Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(91,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.n (of order \(2\), degree \(1\), 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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.20 | ||
Character | \(\chi\) | \(=\) | 552.91 |
Dual form | 552.2.n.b.91.18 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.07870 | + | 0.914558i | 0.762753 | + | 0.646690i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.327167 | + | 1.97306i | 0.163583 | + | 0.986530i | ||||
\(5\) | 0.969269 | 0.433470 | 0.216735 | − | 0.976230i | \(-0.430459\pi\) | ||||
0.216735 | + | 0.976230i | \(0.430459\pi\) | |||||||
\(6\) | −1.07870 | − | 0.914558i | −0.440375 | − | 0.373367i | ||||
\(7\) | 4.55308 | 1.72090 | 0.860451 | − | 0.509533i | \(-0.170182\pi\) | ||||
0.860451 | + | 0.509533i | \(0.170182\pi\) | |||||||
\(8\) | −1.45156 | + | 2.42754i | −0.513205 | + | 0.858266i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.04555 | + | 0.886452i | 0.330630 | + | 0.280321i | ||||
\(11\) | − | 0.915699i | − | 0.276094i | −0.990426 | − | 0.138047i | \(-0.955918\pi\) | ||
0.990426 | − | 0.138047i | \(-0.0440825\pi\) | |||||||
\(12\) | −0.327167 | − | 1.97306i | −0.0944449 | − | 0.569573i | ||||
\(13\) | − | 4.49735i | − | 1.24734i | −0.781687 | − | 0.623671i | \(-0.785641\pi\) | ||
0.781687 | − | 0.623671i | \(-0.214359\pi\) | |||||||
\(14\) | 4.91139 | + | 4.16406i | 1.31262 | + | 1.11289i | ||||
\(15\) | −0.969269 | −0.250264 | ||||||||
\(16\) | −3.78592 | + | 1.29104i | −0.946481 | + | 0.322760i | ||||
\(17\) | 5.37023i | 1.30247i | 0.758875 | + | 0.651236i | \(0.225749\pi\) | ||||
−0.758875 | + | 0.651236i | \(0.774251\pi\) | |||||||
\(18\) | 1.07870 | + | 0.914558i | 0.254251 | + | 0.215563i | ||||
\(19\) | − | 0.688174i | − | 0.157878i | −0.996879 | − | 0.0789390i | \(-0.974847\pi\) | ||
0.996879 | − | 0.0789390i | \(-0.0251532\pi\) | |||||||
\(20\) | 0.317112 | + | 1.91242i | 0.0709085 | + | 0.427631i | ||||
\(21\) | −4.55308 | −0.993564 | ||||||||
\(22\) | 0.837460 | − | 0.987761i | 0.178547 | − | 0.210591i | ||||
\(23\) | 4.70330 | − | 0.937530i | 0.980706 | − | 0.195489i | ||||
\(24\) | 1.45156 | − | 2.42754i | 0.296299 | − | 0.495520i | ||||
\(25\) | −4.06052 | −0.812104 | ||||||||
\(26\) | 4.11309 | − | 4.85127i | 0.806643 | − | 0.951413i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.48962 | + | 8.98350i | 0.281511 | + | 1.69772i | ||||
\(29\) | 6.35610i | 1.18030i | 0.807294 | + | 0.590149i | \(0.200931\pi\) | ||||
−0.807294 | + | 0.590149i | \(0.799069\pi\) | |||||||
\(30\) | −1.04555 | − | 0.886452i | −0.190890 | − | 0.161843i | ||||
\(31\) | 5.64064i | 1.01309i | 0.862214 | + | 0.506544i | \(0.169077\pi\) | ||||
−0.862214 | + | 0.506544i | \(0.830923\pi\) | |||||||
\(32\) | −5.26459 | − | 2.06981i | −0.930656 | − | 0.365894i | ||||
\(33\) | 0.915699i | 0.159403i | ||||||||
\(34\) | −4.91139 | + | 5.79284i | −0.842296 | + | 0.993464i | ||||
\(35\) | 4.41316 | 0.745960 | ||||||||
\(36\) | 0.327167 | + | 1.97306i | 0.0545278 | + | 0.328843i | ||||
\(37\) | 3.25973 | 0.535896 | 0.267948 | − | 0.963433i | \(-0.413654\pi\) | ||||
0.267948 | + | 0.963433i | \(0.413654\pi\) | |||||||
\(38\) | 0.629375 | − | 0.742330i | 0.102098 | − | 0.120422i | ||||
\(39\) | 4.49735i | 0.720153i | ||||||||
\(40\) | −1.40696 | + | 2.35294i | −0.222459 | + | 0.372033i | ||||
\(41\) | −8.87354 | −1.38581 | −0.692907 | − | 0.721027i | \(-0.743670\pi\) | ||||
−0.692907 | + | 0.721027i | \(0.743670\pi\) | |||||||
\(42\) | −4.91139 | − | 4.16406i | −0.757843 | − | 0.642528i | ||||
\(43\) | − | 9.54349i | − | 1.45537i | −0.685912 | − | 0.727684i | \(-0.740597\pi\) | ||
0.685912 | − | 0.727684i | \(-0.259403\pi\) | |||||||
\(44\) | 1.80673 | − | 0.299586i | 0.272375 | − | 0.0451643i | ||||
\(45\) | 0.969269 | 0.144490 | ||||||||
\(46\) | 5.93085 | + | 3.29013i | 0.874457 | + | 0.485104i | ||||
\(47\) | 0.156006i | 0.0227558i | 0.999935 | + | 0.0113779i | \(0.00362177\pi\) | ||||
−0.999935 | + | 0.0113779i | \(0.996378\pi\) | |||||||
\(48\) | 3.78592 | − | 1.29104i | 0.546451 | − | 0.186345i | ||||
\(49\) | 13.7305 | 1.96151 | ||||||||
\(50\) | −4.38006 | − | 3.71358i | −0.619434 | − | 0.525180i | ||||
\(51\) | − | 5.37023i | − | 0.751982i | ||||||
\(52\) | 8.87354 | − | 1.47138i | 1.23054 | − | 0.204044i | ||||
\(53\) | −2.42613 | −0.333255 | −0.166628 | − | 0.986020i | \(-0.553288\pi\) | ||||
−0.166628 | + | 0.986020i | \(0.553288\pi\) | |||||||
\(54\) | −1.07870 | − | 0.914558i | −0.146792 | − | 0.124456i | ||||
\(55\) | − | 0.887559i | − | 0.119678i | ||||||
\(56\) | −6.60909 | + | 11.0528i | −0.883176 | + | 1.47699i | ||||
\(57\) | 0.688174i | 0.0911509i | ||||||||
\(58\) | −5.81302 | + | 6.85630i | −0.763287 | + | 0.900276i | ||||
\(59\) | 3.81302 | 0.496413 | 0.248207 | − | 0.968707i | \(-0.420159\pi\) | ||||
0.248207 | + | 0.968707i | \(0.420159\pi\) | |||||||
\(60\) | −0.317112 | − | 1.91242i | −0.0409390 | − | 0.246893i | ||||
\(61\) | −12.2676 | −1.57070 | −0.785352 | − | 0.619049i | \(-0.787518\pi\) | ||||
−0.785352 | + | 0.619049i | \(0.787518\pi\) | |||||||
\(62\) | −5.15869 | + | 6.08453i | −0.655154 | + | 0.772736i | ||||
\(63\) | 4.55308 | 0.573634 | ||||||||
\(64\) | −3.78592 | − | 7.04747i | −0.473240 | − | 0.880933i | ||||
\(65\) | − | 4.35914i | − | 0.540685i | ||||||
\(66\) | −0.837460 | + | 0.987761i | −0.103084 | + | 0.121585i | ||||
\(67\) | − | 10.6451i | − | 1.30050i | −0.759719 | − | 0.650251i | \(-0.774664\pi\) | ||
0.759719 | − | 0.650251i | \(-0.225336\pi\) | |||||||
\(68\) | −10.5958 | + | 1.75696i | −1.28493 | + | 0.213063i | ||||
\(69\) | −4.70330 | + | 0.937530i | −0.566211 | + | 0.112865i | ||||
\(70\) | 4.76045 | + | 4.03609i | 0.568983 | + | 0.482405i | ||||
\(71\) | − | 14.9045i | − | 1.76884i | −0.466689 | − | 0.884422i | \(-0.654553\pi\) | ||
0.466689 | − | 0.884422i | \(-0.345447\pi\) | |||||||
\(72\) | −1.45156 | + | 2.42754i | −0.171068 | + | 0.286089i | ||||
\(73\) | −8.18221 | −0.957655 | −0.478828 | − | 0.877909i | \(-0.658938\pi\) | ||||
−0.478828 | + | 0.877909i | \(0.658938\pi\) | |||||||
\(74\) | 3.51625 | + | 2.98121i | 0.408756 | + | 0.346559i | ||||
\(75\) | 4.06052 | 0.468868 | ||||||||
\(76\) | 1.35781 | − | 0.225148i | 0.155751 | − | 0.0258262i | ||||
\(77\) | − | 4.16925i | − | 0.475130i | ||||||
\(78\) | −4.11309 | + | 4.85127i | −0.465716 | + | 0.549298i | ||||
\(79\) | 12.0667 | 1.35761 | 0.678805 | − | 0.734318i | \(-0.262498\pi\) | ||||
0.678805 | + | 0.734318i | \(0.262498\pi\) | |||||||
\(80\) | −3.66958 | + | 1.25136i | −0.410271 | + | 0.139907i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.57185 | − | 8.11537i | −1.05703 | − | 0.896193i | ||||
\(83\) | 11.1608i | 1.22506i | 0.790447 | + | 0.612531i | \(0.209848\pi\) | ||||
−0.790447 | + | 0.612531i | \(0.790152\pi\) | |||||||
\(84\) | −1.48962 | − | 8.98350i | −0.162530 | − | 0.980180i | ||||
\(85\) | 5.20519i | 0.564582i | ||||||||
\(86\) | 8.72808 | − | 10.2945i | 0.941173 | − | 1.11009i | ||||
\(87\) | − | 6.35610i | − | 0.681446i | ||||||
\(88\) | 2.22290 | + | 1.32920i | 0.236962 | + | 0.141693i | ||||
\(89\) | − | 10.9680i | − | 1.16260i | −0.813688 | − | 0.581302i | \(-0.802544\pi\) | ||
0.813688 | − | 0.581302i | \(-0.197456\pi\) | |||||||
\(90\) | 1.04555 | + | 0.886452i | 0.110210 | + | 0.0934403i | ||||
\(91\) | − | 20.4768i | − | 2.14655i | ||||||
\(92\) | 3.38857 | + | 8.97316i | 0.353282 | + | 0.935517i | ||||
\(93\) | − | 5.64064i | − | 0.584907i | ||||||
\(94\) | −0.142676 | + | 0.168283i | −0.0147159 | + | 0.0173570i | ||||
\(95\) | − | 0.667026i | − | 0.0684354i | ||||||
\(96\) | 5.26459 | + | 2.06981i | 0.537315 | + | 0.211249i | ||||
\(97\) | − | 17.8948i | − | 1.81695i | −0.417944 | − | 0.908473i | \(-0.637249\pi\) | ||
0.417944 | − | 0.908473i | \(-0.362751\pi\) | |||||||
\(98\) | 14.8111 | + | 12.5574i | 1.49614 | + | 1.26849i | ||||
\(99\) | − | 0.915699i | − | 0.0920312i | ||||||
\(100\) | −1.32847 | − | 8.01164i | −0.132847 | − | 0.801164i | ||||
\(101\) | − | 2.18685i | − | 0.217600i | −0.994064 | − | 0.108800i | \(-0.965299\pi\) | ||
0.994064 | − | 0.108800i | \(-0.0347007\pi\) | |||||||
\(102\) | 4.91139 | − | 5.79284i | 0.486300 | − | 0.573577i | ||||
\(103\) | 1.82776 | 0.180095 | 0.0900475 | − | 0.995937i | \(-0.471298\pi\) | ||||
0.0900475 | + | 0.995937i | \(0.471298\pi\) | |||||||
\(104\) | 10.9175 | + | 6.52820i | 1.07055 | + | 0.640142i | ||||
\(105\) | −4.41316 | −0.430680 | ||||||||
\(106\) | −2.61706 | − | 2.21884i | −0.254191 | − | 0.215513i | ||||
\(107\) | − | 2.63011i | − | 0.254262i | −0.991886 | − | 0.127131i | \(-0.959423\pi\) | ||
0.991886 | − | 0.127131i | \(-0.0405769\pi\) | |||||||
\(108\) | −0.327167 | − | 1.97306i | −0.0314816 | − | 0.189858i | ||||
\(109\) | −6.14687 | −0.588764 | −0.294382 | − | 0.955688i | \(-0.595114\pi\) | ||||
−0.294382 | + | 0.955688i | \(0.595114\pi\) | |||||||
\(110\) | 0.811724 | − | 0.957405i | 0.0773948 | − | 0.0912850i | ||||
\(111\) | −3.25973 | −0.309400 | ||||||||
\(112\) | −17.2376 | + | 5.87820i | −1.62880 | + | 0.555438i | ||||
\(113\) | 18.8052i | 1.76905i | 0.466495 | + | 0.884524i | \(0.345517\pi\) | ||||
