Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(370,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.370");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.fm (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 370.8 | ||
Character | \(\chi\) | \(=\) | 819.370 |
Dual form | 819.2.fm.g.622.8 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.607529 | + | 2.26733i | 0.429588 | + | 1.60324i | 0.753696 | + | 0.657223i | \(0.228269\pi\) |
−0.324108 | + | 0.946020i | \(0.605064\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.03963 | + | 1.75493i | −1.51982 | + | 0.877467i | ||||
\(5\) | 1.12678 | + | 1.12678i | 0.503911 | + | 0.503911i | 0.912651 | − | 0.408740i | \(-0.134032\pi\) |
−0.408740 | + | 0.912651i | \(0.634032\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.68394 | − | 2.04067i | 0.636469 | − | 0.771303i | ||||
\(8\) | −2.50608 | − | 2.50608i | −0.886032 | − | 0.886032i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.87023 | + | 3.23933i | −0.591418 | + | 1.02437i | ||||
\(11\) | 3.03446 | − | 0.813080i | 0.914923 | − | 0.245153i | 0.229509 | − | 0.973306i | \(-0.426288\pi\) |
0.685414 | + | 0.728154i | \(0.259621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.04831 | + | 3.44979i | 0.290748 | + | 0.956800i | ||||
\(14\) | 5.64992 | + | 2.57827i | 1.51000 | + | 0.689072i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.649718 | − | 1.12534i | 0.162430 | − | 0.281336i | ||||
\(17\) | 0.320795 | + | 0.555633i | 0.0778042 | + | 0.134761i | 0.902302 | − | 0.431104i | \(-0.141876\pi\) |
−0.824498 | + | 0.565865i | \(0.808542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.04036 | + | 7.61472i | −0.468090 | + | 1.74694i | 0.178346 | + | 0.983968i | \(0.442925\pi\) |
−0.646436 | + | 0.762968i | \(0.723741\pi\) | |||||||
\(20\) | −5.40242 | − | 1.44757i | −1.20802 | − | 0.323687i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.68704 | + | 6.38614i | 0.786080 | + | 1.36153i | ||||
\(23\) | 0.126569 | + | 0.0730744i | 0.0263914 | + | 0.0152371i | 0.513138 | − | 0.858306i | \(-0.328483\pi\) |
−0.486746 | + | 0.873543i | \(0.661816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 2.46074i | − | 0.492147i | ||||||
\(26\) | −7.18493 | + | 4.47270i | −1.40908 | + | 0.877169i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.53731 | + | 9.15811i | −0.290523 | + | 1.73072i | ||||
\(29\) | −1.49412 | + | 2.58790i | −0.277452 | + | 0.480561i | −0.970751 | − | 0.240089i | \(-0.922823\pi\) |
0.693299 | + | 0.720650i | \(0.256157\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.73334 | − | 4.73334i | −0.850132 | − | 0.850132i | 0.140017 | − | 0.990149i | \(-0.455284\pi\) |
−0.990149 | + | 0.140017i | \(0.955284\pi\) | |||||||
\(32\) | −3.90048 | − | 1.04513i | −0.689514 | − | 0.184755i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.06491 | + | 1.06491i | −0.182631 | + | 0.182631i | ||||
\(35\) | 4.19682 | − | 0.401964i | 0.709391 | − | 0.0679444i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.75725 | − | 1.00675i | 0.617688 | − | 0.165509i | 0.0636115 | − | 0.997975i | \(-0.479738\pi\) |
0.554077 | + | 0.832466i | \(0.313071\pi\) | |||||||
\(38\) | −18.5046 | −3.00185 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 5.64759i | − | 0.892963i | ||||||
\(41\) | 5.60356 | − | 1.50147i | 0.875129 | − | 0.234490i | 0.206825 | − | 0.978378i | \(-0.433687\pi\) |
0.668305 | + | 0.743888i | \(0.267020\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.42713 | − | 1.40130i | 0.370133 | − | 0.213697i | −0.303383 | − | 0.952869i | \(-0.598116\pi\) |
0.673517 | + | 0.739172i | \(0.264783\pi\) | |||||||
\(44\) | −7.79674 | + | 7.79674i | −1.17540 | + | 1.17540i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0887896 | + | 0.331367i | −0.0130913 | + | 0.0488574i | ||||
\(47\) | −2.22937 | + | 2.22937i | −0.325187 | + | 0.325187i | −0.850753 | − | 0.525566i | \(-0.823854\pi\) |
0.525566 | + | 0.850753i | \(0.323854\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.32871 | − | 6.87274i | −0.189815 | − | 0.981820i | ||||
\(50\) | 5.57930 | − | 1.49497i | 0.789032 | − | 0.211420i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.24062 | − | 8.64639i | −1.28144 | − | 1.19904i | ||||
\(53\) | 7.32119 | 1.00564 | 0.502821 | − | 0.864390i | \(-0.332295\pi\) | ||||
0.502821 | + | 0.864390i | \(0.332295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.33533 | + | 2.50300i | 0.584575 | + | 0.337505i | ||||
\(56\) | −9.33417 | + | 0.894011i | −1.24733 | + | 0.119467i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.77534 | − | 1.81545i | −0.889646 | − | 0.238380i | ||||
\(59\) | −4.00631 | − | 1.07349i | −0.521578 | − | 0.139756i | −0.0115814 | − | 0.999933i | \(-0.503687\pi\) |
−0.509996 | + | 0.860177i | \(0.670353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.90292 | − | 2.25335i | 0.499718 | − | 0.288512i | −0.228879 | − | 0.973455i | \(-0.573506\pi\) |
0.728597 | + | 0.684942i | \(0.240173\pi\) | |||||||
\(62\) | 7.85639 | − | 13.6077i | 0.997763 | − | 1.72818i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 12.0775i | − | 1.50969i | ||||||
\(65\) | −2.70594 | + | 5.06836i | −0.335631 | + | 0.628653i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.366486 | − | 1.36775i | −0.0447734 | − | 0.167097i | 0.939919 | − | 0.341397i | \(-0.110900\pi\) |
−0.984692 | + | 0.174301i | \(0.944234\pi\) | |||||||
\(68\) | −1.95020 | − | 1.12595i | −0.236496 | − | 0.136541i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.46107 | + | 9.27135i | 0.413677 | + | 1.10814i | ||||
\(71\) | −13.8300 | − | 3.70574i | −1.64132 | − | 0.439791i | −0.684157 | − | 0.729335i | \(-0.739830\pi\) |
−0.957165 | + | 0.289544i | \(0.906496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.99083 | + | 4.99083i | −0.584133 | + | 0.584133i | −0.936036 | − | 0.351904i | \(-0.885534\pi\) |
0.351904 | + | 0.936036i | \(0.385534\pi\) | |||||||
\(74\) | 4.56527 | + | 7.90729i | 0.530702 | + | 0.919203i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.16138 | − | 26.7267i | −0.821467 | − | 3.06576i | ||||
\(77\) | 3.45060 | − | 7.56152i | 0.393233 | − | 0.861715i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.632916 | −0.0712086 | −0.0356043 | − | 0.999366i | \(-0.511336\pi\) | ||||
−0.0356043 | + | 0.999366i | \(0.511336\pi\) | |||||||
\(80\) | 2.00010 | − | 0.535926i | 0.223618 | − | 0.0599184i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.80865 | + | 11.7929i | 0.751890 | + | 1.30231i | ||||
\(83\) | 1.07813 | + | 1.07813i | 0.118340 | + | 0.118340i | 0.763797 | − | 0.645457i | \(-0.223333\pi\) |
−0.645457 | + | 0.763797i | \(0.723333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.264611 | + | 0.987541i | −0.0287011 | + | 0.107114i | ||||
\(86\) | 4.65176 | + | 4.65176i | 0.501612 | + | 0.501612i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.64223 | − | 5.56694i | −1.02786 | − | 0.593438i | ||||
\(89\) | 3.51557 | + | 13.1203i | 0.372649 | + | 1.39075i | 0.856749 | + | 0.515734i | \(0.172481\pi\) |
−0.484099 | + | 0.875013i | \(0.660853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.80518 | + | 3.66998i | 0.923034 | + | 0.384718i | ||||
\(92\) | −0.512963 | −0.0534801 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.40911 | − | 3.70030i | −0.661049 | − | 0.381657i | ||||
\(95\) | −10.8791 | + | 6.28107i | −1.11618 | + | 0.644425i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0487160 | + | 0.181811i | −0.00494637 | + | 0.0184601i | −0.968355 | − | 0.249577i | \(-0.919708\pi\) |
0.963409 | + | 0.268037i | \(0.0863750\pi\) | |||||||
\(98\) | 14.7755 | − | 7.18800i | 1.49255 | − | 0.726098i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.31843 | + | 7.47974i | 0.431843 | + | 0.747974i | ||||
\(101\) | −0.596904 | + | 1.03387i | −0.0593942 | + | 0.102874i | −0.894194 | − | 0.447680i | \(-0.852250\pi\) |
0.834799 | + | 0.550554i | \(0.185584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.79583 | −0.472548 | −0.236274 | − | 0.971687i | \(-0.575926\pi\) | ||||
−0.236274 | + | 0.971687i | \(0.575926\pi\) | |||||||
\(104\) | 6.01830 | − | 11.2726i | 0.590143 | − | 1.10537i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.44783 | + | 16.5995i | 0.432012 | + | 1.61229i | ||||
\(107\) | 7.64819 | − | 13.2471i | 0.739378 | − | 1.28064i | −0.213397 | − | 0.976966i | \(-0.568453\pi\) |
0.952776 | − | 0.303675i | \(-0.0982138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.12415 | − | 9.12415i | 0.873935 | − | 0.873935i | −0.118963 | − | 0.992899i | \(-0.537957\pi\) |
0.992899 | + | 0.118963i | \(0.0379571\pi\) | |||||||
\(110\) | −3.04129 | + | 11.3503i | −0.289976 | + | 1.08220i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.20238 | − | 3.22087i | −0.113614 | − | 0.304344i | ||||
\(113\) | 0.770731 | + | 1.33494i | 0.0725042 | + | 0.125581i | 0.899998 | − | 0.435894i | \(-0.143568\pi\) |
