Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 697.15 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.a.43.15 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.17211 | + | 0.530977i | −0.971397 | + | 0.237460i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −1.93388 | − | 1.93388i | −0.730937 | − | 0.730937i | 0.239869 | − | 0.970805i | \(-0.422896\pi\) |
−0.970805 | + | 0.239869i | \(0.922896\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.530977 | + | 2.17211i | 0.167910 | + | 0.686882i | ||||
\(11\) | − | 2.54109i | − | 0.766168i | −0.923714 | − | 0.383084i | \(-0.874862\pi\) | ||
0.923714 | − | 0.383084i | \(-0.125138\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | 2.64021i | 0.732261i | 0.930563 | + | 0.366131i | \(0.119318\pi\) | ||||
−0.930563 | + | 0.366131i | \(0.880682\pi\) | |||||||
\(14\) | −1.93388 | + | 1.93388i | −0.516850 | + | 0.516850i | ||||
\(15\) | −1.91137 | − | 1.16046i | −0.493514 | − | 0.299629i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.60448 | 0.874214 | 0.437107 | − | 0.899410i | \(-0.356003\pi\) | ||||
0.437107 | + | 0.899410i | \(0.356003\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.47157 | + | 2.47157i | 0.567017 | + | 0.567017i | 0.931291 | − | 0.364275i | \(-0.118683\pi\) |
−0.364275 | + | 0.931291i | \(0.618683\pi\) | |||||||
\(20\) | 2.17211 | − | 0.530977i | 0.485699 | − | 0.118730i | ||||
\(21\) | − | 2.73491i | − | 0.596807i | ||||||
\(22\) | −2.54109 | −0.541763 | ||||||||
\(23\) | 4.49206i | 0.936659i | 0.883554 | + | 0.468329i | \(0.155144\pi\) | ||||
−0.883554 | + | 0.468329i | \(0.844856\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | 4.43613 | − | 2.30668i | 0.887225 | − | 0.461336i | ||||
\(26\) | 2.64021 | 0.517787 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 1.93388 | + | 1.93388i | 0.365468 | + | 0.365468i | ||||
\(29\) | −4.58885 | + | 4.58885i | −0.852129 | + | 0.852129i | −0.990395 | − | 0.138266i | \(-0.955847\pi\) |
0.138266 | + | 0.990395i | \(0.455847\pi\) | |||||||
\(30\) | −1.16046 | + | 1.91137i | −0.211869 | + | 0.348967i | ||||
\(31\) | 7.33111 | + | 7.33111i | 1.31671 | + | 1.31671i | 0.916368 | + | 0.400338i | \(0.131107\pi\) |
0.400338 | + | 0.916368i | \(0.368893\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.79682 | − | 1.79682i | 0.312787 | − | 0.312787i | ||||
\(34\) | − | 3.60448i | − | 0.618163i | ||||||
\(35\) | 5.22744 | + | 3.17375i | 0.883598 | + | 0.536461i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −1.59211 | + | 5.87071i | −0.261741 | + | 0.965138i | ||||
\(38\) | 2.47157 | − | 2.47157i | 0.400941 | − | 0.400941i | ||||
\(39\) | −1.86691 | + | 1.86691i | −0.298944 | + | 0.298944i | ||||
\(40\) | −0.530977 | − | 2.17211i | −0.0839549 | − | 0.343441i | ||||
\(41\) | − | 4.31993i | − | 0.674660i | −0.941387 | − | 0.337330i | \(-0.890476\pi\) | ||
0.941387 | − | 0.337330i | \(-0.109524\pi\) | |||||||
\(42\) | −2.73491 | −0.422006 | ||||||||
\(43\) | 3.12360i | 0.476344i | 0.971223 | + | 0.238172i | \(0.0765483\pi\) | ||||
−0.971223 | + | 0.238172i | \(0.923452\pi\) | |||||||
\(44\) | 2.54109i | 0.383084i | ||||||||
\(45\) | −0.530977 | − | 2.17211i | −0.0791534 | − | 0.323799i | ||||
\(46\) | 4.49206 | 0.662318 | ||||||||
\(47\) | 4.51187 | + | 4.51187i | 0.658123 | + | 0.658123i | 0.954936 | − | 0.296812i | \(-0.0959236\pi\) |
−0.296812 | + | 0.954936i | \(0.595924\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 0.479758i | 0.0685368i | ||||||||
\(50\) | −2.30668 | − | 4.43613i | −0.326214 | − | 0.627363i | ||||
\(51\) | 2.54875 | + | 2.54875i | 0.356896 | + | 0.356896i | ||||
\(52\) | − | 2.64021i | − | 0.366131i | ||||||
\(53\) | −0.301411 | + | 0.301411i | −0.0414020 | + | 0.0414020i | −0.727505 | − | 0.686103i | \(-0.759320\pi\) |
0.686103 | + | 0.727505i | \(0.259320\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 1.34926 | + | 5.51953i | 0.181934 | + | 0.744253i | ||||
\(56\) | 1.93388 | − | 1.93388i | 0.258425 | − | 0.258425i | ||||
\(57\) | 3.49532i | 0.462967i | ||||||||
\(58\) | 4.58885 | + | 4.58885i | 0.602546 | + | 0.602546i | ||||
\(59\) | 0.813625 | + | 0.813625i | 0.105925 | + | 0.105925i | 0.758083 | − | 0.652158i | \(-0.226136\pi\) |
−0.652158 | + | 0.758083i | \(0.726136\pi\) | |||||||
\(60\) | 1.91137 | + | 1.16046i | 0.246757 | + | 0.149814i | ||||
\(61\) | −0.867564 | − | 0.867564i | −0.111080 | − | 0.111080i | 0.649382 | − | 0.760462i | \(-0.275028\pi\) |
−0.760462 | + | 0.649382i | \(0.775028\pi\) | |||||||
\(62\) | 7.33111 | − | 7.33111i | 0.931051 | − | 0.931051i | ||||
\(63\) | 1.93388 | − | 1.93388i | 0.243646 | − | 0.243646i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.40189 | − | 5.73482i | −0.173883 | − | 0.711317i | ||||
\(66\) | −1.79682 | − | 1.79682i | −0.221174 | − | 0.221174i | ||||
\(67\) | −5.77261 | + | 5.77261i | −0.705237 | + | 0.705237i | −0.965530 | − | 0.260293i | \(-0.916181\pi\) |
0.260293 | + | 0.965530i | \(0.416181\pi\) | |||||||
\(68\) | −3.60448 | −0.437107 | ||||||||
\(69\) | −3.17637 | + | 3.17637i | −0.382389 | + | 0.382389i | ||||
\(70\) | 3.17375 | − | 5.22744i | 0.379336 | − | 0.624798i | ||||
\(71\) | −2.30317 | −0.273336 | −0.136668 | − | 0.990617i | \(-0.543639\pi\) | ||||
−0.136668 | + | 0.990617i | \(0.543639\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.70992 | + | 3.70992i | 0.434213 | + | 0.434213i | 0.890059 | − | 0.455846i | \(-0.150663\pi\) |
−0.455846 | + | 0.890059i | \(0.650663\pi\) | |||||||
\(74\) | 5.87071 | + | 1.59211i | 0.682456 | + | 0.185079i | ||||
\(75\) | 4.76789 | + | 1.50574i | 0.550548 | + | 0.173868i | ||||
\(76\) | −2.47157 | − | 2.47157i | −0.283508 | − | 0.283508i | ||||
\(77\) | −4.91416 | + | 4.91416i | −0.560020 | + | 0.560020i | ||||
\(78\) | 1.86691 | + | 1.86691i | 0.211386 | + | 0.211386i | ||||
\(79\) | 4.70094 | + | 4.70094i | 0.528897 | + | 0.528897i | 0.920243 | − | 0.391347i | \(-0.127991\pi\) |
−0.391347 | + | 0.920243i | \(0.627991\pi\) | |||||||
\(80\) | −2.17211 | + | 0.530977i | −0.242849 | + | 0.0593651i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −4.31993 | −0.477056 | ||||||||
\(83\) | −0.524568 | + | 0.524568i | −0.0575788 | + | 0.0575788i | −0.735310 | − | 0.677731i | \(-0.762963\pi\) |
0.677731 | + | 0.735310i | \(0.262963\pi\) | |||||||
\(84\) | 2.73491i | 0.298404i | ||||||||
\(85\) | −7.82932 | + | 1.91389i | −0.849209 | + | 0.207591i | ||||
\(86\) | 3.12360 | 0.336826 | ||||||||
\(87\) | −6.48962 | −0.695760 | ||||||||
\(88\) | 2.54109 | 0.270881 | ||||||||
\(89\) | −6.69075 | + | 6.69075i | −0.709218 | + | 0.709218i | −0.966371 | − | 0.257153i | \(-0.917216\pi\) |
0.257153 | + | 0.966371i | \(0.417216\pi\) | |||||||
\(90\) | −2.17211 | + | 0.530977i | −0.228961 | + | 0.0559699i | ||||
\(91\) | 5.10583 | − | 5.10583i | 0.535237 | − | 0.535237i | ||||
\(92\) | − | 4.49206i | − | 0.468329i | ||||||
\(93\) | 10.3677i | 1.07509i | ||||||||
\(94\) | 4.51187 | − | 4.51187i | 0.465363 | − | 0.465363i | ||||
\(95\) | −6.68086 | − | 4.05617i | −0.685442 | − | 0.416154i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 17.0294 | 1.72908 | 0.864539 | − | 0.502565i | \(-0.167610\pi\) | ||||
0.864539 | + | 0.502565i | \(0.167610\pi\) | |||||||
\(98\) | 0.479758 | 0.0484628 | ||||||||
\(99\) | 2.54109 | 0.255389 | ||||||||
\(100\) | −4.43613 | + | 2.30668i | −0.443613 | + | 0.230668i | ||||
\(101\) | − | 18.0572i | − | 1.79675i | −0.439225 | − | 0.898377i | \(-0.644747\pi\) | ||
0.439225 | − | 0.898377i | \(-0.355253\pi\) | |||||||
\(102\) | 2.54875 | − | 2.54875i | 0.252364 | − | 0.252364i | ||||
\(103\) | −2.66961 | −0.263044 | −0.131522 | − | 0.991313i | \(-0.541986\pi\) | ||||
−0.131522 | + | 0.991313i | \(0.541986\pi\) | |||||||
\(104\) | −2.64021 | −0.258894 | ||||||||
\(105\) | 1.45218 | + | 5.94054i | 0.141718 | + | 0.579737i | ||||
\(106\) | 0.301411 | + | 0.301411i | 0.0292757 | + | 0.0292757i | ||||
\(107\) | −0.404456 | − | 0.404456i | −0.0391002 | − | 0.0391002i | 0.687286 | − | 0.726387i | \(-0.258802\pi\) |
−0.726387 | + | 0.687286i | \(0.758802\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 1.04982 | + | 1.04982i | 0.100554 | + | 0.100554i | 0.755594 | − | 0.655040i | \(-0.227348\pi\) |
−0.655040 | + | 0.755594i | \(0.727348\pi\) | |||||||
\(110\) | 5.51953 | − | 1.34926i | 0.526267 | − | 0.128647i | ||||
\(111\) | −5.27701 | + | 3.02543i | −0.500871 | + | 0.287161i | ||||
\(112\) | −1.93388 | − | 1.93388i | −0.182734 | − | 0.182734i | ||||
\(113\) | −5.71763 | −0.537869 | −0.268935 | − | 0.963158i | \(-0.586672\pi\) | ||||
−0.268935 | + | 0.963158i | \(0.586672\pi\) | |||||||
\(114\) | 3.49532 | 0.327367 | ||||||||
\(115\) | −2.38518 | − | 9.75725i | −0.222419 | − | 0.909868i | ||||
\(116\) | 4.58885 | − | 4.58885i | 0.426064 | − | 0.426064i | ||||
\(117\) | −2.64021 | −0.244087 | ||||||||
\(118\) | 0.813625 | − | 0.813625i | 0.0749002 | − | 0.0749002i | ||||
\(119\) | −6.97061 | − | 6.97061i | −0.638995 | − | 0.638995i | ||||
\(120\) | 1.16046 | − | 1.91137i | 0.105935 | − | 0.174484i | ||||
\(121\) | 4.54285 | 0.412987 | ||||||||
\(122\) | −0.867564 | + | 0.867564i | −0.0785456 | + | 0.0785456i | ||||
\(123\) | 3.05465 | − | 3.05465i | 0.275429 | − | 0.275429i | ||||
\(124\) | −7.33111 | − | 7.33111i | −0.658353 | − | 0.658353i | ||||
