Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(178,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.178");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.v (of order \(12\), degree \(4\), not 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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 607.5 | ||
Character | \(\chi\) | \(=\) | 735.607 |
Dual form | 735.2.v.a.178.5 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.228203 | − | 0.0611467i | 0.161364 | − | 0.0432372i | −0.177233 | − | 0.984169i | \(-0.556715\pi\) |
0.338596 | + | 0.940932i | \(0.390048\pi\) | |||||||
\(3\) | −0.258819 | + | 0.965926i | −0.149429 | + | 0.557678i | ||||
\(4\) | −1.68371 | + | 0.972092i | −0.841857 | + | 0.486046i | ||||
\(5\) | 1.18965 | − | 1.89334i | 0.532029 | − | 0.846726i | ||||
\(6\) | 0.236253i | 0.0964497i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.658899 | + | 0.658899i | −0.232956 | + | 0.232956i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0.155711 | − | 0.504808i | 0.0492400 | − | 0.159634i | ||||
\(11\) | −1.99301 | − | 3.45200i | −0.600915 | − | 1.04082i | −0.992683 | − | 0.120752i | \(-0.961470\pi\) |
0.391767 | − | 0.920064i | \(-0.371864\pi\) | |||||||
\(12\) | −0.503192 | − | 1.87794i | −0.145259 | − | 0.542114i | ||||
\(13\) | −0.500437 | − | 0.500437i | −0.138796 | − | 0.138796i | 0.634295 | − | 0.773091i | \(-0.281291\pi\) |
−0.773091 | + | 0.634295i | \(0.781291\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.52092 | + | 1.63915i | 0.392699 | + | 0.423226i | ||||
\(16\) | 1.83411 | − | 3.17677i | 0.458528 | − | 0.794194i | ||||
\(17\) | −2.29273 | − | 0.614336i | −0.556070 | − | 0.148998i | −0.0301697 | − | 0.999545i | \(-0.509605\pi\) |
−0.525900 | + | 0.850546i | \(0.676271\pi\) | |||||||
\(18\) | −0.228203 | − | 0.0611467i | −0.0537879 | − | 0.0144124i | ||||
\(19\) | −3.60925 | + | 6.25141i | −0.828019 | + | 1.43417i | 0.0715711 | + | 0.997435i | \(0.477199\pi\) |
−0.899590 | + | 0.436735i | \(0.856135\pi\) | |||||||
\(20\) | −0.162536 | + | 4.34429i | −0.0363441 | + | 0.971413i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.665888 | − | 0.665888i | −0.141968 | − | 0.141968i | ||||
\(23\) | −1.88872 | − | 7.04878i | −0.393824 | − | 1.46977i | −0.823773 | − | 0.566919i | \(-0.808135\pi\) |
0.429949 | − | 0.902853i | \(-0.358532\pi\) | |||||||
\(24\) | −0.465912 | − | 0.806983i | −0.0951039 | − | 0.164725i | ||||
\(25\) | −2.16945 | − | 4.50483i | −0.433890 | − | 0.900966i | ||||
\(26\) | −0.144801 | − | 0.0836010i | −0.0283978 | − | 0.0163955i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.65191i | − | 0.678143i | −0.940761 | − | 0.339071i | \(-0.889887\pi\) | ||
0.940761 | − | 0.339071i | \(-0.110113\pi\) | |||||||
\(30\) | 0.447306 | + | 0.281059i | 0.0816665 | + | 0.0513141i | ||||
\(31\) | 4.27662 | − | 2.46911i | 0.768103 | − | 0.443465i | −0.0640944 | − | 0.997944i | \(-0.520416\pi\) |
0.832198 | + | 0.554479i | \(0.187083\pi\) | |||||||
\(32\) | 0.706647 | − | 2.63724i | 0.124919 | − | 0.466203i | ||||
\(33\) | 3.85020 | − | 1.03166i | 0.670234 | − | 0.179589i | ||||
\(34\) | −0.560773 | −0.0961717 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.94418 | 0.324031 | ||||||||
\(37\) | −0.399255 | + | 0.106980i | −0.0656371 | + | 0.0175874i | −0.291488 | − | 0.956574i | \(-0.594150\pi\) |
0.225851 | + | 0.974162i | \(0.427484\pi\) | |||||||
\(38\) | −0.441387 | + | 1.64728i | −0.0716025 | + | 0.267224i | ||||
\(39\) | 0.612908 | − | 0.353863i | 0.0981438 | − | 0.0566634i | ||||
\(40\) | 0.463657 | + | 2.03138i | 0.0733106 | + | 0.321189i | ||||
\(41\) | − | 7.63184i | − | 1.19189i | −0.803024 | − | 0.595947i | \(-0.796777\pi\) | ||
0.803024 | − | 0.595947i | \(-0.203223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.65191 | − | 3.65191i | 0.556911 | − | 0.556911i | −0.371516 | − | 0.928427i | \(-0.621162\pi\) |
0.928427 | + | 0.371516i | \(0.121162\pi\) | |||||||
\(44\) | 6.71132 | + | 3.87478i | 1.01177 | + | 0.584145i | ||||
\(45\) | −1.97694 | + | 1.04485i | −0.294705 | + | 0.155757i | ||||
\(46\) | −0.862019 | − | 1.49306i | −0.127098 | − | 0.220140i | ||||
\(47\) | 0.111749 | + | 0.417052i | 0.0163002 | + | 0.0608333i | 0.973597 | − | 0.228274i | \(-0.0733082\pi\) |
−0.957297 | + | 0.289107i | \(0.906642\pi\) | |||||||
\(48\) | 2.59383 | + | 2.59383i | 0.374386 | + | 0.374386i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.770530 | − | 0.895358i | −0.108969 | − | 0.126623i | ||||
\(51\) | 1.18681 | − | 2.05561i | 0.166186 | − | 0.287843i | ||||
\(52\) | 1.32906 | + | 0.356122i | 0.184308 | + | 0.0493852i | ||||
\(53\) | −7.37179 | − | 1.97527i | −1.01259 | − | 0.271324i | −0.285881 | − | 0.958265i | \(-0.592286\pi\) |
−0.726713 | + | 0.686942i | \(0.758953\pi\) | |||||||
\(54\) | 0.118126 | − | 0.204601i | 0.0160750 | − | 0.0278426i | ||||
\(55\) | −8.90678 | − | 0.333235i | −1.20099 | − | 0.0449335i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.10425 | − | 5.10425i | −0.676075 | − | 0.676075i | ||||
\(58\) | −0.223302 | − | 0.833375i | −0.0293210 | − | 0.109428i | ||||
\(59\) | 3.05480 | + | 5.29106i | 0.397701 | + | 0.688838i | 0.993442 | − | 0.114339i | \(-0.0364750\pi\) |
−0.595741 | + | 0.803176i | \(0.703142\pi\) | |||||||
\(60\) | −4.15419 | − | 1.28138i | −0.536304 | − | 0.165426i | ||||
\(61\) | −6.15784 | − | 3.55523i | −0.788431 | − | 0.455201i | 0.0509788 | − | 0.998700i | \(-0.483766\pi\) |
−0.839410 | + | 0.543499i | \(0.817099\pi\) | |||||||
\(62\) | 0.824957 | − | 0.824957i | 0.104770 | − | 0.104770i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.69141i | 0.836426i | ||||||||
\(65\) | −1.54284 | + | 0.352150i | −0.191366 | + | 0.0436788i | ||||
\(66\) | 0.815543 | − | 0.470854i | 0.100386 | − | 0.0579581i | ||||
\(67\) | 0.345596 | − | 1.28978i | 0.0422212 | − | 0.157572i | −0.941597 | − | 0.336743i | \(-0.890675\pi\) |
0.983818 | + | 0.179171i | \(0.0573415\pi\) | |||||||
\(68\) | 4.45750 | − | 1.19438i | 0.540551 | − | 0.144840i | ||||
\(69\) | 7.29744 | 0.878508 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.19297 | 0.141579 | 0.0707897 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707897 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(72\) | 0.900073 | − | 0.241174i | 0.106075 | − | 0.0284226i | ||||
\(73\) | −0.506205 | + | 1.88918i | −0.0592469 | + | 0.221112i | −0.989201 | − | 0.146562i | \(-0.953179\pi\) |
0.929955 | + | 0.367674i | \(0.119846\pi\) | |||||||
\(74\) | −0.0845694 | + | 0.0488262i | −0.00983100 | + | 0.00567593i | ||||
\(75\) | 4.91283 | − | 0.929594i | 0.567284 | − | 0.107340i | ||||
\(76\) | − | 14.0341i | − | 1.60982i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.118230 | − | 0.118230i | 0.0133869 | − | 0.0133869i | ||||
\(79\) | −7.48269 | − | 4.32013i | −0.841868 | − | 0.486053i | 0.0160304 | − | 0.999872i | \(-0.494897\pi\) |
−0.857899 | + | 0.513819i | \(0.828230\pi\) | |||||||
\(80\) | −3.83275 | − | 7.25185i | −0.428514 | − | 0.810782i | ||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.466662 | − | 1.74161i | −0.0515342 | − | 0.192328i | ||||
\(83\) | 11.9895 | + | 11.9895i | 1.31602 | + | 1.31602i | 0.916898 | + | 0.399122i | \(0.130685\pi\) |
0.399122 | + | 0.916898i | \(0.369315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.89070 | + | 3.61007i | −0.422006 | + | 0.391567i | ||||
\(86\) | 0.610073 | − | 1.05668i | 0.0657859 | − | 0.113944i | ||||
\(87\) | 3.52747 | + | 0.945184i | 0.378185 | + | 0.101334i | ||||
\(88\) | 3.58771 | + | 0.961324i | 0.382451 | + | 0.102477i | ||||
\(89\) | 3.91290 | − | 6.77735i | 0.414767 | − | 0.718397i | −0.580637 | − | 0.814163i | \(-0.697196\pi\) |
0.995404 | + | 0.0957652i | \(0.0305298\pi\) | |||||||
\(90\) | −0.387253 | + | 0.359321i | −0.0408201 | + | 0.0378758i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.0321 | + | 10.0321i | 1.04592 | + | 1.04592i | ||||
\(93\) | 1.27810 | + | 4.76995i | 0.132533 | + | 0.494620i | ||||
\(94\) | 0.0510027 | + | 0.0883393i | 0.00526053 | + | 0.00911150i | ||||
\(95\) | 7.54226 | + | 14.2705i | 0.773820 | + | 1.46413i | ||||
\(96\) | 2.36449 | + | 1.36514i | 0.241325 | + | 0.139329i | ||||
\(97\) | −7.43671 | + | 7.43671i | −0.755083 | + | 0.755083i | −0.975423 | − | 0.220340i | \(-0.929283\pi\) |
0.220340 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.98602i | 0.400610i | ||||||||
\(100\) | 8.03184 | + | 5.47593i | 0.803184 | + | 0.547593i | ||||
\(101\) | 5.47010 | − | 3.15816i | 0.544295 | − | 0.314249i | −0.202523 | − | 0.979278i | \(-0.564914\pi\) |
0.746818 | + | 0.665028i | \(0.231581\pi\) | |||||||
\(102\) | 0.145139 | − | 0.541665i | 0.0143709 | − | 0.0536328i | ||||
\(103\) | −17.1313 | + | 4.59031i | −1.68799 | + | 0.452296i | −0.969871 | − | 0.243620i | \(-0.921665\pi\) |
−0.718122 | + | 0.695917i | \(0.754998\pi\) | |||||||
\(104\) | 0.659476 | 0.0646669 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.80304 | −0.175127 | ||||||||
\(107\) | −10.2181 | + | 2.73794i | −0.987825 | + | 0.264687i | −0.716337 | − | 0.697755i | \(-0.754183\pi\) |
−0.271488 | + | 0.962442i | \(0.587516\pi\) | |||||||
\(108\) | −0.503192 | + | 1.87794i | −0.0484197 | + | 0.180705i | ||||
\(109\) | 0.578698 | − | 0.334112i | 0.0554293 | − | 0.0320021i | −0.472029 | − | 0.881583i | \(-0.656478\pi\) |
0.527459 | + | 0.849581i | \(0.323145\pi\) | |||||||
\(110\) | −2.05293 | + | 0.468575i | −0.195739 | + | 0.0446769i | ||||
\(111\) | − | 0.413339i | − | 0.0392324i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.39653 | + | 3.39653i | −0.319518 | + | 0.319518i | −0.848582 | − | 0.529064i | \(-0.822543\pi\) |
0.529064 | + | 0.848582i | \(0.322543\pi\) | |||||||
\(114\) | −1.47691 | − | 0.852695i | −0.138325 | − | 0.0798622i | ||||
\(115\) | −15.5926 | − | 4.80963i | −1.45402 | − | 0.448500i | ||||
\(116\) | 3.54999 | + | 6.14877i | 0.329609 | + | 0.570899i | ||||