−0.827494 | + | 0.561475i | \(0.810234\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0602761 | + | 0.224953i | 0.00562078 | + | 0.0209770i | ||||
\(116\) | − | 10.4884i | − | 0.973819i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 9.73580i | − | 0.896253i | ||||||
\(119\) | 1.67407 | + | 0.281013i | 0.153461 | + | 0.0257605i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.979449 | + | 0.565485i | −0.0890408 | + | 0.0514077i | ||||
\(122\) | 7.48023 | + | 7.48023i | 0.677228 | + | 0.677228i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 22.6943 | + | 6.08092i | 2.03801 | + | 0.546083i | ||||
\(125\) | 8.40660 | − | 8.40660i | 0.751910 | − | 0.751910i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.81842 | + | 1.62722i | 0.250095 | + | 0.144392i | 0.619808 | − | 0.784754i | \(-0.287211\pi\) |
−0.369713 | + | 0.929146i | \(0.620544\pi\) | |||||||
\(128\) | 19.5827 | − | 5.24716i | 1.73088 | − | 0.463788i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13.1356 | − | 3.05608i | −1.15207 | − | 0.268036i | ||||
\(131\) | − | 16.4678i | − | 1.43880i | −0.694597 | − | 0.719400i | \(-0.744417\pi\) | ||
0.694597 | − | 0.719400i | \(-0.255583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1033 | + | 16.9864i | 1.04949 | + | 1.47291i | ||||
\(134\) | 2.87848 | − | 1.66189i | 0.248663 | − | 0.143565i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.588523 | − | 2.19640i | 0.0504654 | − | 0.188339i | ||||
\(137\) | 0.0978163 | − | 0.365056i | 0.00835701 | − | 0.0311888i | −0.961621 | − | 0.274380i | \(-0.911527\pi\) |
0.969978 | + | 0.243191i | \(0.0781942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.52132 | − | 4.91978i | 0.722769 | − | 0.417291i | −0.0930022 | − | 0.995666i | \(-0.529646\pi\) |
0.815771 | + | 0.578375i | \(0.196313\pi\) | |||||||
\(140\) | −12.0514 | + | 8.58696i | −1.01853 | + | 0.725731i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 33.6085i | − | 2.82037i | ||||||
\(143\) | 5.98600 | + | 9.61588i | 0.500574 | + | 0.804121i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.59954 | + | 1.23244i | −0.381971 | + | 0.102349i | ||||
\(146\) | −14.3479 | − | 8.28378i | −1.18744 | − | 0.685570i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.65388 | + | 9.65388i | −0.793544 | + | 0.793544i | ||||
\(149\) | 5.36436 | + | 1.43738i | 0.439465 | + | 0.117754i | 0.471766 | − | 0.881724i | \(-0.343617\pi\) |
−0.0323006 | + | 0.999478i | \(0.510283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.35521 | + | 3.35521i | 0.273043 | + | 0.273043i | 0.830324 | − | 0.557281i | \(-0.188155\pi\) |
−0.557281 | + | 0.830324i | \(0.688155\pi\) | |||||||
\(152\) | 24.1964 | − | 13.9698i | 1.96258 | − | 1.13310i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.2408 | + | 3.22981i | 1.55047 | + | 0.260266i | ||||
\(155\) | − | 10.6669i | − | 0.856782i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.6201i | − | 1.00720i | −0.863938 | − | 0.503598i | \(-0.832009\pi\) | ||
0.863938 | − | 0.503598i | \(-0.167991\pi\) | |||||||
\(158\) | −0.384515 | − | 1.43503i | −0.0305904 | − | 0.114165i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.21735 | − | 5.57262i | −0.254354 | − | 0.440554i | ||||
\(161\) | 0.362255 | − | 0.135233i | 0.0285497 | − | 0.0106578i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.37843 | + | 12.6085i | −0.264619 | + | 0.987571i | 0.697864 | + | 0.716230i | \(0.254134\pi\) |
−0.962483 | + | 0.271341i | \(0.912533\pi\) | |||||||
\(164\) | −14.3978 | + | 14.3978i | −1.12428 | + | 1.12428i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.78948 | + | 3.09948i | −0.138891 | + | 0.240566i | ||||
\(167\) | −4.79697 | − | 17.9025i | −0.371201 | − | 1.38534i | −0.858817 | − | 0.512282i | \(-0.828800\pi\) |
0.487616 | − | 0.873058i | \(-0.337867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8021 | + | 7.23288i | −0.830931 | + | 0.556375i | ||||
\(170\) | −2.39984 | −0.184059 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.91839 | + | 8.51890i | −0.375024 | + | 0.649560i | ||||
\(173\) | −2.79684 | − | 4.84427i | −0.212640 | − | 0.368303i | 0.739900 | − | 0.672717i | \(-0.234873\pi\) |
−0.952540 | + | 0.304414i | \(0.901540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.02156 | − | 4.14373i | −0.379595 | − | 0.313236i | ||||
\(176\) | 1.05655 | − | 3.94308i | 0.0796402 | − | 0.297221i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.6122 | + | 15.9419i | −2.06962 | + | 1.19490i | ||||
\(179\) | −8.21928 | − | 4.74540i | −0.614338 | − | 0.354688i | 0.160324 | − | 0.987065i | \(-0.448746\pi\) |
−0.774661 | + | 0.632377i | \(0.782080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.91516 | −0.514000 | −0.257000 | − | 0.966411i | \(-0.582734\pi\) | ||||
−0.257000 | + | 0.966411i | \(0.582734\pi\) | |||||||
\(182\) | −2.97164 | + | 22.1939i | −0.220273 | + | 1.64512i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.134060 | − | 0.500321i | −0.00988307 | − | 0.0368841i | ||||
\(185\) | 5.36798 | + | 3.09920i | 0.394662 | + | 0.227858i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.42521 | + | 1.42521i | 0.104222 | + | 0.104222i | ||||
\(188\) | 2.86407 | − | 10.6889i | 0.208884 | − | 0.779565i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.8506 | − | 20.8506i | −1.51266 | − | 1.51266i | ||||
\(191\) | −1.25251 | − | 2.16942i | −0.0906287 | − | 0.156974i | 0.817147 | − | 0.576429i | \(-0.195554\pi\) |
−0.907776 | + | 0.419456i | \(0.862221\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7882 | − | 5.83813i | 1.56835 | − | 0.420238i | 0.633054 | − | 0.774108i | \(-0.281801\pi\) |
0.935295 | + | 0.353870i | \(0.115134\pi\) | |||||||
\(194\) | −0.441821 | −0.0317209 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.1000 | + | 18.5588i | 1.15000 | + | 1.32563i | ||||
\(197\) | 4.63560 | + | 17.3003i | 0.330273 | + | 1.23259i | 0.908904 | + | 0.417005i | \(0.136920\pi\) |
−0.578631 | + | 0.815589i | \(0.696413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.20617 | + | 14.2135i | 0.581720 | + | 1.00757i | 0.995276 | + | 0.0970896i | \(0.0309533\pi\) |
−0.413556 | + | 0.910479i | \(0.635713\pi\) | |||||||
\(200\) | −6.16680 | + | 6.16680i | −0.436058 | + | 0.436058i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.70675 | − | 0.725273i | −0.190447 | − | 0.0510300i | ||||
\(203\) | 2.76505 | + | 7.40688i | 0.194068 | + | 0.519861i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00580 | + | 4.62215i | 0.559150 | + | 0.322825i | ||||
\(206\) | −2.91361 | − | 10.8737i | −0.203001 | − | 0.757609i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.56331 | + | 1.06169i | 0.316408 | + | 0.0736146i | ||||
\(209\) | 24.7655i | 1.71307i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.93176 | − | 8.54207i | 0.339517 | − | 0.588060i | −0.644825 | − | 0.764330i | \(-0.723070\pi\) |
0.984342 | + | 0.176270i | \(0.0564032\pi\) | |||||||
\(212\) | −22.2537 | + | 12.8482i | −1.52839 | + | 0.882418i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 34.6819 | + | 9.29299i | 2.37081 | + | 0.635256i | ||||
\(215\) | 4.31380 | + | 1.15588i | 0.294198 | + | 0.0788302i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.6298 | + | 1.68856i | −1.19679 | + | 0.114627i | ||||
\(218\) | 26.2306 | + | 15.1443i | 1.77656 | + | 1.02570i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.5704 | −1.18460 | ||||||||
\(221\) | −1.58053 | + | 1.68915i | −0.106318 | + | 0.113624i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.41926 | − | 2.25594i | 0.563796 | − | 0.151069i | 0.0343461 | − | 0.999410i | \(-0.489065\pi\) |
0.529450 | + | 0.848341i | \(0.322398\pi\) | |||||||
\(224\) | −8.70094 | + | 6.19968i | −0.581356 | + | 0.414234i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.55852 | + | 2.55852i | −0.170190 | + | 0.170190i | ||||
\(227\) | 4.37226 | − | 16.3175i | 0.290197 | − | 1.08303i | −0.654760 | − | 0.755837i | \(-0.727230\pi\) |
0.944957 | − | 0.327194i | \(-0.106103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.72909 | + | 1.72909i | −0.114262 | + | 0.114262i | −0.761926 | − | 0.647664i | \(-0.775746\pi\) |
0.647664 | + | 0.761926i | \(0.275746\pi\) | |||||||
\(230\) | −0.473424 | + | 0.273331i | −0.0312166 | + | 0.0180229i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.2299 | − | 2.74108i | 0.671624 | − | 0.179961i | ||||
\(233\) | − | 5.37483i | − | 0.352117i | −0.984380 | − | 0.176058i | \(-0.943665\pi\) | ||
0.984380 | − | 0.176058i | \(-0.0563348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.02401 | −0.327730 | ||||||||
\(236\) | 14.0616 | − | 3.76780i | 0.915334 | − | 0.245263i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.379893 | + | 3.96638i | 0.0246248 | + | 0.257102i | ||||
\(239\) | 11.9572 | − | 11.9572i | 0.773448 | − | 0.773448i | −0.205260 | − | 0.978708i | \(-0.565804\pi\) |
0.978708 | + | 0.205260i | \(0.0658038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9893 | − | 3.48047i | −0.836713 | − | 0.224197i | −0.185073 | − | 0.982725i | \(-0.559252\pi\) |
