Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(73,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 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("945.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.bv (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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 262.28 | ||
Character | \(\chi\) | \(=\) | 945.262 |
Dual form | 945.2.bv.e.523.28 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.690838 | + | 0.690838i | 0.488496 | + | 0.488496i | 0.907832 | − | 0.419335i | \(-0.137737\pi\) |
−0.419335 | + | 0.907832i | \(0.637737\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.04549i | − | 0.522743i | ||||||
\(5\) | −1.77477 | − | 1.36022i | −0.793700 | − | 0.608310i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.704044 | + | 2.55036i | −0.266104 | + | 0.963944i | ||||
\(8\) | 2.10394 | − | 2.10394i | 0.743854 | − | 0.743854i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.286383 | − | 2.16577i | −0.0905622 | − | 0.684877i | ||||
\(11\) | −0.816710 | − | 1.41458i | −0.246247 | − | 0.426513i | 0.716234 | − | 0.697860i | \(-0.245864\pi\) |
−0.962482 | + | 0.271347i | \(0.912531\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.137573 | + | 0.513429i | −0.0381558 | + | 0.142400i | −0.982376 | − | 0.186915i | \(-0.940151\pi\) |
0.944220 | + | 0.329315i | \(0.106818\pi\) | |||||||
\(14\) | −2.24826 | + | 1.27550i | −0.600874 | + | 0.340893i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.815990 | 0.203998 | ||||||||
\(17\) | −0.265268 | − | 0.989992i | −0.0643369 | − | 0.240108i | 0.926268 | − | 0.376866i | \(-0.122998\pi\) |
−0.990604 | + | 0.136758i | \(0.956332\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.99374 | − | 5.18531i | −0.686811 | − | 1.18959i | −0.972864 | − | 0.231377i | \(-0.925677\pi\) |
0.286053 | − | 0.958214i | \(-0.407657\pi\) | |||||||
\(20\) | −1.42209 | + | 1.85549i | −0.317989 | + | 0.414901i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.413034 | − | 1.54146i | 0.0880591 | − | 0.328641i | ||||
\(23\) | −1.92122 | − | 7.17009i | −0.400602 | − | 1.49507i | −0.812025 | − | 0.583622i | \(-0.801635\pi\) |
0.411423 | − | 0.911444i | \(-0.365032\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.29959 | + | 4.82815i | 0.259918 | + | 0.965631i | ||||
\(26\) | −0.449737 | + | 0.259656i | −0.0882006 | + | 0.0509227i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.66636 | + | 0.736068i | 0.503895 | + | 0.139104i | ||||
\(29\) | −5.82340 | − | 3.36214i | −1.08138 | − | 0.624334i | −0.150110 | − | 0.988669i | \(-0.547963\pi\) |
−0.931268 | + | 0.364335i | \(0.881296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.35659i | 1.50089i | 0.660934 | + | 0.750444i | \(0.270160\pi\) | ||||
−0.660934 | + | 0.750444i | \(0.729840\pi\) | |||||||
\(32\) | −3.64416 | − | 3.64416i | −0.644202 | − | 0.644202i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.500668 | − | 0.867182i | 0.0858638 | − | 0.148720i | ||||
\(35\) | 4.71857 | − | 3.56863i | 0.797583 | − | 0.603209i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.47305 | − | 5.49748i | 0.242167 | − | 0.903780i | −0.732619 | − | 0.680639i | \(-0.761702\pi\) |
0.974786 | − | 0.223141i | \(-0.0716311\pi\) | |||||||
\(38\) | 1.51402 | − | 5.65040i | 0.245606 | − | 0.916615i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.59582 | + | 0.872175i | −1.04289 | + | 0.137903i | ||||
\(41\) | −6.13816 | + | 3.54387i | −0.958619 | + | 0.553459i | −0.895748 | − | 0.444563i | \(-0.853359\pi\) |
−0.0628714 | + | 0.998022i | \(0.520026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.98612 | − | 7.41230i | −0.302880 | − | 1.13036i | −0.934755 | − | 0.355294i | \(-0.884381\pi\) |
0.631874 | − | 0.775071i | \(-0.282286\pi\) | |||||||
\(44\) | −1.47893 | + | 0.853858i | −0.222956 | + | 0.128724i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.62612 | − | 6.28062i | 0.534642 | − | 0.926027i | ||||
\(47\) | −1.39656 | + | 1.39656i | −0.203709 | + | 0.203709i | −0.801587 | − | 0.597878i | \(-0.796011\pi\) |
0.597878 | + | 0.801587i | \(0.296011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00864 | − | 3.59113i | −0.858378 | − | 0.513018i | ||||
\(50\) | −2.43767 | + | 4.23328i | −0.344738 | + | 0.598676i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.536782 | + | 0.143830i | 0.0744383 | + | 0.0199457i | ||||
\(53\) | −0.361997 | − | 1.35099i | −0.0497241 | − | 0.185573i | 0.936597 | − | 0.350409i | \(-0.113957\pi\) |
−0.986321 | + | 0.164836i | \(0.947291\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.474678 | + | 3.62146i | −0.0640056 | + | 0.488318i | ||||
\(56\) | 3.88453 | + | 6.84706i | 0.519092 | + | 0.914976i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.70033 | − | 6.34572i | −0.223264 | − | 0.833234i | ||||
\(59\) | 1.10522 | 0.143887 | 0.0719437 | − | 0.997409i | \(-0.477080\pi\) | ||||
0.0719437 | + | 0.997409i | \(0.477080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.7361i | − | 1.75873i | −0.476153 | − | 0.879363i | \(-0.657969\pi\) | ||
0.476153 | − | 0.879363i | \(-0.342031\pi\) | |||||||
\(62\) | −5.77305 | + | 5.77305i | −0.733178 | + | 0.733178i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 6.66703i | − | 0.833378i | ||||||
\(65\) | 0.942537 | − | 0.724087i | 0.116907 | − | 0.0898119i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.95260 | + | 3.95260i | 0.482886 | + | 0.482886i | 0.906052 | − | 0.423166i | \(-0.139081\pi\) |
−0.423166 | + | 0.906052i | \(0.639081\pi\) | |||||||
\(68\) | −1.03502 | + | 0.277333i | −0.125515 | + | 0.0336316i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.72511 | + | 0.794419i | 0.684282 | + | 0.0949512i | ||||
\(71\) | 6.35753 | 0.754500 | 0.377250 | − | 0.926112i | \(-0.376870\pi\) | ||||
0.377250 | + | 0.926112i | \(0.376870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.07255 | − | 1.62714i | 0.710739 | − | 0.190442i | 0.114703 | − | 0.993400i | \(-0.463408\pi\) |
0.596036 | + | 0.802958i | \(0.296742\pi\) | |||||||
\(74\) | 4.81551 | − | 2.78023i | 0.559791 | − | 0.323196i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.42116 | + | 3.12991i | −0.621850 | + | 0.359025i | ||||
\(77\) | 4.18269 | − | 1.08697i | 0.476662 | − | 0.123872i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.73743i | 0.758020i | 0.925393 | + | 0.379010i | \(0.123735\pi\) | ||||
−0.925393 | + | 0.379010i | \(0.876265\pi\) | |||||||
\(80\) | −1.44819 | − | 1.10993i | −0.161913 | − | 0.124094i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.68871 | − | 1.79224i | −0.738645 | − | 0.197919i | ||||
\(83\) | −3.78491 | + | 1.01416i | −0.415448 | + | 0.111319i | −0.460488 | − | 0.887666i | \(-0.652325\pi\) |
0.0450392 | + | 0.998985i | \(0.485659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.875822 | + | 2.11783i | −0.0949962 | + | 0.229711i | ||||
\(86\) | 3.74861 | − | 6.49278i | 0.404223 | − | 0.700135i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.69450 | − | 1.25789i | −0.500436 | − | 0.134091i | ||||
\(89\) | 9.04644 | + | 15.6689i | 0.958921 | + | 1.66090i | 0.725128 | + | 0.688614i | \(0.241780\pi\) |
0.233793 | + | 0.972286i | \(0.424886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.21257 | − | 0.712336i | −0.127112 | − | 0.0746731i | ||||
\(92\) | −7.49622 | + | 2.00861i | −0.781535 | + | 0.209412i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.92959 | −0.199022 | ||||||||
\(95\) | −1.73998 | + | 13.2749i | −0.178519 | + | 1.36197i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0399199 | + | 0.148983i | 0.00405325 | + | 0.0151270i | 0.967923 | − | 0.251248i | \(-0.0808409\pi\) |
−0.963870 | + | 0.266375i | \(0.914174\pi\) | |||||||
\(98\) | −1.67011 | − | 6.63189i | −0.168707 | − | 0.669922i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.04776 | − | 1.35870i | 0.504776 | − | 0.135870i | ||||
\(101\) | −7.05201 | + | 4.07148i | −0.701701 | + | 0.405127i | −0.807981 | − | 0.589209i | \(-0.799439\pi\) |
0.106280 | + | 0.994336i | \(0.466106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.91904 | − | 2.65780i | 0.977352 | − | 0.261881i | 0.265423 | − | 0.964132i | \(-0.414488\pi\) |
0.711929 | + | 0.702252i | \(0.247822\pi\) | |||||||
\(104\) | 0.790777 | + | 1.36967i | 0.0775421 | + | 0.134307i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.683235 | − | 1.18340i | 0.0663616 | − | 0.114942i | ||||
\(107\) | 0.329306 | − | 1.22899i | 0.0318352 | − | 0.118811i | −0.948180 | − | 0.317734i | \(-0.897078\pi\) |
0.980015 | + | 0.198924i | \(0.0637446\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0397 | + | 5.79643i | 0.961630 | + | 0.555197i | 0.896674 | − | 0.442691i | \(-0.145976\pi\) |
0.0649556 | + | 0.997888i | \(0.479309\pi\) | |||||||
\(110\) | −2.82977 | + | 2.17392i | −0.269808 | + | 0.207275i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.574493 | + | 2.08107i | −0.0542845 | + | 0.196642i | ||||
\(113\) | 20.1005 | + | 5.38592i | 1.89090 | + | 0.506664i | 0.998459 | + | 0.0554944i | \(0.0176735\pi\) |
