Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, 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("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.15 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.18 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.475674i | − | 0.336352i | −0.985757 | − | 0.168176i | \(-0.946212\pi\) | ||
0.985757 | − | 0.168176i | \(-0.0537877\pi\) | |||||||
\(3\) | 0.345654 | 0.199564 | 0.0997818 | − | 0.995009i | \(-0.468186\pi\) | ||||
0.0997818 | + | 0.995009i | \(0.468186\pi\) | |||||||
\(4\) | 1.77373 | 0.886867 | ||||||||
\(5\) | − | 0.161594i | − | 0.0722671i | −0.999347 | − | 0.0361336i | \(-0.988496\pi\) | ||
0.999347 | − | 0.0361336i | \(-0.0115042\pi\) | |||||||
\(6\) | − | 0.164419i | − | 0.0671236i | ||||||
\(7\) | − | 4.07996i | − | 1.54208i | −0.636787 | − | 0.771039i | \(-0.719737\pi\) | ||
0.636787 | − | 0.771039i | \(-0.280263\pi\) | |||||||
\(8\) | − | 1.79507i | − | 0.634652i | ||||||
\(9\) | −2.88052 | −0.960174 | ||||||||
\(10\) | −0.0768661 | −0.0243072 | ||||||||
\(11\) | − | 3.77693i | − | 1.13879i | −0.822065 | − | 0.569394i | \(-0.807178\pi\) | ||
0.822065 | − | 0.569394i | \(-0.192822\pi\) | |||||||
\(12\) | 0.613099 | 0.176986 | ||||||||
\(13\) | −3.57244 | + | 0.487542i | −0.990816 | + | 0.135220i | ||||
\(14\) | −1.94073 | −0.518681 | ||||||||
\(15\) | − | 0.0558557i | − | 0.0144219i | ||||||
\(16\) | 2.69360 | 0.673401 | ||||||||
\(17\) | 1.83266 | 0.444485 | 0.222243 | − | 0.974991i | \(-0.428662\pi\) | ||||
0.222243 | + | 0.974991i | \(0.428662\pi\) | |||||||
\(18\) | 1.37019i | 0.322957i | ||||||||
\(19\) | 6.07852i | 1.39451i | 0.716825 | + | 0.697254i | \(0.245595\pi\) | ||||
−0.716825 | + | 0.697254i | \(0.754405\pi\) | |||||||
\(20\) | − | 0.286625i | − | 0.0640913i | ||||||
\(21\) | − | 1.41025i | − | 0.307743i | ||||||
\(22\) | −1.79659 | −0.383033 | ||||||||
\(23\) | 8.58551 | 1.79020 | 0.895102 | − | 0.445862i | \(-0.147103\pi\) | ||||
0.895102 | + | 0.445862i | \(0.147103\pi\) | |||||||
\(24\) | − | 0.620472i | − | 0.126653i | ||||||
\(25\) | 4.97389 | 0.994777 | ||||||||
\(26\) | 0.231911 | + | 1.69931i | 0.0454814 | + | 0.333263i | ||||
\(27\) | −2.03263 | −0.391179 | ||||||||
\(28\) | − | 7.23676i | − | 1.36762i | ||||||
\(29\) | −5.21592 | −0.968571 | −0.484286 | − | 0.874910i | \(-0.660920\pi\) | ||||
−0.484286 | + | 0.874910i | \(0.660920\pi\) | |||||||
\(30\) | −0.0265691 | −0.00485083 | ||||||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | − | 4.87141i | − | 0.861151i | ||||||
\(33\) | − | 1.30551i | − | 0.227261i | ||||||
\(34\) | − | 0.871748i | − | 0.149504i | ||||||
\(35\) | −0.659297 | −0.111442 | ||||||||
\(36\) | −5.10928 | −0.851547 | ||||||||
\(37\) | 11.7559i | 1.93266i | 0.257313 | + | 0.966328i | \(0.417163\pi\) | ||||
−0.257313 | + | 0.966328i | \(0.582837\pi\) | |||||||
\(38\) | 2.89139 | 0.469045 | ||||||||
\(39\) | −1.23483 | + | 0.168521i | −0.197731 | + | 0.0269849i | ||||
\(40\) | −0.290072 | −0.0458644 | ||||||||
\(41\) | − | 4.76311i | − | 0.743873i | −0.928258 | − | 0.371937i | \(-0.878694\pi\) | ||
0.928258 | − | 0.371937i | \(-0.121306\pi\) | |||||||
\(42\) | −0.670821 | −0.103510 | ||||||||
\(43\) | 6.24514 | 0.952374 | 0.476187 | − | 0.879344i | \(-0.342018\pi\) | ||||
0.476187 | + | 0.879344i | \(0.342018\pi\) | |||||||
\(44\) | − | 6.69927i | − | 1.00995i | ||||||
\(45\) | 0.465476i | 0.0693890i | ||||||||
\(46\) | − | 4.08390i | − | 0.602138i | ||||||
\(47\) | 4.70897i | 0.686874i | 0.939176 | + | 0.343437i | \(0.111591\pi\) | ||||
−0.939176 | + | 0.343437i | \(0.888409\pi\) | |||||||
\(48\) | 0.931056 | 0.134386 | ||||||||
\(49\) | −9.64605 | −1.37801 | ||||||||
\(50\) | − | 2.36595i | − | 0.334595i | ||||||
\(51\) | 0.633467 | 0.0887031 | ||||||||
\(52\) | −6.33655 | + | 0.864769i | −0.878722 | + | 0.119922i | ||||
\(53\) | 6.16063 | 0.846227 | 0.423113 | − | 0.906077i | \(-0.360937\pi\) | ||||
0.423113 | + | 0.906077i | \(0.360937\pi\) | |||||||
\(54\) | 0.966867i | 0.131574i | ||||||||
\(55\) | −0.610330 | −0.0822969 | ||||||||
\(56\) | −7.32379 | −0.978683 | ||||||||
\(57\) | 2.10107i | 0.278293i | ||||||||
\(58\) | 2.48107i | 0.325781i | ||||||||
\(59\) | − | 7.98069i | − | 1.03900i | −0.854471 | − | 0.519499i | \(-0.826119\pi\) | ||
0.854471 | − | 0.519499i | \(-0.173881\pi\) | |||||||
\(60\) | − | 0.0990732i | − | 0.0127903i | ||||||
\(61\) | −4.52134 | −0.578899 | −0.289449 | − | 0.957193i | \(-0.593472\pi\) | ||||
−0.289449 | + | 0.957193i | \(0.593472\pi\) | |||||||
\(62\) | 0.475674 | 0.0604106 | ||||||||
\(63\) | 11.7524i | 1.48066i | ||||||||
\(64\) | 3.07001 | 0.383751 | ||||||||
\(65\) | 0.0787839 | + | 0.577285i | 0.00977194 | + | 0.0716034i | ||||
\(66\) | −0.620998 | −0.0764395 | ||||||||
\(67\) | 7.69808i | 0.940470i | 0.882541 | + | 0.470235i | \(0.155831\pi\) | ||||
−0.882541 | + | 0.470235i | \(0.844169\pi\) | |||||||
\(68\) | 3.25065 | 0.394199 | ||||||||
\(69\) | 2.96762 | 0.357259 | ||||||||
\(70\) | 0.313610i | 0.0374836i | ||||||||
\(71\) | − | 7.77152i | − | 0.922310i | −0.887320 | − | 0.461155i | \(-0.847435\pi\) | ||
0.887320 | − | 0.461155i | \(-0.152565\pi\) | |||||||
\(72\) | 5.17073i | 0.609376i | ||||||||
\(73\) | − | 4.96395i | − | 0.580986i | −0.956877 | − | 0.290493i | \(-0.906181\pi\) | ||
0.956877 | − | 0.290493i | \(-0.0938194\pi\) | |||||||
\(74\) | 5.59197 | 0.650053 | ||||||||
\(75\) | 1.71925 | 0.198521 | ||||||||
\(76\) | 10.7817i | 1.23674i | ||||||||
\(77\) | −15.4097 | −1.75610 | ||||||||
\(78\) | 0.0801609 | + | 0.587375i | 0.00907644 | + | 0.0665071i | ||||
\(79\) | 8.26843 | 0.930271 | 0.465135 | − | 0.885240i | \(-0.346006\pi\) | ||||
0.465135 | + | 0.885240i | \(0.346006\pi\) | |||||||
\(80\) | − | 0.435271i | − | 0.0486648i | ||||||
\(81\) | 7.93898 | 0.882109 | ||||||||
\(82\) | −2.26569 | −0.250203 | ||||||||
\(83\) | 12.1642i | 1.33520i | 0.744522 | + | 0.667598i | \(0.232678\pi\) | ||||
−0.744522 | + | 0.667598i | \(0.767322\pi\) | |||||||
\(84\) | − | 2.50142i | − | 0.272927i | ||||||
\(85\) | − | 0.296147i | − | 0.0321217i | ||||||
\(86\) | − | 2.97065i | − | 0.320333i | ||||||
\(87\) | −1.80290 | −0.193292 | ||||||||
\(88\) | −6.77984 | −0.722733 | ||||||||
\(89\) | 3.17056i | 0.336079i | 0.985780 | + | 0.168040i | \(0.0537436\pi\) | ||||
−0.985780 | + | 0.168040i | \(0.946256\pi\) | |||||||
\(90\) | 0.221415 | 0.0233391 | ||||||||
\(91\) | 1.98915 | + | 14.5754i | 0.208519 | + | 1.52792i | ||||
\(92\) | 15.2284 | 1.58767 | ||||||||
\(93\) | 0.345654i | 0.0358427i | ||||||||
\(94\) | 2.23993 | 0.231031 | ||||||||
\(95\) | 0.982253 | 0.100777 | ||||||||
\(96\) | − | 1.68382i | − | 0.171854i | ||||||
\(97\) | 0.366185i | 0.0371804i | 0.999827 | + | 0.0185902i | \(0.00591779\pi\) | ||||
−0.999827 | + | 0.0185902i | \(0.994082\pi\) | |||||||
\(98\) | 4.58837i | 0.463495i | ||||||||
\(99\) | 10.8795i | 1.09343i | ||||||||
\(100\) | 8.82236 | 0.882236 | ||||||||
\(101\) | 4.41069 | 0.438880 | 0.219440 | − | 0.975626i | \(-0.429577\pi\) | ||||
0.219440 | + | 0.975626i | \(0.429577\pi\) | |||||||
\(102\) | − | 0.301323i | − | 0.0298355i | ||||||
\(103\) | −5.82239 | −0.573697 | −0.286849 | − | 0.957976i | \(-0.592608\pi\) | ||||
−0.286849 | + | 0.957976i | \(0.592608\pi\) | |||||||
\(104\) | 0.875169 | + | 6.41276i | 0.0858174 | + | 0.628823i | ||||
\(105\) | −0.227889 | −0.0222397 | ||||||||
\(106\) | − | 2.93045i | − | 0.284630i | ||||||
\(107\) | −16.7531 | −1.61958 | −0.809790 | − | 0.586720i | \(-0.800419\pi\) | ||||
−0.809790 | + | 0.586720i | \(0.800419\pi\) | |||||||
\(108\) | −3.60534 | −0.346924 | ||||||||
\(109\) | 7.98649i | 0.764967i | 0.923962 | + | 0.382484i | \(0.124931\pi\) | ||||
−0.923962 | + | 0.382484i | \(0.875069\pi\) | |||||||
\(110\) | 0.290318i | 0.0276807i | ||||||||