−0.651640 | + | 0.758528i | \(0.725919\pi\) | |||||||
\(242\) | −1.87718 | − | 1.87718i | −0.120670 | − | 0.120670i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.90898 | + | 13.6987i | −0.506320 | + | 0.876972i | ||||
\(245\) | 6.24690 | − | 9.24122i | 0.399100 | − | 0.590400i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.4081 | + | 0.943754i | −1.80756 | + | 0.0600496i | ||||
\(248\) | 23.7242i | 1.50649i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.1678 | + | 13.9533i | 1.52850 | + | 0.882483i | ||||
\(251\) | 6.40248 | + | 11.0894i | 0.404121 | + | 0.699958i | 0.994219 | − | 0.107374i | \(-0.0342441\pi\) |
−0.590098 | + | 0.807332i | \(0.700911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.443482 | + | 0.118831i | 0.0278815 | + | 0.00747082i | ||||
\(254\) | −1.97716 | + | 7.37887i | −0.124058 | + | 0.462992i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.7166 | + | 20.2937i | 0.732286 | + | 1.26836i | ||||
\(257\) | 5.19036 | − | 8.98997i | 0.323766 | − | 0.560779i | −0.657496 | − | 0.753458i | \(-0.728384\pi\) |
0.981262 | + | 0.192679i | \(0.0617176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.27252 | − | 9.36263i | 0.265482 | − | 0.581766i | ||||
\(260\) | −0.669566 | − | 20.1547i | −0.0415247 | − | 1.24994i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 37.3379 | − | 10.0047i | 2.30674 | − | 0.618090i | ||||
\(263\) | −2.18977 | + | 3.79279i | −0.135027 | + | 0.233873i | −0.925608 | − | 0.378484i | \(-0.876445\pi\) |
0.790581 | + | 0.612358i | \(0.209779\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.24936 | + | 8.24936i | 0.506754 | + | 0.506754i | ||||
\(266\) | −31.1607 | + | 37.7620i | −1.91058 | + | 2.31533i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.51429 | + | 3.51429i | 0.214669 | + | 0.214669i | ||||
\(269\) | −10.1192 | + | 5.84233i | −0.616980 | + | 0.356213i | −0.775692 | − | 0.631112i | \(-0.782599\pi\) |
0.158713 | + | 0.987325i | \(0.449266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.94389 | − | 29.6470i | −0.482557 | − | 1.80093i | −0.590819 | − | 0.806804i | \(-0.701195\pi\) |
0.108262 | − | 0.994122i | \(-0.465471\pi\) | |||||||
\(272\) | 0.833705 | 0.0505508 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.887127 | 0.0535933 | ||||||||
\(275\) | −2.00078 | − | 7.46700i | −0.120651 | − | 0.450277i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.5109 | + | 9.53260i | −0.992047 | + | 0.572758i | −0.905885 | − | 0.423523i | \(-0.860793\pi\) |
−0.0861613 | + | 0.996281i | \(0.527460\pi\) | |||||||
\(278\) | 16.3317 | + | 16.3317i | 0.979511 | + | 0.979511i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.5249 | − | 9.51019i | −0.688745 | − | 0.568343i | ||||
\(281\) | −11.8671 | − | 11.8671i | −0.707931 | − | 0.707931i | 0.258169 | − | 0.966100i | \(-0.416881\pi\) |
−0.966100 | + | 0.258169i | \(0.916881\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.21864 | + | 7.30690i | −0.250772 | + | 0.434350i | −0.963739 | − | 0.266848i | \(-0.914018\pi\) |
0.712966 | + | 0.701198i | \(0.247351\pi\) | |||||||
\(284\) | 48.5415 | − | 13.0067i | 2.88041 | − | 0.771804i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.1657 | + | 19.4141i | −1.07416 | + | 1.14798i | ||||
\(287\) | 6.37204 | − | 13.9634i | 0.376129 | − | 0.824235i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.29418 | − | 14.3659i | 0.487893 | − | 0.845055i | ||||
\(290\) | −5.58870 | − | 9.67992i | −0.328180 | − | 0.568424i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.41172 | − | 23.9289i | 0.375218 | − | 1.40033i | ||||
\(293\) | −8.00676 | − | 2.14541i | −0.467760 | − | 0.125336i | 0.0172376 | − | 0.999851i | \(-0.494513\pi\) |
−0.484998 | + | 0.874516i | \(0.661180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.30465 | − | 5.72382i | −0.192404 | − | 0.333253i | ||||
\(296\) | −11.9390 | − | 6.89296i | −0.693938 | − | 0.400645i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.0360i | 0.755156i | ||||||||
\(299\) | −0.119409 | + | 0.513239i | −0.00690558 | + | 0.0296814i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.22753 | − | 7.31268i | 0.0707535 | − | 0.421496i | ||||
\(302\) | −5.56897 | + | 9.64574i | −0.320458 | + | 0.555050i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.24353 | + | 7.24353i | 0.415445 | + | 0.415445i | ||||
\(305\) | 6.93677 | + | 1.85870i | 0.397198 | + | 0.106429i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3438 | − | 17.3438i | 0.989863 | − | 0.989863i | −0.0100865 | − | 0.999949i | \(-0.503211\pi\) |
0.999949 | + | 0.0100865i | \(0.00321069\pi\) | |||||||
\(308\) | 2.78139 | + | 29.0398i | 0.158484 | + | 1.65470i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.1853 | − | 6.48042i | 1.37363 | − | 0.368063i | ||||
\(311\) | 23.7121 | 1.34459 | 0.672294 | − | 0.740284i | \(-0.265309\pi\) | ||||
0.672294 | + | 0.740284i | \(0.265309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0715i | 0.795366i | 0.917523 | + | 0.397683i | \(0.130186\pi\) | ||||
−0.917523 | + | 0.397683i | \(0.869814\pi\) | |||||||
\(314\) | 28.6140 | − | 7.66709i | 1.61478 | − | 0.432679i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.92383 | − | 1.11073i | 0.108224 | − | 0.0624832i | ||||
\(317\) | −11.8369 | + | 11.8369i | −0.664828 | + | 0.664828i | −0.956514 | − | 0.291686i | \(-0.905784\pi\) |
0.291686 | + | 0.956514i | \(0.405784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.42969 | + | 9.06771i | −0.136036 | + | 0.507694i | ||||
\(320\) | 13.6087 | − | 13.6087i | 0.760748 | − | 0.760748i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.526697 | + | 0.739192i | 0.0293517 | + | 0.0411936i | ||||
\(323\) | −4.88553 | + | 1.30907i | −0.271838 | + | 0.0728388i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.48903 | − | 2.57961i | 0.470886 | − | 0.143091i | ||||
\(326\) | −30.6400 | −1.69699 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.8058 | − | 10.2802i | −0.983159 | − | 0.567627i | ||||
\(329\) | 0.795298 | + | 8.30353i | 0.0438462 | + | 0.457788i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.34837 | + | 2.50489i | 0.513833 | + | 0.137681i | 0.506413 | − | 0.862291i | \(-0.330971\pi\) |
0.00742049 | + | 0.999972i | \(0.497638\pi\) | |||||||
\(332\) | −5.16918 | − | 1.38508i | −0.283696 | − | 0.0760160i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 37.6766 | − | 21.7526i | 2.06157 | − | 1.19025i | ||||
\(335\) | 1.12820 | − | 1.95410i | 0.0616401 | − | 0.106764i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0838i | 1.09403i | 0.837122 | + | 0.547016i | \(0.184236\pi\) | ||||
−0.837122 | + | 0.547016i | \(0.815764\pi\) | |||||||
\(338\) | −22.9619 | − | 20.0977i | −1.24896 | − | 1.09317i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.928749 | − | 3.46614i | −0.0503685 | − | 0.187978i | ||||
\(341\) | −18.2117 | − | 10.5145i | −0.986218 | − | 0.569393i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.2625 | − | 8.86180i | −0.878092 | − | 0.478492i | ||||
\(344\) | −9.59434 | − | 2.57080i | −0.517292 | − | 0.138608i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.28440 | − | 9.28440i | 0.499132 | − | 0.499132i | ||||
\(347\) | −11.1008 | − | 19.2271i | −0.595920 | − | 1.03216i | −0.993416 | − | 0.114560i | \(-0.963454\pi\) |
0.397496 | − | 0.917604i | \(-0.369879\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.38593 | + | 5.17235i | 0.0741869 | + | 0.276869i | 0.993048 | − | 0.117713i | \(-0.0375561\pi\) |
−0.918861 | + | 0.394582i | \(0.870889\pi\) | |||||||
\(350\) | 6.34444 | − | 13.9030i | 0.339125 | − | 0.743145i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.6856 | −0.676146 | ||||||||
\(353\) | −25.2105 | + | 6.75514i | −1.34182 | + | 0.359540i | −0.857110 | − | 0.515134i | \(-0.827742\pi\) |
−0.484712 | + | 0.874674i | \(0.661075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.4078 | − | 19.7589i | −0.605465 | − | 1.04870i | ||||
\(356\) | −33.7113 | − | 33.7113i | −1.78669 | − | 1.78669i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.76594 | − | 21.5188i | 0.304739 | − | 1.13730i | ||||
\(359\) | 16.0116 | + | 16.0116i | 0.845061 | + | 0.845061i | 0.989512 | − | 0.144451i | \(-0.0461416\pi\) |
−0.144451 | + | 0.989512i | \(0.546142\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −37.3664 | − | 21.5735i | −1.96665 | − | 1.13545i | ||||
\(362\) | −4.20116 | − | 15.6789i | −0.220808 | − | 0.824066i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −33.2051 | + | 4.29712i | −1.74042 | + | 0.225230i | ||||
\(365\) | −11.2471 | −0.588702 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.2942 | − | 7.09806i | −0.641752 | − | 0.370516i | 0.143537 | − | 0.989645i | \(-0.454152\pi\) |
−0.785289 | + | 0.619129i | \(0.787486\pi\) | |||||||