0.892438 | + | 0.451170i | \(0.148993\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.34320 | + | 15.3385i | −0.591506 | + | 1.43032i | ||||
\(116\) | −3.51507 | + | 6.08828i | −0.326366 | + | 0.565282i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.763528 | + | 0.763528i | 0.0702884 | + | 0.0702884i | ||||
\(119\) | 2.71159 | + | 0.0204710i | 0.248571 | + | 0.00187657i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.16597 | − | 7.21567i | 0.378724 | − | 0.655970i | ||||
\(122\) | 9.48941 | − | 9.48941i | 0.859131 | − | 0.859131i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.73669 | 0.784578 | ||||||||
\(125\) | 4.26089 | − | 10.3366i | 0.381106 | − | 0.924531i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.86063 | − | 1.86063i | −0.165104 | − | 0.165104i | 0.619719 | − | 0.784824i | \(-0.287246\pi\) |
−0.784824 | + | 0.619719i | \(0.787246\pi\) | |||||||
\(128\) | −2.68248 | + | 2.68248i | −0.237100 | + | 0.237100i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.15137 | + | 0.150914i | 0.100982 | + | 0.0132360i | ||||
\(131\) | −1.82517 | − | 1.05376i | −0.159465 | − | 0.0920674i | 0.418144 | − | 0.908381i | \(-0.362681\pi\) |
−0.577609 | + | 0.816313i | \(0.696014\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.3321 | − | 3.98442i | 1.32946 | − | 0.345493i | ||||
\(134\) | 5.46121i | 0.471777i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.64099 | − | 1.52478i | −0.226463 | − | 0.130748i | ||||
\(137\) | 3.50159 | − | 13.0681i | 0.299161 | − | 1.11648i | −0.638695 | − | 0.769460i | \(-0.720526\pi\) |
0.937856 | − | 0.347024i | \(-0.112808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.44269 | + | 11.1591i | 0.546461 | + | 0.946499i | 0.998513 | + | 0.0545074i | \(0.0173588\pi\) |
−0.452052 | + | 0.891992i | \(0.649308\pi\) | |||||||
\(140\) | −3.73095 | − | 4.93319i | −0.315323 | − | 0.416931i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.39202 | + | 4.39202i | 0.368570 | + | 0.368570i | ||||
\(143\) | 0.838645 | − | 0.224714i | 0.0701310 | − | 0.0187915i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.76191 | + | 13.8881i | 0.478501 | + | 1.15335i | ||||
\(146\) | 5.31924 | + | 3.07106i | 0.440223 | + | 0.254163i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.74753 | − | 1.54005i | −0.472444 | − | 0.126591i | ||||
\(149\) | −3.17238 | − | 1.83158i | −0.259892 | − | 0.150049i | 0.364393 | − | 0.931245i | \(-0.381276\pi\) |
−0.624285 | + | 0.781197i | \(0.714610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.998652 | − | 1.72972i | −0.0812691 | − | 0.140762i | 0.822526 | − | 0.568727i | \(-0.192564\pi\) |
−0.903795 | + | 0.427965i | \(0.859231\pi\) | |||||||
\(152\) | −17.2082 | − | 4.61092i | −1.39577 | − | 0.373995i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.64049 | + | 2.13864i | 0.293359 | + | 0.172337i | ||||
\(155\) | 11.3668 | − | 14.8310i | 0.913005 | − | 1.19125i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.97391 | + | 5.97391i | −0.476770 | + | 0.476770i | −0.904097 | − | 0.427327i | \(-0.859455\pi\) |
0.427327 | + | 0.904097i | \(0.359455\pi\) | |||||||
\(158\) | −4.65447 | + | 4.65447i | −0.370290 | + | 0.370290i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.51066 | + | 11.4244i | 0.119428 | + | 0.903178i | ||||
\(161\) | 19.6389 | + | 0.148263i | 1.54776 | + | 0.0116847i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.14187 | − | 0.573913i | −0.167764 | − | 0.0449523i | 0.173959 | − | 0.984753i | \(-0.444344\pi\) |
−0.341723 | + | 0.939801i | \(0.611011\pi\) | |||||||
\(164\) | 3.70506 | + | 6.41735i | 0.289317 | + | 0.501111i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.31539 | − | 1.91414i | −0.257324 | − | 0.148566i | ||||
\(167\) | −1.31306 | − | 0.351833i | −0.101607 | − | 0.0272256i | 0.207657 | − | 0.978202i | \(-0.433416\pi\) |
−0.309265 | + | 0.950976i | \(0.600083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0136 | + | 6.35873i | 0.847204 | + | 0.489133i | ||||
\(170\) | −2.06813 | + | 0.858026i | −0.158618 | + | 0.0658076i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.74945 | + | 2.07646i | −0.590890 | + | 0.158328i | ||||
\(173\) | −1.45010 | − | 1.45010i | −0.110249 | − | 0.110249i | 0.649830 | − | 0.760079i | \(-0.274840\pi\) |
−0.760079 | + | 0.649830i | \(0.774840\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2285 | − | 0.0848112i | −0.999979 | − | 0.00641112i | ||||
\(176\) | −0.666427 | − | 1.15429i | −0.0502339 | − | 0.0870076i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.57505 | + | 17.0743i | −0.342914 | + | 1.27977i | ||||
\(179\) | −14.6028 | − | 8.43092i | −1.09146 | − | 0.630157i | −0.157498 | − | 0.987519i | \(-0.550343\pi\) |
−0.933966 | + | 0.357362i | \(0.883676\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.3678i | − | 1.51392i | −0.653459 | − | 0.756962i | \(-0.726683\pi\) | ||
0.653459 | − | 0.756962i | \(-0.273317\pi\) | |||||||
\(182\) | −0.345580 | − | 1.32980i | −0.0256161 | − | 0.0985712i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.1275 | − | 11.0433i | −1.41010 | − | 0.814122i | ||||
\(185\) | −10.0921 | + | 7.75307i | −0.741986 | + | 0.570017i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.18378 | + | 1.18378i | −0.0865666 | + | 0.0865666i | ||||
\(188\) | 1.46008 | + | 1.46008i | 0.106487 | + | 0.106487i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.3728 | + | 7.96873i | −0.752524 | + | 0.578113i | ||||
\(191\) | −17.2341 | −1.24701 | −0.623506 | − | 0.781818i | \(-0.714292\pi\) | ||||
−0.623506 | + | 0.781818i | \(0.714292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.64872 | − | 7.64872i | 0.550567 | − | 0.550567i | −0.376038 | − | 0.926604i | \(-0.622714\pi\) |
0.926604 | + | 0.376038i | \(0.122714\pi\) | |||||||
\(194\) | −0.0753451 | + | 0.130501i | −0.00540946 | + | 0.00936946i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.75447 | + | 6.28195i | −0.268176 | + | 0.448711i | ||||
\(197\) | −4.66542 | − | 4.66542i | −0.332398 | − | 0.332398i | 0.521099 | − | 0.853496i | \(-0.325522\pi\) |
−0.853496 | + | 0.521099i | \(0.825522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.58318 | + | 4.47420i | −0.183117 | + | 0.317168i | −0.942940 | − | 0.332962i | \(-0.891952\pi\) |
0.759823 | + | 0.650130i | \(0.225285\pi\) | |||||||
\(200\) | 12.8924 | + | 7.42387i | 0.911630 | + | 0.524947i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.68453 | − | 2.05906i | −0.540682 | − | 0.144875i | ||||
\(203\) | 12.6746 | − | 12.4847i | 0.889582 | − | 0.876251i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.7142 | + | 2.05972i | 1.09753 | + | 0.143857i | ||||
\(206\) | 8.68856 | + | 5.01634i | 0.605360 | + | 0.349505i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.112258 | + | 0.418953i | −0.00778370 | + | 0.0290492i | ||||
\(209\) | −4.89003 | + | 8.46978i | −0.338251 | + | 0.585867i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.273339 | + | 0.473437i | 0.0188174 | + | 0.0325927i | 0.875281 | − | 0.483615i | \(-0.160677\pi\) |
−0.856463 | + | 0.516208i | \(0.827343\pi\) | |||||||
\(212\) | −1.41244 | + | 0.378462i | −0.0970068 | + | 0.0259929i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.07653 | − | 0.621534i | 0.0735900 | − | 0.0424872i | ||||
\(215\) | −6.55747 | + | 15.8567i | −0.447216 | + | 1.08141i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.3123 | − | 5.88341i | −1.44677 | − | 0.399392i | ||||
\(218\) | 2.93142 | + | 10.9402i | 0.198541 | + | 0.740965i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.78618 | + | 0.496269i | 0.255265 | + | 0.0334584i | ||||
\(221\) | 0.544784 | 0.0366462 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.6042 | + | 6.86061i | −1.71458 | + | 0.459421i | −0.976540 | − | 0.215335i | \(-0.930916\pi\) |
−0.738041 | + | 0.674756i | \(0.764249\pi\) | |||||||
\(224\) | 11.8596 | − | 6.72826i | 0.792400 | − | 0.449551i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1654 | + | 17.6070i | 0.676193 | + | 1.17120i | ||||
\(227\) | 16.4370 | + | 4.40428i | 1.09096 | + | 0.292323i | 0.759079 | − | 0.650998i | \(-0.225649\pi\) |
0.331883 | + | 0.943321i | \(0.392316\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.99567 | + | 12.1169i | −0.462287 | + | 0.800705i | −0.999075 | − | 0.0430129i | \(-0.986304\pi\) |
0.536787 | + | 0.843717i | \(0.319638\pi\) | |||||||
\(230\) | −14.9786 | + | 6.21431i | −0.987657 | + | 0.409759i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.3258 | + | 5.17833i | −1.26880 | + | 0.339974i | ||||
\(233\) | −11.8929 | − | 3.18669i | −0.779130 | − | 0.208767i | −0.152729 | − | 0.988268i | \(-0.548806\pi\) |
−0.626401 | + | 0.779501i | \(0.715473\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.37819 | − | 0.578935i | 0.285602 | − | 0.0377656i | ||||
\(236\) | − | 1.15549i | − | 0.0752160i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.85913 | + | 1.88742i | 0.120510 | + | 0.122343i | ||||