−0.466495 | + | 0.884524i | \(0.654483\pi\) | |||||||
\(114\) | −0.629375 | + | 0.742330i | −0.0589464 | + | 0.0695256i | ||||
\(115\) | 4.55876 | − | 0.908719i | 0.425107 | − | 0.0847385i | ||||
\(116\) | −12.5410 | + | 2.07950i | −1.16440 | + | 0.193077i | ||||
\(117\) | − | 4.49735i | − | 0.415780i | ||||||
\(118\) | 4.11309 | + | 3.48723i | 0.378641 | + | 0.321026i | ||||
\(119\) | 24.4511i | 2.24143i | ||||||||
\(120\) | 1.40696 | − | 2.35294i | 0.128437 | − | 0.214793i | ||||
\(121\) | 10.1615 | 0.923772 | ||||||||
\(122\) | −13.2330 | − | 11.2194i | −1.19806 | − | 1.01576i | ||||
\(123\) | 8.87354 | 0.800100 | ||||||||
\(124\) | −11.1293 | + | 1.84543i | −0.999441 | + | 0.165724i | ||||
\(125\) | −8.78208 | −0.785493 | ||||||||
\(126\) | 4.91139 | + | 4.16406i | 0.437541 | + | 0.370964i | ||||
\(127\) | − | 0.261572i | − | 0.0232107i | −0.999933 | − | 0.0116054i | \(-0.996306\pi\) | ||
0.999933 | − | 0.0116054i | \(-0.00369418\pi\) | |||||||
\(128\) | 2.36146 | − | 11.0645i | 0.208726 | − | 0.977974i | ||||
\(129\) | 9.54349i | 0.840258i | ||||||||
\(130\) | 3.98669 | − | 4.70219i | 0.349656 | − | 0.412409i | ||||
\(131\) | −8.22618 | −0.718725 | −0.359362 | − | 0.933198i | \(-0.617006\pi\) | ||||
−0.359362 | + | 0.933198i | \(0.617006\pi\) | |||||||
\(132\) | −1.80673 | + | 0.299586i | −0.157256 | + | 0.0260756i | ||||
\(133\) | − | 3.13331i | − | 0.271693i | ||||||
\(134\) | 9.73554 | − | 11.4828i | 0.841022 | − | 0.991962i | ||||
\(135\) | −0.969269 | −0.0834214 | ||||||||
\(136\) | −13.0365 | − | 7.79523i | −1.11787 | − | 0.668435i | ||||
\(137\) | 6.70631i | 0.572959i | 0.958086 | + | 0.286479i | \(0.0924850\pi\) | ||||
−0.958086 | + | 0.286479i | \(0.907515\pi\) | |||||||
\(138\) | −5.93085 | − | 3.29013i | −0.504868 | − | 0.280075i | ||||
\(139\) | −7.42604 | −0.629868 | −0.314934 | − | 0.949114i | \(-0.601982\pi\) | ||||
−0.314934 | + | 0.949114i | \(0.601982\pi\) | |||||||
\(140\) | 1.44384 | + | 8.70742i | 0.122027 | + | 0.735911i | ||||
\(141\) | − | 0.156006i | − | 0.0131381i | ||||||
\(142\) | 13.6311 | − | 16.0775i | 1.14389 | − | 1.34919i | ||||
\(143\) | −4.11822 | −0.344383 | ||||||||
\(144\) | −3.78592 | + | 1.29104i | −0.315494 | + | 0.107587i | ||||
\(145\) | 6.16077i | 0.511624i | ||||||||
\(146\) | −8.82611 | − | 7.48311i | −0.730454 | − | 0.619306i | ||||
\(147\) | −13.7305 | −1.13248 | ||||||||
\(148\) | 1.06647 | + | 6.43163i | 0.0876636 | + | 0.528677i | ||||
\(149\) | 16.0149 | 1.31199 | 0.655997 | − | 0.754764i | \(-0.272249\pi\) | ||||
0.655997 | + | 0.754764i | \(0.272249\pi\) | |||||||
\(150\) | 4.38006 | + | 3.71358i | 0.357631 | + | 0.303213i | ||||
\(151\) | 8.36872i | 0.681037i | 0.940238 | + | 0.340518i | \(0.110603\pi\) | ||||
−0.940238 | + | 0.340518i | \(0.889397\pi\) | |||||||
\(152\) | 1.67057 | + | 0.998929i | 0.135501 | + | 0.0810238i | ||||
\(153\) | 5.37023i | 0.434157i | ||||||||
\(154\) | 3.81302 | − | 4.49735i | 0.307262 | − | 0.362407i | ||||
\(155\) | 5.46729i | 0.439143i | ||||||||
\(156\) | −8.87354 | + | 1.47138i | −0.710452 | + | 0.117805i | ||||
\(157\) | −0.188409 | −0.0150366 | −0.00751832 | − | 0.999972i | \(-0.502393\pi\) | ||||
−0.00751832 | + | 0.999972i | \(0.502393\pi\) | |||||||
\(158\) | 13.0163 | + | 11.0357i | 1.03552 | + | 0.877953i | ||||
\(159\) | 2.42613 | 0.192405 | ||||||||
\(160\) | −5.10280 | − | 2.00620i | −0.403412 | − | 0.158604i | ||||
\(161\) | 21.4145 | − | 4.26865i | 1.68770 | − | 0.336417i | ||||
\(162\) | 1.07870 | + | 0.914558i | 0.0847503 | + | 0.0718545i | ||||
\(163\) | 6.04337 | 0.473354 | 0.236677 | − | 0.971588i | \(-0.423942\pi\) | ||||
0.236677 | + | 0.971588i | \(0.423942\pi\) | |||||||
\(164\) | −2.90313 | − | 17.5080i | −0.226696 | − | 1.36715i | ||||
\(165\) | 0.887559i | 0.0690963i | ||||||||
\(166\) | −10.2072 | + | 12.0391i | −0.792235 | + | 0.934419i | ||||
\(167\) | 3.28126i | 0.253912i | 0.991908 | + | 0.126956i | \(0.0405207\pi\) | ||||
−0.991908 | + | 0.126956i | \(0.959479\pi\) | |||||||
\(168\) | 6.60909 | − | 11.0528i | 0.509902 | − | 0.852742i | ||||
\(169\) | −7.22618 | −0.555860 | ||||||||
\(170\) | −4.76045 | + | 5.61482i | −0.365110 | + | 0.430637i | ||||
\(171\) | − | 0.688174i | − | 0.0526260i | ||||||
\(172\) | 18.8299 | − | 3.12231i | 1.43576 | − | 0.238074i | ||||
\(173\) | 4.28422i | 0.325723i | 0.986649 | + | 0.162862i | \(0.0520724\pi\) | ||||
−0.986649 | + | 0.162862i | \(0.947928\pi\) | |||||||
\(174\) | 5.81302 | − | 6.85630i | 0.440684 | − | 0.519774i | ||||
\(175\) | −18.4879 | −1.39755 | ||||||||
\(176\) | 1.18220 | + | 3.46677i | 0.0891119 | + | 0.261317i | ||||
\(177\) | −3.81302 | −0.286604 | ||||||||
\(178\) | 10.0309 | − | 11.8311i | 0.751844 | − | 0.886779i | ||||
\(179\) | −21.7569 | −1.62618 | −0.813092 | − | 0.582135i | \(-0.802217\pi\) | ||||
−0.813092 | + | 0.582135i | \(0.802217\pi\) | |||||||
\(180\) | 0.317112 | + | 1.91242i | 0.0236362 | + | 0.142544i | ||||
\(181\) | 2.42739 | 0.180426 | 0.0902131 | − | 0.995922i | \(-0.471245\pi\) | ||||
0.0902131 | + | 0.995922i | \(0.471245\pi\) | |||||||
\(182\) | 18.7272 | − | 22.0882i | 1.38815 | − | 1.63729i | ||||
\(183\) | 12.2676 | 0.906847 | ||||||||
\(184\) | −4.55125 | + | 12.7783i | −0.335522 | + | 0.942032i | ||||
\(185\) | 3.15955 | 0.232295 | ||||||||
\(186\) | 5.15869 | − | 6.08453i | 0.378254 | − | 0.446139i | ||||
\(187\) | 4.91751 | 0.359604 | ||||||||
\(188\) | −0.307809 | + | 0.0510399i | −0.0224492 | + | 0.00372247i | ||||
\(189\) | −4.55308 | −0.331188 | ||||||||
\(190\) | 0.610034 | − | 0.719517i | 0.0442565 | − | 0.0521993i | ||||
\(191\) | −8.94391 | −0.647158 | −0.323579 | − | 0.946201i | \(-0.604886\pi\) | ||||
−0.323579 | + | 0.946201i | \(0.604886\pi\) | |||||||
\(192\) | 3.78592 | + | 7.04747i | 0.273226 | + | 0.508607i | ||||
\(193\) | −12.2220 | −0.879760 | −0.439880 | − | 0.898057i | \(-0.644979\pi\) | ||||
−0.439880 | + | 0.898057i | \(0.644979\pi\) | |||||||
\(194\) | 16.3659 | − | 19.3031i | 1.17500 | − | 1.38588i | ||||
\(195\) | 4.35914i | 0.312165i | ||||||||
\(196\) | 4.49218 | + | 27.0912i | 0.320870 | + | 1.93508i | ||||
\(197\) | − | 10.5254i | − | 0.749900i | −0.927045 | − | 0.374950i | \(-0.877660\pi\) | ||
0.927045 | − | 0.374950i | \(-0.122340\pi\) | |||||||
\(198\) | 0.837460 | − | 0.987761i | 0.0595157 | − | 0.0701971i | ||||
\(199\) | 16.2033 | 1.14862 | 0.574312 | − | 0.818637i | \(-0.305270\pi\) | ||||
0.574312 | + | 0.818637i | \(0.305270\pi\) | |||||||
\(200\) | 5.89410 | − | 9.85708i | 0.416776 | − | 0.697001i | ||||
\(201\) | 10.6451i | 0.750845i | ||||||||
\(202\) | 2.00000 | − | 2.35894i | 0.140720 | − | 0.165975i | ||||
\(203\) | 28.9398i | 2.03118i | ||||||||
\(204\) | 10.5958 | − | 1.75696i | 0.741853 | − | 0.123012i | ||||
\(205\) | −8.60085 | −0.600709 | ||||||||
\(206\) | 1.97160 | + | 1.67160i | 0.137368 | + | 0.116466i | ||||
\(207\) | 4.70330 | − | 0.937530i | 0.326902 | − | 0.0651629i | ||||
\(208\) | 5.80626 | + | 17.0266i | 0.402591 | + | 1.18058i | ||||
\(209\) | −0.630161 | −0.0435891 | ||||||||
\(210\) | −4.76045 | − | 4.03609i | −0.328502 | − | 0.278517i | ||||
\(211\) | 6.20898 | 0.427444 | 0.213722 | − | 0.976895i | \(-0.431441\pi\) | ||||
0.213722 | + | 0.976895i | \(0.431441\pi\) | |||||||
\(212\) | −0.793751 | − | 4.78691i | −0.0545150 | − | 0.328766i | ||||
\(213\) | 14.9045i | 1.02124i | ||||||||
\(214\) | 2.40539 | − | 2.83709i | 0.164429 | − | 0.193939i | ||||
\(215\) | − | 9.25021i | − | 0.630859i | ||||||
\(216\) | 1.45156 | − | 2.42754i | 0.0987664 | − | 0.165173i | ||||
\(217\) | 25.6823i | 1.74343i | ||||||||
\(218\) | −6.63060 | − | 5.62167i | −0.449081 | − | 0.380748i | ||||
\(219\) | 8.18221 | 0.552902 | ||||||||
\(220\) | 1.75121 | − | 0.290380i | 0.118066 | − | 0.0195774i | ||||
\(221\) | 24.1518 | 1.62463 | ||||||||
\(222\) | −3.51625 | − | 2.98121i | −0.235995 | − | 0.200086i | ||||
\(223\) | − | 22.7592i | − | 1.52407i | −0.647538 | − | 0.762033i | \(-0.724201\pi\) | ||
0.647538 | − | 0.762033i | \(-0.275799\pi\) | |||||||
\(224\) | −23.9701 | − | 9.42401i | −1.60157 | − | 0.629668i | ||||
\(225\) | −4.06052 | −0.270701 | ||||||||
\(226\) | −17.1985 | + | 20.2851i | −1.14403 | + | 1.34935i | ||||
\(227\) | − | 5.19084i | − | 0.344528i | −0.985051 | − | 0.172264i | \(-0.944892\pi\) | ||
0.985051 | − | 0.172264i | \(-0.0551083\pi\) | |||||||
\(228\) | −1.35781 | + | 0.225148i | −0.0899230 | + | 0.0149108i | ||||
\(229\) | −16.5481 | −1.09353 | −0.546764 | − | 0.837287i | \(-0.684140\pi\) | ||||
−0.546764 | + | 0.837287i | \(0.684140\pi\) | |||||||
\(230\) | 5.74859 | + | 3.18902i | 0.379051 | + | 0.210278i | ||||
\(231\) | 4.16925i | 0.274317i | ||||||||
\(232\) | −15.4297 | − | 9.22629i | −1.01301 | − | 0.605735i | ||||
\(233\) | −15.1175 | −0.990382 | −0.495191 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495191 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(234\) | 4.11309 | − | 4.85127i | 0.268881 | − | 0.317138i | ||||
\(235\) | 0.151211i | 0.00986395i | ||||||||
\(236\) | 1.24749 | + | 7.52332i | 0.0812050 | + | 0.489726i | ||||
\(237\) | −12.0667 | −0.783817 | ||||||||
\(238\) | −22.3619 | + | 26.3753i | −1.44951 | + | 1.70965i | ||||
\(239\) | 4.20687i | 0.272120i | 0.990701 | + | 0.136060i | \(0.0434439\pi\) | ||||