\(368\) | 0.164468 | − | 0.0949555i | 0.00857347 | − | 0.00494990i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.76571 | + | 14.0538i | −0.195770 | + | 0.730624i | ||||
\(371\) | 12.3284 | − | 14.9402i | 0.640060 | − | 0.775655i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.75321 | − | 3.03665i | −0.0907778 | − | 0.157232i | 0.817061 | − | 0.576551i | \(-0.195602\pi\) |
−0.907839 | + | 0.419320i | \(0.862269\pi\) | |||||||
\(374\) | −2.36557 | + | 4.09728i | −0.122321 | + | 0.211865i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.1739 | 0.576252 | ||||||||
\(377\) | −10.4940 | − | 2.44150i | −0.540469 | − | 0.125744i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.94797 | + | 25.9302i | 0.356893 | + | 1.33194i | 0.878085 | + | 0.478504i | \(0.158821\pi\) |
−0.521192 | + | 0.853439i | \(0.674513\pi\) | |||||||
\(380\) | 22.0457 | − | 38.1843i | 1.13092 | − | 1.95882i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.15784 | − | 4.15784i | 0.212734 | − | 0.212734i | ||||
\(383\) | 8.83941 | − | 32.9891i | 0.451673 | − | 1.68567i | −0.246017 | − | 0.969266i | \(-0.579122\pi\) |
0.697690 | − | 0.716400i | \(-0.254211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4082 | − | 4.63209i | 0.632382 | − | 0.236073i | ||||
\(386\) | 26.4739 | + | 45.8542i | 1.34749 | + | 2.33392i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.170987 | − | 0.638132i | −0.00868054 | − | 0.0323962i | ||||
\(389\) | 27.4644i | 1.39250i | 0.717798 | + | 0.696251i | \(0.245150\pi\) | ||||
−0.717798 | + | 0.696251i | \(0.754850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0937676i | 0.00474203i | ||||||||
\(392\) | −13.8938 | + | 20.5535i | −0.701741 | + | 1.03811i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −36.4092 | + | 21.0208i | −1.83427 | + | 1.05901i | ||||
\(395\) | −0.713157 | − | 0.713157i | −0.0358828 | − | 0.0358828i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.8032 | − | 9.59343i | −1.79691 | − | 0.481480i | −0.803420 | − | 0.595412i | \(-0.796989\pi\) |
−0.993489 | + | 0.113932i | \(0.963655\pi\) | |||||||
\(398\) | −27.2412 | + | 27.2412i | −1.36548 | + | 1.36548i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.76918 | − | 1.59879i | −0.138459 | − | 0.0799393i | ||||
\(401\) | 16.7841 | − | 4.49729i | 0.838158 | − | 0.224584i | 0.185888 | − | 0.982571i | \(-0.440484\pi\) |
0.652269 | + | 0.757987i | \(0.273817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3670 | − | 21.2910i | 0.566232 | − | 1.06058i | ||||
\(404\) | − | 4.19011i | − | 0.208466i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.1140 | + | 10.7692i | −0.750095 | + | 0.534465i | ||||
\(407\) | 10.5826 | − | 6.10989i | 0.524562 | − | 0.302856i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.92033 | + | 10.8988i | −0.144401 | + | 0.538913i | 0.855380 | + | 0.518001i | \(0.173324\pi\) |
−0.999781 | + | 0.0209119i | \(0.993343\pi\) | |||||||
\(410\) | −5.61618 | + | 20.9599i | −0.277363 | + | 1.03513i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.5776 | − | 8.41637i | 0.718186 | − | 0.414645i | ||||
\(413\) | −8.93702 | + | 6.36790i | −0.439762 | + | 0.313344i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.42963i | 0.119266i | ||||||||
\(416\) | −0.483418 | − | 14.5515i | −0.0237015 | − | 0.713444i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −56.1515 | + | 15.0458i | −2.74646 | + | 0.735912i | ||||
\(419\) | 16.1248 | + | 9.30964i | 0.787747 | + | 0.454806i | 0.839169 | − | 0.543871i | \(-0.183042\pi\) |
−0.0514220 | + | 0.998677i | \(0.516375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9024 | − | 18.9024i | 0.921247 | − | 0.921247i | −0.0758709 | − | 0.997118i | \(-0.524174\pi\) |
0.997118 | + | 0.0758709i | \(0.0241737\pi\) | |||||||
\(422\) | 22.3639 | + | 5.99238i | 1.08866 | + | 0.291704i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.3475 | − | 18.3475i | −0.891032 | − | 0.891032i | ||||
\(425\) | 1.36727 | − | 0.789392i | 0.0663222 | − | 0.0382911i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.97392 | − | 11.7591i | 0.0955245 | − | 0.569063i | ||||
\(428\) | 53.6883i | 2.59512i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.4830i | 0.505536i | ||||||||
\(431\) | 7.64079 | + | 28.5158i | 0.368044 | + | 1.37356i | 0.863247 | + | 0.504782i | \(0.168427\pi\) |
−0.495203 | + | 0.868777i | \(0.664906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.9660 | − | 31.1180i | −0.863390 | − | 1.49543i | −0.868637 | − | 0.495449i | \(-0.835004\pi\) |
0.00524758 | − | 0.999986i | \(-0.498330\pi\) | |||||||
\(434\) | −14.5392 | − | 38.9468i | −0.697902 | − | 1.86951i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.7218 | + | 43.7464i | −0.561373 | + | 2.09507i | ||||
\(437\) | −0.814686 | + | 0.814686i | −0.0389717 | + | 0.0389717i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.87991 | − | 8.45226i | 0.232906 | − | 0.403404i | −0.725756 | − | 0.687952i | \(-0.758510\pi\) |
0.958662 | + | 0.284548i | \(0.0918434\pi\) | |||||||
\(440\) | −4.59195 | − | 17.1374i | −0.218912 | − | 0.816992i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.79007 | − | 2.55737i | −0.227840 | − | 0.121641i | ||||
\(443\) | −38.7798 | −1.84248 | −0.921241 | − | 0.388992i | \(-0.872824\pi\) | ||||
−0.921241 | + | 0.388992i | \(0.872824\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.8224 | + | 18.7449i | −0.513030 | + | 0.888595i | ||||
\(446\) | 10.2299 | + | 17.7187i | 0.484399 | + | 0.839004i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −24.6462 | − | 20.3377i | −1.16443 | − | 0.960868i | ||||
\(449\) | 2.42216 | − | 9.03963i | 0.114309 | − | 0.426606i | −0.884925 | − | 0.465733i | \(-0.845791\pi\) |
0.999234 | + | 0.0391263i | \(0.0124575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7830 | − | 9.11229i | 0.743190 | − | 0.429081i | ||||
\(452\) | −4.68548 | − | 2.70516i | −0.220386 | − | 0.127240i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 39.6534 | 1.86103 | ||||||||
\(455\) | 5.78624 | + | 14.0568i | 0.271263 | + | 0.658991i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.97477 | + | 18.5661i | 0.232710 | + | 0.868485i | 0.979168 | + | 0.203053i | \(0.0650863\pi\) |
−0.746458 | + | 0.665433i | \(0.768247\pi\) | |||||||
\(458\) | −4.97089 | − | 2.86995i | −0.232275 | − | 0.134104i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.577996 | − | 0.577996i | −0.0269492 | − | 0.0269492i | ||||
\(461\) | 3.50466 | − | 13.0796i | 0.163228 | − | 0.609175i | −0.835031 | − | 0.550202i | \(-0.814551\pi\) |
0.998260 | − | 0.0589733i | \(-0.0187827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6336 | − | 14.6336i | −0.680081 | − | 0.680081i | 0.279937 | − | 0.960018i | \(-0.409686\pi\) |
−0.960018 | + | 0.279937i | \(0.909686\pi\) | |||||||
\(464\) | 1.94152 | + | 3.36281i | 0.0901328 | + | 0.156115i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.1865 | − | 3.26536i | 0.564529 | − | 0.151265i | ||||
\(467\) | −30.9732 | −1.43327 | −0.716634 | − | 0.697449i | \(-0.754318\pi\) | ||||
−0.716634 | + | 0.697449i | \(0.754318\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.40826 | − | 1.55532i | −0.157379 | − | 0.0718179i | ||||
\(470\) | −3.05223 | − | 11.3911i | −0.140789 | − | 0.525431i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.34989 | + | 12.7304i | 0.338306 | + | 0.585963i | ||||
\(473\) | 6.22564 | − | 6.22564i | 0.286255 | − | 0.286255i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.7378 | + | 5.02078i | 0.859750 | + | 0.230369i | ||||
\(476\) | −5.58171 | + | 2.08370i | −0.255837 | + | 0.0955061i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.3753 | + | 19.8466i | 1.57229 | + | 0.907761i | ||||
\(479\) | −1.90105 | − | 7.09483i | −0.0868613 | − | 0.324171i | 0.908799 | − | 0.417235i | \(-0.137001\pi\) |
−0.995660 | + | 0.0930636i | \(0.970334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.41183 | + | 11.9063i | 0.337951 | + | 0.542882i | ||||
\(482\) | − | 31.5654i | − | 1.43777i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.98478 | − | 3.43773i | 0.0902171 | − | 0.156261i | ||||
\(485\) | −0.259753 | + | 0.149968i | −0.0117948 | + | 0.00680971i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.52611 | + | 2.55251i | 0.431669 | + | 0.115665i | 0.468110 | − | 0.883670i | \(-0.344935\pi\) |
−0.0364405 | + | 0.999336i | \(0.511602\pi\) | |||||||
\(488\) | −15.4281 | − | 4.13395i | −0.698398 | − | 0.187135i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 24.7480 | + | 8.54946i | 1.11800 | + | 0.386225i | ||||
\(491\) | −33.1372 | − | 19.1318i | −1.49546 | − | 0.863404i | −0.495473 | − | 0.868623i | \(-0.665005\pi\) |
−0.999986 | + | 0.00521946i | \(0.998339\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.91723 | −0.0863477 | ||||||||
\(494\) | −19.3985 | − | 63.8371i | −0.872781 | − | 2.87217i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.40197 | + | 2.25130i | −0.377260 | + | 0.101086i | ||||