\(125\) | −8.41096 | + | 7.36585i | −0.752299 | + | 0.658822i | ||||
\(126\) | −1.93388 | − | 1.93388i | −0.172283 | − | 0.172283i | ||||
\(127\) | 3.15767 | + | 3.15767i | 0.280198 | + | 0.280198i | 0.833188 | − | 0.552990i | \(-0.186513\pi\) |
−0.552990 | + | 0.833188i | \(0.686513\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −2.20872 | + | 2.20872i | −0.194467 | + | 0.194467i | ||||
\(130\) | −5.73482 | + | 1.40189i | −0.502977 | + | 0.122954i | ||||
\(131\) | −12.5592 | − | 12.5592i | −1.09730 | − | 1.09730i | −0.994725 | − | 0.102577i | \(-0.967291\pi\) |
−0.102577 | − | 0.994725i | \(-0.532709\pi\) | |||||||
\(132\) | −1.79682 | + | 1.79682i | −0.156393 | + | 0.156393i | ||||
\(133\) | − | 9.55941i | − | 0.828906i | ||||||
\(134\) | 5.77261 | + | 5.77261i | 0.498678 | + | 0.498678i | ||||
\(135\) | 1.16046 | − | 1.91137i | 0.0998762 | − | 0.164505i | ||||
\(136\) | 3.60448i | 0.309081i | ||||||||
\(137\) | −12.7858 | − | 12.7858i | −1.09236 | − | 1.09236i | −0.995276 | − | 0.0970857i | \(-0.969048\pi\) |
−0.0970857 | − | 0.995276i | \(-0.530952\pi\) | |||||||
\(138\) | 3.17637 | + | 3.17637i | 0.270390 | + | 0.270390i | ||||
\(139\) | 3.82368 | 0.324321 | 0.162160 | − | 0.986764i | \(-0.448154\pi\) | ||||
0.162160 | + | 0.986764i | \(0.448154\pi\) | |||||||
\(140\) | −5.22744 | − | 3.17375i | −0.441799 | − | 0.268231i | ||||
\(141\) | 6.38074i | 0.537355i | ||||||||
\(142\) | 2.30317i | 0.193278i | ||||||||
\(143\) | 6.70901 | 0.561035 | ||||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 7.53092 | − | 12.4041i | 0.625409 | − | 1.03010i | ||||
\(146\) | 3.70992 | − | 3.70992i | 0.307035 | − | 0.307035i | ||||
\(147\) | −0.339240 | + | 0.339240i | −0.0279800 | + | 0.0279800i | ||||
\(148\) | 1.59211 | − | 5.87071i | 0.130870 | − | 0.482569i | ||||
\(149\) | 4.92924i | 0.403819i | 0.979404 | + | 0.201909i | \(0.0647147\pi\) | ||||
−0.979404 | + | 0.201909i | \(0.935285\pi\) | |||||||
\(150\) | 1.50574 | − | 4.76789i | 0.122943 | − | 0.389296i | ||||
\(151\) | 2.56917i | 0.209076i | 0.994521 | + | 0.104538i | \(0.0333363\pi\) | ||||
−0.994521 | + | 0.104538i | \(0.966664\pi\) | |||||||
\(152\) | −2.47157 | + | 2.47157i | −0.200471 | + | 0.200471i | ||||
\(153\) | 3.60448i | 0.291405i | ||||||||
\(154\) | 4.91416 | + | 4.91416i | 0.395994 | + | 0.395994i | ||||
\(155\) | −19.8166 | − | 12.0313i | −1.59171 | − | 0.966379i | ||||
\(156\) | 1.86691 | − | 1.86691i | 0.149472 | − | 0.149472i | ||||
\(157\) | 10.7956 | + | 10.7956i | 0.861586 | + | 0.861586i | 0.991522 | − | 0.129937i | \(-0.0414774\pi\) |
−0.129937 | + | 0.991522i | \(0.541477\pi\) | |||||||
\(158\) | 4.70094 | − | 4.70094i | 0.373986 | − | 0.373986i | ||||
\(159\) | −0.426260 | −0.0338046 | ||||||||
\(160\) | 0.530977 | + | 2.17211i | 0.0419774 | + | 0.171720i | ||||
\(161\) | 8.68709 | − | 8.68709i | 0.684638 | − | 0.684638i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 2.00094 | 0.156726 | 0.0783628 | − | 0.996925i | \(-0.475031\pi\) | ||||
0.0783628 | + | 0.996925i | \(0.475031\pi\) | |||||||
\(164\) | 4.31993i | 0.337330i | ||||||||
\(165\) | −2.94883 | + | 4.85697i | −0.229566 | + | 0.378115i | ||||
\(166\) | 0.524568 | + | 0.524568i | 0.0407144 | + | 0.0407144i | ||||
\(167\) | 3.34903 | 0.259156 | 0.129578 | − | 0.991569i | \(-0.458638\pi\) | ||||
0.129578 | + | 0.991569i | \(0.458638\pi\) | |||||||
\(168\) | 2.73491 | 0.211003 | ||||||||
\(169\) | 6.02931 | 0.463793 | ||||||||
\(170\) | 1.91389 | + | 7.82932i | 0.146789 | + | 0.600481i | ||||
\(171\) | −2.47157 | + | 2.47157i | −0.189006 | + | 0.189006i | ||||
\(172\) | − | 3.12360i | − | 0.238172i | ||||||
\(173\) | −7.11846 | − | 7.11846i | −0.541206 | − | 0.541206i | 0.382676 | − | 0.923882i | \(-0.375002\pi\) |
−0.923882 | + | 0.382676i | \(0.875002\pi\) | |||||||
\(174\) | 6.48962i | 0.491977i | ||||||||
\(175\) | −13.0398 | − | 4.11808i | −0.985713 | − | 0.311298i | ||||
\(176\) | − | 2.54109i | − | 0.191542i | ||||||
\(177\) | 1.15064i | 0.0864873i | ||||||||
\(178\) | 6.69075 | + | 6.69075i | 0.501493 | + | 0.501493i | ||||
\(179\) | 8.68094 | − | 8.68094i | 0.648844 | − | 0.648844i | −0.303869 | − | 0.952714i | \(-0.598279\pi\) |
0.952714 | + | 0.303869i | \(0.0982787\pi\) | |||||||
\(180\) | 0.530977 | + | 2.17211i | 0.0395767 | + | 0.161900i | ||||
\(181\) | 14.0432 | 1.04382 | 0.521912 | − | 0.852999i | \(-0.325219\pi\) | ||||
0.521912 | + | 0.852999i | \(0.325219\pi\) | |||||||
\(182\) | −5.10583 | − | 5.10583i | −0.378470 | − | 0.378470i | ||||
\(183\) | − | 1.22692i | − | 0.0906966i | ||||||
\(184\) | −4.49206 | −0.331159 | ||||||||
\(185\) | 0.341020 | − | 13.5972i | 0.0250723 | − | 0.999686i | ||||
\(186\) | 10.3677 | 0.760200 | ||||||||
\(187\) | − | 9.15930i | − | 0.669795i | ||||||
\(188\) | −4.51187 | − | 4.51187i | −0.329062 | − | 0.329062i | ||||
\(189\) | 2.73491 | 0.198936 | ||||||||
\(190\) | −4.05617 | + | 6.68086i | −0.294266 | + | 0.484681i | ||||
\(191\) | −1.64289 | + | 1.64289i | −0.118876 | + | 0.118876i | −0.764042 | − | 0.645166i | \(-0.776788\pi\) |
0.645166 | + | 0.764042i | \(0.276788\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 13.9313i | 1.00280i | 0.865217 | + | 0.501398i | \(0.167181\pi\) | ||||
−0.865217 | + | 0.501398i | \(0.832819\pi\) | |||||||
\(194\) | − | 17.0294i | − | 1.22264i | ||||||
\(195\) | 3.06384 | − | 5.04642i | 0.219406 | − | 0.361381i | ||||
\(196\) | − | 0.479758i | − | 0.0342684i | ||||||
\(197\) | 18.7947 | + | 18.7947i | 1.33907 | + | 1.33907i | 0.896962 | + | 0.442107i | \(0.145769\pi\) |
0.442107 | + | 0.896962i | \(0.354231\pi\) | |||||||
\(198\) | − | 2.54109i | − | 0.180588i | ||||||
\(199\) | −3.23872 | + | 3.23872i | −0.229587 | + | 0.229587i | −0.812520 | − | 0.582933i | \(-0.801905\pi\) |
0.582933 | + | 0.812520i | \(0.301905\pi\) | |||||||
\(200\) | 2.30668 | + | 4.43613i | 0.163107 | + | 0.313681i | ||||
\(201\) | −8.16371 | −0.575824 | ||||||||
\(202\) | −18.0572 | −1.27050 | ||||||||
\(203\) | 17.7486 | 1.24570 | ||||||||
\(204\) | −2.54875 | − | 2.54875i | −0.178448 | − | 0.178448i | ||||
\(205\) | 2.29378 | + | 9.38336i | 0.160205 | + | 0.655362i | ||||
\(206\) | 2.66961i | 0.186000i | ||||||||
\(207\) | −4.49206 | −0.312220 | ||||||||
\(208\) | 2.64021i | 0.183065i | ||||||||
\(209\) | 6.28048 | − | 6.28048i | 0.434430 | − | 0.434430i | ||||
\(210\) | 5.94054 | − | 1.45218i | 0.409936 | − | 0.100210i | ||||
\(211\) | −13.4040 | −0.922767 | −0.461384 | − | 0.887201i | \(-0.652647\pi\) | ||||
−0.461384 | + | 0.887201i | \(0.652647\pi\) | |||||||
\(212\) | 0.301411 | − | 0.301411i | 0.0207010 | − | 0.0207010i | ||||
\(213\) | −1.62859 | − | 1.62859i | −0.111589 | − | 0.111589i | ||||
\(214\) | −0.404456 | + | 0.404456i | −0.0276480 | + | 0.0276480i | ||||
\(215\) | −1.65856 | − | 6.78480i | −0.113113 | − | 0.462720i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | − | 28.3549i | − | 1.92486i | ||||||
\(218\) | 1.04982 | − | 1.04982i | 0.0711026 | − | 0.0711026i | ||||
\(219\) | 5.24662i | 0.354534i | ||||||||
\(220\) | −1.34926 | − | 5.51953i | −0.0909672 | − | 0.372127i | ||||
\(221\) | 9.51656i | 0.640153i | ||||||||
\(222\) | 3.02543 | + | 5.27701i | 0.203053 | + | 0.354169i | ||||
\(223\) | −18.2552 | + | 18.2552i | −1.22246 | + | 1.22246i | −0.255707 | + | 0.966754i | \(0.582308\pi\) |
−0.966754 | + | 0.255707i | \(0.917692\pi\) | |||||||
\(224\) | −1.93388 | + | 1.93388i | −0.129213 | + | 0.129213i | ||||
\(225\) | 2.30668 | + | 4.43613i | 0.153779 | + | 0.295742i | ||||
\(226\) | 5.71763i | 0.380331i | ||||||||
\(227\) | −20.3161 | −1.34843 | −0.674215 | − | 0.738535i | \(-0.735518\pi\) | ||||
−0.674215 | + | 0.738535i | \(0.735518\pi\) | |||||||
\(228\) | − | 3.49532i | − | 0.231484i | ||||||
\(229\) | − | 23.8741i | − | 1.57764i | −0.614623 | − | 0.788821i | \(-0.710692\pi\) | ||
0.614623 | − | 0.788821i | \(-0.289308\pi\) | |||||||
\(230\) | −9.75725 | + | 2.38518i | −0.643374 | + | 0.157274i | ||||
\(231\) | −6.94967 | −0.457255 | ||||||||
\(232\) | −4.58885 | − | 4.58885i | −0.301273 | − | 0.301273i | ||||
\(233\) | 0.0502450 | + | 0.0502450i | 0.00329166 | + | 0.00329166i | 0.708751 | − | 0.705459i | \(-0.249259\pi\) |
−0.705459 | + | 0.708751i | \(0.749259\pi\) | |||||||
\(234\) | 2.64021i | 0.172596i | ||||||||
\(235\) | −12.1960 | − | 7.40457i | −0.795577 | − | 0.483021i | ||||
\(236\) | −0.813625 | − | 0.813625i | −0.0529625 | − | 0.0529625i | ||||
\(237\) | 6.64813i | 0.431842i | ||||||||
\(238\) | −6.97061 | + | 6.97061i | −0.451838 | + | 0.451838i | ||||
\(239\) | 11.3273 | + | 11.3273i | 0.732705 | + | 0.732705i | 0.971155 | − | 0.238450i | \(-0.0766394\pi\) |
−0.238450 | + | 0.971155i | \(0.576639\pi\) | |||||||
\(240\) | −1.91137 | − | 1.16046i | −0.123379 | − | 0.0749071i | ||||
\(241\) | −3.69272 | + | 3.69272i | −0.237869 | + | 0.237869i | −0.815967 | − | 0.578098i | \(-0.803795\pi\) |
0.578098 | + | 0.815967i | \(0.303795\pi\) | |||||||
\(242\) | − | 4.54285i | − | 0.292026i | ||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0.867564 | + | 0.867564i | 0.0555401 | + | 0.0555401i | ||||
\(245\) | −0.254740 | − | 1.04209i | −0.0162748 | − | 0.0665765i | ||||
\(246\) | −3.05465 | − | 3.05465i | −0.194757 | − | 0.194757i | ||||
\(247\) | −6.52545 | + | 6.52545i | −0.415204 | + | 0.415204i | ||||