−0.990701 | + | 0.136060i | \(0.956556\pi\) | |||||||
\(240\) | 3.66958 | − | 1.25136i | 0.236870 | − | 0.0807751i | ||||
\(241\) | − | 11.2163i | − | 0.722503i | −0.932469 | − | 0.361251i | \(-0.882350\pi\) | ||
0.932469 | − | 0.361251i | \(-0.117650\pi\) | |||||||
\(242\) | 10.9612 | + | 9.29328i | 0.704610 | + | 0.597395i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.01355 | − | 24.2047i | −0.256941 | − | 1.54955i | ||||
\(245\) | 13.3086 | 0.850254 | ||||||||
\(246\) | 9.57185 | + | 8.11537i | 0.610279 | + | 0.517417i | ||||
\(247\) | −3.09496 | −0.196928 | ||||||||
\(248\) | −13.6929 | − | 8.18775i | −0.869499 | − | 0.519922i | ||||
\(249\) | − | 11.1608i | − | 0.707289i | ||||||
\(250\) | −9.47318 | − | 8.03172i | −0.599137 | − | 0.507971i | ||||
\(251\) | 19.6483i | 1.24019i | 0.784526 | + | 0.620096i | \(0.212906\pi\) | ||||
−0.784526 | + | 0.620096i | \(0.787094\pi\) | |||||||
\(252\) | 1.48962 | + | 8.98350i | 0.0938370 | + | 0.565907i | ||||
\(253\) | −0.858496 | − | 4.30681i | −0.0539732 | − | 0.270767i | ||||
\(254\) | 0.239222 | − | 0.282156i | 0.0150101 | − | 0.0177040i | ||||
\(255\) | − | 5.20519i | − | 0.325962i | ||||||
\(256\) | 12.6664 | − | 9.77555i | 0.791652 | − | 0.610972i | ||||
\(257\) | 12.3772 | 0.772071 | 0.386036 | − | 0.922484i | \(-0.373844\pi\) | ||||
0.386036 | + | 0.922484i | \(0.373844\pi\) | |||||||
\(258\) | −8.72808 | + | 10.2945i | −0.543386 | + | 0.640909i | ||||
\(259\) | 14.8418 | 0.922224 | ||||||||
\(260\) | 8.60085 | − | 1.42617i | 0.533402 | − | 0.0884471i | ||||
\(261\) | 6.35610i | 0.393433i | ||||||||
\(262\) | −8.87354 | − | 7.52332i | −0.548209 | − | 0.464792i | ||||
\(263\) | 0.300441 | 0.0185260 | 0.00926300 | − | 0.999957i | \(-0.497051\pi\) | ||||
0.00926300 | + | 0.999957i | \(0.497051\pi\) | |||||||
\(264\) | −2.22290 | − | 1.32920i | −0.136810 | − | 0.0818064i | ||||
\(265\) | −2.35158 | −0.144456 | ||||||||
\(266\) | 2.86560 | − | 3.37989i | 0.175701 | − | 0.207234i | ||||
\(267\) | 10.9680i | 0.671230i | ||||||||
\(268\) | 21.0034 | − | 3.48271i | 1.28298 | − | 0.212741i | ||||
\(269\) | − | 1.53065i | − | 0.0933252i | −0.998911 | − | 0.0466626i | \(-0.985141\pi\) | ||
0.998911 | − | 0.0466626i | \(-0.0148586\pi\) | |||||||
\(270\) | −1.04555 | − | 0.886452i | −0.0636299 | − | 0.0539478i | ||||
\(271\) | − | 6.52820i | − | 0.396560i | −0.980145 | − | 0.198280i | \(-0.936465\pi\) | ||
0.980145 | − | 0.198280i | \(-0.0635355\pi\) | |||||||
\(272\) | −6.93317 | − | 20.3313i | −0.420385 | − | 1.23276i | ||||
\(273\) | 20.4768i | 1.23931i | ||||||||
\(274\) | −6.13331 | + | 7.23407i | −0.370527 | + | 0.437026i | ||||
\(275\) | 3.71821i | 0.224217i | ||||||||
\(276\) | −3.38857 | − | 8.97316i | −0.203968 | − | 0.540121i | ||||
\(277\) | 7.38599i | 0.443781i | 0.975072 | + | 0.221891i | \(0.0712228\pi\) | ||||
−0.975072 | + | 0.221891i | \(0.928777\pi\) | |||||||
\(278\) | −8.01043 | − | 6.79154i | −0.480434 | − | 0.407330i | ||||
\(279\) | 5.64064i | 0.337696i | ||||||||
\(280\) | −6.40598 | + | 10.7131i | −0.382831 | + | 0.640232i | ||||
\(281\) | − | 7.79441i | − | 0.464976i | −0.972599 | − | 0.232488i | \(-0.925313\pi\) | ||
0.972599 | − | 0.232488i | \(-0.0746866\pi\) | |||||||
\(282\) | 0.142676 | − | 0.168283i | 0.00849625 | − | 0.0100211i | ||||
\(283\) | 27.8464i | 1.65530i | 0.561246 | + | 0.827649i | \(0.310322\pi\) | ||||
−0.561246 | + | 0.827649i | \(0.689678\pi\) | |||||||
\(284\) | 29.4075 | − | 4.87627i | 1.74502 | − | 0.289353i | ||||
\(285\) | 0.667026i | 0.0395112i | ||||||||
\(286\) | −4.44231 | − | 3.76635i | −0.262679 | − | 0.222709i | ||||
\(287\) | −40.4019 | −2.38485 | ||||||||
\(288\) | −5.26459 | − | 2.06981i | −0.310219 | − | 0.121965i | ||||
\(289\) | −11.8393 | −0.696432 | ||||||||
\(290\) | −5.63438 | + | 6.64559i | −0.330862 | + | 0.390243i | ||||
\(291\) | 17.8948i | 1.04901i | ||||||||
\(292\) | −2.67695 | − | 16.1440i | −0.156656 | − | 0.944755i | ||||
\(293\) | −12.2770 | −0.717232 | −0.358616 | − | 0.933485i | \(-0.616751\pi\) | ||||
−0.358616 | + | 0.933485i | \(0.616751\pi\) | |||||||
\(294\) | −14.8111 | − | 12.5574i | −0.863799 | − | 0.732361i | ||||
\(295\) | 3.69584 | 0.215180 | ||||||||
\(296\) | −4.73170 | + | 7.91313i | −0.275025 | + | 0.459941i | ||||
\(297\) | 0.915699i | 0.0531343i | ||||||||
\(298\) | 17.2752 | + | 14.6466i | 1.00073 | + | 0.848453i | ||||
\(299\) | −4.21640 | − | 21.1524i | −0.243841 | − | 1.22327i | ||||
\(300\) | 1.32847 | + | 8.01164i | 0.0766991 | + | 0.462552i | ||||
\(301\) | − | 43.4523i | − | 2.50455i | ||||||
\(302\) | −7.65368 | + | 9.02730i | −0.440420 | + | 0.519463i | ||||
\(303\) | 2.18685i | 0.125631i | ||||||||
\(304\) | 0.888459 | + | 2.60537i | 0.0509566 | + | 0.149428i | ||||
\(305\) | −11.8906 | −0.680853 | ||||||||
\(306\) | −4.91139 | + | 5.79284i | −0.280765 | + | 0.331155i | ||||
\(307\) | −0.0911995 | −0.00520503 | −0.00260251 | − | 0.999997i | \(-0.500828\pi\) | ||||
−0.00260251 | + | 0.999997i | \(0.500828\pi\) | |||||||
\(308\) | 8.22618 | − | 1.36404i | 0.468730 | − | 0.0777234i | ||||
\(309\) | −1.82776 | −0.103978 | ||||||||
\(310\) | −5.00016 | + | 5.89754i | −0.283990 | + | 0.334958i | ||||
\(311\) | − | 2.75985i | − | 0.156497i | −0.996934 | − | 0.0782483i | \(-0.975067\pi\) | ||
0.996934 | − | 0.0782483i | \(-0.0249327\pi\) | |||||||
\(312\) | −10.9175 | − | 6.52820i | −0.618083 | − | 0.369586i | ||||
\(313\) | − | 11.2930i | − | 0.638317i | −0.947701 | − | 0.319158i | \(-0.896600\pi\) | ||
0.947701 | − | 0.319158i | \(-0.103400\pi\) | |||||||
\(314\) | −0.203235 | − | 0.172311i | −0.0114692 | − | 0.00972405i | ||||
\(315\) | 4.41316 | 0.248653 | ||||||||
\(316\) | 3.94783 | + | 23.8083i | 0.222083 | + | 1.33932i | ||||
\(317\) | 23.3082i | 1.30912i | 0.756010 | + | 0.654560i | \(0.227146\pi\) | ||||
−0.756010 | + | 0.654560i | \(0.772854\pi\) | |||||||
\(318\) | 2.61706 | + | 2.21884i | 0.146757 | + | 0.124426i | ||||
\(319\) | 5.82028 | 0.325873 | ||||||||
\(320\) | −3.66958 | − | 6.83089i | −0.205136 | − | 0.381858i | ||||
\(321\) | 2.63011i | 0.146798i | ||||||||
\(322\) | 27.0037 | + | 14.9802i | 1.50485 | + | 0.834816i | ||||
\(323\) | 3.69565 | 0.205632 | ||||||||
\(324\) | 0.327167 | + | 1.97306i | 0.0181759 | + | 0.109614i | ||||
\(325\) | 18.2616i | 1.01297i | ||||||||
\(326\) | 6.51896 | + | 5.52702i | 0.361052 | + | 0.306113i | ||||
\(327\) | 6.14687 | 0.339923 | ||||||||
\(328\) | 12.8805 | − | 21.5409i | 0.711207 | − | 1.18940i | ||||
\(329\) | 0.710307i | 0.0391605i | ||||||||
\(330\) | −0.811724 | + | 0.957405i | −0.0446839 | + | 0.0527034i | ||||
\(331\) | −14.7506 | −0.810766 | −0.405383 | − | 0.914147i | \(-0.632862\pi\) | ||||
−0.405383 | + | 0.914147i | \(0.632862\pi\) | |||||||
\(332\) | −22.0210 | + | 3.65146i | −1.20856 | + | 0.200400i | ||||
\(333\) | 3.25973 | 0.178632 | ||||||||
\(334\) | −3.00091 | + | 3.53948i | −0.164202 | + | 0.193672i | ||||
\(335\) | − | 10.3179i | − | 0.563729i | ||||||
\(336\) | 17.2376 | − | 5.87820i | 0.940389 | − | 0.320682i | ||||
\(337\) | 22.4118i | 1.22085i | 0.792075 | + | 0.610423i | \(0.209001\pi\) | ||||
−0.792075 | + | 0.610423i | \(0.790999\pi\) | |||||||
\(338\) | −7.79485 | − | 6.60876i | −0.423984 | − | 0.359469i | ||||
\(339\) | − | 18.8052i | − | 1.02136i | ||||||
\(340\) | −10.2702 | + | 1.70297i | −0.556977 | + | 0.0923563i | ||||
\(341\) | 5.16513 | 0.279707 | ||||||||
\(342\) | 0.629375 | − | 0.742330i | 0.0340327 | − | 0.0401406i | ||||
\(343\) | 30.6447 | 1.65466 | ||||||||
\(344\) | 23.1672 | + | 13.8530i | 1.24909 | + | 0.746903i | ||||
\(345\) | −4.55876 | + | 0.908719i | −0.245435 | + | 0.0489238i | ||||
\(346\) | −3.91817 | + | 4.62137i | −0.210642 | + | 0.248446i | ||||
\(347\) | 8.93888 | 0.479864 | 0.239932 | − | 0.970790i | \(-0.422875\pi\) | ||||
0.239932 | + | 0.970790i | \(0.422875\pi\) | |||||||
\(348\) | 12.5410 | − | 2.07950i | 0.672266 | − | 0.111473i | ||||
\(349\) | 33.9944i | 1.81968i | 0.414960 | + | 0.909840i | \(0.363796\pi\) | ||||
−0.414960 | + | 0.909840i | \(0.636204\pi\) | |||||||
\(350\) | −19.9428 | − | 16.9082i | −1.06599 | − | 0.903783i | ||||
\(351\) | 4.49735i | 0.240051i | ||||||||
\(352\) | −1.89532 | + | 4.82078i | −0.101021 | + | 0.256948i | ||||
\(353\) | −14.3436 | −0.763430 | −0.381715 | − | 0.924280i | \(-0.624666\pi\) | ||||
−0.381715 | + | 0.924280i | \(0.624666\pi\) | |||||||
\(354\) | −4.11309 | − | 3.48723i | −0.218608 | − | 0.185344i | ||||
\(355\) | − | 14.4465i | − | 0.766741i | ||||||
\(356\) | 21.6405 | − | 3.58836i | 1.14694 | − | 0.190183i | ||||
\(357\) | − | 24.4511i | − | 1.29409i | ||||||
\(358\) | −23.4690 | − | 19.8979i | −1.24038 | − | 1.05164i | ||||
\(359\) | −17.4705 | −0.922059 | −0.461029 | − | 0.887385i | \(-0.652520\pi\) | ||||
−0.461029 | + | 0.887385i | \(0.652520\pi\) | |||||||
\(360\) | −1.40696 | + | 2.35294i | −0.0741531 | + | 0.124011i | ||||
\(361\) | 18.5264 | 0.975075 | ||||||||
\(362\) | 2.61841 | + | 2.21999i | 0.137621 | + | 0.116680i | ||||
\(363\) | −10.1615 | −0.533340 | ||||||||
\(364\) | 40.4019 | − | 6.69933i | 2.11764 | − | 0.351140i | ||||
\(365\) | −7.93076 | −0.415115 | ||||||||
\(366\) | 13.2330 | + | 11.2194i | 0.691700 | + | 0.586449i | ||||
