Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(85,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.w (of order \(4\), degree \(2\), 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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 85.5 | ||
Character | \(\chi\) | \(=\) | 336.85 |
Dual form | 336.2.w.b.253.5 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.819262 | + | 1.15274i | −0.579305 | + | 0.815111i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | −0.657621 | − | 1.88879i | −0.328811 | − | 0.944396i | ||||
\(5\) | −0.979857 | − | 0.979857i | −0.438205 | − | 0.438205i | 0.453202 | − | 0.891408i | \(-0.350282\pi\) |
−0.891408 | + | 0.453202i | \(0.850282\pi\) | |||||||
\(6\) | −0.235805 | − | 1.39442i | −0.0962671 | − | 0.569268i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 2.71605 | + | 0.789348i | 0.960269 | + | 0.279077i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 1.93228 | − | 0.326762i | 0.611041 | − | 0.103331i | ||||
\(11\) | 2.99092 | + | 2.99092i | 0.901796 | + | 0.901796i | 0.995591 | − | 0.0937956i | \(-0.0299000\pi\) |
−0.0937956 | + | 0.995591i | \(0.529900\pi\) | |||||||
\(12\) | 1.80059 | + | 0.870569i | 0.519784 | + | 0.251312i | ||||
\(13\) | −0.686333 | + | 0.686333i | −0.190355 | + | 0.190355i | −0.795849 | − | 0.605495i | \(-0.792975\pi\) |
0.605495 | + | 0.795849i | \(0.292975\pi\) | |||||||
\(14\) | 1.15274 | + | 0.819262i | 0.308083 | + | 0.218957i | ||||
\(15\) | 1.38573 | 0.357793 | ||||||||
\(16\) | −3.13507 | + | 2.48422i | −0.783767 | + | 0.621055i | ||||
\(17\) | 7.74860 | 1.87931 | 0.939655 | − | 0.342122i | \(-0.111146\pi\) | ||||
0.939655 | + | 0.342122i | \(0.111146\pi\) | |||||||
\(18\) | 1.15274 | + | 0.819262i | 0.271704 | + | 0.193102i | ||||
\(19\) | 2.46495 | − | 2.46495i | 0.565498 | − | 0.565498i | −0.365366 | − | 0.930864i | \(-0.619056\pi\) |
0.930864 | + | 0.365366i | \(0.119056\pi\) | |||||||
\(20\) | −1.20637 | + | 2.49512i | −0.269753 | + | 0.557926i | ||||
\(21\) | 0.707107 | + | 0.707107i | 0.154303 | + | 0.154303i | ||||
\(22\) | −5.89810 | + | 0.997408i | −1.25748 | + | 0.212648i | ||||
\(23\) | 8.35641i | 1.74243i | 0.490900 | + | 0.871216i | \(0.336668\pi\) | ||||
−0.490900 | + | 0.871216i | \(0.663332\pi\) | |||||||
\(24\) | −2.47869 | + | 1.36238i | −0.505961 | + | 0.278096i | ||||
\(25\) | − | 3.07976i | − | 0.615952i | ||||||
\(26\) | −0.228878 | − | 1.35345i | −0.0448866 | − | 0.265433i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −1.88879 | + | 0.657621i | −0.356948 | + | 0.124279i | ||||
\(29\) | −3.68876 | + | 3.68876i | −0.684985 | + | 0.684985i | −0.961119 | − | 0.276134i | \(-0.910947\pi\) |
0.276134 | + | 0.961119i | \(0.410947\pi\) | |||||||
\(30\) | −1.13527 | + | 1.59738i | −0.207271 | + | 0.291641i | ||||
\(31\) | 7.60568 | 1.36602 | 0.683010 | − | 0.730409i | \(-0.260671\pi\) | ||||
0.683010 | + | 0.730409i | \(0.260671\pi\) | |||||||
\(32\) | −0.295218 | − | 5.64915i | −0.0521877 | − | 0.998637i | ||||
\(33\) | −4.22980 | −0.736313 | ||||||||
\(34\) | −6.34813 | + | 8.93212i | −1.08869 | + | 1.53185i | ||||
\(35\) | −0.979857 | + | 0.979857i | −0.165626 | + | 0.165626i | ||||
\(36\) | −1.88879 | + | 0.657621i | −0.314799 | + | 0.109604i | ||||
\(37\) | −4.63198 | − | 4.63198i | −0.761492 | − | 0.761492i | 0.215100 | − | 0.976592i | \(-0.430992\pi\) |
−0.976592 | + | 0.215100i | \(0.930992\pi\) | |||||||
\(38\) | 0.822008 | + | 4.86088i | 0.133347 | + | 0.788539i | ||||
\(39\) | − | 0.970621i | − | 0.155424i | ||||||
\(40\) | −1.88789 | − | 3.43479i | −0.298502 | − | 0.543088i | ||||
\(41\) | − | 7.39378i | − | 1.15471i | −0.816492 | − | 0.577357i | \(-0.804084\pi\) | ||
0.816492 | − | 0.577357i | \(-0.195916\pi\) | |||||||
\(42\) | −1.39442 | + | 0.235805i | −0.215163 | + | 0.0363855i | ||||
\(43\) | 7.06672 | + | 7.06672i | 1.07767 | + | 1.07767i | 0.996718 | + | 0.0809467i | \(0.0257944\pi\) |
0.0809467 | + | 0.996718i | \(0.474206\pi\) | |||||||
\(44\) | 3.68233 | − | 7.61611i | 0.555132 | − | 1.14817i | ||||
\(45\) | −0.979857 | + | 0.979857i | −0.146068 | + | 0.146068i | ||||
\(46\) | −9.63277 | − | 6.84608i | −1.42027 | − | 1.00940i | ||||
\(47\) | 2.46578 | 0.359671 | 0.179836 | − | 0.983697i | \(-0.442443\pi\) | ||||
0.179836 | + | 0.983697i | \(0.442443\pi\) | |||||||
\(48\) | 0.460221 | − | 3.97344i | 0.0664271 | − | 0.573516i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 3.55016 | + | 2.52313i | 0.502069 | + | 0.356824i | ||||
\(51\) | −5.47909 | + | 5.47909i | −0.767225 | + | 0.767225i | ||||
\(52\) | 1.74769 | + | 0.844993i | 0.242361 | + | 0.117179i | ||||
\(53\) | 6.50509 | + | 6.50509i | 0.893543 | + | 0.893543i | 0.994855 | − | 0.101312i | \(-0.0323040\pi\) |
−0.101312 | + | 0.994855i | \(0.532304\pi\) | |||||||
\(54\) | −1.39442 | + | 0.235805i | −0.189756 | + | 0.0320890i | ||||
\(55\) | − | 5.86134i | − | 0.790343i | ||||||
\(56\) | 0.789348 | − | 2.71605i | 0.105481 | − | 0.362948i | ||||
\(57\) | 3.48596i | 0.461727i | ||||||||
\(58\) | −1.23012 | − | 7.27423i | −0.161523 | − | 0.955154i | ||||
\(59\) | 2.18485 | + | 2.18485i | 0.284443 | + | 0.284443i | 0.834878 | − | 0.550435i | \(-0.185538\pi\) |
−0.550435 | + | 0.834878i | \(0.685538\pi\) | |||||||
\(60\) | −0.911283 | − | 2.61735i | −0.117646 | − | 0.337898i | ||||
\(61\) | −1.02350 | + | 1.02350i | −0.131045 | + | 0.131045i | −0.769587 | − | 0.638542i | \(-0.779538\pi\) |
0.638542 | + | 0.769587i | \(0.279538\pi\) | |||||||
\(62\) | −6.23104 | + | 8.76737i | −0.791343 | + | 1.11346i | ||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 6.75386 | + | 4.28782i | 0.844232 | + | 0.535977i | ||||
\(65\) | 1.34502 | 0.166829 | ||||||||
\(66\) | 3.46531 | − | 4.87586i | 0.426550 | − | 0.600177i | ||||
\(67\) | 2.22728 | − | 2.22728i | 0.272106 | − | 0.272106i | −0.557842 | − | 0.829947i | \(-0.688370\pi\) |
0.829947 | + | 0.557842i | \(0.188370\pi\) | |||||||
\(68\) | −5.09564 | − | 14.6355i | −0.617937 | − | 1.77481i | ||||
\(69\) | −5.90887 | − | 5.90887i | −0.711345 | − | 0.711345i | ||||
\(70\) | −0.326762 | − | 1.93228i | −0.0390555 | − | 0.230952i | ||||
\(71\) | − | 14.1741i | − | 1.68216i | −0.540914 | − | 0.841078i | \(-0.681922\pi\) | ||
0.540914 | − | 0.841078i | \(-0.318078\pi\) | |||||||
\(72\) | 0.789348 | − | 2.71605i | 0.0930255 | − | 0.320090i | ||||
\(73\) | − | 5.93888i | − | 0.695093i | −0.937663 | − | 0.347546i | \(-0.887015\pi\) | ||
0.937663 | − | 0.347546i | \(-0.112985\pi\) | |||||||
\(74\) | 9.13427 | − | 1.54467i | 1.06184 | − | 0.179564i | ||||
\(75\) | 2.17772 | + | 2.17772i | 0.251461 | + | 0.251461i | ||||
\(76\) | −6.27678 | − | 3.03477i | −0.719996 | − | 0.348112i | ||||
\(77\) | 2.99092 | − | 2.99092i | 0.340847 | − | 0.340847i | ||||
\(78\) | 1.11887 | + | 0.795193i | 0.126688 | + | 0.0900378i | ||||
\(79\) | −2.58459 | −0.290789 | −0.145394 | − | 0.989374i | \(-0.546445\pi\) | ||||
−0.145394 | + | 0.989374i | \(0.546445\pi\) | |||||||
\(80\) | 5.50610 | + | 0.637740i | 0.615600 | + | 0.0713015i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 8.52311 | + | 6.05744i | 0.941220 | + | 0.668932i | ||||
\(83\) | −4.80684 | + | 4.80684i | −0.527619 | + | 0.527619i | −0.919862 | − | 0.392243i | \(-0.871699\pi\) |
0.392243 | + | 0.919862i | \(0.371699\pi\) | |||||||
\(84\) | 0.870569 | − | 1.80059i | 0.0949869 | − | 0.196460i | ||||
\(85\) | −7.59252 | − | 7.59252i | −0.823524 | − | 0.823524i | ||||
\(86\) | −13.9356 | + | 2.35660i | −1.50271 | + | 0.254119i | ||||
\(87\) | − | 5.21669i | − | 0.559288i | ||||||
\(88\) | 5.76261 | + | 10.4844i | 0.614296 | + | 1.11764i | ||||
\(89\) | − | 5.96557i | − | 0.632349i | −0.948701 | − | 0.316174i | \(-0.897602\pi\) | ||
0.948701 | − | 0.316174i | \(-0.102398\pi\) | |||||||
\(90\) | −0.326762 | − | 1.93228i | −0.0344437 | − | 0.203680i | ||||
\(91\) | 0.686333 | + | 0.686333i | 0.0719472 | + | 0.0719472i | ||||
\(92\) | 15.7835 | − | 5.49535i | 1.64555 | − | 0.572930i | ||||
\(93\) | −5.37803 | + | 5.37803i | −0.557675 | + | 0.557675i | ||||
\(94\) | −2.02012 | + | 2.84241i | −0.208360 | + | 0.293172i | ||||
\(95\) | −4.83059 | −0.495608 | ||||||||
\(96\) | 4.20330 | + | 3.78580i | 0.428998 | + | 0.386386i | ||||
\(97\) | 11.2310 | 1.14033 | 0.570166 | − | 0.821529i | \(-0.306879\pi\) | ||||
0.570166 | + | 0.821529i | \(0.306879\pi\) | |||||||
\(98\) | 0.819262 | − | 1.15274i | 0.0827579 | − | 0.116444i | ||||
\(99\) | 2.99092 | − | 2.99092i | 0.300599 | − | 0.300599i | ||||
\(100\) | −5.81703 | + | 2.02532i | −0.581703 | + | 0.202532i | ||||
\(101\) | −10.0023 | − | 10.0023i | −0.995271 | − | 0.995271i | 0.00471790 | − | 0.999989i | \(-0.498498\pi\) |
−0.999989 | + | 0.00471790i | \(0.998498\pi\) | |||||||
\(102\) | −1.82716 | − | 10.8048i | −0.180916 | − | 1.06983i | ||||
\(103\) | 7.61089i | 0.749924i | 0.927040 | + | 0.374962i | \(0.122344\pi\) | ||||
−0.927040 | + | 0.374962i | \(0.877656\pi\) | |||||||
\(104\) | −2.40587 | + | 1.32236i | −0.235915 | + | 0.129668i | ||||
\(105\) | − | 1.38573i | − | 0.135233i | ||||||
\(106\) | −12.8280 | + | 2.16931i | −1.24597 | + | 0.210702i | ||||
\(107\) | −2.75768 | − | 2.75768i | −0.266595 | − | 0.266595i | 0.561132 | − | 0.827727i | \(-0.310366\pi\) |
−0.827727 | + | 0.561132i | \(0.810366\pi\) | |||||||
\(108\) | 0.870569 | − | 1.80059i | 0.0837706 | − | 0.173261i | ||||
\(109\) | −7.69583 | + | 7.69583i | −0.737127 | + | 0.737127i | −0.972021 | − | 0.234894i | \(-0.924526\pi\) |
0.234894 | + | 0.972021i | \(0.424526\pi\) | |||||||
\(110\) | 6.75661 | + | 4.80197i | 0.644217 | + | 0.457850i | ||||
\(111\) | 6.55060 | 0.621756 | ||||||||
\(112\) | 2.48422 | + | 3.13507i | 0.234737 | + | 0.296236i | ||||
\(113\) | −4.68183 | −0.440430 | −0.220215 | − | 0.975451i | \(-0.570676\pi\) | ||||
−0.220215 | + | 0.975451i | \(0.570676\pi\) | |||||||
\(114\) | −4.01841 | − | 2.85592i | −0.376359 | − | 0.267481i | ||||