\(497\) | −30.8511 | + | 21.9823i | −1.38386 | + | 0.986042i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.00102712 | − | 0.00102712i | 4.59801e−5 | − | 4.59801e-5i | −0.707084 | − | 0.707130i | \(-0.749990\pi\) |
0.707130 | + | 0.707084i | \(0.249990\pi\) | |||||||
\(500\) | −10.8000 | + | 40.3060i | −0.482989 | + | 1.80254i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.2537 | + | 21.2537i | −0.948598 | + | 0.948598i | ||||
\(503\) | −21.6205 | + | 12.4826i | −0.964012 | + | 0.556573i | −0.897406 | − | 0.441206i | \(-0.854551\pi\) |
−0.0666068 | + | 0.997779i | \(0.521217\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.83752 | + | 0.492362i | −0.0817686 | + | 0.0219098i | ||||
\(506\) | 1.07771i | 0.0479102i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.4226 | −0.506798 | ||||||||
\(509\) | 2.53176 | − | 0.678383i | 0.112218 | − | 0.0300688i | −0.202273 | − | 0.979329i | \(-0.564833\pi\) |
0.314491 | + | 0.949260i | \(0.398166\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.78042 | + | 18.5889i | 0.0787610 | + | 0.822325i | ||||
\(512\) | −10.2233 | + | 10.2233i | −0.451811 | + | 0.451811i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.5365 | + | 6.30659i | 1.03815 | + | 0.278172i | ||||
\(515\) | −5.40385 | − | 5.40385i | −0.238122 | − | 0.238122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.95226 | + | 8.57757i | −0.217800 | + | 0.377241i | ||||
\(518\) | 23.8238 | + | 3.99914i | 1.04676 | + | 0.175712i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.4830 | − | 5.92041i | 0.854387 | − | 0.259627i | ||||
\(521\) | 29.8603i | 1.30820i | 0.756406 | + | 0.654102i | \(0.226953\pi\) | ||||
−0.756406 | + | 0.654102i | \(0.773047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9268 | − | 8.04062i | −0.608975 | − | 0.351592i | 0.163589 | − | 0.986529i | \(-0.447693\pi\) |
−0.772564 | + | 0.634937i | \(0.781026\pi\) | |||||||
\(524\) | 28.8999 | + | 50.0561i | 1.26250 | + | 2.18671i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.92985 | − | 2.66069i | −0.432962 | − | 0.116012i | ||||
\(527\) | 1.11157 | − | 4.14843i | 0.0484207 | − | 0.180708i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4893 | − | 19.9001i | −0.499536 | − | 0.865221i | ||||
\(530\) | −13.6923 | + | 23.7157i | −0.594755 | + | 1.03015i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −66.5997 | − | 30.3920i | −2.88746 | − | 1.31766i | ||||
\(533\) | 11.0540 | + | 17.7571i | 0.478802 | + | 0.769146i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.5443 | − | 6.30868i | 1.01791 | − | 0.272748i | ||||
\(536\) | −2.50923 | + | 4.34612i | −0.108382 | + | 0.187724i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.3942 | − | 19.3942i | −0.836143 | − | 0.836143i | ||||
\(539\) | −9.62000 | − | 19.7747i | −0.414363 | − | 0.851756i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4465 | + | 12.4465i | 0.535115 | + | 0.535115i | 0.922090 | − | 0.386975i | \(-0.126480\pi\) |
−0.386975 | + | 0.922090i | \(0.626480\pi\) | |||||||
\(542\) | 62.3933 | − | 36.0228i | 2.68002 | − | 1.54731i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.670546 | − | 2.50251i | −0.0287494 | − | 0.107294i | ||||
\(545\) | 20.5618 | 0.880771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.8734 | −0.678698 | −0.339349 | − | 0.940661i | \(-0.610207\pi\) | ||||
−0.339349 | + | 0.940661i | \(0.610207\pi\) | |||||||
\(548\) | 0.343322 | + | 1.28130i | 0.0146660 | + | 0.0547343i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.7146 | − | 9.07284i | 0.670073 | − | 0.386867i | ||||
\(551\) | −16.6576 | − | 16.6576i | −0.709636 | − | 0.709636i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.06579 | + | 1.29158i | −0.0453221 | + | 0.0549234i | ||||
\(554\) | −31.6444 | − | 31.6444i | −1.34444 | − | 1.34444i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2678 | + | 29.9087i | −0.732318 | + | 1.26841i | ||||
\(557\) | 2.44666 | − | 0.655582i | 0.103668 | − | 0.0277779i | −0.206612 | − | 0.978423i | \(-0.566244\pi\) |
0.310280 | + | 0.950645i | \(0.399577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.37857 | + | 6.90409i | 0.312080 | + | 0.292012i | ||||
\(560\) | 2.27440 | − | 4.98403i | 0.0961109 | − | 0.210614i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.6970 | − | 34.1162i | 0.830867 | − | 1.43910i | ||||
\(563\) | 10.1159 | + | 17.5213i | 0.426336 | + | 0.738436i | 0.996544 | − | 0.0830642i | \(-0.0264707\pi\) |
−0.570208 | + | 0.821500i | \(0.693137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.635745 | + | 2.37263i | −0.0267460 | + | 0.0998174i | ||||
\(566\) | −19.1301 | − | 5.12589i | −0.804098 | − | 0.215457i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.3722 | + | 43.9460i | 1.06459 | + | 1.84393i | ||||
\(569\) | 12.8801 | + | 7.43632i | 0.539961 | + | 0.311747i | 0.745063 | − | 0.666994i | \(-0.232419\pi\) |
−0.205102 | + | 0.978741i | \(0.565753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.9235i | 1.54520i | 0.634893 | + | 0.772600i | \(0.281044\pi\) | ||||
−0.634893 | + | 0.772600i | \(0.718956\pi\) | |||||||
\(572\) | −35.0705 | − | 18.7237i | −1.46637 | − | 0.782879i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 35.5309 | + | 5.96431i | 1.48303 | + | 0.248946i | ||||
\(575\) | 0.179817 | − | 0.311452i | 0.00749888 | − | 0.0129884i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.5105 | + | 14.5105i | 0.604080 | + | 0.604080i | 0.941393 | − | 0.337312i | \(-0.109518\pi\) |
−0.337312 | + | 0.941393i | \(0.609518\pi\) | |||||||
\(578\) | 37.6113 | + | 10.0779i | 1.56442 | + | 0.419186i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.8181 | − | 11.8181i | 0.490718 | − | 0.490718i | ||||
\(581\) | 4.01563 | − | 0.384610i | 0.166596 | − | 0.0159563i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.2158 | − | 5.95271i | 0.920086 | − | 0.246536i | ||||
\(584\) | 25.0148 | 1.03512 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 19.4573i | − | 0.803776i | ||||||
\(587\) | 19.8321 | − | 5.31399i | 0.818557 | − | 0.219332i | 0.174842 | − | 0.984597i | \(-0.444059\pi\) |
0.643715 | + | 0.765265i | \(0.277392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.7007 | − | 26.3853i | 1.88307 | − | 1.08719i | ||||
\(590\) | 10.9701 | − | 10.9701i | 0.451632 | − | 0.451632i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.30821 | − | 4.88231i | 0.0537671 | − | 0.200662i | ||||
\(593\) | −29.4133 | + | 29.4133i | −1.20786 | + | 1.20786i | −0.236140 | + | 0.971719i | \(0.575882\pi\) |
−0.971719 | + | 0.236140i | \(0.924118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.56966 | + | 2.20294i | 0.0643499 | + | 0.0903118i | ||||
\(596\) | −18.8282 | + | 5.04500i | −0.771233 | + | 0.206651i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.23623 | + | 0.0410690i | −0.0505530 | + | 0.00167944i | ||||
\(599\) | 4.33998 | 0.177327 | 0.0886634 | − | 0.996062i | \(-0.471740\pi\) | ||||
0.0886634 | + | 0.996062i | \(0.471740\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.72067 | + | 3.30283i | 0.233351 | + | 0.134725i | 0.612117 | − | 0.790767i | \(-0.290318\pi\) |
−0.378766 | + | 0.925492i | \(0.623652\pi\) | |||||||
\(602\) | 17.3260 | − | 1.65946i | 0.706156 | − | 0.0676344i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.0868 | − | 4.31044i | −0.654561 | − | 0.175389i | ||||
\(605\) | −1.74080 | − | 0.466446i | −0.0707735 | − | 0.0189637i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.8777 | + | 23.0234i | −1.61859 | + | 0.934492i | −0.631301 | + | 0.775538i | \(0.717479\pi\) |
−0.987286 | + | 0.158954i | \(0.949188\pi\) | |||||||
\(608\) | 15.9168 | − | 27.5686i | 0.645510 | − | 1.11806i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.8571i | 0.682526i | ||||||||
\(611\) | −10.0279 | − | 5.35379i | −0.405686 | − | 0.216591i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.42773 | + | 27.7207i | 0.300003 | + | 1.11963i | 0.937162 | + | 0.348895i | \(0.113443\pi\) |
−0.637159 | + | 0.770733i | \(0.719890\pi\) | |||||||
\(614\) | 49.8609 | + | 28.7872i | 2.01222 | + | 1.16176i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −27.5972 | + | 10.3023i | −1.11192 | + | 0.415090i | ||||
\(617\) | −0.0947548 | − | 0.0253895i | −0.00381469 | − | 0.00102214i | 0.256911 | − | 0.966435i | \(-0.417295\pi\) |
−0.260726 | + | 0.965413i | \(0.583962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.9073 | + | 29.9073i | −1.20208 | + | 1.20208i | −0.228543 | + | 0.973534i | \(0.573396\pi\) |
−0.973534 | + | 0.228543i | \(0.926604\pi\) | |||||||
\(620\) | 18.7196 | + | 32.4233i | 0.751798 | + | 1.30215i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.4058 | + | 53.7630i | 0.577619 | + | 2.15570i | ||||
\(623\) | 32.6942 | + | 14.9196i | 1.30987 | + | 0.597741i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.64109 | 0.265644 | ||||||||
\(626\) | −31.9046 | + | 8.54882i | −1.27517 | + | 0.341680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.1475 | + | 38.3606i | 0.883781 | + | 1.53075i | ||||
