687i | \(-0.0659428\pi\) | |||||||
\(774\) | −2.49087 | −0.0895325 | ||||||||
\(775\) | 9.92864 | + | 19.7814i | 0.356647 | + | 0.710570i | ||||
\(776\) | 0.499569 | 0.0179335 | ||||||||
\(777\) | 7.63062i | 0.273747i | ||||||||
\(778\) | − | 10.7410i | − | 0.385083i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 60.2352 | − | 97.6298i | 2.15677 | − | 3.49571i | ||||
\(781\) | −7.18673 | −0.257162 | ||||||||
\(782\) | 54.0721i | 1.93361i | ||||||||
\(783\) | − | 3.95817i | − | 0.141453i | ||||||
\(784\) | 8.08980 | 0.288921 | ||||||||
\(785\) | 38.5648 | + | 23.7936i | 1.37644 | + | 0.849229i | ||||
\(786\) | −57.1372 | −2.03802 | ||||||||
\(787\) | 6.64024i | 0.236699i | 0.992972 | + | 0.118350i | \(0.0377603\pi\) | ||||
−0.992972 | + | 0.118350i | \(0.962240\pi\) | |||||||
\(788\) | − | 9.87488i | − | 0.351778i | ||||||
\(789\) | 4.84347 | 0.172432 | ||||||||
\(790\) | −18.5901 | − | 11.4696i | −0.661407 | − | 0.408072i | ||||
\(791\) | −21.7493 | −0.773315 | ||||||||
\(792\) | − | 23.2969i | − | 0.827819i | ||||||
\(793\) | 29.6995i | 1.05466i | ||||||||
\(794\) | 59.5938 | 2.11490 | ||||||||
\(795\) | 17.0742 | − | 27.6740i | 0.605558 | − | 0.981495i | ||||
\(796\) | 16.2184 | 0.574847 | ||||||||
\(797\) | − | 0.186468i | − | 0.00660502i | −0.999995 | − | 0.00330251i | \(-0.998949\pi\) | ||
0.999995 | − | 0.00330251i | \(-0.00105122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.19137 | 0.254412 | ||||||||
\(800\) | 14.5235 | − | 7.28959i | 0.513483 | − | 0.257726i | ||||
\(801\) | −38.4461 | −1.35843 | ||||||||
\(802\) | 68.5485i | 2.42053i | ||||||||
\(803\) | − | 17.7640i | − | 0.626878i | ||||||
\(804\) | 5.55255 | 0.195823 | ||||||||
\(805\) | 14.0270 | − | 22.7350i | 0.494385 | − | 0.801305i | ||||
\(806\) | 65.0649 | 2.29181 | ||||||||
\(807\) | 8.97655i | 0.315989i | ||||||||
\(808\) | 14.3610i | 0.505219i | ||||||||
\(809\) | −1.21997 | −0.0428918 | −0.0214459 | − | 0.999770i | \(-0.506827\pi\) | ||||
−0.0214459 | + | 0.999770i | \(0.506827\pi\) | |||||||
\(810\) | 48.4094 | + | 29.8674i | 1.70093 | + | 1.04943i | ||||
\(811\) | 19.0938 | 0.670474 | 0.335237 | − | 0.942134i | \(-0.391184\pi\) | ||||
0.335237 | + | 0.942134i | \(0.391184\pi\) | |||||||
\(812\) | 13.1931i | 0.462986i | ||||||||
\(813\) | − | 43.2706i | − | 1.51757i | ||||||
\(814\) | −13.1932 | −0.462422 | ||||||||
\(815\) | −29.7992 | − | 18.3854i | −1.04382 | − | 0.644012i | ||||
\(816\) | 13.3674 | 0.467951 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 54.4413i | 1.90349i | ||||||||
\(819\) | 22.5439 | 0.787748 | ||||||||