\(115\) | 8.18808 | − | 8.18808i | 0.763543 | − | 0.763543i | ||||
\(116\) | 9.39310 | + | 4.54149i | 0.872127 | + | 0.421667i | ||||
\(117\) | 0.686333 | + | 0.686333i | 0.0634515 | + | 0.0634515i | ||||
\(118\) | −4.30852 | + | 0.728600i | −0.396631 | + | 0.0670731i | ||||
\(119\) | − | 7.74860i | − | 0.710313i | ||||||
\(120\) | 3.76370 | + | 1.09382i | 0.343578 | + | 0.0998517i | ||||
\(121\) | 6.89119i | 0.626472i | ||||||||
\(122\) | −0.341314 | − | 2.01834i | −0.0309011 | − | 0.182732i | ||||
\(123\) | 5.22819 | + | 5.22819i | 0.471410 | + | 0.471410i | ||||
\(124\) | −5.00165 | − | 14.3655i | −0.449162 | − | 1.29006i | ||||
\(125\) | −7.91701 | + | 7.91701i | −0.708119 | + | 0.708119i | ||||
\(126\) | 0.819262 | − | 1.15274i | 0.0729856 | − | 0.102694i | ||||
\(127\) | −1.79855 | −0.159596 | −0.0797978 | − | 0.996811i | \(-0.525427\pi\) | ||||
−0.0797978 | + | 0.996811i | \(0.525427\pi\) | |||||||
\(128\) | −10.4759 | + | 4.27260i | −0.925949 | + | 0.377648i | ||||
\(129\) | −9.99386 | −0.879910 | ||||||||
\(130\) | −1.10192 | + | 1.55045i | −0.0966448 | + | 0.135984i | ||||
\(131\) | −12.8298 | + | 12.8298i | −1.12094 | + | 1.12094i | −0.129344 | + | 0.991600i | \(0.541287\pi\) |
−0.991600 | + | 0.129344i | \(0.958713\pi\) | |||||||
\(132\) | 2.78160 | + | 7.98921i | 0.242108 | + | 0.695371i | ||||
\(133\) | −2.46495 | − | 2.46495i | −0.213738 | − | 0.213738i | ||||
\(134\) | 0.742752 | + | 4.39220i | 0.0641640 | + | 0.379429i | ||||
\(135\) | − | 1.38573i | − | 0.119264i | ||||||
\(136\) | 21.0456 | + | 6.11634i | 1.80464 | + | 0.524472i | ||||
\(137\) | 14.2550i | 1.21789i | 0.793213 | + | 0.608944i | \(0.208407\pi\) | ||||
−0.793213 | + | 0.608944i | \(0.791593\pi\) | |||||||
\(138\) | 11.6523 | − | 1.97048i | 0.991910 | − | 0.167739i | ||||
\(139\) | −6.97271 | − | 6.97271i | −0.591418 | − | 0.591418i | 0.346597 | − | 0.938014i | \(-0.387337\pi\) |
−0.938014 | + | 0.346597i | \(0.887337\pi\) | |||||||
\(140\) | 2.49512 | + | 1.20637i | 0.210876 | + | 0.101957i | ||||
\(141\) | −1.74357 | + | 1.74357i | −0.146835 | + | 0.146835i | ||||
\(142\) | 16.3391 | + | 11.6123i | 1.37114 | + | 0.974482i | ||||
\(143\) | −4.10553 | −0.343322 | ||||||||
\(144\) | 2.48422 | + | 3.13507i | 0.207018 | + | 0.261256i | ||||
\(145\) | 7.22891 | 0.600328 | ||||||||
\(146\) | 6.84598 | + | 4.86549i | 0.566578 | + | 0.402671i | ||||
\(147\) | 0.707107 | − | 0.707107i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | −5.70275 | + | 11.7949i | −0.468764 | + | 0.969537i | ||||
\(149\) | 1.43696 | + | 1.43696i | 0.117721 | + | 0.117721i | 0.763513 | − | 0.645792i | \(-0.223473\pi\) |
−0.645792 | + | 0.763513i | \(0.723473\pi\) | |||||||
\(150\) | −4.29447 | + | 0.726224i | −0.350642 | + | 0.0592959i | ||||
\(151\) | 7.09120i | 0.577073i | 0.957469 | + | 0.288537i | \(0.0931687\pi\) | ||||
−0.957469 | + | 0.288537i | \(0.906831\pi\) | |||||||
\(152\) | 8.64063 | − | 4.74922i | 0.700847 | − | 0.385213i | ||||
\(153\) | − | 7.74860i | − | 0.626437i | ||||||
\(154\) | 0.997408 | + | 5.89810i | 0.0803735 | + | 0.475282i | ||||
\(155\) | −7.45248 | − | 7.45248i | −0.598597 | − | 0.598597i | ||||
\(156\) | −1.83330 | + | 0.638301i | −0.146782 | + | 0.0511050i | ||||
\(157\) | 12.1843 | − | 12.1843i | 0.972413 | − | 0.972413i | −0.0272169 | − | 0.999630i | \(-0.508664\pi\) |
0.999630 | + | 0.0272169i | \(0.00866448\pi\) | |||||||
\(158\) | 2.11745 | − | 2.97936i | 0.168455 | − | 0.237025i | ||||
\(159\) | −9.19959 | −0.729575 | ||||||||
\(160\) | −5.24608 | + | 5.82463i | −0.414739 | + | 0.460477i | ||||
\(161\) | 8.35641 | 0.658577 | ||||||||
\(162\) | 0.819262 | − | 1.15274i | 0.0643673 | − | 0.0905678i | ||||
\(163\) | −6.78971 | + | 6.78971i | −0.531811 | + | 0.531811i | −0.921111 | − | 0.389300i | \(-0.872717\pi\) |
0.389300 | + | 0.921111i | \(0.372717\pi\) | |||||||
\(164\) | −13.9653 | + | 4.86231i | −1.09051 | + | 0.379682i | ||||
\(165\) | 4.14460 | + | 4.14460i | 0.322656 | + | 0.322656i | ||||
\(166\) | −1.60298 | − | 9.47910i | −0.124415 | − | 0.735721i | ||||
\(167\) | 5.53606i | 0.428393i | 0.976791 | + | 0.214197i | \(0.0687133\pi\) | ||||
−0.976791 | + | 0.214197i | \(0.931287\pi\) | |||||||
\(168\) | 1.36238 | + | 2.47869i | 0.105110 | + | 0.191235i | ||||
\(169\) | 12.0579i | 0.927530i | ||||||||
\(170\) | 14.9725 | − | 2.53194i | 1.14834 | − | 0.194191i | ||||
\(171\) | −2.46495 | − | 2.46495i | −0.188499 | − | 0.188499i | ||||
\(172\) | 8.70034 | − | 17.9948i | 0.663395 | − | 1.37209i | ||||
\(173\) | 7.62433 | − | 7.62433i | 0.579667 | − | 0.579667i | −0.355144 | − | 0.934812i | \(-0.615568\pi\) |
0.934812 | + | 0.355144i | \(0.115568\pi\) | |||||||
\(174\) | 6.01349 | + | 4.27383i | 0.455881 | + | 0.323998i | ||||
\(175\) | −3.07976 | −0.232808 | ||||||||
\(176\) | −16.8068 | − | 1.94664i | −1.26686 | − | 0.146733i | ||||
\(177\) | −3.08984 | −0.232246 | ||||||||
\(178\) | 6.87675 | + | 4.88736i | 0.515434 | + | 0.366323i | ||||
\(179\) | −8.96337 | + | 8.96337i | −0.669954 | + | 0.669954i | −0.957705 | − | 0.287751i | \(-0.907092\pi\) |
0.287751 | + | 0.957705i | \(0.407092\pi\) | |||||||
\(180\) | 2.49512 | + | 1.20637i | 0.185975 | + | 0.0899176i | ||||
\(181\) | −5.90281 | − | 5.90281i | −0.438752 | − | 0.438752i | 0.452840 | − | 0.891592i | \(-0.350411\pi\) |
−0.891592 | + | 0.452840i | \(0.850411\pi\) | |||||||
\(182\) | −1.35345 | + | 0.228878i | −0.100324 | + | 0.0169655i | ||||
\(183\) | − | 1.44744i | − | 0.106998i | ||||||
\(184\) | −6.59611 | + | 22.6964i | −0.486272 | + | 1.67320i | ||||
\(185\) | 9.07735i | 0.667380i | ||||||||
\(186\) | −1.79346 | − | 10.6055i | −0.131503 | − | 0.777631i | ||||
\(187\) | 23.1754 | + | 23.1754i | 1.69475 | + | 1.69475i | ||||
\(188\) | −1.62155 | − | 4.65735i | −0.118264 | − | 0.339672i | ||||
\(189\) | 0.707107 | − | 0.707107i | 0.0514344 | − | 0.0514344i | ||||
\(190\) | 3.95752 | − | 5.56842i | 0.287109 | − | 0.403976i | ||||
\(191\) | −21.8175 | −1.57866 | −0.789330 | − | 0.613969i | \(-0.789572\pi\) | ||||
−0.789330 | + | 0.613969i | \(0.789572\pi\) | |||||||
\(192\) | −7.80764 | + | 1.74376i | −0.563468 | + | 0.125845i | ||||
\(193\) | 6.18705 | 0.445354 | 0.222677 | − | 0.974892i | \(-0.428521\pi\) | ||||
0.222677 | + | 0.974892i | \(0.428521\pi\) | |||||||
\(194\) | −9.20110 | + | 12.9464i | −0.660601 | + | 0.929497i | ||||
\(195\) | −0.951070 | + | 0.951070i | −0.0681075 | + | 0.0681075i | ||||
\(196\) | 0.657621 | + | 1.88879i | 0.0469729 | + | 0.134914i | ||||
\(197\) | 4.73831 | + | 4.73831i | 0.337590 | + | 0.337590i | 0.855460 | − | 0.517869i | \(-0.173275\pi\) |
−0.517869 | + | 0.855460i | \(0.673275\pi\) | |||||||
\(198\) | 0.997408 | + | 5.89810i | 0.0708827 | + | 0.419160i | ||||
\(199\) | − | 17.6373i | − | 1.25027i | −0.780516 | − | 0.625136i | \(-0.785043\pi\) | ||
0.780516 | − | 0.625136i | \(-0.214957\pi\) | |||||||
\(200\) | 2.43100 | − | 8.36479i | 0.171898 | − | 0.591480i | ||||
\(201\) | 3.14985i | 0.222173i | ||||||||
\(202\) | 19.7247 | − | 3.33557i | 1.38782 | − | 0.234690i | ||||
\(203\) | 3.68876 | + | 3.68876i | 0.258900 | + | 0.258900i | ||||
\(204\) | 13.9520 | + | 6.74569i | 0.976836 | + | 0.472293i | ||||
\(205\) | −7.24485 | + | 7.24485i | −0.506002 | + | 0.506002i | ||||
\(206\) | −8.77338 | − | 6.23531i | −0.611271 | − | 0.434435i | ||||
\(207\) | 8.35641 | 0.580811 | ||||||||
\(208\) | 0.446700 | − | 3.85670i | 0.0309731 | − | 0.267414i | ||||
\(209\) | 14.7449 | 1.01993 | ||||||||
\(210\) | 1.59738 | + | 1.13527i | 0.110230 | + | 0.0783413i | ||||
\(211\) | 16.9192 | − | 16.9192i | 1.16476 | − | 1.16476i | 0.181344 | − | 0.983420i | \(-0.441955\pi\) |
0.983420 | − | 0.181344i | \(-0.0580449\pi\) | |||||||
\(212\) | 8.00888 | − | 16.5646i | 0.550052 | − | 1.13766i | ||||
\(213\) | 10.0226 | + | 10.0226i | 0.686737 | + | 0.686737i | ||||
\(214\) | 5.43815 | − | 0.919628i | 0.371744 | − | 0.0628645i | ||||
\(215\) | − | 13.8488i | − | 0.944477i | ||||||
\(216\) | 1.36238 | + | 2.47869i | 0.0926985 | + | 0.168654i | ||||
\(217\) | − | 7.60568i | − | 0.516307i | ||||||
\(218\) | −2.56640 | − | 15.1762i | −0.173818 | − | 1.02786i | ||||
\(219\) | 4.19942 | + | 4.19942i | 0.283770 | + | 0.283770i | ||||
\(220\) | −11.0709 | + | 3.85454i | −0.746397 | + | 0.259873i | ||||
\(221\) | −5.31812 | + | 5.31812i | −0.357735 | + | 0.357735i | ||||
\(222\) | −5.36666 | + | 7.55115i | −0.360187 | + | 0.506800i | ||||
\(223\) | −10.0690 | −0.674271 | −0.337136 | − | 0.941456i | \(-0.609458\pi\) | ||||
−0.337136 | + | 0.941456i | \(0.609458\pi\) | |||||||
\(224\) | −5.64915 | + | 0.295218i | −0.377449 | + | 0.0197251i | ||||
\(225\) | −3.07976 | −0.205317 | ||||||||
\(226\) | 3.83565 | − | 5.39694i | 0.255143 | − | 0.358999i | ||||
\(227\) | −14.9150 | + | 14.9150i | −0.989946 | + | 0.989946i | −0.999950 | − | 0.0100043i | \(-0.996815\pi\) |
0.0100043 | + | 0.999950i | \(0.496815\pi\) | |||||||
\(228\) | 6.58426 | − | 2.29244i | 0.436053 | − | 0.151821i | ||||
\(229\) | −3.15436 | − | 3.15436i | −0.208446 | − | 0.208446i | 0.595161 | − | 0.803607i | \(-0.297088\pi\) |
−0.803607 | + | 0.595161i | \(0.797088\pi\) | |||||||
\(230\) | 2.73055 | + | 16.1469i | 0.180047 | + | 1.06470i | ||||
\(231\) | 4.22980i | 0.278300i | ||||||||
\(232\) | −12.9306 | + | 7.10714i | −0.848933 | + | 0.466606i | ||||
\(233\) | − | 7.66530i | − | 0.502171i | −0.967965 | − | 0.251085i | \(-0.919213\pi\) | ||
0.967965 | − | 0.251085i | \(-0.0807875\pi\) | |||||||
\(234\) | −1.35345 | + | 0.228878i | −0.0884778 | + | 0.0149622i | ||||
\(235\) | −2.41612 | − | 2.41612i | −0.157610 | − | 0.157610i | ||||
\(236\) | 2.68992 | − | 5.56352i | 0.175099 | − | 0.362154i | ||||
\(237\) | 1.82758 | − | 1.82758i | 0.118714 | − | 0.118714i | ||||
\(238\) | 8.93212 | + | 6.34813i | 0.578983 | + | 0.411488i | ||||
\(239\) | 3.16599 | 0.204791 | 0.102396 | − | 0.994744i | \(-0.467349\pi\) | ||||
0.102396 | + | 0.994744i | \(0.467349\pi\) | |||||||