\(367\) | −4.20241 | −0.219364 | −0.109682 | − | 0.993967i | \(-0.534983\pi\) | ||||
−0.109682 | + | 0.993967i | \(0.534983\pi\) | |||||||
\(368\) | −16.5960 | + | 9.62156i | −0.865124 | + | 0.501559i | ||||
\(369\) | −8.87354 | −0.461938 | ||||||||
\(370\) | 3.40819 | + | 2.88959i | 0.177183 | + | 0.150223i | ||||
\(371\) | −11.0464 | −0.573500 | ||||||||
\(372\) | 11.1293 | − | 1.84543i | 0.577028 | − | 0.0956810i | ||||
\(373\) | 37.2998 | 1.93131 | 0.965655 | − | 0.259826i | \(-0.0836652\pi\) | ||||
0.965655 | + | 0.259826i | \(0.0836652\pi\) | |||||||
\(374\) | 5.30450 | + | 4.49735i | 0.274289 | + | 0.232553i | ||||
\(375\) | 8.78208 | 0.453504 | ||||||||
\(376\) | −0.378711 | − | 0.226452i | −0.0195305 | − | 0.0116784i | ||||
\(377\) | 28.5856 | 1.47223 | ||||||||
\(378\) | −4.91139 | − | 4.16406i | −0.252614 | − | 0.214176i | ||||
\(379\) | 12.0640i | 0.619684i | 0.950788 | + | 0.309842i | \(0.100276\pi\) | ||||
−0.950788 | + | 0.309842i | \(0.899724\pi\) | |||||||
\(380\) | 1.31608 | − | 0.218229i | 0.0675135 | − | 0.0111949i | ||||
\(381\) | 0.261572i | 0.0134007i | ||||||||
\(382\) | −9.64775 | − | 8.17972i | −0.493622 | − | 0.418511i | ||||
\(383\) | −15.8402 | −0.809395 | −0.404698 | − | 0.914451i | \(-0.632623\pi\) | ||||
−0.404698 | + | 0.914451i | \(0.632623\pi\) | |||||||
\(384\) | −2.36146 | + | 11.0645i | −0.120508 | + | 0.564634i | ||||
\(385\) | − | 4.04113i | − | 0.205955i | ||||||
\(386\) | −13.1838 | − | 11.1777i | −0.671039 | − | 0.568932i | ||||
\(387\) | − | 9.54349i | − | 0.485123i | ||||||
\(388\) | 35.3076 | − | 5.85460i | 1.79247 | − | 0.297222i | ||||
\(389\) | 2.04276 | 0.103572 | 0.0517860 | − | 0.998658i | \(-0.483509\pi\) | ||||
0.0517860 | + | 0.998658i | \(0.483509\pi\) | |||||||
\(390\) | −3.98669 | + | 4.70219i | −0.201874 | + | 0.238104i | ||||
\(391\) | 5.03475 | + | 25.2578i | 0.254618 | + | 1.27734i | ||||
\(392\) | −19.9308 | + | 33.3315i | −1.00666 | + | 1.68349i | ||||
\(393\) | 8.22618 | 0.414956 | ||||||||
\(394\) | 9.62605 | − | 11.3536i | 0.484953 | − | 0.571989i | ||||
\(395\) | 11.6959 | 0.588484 | ||||||||
\(396\) | 1.80673 | − | 0.299586i | 0.0907915 | − | 0.0150548i | ||||
\(397\) | 34.7911i | 1.74612i | 0.487617 | + | 0.873058i | \(0.337866\pi\) | ||||
−0.487617 | + | 0.873058i | \(0.662134\pi\) | |||||||
\(398\) | 17.4784 | + | 14.8189i | 0.876116 | + | 0.742804i | ||||
\(399\) | 3.13331i | 0.156862i | ||||||||
\(400\) | 15.3728 | − | 5.24229i | 0.768641 | − | 0.262114i | ||||
\(401\) | − | 27.9532i | − | 1.39592i | −0.716138 | − | 0.697958i | \(-0.754092\pi\) | ||
0.716138 | − | 0.697958i | \(-0.245908\pi\) | |||||||
\(402\) | −9.73554 | + | 11.4828i | −0.485564 | + | 0.572709i | ||||
\(403\) | 25.3679 | 1.26367 | ||||||||
\(404\) | 4.31478 | − | 0.715464i | 0.214668 | − | 0.0355957i | ||||
\(405\) | 0.969269 | 0.0481633 | ||||||||
\(406\) | −26.4672 | + | 31.2173i | −1.31354 | + | 1.54929i | ||||
\(407\) | − | 2.98493i | − | 0.147957i | ||||||
\(408\) | 13.0365 | + | 7.79523i | 0.645401 | + | 0.385921i | ||||
\(409\) | −10.4393 | −0.516192 | −0.258096 | − | 0.966119i | \(-0.583095\pi\) | ||||
−0.258096 | + | 0.966119i | \(0.583095\pi\) | |||||||
\(410\) | −9.27769 | − | 7.86597i | −0.458192 | − | 0.388473i | ||||
\(411\) | − | 6.70631i | − | 0.330798i | ||||||
\(412\) | 0.597984 | + | 3.60629i | 0.0294605 | + | 0.177669i | ||||
\(413\) | 17.3610 | 0.854279 | ||||||||
\(414\) | 5.93085 | + | 3.29013i | 0.291486 | + | 0.161701i | ||||
\(415\) | 10.8179i | 0.531027i | ||||||||
\(416\) | −9.30867 | + | 23.6767i | −0.456395 | + | 1.16085i | ||||
\(417\) | 7.42604 | 0.363655 | ||||||||
\(418\) | −0.679751 | − | 0.576319i | −0.0332477 | − | 0.0281887i | ||||
\(419\) | 27.9406i | 1.36499i | 0.730891 | + | 0.682494i | \(0.239105\pi\) | ||||
−0.730891 | + | 0.682494i | \(0.760895\pi\) | |||||||
\(420\) | −1.44384 | − | 8.70742i | −0.0704521 | − | 0.424879i | ||||
\(421\) | 32.6815 | 1.59280 | 0.796400 | − | 0.604770i | \(-0.206735\pi\) | ||||
0.796400 | + | 0.604770i | \(0.206735\pi\) | |||||||
\(422\) | 6.69760 | + | 5.67847i | 0.326034 | + | 0.276424i | ||||
\(423\) | 0.156006i | 0.00758526i | ||||||||
\(424\) | 3.52169 | − | 5.88954i | 0.171028 | − | 0.286022i | ||||
\(425\) | − | 21.8059i | − | 1.05774i | ||||||
\(426\) | −13.6311 | + | 16.0775i | −0.660427 | + | 0.778955i | ||||
\(427\) | −55.8553 | −2.70303 | ||||||||
\(428\) | 5.18936 | − | 0.860485i | 0.250837 | − | 0.0415931i | ||||
\(429\) | 4.11822 | 0.198830 | ||||||||
\(430\) | 8.45985 | − | 9.97815i | 0.407970 | − | 0.481189i | ||||
\(431\) | 16.1528 | 0.778055 | 0.389028 | − | 0.921226i | \(-0.372811\pi\) | ||||
0.389028 | + | 0.921226i | \(0.372811\pi\) | |||||||
\(432\) | 3.78592 | − | 1.29104i | 0.182150 | − | 0.0621151i | ||||
\(433\) | 19.9138i | 0.956996i | 0.878089 | + | 0.478498i | \(0.158819\pi\) | ||||
−0.878089 | + | 0.478498i | \(0.841181\pi\) | |||||||
\(434\) | −23.4879 | + | 27.7033i | −1.12746 | + | 1.32980i | ||||
\(435\) | − | 6.16077i | − | 0.295386i | ||||||
\(436\) | −2.01105 | − | 12.1281i | −0.0963120 | − | 0.580833i | ||||
\(437\) | −0.645184 | − | 3.23669i | −0.0308633 | − | 0.154832i | ||||
\(438\) | 8.82611 | + | 7.48311i | 0.421728 | + | 0.357557i | ||||
\(439\) | − | 29.3002i | − | 1.39842i | −0.714915 | − | 0.699211i | \(-0.753535\pi\) | ||
0.714915 | − | 0.699211i | \(-0.246465\pi\) | |||||||
\(440\) | 2.15459 | + | 1.28835i | 0.102716 | + | 0.0614196i | ||||
\(441\) | 13.7305 | 0.653835 | ||||||||
\(442\) | 26.0524 | + | 22.0882i | 1.23919 | + | 1.05063i | ||||
\(443\) | 32.9596 | 1.56596 | 0.782978 | − | 0.622049i | \(-0.213699\pi\) | ||||
0.782978 | + | 0.622049i | \(0.213699\pi\) | |||||||
\(444\) | −1.06647 | − | 6.43163i | −0.0506126 | − | 0.305232i | ||||
\(445\) | − | 10.6309i | − | 0.503954i | ||||||
\(446\) | 20.8146 | − | 24.5502i | 0.985599 | − | 1.16249i | ||||
\(447\) | −16.0149 | −0.757480 | ||||||||
\(448\) | −17.2376 | − | 32.0877i | −0.814401 | − | 1.51600i | ||||
\(449\) | 16.6963 | 0.787949 | 0.393975 | − | 0.919121i | \(-0.371100\pi\) | ||||
0.393975 | + | 0.919121i | \(0.371100\pi\) | |||||||
\(450\) | −4.38006 | − | 3.71358i | −0.206478 | − | 0.175060i | ||||
\(451\) | 8.12550i | 0.382615i | ||||||||
\(452\) | −37.1038 | + | 6.15245i | −1.74522 | + | 0.289387i | ||||
\(453\) | − | 8.36872i | − | 0.393197i | ||||||
\(454\) | 4.74733 | − | 5.59934i | 0.222803 | − | 0.262790i | ||||
\(455\) | − | 19.8475i | − | 0.930466i | ||||||
\(456\) | −1.67057 | − | 0.998929i | −0.0782317 | − | 0.0467791i | ||||
\(457\) | 7.54667i | 0.353018i | 0.984299 | + | 0.176509i | \(0.0564805\pi\) | ||||
−0.984299 | + | 0.176509i | \(0.943519\pi\) | |||||||
\(458\) | −17.8503 | − | 15.1342i | −0.834091 | − | 0.707173i | ||||
\(459\) | − | 5.37023i | − | 0.250661i | ||||||
\(460\) | 3.28443 | + | 8.69740i | 0.153137 | + | 0.405518i | ||||
\(461\) | − | 22.0330i | − | 1.02618i | −0.858335 | − | 0.513090i | \(-0.828501\pi\) | ||
0.858335 | − | 0.513090i | \(-0.171499\pi\) | |||||||
\(462\) | −3.81302 | + | 4.49735i | −0.177398 | + | 0.209236i | ||||
\(463\) | 10.5899i | 0.492153i | 0.969250 | + | 0.246077i | \(0.0791415\pi\) | ||||
−0.969250 | + | 0.246077i | \(0.920858\pi\) | |||||||
\(464\) | −8.20597 | − | 24.0637i | −0.380953 | − | 1.11713i | ||||
\(465\) | − | 5.46729i | − | 0.253540i | ||||||
\(466\) | −16.3072 | − | 13.8259i | −0.755416 | − | 0.640470i | ||||
\(467\) | − | 23.8323i | − | 1.10283i | −0.834231 | − | 0.551414i | \(-0.814088\pi\) | ||
0.834231 | − | 0.551414i | \(-0.185912\pi\) | |||||||
\(468\) | 8.87354 | − | 1.47138i | 0.410180 | − | 0.0680148i | ||||
\(469\) | − | 48.4679i | − | 2.23804i | ||||||
\(470\) | −0.138292 | + | 0.163111i | −0.00637892 | + | 0.00752375i | ||||
\(471\) | 0.188409 | 0.00868141 | ||||||||
\(472\) | −5.53485 | + | 9.25628i | −0.254762 | + | 0.426055i | ||||
\(473\) | −8.73897 | −0.401818 | ||||||||
\(474\) | −13.0163 | − | 11.0357i | −0.597858 | − | 0.506887i | ||||
\(475\) | 2.79434i | 0.128213i | ||||||||
\(476\) | −48.2434 | + | 7.99958i | −2.21123 | + | 0.366660i | ||||
\(477\) | −2.42613 | −0.111085 | ||||||||
\(478\) | −3.84742 | + | 4.53793i | −0.175977 | + | 0.207560i | ||||
\(479\) | −18.4098 | −0.841165 | −0.420583 | − | 0.907254i | \(-0.638174\pi\) | ||||
−0.420583 | + | 0.907254i | \(0.638174\pi\) | |||||||
\(480\) | 5.10280 | + | 2.00620i | 0.232910 | + | 0.0915702i | ||||
\(481\) | − | 14.6601i | − | 0.668445i | ||||||
\(482\) | 10.2579 | − | 12.0989i | 0.467235 | − | 0.551091i | ||||
\(483\) | −21.4145 | + | 4.26865i | −0.974394 | + | 0.194230i | ||||
\(484\) | 3.32450 | + | 20.0492i | 0.151114 | + | 0.911329i | ||||
\(485\) | − | 17.3449i | − | 0.787591i | ||||||
\(486\) | −1.07870 | − | 0.914558i | −0.0489306 | − | 0.0414852i | ||||
\(487\) | 39.6459i | 1.79653i | 0.439458 | + | 0.898263i | \(0.355171\pi\) | ||||
−0.439458 | + | 0.898263i | \(0.644829\pi\) | |||||||
\(488\) | 17.8072 | − | 29.7801i | 0.806094 | − | 1.34808i | ||||
\(489\) | −6.04337 | −0.273291 | ||||||||
\(490\) | 14.3559 | + | 12.1715i | 0.648533 | + | 0.549851i | ||||
\(491\) | −30.1004 | −1.35841 | −0.679206 | − | 0.733947i | \(-0.737676\pi\) | ||||
−0.679206 | + | 0.733947i | \(0.737676\pi\) | |||||||