\(248\) | −7.33111 | + | 7.33111i | −0.465526 | + | 0.465526i | ||||
\(249\) | −0.741852 | −0.0470129 | ||||||||
\(250\) | 7.36585 | + | 8.41096i | 0.465857 | + | 0.531956i | ||||
\(251\) | −8.29215 | − | 8.29215i | −0.523396 | − | 0.523396i | 0.395199 | − | 0.918595i | \(-0.370675\pi\) |
−0.918595 | + | 0.395199i | \(0.870675\pi\) | |||||||
\(252\) | −1.93388 | + | 1.93388i | −0.121823 | + | 0.121823i | ||||
\(253\) | 11.4147 | 0.717638 | ||||||||
\(254\) | 3.15767 | − | 3.15767i | 0.198130 | − | 0.198130i | ||||
\(255\) | −6.88949 | − | 4.18284i | −0.431437 | − | 0.261939i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.06813 | 0.0666279 | 0.0333140 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333140 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(258\) | 2.20872 | + | 2.20872i | 0.137509 | + | 0.137509i | ||||
\(259\) | 14.4322 | − | 8.27428i | 0.896771 | − | 0.514139i | ||||
\(260\) | 1.40189 | + | 5.73482i | 0.0869415 | + | 0.355658i | ||||
\(261\) | −4.58885 | − | 4.58885i | −0.284043 | − | 0.284043i | ||||
\(262\) | −12.5592 | + | 12.5592i | −0.775909 | + | 0.775909i | ||||
\(263\) | 22.2567 | + | 22.2567i | 1.37240 | + | 1.37240i | 0.856867 | + | 0.515538i | \(0.172408\pi\) |
0.515538 | + | 0.856867i | \(0.327592\pi\) | |||||||
\(264\) | 1.79682 | + | 1.79682i | 0.110587 | + | 0.110587i | ||||
\(265\) | 0.494656 | − | 0.814742i | 0.0303865 | − | 0.0500492i | ||||
\(266\) | −9.55941 | −0.586125 | ||||||||
\(267\) | −9.46214 | −0.579074 | ||||||||
\(268\) | 5.77261 | − | 5.77261i | 0.352618 | − | 0.352618i | ||||
\(269\) | − | 1.98048i | − | 0.120752i | −0.998176 | − | 0.0603760i | \(-0.980770\pi\) | ||
0.998176 | − | 0.0603760i | \(-0.0192300\pi\) | |||||||
\(270\) | −1.91137 | − | 1.16046i | −0.116322 | − | 0.0706231i | ||||
\(271\) | −20.2119 | −1.22779 | −0.613894 | − | 0.789389i | \(-0.710398\pi\) | ||||
−0.613894 | + | 0.789389i | \(0.710398\pi\) | |||||||
\(272\) | 3.60448 | 0.218553 | ||||||||
\(273\) | 7.22074 | 0.437019 | ||||||||
\(274\) | −12.7858 | + | 12.7858i | −0.772416 | + | 0.772416i | ||||
\(275\) | −5.86149 | − | 11.2726i | −0.353461 | − | 0.679763i | ||||
\(276\) | 3.17637 | − | 3.17637i | 0.191195 | − | 0.191195i | ||||
\(277\) | − | 26.8225i | − | 1.61161i | −0.592181 | − | 0.805805i | \(-0.701733\pi\) | ||
0.592181 | − | 0.805805i | \(-0.298267\pi\) | |||||||
\(278\) | − | 3.82368i | − | 0.229329i | ||||||
\(279\) | −7.33111 | + | 7.33111i | −0.438902 | + | 0.438902i | ||||
\(280\) | −3.17375 | + | 5.22744i | −0.189668 | + | 0.312399i | ||||
\(281\) | 11.8287 | − | 11.8287i | 0.705642 | − | 0.705642i | −0.259974 | − | 0.965616i | \(-0.583714\pi\) |
0.965616 | + | 0.259974i | \(0.0837140\pi\) | |||||||
\(282\) | 6.38074 | 0.379968 | ||||||||
\(283\) | −20.4845 | −1.21768 | −0.608840 | − | 0.793293i | \(-0.708365\pi\) | ||||
−0.608840 | + | 0.793293i | \(0.708365\pi\) | |||||||
\(284\) | 2.30317 | 0.136668 | ||||||||
\(285\) | −1.85594 | − | 7.59223i | −0.109936 | − | 0.449725i | ||||
\(286\) | − | 6.70901i | − | 0.396712i | ||||||
\(287\) | −8.35421 | + | 8.35421i | −0.493133 | + | 0.493133i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −4.00775 | −0.235750 | ||||||||
\(290\) | −12.4041 | − | 7.53092i | −0.728392 | − | 0.442231i | ||||
\(291\) | 12.0416 | + | 12.0416i | 0.705893 | + | 0.705893i | ||||
\(292\) | −3.70992 | − | 3.70992i | −0.217107 | − | 0.217107i | ||||
\(293\) | −18.0953 | + | 18.0953i | −1.05714 | + | 1.05714i | −0.0588702 | + | 0.998266i | \(0.518750\pi\) |
−0.998266 | + | 0.0588702i | \(0.981250\pi\) | |||||||
\(294\) | 0.339240 | + | 0.339240i | 0.0197849 | + | 0.0197849i | ||||
\(295\) | −2.19930 | − | 1.33527i | −0.128048 | − | 0.0777422i | ||||
\(296\) | −5.87071 | − | 1.59211i | −0.341228 | − | 0.0925393i | ||||
\(297\) | 1.79682 | + | 1.79682i | 0.104262 | + | 0.104262i | ||||
\(298\) | 4.92924 | 0.285543 | ||||||||
\(299\) | −11.8600 | −0.685879 | ||||||||
\(300\) | −4.76789 | − | 1.50574i | −0.275274 | − | 0.0869342i | ||||
\(301\) | 6.04066 | − | 6.04066i | 0.348178 | − | 0.348178i | ||||
\(302\) | 2.56917 | 0.147839 | ||||||||
\(303\) | 12.7683 | − | 12.7683i | 0.733522 | − | 0.733522i | ||||
\(304\) | 2.47157 | + | 2.47157i | 0.141754 | + | 0.141754i | ||||
\(305\) | 2.34510 | + | 1.42379i | 0.134280 | + | 0.0815259i | ||||
\(306\) | 3.60448 | 0.206054 | ||||||||
\(307\) | −22.5634 | + | 22.5634i | −1.28776 | + | 1.28776i | −0.351616 | + | 0.936144i | \(0.614368\pi\) |
−0.936144 | + | 0.351616i | \(0.885632\pi\) | |||||||
\(308\) | 4.91416 | − | 4.91416i | 0.280010 | − | 0.280010i | ||||
\(309\) | −1.88770 | − | 1.88770i | −0.107387 | − | 0.107387i | ||||
\(310\) | −12.0313 | + | 19.8166i | −0.683333 | + | 1.12551i | ||||
\(311\) | 17.2148 | + | 17.2148i | 0.976159 | + | 0.976159i | 0.999722 | − | 0.0235634i | \(-0.00750115\pi\) |
−0.0235634 | + | 0.999722i | \(0.507501\pi\) | |||||||
\(312\) | −1.86691 | − | 1.86691i | −0.105693 | − | 0.105693i | ||||
\(313\) | 30.7702i | 1.73923i | 0.493729 | + | 0.869616i | \(0.335634\pi\) | ||||
−0.493729 | + | 0.869616i | \(0.664366\pi\) | |||||||
\(314\) | 10.7956 | − | 10.7956i | 0.609233 | − | 0.609233i | ||||
\(315\) | −3.17375 | + | 5.22744i | −0.178820 | + | 0.294533i | ||||
\(316\) | −4.70094 | − | 4.70094i | −0.264448 | − | 0.264448i | ||||
\(317\) | −12.5932 | + | 12.5932i | −0.707307 | + | 0.707307i | −0.965968 | − | 0.258661i | \(-0.916719\pi\) |
0.258661 | + | 0.965968i | \(0.416719\pi\) | |||||||
\(318\) | 0.426260i | 0.0239035i | ||||||||
\(319\) | 11.6607 | + | 11.6607i | 0.652874 | + | 0.652874i | ||||
\(320\) | 2.17211 | − | 0.530977i | 0.121425 | − | 0.0296825i | ||||
\(321\) | − | 0.571987i | − | 0.0319252i | ||||||
\(322\) | −8.68709 | − | 8.68709i | −0.484112 | − | 0.484112i | ||||
\(323\) | 8.90871 | + | 8.90871i | 0.495694 | + | 0.495694i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 6.09012 | + | 11.7123i | 0.337819 | + | 0.649681i | ||||
\(326\) | − | 2.00094i | − | 0.110822i | ||||||
\(327\) | 1.48467i | 0.0821022i | ||||||||
\(328\) | 4.31993 | 0.238528 | ||||||||
\(329\) | − | 17.4508i | − | 0.962093i | ||||||
\(330\) | 4.85697 | + | 2.94883i | 0.267367 | + | 0.162327i | ||||
\(331\) | 12.4856 | − | 12.4856i | 0.686272 | − | 0.686272i | −0.275134 | − | 0.961406i | \(-0.588722\pi\) |
0.961406 | + | 0.275134i | \(0.0887222\pi\) | |||||||
\(332\) | 0.524568 | − | 0.524568i | 0.0287894 | − | 0.0287894i | ||||
\(333\) | −5.87071 | − | 1.59211i | −0.321713 | − | 0.0872469i | ||||
\(334\) | − | 3.34903i | − | 0.183251i | ||||||
\(335\) | 9.47363 | − | 15.6039i | 0.517599 | − | 0.852531i | ||||
\(336\) | − | 2.73491i | − | 0.149202i | ||||||
\(337\) | −2.01004 | + | 2.01004i | −0.109494 | + | 0.109494i | −0.759731 | − | 0.650237i | \(-0.774669\pi\) |
0.650237 | + | 0.759731i | \(0.274669\pi\) | |||||||
\(338\) | − | 6.02931i | − | 0.327951i | ||||||
\(339\) | −4.04297 | − | 4.04297i | −0.219584 | − | 0.219584i | ||||
\(340\) | 7.82932 | − | 1.91389i | 0.424604 | − | 0.103796i | ||||
\(341\) | 18.6290 | − | 18.6290i | 1.00882 | − | 1.00882i | ||||
\(342\) | 2.47157 | + | 2.47157i | 0.133647 | + | 0.133647i | ||||
\(343\) | −12.6093 | + | 12.6093i | −0.680841 | + | 0.680841i | ||||
\(344\) | −3.12360 | −0.168413 | ||||||||
\(345\) | 5.21284 | − | 8.58599i | 0.280650 | − | 0.462254i | ||||
\(346\) | −7.11846 | + | 7.11846i | −0.382691 | + | 0.382691i | ||||
\(347\) | 15.1173i | 0.811539i | 0.913975 | + | 0.405770i | \(0.132996\pi\) | ||||
−0.913975 | + | 0.405770i | \(0.867004\pi\) | |||||||
\(348\) | 6.48962 | 0.347880 | ||||||||
\(349\) | 13.6893i | 0.732771i | 0.930463 | + | 0.366386i | \(0.119405\pi\) | ||||
−0.930463 | + | 0.366386i | \(0.880595\pi\) | |||||||
\(350\) | −4.11808 | + | 13.0398i | −0.220121 | + | 0.697005i | ||||
\(351\) | −1.86691 | − | 1.86691i | −0.0996482 | − | 0.0996482i | ||||
\(352\) | −2.54109 | −0.135441 | ||||||||
\(353\) | −31.3775 | −1.67006 | −0.835029 | − | 0.550206i | \(-0.814549\pi\) | ||||
−0.835029 | + | 0.550206i | \(0.814549\pi\) | |||||||
\(354\) | 1.15064 | 0.0611558 | ||||||||
\(355\) | 5.00274 | − | 1.22293i | 0.265518 | − | 0.0649065i | ||||
\(356\) | 6.69075 | − | 6.69075i | 0.354609 | − | 0.354609i | ||||
\(357\) | − | 9.85793i | − | 0.521737i | ||||||
\(358\) | −8.68094 | − | 8.68094i | −0.458802 | − | 0.458802i | ||||
\(359\) | − | 32.4157i | − | 1.71083i | −0.517941 | − | 0.855416i | \(-0.673301\pi\) | ||
0.517941 | − | 0.855416i | \(-0.326699\pi\) | |||||||
\(360\) | 2.17211 | − | 0.530977i | 0.114480 | − | 0.0279850i | ||||
\(361\) | − | 6.78271i | − | 0.356985i | ||||||
\(362\) | − | 14.0432i | − | 0.738096i | ||||||
\(363\) | 3.21228 | + | 3.21228i | 0.168601 | + | 0.168601i | ||||
\(364\) | −5.10583 | + | 5.10583i | −0.267618 | + | 0.267618i | ||||
\(365\) | −10.0282 | − | 6.08847i | −0.524902 | − | 0.318685i | ||||
\(366\) | −1.22692 | −0.0641322 | ||||||||
\(367\) | 9.63234 | + | 9.63234i | 0.502804 | + | 0.502804i | 0.912308 | − | 0.409504i | \(-0.134298\pi\) |
−0.409504 | + | 0.912308i | \(0.634298\pi\) | |||||||
\(368\) | 4.49206i | 0.234165i | ||||||||
\(369\) | 4.31993 | 0.224887 | ||||||||
\(370\) | −13.5972 | − | 0.341020i | −0.706884 | − | 0.0177288i | ||||
\(371\) | 1.16579 | 0.0605245 | ||||||||
\(372\) | − | 10.3677i | − | 0.537543i | ||||||