\(117\) | 0.183173 | + | 0.683610i | 0.0169343 | + | 0.0631998i | ||||
\(118\) | 1.02064 | + | 1.02064i | 0.0939578 | + | 0.0939578i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.08217 | − | 0.0779014i | −0.190075 | − | 0.00711139i | ||||
\(121\) | −2.44418 | + | 4.23345i | −0.222199 | + | 0.384859i | ||||
\(122\) | −1.62263 | − | 0.434781i | −0.146906 | − | 0.0393633i | ||||
\(123\) | 7.37179 | + | 1.97527i | 0.664692 | + | 0.178104i | ||||
\(124\) | −4.80040 | + | 8.31453i | −0.431088 | + | 0.746667i | ||||
\(125\) | −11.1101 | − | 1.25168i | −0.993713 | − | 0.111953i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.88837 | − | 5.88837i | −0.522508 | − | 0.522508i | 0.395820 | − | 0.918328i | \(-0.370460\pi\) |
−0.918328 | + | 0.395820i | \(0.870460\pi\) | |||||||
\(128\) | 1.82245 | + | 6.80149i | 0.161084 | + | 0.601172i | ||||
\(129\) | 2.58229 | + | 4.47266i | 0.227358 | + | 0.393796i | ||||
\(130\) | −0.330548 | + | 0.174701i | −0.0289910 | + | 0.0153223i | ||||
\(131\) | 16.2938 | + | 9.40722i | 1.42359 | + | 0.821913i | 0.996604 | − | 0.0823433i | \(-0.0262404\pi\) |
0.426991 | + | 0.904256i | \(0.359574\pi\) | |||||||
\(132\) | −5.47977 | + | 5.47977i | −0.476953 | + | 0.476953i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.315463i | − | 0.0272519i | ||||||
\(135\) | −0.497580 | − | 2.18000i | −0.0428249 | − | 0.187625i | ||||
\(136\) | 1.91547 | − | 1.10590i | 0.164250 | − | 0.0948297i | ||||
\(137\) | −0.297204 | + | 1.10918i | −0.0253919 | + | 0.0947637i | −0.977459 | − | 0.211126i | \(-0.932287\pi\) |
0.952067 | + | 0.305889i | \(0.0989538\pi\) | |||||||
\(138\) | 1.66529 | − | 0.446214i | 0.141759 | − | 0.0379843i | ||||
\(139\) | 0.442439 | 0.0375272 | 0.0187636 | − | 0.999824i | \(-0.494027\pi\) | ||||
0.0187636 | + | 0.999824i | \(0.494027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.431764 | −0.0363611 | ||||||||
\(142\) | 0.272239 | − | 0.0729461i | 0.0228458 | − | 0.00612150i | ||||
\(143\) | −0.730131 | + | 2.72489i | −0.0610566 | + | 0.227866i | ||||
\(144\) | −3.17677 | + | 1.83411i | −0.264731 | + | 0.152843i | ||||
\(145\) | −6.91430 | − | 4.34451i | −0.574201 | − | 0.360792i | ||||
\(146\) | 0.462070i | 0.0382411i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.568236 | − | 0.568236i | 0.0467087 | − | 0.0467087i | ||||
\(149\) | 2.72031 | + | 1.57057i | 0.222856 | + | 0.128666i | 0.607272 | − | 0.794494i | \(-0.292264\pi\) |
−0.384416 | + | 0.923160i | \(0.625597\pi\) | |||||||
\(150\) | 1.06428 | − | 0.512539i | 0.0868979 | − | 0.0418486i | ||||
\(151\) | 7.36197 | + | 12.7513i | 0.599109 | + | 1.03769i | 0.992953 | + | 0.118509i | \(0.0378116\pi\) |
−0.393844 | + | 0.919177i | \(0.628855\pi\) | |||||||
\(152\) | −1.74091 | − | 6.49718i | −0.141207 | − | 0.526991i | ||||
\(153\) | 1.67840 | + | 1.67840i | 0.135690 | + | 0.135690i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.412839 | − | 11.0345i | 0.0331601 | − | 0.886309i | ||||
\(156\) | −0.687974 | + | 1.19161i | −0.0550820 | + | 0.0954049i | ||||
\(157\) | −10.8805 | − | 2.91542i | −0.868358 | − | 0.232676i | −0.202980 | − | 0.979183i | \(-0.565063\pi\) |
−0.665378 | + | 0.746507i | \(0.731729\pi\) | |||||||
\(158\) | −1.97173 | − | 0.528324i | −0.156862 | − | 0.0420312i | ||||
\(159\) | 3.81592 | − | 6.60937i | 0.302622 | − | 0.524157i | ||||
\(160\) | −4.15253 | − | 4.47533i | −0.328286 | − | 0.353806i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.167056 | + | 0.167056i | 0.0131251 | + | 0.0131251i | ||||
\(163\) | 3.82312 | + | 14.2681i | 0.299450 | + | 1.11756i | 0.937619 | + | 0.347666i | \(0.113026\pi\) |
−0.638169 | + | 0.769897i | \(0.720308\pi\) | |||||||
\(164\) | 7.41885 | + | 12.8498i | 0.579315 | + | 1.00340i | ||||
\(165\) | 2.62713 | − | 8.51705i | 0.204521 | − | 0.663051i | ||||
\(166\) | 3.46916 | + | 2.00292i | 0.269259 | + | 0.155457i | ||||
\(167\) | −4.63621 | + | 4.63621i | −0.358761 | + | 0.358761i | −0.863356 | − | 0.504595i | \(-0.831642\pi\) |
0.504595 | + | 0.863356i | \(0.331642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.4991i | − | 0.961471i | ||||||
\(170\) | −0.667125 | + | 1.06173i | −0.0511661 | + | 0.0814311i | ||||
\(171\) | 6.25141 | − | 3.60925i | 0.478057 | − | 0.276006i | ||||
\(172\) | −2.59878 | + | 9.69876i | −0.198155 | + | 0.739524i | ||||
\(173\) | −3.39499 | + | 0.909686i | −0.258117 | + | 0.0691621i | −0.385557 | − | 0.922684i | \(-0.625991\pi\) |
0.127440 | + | 0.991846i | \(0.459324\pi\) | |||||||
\(174\) | 0.862773 | 0.0654067 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.6216 | −1.10215 | ||||||||
\(177\) | −5.90141 | + | 1.58128i | −0.443577 | + | 0.118856i | ||||
\(178\) | 0.478522 | − | 1.78587i | 0.0358667 | − | 0.133857i | ||||
\(179\) | 19.1486 | − | 11.0554i | 1.43123 | − | 0.826321i | 0.434016 | − | 0.900905i | \(-0.357096\pi\) |
0.997215 | + | 0.0745840i | \(0.0237629\pi\) | |||||||
\(180\) | 2.31290 | − | 3.68100i | 0.172394 | − | 0.274365i | ||||
\(181\) | − | 8.48528i | − | 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.02786 | − | 5.02786i | 0.371670 | − | 0.371670i | ||||
\(184\) | 5.88891 | + | 3.39996i | 0.434136 | + | 0.250649i | ||||
\(185\) | −0.272425 | + | 0.883193i | −0.0200291 | + | 0.0649336i | ||||
\(186\) | 0.583333 | + | 1.01036i | 0.0427720 | + | 0.0740833i | ||||
\(187\) | 2.44876 | + | 9.13889i | 0.179071 | + | 0.668302i | ||||
\(188\) | −0.593566 | − | 0.593566i | −0.0432903 | − | 0.0432903i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.59376 | + | 2.79539i | 0.188171 | + | 0.202799i | ||||
\(191\) | −7.64492 | + | 13.2414i | −0.553167 | + | 0.958113i | 0.444877 | + | 0.895592i | \(0.353248\pi\) |
−0.998044 | + | 0.0625216i | \(0.980086\pi\) | |||||||
\(192\) | −6.46341 | − | 1.73186i | −0.466456 | − | 0.124987i | ||||
\(193\) | 12.1957 | + | 3.26783i | 0.877866 | + | 0.235223i | 0.669486 | − | 0.742825i | \(-0.266514\pi\) |
0.208380 | + | 0.978048i | \(0.433181\pi\) | |||||||
\(194\) | −1.24235 | + | 2.15181i | −0.0891952 | + | 0.154491i | ||||
\(195\) | 0.0591665 | − | 1.58142i | 0.00423700 | − | 0.113248i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.68715 | − | 2.68715i | −0.191451 | − | 0.191451i | 0.604872 | − | 0.796323i | \(-0.293224\pi\) |
−0.796323 | + | 0.604872i | \(0.793224\pi\) | |||||||
\(198\) | 0.243732 | + | 0.909620i | 0.0173213 | + | 0.0646439i | ||||
\(199\) | 0.308318 | + | 0.534023i | 0.0218561 | + | 0.0378559i | 0.876747 | − | 0.480953i | \(-0.159709\pi\) |
−0.854890 | + | 0.518809i | \(0.826376\pi\) | |||||||
\(200\) | 4.39768 | + | 1.53878i | 0.310963 | + | 0.108808i | ||||
\(201\) | 1.15639 | + | 0.667639i | 0.0815651 | + | 0.0470917i | ||||
\(202\) | 1.05518 | − | 1.05518i | 0.0742422 | − | 0.0742422i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.61474i | 0.323097i | ||||||||
\(205\) | −14.4496 | − | 9.07924i | −1.00921 | − | 0.634122i | ||||
\(206\) | −3.62871 | + | 2.09504i | −0.252825 | + | 0.145968i | ||||
\(207\) | −1.88872 | + | 7.04878i | −0.131275 | + | 0.489924i | ||||
\(208\) | −2.50763 | + | 0.671919i | −0.173873 | + | 0.0465892i | ||||
\(209\) | 28.7731 | 1.99028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.30849 | 0.640823 | 0.320411 | − | 0.947278i | \(-0.396179\pi\) | ||||
0.320411 | + | 0.947278i | \(0.396179\pi\) | |||||||
\(212\) | 14.3321 | − | 3.84028i | 0.984334 | − | 0.263752i | ||||
\(213\) | −0.308763 | + | 1.15232i | −0.0211561 | + | 0.0789557i | ||||
\(214\) | −2.16439 | + | 1.24961i | −0.147955 | + | 0.0854217i | ||||
\(215\) | −2.56979 | − | 11.2588i | −0.175258 | − | 0.767844i | ||||
\(216\) | 0.931824i | 0.0634026i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.111631 | − | 0.111631i | 0.00756058 | − | 0.00756058i | ||||
\(219\) | −1.69380 | − | 0.977914i | −0.114456 | − | 0.0660813i | ||||
\(220\) | 15.3204 | − | 8.09714i | 1.03290 | − | 0.545909i | ||||
\(221\) | 0.839933 | + | 1.45481i | 0.0565000 | + | 0.0978609i | ||||
\(222\) | −0.0252743 | − | 0.0943250i | −0.00169630 | − | 0.00633068i | ||||
\(223\) | 1.35505 | + | 1.35505i | 0.0907407 | + | 0.0907407i | 0.751020 | − | 0.660279i | \(-0.229562\pi\) |
−0.660279 | + | 0.751020i | \(0.729562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.373614 | + | 4.98602i | −0.0249076 | + | 0.332401i | ||||
\(226\) | −0.567410 | + | 0.982782i | −0.0377435 | + | 0.0653737i | ||||
\(227\) | 5.67498 | + | 1.52061i | 0.376662 | + | 0.100926i | 0.442183 | − | 0.896925i | \(-0.354204\pi\) |
−0.0655211 | + | 0.997851i | \(0.520871\pi\) | |||||||
\(228\) | 13.5559 | + | 3.63229i | 0.897761 | + | 0.240554i | ||||
\(229\) | 6.49500 | − | 11.2497i | 0.429202 | − | 0.743399i | −0.567601 | − | 0.823304i | \(-0.692128\pi\) |
0.996802 | + | 0.0799049i | \(0.0254617\pi\) | |||||||
\(230\) | −3.85237 | − | 0.144131i | −0.254018 | − | 0.00950374i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.40624 | + | 2.40624i | 0.157977 | + | 0.157977i | ||||
\(233\) | −6.02620 | − | 22.4901i | −0.394790 | − | 1.47337i | −0.822138 | − | 0.569288i | \(-0.807219\pi\) |
0.427349 | − | 0.904087i | \(-0.359448\pi\) | |||||||
\(234\) | 0.0836010 | + | 0.144801i | 0.00546517 | + | 0.00946595i | ||||
\(235\) | 0.922563 | + | 0.284569i | 0.0601813 | + | 0.0185632i | ||||
\(236\) | −10.2868 | − | 5.93909i | −0.669614 | − | 0.386602i | ||||
\(237\) | 6.10959 | − | 6.10959i | 0.396861 | − | 0.396861i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.48048i | 0.354503i | 0.984166 | + | 0.177251i | \(0.0567205\pi\) | ||||
−0.984166 | + | 0.177251i | \(0.943279\pi\) | |||||||
\(240\) | 7.99674 | − | 1.82523i | 0.516187 | − | 0.117818i | ||||
\(241\) | 12.6879 | − | 7.32537i | 0.817300 | − | 0.471868i | −0.0321844 | − | 0.999482i | \(-0.510246\pi\) |
0.849485 | + | 0.527613i | \(0.176913\pi\) | |||||||
\(242\) | −0.298908 | + | 1.11554i | −0.0192145 | + | 0.0717095i | ||||
\(243\) | −0.965926 | + | 0.258819i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | 13.8241 | 0.884995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.80304 | 0.114958 | ||||||||