\(492\) | 2.90313 | + | 17.5080i | 0.130883 | + | 0.789323i | ||||
\(493\) | −34.1337 | −1.53730 | ||||||||
\(494\) | −3.33852 | − | 2.83052i | −0.150207 | − | 0.127351i | ||||
\(495\) | − | 0.887559i | − | 0.0398928i | ||||||
\(496\) | −7.28228 | − | 21.3550i | −0.326984 | − | 0.958869i | ||||
\(497\) | − | 67.8616i | − | 3.04401i | ||||||
\(498\) | 10.2072 | − | 12.0391i | 0.457397 | − | 0.539487i | ||||
\(499\) | −21.5335 | −0.963974 | −0.481987 | − | 0.876178i | \(-0.660085\pi\) | ||||
−0.481987 | + | 0.876178i | \(0.660085\pi\) | |||||||
\(500\) | −2.87320 | − | 17.3276i | −0.128494 | − | 0.774912i | ||||
\(501\) | − | 3.28126i | − | 0.146596i | ||||||
\(502\) | −17.9695 | + | 21.1946i | −0.802020 | + | 0.945959i | ||||
\(503\) | 22.2489 | 0.992030 | 0.496015 | − | 0.868314i | \(-0.334796\pi\) | ||||
0.496015 | + | 0.868314i | \(0.334796\pi\) | |||||||
\(504\) | −6.60909 | + | 11.0528i | −0.294392 | + | 0.492331i | ||||
\(505\) | − | 2.11964i | − | 0.0943229i | ||||||
\(506\) | 3.01277 | − | 5.43088i | 0.133934 | − | 0.241432i | ||||
\(507\) | 7.22618 | 0.320926 | ||||||||
\(508\) | 0.516096 | − | 0.0855775i | 0.0228981 | − | 0.00379689i | ||||
\(509\) | − | 30.3648i | − | 1.34590i | −0.739689 | − | 0.672949i | \(-0.765028\pi\) | ||
0.739689 | − | 0.672949i | \(-0.234972\pi\) | |||||||
\(510\) | 4.76045 | − | 5.61482i | 0.210796 | − | 0.248628i | ||||
\(511\) | −37.2543 | −1.64803 | ||||||||
\(512\) | 22.6035 | + | 1.03936i | 0.998944 | + | 0.0459336i | ||||
\(513\) | 0.688174i | 0.0303836i | ||||||||
\(514\) | 13.3513 | + | 11.3197i | 0.588900 | + | 0.499291i | ||||
\(515\) | 1.77159 | 0.0780658 | ||||||||
\(516\) | −18.8299 | + | 3.12231i | −0.828939 | + | 0.137452i | ||||
\(517\) | 0.142854 | 0.00628273 | ||||||||
\(518\) | 16.0098 | + | 13.5737i | 0.703429 | + | 0.596394i | ||||
\(519\) | − | 4.28422i | − | 0.188056i | ||||||
\(520\) | 10.5820 | + | 6.32757i | 0.464052 | + | 0.277482i | ||||
\(521\) | − | 35.7402i | − | 1.56580i | −0.622145 | − | 0.782902i | \(-0.713738\pi\) | ||
0.622145 | − | 0.782902i | \(-0.286262\pi\) | |||||||
\(522\) | −5.81302 | + | 6.85630i | −0.254429 | + | 0.300092i | ||||
\(523\) | − | 9.30899i | − | 0.407054i | −0.979069 | − | 0.203527i | \(-0.934760\pi\) | ||
0.979069 | − | 0.203527i | \(-0.0652404\pi\) | |||||||
\(524\) | −2.69133 | − | 16.2307i | −0.117571 | − | 0.709043i | ||||
\(525\) | 18.4879 | 0.806877 | ||||||||
\(526\) | 0.324084 | + | 0.274771i | 0.0141308 | + | 0.0119806i | ||||
\(527\) | −30.2915 | −1.31952 | ||||||||
\(528\) | −1.18220 | − | 3.46677i | −0.0514488 | − | 0.150872i | ||||
\(529\) | 21.2421 | − | 8.81897i | 0.923568 | − | 0.383434i | ||||
\(530\) | −2.53663 | − | 2.15065i | −0.110184 | − | 0.0934184i | ||||
\(531\) | 3.81302 | 0.165471 | ||||||||
\(532\) | 6.18221 | − | 1.02512i | 0.268033 | − | 0.0444444i | ||||
\(533\) | 39.9074i | 1.72858i | ||||||||
\(534\) | −10.0309 | + | 11.8311i | −0.434078 | + | 0.511982i | ||||
\(535\) | − | 2.54928i | − | 0.110215i | ||||||
\(536\) | 25.8414 | + | 15.4520i | 1.11618 | + | 0.667425i | ||||
\(537\) | 21.7569 | 0.938878 | ||||||||
\(538\) | 1.39987 | − | 1.65110i | 0.0603525 | − | 0.0711841i | ||||
\(539\) | − | 12.5730i | − | 0.541559i | ||||||
\(540\) | −0.317112 | − | 1.91242i | −0.0136463 | − | 0.0822976i | ||||
\(541\) | 20.3348i | 0.874263i | 0.899398 | + | 0.437131i | \(0.144006\pi\) | ||||
−0.899398 | + | 0.437131i | \(0.855994\pi\) | |||||||
\(542\) | 5.97041 | − | 7.04193i | 0.256451 | − | 0.302477i | ||||
\(543\) | −2.42739 | −0.104169 | ||||||||
\(544\) | 11.1154 | − | 28.2720i | 0.476567 | − | 1.21215i | ||||
\(545\) | −5.95797 | −0.255211 | ||||||||
\(546\) | −18.7272 | + | 22.0882i | −0.801451 | + | 0.945289i | ||||
\(547\) | 39.4942 | 1.68865 | 0.844324 | − | 0.535832i | \(-0.180002\pi\) | ||||
0.844324 | + | 0.535832i | \(0.180002\pi\) | |||||||
\(548\) | −13.2319 | + | 2.19408i | −0.565241 | + | 0.0937265i | ||||
\(549\) | −12.2676 | −0.523568 | ||||||||
\(550\) | −3.40052 | + | 4.01082i | −0.144999 | + | 0.171022i | ||||
\(551\) | 4.37410 | 0.186343 | ||||||||
\(552\) | 4.55125 | − | 12.7783i | 0.193714 | − | 0.543883i | ||||
\(553\) | 54.9407 | 2.33632 | ||||||||
\(554\) | −6.75492 | + | 7.96723i | −0.286989 | + | 0.338495i | ||||
\(555\) | −3.15955 | −0.134115 | ||||||||
\(556\) | −2.42955 | − | 14.6520i | −0.103036 | − | 0.621384i | ||||
\(557\) | 0.909976 | 0.0385569 | 0.0192785 | − | 0.999814i | \(-0.493863\pi\) | ||||
0.0192785 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(558\) | −5.15869 | + | 6.08453i | −0.218385 | + | 0.257579i | ||||
\(559\) | −42.9205 | −1.81534 | ||||||||
\(560\) | −16.7079 | + | 5.69756i | −0.706037 | + | 0.240766i | ||||
\(561\) | −4.91751 | −0.207618 | ||||||||
\(562\) | 7.12845 | − | 8.40780i | 0.300695 | − | 0.354662i | ||||
\(563\) | 24.7038i | 1.04114i | 0.853819 | + | 0.520571i | \(0.174281\pi\) | ||||
−0.853819 | + | 0.520571i | \(0.825719\pi\) | |||||||
\(564\) | 0.307809 | − | 0.0510399i | 0.0129611 | − | 0.00214917i | ||||
\(565\) | 18.2273i | 0.766829i | ||||||||
\(566\) | −25.4672 | + | 30.0378i | −1.07047 | + | 1.26258i | ||||
\(567\) | 4.55308 | 0.191211 | ||||||||
\(568\) | 36.1814 | + | 21.6349i | 1.51814 | + | 0.907780i | ||||
\(569\) | 4.12434i | 0.172901i | 0.996256 | + | 0.0864507i | \(0.0275525\pi\) | ||||
−0.996256 | + | 0.0864507i | \(0.972448\pi\) | |||||||
\(570\) | −0.610034 | + | 0.719517i | −0.0255515 | + | 0.0301373i | ||||
\(571\) | − | 27.5717i | − | 1.15384i | −0.816801 | − | 0.576919i | \(-0.804255\pi\) | ||
0.816801 | − | 0.576919i | \(-0.195745\pi\) | |||||||
\(572\) | −1.34735 | − | 8.12550i | −0.0563354 | − | 0.339744i | ||||
\(573\) | 8.94391 | 0.373637 | ||||||||
\(574\) | −43.5814 | − | 36.9499i | −1.81905 | − | 1.54226i | ||||
\(575\) | −19.0978 | + | 3.80686i | −0.796435 | + | 0.158757i | ||||
\(576\) | −3.78592 | − | 7.04747i | −0.157747 | − | 0.293644i | ||||
\(577\) | −30.3113 | −1.26188 | −0.630938 | − | 0.775833i | \(-0.717330\pi\) | ||||
−0.630938 | + | 0.775833i | \(0.717330\pi\) | |||||||
\(578\) | −12.7710 | − | 10.8278i | −0.531206 | − | 0.450376i | ||||
\(579\) | 12.2220 | 0.507930 | ||||||||
\(580\) | −12.1556 | + | 2.01560i | −0.504732 | + | 0.0836932i | ||||
\(581\) | 50.8162i | 2.10821i | ||||||||
\(582\) | −16.3659 | + | 19.3031i | −0.678387 | + | 0.800138i | ||||
\(583\) | 2.22161i | 0.0920097i | ||||||||
\(584\) | 11.8770 | − | 19.8627i | 0.491474 | − | 0.821923i | ||||
\(585\) | − | 4.35914i | − | 0.180228i | ||||||
\(586\) | −13.2432 | − | 11.2281i | −0.547071 | − | 0.463827i | ||||
\(587\) | 14.3608 | 0.592732 | 0.296366 | − | 0.955074i | \(-0.404225\pi\) | ||||
0.296366 | + | 0.955074i | \(0.404225\pi\) | |||||||
\(588\) | −4.49218 | − | 27.0912i | −0.185254 | − | 1.11722i | ||||
\(589\) | 3.88174 | 0.159944 | ||||||||
\(590\) | 3.98669 | + | 3.38006i | 0.164129 | + | 0.139155i | ||||
\(591\) | 10.5254i | 0.432955i | ||||||||
\(592\) | −12.3411 | + | 4.20843i | −0.507215 | + | 0.172966i | ||||
\(593\) | −25.1240 | −1.03172 | −0.515859 | − | 0.856674i | \(-0.672527\pi\) | ||||
−0.515859 | + | 0.856674i | \(0.672527\pi\) | |||||||
\(594\) | −0.837460 | + | 0.987761i | −0.0343614 | + | 0.0405283i | ||||
\(595\) | 23.6997i | 0.971591i | ||||||||
\(596\) | 5.23955 | + | 31.5984i | 0.214620 | + | 1.29432i | ||||
\(597\) | −16.2033 | −0.663158 | ||||||||
\(598\) | 14.7969 | − | 26.6731i | 0.605090 | − | 1.09075i | ||||
\(599\) | 3.10960i | 0.127055i | 0.997980 | + | 0.0635274i | \(0.0202350\pi\) | ||||
−0.997980 | + | 0.0635274i | \(0.979765\pi\) | |||||||
\(600\) | −5.89410 | + | 9.85708i | −0.240626 | + | 0.402414i | ||||
\(601\) | −14.1864 | −0.578674 | −0.289337 | − | 0.957227i | \(-0.593435\pi\) | ||||
−0.289337 | + | 0.957227i | \(0.593435\pi\) | |||||||
\(602\) | 39.7396 | − | 46.8718i | 1.61967 | − | 1.91035i | ||||
\(603\) | − | 10.6451i | − | 0.433501i | ||||||
\(604\) | −16.5120 | + | 2.73797i | −0.671863 | + | 0.111406i | ||||
\(605\) | 9.84922 | 0.400428 | ||||||||
\(606\) | −2.00000 | + | 2.35894i | −0.0812444 | + | 0.0958255i | ||||
\(607\) | 6.65785i | 0.270234i | 0.990830 | + | 0.135117i | \(0.0431410\pi\) | ||||
−0.990830 | + | 0.135117i | \(0.956859\pi\) | |||||||
\(608\) | −1.42439 | + | 3.62295i | −0.0577666 | + | 0.146930i | ||||
\(609\) | − | 28.9398i | − | 1.17270i | ||||||
\(610\) | −12.8263 | − | 10.8746i | −0.519323 | − | 0.440301i | ||||
\(611\) | 0.701613 | 0.0283842 | ||||||||
\(612\) | −10.5958 | + | 1.75696i | −0.428309 | + | 0.0710209i | ||||
\(613\) | −8.35314 | −0.337380 | −0.168690 | − | 0.985669i | \(-0.553954\pi\) | ||||
−0.168690 | + | 0.985669i | \(0.553954\pi\) | |||||||
\(614\) | −0.0983765 | − | 0.0834072i | −0.00397015 | − | 0.00336604i | ||||
\(615\) | 8.60085 | 0.346820 | ||||||||
\(616\) | 10.1210 | + | 6.05194i | 0.407788 | + | 0.243839i | ||||
\(617\) | 8.98374i | 0.361672i | 0.983513 | + | 0.180836i | \(0.0578803\pi\) | ||||
−0.983513 | + | 0.180836i | \(0.942120\pi\) | |||||||
\(618\) | −1.97160 | − | 1.67160i | −0.0793094 | − | 0.0672415i | ||||
\(619\) | − | 25.1148i | − | 1.00945i | −0.863280 | − | 0.504725i | \(-0.831594\pi\) | ||
0.863280 | − | 0.504725i | \(-0.168406\pi\) | |||||||
