Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,3,Mod(7,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.c (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: | \(0.681200660901\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.7 |
Dual form | 25.3.c.a.18.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 1.22474i | −0.612372 | − | 0.612372i | 0.331191 | − | 0.943564i | \(-0.392549\pi\) |
−0.943564 | + | 0.331191i | \(0.892549\pi\) | |||||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | −0.472879 | − | 0.881127i | \(-0.656785\pi\) |
0.881127 | + | 0.472879i | \(0.156785\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.250000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.00000 | −0.500000 | ||||||||
\(7\) | 4.89898 | + | 4.89898i | 0.699854 | + | 0.699854i | 0.964379 | − | 0.264525i | \(-0.0852151\pi\) |
−0.264525 | + | 0.964379i | \(0.585215\pi\) | |||||||
\(8\) | −6.12372 | + | 6.12372i | −0.765466 | + | 0.765466i | ||||
\(9\) | 6.00000i | 0.666667i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.272727 | −0.136364 | − | 0.990659i | \(-0.543542\pi\) | ||||
−0.136364 | + | 0.990659i | \(0.543542\pi\) | |||||||
\(12\) | −1.22474 | − | 1.22474i | −0.102062 | − | 0.102062i | ||||
\(13\) | 7.34847 | − | 7.34847i | 0.565267 | − | 0.565267i | −0.365532 | − | 0.930799i | \(-0.619113\pi\) |
0.930799 | + | 0.365532i | \(0.119113\pi\) | |||||||
\(14\) | − | 12.0000i | − | 0.857143i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.0000 | 0.687500 | ||||||||
\(17\) | −13.4722 | − | 13.4722i | −0.792482 | − | 0.792482i | 0.189415 | − | 0.981897i | \(-0.439341\pi\) |
−0.981897 | + | 0.189415i | \(0.939341\pi\) | |||||||
\(18\) | 7.34847 | − | 7.34847i | 0.408248 | − | 0.408248i | ||||
\(19\) | 5.00000i | 0.263158i | 0.991306 | + | 0.131579i | \(0.0420047\pi\) | ||||
−0.991306 | + | 0.131579i | \(0.957995\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0000 | 0.571429 | ||||||||
\(22\) | 3.67423 | + | 3.67423i | 0.167011 | + | 0.167011i | ||||
\(23\) | −17.1464 | + | 17.1464i | −0.745497 | + | 0.745497i | −0.973630 | − | 0.228133i | \(-0.926738\pi\) |
0.228133 | + | 0.973630i | \(0.426738\pi\) | |||||||
\(24\) | 15.0000i | 0.625000i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −18.0000 | −0.692308 | ||||||||
\(27\) | 18.3712 | + | 18.3712i | 0.680414 | + | 0.680414i | ||||
\(28\) | 4.89898 | − | 4.89898i | 0.174964 | − | 0.174964i | ||||
\(29\) | − | 30.0000i | − | 1.03448i | −0.855840 | − | 0.517241i | \(-0.826959\pi\) | ||
0.855840 | − | 0.517241i | \(-0.173041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.0000 | −1.22581 | −0.612903 | − | 0.790158i | \(-0.709998\pi\) | ||||
−0.612903 | + | 0.790158i | \(0.709998\pi\) | |||||||
\(32\) | 11.0227 | + | 11.0227i | 0.344459 | + | 0.344459i | ||||
\(33\) | −3.67423 | + | 3.67423i | −0.111340 | + | 0.111340i | ||||
\(34\) | 33.0000i | 0.970588i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −19.5959 | − | 19.5959i | −0.529619 | − | 0.529619i | 0.390839 | − | 0.920459i | \(-0.372185\pi\) |
−0.920459 | + | 0.390839i | \(0.872185\pi\) | |||||||
\(38\) | 6.12372 | − | 6.12372i | 0.161151 | − | 0.161151i | ||||
\(39\) | − | 18.0000i | − | 0.461538i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 57.0000 | 1.39024 | 0.695122 | − | 0.718892i | \(-0.255350\pi\) | ||||
0.695122 | + | 0.718892i | \(0.255350\pi\) | |||||||
\(42\) | −14.6969 | − | 14.6969i | −0.349927 | − | 0.349927i | ||||
\(43\) | −4.89898 | + | 4.89898i | −0.113930 | + | 0.113930i | −0.761773 | − | 0.647844i | \(-0.775671\pi\) |
0.647844 | + | 0.761773i | \(0.275671\pi\) | |||||||
\(44\) | 3.00000i | 0.0681818i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 42.0000 | 0.913043 | ||||||||