\(247\) | 4.93464 | − | 1.32223i | 0.313984 | − | 0.0841317i | ||||
\(248\) | −1.19097 | + | 4.44475i | −0.0756265 | + | 0.282242i | ||||
\(249\) | −14.6841 | + | 8.47787i | −0.930567 | + | 0.537263i | ||||
\(250\) | −2.61188 | + | 0.393707i | −0.165190 | + | 0.0249002i | ||||
\(251\) | − | 21.1506i | − | 1.33501i | −0.744604 | − | 0.667507i | \(-0.767361\pi\) | ||
0.744604 | − | 0.667507i | \(-0.232639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.5681 | + | 20.5681i | −1.29311 | + | 1.29311i | ||||
\(254\) | −1.70380 | − | 0.983687i | −0.106906 | − | 0.0617220i | ||||
\(255\) | −2.48007 | − | 4.69249i | −0.155308 | − | 0.293855i | ||||
\(256\) | −5.85964 | − | 10.1492i | −0.366227 | − | 0.634324i | ||||
\(257\) | 3.43788 | + | 12.8304i | 0.214449 | + | 0.800336i | 0.986360 | + | 0.164604i | \(0.0526348\pi\) |
−0.771910 | + | 0.635731i | \(0.780699\pi\) | |||||||
\(258\) | 0.862773 | + | 0.862773i | 0.0537139 | + | 0.0537139i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.25538 | − | 2.09271i | 0.139873 | − | 0.129784i | ||||
\(261\) | −1.82596 | + | 3.16265i | −0.113024 | + | 0.195763i | ||||
\(262\) | 4.29350 | + | 1.15044i | 0.265254 | + | 0.0710745i | ||||
\(263\) | −21.0066 | − | 5.62869i | −1.29532 | − | 0.347080i | −0.455642 | − | 0.890163i | \(-0.650590\pi\) |
−0.839679 | + | 0.543083i | \(0.817257\pi\) | |||||||
\(264\) | −1.85714 | + | 3.21665i | −0.114299 | + | 0.197971i | ||||
\(265\) | −12.5097 | + | 11.6074i | −0.768466 | + | 0.713037i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.53368 | + | 5.53368i | 0.338656 | + | 0.338656i | ||||
\(268\) | 0.671902 | + | 2.50757i | 0.0410429 | + | 0.153174i | ||||
\(269\) | −11.4926 | − | 19.9057i | −0.700714 | − | 1.21367i | −0.968216 | − | 0.250116i | \(-0.919531\pi\) |
0.267501 | − | 0.963557i | \(-0.413802\pi\) | |||||||
\(270\) | −0.246849 | − | 0.467057i | −0.0150228 | − | 0.0284242i | ||||
\(271\) | 13.6483 | + | 7.87982i | 0.829072 | + | 0.478665i | 0.853535 | − | 0.521036i | \(-0.174454\pi\) |
−0.0244625 | + | 0.999701i | \(0.507787\pi\) | |||||||
\(272\) | −6.15674 | + | 6.15674i | −0.373307 | + | 0.373307i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.271291i | 0.0163893i | ||||||||
\(275\) | −11.2269 | + | 16.4671i | −0.677008 | + | 0.993004i | ||||
\(276\) | −12.2868 | + | 7.09378i | −0.739578 | + | 0.426995i | ||||
\(277\) | 1.75975 | − | 6.56746i | 0.105733 | − | 0.394600i | −0.892694 | − | 0.450662i | \(-0.851188\pi\) |
0.998427 | + | 0.0560621i | \(0.0178545\pi\) | |||||||
\(278\) | 0.100966 | − | 0.0270537i | 0.00605553 | − | 0.00162257i | ||||
\(279\) | −4.93821 | −0.295643 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.65658 | −0.576063 | −0.288032 | − | 0.957621i | \(-0.593001\pi\) | ||||
−0.288032 | + | 0.957621i | \(0.593001\pi\) | |||||||
\(282\) | −0.0985297 | + | 0.0264009i | −0.00586736 | + | 0.00157215i | ||||
\(283\) | −5.45726 | + | 20.3668i | −0.324400 | + | 1.21068i | 0.590513 | + | 0.807028i | \(0.298925\pi\) |
−0.914913 | + | 0.403650i | \(0.867741\pi\) | |||||||
\(284\) | −2.00862 | + | 1.15968i | −0.119190 | + | 0.0688141i | ||||
\(285\) | −15.7364 | + | 3.59178i | −0.932141 | + | 0.212759i | ||||
\(286\) | 0.666471i | 0.0394092i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.93060 | + | 1.93060i | −0.113761 | + | 0.113761i | ||||
\(289\) | −9.84321 | − | 5.68298i | −0.579012 | − | 0.334293i | ||||
\(290\) | −1.84351 | − | 0.568641i | −0.108255 | − | 0.0333917i | ||||
\(291\) | −5.25855 | − | 9.10807i | −0.308261 | − | 0.533924i | ||||
\(292\) | −0.984157 | − | 3.67292i | −0.0575934 | − | 0.214942i | ||||
\(293\) | −4.79236 | − | 4.79236i | −0.279973 | − | 0.279973i | 0.553125 | − | 0.833098i | \(-0.313435\pi\) |
−0.833098 | + | 0.553125i | \(0.813435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6519 | + | 0.510768i | 0.794845 | + | 0.0297381i | ||||
\(296\) | 0.192580 | − | 0.333558i | 0.0111935 | − | 0.0193876i | ||||
\(297\) | −3.85020 | − | 1.03166i | −0.223411 | − | 0.0598629i | ||||
\(298\) | 0.716817 | + | 0.192070i | 0.0415241 | + | 0.0111263i | ||||
\(299\) | −2.58229 | + | 4.47266i | −0.149338 | + | 0.258660i | ||||
\(300\) | −7.36814 | + | 6.34089i | −0.425400 | + | 0.366091i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.45972 | + | 2.45972i | 0.141541 | + | 0.141541i | ||||
\(303\) | 1.63479 | + | 6.10111i | 0.0939160 | + | 0.350499i | ||||
\(304\) | 13.2395 | + | 22.9316i | 0.759340 | + | 1.31521i | ||||
\(305\) | −14.0570 | + | 7.42938i | −0.804899 | + | 0.425405i | ||||
\(306\) | 0.485643 | + | 0.280386i | 0.0277624 | + | 0.0160286i | ||||
\(307\) | −9.85063 | + | 9.85063i | −0.562205 | + | 0.562205i | −0.929933 | − | 0.367728i | \(-0.880136\pi\) |
0.367728 | + | 0.929933i | \(0.380136\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 17.7356i | − | 1.00894i | ||||||
\(310\) | −0.580510 | − | 2.54334i | −0.0329707 | − | 0.144452i | ||||
\(311\) | 23.6480 | − | 13.6532i | 1.34095 | − | 0.774200i | 0.354006 | − | 0.935243i | \(-0.384819\pi\) |
0.986947 | + | 0.161043i | \(0.0514858\pi\) | |||||||
\(312\) | −0.170685 | + | 0.637004i | −0.00966313 | + | 0.0360633i | ||||
\(313\) | 25.2824 | − | 6.77439i | 1.42904 | − | 0.382911i | 0.540361 | − | 0.841434i | \(-0.318288\pi\) |
0.888683 | + | 0.458523i | \(0.151621\pi\) | |||||||
\(314\) | −2.66123 | −0.150182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.7983 | 0.944977 | ||||||||
\(317\) | 29.8877 | − | 8.00839i | 1.67866 | − | 0.449796i | 0.711237 | − | 0.702952i | \(-0.248135\pi\) |
0.967425 | + | 0.253156i | \(0.0814687\pi\) | |||||||
\(318\) | 0.466662 | − | 1.74161i | 0.0261691 | − | 0.0976644i | ||||
\(319\) | −12.6064 | + | 7.27830i | −0.705822 | + | 0.407506i | ||||
\(320\) | 12.6691 | + | 7.96046i | 0.708224 | + | 0.445003i | ||||
\(321\) | − | 10.5786i | − | 0.590440i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.1155 | − | 12.1155i | 0.674126 | − | 0.674126i | ||||
\(324\) | −1.68371 | − | 0.972092i | −0.0935396 | − | 0.0540051i | ||||
\(325\) | −1.16871 | + | 3.34006i | −0.0648283 | + | 0.185273i | ||||
\(326\) | 1.74489 | + | 3.02224i | 0.0966406 | + | 0.167386i | ||||
\(327\) | 0.172949 | + | 0.645454i | 0.00956410 | + | 0.0356937i | ||||
\(328\) | 5.02861 | + | 5.02861i | 0.277659 | + | 0.277659i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.0787277 | − | 2.10425i | 0.00433382 | − | 0.115835i | ||||
\(331\) | 8.34566 | − | 14.4551i | 0.458719 | − | 0.794524i | −0.540175 | − | 0.841553i | \(-0.681642\pi\) |
0.998894 | + | 0.0470286i | \(0.0149752\pi\) | |||||||
\(332\) | −31.8418 | − | 8.53199i | −1.74755 | − | 0.468254i | ||||
\(333\) | 0.399255 | + | 0.106980i | 0.0218790 | + | 0.00586246i | ||||
\(334\) | −0.774506 | + | 1.34148i | −0.0423791 | + | 0.0734027i | ||||
\(335\) | −2.03085 | − | 2.18872i | −0.110957 | − | 0.119583i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.54028 | + | 2.54028i | 0.138378 | + | 0.138378i | 0.772903 | − | 0.634525i | \(-0.218804\pi\) |
−0.634525 | + | 0.772903i | \(0.718804\pi\) | |||||||
\(338\) | −0.764280 | − | 2.85233i | −0.0415714 | − | 0.155146i | ||||
\(339\) | −2.40171 | − | 4.15988i | −0.130443 | − | 0.225934i | ||||
\(340\) | 3.04151 | − | 9.86045i | 0.164949 | − | 0.534758i | ||||
\(341\) | −17.0467 | − | 9.84191i | −0.923130 | − | 0.532969i | ||||
\(342\) | 1.20589 | − | 1.20589i | 0.0652072 | − | 0.0652072i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.81248i | 0.259472i | ||||||||
\(345\) | 8.68142 | − | 13.8165i | 0.467392 | − | 0.743856i | ||||
\(346\) | −0.719122 | + | 0.415185i | −0.0386602 | + | 0.0223205i | ||||
\(347\) | 5.01382 | − | 18.7118i | 0.269156 | − | 1.00450i | −0.690501 | − | 0.723331i | \(-0.742610\pi\) |
0.959657 | − | 0.281173i | \(-0.0907233\pi\) | |||||||
\(348\) | −6.85806 | + | 1.83761i | −0.367631 | + | 0.0985063i | ||||
\(349\) | −0.508601 | −0.0272248 | −0.0136124 | − | 0.999907i | \(-0.504333\pi\) | ||||
−0.0136124 | + | 0.999907i | \(0.504333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.707725 | −0.0377756 | ||||||||
\(352\) | −10.5121 | + | 2.81671i | −0.560297 | + | 0.150131i | ||||
\(353\) | −3.99763 | + | 14.9193i | −0.212772 | + | 0.794077i | 0.774167 | + | 0.632982i | \(0.218169\pi\) |
−0.986939 | + | 0.161095i | \(0.948497\pi\) | |||||||
\(354\) | −1.25003 | + | 0.721704i | −0.0664382 | + | 0.0383581i | ||||
\(355\) | 1.41922 | − | 2.25869i | 0.0753244 | − | 0.119879i | ||||
\(356\) | 15.2148i | 0.806383i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.69375 | − | 3.69375i | 0.195221 | − | 0.195221i | ||||
\(359\) | 13.8443 | + | 7.99301i | 0.730674 | + | 0.421855i | 0.818669 | − | 0.574266i | \(-0.194712\pi\) |
−0.0879945 | + | 0.996121i | \(0.528046\pi\) | |||||||
\(360\) | 0.614151 | − | 1.99105i | 0.0323686 | − | 0.104938i | ||||
\(361\) | −16.5534 | − | 28.6713i | −0.871231 | − | 1.50902i | ||||
\(362\) | −0.518847 | − | 1.93636i | −0.0272700 | − | 0.101773i | ||||
\(363\) | −3.45660 | − | 3.45660i | −0.181424 | − | 0.181424i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.97465 | + | 3.20589i | 0.155701 | + | 0.167804i | ||||
\(366\) | 0.839933 | − | 1.45481i | 0.0439040 | − | 0.0760440i | ||||
\(367\) | 0.560120 | + | 0.150084i | 0.0292380 | + | 0.00783431i | 0.273408 | − | 0.961898i | \(-0.411849\pi\) |
−0.244170 | + | 0.969732i | \(0.578516\pi\) | |||||||
\(368\) | −25.8565 | − | 6.92823i | −1.34786 | − | 0.361159i | ||||
\(369\) | −3.81592 | + | 6.60937i | −0.198649 | + | 0.344070i | ||||
\(370\) | −0.00816384 | + | 0.218205i | −0.000424418 | + | 0.0113439i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.78879 | − | 6.78879i | −0.351982 | − | 0.351982i | ||||
\(373\) | −1.26094 | − | 4.70591i | −0.0652892 | − | 0.243663i | 0.925567 | − | 0.378583i | \(-0.123589\pi\) |
−0.990856 | + | 0.134921i | \(0.956922\pi\) | |||||||