\(820\) | 16.6885 | − | 27.0489i | 0.582787 | − | 0.944587i | ||||
\(821\) | −9.97729 | −0.348210 | −0.174105 | − | 0.984727i | \(-0.555703\pi\) | ||||
−0.174105 | + | 0.984727i | \(0.555703\pi\) | |||||||
\(822\) | 2.15211i | 0.0750633i | ||||||||
\(823\) | − | 28.2077i | − | 0.983260i | −0.870804 | − | 0.491630i | \(-0.836401\pi\) | ||
0.870804 | − | 0.491630i | \(-0.163599\pi\) | |||||||
\(824\) | −25.3719 | −0.883873 | ||||||||
\(825\) | −27.8517 | + | 13.9792i | −0.969670 | + | 0.486694i | ||||
\(826\) | −47.6014 | −1.65626 | ||||||||
\(827\) | 8.85297i | 0.307848i | 0.988083 | + | 0.153924i | \(0.0491911\pi\) | ||||
−0.988083 | + | 0.153924i | \(0.950809\pi\) | |||||||
\(828\) | 58.7286i | 2.04096i | ||||||||
\(829\) | 45.6892 | 1.58685 | 0.793425 | − | 0.608668i | \(-0.208296\pi\) | ||||
0.793425 | + | 0.608668i | \(0.208296\pi\) | |||||||
\(830\) | 17.8829 | − | 28.9848i | 0.620725 | − | 1.00608i | ||||
\(831\) | 34.3393 | 1.19122 | ||||||||
\(832\) | − | 70.9835i | − | 2.46091i | ||||||
\(833\) | 13.5009i | 0.467779i | ||||||||
\(834\) | −40.6640 | −1.40808 | ||||||||
\(835\) | −11.5051 | − | 7.09834i | −0.398149 | − | 0.245648i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.87227i | 0.272105i | ||||||||
\(838\) | 21.2927i | 0.735543i | ||||||||
\(839\) | 0.182558 | 0.00630259 | 0.00315130 | − | 0.999995i | \(-0.498997\pi\) | ||||
0.00315130 | + | 0.999995i | \(0.498997\pi\) | |||||||
\(840\) | −27.3639 | − | 16.8829i | −0.944146 | − | 0.582515i | ||||
\(841\) | −24.0462 | −0.829178 | ||||||||
\(842\) | − | 80.7092i | − | 2.78142i | ||||||
\(843\) | 62.8019i | 2.16301i | ||||||||
\(844\) | −26.5826 | −0.915010 | ||||||||
\(845\) | −29.8597 | + | 48.3968i | −1.02720 | + | 1.66490i | ||||
\(846\) | 12.1242 | 0.416838 | ||||||||
\(847\) | 5.82833i | 0.200264i | ||||||||
\(848\) | 11.9145i | 0.409147i | ||||||||
\(849\) | −46.4694 | −1.59483 | ||||||||
\(850\) | −16.6158 | − | 33.1046i | −0.569917 | − | 1.13548i | ||||
\(851\) | 14.8912 | 0.510463 | ||||||||
\(852\) | − | 21.8055i | − | 0.747044i | ||||||
\(853\) | 49.2184i | 1.68520i | 0.538537 | + | 0.842602i | \(0.318977\pi\) | ||||
−0.538537 | + | 0.842602i | \(0.681023\pi\) | |||||||
\(854\) | 18.5917 | 0.636193 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 45.3470 | 1.54993 | ||||||||
\(857\) | − | 31.5699i | − | 1.07841i | −0.842175 | − | 0.539204i | \(-0.818725\pi\) | ||
0.842175 | − | 0.539204i | \(-0.181275\pi\) | |||||||
\(858\) | 91.6094i | 3.12749i | ||||||||
\(859\) | 10.6896 | 0.364723 | 0.182362 | − | 0.983232i | \(-0.441626\pi\) | ||||
0.182362 | + | 0.983232i | \(0.441626\pi\) | |||||||