\(47\) | −7.34847 | − | 7.34847i | −0.156350 | − | 0.156350i | 0.624597 | − | 0.780947i | \(-0.285263\pi\) |
−0.780947 | + | 0.624597i | \(0.785263\pi\) | |||||||
\(48\) | 13.4722 | − | 13.4722i | 0.280671 | − | 0.280671i | ||||
\(49\) | − | 1.00000i | − | 0.0204082i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −33.0000 | −0.647059 | ||||||||
\(52\) | −7.34847 | − | 7.34847i | −0.141317 | − | 0.141317i | ||||
\(53\) | 31.8434 | − | 31.8434i | 0.600818 | − | 0.600818i | −0.339711 | − | 0.940530i | \(-0.610329\pi\) |
0.940530 | + | 0.339711i | \(0.110329\pi\) | |||||||
\(54\) | − | 45.0000i | − | 0.833333i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −60.0000 | −1.07143 | ||||||||
\(57\) | 6.12372 | + | 6.12372i | 0.107434 | + | 0.107434i | ||||
\(58\) | −36.7423 | + | 36.7423i | −0.633489 | + | 0.633489i | ||||
\(59\) | 90.0000i | 1.52542i | 0.646738 | + | 0.762712i | \(0.276133\pi\) | ||||
−0.646738 | + | 0.762712i | \(0.723867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.0000 | −0.459016 | −0.229508 | − | 0.973307i | \(-0.573712\pi\) | ||||
−0.229508 | + | 0.973307i | \(0.573712\pi\) | |||||||
\(62\) | 46.5403 | + | 46.5403i | 0.750650 | + | 0.750650i | ||||
\(63\) | −29.3939 | + | 29.3939i | −0.466569 | + | 0.466569i | ||||
\(64\) | − | 71.0000i | − | 1.10938i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.00000 | 0.136364 | ||||||||
\(67\) | 47.7650 | + | 47.7650i | 0.712911 | + | 0.712911i | 0.967143 | − | 0.254232i | \(-0.0818227\pi\) |
−0.254232 | + | 0.967143i | \(0.581823\pi\) | |||||||
\(68\) | −13.4722 | + | 13.4722i | −0.198120 | + | 0.198120i | ||||
\(69\) | 42.0000i | 0.608696i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42.0000 | 0.591549 | 0.295775 | − | 0.955258i | \(-0.404422\pi\) | ||||
0.295775 | + | 0.955258i | \(0.404422\pi\) | |||||||
\(72\) | −36.7423 | − | 36.7423i | −0.510310 | − | 0.510310i | ||||
\(73\) | 13.4722 | − | 13.4722i | 0.184551 | − | 0.184551i | −0.608785 | − | 0.793335i | \(-0.708343\pi\) |
0.793335 | + | 0.608785i | \(0.208343\pi\) | |||||||
\(74\) | 48.0000i | 0.648649i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.00000 | 0.0657895 | ||||||||
\(77\) | −14.6969 | − | 14.6969i | −0.190869 | − | 0.190869i | ||||
\(78\) | −22.0454 | + | 22.0454i | −0.282633 | + | 0.282633i | ||||
\(79\) | − | 80.0000i | − | 1.01266i | −0.862340 | − | 0.506329i | \(-0.831002\pi\) | ||
0.862340 | − | 0.506329i | \(-0.168998\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −69.8105 | − | 69.8105i | −0.851347 | − | 0.851347i | ||||
\(83\) | 111.452 | − | 111.452i | 1.34279 | − | 1.34279i | 0.449525 | − | 0.893268i | \(-0.351593\pi\) |
0.893268 | − | 0.449525i | \(-0.148407\pi\) | |||||||
\(84\) | − | 12.0000i | − | 0.142857i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.0000 | 0.139535 | ||||||||
\(87\) | −36.7423 | − | 36.7423i | −0.422326 | − | 0.422326i | ||||
\(88\) | 18.3712 | − | 18.3712i | 0.208763 | − | 0.208763i | ||||
\(89\) | − | 15.0000i | − | 0.168539i | −0.996443 | − | 0.0842697i | \(-0.973144\pi\) | ||
0.996443 | − | 0.0842697i | \(-0.0268557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 72.0000 | 0.791209 | ||||||||
\(92\) | 17.1464 | + | 17.1464i | 0.186374 | + | 0.186374i | ||||
\(93\) | −46.5403 | + | 46.5403i | −0.500433 | + | 0.500433i | ||||
\(94\) | 18.0000i | 0.191489i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 27.0000 | 0.281250 | ||||||||
\(97\) | 53.8888 | + | 53.8888i | 0.555554 | + | 0.555554i | 0.928039 | − | 0.372484i | \(-0.121494\pi\) |
−0.372484 | + | 0.928039i | \(0.621494\pi\) | |||||||
\(98\) | −1.22474 | + | 1.22474i | −0.0124974 | + | 0.0124974i | ||||
\(99\) | − | 18.0000i | − | 0.181818i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −48.0000 | −0.475248 | −0.237624 | − | 0.971357i | \(-0.576369\pi\) | ||||