\(111\) | 4.06347i | 0.385688i | ||||||||
\(112\) | − | 10.9898i | − | 1.03844i | ||||||
\(113\) | −8.73574 | −0.821789 | −0.410895 | − | 0.911683i | \(-0.634784\pi\) | ||||
−0.410895 | + | 0.911683i | \(0.634784\pi\) | |||||||
\(114\) | 0.999421 | 0.0936044 | ||||||||
\(115\) | − | 1.38737i | − | 0.129373i | ||||||
\(116\) | −9.25165 | −0.858994 | ||||||||
\(117\) | 10.2905 | − | 1.40437i | 0.951356 | − | 0.129834i | ||||
\(118\) | −3.79620 | −0.349469 | ||||||||
\(119\) | − | 7.47717i | − | 0.685431i | ||||||
\(120\) | −0.100265 | −0.00915287 | ||||||||
\(121\) | −3.26520 | −0.296837 | ||||||||
\(122\) | 2.15068i | 0.194714i | ||||||||
\(123\) | − | 1.64639i | − | 0.148450i | ||||||
\(124\) | 1.77373i | 0.159286i | ||||||||
\(125\) | − | 1.61172i | − | 0.144157i | ||||||
\(126\) | 5.59031 | 0.498024 | ||||||||
\(127\) | 10.6754 | 0.947291 | 0.473646 | − | 0.880715i | \(-0.342938\pi\) | ||||
0.473646 | + | 0.880715i | \(0.342938\pi\) | |||||||
\(128\) | − | 11.2031i | − | 0.990227i | ||||||
\(129\) | 2.15866 | 0.190059 | ||||||||
\(130\) | 0.274599 | − | 0.0374754i | 0.0240839 | − | 0.00328681i | ||||
\(131\) | −19.6250 | −1.71464 | −0.857322 | − | 0.514780i | \(-0.827873\pi\) | ||||
−0.857322 | + | 0.514780i | \(0.827873\pi\) | |||||||
\(132\) | − | 2.31563i | − | 0.201550i | ||||||
\(133\) | 24.8001 | 2.15044 | ||||||||
\(134\) | 3.66177 | 0.316329 | ||||||||
\(135\) | 0.328461i | 0.0282694i | ||||||||
\(136\) | − | 3.28974i | − | 0.282093i | ||||||
\(137\) | 2.38607i | 0.203856i | 0.994792 | + | 0.101928i | \(0.0325012\pi\) | ||||
−0.994792 | + | 0.101928i | \(0.967499\pi\) | |||||||
\(138\) | − | 1.41162i | − | 0.120165i | ||||||
\(139\) | −16.6882 | −1.41547 | −0.707735 | − | 0.706478i | \(-0.750283\pi\) | ||||
−0.707735 | + | 0.706478i | \(0.750283\pi\) | |||||||
\(140\) | −1.16942 | −0.0988339 | ||||||||
\(141\) | 1.62768i | 0.137075i | ||||||||
\(142\) | −3.69671 | −0.310221 | ||||||||
\(143\) | 1.84141 | + | 13.4928i | 0.153986 | + | 1.12833i | ||||
\(144\) | −7.75899 | −0.646582 | ||||||||
\(145\) | 0.842862i | 0.0699959i | ||||||||
\(146\) | −2.36122 | −0.195416 | ||||||||
\(147\) | −3.33420 | −0.275000 | ||||||||
\(148\) | 20.8518i | 1.71401i | ||||||||
\(149\) | − | 17.0531i | − | 1.39705i | −0.715588 | − | 0.698523i | \(-0.753841\pi\) | ||
0.715588 | − | 0.698523i | \(-0.246159\pi\) | |||||||
\(150\) | − | 0.817800i | − | 0.0667731i | ||||||
\(151\) | 14.6889i | 1.19537i | 0.801733 | + | 0.597683i | \(0.203912\pi\) | ||||
−0.801733 | + | 0.597683i | \(0.796088\pi\) | |||||||
\(152\) | 10.9113 | 0.885026 | ||||||||
\(153\) | −5.27902 | −0.426783 | ||||||||
\(154\) | 7.32999i | 0.590668i | ||||||||
\(155\) | 0.161594 | 0.0129796 | ||||||||
\(156\) | −2.19026 | + | 0.298911i | −0.175361 | + | 0.0239321i | ||||
\(157\) | 3.04722 | 0.243195 | 0.121597 | − | 0.992580i | \(-0.461198\pi\) | ||||
0.121597 | + | 0.992580i | \(0.461198\pi\) | |||||||
\(158\) | − | 3.93307i | − | 0.312898i | ||||||
\(159\) | 2.12945 | 0.168876 | ||||||||
\(160\) | −0.787191 | −0.0622329 | ||||||||
\(161\) | − | 35.0285i | − | 2.76063i | ||||||
\(162\) | − | 3.77636i | − | 0.296699i | ||||||
\(163\) | − | 13.4400i | − | 1.05270i | −0.850267 | − | 0.526351i | \(-0.823560\pi\) | ||
0.850267 | − | 0.526351i | \(-0.176440\pi\) | |||||||
\(164\) | − | 8.44850i | − | 0.659717i | ||||||
\(165\) | −0.210963 | −0.0164235 | ||||||||
\(166\) | 5.78620 | 0.449096 | ||||||||
\(167\) | 18.9746i | 1.46830i | 0.678990 | + | 0.734148i | \(0.262418\pi\) | ||||
−0.678990 | + | 0.734148i | \(0.737582\pi\) | |||||||
\(168\) | −2.53150 | −0.195309 | ||||||||
\(169\) | 12.5246 | − | 3.48342i | 0.963431 | − | 0.267956i | ||||
\(170\) | −0.140869 | −0.0108042 | ||||||||
\(171\) | − | 17.5093i | − | 1.33897i | ||||||
\(172\) | 11.0772 | 0.844630 | ||||||||
\(173\) | −4.56058 | −0.346735 | −0.173367 | − | 0.984857i | \(-0.555465\pi\) | ||||
−0.173367 | + | 0.984857i | \(0.555465\pi\) | |||||||
\(174\) | 0.857594i | 0.0650140i | ||||||||
\(175\) | − | 20.2932i | − | 1.53403i | ||||||
\(176\) | − | 10.1736i | − | 0.766861i | ||||||
\(177\) | − | 2.75856i | − | 0.207346i | ||||||
\(178\) | 1.50815 | 0.113041 | ||||||||
\(179\) | 3.85639 | 0.288240 | 0.144120 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144120 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(180\) | 0.825631i | 0.0615389i | ||||||||
\(181\) | 8.51055 | 0.632584 | 0.316292 | − | 0.948662i | \(-0.397562\pi\) | ||||
0.316292 | + | 0.948662i | \(0.397562\pi\) | |||||||
\(182\) | 6.93313 | − | 0.946185i | 0.513918 | − | 0.0701359i | ||||
\(183\) | −1.56282 | −0.115527 | ||||||||
\(184\) | − | 15.4116i | − | 1.13616i | ||||||
\(185\) | 1.89968 | 0.139667 | ||||||||
\(186\) | 0.164419 | 0.0120558 | ||||||||
\(187\) | − | 6.92183i | − | 0.506174i | ||||||
\(188\) | 8.35246i | 0.609166i | ||||||||
\(189\) | 8.29304i | 0.603230i | ||||||||
\(190\) | − | 0.467232i | − | 0.0338965i | ||||||
\(191\) | 8.46629 | 0.612599 | 0.306300 | − | 0.951935i | \(-0.400909\pi\) | ||||
0.306300 | + | 0.951935i | \(0.400909\pi\) | |||||||
\(192\) | 1.06116 | 0.0765827 | ||||||||
\(193\) | − | 1.35305i | − | 0.0973950i | −0.998814 | − | 0.0486975i | \(-0.984493\pi\) | ||
0.998814 | − | 0.0486975i | \(-0.0155070\pi\) | |||||||
\(194\) | 0.174184 | 0.0125057 | ||||||||
\(195\) | 0.0272320 | + | 0.199541i | 0.00195012 | + | 0.0142894i | ||||
\(196\) | −17.1095 | −1.22211 | ||||||||
\(197\) | − | 4.99593i | − | 0.355946i | −0.984035 | − | 0.177973i | \(-0.943046\pi\) | ||
0.984035 | − | 0.177973i | \(-0.0569539\pi\) | |||||||
\(198\) | 5.17511 | 0.367779 | ||||||||
\(199\) | −18.1523 | −1.28678 | −0.643390 | − | 0.765539i | \(-0.722472\pi\) | ||||
−0.643390 | + | 0.765539i | \(0.722472\pi\) | |||||||
\(200\) | − | 8.92845i | − | 0.631337i | ||||||
\(201\) | 2.66087i | 0.187684i | ||||||||
\(202\) | − | 2.09805i | − | 0.147618i | ||||||
\(203\) | 21.2807i | 1.49361i | ||||||||
\(204\) | 1.12360 | 0.0786679 | ||||||||
\(205\) | −0.769691 | −0.0537576 | ||||||||
\(206\) | 2.76956i | 0.192964i | ||||||||
\(207\) | −24.7308 | −1.71891 | ||||||||
\(208\) | −9.62273 | + | 1.31324i | −0.667216 | + | 0.0910571i | ||||
\(209\) | 22.9581 | 1.58805 | ||||||||
\(210\) | 0.108401i | 0.00748036i | ||||||||
\(211\) | −17.5202 | −1.20614 | −0.603069 | − | 0.797689i | \(-0.706056\pi\) | ||||
−0.603069 | + | 0.797689i | \(0.706056\pi\) | |||||||
\(212\) | 10.9273 | 0.750491 | ||||||||
\(213\) | − | 2.68626i | − | 0.184060i | ||||||
\(214\) | 7.96899i | 0.544749i | ||||||||
\(215\) | − | 1.00918i | − | 0.0688254i | ||||||
\(216\) | 3.64870i | 0.248263i | ||||||||
\(217\) | 4.07996 | 0.276966 | ||||||||
\(218\) | 3.79896 | 0.257298 | ||||||||
\(219\) | − | 1.71581i | − | 0.115944i | ||||||
\(220\) | −1.08256 | −0.0729864 | ||||||||
\(221\) | −6.54706 | + | 0.893498i | −0.440403 | + | 0.0601032i | ||||
\(222\) | 1.93289 | 0.129727 | ||||||||
\(223\) | 14.9046i | 0.998084i | 0.866578 | + | 0.499042i | \(0.166315\pi\) | ||||
−0.866578 | + | 0.499042i | \(0.833685\pi\) | |||||||
\(224\) | −19.8751 | −1.32796 | ||||||||
\(225\) | −14.3274 | −0.955160 | ||||||||
\(226\) | 4.15536i | 0.276410i | ||||||||
\(227\) | − | 23.7120i | − | 1.57382i | −0.617068 | − | 0.786910i | \(-0.711680\pi\) | ||
0.617068 | − | 0.786910i | \(-0.288320\pi\) | |||||||
\(228\) | 3.72673i | 0.246809i | ||||||||
\(229\) | − | 13.5862i | − | 0.897804i | −0.893581 | − | 0.448902i | \(-0.851815\pi\) | ||
0.893581 | − | 0.448902i | \(-0.148185\pi\) | |||||||
\(230\) | −0.659935 | −0.0435148 | ||||||||
\(231\) | −5.32643 | −0.350454 | ||||||||
\(232\) | 9.36291i | 0.614705i | ||||||||
\(233\) | −12.3027 | −0.805980 | −0.402990 | − | 0.915204i | \(-0.632029\pi\) | ||||
−0.402990 | + | 0.915204i | \(0.632029\pi\) | |||||||