\(239\) | 6.57367 | − | 3.79531i | 0.425215 | − | 0.245498i | −0.272091 | − | 0.962272i | \(-0.587715\pi\) |
0.697306 | + | 0.716773i | \(0.254382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.21861 | − | 3.01296i | 0.336160 | − | 0.194082i | −0.322413 | − | 0.946599i | \(-0.604494\pi\) |
0.658573 | + | 0.752517i | \(0.271161\pi\) | |||||||
\(242\) | 7.86287 | − | 2.10685i | 0.505445 | − | 0.135433i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.3609 | −0.919361 | ||||||||
\(245\) | 5.77921 | + | 14.5465i | 0.369220 | + | 0.929342i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.07414 | − | 0.823714i | 0.195603 | − | 0.0524117i | ||||
\(248\) | 17.5817 | + | 17.5817i | 1.11644 | + | 1.11644i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.0845 | − | 4.19732i | 0.637799 | − | 0.265462i | ||||
\(251\) | 4.81059i | 0.303642i | 0.988408 | + | 0.151821i | \(0.0485137\pi\) | ||||
−0.988408 | + | 0.151821i | \(0.951486\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.57361 | + | 8.57361i | −0.539018 | + | 0.539018i | ||||
\(254\) | − | 2.57079i | − | 0.161306i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0404 | −1.06502 | ||||||||
\(257\) | −4.23796 | − | 15.8163i | −0.264357 | − | 0.986592i | −0.962643 | − | 0.270774i | \(-0.912721\pi\) |
0.698287 | − | 0.715818i | \(-0.253946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.9835 | + | 7.62726i | 0.806752 | + | 0.473935i | ||||
\(260\) | −0.757022 | − | 0.985408i | −0.0469485 | − | 0.0611124i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.532917 | − | 1.98887i | −0.0329237 | − | 0.122873i | ||||
\(263\) | 8.05555 | + | 2.15848i | 0.496726 | + | 0.133097i | 0.498480 | − | 0.866901i | \(-0.333892\pi\) |
−0.00175401 | + | 0.999998i | \(0.500558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.19519 | + | 2.89009i | −0.0734198 | + | 0.177537i | ||||
\(266\) | 13.3446 | + | 7.83942i | 0.818210 | + | 0.480666i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.13238 | − | 4.13238i | 0.252425 | − | 0.252425i | ||||
\(269\) | 1.86662 | − | 3.23307i | 0.113810 | − | 0.197124i | −0.803494 | − | 0.595313i | \(-0.797028\pi\) |
0.917303 | + | 0.398189i | \(0.130361\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.54325 | − | 3.20039i | 0.336728 | − | 0.194410i | −0.322096 | − | 0.946707i | \(-0.604387\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(272\) | −0.216456 | − | 0.807824i | −0.0131246 | − | 0.0489815i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.4470 | − | 6.60892i | 0.691537 | − | 0.399259i | ||||
\(275\) | 5.76844 | − | 5.78158i | 0.347850 | − | 0.348642i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.148632 | − | 0.554701i | 0.00893041 | − | 0.0333287i | −0.961317 | − | 0.275445i | \(-0.911175\pi\) |
0.970247 | + | 0.242116i | \(0.0778415\pi\) | |||||||
\(278\) | −3.25825 | + | 12.1600i | −0.195417 | + | 0.729306i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.41939 | − | 17.4357i | 0.144586 | − | 1.04199i | ||||
\(281\) | −2.21693 | + | 3.83984i | −0.132251 | + | 0.229065i | −0.924544 | − | 0.381075i | \(-0.875554\pi\) |
0.792293 | + | 0.610141i | \(0.208887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.26619 | + | 5.26619i | 0.313043 | + | 0.313043i | 0.846087 | − | 0.533044i | \(-0.178952\pi\) |
−0.533044 | + | 0.846087i | \(0.678952\pi\) | |||||||
\(284\) | − | 6.64670i | − | 0.394409i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.734609 | + | 0.424127i | 0.0434383 | + | 0.0250791i | ||||
\(287\) | −4.71659 | − | 18.1495i | −0.278412 | − | 1.07133i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.8127 | − | 7.97477i | 0.812513 | − | 0.469104i | ||||
\(290\) | −5.61390 | + | 13.5750i | −0.329660 | + | 0.797152i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.70115 | − | 6.34877i | −0.0995521 | − | 0.371533i | ||||
\(293\) | 4.98512 | − | 18.6047i | 0.291234 | − | 1.08690i | −0.652929 | − | 0.757419i | \(-0.726460\pi\) |
0.944163 | − | 0.329480i | \(-0.106873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.96151 | − | 1.50334i | −0.114203 | − | 0.0875281i | ||||
\(296\) | −8.46716 | − | 14.6656i | −0.492144 | − | 0.852418i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.926280 | − | 3.45692i | −0.0536580 | − | 0.200254i | ||||
\(299\) | 3.94564 | 0.228182 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3023 | + | 0.153271i | 1.17021 | + | 0.00883439i | ||||
\(302\) | 0.505047 | − | 1.88486i | 0.0290622 | − | 0.108462i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.44286 | − | 4.23116i | −0.140108 | − | 0.242674i | ||||
\(305\) | −18.6841 | + | 24.3783i | −1.06985 | + | 1.39590i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.54479 | − | 6.54479i | 0.373531 | − | 0.373531i | −0.495231 | − | 0.868761i | \(-0.664916\pi\) |
0.868761 | + | 0.495231i | \(0.164916\pi\) | |||||||
\(308\) | −1.13641 | − | 4.37294i | −0.0647532 | − | 0.249172i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.0985 | − | 2.39319i | 1.02792 | − | 0.135924i | ||||
\(311\) | 24.6330i | 1.39681i | 0.715702 | + | 0.698406i | \(0.246107\pi\) | ||||
−0.715702 | + | 0.698406i | \(0.753893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.9429 | − | 17.9429i | −1.01419 | − | 1.01419i | −0.999898 | − | 0.0142930i | \(-0.995450\pi\) |
−0.0142930 | − | 0.999898i | \(-0.504550\pi\) | |||||||
\(314\) | −8.25401 | −0.465801 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.04388 | 0.396249 | ||||||||
\(317\) | 7.53443 | + | 7.53443i | 0.423176 | + | 0.423176i | 0.886296 | − | 0.463120i | \(-0.153270\pi\) |
−0.463120 | + | 0.886296i | \(0.653270\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.9836i | 0.614962i | ||||||||
\(320\) | −9.06864 | + | 11.8324i | −0.506952 | + | 0.661452i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.4649 | + | 13.6697i | 0.750369 | + | 0.761785i | ||||
\(323\) | −4.33927 | + | 4.33927i | −0.241444 | + | 0.241444i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.65770 | + | 0.00302479i | −0.147423 | + | 0.000167785i | ||||
\(326\) | −1.08321 | − | 1.87617i | −0.0599932 | − | 0.103911i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.45823 | + | 20.3704i | −0.301380 | + | 1.12477i | ||||
\(329\) | −2.57848 | − | 4.54496i | −0.142156 | − | 0.250572i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.24703 | 0.343368 | 0.171684 | − | 0.985152i | \(-0.445079\pi\) | ||||
0.171684 | + | 0.985152i | \(0.445079\pi\) | |||||||
\(332\) | 1.06029 | + | 3.95707i | 0.0581912 | + | 0.217173i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.664051 | − | 1.15017i | −0.0363352 | − | 0.0629345i | ||||
\(335\) | −1.63853 | − | 12.3913i | −0.0895222 | − | 0.677011i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.31266 | + | 12.3630i | −0.180452 | + | 0.673457i | 0.815106 | + | 0.579311i | \(0.196678\pi\) |
−0.995558 | + | 0.0941452i | \(0.969988\pi\) | |||||||
\(338\) | 3.21579 | + | 12.0015i | 0.174916 | + | 0.652796i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.21416 | + | 0.915659i | 0.120080 | + | 0.0496586i | ||||
\(341\) | 11.8211 | − | 6.82491i | 0.640148 | − | 0.369590i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.3890 | − | 12.7959i | 0.722939 | − | 0.690912i | ||||
\(344\) | −19.7737 | − | 11.4163i | −1.06613 | − | 0.615528i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 2.00357i | − | 0.107712i | ||||||
\(347\) | 9.47519 | + | 9.47519i | 0.508655 | + | 0.508655i | 0.914113 | − | 0.405459i | \(-0.132888\pi\) |
−0.405459 | + | 0.914113i | \(0.632888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4350 | − | 26.7341i | 0.826215 | − | 1.43105i | −0.0747724 | − | 0.997201i | \(-0.523823\pi\) |
0.900987 | − | 0.433846i | \(-0.142844\pi\) | |||||||
\(350\) | −9.08015 | − | 9.19733i | −0.485355 | − | 0.491618i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.17874 | + | 8.13118i | −0.116127 | + | 0.433394i | ||||
\(353\) | 4.25417 | − | 15.8768i | 0.226426 | − | 0.845035i | −0.755402 | − | 0.655262i | \(-0.772558\pi\) |
0.981828 | − | 0.189773i | \(-0.0607752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.2831 | − | 8.64765i | −0.598846 | − | 0.458970i | ||||
\(356\) | 16.3816 | − | 9.45792i | 0.868223 | − | 0.501269i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.26376 | − | 15.9126i | −0.225347 | − | 0.841005i | ||||
\(359\) | −1.40486 | + | 0.811094i | −0.0741455 | + | 0.0428079i | −0.536614 | − | 0.843828i | \(-0.680297\pi\) |
0.462469 | + | 0.886635i | \(0.346964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.42494 | + | 14.5924i | −0.443418 | + | 0.768022i | ||||
\(362\) | 14.0708 | − | 14.0708i | 0.739546 | − | 0.739546i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.744737 | + | 1.26772i | −0.0390348 | + | 0.0664468i | ||||
\(365\) | −12.9906 | − | 5.37224i | −0.679961 | − | 0.281196i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.34101 | + | 0.627271i | 0.122200 | + | 0.0327433i | 0.319401 | − | 0.947620i | \(-0.396518\pi\) |
−0.197201 | + | 0.980363i | \(0.563185\pi\) | |||||||
