Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(17,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.ci (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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Character | \(\chi\) | \(=\) | 560.33 |
Dual form | 560.2.ci.e.17.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −3.19510 | − | 0.856125i | −1.84469 | − | 0.494284i | −0.845482 | − | 0.534004i | \(-0.820687\pi\) |
−0.999211 | + | 0.0397200i | \(0.987353\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.672461 | − | 2.13256i | 0.300734 | − | 0.953708i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.52104 | − | 0.802724i | 0.952863 | − | 0.303401i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.87765 | + | 3.97081i | 2.29255 | + | 1.32360i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.05351 | + | 1.82473i | 0.317644 | + | 0.550175i | 0.979996 | − | 0.199017i | \(-0.0637750\pi\) |
−0.662352 | + | 0.749193i | \(0.730442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.20510 | + | 1.20510i | −0.334235 | + | 0.334235i | −0.854192 | − | 0.519957i | \(-0.825948\pi\) |
0.519957 | + | 0.854192i | \(0.325948\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.97432 | + | 6.23802i | −1.02616 | + | 1.61065i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.850985 | − | 3.17592i | 0.206394 | − | 0.770273i | −0.782626 | − | 0.622492i | \(-0.786120\pi\) |
0.989020 | − | 0.147781i | \(-0.0472131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.36491 | − | 4.09614i | 0.542547 | − | 0.939718i | −0.456210 | − | 0.889872i | \(-0.650794\pi\) |
0.998757 | − | 0.0498463i | \(-0.0158731\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.74221 | + | 0.406461i | −1.90771 | + | 0.0886970i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00492 | − | 1.07312i | 0.835084 | − | 0.223760i | 0.184154 | − | 0.982897i | \(-0.441046\pi\) |
0.650931 | + | 0.759137i | \(0.274379\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.09559 | − | 2.86812i | −0.819118 | − | 0.573624i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.5583 | − | 11.5583i | −2.22440 | − | 2.22440i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65910i | 0.679478i | 0.940520 | + | 0.339739i | \(0.110339\pi\) | ||||
−0.940520 | + | 0.339739i | \(0.889661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.63858 | − | 0.946036i | 0.294298 | − | 0.169913i | −0.345581 | − | 0.938389i | \(-0.612318\pi\) |
0.639879 | + | 0.768476i | \(0.278985\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.80387 | − | 6.73212i | −0.314013 | − | 1.17191i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0165540 | − | 5.91606i | −0.00279813 | − | 0.999996i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.65625 | − | 9.91327i | −0.436685 | − | 1.62973i | −0.737001 | − | 0.675891i | \(-0.763759\pi\) |
0.300316 | − | 0.953840i | \(-0.402908\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.88214 | − | 2.81870i | 0.781768 | − | 0.451354i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.826081i | 0.129012i | 0.997917 | + | 0.0645061i | \(0.0205472\pi\) | ||||
−0.997917 | + | 0.0645061i | \(0.979453\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70172 | − | 4.70172i | −0.717005 | − | 0.717005i | 0.250985 | − | 0.967991i | \(-0.419245\pi\) |
−0.967991 | + | 0.250985i | \(0.919245\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.0929 | − | 11.9968i | 1.95178 | − | 1.78837i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.90561 | + | 1.04650i | −0.569692 | + | 0.152648i | −0.532155 | − | 0.846647i | \(-0.678618\pi\) |
−0.0375365 | + | 0.999295i | \(0.511951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.71127 | − | 4.04740i | 0.815896 | − | 0.578199i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.43796 | + | 9.41883i | −0.761467 | + | 1.31890i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.645746 | + | 2.40996i | −0.0887000 | + | 0.331033i | −0.995989 | − | 0.0894744i | \(-0.971481\pi\) |
0.907289 | + | 0.420507i | \(0.138148\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.59977 | − | 1.01960i | 0.620233 | − | 0.137483i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.0629 | + | 11.0629i | −1.46532 | + | 1.46532i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.15566 | + | 2.00166i | 0.150454 | + | 0.260594i | 0.931394 | − | 0.364011i | \(-0.118593\pi\) |
−0.780940 | + | 0.624606i | \(0.785260\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.44974 | + | 0.837008i | 0.185620 | + | 0.107168i | 0.589931 | − | 0.807454i | \(-0.299155\pi\) |
−0.404310 | + | 0.914622i | \(0.632488\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.5263 | + | 4.48972i | 2.58607 | + | 0.565651i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75956 | + | 3.38033i | 0.218247 | + | 0.419278i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.2602 | + | 3.28512i | 1.49783 | + | 0.401342i | 0.912372 | − | 0.409363i | \(-0.134249\pi\) |
0.585456 | + | 0.810704i | \(0.300916\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.7149 | −1.65108 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7915 | −1.28071 | −0.640356 | − | 0.768079i | \(-0.721213\pi\) | ||||
−0.640356 | + | 0.768079i | \(0.721213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.6133 | − | 3.37973i | −1.47628 | − | 0.395567i | −0.571198 | − | 0.820812i | \(-0.693521\pi\) |
−0.905078 | + | 0.425245i | \(0.860188\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.6304 | + | 12.6703i | 1.22749 | + | 1.46304i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.12068 | + | 3.75453i | 0.469595 | + | 0.427868i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.29280 | − | 4.78785i | −0.933013 | − | 0.538675i | −0.0452496 | − | 0.998976i | \(-0.514408\pi\) |
−0.887763 | + | 0.460301i | \(0.847742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.1223 | + | 26.1925i | 1.68025 | + | 2.91028i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.47691 | − | 3.47691i | 0.381641 | − | 0.381641i | −0.490052 | − | 0.871693i | \(-0.663022\pi\) |
0.871693 | + | 0.490052i | \(0.163022\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.20057 | − | 3.95045i | −0.672546 | − | 0.428487i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.13265 | − | 11.6912i | 0.335855 | − | 1.25343i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.86698 | − | 4.96576i | 0.303900 | − | 0.526370i | −0.673116 | − | 0.739537i | \(-0.735045\pi\) |
0.977016 | + | 0.213167i | \(0.0683779\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.07074 | + | 4.00547i | −0.217073 | + | 0.419887i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.04536 | + | 1.61985i | −0.626875 | + | 0.167971i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.14494 | − | 7.79779i | −0.733055 | − | 0.800036i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.02714 | − | 1.02714i | −0.104290 | − | 0.104290i | 0.653036 | − | 0.757327i | \(-0.273495\pi\) |
−0.757327 | + | 0.653036i | \(0.773495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.7331i | 1.68174i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.11869 | − | 0.645878i | 0.111314 | − | 0.0642672i | −0.443309 | − | 0.896369i | \(-0.646196\pi\) |
0.554623 | + | 0.832101i | \(0.312862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.82954 | + | 10.5600i | 0.278803 | + | 1.04051i | 0.953250 | + | 0.302184i | \(0.0977155\pi\) |
−0.674447 | + | 0.738324i | \(0.735618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.01199 | + | 18.9166i | −0.489120 | + | 1.84607i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.770212 | + | 2.87447i | 0.0744592 | + | 0.277885i | 0.993110 | − | 0.117185i | \(-0.0373870\pi\) |
−0.918651 | + | 0.395070i | \(0.870720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0694 | − | 7.54561i | 1.25182 | − | 0.722739i | 0.280349 | − | 0.959898i | \(-0.409550\pi\) |
0.971471 | + | 0.237160i | \(0.0762164\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 33.9480i | 3.22220i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.23171 | + | 4.23171i | 0.398086 | + | 0.398086i | 0.877558 | − | 0.479471i | \(-0.159172\pi\) |