−0.237624 | + | 0.971357i | \(0.576369\pi\) | |||||||
\(102\) | 40.4166 | + | 40.4166i | 0.396241 | + | 0.396241i | ||||
\(103\) | −90.6311 | + | 90.6311i | −0.879914 | + | 0.879914i | −0.993525 | − | 0.113611i | \(-0.963758\pi\) |
0.113611 | + | 0.993525i | \(0.463758\pi\) | |||||||
\(104\) | 90.0000i | 0.865385i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −78.0000 | −0.735849 | ||||||||
\(107\) | −25.7196 | − | 25.7196i | −0.240370 | − | 0.240370i | 0.576633 | − | 0.817003i | \(-0.304366\pi\) |
−0.817003 | + | 0.576633i | \(0.804366\pi\) | |||||||
\(108\) | 18.3712 | − | 18.3712i | 0.170103 | − | 0.170103i | ||||
\(109\) | 40.0000i | 0.366972i | 0.983022 | + | 0.183486i | \(0.0587383\pi\) | ||||
−0.983022 | + | 0.183486i | \(0.941262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −48.0000 | −0.432432 | ||||||||
\(112\) | 53.8888 | + | 53.8888i | 0.481150 | + | 0.481150i | ||||
\(113\) | −84.5074 | + | 84.5074i | −0.747853 | + | 0.747853i | −0.974076 | − | 0.226223i | \(-0.927362\pi\) |
0.226223 | + | 0.974076i | \(0.427362\pi\) | |||||||
\(114\) | − | 15.0000i | − | 0.131579i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −30.0000 | −0.258621 | ||||||||
\(117\) | 44.0908 | + | 44.0908i | 0.376845 | + | 0.376845i | ||||
\(118\) | 110.227 | − | 110.227i | 0.934127 | − | 0.934127i | ||||
\(119\) | − | 132.000i | − | 1.10924i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −112.000 | −0.925620 | ||||||||
\(122\) | 34.2929 | + | 34.2929i | 0.281089 | + | 0.281089i | ||||
\(123\) | 69.8105 | − | 69.8105i | 0.567565 | − | 0.567565i | ||||
\(124\) | 38.0000i | 0.306452i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 72.0000 | 0.571429 | ||||||||
\(127\) | −154.318 | − | 154.318i | −1.21510 | − | 1.21510i | −0.969327 | − | 0.245774i | \(-0.920958\pi\) |
−0.245774 | − | 0.969327i | \(-0.579042\pi\) | |||||||
\(128\) | −42.8661 | + | 42.8661i | −0.334891 | + | 0.334891i | ||||
\(129\) | 12.0000i | 0.0930233i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 162.000 | 1.23664 | 0.618321 | − | 0.785926i | \(-0.287813\pi\) | ||||
0.618321 | + | 0.785926i | \(0.287813\pi\) | |||||||
\(132\) | 3.67423 | + | 3.67423i | 0.0278351 | + | 0.0278351i | ||||
\(133\) | −24.4949 | + | 24.4949i | −0.184172 | + | 0.184172i | ||||
\(134\) | − | 117.000i | − | 0.873134i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 165.000 | 1.21324 | ||||||||
\(137\) | −50.2145 | − | 50.2145i | −0.366529 | − | 0.366529i | 0.499680 | − | 0.866210i | \(-0.333451\pi\) |
−0.866210 | + | 0.499680i | \(0.833451\pi\) | |||||||
\(138\) | 51.4393 | − | 51.4393i | 0.372748 | − | 0.372748i | ||||
\(139\) | 185.000i | 1.33094i | 0.746427 | + | 0.665468i | \(0.231768\pi\) | ||||
−0.746427 | + | 0.665468i | \(0.768232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0000 | −0.127660 | ||||||||
\(142\) | −51.4393 | − | 51.4393i | −0.362248 | − | 0.362248i | ||||
\(143\) | −22.0454 | + | 22.0454i | −0.154164 | + | 0.154164i | ||||
\(144\) | 66.0000i | 0.458333i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −33.0000 | −0.226027 | ||||||||
\(147\) | −1.22474 | − | 1.22474i | −0.00833160 | − | 0.00833160i | ||||
\(148\) | −19.5959 | + | 19.5959i | −0.132405 | + | 0.132405i | ||||
\(149\) | − | 150.000i | − | 1.00671i | −0.864079 | − | 0.503356i | \(-0.832099\pi\) | ||
0.864079 | − | 0.503356i | \(-0.167901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 52.0000 | 0.344371 | 0.172185 | − | 0.985065i | \(-0.444917\pi\) | ||||
0.172185 | + | 0.985065i | \(0.444917\pi\) | |||||||
\(152\) | −30.6186 | − | 30.6186i | −0.201438 | − | 0.201438i | ||||
\(153\) | 80.8332 | − | 80.8332i | 0.528321 | − | 0.528321i | ||||
\(154\) | 36.0000i | 0.233766i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −18.0000 | −0.115385 | ||||||||