\(629\) | 1.76469 | + | 1.76469i | 0.0703629 | + | 0.0703629i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.02584 | − | 7.56053i | 0.0806473 | − | 0.300980i | −0.913807 | − | 0.406148i | \(-0.866872\pi\) |
0.994454 | + | 0.105169i | \(0.0335383\pi\) | |||||||
\(632\) | 1.58614 | + | 1.58614i | 0.0630931 | + | 0.0630931i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −34.0295 | − | 19.6469i | −1.35148 | − | 0.780279i | ||||
\(635\) | 1.34223 | + | 5.00926i | 0.0532646 | + | 0.198786i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3166 | − | 11.7885i | 0.884216 | − | 0.467077i | ||||
\(638\) | −22.0356 | −0.872397 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 27.9777 | + | 16.1530i | 1.10592 | + | 0.638502i | ||||
\(641\) | 28.9275 | − | 16.7013i | 1.14257 | − | 0.659661i | 0.195502 | − | 0.980703i | \(-0.437366\pi\) |
0.947065 | + | 0.321042i | \(0.104033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.94009 | + | 18.4367i | −0.194818 | + | 0.727071i | 0.797496 | + | 0.603324i | \(0.206158\pi\) |
−0.992314 | + | 0.123746i | \(0.960509\pi\) | |||||||
\(644\) | −0.863797 | + | 1.04679i | −0.0340384 | + | 0.0412493i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.93619 | − | 10.2818i | −0.233556 | − | 0.404532i | ||||
\(647\) | −16.4522 | + | 28.4961i | −0.646804 | + | 1.12030i | 0.337078 | + | 0.941477i | \(0.390561\pi\) |
−0.983882 | + | 0.178821i | \(0.942772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.0298 | −0.511465 | ||||||||
\(650\) | 11.0061 | + | 17.6802i | 0.431696 | + | 0.693475i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.8578 | − | 44.2541i | −0.464389 | − | 1.73312i | ||||
\(653\) | 13.9982 | − | 24.2457i | 0.547793 | − | 0.948806i | −0.450632 | − | 0.892710i | \(-0.648801\pi\) |
0.998425 | − | 0.0560961i | \(-0.0178653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.5556 | − | 18.5556i | 0.725027 | − | 0.725027i | ||||
\(656\) | 1.95106 | − | 7.28147i | 0.0761763 | − | 0.284294i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.3437 | + | 6.84783i | −0.715110 | + | 0.266956i | ||||
\(659\) | 5.35203 | + | 9.27000i | 0.208486 | + | 0.361108i | 0.951238 | − | 0.308459i | \(-0.0998132\pi\) |
−0.742752 | + | 0.669567i | \(0.766480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.21818 | + | 23.2066i | 0.241859 | + | 0.902631i | 0.974936 | + | 0.222485i | \(0.0714169\pi\) |
−0.733077 | + | 0.680146i | \(0.761916\pi\) | |||||||
\(662\) | 22.7176i | 0.882945i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 5.40377i | − | 0.209707i | ||||||
\(665\) | −5.50216 | + | 32.7777i | −0.213365 | + | 1.27107i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.378218 | + | 0.218364i | −0.0146447 | + | 0.00845510i | ||||
\(668\) | 45.9988 | + | 45.9988i | 1.77975 | + | 1.77975i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.11599 | + | 1.37083i | 0.197648 | + | 0.0529596i | ||||
\(671\) | 10.0111 | − | 10.0111i | 0.386474 | − | 0.386474i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.79792 | + | 2.77008i | 0.184946 | + | 0.106779i | 0.589615 | − | 0.807685i | \(-0.299280\pi\) |
−0.404668 | + | 0.914464i | \(0.632613\pi\) | |||||||
\(674\) | −45.5365 | + | 12.2015i | −1.75400 | + | 0.469983i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.1412 | − | 40.9423i | 0.774663 | − | 1.57470i | ||||
\(677\) | 44.0680i | 1.69367i | 0.531855 | + | 0.846835i | \(0.321495\pi\) | ||||
−0.531855 | + | 0.846835i | \(0.678505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.288982 | + | 0.405572i | 0.0110901 | + | 0.0155644i | ||||
\(680\) | 3.13799 | − | 1.81172i | 0.120336 | − | 0.0694763i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.7758 | − | 47.6798i | 0.489209 | − | 1.82575i | ||||
\(683\) | −1.33328 | + | 4.97587i | −0.0510166 | + | 0.190396i | −0.986731 | − | 0.162361i | \(-0.948089\pi\) |
0.935715 | + | 0.352757i | \(0.114756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.521554 | − | 0.301120i | 0.0199276 | − | 0.0115052i | ||||
\(686\) | 10.2127 | − | 42.2562i | 0.389922 | − | 1.61335i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 3.64181i | − | 0.138843i | ||||||
\(689\) | 7.67485 | + | 25.2566i | 0.292388 | + | 0.962198i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.95186 | − | 0.790947i | 0.112294 | − | 0.0300891i | −0.202234 | − | 0.979337i | \(-0.564820\pi\) |
0.314528 | + | 0.949248i | \(0.398154\pi\) | |||||||
\(692\) | 17.0028 | + | 9.81655i | 0.646348 | + | 0.373169i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.8501 | − | 36.8501i | 1.39881 | − | 1.39881i | ||||
\(695\) | 15.1452 | + | 4.05813i | 0.574489 | + | 0.153934i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.63186 | + | 2.63186i | 0.0996888 | + | 0.0996888i | ||||
\(698\) | −10.8854 | + | 6.28470i | −0.412019 | + | 0.237879i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 22.5357 | + | 3.78290i | 0.851769 | + | 0.142980i | ||||
\(701\) | 11.0158i | 0.416061i | 0.978122 | + | 0.208031i | \(0.0667054\pi\) | ||||
−0.978122 | + | 0.208031i | \(0.933295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.6645i | 1.15653i | ||||||||
\(704\) | −9.81997 | − | 36.6486i | −0.370104 | − | 1.38125i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.6322 | − | 53.0566i | −1.15286 | − | 1.99681i | ||||
\(707\) | 1.10464 | + | 2.95906i | 0.0415443 | + | 0.111287i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.29113 | − | 27.2109i | 0.273824 | − | 1.02192i | −0.682801 | − | 0.730604i | \(-0.739239\pi\) |
0.956625 | − | 0.291321i | \(-0.0940948\pi\) | |||||||
\(710\) | 37.8694 | − | 37.8694i | 1.42121 | − | 1.42121i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.0702 | − | 41.6907i | 0.902067 | − | 1.56243i | ||||
\(713\) | −0.253206 | − | 0.944977i | −0.00948263 | − | 0.0353897i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09008 | + | 17.5799i | −0.152960 | + | 0.657450i | ||||
\(716\) | 33.3115 | 1.24491 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −26.5761 | + | 46.0311i | −0.991811 | + | 1.71787i | ||||
\(719\) | −21.0559 | − | 36.4699i | −0.785252 | − | 1.36010i | −0.928848 | − | 0.370460i | \(-0.879200\pi\) |
0.143596 | − | 0.989636i | \(-0.454133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.07589 | + | 9.78674i | −0.300762 | + | 0.364477i | ||||
\(722\) | 26.2130 | − | 97.8284i | 0.975548 | − | 3.64079i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.0195 | − | 12.1356i | 0.781185 | − | 0.451018i | ||||
\(725\) | 6.36814 | + | 3.67665i | 0.236507 | + | 0.136547i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0901 | 0.374223 | 0.187111 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187111 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(728\) | −12.8692 | − | 31.2637i | −0.476965 | − | 1.15871i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.83295 | − | 25.5009i | −0.252899 | − | 0.943832i | ||||
\(731\) | 1.55722 | + | 0.899062i | 0.0575959 | + | 0.0332530i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.7908 | − | 18.7908i | −0.694053 | − | 0.694053i | 0.269068 | − | 0.963121i | \(-0.413284\pi\) |
−0.963121 | + | 0.269068i | \(0.913284\pi\) | |||||||
\(734\) | 8.62455 | − | 32.1873i | 0.318338 | − | 1.18805i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.417306 | − | 0.417306i | −0.0153821 | − | 0.0153821i | ||||
\(737\) | −2.22417 | − | 3.85238i | −0.0819285 | − | 0.141904i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.3011 | + | 6.51146i | −0.893930 | + | 0.239528i | −0.676407 | − | 0.736528i | \(-0.736464\pi\) |
−0.217522 | + | 0.976055i | \(0.569797\pi\) | |||||||
\(740\) | −21.7556 | −0.799751 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 41.3641 | + | 18.8760i | 1.51852 | + | 0.692960i | ||||
\(743\) | 2.81817 | + | 10.5175i | 0.103388 | + | 0.385851i | 0.998157 | − | 0.0606785i | \(-0.0193264\pi\) |
−0.894769 | + | 0.446530i | \(0.852660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.42484 | + | 7.66405i | 0.162114 | + | 0.280789i | ||||
\(746\) | 5.81996 | − | 5.81996i | 0.213084 | − | 0.213084i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.83328 | − | 1.83097i | −0.249850 | − | 0.0669470i | ||||
\(749\) | −14.1539 | − | 37.9147i | −0.517171 | − | 1.38537i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.9154 | − | 16.1170i | −1.01865 | − | 0.588117i | −0.104936 | − | 0.994479i | \(-0.533464\pi\) |
−0.913712 | + | 0.406362i | \(0.866797\pi\) | |||||||
\(752\) | 1.06035 | + | 3.95727i | 0.0386669 | + | 0.144307i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.839723 | − | 25.2766i | −0.0305809 | − | 0.920521i | ||||
\(755\) | 7.56115i | 0.275179i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.9609 | + | 29.3771i | −0.616453 | + | 1.06773i | 0.373675 | + | 0.927560i | \(0.378098\pi\) |
−0.990128 | + | 0.140168i | \(0.955236\pi\) | |||||||