−0.479471 | + | 0.877558i | \(0.659172\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.404675 | − | 9.26236i | 0.0377361 | − | 0.863719i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.0735 | + | 3.50303i | −1.20865 | + | 0.323855i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.404020 | − | 8.68972i | −0.0370365 | − | 0.796585i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.28025 | − | 5.68156i | 0.298205 | − | 0.516506i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.707229 | − | 2.63941i | 0.0637687 | − | 0.237988i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.87056 | + | 6.80538i | −0.793407 | + | 0.608692i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.53114 | − | 4.53114i | 0.402073 | − | 0.402073i | −0.476890 | − | 0.878963i | \(-0.658236\pi\) |
0.878963 | + | 0.476890i | \(0.158236\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.9972 | + | 19.0477i | 0.968250 | + | 1.67706i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.40936 | + | 1.39105i | 0.210507 | + | 0.121536i | 0.601547 | − | 0.798837i | \(-0.294551\pi\) |
−0.391040 | + | 0.920374i | \(0.627885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.67395 | − | 12.2249i | 0.231861 | − | 1.06003i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −32.4214 | + | 16.8763i | −2.79039 | + | 1.45248i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.7199 | + | 5.81982i | 1.85565 | + | 0.497221i | 0.999800 | − | 0.0199984i | \(-0.00636610\pi\) |
0.855853 | + | 0.517219i | \(0.173033\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.33499 | 0.706965 | 0.353482 | − | 0.935441i | \(-0.384997\pi\) | ||||
0.353482 | + | 0.935441i | \(0.384997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3748 | 1.12636 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.46856 | − | 0.929398i | −0.290056 | − | 0.0777202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.80324 | + | 2.46060i | 0.648024 | + | 0.204342i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21.7132 | + | 8.04228i | −1.79087 | + | 0.663316i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.44844 | + | 4.30036i | 0.610200 | + | 0.352299i | 0.773044 | − | 0.634353i | \(-0.218733\pi\) |
−0.162844 | + | 0.986652i | \(0.552067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.13200 | − | 8.88888i | −0.417636 | − | 0.723366i | 0.578065 | − | 0.815990i | \(-0.303808\pi\) |
−0.995701 | + | 0.0926240i | \(0.970475\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.4637 | − | 18.4637i | 1.49271 | − | 1.49271i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.915592 | − | 4.13054i | −0.0735421 | − | 0.331773i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.63385 | − | 9.82966i | 0.210204 | − | 0.784492i | −0.777596 | − | 0.628764i | \(-0.783561\pi\) |
0.987800 | − | 0.155728i | \(-0.0497723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.12645 | − | 7.14722i | 0.327249 | − | 0.566811i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.23515 | − | 5.92022i | 0.727832 | − | 0.466578i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.79779 | + | 0.749665i | −0.219140 | + | 0.0587183i | −0.366718 | − | 0.930332i | \(-0.619519\pi\) |
0.147579 | + | 0.989050i | \(0.452852\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.5696 | − | 0.680242i | −1.21210 | − | 0.0529567i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.39226 | − | 8.39226i | −0.649412 | − | 0.649412i | 0.303439 | − | 0.952851i | \(-0.401865\pi\) |
−0.952851 | + | 0.303439i | \(0.901865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0955i | 0.776574i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 32.5300 | − | 18.7812i | 2.48763 | − | 1.43623i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0653257 | + | 0.243799i | 0.00496662 | + | 0.0185357i | 0.968365 | − | 0.249539i | \(-0.0802792\pi\) |
−0.963398 | + | 0.268075i | \(0.913613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.6275 | − | 3.94301i | −0.954546 | − | 0.298064i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.97878 | − | 7.38490i | −0.148734 | − | 0.555083i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8244 | + | 10.8683i | −1.40700 | + | 0.812331i | −0.995098 | − | 0.0988972i | \(-0.968469\pi\) |
−0.411901 | + | 0.911228i | \(0.635135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.06050i | 0.227485i | 0.993510 | + | 0.113743i | \(0.0362839\pi\) | ||||
−0.993510 | + | 0.113743i | \(0.963716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.91548 | − | 3.91548i | −0.289441 | − | 0.289441i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.9268 | − | 1.00168i | −1.68561 | − | 0.0736449i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.69170 | − | 1.79303i | 0.489345 | − | 0.131120i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −38.4172 | − | 19.8609i | −2.79444 | − | 1.44467i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5499 | − | 18.2729i | 0.763361 | − | 1.32218i | −0.177748 | − | 0.984076i | \(-0.556881\pi\) |
0.941109 | − | 0.338103i | \(-0.109785\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.39085 | + | 20.1189i | −0.388042 | + | 1.44819i | 0.445273 | + | 0.895395i | \(0.353106\pi\) |
−0.833315 | + | 0.552798i | \(0.813560\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.72800 | − | 12.3069i | −0.195356 | − | 0.881316i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.29732 | + | 9.29732i | −0.662406 | + | 0.662406i | −0.955947 | − | 0.293540i | \(-0.905167\pi\) |
0.293540 | + | 0.955947i | \(0.405167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.77827 | − | 6.54415i | −0.267834 | − | 0.463902i | 0.700468 | − | 0.713684i | \(-0.252975\pi\) |
−0.968302 | + | 0.249781i | \(0.919641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −36.3603 | − | 20.9926i | −2.56465 | − | 1.48070i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.93725 | + | 9.22474i | 0.206154 | + | 0.647450i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.76167 | + | 0.555508i | 0.123040 | + | 0.0387983i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 31.8056 | + | 8.52229i | 2.21064 | + | 0.592340i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.96577 | 0.689347 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.32737 | 0.0913799 | 0.0456900 | − | 0.998956i | \(-0.485451\pi\) | ||||
0.0456900 | + | 0.998956i | \(0.485451\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.4798 | + | 9.23884i | 2.36252 | + | 0.633035i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.1884 | + | 6.86496i | −0.899442 | + | 0.468186i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.37152 | − | 3.70032i | 0.228874 | − | 0.251194i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.4074 | + | 21.5971i | 2.52775 | + | 1.45940i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.80178 | + | 4.85282i | 0.188468 | + | 0.326436i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.24966 | − | 7.24966i | 0.485473 | − | 0.485473i | −0.421401 | − | 0.906874i | \(-0.638462\pi\) |
0.906874 | + | 0.421401i | \(0.138462\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.7793 | − | 35.9888i | −1.11862 | − | 2.39925i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.76791 | + | 28.9902i | −0.515574 | + | 1.92415i | −0.171618 | + | 0.985164i | \(0.554899\pi\) |
−0.343956 | + | 0.938986i | \(0.611767\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3484 | − | 17.9239i | 0.683841 | − | 1.18445i | −0.289958 | − | 0.957039i | \(-0.593641\pi\) |
0.973800 | − | 0.227408i | \(-0.0730252\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.95164 | − | 15.5239i | −0.654770 | − | 1.02140i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.82659 | − | 1.02533i | 0.250688 | − | 0.0671717i | −0.131287 | − | 0.991344i | \(-0.541911\pi\) |
0.381975 | + | 0.924173i | \(0.375244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.394639 | + | 9.03266i | −0.0257434 | + | 0.589226i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.3973 | + | 22.3973i | 1.45486 | + | 1.45486i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 14.2588i | − | 0.922325i | −0.887316 | − | 0.461163i | \(-0.847432\pi\) | ||