\(157\) | 188.611 | + | 188.611i | 1.20134 | + | 1.20134i | 0.973759 | + | 0.227584i | \(0.0730825\pi\) |
0.227584 | + | 0.973759i | \(0.426918\pi\) | |||||||
\(158\) | −97.9796 | + | 97.9796i | −0.620124 | + | 0.620124i | ||||
\(159\) | − | 78.0000i | − | 0.490566i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −168.000 | −1.04348 | ||||||||
\(162\) | 11.0227 | + | 11.0227i | 0.0680414 | + | 0.0680414i | ||||
\(163\) | 99.2043 | − | 99.2043i | 0.608616 | − | 0.608616i | −0.333969 | − | 0.942584i | \(-0.608388\pi\) |
0.942584 | + | 0.333969i | \(0.108388\pi\) | |||||||
\(164\) | − | 57.0000i | − | 0.347561i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −273.000 | −1.64458 | ||||||||
\(167\) | 17.1464 | + | 17.1464i | 0.102673 | + | 0.102673i | 0.756577 | − | 0.653904i | \(-0.226870\pi\) |
−0.653904 | + | 0.756577i | \(0.726870\pi\) | |||||||
\(168\) | −73.4847 | + | 73.4847i | −0.437409 | + | 0.437409i | ||||
\(169\) | 61.0000i | 0.360947i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30.0000 | −0.175439 | ||||||||
\(172\) | 4.89898 | + | 4.89898i | 0.0284824 | + | 0.0284824i | ||||
\(173\) | −78.3837 | + | 78.3837i | −0.453085 | + | 0.453085i | −0.896377 | − | 0.443292i | \(-0.853810\pi\) |
0.443292 | + | 0.896377i | \(0.353810\pi\) | |||||||
\(174\) | 90.0000i | 0.517241i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −33.0000 | −0.187500 | ||||||||
\(177\) | 110.227 | + | 110.227i | 0.622752 | + | 0.622752i | ||||
\(178\) | −18.3712 | + | 18.3712i | −0.103209 | + | 0.103209i | ||||
\(179\) | 195.000i | 1.08939i | 0.838636 | + | 0.544693i | \(0.183354\pi\) | ||||
−0.838636 | + | 0.544693i | \(0.816646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 262.000 | 1.44751 | 0.723757 | − | 0.690055i | \(-0.242414\pi\) | ||||
0.723757 | + | 0.690055i | \(0.242414\pi\) | |||||||
\(182\) | −88.1816 | − | 88.1816i | −0.484514 | − | 0.484514i | ||||
\(183\) | −34.2929 | + | 34.2929i | −0.187393 | + | 0.187393i | ||||
\(184\) | − | 210.000i | − | 1.14130i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 114.000 | 0.612903 | ||||||||
\(187\) | 40.4166 | + | 40.4166i | 0.216131 | + | 0.216131i | ||||
\(188\) | −7.34847 | + | 7.34847i | −0.0390876 | + | 0.0390876i | ||||
\(189\) | 180.000i | 0.952381i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.0000 | −0.0942408 | −0.0471204 | − | 0.998889i | \(-0.515004\pi\) | ||||
−0.0471204 | + | 0.998889i | \(0.515004\pi\) | |||||||
\(192\) | −86.9569 | − | 86.9569i | −0.452900 | − | 0.452900i | ||||
\(193\) | 86.9569 | − | 86.9569i | 0.450554 | − | 0.450554i | −0.444984 | − | 0.895538i | \(-0.646791\pi\) |
0.895538 | + | 0.444984i | \(0.146791\pi\) | |||||||
\(194\) | − | 132.000i | − | 0.680412i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.00510204 | ||||||||
\(197\) | −129.823 | − | 129.823i | −0.659000 | − | 0.659000i | 0.296144 | − | 0.955143i | \(-0.404299\pi\) |
−0.955143 | + | 0.296144i | \(0.904299\pi\) | |||||||
\(198\) | −22.0454 | + | 22.0454i | −0.111340 | + | 0.111340i | ||||
\(199\) | − | 200.000i | − | 1.00503i | −0.864570 | − | 0.502513i | \(-0.832409\pi\) | ||
0.864570 | − | 0.502513i | \(-0.167591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 117.000 | 0.582090 | ||||||||
\(202\) | 58.7878 | + | 58.7878i | 0.291028 | + | 0.291028i | ||||
\(203\) | 146.969 | − | 146.969i | 0.723987 | − | 0.723987i | ||||
\(204\) | 33.0000i | 0.161765i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 222.000 | 1.07767 | ||||||||
\(207\) | −102.879 | − | 102.879i | −0.496998 | − | 0.496998i | ||||
\(208\) | 80.8332 | − | 80.8332i | 0.388621 | − | 0.388621i | ||||
\(209\) | − | 15.0000i | − | 0.0717703i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −103.000 | −0.488152 | −0.244076 | − | 0.969756i | \(-0.578485\pi\) | ||||
