Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (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 | 253.4 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.a.487.4 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.530977 | + | 2.17211i | −0.237460 | + | 0.971397i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | −1.93388 | + | 1.93388i | −0.730937 | + | 0.730937i | −0.970805 | − | 0.239869i | \(-0.922896\pi\) |
0.239869 | + | 0.970805i | \(0.422896\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 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 | ||||
\(13\) | −2.64021 | −0.732261 | −0.366131 | − | 0.930563i | \(-0.619318\pi\) | ||||
−0.366131 | + | 0.930563i | \(0.619318\pi\) | |||||||
\(14\) | 1.93388 | − | 1.93388i | 0.516850 | − | 0.516850i | ||||
\(15\) | −1.16046 | − | 1.91137i | −0.299629 | − | 0.493514i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.60448i | − | 0.874214i | −0.899410 | − | 0.437107i | \(-0.856003\pi\) | ||
0.899410 | − | 0.437107i | \(-0.143997\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −2.47157 | − | 2.47157i | −0.567017 | − | 0.567017i | 0.364275 | − | 0.931291i | \(-0.381317\pi\) |
−0.931291 | + | 0.364275i | \(0.881317\pi\) | |||||||
\(20\) | −0.530977 | + | 2.17211i | −0.118730 | + | 0.485699i | ||||
\(21\) | − | 2.73491i | − | 0.596807i | ||||||
\(22\) | 2.54109i | 0.541763i | ||||||||
\(23\) | −4.49206 | −0.936659 | −0.468329 | − | 0.883554i | \(-0.655144\pi\) | ||||
−0.468329 | + | 0.883554i | \(0.655144\pi\) | |||||||
\(24\) | 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 | −0.138266 | − | 0.990395i | \(-0.544153\pi\) |
0.990395 | + | 0.138266i | \(0.0441530\pi\) | |||||||
\(30\) | 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 | \(0.368893\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.79682 | + | 1.79682i | 0.312787 | + | 0.312787i | ||||
\(34\) | 3.60448i | 0.618163i | ||||||||
\(35\) | −3.17375 | − | 5.22744i | −0.536461 | − | 0.883598i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 5.87071 | + | 1.59211i | 0.965138 | + | 0.261741i | ||||
\(38\) | 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 | \(-0.109524\pi\) | |||||||
\(42\) | 2.73491i | 0.422006i | ||||||||
\(43\) | −3.12360 | −0.476344 | −0.238172 | − | 0.971223i | \(-0.576548\pi\) | ||||
−0.238172 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(44\) | − | 2.54109i | − | 0.383084i | ||||||
\(45\) | 2.17211 | + | 0.530977i | 0.323799 | + | 0.0791534i | ||||
\(46\) | 4.49206 | 0.662318 | ||||||||
\(47\) | 4.51187 | − | 4.51187i | 0.658123 | − | 0.658123i | −0.296812 | − | 0.954936i | \(-0.595924\pi\) |
0.954936 | + | 0.296812i | \(0.0959236\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | − | 0.479758i | − | 0.0685368i | ||||||
\(50\) | 4.43613 | + | 2.30668i | 0.627363 | + | 0.326214i | ||||
\(51\) | 2.54875 | + | 2.54875i | 0.356896 | + | 0.356896i | ||||
\(52\) | −2.64021 | −0.366131 | ||||||||
\(53\) | −0.301411 | − | 0.301411i | −0.0414020 | − | 0.0414020i | 0.686103 | − | 0.727505i | \(-0.259320\pi\) |
−0.727505 | + | 0.686103i | \(0.759320\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | 5.51953 | + | 1.34926i | 0.744253 | + | 0.181934i | ||||
\(56\) | 1.93388 | − | 1.93388i | 0.258425 | − | 0.258425i | ||||
\(57\) | 3.49532 | 0.462967 | ||||||||
\(58\) | −4.58885 | + | 4.58885i | −0.602546 | + | 0.602546i | ||||
\(59\) | −0.813625 | − | 0.813625i | −0.105925 | − | 0.105925i | 0.652158 | − | 0.758083i | \(-0.273864\pi\) |
−0.758083 | + | 0.652158i | \(0.773864\pi\) | |||||||
\(60\) | −1.16046 | − | 1.91137i | −0.149814 | − | 0.246757i | ||||
\(61\) | −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 | \(-0.0838191\pi\) |
−0.260293 | + | 0.965530i | \(0.583819\pi\) | |||||||
\(68\) | − | 3.60448i | − | 0.437107i | ||||||
\(69\) | 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 | \(0.543639\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −3.70992 | + | 3.70992i | −0.434213 | + | 0.434213i | −0.890059 | − | 0.455846i | \(-0.849337\pi\) |
0.455846 | + | 0.890059i | \(0.349337\pi\) | |||||||
\(74\) | −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 | 0.391347 | − | 0.920243i | \(-0.372009\pi\) |
−0.920243 | + | 0.391347i | \(0.872009\pi\) | |||||||
\(80\) | −0.530977 | + | 2.17211i | −0.0593651 | + | 0.242849i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.31993i | 0.477056i | ||||||||
\(83\) | −0.524568 | − | 0.524568i | −0.0575788 | − | 0.0575788i | 0.677731 | − | 0.735310i | \(-0.262963\pi\) |
−0.735310 | + | 0.677731i | \(0.762963\pi\) | |||||||
\(84\) | − | 2.73491i | − | 0.298404i | ||||||
\(85\) | 7.82932 | + | 1.91389i | 0.849209 | + | 0.207591i | ||||
\(86\) | 3.12360 | 0.336826 | ||||||||
\(87\) | 6.48962i | 0.695760i | ||||||||
\(88\) | 2.54109i | 0.270881i | ||||||||
\(89\) | 6.69075 | − | 6.69075i | 0.709218 | − | 0.709218i | −0.257153 | − | 0.966371i | \(-0.582784\pi\) |
0.966371 | + | 0.257153i | \(0.0827844\pi\) | |||||||
\(90\) | −2.17211 | − | 0.530977i | −0.228961 | − | 0.0559699i | ||||
\(91\) | 5.10583 | − | 5.10583i | 0.535237 | − | 0.535237i | ||||
\(92\) | −4.49206 | −0.468329 | ||||||||
\(93\) | −10.3677 | −1.07509 | ||||||||
\(94\) | −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 | ||||
\(97\) | − | 17.0294i | − | 1.72908i | −0.502565 | − | 0.864539i | \(-0.667610\pi\) | ||
0.502565 | − | 0.864539i | \(-0.332390\pi\) | |||||||
\(98\) | 0.479758i | 0.0484628i | ||||||||
\(99\) | −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 | ||||
\(103\) | − | 2.66961i | − | 0.263044i | −0.991313 | − | 0.131522i | \(-0.958014\pi\) | ||
0.991313 | − | 0.131522i | \(-0.0419864\pi\) | |||||||
\(104\) | 2.64021 | 0.258894 | ||||||||
\(105\) | 5.94054 | + | 1.45218i | 0.579737 | + | 0.141718i | ||||
\(106\) | 0.301411 | + | 0.301411i | 0.0292757 | + | 0.0292757i | ||||
\(107\) | −0.404456 | + | 0.404456i | −0.0391002 | + | 0.0391002i | −0.726387 | − | 0.687286i | \(-0.758802\pi\) |
0.687286 | + | 0.726387i | \(0.258802\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −1.04982 | − | 1.04982i | −0.100554 | − | 0.100554i | 0.655040 | − | 0.755594i | \(-0.272652\pi\) |
−0.755594 | + | 0.655040i | \(0.772652\pi\) | |||||||
\(110\) | −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 | ||||
\(113\) | − | 5.71763i | − | 0.537869i | −0.963158 | − | 0.268935i | \(-0.913328\pi\) | ||
0.963158 | − | 0.268935i | \(-0.0866715\pi\) | |||||||
\(114\) | −3.49532 | −0.327367 | ||||||||
\(115\) | 2.38518 | − | 9.75725i | 0.222419 | − | 0.909868i | ||||
\(116\) | 4.58885 | − | 4.58885i | 0.426064 | − | 0.426064i | ||||
\(117\) | 2.64021i | 0.244087i | ||||||||
\(118\) | 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 | ||||
\(125\) | 7.36585 | − | 8.41096i | 0.658822 | − | 0.752299i | ||||