0.887316 | − | 0.461163i | \(-0.152568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.21711 | + | 2.43475i | −0.271648 | + | 0.156836i | −0.629636 | − | 0.776890i | \(-0.716796\pi\) |
0.357989 | + | 0.933726i | \(0.383463\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.2012 | − | 49.2674i | −0.846854 | − | 3.16050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.79069 | − | 14.9013i | −0.306066 | − | 0.952010i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.08631 | + | 7.78621i | 0.132749 | + | 0.495425i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.0858 | + | 8.13241i | −0.892648 | + | 0.515371i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.5118i | 1.04222i | 0.853491 | + | 0.521108i | \(0.174481\pi\) | ||||
−0.853491 | + | 0.521108i | \(0.825519\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.17735 | + | 6.17735i | 0.388367 | + | 0.388367i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.4294 | + | 17.9306i | 1.02885 | + | 1.12286i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.47367 | + | 2.53846i | −0.590951 | + | 0.158345i | −0.541888 | − | 0.840451i | \(-0.682290\pi\) |
−0.0490634 | + | 0.998796i | \(0.515624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.6541 | − | 22.8595i | −0.910563 | − | 1.42042i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.5296 | + | 25.1660i | −0.899360 | + | 1.55774i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.21180 | + | 11.9866i | −0.198048 | + | 0.739125i | 0.793409 | + | 0.608689i | \(0.208304\pi\) |
−0.991457 | + | 0.130436i | \(0.958362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.70513 | + | 2.99769i | 0.289034 | + | 0.184147i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.4116 | + | 13.4116i | −0.820778 | + | 0.820778i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.86530 | + | 3.23079i | 0.113729 | + | 0.196985i | 0.917271 | − | 0.398264i | \(-0.130387\pi\) |
−0.803542 | + | 0.595248i | \(0.797054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.43539 | + | 0.828725i | 0.0871940 | + | 0.0503415i | 0.542963 | − | 0.839757i | \(-0.317302\pi\) |
−0.455769 | + | 0.890098i | \(0.650636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.0454 | − | 11.0251i | 0.607976 | − | 0.667268i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.918805 | − | 10.4949i | 0.0554060 | − | 0.632867i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.7235 | − | 3.94516i | −0.884652 | − | 0.237042i | −0.212239 | − | 0.977218i | \(-0.568076\pi\) |
−0.672413 | + | 0.740176i | \(0.734742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.0261 | 0.899590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.25722 | −0.134655 | −0.0673273 | − | 0.997731i | \(-0.521447\pi\) | ||||
−0.0673273 | + | 0.997731i | \(0.521447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.87101 | + | 1.57313i | 0.348995 | + | 0.0935130i | 0.429058 | − | 0.903277i | \(-0.358846\pi\) |
−0.0800631 | + | 0.996790i | \(0.525512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.1529 | + | 31.0317i | 0.956816 | + | 1.83816i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.663115 | + | 2.08258i | 0.0391425 | + | 0.122931i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.36015 | + | 3.09469i | 0.315303 | + | 0.182040i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.40246 | + | 4.16118i | 0.140834 | + | 0.243932i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5770 | + | 17.5770i | −1.02686 | + | 1.02686i | −0.0272289 | + | 0.999629i | \(0.508668\pi\) |
−0.999629 | + | 0.0272289i | \(0.991332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.04579 | − | 1.11847i | 0.293777 | − | 0.0651198i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.91403 | − | 33.2676i | 0.517244 | − | 1.93038i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.53313 | + | 6.11955i | −0.204326 | + | 0.353903i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.6274 | − | 8.07903i | −0.900748 | − | 0.465668i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.12729 | + | 1.10590i | −0.237107 | + | 0.0635325i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.75986 | − | 2.52880i | 0.158029 | − | 0.144798i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.1121 | + | 21.1121i | 1.20493 | + | 1.20493i | 0.972648 | + | 0.232283i | \(0.0746195\pi\) |
0.232283 | + | 0.972648i | \(0.425380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 36.1627i | − | 2.05722i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3420 | + | 9.43506i | −0.926670 | + | 0.535013i | −0.885757 | − | 0.464150i | \(-0.846360\pi\) |
−0.0409129 | + | 0.999163i | \(0.513027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.71594 | + | 25.0642i | 0.379607 | + | 1.41671i | 0.846495 | + | 0.532397i | \(0.178709\pi\) |
−0.466888 | + | 0.884317i | \(0.654625\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.3777 | − | 40.7543i | 1.31718 | − | 2.29624i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.370421 | + | 1.38243i | 0.0208049 | + | 0.0776451i | 0.975548 | − | 0.219787i | \(-0.0705364\pi\) |
−0.954743 | + | 0.297432i | \(0.903870\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.67686 | + | 3.85489i | −0.373832 | + | 0.215832i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 9.84362i | − | 0.549417i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.9965 | − | 10.9965i | −0.611861 | − | 0.611861i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.39198 | − | 1.47923i | 0.465503 | − | 0.0820527i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −48.2180 | + | 12.9200i | −2.66646 | + | 0.714476i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.00614 | + | 5.77340i | −0.496524 | + | 0.318298i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.21858 | − | 14.2350i | 0.451734 | − | 0.782426i | −0.546760 | − | 0.837290i | \(-0.684139\pi\) |
0.998494 | + | 0.0548631i | \(0.0174722\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.0950 | − | 78.7275i | 1.15600 | − | 4.31424i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.2502 | − | 23.9365i | 0.833210 | − | 1.30779i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4453 | − | 16.4453i | 0.895835 | − | 0.895835i | −0.0992293 | − | 0.995065i | \(-0.531638\pi\) |
0.995065 | + | 0.0992293i | \(0.0316377\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.89788 | − | 17.1436i | −0.537579 | − | 0.931115i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.45251 | + | 1.99331i | 0.186964 | + | 0.107944i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1494 | − | 14.7882i | 0.602010 | − | 0.798488i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.22271 | + | 29.2477i | −0.496534 | + | 1.57464i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.43767 | + | 0.921122i | 0.184544 | + | 0.0494484i | 0.349907 | − | 0.936784i | \(-0.386213\pi\) |
−0.165363 | + | 0.986233i | \(0.552880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.16515 | −0.437070 | −0.218535 | − | 0.975829i | \(-0.570128\pi\) | ||||
−0.218535 | + | 0.975829i | \(0.570128\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.8580 | 1.48695 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.779678 | − | 0.208914i | −0.0414981 | − | 0.0111194i | 0.238010 | − | 0.971263i | \(-0.423505\pi\) |
−0.279508 | + | 0.960143i | \(0.590171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.25684 | + | 23.0134i | −0.385153 | + | 1.22142i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.14860 | + | 28.1104i | −0.325418 | + | 1.48776i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.7687 | + | 13.7228i | 1.25446 | + | 0.724264i | 0.971992 | − | 0.235012i | \(-0.0755131\pi\) |
0.282469 | + | 0.959276i | \(0.408846\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.68556 | − | 2.91947i | −0.0887136 | − | 0.153656i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.3449 | + | 15.3449i | −0.805396 | + | 0.805396i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6894 | + | 24.6259i | −0.821222 | + | 1.28898i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.44136 | − | 12.8433i | 0.179637 | − | 0.670416i | −0.816078 | − | 0.577942i | \(-0.803856\pi\) |