\(620\) | −10.7873 | + | 1.78872i | −0.433228 | + | 0.0718366i | ||||
\(621\) | −4.70330 | + | 0.937530i | −0.188737 | + | 0.0376218i | ||||
\(622\) | 2.52404 | − | 2.97704i | 0.101205 | − | 0.119368i | ||||
\(623\) | − | 49.9381i | − | 2.00073i | ||||||
\(624\) | −5.80626 | − | 17.0266i | −0.232436 | − | 0.681611i | ||||
\(625\) | 11.7904 | 0.471616 | ||||||||
\(626\) | 10.3281 | − | 12.1817i | 0.412793 | − | 0.486878i | ||||
\(627\) | 0.630161 | 0.0251662 | ||||||||
\(628\) | −0.0616410 | − | 0.371741i | −0.00245974 | − | 0.0148341i | ||||
\(629\) | 17.5055i | 0.697989i | ||||||||
\(630\) | 4.76045 | + | 4.03609i | 0.189661 | + | 0.160802i | ||||
\(631\) | 16.1347 | 0.642312 | 0.321156 | − | 0.947026i | \(-0.395929\pi\) | ||||
0.321156 | + | 0.947026i | \(0.395929\pi\) | |||||||
\(632\) | −17.5156 | + | 29.2924i | −0.696733 | + | 1.16519i | ||||
\(633\) | −6.20898 | −0.246785 | ||||||||
\(634\) | −21.3167 | + | 25.1425i | −0.846595 | + | 0.998535i | ||||
\(635\) | − | 0.253533i | − | 0.0100612i | ||||||
\(636\) | 0.793751 | + | 4.78691i | 0.0314743 | + | 0.189813i | ||||
\(637\) | − | 61.7511i | − | 2.44667i | ||||||
\(638\) | 6.27831 | + | 5.32298i | 0.248560 | + | 0.210739i | ||||
\(639\) | − | 14.9045i | − | 0.589614i | ||||||
\(640\) | 2.28889 | − | 10.7245i | 0.0904763 | − | 0.423923i | ||||
\(641\) | − | 17.9723i | − | 0.709865i | −0.934892 | − | 0.354932i | \(-0.884504\pi\) | ||
0.934892 | − | 0.354932i | \(-0.115496\pi\) | |||||||
\(642\) | −2.40539 | + | 2.83709i | −0.0949331 | + | 0.111971i | ||||
\(643\) | 37.3857i | 1.47435i | 0.675704 | + | 0.737173i | \(0.263840\pi\) | ||||
−0.675704 | + | 0.737173i | \(0.736160\pi\) | |||||||
\(644\) | 15.4284 | + | 40.8555i | 0.607965 | + | 1.60993i | ||||
\(645\) | 9.25021i | 0.364227i | ||||||||
\(646\) | 3.98648 | + | 3.37989i | 0.156846 | + | 0.132980i | ||||
\(647\) | − | 0.412854i | − | 0.0162310i | −0.999967 | − | 0.00811548i | \(-0.997417\pi\) | ||
0.999967 | − | 0.00811548i | \(-0.00258327\pi\) | |||||||
\(648\) | −1.45156 | + | 2.42754i | −0.0570228 | + | 0.0953629i | ||||
\(649\) | − | 3.49158i | − | 0.137057i | ||||||
\(650\) | −16.7013 | + | 19.6987i | −0.655078 | + | 0.772646i | ||||
\(651\) | − | 25.6823i | − | 1.00657i | ||||||
\(652\) | 1.97719 | + | 11.9239i | 0.0774328 | + | 0.466977i | ||||
\(653\) | 47.0964i | 1.84302i | 0.388350 | + | 0.921512i | \(0.373045\pi\) | ||||
−0.388350 | + | 0.921512i | \(0.626955\pi\) | |||||||
\(654\) | 6.63060 | + | 5.62167i | 0.259277 | + | 0.219825i | ||||
\(655\) | −7.97338 | −0.311546 | ||||||||
\(656\) | 33.5946 | − | 11.4561i | 1.31165 | − | 0.447285i | ||||
\(657\) | −8.18221 | −0.319218 | ||||||||
\(658\) | −0.649617 | + | 0.766204i | −0.0253247 | + | 0.0298698i | ||||
\(659\) | − | 35.5752i | − | 1.38581i | −0.721027 | − | 0.692907i | \(-0.756330\pi\) | ||
0.721027 | − | 0.692907i | \(-0.243670\pi\) | |||||||
\(660\) | −1.75121 | + | 0.290380i | −0.0681656 | + | 0.0113030i | ||||
\(661\) | 24.5240 | 0.953872 | 0.476936 | − | 0.878938i | \(-0.341747\pi\) | ||||
0.476936 | + | 0.878938i | \(0.341747\pi\) | |||||||
\(662\) | −15.9114 | − | 13.4903i | −0.618414 | − | 0.524315i | ||||
\(663\) | −24.1518 | −0.937979 | ||||||||
\(664\) | −27.0934 | − | 16.2007i | −1.05143 | − | 0.628708i | ||||
\(665\) | − | 3.03702i | − | 0.117771i | ||||||
\(666\) | 3.51625 | + | 2.98121i | 0.136252 | + | 0.115520i | ||||
\(667\) | 5.95904 | + | 29.8947i | 0.230735 | + | 1.15753i | ||||
\(668\) | −6.47413 | + | 1.07352i | −0.250491 | + | 0.0415357i | ||||
\(669\) | 22.7592i | 0.879920i | ||||||||
\(670\) | 9.43635 | − | 11.1299i | 0.364558 | − | 0.429986i | ||||
\(671\) | 11.2334i | 0.433662i | ||||||||
\(672\) | 23.9701 | + | 9.42401i | 0.924666 | + | 0.363539i | ||||
\(673\) | −49.3893 | −1.90382 | −0.951910 | − | 0.306379i | \(-0.900882\pi\) | ||||
−0.951910 | + | 0.306379i | \(0.900882\pi\) | |||||||
\(674\) | −20.4969 | + | 24.1755i | −0.789510 | + | 0.931204i | ||||
\(675\) | 4.06052 | 0.156289 | ||||||||
\(676\) | −2.36417 | − | 14.2577i | −0.0909295 | − | 0.548372i | ||||
\(677\) | 38.7298 | 1.48851 | 0.744254 | − | 0.667896i | \(-0.232805\pi\) | ||||
0.744254 | + | 0.667896i | \(0.232805\pi\) | |||||||
\(678\) | 17.1985 | − | 20.2851i | 0.660504 | − | 0.779045i | ||||
\(679\) | − | 81.4766i | − | 3.12679i | ||||||
\(680\) | −12.6358 | − | 7.55567i | −0.484562 | − | 0.289747i | ||||
\(681\) | 5.19084i | 0.198914i | ||||||||
\(682\) | 5.57160 | + | 4.72381i | 0.213348 | + | 0.180884i | ||||
\(683\) | −11.5331 | −0.441303 | −0.220651 | − | 0.975353i | \(-0.570818\pi\) | ||||
−0.220651 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(684\) | 1.35781 | − | 0.225148i | 0.0519171 | − | 0.00860874i | ||||
\(685\) | 6.50022i | 0.248361i | ||||||||
\(686\) | 33.0563 | + | 28.0263i | 1.26209 | + | 1.07005i | ||||
\(687\) | 16.5481 | 0.631348 | ||||||||
\(688\) | 12.3210 | + | 36.1309i | 0.469734 | + | 1.37748i | ||||
\(689\) | 10.9112i | 0.415683i | ||||||||
\(690\) | −5.74859 | − | 3.18902i | −0.218845 | − | 0.121404i | ||||
\(691\) | −19.3937 | −0.737771 | −0.368885 | − | 0.929475i | \(-0.620261\pi\) | ||||
−0.368885 | + | 0.929475i | \(0.620261\pi\) | |||||||
\(692\) | −8.45302 | + | 1.40165i | −0.321336 | + | 0.0532829i | ||||
\(693\) | − | 4.16925i | − | 0.158377i | ||||||
\(694\) | 9.64233 | + | 8.17513i | 0.366018 | + | 0.310324i | ||||
\(695\) | −7.19783 | −0.273029 | ||||||||
\(696\) | 15.4297 | + | 9.22629i | 0.584861 | + | 0.349722i | ||||
\(697\) | − | 47.6529i | − | 1.80498i | ||||||
\(698\) | −31.0899 | + | 36.6696i | −1.17677 | + | 1.38797i | ||||
\(699\) | 15.1175 | 0.571797 | ||||||||
\(700\) | −6.04861 | − | 36.4777i | −0.228616 | − | 1.37873i | ||||
\(701\) | 42.0341 | 1.58761 | 0.793803 | − | 0.608174i | \(-0.208098\pi\) | ||||
0.793803 | + | 0.608174i | \(0.208098\pi\) | |||||||
\(702\) | −4.11309 | + | 4.85127i | −0.155239 | + | 0.183099i | ||||
\(703\) | − | 2.24326i | − | 0.0846061i | ||||||
\(704\) | −6.45336 | + | 3.46677i | −0.243220 | + | 0.130659i | ||||
\(705\) | − | 0.151211i | − | 0.00569495i | ||||||
\(706\) | −15.4723 | − | 13.1180i | −0.582309 | − | 0.493703i | ||||
\(707\) | − | 9.95690i | − | 0.374468i | ||||||
\(708\) | −1.24749 | − | 7.52332i | −0.0468837 | − | 0.282744i | ||||
\(709\) | −7.00113 | −0.262933 | −0.131467 | − | 0.991321i | \(-0.541969\pi\) | ||||
−0.131467 | + | 0.991321i | \(0.541969\pi\) | |||||||
\(710\) | 13.2122 | − | 15.5834i | 0.495844 | − | 0.584833i | ||||
\(711\) | 12.0667 | 0.452537 | ||||||||
\(712\) | 26.6252 | + | 15.9207i | 0.997823 | + | 0.596654i | ||||
\(713\) | 5.28827 | + | 26.5296i | 0.198047 | + | 0.993542i | ||||
\(714\) | 22.3619 | − | 26.3753i | 0.836874 | − | 0.987069i | ||||
\(715\) | −3.99166 | −0.149280 | ||||||||
\(716\) | −7.11812 | − | 42.9276i | −0.266017 | − | 1.60428i | ||||
\(717\) | − | 4.20687i | − | 0.157108i | ||||||
\(718\) | −18.8454 | − | 15.9778i | −0.703303 | − | 0.596287i | ||||
\(719\) | 32.5628i | 1.21439i | 0.794554 | + | 0.607193i | \(0.207705\pi\) | ||||
−0.794554 | + | 0.607193i | \(0.792295\pi\) | |||||||
\(720\) | −3.66958 | + | 1.25136i | −0.136757 | + | 0.0466356i | ||||
\(721\) | 8.32196 | 0.309926 | ||||||||
\(722\) | 19.9844 | + | 16.9435i | 0.743741 | + | 0.630571i | ||||
\(723\) | 11.2163i | 0.417137i | ||||||||
\(724\) | 0.794160 | + | 4.78938i | 0.0295147 | + | 0.177996i | ||||
\(725\) | − | 25.8091i | − | 0.958525i | ||||||
\(726\) | −10.9612 | − | 9.29328i | −0.406807 | − | 0.344906i | ||||
\(727\) | 8.30822 | 0.308135 | 0.154067 | − | 0.988060i | \(-0.450763\pi\) | ||||
0.154067 | + | 0.988060i | \(0.450763\pi\) | |||||||
\(728\) | 49.7083 | + | 29.7234i | 1.84231 | + | 1.10162i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.55487 | − | 7.25314i | −0.316630 | − | 0.268451i | ||||
\(731\) | 51.2507 | 1.89558 | ||||||||
\(732\) | 4.01355 | + | 24.2047i | 0.148345 | + | 0.894631i | ||||
\(733\) | 5.54133 | 0.204674 | 0.102337 | − | 0.994750i | \(-0.467368\pi\) | ||||
0.102337 | + | 0.994750i | \(0.467368\pi\) | |||||||
\(734\) | −4.53312 | − | 3.84335i | −0.167321 | − | 0.141861i | ||||
\(735\) | −13.3086 | −0.490894 | ||||||||
\(736\) | −26.7014 | − | 4.79923i | −0.984228 | − | 0.176902i | ||||
\(737\) | −9.74768 | −0.359061 | ||||||||
\(738\) | −9.57185 | − | 8.11537i | −0.352345 | − | 0.298731i | ||||
\(739\) | 16.1333 | 0.593472 | 0.296736 | − | 0.954960i | \(-0.404102\pi\) | ||||
0.296736 | + | 0.954960i | \(0.404102\pi\) | |||||||
\(740\) | 1.03370 | + | 6.23398i | 0.0379996 | + | 0.229166i | ||||
\(741\) | 3.09496 | 0.113696 | ||||||||
\(742\) | −11.9157 | − | 10.1026i | −0.437438 | − | 0.370877i | ||||
\(743\) | 46.0973 | 1.69115 | 0.845574 | − | 0.533859i | \(-0.179259\pi\) | ||||
0.845574 | + | 0.533859i | \(0.179259\pi\) | |||||||
\(744\) | 13.6929 | + | 8.18775i | 0.502006 | + | 0.300177i | ||||
\(745\) | 15.5228 | 0.568710 | ||||||||
\(746\) | 40.2351 | + | 34.1128i | 1.47311 | + | 1.24896i | ||||
\(747\) | 11.1608i | 0.408354i | ||||||||
\(748\) | 1.60885 | + | 9.70255i | 0.0588253 | + | 0.354760i | ||||
\(749\) | − | 11.9751i | − | 0.437561i | ||||||
\(750\) | 9.47318 | + | 8.03172i | 0.345912 | + | 0.293277i | ||||
\(751\) | −2.29470 | −0.0837349 | −0.0418675 | − | 0.999123i | \(-0.513331\pi\) | ||||