\(234\) | −0.668024 | − | 4.89491i | −0.0436701 | − | 0.319990i | ||||
\(235\) | 0.760942 | 0.0496384 | ||||||||
\(236\) | − | 14.1556i | − | 0.921453i | ||||||
\(237\) | 2.85802 | 0.185648 | ||||||||
\(238\) | −3.55669 | −0.230546 | ||||||||
\(239\) | 21.8890i | 1.41588i | 0.706273 | + | 0.707940i | \(0.250375\pi\) | ||||
−0.706273 | + | 0.707940i | \(0.749625\pi\) | |||||||
\(240\) | − | 0.150453i | − | 0.00971171i | ||||||
\(241\) | − | 7.21497i | − | 0.464757i | −0.972625 | − | 0.232379i | \(-0.925349\pi\) | ||
0.972625 | − | 0.232379i | \(-0.0746509\pi\) | |||||||
\(242\) | 1.55317i | 0.0998416i | ||||||||
\(243\) | 8.84203 | 0.567216 | ||||||||
\(244\) | −8.01967 | −0.513406 | ||||||||
\(245\) | 1.55875i | 0.0995846i | ||||||||
\(246\) | −0.783144 | −0.0499315 | ||||||||
\(247\) | −2.96353 | − | 21.7151i | −0.188565 | − | 1.38170i | ||||
\(248\) | 1.79507 | 0.113987 | ||||||||
\(249\) | 4.20462i | 0.266457i | ||||||||
\(250\) | −0.766654 | −0.0484874 | ||||||||
\(251\) | 13.8037 | 0.871280 | 0.435640 | − | 0.900121i | \(-0.356522\pi\) | ||||
0.435640 | + | 0.900121i | \(0.356522\pi\) | |||||||
\(252\) | 20.8457i | 1.31315i | ||||||||
\(253\) | − | 32.4269i | − | 2.03866i | ||||||
\(254\) | − | 5.07802i | − | 0.318623i | ||||||
\(255\) | − | 0.102365i | − | 0.00641032i | ||||||
\(256\) | 0.810980 | 0.0506863 | ||||||||
\(257\) | 10.4274 | 0.650446 | 0.325223 | − | 0.945637i | \(-0.394561\pi\) | ||||
0.325223 | + | 0.945637i | \(0.394561\pi\) | |||||||
\(258\) | − | 1.02682i | − | 0.0639268i | ||||||
\(259\) | 47.9635 | 2.98031 | ||||||||
\(260\) | 0.139742 | + | 1.02395i | 0.00866641 | + | 0.0635027i | ||||
\(261\) | 15.0246 | 0.929997 | ||||||||
\(262\) | 9.33509i | 0.576724i | ||||||||
\(263\) | 21.8967 | 1.35021 | 0.675105 | − | 0.737721i | \(-0.264098\pi\) | ||||
0.675105 | + | 0.737721i | \(0.264098\pi\) | |||||||
\(264\) | −2.34348 | −0.144231 | ||||||||
\(265\) | − | 0.995521i | − | 0.0611544i | ||||||
\(266\) | − | 11.7967i | − | 0.723305i | ||||||
\(267\) | 1.09592i | 0.0670692i | ||||||||
\(268\) | 13.6543i | 0.834072i | ||||||||
\(269\) | −4.19670 | −0.255877 | −0.127939 | − | 0.991782i | \(-0.540836\pi\) | ||||
−0.127939 | + | 0.991782i | \(0.540836\pi\) | |||||||
\(270\) | 0.156240 | 0.00950847 | ||||||||
\(271\) | − | 4.89966i | − | 0.297633i | −0.988865 | − | 0.148817i | \(-0.952454\pi\) | ||
0.988865 | − | 0.148817i | \(-0.0475464\pi\) | |||||||
\(272\) | 4.93646 | 0.299317 | ||||||||
\(273\) | 0.687558 | + | 5.03805i | 0.0416129 | + | 0.304916i | ||||
\(274\) | 1.13499 | 0.0685674 | ||||||||
\(275\) | − | 18.7860i | − | 1.13284i | ||||||
\(276\) | 5.26377 | 0.316842 | ||||||||
\(277\) | −15.9569 | −0.958760 | −0.479380 | − | 0.877608i | \(-0.659138\pi\) | ||||
−0.479380 | + | 0.877608i | \(0.659138\pi\) | |||||||
\(278\) | 7.93811i | 0.476096i | ||||||||
\(279\) | − | 2.88052i | − | 0.172452i | ||||||
\(280\) | 1.18348i | 0.0707266i | ||||||||
\(281\) | 8.30204i | 0.495258i | 0.968855 | + | 0.247629i | \(0.0796514\pi\) | ||||
−0.968855 | + | 0.247629i | \(0.920349\pi\) | |||||||
\(282\) | 0.774242 | 0.0461055 | ||||||||
\(283\) | 21.4803 | 1.27687 | 0.638436 | − | 0.769675i | \(-0.279582\pi\) | ||||
0.638436 | + | 0.769675i | \(0.279582\pi\) | |||||||
\(284\) | − | 13.7846i | − | 0.817967i | ||||||
\(285\) | 0.339520 | 0.0201114 | ||||||||
\(286\) | 6.41819 | − | 0.875910i | 0.379515 | − | 0.0517937i | ||||
\(287\) | −19.4333 | −1.14711 | ||||||||
\(288\) | 14.0322i | 0.826855i | ||||||||
\(289\) | −13.6414 | −0.802433 | ||||||||
\(290\) | 0.400927 | 0.0235432 | ||||||||
\(291\) | 0.126573i | 0.00741986i | ||||||||
\(292\) | − | 8.80473i | − | 0.515258i | ||||||
\(293\) | − | 25.3620i | − | 1.48166i | −0.671690 | − | 0.740832i | \(-0.734431\pi\) | ||
0.671690 | − | 0.740832i | \(-0.265569\pi\) | |||||||
\(294\) | 1.58599i | 0.0924968i | ||||||||
\(295\) | −1.28963 | −0.0750854 | ||||||||
\(296\) | 21.1026 | 1.22656 | ||||||||
\(297\) | 7.67710i | 0.445470i | ||||||||
\(298\) | −8.11171 | −0.469899 | ||||||||
\(299\) | −30.6712 | + | 4.18579i | −1.77376 | + | 0.242071i | ||||
\(300\) | 3.04949 | 0.176062 | ||||||||
\(301\) | − | 25.4799i | − | 1.46864i | ||||||
\(302\) | 6.98712 | 0.402064 | ||||||||
\(303\) | 1.52457 | 0.0875845 | ||||||||
\(304\) | 16.3731i | 0.939063i | ||||||||
\(305\) | 0.730623i | 0.0418354i | ||||||||
\(306\) | 2.51109i | 0.143549i | ||||||||
\(307\) | 24.5792i | 1.40281i | 0.712765 | + | 0.701403i | \(0.247443\pi\) | ||||
−0.712765 | + | 0.701403i | \(0.752557\pi\) | |||||||
\(308\) | −27.3327 | −1.55743 | ||||||||
\(309\) | −2.01253 | −0.114489 | ||||||||
\(310\) | − | 0.0768661i | − | 0.00436570i | ||||||
\(311\) | 11.9767 | 0.679138 | 0.339569 | − | 0.940581i | \(-0.389719\pi\) | ||||
0.339569 | + | 0.940581i | \(0.389719\pi\) | |||||||
\(312\) | 0.302506 | + | 2.21660i | 0.0171260 | + | 0.125490i | ||||
\(313\) | 4.14553 | 0.234319 | 0.117160 | − | 0.993113i | \(-0.462621\pi\) | ||||
0.117160 | + | 0.993113i | \(0.462621\pi\) | |||||||
\(314\) | − | 1.44948i | − | 0.0817990i | ||||||
\(315\) | 1.89912 | 0.107003 | ||||||||
\(316\) | 14.6660 | 0.825027 | ||||||||
\(317\) | 31.3673i | 1.76176i | 0.473335 | + | 0.880882i | \(0.343050\pi\) | ||||
−0.473335 | + | 0.880882i | \(0.656950\pi\) | |||||||
\(318\) | − | 1.01292i | − | 0.0568018i | ||||||
\(319\) | 19.7002i | 1.10300i | ||||||||
\(320\) | − | 0.496095i | − | 0.0277326i | ||||||
\(321\) | −5.79077 | −0.323209 | ||||||||
\(322\) | −16.6621 | −0.928545 | ||||||||
\(323\) | 11.1399i | 0.619838i | ||||||||
\(324\) | 14.0816 | 0.782314 | ||||||||
\(325\) | −17.7689 | + | 2.42498i | −0.985641 | + | 0.134514i | ||||
\(326\) | −6.39305 | −0.354078 | ||||||||
\(327\) | 2.76056i | 0.152660i | ||||||||
\(328\) | −8.55010 | −0.472100 | ||||||||
\(329\) | 19.2124 | 1.05921 | ||||||||
\(330\) | 0.100350i | 0.00552406i | ||||||||
\(331\) | 0.485651i | 0.0266938i | 0.999911 | + | 0.0133469i | \(0.00424858\pi\) | ||||
−0.999911 | + | 0.0133469i | \(0.995751\pi\) | |||||||
\(332\) | 21.5761i | 1.18414i | ||||||||
\(333\) | − | 33.8631i | − | 1.85569i | ||||||
\(334\) | 9.02569 | 0.493864 | ||||||||
\(335\) | 1.24396 | 0.0679650 | ||||||||
\(336\) | − | 3.79867i | − | 0.207234i | ||||||
\(337\) | −10.4733 | −0.570518 | −0.285259 | − | 0.958451i | \(-0.592080\pi\) | ||||
−0.285259 | + | 0.958451i | \(0.592080\pi\) | |||||||
\(338\) | −1.65697 | − | 5.95762i | −0.0901274 | − | 0.324052i | ||||
\(339\) | −3.01955 | −0.163999 | ||||||||
\(340\) | − | 0.525286i | − | 0.0284877i | ||||||
\(341\) | 3.77693 | 0.204532 | ||||||||
\(342\) | −8.32871 | −0.450365 | ||||||||
\(343\) | 10.7958i | 0.582917i | ||||||||
\(344\) | − | 11.2104i | − | 0.604426i | ||||||
\(345\) | − | 0.479550i | − | 0.0258181i | ||||||
\(346\) | 2.16935i | 0.116625i | ||||||||
\(347\) | 16.0801 | 0.863225 | 0.431613 | − | 0.902059i | \(-0.357945\pi\) | ||||
0.431613 | + | 0.902059i | \(0.357945\pi\) | |||||||
\(348\) | −3.19787 | −0.171424 | ||||||||
\(349\) | 27.1125i | 1.45130i | 0.688064 | + | 0.725650i | \(0.258461\pi\) | ||||
−0.688064 | + | 0.725650i | \(0.741539\pi\) | |||||||
\(350\) | −9.65296 | −0.515972 | ||||||||
\(351\) | 7.26144 | − | 0.990991i | 0.387587 | − | 0.0528952i | ||||
\(352\) | −18.3990 | −0.980668 | ||||||||
\(353\) | − | 2.27544i | − | 0.121109i | −0.998165 | − | 0.0605547i | \(-0.980713\pi\) | ||
0.998165 | − | 0.0605547i | \(-0.0192869\pi\) | |||||||
\(354\) | −1.31217 | −0.0697413 | ||||||||
\(355\) | −1.25583 | −0.0666527 | ||||||||
\(356\) | 5.62374i | 0.298058i | ||||||||
\(357\) | − | 2.58452i | − | 0.136787i | ||||||
\(358\) | − | 1.83438i | − | 0.0969502i | ||||||
\(359\) | 2.58251i | 0.136300i | 0.997675 | + | 0.0681498i | \(0.0217096\pi\) | ||||
−0.997675 | + | 0.0681498i | \(0.978290\pi\) | |||||||
\(360\) | 0.835560 | 0.0440379 | ||||||||