0.995715 | − | 0.0924739i | \(-0.0294775\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.28021 | + | 5.68150i | −0.170761 | + | 0.295767i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.306579 | + | 6.59395i | 0.0159168 | + | 0.342341i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3794 | + | 3.31706i | −0.640982 | + | 0.171751i | −0.564648 | − | 0.825332i | \(-0.690988\pi\) |
−0.0763341 | + | 0.997082i | \(0.524322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 34.1686 | − | 14.1496i | 1.76446 | − | 0.730681i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.40959 | − | 4.40959i | −0.227105 | − | 0.227105i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.65754i | − | 0.187875i | −0.995578 | − | 0.0939375i | \(-0.970055\pi\) | ||
0.995578 | − | 0.0939375i | \(-0.0299454\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.3567 | + | 10.5982i | −0.940441 | + | 0.542964i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.80691 | + | 29.1358i | 0.398915 | + | 1.48877i | 0.815009 | + | 0.579448i | \(0.196732\pi\) |
−0.416095 | + | 0.909321i | \(0.636601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.7777 | − | 6.26281i | 0.549285 | − | 0.319182i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.6671 | − | 51.0064i | −0.694739 | − | 2.59280i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.17854 | + | 2.98983i | −0.262562 | + | 0.151591i | −0.625503 | − | 0.780222i | \(-0.715106\pi\) |
0.362940 | + | 0.931812i | \(0.381773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.6325i | − | 0.689426i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.50725 | − | 6.50725i | −0.328247 | − | 0.328247i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.7869 | + | 14.4652i | −0.794327 | + | 0.727824i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.45836 | + | 0.390768i | −0.0731932 | + | 0.0196121i | −0.295230 | − | 0.955426i | \(-0.595396\pi\) |
0.222037 | + | 0.975038i | \(0.428730\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.0096 | + | 36.7705i | −0.951669 | + | 1.84083i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.6011 | − | 21.8258i | 0.629269 | − | 1.08993i | −0.358429 | − | 0.933557i | \(-0.616688\pi\) |
0.987699 | − | 0.156370i | \(-0.0499791\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.834588 | + | 3.11473i | −0.0415738 | + | 0.155156i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 66.0262 | − | 14.6356i | 3.28087 | − | 0.727250i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.2906 | − | 15.2906i | 0.757928 | − | 0.757928i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.7806 | − | 20.4046i | −0.582513 | − | 1.00894i | −0.995180 | − | 0.0980604i | \(-0.968736\pi\) |
0.412667 | − | 0.910882i | \(-0.364597\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −64.4147 | − | 37.1898i | −3.17734 | − | 1.83444i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.52024 | + | 4.11859i | 0.222427 | + | 0.202663i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.07662 | − | 9.75280i | −0.249202 | − | 0.478746i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.6312 | − | 7.13580i | −1.30413 | − | 0.349441i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.614382 | 0.0300145 | 0.0150073 | − | 0.999887i | \(-0.495223\pi\) | ||||
0.0150073 | + | 0.999887i | \(0.495223\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0643 | 0.636713 | 0.318356 | − | 0.947971i | \(-0.396869\pi\) | ||||
0.318356 | + | 0.947971i | \(0.396869\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.0169 | − | 8.31095i | −1.50809 | − | 0.404092i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.5942 | + | 10.5665i | −0.610909 | + | 0.512552i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.32674 | + | 0.946388i | 0.209385 | + | 0.0457989i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.2867 | + | 5.93904i | 0.496648 | + | 0.286740i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.52522 | + | 13.0341i | 0.362477 | + | 0.627828i | 0.988368 | − | 0.152082i | \(-0.0485979\pi\) |
−0.625891 | + | 0.779911i | \(0.715265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5694 | + | 18.5694i | −0.892387 | + | 0.892387i | −0.994747 | − | 0.102361i | \(-0.967360\pi\) |
0.102361 | + | 0.994747i | \(0.467360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.8256 | − | 14.5424i | −1.09440 | − | 0.697256i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.07564 | − | 18.9425i | 0.242801 | − | 0.906144i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.96987 | − | 6.87601i | 0.189471 | − | 0.328174i | −0.755603 | − | 0.655030i | \(-0.772656\pi\) |
0.945074 | + | 0.326856i | \(0.105989\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 55.3516 | − | 5.15819i | 2.63579 | − | 0.245628i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.70480 | + | 2.60039i | −0.461089 | + | 0.123548i | −0.481883 | − | 0.876235i | \(-0.660047\pi\) |
0.0207943 | + | 0.999784i | \(0.493380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.66183 | − | 9.45329i | −0.410610 | − | 0.448129i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.1169 | − | 20.1169i | −0.951496 | − | 0.951496i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.6484i | 0.738492i | 0.929332 | + | 0.369246i | \(0.120384\pi\) | ||||
−0.929332 | + | 0.369246i | \(0.879616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.50737 | + | 0.870282i | −0.0709794 | + | 0.0409800i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.78726 | + | 32.7945i | 0.412861 | + | 1.54082i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.14940 | + | 7.10950i | 0.335169 | + | 0.333298i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.39543 | − | 23.8681i | −0.299165 | − | 1.11650i | −0.937853 | − | 0.347034i | \(-0.887189\pi\) |
0.638687 | − | 0.769467i | \(-0.279478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −46.5443 | + | 26.8724i | −2.17250 | + | 1.25430i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.2862i | − | 0.805099i | −0.915398 | − | 0.402550i | \(-0.868124\pi\) | ||
0.915398 | − | 0.402550i | \(-0.131876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.61564 | + | 5.61564i | 0.260981 | + | 0.260981i | 0.825453 | − | 0.564472i | \(-0.190920\pi\) |
−0.564472 | + | 0.825453i | \(0.690920\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.610849 | + | 13.9814i | −0.0283274 | + | 0.648370i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.3828 | − | 10.8205i | 1.86869 | − | 0.500715i | 0.868709 | − | 0.495322i | \(-0.164950\pi\) |
0.999985 | − | 0.00539309i | \(-0.00171668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.5456 | − | 1.55967i | 1.54899 | − | 0.0720189i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.8308 | + | 29.1519i | −0.775524 | + | 1.34325i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.62606 | − | 13.5326i | 0.166726 | − | 0.622231i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.4339 | + | 9.99327i | −0.983455 | + | 0.458523i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.0107 | + | 14.0107i | −0.641506 | + | 0.641506i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.2812 | + | 31.6639i | 0.835287 | + | 1.44676i | 0.893796 | + | 0.448473i | \(0.148032\pi\) |
−0.0585091 | + | 0.998287i | \(0.518635\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.1475 | + | 8.74544i | 0.690669 | + | 0.398758i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.5757 | + | 11.0092i | −1.57325 | + | 0.500938i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.88114 | + | 1.49972i | −0.130826 | + | 0.0680989i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.00674 | − | 0.805655i | −0.136249 | − | 0.0365077i | 0.190050 | − | 0.981774i | \(-0.439135\pi\) |
−0.326299 | + | 0.945267i | \(0.605802\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.58102 | 0.433269 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.3286 | 1.45897 | 0.729484 | − | 0.683998i | \(-0.239760\pi\) | ||||