\(373\) | −21.6306 | − | 21.6306i | −1.11999 | − | 1.11999i | −0.991742 | − | 0.128250i | \(-0.959064\pi\) |
−0.128250 | − | 0.991742i | \(-0.540936\pi\) | |||||||
\(374\) | −9.15930 | −0.473616 | ||||||||
\(375\) | −11.1559 | − | 0.739003i | −0.576088 | − | 0.0381620i | ||||
\(376\) | −4.51187 | + | 4.51187i | −0.232682 | + | 0.232682i | ||||
\(377\) | −12.1155 | − | 12.1155i | −0.623981 | − | 0.623981i | ||||
\(378\) | − | 2.73491i | − | 0.140669i | ||||||
\(379\) | 0.115662i | 0.00594116i | 0.999996 | + | 0.00297058i | \(0.000945566\pi\) | ||||
−0.999996 | + | 0.00297058i | \(0.999054\pi\) | |||||||
\(380\) | 6.68086 | + | 4.05617i | 0.342721 | + | 0.208077i | ||||
\(381\) | 4.46562i | 0.228781i | ||||||||
\(382\) | 1.64289 | + | 1.64289i | 0.0840578 | + | 0.0840578i | ||||
\(383\) | − | 1.75588i | − | 0.0897211i | −0.998993 | − | 0.0448606i | \(-0.985716\pi\) | ||
0.998993 | − | 0.0448606i | \(-0.0142844\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 8.06479 | − | 13.2834i | 0.411020 | − | 0.676985i | ||||
\(386\) | 13.9313 | 0.709084 | ||||||||
\(387\) | −3.12360 | −0.158781 | ||||||||
\(388\) | −17.0294 | −0.864539 | ||||||||
\(389\) | −11.3156 | − | 11.3156i | −0.573722 | − | 0.573722i | 0.359445 | − | 0.933166i | \(-0.382966\pi\) |
−0.933166 | + | 0.359445i | \(0.882966\pi\) | |||||||
\(390\) | −5.04642 | − | 3.06384i | −0.255535 | − | 0.155144i | ||||
\(391\) | 16.1915i | 0.818840i | ||||||||
\(392\) | −0.479758 | −0.0242314 | ||||||||
\(393\) | − | 17.7614i | − | 0.895943i | ||||||
\(394\) | 18.7947 | − | 18.7947i | 0.946865 | − | 0.946865i | ||||
\(395\) | −12.7070 | − | 7.71486i | −0.639361 | − | 0.388177i | ||||
\(396\) | −2.54109 | −0.127695 | ||||||||
\(397\) | 10.5898 | − | 10.5898i | 0.531488 | − | 0.531488i | −0.389527 | − | 0.921015i | \(-0.627361\pi\) |
0.921015 | + | 0.389527i | \(0.127361\pi\) | |||||||
\(398\) | 3.23872 | + | 3.23872i | 0.162342 | + | 0.162342i | ||||
\(399\) | 6.75953 | − | 6.75953i | 0.338400 | − | 0.338400i | ||||
\(400\) | 4.43613 | − | 2.30668i | 0.221806 | − | 0.115334i | ||||
\(401\) | 6.78291 | + | 6.78291i | 0.338722 | + | 0.338722i | 0.855886 | − | 0.517164i | \(-0.173012\pi\) |
−0.517164 | + | 0.855886i | \(0.673012\pi\) | |||||||
\(402\) | 8.16371i | 0.407169i | ||||||||
\(403\) | −19.3556 | + | 19.3556i | −0.964173 | + | 0.964173i | ||||
\(404\) | 18.0572i | 0.898377i | ||||||||
\(405\) | 2.17211 | − | 0.530977i | 0.107933 | − | 0.0263845i | ||||
\(406\) | − | 17.7486i | − | 0.880846i | ||||||
\(407\) | 14.9180 | + | 4.04569i | 0.739458 | + | 0.200537i | ||||
\(408\) | −2.54875 | + | 2.54875i | −0.126182 | + | 0.126182i | ||||
\(409\) | 12.5316 | − | 12.5316i | 0.619650 | − | 0.619650i | −0.325792 | − | 0.945442i | \(-0.605631\pi\) |
0.945442 | + | 0.325792i | \(0.105631\pi\) | |||||||
\(410\) | 9.38336 | − | 2.29378i | 0.463411 | − | 0.113282i | ||||
\(411\) | − | 18.0818i | − | 0.891910i | ||||||
\(412\) | 2.66961 | 0.131522 | ||||||||
\(413\) | − | 3.14690i | − | 0.154849i | ||||||
\(414\) | 4.49206i | 0.220773i | ||||||||
\(415\) | 0.860886 | − | 1.41795i | 0.0422592 | − | 0.0696046i | ||||
\(416\) | 2.64021 | 0.129447 | ||||||||
\(417\) | 2.70375 | + | 2.70375i | 0.132403 | + | 0.132403i | ||||
\(418\) | −6.28048 | − | 6.28048i | −0.307188 | − | 0.307188i | ||||
\(419\) | 21.4066i | 1.04578i | 0.852400 | + | 0.522891i | \(0.175146\pi\) | ||||
−0.852400 | + | 0.522891i | \(0.824854\pi\) | |||||||
\(420\) | −1.45218 | − | 5.94054i | −0.0708590 | − | 0.289868i | ||||
\(421\) | 10.7024 | + | 10.7024i | 0.521601 | + | 0.521601i | 0.918055 | − | 0.396454i | \(-0.129759\pi\) |
−0.396454 | + | 0.918055i | \(0.629759\pi\) | |||||||
\(422\) | 13.4040i | 0.652495i | ||||||||
\(423\) | −4.51187 | + | 4.51187i | −0.219374 | + | 0.219374i | ||||
\(424\) | −0.301411 | − | 0.301411i | −0.0146378 | − | 0.0146378i | ||||
\(425\) | 15.9899 | − | 8.31438i | 0.775625 | − | 0.403307i | ||||
\(426\) | −1.62859 | + | 1.62859i | −0.0789053 | + | 0.0789053i | ||||
\(427\) | 3.35552i | 0.162385i | ||||||||
\(428\) | 0.404456 | + | 0.404456i | 0.0195501 | + | 0.0195501i | ||||
\(429\) | 4.74398 | + | 4.74398i | 0.229042 | + | 0.229042i | ||||
\(430\) | −6.78480 | + | 1.65856i | −0.327192 | + | 0.0799829i | ||||
\(431\) | −11.7768 | − | 11.7768i | −0.567266 | − | 0.567266i | 0.364095 | − | 0.931362i | \(-0.381378\pi\) |
−0.931362 | + | 0.364095i | \(0.881378\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 12.9115 | − | 12.9115i | 0.620487 | − | 0.620487i | −0.325169 | − | 0.945656i | \(-0.605421\pi\) |
0.945656 | + | 0.325169i | \(0.105421\pi\) | |||||||
\(434\) | −28.3549 | −1.36108 | ||||||||
\(435\) | 14.0962 | − | 3.44584i | 0.675860 | − | 0.165215i | ||||
\(436\) | −1.04982 | − | 1.04982i | −0.0502771 | − | 0.0502771i | ||||
\(437\) | −11.1024 | + | 11.1024i | −0.531101 | + | 0.531101i | ||||
\(438\) | 5.24662 | 0.250693 | ||||||||
\(439\) | 12.6631 | − | 12.6631i | 0.604375 | − | 0.604375i | −0.337095 | − | 0.941471i | \(-0.609444\pi\) |
0.941471 | + | 0.337095i | \(0.109444\pi\) | |||||||
\(440\) | −5.51953 | + | 1.34926i | −0.263133 | + | 0.0643235i | ||||
\(441\) | −0.479758 | −0.0228456 | ||||||||
\(442\) | 9.51656 | 0.452657 | ||||||||
\(443\) | 19.8789 | + | 19.8789i | 0.944476 | + | 0.944476i | 0.998538 | − | 0.0540616i | \(-0.0172167\pi\) |
−0.0540616 | + | 0.998538i | \(0.517217\pi\) | |||||||
\(444\) | 5.27701 | − | 3.02543i | 0.250436 | − | 0.143580i | ||||
\(445\) | 10.9804 | − | 18.0857i | 0.520521 | − | 0.857343i | ||||
\(446\) | 18.2552 | + | 18.2552i | 0.864411 | + | 0.864411i | ||||
\(447\) | −3.48550 | + | 3.48550i | −0.164858 | + | 0.164858i | ||||
\(448\) | 1.93388 | + | 1.93388i | 0.0913671 | + | 0.0913671i | ||||
\(449\) | 10.2591 | + | 10.2591i | 0.484159 | + | 0.484159i | 0.906457 | − | 0.422298i | \(-0.138776\pi\) |
−0.422298 | + | 0.906457i | \(0.638776\pi\) | |||||||
\(450\) | 4.43613 | − | 2.30668i | 0.209121 | − | 0.108738i | ||||
\(451\) | −10.9773 | −0.516902 | ||||||||
\(452\) | 5.71763 | 0.268935 | ||||||||
\(453\) | −1.81667 | + | 1.81667i | −0.0853548 | + | 0.0853548i | ||||
\(454\) | 20.3161i | 0.953483i | ||||||||
\(455\) | −8.37935 | + | 13.8015i | −0.392830 | + | 0.647025i | ||||
\(456\) | −3.49532 | −0.163684 | ||||||||
\(457\) | −3.03992 | −0.142202 | −0.0711008 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0711008 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(458\) | −23.8741 | −1.11556 | ||||||||
\(459\) | −2.54875 | + | 2.54875i | −0.118965 | + | 0.118965i | ||||
\(460\) | 2.38518 | + | 9.75725i | 0.111210 | + | 0.454934i | ||||
\(461\) | −2.13391 | + | 2.13391i | −0.0993859 | + | 0.0993859i | −0.755051 | − | 0.655666i | \(-0.772388\pi\) |
0.655666 | + | 0.755051i | \(0.272388\pi\) | |||||||
\(462\) | 6.94967i | 0.323328i | ||||||||
\(463\) | 20.8314i | 0.968118i | 0.875035 | + | 0.484059i | \(0.160838\pi\) | ||||
−0.875035 | + | 0.484059i | \(0.839162\pi\) | |||||||
\(464\) | −4.58885 | + | 4.58885i | −0.213032 | + | 0.213032i | ||||
\(465\) | −5.50504 | − | 22.5199i | −0.255290 | − | 1.04434i | ||||
\(466\) | 0.0502450 | − | 0.0502450i | 0.00232756 | − | 0.00232756i | ||||
\(467\) | 30.6842 | 1.41990 | 0.709949 | − | 0.704253i | \(-0.248718\pi\) | ||||
0.709949 | + | 0.704253i | \(0.248718\pi\) | |||||||
\(468\) | 2.64021 | 0.122044 | ||||||||
\(469\) | 22.3270 | 1.03097 | ||||||||
\(470\) | −7.40457 | + | 12.1960i | −0.341547 | + | 0.562558i | ||||
\(471\) | 15.2673i | 0.703482i | ||||||||
\(472\) | −0.813625 | + | 0.813625i | −0.0374501 | + | 0.0374501i | ||||
\(473\) | 7.93735 | 0.364960 | ||||||||
\(474\) | 6.64813 | 0.305359 | ||||||||
\(475\) | 16.6653 | + | 5.26306i | 0.764657 | + | 0.241486i | ||||
\(476\) | 6.97061 | + | 6.97061i | 0.319497 | + | 0.319497i | ||||
\(477\) | −0.301411 | − | 0.301411i | −0.0138007 | − | 0.0138007i | ||||
\(478\) | 11.3273 | − | 11.3273i | 0.518100 | − | 0.518100i | ||||
\(479\) | −3.72623 | − | 3.72623i | −0.170256 | − | 0.170256i | 0.616836 | − | 0.787092i | \(-0.288414\pi\) |
−0.787092 | + | 0.616836i | \(0.788414\pi\) | |||||||
\(480\) | −1.16046 | + | 1.91137i | −0.0529673 | + | 0.0872418i | ||||
\(481\) | −15.4999 | − | 4.20349i | −0.706734 | − | 0.191663i | ||||
\(482\) | 3.69272 | + | 3.69272i | 0.168199 | + | 0.168199i | ||||
\(483\) | 12.2854 | 0.559005 | ||||||||
\(484\) | −4.54285 | −0.206493 | ||||||||
\(485\) | −36.9898 | + | 9.04225i | −1.67962 | + | 0.410587i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 19.2486 | 0.872239 | 0.436120 | − | 0.899889i | \(-0.356352\pi\) | ||||
0.436120 | + | 0.899889i | \(0.356352\pi\) | |||||||
\(488\) | 0.867564 | − | 0.867564i | 0.0392728 | − | 0.0392728i | ||||
\(489\) | 1.41488 | + | 1.41488i | 0.0639830 | + | 0.0639830i | ||||
\(490\) | −1.04209 | + | 0.254740i | −0.0470767 | + | 0.0115080i | ||||
\(491\) | −7.57274 | −0.341753 | −0.170877 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170877 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(492\) | −3.05465 | + | 3.05465i | −0.137714 | + | 0.137714i | ||||
\(493\) | −16.5404 | + | 16.5404i | −0.744943 | + | 0.744943i | ||||
\(494\) | 6.52545 | + | 6.52545i | 0.293594 | + | 0.293594i | ||||
\(495\) | −5.51953 | + | 1.34926i | −0.248084 | + | 0.0606448i | ||||
\(496\) | 7.33111 | + | 7.33111i | 0.329176 | + | 0.329176i | ||||