−0.244076 | + | 0.969756i | \(0.578485\pi\) | |||||||
\(212\) | −31.8434 | − | 31.8434i | −0.150205 | − | 0.150205i | ||||
\(213\) | 51.4393 | − | 51.4393i | 0.241499 | − | 0.241499i | ||||
\(214\) | 63.0000i | 0.294393i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −225.000 | −1.04167 | ||||||||
\(217\) | −186.161 | − | 186.161i | −0.857886 | − | 0.857886i | ||||
\(218\) | 48.9898 | − | 48.9898i | 0.224724 | − | 0.224724i | ||||
\(219\) | − | 33.0000i | − | 0.150685i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −198.000 | −0.895928 | ||||||||
\(222\) | 58.7878 | + | 58.7878i | 0.264810 | + | 0.264810i | ||||
\(223\) | −200.858 | + | 200.858i | −0.900709 | + | 0.900709i | −0.995497 | − | 0.0947882i | \(-0.969783\pi\) |
0.0947882 | + | 0.995497i | \(0.469783\pi\) | |||||||
\(224\) | 108.000i | 0.482143i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 207.000 | 0.915929 | ||||||||
\(227\) | 274.343 | + | 274.343i | 1.20856 | + | 1.20856i | 0.971494 | + | 0.237065i | \(0.0761854\pi\) |
0.237065 | + | 0.971494i | \(0.423815\pi\) | |||||||
\(228\) | 6.12372 | − | 6.12372i | 0.0268584 | − | 0.0268584i | ||||
\(229\) | 20.0000i | 0.0873362i | 0.999046 | + | 0.0436681i | \(0.0139044\pi\) | ||||
−0.999046 | + | 0.0436681i | \(0.986096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −36.0000 | −0.155844 | ||||||||
\(232\) | 183.712 | + | 183.712i | 0.791861 | + | 0.791861i | ||||
\(233\) | −102.879 | + | 102.879i | −0.441539 | + | 0.441539i | −0.892529 | − | 0.450990i | \(-0.851071\pi\) |
0.450990 | + | 0.892529i | \(0.351071\pi\) | |||||||
\(234\) | − | 108.000i | − | 0.461538i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 90.0000 | 0.381356 | ||||||||
\(237\) | −97.9796 | − | 97.9796i | −0.413416 | − | 0.413416i | ||||
\(238\) | −161.666 | + | 161.666i | −0.679270 | + | 0.679270i | ||||
\(239\) | 210.000i | 0.878661i | 0.898325 | + | 0.439331i | \(0.144784\pi\) | ||||
−0.898325 | + | 0.439331i | \(0.855216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −43.0000 | −0.178423 | −0.0892116 | − | 0.996013i | \(-0.528435\pi\) | ||||
−0.0892116 | + | 0.996013i | \(0.528435\pi\) | |||||||
\(242\) | 137.171 | + | 137.171i | 0.566824 | + | 0.566824i | ||||
\(243\) | −176.363 | + | 176.363i | −0.725775 | + | 0.725775i | ||||
\(244\) | 28.0000i | 0.114754i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −171.000 | −0.695122 | ||||||||
\(247\) | 36.7423 | + | 36.7423i | 0.148754 | + | 0.148754i | ||||
\(248\) | 232.702 | − | 232.702i | 0.938313 | − | 0.938313i | ||||
\(249\) | − | 273.000i | − | 1.09639i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −123.000 | −0.490040 | −0.245020 | − | 0.969518i | \(-0.578795\pi\) | ||||
−0.245020 | + | 0.969518i | \(0.578795\pi\) | |||||||
\(252\) | 29.3939 | + | 29.3939i | 0.116642 | + | 0.116642i | ||||
\(253\) | 51.4393 | − | 51.4393i | 0.203317 | − | 0.203317i | ||||
\(254\) | 378.000i | 1.48819i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −179.000 | −0.699219 | ||||||||
\(257\) | 4.89898 | + | 4.89898i | 0.0190622 | + | 0.0190622i | 0.716574 | − | 0.697511i | \(-0.245709\pi\) |
−0.697511 | + | 0.716574i | \(0.745709\pi\) | |||||||
\(258\) | 14.6969 | − | 14.6969i | 0.0569649 | − | 0.0569649i | ||||
\(259\) | − | 192.000i | − | 0.741313i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 180.000 | 0.689655 | ||||||||
\(262\) | −198.409 | − | 198.409i | −0.757285 | − | 0.757285i | ||||
\(263\) | 7.34847 | − | 7.34847i | 0.0279409 | − | 0.0279409i | −0.692998 | − | 0.720939i | \(-0.743711\pi\) |
0.720939 | + | 0.692998i | \(0.243711\pi\) | |||||||
\(264\) | − | 45.0000i | − | 0.170455i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 60.0000 | 0.225564 | ||||||||
\(267\) | −18.3712 | − | 18.3712i | −0.0688059 | − | 0.0688059i | ||||