\(126\) | −1.93388 | − | 1.93388i | −0.172283 | − | 0.172283i | ||||
\(127\) | 3.15767 | − | 3.15767i | 0.280198 | − | 0.280198i | −0.552990 | − | 0.833188i | \(-0.686513\pi\) |
0.833188 | + | 0.552990i | \(0.186513\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.20872 | − | 2.20872i | 0.194467 | − | 0.194467i | ||||
\(130\) | −1.40189 | + | 5.73482i | −0.122954 | + | 0.502977i | ||||
\(131\) | −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 | ||||
\(133\) | 9.55941 | 0.828906 | ||||||||
\(134\) | −5.77261 | − | 5.77261i | −0.498678 | − | 0.498678i | ||||
\(135\) | −1.91137 | + | 1.16046i | −0.164505 | + | 0.0998762i | ||||
\(136\) | 3.60448i | 0.309081i | ||||||||
\(137\) | −12.7858 | + | 12.7858i | −1.09236 | + | 1.09236i | −0.0970857 | + | 0.995276i | \(0.530952\pi\) |
−0.995276 | + | 0.0970857i | \(0.969048\pi\) | |||||||
\(138\) | −3.17637 | + | 3.17637i | −0.270390 | + | 0.270390i | ||||
\(139\) | −3.82368 | −0.324321 | −0.162160 | − | 0.986764i | \(-0.551846\pi\) | ||||
−0.162160 | + | 0.986764i | \(0.551846\pi\) | |||||||
\(140\) | −3.17375 | − | 5.22744i | −0.268231 | − | 0.441799i | ||||
\(141\) | 6.38074i | 0.537355i | ||||||||
\(142\) | 2.30317 | 0.193278 | ||||||||
\(143\) | 6.70901i | 0.561035i | ||||||||
\(144\) | − | 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 | ||||
\(148\) | 5.87071 | + | 1.59211i | 0.482569 | + | 0.130870i | ||||
\(149\) | − | 4.92924i | − | 0.403819i | −0.979404 | − | 0.201909i | \(-0.935285\pi\) | ||
0.979404 | − | 0.201909i | \(-0.0647147\pi\) | |||||||
\(150\) | −4.76789 | + | 1.50574i | −0.389296 | + | 0.122943i | ||||
\(151\) | 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 | ||||
\(153\) | −3.60448 | −0.291405 | ||||||||
\(154\) | −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 | −0.129937 | − | 0.991522i | \(-0.541477\pi\) |
0.991522 | + | 0.129937i | \(0.0414774\pi\) | |||||||
\(158\) | 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 | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.00094i | 0.156726i | 0.996925 | + | 0.0783628i | \(0.0249693\pi\) | ||||
−0.996925 | + | 0.0783628i | \(0.975031\pi\) | |||||||
\(164\) | − | 4.31993i | − | 0.337330i | ||||||
\(165\) | −4.85697 | + | 2.94883i | −0.378115 | + | 0.229566i | ||||
\(166\) | 0.524568 | + | 0.524568i | 0.0407144 | + | 0.0407144i | ||||
\(167\) | − | 3.34903i | − | 0.259156i | −0.991569 | − | 0.129578i | \(-0.958638\pi\) | ||
0.991569 | − | 0.129578i | \(-0.0413622\pi\) | |||||||
\(168\) | 2.73491i | 0.211003i | ||||||||
\(169\) | −6.02931 | −0.463793 | ||||||||
\(170\) | −7.82932 | − | 1.91389i | −0.600481 | − | 0.146789i | ||||
\(171\) | −2.47157 | + | 2.47157i | −0.189006 | + | 0.189006i | ||||
\(172\) | −3.12360 | −0.238172 | ||||||||
\(173\) | 7.11846 | − | 7.11846i | 0.541206 | − | 0.541206i | −0.382676 | − | 0.923882i | \(-0.624998\pi\) |
0.923882 | + | 0.382676i | \(0.124998\pi\) | |||||||
\(174\) | − | 6.48962i | − | 0.491977i | ||||||
\(175\) | 13.0398 | − | 4.11808i | 0.985713 | − | 0.311298i | ||||
\(176\) | − | 2.54109i | − | 0.191542i | ||||||
\(177\) | 1.15064 | 0.0864873 | ||||||||
\(178\) | −6.69075 | + | 6.69075i | −0.501493 | + | 0.501493i | ||||
\(179\) | −8.68094 | + | 8.68094i | −0.648844 | + | 0.648844i | −0.952714 | − | 0.303869i | \(-0.901721\pi\) |
0.303869 | + | 0.952714i | \(0.401721\pi\) | |||||||
\(180\) | 2.17211 | + | 0.530977i | 0.161900 | + | 0.0395767i | ||||
\(181\) | 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 | ||||
\(183\) | 1.22692 | 0.0906966 | ||||||||
\(184\) | 4.49206 | 0.331159 | ||||||||
\(185\) | −6.57544 | + | 11.9064i | −0.483436 | + | 0.875380i | ||||
\(186\) | 10.3677 | 0.760200 | ||||||||
\(187\) | −9.15930 | −0.669795 | ||||||||
\(188\) | 4.51187 | − | 4.51187i | 0.329062 | − | 0.329062i | ||||
\(189\) | −2.73491 | −0.198936 | ||||||||
\(190\) | −6.68086 | + | 4.05617i | −0.484681 | + | 0.294266i | ||||
\(191\) | −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 | ||||
\(193\) | −13.9313 | −1.00280 | −0.501398 | − | 0.865217i | \(-0.667181\pi\) | ||||
−0.501398 | + | 0.865217i | \(0.667181\pi\) | |||||||
\(194\) | 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 | 0.442107 | − | 0.896962i | \(-0.354231\pi\) |
0.896962 | − | 0.442107i | \(-0.145769\pi\) | |||||||
\(198\) | 2.54109 | 0.180588 | ||||||||
\(199\) | 3.23872 | − | 3.23872i | 0.229587 | − | 0.229587i | −0.582933 | − | 0.812520i | \(-0.698095\pi\) |
0.812520 | + | 0.582933i | \(0.198095\pi\) | |||||||
\(200\) | 4.43613 | + | 2.30668i | 0.313681 | + | 0.163107i | ||||
\(201\) | −8.16371 | −0.575824 | ||||||||
\(202\) | 18.0572i | 1.27050i | ||||||||
\(203\) | 17.7486i | 1.24570i | ||||||||
\(204\) | 2.54875 | + | 2.54875i | 0.178448 | + | 0.178448i | ||||
\(205\) | 9.38336 | + | 2.29378i | 0.655362 | + | 0.160205i | ||||
\(206\) | 2.66961i | 0.186000i | ||||||||
\(207\) | 4.49206i | 0.312220i | ||||||||
\(208\) | −2.64021 | −0.183065 | ||||||||
\(209\) | −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 | ||||
\(217\) | −28.3549 | −1.92486 | ||||||||
\(218\) | 1.04982 | + | 1.04982i | 0.0711026 | + | 0.0711026i | ||||
\(219\) | − | 5.24662i | − | 0.354534i | ||||||
\(220\) | 5.51953 | + | 1.34926i | 0.372127 | + | 0.0909672i | ||||
\(221\) | 9.51656i | 0.640153i | ||||||||
\(222\) | 5.27701 | − | 3.02543i | 0.354169 | − | 0.203053i | ||||
\(223\) | −18.2552 | − | 18.2552i | −1.22246 | − | 1.22246i | −0.966754 | − | 0.255707i | \(-0.917692\pi\) |
−0.255707 | − | 0.966754i | \(-0.582308\pi\) | |||||||
\(224\) | 1.93388 | − | 1.93388i | 0.129213 | − | 0.129213i | ||||
\(225\) | −2.30668 | + | 4.43613i | −0.153779 | + | 0.295742i | ||||
\(226\) | 5.71763i | 0.380331i | ||||||||
\(227\) | 20.3161i | 1.34843i | 0.738535 | + | 0.674215i | \(0.235518\pi\) | ||||
−0.738535 | + | 0.674215i | \(0.764482\pi\) | |||||||
\(228\) | 3.49532 | 0.231484 | ||||||||
\(229\) | 23.8741i | 1.57764i | 0.614623 | + | 0.788821i | \(0.289308\pi\) | ||||
−0.614623 | + | 0.788821i | \(0.710692\pi\) | |||||||
\(230\) | −2.38518 | + | 9.75725i | −0.157274 | + | 0.643374i | ||||
\(231\) | −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 | \(-0.750741\pi\) |
0.705459 | + | 0.708751i | \(0.250741\pi\) | |||||||
\(234\) | − | 2.64021i | − | 0.172596i | ||||||
\(235\) | 7.40457 | + | 12.1960i | 0.483021 | + | 0.795577i | ||||
\(236\) | −0.813625 | − | 0.813625i | −0.0529625 | − | 0.0529625i | ||||
\(237\) | 6.64813 | 0.431842 | ||||||||
\(238\) | −6.97061 | − | 6.97061i | −0.451838 | − | 0.451838i | ||||
\(239\) | −11.3273 | − | 11.3273i | −0.732705 | − | 0.732705i | 0.238450 | − | 0.971155i | \(-0.423361\pi\) |
−0.971155 | + | 0.238450i | \(0.923361\pi\) | |||||||
\(240\) | −1.16046 | − | 1.91137i | −0.0749071 | − | 0.123379i | ||||