\(758\) | −54.5711 | + | 31.5066i | −1.98211 | + | 1.14437i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 43.0048 | + | 11.5231i | 1.55995 | + | 0.417987i | ||||
\(761\) | −9.36045 | − | 2.50812i | −0.339316 | − | 0.0909194i | 0.0851375 | − | 0.996369i | \(-0.472867\pi\) |
−0.424453 | + | 0.905450i | \(0.639534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.25493 | − | 33.9839i | −0.117836 | − | 1.23030i | ||||
\(764\) | 7.61437 | + | 4.39616i | 0.275478 | + | 0.159047i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 80.1674 | 2.89656 | ||||||||
\(767\) | −0.496535 | − | 14.9463i | −0.0179288 | − | 0.539679i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6001 | + | 3.91210i | −0.526495 | + | 0.141074i | −0.512269 | − | 0.858825i | \(-0.671195\pi\) |
−0.0142256 | + | 0.999899i | \(0.504528\pi\) | |||||||
\(770\) | 18.0408 | + | 25.3194i | 0.650146 | + | 0.912448i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −55.9826 | + | 55.9826i | −2.01486 | + | 2.01486i | ||||
\(773\) | −10.1225 | + | 37.7776i | −0.364081 | + | 1.35877i | 0.504582 | + | 0.863364i | \(0.331647\pi\) |
−0.868663 | + | 0.495404i | \(0.835020\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.6475 | + | 11.6475i | −0.418390 | + | 0.418390i | ||||
\(776\) | 0.577718 | − | 0.333546i | 0.0207389 | − | 0.0119736i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −62.2709 | + | 16.6854i | −2.23252 | + | 0.598202i | ||||
\(779\) | 45.7331i | 1.63856i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44.9797 | −1.60950 | ||||||||
\(782\) | −0.212602 | + | 0.0569665i | −0.00760263 | + | 0.00203712i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.59749 | − | 2.97009i | −0.307053 | − | 0.106075i | ||||
\(785\) | 14.2201 | − | 14.2201i | 0.507537 | − | 0.507537i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.68505 | + | 0.451508i | 0.0600656 | + | 0.0160945i | 0.288727 | − | 0.957412i | \(-0.406768\pi\) |
−0.228661 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(788\) | −44.4514 | − | 44.4514i | −1.58352 | − | 1.58352i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.18370 | − | 2.05022i | 0.0421141 | − | 0.0729437i | ||||
\(791\) | 4.02205 | + | 0.675153i | 0.143008 | + | 0.0240057i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.8651 | + | 11.1021i | 0.421341 | + | 0.394246i | ||||
\(794\) | − | 87.0058i | − | 3.08772i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −49.8875 | − | 28.8026i | −1.76822 | − | 1.02088i | ||||
\(797\) | −12.2921 | − | 21.2905i | −0.435407 | − | 0.754148i | 0.561921 | − | 0.827191i | \(-0.310062\pi\) |
−0.997329 | + | 0.0730430i | \(0.976729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.95388 | − | 0.523540i | −0.0691233 | − | 0.0185215i | ||||
\(800\) | −2.57179 | + | 9.59806i | −0.0909266 | + | 0.339343i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.3936 | + | 35.3228i | 0.720125 | + | 1.24729i | ||||
\(803\) | −11.0865 | + | 19.2024i | −0.391235 | + | 0.677638i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.560558 | + | 0.255804i | 0.0197571 | + | 0.00901590i | ||||
\(806\) | 55.1795 | + | 12.8379i | 1.94362 | + | 0.452195i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.08684 | − | 1.09507i | 0.143775 | − | 0.0385243i | ||||
\(809\) | −1.41467 | + | 2.45029i | −0.0497373 | + | 0.0861475i | −0.889822 | − | 0.456307i | \(-0.849172\pi\) |
0.840085 | + | 0.542455i | \(0.182505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.39483 | + | 6.39483i | 0.224553 | + | 0.224553i | 0.810412 | − | 0.585860i | \(-0.199243\pi\) |
−0.585860 | + | 0.810412i | \(0.699243\pi\) | |||||||
\(812\) | −21.4033 | − | 17.6617i | −0.751110 | − | 0.619806i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.2824 | + | 20.2824i | 0.710897 | + | 0.710897i | ||||
\(815\) | −18.0137 | + | 10.4002i | −0.630993 | + | 0.364304i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.71832 | + | 21.3410i | 0.200059 | + | 0.746629i | ||||
\(818\) | −26.4854 | −0.926041 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −32.4463 | −1.13307 | ||||||||
\(821\) | −9.65789 | − | 36.0437i | −0.337063 | − | 1.25793i | −0.901616 | − | 0.432538i | \(-0.857618\pi\) |
0.564553 | − | 0.825397i | \(-0.309049\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.1966 | − | 19.7434i | 1.19202 | − | 0.688212i | 0.233254 | − | 0.972416i | \(-0.425063\pi\) |
0.958764 | + | 0.284204i | \(0.0917293\pi\) | |||||||
\(824\) | 12.0187 | + | 12.0187i | 0.418692 | + | 0.418692i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.8676 | − | 16.3945i | −0.691283 | − | 0.570437i | ||||
\(827\) | 24.4804 | + | 24.4804i | 0.851267 | + | 0.851267i | 0.990289 | − | 0.139022i | \(-0.0443958\pi\) |
−0.139022 | + | 0.990289i | \(0.544396\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.73903 | − | 11.6723i | 0.234056 | − | 0.405397i | −0.724942 | − | 0.688810i | \(-0.758133\pi\) |
0.958998 | + | 0.283413i | \(0.0914667\pi\) | |||||||
\(830\) | −5.50878 | + | 1.47607i | −0.191212 | + | 0.0512352i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.6648 | − | 12.6609i | 1.44447 | − | 0.438938i | ||||
\(833\) | 3.39248 | − | 2.94301i | 0.117542 | − | 0.101969i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.7671 | − | 25.5773i | 0.511036 | − | 0.885141i | ||||
\(836\) | −43.4618 | − | 75.2781i | −1.50316 | − | 2.60355i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.3118 | + | 42.2160i | −0.390758 | + | 1.45833i | ||||
\(839\) | 48.1190 | + | 12.8935i | 1.66125 | + | 0.445132i | 0.962732 | − | 0.270457i | \(-0.0871749\pi\) |
0.698522 | + | 0.715589i | \(0.253842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0352 | + | 17.3815i | 0.346041 | + | 0.599360i | ||||
\(842\) | 54.3417 | + | 31.3742i | 1.87274 | + | 1.08123i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 34.6197i | 1.19166i | ||||||||
\(845\) | −20.3214 | − | 4.02173i | −0.699079 | − | 0.138352i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.495359 | + | 2.95098i | −0.0170208 | + | 0.101397i | ||||
\(848\) | 4.75671 | − | 8.23886i | 0.163346 | − | 0.282924i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.62046 | + | 2.62046i | 0.0898812 | + | 0.0898812i | ||||
\(851\) | 0.549117 | + | 0.147136i | 0.0188235 | + | 0.00504374i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4604 | − | 15.4604i | 0.529355 | − | 0.529355i | −0.391025 | − | 0.920380i | \(-0.627879\pi\) |
0.920380 | + | 0.391025i | \(0.127879\pi\) | |||||||
\(854\) | 27.8610 | − | 2.66848i | 0.953383 | − | 0.0913134i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −52.3651 | + | 14.0312i | −1.78980 | + | 0.479576i | ||||
\(857\) | 25.0101 | 0.854328 | 0.427164 | − | 0.904174i | \(-0.359513\pi\) | ||||
0.427164 | + | 0.904174i | \(0.359513\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 35.7674i | − | 1.22037i | −0.792260 | − | 0.610183i | \(-0.791096\pi\) | ||
0.792260 | − | 0.610183i | \(-0.208904\pi\) | |||||||
\(860\) | −15.1409 | + | 4.05698i | −0.516299 | + | 0.138342i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −60.0127 | + | 34.6484i | −2.04404 | + | 1.18013i | ||||
\(863\) | −29.2685 | + | 29.2685i | −0.996311 | + | 0.996311i | −0.999993 | − | 0.00368256i | \(-0.998828\pi\) |
0.00368256 | + | 0.999993i | \(0.498828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.30700 | − | 8.60985i | 0.0784405 | − | 0.292744i | ||||
\(866\) | 59.6398 | − | 59.6398i | 2.02664 | − | 2.02664i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 50.6250 | − | 36.0718i | 1.71832 | − | 1.22436i | ||||
\(869\) | −1.92056 | + | 0.514612i | −0.0651504 | + | 0.0174570i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.33425 | − | 2.69812i | 0.146860 | − | 0.0914222i | ||||
\(872\) | −45.7317 | −1.54867 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.34210 | − | 1.35221i | −0.0792229 | − | 0.0457393i | ||||
\(875\) | −2.99895 | − | 31.3113i | −0.101383 | − | 1.05852i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.2371 | − | 6.49432i | −0.818430 | − | 0.219298i | −0.174770 | − | 0.984609i | \(-0.555918\pi\) |
−0.643660 | + | 0.765312i | \(0.722585\pi\) | |||||||
\(878\) | 22.1287 | + | 5.92937i | 0.746808 | + | 0.200107i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.63348 | − | 3.25249i | 0.189905 | − | 0.109641i | ||||
\(881\) | −18.7477 | + | 32.4719i | −0.631624 | + | 1.09401i | 0.355595 | + | 0.934640i | \(0.384278\pi\) |
−0.987220 | + | 0.159365i | \(0.949055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.9652i | 0.671881i | 0.941883 | + | 0.335941i | \(0.109054\pi\) | ||||
−0.941883 | + | 0.335941i | \(0.890946\pi\) | |||||||
\(884\) | 1.83988 | − | 7.90812i | 0.0618818 | − | 0.265979i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.5598 | − | 87.9265i | −0.791508 | − | 2.95395i | ||||
\(887\) | −44.5877 | − | 25.7427i | −1.49711 | − | 0.864355i | −0.497113 | − | 0.867686i | \(-0.665606\pi\) |