\(374\) | 1.11763 | + | 1.93578i | 0.0577911 | + | 0.100097i | ||||
\(375\) | 4.08452 | − | 10.4075i | 0.210924 | − | 0.537443i | ||||
\(376\) | −0.348426 | − | 0.201164i | −0.0179687 | − | 0.0103742i | ||||
\(377\) | −1.82755 | + | 1.82755i | −0.0941237 | + | 0.0941237i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.9179i | − | 0.663547i | −0.943359 | − | 0.331773i | \(-0.892353\pi\) | ||
0.943359 | − | 0.331773i | \(-0.107647\pi\) | |||||||
\(380\) | −26.5713 | − | 16.6957i | −1.36308 | − | 0.856472i | ||||
\(381\) | 7.21175 | − | 4.16371i | 0.369469 | − | 0.213313i | ||||
\(382\) | −0.934923 | + | 3.48918i | −0.0478348 | + | 0.178522i | ||||
\(383\) | −13.7654 | + | 3.68844i | −0.703381 | + | 0.188470i | −0.592744 | − | 0.805391i | \(-0.701956\pi\) |
−0.110636 | + | 0.993861i | \(0.535289\pi\) | |||||||
\(384\) | −7.04142 | −0.359331 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.98291 | 0.151826 | ||||||||
\(387\) | −4.98860 | + | 1.33669i | −0.253585 | + | 0.0679479i | ||||
\(388\) | 5.29212 | − | 19.7504i | 0.268666 | − | 1.00268i | ||||
\(389\) | 21.0704 | − | 12.1650i | 1.06831 | − | 0.616791i | 0.140593 | − | 0.990068i | \(-0.455099\pi\) |
0.927720 | + | 0.373277i | \(0.121766\pi\) | |||||||
\(390\) | −0.0831964 | − | 0.364501i | −0.00421281 | − | 0.0184572i | ||||
\(391\) | 17.3213i | 0.875976i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.3038 | + | 13.3038i | −0.671089 | + | 0.671089i | ||||
\(394\) | −0.777524 | − | 0.448904i | −0.0391711 | − | 0.0226154i | ||||
\(395\) | −17.0813 | + | 9.02780i | −0.859452 | + | 0.454238i | ||||
\(396\) | −3.87478 | − | 6.71132i | −0.194715 | − | 0.337256i | ||||
\(397\) | −2.49129 | − | 9.29762i | −0.125034 | − | 0.466634i | 0.874807 | − | 0.484472i | \(-0.160988\pi\) |
−0.999841 | + | 0.0178380i | \(0.994322\pi\) | |||||||
\(398\) | 0.103013 | + | 0.103013i | 0.00516356 | + | 0.00516356i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.2898 | − | 1.37050i | −0.914492 | − | 0.0685249i | ||||
\(401\) | 4.41545 | − | 7.64778i | 0.220497 | − | 0.381912i | −0.734462 | − | 0.678650i | \(-0.762565\pi\) |
0.954959 | + | 0.296738i | \(0.0958987\pi\) | |||||||
\(402\) | 0.304714 | + | 0.0816479i | 0.0151978 | + | 0.00407223i | ||||
\(403\) | −3.37581 | − | 0.904546i | −0.168161 | − | 0.0450587i | ||||
\(404\) | −6.14006 | + | 10.6349i | −0.305479 | + | 0.529105i | ||||
\(405\) | 2.23450 | + | 0.0836010i | 0.111033 | + | 0.00415417i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.16501 | + | 1.16501i | 0.0577476 | + | 0.0577476i | ||||
\(408\) | 0.572453 | + | 2.13643i | 0.0283407 | + | 0.105769i | ||||
\(409\) | −11.5992 | − | 20.0905i | −0.573546 | − | 0.993410i | −0.996198 | − | 0.0871183i | \(-0.972234\pi\) |
0.422652 | − | 0.906292i | \(-0.361099\pi\) | |||||||
\(410\) | −3.85261 | − | 1.18836i | −0.190267 | − | 0.0586888i | ||||
\(411\) | −0.994464 | − | 0.574154i | −0.0490533 | − | 0.0283209i | ||||
\(412\) | 24.3819 | − | 24.3819i | 1.20121 | − | 1.20121i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.72404i | 0.0847319i | ||||||||
\(415\) | 36.9635 | − | 8.43683i | 1.81447 | − | 0.414148i | ||||
\(416\) | −1.67341 | + | 0.966143i | −0.0820456 | + | 0.0473690i | ||||
\(417\) | −0.114512 | + | 0.427364i | −0.00560766 | + | 0.0209281i | ||||
\(418\) | 6.56610 | − | 1.75938i | 0.321158 | − | 0.0860541i | ||||
\(419\) | −13.0393 | −0.637009 | −0.318505 | − | 0.947921i | \(-0.603181\pi\) | ||||
−0.318505 | + | 0.947921i | \(0.603181\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.3549 | −1.52814 | −0.764071 | − | 0.645132i | \(-0.776802\pi\) | ||||
−0.764071 | + | 0.645132i | \(0.776802\pi\) | |||||||
\(422\) | 2.12422 | − | 0.569183i | 0.103405 | − | 0.0277074i | ||||
\(423\) | 0.111749 | − | 0.417052i | 0.00543341 | − | 0.0202778i | ||||
\(424\) | 6.15877 | − | 3.55577i | 0.299096 | − | 0.172683i | ||||
\(425\) | 2.20650 | + | 11.6611i | 0.107031 | + | 0.565649i | ||||
\(426\) | 0.281842i | 0.0136553i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.5429 | − | 14.5429i | 0.702957 | − | 0.702957i | ||||
\(429\) | −2.44307 | − | 1.41050i | −0.117952 | − | 0.0680998i | ||||
\(430\) | −1.27487 | − | 2.41215i | −0.0614798 | − | 0.116324i | ||||
\(431\) | 11.2779 | + | 19.5339i | 0.543238 | + | 0.940915i | 0.998716 | + | 0.0506681i | \(0.0161351\pi\) |
−0.455478 | + | 0.890247i | \(0.650532\pi\) | |||||||
\(432\) | −0.949406 | − | 3.54323i | −0.0456783 | − | 0.170474i | ||||
\(433\) | 19.9639 | + | 19.9639i | 0.959405 | + | 0.959405i | 0.999208 | − | 0.0398028i | \(-0.0126730\pi\) |
−0.0398028 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.98602 | − | 5.55426i | 0.287008 | − | 0.266306i | ||||
\(436\) | −0.649575 | + | 1.12510i | −0.0311090 | + | 0.0538824i | ||||
\(437\) | 50.8816 | + | 13.6337i | 2.43400 | + | 0.652188i | ||||
\(438\) | −0.446325 | − | 0.119592i | −0.0213262 | − | 0.00571435i | ||||
\(439\) | 15.0972 | − | 26.1490i | 0.720548 | − | 1.24803i | −0.240232 | − | 0.970715i | \(-0.577224\pi\) |
0.960780 | − | 0.277310i | \(-0.0894430\pi\) | |||||||
\(440\) | 6.08824 | − | 5.64910i | 0.290246 | − | 0.269310i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.280632 | + | 0.280632i | 0.0133483 | + | 0.0133483i | ||||
\(443\) | −4.66400 | − | 17.4063i | −0.221593 | − | 0.826997i | −0.983741 | − | 0.179594i | \(-0.942522\pi\) |
0.762148 | − | 0.647403i | \(-0.224145\pi\) | |||||||
\(444\) | 0.401803 | + | 0.695944i | 0.0190687 | + | 0.0330280i | ||||
\(445\) | −8.17681 | − | 15.4711i | −0.387618 | − | 0.733402i | ||||
\(446\) | 0.392082 | + | 0.226369i | 0.0185656 | + | 0.0107189i | ||||
\(447\) | −2.22112 | + | 2.22112i | −0.105056 | + | 0.105056i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4170i | 1.43547i | 0.696318 | + | 0.717734i | \(0.254820\pi\) | ||||
−0.696318 | + | 0.717734i | \(0.745180\pi\) | |||||||
\(450\) | 0.219619 | + | 1.16067i | 0.0103529 | + | 0.0547144i | ||||
\(451\) | −26.3451 | + | 15.2103i | −1.24054 | + | 0.716227i | ||||
\(452\) | 2.41704 | − | 9.02051i | 0.113688 | − | 0.424289i | ||||
\(453\) | −14.2222 | + | 3.81084i | −0.668219 | + | 0.179049i | ||||
\(454\) | 1.38802 | 0.0651432 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.72637 | 0.314991 | ||||||||
\(457\) | −1.79696 | + | 0.481493i | −0.0840581 | + | 0.0225233i | −0.300603 | − | 0.953749i | \(-0.597188\pi\) |
0.216545 | + | 0.976273i | \(0.430521\pi\) | |||||||
\(458\) | 0.794295 | − | 2.96435i | 0.0371150 | − | 0.138515i | ||||
\(459\) | −2.05561 | + | 1.18681i | −0.0959476 | + | 0.0553954i | ||||
\(460\) | 30.9289 | − | 7.05945i | 1.44207 | − | 0.329148i | ||||
\(461\) | 1.29957i | 0.0605272i | 0.999542 | + | 0.0302636i | \(0.00963467\pi\) | ||||
−0.999542 | + | 0.0302636i | \(0.990365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.5240 | − | 16.5240i | 0.767934 | − | 0.767934i | −0.209809 | − | 0.977742i | \(-0.567284\pi\) |
0.977742 | + | 0.209809i | \(0.0672841\pi\) | |||||||
\(464\) | −11.6013 | − | 6.69801i | −0.538577 | − | 0.310947i | ||||
\(465\) | 10.5516 | + | 3.25470i | 0.489320 | + | 0.150933i | ||||
\(466\) | −2.75039 | − | 4.76381i | −0.127409 | − | 0.220679i | ||||
\(467\) | −7.35742 | − | 27.4583i | −0.340461 | − | 1.27062i | −0.897826 | − | 0.440350i | \(-0.854854\pi\) |
0.557365 | − | 0.830267i | \(-0.311812\pi\) | |||||||
\(468\) | −0.972943 | − | 0.972943i | −0.0449743 | − | 0.0449743i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.227932 | + | 0.00852775i | 0.0105137 | + | 0.000393356i | ||||
\(471\) | 5.63216 | − | 9.75519i | 0.259516 | − | 0.449495i | ||||
\(472\) | −5.49908 | − | 1.47347i | −0.253116 | − | 0.0678221i | ||||
\(473\) | −19.8847 | − | 5.32808i | −0.914298 | − | 0.244986i | ||||
\(474\) | 1.02064 | − | 1.76781i | 0.0468797 | − | 0.0811980i | ||||
\(475\) | 35.9916 | + | 2.69693i | 1.65141 | + | 0.123744i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.39653 | + | 5.39653i | 0.247090 | + | 0.247090i | ||||
\(478\) | 0.335113 | + | 1.25066i | 0.0153277 | + | 0.0572038i | ||||
\(479\) | −5.54182 | − | 9.59872i | −0.253212 | − | 0.438577i | 0.711196 | − | 0.702994i | \(-0.248154\pi\) |
−0.964408 | + | 0.264417i | \(0.914820\pi\) | |||||||
\(480\) | 5.39759 | − | 2.85273i | 0.246365 | − | 0.130209i | ||||
\(481\) | 0.253339 | + | 0.146265i | 0.0115513 | + | 0.00666912i | ||||
\(482\) | 2.44749 | − | 2.44749i | 0.111480 | − | 0.111480i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 9.50389i | − | 0.431995i | ||||||
\(485\) | 5.23309 | + | 22.9273i | 0.237623 | + | 1.04107i | ||||
\(486\) | −0.204601 | + | 0.118126i | −0.00928088 | + | 0.00535832i | ||||
\(487\) | −4.99695 | + | 18.6489i | −0.226433 | + | 0.845060i | 0.755392 | + | 0.655273i | \(0.227446\pi\) |
−0.981825 | + | 0.189787i | \(0.939220\pi\) | |||||||
\(488\) | 6.39994 | − | 1.71486i | 0.289712 | − | 0.0776280i | ||||
\(489\) | −14.7714 | −0.667986 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1155 | 1.44935 | 0.724677 | − | 0.689089i | \(-0.241989\pi\) | ||||
0.724677 | + | 0.689089i | \(0.241989\pi\) | |||||||
\(492\) | −14.3321 | + | 3.84028i | −0.646142 | + | 0.173133i | ||||
\(493\) | −2.24350 | + | 8.37286i | −0.101042 | + | 0.377095i | ||||
\(494\) | 1.04525 | − | 0.603474i | 0.0470279 | − | 0.0271516i | ||||
\(495\) | 7.54688 | + | 4.74198i | 0.339207 | + | 0.213136i | ||||
\(496\) | − | 18.1145i | − | 0.813364i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.83255 | + | 2.83255i | −0.126930 | + | 0.126930i | ||||
\(499\) | −3.70166 | − | 2.13715i | −0.165709 | − | 0.0956722i | 0.414852 | − | 0.909889i | \(-0.363833\pi\) |
−0.580561 | + | 0.814217i | \(0.697167\pi\) | |||||||
\(500\) | 19.9229 | − | 8.69253i | 0.890979 | − | 0.388742i | ||||
\(501\) | −3.27830 | − | 5.67818i | −0.146463 | − | 0.253682i | ||||
\(502\) | −1.29329 | − | 4.82662i | −0.0577223 | − | 0.215423i | ||||
\(503\) | −17.5637 | − | 17.5637i | −0.783128 | − | 0.783128i | 0.197229 | − | 0.980357i | \(-0.436806\pi\) |