\(268\) | 47.7650 | − | 47.7650i | 0.178228 | − | 0.178228i | ||||
\(269\) | − | 120.000i | − | 0.446097i | −0.974807 | − | 0.223048i | \(-0.928399\pi\) | ||
0.974807 | − | 0.223048i | \(-0.0716008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −58.0000 | −0.214022 | −0.107011 | − | 0.994258i | \(-0.534128\pi\) | ||||
−0.107011 | + | 0.994258i | \(0.534128\pi\) | |||||||
\(272\) | −148.194 | − | 148.194i | −0.544831 | − | 0.544831i | ||||
\(273\) | 88.1816 | − | 88.1816i | 0.323010 | − | 0.323010i | ||||
\(274\) | 123.000i | 0.448905i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 42.0000 | 0.152174 | ||||||||
\(277\) | −276.792 | − | 276.792i | −0.999250 | − | 0.999250i | 0.000749391 | − | 1.00000i | \(-0.499761\pi\) |
−1.00000 | 0.000749391i | \(0.999761\pi\) | ||||||||
\(278\) | 226.578 | − | 226.578i | 0.815028 | − | 0.815028i | ||||
\(279\) | − | 228.000i | − | 0.817204i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 462.000 | 1.64413 | 0.822064 | − | 0.569395i | \(-0.192822\pi\) | ||||
0.822064 | + | 0.569395i | \(0.192822\pi\) | |||||||
\(282\) | 22.0454 | + | 22.0454i | 0.0781752 | + | 0.0781752i | ||||
\(283\) | −72.2599 | + | 72.2599i | −0.255336 | + | 0.255336i | −0.823154 | − | 0.567818i | \(-0.807788\pi\) |
0.567818 | + | 0.823154i | \(0.307788\pi\) | |||||||
\(284\) | − | 42.0000i | − | 0.147887i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 54.0000 | 0.188811 | ||||||||
\(287\) | 279.242 | + | 279.242i | 0.972968 | + | 0.972968i | ||||
\(288\) | −66.1362 | + | 66.1362i | −0.229640 | + | 0.229640i | ||||
\(289\) | 74.0000i | 0.256055i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 132.000 | 0.453608 | ||||||||
\(292\) | −13.4722 | − | 13.4722i | −0.0461376 | − | 0.0461376i | ||||
\(293\) | −4.89898 | + | 4.89898i | −0.0167201 | + | 0.0167201i | −0.715417 | − | 0.698697i | \(-0.753763\pi\) |
0.698697 | + | 0.715417i | \(0.253763\pi\) | |||||||
\(294\) | 3.00000i | 0.0102041i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 240.000 | 0.810811 | ||||||||
\(297\) | −55.1135 | − | 55.1135i | −0.185567 | − | 0.185567i | ||||
\(298\) | −183.712 | + | 183.712i | −0.616482 | + | 0.616482i | ||||
\(299\) | 252.000i | 0.842809i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −48.0000 | −0.159468 | ||||||||
\(302\) | −63.6867 | − | 63.6867i | −0.210883 | − | 0.210883i | ||||
\(303\) | −58.7878 | + | 58.7878i | −0.194019 | + | 0.194019i | ||||
\(304\) | 55.0000i | 0.180921i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −198.000 | −0.647059 | ||||||||
\(307\) | −86.9569 | − | 86.9569i | −0.283247 | − | 0.283247i | 0.551155 | − | 0.834403i | \(-0.314187\pi\) |
−0.834403 | + | 0.551155i | \(0.814187\pi\) | |||||||
\(308\) | −14.6969 | + | 14.6969i | −0.0477173 | + | 0.0477173i | ||||
\(309\) | 222.000i | 0.718447i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −528.000 | −1.69775 | −0.848875 | − | 0.528594i | \(-0.822719\pi\) | ||||
−0.848875 | + | 0.528594i | \(0.822719\pi\) | |||||||
\(312\) | 110.227 | + | 110.227i | 0.353292 | + | 0.353292i | ||||
\(313\) | 191.060 | − | 191.060i | 0.610416 | − | 0.610416i | −0.332638 | − | 0.943054i | \(-0.607939\pi\) |
0.943054 | + | 0.332638i | \(0.107939\pi\) | |||||||
\(314\) | − | 462.000i | − | 1.47134i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −80.0000 | −0.253165 | ||||||||
\(317\) | 200.858 | + | 200.858i | 0.633622 | + | 0.633622i | 0.948975 | − | 0.315353i | \(-0.102123\pi\) |
−0.315353 | + | 0.948975i | \(0.602123\pi\) | |||||||
\(318\) | −95.5301 | + | 95.5301i | −0.300409 | + | 0.300409i | ||||
\(319\) | 90.0000i | 0.282132i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −63.0000 | −0.196262 | ||||||||
\(322\) | 205.757 | + | 205.757i | 0.638997 | + | 0.638997i | ||||
\(323\) | 67.3610 | − | 67.3610i | 0.208548 | − | 0.208548i | ||||