\(361\) | −17.9484 | −0.944650 | ||||||||
\(362\) | − | 4.04824i | − | 0.212771i | ||||||
\(363\) | −1.12863 | −0.0592378 | ||||||||
\(364\) | 3.52822 | + | 25.8529i | 0.184929 | + | 1.35506i | ||||
\(365\) | −0.802146 | −0.0419862 | ||||||||
\(366\) | 0.743393i | 0.0388578i | ||||||||
\(367\) | −15.6380 | −0.816296 | −0.408148 | − | 0.912916i | \(-0.633825\pi\) | ||||
−0.408148 | + | 0.912916i | \(0.633825\pi\) | |||||||
\(368\) | 23.1260 | 1.20552 | ||||||||
\(369\) | 13.7203i | 0.714248i | ||||||||
\(370\) | − | 0.903629i | − | 0.0469774i | ||||||
\(371\) | − | 25.1351i | − | 1.30495i | ||||||
\(372\) | 0.613099i | 0.0317877i | ||||||||
\(373\) | −28.3986 | −1.47042 | −0.735211 | − | 0.677839i | \(-0.762917\pi\) | ||||
−0.735211 | + | 0.677839i | \(0.762917\pi\) | |||||||
\(374\) | −3.29253 | −0.170253 | ||||||||
\(375\) | − | 0.557099i | − | 0.0287685i | ||||||
\(376\) | 8.45291 | 0.435926 | ||||||||
\(377\) | 18.6335 | − | 2.54298i | 0.959676 | − | 0.130970i | ||||
\(378\) | 3.94478 | 0.202897 | ||||||||
\(379\) | − | 3.66801i | − | 0.188413i | −0.995553 | − | 0.0942066i | \(-0.969969\pi\) | ||
0.995553 | − | 0.0942066i | \(-0.0300314\pi\) | |||||||
\(380\) | 1.74226 | 0.0893758 | ||||||||
\(381\) | 3.69001 | 0.189045 | ||||||||
\(382\) | − | 4.02719i | − | 0.206049i | ||||||
\(383\) | 27.7530i | 1.41811i | 0.705153 | + | 0.709056i | \(0.250878\pi\) | ||||
−0.705153 | + | 0.709056i | \(0.749122\pi\) | |||||||
\(384\) | − | 3.87241i | − | 0.197613i | ||||||
\(385\) | 2.49012i | 0.126908i | ||||||||
\(386\) | −0.643612 | −0.0327590 | ||||||||
\(387\) | −17.9893 | −0.914446 | ||||||||
\(388\) | 0.649514i | 0.0329741i | ||||||||
\(389\) | 7.80800 | 0.395881 | 0.197941 | − | 0.980214i | \(-0.436575\pi\) | ||||
0.197941 | + | 0.980214i | \(0.436575\pi\) | |||||||
\(390\) | 0.0949164 | − | 0.0129535i | 0.00480628 | − | 0.000655928i | ||||
\(391\) | 15.7343 | 0.795719 | ||||||||
\(392\) | 17.3153i | 0.874554i | ||||||||
\(393\) | −6.78347 | −0.342181 | ||||||||
\(394\) | −2.37643 | −0.119723 | ||||||||
\(395\) | − | 1.33613i | − | 0.0672280i | ||||||
\(396\) | 19.2974i | 0.969731i | ||||||||
\(397\) | 32.5182i | 1.63204i | 0.578024 | + | 0.816020i | \(0.303824\pi\) | ||||
−0.578024 | + | 0.816020i | \(0.696176\pi\) | |||||||
\(398\) | 8.63455i | 0.432811i | ||||||||
\(399\) | 8.57226 | 0.429150 | ||||||||
\(400\) | 13.3977 | 0.669884 | ||||||||
\(401\) | − | 18.4545i | − | 0.921574i | −0.887511 | − | 0.460787i | \(-0.847567\pi\) | ||
0.887511 | − | 0.460787i | \(-0.152433\pi\) | |||||||
\(402\) | 1.26571 | 0.0631277 | ||||||||
\(403\) | −0.487542 | − | 3.57244i | −0.0242862 | − | 0.177956i | ||||
\(404\) | 7.82340 | 0.389228 | ||||||||
\(405\) | − | 1.28289i | − | 0.0637475i | ||||||
\(406\) | 10.1227 | 0.502380 | ||||||||
\(407\) | 44.4012 | 2.20088 | ||||||||
\(408\) | − | 1.13711i | − | 0.0562956i | ||||||
\(409\) | − | 20.3559i | − | 1.00653i | −0.864132 | − | 0.503266i | \(-0.832132\pi\) | ||
0.864132 | − | 0.503266i | \(-0.167868\pi\) | |||||||
\(410\) | 0.366122i | 0.0180815i | ||||||||
\(411\) | 0.824757i | 0.0406823i | ||||||||
\(412\) | −10.3274 | −0.508793 | ||||||||
\(413\) | −32.5609 | −1.60222 | ||||||||
\(414\) | 11.7638i | 0.578158i | ||||||||
\(415\) | 1.96567 | 0.0964908 | ||||||||
\(416\) | 2.37501 | + | 17.4028i | 0.116445 | + | 0.853242i | ||||
\(417\) | −5.76833 | −0.282477 | ||||||||
\(418\) | − | 10.9206i | − | 0.534143i | ||||||
\(419\) | −32.6649 | −1.59578 | −0.797891 | − | 0.602801i | \(-0.794051\pi\) | ||||
−0.797891 | + | 0.602801i | \(0.794051\pi\) | |||||||
\(420\) | −0.404215 | −0.0197237 | ||||||||
\(421\) | 10.0153i | 0.488114i | 0.969761 | + | 0.244057i | \(0.0784783\pi\) | ||||
−0.969761 | + | 0.244057i | \(0.921522\pi\) | |||||||
\(422\) | 8.33388i | 0.405687i | ||||||||
\(423\) | − | 13.5643i | − | 0.659519i | ||||||
\(424\) | − | 11.0587i | − | 0.537059i | ||||||
\(425\) | 9.11544 | 0.442164 | ||||||||
\(426\) | −1.27778 | −0.0619088 | ||||||||
\(427\) | 18.4469i | 0.892708i | ||||||||
\(428\) | −29.7155 | −1.43635 | ||||||||
\(429\) | 0.636492 | + | 4.66386i | 0.0307301 | + | 0.225173i | ||||
\(430\) | −0.480039 | −0.0231495 | ||||||||
\(431\) | − | 15.7075i | − | 0.756604i | −0.925682 | − | 0.378302i | \(-0.876508\pi\) | ||
0.925682 | − | 0.378302i | \(-0.123492\pi\) | |||||||
\(432\) | −5.47510 | −0.263421 | ||||||||
\(433\) | 23.0783 | 1.10907 | 0.554537 | − | 0.832159i | \(-0.312895\pi\) | ||||
0.554537 | + | 0.832159i | \(0.312895\pi\) | |||||||
\(434\) | − | 1.94073i | − | 0.0931579i | ||||||
\(435\) | 0.291339i | 0.0139686i | ||||||||
\(436\) | 14.1659i | 0.678424i | ||||||||
\(437\) | 52.1872i | 2.49645i | ||||||||
\(438\) | −0.816166 | −0.0389979 | ||||||||
\(439\) | −9.91131 | −0.473041 | −0.236520 | − | 0.971627i | \(-0.576007\pi\) | ||||
−0.236520 | + | 0.971627i | \(0.576007\pi\) | |||||||
\(440\) | 1.09558i | 0.0522298i | ||||||||
\(441\) | 27.7857 | 1.32313 | ||||||||
\(442\) | 0.425013 | + | 3.11426i | 0.0202158 | + | 0.148130i | ||||
\(443\) | −10.2386 | −0.486452 | −0.243226 | − | 0.969970i | \(-0.578206\pi\) | ||||
−0.243226 | + | 0.969970i | \(0.578206\pi\) | |||||||
\(444\) | 7.20752i | 0.342054i | ||||||||
\(445\) | 0.512345 | 0.0242875 | ||||||||
\(446\) | 7.08971 | 0.335708 | ||||||||
\(447\) | − | 5.89448i | − | 0.278799i | ||||||
\(448\) | − | 12.5255i | − | 0.591774i | ||||||
\(449\) | − | 37.8155i | − | 1.78462i | −0.451421 | − | 0.892311i | \(-0.649083\pi\) | ||
0.451421 | − | 0.892311i | \(-0.350917\pi\) | |||||||
\(450\) | 6.81516i | 0.321270i | ||||||||
\(451\) | −17.9899 | −0.847113 | ||||||||
\(452\) | −15.4949 | −0.728818 | ||||||||
\(453\) | 5.07728i | 0.238552i | ||||||||
\(454\) | −11.2792 | −0.529357 | ||||||||
\(455\) | 2.35530 | − | 0.321435i | 0.110418 | − | 0.0150691i | ||||
\(456\) | 3.77155 | 0.176619 | ||||||||
\(457\) | − | 5.76721i | − | 0.269779i | −0.990861 | − | 0.134889i | \(-0.956932\pi\) | ||
0.990861 | − | 0.134889i | \(-0.0430679\pi\) | |||||||
\(458\) | −6.46261 | −0.301978 | ||||||||
\(459\) | −3.72512 | −0.173874 | ||||||||
\(460\) | − | 2.46082i | − | 0.114737i | ||||||
\(461\) | − | 19.4478i | − | 0.905775i | −0.891568 | − | 0.452888i | \(-0.850394\pi\) | ||
0.891568 | − | 0.452888i | \(-0.149606\pi\) | |||||||
\(462\) | 2.53364i | 0.117876i | ||||||||
\(463\) | − | 17.5592i | − | 0.816046i | −0.912972 | − | 0.408023i | \(-0.866218\pi\) | ||
0.912972 | − | 0.408023i | \(-0.133782\pi\) | |||||||
\(464\) | −14.0496 | −0.652237 | ||||||||
\(465\) | 0.0558557 | 0.00259025 | ||||||||
\(466\) | 5.85209i | 0.271093i | ||||||||
\(467\) | 21.5159 | 0.995637 | 0.497818 | − | 0.867281i | \(-0.334135\pi\) | ||||
0.497818 | + | 0.867281i | \(0.334135\pi\) | |||||||
\(468\) | 18.2526 | − | 2.49099i | 0.843726 | − | 0.115146i | ||||
\(469\) | 31.4078 | 1.45028 | ||||||||
\(470\) | − | 0.361960i | − | 0.0166960i | ||||||
\(471\) | 1.05328 | 0.0485328 | ||||||||
\(472\) | −14.3259 | −0.659401 | ||||||||
\(473\) | − | 23.5874i | − | 1.08455i | ||||||
\(474\) | − | 1.35948i | − | 0.0624432i | ||||||
\(475\) | 30.2339i | 1.38722i | ||||||||
\(476\) | − | 13.2625i | − | 0.607887i | ||||||
\(477\) | −17.7458 | −0.812525 | ||||||||
\(478\) | 10.4120 | 0.476234 | ||||||||
\(479\) | 40.4137i | 1.84655i | 0.384139 | + | 0.923275i | \(0.374498\pi\) | ||||
−0.384139 | + | 0.923275i | \(0.625502\pi\) | |||||||
\(480\) | −0.272096 | −0.0124194 | ||||||||
\(481\) | −5.73148 | − | 41.9972i | −0.261333 | − | 1.91491i | ||||
\(482\) | −3.43197 | −0.156322 | ||||||||
\(483\) | − | 12.1078i | − | 0.550922i | ||||||
\(484\) | −5.79160 | −0.263255 | ||||||||
\(485\) | 0.0591733 | 0.00268692 | ||||||||
\(486\) | − | 4.20592i | − | 0.190784i | ||||||
\(487\) | 0.476889i | 0.0216099i | 0.999942 | + | 0.0108050i | \(0.00343939\pi\) | ||||