\(241\) | −3.69272 | + | 3.69272i | −0.237869 | + | 0.237869i | −0.815967 | − | 0.578098i | \(-0.803795\pi\) |
0.578098 | + | 0.815967i | \(0.303795\pi\) | |||||||
\(242\) | −4.54285 | −0.292026 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −0.867564 | − | 0.867564i | −0.0555401 | − | 0.0555401i | ||||
\(245\) | 1.04209 | + | 0.254740i | 0.0665765 | + | 0.0162748i | ||||
\(246\) | −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 | ||||
\(253\) | 11.4147i | 0.717638i | ||||||||
\(254\) | −3.15767 | + | 3.15767i | −0.198130 | + | 0.198130i | ||||
\(255\) | −6.88949 | + | 4.18284i | −0.431437 | + | 0.261939i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 1.06813i | − | 0.0666279i | −0.999445 | − | 0.0333140i | \(-0.989394\pi\) | ||
0.999445 | − | 0.0333140i | \(-0.0106061\pi\) | |||||||
\(258\) | −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 | −0.515538 | + | 0.856867i | \(0.672408\pi\) |
−0.856867 | + | 0.515538i | \(0.827592\pi\) | |||||||
\(264\) | −1.79682 | − | 1.79682i | −0.110587 | − | 0.110587i | ||||
\(265\) | 0.814742 | − | 0.494656i | 0.0500492 | − | 0.0303865i | ||||
\(266\) | −9.55941 | −0.586125 | ||||||||
\(267\) | 9.46214i | 0.579074i | ||||||||
\(268\) | 5.77261 | + | 5.77261i | 0.352618 | + | 0.352618i | ||||
\(269\) | 1.98048i | 0.120752i | 0.998176 | + | 0.0603760i | \(0.0192300\pi\) | ||||
−0.998176 | + | 0.0603760i | \(0.980770\pi\) | |||||||
\(270\) | 1.91137 | − | 1.16046i | 0.116322 | − | 0.0706231i | ||||
\(271\) | −20.2119 | −1.22779 | −0.613894 | − | 0.789389i | \(-0.710398\pi\) | ||||
−0.613894 | + | 0.789389i | \(0.710398\pi\) | |||||||
\(272\) | − | 3.60448i | − | 0.218553i | ||||||
\(273\) | 7.22074i | 0.437019i | ||||||||
\(274\) | 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 | ||||
\(277\) | −26.8225 | −1.61161 | −0.805805 | − | 0.592181i | \(-0.798267\pi\) | ||||
−0.805805 | + | 0.592181i | \(0.798267\pi\) | |||||||
\(278\) | 3.82368 | 0.229329 | ||||||||
\(279\) | 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 | \(0.0837140\pi\) | |||||||
\(282\) | − | 6.38074i | − | 0.379968i | ||||||
\(283\) | − | 20.4845i | − | 1.21768i | −0.793293 | − | 0.608840i | \(-0.791635\pi\) | ||
0.793293 | − | 0.608840i | \(-0.208365\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 4.00775 | 0.235750 | ||||||||
\(290\) | −7.53092 | − | 12.4041i | −0.442231 | − | 0.728392i | ||||
\(291\) | 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 | −0.998266 | − | 0.0588702i | \(-0.981250\pi\) |
−0.0588702 | − | 0.998266i | \(-0.518750\pi\) | |||||||
\(294\) | −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 | ||||
\(298\) | 4.92924i | 0.285543i | ||||||||
\(299\) | 11.8600 | 0.685879 | ||||||||
\(300\) | 4.76789 | − | 1.50574i | 0.275274 | − | 0.0869342i | ||||
\(301\) | 6.04066 | − | 6.04066i | 0.348178 | − | 0.348178i | ||||
\(302\) | − | 2.56917i | − | 0.147839i | ||||||
\(303\) | 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 | 0.936144 | + | 0.351616i | \(0.114368\pi\) |
0.351616 | + | 0.936144i | \(0.385632\pi\) | |||||||
\(308\) | 4.91416 | + | 4.91416i | 0.280010 | + | 0.280010i | ||||
\(309\) | 1.88770 | + | 1.88770i | 0.107387 | + | 0.107387i | ||||
\(310\) | 19.8166 | − | 12.0313i | 1.12551 | − | 0.683333i | ||||
\(311\) | 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 | ||||
\(313\) | −30.7702 | −1.73923 | −0.869616 | − | 0.493729i | \(-0.835634\pi\) | ||||
−0.869616 | + | 0.493729i | \(0.835634\pi\) | |||||||
\(314\) | −10.7956 | + | 10.7956i | −0.609233 | + | 0.609233i | ||||
\(315\) | −5.22744 | + | 3.17375i | −0.294533 | + | 0.178820i | ||||
\(316\) | −4.70094 | − | 4.70094i | −0.264448 | − | 0.264448i | ||||
\(317\) | 12.5932 | + | 12.5932i | 0.707307 | + | 0.707307i | 0.965968 | − | 0.258661i | \(-0.0832813\pi\) |
−0.258661 | + | 0.965968i | \(0.583281\pi\) | |||||||
\(318\) | −0.426260 | −0.0239035 | ||||||||
\(319\) | −11.6607 | − | 11.6607i | −0.652874 | − | 0.652874i | ||||
\(320\) | −0.530977 | + | 2.17211i | −0.0296825 | + | 0.121425i | ||||
\(321\) | − | 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 | ||||||||
\(325\) | 11.7123 | + | 6.09012i | 0.649681 | + | 0.337819i | ||||
\(326\) | − | 2.00094i | − | 0.110822i | ||||||
\(327\) | 1.48467 | 0.0821022 | ||||||||
\(328\) | 4.31993i | 0.238528i | ||||||||
\(329\) | 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 | ||||
\(333\) | 1.59211 | − | 5.87071i | 0.0872469 | − | 0.321713i | ||||
\(334\) | 3.34903i | 0.183251i | ||||||||
\(335\) | −15.6039 | + | 9.47363i | −0.852531 | + | 0.517599i | ||||
\(336\) | − | 2.73491i | − | 0.149202i | ||||||
\(337\) | 2.01004 | + | 2.01004i | 0.109494 | + | 0.109494i | 0.759731 | − | 0.650237i | \(-0.225331\pi\) |
−0.650237 | + | 0.759731i | \(0.725331\pi\) | |||||||
\(338\) | 6.02931 | 0.327951 | ||||||||
\(339\) | 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 | ||||
\(347\) | 15.1173 | 0.811539 | 0.405770 | − | 0.913975i | \(-0.367004\pi\) | ||||
0.405770 | + | 0.913975i | \(0.367004\pi\) | |||||||
\(348\) | 6.48962i | 0.347880i | ||||||||
\(349\) | − | 13.6893i | − | 0.732771i | −0.930463 | − | 0.366386i | \(-0.880595\pi\) | ||
0.930463 | − | 0.366386i | \(-0.119405\pi\) | |||||||
\(350\) | −13.0398 | + | 4.11808i | −0.697005 | + | 0.220121i | ||||
\(351\) | −1.86691 | − | 1.86691i | −0.0996482 | − | 0.0996482i | ||||
\(352\) | 2.54109i | 0.135441i | ||||||||
\(353\) | − | 31.3775i | − | 1.67006i | −0.550206 | − | 0.835029i | \(-0.685451\pi\) | ||
0.550206 | − | 0.835029i | \(-0.314549\pi\) | |||||||
\(354\) | −1.15064 | −0.0611558 | ||||||||
\(355\) | 1.22293 | − | 5.00274i | 0.0649065 | − | 0.265518i | ||||
\(356\) | 6.69075 | − | 6.69075i | 0.354609 | − | 0.354609i | ||||
\(357\) | −9.85793 | −0.521737 | ||||||||
\(358\) | 8.68094 | − | 8.68094i | 0.458802 | − | 0.458802i | ||||
\(359\) | 32.4157i | 1.71083i | 0.517941 | + | 0.855416i | \(0.326699\pi\) | ||||
−0.517941 | + | 0.855416i | \(0.673301\pi\) | |||||||
\(360\) | −2.17211 | − | 0.530977i | −0.114480 | − | 0.0279850i | ||||
\(361\) | − | 6.78271i | − | 0.356985i | ||||||
\(362\) | −14.0432 | −0.738096 | ||||||||
\(363\) | −3.21228 | + | 3.21228i | −0.168601 | + | 0.168601i | ||||
\(364\) | 5.10583 | − | 5.10583i | 0.267618 | − | 0.267618i | ||||
\(365\) | −6.08847 | − | 10.0282i | −0.318685 | − | 0.524902i | ||||
\(366\) | −1.22692 | −0.0641322 | ||||||||
\(367\) | 9.63234 | − | 9.63234i | 0.502804 | − | 0.502804i | −0.409504 | − | 0.912308i | \(-0.634298\pi\) |
0.912308 | + | 0.409504i | \(0.134298\pi\) | |||||||
\(368\) | −4.49206 | −0.234165 | ||||||||
\(369\) | −4.31993 | −0.224887 | ||||||||
\(370\) | 6.57544 | − | 11.9064i | 0.341841 | − | 0.618987i | ||||
\(371\) | 1.16579 | 0.0605245 | ||||||||
\(372\) | −10.3677 | −0.537543 | ||||||||