\(860\) | −3.25880 | − | 2.01060i | −0.111124 | − | 0.0685610i | ||||
\(861\) | 14.6797 | 0.500282 | ||||||||
\(862\) | 90.0327i | 3.06653i | ||||||||
\(863\) | 25.5826i | 0.870841i | 0.900227 | + | 0.435420i | \(0.143400\pi\) | ||||
−0.900227 | + | 0.435420i | \(0.856600\pi\) | |||||||
\(864\) | 5.77981 | 0.196633 | ||||||||
\(865\) | 3.12170 | + | 1.92601i | 0.106141 | + | 0.0654864i | ||||
\(866\) | −87.6783 | −2.97943 | ||||||||
\(867\) | − | 16.5384i | − | 0.561674i | ||||||
\(868\) | − | 26.2393i | − | 0.890619i | ||||||
\(869\) | 11.2377 | 0.381211 | ||||||||
\(870\) | −14.1584 | + | 22.9481i | −0.480015 | + | 0.778013i | ||||
\(871\) | −4.15950 | −0.140939 | ||||||||
\(872\) | 27.8268i | 0.942333i | ||||||||
\(873\) | 0.288703i | 0.00977113i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.60151 | + | 18.2295i | −0.0541409 | + | 0.616268i | ||||
\(876\) | 53.8984 | 1.82106 | ||||||||
\(877\) | 31.0952i | 1.05001i | 0.851099 | + | 0.525005i | \(0.175937\pi\) | ||||
−0.851099 | + | 0.525005i | \(0.824063\pi\) | |||||||
\(878\) | − | 52.5953i | − | 1.77500i | ||||||
\(879\) | 10.4809 | 0.353511 | ||||||||
\(880\) | 5.99552 | − | 9.71759i | 0.202109 | − | 0.327580i | ||||
\(881\) | −47.4465 | −1.59851 | −0.799257 | − | 0.600990i | \(-0.794773\pi\) | ||||
−0.799257 | + | 0.600990i | \(0.794773\pi\) | |||||||
\(882\) | 22.7617i | 0.766425i | ||||||||
\(883\) | − | 14.5332i | − | 0.489082i | −0.969639 | − | 0.244541i | \(-0.921363\pi\) | ||
0.969639 | − | 0.244541i | \(-0.0786372\pi\) | |||||||
\(884\) | −70.1477 | −2.35932 | ||||||||
\(885\) | −53.3403 | − | 32.9097i | −1.79302 | − | 1.10625i | ||||
\(886\) | 23.3512 | 0.784498 | ||||||||
\(887\) | 37.1270i | 1.24660i | 0.781982 | + | 0.623301i | \(0.214209\pi\) | ||||
−0.781982 | + | 0.623301i | \(0.785791\pi\) | |||||||
\(888\) | − | 17.9230i | − | 0.601458i | ||||||
\(889\) | −14.2296 | −0.477245 | ||||||||
\(890\) | −78.0770 | − | 48.1716i | −2.61715 | − | 1.61472i | ||||
\(891\) | −29.2633 | −0.980357 | ||||||||
\(892\) | − | 60.0483i | − | 2.01057i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −19.9695 | −0.667879 | ||||||||
\(895\) | −16.6589 | + | 27.0009i | −0.556845 | + | 0.902539i | ||||
\(896\) | −33.7960 | −1.12904 | ||||||||
\(897\) | − | 103.400i | − | 3.45241i | ||||||
\(898\) | 88.4464i | 2.95150i | ||||||||
\(899\) | −9.85251 | −0.328600 | ||||||||
\(900\) | −18.0467 | − | 35.9555i | −0.601556 | − | 1.19852i | ||||
\(901\) | −19.8840 | −0.662431 | ||||||||
\(902\) | 25.3809i | 0.845091i | ||||||||
\(903\) | − | 1.76858i | − | 0.0588548i | ||||||
\(904\) | 51.0854 | 1.69907 | ||||||||