\(497\) | 4.45405 | + | 4.45405i | 0.199791 | + | 0.199791i | ||||
\(498\) | 0.741852i | 0.0332432i | ||||||||
\(499\) | −8.46141 | + | 8.46141i | −0.378785 | + | 0.378785i | −0.870664 | − | 0.491879i | \(-0.836310\pi\) |
0.491879 | + | 0.870664i | \(0.336310\pi\) | |||||||
\(500\) | 8.41096 | − | 7.36585i | 0.376150 | − | 0.329411i | ||||
\(501\) | 2.36812 | + | 2.36812i | 0.105800 | + | 0.105800i | ||||
\(502\) | −8.29215 | + | 8.29215i | −0.370097 | + | 0.370097i | ||||
\(503\) | 16.8793i | 0.752612i | 0.926495 | + | 0.376306i | \(0.122806\pi\) | ||||
−0.926495 | + | 0.376306i | \(0.877194\pi\) | |||||||
\(504\) | 1.93388 | + | 1.93388i | 0.0861417 | + | 0.0861417i | ||||
\(505\) | 9.58794 | + | 39.2221i | 0.426658 | + | 1.74536i | ||||
\(506\) | − | 11.4147i | − | 0.507447i | ||||||
\(507\) | 4.26337 | + | 4.26337i | 0.189343 | + | 0.189343i | ||||
\(508\) | −3.15767 | − | 3.15767i | −0.140099 | − | 0.140099i | ||||
\(509\) | 24.8021 | 1.09933 | 0.549667 | − | 0.835384i | \(-0.314755\pi\) | ||||
0.549667 | + | 0.835384i | \(0.314755\pi\) | |||||||
\(510\) | −4.18284 | + | 6.88949i | −0.185219 | + | 0.305072i | ||||
\(511\) | − | 14.3491i | − | 0.634765i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.49532 | −0.154322 | ||||||||
\(514\) | − | 1.06813i | − | 0.0471131i | ||||||
\(515\) | 5.79868 | − | 1.41750i | 0.255520 | − | 0.0624625i | ||||
\(516\) | 2.20872 | − | 2.20872i | 0.0972334 | − | 0.0972334i | ||||
\(517\) | 11.4651 | − | 11.4651i | 0.504233 | − | 0.504233i | ||||
\(518\) | −8.27428 | − | 14.4322i | −0.363551 | − | 0.634113i | ||||
\(519\) | − | 10.0670i | − | 0.441893i | ||||||
\(520\) | 5.73482 | − | 1.40189i | 0.251488 | − | 0.0614769i | ||||
\(521\) | − | 25.4431i | − | 1.11468i | −0.830283 | − | 0.557342i | \(-0.811821\pi\) | ||
0.830283 | − | 0.557342i | \(-0.188179\pi\) | |||||||
\(522\) | −4.58885 | + | 4.58885i | −0.200849 | + | 0.200849i | ||||
\(523\) | − | 43.8527i | − | 1.91755i | −0.284174 | − | 0.958773i | \(-0.591720\pi\) | ||
0.284174 | − | 0.958773i | \(-0.408280\pi\) | |||||||
\(524\) | 12.5592 | + | 12.5592i | 0.548651 | + | 0.548651i | ||||
\(525\) | −6.30858 | − | 12.1324i | −0.275329 | − | 0.529502i | ||||
\(526\) | 22.2567 | − | 22.2567i | 0.970437 | − | 0.970437i | ||||
\(527\) | 26.4248 | + | 26.4248i | 1.15108 | + | 1.15108i | ||||
\(528\) | 1.79682 | − | 1.79682i | 0.0781967 | − | 0.0781967i | ||||
\(529\) | 2.82141 | 0.122670 | ||||||||
\(530\) | −0.814742 | − | 0.494656i | −0.0353901 | − | 0.0214865i | ||||
\(531\) | −0.813625 | + | 0.813625i | −0.0353083 | + | 0.0353083i | ||||
\(532\) | 9.55941i | 0.414453i | ||||||||
\(533\) | 11.4055 | 0.494027 | ||||||||
\(534\) | 9.46214i | 0.409467i | ||||||||
\(535\) | 1.09328 | + | 0.663765i | 0.0472666 | + | 0.0286971i | ||||
\(536\) | −5.77261 | − | 5.77261i | −0.249339 | − | 0.249339i | ||||
\(537\) | 12.2767 | 0.529779 | ||||||||
\(538\) | −1.98048 | −0.0853845 | ||||||||
\(539\) | 1.21911 | 0.0525107 | ||||||||
\(540\) | −1.16046 | + | 1.91137i | −0.0499381 | + | 0.0822523i | ||||
\(541\) | 25.4345 | − | 25.4345i | 1.09351 | − | 1.09351i | 0.0983645 | − | 0.995150i | \(-0.468639\pi\) |
0.995150 | − | 0.0983645i | \(-0.0313611\pi\) | |||||||
\(542\) | 20.2119i | 0.868177i | ||||||||
\(543\) | 9.93006 | + | 9.93006i | 0.426140 | + | 0.426140i | ||||
\(544\) | − | 3.60448i | − | 0.154541i | ||||||
\(545\) | −2.83775 | − | 1.72289i | −0.121556 | − | 0.0738005i | ||||
\(546\) | − | 7.22074i | − | 0.309019i | ||||||
\(547\) | − | 13.3671i | − | 0.571538i | −0.958299 | − | 0.285769i | \(-0.907751\pi\) | ||
0.958299 | − | 0.285769i | \(-0.0922489\pi\) | |||||||
\(548\) | 12.7858 | + | 12.7858i | 0.546181 | + | 0.546181i | ||||
\(549\) | 0.867564 | − | 0.867564i | 0.0370267 | − | 0.0370267i | ||||
\(550\) | −11.2726 | + | 5.86149i | −0.480665 | + | 0.249935i | ||||
\(551\) | −22.6833 | −0.966342 | ||||||||
\(552\) | −3.17637 | − | 3.17637i | −0.135195 | − | 0.135195i | ||||
\(553\) | − | 18.1821i | − | 0.773180i | ||||||
\(554\) | −26.8225 | −1.13958 | ||||||||
\(555\) | 9.85581 | − | 9.37353i | 0.418356 | − | 0.397884i | ||||
\(556\) | −3.82368 | −0.162160 | ||||||||
\(557\) | 17.4429i | 0.739080i | 0.929215 | + | 0.369540i | \(0.120485\pi\) | ||||
−0.929215 | + | 0.369540i | \(0.879515\pi\) | |||||||
\(558\) | 7.33111 | + | 7.33111i | 0.310350 | + | 0.310350i | ||||
\(559\) | −8.24695 | −0.348809 | ||||||||
\(560\) | 5.22744 | + | 3.17375i | 0.220900 | + | 0.134115i | ||||
\(561\) | 6.47661 | − | 6.47661i | 0.273442 | − | 0.273442i | ||||
\(562\) | −11.8287 | − | 11.8287i | −0.498964 | − | 0.498964i | ||||
\(563\) | − | 2.58551i | − | 0.108966i | −0.998515 | − | 0.0544831i | \(-0.982649\pi\) | ||
0.998515 | − | 0.0544831i | \(-0.0173511\pi\) | |||||||
\(564\) | − | 6.38074i | − | 0.268678i | ||||||
\(565\) | 12.4193 | − | 3.03593i | 0.522485 | − | 0.127723i | ||||
\(566\) | 20.4845i | 0.861029i | ||||||||
\(567\) | 1.93388 | + | 1.93388i | 0.0812152 | + | 0.0812152i | ||||
\(568\) | − | 2.30317i | − | 0.0966389i | ||||||
\(569\) | 19.1350 | − | 19.1350i | 0.802180 | − | 0.802180i | −0.181256 | − | 0.983436i | \(-0.558016\pi\) |
0.983436 | + | 0.181256i | \(0.0580162\pi\) | |||||||
\(570\) | −7.59223 | + | 1.85594i | −0.318004 | + | 0.0777367i | ||||
\(571\) | 6.72822 | 0.281567 | 0.140784 | − | 0.990040i | \(-0.455038\pi\) | ||||
0.140784 | + | 0.990040i | \(0.455038\pi\) | |||||||
\(572\) | −6.70901 | −0.280518 | ||||||||
\(573\) | −2.32340 | −0.0970616 | ||||||||
\(574\) | 8.35421 | + | 8.35421i | 0.348698 | + | 0.348698i | ||||
\(575\) | 10.3618 | + | 19.9273i | 0.432115 | + | 0.831027i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 32.3098 | 1.34507 | 0.672537 | − | 0.740063i | \(-0.265204\pi\) | ||||
0.672537 | + | 0.740063i | \(0.265204\pi\) | |||||||
\(578\) | 4.00775i | 0.166701i | ||||||||
\(579\) | −9.85090 | + | 9.85090i | −0.409390 | + | 0.409390i | ||||
\(580\) | −7.53092 | + | 12.4041i | −0.312704 | + | 0.515051i | ||||
\(581\) | 2.02890 | 0.0841730 | ||||||||
\(582\) | 12.0416 | − | 12.0416i | 0.499142 | − | 0.499142i | ||||
\(583\) | 0.765914 | + | 0.765914i | 0.0317209 | + | 0.0317209i | ||||
\(584\) | −3.70992 | + | 3.70992i | −0.153518 | + | 0.153518i | ||||
\(585\) | 5.73482 | − | 1.40189i | 0.237106 | − | 0.0579610i | ||||
\(586\) | 18.0953 | + | 18.0953i | 0.747508 | + | 0.747508i | ||||
\(587\) | 13.1138i | 0.541266i | 0.962683 | + | 0.270633i | \(0.0872330\pi\) | ||||
−0.962683 | + | 0.270633i | \(0.912767\pi\) | |||||||
\(588\) | 0.339240 | − | 0.339240i | 0.0139900 | − | 0.0139900i | ||||
\(589\) | 36.2386i | 1.49319i | ||||||||
\(590\) | −1.33527 | + | 2.19930i | −0.0549721 | + | 0.0905437i | ||||
\(591\) | 26.5798i | 1.09335i | ||||||||
\(592\) | −1.59211 | + | 5.87071i | −0.0654352 | + | 0.241285i | ||||
\(593\) | 28.5182 | − | 28.5182i | 1.17110 | − | 1.17110i | 0.189155 | − | 0.981947i | \(-0.439425\pi\) |
0.981947 | − | 0.189155i | \(-0.0605749\pi\) | |||||||
\(594\) | 1.79682 | − | 1.79682i | 0.0737245 | − | 0.0737245i | ||||
\(595\) | 18.8422 | + | 11.4397i | 0.772454 | + | 0.468982i | ||||
\(596\) | − | 4.92924i | − | 0.201909i | ||||||
\(597\) | −4.58024 | −0.187457 | ||||||||
\(598\) | 11.8600i | 0.484990i | ||||||||
\(599\) | − | 13.3830i | − | 0.546815i | −0.961898 | − | 0.273407i | \(-0.911849\pi\) | ||
0.961898 | − | 0.273407i | \(-0.0881507\pi\) | |||||||
\(600\) | −1.50574 | + | 4.76789i | −0.0614717 | + | 0.194648i | ||||
\(601\) | 11.5916 | 0.472833 | 0.236417 | − | 0.971652i | \(-0.424027\pi\) | ||||
0.236417 | + | 0.971652i | \(0.424027\pi\) | |||||||
\(602\) | −6.04066 | − | 6.04066i | −0.246199 | − | 0.246199i | ||||
\(603\) | −5.77261 | − | 5.77261i | −0.235079 | − | 0.235079i | ||||
\(604\) | − | 2.56917i | − | 0.104538i | ||||||
\(605\) | −9.86758 | + | 2.41215i | −0.401174 | + | 0.0980679i | ||||
\(606\) | −12.7683 | − | 12.7683i | −0.518678 | − | 0.518678i | ||||
\(607\) | − | 34.6374i | − | 1.40589i | −0.711246 | − | 0.702944i | \(-0.751869\pi\) | ||
0.711246 | − | 0.702944i | \(-0.248131\pi\) | |||||||
\(608\) | 2.47157 | − | 2.47157i | 0.100235 | − | 0.100235i | ||||
\(609\) | 12.5501 | + | 12.5501i | 0.508557 | + | 0.508557i | ||||
\(610\) | 1.42379 | − | 2.34510i | 0.0576475 | − | 0.0949504i | ||||
\(611\) | −11.9123 | + | 11.9123i | −0.481918 | + | 0.481918i | ||||
\(612\) | − | 3.60448i | − | 0.145702i | ||||||
\(613\) | −13.5656 | − | 13.5656i | −0.547908 | − | 0.547908i | 0.377928 | − | 0.925835i | \(-0.376637\pi\) |
−0.925835 | + | 0.377928i | \(0.876637\pi\) | |||||||
\(614\) | 22.5634 | + | 22.5634i | 0.910584 | + | 0.910584i | ||||
\(615\) | −5.01309 | + | 8.25699i | −0.202147 | + | 0.332954i | ||||
\(616\) | −4.91416 | − | 4.91416i | −0.197997 | − | 0.197997i | ||||
\(617\) | 29.4000 | − | 29.4000i | 1.18360 | − | 1.18360i | 0.204793 | − | 0.978805i | \(-0.434348\pi\) |
0.978805 | − | 0.204793i | \(-0.0656522\pi\) | |||||||
\(618\) | −1.88770 | + | 1.88770i | −0.0759343 | + | 0.0759343i | ||||
\(619\) | 8.71796 | 0.350404 | 0.175202 | − | 0.984532i | \(-0.443942\pi\) | ||||
0.175202 | + | 0.984532i | \(0.443942\pi\) | |||||||
\(620\) | 19.8166 | + | 12.0313i | 0.795855 | + | 0.483189i | ||||
\(621\) | −3.17637 | − | 3.17637i | −0.127463 | − | 0.127463i | ||||