\(240\) | −4.34435 | + | 3.44245i | −0.280427 | + | 0.222209i | ||||
\(241\) | −11.6790 | −0.752313 | −0.376157 | − | 0.926556i | \(-0.622755\pi\) | ||||
−0.376157 | + | 0.926556i | \(0.622755\pi\) | |||||||
\(242\) | −7.94375 | − | 5.64568i | −0.510644 | − | 0.362918i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 2.60624 | + | 1.26010i | 0.166848 | + | 0.0806695i | ||||
\(245\) | 0.979857 | + | 0.979857i | 0.0626008 | + | 0.0626008i | ||||
\(246\) | −10.3100 | + | 1.74349i | −0.657342 | + | 0.111161i | ||||
\(247\) | 3.38355i | 0.215290i | ||||||||
\(248\) | 20.6574 | + | 6.00353i | 1.31175 | + | 0.381224i | ||||
\(249\) | − | 6.79790i | − | 0.430799i | ||||||
\(250\) | −2.64016 | − | 15.6124i | −0.166978 | − | 0.987412i | ||||
\(251\) | −2.02154 | − | 2.02154i | −0.127599 | − | 0.127599i | 0.640423 | − | 0.768022i | \(-0.278759\pi\) |
−0.768022 | + | 0.640423i | \(0.778759\pi\) | |||||||
\(252\) | 0.657621 | + | 1.88879i | 0.0414262 | + | 0.118983i | ||||
\(253\) | −24.9933 | + | 24.9933i | −1.57132 | + | 1.57132i | ||||
\(254\) | 1.47348 | − | 2.07326i | 0.0924546 | − | 0.130088i | ||||
\(255\) | 10.7374 | 0.672405 | ||||||||
\(256\) | 3.65731 | − | 15.5764i | 0.228582 | − | 0.973525i | ||||
\(257\) | −3.57377 | −0.222926 | −0.111463 | − | 0.993769i | \(-0.535554\pi\) | ||||
−0.111463 | + | 0.993769i | \(0.535554\pi\) | |||||||
\(258\) | 8.18758 | − | 11.5203i | 0.509737 | − | 0.717224i | ||||
\(259\) | −4.63198 | + | 4.63198i | −0.287817 | + | 0.287817i | ||||
\(260\) | −0.884511 | − | 2.54046i | −0.0548550 | − | 0.157552i | ||||
\(261\) | 3.68876 | + | 3.68876i | 0.228328 | + | 0.228328i | ||||
\(262\) | −4.27847 | − | 25.3004i | −0.264324 | − | 1.56306i | ||||
\(263\) | − | 4.46531i | − | 0.275343i | −0.990478 | − | 0.137672i | \(-0.956038\pi\) | ||
0.990478 | − | 0.137672i | \(-0.0439618\pi\) | |||||||
\(264\) | −11.4883 | − | 3.33878i | −0.707059 | − | 0.205488i | ||||
\(265\) | − | 12.7481i | − | 0.783110i | ||||||
\(266\) | 4.86088 | − | 0.822008i | 0.298040 | − | 0.0504006i | ||||
\(267\) | 4.21829 | + | 4.21829i | 0.258155 | + | 0.258155i | ||||
\(268\) | −5.67158 | − | 2.74216i | −0.346447 | − | 0.167504i | ||||
\(269\) | 11.0579 | − | 11.0579i | 0.674211 | − | 0.674211i | −0.284473 | − | 0.958684i | \(-0.591819\pi\) |
0.958684 | + | 0.284473i | \(0.0918185\pi\) | |||||||
\(270\) | 1.59738 | + | 1.13527i | 0.0972137 | + | 0.0690905i | ||||
\(271\) | 7.19248 | 0.436912 | 0.218456 | − | 0.975847i | \(-0.429898\pi\) | ||||
0.218456 | + | 0.975847i | \(0.429898\pi\) | |||||||
\(272\) | −24.2924 | + | 19.2492i | −1.47294 | + | 1.16715i | ||||
\(273\) | −0.970621 | −0.0587447 | ||||||||
\(274\) | −16.4323 | − | 11.6786i | −0.992714 | − | 0.705529i | ||||
\(275\) | 9.21131 | − | 9.21131i | 0.555463 | − | 0.555463i | ||||
\(276\) | −7.27483 | + | 15.0464i | −0.437893 | + | 0.905689i | ||||
\(277\) | −6.19860 | − | 6.19860i | −0.372438 | − | 0.372438i | 0.495927 | − | 0.868364i | \(-0.334828\pi\) |
−0.868364 | + | 0.495927i | \(0.834828\pi\) | |||||||
\(278\) | 13.7502 | − | 2.32525i | 0.824682 | − | 0.139459i | ||||
\(279\) | − | 7.60568i | − | 0.455340i | ||||||
\(280\) | −3.43479 | + | 1.88789i | −0.205268 | + | 0.112823i | ||||
\(281\) | − | 12.6024i | − | 0.751795i | −0.926661 | − | 0.375898i | \(-0.877334\pi\) | ||
0.926661 | − | 0.375898i | \(-0.122666\pi\) | |||||||
\(282\) | −0.581445 | − | 3.43833i | −0.0346245 | − | 0.204749i | ||||
\(283\) | −6.24349 | − | 6.24349i | −0.371137 | − | 0.371137i | 0.496754 | − | 0.867891i | \(-0.334525\pi\) |
−0.867891 | + | 0.496754i | \(0.834525\pi\) | |||||||
\(284\) | −26.7719 | + | 9.32118i | −1.58862 | + | 0.553111i | ||||
\(285\) | 3.41575 | − | 3.41575i | 0.202331 | − | 0.202331i | ||||
\(286\) | 3.36350 | − | 4.73261i | 0.198888 | − | 0.279845i | ||||
\(287\) | −7.39378 | −0.436441 | ||||||||
\(288\) | −5.64915 | + | 0.295218i | −0.332879 | + | 0.0173959i | ||||
\(289\) | 43.0408 | 2.53181 | ||||||||
\(290\) | −5.92236 | + | 8.33305i | −0.347773 | + | 0.489334i | ||||
\(291\) | −7.94149 | + | 7.94149i | −0.465539 | + | 0.465539i | ||||
\(292\) | −11.2173 | + | 3.90553i | −0.656443 | + | 0.228554i | ||||
\(293\) | 10.7496 | + | 10.7496i | 0.627997 | + | 0.627997i | 0.947564 | − | 0.319567i | \(-0.103537\pi\) |
−0.319567 | + | 0.947564i | \(0.603537\pi\) | |||||||
\(294\) | 0.235805 | + | 1.39442i | 0.0137524 | + | 0.0813240i | ||||
\(295\) | − | 4.28167i | − | 0.249289i | ||||||
\(296\) | −8.92444 | − | 16.2369i | −0.518723 | − | 0.943752i | ||||
\(297\) | 4.22980i | 0.245438i | ||||||||
\(298\) | −2.83369 | + | 0.479197i | −0.164151 | + | 0.0277591i | ||||
\(299\) | −5.73528 | − | 5.73528i | −0.331680 | − | 0.331680i | ||||
\(300\) | 2.68114 | − | 5.54537i | 0.154796 | − | 0.320162i | ||||
\(301\) | 7.06672 | − | 7.06672i | 0.407319 | − | 0.407319i | ||||
\(302\) | −8.17431 | − | 5.80954i | −0.470379 | − | 0.334302i | ||||
\(303\) | 14.1455 | 0.812635 | ||||||||
\(304\) | −1.60431 | + | 13.8513i | −0.0920136 | + | 0.794424i | ||||
\(305\) | 2.00576 | 0.114849 | ||||||||
\(306\) | 8.93212 | + | 6.34813i | 0.510615 | + | 0.362898i | ||||
\(307\) | 18.4139 | − | 18.4139i | 1.05094 | − | 1.05094i | 0.0523045 | − | 0.998631i | \(-0.483343\pi\) |
0.998631 | − | 0.0523045i | \(-0.0166566\pi\) | |||||||
\(308\) | −7.61611 | − | 3.68233i | −0.433968 | − | 0.209820i | ||||
\(309\) | −5.38171 | − | 5.38171i | −0.306155 | − | 0.306155i | ||||
\(310\) | 14.6963 | − | 2.48524i | 0.834694 | − | 0.141152i | ||||
\(311\) | − | 19.1317i | − | 1.08486i | −0.840101 | − | 0.542430i | \(-0.817504\pi\) | ||
0.840101 | − | 0.542430i | \(-0.182496\pi\) | |||||||
\(312\) | 0.766158 | − | 2.63626i | 0.0433752 | − | 0.149249i | ||||
\(313\) | 32.5993i | 1.84262i | 0.388827 | + | 0.921311i | \(0.372880\pi\) | ||||
−0.388827 | + | 0.921311i | \(0.627120\pi\) | |||||||
\(314\) | 4.06321 | + | 24.0275i | 0.229300 | + | 1.35595i | ||||
\(315\) | 0.979857 | + | 0.979857i | 0.0552087 | + | 0.0552087i | ||||
\(316\) | 1.69968 | + | 4.88174i | 0.0956143 | + | 0.274619i | ||||
\(317\) | 16.8042 | − | 16.8042i | 0.943819 | − | 0.943819i | −0.0546847 | − | 0.998504i | \(-0.517415\pi\) |
0.998504 | + | 0.0546847i | \(0.0174154\pi\) | |||||||
\(318\) | 7.53687 | − | 10.6047i | 0.422646 | − | 0.594684i | ||||
\(319\) | −22.0655 | −1.23543 | ||||||||
\(320\) | −2.41637 | − | 10.8193i | −0.135079 | − | 0.604815i | ||||
\(321\) | 3.89995 | 0.217674 | ||||||||
\(322\) | −6.84608 | + | 9.63277i | −0.381517 | + | 0.536813i | ||||
\(323\) | 19.0999 | − | 19.0999i | 1.06275 | − | 1.06275i | ||||
\(324\) | 0.657621 | + | 1.88879i | 0.0365345 | + | 0.104933i | ||||
\(325\) | 2.11374 | + | 2.11374i | 0.117249 | + | 0.117249i | ||||
\(326\) | −2.26422 | − | 13.3893i | −0.125404 | − | 0.741565i | ||||
\(327\) | − | 10.8835i | − | 0.601861i | ||||||
\(328\) | 5.83627 | − | 20.0819i | 0.322254 | − | 1.10884i | ||||
\(329\) | − | 2.46578i | − | 0.135943i | ||||||
\(330\) | −8.17315 | + | 1.38214i | −0.449917 | + | 0.0760841i | ||||
\(331\) | −23.2036 | − | 23.2036i | −1.27539 | − | 1.27539i | −0.943221 | − | 0.332165i | \(-0.892221\pi\) |
−0.332165 | − | 0.943221i | \(-0.607779\pi\) | |||||||
\(332\) | 12.2402 | + | 5.91804i | 0.671768 | + | 0.324795i | ||||
\(333\) | −4.63198 | + | 4.63198i | −0.253831 | + | 0.253831i | ||||
\(334\) | −6.38164 | − | 4.53548i | −0.349188 | − | 0.248171i | ||||
\(335\) | −4.36484 | −0.238476 | ||||||||
\(336\) | −3.97344 | − | 0.460221i | −0.216769 | − | 0.0251071i | ||||
\(337\) | 2.77461 | 0.151143 | 0.0755714 | − | 0.997140i | \(-0.475922\pi\) | ||||
0.0755714 | + | 0.997140i | \(0.475922\pi\) | |||||||
\(338\) | −13.8996 | − | 9.87857i | −0.756040 | − | 0.537323i | ||||
\(339\) | 3.31056 | − | 3.31056i | 0.179805 | − | 0.179805i | ||||
\(340\) | −9.34768 | + | 19.3337i | −0.506949 | + | 1.04852i | ||||
\(341\) | 22.7480 | + | 22.7480i | 1.23187 | + | 1.23187i | ||||
\(342\) | 4.86088 | − | 0.822008i | 0.262846 | − | 0.0444491i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 13.6155 | + | 24.7717i | 0.734097 | + | 1.33560i | ||||
\(345\) | 11.5797i | 0.623430i | ||||||||
\(346\) | 2.54255 | + | 15.0352i | 0.136689 | + | 0.808297i | ||||
\(347\) | 4.58489 | + | 4.58489i | 0.246130 | + | 0.246130i | 0.819380 | − | 0.573250i | \(-0.194318\pi\) |
−0.573250 | + | 0.819380i | \(0.694318\pi\) | |||||||
\(348\) | −9.85324 | + | 3.43060i | −0.528189 | + | 0.183900i | ||||
\(349\) | 7.19823 | − | 7.19823i | 0.385313 | − | 0.385313i | −0.487699 | − | 0.873012i | \(-0.662164\pi\) |
0.873012 | + | 0.487699i | \(0.162164\pi\) | |||||||
\(350\) | 2.52313 | − | 3.55016i | 0.134867 | − | 0.189764i | ||||
\(351\) | −0.970621 | −0.0518079 | ||||||||
\(352\) | 16.0132 | − | 17.7791i | 0.853504 | − | 0.947630i | ||||
\(353\) | −33.3957 | −1.77748 | −0.888738 | − | 0.458416i | \(-0.848417\pi\) | ||||
−0.888738 | + | 0.458416i | \(0.848417\pi\) | |||||||
\(354\) | 2.53139 | − | 3.56178i | 0.134542 | − | 0.189307i | ||||
\(355\) | −13.8886 | + | 13.8886i | −0.737130 | + | 0.737130i | ||||
\(356\) | −11.2677 | + | 3.92308i | −0.597188 | + | 0.207923i | ||||
\(357\) | 5.47909 | + | 5.47909i | 0.289984 | + | 0.289984i | ||||
\(358\) | −2.98909 | − | 17.6758i | −0.157979 | − | 0.934194i | ||||
\(359\) | 30.4485i | 1.60701i | 0.595296 | + | 0.803506i | \(0.297035\pi\) | ||||
−0.595296 | + | 0.803506i | \(0.702965\pi\) | |||||||
\(360\) | −3.43479 | + | 1.88789i | −0.181029 | + | 0.0995007i | ||||
\(361\) | 6.84806i | 0.360424i | ||||||||
\(362\) | 11.6403 | − | 1.96846i | 0.611803 | − | 0.103460i | ||||
\(363\) | −4.87280 | − | 4.87280i | −0.255756 | − | 0.255756i | ||||
\(364\) | 0.844993 | − | 1.74769i | 0.0442897 | − | 0.0916037i | ||||
\(365\) | −5.81925 | + | 5.81925i | −0.304593 | + | 0.304593i | ||||
\(366\) | 1.66852 | + | 1.18583i | 0.0872152 | + | 0.0619845i | ||||