−0.980357 | + | 0.197229i | \(0.936806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.528051 | − | 14.1139i | 0.0234980 | − | 0.628059i | ||||
\(506\) | −3.43603 | + | 5.95138i | −0.152750 | + | 0.264571i | ||||
\(507\) | 12.0732 | + | 3.23501i | 0.536191 | + | 0.143672i | ||||
\(508\) | 15.6384 | + | 4.19029i | 0.693840 | + | 0.185914i | ||||
\(509\) | −13.9581 | + | 24.1762i | −0.618682 | + | 1.07159i | 0.371044 | + | 0.928615i | \(0.379000\pi\) |
−0.989726 | + | 0.142974i | \(0.954333\pi\) | |||||||
\(510\) | −0.852889 | − | 0.919189i | −0.0377666 | − | 0.0407024i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.9158 | − | 11.9158i | −0.526611 | − | 0.526611i | ||||
\(513\) | 1.86829 | + | 6.97254i | 0.0824868 | + | 0.307845i | ||||
\(514\) | 1.56907 | + | 2.71771i | 0.0692086 | + | 0.119873i | ||||
\(515\) | −11.6893 | + | 37.8961i | −0.515090 | + | 1.66990i | ||||
\(516\) | −8.69567 | − | 5.02045i | −0.382806 | − | 0.221013i | ||||
\(517\) | 1.21695 | − | 1.21695i | 0.0535212 | − | 0.0535212i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.51476i | − | 0.154281i | ||||||
\(520\) | 0.784547 | − | 1.24861i | 0.0344047 | − | 0.0547552i | ||||
\(521\) | −24.9975 | + | 14.4323i | −1.09516 | + | 0.632292i | −0.934946 | − | 0.354790i | \(-0.884552\pi\) |
−0.160216 | + | 0.987082i | \(0.551219\pi\) | |||||||
\(522\) | −0.223302 | + | 0.833375i | −0.00977367 | + | 0.0364758i | ||||
\(523\) | −4.84539 | + | 1.29832i | −0.211874 | + | 0.0567715i | −0.363195 | − | 0.931713i | \(-0.618314\pi\) |
0.151321 | + | 0.988485i | \(0.451647\pi\) | |||||||
\(524\) | −36.5788 | −1.59795 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.13793 | −0.224024 | ||||||||
\(527\) | −11.3220 | + | 3.03372i | −0.493195 | + | 0.132151i | ||||
\(528\) | 3.78435 | − | 14.1234i | 0.164693 | − | 0.614642i | ||||
\(529\) | −26.1995 | + | 15.1263i | −1.13911 | + | 0.657665i | ||||
\(530\) | −2.14499 | + | 3.41377i | −0.0931726 | + | 0.148285i | ||||
\(531\) | − | 6.10959i | − | 0.265134i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.81926 | + | 3.81926i | −0.165430 | + | 0.165430i | ||||
\(534\) | 1.60117 | + | 0.924434i | 0.0692892 | + | 0.0400042i | ||||
\(535\) | −6.97219 | + | 22.6036i | −0.301434 | + | 0.977239i | ||||
\(536\) | 0.622122 | + | 1.07755i | 0.0268716 | + | 0.0465430i | ||||
\(537\) | 5.72271 | + | 21.3574i | 0.246953 | + | 0.921642i | ||||
\(538\) | −3.83980 | − | 3.83980i | −0.165546 | − | 0.165546i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.95695 | + | 3.18681i | 0.127247 | + | 0.137138i | ||||
\(541\) | 2.04349 | − | 3.53943i | 0.0878565 | − | 0.152172i | −0.818748 | − | 0.574153i | \(-0.805332\pi\) |
0.906605 | + | 0.421981i | \(0.138665\pi\) | |||||||
\(542\) | 3.59639 | + | 0.963650i | 0.154478 | + | 0.0413923i | ||||
\(543\) | 8.19615 | + | 2.19615i | 0.351731 | + | 0.0942459i | ||||
\(544\) | −3.24031 | + | 5.61238i | −0.138927 | + | 0.240629i | ||||
\(545\) | 0.0558641 | − | 1.49315i | 0.00239296 | − | 0.0639594i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2200 | + | 28.2200i | 1.20660 | + | 1.20660i | 0.972121 | + | 0.234482i | \(0.0753392\pi\) |
0.234482 | + | 0.972121i | \(0.424661\pi\) | |||||||
\(548\) | −0.577820 | − | 2.15645i | −0.0246832 | − | 0.0921191i | ||||
\(549\) | 3.55523 | + | 6.15784i | 0.151734 | + | 0.262810i | ||||
\(550\) | −1.55510 | + | 4.44433i | −0.0663097 | + | 0.189507i | ||||
\(551\) | 22.8296 | + | 13.1807i | 0.972572 | + | 0.561515i | ||||
\(552\) | −4.80827 | + | 4.80827i | −0.204654 | + | 0.204654i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 1.60631i | − | 0.0682457i | ||||||
\(555\) | −0.782590 | − | 0.491730i | −0.0332191 | − | 0.0208728i | ||||
\(556\) | −0.744941 | + | 0.430092i | −0.0315925 | + | 0.0182400i | ||||
\(557\) | 10.3079 | − | 38.4695i | 0.436758 | − | 1.63000i | −0.300065 | − | 0.953919i | \(-0.597008\pi\) |
0.736823 | − | 0.676086i | \(-0.236325\pi\) | |||||||
\(558\) | −1.12691 | + | 0.301955i | −0.0477060 | + | 0.0127828i | ||||
\(559\) | −3.65510 | −0.154594 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.46128 | −0.399455 | ||||||||
\(562\) | −2.20366 | + | 0.590468i | −0.0929556 | + | 0.0249074i | ||||
\(563\) | 10.0161 | − | 37.3806i | 0.422129 | − | 1.57541i | −0.347985 | − | 0.937500i | \(-0.613134\pi\) |
0.770114 | − | 0.637906i | \(-0.220199\pi\) | |||||||
\(564\) | 0.726967 | − | 0.419715i | 0.0306108 | − | 0.0176732i | ||||
\(565\) | 2.39008 | + | 10.4715i | 0.100552 | + | 0.440537i | ||||
\(566\) | 4.98144i | 0.209386i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.786047 | + | 0.786047i | −0.0329818 | + | 0.0329818i | ||||
\(569\) | 15.3951 | + | 8.88837i | 0.645396 | + | 0.372620i | 0.786690 | − | 0.617348i | \(-0.211793\pi\) |
−0.141294 | + | 0.989968i | \(0.545126\pi\) | |||||||
\(570\) | −3.37145 | + | 1.78188i | −0.141215 | + | 0.0746347i | ||||
\(571\) | 8.44331 | + | 14.6242i | 0.353342 | + | 0.612005i | 0.986833 | − | 0.161744i | \(-0.0517120\pi\) |
−0.633491 | + | 0.773750i | \(0.718379\pi\) | |||||||
\(572\) | −1.41951 | − | 5.29768i | −0.0593527 | − | 0.221507i | ||||
\(573\) | −10.8116 | − | 10.8116i | −0.451659 | − | 0.451659i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.6561 | + | 23.8003i | −1.15334 | + | 0.992543i | ||||
\(576\) | 3.34571 | − | 5.79493i | 0.139404 | − | 0.241456i | ||||
\(577\) | 5.32309 | + | 1.42632i | 0.221603 | + | 0.0593784i | 0.367912 | − | 0.929861i | \(-0.380073\pi\) |
−0.146309 | + | 0.989239i | \(0.546739\pi\) | |||||||
\(578\) | −2.59374 | − | 0.694991i | −0.107885 | − | 0.0289078i | ||||
\(579\) | −6.31296 | + | 10.9344i | −0.262358 | + | 0.454417i | ||||
\(580\) | 15.8650 | + | 0.593566i | 0.658756 | + | 0.0246465i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.75694 | − | 1.75694i | −0.0728276 | − | 0.0728276i | ||||
\(583\) | 7.87345 | + | 29.3841i | 0.326085 | + | 1.21697i | ||||
\(584\) | −0.911244 | − | 1.57832i | −0.0377075 | − | 0.0653114i | ||||
\(585\) | 1.51222 | + | 0.466451i | 0.0625225 | + | 0.0192854i | ||||
\(586\) | −1.38667 | − | 0.800592i | −0.0572826 | − | 0.0330721i | ||||
\(587\) | 15.1058 | − | 15.1058i | 0.623484 | − | 0.623484i | −0.322937 | − | 0.946420i | \(-0.604670\pi\) |
0.946420 | + | 0.322937i | \(0.104670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6465i | 1.46879i | ||||||||
\(590\) | 3.14663 | − | 0.718211i | 0.129545 | − | 0.0295683i | ||||
\(591\) | 3.29107 | − | 1.90010i | 0.135377 | − | 0.0781597i | ||||
\(592\) | −0.392426 | + | 1.46456i | −0.0161286 | + | 0.0601928i | ||||
\(593\) | −4.68590 | + | 1.25558i | −0.192427 | + | 0.0515606i | −0.353745 | − | 0.935342i | \(-0.615092\pi\) |
0.161318 | + | 0.986902i | \(0.448425\pi\) | |||||||
\(594\) | −0.941708 | −0.0386388 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.10696 | −0.250151 | ||||||||
\(597\) | −0.595625 | + | 0.159597i | −0.0243773 | + | 0.00653188i | ||||
\(598\) | −0.315797 | + | 1.17857i | −0.0129139 | + | 0.0481953i | ||||
\(599\) | 8.74769 | − | 5.05048i | 0.357421 | − | 0.206357i | −0.310528 | − | 0.950564i | \(-0.600506\pi\) |
0.667949 | + | 0.744207i | \(0.267173\pi\) | |||||||
\(600\) | −2.62455 | + | 3.84957i | −0.107147 | + | 0.157158i | ||||
\(601\) | 38.4063i | 1.56663i | 0.621628 | + | 0.783313i | \(0.286472\pi\) | ||||
−0.621628 | + | 0.783313i | \(0.713528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.944185 | + | 0.944185i | −0.0384502 | + | 0.0384502i | ||||
\(604\) | −24.7909 | − | 14.3130i | −1.00873 | − | 0.582389i | ||||
\(605\) | 5.10762 | + | 9.66400i | 0.207654 | + | 0.392898i | ||||
\(606\) | 0.746125 | + | 1.29233i | 0.0303093 | + | 0.0524972i | ||||
\(607\) | −3.76752 | − | 14.0606i | −0.152919 | − | 0.570702i | −0.999275 | − | 0.0380833i | \(-0.987875\pi\) |
0.846356 | − | 0.532618i | \(-0.178792\pi\) | |||||||
\(608\) | 13.9360 | + | 13.9360i | 0.565180 | + | 0.565180i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.75355 | + | 2.55494i | −0.111488 | + | 0.103447i | ||||
\(611\) | 0.152785 | − | 0.264632i | 0.00618103 | − | 0.0107059i | ||||
\(612\) | −4.45750 | − | 1.19438i | −0.180184 | − | 0.0482801i | ||||
\(613\) | 19.6919 | + | 5.27642i | 0.795347 | + | 0.213113i | 0.633540 | − | 0.773710i | \(-0.281601\pi\) |
0.161807 | + | 0.986822i | \(0.448268\pi\) | |||||||
\(614\) | −1.64560 | + | 2.85027i | −0.0664112 | + | 0.115028i | ||||
\(615\) | 12.5097 | − | 11.6074i | 0.504440 | − | 0.468056i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4196 | − | 25.4196i | −1.02336 | − | 1.02336i | −0.999721 | − | 0.0236346i | \(-0.992476\pi\) |
−0.0236346 | − | 0.999721i | \(-0.507524\pi\) | |||||||
\(618\) | −1.08447 | − | 4.04731i | −0.0436239 | − | 0.162807i | ||||
\(619\) | −5.59953 | − | 9.69868i | −0.225064 | − | 0.389823i | 0.731274 | − | 0.682083i | \(-0.238926\pi\) |
−0.956339 | + | 0.292261i | \(0.905593\pi\) | |||||||
\(620\) | 10.0314 | + | 18.9802i | 0.402871 | + | 0.762262i | ||||
\(621\) | −6.31977 | − | 3.64872i | −0.253603 | − | 0.146418i | ||||
\(622\) | 4.56168 | − | 4.56168i | 0.182907 | − | 0.182907i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 2.59609i | − | 0.103927i | ||||||
\(625\) | −15.5870 | + | 19.5460i | −0.623478 | + | 0.781841i | ||||
\(626\) | 5.35527 | − | 3.09186i | 0.214040 | − | 0.123576i | ||||
\(627\) | −7.44703 | + | 27.7927i | −0.297406 | + | 1.10993i | ||||
\(628\) | 21.1537 | − | 5.66812i | 0.844124 | − | 0.226182i | ||||
\(629\) | 0.981107 | 0.0391193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.2015 | 0.844020 | 0.422010 | − | 0.906591i | \(-0.361325\pi\) | ||||
0.422010 | + | 0.906591i | \(0.361325\pi\) | |||||||
\(632\) | 7.77687 | − | 2.08381i | 0.309347 | − | 0.0828894i | ||||
\(633\) | −2.40921 | + | 8.99131i | −0.0957577 | + | 0.357373i | ||||
\(634\) | 6.33077 | − | 3.65507i | 0.251427 | − | 0.145161i | ||||