−0.999942 | + | 0.0108050i | \(0.996561\pi\) | |||||||
\(488\) | 8.11611i | 0.367399i | ||||||||
\(489\) | − | 4.64559i | − | 0.210081i | ||||||
\(490\) | 0.741454 | 0.0334955 | ||||||||
\(491\) | −5.42032 | −0.244616 | −0.122308 | − | 0.992492i | \(-0.539030\pi\) | ||||
−0.122308 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(492\) | − | 2.92026i | − | 0.131655i | ||||||
\(493\) | −9.55900 | −0.430516 | ||||||||
\(494\) | −10.3293 | + | 1.40967i | −0.464737 | + | 0.0634242i | ||||
\(495\) | 1.75807 | 0.0790194 | ||||||||
\(496\) | 2.69360i | 0.120946i | ||||||||
\(497\) | −31.7075 | −1.42227 | ||||||||
\(498\) | 2.00002 | 0.0896232 | ||||||||
\(499\) | − | 12.7183i | − | 0.569350i | −0.958624 | − | 0.284675i | \(-0.908114\pi\) | ||
0.958624 | − | 0.284675i | \(-0.0918856\pi\) | |||||||
\(500\) | − | 2.85877i | − | 0.127848i | ||||||
\(501\) | 6.55864i | 0.293018i | ||||||||
\(502\) | − | 6.56604i | − | 0.293057i | ||||||
\(503\) | 3.19745 | 0.142567 | 0.0712835 | − | 0.997456i | \(-0.477290\pi\) | ||||
0.0712835 | + | 0.997456i | \(0.477290\pi\) | |||||||
\(504\) | 21.0964 | 0.939706 | ||||||||
\(505\) | − | 0.712742i | − | 0.0317166i | ||||||
\(506\) | −15.4246 | −0.685708 | ||||||||
\(507\) | 4.32918 | − | 1.20406i | 0.192266 | − | 0.0534742i | ||||
\(508\) | 18.9354 | 0.840122 | ||||||||
\(509\) | 29.0567i | 1.28791i | 0.765061 | + | 0.643957i | \(0.222709\pi\) | ||||
−0.765061 | + | 0.643957i | \(0.777291\pi\) | |||||||
\(510\) | −0.0486921 | −0.00215612 | ||||||||
\(511\) | −20.2527 | −0.895927 | ||||||||
\(512\) | − | 22.7920i | − | 1.00728i | ||||||
\(513\) | − | 12.3554i | − | 0.545503i | ||||||
\(514\) | − | 4.96006i | − | 0.218779i | ||||||
\(515\) | 0.940864i | 0.0414594i | ||||||||
\(516\) | 3.82889 | 0.168557 | ||||||||
\(517\) | 17.7855 | 0.782203 | ||||||||
\(518\) | − | 22.8150i | − | 1.00243i | ||||||
\(519\) | −1.57639 | −0.0691956 | ||||||||
\(520\) | 1.03626 | − | 0.141422i | 0.0454432 | − | 0.00620178i | ||||
\(521\) | −32.5948 | −1.42800 | −0.714001 | − | 0.700145i | \(-0.753119\pi\) | ||||
−0.714001 | + | 0.700145i | \(0.753119\pi\) | |||||||
\(522\) | − | 7.14679i | − | 0.312806i | ||||||
\(523\) | 24.3813 | 1.06612 | 0.533059 | − | 0.846078i | \(-0.321042\pi\) | ||||
0.533059 | + | 0.846078i | \(0.321042\pi\) | |||||||
\(524\) | −34.8095 | −1.52066 | ||||||||
\(525\) | − | 7.01445i | − | 0.306136i | ||||||
\(526\) | − | 10.4157i | − | 0.454146i | ||||||
\(527\) | 1.83266i | 0.0798319i | ||||||||
\(528\) | − | 3.51653i | − | 0.153037i | ||||||
\(529\) | 50.7110 | 2.20483 | ||||||||
\(530\) | −0.473543 | −0.0205694 | ||||||||
\(531\) | 22.9886i | 0.997619i | ||||||||
\(532\) | 43.9888 | 1.90716 | ||||||||
\(533\) | 2.32221 | + | 17.0159i | 0.100586 | + | 0.737041i | ||||
\(534\) | 0.521300 | 0.0225588 | ||||||||
\(535\) | 2.70720i | 0.117042i | ||||||||
\(536\) | 13.8186 | 0.596871 | ||||||||
\(537\) | 1.33298 | 0.0575223 | ||||||||
\(538\) | 1.99626i | 0.0860649i | ||||||||
\(539\) | 36.4325i | 1.56926i | ||||||||
\(540\) | 0.582603i | 0.0250712i | ||||||||
\(541\) | − | 36.9850i | − | 1.59011i | −0.606537 | − | 0.795055i | \(-0.707442\pi\) | ||
0.606537 | − | 0.795055i | \(-0.292558\pi\) | |||||||
\(542\) | −2.33064 | −0.100110 | ||||||||
\(543\) | 2.94171 | 0.126241 | ||||||||
\(544\) | − | 8.92763i | − | 0.382769i | ||||||
\(545\) | 1.29057 | 0.0552820 | ||||||||
\(546\) | 2.39647 | − | 0.327053i | 0.102559 | − | 0.0139966i | ||||
\(547\) | 10.3345 | 0.441872 | 0.220936 | − | 0.975288i | \(-0.429089\pi\) | ||||
0.220936 | + | 0.975288i | \(0.429089\pi\) | |||||||
\(548\) | 4.23226i | 0.180793i | ||||||||
\(549\) | 13.0238 | 0.555844 | ||||||||
\(550\) | −8.93602 | −0.381033 | ||||||||
\(551\) | − | 31.7050i | − | 1.35068i | ||||||
\(552\) | − | 5.32707i | − | 0.226735i | ||||||
\(553\) | − | 33.7348i | − | 1.43455i | ||||||
\(554\) | 7.59029i | 0.322481i | ||||||||
\(555\) | 0.656634 | 0.0278726 | ||||||||
\(556\) | −29.6004 | −1.25533 | ||||||||
\(557\) | − | 5.13754i | − | 0.217685i | −0.994059 | − | 0.108842i | \(-0.965286\pi\) | ||
0.994059 | − | 0.108842i | \(-0.0347143\pi\) | |||||||
\(558\) | −1.37019 | −0.0580047 | ||||||||
\(559\) | −22.3104 | + | 3.04476i | −0.943627 | + | 0.128780i | ||||
\(560\) | −1.77589 | −0.0750449 | ||||||||
\(561\) | − | 2.39256i | − | 0.101014i | ||||||
\(562\) | 3.94906 | 0.166581 | ||||||||
\(563\) | −5.84576 | −0.246370 | −0.123185 | − | 0.992384i | \(-0.539311\pi\) | ||||
−0.123185 | + | 0.992384i | \(0.539311\pi\) | |||||||
\(564\) | 2.88706i | 0.121567i | ||||||||
\(565\) | 1.41164i | 0.0593883i | ||||||||
\(566\) | − | 10.2176i | − | 0.429478i | ||||||
\(567\) | − | 32.3907i | − | 1.36028i | ||||||
\(568\) | −13.9504 | −0.585346 | ||||||||
\(569\) | −19.4506 | −0.815413 | −0.407706 | − | 0.913113i | \(-0.633671\pi\) | ||||
−0.407706 | + | 0.913113i | \(0.633671\pi\) | |||||||
\(570\) | − | 0.161501i | − | 0.00676452i | ||||||
\(571\) | 4.61628 | 0.193185 | 0.0965927 | − | 0.995324i | \(-0.469206\pi\) | ||||
0.0965927 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(572\) | 3.26617 | + | 23.9327i | 0.136566 | + | 1.00068i | ||||
\(573\) | 2.92641 | 0.122253 | ||||||||
\(574\) | 9.24390i | 0.385833i | ||||||||
\(575\) | 42.7034 | 1.78085 | ||||||||
\(576\) | −8.84323 | −0.368468 | ||||||||
\(577\) | − | 26.1386i | − | 1.08817i | −0.839032 | − | 0.544083i | \(-0.816878\pi\) | ||
0.839032 | − | 0.544083i | \(-0.183122\pi\) | |||||||
\(578\) | 6.48883i | 0.269900i | ||||||||
\(579\) | − | 0.467689i | − | 0.0194365i | ||||||
\(580\) | 1.49501i | 0.0620770i | ||||||||
\(581\) | 49.6295 | 2.05898 | ||||||||
\(582\) | 0.0602076 | 0.00249568 | ||||||||
\(583\) | − | 23.2683i | − | 0.963673i | ||||||
\(584\) | −8.91062 | −0.368724 | ||||||||
\(585\) | −0.226939 | − | 1.66288i | −0.00938276 | − | 0.0687517i | ||||
\(586\) | −12.0640 | −0.498361 | ||||||||
\(587\) | 19.2852i | 0.795983i | 0.917389 | + | 0.397992i | \(0.130293\pi\) | ||||
−0.917389 | + | 0.397992i | \(0.869707\pi\) | |||||||
\(588\) | −5.91398 | −0.243889 | ||||||||
\(589\) | −6.07852 | −0.250461 | ||||||||
\(590\) | 0.613445i | 0.0252551i | ||||||||
\(591\) | − | 1.72687i | − | 0.0710338i | ||||||
\(592\) | 31.6657i | 1.30145i | ||||||||
\(593\) | − | 16.2964i | − | 0.669214i | −0.942358 | − | 0.334607i | \(-0.891397\pi\) | ||
0.942358 | − | 0.334607i | \(-0.108603\pi\) | |||||||
\(594\) | 3.65179 | 0.149835 | ||||||||
\(595\) | −1.20827 | −0.0495341 | ||||||||
\(596\) | − | 30.2477i | − | 1.23899i | ||||||
\(597\) | −6.27441 | −0.256794 | ||||||||
\(598\) | 1.99107 | + | 14.5895i | 0.0814210 | + | 0.596608i | ||||
\(599\) | −24.5049 | −1.00124 | −0.500622 | − | 0.865666i | \(-0.666895\pi\) | ||||
−0.500622 | + | 0.865666i | \(0.666895\pi\) | |||||||
\(600\) | − | 3.08616i | − | 0.125992i | ||||||
\(601\) | −6.30942 | −0.257367 | −0.128683 | − | 0.991686i | \(-0.541075\pi\) | ||||
−0.128683 | + | 0.991686i | \(0.541075\pi\) | |||||||
\(602\) | −12.1201 | −0.493979 | ||||||||
\(603\) | − | 22.1745i | − | 0.903015i | ||||||
\(604\) | 26.0542i | 1.06013i | ||||||||
\(605\) | 0.527638i | 0.0214515i | ||||||||
\(606\) | − | 0.725200i | − | 0.0294592i | ||||||
\(607\) | 1.35917 | 0.0551672 | 0.0275836 | − | 0.999620i | \(-0.491219\pi\) | ||||
0.0275836 | + | 0.999620i | \(0.491219\pi\) | |||||||
\(608\) | 29.6109 | 1.20088 | ||||||||
\(609\) | 7.35577i | 0.298071i | ||||||||
\(610\) | 0.347538 | 0.0140714 | ||||||||
\(611\) | −2.29582 | − | 16.8225i | −0.0928789 | − | 0.680565i | ||||
\(612\) | −9.36358 | −0.378500 | ||||||||
\(613\) | 29.2724i | 1.18230i | 0.806562 | + | 0.591150i | \(0.201326\pi\) | ||||
−0.806562 | + | 0.591150i | \(0.798674\pi\) | |||||||
\(614\) | 11.6917 | 0.471837 | ||||||||
\(615\) | −0.266047 | −0.0107281 | ||||||||