\(367\) | −7.37192 | −0.384811 | −0.192405 | − | 0.981316i | \(-0.561629\pi\) | ||||
−0.192405 | + | 0.981316i | \(0.561629\pi\) | |||||||
\(368\) | −20.7591 | − | 26.1979i | −1.08215 | − | 1.36566i | ||||
\(369\) | −7.39378 | −0.384905 | ||||||||
\(370\) | −10.4638 | − | 7.43672i | −0.543988 | − | 0.386617i | ||||
\(371\) | 6.50509 | − | 6.50509i | 0.337727 | − | 0.337727i | ||||
\(372\) | 13.6947 | + | 6.62127i | 0.710036 | + | 0.343297i | ||||
\(373\) | −12.6122 | − | 12.6122i | −0.653034 | − | 0.653034i | 0.300688 | − | 0.953722i | \(-0.402784\pi\) |
−0.953722 | + | 0.300688i | \(0.902784\pi\) | |||||||
\(374\) | −45.7020 | + | 7.72852i | −2.36319 | + | 0.399632i | ||||
\(375\) | − | 11.1963i | − | 0.578177i | ||||||
\(376\) | 6.69719 | + | 1.94636i | 0.345381 | + | 0.100376i | ||||
\(377\) | − | 5.06343i | − | 0.260780i | ||||||
\(378\) | 0.235805 | + | 1.39442i | 0.0121285 | + | 0.0717210i | ||||
\(379\) | −9.17933 | − | 9.17933i | −0.471511 | − | 0.471511i | 0.430893 | − | 0.902403i | \(-0.358199\pi\) |
−0.902403 | + | 0.430893i | \(0.858199\pi\) | |||||||
\(380\) | 3.17670 | + | 9.12399i | 0.162961 | + | 0.468051i | ||||
\(381\) | 1.27177 | − | 1.27177i | 0.0651546 | − | 0.0651546i | ||||
\(382\) | 17.8742 | − | 25.1499i | 0.914526 | − | 1.28678i | ||||
\(383\) | −6.35061 | −0.324501 | −0.162251 | − | 0.986750i | \(-0.551875\pi\) | ||||
−0.162251 | + | 0.986750i | \(0.551875\pi\) | |||||||
\(384\) | 4.38641 | − | 10.4288i | 0.223843 | − | 0.532191i | ||||
\(385\) | −5.86134 | −0.298722 | ||||||||
\(386\) | −5.06881 | + | 7.13206i | −0.257996 | + | 0.363012i | ||||
\(387\) | 7.06672 | − | 7.06672i | 0.359222 | − | 0.359222i | ||||
\(388\) | −7.38572 | − | 21.2130i | −0.374953 | − | 1.07693i | ||||
\(389\) | 10.1588 | + | 10.1588i | 0.515070 | + | 0.515070i | 0.916076 | − | 0.401006i | \(-0.131339\pi\) |
−0.401006 | + | 0.916076i | \(0.631339\pi\) | |||||||
\(390\) | −0.317162 | − | 1.87551i | −0.0160601 | − | 0.0949702i | ||||
\(391\) | 64.7504i | 3.27457i | ||||||||
\(392\) | −2.71605 | − | 0.789348i | −0.137181 | − | 0.0398681i | ||||
\(393\) | − | 18.1441i | − | 0.915247i | ||||||
\(394\) | −9.34395 | + | 1.58013i | −0.470741 | + | 0.0796056i | ||||
\(395\) | 2.53252 | + | 2.53252i | 0.127425 | + | 0.127425i | ||||
\(396\) | −7.61611 | − | 3.68233i | −0.382724 | − | 0.185044i | ||||
\(397\) | 14.2143 | − | 14.2143i | 0.713397 | − | 0.713397i | −0.253847 | − | 0.967244i | \(-0.581696\pi\) |
0.967244 | + | 0.253847i | \(0.0816961\pi\) | |||||||
\(398\) | 20.3312 | + | 14.4495i | 1.01911 | + | 0.724290i | ||||
\(399\) | 3.48596 | 0.174516 | ||||||||
\(400\) | 7.65080 | + | 9.65526i | 0.382540 | + | 0.482763i | ||||
\(401\) | 17.0760 | 0.852733 | 0.426367 | − | 0.904550i | \(-0.359793\pi\) | ||||
0.426367 | + | 0.904550i | \(0.359793\pi\) | |||||||
\(402\) | −3.63096 | − | 2.58055i | −0.181096 | − | 0.128706i | ||||
\(403\) | −5.22003 | + | 5.22003i | −0.260028 | + | 0.260028i | ||||
\(404\) | −12.3146 | + | 25.4701i | −0.612674 | + | 1.26719i | ||||
\(405\) | 0.979857 | + | 0.979857i | 0.0486895 | + | 0.0486895i | ||||
\(406\) | −7.27423 | + | 1.23012i | −0.361014 | + | 0.0610500i | ||||
\(407\) | − | 27.7077i | − | 1.37342i | ||||||
\(408\) | −19.2064 | + | 10.5566i | −0.950857 | + | 0.522628i | ||||
\(409\) | 35.3057i | 1.74575i | 0.487941 | + | 0.872877i | \(0.337748\pi\) | ||||
−0.487941 | + | 0.872877i | \(0.662252\pi\) | |||||||
\(410\) | −2.41600 | − | 14.2869i | −0.119318 | − | 0.705578i | ||||
\(411\) | −10.0798 | − | 10.0798i | −0.497201 | − | 0.497201i | ||||
\(412\) | 14.3754 | − | 5.00508i | 0.708225 | − | 0.246583i | ||||
\(413\) | 2.18485 | − | 2.18485i | 0.107509 | − | 0.107509i | ||||
\(414\) | −6.84608 | + | 9.63277i | −0.336467 | + | 0.473425i | ||||
\(415\) | 9.42003 | 0.462411 | ||||||||
\(416\) | 4.07981 | + | 3.67458i | 0.200029 | + | 0.180161i | ||||
\(417\) | 9.86090 | 0.482890 | ||||||||
\(418\) | −12.0799 | + | 16.9971i | −0.590849 | + | 0.831354i | ||||
\(419\) | −17.0370 | + | 17.0370i | −0.832314 | + | 0.832314i | −0.987833 | − | 0.155519i | \(-0.950295\pi\) |
0.155519 | + | 0.987833i | \(0.450295\pi\) | |||||||
\(420\) | −2.61735 | + | 0.911283i | −0.127714 | + | 0.0444661i | ||||
\(421\) | 5.35804 | + | 5.35804i | 0.261135 | + | 0.261135i | 0.825515 | − | 0.564380i | \(-0.190885\pi\) |
−0.564380 | + | 0.825515i | \(0.690885\pi\) | |||||||
\(422\) | 5.64219 | + | 33.3646i | 0.274657 | + | 1.62417i | ||||
\(423\) | − | 2.46578i | − | 0.119890i | ||||||
\(424\) | 12.5334 | + | 22.8029i | 0.608674 | + | 1.10741i | ||||
\(425\) | − | 23.8638i | − | 1.15757i | ||||||
\(426\) | −19.7646 | + | 3.34233i | −0.957597 | + | 0.161936i | ||||
\(427\) | 1.02350 | + | 1.02350i | 0.0495304 | + | 0.0495304i | ||||
\(428\) | −3.39517 | + | 7.02219i | −0.164112 | + | 0.339430i | ||||
\(429\) | 2.90305 | − | 2.90305i | 0.140161 | − | 0.140161i | ||||
\(430\) | 15.9640 | + | 11.3458i | 0.769853 | + | 0.547141i | ||||
\(431\) | 8.52604 | 0.410685 | 0.205342 | − | 0.978690i | \(-0.434169\pi\) | ||||
0.205342 | + | 0.978690i | \(0.434169\pi\) | |||||||
\(432\) | −3.97344 | − | 0.460221i | −0.191172 | − | 0.0221424i | ||||
\(433\) | −2.15043 | −0.103343 | −0.0516715 | − | 0.998664i | \(-0.516455\pi\) | ||||
−0.0516715 | + | 0.998664i | \(0.516455\pi\) | |||||||
\(434\) | 8.76737 | + | 6.23104i | 0.420847 | + | 0.299099i | ||||
\(435\) | −5.11161 | + | 5.11161i | −0.245083 | + | 0.245083i | ||||
\(436\) | 19.5968 | + | 9.47488i | 0.938514 | + | 0.453764i | ||||
\(437\) | 20.5981 | + | 20.5981i | 0.985342 | + | 0.985342i | ||||
\(438\) | −8.28126 | + | 1.40042i | −0.395694 | + | 0.0669146i | ||||
\(439\) | 23.1132i | 1.10313i | 0.834132 | + | 0.551566i | \(0.185969\pi\) | ||||
−0.834132 | + | 0.551566i | \(0.814031\pi\) | |||||||
\(440\) | 4.62664 | − | 15.9197i | 0.220566 | − | 0.758942i | ||||
\(441\) | 1.00000i | 0.0476190i | ||||||||
\(442\) | −1.77348 | − | 10.4873i | −0.0843558 | − | 0.498832i | ||||
\(443\) | −1.94184 | − | 1.94184i | −0.0922594 | − | 0.0922594i | 0.659471 | − | 0.751730i | \(-0.270780\pi\) |
−0.751730 | + | 0.659471i | \(0.770780\pi\) | |||||||
\(444\) | −4.30782 | − | 12.3727i | −0.204440 | − | 0.587184i | ||||
\(445\) | −5.84540 | + | 5.84540i | −0.277099 | + | 0.277099i | ||||
\(446\) | 8.24916 | − | 11.6070i | 0.390609 | − | 0.549606i | ||||
\(447\) | −2.03217 | −0.0961185 | ||||||||
\(448\) | 4.28782 | − | 6.75386i | 0.202580 | − | 0.319090i | ||||
\(449\) | 4.34764 | 0.205178 | 0.102589 | − | 0.994724i | \(-0.467287\pi\) | ||||
0.102589 | + | 0.994724i | \(0.467287\pi\) | |||||||
\(450\) | 2.52313 | − | 3.55016i | 0.118941 | − | 0.167356i | ||||
\(451\) | 22.1142 | − | 22.1142i | 1.04132 | − | 1.04132i | ||||
\(452\) | 3.07887 | + | 8.84301i | 0.144818 | + | 0.415940i | ||||
\(453\) | −5.01423 | − | 5.01423i | −0.235589 | − | 0.235589i | ||||
\(454\) | −4.97385 | − | 29.4125i | −0.233434 | − | 1.38040i | ||||
\(455\) | − | 1.34502i | − | 0.0630553i | ||||||
\(456\) | −2.75164 | + | 9.46805i | −0.128857 | + | 0.443382i | ||||
\(457\) | − | 2.90858i | − | 0.136057i | −0.997683 | − | 0.0680287i | \(-0.978329\pi\) | ||
0.997683 | − | 0.0680287i | \(-0.0216710\pi\) | |||||||
\(458\) | 6.22040 | − | 1.05191i | 0.290660 | − | 0.0491526i | ||||
\(459\) | 5.47909 | + | 5.47909i | 0.255742 | + | 0.255742i | ||||
\(460\) | −20.8502 | − | 10.0809i | −0.972148 | − | 0.470026i | ||||
\(461\) | −0.855011 | + | 0.855011i | −0.0398218 | + | 0.0398218i | −0.726737 | − | 0.686915i | \(-0.758964\pi\) |
0.686915 | + | 0.726737i | \(0.258964\pi\) | |||||||
\(462\) | −4.87586 | − | 3.46531i | −0.226845 | − | 0.161221i | ||||
\(463\) | 18.1432 | 0.843185 | 0.421592 | − | 0.906785i | \(-0.361471\pi\) | ||||
0.421592 | + | 0.906785i | \(0.361471\pi\) | |||||||
\(464\) | 2.40083 | − | 20.7282i | 0.111456 | − | 0.962282i | ||||
\(465\) | 10.5394 | 0.488753 | ||||||||
\(466\) | 8.83610 | + | 6.27989i | 0.409325 | + | 0.290910i | ||||
\(467\) | −9.77872 | + | 9.77872i | −0.452505 | + | 0.452505i | −0.896185 | − | 0.443680i | \(-0.853673\pi\) |
0.443680 | + | 0.896185i | \(0.353673\pi\) | |||||||
\(468\) | 0.844993 | − | 1.74769i | 0.0390598 | − | 0.0807869i | ||||
\(469\) | −2.22728 | − | 2.22728i | −0.102846 | − | 0.102846i | ||||
\(470\) | 4.76458 | − | 0.805723i | 0.219774 | − | 0.0371653i | ||||
\(471\) | 17.2312i | 0.793972i | ||||||||
\(472\) | 4.20955 | + | 7.65875i | 0.193760 | + | 0.352523i | ||||
\(473\) | 42.2720i | 1.94367i | ||||||||
\(474\) | 0.609459 | + | 3.60399i | 0.0279934 | + | 0.165537i | ||||
\(475\) | −7.59145 | − | 7.59145i | −0.348320 | − | 0.348320i | ||||
\(476\) | −14.6355 | + | 5.09564i | −0.670816 | + | 0.233558i | ||||
\(477\) | 6.50509 | − | 6.50509i | 0.297848 | − | 0.297848i | ||||
\(478\) | −2.59378 | + | 3.64957i | −0.118637 | + | 0.166927i | ||||
\(479\) | 23.4030 | 1.06931 | 0.534655 | − | 0.845071i | \(-0.320442\pi\) | ||||
0.534655 | + | 0.845071i | \(0.320442\pi\) | |||||||
\(480\) | −0.409092 | − | 7.82817i | −0.0186724 | − | 0.357306i | ||||
\(481\) | 6.35816 | 0.289907 | ||||||||
\(482\) | 9.56819 | − | 13.4629i | 0.435819 | − | 0.613218i | ||||
\(483\) | −5.90887 | + | 5.90887i | −0.268863 | + | 0.268863i | ||||
\(484\) | 13.0160 | − | 4.53179i | 0.591637 | − | 0.205990i | ||||
\(485\) | −11.0047 | − | 11.0047i | −0.499700 | − | 0.499700i | ||||
\(486\) | 0.235805 | + | 1.39442i | 0.0106963 | + | 0.0632520i | ||||
\(487\) | − | 16.2734i | − | 0.737420i | −0.929544 | − | 0.368710i | \(-0.879800\pi\) | ||
0.929544 | − | 0.368710i | \(-0.120200\pi\) | |||||||
\(488\) | −3.58776 | + | 1.97197i | −0.162410 | + | 0.0892670i | ||||
\(489\) | − | 9.60209i | − | 0.434222i | ||||||
\(490\) | −1.93228 | + | 0.326762i | −0.0872915 | + | 0.0147616i | ||||
\(491\) | 0.0270638 | + | 0.0270638i | 0.00122137 | + | 0.00122137i | 0.707717 | − | 0.706496i | \(-0.249725\pi\) |
−0.706496 | + | 0.707717i | \(0.749725\pi\) | |||||||