\(622\) | 17.2148 | − | 17.2148i | 0.690249 | − | 0.690249i | ||||
\(623\) | 25.8782 | 1.03679 | ||||||||
\(624\) | −1.86691 | + | 1.86691i | −0.0747361 | + | 0.0747361i | ||||
\(625\) | 14.3584 | − | 20.4655i | 0.574337 | − | 0.818619i | ||||
\(626\) | 30.7702 | 1.22982 | ||||||||
\(627\) | 8.88194 | 0.354710 | ||||||||
\(628\) | −10.7956 | − | 10.7956i | −0.430793 | − | 0.430793i | ||||
\(629\) | −5.73871 | + | 21.1608i | −0.228817 | + | 0.843737i | ||||
\(630\) | 5.22744 | + | 3.17375i | 0.208266 | + | 0.126445i | ||||
\(631\) | −20.3687 | − | 20.3687i | −0.810867 | − | 0.810867i | 0.173897 | − | 0.984764i | \(-0.444364\pi\) |
−0.984764 | + | 0.173897i | \(0.944364\pi\) | |||||||
\(632\) | −4.70094 | + | 4.70094i | −0.186993 | + | 0.186993i | ||||
\(633\) | −9.47804 | − | 9.47804i | −0.376718 | − | 0.376718i | ||||
\(634\) | 12.5932 | + | 12.5932i | 0.500141 | + | 0.500141i | ||||
\(635\) | −8.53546 | − | 5.18216i | −0.338719 | − | 0.205648i | ||||
\(636\) | 0.426260 | 0.0169023 | ||||||||
\(637\) | −1.26666 | −0.0501869 | ||||||||
\(638\) | 11.6607 | − | 11.6607i | 0.461651 | − | 0.461651i | ||||
\(639\) | − | 2.30317i | − | 0.0911120i | ||||||
\(640\) | −0.530977 | − | 2.17211i | −0.0209887 | − | 0.0858602i | ||||
\(641\) | 19.7213 | 0.778944 | 0.389472 | − | 0.921038i | \(-0.372658\pi\) | ||||
0.389472 | + | 0.921038i | \(0.372658\pi\) | |||||||
\(642\) | −0.571987 | −0.0225745 | ||||||||
\(643\) | −30.0934 | −1.18677 | −0.593384 | − | 0.804919i | \(-0.702209\pi\) | ||||
−0.593384 | + | 0.804919i | \(0.702209\pi\) | |||||||
\(644\) | −8.68709 | + | 8.68709i | −0.342319 | + | 0.342319i | ||||
\(645\) | 3.62480 | − | 5.97036i | 0.142726 | − | 0.235083i | ||||
\(646\) | 8.90871 | − | 8.90871i | 0.350508 | − | 0.350508i | ||||
\(647\) | 3.58012i | 0.140749i | 0.997521 | + | 0.0703746i | \(0.0224195\pi\) | ||||
−0.997521 | + | 0.0703746i | \(0.977581\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 2.06750 | − | 2.06750i | 0.0811563 | − | 0.0811563i | ||||
\(650\) | 11.7123 | − | 6.09012i | 0.459394 | − | 0.238874i | ||||
\(651\) | 20.0499 | − | 20.0499i | 0.785819 | − | 0.785819i | ||||
\(652\) | −2.00094 | −0.0783628 | ||||||||
\(653\) | 21.6461 | 0.847079 | 0.423540 | − | 0.905878i | \(-0.360787\pi\) | ||||
0.423540 | + | 0.905878i | \(0.360787\pi\) | |||||||
\(654\) | 1.48467 | 0.0580550 | ||||||||
\(655\) | 33.9486 | + | 20.6113i | 1.32648 | + | 0.805350i | ||||
\(656\) | − | 4.31993i | − | 0.168665i | ||||||
\(657\) | −3.70992 | + | 3.70992i | −0.144738 | + | 0.144738i | ||||
\(658\) | −17.4508 | −0.680302 | ||||||||
\(659\) | 24.8071 | 0.966346 | 0.483173 | − | 0.875525i | \(-0.339484\pi\) | ||||
0.483173 | + | 0.875525i | \(0.339484\pi\) | |||||||
\(660\) | 2.94883 | − | 4.85697i | 0.114783 | − | 0.189057i | ||||
\(661\) | −7.55751 | − | 7.55751i | −0.293953 | − | 0.293953i | 0.544687 | − | 0.838640i | \(-0.316649\pi\) |
−0.838640 | + | 0.544687i | \(0.816649\pi\) | |||||||
\(662\) | −12.4856 | − | 12.4856i | −0.485267 | − | 0.485267i | ||||
\(663\) | −6.72922 | + | 6.72922i | −0.261341 | + | 0.261341i | ||||
\(664\) | −0.524568 | − | 0.524568i | −0.0203572 | − | 0.0203572i | ||||
\(665\) | 5.07583 | + | 20.7641i | 0.196832 | + | 0.805197i | ||||
\(666\) | −1.59211 | + | 5.87071i | −0.0616929 | + | 0.227485i | ||||
\(667\) | −20.6134 | − | 20.6134i | −0.798154 | − | 0.798154i | ||||
\(668\) | −3.34903 | −0.129578 | ||||||||
\(669\) | −25.8168 | −0.998135 | ||||||||
\(670\) | −15.6039 | − | 9.47363i | −0.602830 | − | 0.365998i | ||||
\(671\) | −2.20456 | + | 2.20456i | −0.0851061 | + | 0.0851061i | ||||
\(672\) | −2.73491 | −0.105502 | ||||||||
\(673\) | 23.8195 | − | 23.8195i | 0.918173 | − | 0.918173i | −0.0787239 | − | 0.996896i | \(-0.525085\pi\) |
0.996896 | + | 0.0787239i | \(0.0250846\pi\) | |||||||
\(674\) | 2.01004 | + | 2.01004i | 0.0774237 | + | 0.0774237i | ||||
\(675\) | −1.50574 | + | 4.76789i | −0.0579561 | + | 0.183516i | ||||
\(676\) | −6.02931 | −0.231897 | ||||||||
\(677\) | 26.5470 | − | 26.5470i | 1.02028 | − | 1.02028i | 0.0204933 | − | 0.999790i | \(-0.493476\pi\) |
0.999790 | − | 0.0204933i | \(-0.00652367\pi\) | |||||||
\(678\) | −4.04297 | + | 4.04297i | −0.155269 | + | 0.155269i | ||||
\(679\) | −32.9329 | − | 32.9329i | −1.26385 | − | 1.26385i | ||||
\(680\) | −1.91389 | − | 7.82932i | −0.0733945 | − | 0.300241i | ||||
\(681\) | −14.3657 | − | 14.3657i | −0.550494 | − | 0.550494i | ||||
\(682\) | −18.6290 | − | 18.6290i | −0.713342 | − | 0.713342i | ||||
\(683\) | 26.8136i | 1.02599i | 0.858390 | + | 0.512997i | \(0.171465\pi\) | ||||
−0.858390 | + | 0.512997i | \(0.828535\pi\) | |||||||
\(684\) | 2.47157 | − | 2.47157i | 0.0945028 | − | 0.0945028i | ||||
\(685\) | 34.5610 | + | 20.9831i | 1.32051 | + | 0.801725i | ||||
\(686\) | 12.6093 | + | 12.6093i | 0.481427 | + | 0.481427i | ||||
\(687\) | 16.8815 | − | 16.8815i | 0.644070 | − | 0.644070i | ||||
\(688\) | 3.12360i | 0.119086i | ||||||||
\(689\) | −0.795788 | − | 0.795788i | −0.0303171 | − | 0.0303171i | ||||
\(690\) | −8.58599 | − | 5.21284i | −0.326863 | − | 0.198449i | ||||
\(691\) | 39.2996i | 1.49503i | 0.664246 | + | 0.747514i | \(0.268753\pi\) | ||||
−0.664246 | + | 0.747514i | \(0.731247\pi\) | |||||||
\(692\) | 7.11846 | + | 7.11846i | 0.270603 | + | 0.270603i | ||||
\(693\) | −4.91416 | − | 4.91416i | −0.186673 | − | 0.186673i | ||||
\(694\) | 15.1173 | 0.573845 | ||||||||
\(695\) | −8.30546 | + | 2.03029i | −0.315044 | + | 0.0770133i | ||||
\(696\) | − | 6.48962i | − | 0.245988i | ||||||
\(697\) | − | 15.5711i | − | 0.589797i | ||||||
\(698\) | 13.6893 | 0.518148 | ||||||||
\(699\) | 0.0710572i | 0.00268763i | ||||||||
\(700\) | 13.0398 | + | 4.11808i | 0.492857 | + | 0.155649i | ||||
\(701\) | −19.5030 | + | 19.5030i | −0.736617 | + | 0.736617i | −0.971922 | − | 0.235305i | \(-0.924391\pi\) |
0.235305 | + | 0.971922i | \(0.424391\pi\) | |||||||
\(702\) | −1.86691 | + | 1.86691i | −0.0704619 | + | 0.0704619i | ||||
\(703\) | −18.4448 | + | 10.5748i | −0.695661 | + | 0.398838i | ||||
\(704\) | 2.54109i | 0.0957710i | ||||||||
\(705\) | −3.38803 | − | 13.8597i | −0.127601 | − | 0.521986i | ||||
\(706\) | 31.3775i | 1.18091i | ||||||||
\(707\) | −34.9203 | + | 34.9203i | −1.31331 | + | 1.31331i | ||||
\(708\) | − | 1.15064i | − | 0.0432437i | ||||||
\(709\) | −8.21814 | − | 8.21814i | −0.308639 | − | 0.308639i | 0.535743 | − | 0.844381i | \(-0.320032\pi\) |
−0.844381 | + | 0.535743i | \(0.820032\pi\) | |||||||
\(710\) | −1.22293 | − | 5.00274i | −0.0458958 | − | 0.187750i | ||||
\(711\) | −4.70094 | + | 4.70094i | −0.176299 | + | 0.176299i | ||||
\(712\) | −6.69075 | − | 6.69075i | −0.250746 | − | 0.250746i | ||||
\(713\) | −32.9318 | + | 32.9318i | −1.23330 | + | 1.23330i | ||||
\(714\) | −9.85793 | −0.368924 | ||||||||
\(715\) | −14.5727 | + | 3.56233i | −0.544988 | + | 0.133224i | ||||
\(716\) | −8.68094 | + | 8.68094i | −0.324422 | + | 0.324422i | ||||
\(717\) | 16.0193i | 0.598251i | ||||||||
\(718\) | −32.4157 | −1.20974 | ||||||||
\(719\) | − | 9.15541i | − | 0.341439i | −0.985320 | − | 0.170720i | \(-0.945391\pi\) | ||
0.985320 | − | 0.170720i | \(-0.0546092\pi\) | |||||||
\(720\) | −0.530977 | − | 2.17211i | −0.0197884 | − | 0.0809498i | ||||
\(721\) | 5.16269 | + | 5.16269i | 0.192269 | + | 0.192269i | ||||
\(722\) | −6.78271 | −0.252426 | ||||||||
\(723\) | −5.22229 | −0.194219 | ||||||||
\(724\) | −14.0432 | −0.521912 | ||||||||
\(725\) | −9.77171 | + | 30.9418i | −0.362912 | + | 1.14915i | ||||
\(726\) | 3.21228 | − | 3.21228i | 0.119219 | − | 0.119219i | ||||
\(727\) | − | 32.4114i | − | 1.20207i | −0.799222 | − | 0.601036i | \(-0.794755\pi\) | ||
0.799222 | − | 0.601036i | \(-0.205245\pi\) | |||||||
\(728\) | 5.10583 | + | 5.10583i | 0.189235 | + | 0.189235i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −6.08847 | + | 10.0282i | −0.225344 | + | 0.371162i | ||||
\(731\) | 11.2589i | 0.416427i | ||||||||
\(732\) | 1.22692i | 0.0453483i | ||||||||
\(733\) | −35.1555 | − | 35.1555i | −1.29850 | − | 1.29850i | −0.929384 | − | 0.369115i | \(-0.879661\pi\) |
−0.369115 | − | 0.929384i | \(-0.620339\pi\) | |||||||
\(734\) | 9.63234 | − | 9.63234i | 0.355536 | − | 0.355536i | ||||
\(735\) | 0.556738 | − | 0.916995i | 0.0205356 | − | 0.0338239i | ||||
\(736\) | 4.49206 | 0.165579 | ||||||||
\(737\) | 14.6687 | + | 14.6687i | 0.540330 | + | 0.540330i | ||||
\(738\) | − | 4.31993i | − | 0.159019i | ||||||
\(739\) | −11.5902 | −0.426351 | −0.213176 | − | 0.977014i | \(-0.568381\pi\) | ||||
−0.213176 | + | 0.977014i | \(0.568381\pi\) | |||||||
\(740\) | −0.341020 | + | 13.5972i | −0.0125361 | + | 0.499843i | ||||
\(741\) | −9.22838 | −0.339013 | ||||||||
\(742\) | − | 1.16579i | − | 0.0427973i | ||||||
\(743\) | −21.4779 | − | 21.4779i | −0.787949 | − | 0.787949i | 0.193209 | − | 0.981158i | \(-0.438110\pi\) |
−0.981158 | + | 0.193209i | \(0.938110\pi\) | |||||||
\(744\) | −10.3677 | −0.380100 | ||||||||
\(745\) | −2.61731 | − | 10.7068i | −0.0958909 | − | 0.392269i | ||||
\(746\) | −21.6306 | + | 21.6306i | −0.791954 | + | 0.791954i | ||||
\(747\) | −0.524568 | − | 0.524568i | −0.0191929 | − | 0.0191929i | ||||
\(748\) | 9.15930i | 0.334897i | ||||||||
\(749\) | 1.56433i | 0.0571595i | ||||||||
\(750\) | −0.739003 | + | 11.1559i | −0.0269846 | + | 0.407355i | ||||