\(373\) | 21.6306 | − | 21.6306i | 1.11999 | − | 1.11999i | 0.128250 | − | 0.991742i | \(-0.459064\pi\) |
0.991742 | − | 0.128250i | \(-0.0409359\pi\) | |||||||
\(374\) | 9.15930 | 0.473616 | ||||||||
\(375\) | 0.739003 | + | 11.1559i | 0.0381620 | + | 0.576088i | ||||
\(376\) | −4.51187 | + | 4.51187i | −0.232682 | + | 0.232682i | ||||
\(377\) | −12.1155 | + | 12.1155i | −0.623981 | + | 0.623981i | ||||
\(378\) | 2.73491 | 0.140669 | ||||||||
\(379\) | − | 0.115662i | − | 0.00594116i | −0.999996 | − | 0.00297058i | \(-0.999054\pi\) | ||
0.999996 | − | 0.00297058i | \(-0.000945566\pi\) | |||||||
\(380\) | 6.68086 | − | 4.05617i | 0.342721 | − | 0.208077i | ||||
\(381\) | 4.46562i | 0.228781i | ||||||||
\(382\) | 1.64289 | − | 1.64289i | 0.0840578 | − | 0.0840578i | ||||
\(383\) | 1.75588 | 0.0897211 | 0.0448606 | − | 0.998993i | \(-0.485716\pi\) | ||||
0.0448606 | + | 0.998993i | \(0.485716\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | −13.2834 | + | 8.06479i | −0.676985 | + | 0.411020i | ||||
\(386\) | 13.9313 | 0.709084 | ||||||||
\(387\) | 3.12360i | 0.158781i | ||||||||
\(388\) | − | 17.0294i | − | 0.864539i | ||||||
\(389\) | 11.3156 | + | 11.3156i | 0.573722 | + | 0.573722i | 0.933166 | − | 0.359445i | \(-0.117034\pi\) |
−0.359445 | + | 0.933166i | \(0.617034\pi\) | |||||||
\(390\) | −3.06384 | − | 5.04642i | −0.155144 | − | 0.255535i | ||||
\(391\) | 16.1915i | 0.818840i | ||||||||
\(392\) | 0.479758i | 0.0242314i | ||||||||
\(393\) | 17.7614 | 0.895943 | ||||||||
\(394\) | −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 | \(-0.372639\pi\) |
−0.921015 | + | 0.389527i | \(0.872639\pi\) | |||||||
\(398\) | −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 | \(0.673012\pi\) | |||||||
\(402\) | 8.16371 | 0.407169 | ||||||||
\(403\) | −19.3556 | − | 19.3556i | −0.964173 | − | 0.964173i | ||||
\(404\) | − | 18.0572i | − | 0.898377i | ||||||
\(405\) | 0.530977 | − | 2.17211i | 0.0263845 | − | 0.107933i | ||||
\(406\) | − | 17.7486i | − | 0.880846i | ||||||
\(407\) | 4.04569 | − | 14.9180i | 0.200537 | − | 0.739458i | ||||
\(408\) | −2.54875 | − | 2.54875i | −0.126182 | − | 0.126182i | ||||
\(409\) | −12.5316 | + | 12.5316i | −0.619650 | + | 0.619650i | −0.945442 | − | 0.325792i | \(-0.894369\pi\) |
0.325792 | + | 0.945442i | \(0.394369\pi\) | |||||||
\(410\) | −9.38336 | − | 2.29378i | −0.463411 | − | 0.113282i | ||||
\(411\) | − | 18.0818i | − | 0.891910i | ||||||
\(412\) | − | 2.66961i | − | 0.131522i | ||||||
\(413\) | 3.14690 | 0.154849 | ||||||||
\(414\) | − | 4.49206i | − | 0.220773i | ||||||
\(415\) | 1.41795 | − | 0.860886i | 0.0696046 | − | 0.0422592i | ||||
\(416\) | 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 | \(-0.824854\pi\) | ||
0.852400 | − | 0.522891i | \(-0.175146\pi\) | |||||||
\(420\) | 5.94054 | + | 1.45218i | 0.289868 | + | 0.0708590i | ||||
\(421\) | 10.7024 | + | 10.7024i | 0.521601 | + | 0.521601i | 0.918055 | − | 0.396454i | \(-0.129759\pi\) |
−0.396454 | + | 0.918055i | \(0.629759\pi\) | |||||||
\(422\) | 13.4040 | 0.652495 | ||||||||
\(423\) | −4.51187 | − | 4.51187i | −0.219374 | − | 0.219374i | ||||
\(424\) | 0.301411 | + | 0.301411i | 0.0146378 | + | 0.0146378i | ||||
\(425\) | −8.31438 | + | 15.9899i | −0.403307 | + | 0.775625i | ||||
\(426\) | −1.62859 | + | 1.62859i | −0.0789053 | + | 0.0789053i | ||||
\(427\) | 3.35552 | 0.162385 | ||||||||
\(428\) | −0.404456 | + | 0.404456i | −0.0195501 | + | 0.0195501i | ||||
\(429\) | −4.74398 | − | 4.74398i | −0.229042 | − | 0.229042i | ||||
\(430\) | −1.65856 | + | 6.78480i | −0.0799829 | + | 0.327192i | ||||
\(431\) | −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 | 0.945656 | − | 0.325169i | \(-0.105421\pi\) |
−0.325169 | + | 0.945656i | \(0.605421\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | 5.24662i | 0.250693i | ||||||||
\(439\) | −12.6631 | + | 12.6631i | −0.604375 | + | 0.604375i | −0.941471 | − | 0.337095i | \(-0.890556\pi\) |
0.337095 | + | 0.941471i | \(0.390556\pi\) | |||||||
\(440\) | −5.51953 | − | 1.34926i | −0.263133 | − | 0.0643235i | ||||
\(441\) | −0.479758 | −0.0228456 | ||||||||
\(442\) | − | 9.51656i | − | 0.452657i | ||||||
\(443\) | −19.8789 | + | 19.8789i | −0.944476 | + | 0.944476i | −0.998538 | − | 0.0540616i | \(-0.982783\pi\) |
0.0540616 | + | 0.998538i | \(0.482783\pi\) | |||||||
\(444\) | −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 | 0.422298 | − | 0.906457i | \(-0.361224\pi\) |
−0.906457 | + | 0.422298i | \(0.861224\pi\) | |||||||
\(450\) | 2.30668 | − | 4.43613i | 0.108738 | − | 0.209121i | ||||
\(451\) | −10.9773 | −0.516902 | ||||||||
\(452\) | − | 5.71763i | − | 0.268935i | ||||||
\(453\) | −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 | ||||||||
\(457\) | 3.03992i | 0.142202i | 0.997469 | + | 0.0711008i | \(0.0226512\pi\) | ||||
−0.997469 | + | 0.0711008i | \(0.977349\pi\) | |||||||
\(458\) | − | 23.8741i | − | 1.11556i | ||||||
\(459\) | 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 | \(0.272388\pi\) | |||||||
\(462\) | 6.94967 | 0.323328 | ||||||||
\(463\) | −20.8314 | −0.968118 | −0.484059 | − | 0.875035i | \(-0.660838\pi\) | ||||
−0.484059 | + | 0.875035i | \(0.660838\pi\) | |||||||
\(464\) | 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 | ||||
\(467\) | − | 30.6842i | − | 1.41990i | −0.704253 | − | 0.709949i | \(-0.748718\pi\) | ||
0.704253 | − | 0.709949i | \(-0.251282\pi\) | |||||||
\(468\) | 2.64021i | 0.122044i | ||||||||
\(469\) | −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 | ||||
\(473\) | 7.93735i | 0.364960i | ||||||||
\(474\) | −6.64813 | −0.305359 | ||||||||
\(475\) | 5.26306 | + | 16.6653i | 0.241486 | + | 0.764657i | ||||
\(476\) | 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 | 0.787092 | − | 0.616836i | \(-0.211586\pi\) |
−0.616836 | + | 0.787092i | \(0.711586\pi\) | |||||||
\(480\) | 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 | ||||
\(483\) | 12.2854i | 0.559005i | ||||||||
\(484\) | 4.54285 | 0.206493 | ||||||||
\(485\) | 36.9898 | + | 9.04225i | 1.67962 | + | 0.410587i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | − | 19.2486i | − | 0.872239i | −0.899889 | − | 0.436120i | \(-0.856352\pi\) | ||
0.899889 | − | 0.436120i | \(-0.143648\pi\) | |||||||
\(488\) | 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 | ||||
\(495\) | 1.34926 | − | 5.51953i | 0.0606448 | − | 0.248084i | ||||
\(496\) | 7.33111 | + | 7.33111i | 0.329176 | + | 0.329176i | ||||
\(497\) | 4.45405 | − | 4.45405i | 0.199791 | − | 0.199791i | ||||
\(498\) | −0.741852 | −0.0332432 | ||||||||
\(499\) | 8.46141 | − | 8.46141i | 0.378785 | − | 0.378785i | −0.491879 | − | 0.870664i | \(-0.663690\pi\) |
0.870664 | + | 0.491879i | \(0.163690\pi\) | |||||||
\(500\) | 7.36585 | − | 8.41096i | 0.329411 | − | 0.376150i | ||||