\(368\) | −1.56770 | − | 5.85072i | −0.0817218 | − | 0.304990i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.3281 | − | 1.61589i | −0.640909 | − | 0.0840063i | ||||
\(371\) | 3.70037 | + | 0.0279357i | 0.192114 | + | 0.00145035i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.27835 | − | 30.8952i | −0.428637 | − | 1.59969i | −0.755851 | − | 0.654744i | \(-0.772777\pi\) |
0.327214 | − | 0.944950i | \(-0.393890\pi\) | |||||||
\(374\) | −1.63560 | −0.0845749 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.87654i | 0.303060i | ||||||||
\(377\) | 2.52736 | − | 2.52736i | 0.130166 | − | 0.130166i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.9678i | 1.59071i | 0.606146 | + | 0.795353i | \(0.292715\pi\) | ||||
−0.606146 | + | 0.795353i | \(0.707285\pi\) | |||||||
\(380\) | 13.8787 | + | 1.81913i | 0.711961 | + | 0.0933193i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.9059 | − | 11.9059i | −0.609161 | − | 0.609161i | ||||
\(383\) | −18.1872 | + | 4.87326i | −0.929324 | + | 0.249012i | −0.691567 | − | 0.722313i | \(-0.743079\pi\) |
−0.237758 | + | 0.971324i | \(0.576412\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.90183 | − | 3.76027i | −0.453679 | − | 0.191641i | ||||
\(386\) | 10.5681 | 0.537900 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.155760 | − | 0.0417357i | 0.00790750 | − | 0.00211881i | ||||
\(389\) | −20.5140 | + | 11.8438i | −1.04010 | + | 0.600503i | −0.919862 | − | 0.392242i | \(-0.871700\pi\) |
−0.120240 | + | 0.992745i | \(0.538366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.58870 | + | 3.80399i | −0.333205 | + | 0.192376i | ||||
\(392\) | −20.1973 | + | 5.08630i | −1.02012 | + | 0.256897i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 6.44611i | − | 0.324750i | ||||||
\(395\) | 9.16440 | − | 11.9574i | 0.461111 | − | 0.601640i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.2158 | − | 6.22065i | −1.16517 | − | 0.312205i | −0.376139 | − | 0.926563i | \(-0.622748\pi\) |
−0.789027 | + | 0.614358i | \(0.789415\pi\) | |||||||
\(398\) | −4.87551 | + | 1.30639i | −0.244387 | + | 0.0654834i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.06045 | + | 3.93973i | 0.0530227 | + | 0.196986i | ||||
\(401\) | 17.1072 | − | 29.6306i | 0.854295 | − | 1.47968i | −0.0230028 | − | 0.999735i | \(-0.507323\pi\) |
0.877298 | − | 0.479947i | \(-0.159344\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.29051 | − | 1.14964i | −0.213726 | − | 0.0572676i | ||||
\(404\) | 4.25667 | + | 7.37277i | 0.211777 | + | 0.366809i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.3810 | + | 0.131216i | 0.862603 | + | 0.00651216i | ||||
\(407\) | −8.97969 | + | 2.40610i | −0.445107 | + | 0.119266i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0910287 | 0.00450108 | 0.00225054 | − | 0.999997i | \(-0.499284\pi\) | ||||
0.00225054 | + | 0.999997i | \(0.499284\pi\) | |||||||
\(410\) | 9.43306 | + | 12.2789i | 0.465866 | + | 0.606413i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.77869 | − | 10.3702i | −0.136896 | − | 0.510903i | ||||
\(413\) | −0.778123 | + | 2.81870i | −0.0382889 | + | 0.138699i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.09683 | + | 3.34842i | 0.397458 | + | 0.164367i | ||||
\(416\) | 2.37235 | − | 1.36968i | 0.116314 | − | 0.0671540i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.22947 | + | 2.47303i | −0.451428 | + | 0.120960i | ||||
\(419\) | 13.7216 | + | 23.7665i | 0.670343 | + | 1.16107i | 0.977807 | + | 0.209508i | \(0.0671862\pi\) |
−0.307464 | + | 0.951560i | \(0.599480\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.94319 | + | 10.2939i | −0.289653 | + | 0.501695i | −0.973727 | − | 0.227719i | \(-0.926873\pi\) |
0.684074 | + | 0.729413i | \(0.260207\pi\) | |||||||
\(422\) | −0.138235 | + | 0.515901i | −0.00672919 | + | 0.0251137i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.60402 | − | 2.08078i | −0.175027 | − | 0.101052i | ||||
\(425\) | 4.43510 | − | 2.56734i | 0.215134 | − | 0.124534i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.0319 | + | 9.67081i | 1.69531 | + | 0.468003i | ||||
\(428\) | −1.28489 | − | 0.344285i | −0.0621074 | − | 0.0166416i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.4845 | + | 6.42423i | −0.746731 | + | 0.309804i | ||||
\(431\) | 11.1221 | − | 19.2640i | 0.535732 | − | 0.927915i | −0.463396 | − | 0.886152i | \(-0.653369\pi\) |
0.999128 | − | 0.0417634i | \(-0.0132976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.23695 | − | 5.23695i | −0.251672 | − | 0.251672i | 0.569984 | − | 0.821656i | \(-0.306949\pi\) |
−0.821656 | + | 0.569984i | \(0.806949\pi\) | |||||||
\(434\) | −10.6589 | − | 18.7878i | −0.511642 | − | 0.901845i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.06008 | − | 10.4964i | 0.290225 | − | 0.502685i | ||||
\(437\) | −31.4275 | + | 31.4275i | −1.50338 | + | 1.50338i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5501 | −0.933075 | −0.466538 | − | 0.884501i | \(-0.654499\pi\) | ||||
−0.466538 | + | 0.884501i | \(0.654499\pi\) | |||||||
\(440\) | 6.62064 | + | 8.61802i | 0.315626 | + | 0.410848i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.376358 | + | 0.376358i | 0.0179015 | + | 0.0179015i | ||||
\(443\) | 26.5025 | − | 26.5025i | 1.25917 | − | 1.25917i | 0.307685 | − | 0.951488i | \(-0.400446\pi\) |
0.951488 | − | 0.307685i | \(-0.0995544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.25786 | − | 40.1138i | 0.249247 | − | 1.90158i | ||||
\(446\) | −22.4279 | − | 12.9488i | −1.06199 | − | 0.613141i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.0033 | + | 4.69388i | 0.803330 | + | 0.221765i | ||||
\(449\) | 18.6203i | 0.878748i | 0.898304 | + | 0.439374i | \(0.144800\pi\) | ||||
−0.898304 | + | 0.439374i | \(0.855200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0262 | + | 5.78862i | 0.472115 | + | 0.272576i | ||||
\(452\) | 5.63090 | − | 21.0148i | 0.264855 | − | 0.988452i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.31267 | + | 14.3980i | 0.390133 | + | 0.675730i | ||||
\(455\) | 1.18309 | + | 2.91359i | 0.0554642 | + | 0.136591i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.6389 | − | 20.6389i | −0.965445 | − | 0.965445i | 0.0339772 | − | 0.999423i | \(-0.489183\pi\) |
−0.999423 | + | 0.0339772i | \(0.989183\pi\) | |||||||
\(458\) | −13.2037 | + | 3.53791i | −0.616967 | + | 0.165316i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.0362 | + | 6.63172i | 0.747691 | + | 0.309206i | ||||
\(461\) | −13.2237 | − | 7.63473i | −0.615891 | − | 0.355585i | 0.159377 | − | 0.987218i | \(-0.449052\pi\) |
−0.775267 | + | 0.631633i | \(0.782385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.9841 | + | 10.7137i | 1.85822 | + | 0.497908i | 0.999885 | − | 0.0151842i | \(-0.00483345\pi\) |
0.858333 | + | 0.513092i | \(0.171500\pi\) | |||||||
\(464\) | −4.75184 | − | 2.74347i | −0.220599 | − | 0.127363i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.01458 | − | 10.4176i | −0.278620 | − | 0.482584i | ||||
\(467\) | −17.4657 | − | 4.67993i | −0.808217 | − | 0.216561i | −0.169029 | − | 0.985611i | \(-0.554063\pi\) |
−0.639189 | + | 0.769050i | \(0.720730\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8633 | + | 7.29773i | −0.593973 | + | 0.336978i | ||||
\(470\) | 3.42457 | + | 2.62467i | 0.157964 | + | 0.121067i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.32531 | − | 2.32531i | 0.107031 | − | 0.107031i | ||||
\(473\) | −8.86323 | + | 8.86323i | −0.407532 | + | 0.407532i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.1448 | − | 21.1930i | 0.970191 | − | 0.972402i | ||||
\(476\) | 0.0214021 | − | 2.83493i | 0.000980965 | − | 0.129939i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.16329 | + | 1.91940i | 0.327641 | + | 0.0877912i | ||||
\(479\) | −4.07569 | − | 7.05931i | −0.186223 | − | 0.322548i | 0.757765 | − | 0.652528i | \(-0.226291\pi\) |
−0.943988 | + | 0.329980i | \(0.892958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.61991 | + | 1.51261i | 0.119458 | + | 0.0689690i | ||||
\(482\) | 5.68668 | + | 1.52374i | 0.259021 | + | 0.0694045i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.54388 | − | 4.35546i | −0.342903 | − | 0.197975i | ||||
\(485\) | 0.131802 | − | 0.318710i | 0.00598481 | − | 0.0144719i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.93080 | − | 1.05326i | 0.178122 | − | 0.0477276i | −0.168656 | − | 0.985675i | \(-0.553943\pi\) |
0.346777 | + | 0.937947i | \(0.387276\pi\) | |||||||
\(488\) | −28.8999 | − | 28.8999i | −1.30824 | − | 1.30824i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.05678 | + | 14.0418i | −0.273618 | + | 0.634343i | ||||
\(491\) | −14.1237 | − | 24.4629i | −0.637392 | − | 1.10399i | −0.986003 | − | 0.166727i | \(-0.946680\pi\) |
0.348612 | − | 0.937267i | \(-0.386653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.78373 | + | 6.65699i | −0.0803354 | + | 0.299816i | ||||
\(494\) | 2.69279 | + | 1.55468i | 0.121154 | + | 0.0699485i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.81890i | 0.306178i | ||||||||