\(492\) | 6.43680 | − | 13.3131i | 0.290193 | − | 0.600203i | ||||
\(493\) | −28.5827 | + | 28.5827i | −1.28730 | + | 1.28730i | ||||
\(494\) | −3.90036 | − | 2.77201i | −0.175485 | − | 0.124719i | ||||
\(495\) | −5.86134 | −0.263448 | ||||||||
\(496\) | −23.8443 | + | 18.8942i | −1.07064 | + | 0.848373i | ||||
\(497\) | −14.1741 | −0.635795 | ||||||||
\(498\) | 7.83621 | + | 5.56926i | 0.351149 | + | 0.249564i | ||||
\(499\) | 19.4506 | − | 19.4506i | 0.870729 | − | 0.870729i | −0.121823 | − | 0.992552i | \(-0.538874\pi\) |
0.992552 | + | 0.121823i | \(0.0388740\pi\) | |||||||
\(500\) | 20.1600 | + | 9.74719i | 0.901582 | + | 0.435908i | ||||
\(501\) | −3.91459 | − | 3.91459i | −0.174891 | − | 0.174891i | ||||
\(502\) | 3.98648 | − | 0.674142i | 0.177926 | − | 0.0300884i | ||||
\(503\) | − | 11.5571i | − | 0.515305i | −0.966238 | − | 0.257652i | \(-0.917051\pi\) | ||
0.966238 | − | 0.257652i | \(-0.0829490\pi\) | |||||||
\(504\) | −2.71605 | − | 0.789348i | −0.120983 | − | 0.0351604i | ||||
\(505\) | 19.6017i | 0.872266i | ||||||||
\(506\) | −8.33475 | − | 49.2869i | −0.370525 | − | 2.19107i | ||||
\(507\) | −8.52622 | − | 8.52622i | −0.378663 | − | 0.378663i | ||||
\(508\) | 1.18276 | + | 3.39709i | 0.0524767 | + | 0.150721i | ||||
\(509\) | 22.3367 | − | 22.3367i | 0.990056 | − | 0.990056i | −0.00989464 | − | 0.999951i | \(-0.503150\pi\) |
0.999951 | + | 0.00989464i | \(0.00314961\pi\) | |||||||
\(510\) | −8.79677 | + | 12.3775i | −0.389528 | + | 0.548084i | ||||
\(511\) | −5.93888 | −0.262720 | ||||||||
\(512\) | 14.9592 | + | 16.9771i | 0.661111 | + | 0.750288i | ||||
\(513\) | 3.48596 | 0.153909 | ||||||||
\(514\) | 2.92785 | − | 4.11963i | 0.129142 | − | 0.181709i | ||||
\(515\) | 7.45759 | − | 7.45759i | 0.328620 | − | 0.328620i | ||||
\(516\) | 6.57217 | + | 18.8763i | 0.289324 | + | 0.830983i | ||||
\(517\) | 7.37496 | + | 7.37496i | 0.324350 | + | 0.324350i | ||||
\(518\) | −1.54467 | − | 9.13427i | −0.0678688 | − | 0.401337i | ||||
\(519\) | 10.7824i | 0.473296i | ||||||||
\(520\) | 3.65313 | + | 1.06169i | 0.160200 | + | 0.0465580i | ||||
\(521\) | − | 17.5991i | − | 0.771031i | −0.922701 | − | 0.385516i | \(-0.874024\pi\) | ||
0.922701 | − | 0.385516i | \(-0.125976\pi\) | |||||||
\(522\) | −7.27423 | + | 1.23012i | −0.318385 | + | 0.0538410i | ||||
\(523\) | −11.8194 | − | 11.8194i | −0.516828 | − | 0.516828i | 0.399782 | − | 0.916610i | \(-0.369086\pi\) |
−0.916610 | + | 0.399782i | \(0.869086\pi\) | |||||||
\(524\) | 32.6699 | + | 15.7957i | 1.42719 | + | 0.690037i | ||||
\(525\) | 2.17772 | − | 2.17772i | 0.0950435 | − | 0.0950435i | ||||
\(526\) | 5.14735 | + | 3.65826i | 0.224435 | + | 0.159508i | ||||
\(527\) | 58.9333 | 2.56718 | ||||||||
\(528\) | 13.2607 | − | 10.5077i | 0.577098 | − | 0.457291i | ||||
\(529\) | −46.8296 | −2.03607 | ||||||||
\(530\) | 14.6953 | + | 10.4440i | 0.638322 | + | 0.453660i | ||||
\(531\) | 2.18485 | − | 2.18485i | 0.0948142 | − | 0.0948142i | ||||
\(532\) | −3.03477 | + | 6.27678i | −0.131574 | + | 0.272133i | ||||
\(533\) | 5.07460 | + | 5.07460i | 0.219805 | + | 0.219805i | ||||
\(534\) | −8.31848 | + | 1.40671i | −0.359976 | + | 0.0608744i | ||||
\(535\) | 5.40426i | 0.233647i | ||||||||
\(536\) | 7.80751 | − | 4.29131i | 0.337233 | − | 0.185356i | ||||
\(537\) | − | 12.6761i | − | 0.547015i | ||||||
\(538\) | 3.68757 | + | 21.8062i | 0.158983 | + | 0.940131i | ||||
\(539\) | −2.99092 | − | 2.99092i | −0.128828 | − | 0.128828i | ||||
\(540\) | −2.61735 | + | 0.911283i | −0.112633 | + | 0.0392154i | ||||
\(541\) | −17.1403 | + | 17.1403i | −0.736919 | + | 0.736919i | −0.971981 | − | 0.235061i | \(-0.924471\pi\) |
0.235061 | + | 0.971981i | \(0.424471\pi\) | |||||||
\(542\) | −5.89252 | + | 8.29107i | −0.253106 | + | 0.356132i | ||||
\(543\) | 8.34783 | 0.358240 | ||||||||
\(544\) | −2.28753 | − | 43.7730i | −0.0980769 | − | 1.87675i | ||||
\(545\) | 15.0816 | 0.646026 | ||||||||
\(546\) | 0.795193 | − | 1.11887i | 0.0340311 | − | 0.0478834i | ||||
\(547\) | −10.3324 | + | 10.3324i | −0.441782 | + | 0.441782i | −0.892611 | − | 0.450828i | \(-0.851129\pi\) |
0.450828 | + | 0.892611i | \(0.351129\pi\) | |||||||
\(548\) | 26.9248 | − | 9.37440i | 1.15017 | − | 0.400455i | ||||
\(549\) | 1.02350 | + | 1.02350i | 0.0436817 | + | 0.0436817i | ||||
\(550\) | 3.07178 | + | 18.1647i | 0.130981 | + | 0.774547i | ||||
\(551\) | 18.1852i | 0.774715i | ||||||||
\(552\) | −11.3846 | − | 20.7130i | −0.484562 | − | 0.881602i | ||||
\(553\) | 2.58459i | 0.109908i | ||||||||
\(554\) | 12.2236 | − | 2.06710i | 0.519333 | − | 0.0878228i | ||||
\(555\) | −6.41866 | − | 6.41866i | −0.272457 | − | 0.272457i | ||||
\(556\) | −8.58460 | + | 17.7554i | −0.364068 | + | 0.752997i | ||||
\(557\) | 6.71091 | − | 6.71091i | 0.284351 | − | 0.284351i | −0.550491 | − | 0.834841i | \(-0.685559\pi\) |
0.834841 | + | 0.550491i | \(0.185559\pi\) | |||||||
\(558\) | 8.76737 | + | 6.23104i | 0.371152 | + | 0.263781i | ||||
\(559\) | −9.70025 | −0.410277 | ||||||||
\(560\) | 0.637740 | − | 5.50610i | 0.0269494 | − | 0.232675i | ||||
\(561\) | −32.7750 | −1.38376 | ||||||||
\(562\) | 14.5273 | + | 10.3246i | 0.612796 | + | 0.435519i | ||||
\(563\) | 0.997484 | − | 0.997484i | 0.0420389 | − | 0.0420389i | −0.685775 | − | 0.727814i | \(-0.740537\pi\) |
0.727814 | + | 0.685775i | \(0.240537\pi\) | |||||||
\(564\) | 4.43986 | + | 2.14664i | 0.186952 | + | 0.0903896i | ||||
\(565\) | 4.58753 | + | 4.58753i | 0.192999 | + | 0.192999i | ||||
\(566\) | 12.3122 | − | 2.08207i | 0.517520 | − | 0.0875161i | ||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 11.1883 | − | 38.4976i | 0.469450 | − | 1.61532i | ||||
\(569\) | − | 33.8927i | − | 1.42085i | −0.703771 | − | 0.710427i | \(-0.748502\pi\) | ||
0.703771 | − | 0.710427i | \(-0.251498\pi\) | |||||||
\(570\) | 1.13908 | + | 6.73586i | 0.0477108 | + | 0.282134i | ||||
\(571\) | 29.0688 | + | 29.0688i | 1.21649 | + | 1.21649i | 0.968853 | + | 0.247638i | \(0.0796544\pi\) |
0.247638 | + | 0.968853i | \(0.420346\pi\) | |||||||
\(572\) | 2.69988 | + | 7.75449i | 0.112888 | + | 0.324232i | ||||
\(573\) | 15.4273 | − | 15.4273i | 0.644485 | − | 0.644485i | ||||
\(574\) | 6.05744 | − | 8.52311i | 0.252833 | − | 0.355748i | ||||
\(575\) | 25.7357 | 1.07325 | ||||||||
\(576\) | 4.28782 | − | 6.75386i | 0.178659 | − | 0.281411i | ||||
\(577\) | −35.6352 | −1.48351 | −0.741756 | − | 0.670670i | \(-0.766007\pi\) | ||||
−0.741756 | + | 0.670670i | \(0.766007\pi\) | |||||||
\(578\) | −35.2616 | + | 49.6148i | −1.46669 | + | 2.06370i | ||||
\(579\) | −4.37490 | + | 4.37490i | −0.181815 | + | 0.181815i | ||||
\(580\) | −4.75388 | − | 13.6539i | −0.197394 | − | 0.566947i | ||||
\(581\) | 4.80684 | + | 4.80684i | 0.199421 | + | 0.199421i | ||||
\(582\) | −2.64832 | − | 15.6606i | −0.109776 | − | 0.649155i | ||||
\(583\) | 38.9124i | 1.61159i | ||||||||
\(584\) | 4.68784 | − | 16.1303i | 0.193984 | − | 0.667476i | ||||
\(585\) | − | 1.34502i | − | 0.0556096i | ||||||
\(586\) | −21.1982 | + | 3.58476i | −0.875688 | + | 0.148085i | ||||
\(587\) | −6.05112 | − | 6.05112i | −0.249756 | − | 0.249756i | 0.571114 | − | 0.820871i | \(-0.306511\pi\) |
−0.820871 | + | 0.571114i | \(0.806511\pi\) | |||||||
\(588\) | −1.80059 | − | 0.870569i | −0.0742549 | − | 0.0359017i | ||||
\(589\) | 18.7476 | − | 18.7476i | 0.772482 | − | 0.772482i | ||||
\(590\) | 4.93566 | + | 3.50781i | 0.203198 | + | 0.144414i | ||||
\(591\) | −6.70098 | −0.275641 | ||||||||
\(592\) | 26.0284 | + | 3.01472i | 1.06976 | + | 0.123904i | ||||
\(593\) | −42.5490 | −1.74728 | −0.873639 | − | 0.486575i | \(-0.838246\pi\) | ||||
−0.873639 | + | 0.486575i | \(0.838246\pi\) | |||||||
\(594\) | −4.87586 | − | 3.46531i | −0.200059 | − | 0.142183i | ||||
\(595\) | −7.59252 | + | 7.59252i | −0.311263 | + | 0.311263i | ||||
\(596\) | 1.76915 | − | 3.65910i | 0.0724671 | − | 0.149883i | ||||
\(597\) | 12.4714 | + | 12.4714i | 0.510422 | + | 0.510422i | ||||
\(598\) | 11.3100 | − | 1.91259i | 0.462499 | − | 0.0782118i | ||||
\(599\) | 14.9804i | 0.612082i | 0.952018 | + | 0.306041i | \(0.0990045\pi\) | ||||
−0.952018 | + | 0.306041i | \(0.900995\pi\) | |||||||
\(600\) | 4.19582 | + | 7.63378i | 0.171294 | + | 0.311648i | ||||
\(601\) | − | 43.3018i | − | 1.76632i | −0.469075 | − | 0.883158i | \(-0.655413\pi\) | ||
0.469075 | − | 0.883158i | \(-0.344587\pi\) | |||||||
\(602\) | 2.35660 | + | 13.9356i | 0.0960480 | + | 0.567972i | ||||
\(603\) | −2.22728 | − | 2.22728i | −0.0907019 | − | 0.0907019i | ||||
\(604\) | 13.3938 | − | 4.66332i | 0.544986 | − | 0.189748i | ||||
\(605\) | 6.75238 | − | 6.75238i | 0.274523 | − | 0.274523i | ||||
\(606\) | −11.5888 | + | 16.3060i | −0.470764 | + | 0.662388i | ||||
\(607\) | −40.4798 | −1.64303 | −0.821513 | − | 0.570190i | \(-0.806870\pi\) | ||||
−0.821513 | + | 0.570190i | \(0.806870\pi\) | |||||||
\(608\) | −14.6526 | − | 13.1972i | −0.594239 | − | 0.535215i | ||||
\(609\) | −5.21669 | −0.211391 | ||||||||
\(610\) | −1.64324 | + | 2.31212i | −0.0665329 | + | 0.0936150i | ||||
\(611\) | −1.69235 | + | 1.69235i | −0.0684651 | + | 0.0684651i | ||||
\(612\) | −14.6355 | + | 5.09564i | −0.591604 | + | 0.205979i | ||||
\(613\) | −8.87961 | − | 8.87961i | −0.358644 | − | 0.358644i | 0.504669 | − | 0.863313i | \(-0.331615\pi\) |
−0.863313 | + | 0.504669i | \(0.831615\pi\) | |||||||
\(614\) | 6.14064 | + | 36.3122i | 0.247816 | + | 1.46544i | ||||
\(615\) | − | 10.2458i | − | 0.413149i | ||||||
\(616\) | 10.4844 | − | 5.76261i | 0.422427 | − | 0.232182i | ||||
\(617\) | 24.7983i | 0.998342i | 0.866503 | + | 0.499171i | \(0.166362\pi\) | ||||
−0.866503 | + | 0.499171i | \(0.833638\pi\) | |||||||
\(618\) | 10.6128 | − | 1.79469i | 0.426907 | − | 0.0721929i | ||||
\(619\) | −19.1531 | − | 19.1531i | −0.769830 | − | 0.769830i | 0.208246 | − | 0.978076i | \(-0.433224\pi\) |
−0.978076 | + | 0.208246i | \(0.933224\pi\) | |||||||