\(635\) | −18.1538 | + | 4.14355i | −0.720411 | + | 0.164432i | ||||
\(636\) | 14.8377i | 0.588353i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.43176 | + | 2.43176i | −0.0962745 | + | 0.0962745i | ||||
\(639\) | −1.03314 | − | 0.596485i | −0.0408705 | − | 0.0235966i | ||||
\(640\) | 15.0456 | + | 4.64089i | 0.594729 | + | 0.183447i | ||||
\(641\) | 14.9484 | + | 25.8915i | 0.590428 | + | 1.02265i | 0.994175 | + | 0.107781i | \(0.0343745\pi\) |
−0.403746 | + | 0.914871i | \(0.632292\pi\) | |||||||
\(642\) | −0.646846 | − | 2.41406i | −0.0255290 | − | 0.0952755i | ||||
\(643\) | −11.2813 | − | 11.2813i | −0.444891 | − | 0.444891i | 0.448761 | − | 0.893652i | \(-0.351866\pi\) |
−0.893652 | + | 0.448761i | \(0.851866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5403 | + | 0.431764i | 0.454398 | + | 0.0170007i | ||||
\(646\) | 2.02397 | − | 3.50562i | 0.0796320 | − | 0.137927i | ||||
\(647\) | −35.8439 | − | 9.60434i | −1.40917 | − | 0.377586i | −0.527540 | − | 0.849530i | \(-0.676886\pi\) |
−0.881628 | + | 0.471944i | \(0.843552\pi\) | |||||||
\(648\) | −0.900073 | − | 0.241174i | −0.0353582 | − | 0.00947420i | ||||
\(649\) | 12.1765 | − | 21.0903i | 0.477969 | − | 0.827866i | ||||
\(650\) | −0.0624689 | + | 0.833673i | −0.00245023 | + | 0.0326993i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.3069 | − | 20.3069i | −0.795281 | − | 0.795281i | ||||
\(653\) | −0.723414 | − | 2.69982i | −0.0283094 | − | 0.105652i | 0.950326 | − | 0.311258i | \(-0.100750\pi\) |
−0.978635 | + | 0.205606i | \(0.934084\pi\) | |||||||
\(654\) | 0.0789348 | + | 0.136719i | 0.00308659 | + | 0.00534614i | ||||
\(655\) | 37.1950 | − | 19.6583i | 1.45333 | − | 0.768113i | ||||
\(656\) | −24.2446 | − | 13.9976i | −0.946594 | − | 0.546516i | ||||
\(657\) | 1.38298 | − | 1.38298i | 0.0539552 | − | 0.0539552i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 15.1044i | − | 0.588385i | −0.955746 | − | 0.294193i | \(-0.904949\pi\) | ||
0.955746 | − | 0.294193i | \(-0.0950507\pi\) | |||||||
\(660\) | 3.85603 | + | 16.8941i | 0.150096 | + | 0.657601i | ||||
\(661\) | 0.953098 | − | 0.550272i | 0.0370712 | − | 0.0214031i | −0.481350 | − | 0.876529i | \(-0.659853\pi\) |
0.518421 | + | 0.855125i | \(0.326520\pi\) | |||||||
\(662\) | 1.02062 | − | 3.80900i | 0.0396675 | − | 0.148041i | ||||
\(663\) | −1.62263 | + | 0.434781i | −0.0630176 | + | 0.0168855i | ||||
\(664\) | −15.7998 | −0.613150 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0976524 | 0.00378395 | ||||||||
\(667\) | −25.7415 | + | 6.89742i | −0.996716 | + | 0.267069i | ||||
\(668\) | 3.29923 | − | 12.3129i | 0.127651 | − | 0.476399i | ||||
\(669\) | −1.65959 | + | 0.958163i | −0.0641633 | + | 0.0370447i | ||||
\(670\) | −0.597278 | − | 0.375292i | −0.0230749 | − | 0.0144988i | ||||
\(671\) | 28.3425i | 1.09415i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.4381 | + | 11.4381i | −0.440906 | + | 0.440906i | −0.892316 | − | 0.451411i | \(-0.850921\pi\) |
0.451411 | + | 0.892316i | \(0.350921\pi\) | |||||||
\(674\) | 0.735028 | + | 0.424369i | 0.0283122 | + | 0.0163461i | ||||
\(675\) | −4.71943 | − | 1.65136i | −0.181651 | − | 0.0635609i | ||||
\(676\) | 12.1503 | + | 21.0449i | 0.467319 | + | 0.809421i | ||||
\(677\) | 9.00447 | + | 33.6052i | 0.346070 | + | 1.29155i | 0.891357 | + | 0.453302i | \(0.149754\pi\) |
−0.545287 | + | 0.838249i | \(0.683579\pi\) | |||||||
\(678\) | −0.802438 | − | 0.802438i | −0.0308175 | − | 0.0308175i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.184908 | − | 4.94226i | 0.00709089 | − | 0.189527i | ||||
\(681\) | −2.93759 | + | 5.08805i | −0.112569 | + | 0.194974i | ||||
\(682\) | −4.49190 | − | 1.20360i | −0.172004 | − | 0.0460882i | ||||
\(683\) | 18.9404 | + | 5.07507i | 0.724736 | + | 0.194192i | 0.602284 | − | 0.798282i | \(-0.294258\pi\) |
0.122452 | + | 0.992474i | \(0.460924\pi\) | |||||||
\(684\) | −7.01705 | + | 12.1539i | −0.268304 | + | 0.464715i | ||||
\(685\) | 1.74648 | + | 1.88225i | 0.0667297 | + | 0.0719170i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.18531 | + | 9.18531i | 0.350442 | + | 0.350442i | ||||
\(688\) | −4.90328 | − | 18.2993i | −0.186936 | − | 0.697655i | ||||
\(689\) | 2.70062 | + | 4.67762i | 0.102886 | + | 0.178203i | ||||
\(690\) | 1.13629 | − | 3.68380i | 0.0432577 | − | 0.140240i | ||||
\(691\) | −10.7439 | − | 6.20301i | −0.408718 | − | 0.235974i | 0.281521 | − | 0.959555i | \(-0.409161\pi\) |
−0.690239 | + | 0.723582i | \(0.742495\pi\) | |||||||
\(692\) | 4.83190 | − | 4.83190i | 0.183681 | − | 0.183681i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 4.57667i | − | 0.173728i | ||||||
\(695\) | 0.526349 | − | 0.837687i | 0.0199656 | − | 0.0317753i | ||||
\(696\) | −2.94703 | + | 1.70147i | −0.111707 | + | 0.0644940i | ||||
\(697\) | −4.68852 | + | 17.4978i | −0.177590 | + | 0.662776i | ||||
\(698\) | −0.116064 | + | 0.0310993i | −0.00439309 | + | 0.00117713i | ||||
\(699\) | 23.2835 | 0.880661 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.45193 | 0.0548388 | 0.0274194 | − | 0.999624i | \(-0.491271\pi\) | ||||
0.0274194 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(702\) | −0.161505 | + | 0.0432751i | −0.00609560 | + | 0.00163331i | ||||
\(703\) | 0.772235 | − | 2.88202i | 0.0291254 | − | 0.108697i | ||||
\(704\) | 23.0987 | − | 13.3361i | 0.870566 | − | 0.502622i | ||||
\(705\) | −0.513649 | + | 0.817475i | −0.0193452 | + | 0.0307879i | ||||
\(706\) | 3.64907i | 0.137335i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.39914 | − | 8.39914i | 0.315659 | − | 0.315659i | ||||
\(709\) | 42.0269 | + | 24.2642i | 1.57835 | + | 0.911262i | 0.995090 | + | 0.0989781i | \(0.0315574\pi\) |
0.583262 | + | 0.812284i | \(0.301776\pi\) | |||||||
\(710\) | 0.185758 | − | 0.602220i | 0.00697137 | − | 0.0226009i | ||||
\(711\) | 4.32013 | + | 7.48269i | 0.162018 | + | 0.280623i | ||||
\(712\) | 1.88738 | + | 7.04380i | 0.0707325 | + | 0.263977i | ||||
\(713\) | −25.4815 | − | 25.4815i | −0.954290 | − | 0.954290i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.29052 | + | 4.62405i | 0.160457 | + | 0.172930i | ||||
\(716\) | −21.4938 | + | 37.2283i | −0.803261 | + | 1.39129i | ||||
\(717\) | −5.29373 | − | 1.41845i | −0.197698 | − | 0.0529730i | ||||
\(718\) | 3.64805 | + | 0.977492i | 0.136144 | + | 0.0364797i | ||||
\(719\) | 21.7936 | − | 37.7476i | 0.812764 | − | 1.40775i | −0.0981578 | − | 0.995171i | \(-0.531295\pi\) |
0.910922 | − | 0.412578i | \(-0.135372\pi\) | |||||||
\(720\) | −0.306667 | + | 8.19666i | −0.0114288 | + | 0.305472i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.53068 | − | 5.53068i | −0.205831 | − | 0.205831i | ||||
\(723\) | 3.79189 | + | 14.1515i | 0.141022 | + | 0.526301i | ||||
\(724\) | 8.24848 | + | 14.2868i | 0.306552 | + | 0.530964i | ||||
\(725\) | −16.4512 | + | 7.92264i | −0.610983 | + | 0.294240i | ||||
\(726\) | −1.00016 | − | 0.577445i | −0.0371196 | − | 0.0214310i | ||||
\(727\) | −10.4498 | + | 10.4498i | −0.387563 | + | 0.387563i | −0.873817 | − | 0.486254i | \(-0.838363\pi\) |
0.486254 | + | 0.873817i | \(0.338363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0.874853 | + | 0.549702i | 0.0323798 | + | 0.0203454i | ||||
\(731\) | −10.6164 | + | 6.12936i | −0.392660 | + | 0.226703i | ||||
\(732\) | −3.57793 | + | 13.3530i | −0.132244 | + | 0.493542i | ||||
\(733\) | 25.7752 | − | 6.90644i | 0.952028 | − | 0.255095i | 0.250806 | − | 0.968037i | \(-0.419305\pi\) |
0.701223 | + | 0.712942i | \(0.252638\pi\) | |||||||
\(734\) | 0.136998 | 0.00505669 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.9240 | −0.734409 | ||||||||
\(737\) | −5.14109 | + | 1.37755i | −0.189375 | + | 0.0507428i | ||||
\(738\) | −0.466662 | + | 1.74161i | −0.0171781 | + | 0.0641094i | ||||
\(739\) | 18.1596 | − | 10.4845i | 0.668013 | − | 0.385677i | −0.127311 | − | 0.991863i | \(-0.540634\pi\) |
0.795323 | + | 0.606186i | \(0.207301\pi\) | |||||||
\(740\) | −0.399859 | − | 1.75187i | −0.0146991 | − | 0.0643999i | ||||
\(741\) | 5.10872i | 0.187673i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.18724 | − | 9.18724i | 0.337047 | − | 0.337047i | −0.518208 | − | 0.855255i | \(-0.673401\pi\) |
0.855255 | + | 0.518208i | \(0.173401\pi\) | |||||||
\(744\) | −3.98506 | − | 2.30077i | −0.146099 | − | 0.0843504i | ||||
\(745\) | 6.20984 | − | 3.28203i | 0.227511 | − | 0.120244i | ||||
\(746\) | −0.575501 | − | 0.996797i | −0.0210706 | − | 0.0364953i | ||||
\(747\) | −4.38847 | − | 16.3780i | −0.160566 | − | 0.599239i | ||||
\(748\) | −13.0069 | − | 13.0069i | −0.475578 | − | 0.475578i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.295712 | − | 2.62478i | 0.0107979 | − | 0.0958434i | ||||
\(751\) | −5.59843 | + | 9.69676i | −0.204290 | + | 0.353840i | −0.949906 | − | 0.312535i | \(-0.898822\pi\) |
0.745617 | + | 0.666375i | \(0.232155\pi\) | |||||||
\(752\) | 1.52984 | + | 0.409919i | 0.0557875 | + | 0.0149482i | ||||
\(753\) | 20.4299 | + | 5.47418i | 0.744507 | + | 0.199490i | ||||
\(754\) | −0.305303 | + | 0.528801i | −0.0111185 | + | 0.0192578i | ||||
\(755\) | 32.9007 | + | 1.23094i | 1.19738 | + | 0.0447984i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9324 | − | 13.9324i | −0.506383 | − | 0.506383i | 0.407031 | − | 0.913414i | \(-0.366564\pi\) |
−0.913414 | + | 0.407031i | \(0.866564\pi\) | |||||||
\(758\) | −0.789886 | − | 2.94789i | −0.0286899 | − | 0.107072i | ||||
\(759\) | −14.5439 | − | 25.1907i | −0.527909 | − | 0.914365i | ||||
\(760\) | −14.3724 | − | 4.43325i | −0.521343 | − | 0.160811i | ||||
\(761\) | −7.61085 | − | 4.39412i | −0.275893 | − | 0.159287i | 0.355670 | − | 0.934612i | \(-0.384253\pi\) |
−0.631563 | + | 0.775325i | \(0.717586\pi\) | |||||||
\(762\) | 1.39114 | − | 1.39114i | 0.0503958 | − | 0.0503958i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 29.7263i | − | 1.07546i | ||||||
\(765\) | 5.17449 | − | 1.18106i | 0.187084 | − | 0.0427014i | ||||