\(616\) | 27.6615i | 1.11451i | ||||||||
\(617\) | − | 19.6789i | − | 0.792241i | −0.918198 | − | 0.396121i | \(-0.870356\pi\) | ||
0.918198 | − | 0.396121i | \(-0.129644\pi\) | |||||||
\(618\) | 0.957309i | 0.0385086i | ||||||||
\(619\) | 20.4145i | 0.820528i | 0.911967 | + | 0.410264i | \(0.134563\pi\) | ||||
−0.911967 | + | 0.410264i | \(0.865437\pi\) | |||||||
\(620\) | 0.286625 | 0.0115111 | ||||||||
\(621\) | −17.4512 | −0.700291 | ||||||||
\(622\) | − | 5.69701i | − | 0.228429i | ||||||
\(623\) | 12.9358 | 0.518261 | ||||||||
\(624\) | −3.32614 | + | 0.453928i | −0.133152 | + | 0.0181717i | ||||
\(625\) | 24.6090 | 0.984360 | ||||||||
\(626\) | − | 1.97192i | − | 0.0788137i | ||||||
\(627\) | 7.93558 | 0.316916 | ||||||||
\(628\) | 5.40496 | 0.215681 | ||||||||
\(629\) | 21.5445i | 0.859037i | ||||||||
\(630\) | − | 0.903362i | − | 0.0359908i | ||||||
\(631\) | − | 23.8412i | − | 0.949104i | −0.880228 | − | 0.474552i | \(-0.842610\pi\) | ||
0.880228 | − | 0.474552i | \(-0.157390\pi\) | |||||||
\(632\) | − | 14.8424i | − | 0.590398i | ||||||
\(633\) | −6.05592 | −0.240701 | ||||||||
\(634\) | 14.9206 | 0.592573 | ||||||||
\(635\) | − | 1.72509i | − | 0.0684580i | ||||||
\(636\) | 3.77707 | 0.149771 | ||||||||
\(637\) | 34.4599 | − | 4.70285i | 1.36535 | − | 0.186334i | ||||
\(638\) | 9.37084 | 0.370995 | ||||||||
\(639\) | 22.3860i | 0.885578i | ||||||||
\(640\) | −1.81036 | −0.0715608 | ||||||||
\(641\) | 14.6516 | 0.578705 | 0.289352 | − | 0.957223i | \(-0.406560\pi\) | ||||
0.289352 | + | 0.957223i | \(0.406560\pi\) | |||||||
\(642\) | 2.75452i | 0.108712i | ||||||||
\(643\) | 41.7544i | 1.64663i | 0.567582 | + | 0.823317i | \(0.307879\pi\) | ||||
−0.567582 | + | 0.823317i | \(0.692121\pi\) | |||||||
\(644\) | − | 62.1313i | − | 2.44832i | ||||||
\(645\) | − | 0.348827i | − | 0.0137350i | ||||||
\(646\) | 5.29893 | 0.208484 | ||||||||
\(647\) | 48.8162 | 1.91916 | 0.959582 | − | 0.281430i | \(-0.0908087\pi\) | ||||
0.959582 | + | 0.281430i | \(0.0908087\pi\) | |||||||
\(648\) | − | 14.2510i | − | 0.559832i | ||||||
\(649\) | −30.1425 | −1.18320 | ||||||||
\(650\) | 1.15350 | + | 8.45219i | 0.0452439 | + | 0.331522i | ||||
\(651\) | 1.41025 | 0.0552722 | ||||||||
\(652\) | − | 23.8390i | − | 0.933607i | ||||||
\(653\) | −22.5149 | −0.881076 | −0.440538 | − | 0.897734i | \(-0.645212\pi\) | ||||
−0.440538 | + | 0.897734i | \(0.645212\pi\) | |||||||
\(654\) | 1.31313 | 0.0513474 | ||||||||
\(655\) | 3.17129i | 0.123912i | ||||||||
\(656\) | − | 12.8299i | − | 0.500925i | ||||||
\(657\) | 14.2988i | 0.557848i | ||||||||
\(658\) | − | 9.13883i | − | 0.356269i | ||||||
\(659\) | 5.23972 | 0.204110 | 0.102055 | − | 0.994779i | \(-0.467458\pi\) | ||||
0.102055 | + | 0.994779i | \(0.467458\pi\) | |||||||
\(660\) | −0.374193 | −0.0145654 | ||||||||
\(661\) | − | 24.7912i | − | 0.964266i | −0.876098 | − | 0.482133i | \(-0.839862\pi\) | ||
0.876098 | − | 0.482133i | \(-0.160138\pi\) | |||||||
\(662\) | 0.231012 | 0.00897852 | ||||||||
\(663\) | −2.26302 | + | 0.308841i | −0.0878884 | + | 0.0119944i | ||||
\(664\) | 21.8356 | 0.847385 | ||||||||
\(665\) | − | 4.00755i | − | 0.155406i | ||||||
\(666\) | −16.1078 | −0.624164 | ||||||||
\(667\) | −44.7813 | −1.73394 | ||||||||
\(668\) | 33.6558i | 1.30218i | ||||||||
\(669\) | 5.15183i | 0.199181i | ||||||||
\(670\) | − | 0.591721i | − | 0.0228602i | ||||||
\(671\) | 17.0768i | 0.659243i | ||||||||
\(672\) | −6.86993 | −0.265013 | ||||||||
\(673\) | −26.8313 | −1.03427 | −0.517135 | − | 0.855904i | \(-0.673001\pi\) | ||||
−0.517135 | + | 0.855904i | \(0.673001\pi\) | |||||||
\(674\) | 4.98188i | 0.191895i | ||||||||
\(675\) | −10.1101 | −0.389137 | ||||||||
\(676\) | 22.2153 | − | 6.17867i | 0.854436 | − | 0.237641i | ||||
\(677\) | −8.48908 | −0.326262 | −0.163131 | − | 0.986604i | \(-0.552159\pi\) | ||||
−0.163131 | + | 0.986604i | \(0.552159\pi\) | |||||||
\(678\) | 1.43632i | 0.0551615i | ||||||||
\(679\) | 1.49402 | 0.0573351 | ||||||||
\(680\) | −0.531604 | −0.0203861 | ||||||||
\(681\) | − | 8.19615i | − | 0.314077i | ||||||
\(682\) | − | 1.79659i | − | 0.0687948i | ||||||
\(683\) | 33.5723i | 1.28461i | 0.766449 | + | 0.642305i | \(0.222022\pi\) | ||||
−0.766449 | + | 0.642305i | \(0.777978\pi\) | |||||||
\(684\) | − | 31.0569i | − | 1.18749i | ||||||
\(685\) | 0.385576 | 0.0147321 | ||||||||
\(686\) | 5.13526 | 0.196065 | ||||||||
\(687\) | − | 4.69614i | − | 0.179169i | ||||||
\(688\) | 16.8219 | 0.641330 | ||||||||
\(689\) | −22.0084 | + | 3.00356i | −0.838455 | + | 0.114427i | ||||
\(690\) | −0.228109 | −0.00868397 | ||||||||
\(691\) | − | 39.7800i | − | 1.51330i | −0.653818 | − | 0.756652i | \(-0.726834\pi\) | ||
0.653818 | − | 0.756652i | \(-0.273166\pi\) | |||||||
\(692\) | −8.08927 | −0.307508 | ||||||||
\(693\) | 44.3880 | 1.68616 | ||||||||
\(694\) | − | 7.64888i | − | 0.290348i | ||||||
\(695\) | 2.69671i | 0.102292i | ||||||||
\(696\) | 3.23633i | 0.122673i | ||||||||
\(697\) | − | 8.72916i | − | 0.330641i | ||||||
\(698\) | 12.8967 | 0.488148 | ||||||||
\(699\) | −4.25250 | −0.160844 | ||||||||
\(700\) | − | 35.9948i | − | 1.36048i | ||||||
\(701\) | −5.79116 | −0.218729 | −0.109365 | − | 0.994002i | \(-0.534882\pi\) | ||||
−0.109365 | + | 0.994002i | \(0.534882\pi\) | |||||||
\(702\) | −0.471388 | − | 3.45407i | −0.0177914 | − | 0.130366i | ||||
\(703\) | −71.4584 | −2.69510 | ||||||||
\(704\) | − | 11.5952i | − | 0.437011i | ||||||
\(705\) | 0.263023 | 0.00990602 | ||||||||
\(706\) | −1.08237 | −0.0407354 | ||||||||
\(707\) | − | 17.9954i | − | 0.676788i | ||||||
\(708\) | − | 4.89295i | − | 0.183888i | ||||||
\(709\) | 11.9447i | 0.448594i | 0.974521 | + | 0.224297i | \(0.0720086\pi\) | ||||
−0.974521 | + | 0.224297i | \(0.927991\pi\) | |||||||
\(710\) | 0.597366i | 0.0224188i | ||||||||
\(711\) | −23.8174 | −0.893222 | ||||||||
\(712\) | 5.69137 | 0.213293 | ||||||||
\(713\) | 8.58551i | 0.321530i | ||||||||
\(714\) | −1.22939 | −0.0460086 | ||||||||
\(715\) | 2.18037 | − | 0.297561i | 0.0815410 | − | 0.0111282i | ||||
\(716\) | 6.84021 | 0.255631 | ||||||||
\(717\) | 7.56601i | 0.282558i | ||||||||
\(718\) | 1.22843 | 0.0458446 | ||||||||
\(719\) | −39.8697 | −1.48689 | −0.743445 | − | 0.668797i | \(-0.766809\pi\) | ||||
−0.743445 | + | 0.668797i | \(0.766809\pi\) | |||||||
\(720\) | 1.25381i | 0.0467266i | ||||||||
\(721\) | 23.7551i | 0.884686i | ||||||||
\(722\) | 8.53756i | 0.317735i | ||||||||
\(723\) | − | 2.49389i | − | 0.0927486i | ||||||
\(724\) | 15.0955 | 0.561018 | ||||||||
\(725\) | −25.9434 | −0.963513 | ||||||||
\(726\) | 0.536860i | 0.0199248i | ||||||||
\(727\) | −45.0588 | −1.67114 | −0.835569 | − | 0.549385i | \(-0.814862\pi\) | ||||
−0.835569 | + | 0.549385i | \(0.814862\pi\) | |||||||
\(728\) | 26.1638 | − | 3.57065i | 0.969694 | − | 0.132337i | ||||
\(729\) | −20.7607 | −0.768913 | ||||||||
\(730\) | 0.381559i | 0.0141221i | ||||||||
\(731\) | 11.4452 | 0.423316 | ||||||||
\(732\) | −2.77203 | −0.102457 | ||||||||
\(733\) | − | 28.3348i | − | 1.04657i | −0.852158 | − | 0.523285i | \(-0.824706\pi\) | ||
0.852158 | − | 0.523285i | \(-0.175294\pi\) | |||||||
\(734\) | 7.43857i | 0.274563i | ||||||||
\(735\) | 0.538787i | 0.0198735i | ||||||||
\(736\) | − | 41.8235i | − | 1.54164i | ||||||
\(737\) | 29.0751 | 1.07100 | ||||||||
\(738\) | 6.52636 | 0.240239 | ||||||||
\(739\) | 2.93397i | 0.107928i | 0.998543 | + | 0.0539639i | \(0.0171856\pi\) | ||||
−0.998543 | + | 0.0539639i | \(0.982814\pi\) | |||||||
\(740\) | 3.36953 | 0.123867 | ||||||||
\(741\) | −1.02436 | − | 7.50592i | −0.0376307 | − | 0.275737i | ||||
\(742\) | −11.9561 | −0.438922 | ||||||||
\(743\) | 0.923703i | 0.0338874i | 0.999856 | + | 0.0169437i | \(0.00539360\pi\) | ||||
−0.999856 | + | 0.0169437i | \(0.994606\pi\) | |||||||