\(620\) | −9.17527 | + | 18.9771i | −0.368488 | + | 0.762138i | ||||
\(621\) | −5.90887 | + | 5.90887i | −0.237115 | + | 0.237115i | ||||
\(622\) | 22.0539 | + | 15.6739i | 0.884281 | + | 0.628465i | ||||
\(623\) | −5.96557 | −0.239005 | ||||||||
\(624\) | 2.41124 | + | 3.04296i | 0.0965267 | + | 0.121816i | ||||
\(625\) | 0.116268 | 0.00465074 | ||||||||
\(626\) | −37.5785 | − | 26.7073i | −1.50194 | − | 1.06744i | ||||
\(627\) | −10.4262 | + | 10.4262i | −0.416384 | + | 0.416384i | ||||
\(628\) | −31.0262 | − | 15.0009i | −1.23808 | − | 0.598603i | ||||
\(629\) | −35.8913 | − | 35.8913i | −1.43108 | − | 1.43108i | ||||
\(630\) | −1.93228 | + | 0.326762i | −0.0769839 | + | 0.0130185i | ||||
\(631\) | 24.9707i | 0.994068i | 0.867731 | + | 0.497034i | \(0.165578\pi\) | ||||
−0.867731 | + | 0.497034i | \(0.834422\pi\) | |||||||
\(632\) | −7.01986 | − | 2.04014i | −0.279235 | − | 0.0811523i | ||||
\(633\) | 23.9273i | 0.951026i | ||||||||
\(634\) | 5.60385 | + | 33.1380i | 0.222557 | + | 1.31608i | ||||
\(635\) | 1.76232 | + | 1.76232i | 0.0699356 | + | 0.0699356i | ||||
\(636\) | 6.04984 | + | 17.3761i | 0.239892 | + | 0.689007i | ||||
\(637\) | 0.686333 | − | 0.686333i | 0.0271935 | − | 0.0271935i | ||||
\(638\) | 18.0774 | − | 25.4358i | 0.715693 | − | 1.00701i | ||||
\(639\) | −14.1741 | −0.560719 | ||||||||
\(640\) | 14.4514 | + | 6.07836i | 0.571243 | + | 0.240268i | ||||
\(641\) | −46.6091 | −1.84095 | −0.920474 | − | 0.390805i | \(-0.872197\pi\) | ||||
−0.920474 | + | 0.390805i | \(0.872197\pi\) | |||||||
\(642\) | −3.19508 | + | 4.49563i | −0.126100 | + | 0.177428i | ||||
\(643\) | 11.0061 | − | 11.0061i | 0.434037 | − | 0.434037i | −0.455962 | − | 0.889999i | \(-0.650705\pi\) |
0.889999 | + | 0.455962i | \(0.150705\pi\) | |||||||
\(644\) | −5.49535 | − | 15.7835i | −0.216547 | − | 0.621958i | ||||
\(645\) | 9.79255 | + | 9.79255i | 0.385581 | + | 0.385581i | ||||
\(646\) | 6.36941 | + | 37.6650i | 0.250601 | + | 1.48191i | ||||
\(647\) | 38.4788i | 1.51276i | 0.654133 | + | 0.756379i | \(0.273033\pi\) | ||||
−0.654133 | + | 0.756379i | \(0.726967\pi\) | |||||||
\(648\) | −2.71605 | − | 0.789348i | −0.106697 | − | 0.0310085i | ||||
\(649\) | 13.0694i | 0.513018i | ||||||||
\(650\) | −4.16830 | + | 0.704888i | −0.163494 | + | 0.0276480i | ||||
\(651\) | 5.37803 | + | 5.37803i | 0.210781 | + | 0.210781i | ||||
\(652\) | 17.2894 | + | 8.35929i | 0.677105 | + | 0.327375i | ||||
\(653\) | −8.40405 | + | 8.40405i | −0.328876 | + | 0.328876i | −0.852159 | − | 0.523283i | \(-0.824707\pi\) |
0.523283 | + | 0.852159i | \(0.324707\pi\) | |||||||
\(654\) | 12.5459 | + | 8.91647i | 0.490584 | + | 0.348662i | ||||
\(655\) | 25.1427 | 0.982407 | ||||||||
\(656\) | 18.3678 | + | 23.1800i | 0.717141 | + | 0.905028i | ||||
\(657\) | −5.93888 | −0.231698 | ||||||||
\(658\) | 2.84241 | + | 2.02012i | 0.110809 | + | 0.0787525i | ||||
\(659\) | 28.9012 | − | 28.9012i | 1.12583 | − | 1.12583i | 0.134985 | − | 0.990848i | \(-0.456902\pi\) |
0.990848 | − | 0.134985i | \(-0.0430985\pi\) | |||||||
\(660\) | 5.10271 | − | 10.5539i | 0.198623 | − | 0.410808i | ||||
\(661\) | −13.2673 | − | 13.2673i | −0.516037 | − | 0.516037i | 0.400333 | − | 0.916370i | \(-0.368895\pi\) |
−0.916370 | + | 0.400333i | \(0.868895\pi\) | |||||||
\(662\) | 45.7576 | − | 7.73792i | 1.77842 | − | 0.300743i | ||||
\(663\) | − | 7.52095i | − | 0.292090i | ||||||
\(664\) | −16.8499 | + | 9.26135i | −0.653903 | + | 0.359410i | ||||
\(665\) | 4.83059i | 0.187322i | ||||||||
\(666\) | −1.54467 | − | 9.13427i | −0.0598546 | − | 0.353946i | ||||
\(667\) | −30.8248 | − | 30.8248i | −1.19354 | − | 1.19354i | ||||
\(668\) | 10.4565 | − | 3.64063i | 0.404573 | − | 0.140860i | ||||
\(669\) | 7.11987 | − | 7.11987i | 0.275270 | − | 0.275270i | ||||
\(670\) | 3.57594 | − | 5.03152i | 0.138151 | − | 0.194385i | ||||
\(671\) | −6.12238 | −0.236352 | ||||||||
\(672\) | 3.78580 | − | 4.20330i | 0.146040 | − | 0.162146i | ||||
\(673\) | 17.5478 | 0.676417 | 0.338209 | − | 0.941071i | \(-0.390179\pi\) | ||||
0.338209 | + | 0.941071i | \(0.390179\pi\) | |||||||
\(674\) | −2.27313 | + | 3.19841i | −0.0875578 | + | 0.123198i | ||||
\(675\) | 2.17772 | − | 2.17772i | 0.0838205 | − | 0.0838205i | ||||
\(676\) | 22.7749 | − | 7.92953i | 0.875956 | − | 0.304982i | ||||
\(677\) | −33.3465 | − | 33.3465i | −1.28161 | − | 1.28161i | −0.939752 | − | 0.341858i | \(-0.888944\pi\) |
−0.341858 | − | 0.939752i | \(-0.611056\pi\) | |||||||
\(678\) | 1.10400 | + | 6.52842i | 0.0423989 | + | 0.250723i | ||||
\(679\) | − | 11.2310i | − | 0.431005i | ||||||
\(680\) | −14.6285 | − | 26.6148i | −0.560978 | − | 1.02063i | ||||
\(681\) | − | 21.0930i | − | 0.808287i | ||||||
\(682\) | −44.8590 | + | 7.58597i | −1.71774 | + | 0.290482i | ||||
\(683\) | −17.1553 | − | 17.1553i | −0.656431 | − | 0.656431i | 0.298103 | − | 0.954534i | \(-0.403646\pi\) |
−0.954534 | + | 0.298103i | \(0.903646\pi\) | |||||||
\(684\) | −3.03477 | + | 6.27678i | −0.116037 | + | 0.239999i | ||||
\(685\) | 13.9679 | − | 13.9679i | 0.533685 | − | 0.533685i | ||||
\(686\) | −1.15274 | − | 0.819262i | −0.0440118 | − | 0.0312796i | ||||
\(687\) | 4.46094 | 0.170195 | ||||||||
\(688\) | −39.7099 | − | 4.59938i | −1.51393 | − | 0.175350i | ||||
\(689\) | −8.92931 | −0.340180 | ||||||||
\(690\) | −13.3484 | − | 9.48680i | −0.508164 | − | 0.361156i | ||||
\(691\) | −20.0455 | + | 20.0455i | −0.762566 | + | 0.762566i | −0.976786 | − | 0.214220i | \(-0.931279\pi\) |
0.214220 | + | 0.976786i | \(0.431279\pi\) | |||||||
\(692\) | −19.4147 | − | 9.38685i | −0.738036 | − | 0.356835i | ||||
\(693\) | −2.99092 | − | 2.99092i | −0.113616 | − | 0.113616i | ||||
\(694\) | −9.04141 | + | 1.52896i | −0.343207 | + | 0.0580387i | ||||
\(695\) | 13.6645i | 0.518325i | ||||||||
\(696\) | 4.11778 | − | 14.1688i | 0.156084 | − | 0.537067i | ||||
\(697\) | − | 57.2914i | − | 2.17007i | ||||||
\(698\) | 2.40046 | + | 14.1949i | 0.0908587 | + | 0.537286i | ||||
\(699\) | 5.42019 | + | 5.42019i | 0.205010 | + | 0.205010i | ||||
\(700\) | 2.02532 | + | 5.81703i | 0.0765497 | + | 0.219863i | ||||
\(701\) | −34.1260 | + | 34.1260i | −1.28892 | + | 1.28892i | −0.353481 | + | 0.935442i | \(0.615002\pi\) |
−0.935442 | + | 0.353481i | \(0.884998\pi\) | |||||||
\(702\) | 0.795193 | − | 1.11887i | 0.0300126 | − | 0.0422292i | ||||
\(703\) | −22.8352 | −0.861245 | ||||||||
\(704\) | 7.37573 | + | 33.0248i | 0.277983 | + | 1.24467i | ||||
\(705\) | 3.41690 | 0.128688 | ||||||||
\(706\) | 27.3598 | − | 38.4966i | 1.02970 | − | 1.44884i | ||||
\(707\) | −10.0023 | + | 10.0023i | −0.376177 | + | 0.376177i | ||||
\(708\) | 2.03194 | + | 5.83606i | 0.0763651 | + | 0.219333i | ||||
\(709\) | −21.5424 | − | 21.5424i | −0.809040 | − | 0.809040i | 0.175448 | − | 0.984489i | \(-0.443862\pi\) |
−0.984489 | + | 0.175448i | \(0.943862\pi\) | |||||||
\(710\) | −4.63155 | − | 27.3883i | −0.173819 | − | 1.02787i | ||||
\(711\) | 2.58459i | 0.0969295i | ||||||||
\(712\) | 4.70891 | − | 16.2028i | 0.176474 | − | 0.607225i | ||||
\(713\) | 63.5562i | 2.38020i | ||||||||
\(714\) | −10.8048 | + | 1.82716i | −0.404358 | + | 0.0683797i | ||||
\(715\) | 4.02283 | + | 4.02283i | 0.150445 | + | 0.150445i | ||||
\(716\) | 22.8244 | + | 11.0354i | 0.852989 | + | 0.412414i | ||||
\(717\) | −2.23870 | + | 2.23870i | −0.0836056 | + | 0.0836056i | ||||
\(718\) | −35.0993 | − | 24.9453i | −1.30989 | − | 0.930951i | ||||
\(719\) | −18.3813 | −0.685505 | −0.342752 | − | 0.939426i | \(-0.611359\pi\) | ||||
−0.342752 | + | 0.939426i | \(0.611359\pi\) | |||||||
\(720\) | 0.637740 | − | 5.50610i | 0.0237672 | − | 0.205200i | ||||
\(721\) | 7.61089 | 0.283444 | ||||||||
\(722\) | −7.89403 | − | 5.61035i | −0.293785 | − | 0.208796i | ||||
\(723\) | 8.25833 | − | 8.25833i | 0.307131 | − | 0.307131i | ||||
\(724\) | −7.26736 | + | 15.0310i | −0.270089 | + | 0.558622i | ||||
\(725\) | 11.3605 | + | 11.3605i | 0.421918 | + | 0.421918i | ||||
\(726\) | 9.60918 | − | 1.62498i | 0.356630 | − | 0.0603086i | ||||
\(727\) | 14.8076i | 0.549185i | 0.961561 | + | 0.274593i | \(0.0885430\pi\) | ||||
−0.961561 | + | 0.274593i | \(0.911457\pi\) | |||||||
\(728\) | 1.32236 | + | 2.40587i | 0.0490099 | + | 0.0891675i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −1.94060 | − | 11.4756i | −0.0718247 | − | 0.424730i | ||||
\(731\) | 54.7572 | + | 54.7572i | 2.02527 | + | 2.02527i | ||||
\(732\) | −2.73392 | + | 0.951868i | −0.101048 | + | 0.0351821i | ||||
\(733\) | 4.58173 | − | 4.58173i | 0.169230 | − | 0.169230i | −0.617411 | − | 0.786641i | \(-0.711818\pi\) |
0.786641 | + | 0.617411i | \(0.211818\pi\) | |||||||
\(734\) | 6.03953 | − | 8.49791i | 0.222923 | − | 0.313663i | ||||
\(735\) | −1.38573 | −0.0511133 | ||||||||
\(736\) | 47.2066 | − | 2.46696i | 1.74006 | − | 0.0909335i | ||||
\(737\) | 13.3232 | 0.490768 | ||||||||
\(738\) | 6.05744 | − | 8.52311i | 0.222977 | − | 0.313740i | ||||
\(739\) | 20.3064 | − | 20.3064i | 0.746984 | − | 0.746984i | −0.226927 | − | 0.973912i | \(-0.572868\pi\) |
0.973912 | + | 0.226927i | \(0.0728680\pi\) | |||||||
\(740\) | 17.1452 | − | 5.96946i | 0.630271 | − | 0.219442i | ||||
\(741\) | −2.39253 | − | 2.39253i | −0.0878918 | − | 0.0878918i | ||||
\(742\) | 2.16931 | + | 12.8280i | 0.0796379 | + | 0.470933i | ||||
\(743\) | 12.7830i | 0.468964i | 0.972120 | + | 0.234482i | \(0.0753394\pi\) | ||||
−0.972120 | + | 0.234482i | \(0.924661\pi\) | |||||||
\(744\) | −18.8521 | + | 10.3619i | −0.691152 | + | 0.379884i | ||||
\(745\) | − | 2.81604i | − | 0.103172i | ||||||
\(746\) | 24.8712 | − | 4.20590i | 0.910601 | − | 0.153989i | ||||
\(747\) | 4.80684 | + | 4.80684i | 0.175873 | + | 0.175873i | ||||
\(748\) | 28.5329 | − | 59.0142i | 1.04327 | − | 2.15777i | ||||
\(749\) | −2.75768 | + | 2.75768i | −0.100763 | + | 0.100763i | ||||
\(750\) | 12.9065 | + | 9.17273i | 0.471278 | + | 0.334941i | ||||