\(766\) | −2.91577 | + | 1.68342i | −0.105351 | + | 0.0608245i | ||||
\(767\) | 1.11911 | − | 4.17658i | 0.0404088 | − | 0.150808i | ||||
\(768\) | 11.3199 | − | 3.03317i | 0.408473 | − | 0.109450i | ||||
\(769\) | 11.2183 | 0.404543 | 0.202271 | − | 0.979330i | \(-0.435168\pi\) | ||||
0.202271 | + | 0.979330i | \(0.435168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.2830 | −0.478374 | ||||||||
\(772\) | −23.7107 | + | 6.35326i | −0.853366 | + | 0.228659i | ||||
\(773\) | −7.87192 | + | 29.3784i | −0.283133 | + | 1.05667i | 0.667059 | + | 0.745005i | \(0.267553\pi\) |
−0.950193 | + | 0.311663i | \(0.899114\pi\) | |||||||
\(774\) | −1.05668 | + | 0.610073i | −0.0379815 | + | 0.0219286i | ||||
\(775\) | −20.4008 | − | 13.9088i | −0.732819 | − | 0.499620i | ||||
\(776\) | − | 9.80008i | − | 0.351802i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.06447 | − | 4.06447i | 0.145718 | − | 0.145718i | ||||
\(779\) | 47.7097 | + | 27.5452i | 1.70938 | + | 0.986910i | ||||
\(780\) | 1.43766 | + | 2.72017i | 0.0514766 | + | 0.0973976i | ||||
\(781\) | −2.37760 | − | 4.11813i | −0.0850773 | − | 0.147358i | ||||
\(782\) | 1.05914 | + | 3.95276i | 0.0378748 | + | 0.141351i | ||||
\(783\) | −2.58229 | − | 2.58229i | −0.0922835 | − | 0.0922835i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.4639 | + | 17.1321i | −0.659004 | + | 0.611471i | ||||
\(786\) | −2.22248 | + | 3.84945i | −0.0792733 | + | 0.137305i | ||||
\(787\) | 51.1813 | + | 13.7140i | 1.82442 | + | 0.488851i | 0.997317 | − | 0.0732040i | \(-0.0233224\pi\) |
0.827100 | + | 0.562055i | \(0.189989\pi\) | |||||||
\(788\) | 7.13654 | + | 1.91223i | 0.254229 | + | 0.0681204i | ||||
\(789\) | 10.8738 | − | 18.8340i | 0.387118 | − | 0.670507i | ||||
\(790\) | −3.34597 | + | 3.10463i | −0.119044 | + | 0.110458i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.62639 | − | 2.62639i | −0.0933246 | − | 0.0933246i | ||||
\(793\) | 1.30244 | + | 4.86079i | 0.0462511 | + | 0.172612i | ||||
\(794\) | −1.13704 | − | 1.96941i | −0.0403520 | − | 0.0698916i | ||||
\(795\) | −7.97414 | − | 15.0877i | −0.282814 | − | 0.535105i | ||||
\(796\) | −1.03824 | − | 0.599428i | −0.0367994 | − | 0.0212462i | ||||
\(797\) | −6.96365 | + | 6.96365i | −0.246665 | + | 0.246665i | −0.819601 | − | 0.572935i | \(-0.805805\pi\) |
0.572935 | + | 0.819601i | \(0.305805\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.02484i | − | 0.0362563i | ||||||
\(800\) | −13.4134 | + | 2.53805i | −0.474234 | + | 0.0897336i | ||||
\(801\) | −6.77735 | + | 3.91290i | −0.239466 | + | 0.138256i | ||||
\(802\) | 0.539980 | − | 2.01523i | 0.0190674 | − | 0.0711604i | ||||
\(803\) | 7.53033 | − | 2.01775i | 0.265740 | − | 0.0712047i | ||||
\(804\) | −2.59603 | −0.0915549 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.825679 | −0.0290833 | ||||||||
\(807\) | 22.2019 | − | 5.94899i | 0.781545 | − | 0.209414i | ||||
\(808\) | −1.52333 | + | 5.68516i | −0.0535907 | + | 0.200003i | ||||
\(809\) | −36.5817 | + | 21.1205i | −1.28614 | + | 0.742556i | −0.977964 | − | 0.208772i | \(-0.933053\pi\) |
−0.308180 | + | 0.951328i | \(0.599720\pi\) | |||||||
\(810\) | 0.515032 | − | 0.117555i | 0.0180964 | − | 0.00413045i | ||||
\(811\) | 34.9480i | 1.22719i | 0.789620 | + | 0.613596i | \(0.210277\pi\) | ||||
−0.789620 | + | 0.613596i | \(0.789723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.1438 | + | 11.1438i | −0.390828 | + | 0.390828i | ||||
\(814\) | 0.337096 | + | 0.194622i | 0.0118152 | + | 0.00682151i | ||||
\(815\) | 31.5625 | + | 9.73561i | 1.10559 | + | 0.341023i | ||||
\(816\) | −4.35347 | − | 7.54044i | −0.152402 | − | 0.263968i | ||||
\(817\) | 9.64891 | + | 36.0102i | 0.337573 | + | 1.25984i | ||||
\(818\) | −3.87544 | − | 3.87544i | −0.135502 | − | 0.135502i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 33.1549 | + | 1.24045i | 1.15782 | + | 0.0433183i | ||||
\(821\) | 2.06708 | − | 3.58030i | 0.0721418 | − | 0.124953i | −0.827698 | − | 0.561174i | \(-0.810350\pi\) |
0.899840 | + | 0.436221i | \(0.143683\pi\) | |||||||
\(822\) | −0.262047 | − | 0.0702153i | −0.00913994 | − | 0.00244904i | ||||
\(823\) | 7.81506 | + | 2.09404i | 0.272416 | + | 0.0729936i | 0.392441 | − | 0.919777i | \(-0.371631\pi\) |
−0.120025 | + | 0.992771i | \(0.538297\pi\) | |||||||
\(824\) | 8.26322 | − | 14.3123i | 0.287863 | − | 0.498593i | ||||
\(825\) | −13.0003 | − | 15.1064i | −0.452611 | − | 0.525936i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0630 | + | 17.0630i | 0.593339 | + | 0.593339i | 0.938532 | − | 0.345193i | \(-0.112187\pi\) |
−0.345193 | + | 0.938532i | \(0.612187\pi\) | |||||||
\(828\) | −3.67201 | − | 13.7041i | −0.127611 | − | 0.476252i | ||||
\(829\) | −18.8573 | − | 32.6618i | −0.654940 | − | 1.13439i | −0.981909 | − | 0.189355i | \(-0.939360\pi\) |
0.326968 | − | 0.945035i | \(-0.393973\pi\) | |||||||
\(830\) | 7.91929 | − | 4.18550i | 0.274883 | − | 0.145281i | ||||
\(831\) | 5.88822 | + | 3.39957i | 0.204260 | + | 0.117930i | ||||
\(832\) | 3.34863 | − | 3.34863i | 0.116093 | − | 0.116093i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.104527i | 0.00361949i | ||||||||
\(835\) | 3.26243 | + | 14.2934i | 0.112901 | + | 0.494643i | ||||
\(836\) | −48.4457 | + | 27.9701i | −1.67553 | + | 0.967367i | ||||
\(837\) | 1.27810 | − | 4.76995i | 0.0441777 | − | 0.164873i | ||||
\(838\) | −2.97559 | + | 0.797307i | −0.102790 | + | 0.0275425i | ||||
\(839\) | −22.3652 | −0.772133 | −0.386066 | − | 0.922471i | \(-0.626166\pi\) | ||||
−0.386066 | + | 0.922471i | \(0.626166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6636 | 0.540123 | ||||||||
\(842\) | −7.15526 | + | 1.91725i | −0.246587 | + | 0.0660727i | ||||
\(843\) | 2.49931 | − | 9.32754i | 0.0860807 | − | 0.321258i | ||||
\(844\) | −15.6728 | + | 9.04871i | −0.539481 | + | 0.311470i | ||||
\(845\) | −23.6651 | − | 14.8696i | −0.814103 | − | 0.511530i | ||||
\(846\) | − | 0.102005i | − | 0.00350702i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.7957 | + | 19.7957i | −0.679786 | + | 0.679786i | ||||
\(849\) | −18.2603 | − | 10.5426i | −0.626693 | − | 0.361822i | ||||
\(850\) | 1.21657 | + | 2.52618i | 0.0417280 | + | 0.0866474i | ||||
\(851\) | 1.50816 | + | 2.61220i | 0.0516989 | + | 0.0895452i | ||||
\(852\) | −0.600293 | − | 2.24032i | −0.0205657 | − | 0.0767522i | ||||
\(853\) | −24.1276 | − | 24.1276i | −0.826114 | − | 0.826114i | 0.160863 | − | 0.986977i | \(-0.448572\pi\) |
−0.986977 | + | 0.160863i | \(0.948572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.603474 | − | 16.1298i | 0.0206384 | − | 0.551627i | ||||
\(856\) | 4.92870 | − | 8.53675i | 0.168459 | − | 0.291780i | ||||
\(857\) | −2.09134 | − | 0.560372i | −0.0714387 | − | 0.0191419i | 0.222923 | − | 0.974836i | \(-0.428440\pi\) |
−0.294361 | + | 0.955694i | \(0.595107\pi\) | |||||||
\(858\) | −0.643761 | − | 0.172495i | −0.0219777 | − | 0.00588889i | ||||
\(859\) | −20.9047 | + | 36.2081i | −0.713261 | + | 1.23540i | 0.250366 | + | 0.968151i | \(0.419449\pi\) |
−0.963627 | + | 0.267253i | \(0.913884\pi\) | |||||||
\(860\) | 15.2714 | + | 16.4585i | 0.520750 | + | 0.561231i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.76808 | + | 3.76808i | 0.128341 | + | 0.128341i | ||||
\(863\) | −5.14806 | − | 19.2128i | −0.175242 | − | 0.654011i | −0.996510 | − | 0.0834696i | \(-0.973400\pi\) |
0.821268 | − | 0.570542i | \(-0.193267\pi\) | |||||||
\(864\) | −1.36514 | − | 2.36449i | −0.0464429 | − | 0.0804415i | ||||
\(865\) | −2.31652 | + | 7.51008i | −0.0787641 | + | 0.255350i | ||||
\(866\) | 5.77654 | + | 3.33509i | 0.196295 | + | 0.113331i | ||||
\(867\) | 8.03695 | − | 8.03695i | 0.272949 | − | 0.272949i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.4403i | 1.16831i | ||||||||
\(870\) | 1.02640 | − | 1.63352i | 0.0347983 | − | 0.0553816i | ||||
\(871\) | −0.818403 | + | 0.472505i | −0.0277305 | + | 0.0160102i | ||||
\(872\) | −0.161158 | + | 0.601450i | −0.00545750 | + | 0.0203677i | ||||
\(873\) | 10.1587 | − | 2.72202i | 0.343821 | − | 0.0921265i | ||||
\(874\) | 12.4450 | 0.420958 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.80249 | 0.128474 | ||||||||
\(877\) | 53.8001 | − | 14.4157i | 1.81670 | − | 0.486783i | 0.820328 | − | 0.571894i | \(-0.193791\pi\) |
0.996371 | + | 0.0851110i | \(0.0271245\pi\) | |||||||
\(878\) | 1.84628 | − | 6.89042i | 0.0623090 | − | 0.232540i | ||||
\(879\) | 5.86942 | − | 3.38871i | 0.197971 | − | 0.114298i | ||||
\(880\) | −17.3947 | + | 27.6837i | −0.586374 | + | 0.933216i | ||||
\(881\) | 25.7205i | 0.866546i | 0.901263 | + | 0.433273i | \(0.142641\pi\) | ||||
−0.901263 | + | 0.433273i | \(0.857359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.0968 | + | 25.0968i | −0.844574 | + | 0.844574i | −0.989450 | − | 0.144876i | \(-0.953722\pi\) |
0.144876 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(884\) | −2.82841 | − | 1.63299i | −0.0951298 | − | 0.0549232i | ||||
\(885\) | −4.02674 | + | 13.0545i | −0.135357 | + | 0.438823i | ||||
\(886\) | −2.12867 | − | 3.68697i | −0.0715142 | − | 0.123866i | ||||
\(887\) | 13.8704 | + | 51.7651i | 0.465723 | + | 1.73810i | 0.654482 | + | 0.756077i | \(0.272887\pi\) |
−0.188760 | + | 0.982023i | \(0.560447\pi\) | |||||||
\(888\) | 0.272349 | + | 0.272349i | 0.00913942 | + | 0.00913942i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.81198 | − | 3.03057i | −0.0942577 | − | 0.101585i | ||||
\(891\) | 1.99301 | − | 3.45200i | 0.0667684 | − | 0.115646i | ||||
\(892\) | −3.59874 | − | 0.964280i | −0.120495 | − | 0.0322865i | ||||
\(893\) | −3.01049 | − | 0.806659i | −0.100742 | − | 0.0269938i | ||||
\(894\) | −0.371052 | + | 0.642680i | −0.0124098 | + | 0.0214944i | ||||
\(895\) | 1.84849 | − | 49.4068i | 0.0617882 | − | 1.65149i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.65191 | − | 3.65191i | −0.121934 | − | 0.121934i | ||||
\(898\) | 1.85990 | + | 6.94124i | 0.0620656 | + | 0.231632i | ||||