\(905\) | −26.9410 | + | 43.6663i | −0.895550 | + | 1.45152i | ||||
\(906\) | −24.3293 | −0.808287 | ||||||||
\(907\) | − | 10.8657i | − | 0.360789i | −0.983594 | − | 0.180394i | \(-0.942263\pi\) | ||
0.983594 | − | 0.180394i | \(-0.0577374\pi\) | |||||||
\(908\) | − | 42.6713i | − | 1.41610i | ||||||
\(909\) | −8.29929 | −0.275270 | ||||||||
\(910\) | 45.7826 | + | 28.2467i | 1.51768 | + | 0.936371i | ||||
\(911\) | 39.5522 | 1.31042 | 0.655211 | − | 0.755446i | \(-0.272580\pi\) | ||||
0.655211 | + | 0.755446i | \(0.272580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.5212i | 0.579867i | ||||||||
\(914\) | 33.2749 | 1.10064 | ||||||||
\(915\) | 20.8331 | + | 12.8535i | 0.688722 | + | 0.424924i | ||||
\(916\) | −28.3321 | −0.936117 | ||||||||
\(917\) | − | 17.2613i | − | 0.570018i | ||||||
\(918\) | − | 13.1744i | − | 0.434820i | ||||||
\(919\) | −32.1565 | −1.06074 | −0.530372 | − | 0.847765i | \(-0.677948\pi\) | ||||
−0.530372 | + | 0.847765i | \(0.677948\pi\) | |||||||
\(920\) | −32.9470 | + | 53.4008i | −1.08623 | + | 1.76057i | ||||
\(921\) | 55.5805 | 1.83144 | ||||||||
\(922\) | 24.0320i | 0.791451i | ||||||||
\(923\) | 16.3348i | 0.537668i | ||||||||
\(924\) | 36.9441 | 1.21537 | ||||||||
\(925\) | −9.11685 | + | 4.57590i | −0.299760 | + | 0.150455i | ||||
\(926\) | 1.71215 | 0.0562647 | ||||||||
\(927\) | − | 14.6626i | − | 0.481582i | ||||||
\(928\) | 7.23369i | 0.237458i | ||||||||
\(929\) | 10.9336 | 0.358719 | 0.179359 | − | 0.983784i | \(-0.442598\pi\) | ||||
0.179359 | + | 0.983784i | \(0.442598\pi\) | |||||||
\(930\) | 28.1592 | − | 45.6407i | 0.923376 | − | 1.49662i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 24.3355i | 0.797136i | ||||||||
\(933\) | − | 50.3194i | − | 1.64738i | ||||||
\(934\) | −83.0247 | −2.71665 | ||||||||
\(935\) | 16.2175 | + | 10.0058i | 0.530370 | + | 0.327225i | ||||
\(936\) | −52.9519 | −1.73079 | ||||||||
\(937\) | − | 45.0301i | − | 1.47107i | −0.677487 | − | 0.735535i | \(-0.736931\pi\) | ||
0.677487 | − | 0.735535i | \(-0.263069\pi\) | |||||||
\(938\) | 2.60382i | 0.0850177i | ||||||||
\(939\) | 67.3691 | 2.19851 | ||||||||
\(940\) | 15.8621 | + | 9.78650i | 0.517363 | + | 0.319200i | ||||
\(941\) | 42.6516 | 1.39040 | 0.695201 | − | 0.718816i | \(-0.255315\pi\) | ||||
0.695201 | + | 0.718816i | \(0.255315\pi\) | |||||||
\(942\) | − | 109.795i | − | 3.57733i | ||||||
\(943\) | − | 28.6474i | − | 0.932888i | ||||||
\(944\) | 22.9647 | 0.747438 | ||||||||
\(945\) | −3.41760 | + | 5.53929i | −0.111175 | + | 0.180193i | ||||
\(946\) | 3.05785 | 0.0994192 | ||||||||