\(501\) | 2.36812 | + | 2.36812i | 0.105800 | + | 0.105800i | ||||
\(502\) | 8.29215 | + | 8.29215i | 0.370097 | + | 0.370097i | ||||
\(503\) | −16.8793 | −0.752612 | −0.376306 | − | 0.926495i | \(-0.622806\pi\) | ||||
−0.376306 | + | 0.926495i | \(0.622806\pi\) | |||||||
\(504\) | −1.93388 | − | 1.93388i | −0.0861417 | − | 0.0861417i | ||||
\(505\) | 39.2221 | + | 9.58794i | 1.74536 | + | 0.426658i | ||||
\(506\) | − | 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 | \(-0.685245\pi\) | ||||
−0.549667 | + | 0.835384i | \(0.685245\pi\) | |||||||
\(510\) | 6.88949 | − | 4.18284i | 0.305072 | − | 0.185219i | ||||
\(511\) | − | 14.3491i | − | 0.634765i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 3.49532i | − | 0.154322i | ||||||
\(514\) | 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 | ||||
\(518\) | 14.4322 | − | 8.27428i | 0.634113 | − | 0.363551i | ||||
\(519\) | 10.0670i | 0.441893i | ||||||||
\(520\) | −1.40189 | + | 5.73482i | −0.0614769 | + | 0.251488i | ||||
\(521\) | − | 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 | ||||
\(523\) | 43.8527 | 1.91755 | 0.958773 | − | 0.284174i | \(-0.0917195\pi\) | ||||
0.958773 | + | 0.284174i | \(0.0917195\pi\) | |||||||
\(524\) | −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 | ||||
\(532\) | 9.55941 | 0.414453 | ||||||||
\(533\) | 11.4055i | 0.494027i | ||||||||
\(534\) | − | 9.46214i | − | 0.409467i | ||||||
\(535\) | −0.663765 | − | 1.09328i | −0.0286971 | − | 0.0472666i | ||||
\(536\) | −5.77261 | − | 5.77261i | −0.249339 | − | 0.249339i | ||||
\(537\) | − | 12.2767i | − | 0.529779i | ||||||
\(538\) | − | 1.98048i | − | 0.0853845i | ||||||
\(539\) | −1.21911 | −0.0525107 | ||||||||
\(540\) | −1.91137 | + | 1.16046i | −0.0822523 | + | 0.0499381i | ||||
\(541\) | 25.4345 | − | 25.4345i | 1.09351 | − | 1.09351i | 0.0983645 | − | 0.995150i | \(-0.468639\pi\) |
0.995150 | − | 0.0983645i | \(-0.0313611\pi\) | |||||||
\(542\) | 20.2119 | 0.868177 | ||||||||
\(543\) | −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 | ||||||
\(547\) | −13.3671 | −0.571538 | −0.285769 | − | 0.958299i | \(-0.592249\pi\) | ||||
−0.285769 | + | 0.958299i | \(0.592249\pi\) | |||||||
\(548\) | −12.7858 | + | 12.7858i | −0.546181 | + | 0.546181i | ||||
\(549\) | −0.867564 | + | 0.867564i | −0.0370267 | + | 0.0370267i | ||||
\(550\) | 5.86149 | − | 11.2726i | 0.249935 | − | 0.480665i | ||||
\(551\) | −22.6833 | −0.966342 | ||||||||
\(552\) | −3.17637 | + | 3.17637i | −0.135195 | + | 0.135195i | ||||
\(553\) | 18.1821 | 0.773180 | ||||||||
\(554\) | 26.8225 | 1.13958 | ||||||||
\(555\) | −3.76959 | − | 13.0687i | −0.160010 | − | 0.554734i | ||||
\(556\) | −3.82368 | −0.162160 | ||||||||
\(557\) | 17.4429 | 0.739080 | 0.369540 | − | 0.929215i | \(-0.379515\pi\) | ||||
0.369540 | + | 0.929215i | \(0.379515\pi\) | |||||||
\(558\) | −7.33111 | + | 7.33111i | −0.310350 | + | 0.310350i | ||||
\(559\) | 8.24695 | 0.348809 | ||||||||
\(560\) | −3.17375 | − | 5.22744i | −0.134115 | − | 0.220900i | ||||
\(561\) | 6.47661 | − | 6.47661i | 0.273442 | − | 0.273442i | ||||
\(562\) | −11.8287 | + | 11.8287i | −0.498964 | + | 0.498964i | ||||
\(563\) | 2.58551 | 0.108966 | 0.0544831 | − | 0.998515i | \(-0.482649\pi\) | ||||
0.0544831 | + | 0.998515i | \(0.482649\pi\) | |||||||
\(564\) | 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 | ||||
\(568\) | 2.30317 | 0.0966389 | ||||||||
\(569\) | −19.1350 | + | 19.1350i | −0.802180 | + | 0.802180i | −0.983436 | − | 0.181256i | \(-0.941984\pi\) |
0.181256 | + | 0.983436i | \(0.441984\pi\) | |||||||
\(570\) | 1.85594 | − | 7.59223i | 0.0777367 | − | 0.318004i | ||||
\(571\) | 6.72822 | 0.281567 | 0.140784 | − | 0.990040i | \(-0.455038\pi\) | ||||
0.140784 | + | 0.990040i | \(0.455038\pi\) | |||||||
\(572\) | 6.70901i | 0.280518i | ||||||||
\(573\) | − | 2.32340i | − | 0.0970616i | ||||||
\(574\) | −8.35421 | − | 8.35421i | −0.348698 | − | 0.348698i | ||||
\(575\) | 19.9273 | + | 10.3618i | 0.831027 | + | 0.432115i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 32.3098i | − | 1.34507i | −0.740063 | − | 0.672537i | \(-0.765204\pi\) | ||
0.740063 | − | 0.672537i | \(-0.234796\pi\) | |||||||
\(578\) | −4.00775 | −0.166701 | ||||||||
\(579\) | 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 | ||||
\(587\) | 13.1138 | 0.541266 | 0.270633 | − | 0.962683i | \(-0.412767\pi\) | ||||
0.270633 | + | 0.962683i | \(0.412767\pi\) | |||||||
\(588\) | 0.339240 | + | 0.339240i | 0.0139900 | + | 0.0139900i | ||||
\(589\) | − | 36.2386i | − | 1.49319i | ||||||
\(590\) | −2.19930 | + | 1.33527i | −0.0905437 | + | 0.0549721i | ||||
\(591\) | 26.5798i | 1.09335i | ||||||||
\(592\) | 5.87071 | + | 1.59211i | 0.241285 | + | 0.0654352i | ||||
\(593\) | 28.5182 | + | 28.5182i | 1.17110 | + | 1.17110i | 0.981947 | + | 0.189155i | \(0.0605749\pi\) |
0.189155 | + | 0.981947i | \(0.439425\pi\) | |||||||
\(594\) | −1.79682 | + | 1.79682i | −0.0737245 | + | 0.0737245i | ||||
\(595\) | −18.8422 | + | 11.4397i | −0.772454 | + | 0.468982i | ||||
\(596\) | − | 4.92924i | − | 0.201909i | ||||||
\(597\) | 4.58024i | 0.187457i | ||||||||
\(598\) | −11.8600 | −0.484990 | ||||||||
\(599\) | 13.3830i | 0.546815i | 0.961898 | + | 0.273407i | \(0.0881507\pi\) | ||||
−0.961898 | + | 0.273407i | \(0.911849\pi\) | |||||||
\(600\) | −4.76789 | + | 1.50574i | −0.194648 | + | 0.0614717i | ||||
\(601\) | 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 | ||||||||
\(605\) | −2.41215 | + | 9.86758i | −0.0980679 | + | 0.401174i | ||||
\(606\) | −12.7683 | − | 12.7683i | −0.518678 | − | 0.518678i | ||||
\(607\) | −34.6374 | −1.40589 | −0.702944 | − | 0.711246i | \(-0.748131\pi\) | ||||
−0.702944 | + | 0.711246i | \(0.748131\pi\) | |||||||
\(608\) | 2.47157 | + | 2.47157i | 0.100235 | + | 0.100235i | ||||
\(609\) | −12.5501 | − | 12.5501i | −0.508557 | − | 0.508557i | ||||
\(610\) | −2.34510 | + | 1.42379i | −0.0949504 | + | 0.0576475i | ||||
\(611\) | −11.9123 | + | 11.9123i | −0.481918 | + | 0.481918i | ||||
\(612\) | −3.60448 | −0.145702 | ||||||||
\(613\) | 13.5656 | − | 13.5656i | 0.547908 | − | 0.547908i | −0.377928 | − | 0.925835i | \(-0.623363\pi\) |
0.925835 | + | 0.377928i | \(0.123363\pi\) | |||||||
\(614\) | −22.5634 | − | 22.5634i | −0.910584 | − | 0.910584i | ||||
\(615\) | −8.25699 | + | 5.01309i | −0.332954 | + | 0.202147i | ||||
\(616\) | −4.91416 | − | 4.91416i | −0.197997 | − | 0.197997i | ||||
\(617\) | −29.4000 | − | 29.4000i | −1.18360 | − | 1.18360i | −0.978805 | − | 0.204793i | \(-0.934348\pi\) |
−0.204793 | − | 0.978805i | \(-0.565652\pi\) | |||||||
\(618\) | −1.88770 | − | 1.88770i | −0.0759343 | − | 0.0759343i | ||||
\(619\) | −8.71796 | −0.350404 | −0.175202 | − | 0.984532i | \(-0.556058\pi\) | ||||
−0.175202 | + | 0.984532i | \(0.556058\pi\) | |||||||