\(899\) | −9.01695 | − | 15.6178i | −0.300732 | − | 0.520883i | ||||
\(900\) | −4.21782 | − | 8.75822i | −0.140594 | − | 0.291941i | ||||
\(901\) | 15.6881 | + | 9.05752i | 0.522646 | + | 0.301750i | ||||
\(902\) | −5.08195 | + | 5.08195i | −0.169211 | + | 0.169211i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 4.47594i | − | 0.148867i | ||||||
\(905\) | −16.0655 | − | 10.0945i | −0.534035 | − | 0.335554i | ||||
\(906\) | −3.01253 | + | 1.73929i | −0.100085 | + | 0.0577839i | ||||
\(907\) | −11.1989 | + | 41.7950i | −0.371855 | + | 1.38778i | 0.486031 | + | 0.873942i | \(0.338444\pi\) |
−0.857886 | + | 0.513840i | \(0.828222\pi\) | |||||||
\(908\) | −11.0332 | + | 2.95634i | −0.366150 | + | 0.0981096i | ||||
\(909\) | −6.31633 | −0.209499 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7843 | 0.688614 | 0.344307 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344307 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(912\) | −25.5768 | + | 6.85329i | −0.846933 | + | 0.226935i | ||||
\(913\) | 17.4925 | − | 65.2830i | 0.578918 | − | 2.16055i | ||||
\(914\) | −0.380628 | + | 0.219756i | −0.0125901 | + | 0.00726888i | ||||
\(915\) | −3.53803 | − | 15.5008i | −0.116964 | − | 0.512442i | ||||
\(916\) | 25.2550i | 0.834447i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.396526 | + | 0.396526i | −0.0130873 | + | 0.0130873i | ||||
\(919\) | −41.2267 | − | 23.8023i | −1.35994 | − | 0.785164i | −0.370328 | − | 0.928901i | \(-0.620755\pi\) |
−0.989616 | + | 0.143737i | \(0.954088\pi\) | |||||||
\(920\) | 13.4430 | − | 7.10492i | 0.443204 | − | 0.234242i | ||||
\(921\) | −6.96544 | − | 12.0645i | −0.229519 | − | 0.397539i | ||||
\(922\) | 0.0794646 | + | 0.296566i | 0.00261703 | + | 0.00976688i | ||||
\(923\) | −0.597007 | − | 0.597007i | −0.0196507 | − | 0.0196507i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34809 | + | 1.56649i | 0.0443249 | + | 0.0515057i | ||||
\(926\) | 2.76043 | − | 4.78120i | 0.0907132 | − | 0.157120i | ||||
\(927\) | 17.1313 | + | 4.59031i | 0.562664 | + | 0.150765i | ||||
\(928\) | −9.63098 | − | 2.58061i | −0.316152 | − | 0.0847128i | ||||
\(929\) | 20.3266 | − | 35.2067i | 0.666895 | − | 1.15510i | −0.311873 | − | 0.950124i | \(-0.600956\pi\) |
0.978768 | − | 0.204972i | \(-0.0657102\pi\) | |||||||
\(930\) | 2.60692 | + | 0.0975344i | 0.0854843 | + | 0.00319828i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32.0088 | + | 32.0088i | 1.04848 | + | 1.04848i | ||||
\(933\) | 7.06740 | + | 26.3759i | 0.231376 | + | 0.863508i | ||||
\(934\) | −3.35797 | − | 5.81617i | −0.109876 | − | 0.190311i | ||||
\(935\) | 20.2162 | + | 6.23578i | 0.661140 | + | 0.203932i | ||||
\(936\) | −0.571123 | − | 0.329738i | −0.0186677 | − | 0.0107778i | ||||
\(937\) | 8.25994 | − | 8.25994i | 0.269841 | − | 0.269841i | −0.559195 | − | 0.829036i | \(-0.688890\pi\) |
0.829036 | + | 0.559195i | \(0.188890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.1742i | 0.854163i | ||||||||
\(940\) | −1.82996 | + | 0.417683i | −0.0596867 | + | 0.0136233i | ||||
\(941\) | 24.9263 | − | 14.3912i | 0.812575 | − | 0.469140i | −0.0352744 | − | 0.999378i | \(-0.511231\pi\) |
0.847849 | + | 0.530237i | \(0.177897\pi\) | |||||||
\(942\) | 0.688776 | − | 2.57055i | 0.0224415 | − | 0.0837529i | ||||
\(943\) | −53.7952 | + | 14.4144i | −1.75181 | + | 0.469397i | ||||
\(944\) | 22.4113 | 0.729427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.86353 | −0.158127 | ||||||||
\(947\) | −5.83206 | + | 1.56270i | −0.189516 | + | 0.0507808i | −0.352329 | − | 0.935876i | \(-0.614610\pi\) |
0.162812 | + | 0.986657i | \(0.447943\pi\) | |||||||
\(948\) | −4.34771 | + | 16.2259i | −0.141207 | + | 0.526992i | ||||
\(949\) | 1.19874 | − | 0.692094i | 0.0389128 | − | 0.0224663i | ||||
\(950\) | 8.37828 | − | 1.58532i | 0.271827 | − | 0.0514346i | ||||
\(951\) | 30.9421i | 1.00336i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8382 | − | 31.8382i | 1.03134 | − | 1.03134i | 0.0318472 | − | 0.999493i | \(-0.489861\pi\) |
0.999493 | − | 0.0318472i | \(-0.0101390\pi\) | |||||||
\(954\) | 1.56148 | + | 0.901521i | 0.0505548 | + | 0.0291878i | ||||
\(955\) | 15.9756 | + | 30.2271i | 0.516959 | + | 0.978125i | ||||
\(956\) | −5.32753 | − | 9.22755i | −0.172305 | − | 0.298440i | ||||
\(957\) | −3.76752 | − | 14.0606i | −0.121787 | − | 0.454514i | ||||
\(958\) | −1.85159 | − | 1.85159i | −0.0598221 | − | 0.0598221i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.9682 | + | 10.1771i | −0.353998 | + | 0.328464i | ||||
\(961\) | −3.30703 | + | 5.72794i | −0.106678 | + | 0.184772i | ||||
\(962\) | 0.0667562 | + | 0.0178873i | 0.00215231 | + | 0.000576708i | ||||
\(963\) | 10.2181 | + | 2.73794i | 0.329275 | + | 0.0882290i | ||||
\(964\) | −14.2419 | + | 24.6676i | −0.458700 | + | 0.794491i | ||||
\(965\) | 20.6957 | − | 19.2030i | 0.666220 | − | 0.618166i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5518 | − | 17.5518i | −0.564429 | − | 0.564429i | 0.366134 | − | 0.930562i | \(-0.380681\pi\) |
−0.930562 | + | 0.366134i | \(0.880681\pi\) | |||||||
\(968\) | −1.17895 | − | 4.39989i | −0.0378928 | − | 0.141418i | ||||
\(969\) | 8.56697 | + | 14.8384i | 0.275211 | + | 0.476679i | ||||
\(970\) | 2.59613 | + | 4.91208i | 0.0833568 | + | 0.157717i | ||||
\(971\) | 0.0805953 | + | 0.0465317i | 0.00258643 | + | 0.00149327i | 0.501293 | − | 0.865278i | \(-0.332858\pi\) |
−0.498706 | + | 0.866771i | \(0.666191\pi\) | |||||||
\(972\) | 1.37475 | − | 1.37475i | 0.0440950 | − | 0.0440950i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.56126i | 0.146152i | ||||||||
\(975\) | −2.92377 | − | 1.99336i | −0.0936354 | − | 0.0638385i | ||||
\(976\) | −22.5883 | + | 13.0414i | −0.723035 | + | 0.417445i | ||||
\(977\) | 1.90257 | − | 7.10049i | 0.0608686 | − | 0.227165i | −0.928790 | − | 0.370606i | \(-0.879150\pi\) |
0.989659 | + | 0.143441i | \(0.0458168\pi\) | |||||||
\(978\) | −3.37087 | + | 0.903223i | −0.107789 | + | 0.0288819i | ||||
\(979\) | −31.1938 | −0.996959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.668223 | −0.0213347 | ||||||||
\(982\) | 7.32884 | − | 1.96376i | 0.233873 | − | 0.0626660i | ||||
\(983\) | 11.1249 | − | 41.5189i | 0.354831 | − | 1.32425i | −0.525867 | − | 0.850567i | \(-0.676259\pi\) |
0.880697 | − | 0.473679i | \(-0.157074\pi\) | |||||||
\(984\) | −6.15877 | + | 3.55577i | −0.196334 | + | 0.113354i | ||||
\(985\) | −8.28445 | + | 1.89090i | −0.263965 | + | 0.0602492i | ||||
\(986\) | 2.04789i | 0.0652181i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.02319 | + | 7.02319i | −0.223437 | + | 0.223437i | ||||
\(989\) | −32.6389 | − | 18.8441i | −1.03786 | − | 0.599208i | ||||
\(990\) | 2.01217 | + | 0.620666i | 0.0639511 | + | 0.0197260i | ||||
\(991\) | −17.1324 | − | 29.6742i | −0.544228 | − | 0.942631i | −0.998655 | − | 0.0518468i | \(-0.983489\pi\) |
0.454427 | − | 0.890784i | \(-0.349844\pi\) | |||||||
\(992\) | −3.48957 | − | 13.0233i | −0.110794 | − | 0.413489i | ||||
\(993\) | 11.8025 | + | 11.8025i | 0.374542 | + | 0.374542i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.37788 | + | 0.0515514i | 0.0436817 | + | 0.00163429i | ||||
\(996\) | 16.4825 | − | 28.5486i | 0.522269 | − | 0.904597i | ||||
\(997\) | −28.9336 | − | 7.75273i | −0.916336 | − | 0.245532i | −0.230318 | − | 0.973116i | \(-0.573977\pi\) |
−0.686019 | + | 0.727584i | \(0.740643\pi\) | |||||||
\(998\) | −0.975408 | − | 0.261360i | −0.0308760 | − | 0.00827320i | ||||
\(999\) | −0.206669 | + | 0.357962i | −0.00653873 | + | 0.0113254i |
(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 | 735.2.v.a.607.5 | 32 | ||
5.3 | odd | 4 | inner | 735.2.v.a.313.3 | 32 | ||
7.2 | even | 3 | 105.2.m.a.97.3 | yes | 16 | ||
7.3 | odd | 6 | inner | 735.2.v.a.472.3 | 32 | ||
7.4 | even | 3 | inner | 735.2.v.a.472.4 | 32 | ||
7.5 | odd | 6 | 105.2.m.a.97.4 | yes | 16 | ||
7.6 | odd | 2 | inner | 735.2.v.a.607.6 | 32 | ||
21.2 | odd | 6 | 315.2.p.e.307.6 | 16 | |||
21.5 | even | 6 | 315.2.p.e.307.5 | 16 | |||
28.19 | even | 6 | 1680.2.cz.d.97.4 | 16 | |||
28.23 | odd | 6 | 1680.2.cz.d.97.5 | 16 | |||
35.2 | odd | 12 | 525.2.m.b.118.5 | 16 | |||
35.3 | even | 12 | inner | 735.2.v.a.178.5 | 32 | ||
35.9 | even | 6 | 525.2.m.b.307.6 | 16 | |||
35.12 | even | 12 | 525.2.m.b.118.6 | 16 | |||
35.13 | even | 4 | inner | 735.2.v.a.313.4 | 32 | ||
35.18 | odd | 12 | inner | 735.2.v.a.178.6 | 32 | ||
35.19 | odd | 6 | 525.2.m.b.307.5 | 16 | |||
35.23 | odd | 12 | 105.2.m.a.13.4 | yes | 16 | ||
35.33 | even | 12 | 105.2.m.a.13.3 | ✓ | 16 | ||
105.23 | even | 12 | 315.2.p.e.118.5 | 16 | |||
105.68 | odd | 12 | 315.2.p.e.118.6 | 16 | |||
140.23 | even | 12 | 1680.2.cz.d.433.4 | 16 | |||
140.103 | odd | 12 | 1680.2.cz.d.433.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.3 | ✓ | 16 | 35.33 | even | 12 | ||
105.2.m.a.13.4 | yes | 16 | 35.23 | odd | 12 | ||
105.2.m.a.97.3 | yes | 16 | 7.2 | even | 3 | ||
105.2.m.a.97.4 | yes | 16 | 7.5 | odd | 6 | ||
315.2.p.e.118.5 | 16 | 105.23 | even | 12 | |||
315.2.p.e.118.6 | 16 | 105.68 | odd | 12 | |||
315.2.p.e.307.5 | 16 | 21.5 | even | 6 | |||
315.2.p.e.307.6 | 16 | 21.2 | odd | 6 | |||
525.2.m.b.118.5 | 16 | 35.2 | odd | 12 | |||
525.2.m.b.118.6 | 16 | 35.12 | even | 12 | |||
525.2.m.b.307.5 | 16 | 35.19 | odd | 6 | |||
525.2.m.b.307.6 | 16 | 35.9 | even | 6 | |||
735.2.v.a.178.5 | 32 | 35.3 | even | 12 | inner | ||
735.2.v.a.178.6 | 32 | 35.18 | odd | 12 | inner | ||
735.2.v.a.313.3 | 32 | 5.3 | odd | 4 | inner | ||
735.2.v.a.313.4 | 32 | 35.13 | even | 4 | inner | ||
735.2.v.a.472.3 | 32 | 7.3 | odd | 6 | inner | ||
735.2.v.a.472.4 | 32 | 7.4 | even | 3 | inner | ||
735.2.v.a.607.5 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.a.607.6 | 32 | 7.6 | odd | 2 | inner | ||
1680.2.cz.d.97.4 | 16 | 28.19 | even | 6 | |||
1680.2.cz.d.97.5 | 16 | 28.23 | odd | 6 | |||
1680.2.cz.d.433.4 | 16 | 140.23 | even | 12 | |||
1680.2.cz.d.433.5 | 16 | 140.103 | odd | 12 |