−0.999994 | + | 0.00333069i | \(0.998940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.06667 | − | 3.01135i | 0.270547 | − | 0.100998i | ||||
\(890\) | −49.0758 | − | 13.1498i | −1.64502 | − | 0.440783i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.6325 | + | 21.6325i | −0.724309 | + | 0.724309i | ||||
\(893\) | −12.4273 | − | 21.5247i | −0.415863 | − | 0.720297i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.91429 | − | 14.6083i | −0.130840 | − | 0.488303i | ||||
\(896\) | 22.2683 | − | 48.7978i | 0.743930 | − | 1.63022i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.9673 | 0.733059 | ||||||||
\(899\) | 19.3216 | − | 5.17720i | 0.644411 | − | 0.172669i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.34860 | + | 4.06789i | 0.0782432 | + | 0.135521i | ||||
\(902\) | 30.2492 | + | 30.2492i | 1.00719 | + | 1.00719i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.41396 | − | 5.27699i | 0.0470277 | − | 0.175510i | ||||
\(905\) | −7.79185 | − | 7.79185i | −0.259010 | − | 0.259010i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0770 | + | 14.4782i | 0.832669 | + | 0.480742i | 0.854766 | − | 0.519014i | \(-0.173701\pi\) |
−0.0220968 | + | 0.999756i | \(0.507034\pi\) | |||||||
\(908\) | 15.3461 | + | 57.2723i | 0.509277 | + | 1.90065i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28.3560 | + | 21.6592i | −0.939991 | + | 0.717995i | ||||
\(911\) | −3.65299 | −0.121029 | −0.0605144 | − | 0.998167i | \(-0.519274\pi\) | ||||
−0.0605144 | + | 0.998167i | \(0.519274\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.14815 | + | 2.39494i | 0.137284 | + | 0.0792609i | ||||
\(914\) | −39.0731 | + | 22.5589i | −1.29242 | + | 0.746181i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.22137 | − | 8.29025i | 0.0733960 | − | 0.273918i | ||||
\(917\) | −33.6054 | − | 27.7308i | −1.10975 | − | 0.915750i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.3670 | − | 37.0087i | −0.704831 | − | 1.22080i | −0.966753 | − | 0.255714i | \(-0.917690\pi\) |
0.261922 | − | 0.965089i | \(-0.415644\pi\) | |||||||
\(920\) | 0.412694 | − | 0.714807i | 0.0136061 | − | 0.0235665i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.7848 | 1.04678 | ||||||||
\(923\) | −1.71407 | − | 51.5954i | −0.0564192 | − | 1.69828i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.47735 | − | 9.24560i | −0.0814548 | − | 0.303994i | ||||
\(926\) | 24.2888 | − | 42.0695i | 0.798181 | − | 1.38249i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.53250 | − | 8.53250i | 0.280093 | − | 0.280093i | ||||
\(929\) | −4.38107 | + | 16.3504i | −0.143738 | + | 0.536438i | 0.856070 | + | 0.516860i | \(0.172899\pi\) |
−0.999808 | + | 0.0195786i | \(0.993768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 55.0450 | + | 3.90510i | 1.80403 | + | 0.127985i | ||||
\(932\) | 9.43247 | + | 16.3375i | 0.308971 | + | 0.535153i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.8171 | − | 70.2264i | −0.615714 | − | 2.29788i | ||||
\(935\) | 3.21180i | 0.105037i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.5686i | 1.52133i | 0.649145 | + | 0.760665i | \(0.275127\pi\) | ||||
−0.649145 | + | 0.760665i | \(0.724873\pi\) | |||||||
\(938\) | 1.45580 | − | 8.67255i | 0.0475335 | − | 0.283169i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.2712 | − | 8.81680i | 0.498090 | − | 0.287572i | ||||
\(941\) | 8.41532 | + | 8.41532i | 0.274331 | + | 0.274331i | 0.830841 | − | 0.556510i | \(-0.187860\pi\) |
−0.556510 | + | 0.830841i | \(0.687860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.818954 | + | 0.219438i | 0.0266688 | + | 0.00714588i | ||||
\(944\) | −3.81102 | + | 3.81102i | −0.124038 | + | 0.124038i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.8978 | + | 10.3333i | 0.581909 | + | 0.335965i | ||||
\(947\) | 41.7309 | − | 11.1818i | 1.35607 | − | 0.363358i | 0.493699 | − | 0.869633i | \(-0.335644\pi\) |
0.862373 | + | 0.506274i | \(0.168978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4492 | − | 11.9854i | −0.728733 | − | 0.389063i | ||||
\(950\) | 45.5350i | 1.47735i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.49110 | − | 4.89958i | −0.113147 | − | 0.158796i | ||||
\(953\) | 50.8066 | − | 29.3332i | 1.64579 | − | 0.950195i | 0.667066 | − | 0.744999i | \(-0.267550\pi\) |
0.978721 | − | 0.205196i | \(-0.0657832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.03315 | − | 3.85576i | 0.0334319 | − | 0.124770i | ||||
\(956\) | −15.3614 | + | 57.3297i | −0.496825 | + | 1.85417i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.9314 | − | 8.62062i | 0.482410 | − | 0.278520i | ||||
\(959\) | −0.580243 | − | 0.814342i | −0.0187370 | − | 0.0262965i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8090i | 0.445450i | ||||||||
\(962\) | −22.4927 | + | 24.0385i | −0.725193 | + | 0.775032i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 45.5907 | − | 12.2160i | 1.46838 | − | 0.393450i | ||||
\(965\) | 31.1288 | + | 17.9722i | 1.00207 | + | 0.578546i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.53769 | + | 7.53769i | −0.242396 | + | 0.242396i | −0.817841 | − | 0.575445i | \(-0.804829\pi\) |
0.575445 | + | 0.817841i | \(0.304829\pi\) | |||||||
\(968\) | 3.87172 | + | 1.03743i | 0.124442 | + | 0.0333441i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.497835 | − | 0.497835i | −0.0159845 | − | 0.0159845i | ||||
\(971\) | 27.3314 | − | 15.7798i | 0.877107 | − | 0.506398i | 0.00740334 | − | 0.999973i | \(-0.497643\pi\) |
0.869703 | + | 0.493575i | \(0.164310\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.30969 | − | 25.6738i | 0.138162 | − | 0.823066i | ||||
\(974\) | 23.1495i | 0.741759i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 5.85618i | − | 0.187452i | ||||||
\(977\) | 0.295580 | + | 1.10312i | 0.00945644 | + | 0.0352919i | 0.970493 | − | 0.241130i | \(-0.0775180\pi\) |
−0.961036 | + | 0.276422i | \(0.910851\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.3357 | + | 36.9545i | 0.681891 | + | 1.18107i | ||||
\(980\) | −2.77056 | + | 39.0528i | −0.0885022 | + | 1.24750i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.2462 | − | 86.7559i | 0.741815 | − | 2.76849i | ||||
\(983\) | 20.8611 | − | 20.8611i | 0.665366 | − | 0.665366i | −0.291274 | − | 0.956640i | \(-0.594079\pi\) |
0.956640 | + | 0.291274i | \(0.0940791\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.2703 | + | 24.7169i | −0.454690 | + | 0.787546i | ||||
\(986\) | −1.16477 | − | 4.34699i | −0.0370939 | − | 0.138436i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 84.6940 | − | 52.7230i | 2.69448 | − | 1.67734i | ||||
\(989\) | 0.409597 | 0.0130244 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.8046 | − | 39.4987i | 0.724412 | − | 1.25472i | −0.234804 | − | 0.972043i | \(-0.575445\pi\) |
0.959216 | − | 0.282675i | \(-0.0912219\pi\) | |||||||
\(992\) | 13.5153 | + | 23.4093i | 0.429113 | + | 0.743245i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −68.5841 | − | 56.5947i | −2.17536 | − | 1.79507i | ||||
\(995\) | −6.76894 | + | 25.2620i | −0.214590 | + | 0.800860i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.5784 | + | 13.0357i | −0.715065 | + | 0.412843i | −0.812934 | − | 0.582356i | \(-0.802131\pi\) |
0.0978683 | + | 0.995199i | \(0.468798\pi\) | |||||||
\(998\) | 0.00295282 | + | 0.00170481i | 9.34698e−5 | + | 5.39648e-5i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.fm.g.370.8 | 32 | ||
3.2 | odd | 2 | 91.2.bc.a.6.2 | yes | 32 | ||
7.6 | odd | 2 | inner | 819.2.fm.g.370.7 | 32 | ||
13.11 | odd | 12 | inner | 819.2.fm.g.622.7 | 32 | ||
21.2 | odd | 6 | 637.2.bb.b.227.1 | 32 | |||
21.5 | even | 6 | 637.2.bb.b.227.2 | 32 | |||
21.11 | odd | 6 | 637.2.x.b.19.7 | 32 | |||
21.17 | even | 6 | 637.2.x.b.19.8 | 32 | |||
21.20 | even | 2 | 91.2.bc.a.6.1 | ✓ | 32 | ||
39.11 | even | 12 | 91.2.bc.a.76.1 | yes | 32 | ||
91.76 | even | 12 | inner | 819.2.fm.g.622.8 | 32 | ||
273.11 | even | 12 | 637.2.bb.b.362.2 | 32 | |||
273.89 | odd | 12 | 637.2.x.b.570.8 | 32 | |||
273.128 | even | 12 | 637.2.x.b.570.7 | 32 | |||
273.167 | odd | 12 | 91.2.bc.a.76.2 | yes | 32 | ||
273.206 | odd | 12 | 637.2.bb.b.362.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bc.a.6.1 | ✓ | 32 | 21.20 | even | 2 | ||
91.2.bc.a.6.2 | yes | 32 | 3.2 | odd | 2 | ||
91.2.bc.a.76.1 | yes | 32 | 39.11 | even | 12 | ||
91.2.bc.a.76.2 | yes | 32 | 273.167 | odd | 12 | ||
637.2.x.b.19.7 | 32 | 21.11 | odd | 6 | |||
637.2.x.b.19.8 | 32 | 21.17 | even | 6 | |||
637.2.x.b.570.7 | 32 | 273.128 | even | 12 | |||
637.2.x.b.570.8 | 32 | 273.89 | odd | 12 | |||
637.2.bb.b.227.1 | 32 | 21.2 | odd | 6 | |||
637.2.bb.b.227.2 | 32 | 21.5 | even | 6 | |||
637.2.bb.b.362.1 | 32 | 273.206 | odd | 12 | |||
637.2.bb.b.362.2 | 32 | 273.11 | even | 12 | |||
819.2.fm.g.370.7 | 32 | 7.6 | odd | 2 | inner | ||
819.2.fm.g.370.8 | 32 | 1.1 | even | 1 | trivial | ||
819.2.fm.g.622.7 | 32 | 13.11 | odd | 12 | inner | ||
819.2.fm.g.622.8 | 32 | 91.76 | even | 12 | inner |