\(620\) | −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 | ||||
\(623\) | 25.8782i | 1.03679i | ||||||||
\(624\) | 1.86691 | − | 1.86691i | 0.0747361 | − | 0.0747361i | ||||
\(625\) | 14.3584 | + | 20.4655i | 0.574337 | + | 0.818619i | ||||
\(626\) | 30.7702 | 1.22982 | ||||||||
\(627\) | − | 8.88194i | − | 0.354710i | ||||||
\(628\) | 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 | ||||
\(635\) | 5.18216 | + | 8.53546i | 0.205648 | + | 0.338719i | ||||
\(636\) | 0.426260 | 0.0169023 | ||||||||
\(637\) | 1.26666i | 0.0501869i | ||||||||
\(638\) | 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 | \(0.372658\pi\) | |||||||
\(642\) | 0.571987i | 0.0225745i | ||||||||
\(643\) | − | 30.0934i | − | 1.18677i | −0.804919 | − | 0.593384i | \(-0.797791\pi\) | ||
0.804919 | − | 0.593384i | \(-0.202209\pi\) | |||||||
\(644\) | 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 | ||||
\(647\) | 3.58012 | 0.140749 | 0.0703746 | − | 0.997521i | \(-0.477581\pi\) | ||||
0.0703746 | + | 0.997521i | \(0.477581\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −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 | ||||
\(652\) | 2.00094i | 0.0783628i | ||||||||
\(653\) | 21.6461i | 0.847079i | 0.905878 | + | 0.423540i | \(0.139213\pi\) | ||||
−0.905878 | + | 0.423540i | \(0.860787\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | − | 17.4508i | − | 0.680302i | ||||||
\(659\) | −24.8071 | −0.966346 | −0.483173 | − | 0.875525i | \(-0.660516\pi\) | ||||
−0.483173 | + | 0.875525i | \(0.660516\pi\) | |||||||
\(660\) | −4.85697 | + | 2.94883i | −0.189057 | + | 0.114783i | ||||
\(661\) | −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 | ||||
\(668\) | − | 3.34903i | − | 0.129578i | ||||||
\(669\) | 25.8168 | 0.998135 | ||||||||
\(670\) | 15.6039 | − | 9.47363i | 0.602830 | − | 0.365998i | ||||
\(671\) | −2.20456 | + | 2.20456i | −0.0851061 | + | 0.0851061i | ||||
\(672\) | 2.73491i | 0.105502i | ||||||||
\(673\) | 23.8195 | + | 23.8195i | 0.918173 | + | 0.918173i | 0.996896 | − | 0.0787239i | \(-0.0250846\pi\) |
−0.0787239 | + | 0.996896i | \(0.525085\pi\) | |||||||
\(674\) | −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 | −0.999790 | − | 0.0204933i | \(-0.993476\pi\) |
−0.0204933 | − | 0.999790i | \(-0.506524\pi\) | |||||||
\(678\) | −4.04297 | − | 4.04297i | −0.155269 | − | 0.155269i | ||||
\(679\) | 32.9329 | + | 32.9329i | 1.26385 | + | 1.26385i | ||||
\(680\) | −7.82932 | − | 1.91389i | −0.300241 | − | 0.0733945i | ||||
\(681\) | −14.3657 | − | 14.3657i | −0.550494 | − | 0.550494i | ||||
\(682\) | −18.6290 | + | 18.6290i | −0.713342 | + | 0.713342i | ||||
\(683\) | −26.8136 | −1.02599 | −0.512997 | − | 0.858390i | \(-0.671465\pi\) | ||||
−0.512997 | + | 0.858390i | \(0.671465\pi\) | |||||||
\(684\) | −2.47157 | + | 2.47157i | −0.0945028 | + | 0.0945028i | ||||
\(685\) | −20.9831 | − | 34.5610i | −0.801725 | − | 1.32051i | ||||
\(686\) | 12.6093 | + | 12.6093i | 0.481427 | + | 0.481427i | ||||
\(687\) | −16.8815 | − | 16.8815i | −0.644070 | − | 0.644070i | ||||
\(688\) | −3.12360 | −0.119086 | ||||||||
\(689\) | 0.795788 | + | 0.795788i | 0.0303171 | + | 0.0303171i | ||||
\(690\) | −5.21284 | − | 8.58599i | −0.198449 | − | 0.326863i | ||||
\(691\) | 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 | ||||||||
\(695\) | 2.03029 | − | 8.30546i | 0.0770133 | − | 0.315044i | ||||
\(696\) | − | 6.48962i | − | 0.245988i | ||||||
\(697\) | −15.5711 | −0.589797 | ||||||||
\(698\) | 13.6893i | 0.518148i | ||||||||
\(699\) | − | 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 | ||||
\(703\) | −10.5748 | − | 18.4448i | −0.398838 | − | 0.695661i | ||||
\(704\) | − | 2.54109i | − | 0.0957710i | ||||||
\(705\) | −13.8597 | − | 3.38803i | −0.521986 | − | 0.127601i | ||||
\(706\) | 31.3775i | 1.18091i | ||||||||
\(707\) | 34.9203 | + | 34.9203i | 1.31331 | + | 1.31331i | ||||
\(708\) | 1.15064 | 0.0432437 | ||||||||
\(709\) | 8.21814 | + | 8.21814i | 0.308639 | + | 0.308639i | 0.844381 | − | 0.535743i | \(-0.179968\pi\) |
−0.535743 | + | 0.844381i | \(0.679968\pi\) | |||||||
\(710\) | −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 | ||||
\(717\) | 16.0193 | 0.598251 | ||||||||
\(718\) | − | 32.4157i | − | 1.20974i | ||||||
\(719\) | 9.15541i | 0.341439i | 0.985320 | + | 0.170720i | \(0.0546092\pi\) | ||||
−0.985320 | + | 0.170720i | \(0.945391\pi\) | |||||||
\(720\) | 2.17211 | + | 0.530977i | 0.0809498 | + | 0.0197884i | ||||
\(721\) | 5.16269 | + | 5.16269i | 0.192269 | + | 0.192269i | ||||
\(722\) | 6.78271i | 0.252426i | ||||||||
\(723\) | − | 5.22229i | − | 0.194219i | ||||||
\(724\) | 14.0432 | 0.521912 | ||||||||
\(725\) | −30.9418 | + | 9.77171i | −1.14915 | + | 0.362912i | ||||
\(726\) | 3.21228 | − | 3.21228i | 0.119219 | − | 0.119219i | ||||
\(727\) | −32.4114 | −1.20207 | −0.601036 | − | 0.799222i | \(-0.705245\pi\) | ||||
−0.601036 | + | 0.799222i | \(0.705245\pi\) | |||||||
\(728\) | −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 | ||||||||
\(732\) | 1.22692 | 0.0453483 | ||||||||
\(733\) | 35.1555 | − | 35.1555i | 1.29850 | − | 1.29850i | 0.369115 | − | 0.929384i | \(-0.379661\pi\) |
0.929384 | − | 0.369115i | \(-0.120339\pi\) | |||||||
\(734\) | −9.63234 | + | 9.63234i | −0.355536 | + | 0.355536i | ||||
\(735\) | −0.916995 | + | 0.556738i | −0.0338239 | + | 0.0205356i | ||||
\(736\) | 4.49206 | 0.165579 | ||||||||
\(737\) | 14.6687 | − | 14.6687i | 0.540330 | − | 0.540330i | ||||
\(738\) | 4.31993 | 0.159019 | ||||||||
\(739\) | 11.5902 | 0.426351 | 0.213176 | − | 0.977014i | \(-0.431619\pi\) | ||||
0.213176 | + | 0.977014i | \(0.431619\pi\) | |||||||
\(740\) | −6.57544 | + | 11.9064i | −0.241718 | + | 0.437690i | ||||
\(741\) | −9.22838 | −0.339013 | ||||||||
\(742\) | −1.16579 | −0.0427973 | ||||||||
\(743\) | 21.4779 | − | 21.4779i | 0.787949 | − | 0.787949i | −0.193209 | − | 0.981158i | \(-0.561890\pi\) |
0.981158 | + | 0.193209i | \(0.0618895\pi\) | |||||||
\(744\) | 10.3677 | 0.380100 | ||||||||
\(745\) | 10.7068 | + | 2.61731i | 0.392269 | + | 0.0958909i | ||||
\(746\) | −21.6306 | + | 21.6306i | −0.791954 | + | 0.791954i | ||||
\(747\) | −0.524568 | + | 0.524568i | −0.0191929 | + | 0.0191929i | ||||
\(748\) | −9.15930 | −0.334897 | ||||||||
\(749\) | − | 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 | ||||
\(753\) | 11.7269 | 0.427351 | ||||||||
\(754\) | 12.1155 | − | 12.1155i | 0.441221 | − | 0.441221i | ||||
\(755\) | −5.58051 | − | 1.36417i | −0.203096 | − | 0.0496472i | ||||
\(756\) | −2.73491 | −0.0994679 | ||||||||
\(757\) | 28.5100i | 1.03622i | 0.855315 | + | 0.518108i | \(0.173363\pi\) | ||||
−0.855315 | + | 0.518108i | \(0.826637\pi\) | |||||||
\(758\) | 0.115662i | 0.00420103i | ||||||||