\(947\) | − | 24.7131i | − | 0.803069i | −0.915844 | − | 0.401535i | \(-0.868477\pi\) | ||
0.915844 | − | 0.401535i | \(-0.131523\pi\) | |||||||
\(948\) | 34.0965i | 1.10740i | ||||||||
\(949\) | −40.3761 | −1.31066 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.3795 | −0.595996 | ||||||||
\(952\) | 19.6612i | 0.637223i | ||||||||
\(953\) | 15.5170i | 0.502646i | 0.967903 | + | 0.251323i | \(0.0808657\pi\) | ||||
−0.967903 | + | 0.251323i | \(0.919134\pi\) | |||||||
\(954\) | −33.5231 | −1.08535 | ||||||||
\(955\) | 11.9876 | − | 19.4296i | 0.387909 | − | 0.628726i | ||||
\(956\) | −57.8517 | −1.87106 | ||||||||
\(957\) | − | 13.8720i | − | 0.448419i | ||||||
\(958\) | − | 63.9217i | − | 2.06521i | ||||||
\(959\) | −0.650157 | −0.0209946 | ||||||||
\(960\) | −49.7923 | − | 30.7207i | −1.60704 | − | 0.991505i | ||||
\(961\) | −11.4047 | −0.367893 | ||||||||
\(962\) | 29.9871i | 0.966821i | ||||||||
\(963\) | 26.2062i | 0.844484i | ||||||||
\(964\) | 37.8642 | 1.21952 | ||||||||
\(965\) | −22.5150 | − | 13.8912i | −0.724784 | − | 0.447174i | ||||
\(966\) | −64.7274 | −2.08257 | ||||||||
\(967\) | − | 16.0510i | − | 0.516166i | −0.966123 | − | 0.258083i | \(-0.916909\pi\) | ||
0.966123 | − | 0.258083i | \(-0.0830909\pi\) | |||||||
\(968\) | − | 13.6898i | − | 0.440006i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.361735 | + | 0.586304i | −0.0116146 | + | 0.0188251i | ||||
\(971\) | 5.76925 | 0.185144 | 0.0925720 | − | 0.995706i | \(-0.470491\pi\) | ||||
0.0925720 | + | 0.995706i | \(0.470491\pi\) | |||||||
\(972\) | − | 69.4676i | − | 2.22817i | ||||||
\(973\) | − | 12.2847i | − | 0.393829i | ||||||
\(974\) | −7.27312 | −0.233046 | ||||||||
\(975\) | 31.7736 | + | 63.3045i | 1.01757 | + | 2.02737i | ||||
\(976\) | −8.96933 | −0.287101 | ||||||||
\(977\) | 46.7724i | 1.49638i | 0.663484 | + | 0.748190i | \(0.269077\pi\) | ||||
−0.663484 | + | 0.748190i | \(0.730923\pi\) | |||||||
\(978\) | 84.8394i | 2.71286i | ||||||||
\(979\) | 47.1973 | 1.50843 | ||||||||
\(980\) | −18.3730 | + | 29.7791i | −0.586903 | + | 0.951258i | ||||
\(981\) | −16.0812 | −0.513434 | ||||||||
\(982\) | − | 2.96106i | − | 0.0944912i | ||||||
\(983\) | 33.6039i | 1.07180i | 0.844282 | + | 0.535900i | \(0.180028\pi\) | ||||
−0.844282 | + | 0.535900i | \(0.819972\pi\) | |||||||
\(984\) | −34.4801 | −1.09919 | ||||||||
\(985\) | 5.18903 | + | 3.20151i | 0.165336 | + | 0.102008i | ||||
\(986\) | 16.4884 | 0.525097 | ||||||||
\(987\) | 8.60848i | 0.274011i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.45139 | −0.109748 | ||||||||
\(990\) | 27.3417 | + | 16.8691i | 0.868976 | + | 0.536137i | ||||