\(751\) | −34.4832 | −1.25831 | −0.629155 | − | 0.777280i | \(-0.716599\pi\) | ||||
−0.629155 | + | 0.777280i | \(0.716599\pi\) | |||||||
\(752\) | −7.73040 | + | 6.12555i | −0.281899 | + | 0.223376i | ||||
\(753\) | 2.85889 | 0.104184 | ||||||||
\(754\) | 5.83682 | + | 4.14827i | 0.212564 | + | 0.151071i | ||||
\(755\) | 6.94836 | − | 6.94836i | 0.252877 | − | 0.252877i | ||||
\(756\) | −1.80059 | − | 0.870569i | −0.0654867 | − | 0.0316623i | ||||
\(757\) | 0.510274 | + | 0.510274i | 0.0185462 | + | 0.0185462i | 0.716319 | − | 0.697773i | \(-0.245826\pi\) |
−0.697773 | + | 0.716319i | \(0.745826\pi\) | |||||||
\(758\) | 18.1017 | − | 3.06111i | 0.657482 | − | 0.111185i | ||||
\(759\) | − | 35.3459i | − | 1.28298i | ||||||
\(760\) | −13.1201 | − | 3.81302i | −0.475917 | − | 0.138313i | ||||
\(761\) | − | 27.0730i | − | 0.981396i | −0.871330 | − | 0.490698i | \(-0.836742\pi\) | ||
0.871330 | − | 0.490698i | \(-0.163258\pi\) | |||||||
\(762\) | 0.424108 | + | 2.50793i | 0.0153638 | + | 0.0908526i | ||||
\(763\) | 7.69583 | + | 7.69583i | 0.278608 | + | 0.278608i | ||||
\(764\) | 14.3477 | + | 41.2087i | 0.519080 | + | 1.49088i | ||||
\(765\) | −7.59252 | + | 7.59252i | −0.274508 | + | 0.274508i | ||||
\(766\) | 5.20281 | − | 7.32061i | 0.187985 | − | 0.264504i | ||||
\(767\) | −2.99906 | −0.108290 | ||||||||
\(768\) | 8.42806 | + | 13.6003i | 0.304122 | + | 0.490758i | ||||
\(769\) | −8.47674 | −0.305679 | −0.152840 | − | 0.988251i | \(-0.548842\pi\) | ||||
−0.152840 | + | 0.988251i | \(0.548842\pi\) | |||||||
\(770\) | 4.80197 | − | 6.75661i | 0.173051 | − | 0.243491i | ||||
\(771\) | 2.52704 | − | 2.52704i | 0.0910091 | − | 0.0910091i | ||||
\(772\) | −4.06873 | − | 11.6860i | −0.146437 | − | 0.420590i | ||||
\(773\) | −6.94565 | − | 6.94565i | −0.249818 | − | 0.249818i | 0.571078 | − | 0.820896i | \(-0.306525\pi\) |
−0.820896 | + | 0.571078i | \(0.806525\pi\) | |||||||
\(774\) | 2.35660 | + | 13.9356i | 0.0847064 | + | 0.500904i | ||||
\(775\) | − | 23.4237i | − | 0.841403i | ||||||
\(776\) | 30.5039 | + | 8.86514i | 1.09503 | + | 0.318240i | ||||
\(777\) | − | 6.55060i | − | 0.235002i | ||||||
\(778\) | −20.0331 | + | 3.38773i | −0.718221 | + | 0.121456i | ||||
\(779\) | −18.2253 | − | 18.2253i | −0.652989 | − | 0.652989i | ||||
\(780\) | 2.42182 | + | 1.17093i | 0.0867150 | + | 0.0419260i | ||||
\(781\) | 42.3936 | − | 42.3936i | 1.51696 | − | 1.51696i | ||||
\(782\) | −74.6405 | − | 53.0475i | −2.66914 | − | 1.89698i | ||||
\(783\) | −5.21669 | −0.186429 | ||||||||
\(784\) | 3.13507 | − | 2.48422i | 0.111967 | − | 0.0887221i | ||||
\(785\) | −23.8777 | −0.852233 | ||||||||
\(786\) | 20.9154 | + | 14.8647i | 0.746028 | + | 0.530208i | ||||
\(787\) | −25.0044 | + | 25.0044i | −0.891310 | + | 0.891310i | −0.994646 | − | 0.103336i | \(-0.967048\pi\) |
0.103336 | + | 0.994646i | \(0.467048\pi\) | |||||||
\(788\) | 5.83367 | − | 12.0657i | 0.207816 | − | 0.429822i | ||||
\(789\) | 3.15745 | + | 3.15745i | 0.112408 | + | 0.112408i | ||||
\(790\) | −4.99414 | + | 0.844543i | −0.177684 | + | 0.0300475i | ||||
\(791\) | 4.68183i | 0.166467i | ||||||||
\(792\) | 10.4844 | − | 5.76261i | 0.372546 | − | 0.204765i | ||||
\(793\) | − | 1.40492i | − | 0.0498901i | ||||||
\(794\) | 4.74018 | + | 28.0307i | 0.168223 | + | 0.994772i | ||||
\(795\) | 9.01428 | + | 9.01428i | 0.319703 | + | 0.319703i | ||||
\(796\) | −33.3131 | + | 11.5986i | −1.18075 | + | 0.411103i | ||||
\(797\) | −14.3282 | + | 14.3282i | −0.507533 | + | 0.507533i | −0.913768 | − | 0.406236i | \(-0.866841\pi\) |
0.406236 | + | 0.913768i | \(0.366841\pi\) | |||||||
\(798\) | −2.85592 | + | 4.01841i | −0.101098 | + | 0.142250i | ||||
\(799\) | 19.1064 | 0.675935 | ||||||||
\(800\) | −17.3980 | + | 0.909202i | −0.615113 | + | 0.0321451i | ||||
\(801\) | −5.96557 | −0.210783 | ||||||||
\(802\) | −13.9897 | + | 19.6842i | −0.493993 | + | 0.695072i | ||||
\(803\) | 17.7627 | − | 17.7627i | 0.626832 | − | 0.626832i | ||||
\(804\) | 5.94942 | − | 2.07141i | 0.209820 | − | 0.0730530i | ||||
\(805\) | −8.18808 | − | 8.18808i | −0.288592 | − | 0.288592i | ||||
\(806\) | −1.74077 | − | 10.2939i | −0.0613160 | − | 0.362587i | ||||
\(807\) | 15.6382i | 0.550491i | ||||||||
\(808\) | −19.2716 | − | 35.0622i | −0.677971 | − | 1.23348i | ||||
\(809\) | − | 33.4003i | − | 1.17429i | −0.809481 | − | 0.587146i | \(-0.800251\pi\) | ||
0.809481 | − | 0.587146i | \(-0.199749\pi\) | |||||||
\(810\) | −1.93228 | + | 0.326762i | −0.0678934 | + | 0.0114812i | ||||
\(811\) | 21.6080 | + | 21.6080i | 0.758758 | + | 0.758758i | 0.976096 | − | 0.217339i | \(-0.0697376\pi\) |
−0.217339 | + | 0.976096i | \(0.569738\pi\) | |||||||
\(812\) | 4.54149 | − | 9.39310i | 0.159375 | − | 0.329633i | ||||
\(813\) | −5.08585 | + | 5.08585i | −0.178369 | + | 0.178369i | ||||
\(814\) | 31.9398 | + | 22.6999i | 1.11949 | + | 0.795630i | ||||
\(815\) | 13.3059 | 0.466085 | ||||||||
\(816\) | 3.56606 | − | 30.7886i | 0.124837 | − | 1.07782i | ||||
\(817\) | 34.8382 | 1.21883 | ||||||||
\(818\) | −40.6983 | − | 28.9246i | −1.42298 | − | 1.01132i | ||||
\(819\) | 0.686333 | − | 0.686333i | 0.0239824 | − | 0.0239824i | ||||
\(820\) | 18.4484 | + | 8.91965i | 0.644245 | + | 0.311488i | ||||
\(821\) | −19.8197 | − | 19.8197i | −0.691713 | − | 0.691713i | 0.270896 | − | 0.962609i | \(-0.412680\pi\) |
−0.962609 | + | 0.270896i | \(0.912680\pi\) | |||||||
\(822\) | 19.8774 | − | 3.36141i | 0.693305 | − | 0.117243i | ||||
\(823\) | − | 23.2507i | − | 0.810470i | −0.914213 | − | 0.405235i | \(-0.867190\pi\) | ||
0.914213 | − | 0.405235i | \(-0.132810\pi\) | |||||||
\(824\) | −6.00764 | + | 20.6716i | −0.209286 | + | 0.720128i | ||||
\(825\) | 13.0268i | 0.453534i | ||||||||
\(826\) | 0.728600 | + | 4.30852i | 0.0253512 | + | 0.149913i | ||||
\(827\) | −15.1321 | − | 15.1321i | −0.526196 | − | 0.526196i | 0.393240 | − | 0.919436i | \(-0.371354\pi\) |
−0.919436 | + | 0.393240i | \(0.871354\pi\) | |||||||
\(828\) | −5.49535 | − | 15.7835i | −0.190977 | − | 0.548515i | ||||
\(829\) | 30.4205 | − | 30.4205i | 1.05655 | − | 1.05655i | 0.0582469 | − | 0.998302i | \(-0.481449\pi\) |
0.998302 | − | 0.0582469i | \(-0.0185511\pi\) | |||||||
\(830\) | −7.71747 | + | 10.8589i | −0.267877 | + | 0.376916i | ||||
\(831\) | 8.76614 | 0.304094 | ||||||||
\(832\) | −7.57827 | + | 1.69253i | −0.262729 | + | 0.0586778i | ||||
\(833\) | −7.74860 | −0.268473 | ||||||||
\(834\) | −8.07866 | + | 11.3671i | −0.279741 | + | 0.393609i | ||||
\(835\) | 5.42455 | − | 5.42455i | 0.187724 | − | 0.187724i | ||||
\(836\) | −9.69657 | − | 27.8501i | −0.335363 | − | 0.963215i | ||||
\(837\) | 5.37803 | + | 5.37803i | 0.185892 | + | 0.185892i | ||||
\(838\) | −5.68150 | − | 33.5971i | −0.196264 | − | 1.16059i | ||||
\(839\) | − | 10.3618i | − | 0.357728i | −0.983874 | − | 0.178864i | \(-0.942758\pi\) | ||
0.983874 | − | 0.178864i | \(-0.0572423\pi\) | |||||||
\(840\) | 1.09382 | − | 3.76370i | 0.0377404 | − | 0.129860i | ||||
\(841\) | 1.78616i | 0.0615916i | ||||||||
\(842\) | −10.5661 | + | 1.78680i | −0.364131 | + | 0.0615770i | ||||
\(843\) | 8.91123 | + | 8.91123i | 0.306919 | + | 0.306919i | ||||
\(844\) | −43.0832 | − | 20.8304i | −1.48299 | − | 0.717012i | ||||
\(845\) | 11.8150 | − | 11.8150i | 0.406449 | − | 0.406449i | ||||
\(846\) | 2.84241 | + | 2.02012i | 0.0977240 | + | 0.0694532i | ||||
\(847\) | 6.89119 | 0.236784 | ||||||||
\(848\) | −36.5540 | − | 4.23384i | −1.25527 | − | 0.145391i | ||||
\(849\) | 8.82963 | 0.303032 | ||||||||
\(850\) | 27.5088 | + | 19.5507i | 0.943544 | + | 0.670584i | ||||
\(851\) | 38.7067 | − | 38.7067i | 1.32685 | − | 1.32685i | ||||
\(852\) | 12.3395 | − | 25.5217i | 0.422745 | − | 0.874358i | ||||
\(853\) | 24.1840 | + | 24.1840i | 0.828045 | + | 0.828045i | 0.987246 | − | 0.159201i | \(-0.0508918\pi\) |
−0.159201 | + | 0.987246i | \(0.550892\pi\) | |||||||
\(854\) | −2.01834 | + | 0.341314i | −0.0690660 | + | 0.0116795i | ||||
\(855\) | 4.83059i | 0.165203i | ||||||||
\(856\) | −5.31323 | − | 9.66676i | −0.181602 | − | 0.330403i | ||||
\(857\) | − | 24.0977i | − | 0.823163i | −0.911373 | − | 0.411581i | \(-0.864977\pi\) | ||
0.911373 | − | 0.411581i | \(-0.135023\pi\) | |||||||
\(858\) | 0.968106 | + | 5.72482i | 0.0330506 | + | 0.195442i | ||||
\(859\) | 31.4576 | + | 31.4576i | 1.07332 | + | 1.07332i | 0.997090 | + | 0.0762289i | \(0.0242880\pi\) |
0.0762289 | + | 0.997090i | \(0.475712\pi\) | |||||||
\(860\) | −26.1574 | + | 9.10723i | −0.891960 | + | 0.310554i | ||||
\(861\) | 5.22819 | − | 5.22819i | 0.178176 | − | 0.178176i | ||||
\(862\) | −6.98505 | + | 9.82831i | −0.237912 | + | 0.334754i | ||||
\(863\) | 20.4551 | 0.696299 | 0.348149 | − | 0.937439i | \(-0.386810\pi\) | ||||
0.348149 | + | 0.937439i | \(0.386810\pi\) | |||||||
\(864\) | 3.78580 | − | 4.20330i | 0.128795 | − | 0.142999i | ||||
\(865\) | −14.9415 | −0.508027 | ||||||||
\(866\) | 1.76176 | − | 2.47889i | 0.0598671 | − | 0.0842360i | ||||
\(867\) | −30.4344 | + | 30.4344i | −1.03361 | + | 1.03361i | ||||
\(868\) | −14.3655 | + | 5.00165i | −0.487598 | + | 0.169767i | ||||
\(869\) | −7.73028 | − | 7.73028i | −0.262232 | − | 0.262232i | ||||
\(870\) | −1.70461 | − | 10.0801i | −0.0577918 | − | 0.341747i | ||||
\(871\) | 3.05731i | 0.103593i | ||||||||
\(872\) | −26.9769 | + | 14.8276i | −0.913555 | + | 0.502125i | ||||
\(873\) | − | 11.2310i | − | 0.380111i | ||||||
\(874\) | −40.6195 | + | 6.86904i | −1.37398 | + | 0.232349i | ||||
\(875\) | 7.91701 | + | 7.91701i | 0.267644 | + | 0.267644i | ||||
\(876\) | 5.17020 | − | 10.6935i | 0.174685 | − | 0.361298i | ||||
\(877\) | 0.277805 | − | 0.277805i | 0.00938082 | − | 0.00938082i | −0.702401 | − | 0.711782i | \(-0.747889\pi\) |
0.711782 | + | 0.702401i | \(0.247889\pi\) | |||||||
\(878\) | −26.6435 | − | 18.9357i | −0.899174 | − | 0.639050i | ||||
\(879\) | −15.2022 | −0.512757 | ||||||||
\(880\) | 14.5609 | + | 18.3757i | 0.490847 | + | 0.619445i | ||||