\(759\) | −8.07143 | − | 8.07143i | −0.292974 | − | 0.292974i | ||||
\(760\) | −6.68086 | + | 4.05617i | −0.242340 | + | 0.147133i | ||||
\(761\) | 19.7514i | 0.715988i | 0.933724 | + | 0.357994i | \(0.116539\pi\) | ||||
−0.933724 | + | 0.357994i | \(0.883461\pi\) | |||||||
\(762\) | − | 4.46562i | − | 0.161772i | ||||||
\(763\) | 4.06043 | 0.146998 | ||||||||
\(764\) | −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 | −0.0391547 | − | 0.999233i | \(-0.512467\pi\) |
0.999233 | + | 0.0391547i | \(0.0124665\pi\) | |||||||
\(770\) | 13.2834 | − | 8.06479i | 0.478700 | − | 0.290635i | ||||
\(771\) | 0.755280 | + | 0.755280i | 0.0272007 | + | 0.0272007i | ||||
\(772\) | −13.9313 | −0.501398 | ||||||||
\(773\) | −1.41448 | − | 1.41448i | −0.0508753 | − | 0.0508753i | 0.681211 | − | 0.732087i | \(-0.261453\pi\) |
−0.732087 | + | 0.681211i | \(0.761453\pi\) | |||||||
\(774\) | − | 3.12360i | − | 0.112275i | ||||||
\(775\) | −15.6112 | − | 49.4322i | −0.560770 | − | 1.77566i | ||||
\(776\) | 17.0294i | 0.611322i | ||||||||
\(777\) | 4.35428 | − | 16.0559i | 0.156209 | − | 0.576002i | ||||
\(778\) | −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 | ||||||||
\(782\) | − | 16.1915i | − | 0.579007i | ||||||
\(783\) | 6.48962 | 0.231920 | ||||||||
\(784\) | − | 0.479758i | − | 0.0171342i | ||||||
\(785\) | 17.7171 | + | 29.1816i | 0.632350 | + | 1.04153i | ||||
\(786\) | −17.7614 | −0.633527 | ||||||||
\(787\) | 22.3671 | − | 22.3671i | 0.797301 | − | 0.797301i | −0.185368 | − | 0.982669i | \(-0.559348\pi\) |
0.982669 | + | 0.185368i | \(0.0593479\pi\) | |||||||
\(788\) | 18.7947 | − | 18.7947i | 0.669535 | − | 0.669535i | ||||
\(789\) | − | 31.4757i | − | 1.12056i | ||||||
\(790\) | −12.7070 | + | 7.71486i | −0.452096 | + | 0.274483i | ||||
\(791\) | 11.0572 | + | 11.0572i | 0.393148 | + | 0.393148i | ||||
\(792\) | 2.54109 | 0.0902938 | ||||||||
\(793\) | 2.29055 | + | 2.29055i | 0.0813398 | + | 0.0813398i | ||||
\(794\) | 10.5898 | + | 10.5898i | 0.375819 | + | 0.375819i | ||||
\(795\) | −0.226334 | + | 0.925884i | −0.00802726 | + | 0.0328377i | ||||
\(796\) | 3.23872 | − | 3.23872i | 0.114793 | − | 0.114793i | ||||
\(797\) | 3.20231 | 0.113432 | 0.0567159 | − | 0.998390i | \(-0.481937\pi\) | ||||
0.0567159 | + | 0.998390i | \(0.481937\pi\) | |||||||
\(798\) | 6.75953 | − | 6.75953i | 0.239285 | − | 0.239285i | ||||
\(799\) | −16.2629 | − | 16.2629i | −0.575341 | − | 0.575341i | ||||
\(800\) | 4.43613 | + | 2.30668i | 0.156841 | + | 0.0815535i | ||||
\(801\) | −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 | ||||
\(808\) | 18.0572i | 0.635249i | ||||||||
\(809\) | −6.69579 | + | 6.69579i | −0.235412 | + | 0.235412i | −0.814947 | − | 0.579535i | \(-0.803234\pi\) |
0.579535 | + | 0.814947i | \(0.303234\pi\) | |||||||
\(810\) | −0.530977 | + | 2.17211i | −0.0186566 | + | 0.0763202i | ||||
\(811\) | 15.8744 | 0.557425 | 0.278712 | − | 0.960375i | \(-0.410092\pi\) | ||||
0.278712 | + | 0.960375i | \(0.410092\pi\) | |||||||
\(812\) | 17.7486i | 0.622852i | ||||||||
\(813\) | 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 | ||||
\(820\) | 9.38336 | + | 2.29378i | 0.327681 | + | 0.0801024i | ||||
\(821\) | −46.5456 | −1.62445 | −0.812227 | − | 0.583342i | \(-0.801745\pi\) | ||||
−0.812227 | + | 0.583342i | \(0.801745\pi\) | |||||||
\(822\) | 18.0818i | 0.630675i | ||||||||
\(823\) | 15.5996 | + | 15.5996i | 0.543767 | + | 0.543767i | 0.924631 | − | 0.380864i | \(-0.124373\pi\) |
−0.380864 | + | 0.924631i | \(0.624373\pi\) | |||||||
\(824\) | 2.66961i | 0.0930001i | ||||||||
\(825\) | −3.82623 | − | 12.1156i | −0.133212 | − | 0.421812i | ||||
\(826\) | −3.14690 | −0.109495 | ||||||||
\(827\) | 28.5690i | 0.993443i | 0.867910 | + | 0.496721i | \(0.165463\pi\) | ||||
−0.867910 | + | 0.496721i | \(0.834537\pi\) | |||||||
\(828\) | 4.49206i | 0.156110i | ||||||||
\(829\) | −28.7820 | + | 28.7820i | −0.999640 | + | 0.999640i | −1.00000 | 0.000360408i | \(-0.999885\pi\) | |
0.000360408 | 1.00000i | \(0.499885\pi\) | ||||||||
\(830\) | −1.41795 | + | 0.860886i | −0.0492179 | + | 0.0298818i | ||||
\(831\) | 18.9664 | − | 18.9664i | 0.657937 | − | 0.657937i | ||||
\(832\) | −2.64021 | −0.0915327 | ||||||||
\(833\) | −1.72927 | −0.0599158 | ||||||||
\(834\) | −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 | ||||
\(837\) | 10.3677i | 0.358362i | ||||||||
\(838\) | 21.4066i | 0.739479i | ||||||||
\(839\) | 29.3296 | 1.01257 | 0.506285 | − | 0.862366i | \(-0.331018\pi\) | ||||
0.506285 | + | 0.862366i | \(0.331018\pi\) | |||||||
\(840\) | −5.94054 | − | 1.45218i | −0.204968 | − | 0.0501049i | ||||
\(841\) | − | 13.1152i | − | 0.452247i | ||||||
\(842\) | −10.7024 | − | 10.7024i | −0.368827 | − | 0.368827i | ||||
\(843\) | 16.7283i | 0.576154i | ||||||||
\(844\) | −13.4040 | −0.461384 | ||||||||
\(845\) | 3.20143 | − | 13.0963i | 0.110132 | − | 0.450527i | ||||
\(846\) | 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 | ||||
\(853\) | 10.7137i | 0.366831i | 0.983035 | + | 0.183416i | \(0.0587154\pi\) | ||||
−0.983035 | + | 0.183416i | \(0.941285\pi\) | |||||||
\(854\) | −3.35552 | −0.114824 | ||||||||
\(855\) | −4.05617 | − | 6.68086i | −0.138718 | − | 0.228481i | ||||
\(856\) | 0.404456 | − | 0.404456i | 0.0138240 | − | 0.0138240i | ||||
\(857\) | − | 31.9152i | − | 1.09020i | −0.838371 | − | 0.545101i | \(-0.816491\pi\) | ||
0.838371 | − | 0.545101i | \(-0.183509\pi\) | |||||||
\(858\) | 4.74398 | + | 4.74398i | 0.161957 | + | 0.161957i | ||||
\(859\) | 30.9778 | + | 30.9778i | 1.05695 | + | 1.05695i | 0.998277 | + | 0.0586704i | \(0.0186861\pi\) |
0.0586704 | + | 0.998277i | \(0.481314\pi\) | |||||||
\(860\) | 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 | 0.999942 | + | 0.0107769i | \(0.00343045\pi\) |
0.0107769 | + | 0.999942i | \(0.496570\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | 11.6823 | + | 19.2418i | 0.397211 | + | 0.654241i | ||||
\(866\) | −12.9115 | − | 12.9115i | −0.438751 | − | 0.438751i | ||||
\(867\) | −2.83391 | + | 2.83391i | −0.0962446 | + | 0.0962446i | ||||
\(868\) | −28.3549 | −0.962428 | ||||||||
\(869\) | −11.9455 | + | 11.9455i | −0.405224 | + | 0.405224i | ||||
\(870\) | 14.0962 | + | 3.44584i | 0.477905 | + | 0.116825i | ||||
\(871\) | −15.2409 | − | 15.2409i | −0.516418 | − | 0.516418i | ||||
\(872\) | 1.04982 | + | 1.04982i | 0.0355513 | + | 0.0355513i | ||||
\(873\) | −17.0294 | −0.576360 | ||||||||
\(874\) | −11.1024 | − | 11.1024i | −0.375545 | − | 0.375545i | ||||
\(875\) | 2.02111 | + | 30.5104i | 0.0683260 | + | 1.03144i | ||||
\(876\) | − | 5.24662i | − | 0.177267i | ||||||
\(877\) | 13.3438 | − | 13.3438i | 0.450587 | − | 0.450587i | −0.444962 | − | 0.895549i | \(-0.646783\pi\) |
0.895549 | + | 0.444962i | \(0.146783\pi\) | |||||||
\(878\) | 12.6631 | − | 12.6631i | 0.427358 | − | 0.427358i | ||||