\(991\) | 45.6040 | 1.44866 | 0.724329 | − | 0.689454i | \(-0.242150\pi\) | ||||
0.724329 | + | 0.689454i | \(0.242150\pi\) | |||||||
\(992\) | − | 14.3868i | − | 0.456783i | ||||||
\(993\) | 41.6310i | 1.32112i | ||||||||
\(994\) | 10.2255 | 0.324333 | ||||||||
\(995\) | −5.25812 | + | 8.52242i | −0.166694 | + | 0.270179i | ||||
\(996\) | −53.1616 | −1.68449 | ||||||||
\(997\) | − | 4.80126i | − | 0.152057i | −0.997106 | − | 0.0760287i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760287i | \(-0.0242241\pi\) | |||||||
\(998\) | 46.4047i | 1.46892i | ||||||||
\(999\) | −3.62817 | −0.114790 |
(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 | 1805.2.b.l.1084.2 | 24 | ||
5.2 | odd | 4 | 9025.2.a.ct.1.23 | 24 | |||
5.3 | odd | 4 | 9025.2.a.ct.1.2 | 24 | |||
5.4 | even | 2 | inner | 1805.2.b.l.1084.23 | 24 | ||
19.2 | odd | 18 | 95.2.p.a.4.8 | yes | 48 | ||
19.10 | odd | 18 | 95.2.p.a.24.1 | yes | 48 | ||
19.18 | odd | 2 | 1805.2.b.k.1084.23 | 24 | |||
57.2 | even | 18 | 855.2.da.b.289.1 | 48 | |||
57.29 | even | 18 | 855.2.da.b.784.8 | 48 | |||
95.2 | even | 36 | 475.2.l.f.251.8 | 48 | |||
95.18 | even | 4 | 9025.2.a.cu.1.23 | 24 | |||
95.29 | odd | 18 | 95.2.p.a.24.8 | yes | 48 | ||
95.37 | even | 4 | 9025.2.a.cu.1.2 | 24 | |||
95.48 | even | 36 | 475.2.l.f.176.1 | 48 | |||
95.59 | odd | 18 | 95.2.p.a.4.1 | ✓ | 48 | ||
95.67 | even | 36 | 475.2.l.f.176.8 | 48 | |||
95.78 | even | 36 | 475.2.l.f.251.1 | 48 | |||
95.94 | odd | 2 | 1805.2.b.k.1084.2 | 24 | |||
285.29 | even | 18 | 855.2.da.b.784.1 | 48 | |||
285.59 | even | 18 | 855.2.da.b.289.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.4.1 | ✓ | 48 | 95.59 | odd | 18 | ||
95.2.p.a.4.8 | yes | 48 | 19.2 | odd | 18 | ||
95.2.p.a.24.1 | yes | 48 | 19.10 | odd | 18 | ||
95.2.p.a.24.8 | yes | 48 | 95.29 | odd | 18 | ||
475.2.l.f.176.1 | 48 | 95.48 | even | 36 | |||
475.2.l.f.176.8 | 48 | 95.67 | even | 36 | |||
475.2.l.f.251.1 | 48 | 95.78 | even | 36 | |||
475.2.l.f.251.8 | 48 | 95.2 | even | 36 | |||
855.2.da.b.289.1 | 48 | 57.2 | even | 18 | |||
855.2.da.b.289.8 | 48 | 285.59 | even | 18 | |||
855.2.da.b.784.1 | 48 | 285.29 | even | 18 | |||
855.2.da.b.784.8 | 48 | 57.29 | even | 18 | |||
1805.2.b.k.1084.2 | 24 | 95.94 | odd | 2 | |||
1805.2.b.k.1084.23 | 24 | 19.18 | odd | 2 | |||
1805.2.b.l.1084.2 | 24 | 1.1 | even | 1 | trivial | ||
1805.2.b.l.1084.23 | 24 | 5.4 | even | 2 | inner | ||
9025.2.a.ct.1.2 | 24 | 5.3 | odd | 4 | |||
9025.2.a.ct.1.23 | 24 | 5.2 | odd | 4 | |||
9025.2.a.cu.1.2 | 24 | 95.37 | even | 4 | |||
9025.2.a.cu.1.23 | 24 | 95.18 | even | 4 |