0.729484 | + | 0.683998i | \(0.239760\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6210 | + | 3.11384i | 0.523384 | + | 0.140240i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 35.6843 | + | 11.2524i | 1.60389 | + | 0.505756i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.2057 | + | 8.66257i | −1.22034 | + | 0.388569i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.3372 | + | 11.1643i | 0.865651 | + | 0.499784i | 0.865901 | − | 0.500216i | \(-0.166746\pi\) |
−0.000249428 | 1.00000i | \(0.500079\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.6293 | + | 33.9989i | 0.876972 | + | 1.51896i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.3631 | + | 20.3631i | −0.907947 | + | 0.907947i | −0.996106 | − | 0.0881596i | \(-0.971901\pi\) |
0.0881596 | + | 0.996106i | \(0.471901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.625093 | − | 2.82000i | −0.0278163 | − | 0.125489i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.64298 | − | 32.2560i | 0.383848 | − | 1.43254i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.5423 | + | 28.6521i | −0.733224 | + | 1.26998i | 0.222274 | + | 0.974984i | \(0.428652\pi\) |
−0.955498 | + | 0.294997i | \(0.904681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.5116 | + | 1.60459i | −1.52670 | + | 0.0709827i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −74.6790 | + | 20.0102i | −3.29716 | + | 0.883471i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.4225 | + | 1.06703i | 1.07619 | + | 0.0470188i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.02417 | − | 6.02417i | −0.264943 | − | 0.264943i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 0.834889i | − | 0.0366475i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.9365 | + | 12.0877i | −0.917246 | + | 0.529572i | −0.882755 | − | 0.469833i | \(-0.844314\pi\) |
−0.0344903 | + | 0.999405i | \(0.510981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.17690 | + | 23.0525i | 0.270097 | + | 1.00801i | 0.959056 | + | 0.283215i | \(0.0914011\pi\) |
−0.688960 | + | 0.724800i | \(0.741932\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 36.9703 | + | 23.4090i | 1.61352 | + | 1.02165i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.61012 | − | 6.00906i | −0.0701381 | − | 0.261759i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.03074 | + | 2.90450i | −0.218728 | + | 0.126283i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.3556i | 0.796566i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.995512 | − | 0.995512i | −0.0431204 | − | 0.0431204i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.64790 | + | 0.290448i | 0.287414 | + | 0.0125572i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 69.4503 | − | 18.6092i | 2.99700 | − | 0.803045i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.4022 | + | 6.15754i | 0.577275 | + | 0.265224i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.226204 | − | 0.391797i | 0.00972527 | − | 0.0168447i | −0.861122 | − | 0.508399i | \(-0.830238\pi\) |
0.870847 | + | 0.491554i | \(0.163571\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.62017 | − | 9.77860i | 0.112442 | − | 0.419640i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.30279 | − | 32.9453i | −0.312817 | − | 1.41122i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.0665 | + | 24.0665i | −1.02901 | + | 1.02901i | −0.0294424 | + | 0.999566i | \(0.509373\pi\) |
−0.999566 | + | 0.0294424i | \(0.990627\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.64720 | + | 11.5133i | 0.283696 | + | 0.491375i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.9882 | + | 8.65343i | 0.638518 | + | 0.368649i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.7498 | − | 5.41353i | −1.05247 | − | 0.230207i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 72.3960 | + | 22.8287i | 3.07304 | + | 0.969024i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.9643 | + | 11.7802i | 1.86283 | + | 0.499143i | 0.999980 | − | 0.00632392i | \(-0.00201298\pi\) |
0.862846 | + | 0.505467i | \(0.168680\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3321 | 0.479297 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.9157 | −0.967502 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.3526 | + | 5.98936i | 0.942050 | + | 0.252422i | 0.696986 | − | 0.717085i | \(-0.254524\pi\) |
0.245065 | + | 0.969507i | \(0.421191\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.8700 | − | 6.17871i | 0.499376 | − | 0.259940i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 59.1492 | + | 53.8934i | 2.48403 | + | 2.26331i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.46781 | + | 3.73419i | 0.271145 | + | 0.156545i | 0.629408 | − | 0.777075i | \(-0.283298\pi\) |
−0.358263 | + | 0.933621i | \(0.616631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.421350 | − | 0.729799i | −0.0176329 | − | 0.0305412i | 0.857074 | − | 0.515193i | \(-0.172280\pi\) |
−0.874707 | + | 0.484652i | \(0.838946\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −49.3517 | + | 49.3517i | −2.06170 | + | 2.06170i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.4804 | − | 7.09156i | −0.812387 | − | 0.295739i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.36558 | + | 34.9528i | −0.389894 | + | 1.45511i | 0.440411 | + | 0.897796i | \(0.354833\pi\) |
−0.830305 | + | 0.557309i | \(0.811834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.4486 | − | 59.6668i | 1.43164 | − | 2.47967i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.97443 | − | 11.5564i | 0.247861 | − | 0.479441i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.07781 | + | 1.36059i | −0.210301 | + | 0.0563500i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.32100 | + | 30.2356i | −0.0546167 | + | 1.25009i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.777106 | + | 0.777106i | 0.0320746 | + | 0.0320746i | 0.722962 | − | 0.690888i | \(-0.242780\pi\) |
−0.690888 | + | 0.722962i | \(0.742780\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.94914i | − | 0.368743i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.6655 | − | 21.7462i | 1.54935 | − | 0.894519i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.14887 | − | 19.2159i | −0.211439 | − | 0.789101i | −0.987390 | − | 0.158307i | \(-0.949396\pi\) |
0.775951 | − | 0.630793i | \(-0.217270\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.8030 | − | 4.98190i | −0.770848 | − | 0.204238i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.46934 | + | 24.1439i | 0.264772 | + | 0.988144i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.4628 | + | 11.2369i | −0.795229 | + | 0.459126i | −0.841800 | − | 0.539789i | \(-0.818504\pi\) |
0.0465712 | + | 0.998915i | \(0.485171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0046i | 1.22391i | 0.790891 | + | 0.611957i | \(0.209618\pi\) | ||||
−0.790891 | + | 0.611957i | \(0.790382\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 71.2771 | + | 71.2771i | 2.90263 | + | 2.90263i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.91041 | − | 10.8159i | −0.402915 | − | 0.439731i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.14580 | − | 1.11086i | 0.168273 | − | 0.0450886i | −0.173699 | − | 0.984799i | \(-0.555572\pi\) |
0.341972 | + | 0.939710i | \(0.388905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.48728 | − | 31.9886i | −0.0602677 | − | 1.29624i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.44551 | − | 5.96780i | 0.139390 | − | 0.241431i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.74007 | + | 25.1543i | −0.272229 | + | 1.01597i | 0.685447 | + | 0.728123i | \(0.259607\pi\) |
−0.957676 | + | 0.287850i | \(0.907060\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.15312 | − | 3.28311i | −0.207794 | − | 0.132388i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.5489 | − | 18.5489i | 0.746750 | − | 0.746750i | −0.227117 | − | 0.973867i | \(-0.572930\pi\) |
0.973867 | + | 0.227117i | \(0.0729300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9263 | − | 25.8532i | −0.599940 | − | 1.03913i | −0.992829 | − | 0.119541i | \(-0.961858\pi\) |