\(497\) | −4.47598 | + | 16.2140i | −0.200775 | + | 0.727296i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.4496 | + | 12.3840i | 0.960218 | + | 0.554382i | 0.896240 | − | 0.443569i | \(-0.146288\pi\) |
0.0639775 | + | 0.997951i | \(0.479621\pi\) | |||||||
\(500\) | −10.8067 | − | 4.45470i | −0.483292 | − | 0.199220i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.32334 | + | 3.32334i | −0.148328 | + | 0.148328i | ||||
\(503\) | 22.1184 | + | 22.1184i | 0.986211 | + | 0.986211i | 0.999906 | − | 0.0136949i | \(-0.00435937\pi\) |
−0.0136949 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0538 | + | 2.36638i | 0.803383 | + | 0.105302i | ||||
\(506\) | −11.8460 | −0.526617 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.94526 | + | 1.94526i | −0.0863071 | + | 0.0863071i | ||||
\(509\) | 0.687693 | − | 1.19112i | 0.0304815 | − | 0.0527955i | −0.850382 | − | 0.526165i | \(-0.823629\pi\) |
0.880864 | + | 0.473370i | \(0.156963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.125568 | + | 16.6328i | −0.00555480 | + | 0.735790i | ||||
\(512\) | −6.40718 | − | 6.40718i | −0.283160 | − | 0.283160i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.99874 | − | 13.8542i | 0.352809 | − | 0.611084i | ||||
\(515\) | −21.2192 | − | 8.77512i | −0.935028 | − | 0.386678i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.11613 | + | 0.834965i | 0.137047 | + | 0.0367217i | ||||
\(518\) | 3.70026 | + | 14.2387i | 0.162580 | + | 0.625611i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.459606 | − | 3.50647i | 0.0201551 | − | 0.153769i | ||||
\(521\) | 22.4862 | + | 12.9824i | 0.985140 | + | 0.568771i | 0.903818 | − | 0.427917i | \(-0.140752\pi\) |
0.0813222 | + | 0.996688i | \(0.474086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.697525 | − | 2.60320i | 0.0305006 | − | 0.113830i | −0.948997 | − | 0.315284i | \(-0.897900\pi\) |
0.979498 | + | 0.201454i | \(0.0645668\pi\) | |||||||
\(524\) | −1.10169 | + | 1.90818i | −0.0481276 | + | 0.0833594i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.07392 | + | 7.05624i | 0.177631 | + | 0.307667i | ||||
\(527\) | 8.27296 | − | 2.21673i | 0.360376 | − | 0.0965624i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.8005 | + | 16.0506i | −1.20872 | + | 0.697853i | ||||
\(530\) | −2.82226 | + | 1.17090i | −0.122591 | + | 0.0508607i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.16565 | − | 16.0295i | −0.180604 | − | 0.694967i | ||||
\(533\) | −0.975080 | − | 3.63905i | −0.0422354 | − | 0.157625i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.25614 | + | 1.73324i | −0.0975414 | + | 0.0749343i | ||||
\(536\) | 16.6320 | 0.718394 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.52306 | − | 0.944001i | 0.151890 | − | 0.0406988i | ||||
\(539\) | −0.172630 | + | 11.4326i | −0.00743569 | + | 0.492439i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0369 | − | 17.3845i | −0.431522 | − | 0.747418i | 0.565482 | − | 0.824760i | \(-0.308690\pi\) |
−0.997005 | + | 0.0773420i | \(0.975357\pi\) | |||||||
\(542\) | 6.04044 | + | 1.61853i | 0.259459 | + | 0.0695219i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.64101 | + | 4.57437i | −0.113232 | + | 0.196124i | ||||
\(545\) | −9.93371 | − | 23.9435i | −0.425513 | − | 1.02563i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4892 | − | 3.88238i | 0.619515 | − | 0.165999i | 0.0646077 | − | 0.997911i | \(-0.479420\pi\) |
0.554907 | + | 0.831912i | \(0.312754\pi\) | |||||||
\(548\) | −13.6625 | − | 3.66086i | −0.583634 | − | 0.156384i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.97919 | − | 0.00908129i | 0.340234 | − | 0.000387228i | ||||
\(551\) | 40.2615i | 1.71520i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.1829 | − | 4.74345i | −0.730689 | − | 0.201712i | ||||
\(554\) | 0.485889 | − | 0.280528i | 0.0206434 | − | 0.0119185i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.6666 | − | 6.73573i | 0.494775 | − | 0.285659i | ||||
\(557\) | −0.236144 | + | 0.0632745i | −0.0100057 | + | 0.00268103i | −0.263818 | − | 0.964572i | \(-0.584982\pi\) |
0.253813 | + | 0.967253i | \(0.418315\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.07892 | 0.172520 | ||||||||
\(560\) | 3.85030 | − | 2.91197i | 0.162705 | − | 0.123053i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.18424 | + | 1.12117i | −0.176502 | + | 0.0472935i | ||||
\(563\) | −0.0555045 | − | 0.0555045i | −0.00233924 | − | 0.00233924i | 0.705936 | − | 0.708275i | \(-0.250527\pi\) |
−0.708275 | + | 0.705936i | \(0.750527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.3477 | − | 36.8999i | −1.19260 | − | 1.55239i | ||||
\(566\) | 7.27618i | 0.305840i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.3758 | − | 13.3758i | 0.561238 | − | 0.561238i | ||||
\(569\) | − | 14.7549i | − | 0.618556i | −0.950972 | − | 0.309278i | \(-0.899913\pi\) | ||
0.950972 | − | 0.309278i | \(-0.100087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.5516 | −1.23669 | −0.618347 | − | 0.785905i | \(-0.712197\pi\) | ||||
−0.618347 | + | 0.785905i | \(0.712197\pi\) | |||||||
\(572\) | −0.234935 | − | 0.876791i | −0.00982314 | − | 0.0366605i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.27999 | − | 15.7968i | 0.387339 | − | 0.659345i | ||||
\(575\) | 32.1215 | − | 18.5941i | 1.33956 | − | 0.775429i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.16353 | − | 8.07441i | −0.0900690 | − | 0.336142i | 0.906157 | − | 0.422942i | \(-0.139003\pi\) |
−0.996226 | + | 0.0867998i | \(0.972336\pi\) | |||||||
\(578\) | 15.0516 | + | 4.03307i | 0.626065 | + | 0.167754i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.5198 | − | 6.02400i | 0.602903 | − | 0.250133i | ||||
\(581\) | 0.0782642 | − | 10.3669i | 0.00324695 | − | 0.430091i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.61544 | + | 1.61544i | −0.0669048 | + | 0.0669048i | ||||
\(584\) | 9.35288 | − | 16.1997i | 0.387025 | − | 0.670347i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.2968 | − | 9.40894i | 0.673213 | − | 0.388680i | ||||
\(587\) | −2.34352 | − | 8.74614i | −0.0967275 | − | 0.360992i | 0.900548 | − | 0.434756i | \(-0.143165\pi\) |
−0.997276 | + | 0.0737643i | \(0.976499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.3315 | − | 25.0175i | 1.78544 | − | 1.03083i | ||||
\(590\) | −0.316516 | − | 2.39365i | −0.0130308 | − | 0.0985450i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.20199 | − | 4.48589i | 0.0494015 | − | 0.184369i | ||||
\(593\) | 7.48847 | − | 27.9474i | 0.307515 | − | 1.14766i | −0.623244 | − | 0.782027i | \(-0.714186\pi\) |
0.930759 | − | 0.365633i | \(-0.119148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.78460 | − | 3.72470i | −0.196150 | − | 0.152698i | ||||
\(596\) | −1.91489 | + | 3.31668i | −0.0784367 | + | 0.135856i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.72580 | + | 2.72580i | 0.111466 | + | 0.111466i | ||||
\(599\) | 10.0498i | 0.410625i | 0.978696 | + | 0.205313i | \(0.0658211\pi\) | ||||
−0.978696 | + | 0.205313i | \(0.934179\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.4153 | + | 15.8282i | 1.11829 | + | 0.645647i | 0.940965 | − | 0.338505i | \(-0.109921\pi\) |
0.177329 | + | 0.984152i | \(0.443254\pi\) | |||||||
\(602\) | 13.9197 | + | 14.1315i | 0.567326 | + | 0.575957i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.80839 | + | 1.04408i | −0.0735824 | + | 0.0424828i | ||||
\(605\) | −17.2085 | + | 7.13949i | −0.699627 | + | 0.290261i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.86111 | − | 10.6778i | −0.116129 | − | 0.433398i | 0.883240 | − | 0.468921i | \(-0.155357\pi\) |
−0.999369 | + | 0.0355226i | \(0.988690\pi\) | |||||||
\(608\) | −7.98642 | + | 29.8057i | −0.323892 | + | 1.20878i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.7492 | + | 3.93378i | −1.20451 | + | 0.159274i | ||||
\(611\) | −0.524905 | − | 0.909162i | −0.0212354 | − | 0.0367807i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.18919 | + | 23.0984i | 0.249979 | + | 0.932934i | 0.970815 | + | 0.239829i | \(0.0770913\pi\) |
−0.720836 | + | 0.693105i | \(0.756242\pi\) | |||||||
\(614\) | 9.04278 | 0.364937 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.51320 | − | 11.0870i | 0.262424 | − | 0.446710i | ||||
\(617\) | 1.79766 | − | 6.70895i | 0.0723709 | − | 0.270092i | −0.920253 | − | 0.391323i | \(-0.872018\pi\) |
0.992624 | + | 0.121231i | \(0.0386842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.6977 | − | 27.1893i | −0.630945 | − | 1.09283i | −0.987359 | − | 0.158500i | \(-0.949334\pi\) |
0.356414 | − | 0.934328i | \(-0.383999\pi\) | |||||||
\(620\) | −15.5056 | − | 11.8838i | −0.622719 | − | 0.477267i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.0174 | + | 17.0174i | −0.682337 | + | 0.682337i | ||||
\(623\) | −46.3304 | + | 12.0401i | −1.85619 | + | 0.482375i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.6221 | + | 12.5492i | −0.864885 | + | 0.501970i | ||||
\(626\) | − | 24.7912i | − | 0.990857i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.24563 | + | 6.24563i | 0.249228 | + | 0.249228i | ||||