−0.0418675 | + | 0.999123i | \(0.513331\pi\) | |||||||
\(752\) | −0.201409 | − | 0.590626i | −0.00734465 | − | 0.0215379i | ||||
\(753\) | − | 19.6483i | − | 0.716025i | ||||||
\(754\) | 30.8352 | + | 26.1432i | 1.12295 | + | 0.952080i | ||||
\(755\) | 8.11154i | 0.295209i | ||||||||
\(756\) | −1.48962 | − | 8.98350i | −0.0541768 | − | 0.326727i | ||||
\(757\) | −25.5612 | −0.929037 | −0.464518 | − | 0.885563i | \(-0.653773\pi\) | ||||
−0.464518 | + | 0.885563i | \(0.653773\pi\) | |||||||
\(758\) | −11.0332 | + | 13.0133i | −0.400744 | + | 0.472666i | ||||
\(759\) | 0.858496 | + | 4.30681i | 0.0311614 | + | 0.156327i | ||||
\(760\) | 1.61923 | + | 0.968230i | 0.0587357 | + | 0.0351214i | ||||
\(761\) | 16.0610 | 0.582210 | 0.291105 | − | 0.956691i | \(-0.405977\pi\) | ||||
0.291105 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(762\) | −0.239222 | + | 0.282156i | −0.00866611 | + | 0.0102214i | ||||
\(763\) | −27.9872 | −1.01321 | ||||||||
\(764\) | −2.92615 | − | 17.6469i | −0.105864 | − | 0.638441i | ||||
\(765\) | 5.20519i | 0.188194i | ||||||||
\(766\) | −17.0867 | − | 14.4868i | −0.617368 | − | 0.523428i | ||||
\(767\) | − | 17.1485i | − | 0.619197i | ||||||
\(768\) | −12.6664 | + | 9.77555i | −0.457061 | + | 0.352745i | ||||
\(769\) | 28.1563i | 1.01534i | 0.861551 | + | 0.507671i | \(0.169493\pi\) | ||||
−0.861551 | + | 0.507671i | \(0.830507\pi\) | |||||||
\(770\) | 3.69584 | − | 4.35914i | 0.133189 | − | 0.157093i | ||||
\(771\) | −12.3772 | −0.445756 | ||||||||
\(772\) | −3.99864 | − | 24.1148i | −0.143914 | − | 0.867909i | ||||
\(773\) | −24.8284 | −0.893015 | −0.446508 | − | 0.894780i | \(-0.647332\pi\) | ||||
−0.446508 | + | 0.894780i | \(0.647332\pi\) | |||||||
\(774\) | 8.72808 | − | 10.2945i | 0.313724 | − | 0.370029i | ||||
\(775\) | − | 22.9039i | − | 0.822733i | ||||||
\(776\) | 43.4405 | + | 25.9755i | 1.55942 | + | 0.932466i | ||||
\(777\) | −14.8418 | −0.532447 | ||||||||
\(778\) | 2.20351 | + | 1.86822i | 0.0789998 | + | 0.0669789i | ||||
\(779\) | 6.10654i | 0.218790i | ||||||||
\(780\) | −8.60085 | + | 1.42617i | −0.307960 | + | 0.0510650i | ||||
\(781\) | −13.6481 | −0.488367 | ||||||||
\(782\) | −17.6688 | + | 31.8500i | −0.631834 | + | 1.13895i | ||||
\(783\) | − | 6.35610i | − | 0.227149i | ||||||
\(784\) | −51.9828 | + | 17.7267i | −1.85653 | + | 0.633095i | ||||
\(785\) | −0.182618 | −0.00651793 | ||||||||
\(786\) | 8.87354 | + | 7.52332i | 0.316509 | + | 0.268348i | ||||
\(787\) | 30.2006i | 1.07653i | 0.842774 | + | 0.538267i | \(0.180921\pi\) | ||||
−0.842774 | + | 0.538267i | \(0.819079\pi\) | |||||||
\(788\) | 20.7671 | − | 3.44355i | 0.739799 | − | 0.122671i | ||||
\(789\) | −0.300441 | −0.0106960 | ||||||||
\(790\) | 12.6163 | + | 10.6966i | 0.448867 | + | 0.380567i | ||||
\(791\) | 85.6217i | 3.04436i | ||||||||
\(792\) | 2.22290 | + | 1.32920i | 0.0789873 | + | 0.0472309i | ||||
\(793\) | 55.1717i | 1.95920i | ||||||||
\(794\) | −31.8185 | + | 37.5290i | −1.12920 | + | 1.33185i | ||||
\(795\) | 2.35158 | 0.0834018 | ||||||||
\(796\) | 5.30119 | + | 31.9701i | 0.187896 | + | 1.13315i | ||||
\(797\) | −0.413948 | −0.0146628 | −0.00733139 | − | 0.999973i | \(-0.502334\pi\) | ||||
−0.00733139 | + | 0.999973i | \(0.502334\pi\) | |||||||
\(798\) | −2.86560 | + | 3.37989i | −0.101441 | + | 0.119647i | ||||
\(799\) | −0.837786 | −0.0296387 | ||||||||
\(800\) | 21.3770 | + | 8.40450i | 0.755790 | + | 0.297144i | ||||
\(801\) | − | 10.9680i | − | 0.387535i | ||||||
\(802\) | 25.5648 | − | 30.1530i | 0.902726 | − | 1.06474i | ||||
\(803\) | 7.49244i | 0.264403i | ||||||||
\(804\) | −21.0034 | + | 3.48271i | −0.740731 | + | 0.122826i | ||||
\(805\) | 20.7564 | − | 4.13747i | 0.731567 | − | 0.145827i | ||||
\(806\) | 27.3643 | + | 23.2004i | 0.963865 | + | 0.817201i | ||||
\(807\) | 1.53065i | 0.0538814i | ||||||||
\(808\) | 5.30867 | + | 3.17435i | 0.186758 | + | 0.111673i | ||||
\(809\) | 3.27386 | 0.115103 | 0.0575513 | − | 0.998343i | \(-0.481671\pi\) | ||||
0.0575513 | + | 0.998343i | \(0.481671\pi\) | |||||||
\(810\) | 1.04555 | + | 0.886452i | 0.0367367 | + | 0.0311468i | ||||
\(811\) | 5.52427 | 0.193983 | 0.0969916 | − | 0.995285i | \(-0.469078\pi\) | ||||
0.0969916 | + | 0.995285i | \(0.469078\pi\) | |||||||
\(812\) | −57.1000 | + | 9.46815i | −2.00382 | + | 0.332267i | ||||
\(813\) | 6.52820i | 0.228954i | ||||||||
\(814\) | 2.72989 | − | 3.21983i | 0.0956827 | − | 0.112855i | ||||
\(815\) | 5.85765 | 0.205185 | ||||||||
\(816\) | 6.93317 | + | 20.3313i | 0.242710 | + | 0.711737i | ||||
\(817\) | −6.56758 | −0.229771 | ||||||||
\(818\) | −11.2609 | − | 9.54737i | −0.393727 | − | 0.333816i | ||||
\(819\) | − | 20.4768i | − | 0.715518i | ||||||
\(820\) | −2.81391 | − | 16.9700i | −0.0982660 | − | 0.592617i | ||||
\(821\) | − | 40.6786i | − | 1.41969i | −0.704356 | − | 0.709847i | \(-0.748764\pi\) | ||
0.704356 | − | 0.709847i | \(-0.251236\pi\) | |||||||
\(822\) | 6.13331 | − | 7.23407i | 0.213924 | − | 0.252317i | ||||
\(823\) | 31.2641i | 1.08980i | 0.838502 | + | 0.544898i | \(0.183432\pi\) | ||||
−0.838502 | + | 0.544898i | \(0.816568\pi\) | |||||||
\(824\) | −2.65312 | + | 4.43698i | −0.0924257 | + | 0.154569i | ||||
\(825\) | − | 3.71821i | − | 0.129452i | ||||||
\(826\) | 18.7272 | + | 15.8776i | 0.651604 | + | 0.552454i | ||||
\(827\) | 20.8630i | 0.725478i | 0.931891 | + | 0.362739i | \(0.118158\pi\) | ||||
−0.931891 | + | 0.362739i | \(0.881842\pi\) | |||||||
\(828\) | 3.38857 | + | 8.97316i | 0.117761 | + | 0.311839i | ||||
\(829\) | − | 11.6152i | − | 0.403414i | −0.979446 | − | 0.201707i | \(-0.935351\pi\) | ||
0.979446 | − | 0.201707i | \(-0.0646489\pi\) | |||||||
\(830\) | −9.89355 | + | 11.6692i | −0.343410 | + | 0.405043i | ||||
\(831\) | − | 7.38599i | − | 0.256217i | ||||||
\(832\) | −31.6949 | + | 17.0266i | −1.09882 | + | 0.590292i | ||||
\(833\) | 73.7361i | 2.55481i | ||||||||
\(834\) | 8.01043 | + | 6.79154i | 0.277379 | + | 0.235172i | ||||
\(835\) | 3.18042i | 0.110063i | ||||||||
\(836\) | −0.206168 | − | 1.24334i | −0.00713046 | − | 0.0430020i | ||||
\(837\) | − | 5.64064i | − | 0.194969i | ||||||
\(838\) | −25.5533 | + | 30.1394i | −0.882725 | + | 1.04115i | ||||
\(839\) | 35.2227 | 1.21602 | 0.608011 | − | 0.793929i | \(-0.291968\pi\) | ||||
0.608011 | + | 0.793929i | \(0.291968\pi\) | |||||||
\(840\) | 6.40598 | − | 10.7131i | 0.221027 | − | 0.369638i | ||||
\(841\) | −11.4000 | −0.393104 | ||||||||
\(842\) | 35.2534 | + | 29.8891i | 1.21491 | + | 1.03005i | ||||
\(843\) | 7.79441i | 0.268454i | ||||||||
\(844\) | 2.03137 | + | 12.2507i | 0.0699227 | + | 0.421686i | ||||
\(845\) | −7.00411 | −0.240949 | ||||||||
\(846\) | −0.142676 | + | 0.168283i | −0.00490531 | + | 0.00578568i | ||||
\(847\) | 46.2661 | 1.58972 | ||||||||
\(848\) | 9.18516 | − | 3.13223i | 0.315420 | − | 0.107561i | ||||
\(849\) | − | 27.8464i | − | 0.955687i | ||||||
\(850\) | 19.9428 | − | 23.5219i | 0.684031 | − | 0.806796i | ||||
\(851\) | 15.3315 | − | 3.05609i | 0.525556 | − | 0.104762i | ||||
\(852\) | −29.4075 | + | 4.87627i | −1.00749 | + | 0.167058i | ||||
\(853\) | 11.0149i | 0.377145i | 0.982059 | + | 0.188572i | \(0.0603860\pi\) | ||||
−0.982059 | + | 0.188572i | \(0.939614\pi\) | |||||||
\(854\) | −60.2509 | − | 51.0829i | −2.06174 | − | 1.74802i | ||||
\(855\) | − | 0.667026i | − | 0.0228118i | ||||||
\(856\) | 6.38470 | + | 3.81777i | 0.218225 | + | 0.130489i | ||||
\(857\) | 4.44133 | 0.151713 | 0.0758565 | − | 0.997119i | \(-0.475831\pi\) | ||||
0.0758565 | + | 0.997119i | \(0.475831\pi\) | |||||||
\(858\) | 4.44231 | + | 3.76635i | 0.151658 | + | 0.128581i | ||||
\(859\) | 55.9465 | 1.90887 | 0.954436 | − | 0.298417i | \(-0.0964587\pi\) | ||||
0.954436 | + | 0.298417i | \(0.0964587\pi\) | |||||||
\(860\) | 18.2512 | − | 3.02636i | 0.622361 | − | 0.103198i | ||||
\(861\) | 40.4019 | 1.37689 | ||||||||
\(862\) | 17.4240 | + | 14.7727i | 0.593464 | + | 0.503161i | ||||
\(863\) | − | 19.0075i | − | 0.647022i | −0.946224 | − | 0.323511i | \(-0.895137\pi\) | ||
0.946224 | − | 0.323511i | \(-0.104863\pi\) | |||||||
\(864\) | 5.26459 | + | 2.06981i | 0.179105 | + | 0.0704164i | ||||
\(865\) | 4.15256i | 0.141191i | ||||||||
\(866\) | −18.2123 | + | 21.4809i | −0.618880 | + | 0.729951i | ||||
\(867\) | 11.8393 | 0.402085 | ||||||||
\(868\) | −50.6726 | + | 8.40239i | −1.71994 | + | 0.285196i | ||||
\(869\) | − | 11.0495i | − | 0.374828i | ||||||
\(870\) | 5.63438 | − | 6.64559i | 0.191023 | − | 0.225307i | ||||
\(871\) | −47.8746 | −1.62217 | ||||||||
\(872\) | 8.92258 | − | 14.9218i | 0.302157 | − | 0.505316i | ||||
\(873\) | − | 17.8948i | − | 0.605648i | ||||||
\(874\) | 2.26418 | − | 4.08146i | 0.0765872 | − | 0.138057i | ||||
\(875\) | −39.9855 | −1.35176 | ||||||||
\(876\) | 2.67695 | + | 16.1440i | 0.0904457 | + | 0.545455i | ||||
\(877\) | 39.4573i | 1.33238i | 0.745782 | + | 0.666190i | \(0.232076\pi\) | ||||
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(878\) | 26.7967 | − | 31.6060i | 0.904346 | − | 1.06665i | ||||
\(879\) | 12.2770 | 0.414094 | ||||||||
\(880\) | 1.14587 | + | 3.36023i | 0.0386274 | + | 0.113273i | ||||
\(881\) | 17.9584i | 0.605035i | 0.953144 | + | 0.302517i | \(0.0978270\pi\) | ||||