\(879\) | 25.5905 | 0.863148 | ||||||||
\(880\) | 5.51953 | + | 1.34926i | 0.186063 | + | 0.0454836i | ||||
\(881\) | 23.6087i | 0.795397i | 0.917516 | + | 0.397699i | \(0.130191\pi\) | ||||
−0.917516 | + | 0.397699i | \(0.869809\pi\) | |||||||
\(882\) | 0.479758 | 0.0161543 | ||||||||
\(883\) | − | 15.7413i | − | 0.529737i | −0.964285 | − | 0.264868i | \(-0.914671\pi\) | ||
0.964285 | − | 0.264868i | \(-0.0853285\pi\) | |||||||
\(884\) | 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 | \(-0.136026\pi\) |
−0.414450 | + | 0.910072i | \(0.636026\pi\) | |||||||
\(888\) | 5.27701 | − | 3.02543i | 0.177085 | − | 0.101527i | ||||
\(889\) | 12.2131i | 0.409614i | ||||||||
\(890\) | −10.9804 | − | 18.0857i | −0.368064 | − | 0.606233i | ||||
\(891\) | 2.54109i | 0.0851298i | ||||||||
\(892\) | −18.2552 | − | 18.2552i | −0.611231 | − | 0.611231i | ||||
\(893\) | −22.3028 | −0.746334 | ||||||||
\(894\) | −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 | ||||
\(902\) | 10.9773 | 0.365505 | ||||||||
\(903\) | 8.54278i | 0.284286i | ||||||||
\(904\) | 5.71763i | 0.190165i | ||||||||
\(905\) | −7.45663 | + | 30.5034i | −0.247867 | + | 1.01397i | ||||
\(906\) | 1.81667 | + | 1.81667i | 0.0603550 | + | 0.0603550i | ||||
\(907\) | − | 46.5171i | − | 1.54457i | −0.635274 | − | 0.772287i | \(-0.719113\pi\) | ||
0.635274 | − | 0.772287i | \(-0.280887\pi\) | |||||||
\(908\) | 20.3161i | 0.674215i | ||||||||
\(909\) | −18.0572 | −0.598918 | ||||||||
\(910\) | −8.37935 | − | 13.8015i | −0.277773 | − | 0.457516i | ||||
\(911\) | −35.8371 | + | 35.8371i | −1.18734 | + | 1.18734i | −0.209534 | + | 0.977801i | \(0.567195\pi\) |
−0.977801 | + | 0.209534i | \(0.932805\pi\) | |||||||
\(912\) | 3.49532 | 0.115742 | ||||||||
\(913\) | −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 | ||||||||
\(917\) | 48.5759 | 1.60412 | ||||||||
\(918\) | −2.54875 | + | 2.54875i | −0.0841213 | + | 0.0841213i | ||||
\(919\) | −22.7714 | + | 22.7714i | −0.751160 | + | 0.751160i | −0.974696 | − | 0.223536i | \(-0.928240\pi\) |
0.223536 | + | 0.974696i | \(0.428240\pi\) | |||||||
\(920\) | −2.38518 | + | 9.75725i | −0.0786371 | + | 0.321687i | ||||
\(921\) | −31.9094 | −1.05145 | ||||||||
\(922\) | 2.13391 | − | 2.13391i | 0.0702765 | − | 0.0702765i | ||||
\(923\) | 6.08085 | 0.200153 | ||||||||
\(924\) | −6.94967 | −0.228627 | ||||||||
\(925\) | −22.3707 | − | 20.6046i | −0.735544 | − | 0.677476i | ||||
\(926\) | 20.8314 | 0.684563 | ||||||||
\(927\) | −2.66961 | −0.0876814 | ||||||||
\(928\) | −4.58885 | + | 4.58885i | −0.150637 | + | 0.150637i | ||||
\(929\) | 17.7432 | 0.582135 | 0.291068 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291068 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(930\) | −5.50504 | + | 22.5199i | −0.180517 | + | 0.738456i | ||||
\(931\) | −1.18575 | + | 1.18575i | −0.0388615 | + | 0.0388615i | ||||
\(932\) | −0.0502450 | + | 0.0502450i | −0.00164583 | + | 0.00164583i | ||||
\(933\) | −24.3453 | −0.797030 | ||||||||
\(934\) | 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 | −0.177996 | + | 0.984031i | \(0.556961\pi\) |
−0.984031 | + | 0.177996i | \(0.943039\pi\) | |||||||
\(938\) | 22.3270 | 0.729004 | ||||||||
\(939\) | 21.7578 | − | 21.7578i | 0.710038 | − | 0.710038i | ||||
\(940\) | 7.40457 | + | 12.1960i | 0.241511 | + | 0.397789i | ||||
\(941\) | 18.2845 | 0.596058 | 0.298029 | − | 0.954557i | \(-0.403671\pi\) | ||||
0.298029 | + | 0.954557i | \(0.403671\pi\) | |||||||
\(942\) | − | 15.2673i | − | 0.497437i | ||||||
\(943\) | 19.4054i | 0.631926i | ||||||||
\(944\) | −0.813625 | − | 0.813625i | −0.0264812 | − | 0.0264812i | ||||
\(945\) | 1.45218 | − | 5.94054i | 0.0472393 | − | 0.193246i | ||||
\(946\) | − | 7.93735i | − | 0.258066i | ||||||
\(947\) | − | 14.1055i | − | 0.458368i | −0.973383 | − | 0.229184i | \(-0.926394\pi\) | ||
0.973383 | − | 0.229184i | \(-0.0736058\pi\) | |||||||
\(948\) | 6.64813 | 0.215921 | ||||||||
\(949\) | 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 | \(-0.723837\pi\) |
0.762774 | + | 0.646665i | \(0.223837\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | 16.4907 | 0.533069 | ||||||||
\(958\) | −3.72623 | − | 3.72623i | −0.120389 | − | 0.120389i | ||||
\(959\) | − | 49.4522i | − | 1.59689i | ||||||
\(960\) | −1.16046 | − | 1.91137i | −0.0374536 | − | 0.0616893i | ||||
\(961\) | 76.4902i | 2.46743i | ||||||||
\(962\) | 15.4999 | + | 4.20349i | 0.499736 | + | 0.135526i | ||||
\(963\) | 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 | ||||||
\(967\) | − | 21.6520i | − | 0.696280i | −0.937442 | − | 0.348140i | \(-0.886813\pi\) | ||
0.937442 | − | 0.348140i | \(-0.113187\pi\) | |||||||
\(968\) | −4.54285 | −0.146013 | ||||||||
\(969\) | − | 12.5988i | − | 0.404732i | ||||||
\(970\) | −36.9898 | − | 9.04225i | −1.18767 | − | 0.290329i | ||||
\(971\) | 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 | ||||||||
\(975\) | −12.5882 | + | 3.97547i | −0.403145 | + | 0.127317i | ||||
\(976\) | −0.867564 | − | 0.867564i | −0.0277701 | − | 0.0277701i | ||||
\(977\) | −62.4861 | −1.99911 | −0.999553 | − | 0.0298845i | \(-0.990486\pi\) | ||||
−0.999553 | + | 0.0298845i | \(0.990486\pi\) | |||||||
\(978\) | 1.41488 | + | 1.41488i | 0.0452428 | + | 0.0452428i | ||||
\(979\) | −17.0018 | − | 17.0018i | −0.543380 | − | 0.543380i | ||||
\(980\) | 1.04209 | + | 0.254740i | 0.0332882 | + | 0.00813738i | ||||
\(981\) | −1.04982 | + | 1.04982i | −0.0335181 | + | 0.0335181i | ||||
\(982\) | 7.57274 | 0.241656 | ||||||||
\(983\) | 9.77180 | − | 9.77180i | 0.311672 | − | 0.311672i | −0.533885 | − | 0.845557i | \(-0.679268\pi\) |
0.845557 | + | 0.533885i | \(0.179268\pi\) | |||||||
\(984\) | −3.05465 | − | 3.05465i | −0.0973787 | − | 0.0973787i | ||||
\(985\) | 30.8447 | + | 50.8038i | 0.982792 | + | 1.61874i | ||||
\(986\) | 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 | ||||
\(993\) | 17.6573i | 0.560339i | ||||||||
\(994\) | −4.45405 | + | 4.45405i | −0.141274 | + | 0.141274i | ||||
\(995\) | 5.31516 | + | 8.75453i | 0.168502 | + | 0.277537i | ||||
\(996\) | 0.741852 | 0.0235065 | ||||||||
\(997\) | − | 3.43255i | − | 0.108710i | −0.998522 | − | 0.0543550i | \(-0.982690\pi\) | ||
0.998522 | − | 0.0543550i | \(-0.0173103\pi\) | |||||||
\(998\) | −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.o.a.253.4 | yes | 36 | |
5.2 | odd | 4 | 1110.2.l.a.697.15 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.l.a.43.15 | ✓ | 36 | ||
185.117 | even | 4 | inner | 1110.2.o.a.487.4 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.15 | ✓ | 36 | 37.6 | odd | 4 | ||
1110.2.l.a.697.15 | yes | 36 | 5.2 | odd | 4 | ||
1110.2.o.a.253.4 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.487.4 | yes | 36 | 185.117 | even | 4 | inner |