\(629\) | −5.83322 | −0.232586 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.8622 | −1.46746 | −0.733730 | − | 0.679441i | \(-0.762222\pi\) | ||||
−0.733730 | + | 0.679441i | \(0.762222\pi\) | |||||||
\(632\) | 14.1751 | + | 14.1751i | 0.563856 | + | 0.563856i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.4101i | 0.413440i | ||||||||
\(635\) | 0.771314 | + | 5.83306i | 0.0306087 | + | 0.231478i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.67041 | − | 2.59097i | 0.105806 | − | 0.102658i | ||||
\(638\) | −7.58787 | + | 7.58787i | −0.300407 | + | 0.300407i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.40954 | − | 1.11201i | 0.332416 | − | 0.0439559i | ||||
\(641\) | 7.53215 | + | 13.0461i | 0.297502 | + | 0.515289i | 0.975564 | − | 0.219716i | \(-0.0705131\pi\) |
−0.678062 | + | 0.735005i | \(0.737180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.70433 | + | 17.5568i | −0.185521 | + | 0.692372i | 0.808998 | + | 0.587812i | \(0.200010\pi\) |
−0.994518 | + | 0.104561i | \(0.966656\pi\) | |||||||
\(644\) | 0.155006 | − | 20.5322i | 0.00610811 | − | 0.809082i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.99547 | −0.235889 | ||||||||
\(647\) | 1.04775 | + | 3.91026i | 0.0411913 | + | 0.153728i | 0.983458 | − | 0.181134i | \(-0.0579769\pi\) |
−0.942267 | + | 0.334862i | \(0.891310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.902644 | − | 1.56342i | −0.0354319 | − | 0.0613698i | ||||
\(650\) | −1.83813 | − | 1.83395i | −0.0720974 | − | 0.0719335i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.600017 | + | 2.23930i | −0.0234985 | + | 0.0876976i | ||||
\(653\) | −5.98559 | − | 22.3385i | −0.234234 | − | 0.874174i | −0.978493 | − | 0.206282i | \(-0.933864\pi\) |
0.744258 | − | 0.667892i | \(-0.232803\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.80589 | + | 4.35281i | 0.0705622 | + | 0.170078i | ||||
\(656\) | −5.00868 | + | 2.89176i | −0.195556 | + | 0.112904i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.35852 | − | 4.92115i | 0.0529605 | − | 0.191846i | ||||
\(659\) | 38.7647 | + | 22.3808i | 1.51006 | + | 0.871834i | 0.999931 | + | 0.0117356i | \(0.00373563\pi\) |
0.510129 | + | 0.860098i | \(0.329598\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.5421i | − | 0.682309i | −0.940007 | − | 0.341155i | \(-0.889182\pi\) | ||
0.940007 | − | 0.341155i | \(-0.110818\pi\) | |||||||
\(662\) | 4.31569 | + | 4.31569i | 0.167734 | + | 0.167734i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.82948 | + | 10.0970i | −0.226228 | + | 0.391838i | ||||
\(665\) | −32.6306 | − | 13.7837i | −1.26536 | − | 0.534508i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.9188 | + | 48.2137i | −0.500219 | + | 1.86684i | ||||
\(668\) | −0.367836 | + | 1.37278i | −0.0142320 | + | 0.0531145i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.42846 | − | 9.69237i | 0.286986 | − | 0.374449i | ||||
\(671\) | −19.4308 | + | 11.2184i | −0.750119 | + | 0.433081i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8090 | − | 47.8039i | −0.493751 | − | 1.84270i | −0.536914 | − | 0.843637i | \(-0.680410\pi\) |
0.0431629 | − | 0.999068i | \(-0.486257\pi\) | |||||||
\(674\) | −10.8294 | + | 6.25233i | −0.417131 | + | 0.240831i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.64796 | − | 11.5146i | 0.255691 | − | 0.442869i | ||||
\(677\) | −26.4976 | + | 26.4976i | −1.01839 | + | 1.01839i | −0.0185585 | + | 0.999828i | \(0.505908\pi\) |
−0.999828 | + | 0.0185585i | \(0.994092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.408066 | − | 0.00308066i | −0.0156601 | − | 0.000118225i | ||||
\(680\) | 2.61310 | + | 6.29845i | 0.100208 | + | 0.241535i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.8814 | + | 3.45155i | 0.493253 | + | 0.132167i | ||||
\(683\) | 6.76683 | + | 25.2542i | 0.258926 | + | 0.966324i | 0.965864 | + | 0.259049i | \(0.0834090\pi\) |
−0.706939 | + | 0.707275i | \(0.749924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.9900 | + | 18.4299i | −0.916612 | + | 0.704170i | ||||
\(686\) | 18.0895 | + | 0.409759i | 0.690661 | + | 0.0156447i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.62065 | − | 6.04836i | −0.0617868 | − | 0.230592i | ||||
\(689\) | 0.743438 | 0.0283227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.1336i | − | 0.803961i | −0.915648 | − | 0.401980i | \(-0.868322\pi\) | ||
0.915648 | − | 0.401980i | \(-0.131678\pi\) | |||||||
\(692\) | −1.51606 | + | 1.51606i | −0.0576318 | + | 0.0576318i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0916i | 0.496952i | ||||||||
\(695\) | 3.74454 | − | 28.5682i | 0.142038 | − | 1.08365i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.13666 | + | 5.13666i | 0.194565 | + | 0.194565i | ||||
\(698\) | 29.1320 | − | 7.80591i | 1.10266 | − | 0.295458i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.0886688 | + | 13.8302i | −0.00335137 | + | 0.522732i | ||||
\(701\) | −17.0822 | −0.645186 | −0.322593 | − | 0.946538i | \(-0.604554\pi\) | ||||
−0.322593 | + | 0.946538i | \(0.604554\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.9160 | + | 8.81983i | −1.24145 | + | 0.332646i | ||||
\(704\) | −9.43107 | + | 5.44503i | −0.355447 | + | 0.205217i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.9072 | − | 8.02934i | 0.523405 | − | 0.302188i | ||||
\(707\) | −5.41880 | − | 20.8516i | −0.203795 | − | 0.784207i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.7377i | 1.64260i | 0.570494 | + | 0.821302i | \(0.306752\pi\) | ||||
−0.570494 | + | 0.821302i | \(0.693248\pi\) | |||||||
\(710\) | −1.82069 | − | 13.7689i | −0.0683292 | − | 0.516739i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 51.9995 | + | 13.9332i | 1.94877 | + | 0.522170i | ||||
\(713\) | 59.9175 | − | 16.0548i | 2.24393 | − | 0.601259i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.79406 | − | 0.741928i | −0.0670940 | − | 0.0277465i | ||||
\(716\) | −8.81441 | + | 15.2670i | −0.329410 | + | 0.570555i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.53086 | − | 0.410194i | −0.0571313 | − | 0.0153083i | ||||
\(719\) | 9.10099 | + | 15.7634i | 0.339410 | + | 0.587875i | 0.984322 | − | 0.176382i | \(-0.0564394\pi\) |
−0.644912 | + | 0.764257i | \(0.723106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.205105 | + | 27.1683i | −0.00763851 | + | 1.01180i | ||||
\(722\) | −15.9013 | + | 4.26073i | −0.591784 | + | 0.158568i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.2942 | −0.791392 | ||||||||
\(725\) | 8.66489 | − | 32.4857i | 0.321806 | − | 1.20649i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.6674 | − | 47.2752i | −0.469806 | − | 1.75334i | −0.640441 | − | 0.768007i | \(-0.721248\pi\) |
0.170635 | − | 0.985334i | \(-0.445418\pi\) | |||||||
\(728\) | −4.04988 | + | 1.05246i | −0.150099 | + | 0.0390067i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.26308 | − | 12.6858i | −0.194795 | − | 0.469521i | ||||
\(731\) | −6.81126 | + | 3.93249i | −0.251924 | + | 0.145448i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.2445 | − | 5.15655i | 0.710812 | − | 0.190461i | 0.114744 | − | 0.993395i | \(-0.463395\pi\) |
0.596068 | + | 0.802934i | \(0.296729\pi\) | |||||||
\(734\) | 1.18391 | + | 2.05060i | 0.0436991 | + | 0.0756890i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.1277 | + | 33.1302i | −0.705057 | + | 1.22119i | ||||
\(737\) | 2.36315 | − | 8.81940i | 0.0870478 | − | 0.324867i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.8852 | − | 24.1825i | −1.54077 | − | 0.889566i | −0.998790 | − | 0.0491770i | \(-0.984340\pi\) |
−0.541984 | − | 0.840389i | \(-0.682327\pi\) | |||||||
\(740\) | 8.10572 | + | 10.5511i | 0.297972 | + | 0.387868i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.53706 | + | 2.57566i | 0.0931383 | + | 0.0945553i | ||||
\(743\) | 31.7951 | + | 8.51948i | 1.16645 | + | 0.312549i | 0.789539 | − | 0.613700i | \(-0.210320\pi\) |
0.376911 | + | 0.926250i | \(0.376986\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.13889 | + | 7.56576i | 0.115000 | + | 0.277188i | ||||
\(746\) | 15.6246 | − | 27.0626i | 0.572057 | − | 0.990832i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.23762 | + | 1.23762i | 0.0452520 | + | 0.0452520i | ||||
\(749\) | 2.90251 | + | 1.70511i | 0.106055 | + | 0.0623034i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.76017 | − | 11.7090i | 0.246682 | − | 0.427266i | −0.715921 | − | 0.698181i | \(-0.753993\pi\) |
0.962603 | + | 0.270915i | \(0.0873263\pi\) | |||||||
\(752\) | −1.13958 | + | 1.13958i | −0.0415561 | + | 0.0415561i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.49200 | 0.127171 | ||||||||
\(755\) | −0.580424 | + | 4.42823i | −0.0211238 | + | 0.161160i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4104 | + | 28.4104i | 1.03260 | + | 1.03260i | 0.999451 | + | 0.0331447i | \(0.0105522\pi\) |
0.0331447 | + | 0.999451i | \(0.489448\pi\) | |||||||
\(758\) | −21.3937 | + | 21.3937i | −0.777055 | + | 0.777055i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24.2687 | + | 31.5903i | 0.880317 | + | 1.14590i | ||||