\(324\) | 9.00000i | 0.0277778i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −243.000 | −0.745399 | ||||||||
\(327\) | 48.9898 | + | 48.9898i | 0.149816 | + | 0.149816i | ||||
\(328\) | −349.052 | + | 349.052i | −1.06418 | + | 1.06418i | ||||
\(329\) | − | 72.0000i | − | 0.218845i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −313.000 | −0.945619 | −0.472810 | − | 0.881165i | \(-0.656760\pi\) | ||||
−0.472810 | + | 0.881165i | \(0.656760\pi\) | |||||||
\(332\) | −111.452 | − | 111.452i | −0.335698 | − | 0.335698i | ||||
\(333\) | 117.576 | − | 117.576i | 0.353080 | − | 0.353080i | ||||
\(334\) | − | 42.0000i | − | 0.125749i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 132.000 | 0.392857 | ||||||||
\(337\) | 194.734 | + | 194.734i | 0.577847 | + | 0.577847i | 0.934310 | − | 0.356463i | \(-0.116017\pi\) |
−0.356463 | + | 0.934310i | \(0.616017\pi\) | |||||||
\(338\) | 74.7094 | − | 74.7094i | 0.221034 | − | 0.221034i | ||||
\(339\) | 207.000i | 0.610619i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 114.000 | 0.334311 | ||||||||
\(342\) | 36.7423 | + | 36.7423i | 0.107434 | + | 0.107434i | ||||
\(343\) | 244.949 | − | 244.949i | 0.714137 | − | 0.714137i | ||||
\(344\) | − | 60.0000i | − | 0.174419i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 192.000 | 0.554913 | ||||||||
\(347\) | −99.2043 | − | 99.2043i | −0.285891 | − | 0.285891i | 0.549562 | − | 0.835453i | \(-0.314795\pi\) |
−0.835453 | + | 0.549562i | \(0.814795\pi\) | |||||||
\(348\) | −36.7423 | + | 36.7423i | −0.105581 | + | 0.105581i | ||||
\(349\) | − | 100.000i | − | 0.286533i | −0.989684 | − | 0.143266i | \(-0.954239\pi\) | ||
0.989684 | − | 0.143266i | \(-0.0457606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 270.000 | 0.769231 | ||||||||
\(352\) | −33.0681 | − | 33.0681i | −0.0939435 | − | 0.0939435i | ||||
\(353\) | −396.817 | + | 396.817i | −1.12413 | + | 1.12413i | −0.133014 | + | 0.991114i | \(0.542466\pi\) |
−0.991114 | + | 0.133014i | \(0.957534\pi\) | |||||||
\(354\) | − | 270.000i | − | 0.762712i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.0000 | −0.0421348 | ||||||||
\(357\) | −161.666 | − | 161.666i | −0.452847 | − | 0.452847i | ||||
\(358\) | 238.825 | − | 238.825i | 0.667110 | − | 0.667110i | ||||
\(359\) | 540.000i | 1.50418i | 0.659061 | + | 0.752089i | \(0.270954\pi\) | ||||
−0.659061 | + | 0.752089i | \(0.729046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 336.000 | 0.930748 | ||||||||
\(362\) | −320.883 | − | 320.883i | −0.886418 | − | 0.886418i | ||||
\(363\) | −137.171 | + | 137.171i | −0.377883 | + | 0.377883i | ||||
\(364\) | − | 72.0000i | − | 0.197802i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 84.0000 | 0.229508 | ||||||||
\(367\) | −44.0908 | − | 44.0908i | −0.120138 | − | 0.120138i | 0.644481 | − | 0.764620i | \(-0.277073\pi\) |
−0.764620 | + | 0.644481i | \(0.777073\pi\) | |||||||
\(368\) | −188.611 | + | 188.611i | −0.512529 | + | 0.512529i | ||||
\(369\) | 342.000i | 0.926829i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 312.000 | 0.840970 | ||||||||
\(372\) | 46.5403 | + | 46.5403i | 0.125108 | + | 0.125108i | ||||
\(373\) | 350.277 | − | 350.277i | 0.939081 | − | 0.939081i | −0.0591675 | − | 0.998248i | \(-0.518845\pi\) |
0.998248 | + | 0.0591675i | \(0.0188446\pi\) | |||||||
\(374\) | − | 99.0000i | − | 0.264706i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 90.0000 | 0.239362 | ||||||||
\(377\) | −220.454 | − | 220.454i | −0.584759 | − | 0.584759i | ||||
\(378\) | 220.454 | − | 220.454i | 0.583212 | − | 0.583212i | ||||
\(379\) | − | 505.000i | − | 1.33245i | −0.745749 | − | 0.666227i | \(-0.767908\pi\) | ||
0.745749 | − | 0.666227i | \(-0.232092\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −378.000 | −0.992126 | ||||||||