\(744\) | 0.620472 | 0.0227476 | ||||||||
\(745\) | −2.75568 | −0.100960 | ||||||||
\(746\) | 13.5084i | 0.494579i | ||||||||
\(747\) | − | 35.0393i | − | 1.28202i | ||||||
\(748\) | − | 12.2775i | − | 0.448909i | ||||||
\(749\) | 68.3518i | 2.49752i | ||||||||
\(750\) | −0.264997 | −0.00967633 | ||||||||
\(751\) | 28.7114 | 1.04769 | 0.523847 | − | 0.851812i | \(-0.324496\pi\) | ||||
0.523847 | + | 0.851812i | \(0.324496\pi\) | |||||||
\(752\) | 12.6841i | 0.462542i | ||||||||
\(753\) | 4.77130 | 0.173876 | ||||||||
\(754\) | −1.20963 | − | 8.86348i | −0.0440520 | − | 0.322789i | ||||
\(755\) | 2.37364 | 0.0863856 | ||||||||
\(756\) | 14.7096i | 0.534985i | ||||||||
\(757\) | −5.59884 | −0.203493 | −0.101747 | − | 0.994810i | \(-0.532443\pi\) | ||||
−0.101747 | + | 0.994810i | \(0.532443\pi\) | |||||||
\(758\) | −1.74478 | −0.0633731 | ||||||||
\(759\) | − | 11.2085i | − | 0.406843i | ||||||
\(760\) | − | 1.76321i | − | 0.0639583i | ||||||
\(761\) | 15.3752i | 0.557351i | 0.960385 | + | 0.278676i | \(0.0898955\pi\) | ||||
−0.960385 | + | 0.278676i | \(0.910105\pi\) | |||||||
\(762\) | − | 1.75524i | − | 0.0635856i | ||||||
\(763\) | 32.5845 | 1.17964 | ||||||||
\(764\) | 15.0170 | 0.543294 | ||||||||
\(765\) | 0.853059i | 0.0308424i | ||||||||
\(766\) | 13.2014 | 0.476985 | ||||||||
\(767\) | 3.89092 | + | 28.5105i | 0.140493 | + | 1.02946i | ||||
\(768\) | 0.280319 | 0.0101151 | ||||||||
\(769\) | 15.2197i | 0.548838i | 0.961610 | + | 0.274419i | \(0.0884855\pi\) | ||||
−0.961610 | + | 0.274419i | \(0.911515\pi\) | |||||||
\(770\) | 1.18448 | 0.0426859 | ||||||||
\(771\) | 3.60429 | 0.129805 | ||||||||
\(772\) | − | 2.39996i | − | 0.0863764i | ||||||
\(773\) | 22.8328i | 0.821239i | 0.911807 | + | 0.410620i | \(0.134688\pi\) | ||||
−0.911807 | + | 0.410620i | \(0.865312\pi\) | |||||||
\(774\) | 8.55702i | 0.307576i | ||||||||
\(775\) | 4.97389i | 0.178667i | ||||||||
\(776\) | 0.657325 | 0.0235966 | ||||||||
\(777\) | 16.5788 | 0.594761 | ||||||||
\(778\) | − | 3.71406i | − | 0.133155i | ||||||
\(779\) | 28.9526 | 1.03734 | ||||||||
\(780\) | 0.0483023 | + | 0.353933i | 0.00172950 | + | 0.0126728i | ||||
\(781\) | −29.3525 | −1.05031 | ||||||||
\(782\) | − | 7.48440i | − | 0.267642i | ||||||
\(783\) | 10.6020 | 0.378885 | ||||||||
\(784\) | −25.9826 | −0.927951 | ||||||||
\(785\) | − | 0.492413i | − | 0.0175750i | ||||||
\(786\) | 3.22672i | 0.115093i | ||||||||
\(787\) | − | 45.5221i | − | 1.62269i | −0.584570 | − | 0.811343i | \(-0.698737\pi\) | ||
0.584570 | − | 0.811343i | \(-0.301263\pi\) | |||||||
\(788\) | − | 8.86146i | − | 0.315677i | ||||||
\(789\) | 7.56870 | 0.269453 | ||||||||
\(790\) | −0.635562 | −0.0226123 | ||||||||
\(791\) | 35.6414i | 1.26726i | ||||||||
\(792\) | 19.5295 | 0.693950 | ||||||||
\(793\) | 16.1522 | − | 2.20434i | 0.573582 | − | 0.0782785i | ||||
\(794\) | 15.4680 | 0.548940 | ||||||||
\(795\) | − | 0.344106i | − | 0.0122042i | ||||||
\(796\) | −32.1973 | −1.14120 | ||||||||
\(797\) | −32.8209 | −1.16258 | −0.581288 | − | 0.813698i | \(-0.697451\pi\) | ||||
−0.581288 | + | 0.813698i | \(0.697451\pi\) | |||||||
\(798\) | − | 4.07760i | − | 0.144345i | ||||||
\(799\) | 8.62994i | 0.305305i | ||||||||
\(800\) | − | 24.2298i | − | 0.856654i | ||||||
\(801\) | − | 9.13288i | − | 0.322695i | ||||||
\(802\) | −8.77832 | −0.309973 | ||||||||
\(803\) | −18.7485 | −0.661620 | ||||||||
\(804\) | 4.71968i | 0.166450i | ||||||||
\(805\) | −5.66041 | −0.199503 | ||||||||
\(806\) | −1.69931 | + | 0.231911i | −0.0598558 | + | 0.00816870i | ||||
\(807\) | −1.45061 | −0.0510638 | ||||||||
\(808\) | − | 7.91748i | − | 0.278536i | ||||||
\(809\) | −23.3816 | −0.822055 | −0.411027 | − | 0.911623i | \(-0.634830\pi\) | ||||
−0.411027 | + | 0.911623i | \(0.634830\pi\) | |||||||
\(810\) | −0.610238 | −0.0214416 | ||||||||
\(811\) | 20.9233i | 0.734717i | 0.930079 | + | 0.367358i | \(0.119738\pi\) | ||||
−0.930079 | + | 0.367358i | \(0.880262\pi\) | |||||||
\(812\) | 37.7463i | 1.32464i | ||||||||
\(813\) | − | 1.69359i | − | 0.0593968i | ||||||
\(814\) | − | 21.1205i | − | 0.740272i | ||||||
\(815\) | −2.17183 | −0.0760757 | ||||||||
\(816\) | 1.70631 | 0.0597327 | ||||||||
\(817\) | 37.9612i | 1.32809i | ||||||||
\(818\) | −9.68274 | −0.338549 | ||||||||
\(819\) | −5.72979 | − | 41.9847i | −0.200215 | − | 1.46707i | ||||
\(820\) | −1.36523 | −0.0476758 | ||||||||
\(821\) | 33.5027i | 1.16925i | 0.811303 | + | 0.584626i | \(0.198759\pi\) | ||||
−0.811303 | + | 0.584626i | \(0.801241\pi\) | |||||||
\(822\) | 0.392315 | 0.0136836 | ||||||||
\(823\) | 30.7439 | 1.07167 | 0.535833 | − | 0.844324i | \(-0.319998\pi\) | ||||
0.535833 | + | 0.844324i | \(0.319998\pi\) | |||||||
\(824\) | 10.4516i | 0.364098i | ||||||||
\(825\) | − | 6.49347i | − | 0.226074i | ||||||
\(826\) | 15.4883i | 0.538909i | ||||||||
\(827\) | 38.4208i | 1.33602i | 0.744151 | + | 0.668012i | \(0.232854\pi\) | ||||
−0.744151 | + | 0.668012i | \(0.767146\pi\) | |||||||
\(828\) | −43.8658 | −1.52444 | ||||||||
\(829\) | 40.4200 | 1.40385 | 0.701923 | − | 0.712253i | \(-0.252325\pi\) | ||||
0.701923 | + | 0.712253i | \(0.252325\pi\) | |||||||
\(830\) | − | 0.935016i | − | 0.0324549i | ||||||
\(831\) | −5.51559 | −0.191334 | ||||||||
\(832\) | −10.9674 | + | 1.49676i | −0.380227 | + | 0.0518907i | ||||
\(833\) | −17.6779 | −0.612504 | ||||||||
\(834\) | 2.74384i | 0.0950115i | ||||||||
\(835\) | 3.06618 | 0.106109 | ||||||||
\(836\) | 40.7216 | 1.40839 | ||||||||
\(837\) | − | 2.03263i | − | 0.0702579i | ||||||
\(838\) | 15.5378i | 0.536745i | ||||||||
\(839\) | 10.2387i | 0.353478i | 0.984258 | + | 0.176739i | \(0.0565549\pi\) | ||||
−0.984258 | + | 0.176739i | \(0.943445\pi\) | |||||||
\(840\) | 0.409076i | 0.0141145i | ||||||||
\(841\) | −1.79422 | −0.0618695 | ||||||||
\(842\) | 4.76399 | 0.164178 | ||||||||
\(843\) | 2.86964i | 0.0988355i | ||||||||
\(844\) | −31.0761 | −1.06968 | ||||||||
\(845\) | −0.562901 | − | 2.02390i | −0.0193644 | − | 0.0696244i | ||||
\(846\) | −6.45218 | −0.221830 | ||||||||
\(847\) | 13.3219i | 0.457746i | ||||||||
\(848\) | 16.5943 | 0.569850 | ||||||||
\(849\) | 7.42476 | 0.254817 | ||||||||
\(850\) | − | 4.33598i | − | 0.148723i | ||||||
\(851\) | 100.930i | 3.45985i | ||||||||
\(852\) | − | 4.76471i | − | 0.163236i | ||||||
\(853\) | 39.8271i | 1.36365i | 0.731514 | + | 0.681826i | \(0.238814\pi\) | ||||
−0.731514 | + | 0.681826i | \(0.761186\pi\) | |||||||
\(854\) | 8.77470 | 0.300264 | ||||||||
\(855\) | −2.82940 | −0.0967635 | ||||||||
\(856\) | 30.0729i | 1.02787i | ||||||||
\(857\) | 17.2714 | 0.589981 | 0.294990 | − | 0.955500i | \(-0.404684\pi\) | ||||
0.294990 | + | 0.955500i | \(0.404684\pi\) | |||||||
\(858\) | 2.21847 | − | 0.302762i | 0.0757375 | − | 0.0103361i | ||||
\(859\) | 20.0471 | 0.683999 | 0.342000 | − | 0.939700i | \(-0.388896\pi\) | ||||
0.342000 | + | 0.939700i | \(0.388896\pi\) | |||||||
\(860\) | − | 1.79001i | − | 0.0610390i | ||||||
\(861\) | −6.71720 | −0.228922 | ||||||||
\(862\) | −7.47165 | −0.254485 | ||||||||
\(863\) | 17.6248i | 0.599957i | 0.953946 | + | 0.299978i | \(0.0969795\pi\) | ||||
−0.953946 | + | 0.299978i | \(0.903021\pi\) | |||||||
\(864\) | 9.90176i | 0.336865i | ||||||||
\(865\) | 0.736964i | 0.0250575i | ||||||||
\(866\) | − | 10.9778i | − | 0.373039i | ||||||
\(867\) | −4.71519 | −0.160136 | ||||||||
\(868\) | 7.23676 | 0.245632 | ||||||||
\(869\) | − | 31.2293i | − | 1.05938i | ||||||
\(870\) | 0.138582 | 0.00469838 | ||||||||
\(871\) | −3.75313 | − | 27.5009i | −0.127170 | − | 0.931832i | ||||
\(872\) | 14.3363 | 0.485488 | ||||||||
\(873\) | − | 1.05480i | − | 0.0356997i | ||||||
\(874\) | 24.8241 | 0.839686 | ||||||||
\(875\) | −6.57576 | −0.222301 | ||||||||
\(876\) | − | 3.04339i | − | 0.102827i | ||||||