\(761\) | −13.6962 | − | 7.90749i | −0.496486 | − | 0.286646i | 0.230775 | − | 0.973007i | \(-0.425874\pi\) |
−0.727261 | + | 0.686361i | \(0.759207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.8514 | + | 21.5239i | −0.791072 | + | 0.779218i | ||||
\(764\) | 18.0179i | 0.651866i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.9311 | − | 9.19781i | −0.575613 | − | 0.332330i | ||||
\(767\) | −0.152048 | + | 0.567451i | −0.00549014 | + | 0.0204895i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.7002 | − | 18.5333i | −0.385860 | − | 0.668328i | 0.606028 | − | 0.795443i | \(-0.292762\pi\) |
−0.991888 | + | 0.127115i | \(0.959428\pi\) | |||||||
\(770\) | −3.55199 | − | 8.74746i | −0.128005 | − | 0.315237i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.99662 | − | 7.99662i | −0.287805 | − | 0.287805i | ||||
\(773\) | −8.90050 | + | 2.38488i | −0.320129 | + | 0.0857782i | −0.415305 | − | 0.909682i | \(-0.636325\pi\) |
0.0951763 | + | 0.995460i | \(0.469659\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.3469 | + | 10.8602i | −1.44930 | + | 0.390108i | ||||
\(776\) | 0.397440 | + | 0.229462i | 0.0142673 | + | 0.00823722i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.3540 | − | 5.98973i | −0.801430 | − | 0.214742i | ||||
\(779\) | 36.7521 | + | 21.2188i | 1.31678 | + | 0.760243i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.19226 | − | 8.99325i | −0.185794 | − | 0.321804i | ||||
\(782\) | −7.17966 | − | 1.92378i | −0.256744 | − | 0.0687944i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.90300 | − | 2.93033i | −0.175107 | − | 0.104654i | ||||
\(785\) | 18.7281 | − | 2.47645i | 0.668436 | − | 0.0883882i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.7451 | − | 36.7451i | 1.30982 | − | 1.30982i | 0.388282 | − | 0.921541i | \(-0.373069\pi\) |
0.921541 | − | 0.388282i | \(-0.126931\pi\) | |||||||
\(788\) | −4.87763 | + | 4.87763i | −0.173758 | + | 0.173758i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.5917 | − | 1.92948i | 0.519150 | − | 0.0686480i | ||||
\(791\) | −27.8877 | + | 47.4716i | −0.991571 | + | 1.68789i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.05250 | + | 1.88971i | 0.250442 | + | 0.0671056i | ||||
\(794\) | −11.7409 | − | 20.3358i | −0.416668 | − | 0.721691i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.67771 | + | 2.70068i | 0.165797 | + | 0.0957230i | ||||
\(797\) | 4.61563 | + | 1.23676i | 0.163494 | + | 0.0438081i | 0.339638 | − | 0.940556i | \(-0.389696\pi\) |
−0.176143 | + | 0.984365i | \(0.556362\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.75304 | + | 1.01212i | 0.0620182 | + | 0.0358062i | ||||
\(800\) | 12.8586 | − | 22.3305i | 0.454621 | − | 0.789501i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.2883 | − | 8.65162i | 1.14014 | − | 0.305499i | ||||
\(803\) | −7.26124 | − | 7.26124i | −0.256243 | − | 0.256243i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.6528 | − | 26.9764i | −1.22135 | − | 0.950794i | ||||
\(806\) | −2.16984 | − | 3.75827i | −0.0764292 | − | 0.132379i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.27085 | + | 23.4031i | −0.220608 | + | 0.823319i | ||||
\(809\) | −16.7030 | − | 9.64348i | −0.587246 | − | 0.339047i | 0.176762 | − | 0.984254i | \(-0.443438\pi\) |
−0.764008 | + | 0.645207i | \(0.776771\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.57899i | − | 0.266134i | −0.991107 | − | 0.133067i | \(-0.957517\pi\) | ||
0.991107 | − | 0.133067i | \(-0.0424826\pi\) | |||||||
\(812\) | −13.0525 | − | 13.2511i | −0.458054 | − | 0.465022i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.86574 | − | 4.54129i | −0.275694 | − | 0.159172i | ||||
\(815\) | 3.02067 | + | 3.93198i | 0.105810 | + | 0.137731i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.4891 | + | 32.4891i | −1.13665 | + | 1.13665i | ||||
\(818\) | 0.0628861 | + | 0.0628861i | 0.00219876 | + | 0.00219876i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.15341 | − | 16.4290i | 0.0752003 | − | 0.573726i | ||||
\(821\) | −22.8142 | −0.796220 | −0.398110 | − | 0.917338i | \(-0.630334\pi\) | ||||
−0.398110 | + | 0.917338i | \(0.630334\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.27512 | − | 5.27512i | 0.183879 | − | 0.183879i | −0.609165 | − | 0.793044i | \(-0.708495\pi\) |
0.793044 | + | 0.609165i | \(0.208495\pi\) | |||||||
\(824\) | 15.2772 | − | 26.4609i | 0.532206 | − | 0.921808i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.48483 | + | 1.40971i | −0.0864581 | + | 0.0490501i | ||||
\(827\) | 21.2830 | + | 21.2830i | 0.740083 | + | 0.740083i | 0.972594 | − | 0.232511i | \(-0.0746942\pi\) |
−0.232511 | + | 0.972594i | \(0.574694\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.24336 | − | 7.34971i | 0.147378 | − | 0.255266i | −0.782880 | − | 0.622173i | \(-0.786250\pi\) |
0.930258 | + | 0.366907i | \(0.119583\pi\) | |||||||
\(830\) | 3.28038 | + | 7.90681i | 0.113864 | + | 0.274449i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.42304 | + | 0.917202i | 0.118673 | + | 0.0317983i | ||||
\(833\) | −1.96129 | + | 6.90112i | −0.0679547 | + | 0.239110i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.85180 | + | 2.41047i | 0.0640841 | + | 0.0834177i | ||||
\(836\) | 8.85503 | + | 5.11246i | 0.306258 | + | 0.176818i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.93939 | + | 25.8982i | −0.239717 | + | 0.894637i | ||||
\(839\) | −0.839410 | + | 1.45390i | −0.0289797 | + | 0.0501942i | −0.880152 | − | 0.474693i | \(-0.842559\pi\) |
0.851172 | + | 0.524887i | \(0.175892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.10798 | + | 14.0434i | 0.279586 | + | 0.484256i | ||||
\(842\) | −11.2172 | + | 3.00564i | −0.386571 | + | 0.103581i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.494971 | − | 0.285772i | 0.0170376 | − | 0.00983667i | ||||
\(845\) | −10.8974 | − | 26.2663i | −0.374881 | − | 0.903587i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.4695 | + | 15.7049i | 0.531539 | + | 0.539625i | ||||
\(848\) | −0.295386 | − | 1.10240i | −0.0101436 | − | 0.0378564i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.83755 | + | 1.29032i | 0.165927 | + | 0.0442575i | ||||
\(851\) | −42.2475 | −1.44822 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.0407 | − | 10.9968i | 1.40521 | − | 0.376524i | 0.524995 | − | 0.851105i | \(-0.324067\pi\) |
0.880212 | + | 0.474581i | \(0.157401\pi\) | |||||||
\(854\) | 17.5204 | + | 30.8824i | 0.599537 | + | 1.05677i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.89287 | − | 3.27855i | −0.0646971 | − | 0.112059i | ||||
\(857\) | 49.8017 | + | 13.3443i | 1.70119 | + | 0.455833i | 0.973239 | − | 0.229794i | \(-0.0738051\pi\) |
0.727953 | + | 0.685627i | \(0.240472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.69220 | + | 16.7874i | −0.330694 | + | 0.572778i | −0.982648 | − | 0.185480i | \(-0.940616\pi\) |
0.651954 | + | 0.758258i | \(0.273949\pi\) | |||||||
\(860\) | 16.5779 | + | 6.85574i | 0.565302 | + | 0.233779i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.9919 | − | 5.62476i | 0.714986 | − | 0.191580i | ||||
\(863\) | −0.409122 | − | 0.109624i | −0.0139267 | − | 0.00373165i | 0.251849 | − | 0.967767i | \(-0.418961\pi\) |
−0.265776 | + | 0.964035i | \(0.585628\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.601130 | + | 4.54604i | 0.0204390 | + | 0.154570i | ||||
\(866\) | − | 7.23577i | − | 0.245881i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.15102 | + | 22.2817i | −0.208779 | + | 0.756290i | ||||
\(869\) | 9.53065 | − | 5.50253i | 0.323305 | − | 0.186660i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.57315 | + | 1.48561i | −0.0871877 | + | 0.0503379i | ||||
\(872\) | 33.3182 | − | 8.92760i | 1.12830 | − | 0.302327i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −43.4226 | −1.46879 | ||||||||
\(875\) | 23.3621 | + | 18.1442i | 0.789783 | + | 0.613386i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.7802 | + | 10.1232i | −1.27575 | + | 0.341836i | −0.832230 | − | 0.554430i | \(-0.812936\pi\) |
−0.443518 | + | 0.896266i | \(0.646270\pi\) | |||||||
\(878\) | −13.5060 | − | 13.5060i | −0.455804 | − | 0.455804i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.387333 | + | 2.95508i | −0.0130570 | + | 0.0996157i | ||||
\(881\) | − | 34.8974i | − | 1.17572i | −0.808961 | − | 0.587862i | \(-0.799970\pi\) | ||
0.808961 | − | 0.587862i | \(-0.200030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.1289 | + | 38.1289i | −1.28314 | + | 1.28314i | −0.344268 | + | 0.938872i | \(0.611873\pi\) |
−0.938872 | + | 0.344268i | \(0.888127\pi\) | |||||||
\(884\) | − | 0.569564i | − | 0.0191565i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.6179 | 1.23020 | ||||||||
\(887\) | 12.2126 | + | 45.5781i | 0.410060 | + | 1.53036i | 0.794529 | + | 0.607226i | \(0.207718\pi\) |
−0.384469 | + | 0.923138i | \(0.625616\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.05524 | − | 3.43531i | 0.203086 | − | 0.115217i | ||||