0.392889 | − | 0.919586i | \(-0.371476\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −58.6938 | − | 33.8869i | −2.35530 | − | 1.35983i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.24164 | − | 14.8203i | 0.129874 | − | 0.593762i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.54776 | + | 23.4933i | 0.341910 | + | 0.939733i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −31.8416 | − | 8.53194i | −1.27163 | − | 0.340733i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.7441 | −1.34547 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.755612 | −0.0300804 | −0.0150402 | − | 0.999887i | \(-0.504788\pi\) | ||||
−0.0150402 | + | 0.999887i | \(0.504788\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.24108 | − | 1.13639i | −0.168568 | − | 0.0451676i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.61589 | − | 12.7099i | −0.262544 | − | 0.504378i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00514 | + | 11.7602i | −0.0794464 | + | 0.465955i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −74.2199 | − | 42.8509i | −2.93609 | − | 1.69515i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1050 | − | 17.5023i | −0.399122 | − | 0.691299i | 0.594496 | − | 0.804099i | \(-0.297352\pi\) |
−0.993618 | + | 0.112799i | \(0.964018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.933128 | + | 0.933128i | −0.0367990 | + | 0.0367990i | −0.725267 | − | 0.688468i | \(-0.758284\pi\) |
0.688468 | + | 0.725267i | \(0.258284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.0155 | − | 10.6433i | 1.89061 | − | 0.419080i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.85058 | − | 29.2988i | 0.308638 | − | 1.15185i | −0.621130 | − | 0.783708i | \(-0.713326\pi\) |
0.929768 | − | 0.368146i | \(-0.120007\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.43499 | + | 4.21752i | −0.0955816 | + | 0.165552i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.9403 | + | 8.93646i | −0.546363 | + | 0.350247i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.0331 | − | 10.7268i | 1.56662 | − | 0.419774i | 0.631867 | − | 0.775077i | \(-0.282289\pi\) |
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.58669 | − | 4.20268i | 0.179217 | − | 0.164212i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −73.3297 | − | 73.3297i | −2.86086 | − | 2.86086i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7.54235i | − | 0.293808i | −0.989151 | − | 0.146904i | \(-0.953069\pi\) | ||
0.989151 | − | 0.146904i | \(-0.0469309\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.6248 | + | 23.4548i | −1.58012 | + | 0.912284i | −0.585282 | + | 0.810830i | \(0.699016\pi\) |
−0.994840 | + | 0.101455i | \(0.967650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.79735 | − | 17.9039i | −0.186314 | − | 0.695332i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.2721 | − | 13.9231i | −0.941233 | − | 0.539915i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.92664 | + | 14.6544i | 0.152040 | + | 0.567422i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.3700 | + | 16.9568i | −1.13551 | + | 0.655588i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.52717i | 0.136165i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.6391 | + | 29.6391i | 1.14250 | + | 1.14250i | 0.987991 | + | 0.154511i | \(0.0493803\pi\) |
0.154511 | + | 0.987991i | \(0.450620\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.1875 | + | 80.4890i | 0.546078 | + | 3.09802i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.0992 | − | 10.2087i | 1.46427 | − | 0.392351i | 0.563309 | − | 0.826246i | \(-0.309528\pi\) |
0.900963 | + | 0.433896i | \(0.142861\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.41397 | − | 1.76495i | −0.131016 | − | 0.0677325i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 49.6385 | − | 85.9764i | 1.90215 | − | 3.29462i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.10186 | + | 4.11219i | −0.0421615 | + | 0.157349i | −0.983797 | − | 0.179285i | \(-0.942622\pi\) |
0.941636 | + | 0.336633i | \(0.109288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.0169 | − | 42.4052i | 1.03226 | − | 1.62022i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.4093 | + | 48.4093i | −1.84693 | + | 1.84693i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.12605 | − | 3.68243i | −0.0809961 | − | 0.140289i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.538345 | − | 0.310814i | −0.0204796 | − | 0.0118239i | 0.489725 | − | 0.871877i | \(-0.337097\pi\) |
−0.510205 | + | 0.860053i | \(0.670430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.4321 | + | 42.1848i | 0.510242 | + | 1.60247i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.60496 | − | 17.7748i | 0.212608 | − | 0.674238i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.62357 | + | 0.702983i | 0.0993747 | + | 0.0266274i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.1042 | −0.495645 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9626 | −1.16944 | −0.584721 | − | 0.811235i | \(-0.698796\pi\) | ||||
−0.584721 | + | 0.811235i | \(0.698796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.8879 | − | 12.5636i | −1.76841 | − | 0.473844i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.99400 | − | 28.5224i | 0.338734 | − | 1.07422i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.30181 | − | 2.52628i | 0.0865683 | − | 0.0950107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.5831 | − | 15.3478i | −0.998350 | − | 0.576398i | −0.0905903 | − | 0.995888i | \(-0.528875\pi\) |
−0.907760 | + | 0.419491i | \(0.862209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.0233 | − | 65.8583i | −1.42599 | − | 2.46988i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.54719 | − | 5.54719i | 0.207744 | − | 0.207744i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.31446 | + | 6.77192i | −0.161352 | + | 0.253255i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.2073 | + | 45.5583i | −0.455891 | + | 1.70141i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.00357 | − | 6.93439i | 0.149308 | − | 0.258609i | −0.781664 | − | 0.623700i | \(-0.785629\pi\) |
0.930972 | + | 0.365091i | \(0.118962\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.6101 | + | 24.3508i | 0.581352 | + | 0.906871i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.5585 | − | 4.16889i | 0.578628 | − | 0.155043i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.4948 | − | 14.9862i | 0.389765 | − | 0.556573i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.24335 | − | 2.24335i | −0.0832011 | − | 0.0832011i | 0.664281 | − | 0.747483i | \(-0.268738\pi\) |
−0.747483 | + | 0.664281i | \(0.768738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 77.9825i | 2.88824i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.9334 | + | 10.9312i | −0.700276 | + | 0.404304i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.69369 | − | 36.1773i | −0.358045 | − | 1.33624i | −0.876610 | − | 0.481202i | \(-0.840200\pi\) |
0.518565 | − | 0.855038i | \(-0.326466\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.54936 | + | 51.7127i | 0.0940347 | + | 1.90745i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.92179 | + | 25.8325i | 0.254967 | + | 0.951552i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.55973 | − | 4.94196i | 0.314875 | − | 0.181793i | −0.334231 | − | 0.942491i | \(-0.608477\pi\) |
0.649106 | + | 0.760698i | \(0.275143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 26.6639i | − | 0.979522i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.1188 | − | 23.1188i | −0.848147 | − | 0.848147i | 0.141755 | − | 0.989902i | \(-0.454725\pi\) |
−0.989902 | + | 0.141755i | \(0.954725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1795 | − | 12.9924i | 0.519498 | − | 0.476005i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.7191 | − | 10.1068i | 1.38007 | − | 0.369789i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.24914 | + | 6.62838i | 0.155260 | + | 0.242196i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0861 | − | 33.0582i | 0.696463 | − | 1.20631i | −0.273222 | − | 0.961951i | \(-0.588089\pi\) |