\(751\) | 46.7182i | 1.70477i | 0.522914 | + | 0.852385i | \(0.324845\pi\) | ||||
−0.522914 | + | 0.852385i | \(0.675155\pi\) | |||||||
\(752\) | 4.51187 | + | 4.51187i | 0.164531 | + | 0.164531i | ||||
\(753\) | − | 11.7269i | − | 0.427351i | ||||||
\(754\) | −12.1155 | + | 12.1155i | −0.441221 | + | 0.441221i | ||||
\(755\) | −1.36417 | − | 5.58051i | −0.0496472 | − | 0.203096i | ||||
\(756\) | −2.73491 | −0.0994679 | ||||||||
\(757\) | −28.5100 | −1.03622 | −0.518108 | − | 0.855315i | \(-0.673363\pi\) | ||||
−0.518108 | + | 0.855315i | \(0.673363\pi\) | |||||||
\(758\) | 0.115662 | 0.00420103 | ||||||||
\(759\) | 8.07143 | + | 8.07143i | 0.292974 | + | 0.292974i | ||||
\(760\) | 4.05617 | − | 6.68086i | 0.147133 | − | 0.242340i | ||||
\(761\) | 19.7514i | 0.715988i | 0.933724 | + | 0.357994i | \(0.116539\pi\) | ||||
−0.933724 | + | 0.357994i | \(0.883461\pi\) | |||||||
\(762\) | 4.46562 | 0.161772 | ||||||||
\(763\) | − | 4.06043i | − | 0.146998i | ||||||
\(764\) | 1.64289 | − | 1.64289i | 0.0594378 | − | 0.0594378i | ||||
\(765\) | −1.91389 | − | 7.82932i | −0.0691970 | − | 0.283070i | ||||
\(766\) | −1.75588 | −0.0634424 | ||||||||
\(767\) | −2.14814 | + | 2.14814i | −0.0775647 | + | 0.0775647i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −26.6238 | + | 26.6238i | −0.960078 | + | 0.960078i | −0.999233 | − | 0.0391547i | \(-0.987533\pi\) |
0.0391547 | + | 0.999233i | \(0.487533\pi\) | |||||||
\(770\) | −13.2834 | − | 8.06479i | −0.478700 | − | 0.290635i | ||||
\(771\) | 0.755280 | + | 0.755280i | 0.0272007 | + | 0.0272007i | ||||
\(772\) | − | 13.9313i | − | 0.501398i | ||||||
\(773\) | −1.41448 | + | 1.41448i | −0.0508753 | + | 0.0508753i | −0.732087 | − | 0.681211i | \(-0.761453\pi\) |
0.681211 | + | 0.732087i | \(0.261453\pi\) | |||||||
\(774\) | 3.12360i | 0.112275i | ||||||||
\(775\) | 49.4322 | + | 15.6112i | 1.77566 | + | 0.560770i | ||||
\(776\) | 17.0294i | 0.611322i | ||||||||
\(777\) | 16.0559 | + | 4.35428i | 0.576002 | + | 0.156209i | ||||
\(778\) | −11.3156 | + | 11.3156i | −0.405683 | + | 0.405683i | ||||
\(779\) | 10.6770 | − | 10.6770i | 0.382543 | − | 0.382543i | ||||
\(780\) | −3.06384 | + | 5.04642i | −0.109703 | + | 0.180691i | ||||
\(781\) | 5.85257i | 0.209421i | ||||||||
\(782\) | 16.1915 | 0.579007 | ||||||||
\(783\) | − | 6.48962i | − | 0.231920i | ||||||
\(784\) | 0.479758i | 0.0171342i | ||||||||
\(785\) | −29.1816 | − | 17.7171i | −1.04153 | − | 0.632350i | ||||
\(786\) | −17.7614 | −0.633527 | ||||||||
\(787\) | 22.3671 | + | 22.3671i | 0.797301 | + | 0.797301i | 0.982669 | − | 0.185368i | \(-0.0593479\pi\) |
−0.185368 | + | 0.982669i | \(0.559348\pi\) | |||||||
\(788\) | −18.7947 | − | 18.7947i | −0.669535 | − | 0.669535i | ||||
\(789\) | 31.4757i | 1.12056i | ||||||||
\(790\) | −7.71486 | + | 12.7070i | −0.274483 | + | 0.452096i | ||||
\(791\) | 11.0572 | + | 11.0572i | 0.393148 | + | 0.393148i | ||||
\(792\) | 2.54109i | 0.0902938i | ||||||||
\(793\) | 2.29055 | − | 2.29055i | 0.0813398 | − | 0.0813398i | ||||
\(794\) | −10.5898 | − | 10.5898i | −0.375819 | − | 0.375819i | ||||
\(795\) | 0.925884 | − | 0.226334i | 0.0328377 | − | 0.00802726i | ||||
\(796\) | 3.23872 | − | 3.23872i | 0.114793 | − | 0.114793i | ||||
\(797\) | 3.20231i | 0.113432i | 0.998390 | + | 0.0567159i | \(0.0180629\pi\) | ||||
−0.998390 | + | 0.0567159i | \(0.981937\pi\) | |||||||
\(798\) | −6.75953 | − | 6.75953i | −0.239285 | − | 0.239285i | ||||
\(799\) | 16.2629 | + | 16.2629i | 0.575341 | + | 0.575341i | ||||
\(800\) | −2.30668 | − | 4.43613i | −0.0815535 | − | 0.156841i | ||||
\(801\) | −6.69075 | − | 6.69075i | −0.236406 | − | 0.236406i | ||||
\(802\) | 6.78291 | − | 6.78291i | 0.239513 | − | 0.239513i | ||||
\(803\) | 9.42725 | − | 9.42725i | 0.332680 | − | 0.332680i | ||||
\(804\) | 8.16371 | 0.287912 | ||||||||
\(805\) | −14.2567 | + | 23.4820i | −0.502481 | + | 0.827630i | ||||
\(806\) | 19.3556 | + | 19.3556i | 0.681773 | + | 0.681773i | ||||
\(807\) | 1.40041 | − | 1.40041i | 0.0492968 | − | 0.0492968i | ||||
\(808\) | 18.0572 | 0.635249 | ||||||||
\(809\) | 6.69579 | − | 6.69579i | 0.235412 | − | 0.235412i | −0.579535 | − | 0.814947i | \(-0.696766\pi\) |
0.814947 | + | 0.579535i | \(0.196766\pi\) | |||||||
\(810\) | −0.530977 | − | 2.17211i | −0.0186566 | − | 0.0763202i | ||||
\(811\) | 15.8744 | 0.557425 | 0.278712 | − | 0.960375i | \(-0.410092\pi\) | ||||
0.278712 | + | 0.960375i | \(0.410092\pi\) | |||||||
\(812\) | −17.7486 | −0.622852 | ||||||||
\(813\) | −14.2920 | − | 14.2920i | −0.501242 | − | 0.501242i | ||||
\(814\) | 4.04569 | − | 14.9180i | 0.141801 | − | 0.522876i | ||||
\(815\) | −4.34626 | + | 1.06245i | −0.152243 | + | 0.0372161i | ||||
\(816\) | 2.54875 | + | 2.54875i | 0.0892241 | + | 0.0892241i | ||||
\(817\) | −7.72019 | + | 7.72019i | −0.270095 | + | 0.270095i | ||||
\(818\) | −12.5316 | − | 12.5316i | −0.438159 | − | 0.438159i | ||||
\(819\) | 5.10583 | + | 5.10583i | 0.178412 | + | 0.178412i | ||||
\(820\) | −2.29378 | − | 9.38336i | −0.0801024 | − | 0.327681i | ||||
\(821\) | −46.5456 | −1.62445 | −0.812227 | − | 0.583342i | \(-0.801745\pi\) | ||||
−0.812227 | + | 0.583342i | \(0.801745\pi\) | |||||||
\(822\) | −18.0818 | −0.630675 | ||||||||
\(823\) | 15.5996 | − | 15.5996i | 0.543767 | − | 0.543767i | −0.380864 | − | 0.924631i | \(-0.624373\pi\) |
0.924631 | + | 0.380864i | \(0.124373\pi\) | |||||||
\(824\) | − | 2.66961i | − | 0.0930001i | ||||||
\(825\) | 3.82623 | − | 12.1156i | 0.133212 | − | 0.421812i | ||||
\(826\) | −3.14690 | −0.109495 | ||||||||
\(827\) | −28.5690 | −0.993443 | −0.496721 | − | 0.867910i | \(-0.665463\pi\) | ||||
−0.496721 | + | 0.867910i | \(0.665463\pi\) | |||||||
\(828\) | 4.49206 | 0.156110 | ||||||||
\(829\) | 28.7820 | − | 28.7820i | 0.999640 | − | 0.999640i | −0.000360408 | − | 1.00000i | \(-0.500115\pi\) |
1.00000 | 0.000360408i | \(0.000114722\pi\) | ||||||||
\(830\) | −1.41795 | − | 0.860886i | −0.0492179 | − | 0.0298818i | ||||
\(831\) | 18.9664 | − | 18.9664i | 0.657937 | − | 0.657937i | ||||
\(832\) | − | 2.64021i | − | 0.0915327i | ||||||
\(833\) | 1.72927i | 0.0599158i | ||||||||
\(834\) | 2.70375 | − | 2.70375i | 0.0936233 | − | 0.0936233i | ||||
\(835\) | −7.27446 | + | 1.77826i | −0.251743 | + | 0.0615392i | ||||
\(836\) | −6.28048 | + | 6.28048i | −0.217215 | + | 0.217215i | ||||
\(837\) | −10.3677 | −0.358362 | ||||||||
\(838\) | 21.4066 | 0.739479 | ||||||||
\(839\) | −29.3296 | −1.01257 | −0.506285 | − | 0.862366i | \(-0.668982\pi\) | ||||
−0.506285 | + | 0.862366i | \(0.668982\pi\) | |||||||
\(840\) | −5.94054 | + | 1.45218i | −0.204968 | + | 0.0501049i | ||||
\(841\) | − | 13.1152i | − | 0.452247i | ||||||
\(842\) | 10.7024 | − | 10.7024i | 0.368827 | − | 0.368827i | ||||
\(843\) | 16.7283 | 0.576154 | ||||||||
\(844\) | 13.4040 | 0.461384 | ||||||||
\(845\) | −13.0963 | + | 3.20143i | −0.450527 | + | 0.110132i | ||||
\(846\) | 4.51187 | + | 4.51187i | 0.155121 | + | 0.155121i | ||||
\(847\) | −8.78532 | − | 8.78532i | −0.301867 | − | 0.301867i | ||||
\(848\) | −0.301411 | + | 0.301411i | −0.0103505 | + | 0.0103505i | ||||
\(849\) | −14.4848 | − | 14.4848i | −0.497115 | − | 0.497115i | ||||
\(850\) | −8.31438 | − | 15.9899i | −0.285181 | − | 0.548449i | ||||
\(851\) | −26.3716 | − | 7.15184i | −0.904005 | − | 0.245162i | ||||
\(852\) | 1.62859 | + | 1.62859i | 0.0557945 | + | 0.0557945i | ||||
\(853\) | 10.7137 | 0.366831 | 0.183416 | − | 0.983035i | \(-0.441285\pi\) | ||||
0.183416 | + | 0.983035i | \(0.441285\pi\) | |||||||
\(854\) | 3.35552 | 0.114824 | ||||||||
\(855\) | 4.05617 | − | 6.68086i | 0.138718 | − | 0.228481i | ||||
\(856\) | 0.404456 | − | 0.404456i | 0.0138240 | − | 0.0138240i | ||||
\(857\) | 31.9152 | 1.09020 | 0.545101 | − | 0.838371i | \(-0.316491\pi\) | ||||
0.545101 | + | 0.838371i | \(0.316491\pi\) | |||||||
\(858\) | 4.74398 | − | 4.74398i | 0.161957 | − | 0.161957i | ||||
\(859\) | −30.9778 | − | 30.9778i | −1.05695 | − | 1.05695i | −0.998277 | − | 0.0586704i | \(-0.981314\pi\) |
−0.0586704 | − | 0.998277i | \(-0.518686\pi\) | |||||||
\(860\) | 1.65856 | + | 6.78480i | 0.0565564 | + | 0.231360i | ||||
\(861\) | −11.8146 | −0.402642 | ||||||||
\(862\) | −11.7768 | + | 11.7768i | −0.401118 | + | 0.401118i | ||||
\(863\) | 29.6917 | − | 29.6917i | 1.01072 | − | 1.01072i | 0.0107769 | − | 0.999942i | \(-0.496570\pi\) |
0.999942 | − | 0.0107769i | \(-0.00343045\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 19.2418 | + | 11.6823i | 0.654241 | + | 0.397211i | ||||
\(866\) | −12.9115 | − | 12.9115i | −0.438751 | − | 0.438751i | ||||
\(867\) | −2.83391 | − | 2.83391i | −0.0962446 | − | 0.0962446i | ||||
\(868\) | 28.3549i | 0.962428i | ||||||||
\(869\) | 11.9455 | − | 11.9455i | 0.405224 | − | 0.405224i | ||||
\(870\) | −3.44584 | − | 14.0962i | −0.116825 | − | 0.477905i | ||||
\(871\) | −15.2409 | − | 15.2409i | −0.516418 | − | 0.516418i | ||||
\(872\) | −1.04982 | + | 1.04982i | −0.0355513 | + | 0.0355513i | ||||
\(873\) | 17.0294i | 0.576360i | ||||||||
\(874\) | 11.1024 | + | 11.1024i | 0.375545 | + | 0.375545i | ||||
\(875\) | 30.5104 | + | 2.02111i | 1.03144 | + | 0.0683260i | ||||
\(876\) | − | 5.24662i | − | 0.177267i | ||||||
\(877\) | 13.3438 | + | 13.3438i | 0.450587 | + | 0.450587i | 0.895549 | − | 0.444962i | \(-0.146783\pi\) |