−0.953144 | + | 0.302517i | \(0.902173\pi\) | |||||||
\(882\) | 14.8111 | + | 12.5574i | 0.498715 | + | 0.422829i | ||||
\(883\) | −39.4681 | −1.32821 | −0.664104 | − | 0.747640i | \(-0.731187\pi\) | ||||
−0.664104 | + | 0.747640i | \(0.731187\pi\) | |||||||
\(884\) | 7.90167 | + | 47.6529i | 0.265762 | + | 1.60274i | ||||
\(885\) | −3.69584 | −0.124234 | ||||||||
\(886\) | 35.5533 | + | 30.1435i | 1.19444 | + | 1.01269i | ||||
\(887\) | − | 15.0370i | − | 0.504892i | −0.967611 | − | 0.252446i | \(-0.918765\pi\) | ||
0.967611 | − | 0.252446i | \(-0.0812350\pi\) | |||||||
\(888\) | 4.73170 | − | 7.91313i | 0.158786 | − | 0.265547i | ||||
\(889\) | − | 1.19096i | − | 0.0399434i | ||||||
\(890\) | 9.72259 | − | 11.4675i | 0.325902 | − | 0.384392i | ||||
\(891\) | − | 0.915699i | − | 0.0306771i | ||||||
\(892\) | 44.9052 | − | 7.44604i | 1.50354 | − | 0.249312i | ||||
\(893\) | 0.107359 | 0.00359264 | ||||||||
\(894\) | −17.2752 | − | 14.6466i | −0.577770 | − | 0.489855i | ||||
\(895\) | −21.0882 | −0.704902 | ||||||||
\(896\) | 10.7519 | − | 50.3776i | 0.359196 | − | 1.68300i | ||||
\(897\) | 4.21640 | + | 21.1524i | 0.140782 | + | 0.706258i | ||||
\(898\) | 18.0103 | + | 15.2698i | 0.601010 | + | 0.509559i | ||||
\(899\) | −35.8525 | −1.19575 | ||||||||
\(900\) | −1.32847 | − | 8.01164i | −0.0442822 | − | 0.267055i | ||||
\(901\) | − | 13.0289i | − | 0.434055i | ||||||
\(902\) | −7.43124 | + | 8.76493i | −0.247433 | + | 0.291840i | ||||
\(903\) | 43.4523i | 1.44600i | ||||||||
\(904\) | −45.6505 | − | 27.2970i | −1.51831 | − | 0.907885i | ||||
\(905\) | 2.35279 | 0.0782094 | ||||||||
\(906\) | 7.65368 | − | 9.02730i | 0.254276 | − | 0.299912i | ||||
\(907\) | 9.18521i | 0.304990i | 0.988304 | + | 0.152495i | \(0.0487308\pi\) | ||||
−0.988304 | + | 0.152495i | \(0.951269\pi\) | |||||||
\(908\) | 10.2418 | − | 1.69827i | 0.339887 | − | 0.0563591i | ||||
\(909\) | − | 2.18685i | − | 0.0725332i | ||||||
\(910\) | 18.1517 | − | 21.4094i | 0.601724 | − | 0.709716i | ||||
\(911\) | 20.7570 | 0.687710 | 0.343855 | − | 0.939023i | \(-0.388267\pi\) | ||||
0.343855 | + | 0.939023i | \(0.388267\pi\) | |||||||
\(912\) | −0.888459 | − | 2.60537i | −0.0294198 | − | 0.0862726i | ||||
\(913\) | 10.2200 | 0.338232 | ||||||||
\(914\) | −6.90187 | + | 8.14056i | −0.228294 | + | 0.269266i | ||||
\(915\) | 11.8906 | 0.393091 | ||||||||
\(916\) | −5.41398 | − | 32.6503i | −0.178883 | − | 1.07880i | ||||
\(917\) | −37.4545 | −1.23686 | ||||||||
\(918\) | 4.91139 | − | 5.79284i | 0.162100 | − | 0.191192i | ||||
\(919\) | 51.6210 | 1.70282 | 0.851409 | − | 0.524502i | \(-0.175749\pi\) | ||||
0.851409 | + | 0.524502i | \(0.175749\pi\) | |||||||
\(920\) | −4.41138 | + | 12.3856i | −0.145439 | + | 0.408343i | ||||
\(921\) | 0.0911995 | 0.00300513 | ||||||||
\(922\) | 20.1505 | − | 23.7669i | 0.663620 | − | 0.782721i | ||||
\(923\) | −67.0310 | −2.20635 | ||||||||
\(924\) | −8.22618 | + | 1.36404i | −0.270621 | + | 0.0448736i | ||||
\(925\) | −13.2362 | −0.435203 | ||||||||
\(926\) | −9.68506 | + | 11.4233i | −0.318271 | + | 0.375391i | ||||
\(927\) | 1.82776 | 0.0600317 | ||||||||
\(928\) | 13.1559 | − | 33.4623i | 0.431864 | − | 1.09845i | ||||
\(929\) | 36.6120 | 1.20120 | 0.600600 | − | 0.799549i | \(-0.294928\pi\) | ||||
0.600600 | + | 0.799549i | \(0.294928\pi\) | |||||||
\(930\) | 5.00016 | − | 5.89754i | 0.163962 | − | 0.193388i | ||||
\(931\) | − | 9.44900i | − | 0.309679i | ||||||
\(932\) | −4.94595 | − | 29.8278i | −0.162010 | − | 0.977041i | ||||
\(933\) | 2.75985i | 0.0903534i | ||||||||
\(934\) | 21.7961 | − | 25.7078i | 0.713189 | − | 0.841186i | ||||
\(935\) | 4.76639 | 0.155878 | ||||||||
\(936\) | 10.9175 | + | 6.52820i | 0.356850 | + | 0.213381i | ||||
\(937\) | − | 6.16375i | − | 0.201361i | −0.994919 | − | 0.100680i | \(-0.967898\pi\) | ||
0.994919 | − | 0.100680i | \(-0.0321020\pi\) | |||||||
\(938\) | 44.3267 | − | 52.2820i | 1.44732 | − | 1.70707i | ||||
\(939\) | 11.2930i | 0.368532i | ||||||||
\(940\) | −0.298349 | + | 0.0494714i | −0.00973107 | + | 0.00161358i | ||||
\(941\) | 12.0779 | 0.393729 | 0.196865 | − | 0.980431i | \(-0.436924\pi\) | ||||
0.196865 | + | 0.980431i | \(0.436924\pi\) | |||||||
\(942\) | 0.203235 | + | 0.172311i | 0.00662177 | + | 0.00561418i | ||||
\(943\) | −41.7349 | + | 8.31921i | −1.35908 | + | 0.270911i | ||||
\(944\) | −14.4358 | + | 4.92276i | −0.469846 | + | 0.160222i | ||||
\(945\) | −4.41316 | −0.143560 | ||||||||
\(946\) | −9.42668 | − | 7.99230i | −0.306488 | − | 0.259852i | ||||
\(947\) | −51.7679 | −1.68223 | −0.841115 | − | 0.540856i | \(-0.818100\pi\) | ||||
−0.841115 | + | 0.540856i | \(0.818100\pi\) | |||||||
\(948\) | −3.94783 | − | 23.8083i | −0.128219 | − | 0.773258i | ||||
\(949\) | 36.7983i | 1.19452i | ||||||||
\(950\) | −2.55559 | + | 3.01425i | −0.0829143 | + | 0.0977950i | ||||
\(951\) | − | 23.3082i | − | 0.755821i | ||||||
\(952\) | −59.3560 | − | 35.4923i | −1.92374 | − | 1.15031i | ||||
\(953\) | 18.0036i | 0.583193i | 0.956541 | + | 0.291597i | \(0.0941865\pi\) | ||||
−0.956541 | + | 0.291597i | \(0.905813\pi\) | |||||||
\(954\) | −2.61706 | − | 2.21884i | −0.0847304 | − | 0.0718376i | ||||
\(955\) | −8.66905 | −0.280524 | ||||||||
\(956\) | −8.30039 | + | 1.37635i | −0.268454 | + | 0.0445142i | ||||
\(957\) | −5.82028 | −0.188143 | ||||||||
\(958\) | −19.8586 | − | 16.8368i | −0.641601 | − | 0.543973i | ||||
\(959\) | 30.5344i | 0.986006i | ||||||||
\(960\) | 3.66958 | + | 6.83089i | 0.118435 | + | 0.220466i | ||||
\(961\) | −0.816783 | −0.0263478 | ||||||||
\(962\) | 13.4076 | − | 15.8138i | 0.432277 | − | 0.509858i | ||||
\(963\) | − | 2.63011i | − | 0.0847541i | ||||||
\(964\) | 22.1303 | − | 3.66959i | 0.712770 | − | 0.118189i | ||||
\(965\) | −11.8464 | −0.381350 | ||||||||
\(966\) | −27.0037 | − | 14.9802i | −0.868828 | − | 0.481981i | ||||
\(967\) | 51.6314i | 1.66035i | 0.557500 | + | 0.830177i | \(0.311760\pi\) | ||||
−0.557500 | + | 0.830177i | \(0.688240\pi\) | |||||||
\(968\) | −14.7501 | + | 24.6675i | −0.474085 | + | 0.792842i | ||||
\(969\) | −3.69565 | −0.118721 | ||||||||
\(970\) | 15.8629 | − | 18.7099i | 0.509328 | − | 0.600738i | ||||
\(971\) | − | 6.84543i | − | 0.219680i | −0.993949 | − | 0.109840i | \(-0.964966\pi\) | ||
0.993949 | − | 0.109840i | \(-0.0350339\pi\) | |||||||
\(972\) | −0.327167 | − | 1.97306i | −0.0104939 | − | 0.0632859i | ||||
\(973\) | −33.8113 | −1.08394 | ||||||||
\(974\) | −36.2585 | + | 42.7658i | −1.16180 | + | 1.37031i | ||||
\(975\) | − | 18.2616i | − | 0.584839i | ||||||
\(976\) | 46.4442 | − | 15.8379i | 1.48664 | − | 0.506960i | ||||
\(977\) | 18.2136i | 0.582706i | 0.956616 | + | 0.291353i | \(0.0941054\pi\) | ||||
−0.956616 | + | 0.291353i | \(0.905895\pi\) | |||||||
\(978\) | −6.51896 | − | 5.52702i | −0.208453 | − | 0.176734i | ||||
\(979\) | −10.0434 | −0.320988 | ||||||||
\(980\) | 4.35412 | + | 26.2586i | 0.139087 | + | 0.838801i | ||||
\(981\) | −6.14687 | −0.196255 | ||||||||
\(982\) | −32.4692 | − | 27.5286i | −1.03613 | − | 0.878472i | ||||
\(983\) | −9.93131 | −0.316760 | −0.158380 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158380 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(984\) | −12.8805 | + | 21.5409i | −0.410616 | + | 0.686699i | ||||
\(985\) | − | 10.2019i | − | 0.325059i | ||||||
\(986\) | −36.8199 | − | 31.2173i | −1.17258 | − | 0.994160i | ||||
\(987\) | − | 0.710307i | − | 0.0226093i | ||||||
\(988\) | −1.01257 | − | 6.10654i | −0.0322141 | − | 0.194275i | ||||
\(989\) | −8.94731 | − | 44.8859i | −0.284508 | − | 1.42729i | ||||
\(990\) | 0.811724 | − | 0.957405i | 0.0257983 | − | 0.0304283i | ||||
\(991\) | − | 26.5845i | − | 0.844485i | −0.906483 | − | 0.422242i | \(-0.861243\pi\) | ||
0.906483 | − | 0.422242i | \(-0.138757\pi\) | |||||||
\(992\) | 11.6750 | − | 29.6956i | 0.370683 | − | 0.942837i | ||||
\(993\) | 14.7506 | 0.468096 | ||||||||
\(994\) | 62.0633 | − | 73.2019i | 1.96853 | − | 2.32182i | ||||
\(995\) | 15.7054 | 0.497894 | ||||||||
\(996\) | 22.0210 | − | 3.65146i | 0.697762 | − | 0.115701i | ||||
\(997\) | 9.89264i | 0.313303i | 0.987654 | + | 0.156652i | \(0.0500700\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(998\) | −23.2281 | − | 19.6937i | −0.735274 | − | 0.623392i | ||||
\(999\) | −3.25973 | −0.103133 |
(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 | 552.2.n.b.91.20 | yes | 24 | |
4.3 | odd | 2 | 2208.2.n.b.367.16 | 24 | |||
8.3 | odd | 2 | inner | 552.2.n.b.91.17 | ✓ | 24 | |
8.5 | even | 2 | 2208.2.n.b.367.10 | 24 | |||
23.22 | odd | 2 | inner | 552.2.n.b.91.19 | yes | 24 | |
92.91 | even | 2 | 2208.2.n.b.367.9 | 24 | |||
184.45 | odd | 2 | 2208.2.n.b.367.15 | 24 | |||
184.91 | even | 2 | inner | 552.2.n.b.91.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.n.b.91.17 | ✓ | 24 | 8.3 | odd | 2 | inner | |
552.2.n.b.91.18 | yes | 24 | 184.91 | even | 2 | inner | |
552.2.n.b.91.19 | yes | 24 | 23.22 | odd | 2 | inner | |
552.2.n.b.91.20 | yes | 24 | 1.1 | even | 1 | trivial | |
2208.2.n.b.367.9 | 24 | 92.91 | even | 2 | |||
2208.2.n.b.367.10 | 24 | 8.5 | even | 2 | |||
2208.2.n.b.367.15 | 24 | 184.45 | odd | 2 | |||
2208.2.n.b.367.16 | 24 | 4.3 | odd | 2 |