0.969685 | − | 0.244358i | \(-0.0785773\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.1362 | − | 52.7569i | 0.515150 | − | 1.92257i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.4071 | + | 4.96685i | −0.815478 | + | 0.180762i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.5560 | + | 24.5560i | −0.892504 | + | 0.892504i | −0.994758 | − | 0.102255i | \(-0.967394\pi\) |
0.102255 | + | 0.994758i | \(0.467394\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.4487 | − | 25.0259i | −0.524454 | − | 0.908381i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7157 | + | 6.76405i | 0.424693 | + | 0.245197i | 0.697083 | − | 0.716990i | \(-0.254481\pi\) |
−0.272390 | + | 0.962187i | \(0.587814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.8914 | − | 29.5139i | 0.973533 | − | 1.06847i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.9588 | − | 51.7911i | −0.974699 | − | 1.87251i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.80489 | − | 1.01952i | −0.137387 | − | 0.0368126i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.3025 | 1.41728 | 0.708641 | − | 0.705569i | \(-0.249308\pi\) | ||||
0.708641 | + | 0.705569i | \(0.249308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.4426 | 1.16839 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.5742 | − | 7.38848i | −0.991774 | − | 0.265745i | −0.273778 | − | 0.961793i | \(-0.588274\pi\) |
−0.717995 | + | 0.696048i | \(0.754940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.42431 | − | 0.825076i | −0.338531 | − | 0.0296376i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.2509 | + | 85.5842i | 0.977619 | + | 3.07031i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.38374 | + | 1.95360i | 0.121235 | + | 0.0699952i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3689 | − | 19.6915i | −0.406810 | − | 0.704616i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.2932 | − | 42.2932i | 1.51143 | − | 1.51143i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.1911 | − | 12.2269i | −0.684961 | − | 0.436397i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.15609 | + | 15.5107i | −0.148149 | + | 0.552898i | 0.851446 | + | 0.524442i | \(0.175726\pi\) |
−0.999595 | + | 0.0284567i | \(0.990941\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.5240 | − | 35.5487i | 0.730675 | − | 1.26557i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0652 | + | 7.27142i | 0.500101 | + | 0.258542i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.75576 | + | 0.738404i | −0.0978600 | + | 0.0262215i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.4670 | − | 13.6061i | −0.442158 | − | 0.482559i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.4141 | + | 11.4141i | 0.404310 | + | 0.404310i | 0.879749 | − | 0.475439i | \(-0.157711\pi\) |
−0.475439 | + | 0.879749i | \(0.657711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2945i | 0.470324i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.4362 | − | 22.7685i | 1.39341 | − | 0.804486i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.12113 | − | 26.5764i | −0.251299 | − | 0.937861i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.41491 | − | 23.6756i | −0.226096 | − | 0.834455i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.19385 | − | 11.9196i | −0.112429 | − | 0.419591i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.1396 | − | 8.74085i | 0.532280 | − | 0.307312i | −0.209665 | − | 0.977773i | \(-0.567237\pi\) |
0.741944 | + | 0.670461i | \(0.233904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.1883i | − | 1.79747i | −0.438497 | − | 0.898733i | \(-0.644489\pi\) | ||
0.438497 | − | 0.898733i | \(-0.355511\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.87674 | − | 3.87674i | −0.135963 | − | 0.135963i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.282700 | + | 6.47056i | −0.00990256 | + | 0.226654i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.3780 | + | 8.13976i | −1.06279 | + | 0.284774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −30.1468 | + | 19.3257i | −1.05341 | + | 0.675294i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.0218989 | − | 0.0379301i | 0.000764278 | − | 0.00132377i | −0.865643 | − | 0.500662i | \(-0.833090\pi\) |
0.866407 | + | 0.499338i | \(0.166423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.97965 | + | 7.38815i | −0.0690062 | + | 0.257535i | −0.991807 | − | 0.127742i | \(-0.959227\pi\) |
0.922801 | + | 0.385276i | \(0.125894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.9206 | + | 32.7457i | −0.415023 | + | 1.14006i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9919 | − | 25.9919i | 0.903826 | − | 0.903826i | −0.0919384 | − | 0.995765i | \(-0.529306\pi\) |
0.995765 | + | 0.0919384i | \(0.0293063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5010 | + | 18.1883i | 0.364715 | + | 0.631704i | 0.988730 | − | 0.149708i | \(-0.0478332\pi\) |
−0.624016 | + | 0.781412i | \(0.714500\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.6657 | + | 25.2104i | 1.51475 | + | 0.874539i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.99399 | − | 21.5828i | −0.276975 | − | 0.747799i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.5404 | + | 12.2535i | −0.814650 | + | 0.424050i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.8739 | − | 8.00469i | −1.03259 | − | 0.276683i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.5751 | −1.50438 | −0.752189 | − | 0.658947i | \(-0.771002\pi\) | ||||
−0.752189 | + | 0.658947i | \(0.771002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6110 | 0.538309 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.21205 | + | 1.93246i | 0.248396 | + | 0.0665576i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.5291 | + | 6.78880i | 0.740625 | + | 0.233542i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.70891 | − | 16.9566i | 0.127440 | − | 0.582635i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.4117 | − | 10.0526i | −0.597567 | − | 0.345005i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.2762 | − | 36.8514i | −0.729338 | − | 1.26325i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.6117 | − | 17.6117i | 0.603014 | − | 0.603014i | −0.338098 | − | 0.941111i | \(-0.609783\pi\) |
0.941111 | + | 0.338098i | \(0.109783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.1768 | − | 82.0016i | −0.621634 | − | 2.80440i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.04624 | − | 33.7610i | 0.309014 | − | 1.15325i | −0.620422 | − | 0.784268i | \(-0.713038\pi\) |
0.929435 | − | 0.368986i | \(-0.120295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2794 | + | 29.9288i | −0.589565 | + | 1.02116i | 0.404724 | + | 0.914439i | \(0.367367\pi\) |
−0.994289 | + | 0.106718i | \(0.965966\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.335770 | − | 7.22177i | −0.0114430 | − | 0.246117i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.6135 | + | 11.4183i | −1.45058 | + | 0.388682i | −0.896226 | − | 0.443598i | \(-0.853702\pi\) |
−0.554355 | + | 0.832280i | \(0.687035\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.563844 | + | 0.0246345i | 0.0191713 | + | 0.000837597i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.4768 | − | 14.4768i | −0.491658 | − | 0.491658i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 20.1761i | − | 0.684428i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7337 | + | 10.8159i | −0.634769 | + | 0.366484i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.98573 | − | 11.1429i | −0.101052 | − | 0.377130i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.9002 | + | 24.2772i | −0.571330 | + | 0.820720i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.217309 | − | 0.811006i | −0.00733799 | − | 0.0273857i | 0.962160 | − | 0.272486i | \(-0.0878458\pi\) |
−0.969498 | + | 0.245100i | \(0.921179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 71.2083 | − | 41.1121i | 2.40180 | − | 1.38668i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.6633i | 1.33629i | 0.744031 | + | 0.668145i | \(0.232911\pi\) | ||||