−0.444962 | + | 0.895549i | \(0.646783\pi\) | |||||||
\(878\) | −12.6631 | − | 12.6631i | −0.427358 | − | 0.427358i | ||||
\(879\) | −25.5905 | −0.863148 | ||||||||
\(880\) | 1.34926 | + | 5.51953i | 0.0454836 | + | 0.186063i | ||||
\(881\) | 23.6087i | 0.795397i | 0.917516 | + | 0.397699i | \(0.130191\pi\) | ||||
−0.917516 | + | 0.397699i | \(0.869809\pi\) | |||||||
\(882\) | 0.479758i | 0.0161543i | ||||||||
\(883\) | −15.7413 | −0.529737 | −0.264868 | − | 0.964285i | \(-0.585329\pi\) | ||||
−0.264868 | + | 0.964285i | \(0.585329\pi\) | |||||||
\(884\) | − | 9.51656i | − | 0.320077i | ||||||
\(885\) | −0.610963 | − | 2.49932i | −0.0205373 | − | 0.0840136i | ||||
\(886\) | 19.8789 | − | 19.8789i | 0.667845 | − | 0.667845i | ||||
\(887\) | −14.7609 | + | 14.7609i | −0.495622 | + | 0.495622i | −0.910072 | − | 0.414450i | \(-0.863974\pi\) |
0.414450 | + | 0.910072i | \(0.363974\pi\) | |||||||
\(888\) | −3.02543 | − | 5.27701i | −0.101527 | − | 0.177085i | ||||
\(889\) | − | 12.2131i | − | 0.409614i | ||||||
\(890\) | −18.0857 | − | 10.9804i | −0.606233 | − | 0.368064i | ||||
\(891\) | 2.54109i | 0.0851298i | ||||||||
\(892\) | 18.2552 | − | 18.2552i | 0.611231 | − | 0.611231i | ||||
\(893\) | 22.3028i | 0.746334i | ||||||||
\(894\) | 3.48550 | + | 3.48550i | 0.116572 | + | 0.116572i | ||||
\(895\) | −14.2466 | + | 23.4654i | −0.476211 | + | 0.784360i | ||||
\(896\) | 1.93388 | − | 1.93388i | 0.0646063 | − | 0.0646063i | ||||
\(897\) | −8.38626 | − | 8.38626i | −0.280009 | − | 0.280009i | ||||
\(898\) | 10.2591 | − | 10.2591i | 0.342352 | − | 0.342352i | ||||
\(899\) | −67.2827 | −2.24401 | ||||||||
\(900\) | −2.30668 | − | 4.43613i | −0.0768894 | − | 0.147871i | ||||
\(901\) | −1.08643 | + | 1.08643i | −0.0361942 | + | 0.0361942i | ||||
\(902\) | 10.9773i | 0.365505i | ||||||||
\(903\) | 8.54278 | 0.284286 | ||||||||
\(904\) | − | 5.71763i | − | 0.190165i | ||||||
\(905\) | −30.5034 | + | 7.45663i | −1.01397 | + | 0.247867i | ||||
\(906\) | 1.81667 | + | 1.81667i | 0.0603550 | + | 0.0603550i | ||||
\(907\) | 46.5171 | 1.54457 | 0.772287 | − | 0.635274i | \(-0.219113\pi\) | ||||
0.772287 | + | 0.635274i | \(0.219113\pi\) | |||||||
\(908\) | 20.3161 | 0.674215 | ||||||||
\(909\) | 18.0572 | 0.598918 | ||||||||
\(910\) | 13.8015 | + | 8.37935i | 0.457516 | + | 0.277773i | ||||
\(911\) | −35.8371 | + | 35.8371i | −1.18734 | + | 1.18734i | −0.209534 | + | 0.977801i | \(0.567195\pi\) |
−0.977801 | + | 0.209534i | \(0.932805\pi\) | |||||||
\(912\) | 3.49532i | 0.115742i | ||||||||
\(913\) | 1.33298 | + | 1.33298i | 0.0441151 | + | 0.0441151i | ||||
\(914\) | 3.03992i | 0.100552i | ||||||||
\(915\) | 0.651467 | + | 2.66501i | 0.0215368 | + | 0.0881025i | ||||
\(916\) | 23.8741i | 0.788821i | ||||||||
\(917\) | 48.5759i | 1.60412i | ||||||||
\(918\) | 2.54875 | + | 2.54875i | 0.0841213 | + | 0.0841213i | ||||
\(919\) | 22.7714 | − | 22.7714i | 0.751160 | − | 0.751160i | −0.223536 | − | 0.974696i | \(-0.571760\pi\) |
0.974696 | + | 0.223536i | \(0.0717599\pi\) | |||||||
\(920\) | 9.75725 | − | 2.38518i | 0.321687 | − | 0.0786371i | ||||
\(921\) | −31.9094 | −1.05145 | ||||||||
\(922\) | 2.13391 | + | 2.13391i | 0.0702765 | + | 0.0702765i | ||||
\(923\) | − | 6.08085i | − | 0.200153i | ||||||
\(924\) | 6.94967 | 0.228627 | ||||||||
\(925\) | 6.47907 | + | 29.7157i | 0.213030 | + | 0.977046i | ||||
\(926\) | 20.8314 | 0.684563 | ||||||||
\(927\) | − | 2.66961i | − | 0.0876814i | ||||||
\(928\) | 4.58885 | + | 4.58885i | 0.150637 | + | 0.150637i | ||||
\(929\) | −17.7432 | −0.582135 | −0.291068 | − | 0.956702i | \(-0.594011\pi\) | ||||
−0.291068 | + | 0.956702i | \(0.594011\pi\) | |||||||
\(930\) | −22.5199 | + | 5.50504i | −0.738456 | + | 0.180517i | ||||
\(931\) | −1.18575 | + | 1.18575i | −0.0388615 | + | 0.0388615i | ||||
\(932\) | −0.0502450 | − | 0.0502450i | −0.00164583 | − | 0.00164583i | ||||
\(933\) | 24.3453i | 0.797030i | ||||||||
\(934\) | − | 30.6842i | − | 1.00402i | ||||||
\(935\) | 4.86338 | + | 19.8950i | 0.159050 | + | 0.650637i | ||||
\(936\) | − | 2.64021i | − | 0.0862978i | ||||||
\(937\) | −35.5702 | − | 35.5702i | −1.16203 | − | 1.16203i | −0.984031 | − | 0.177996i | \(-0.943039\pi\) |
−0.177996 | − | 0.984031i | \(-0.556961\pi\) | |||||||
\(938\) | − | 22.3270i | − | 0.729004i | ||||||
\(939\) | −21.7578 | + | 21.7578i | −0.710038 | + | 0.710038i | ||||
\(940\) | 12.1960 | + | 7.40457i | 0.397789 | + | 0.241511i | ||||
\(941\) | 18.2845 | 0.596058 | 0.298029 | − | 0.954557i | \(-0.403671\pi\) | ||||
0.298029 | + | 0.954557i | \(0.403671\pi\) | |||||||
\(942\) | 15.2673 | 0.497437 | ||||||||
\(943\) | 19.4054 | 0.631926 | ||||||||
\(944\) | 0.813625 | + | 0.813625i | 0.0264812 | + | 0.0264812i | ||||
\(945\) | −5.94054 | + | 1.45218i | −0.193246 | + | 0.0472393i | ||||
\(946\) | − | 7.93735i | − | 0.258066i | ||||||
\(947\) | 14.1055 | 0.458368 | 0.229184 | − | 0.973383i | \(-0.426394\pi\) | ||||
0.229184 | + | 0.973383i | \(0.426394\pi\) | |||||||
\(948\) | − | 6.64813i | − | 0.215921i | ||||||
\(949\) | −9.79495 | + | 9.79495i | −0.317958 | + | 0.317958i | ||||
\(950\) | 5.26306 | − | 16.6653i | 0.170756 | − | 0.540694i | ||||
\(951\) | −17.8095 | −0.577514 | ||||||||
\(952\) | 6.97061 | − | 6.97061i | 0.225919 | − | 0.225919i | ||||
\(953\) | −3.58438 | − | 3.58438i | −0.116109 | − | 0.116109i | 0.646665 | − | 0.762774i | \(-0.276163\pi\) |
−0.762774 | + | 0.646665i | \(0.776163\pi\) | |||||||
\(954\) | −0.301411 | + | 0.301411i | −0.00975856 | + | 0.00975856i | ||||
\(955\) | 2.69621 | − | 4.44089i | 0.0872473 | − | 0.143704i | ||||
\(956\) | −11.3273 | − | 11.3273i | −0.366352 | − | 0.366352i | ||||
\(957\) | 16.4907i | 0.533069i | ||||||||
\(958\) | −3.72623 | + | 3.72623i | −0.120389 | + | 0.120389i | ||||
\(959\) | 49.4522i | 1.59689i | ||||||||
\(960\) | 1.91137 | + | 1.16046i | 0.0616893 | + | 0.0374536i | ||||
\(961\) | 76.4902i | 2.46743i | ||||||||
\(962\) | −4.20349 | + | 15.4999i | −0.135526 | + | 0.499736i | ||||
\(963\) | 0.404456 | − | 0.404456i | 0.0130334 | − | 0.0130334i | ||||
\(964\) | 3.69272 | − | 3.69272i | 0.118934 | − | 0.118934i | ||||
\(965\) | −7.39719 | − | 30.2603i | −0.238124 | − | 0.974113i | ||||
\(966\) | − | 12.2854i | − | 0.395276i | ||||||
\(967\) | 21.6520 | 0.696280 | 0.348140 | − | 0.937442i | \(-0.386813\pi\) | ||||
0.348140 | + | 0.937442i | \(0.386813\pi\) | |||||||
\(968\) | 4.54285i | 0.146013i | ||||||||
\(969\) | 12.5988i | 0.404732i | ||||||||
\(970\) | 9.04225 | + | 36.9898i | 0.290329 | + | 1.18767i | ||||
\(971\) | 10.5284 | 0.337872 | 0.168936 | − | 0.985627i | \(-0.445967\pi\) | ||||
0.168936 | + | 0.985627i | \(0.445967\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −7.39453 | − | 7.39453i | −0.237058 | − | 0.237058i | ||||
\(974\) | − | 19.2486i | − | 0.616766i | ||||||
\(975\) | −3.97547 | + | 12.5882i | −0.127317 | + | 0.403145i | ||||
\(976\) | −0.867564 | − | 0.867564i | −0.0277701 | − | 0.0277701i | ||||
\(977\) | − | 62.4861i | − | 1.99911i | −0.0298845 | − | 0.999553i | \(-0.509514\pi\) | ||
0.0298845 | − | 0.999553i | \(-0.490486\pi\) | |||||||
\(978\) | 1.41488 | − | 1.41488i | 0.0452428 | − | 0.0452428i | ||||
\(979\) | 17.0018 | + | 17.0018i | 0.543380 | + | 0.543380i | ||||
\(980\) | 0.254740 | + | 1.04209i | 0.00813738 | + | 0.0332882i | ||||
\(981\) | −1.04982 | + | 1.04982i | −0.0335181 | + | 0.0335181i | ||||
\(982\) | 7.57274i | 0.241656i | ||||||||
\(983\) | −9.77180 | − | 9.77180i | −0.311672 | − | 0.311672i | 0.533885 | − | 0.845557i | \(-0.320732\pi\) |
−0.845557 | + | 0.533885i | \(0.820732\pi\) | |||||||
\(984\) | 3.05465 | + | 3.05465i | 0.0973787 | + | 0.0973787i | ||||
\(985\) | −50.8038 | − | 30.8447i | −1.61874 | − | 0.982792i | ||||
\(986\) | 16.5404 | + | 16.5404i | 0.526754 | + | 0.526754i | ||||
\(987\) | 12.3396 | − | 12.3396i | 0.392773 | − | 0.392773i | ||||
\(988\) | 6.52545 | − | 6.52545i | 0.207602 | − | 0.207602i | ||||
\(989\) | −14.0314 | −0.446172 | ||||||||
\(990\) | 1.34926 | + | 5.51953i | 0.0428824 | + | 0.175422i | ||||
\(991\) | −39.3415 | − | 39.3415i | −1.24972 | − | 1.24972i | −0.955842 | − | 0.293883i | \(-0.905053\pi\) |
−0.293883 | − | 0.955842i | \(-0.594947\pi\) | |||||||
\(992\) | 7.33111 | − | 7.33111i | 0.232763 | − | 0.232763i | ||||
\(993\) | 17.6573 | 0.560339 | ||||||||
\(994\) | 4.45405 | − | 4.45405i | 0.141274 | − | 0.141274i | ||||
\(995\) | 5.31516 | − | 8.75453i | 0.168502 | − | 0.277537i | ||||
\(996\) | 0.741852 | 0.0235065 | ||||||||
\(997\) | 3.43255 | 0.108710 | 0.0543550 | − | 0.998522i | \(-0.482690\pi\) | ||||
0.0543550 | + | 0.998522i | \(0.482690\pi\) | |||||||
\(998\) | 8.46141 | + | 8.46141i | 0.267841 | + | 0.267841i | ||||
\(999\) | −3.02543 | − | 5.27701i | −0.0957203 | − | 0.166957i |
(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 | 1110.2.l.a.697.15 | yes | 36 | |
5.3 | odd | 4 | 1110.2.o.a.253.4 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.o.a.487.4 | yes | 36 | ||
185.43 | even | 4 | inner | 1110.2.l.a.43.15 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.15 | ✓ | 36 | 185.43 | even | 4 | inner | |
1110.2.l.a.697.15 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.253.4 | yes | 36 | 5.3 | odd | 4 | ||
1110.2.o.a.487.4 | yes | 36 | 37.6 | odd | 4 |