\(890\) | 31.3445 | − | 24.0798i | 1.05067 | − | 0.807157i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.17267 | + | 26.7688i | 0.240159 | + | 0.896285i | ||||
\(893\) | 11.4225 | + | 3.06065i | 0.382240 | + | 0.102421i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.4486 | + | 34.8260i | 0.482964 | + | 1.16410i | ||||
\(896\) | −4.95269 | − | 8.72986i | −0.165458 | − | 0.291644i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8636 | + | 12.8636i | −0.429265 | + | 0.429265i | ||||
\(899\) | 28.0960 | − | 48.6638i | 0.937055 | − | 1.62303i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.24144 | + | 0.716748i | −0.0413585 | + | 0.0238783i | ||||
\(902\) | 2.92747 | + | 10.9255i | 0.0974742 | + | 0.363779i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 53.6218 | − | 30.9586i | 1.78344 | − | 1.02967i | ||||
\(905\) | −27.7047 | + | 36.1480i | −0.920935 | + | 1.20160i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.49758 | − | 24.2493i | 0.215749 | − | 0.805185i | −0.770153 | − | 0.637859i | \(-0.779820\pi\) |
0.985902 | − | 0.167326i | \(-0.0535131\pi\) | |||||||
\(908\) | 4.60461 | − | 17.1846i | 0.152809 | − | 0.570293i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.19550 | + | 2.83015i | −0.0396304 | + | 0.0938185i | ||||
\(911\) | −18.7147 | + | 32.4148i | −0.620045 | + | 1.07395i | 0.369431 | + | 0.929258i | \(0.379552\pi\) |
−0.989477 | + | 0.144692i | \(0.953781\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.52580 | + | 4.52580i | 0.149782 | + | 0.149782i | ||||
\(914\) | − | 28.5162i | − | 0.943233i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6680 | + | 7.31387i | 0.418562 | + | 0.241657i | ||||
\(917\) | 3.97246 | − | 3.91293i | 0.131182 | − | 0.129216i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.8867 | − | 18.4098i | 1.05184 | − | 0.607283i | 0.128680 | − | 0.991686i | \(-0.458926\pi\) |
0.923165 | + | 0.384403i | \(0.125593\pi\) | |||||||
\(920\) | 18.9256 | + | 45.6170i | 0.623958 | + | 1.50395i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.86110 | − | 14.4098i | −0.127159 | − | 0.474562i | ||||
\(923\) | −0.874623 | + | 3.26414i | −0.0287886 | + | 0.107440i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.4570 | − | 0.0323876i | 0.935662 | − | 0.00106490i | ||||
\(926\) | 20.2211 | + | 35.0240i | 0.664507 | + | 1.15096i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.96921 | + | 33.4736i | 0.294429 | + | 1.09882i | ||||
\(929\) | −10.8700 | −0.356635 | −0.178317 | − | 0.983973i | \(-0.557065\pi\) | ||||
−0.178317 | + | 0.983973i | \(0.557065\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.632793 | + | 41.9076i | −0.0207389 | + | 1.37346i | ||||
\(932\) | −3.33164 | + | 12.4339i | −0.109132 | + | 0.407284i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.83292 | − | 15.2991i | −0.289022 | − | 0.500600i | ||||
\(935\) | 3.71114 | − | 0.490729i | 0.121367 | − | 0.0160486i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.9760 | − | 22.9760i | 0.750592 | − | 0.750592i | −0.223998 | − | 0.974590i | \(-0.571911\pi\) |
0.974590 | + | 0.223998i | \(0.0719108\pi\) | |||||||
\(938\) | −13.9280 | − | 3.84493i | −0.454766 | − | 0.125541i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.605268 | − | 4.57734i | −0.0197417 | − | 0.149296i | ||||
\(941\) | − | 36.3208i | − | 1.18402i | −0.805929 | − | 0.592012i | \(-0.798334\pi\) | ||
0.805929 | − | 0.592012i | \(-0.201666\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.2026 | + | 37.2026i | 1.21148 | + | 1.21148i | ||||
\(944\) | 0.901848 | 0.0293527 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2461 | −0.398155 | ||||||||
\(947\) | 8.17811 | + | 8.17811i | 0.265753 | + | 0.265753i | 0.827386 | − | 0.561633i | \(-0.189827\pi\) |
−0.561633 | + | 0.827386i | \(0.689827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.34167i | 0.108475i | ||||||||
\(950\) | 29.2486 | − | 0.0332885i | 0.948950 | − | 0.00108002i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.74810 | − | 5.66196i | 0.186297 | − | 0.183505i | ||||
\(953\) | −39.2129 | + | 39.2129i | −1.27023 | + | 1.27023i | −0.324263 | + | 0.945967i | \(0.605116\pi\) |
−0.945967 | + | 0.324263i | \(0.894884\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.5864 | + | 23.4421i | 0.989753 | + | 0.758570i | ||||
\(956\) | −3.96794 | − | 6.87267i | −0.128332 | − | 0.222278i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.06120 | − | 7.69249i | 0.0665942 | − | 0.248533i | ||||
\(959\) | 30.8631 | + | 18.1308i | 0.996621 | + | 0.585475i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38.8326 | −1.25267 | ||||||||
\(962\) | 0.764969 | + | 2.85490i | 0.0246636 | + | 0.0920458i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.15001 | − | 5.45598i | −0.101455 | − | 0.175725i | ||||
\(965\) | −23.9786 | + | 3.17073i | −0.771900 | + | 0.102069i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.320359 | + | 1.19560i | −0.0103021 | + | 0.0384478i | −0.970886 | − | 0.239544i | \(-0.923002\pi\) |
0.960583 | + | 0.277992i | \(0.0896688\pi\) | |||||||
\(968\) | −6.41638 | − | 23.9463i | −0.206230 | − | 0.769662i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.311231 | − | 0.129124i | 0.00999302 | − | 0.00414591i | ||||
\(971\) | 36.8435 | − | 21.2716i | 1.18237 | − | 0.682639i | 0.225805 | − | 0.974173i | \(-0.427499\pi\) |
0.956561 | + | 0.291533i | \(0.0941654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.9955 | + | 8.57468i | −1.05779 | + | 0.274892i | ||||
\(974\) | 3.44318 | + | 1.98792i | 0.110327 | + | 0.0636971i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 11.2085i | − | 0.358776i | ||||||
\(977\) | 5.18957 | + | 5.18957i | 0.166029 | + | 0.166029i | 0.785231 | − | 0.619202i | \(-0.212544\pi\) |
−0.619202 | + | 0.785231i | \(0.712544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.7766 | − | 25.5939i | 0.472264 | − | 0.817985i | ||||
\(980\) | 15.2082 | − | 6.04208i | 0.485807 | − | 0.193007i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.14274 | − | 26.6571i | 0.227934 | − | 0.850661i | ||||
\(983\) | −7.81104 | + | 29.1512i | −0.249133 | + | 0.929778i | 0.722127 | + | 0.691760i | \(0.243164\pi\) |
−0.971261 | + | 0.238018i | \(0.923502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.93402 | + | 14.6261i | 0.0616231 | + | 0.466025i | ||||
\(986\) | −5.83117 | + | 3.36663i | −0.185702 | + | 0.107215i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.861181 | − | 3.21397i | −0.0273978 | − | 0.102250i | ||||
\(989\) | −49.3310 | + | 28.4813i | −1.56864 | + | 0.905652i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4329 | + | 44.0511i | −0.807903 | + | 1.39933i | 0.106411 | + | 0.994322i | \(0.466064\pi\) |
−0.914314 | + | 0.405007i | \(0.867269\pi\) | |||||||
\(992\) | 30.4527 | − | 30.4527i | 0.966875 | − | 0.966875i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.2934 | + | 8.10905i | −0.453359 | + | 0.257203i | ||||
\(995\) | 10.6705 | − | 4.42696i | 0.338276 | − | 0.140344i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.06203 | − | 1.62432i | −0.191986 | − | 0.0514426i | 0.161545 | − | 0.986865i | \(-0.448352\pi\) |
−0.353531 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(998\) | 6.26292 | + | 23.3735i | 0.198249 | + | 0.739876i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.bv.e.262.28 | 160 | ||
3.2 | odd | 2 | 315.2.bs.e.52.13 | ✓ | 160 | ||
5.3 | odd | 4 | inner | 945.2.bv.e.73.28 | 160 | ||
7.5 | odd | 6 | 945.2.cj.e.397.28 | 160 | |||
9.4 | even | 3 | 945.2.cj.e.577.13 | 160 | |||
9.5 | odd | 6 | 315.2.cg.e.157.28 | yes | 160 | ||
15.8 | even | 4 | 315.2.bs.e.178.13 | yes | 160 | ||
21.5 | even | 6 | 315.2.cg.e.187.13 | yes | 160 | ||
35.33 | even | 12 | 945.2.cj.e.208.13 | 160 | |||
45.13 | odd | 12 | 945.2.cj.e.388.28 | 160 | |||
45.23 | even | 12 | 315.2.cg.e.283.13 | yes | 160 | ||
63.5 | even | 6 | 315.2.bs.e.292.13 | yes | 160 | ||
63.40 | odd | 6 | inner | 945.2.bv.e.712.28 | 160 | ||
105.68 | odd | 12 | 315.2.cg.e.313.28 | yes | 160 | ||
315.68 | odd | 12 | 315.2.bs.e.103.13 | yes | 160 | ||
315.103 | even | 12 | inner | 945.2.bv.e.523.28 | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bs.e.52.13 | ✓ | 160 | 3.2 | odd | 2 | ||
315.2.bs.e.103.13 | yes | 160 | 315.68 | odd | 12 | ||
315.2.bs.e.178.13 | yes | 160 | 15.8 | even | 4 | ||
315.2.bs.e.292.13 | yes | 160 | 63.5 | even | 6 | ||
315.2.cg.e.157.28 | yes | 160 | 9.5 | odd | 6 | ||
315.2.cg.e.187.13 | yes | 160 | 21.5 | even | 6 | ||
315.2.cg.e.283.13 | yes | 160 | 45.23 | even | 12 | ||
315.2.cg.e.313.28 | yes | 160 | 105.68 | odd | 12 | ||
945.2.bv.e.73.28 | 160 | 5.3 | odd | 4 | inner | ||
945.2.bv.e.262.28 | 160 | 1.1 | even | 1 | trivial | ||
945.2.bv.e.523.28 | 160 | 315.103 | even | 12 | inner | ||
945.2.bv.e.712.28 | 160 | 63.40 | odd | 6 | inner | ||
945.2.cj.e.208.13 | 160 | 35.33 | even | 12 | |||
945.2.cj.e.388.28 | 160 | 45.13 | odd | 12 | |||
945.2.cj.e.397.28 | 160 | 7.5 | odd | 6 | |||
945.2.cj.e.577.13 | 160 | 9.4 | even | 3 |