\(877\) | 21.4082i | 0.722902i | 0.932391 | + | 0.361451i | \(0.117719\pi\) | ||||
−0.932391 | + | 0.361451i | \(0.882281\pi\) | |||||||
\(878\) | 4.71455i | 0.159108i | ||||||||
\(879\) | − | 8.76649i | − | 0.295686i | ||||||
\(880\) | −1.64399 | −0.0554188 | ||||||||
\(881\) | −30.4594 | −1.02620 | −0.513102 | − | 0.858328i | \(-0.671504\pi\) | ||||
−0.513102 | + | 0.858328i | \(0.671504\pi\) | |||||||
\(882\) | − | 13.2169i | − | 0.445036i | ||||||
\(883\) | 25.8122 | 0.868651 | 0.434326 | − | 0.900756i | \(-0.356987\pi\) | ||||
0.434326 | + | 0.900756i | \(0.356987\pi\) | |||||||
\(884\) | −11.6127 | + | 1.58483i | −0.390579 | + | 0.0533035i | ||||
\(885\) | −0.445767 | −0.0149843 | ||||||||
\(886\) | 4.87025i | 0.163619i | ||||||||
\(887\) | 17.1989 | 0.577484 | 0.288742 | − | 0.957407i | \(-0.406763\pi\) | ||||
0.288742 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(888\) | 7.29420 | 0.244777 | ||||||||
\(889\) | − | 43.5553i | − | 1.46080i | ||||||
\(890\) | − | 0.243709i | − | 0.00816914i | ||||||
\(891\) | − | 29.9850i | − | 1.00453i | ||||||
\(892\) | 26.4368i | 0.885168i | ||||||||
\(893\) | −28.6235 | −0.957851 | ||||||||
\(894\) | −2.80385 | −0.0937747 | ||||||||
\(895\) | − | 0.623170i | − | 0.0208303i | ||||||
\(896\) | −45.7083 | −1.52701 | ||||||||
\(897\) | −10.6016 | + | 1.44684i | −0.353978 | + | 0.0483085i | ||||
\(898\) | −17.9878 | −0.600261 | ||||||||
\(899\) | − | 5.21592i | − | 0.173961i | ||||||
\(900\) | −25.4130 | −0.847100 | ||||||||
\(901\) | 11.2903 | 0.376135 | ||||||||
\(902\) | 8.55734i | 0.284928i | ||||||||
\(903\) | − | 8.80723i | − | 0.293086i | ||||||
\(904\) | 15.6812i | 0.521550i | ||||||||
\(905\) | − | 1.37525i | − | 0.0457150i | ||||||
\(906\) | 2.41513 | 0.0802373 | ||||||||
\(907\) | −19.7028 | −0.654220 | −0.327110 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327110 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(908\) | − | 42.0588i | − | 1.39577i | ||||||
\(909\) | −12.7051 | −0.421402 | ||||||||
\(910\) | −0.152898 | − | 1.12035i | −0.00506852 | − | 0.0371393i | ||||
\(911\) | −21.7935 | −0.722050 | −0.361025 | − | 0.932556i | \(-0.617573\pi\) | ||||
−0.361025 | + | 0.932556i | \(0.617573\pi\) | |||||||
\(912\) | 5.65944i | 0.187403i | ||||||||
\(913\) | 45.9434 | 1.52051 | ||||||||
\(914\) | −2.74331 | −0.0907406 | ||||||||
\(915\) | 0.252543i | 0.00834881i | ||||||||
\(916\) | − | 24.0984i | − | 0.796233i | ||||||
\(917\) | 80.0692i | 2.64412i | ||||||||
\(918\) | 1.77194i | 0.0584827i | ||||||||
\(919\) | −17.9983 | −0.593709 | −0.296855 | − | 0.954923i | \(-0.595938\pi\) | ||||
−0.296855 | + | 0.954923i | \(0.595938\pi\) | |||||||
\(920\) | −2.49042 | −0.0821067 | ||||||||
\(921\) | 8.49589i | 0.279949i | ||||||||
\(922\) | −9.25081 | −0.304659 | ||||||||
\(923\) | 3.78894 | + | 27.7633i | 0.124714 | + | 0.913839i | ||||
\(924\) | −9.44768 | −0.310806 | ||||||||
\(925\) | 58.4725i | 1.92256i | ||||||||
\(926\) | −8.35246 | −0.274479 | ||||||||
\(927\) | 16.7715 | 0.550849 | ||||||||
\(928\) | 25.4089i | 0.834087i | ||||||||
\(929\) | 41.5350i | 1.36272i | 0.731949 | + | 0.681360i | \(0.238611\pi\) | ||||
−0.731949 | + | 0.681360i | \(0.761389\pi\) | |||||||
\(930\) | − | 0.0265691i | − | 0.000871235i | ||||||
\(931\) | − | 58.6337i | − | 1.92164i | ||||||
\(932\) | −21.8218 | −0.714797 | ||||||||
\(933\) | 4.13981 | 0.135531 | ||||||||
\(934\) | − | 10.2345i | − | 0.334884i | ||||||
\(935\) | −1.11853 | −0.0365798 | ||||||||
\(936\) | −2.52094 | − | 18.4721i | −0.0823997 | − | 0.603779i | ||||
\(937\) | 32.8134 | 1.07197 | 0.535983 | − | 0.844229i | \(-0.319941\pi\) | ||||
0.535983 | + | 0.844229i | \(0.319941\pi\) | |||||||
\(938\) | − | 14.9399i | − | 0.487804i | ||||||
\(939\) | 1.43292 | 0.0467616 | ||||||||
\(940\) | 1.34971 | 0.0440227 | ||||||||
\(941\) | − | 47.4967i | − | 1.54835i | −0.632972 | − | 0.774174i | \(-0.718165\pi\) | ||
0.632972 | − | 0.774174i | \(-0.281835\pi\) | |||||||
\(942\) | − | 0.501019i | − | 0.0163241i | ||||||
\(943\) | − | 40.8938i | − | 1.33168i | ||||||
\(944\) | − | 21.4968i | − | 0.699662i | ||||||
\(945\) | 1.34011 | 0.0435937 | ||||||||
\(946\) | −11.2199 | −0.364791 | ||||||||
\(947\) | − | 32.9725i | − | 1.07146i | −0.844388 | − | 0.535731i | \(-0.820036\pi\) | ||
0.844388 | − | 0.535731i | \(-0.179964\pi\) | |||||||
\(948\) | 5.06937 | 0.164645 | ||||||||
\(949\) | 2.42013 | + | 17.7334i | 0.0785608 | + | 0.575650i | ||||
\(950\) | 14.3814 | 0.466596 | ||||||||
\(951\) | 10.8423i | 0.351584i | ||||||||
\(952\) | −13.4220 | −0.435010 | ||||||||
\(953\) | −8.49881 | −0.275304 | −0.137652 | − | 0.990481i | \(-0.543955\pi\) | ||||
−0.137652 | + | 0.990481i | \(0.543955\pi\) | |||||||
\(954\) | 8.44122i | 0.273295i | ||||||||
\(955\) | − | 1.36810i | − | 0.0442708i | ||||||
\(956\) | 38.8252i | 1.25570i | ||||||||
\(957\) | 6.80944i | 0.220118i | ||||||||
\(958\) | 19.2237 | 0.621091 | ||||||||
\(959\) | 9.73508 | 0.314362 | ||||||||
\(960\) | − | 0.171478i | − | 0.00553441i | ||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −19.9769 | + | 2.72632i | −0.644082 | + | 0.0878999i | ||||
\(963\) | 48.2576 | 1.55508 | ||||||||
\(964\) | − | 12.7974i | − | 0.412178i | ||||||
\(965\) | −0.218646 | −0.00703846 | ||||||||
\(966\) | −5.75934 | −0.185304 | ||||||||
\(967\) | 10.3380i | 0.332448i | 0.986088 | + | 0.166224i | \(0.0531575\pi\) | ||||
−0.986088 | + | 0.166224i | \(0.946842\pi\) | |||||||
\(968\) | 5.86125i | 0.188388i | ||||||||
\(969\) | 3.85054i | 0.123697i | ||||||||
\(970\) | − | 0.0281472i | − | 0.000903751i | ||||||
\(971\) | −42.4243 | −1.36146 | −0.680730 | − | 0.732534i | \(-0.738337\pi\) | ||||
−0.680730 | + | 0.732534i | \(0.738337\pi\) | |||||||
\(972\) | 15.6834 | 0.503046 | ||||||||
\(973\) | 68.0870i | 2.18277i | ||||||||
\(974\) | 0.226844 | 0.00726853 | ||||||||
\(975\) | −6.14190 | + | 0.838204i | −0.196698 | + | 0.0268440i | ||||
\(976\) | −12.1787 | −0.389831 | ||||||||
\(977\) | 9.45047i | 0.302347i | 0.988507 | + | 0.151174i | \(0.0483053\pi\) | ||||
−0.988507 | + | 0.151174i | \(0.951695\pi\) | |||||||
\(978\) | −2.20979 | −0.0706612 | ||||||||
\(979\) | 11.9750 | 0.382723 | ||||||||
\(980\) | 2.76480i | 0.0883183i | ||||||||
\(981\) | − | 23.0053i | − | 0.734502i | ||||||
\(982\) | 2.57830i | 0.0822770i | ||||||||
\(983\) | 47.9698i | 1.53000i | 0.644031 | + | 0.765000i | \(0.277261\pi\) | ||||
−0.644031 | + | 0.765000i | \(0.722739\pi\) | |||||||
\(984\) | −2.95538 | −0.0942140 | ||||||||
\(985\) | −0.807314 | −0.0257232 | ||||||||
\(986\) | 4.54696i | 0.144805i | ||||||||
\(987\) | 6.64085 | 0.211381 | ||||||||
\(988\) | −5.25651 | − | 38.5168i | −0.167232 | − | 1.22538i | ||||
\(989\) | 53.6177 | 1.70494 | ||||||||
\(990\) | − | 0.836267i | − | 0.0265783i | ||||||
\(991\) | −12.1349 | −0.385477 | −0.192739 | − | 0.981250i | \(-0.561737\pi\) | ||||
−0.192739 | + | 0.981250i | \(0.561737\pi\) | |||||||
\(992\) | 4.87141 | 0.154667 | ||||||||
\(993\) | 0.167868i | 0.00532711i | ||||||||
\(994\) | 15.0824i | 0.478385i | ||||||||
\(995\) | 2.93330i | 0.0929918i | ||||||||
\(996\) | 7.45787i | 0.236312i | ||||||||
\(997\) | 15.1463 | 0.479688 | 0.239844 | − | 0.970811i | \(-0.422904\pi\) | ||||
0.239844 | + | 0.970811i | \(0.422904\pi\) | |||||||
\(998\) | −6.04976 | −0.191502 | ||||||||
\(999\) | − | 23.8954i | − | 0.756015i |
(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 | 403.2.c.b.311.15 | ✓ | 32 | |
13.5 | odd | 4 | 5239.2.a.k.1.9 | 16 | |||
13.8 | odd | 4 | 5239.2.a.l.1.8 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.18 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.15 | ✓ | 32 | 1.1 | even | 1 | trivial | |
403.2.c.b.311.18 | yes | 32 | 13.12 | even | 2 | inner | |
5239.2.a.k.1.9 | 16 | 13.5 | odd | 4 | |||
5239.2.a.l.1.8 | 16 | 13.8 | odd | 4 |