−0.744031 | + | 0.668145i | \(0.767089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9598 | + | 28.9598i | 0.974576 | + | 0.974576i | 0.999685 | − | 0.0251084i | \(-0.00799308\pi\) |
−0.0251084 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.0794 | − | 0.746202i | −0.574117 | − | 0.0250833i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.40217 | − | 1.44751i | 0.181387 | − | 0.0486025i | −0.166982 | − | 0.985960i | \(-0.553402\pi\) |
0.348369 | + | 0.937357i | \(0.386736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.78592 | − | 15.0604i | 0.261131 | − | 0.505110i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.8628 | + | 55.1880i | −1.06744 | + | 1.84887i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.94977 | + | 18.4728i | −0.165638 | + | 0.618168i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.5185 | + | 47.4525i | 0.351595 | + | 1.58616i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.5278 | − | 16.5278i | 0.551847 | − | 0.551847i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.46164 | + | 5.99574i | 0.115452 | + | 0.199969i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.10430 | + | 4.10167i | 0.236679 | + | 0.136646i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 43.0145 | + | 39.1923i | 1.43143 | + | 1.30424i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.52668 | + | 2.05807i | 0.216954 | + | 0.0684124i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.2095 | + | 5.41512i | 0.671046 | + | 0.179806i | 0.578226 | − | 0.815877i | \(-0.303745\pi\) |
0.0928200 | + | 0.995683i | \(0.470412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.2586 | 0.340258 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.0212 | 0.431413 | 0.215707 | − | 0.976458i | \(-0.430795\pi\) | ||||
0.215707 | + | 0.976458i | \(0.430795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0074 | + | 2.68146i | 0.331195 | + | 0.0887435i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.9830 | + | 5.71698i | −0.363087 | + | 0.188997i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.19072 | + | 1.57283i | 0.237459 | + | 0.0519394i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.38681 | + | 2.53273i | 0.144708 | + | 0.0835470i | 0.570606 | − | 0.821224i | \(-0.306708\pi\) |
−0.425898 | + | 0.904771i | \(0.640042\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −49.3807 | − | 85.5299i | −1.62715 | − | 2.81831i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.0048 | − | 13.0048i | 0.428059 | − | 0.428059i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.5535 | + | 48.2192i | −0.577157 | + | 1.58544i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.4712 | + | 83.8635i | −0.738050 | + | 2.75444i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.7411 | + | 42.8528i | −0.811728 | + | 1.40595i | 0.0999258 | + | 0.994995i | \(0.468139\pi\) |
−0.911654 | + | 0.410959i | \(0.865194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.07207 | − | 32.9658i | −0.100683 | − | 1.08041i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 60.2919 | − | 16.1552i | 1.97387 | − | 0.528897i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.676157 | − | 15.4762i | 0.0221127 | − | 0.506125i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1742 | + | 22.1742i | 0.724399 | + | 0.724399i | 0.969498 | − | 0.245099i | \(-0.0788204\pi\) |
−0.245099 | + | 0.969498i | \(0.578820\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 85.8324i | − | 2.80103i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.5134 | − | 15.3075i | 0.864313 | − | 0.499011i | −0.00114123 | − | 0.999999i | \(-0.500363\pi\) |
0.865454 | + | 0.500988i | \(0.167030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.886481 | + | 3.30839i | 0.0288678 | + | 0.107736i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −68.1885 | + | 68.5712i | −2.21817 | + | 2.23062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.48860 | − | 20.4837i | −0.178355 | − | 0.665632i | −0.995956 | − | 0.0898453i | \(-0.971363\pi\) |
0.817600 | − | 0.575786i | \(-0.195304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.2732 | − | 11.1274i | 0.625636 | − | 0.361211i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.73414i | − | 0.153515i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.4466 | − | 30.4466i | −0.986262 | − | 0.986262i | 0.0136447 | − | 0.999907i | \(-0.495657\pi\) |
−0.999907 | + | 0.0136447i | \(0.995657\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.8736 | − | 34.7860i | −1.03140 | − | 1.12565i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.6335 | − | 6.60053i | 0.796288 | − | 0.213365i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 59.4283 | − | 2.76306i | 1.91904 | − | 0.0892240i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7100 | + | 23.7465i | −0.442259 | + | 0.766015i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.11673 | + | 22.8280i | −0.197109 | + | 0.735620i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.2796 | + | 25.0255i | 1.26446 | + | 0.805599i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.2212 | + | 40.2212i | −1.29343 | + | 1.29343i | −0.360774 | + | 0.932653i | \(0.617487\pi\) |
−0.932653 | + | 0.360774i | \(0.882513\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.7205 | + | 44.5493i | 0.826263 | + | 1.43113i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.4574 | + | 6.61493i | 0.367685 | + | 0.212283i | 0.672447 | − | 0.740145i | \(-0.265243\pi\) |
−0.304761 | + | 0.952429i | \(0.598577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.0128 | − | 6.69070i | 0.673641 | − | 0.214494i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −28.0796 | − | 2.45830i | −0.899268 | − | 0.0787288i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.2330 | + | 7.56500i | 0.903253 | + | 0.242026i | 0.680413 | − | 0.732829i | \(-0.261800\pi\) |
0.222840 | + | 0.974855i | \(0.428467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0815 | 0.386128 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 119.849 | 3.82648 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.3912 | − | 3.58817i | −0.427114 | − | 0.114445i | 0.0388569 | − | 0.999245i | \(-0.487628\pi\) |
−0.465971 | + | 0.884800i | \(0.654295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.5750 | + | 26.0791i | 0.432534 | + | 0.830950i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 33.7183 | − | 10.7362i | 1.07326 | − | 0.341738i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.8755 | − | 13.7845i | −0.759197 | − | 0.438323i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.37408 | − | 4.11203i | −0.0754152 | − | 0.130623i | 0.825852 | − | 0.563888i | \(-0.190695\pi\) |
−0.901267 | + | 0.433265i | \(0.857362\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −38.4461 | + | 38.4461i | −1.22005 | + | 1.22005i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.4965 | + | 3.65668i | −0.522974 | + | 0.115925i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.26721 | − | 4.72928i | 0.0401329 | − | 0.149778i | −0.942952 | − | 0.332929i | \(-0.891963\pi\) |
0.983085 | + | 0.183151i | \(0.0586297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −83.8791 | + | 145.283i | −2.65382 | + | 4.59655i |
(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 | 560.2.ci.e.33.1 | 48 | ||
4.3 | odd | 2 | 280.2.bo.a.33.12 | yes | 48 | ||
5.2 | odd | 4 | inner | 560.2.ci.e.257.1 | 48 | ||
7.3 | odd | 6 | inner | 560.2.ci.e.353.1 | 48 | ||
20.7 | even | 4 | 280.2.bo.a.257.12 | yes | 48 | ||
28.3 | even | 6 | 280.2.bo.a.73.12 | yes | 48 | ||
35.17 | even | 12 | inner | 560.2.ci.e.17.1 | 48 | ||
140.87 | odd | 12 | 280.2.bo.a.17.12 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bo.a.17.12 | ✓ | 48 | 140.87 | odd | 12 | ||
280.2.bo.a.33.12 | yes | 48 | 4.3 | odd | 2 | ||
280.2.bo.a.73.12 | yes | 48 | 28.3 | even | 6 | ||
280.2.bo.a.257.12 | yes | 48 | 20.7 | even | 4 | ||
560.2.ci.e.17.1 | 48 | 35.17 | even | 12 | inner | ||
560.2.ci.e.33.1 | 48 | 1.1 | even | 1 | trivial | ||
560.2.ci.e.257.1 | 48 | 5.2 | odd | 4 | inner | ||
560.2.ci.e.353.1 | 48 | 7.3 | odd | 6 | inner |