\(881\) | 22.5049 | 0.758208 | 0.379104 | − | 0.925354i | \(-0.376232\pi\) | ||||
0.379104 | + | 0.925354i | \(0.376232\pi\) | |||||||
\(882\) | −1.15274 | − | 0.819262i | −0.0388148 | − | 0.0275860i | ||||
\(883\) | 5.44565 | − | 5.44565i | 0.183261 | − | 0.183261i | −0.609514 | − | 0.792775i | \(-0.708636\pi\) |
0.792775 | + | 0.609514i | \(0.208636\pi\) | |||||||
\(884\) | 13.5421 | + | 6.54751i | 0.455471 | + | 0.220217i | ||||
\(885\) | 3.02760 | + | 3.02760i | 0.101772 | + | 0.101772i | ||||
\(886\) | 3.82930 | − | 0.647561i | 0.128648 | − | 0.0217552i | ||||
\(887\) | 4.18811i | 0.140623i | 0.997525 | + | 0.0703114i | \(0.0223993\pi\) | ||||
−0.997525 | + | 0.0703114i | \(0.977601\pi\) | |||||||
\(888\) | 17.7918 | + | 5.17071i | 0.597053 | + | 0.173518i | ||||
\(889\) | 1.79855i | 0.0603214i | ||||||||
\(890\) | −1.94932 | − | 11.5271i | −0.0653413 | − | 0.386391i | ||||
\(891\) | −2.99092 | − | 2.99092i | −0.100200 | − | 0.100200i | ||||
\(892\) | 6.62160 | + | 19.0183i | 0.221708 | + | 0.636779i | ||||
\(893\) | 6.07803 | − | 6.07803i | 0.203394 | − | 0.203394i | ||||
\(894\) | 1.66488 | − | 2.34257i | 0.0556819 | − | 0.0783472i | ||||
\(895\) | 17.5656 | 0.587155 | ||||||||
\(896\) | 4.27260 | + | 10.4759i | 0.142738 | + | 0.349976i | ||||
\(897\) | 8.11091 | 0.270815 | ||||||||
\(898\) | −3.56185 | + | 5.01170i | −0.118861 | + | 0.167243i | ||||
\(899\) | −28.0555 | + | 28.0555i | −0.935703 | + | 0.935703i | ||||
\(900\) | 2.02532 | + | 5.81703i | 0.0675105 | + | 0.193901i | ||||
\(901\) | 50.4053 | + | 50.4053i | 1.67924 | + | 1.67924i | ||||
\(902\) | 7.37462 | + | 43.6092i | 0.245548 | + | 1.45203i | ||||
\(903\) | 9.99386i | 0.332575i | ||||||||
\(904\) | −12.7161 | − | 3.69560i | −0.422931 | − | 0.122914i | ||||
\(905\) | 11.5678i | 0.384527i | ||||||||
\(906\) | 9.88808 | − | 1.67214i | 0.328509 | − | 0.0555532i | ||||
\(907\) | −36.9451 | − | 36.9451i | −1.22674 | − | 1.22674i | −0.965189 | − | 0.261553i | \(-0.915765\pi\) |
−0.261553 | − | 0.965189i | \(-0.584235\pi\) | |||||||
\(908\) | 37.9798 | + | 18.3630i | 1.26041 | + | 0.609396i | ||||
\(909\) | −10.0023 | + | 10.0023i | −0.331757 | + | 0.331757i | ||||
\(910\) | 1.55045 | + | 1.10192i | 0.0513971 | + | 0.0365283i | ||||
\(911\) | −18.8612 | −0.624900 | −0.312450 | − | 0.949934i | \(-0.601150\pi\) | ||||
−0.312450 | + | 0.949934i | \(0.601150\pi\) | |||||||
\(912\) | −8.65990 | − | 10.9287i | −0.286758 | − | 0.361887i | ||||
\(913\) | −28.7537 | −0.951610 | ||||||||
\(914\) | 3.35283 | + | 2.38288i | 0.110902 | + | 0.0788188i | ||||
\(915\) | −1.41829 | + | 1.41829i | −0.0468871 | + | 0.0468871i | ||||
\(916\) | −3.88355 | + | 8.03230i | −0.128316 | + | 0.265395i | ||||
\(917\) | 12.8298 | + | 12.8298i | 0.423677 | + | 0.423677i | ||||
\(918\) | −10.8048 | + | 1.82716i | −0.356610 | + | 0.0603053i | ||||
\(919\) | − | 37.4649i | − | 1.23585i | −0.786236 | − | 0.617926i | \(-0.787973\pi\) | ||
0.786236 | − | 0.617926i | \(-0.212027\pi\) | |||||||
\(920\) | 28.7025 | − | 15.7760i | 0.946293 | − | 0.520119i | ||||
\(921\) | 26.0412i | 0.858085i | ||||||||
\(922\) | −0.285128 | − | 1.68608i | −0.00939020 | − | 0.0555282i | ||||
\(923\) | 9.72815 | + | 9.72815i | 0.320206 | + | 0.320206i | ||||
\(924\) | 7.98921 | − | 2.78160i | 0.262826 | − | 0.0915081i | ||||
\(925\) | −14.2654 | + | 14.2654i | −0.469043 | + | 0.469043i | ||||
\(926\) | −14.8640 | + | 20.9144i | −0.488461 | + | 0.687289i | ||||
\(927\) | 7.61089 | 0.249975 | ||||||||
\(928\) | 21.9273 | + | 19.7493i | 0.719799 | + | 0.648304i | ||||
\(929\) | −36.1739 | −1.18683 | −0.593413 | − | 0.804898i | \(-0.702220\pi\) | ||||
−0.593413 | + | 0.804898i | \(0.702220\pi\) | |||||||
\(930\) | −8.63452 | + | 12.1492i | −0.283137 | + | 0.398387i | ||||
\(931\) | −2.46495 | + | 2.46495i | −0.0807854 | + | 0.0807854i | ||||
\(932\) | −14.4782 | + | 5.04086i | −0.474248 | + | 0.165119i | ||||
\(933\) | 13.5282 | + | 13.5282i | 0.442892 | + | 0.442892i | ||||
\(934\) | −3.26100 | − | 19.2836i | −0.106703 | − | 0.630980i | ||||
\(935\) | − | 45.4172i | − | 1.48530i | ||||||
\(936\) | 1.32236 | + | 2.40587i | 0.0432227 | + | 0.0786383i | ||||
\(937\) | 50.8408i | 1.66090i | 0.557096 | + | 0.830448i | \(0.311916\pi\) | ||||
−0.557096 | + | 0.830448i | \(0.688084\pi\) | |||||||
\(938\) | 4.39220 | − | 0.742752i | 0.143411 | − | 0.0242517i | ||||
\(939\) | −23.0512 | − | 23.0512i | −0.752247 | − | 0.752247i | ||||
\(940\) | −2.97465 | + | 6.15243i | −0.0970224 | + | 0.200670i | ||||
\(941\) | 24.8105 | − | 24.8105i | 0.808801 | − | 0.808801i | −0.175652 | − | 0.984452i | \(-0.556203\pi\) |
0.984452 | + | 0.175652i | \(0.0562033\pi\) | |||||||
\(942\) | −19.8631 | − | 14.1169i | −0.647175 | − | 0.459952i | ||||
\(943\) | 61.7855 | 2.01201 | ||||||||
\(944\) | −12.2773 | − | 1.42201i | −0.399591 | − | 0.0462824i | ||||
\(945\) | −1.38573 | −0.0450777 | ||||||||
\(946\) | −48.7286 | − | 34.6318i | −1.58430 | − | 1.12598i | ||||
\(947\) | −9.91506 | + | 9.91506i | −0.322196 | + | 0.322196i | −0.849609 | − | 0.527413i | \(-0.823162\pi\) |
0.527413 | + | 0.849609i | \(0.323162\pi\) | |||||||
\(948\) | −4.65377 | − | 2.25006i | −0.151147 | − | 0.0730785i | ||||
\(949\) | 4.07605 | + | 4.07605i | 0.132314 | + | 0.132314i | ||||
\(950\) | 14.9704 | − | 2.53159i | 0.485703 | − | 0.0821356i | ||||
\(951\) | 23.7648i | 0.770625i | ||||||||
\(952\) | 6.11634 | − | 21.0456i | 0.198232 | − | 0.682091i | ||||
\(953\) | 28.5778i | 0.925726i | 0.886430 | + | 0.462863i | \(0.153178\pi\) | ||||
−0.886430 | + | 0.462863i | \(0.846822\pi\) | |||||||
\(954\) | 2.16931 | + | 12.8280i | 0.0702340 | + | 0.415323i | ||||
\(955\) | 21.3780 | + | 21.3780i | 0.691777 | + | 0.691777i | ||||
\(956\) | −2.08202 | − | 5.97990i | −0.0673375 | − | 0.193404i | ||||
\(957\) | 15.6027 | − | 15.6027i | 0.504363 | − | 0.504363i | ||||
\(958\) | −19.1732 | + | 26.9776i | −0.619457 | + | 0.871605i | ||||
\(959\) | 14.2550 | 0.460319 | ||||||||
\(960\) | 9.35901 | + | 5.94174i | 0.302061 | + | 0.191769i | ||||
\(961\) | 26.8463 | 0.866011 | ||||||||
\(962\) | −5.20899 | + | 7.32930i | −0.167945 | + | 0.236306i | ||||
\(963\) | −2.75768 | + | 2.75768i | −0.0888649 | + | 0.0888649i | ||||
\(964\) | 7.68038 | + | 22.0593i | 0.247368 | + | 0.710481i | ||||
\(965\) | −6.06242 | − | 6.06242i | −0.195156 | − | 0.195156i | ||||
\(966\) | −1.97048 | − | 11.6523i | −0.0633993 | − | 0.374907i | ||||
\(967\) | 20.7125i | 0.666068i | 0.942915 | + | 0.333034i | \(0.108072\pi\) | ||||
−0.942915 | + | 0.333034i | \(0.891928\pi\) | |||||||
\(968\) | −5.43954 | + | 18.7168i | −0.174834 | + | 0.601581i | ||||
\(969\) | 27.0113i | 0.867729i | ||||||||
\(970\) | 21.7014 | − | 3.66985i | 0.696789 | − | 0.117832i | ||||
\(971\) | −3.26325 | − | 3.26325i | −0.104723 | − | 0.104723i | 0.652804 | − | 0.757527i | \(-0.273592\pi\) |
−0.757527 | + | 0.652804i | \(0.773592\pi\) | |||||||
\(972\) | −1.80059 | − | 0.870569i | −0.0577538 | − | 0.0279235i | ||||
\(973\) | −6.97271 | + | 6.97271i | −0.223535 | + | 0.223535i | ||||
\(974\) | 18.7591 | + | 13.3322i | 0.601079 | + | 0.427191i | ||||
\(975\) | −2.98928 | −0.0957336 | ||||||||
\(976\) | 0.666142 | − | 5.75132i | 0.0213227 | − | 0.184095i | ||||
\(977\) | −5.01098 | −0.160315 | −0.0801577 | − | 0.996782i | \(-0.525542\pi\) | ||||
−0.0801577 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(978\) | 11.0687 | + | 7.86663i | 0.353939 | + | 0.251547i | ||||
\(979\) | 17.8425 | − | 17.8425i | 0.570250 | − | 0.570250i | ||||
\(980\) | 1.20637 | − | 2.49512i | 0.0385361 | − | 0.0797037i | ||||
\(981\) | 7.69583 | + | 7.69583i | 0.245709 | + | 0.245709i | ||||
\(982\) | −0.0533699 | + | 0.00902522i | −0.00170310 | + | 0.000288006i | ||||
\(983\) | − | 29.7225i | − | 0.947999i | −0.880525 | − | 0.474000i | \(-0.842810\pi\) | ||
0.880525 | − | 0.474000i | \(-0.157190\pi\) | |||||||
\(984\) | 10.0732 | + | 18.3269i | 0.321121 | + | 0.584240i | ||||
\(985\) | − | 9.28573i | − | 0.295868i | ||||||
\(986\) | −9.53172 | − | 56.3651i | −0.303552 | − | 1.79503i | ||||
\(987\) | 1.74357 | + | 1.74357i | 0.0554985 | + | 0.0554985i | ||||
\(988\) | 6.39082 | − | 2.22509i | 0.203319 | − | 0.0707897i | ||||
\(989\) | −59.0524 | + | 59.0524i | −1.87776 | + | 1.87776i | ||||
\(990\) | 4.80197 | − | 6.75661i | 0.152617 | − | 0.214739i | ||||
\(991\) | −56.2320 | −1.78627 | −0.893135 | − | 0.449789i | \(-0.851499\pi\) | ||||
−0.893135 | + | 0.449789i | \(0.851499\pi\) | |||||||
\(992\) | −2.24533 | − | 42.9656i | −0.0712894 | − | 1.36416i | ||||
\(993\) | 32.8149 | 1.04135 | ||||||||
\(994\) | 11.6123 | − | 16.3391i | 0.368319 | − | 0.518243i | ||||
\(995\) | −17.2820 | + | 17.2820i | −0.547876 | + | 0.547876i | ||||
\(996\) | −12.8398 | + | 4.47044i | −0.406845 | + | 0.141651i | ||||
\(997\) | 27.0545 | + | 27.0545i | 0.856826 | + | 0.856826i | 0.990963 | − | 0.134137i | \(-0.0428262\pi\) |
−0.134137 | + | 0.990963i | \(0.542826\pi\) | |||||||
\(998\) | 6.48637 | + | 38.3566i | 0.205322 | + | 1.21416i | ||||
\(999\) | − | 6.55060i | − | 0.207252i |
(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 | 336.2.w.b.85.5 | ✓ | 28 | |
4.3 | odd | 2 | 1344.2.w.b.1009.10 | 28 | |||
8.3 | odd | 2 | 2688.2.w.c.2017.5 | 28 | |||
8.5 | even | 2 | 2688.2.w.d.2017.10 | 28 | |||
16.3 | odd | 4 | 1344.2.w.b.337.10 | 28 | |||
16.5 | even | 4 | 2688.2.w.d.673.10 | 28 | |||
16.11 | odd | 4 | 2688.2.w.c.673.5 | 28 | |||
16.13 | even | 4 | inner | 336.2.w.b.253.5 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.w.b.85.5 | ✓ | 28 | 1.1 | even | 1 | trivial | |
336.2.w.b.253.5 | yes | 28 | 16.13 | even | 4 | inner | |
1344.2.w.b.337.10 | 28 | 16.3 | odd | 4 | |||
1344.2.w.b.1009.10 | 28 | 4.3 | odd | 2 | |||
2688.2.w.c.673.5 | 28 | 16.11 | odd | 4 | |||
2688.2.w.c.2017.5 | 28 | 8.3 | odd | 2 | |||
2688.2.w.d.673.10 | 28 | 16.5 | even | 4 | |||
2688.2.w.d.2017.10 | 28 | 8.5 | even | 2 |