\(382\) | 22.0454 | + | 22.0454i | 0.0577105 | + | 0.0577105i | ||||
\(383\) | 142.070 | − | 142.070i | 0.370941 | − | 0.370941i | −0.496879 | − | 0.867820i | \(-0.665521\pi\) |
0.867820 | + | 0.496879i | \(0.165521\pi\) | |||||||
\(384\) | 105.000i | 0.273438i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −213.000 | −0.551813 | ||||||||
\(387\) | −29.3939 | − | 29.3939i | −0.0759532 | − | 0.0759532i | ||||
\(388\) | 53.8888 | − | 53.8888i | 0.138889 | − | 0.138889i | ||||
\(389\) | − | 690.000i | − | 1.77378i | −0.461982 | − | 0.886889i | \(-0.652861\pi\) | ||
0.461982 | − | 0.886889i | \(-0.347139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 462.000 | 1.18159 | ||||||||
\(392\) | 6.12372 | + | 6.12372i | 0.0156217 | + | 0.0156217i | ||||
\(393\) | 198.409 | − | 198.409i | 0.504857 | − | 0.504857i | ||||
\(394\) | 318.000i | 0.807107i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.0000 | −0.0454545 | ||||||||
\(397\) | 421.312 | + | 421.312i | 1.06124 | + | 1.06124i | 0.997998 | + | 0.0632416i | \(0.0201439\pi\) |
0.0632416 | + | 0.997998i | \(0.479856\pi\) | |||||||
\(398\) | −244.949 | + | 244.949i | −0.615450 | + | 0.615450i | ||||
\(399\) | 60.0000i | 0.150376i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −573.000 | −1.42893 | −0.714464 | − | 0.699672i | \(-0.753329\pi\) | ||||
−0.714464 | + | 0.699672i | \(0.753329\pi\) | |||||||
\(402\) | −143.295 | − | 143.295i | −0.356456 | − | 0.356456i | ||||
\(403\) | −279.242 | + | 279.242i | −0.692908 | + | 0.692908i | ||||
\(404\) | 48.0000i | 0.118812i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −360.000 | −0.886700 | ||||||||
\(407\) | 58.7878 | + | 58.7878i | 0.144442 | + | 0.144442i | ||||
\(408\) | 202.083 | − | 202.083i | 0.495301 | − | 0.495301i | ||||
\(409\) | 365.000i | 0.892421i | 0.894928 | + | 0.446210i | \(0.147227\pi\) | ||||
−0.894928 | + | 0.446210i | \(0.852773\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −123.000 | −0.299270 | ||||||||
\(412\) | 90.6311 | + | 90.6311i | 0.219978 | + | 0.219978i | ||||
\(413\) | −440.908 | + | 440.908i | −1.06757 | + | 1.06757i | ||||
\(414\) | 252.000i | 0.608696i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 162.000 | 0.389423 | ||||||||
\(417\) | 226.578 | + | 226.578i | 0.543352 | + | 0.543352i | ||||
\(418\) | −18.3712 | + | 18.3712i | −0.0439502 | + | 0.0439502i | ||||
\(419\) | − | 645.000i | − | 1.53938i | −0.638418 | − | 0.769690i | \(-0.720411\pi\) | ||
0.638418 | − | 0.769690i | \(-0.279589\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.0190024 | −0.00950119 | − | 0.999955i | \(-0.503024\pi\) | ||||
−0.00950119 | + | 0.999955i | \(0.503024\pi\) | |||||||
\(422\) | 126.149 | + | 126.149i | 0.298931 | + | 0.298931i | ||||
\(423\) | 44.0908 | − | 44.0908i | 0.104234 | − | 0.104234i | ||||
\(424\) | 390.000i | 0.919811i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −126.000 | −0.295775 | ||||||||
\(427\) | −137.171 | − | 137.171i | −0.321245 | − | 0.321245i | ||||
\(428\) | −25.7196 | + | 25.7196i | −0.0600926 | + | 0.0600926i | ||||
\(429\) | 54.0000i | 0.125874i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | 0.0278422 | 0.0139211 | − | 0.999903i | \(-0.495569\pi\) | ||||
0.0139211 | + | 0.999903i | \(0.495569\pi\) | |||||||
\(432\) | 202.083 | + | 202.083i | 0.467784 | + | 0.467784i | ||||
\(433\) | −439.683 | + | 439.683i | −1.01544 | + | 1.01544i | −0.0155561 | + | 0.999879i | \(0.504952\pi\) |
−0.999879 | + | 0.0155561i | \(0.995048\pi\) | |||||||
\(434\) | 456.000i | 1.05069i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 40.0000 | 0.0917431 | ||||||||
\(437\) | −85.7321 | − | 85.7321i | −0.196183 | − | 0.196183i | ||||
\(438\) | −40.4166 | + | 40.4166i | −0.0922753 | + | 0.0922753i | ||||
\(439\) | 10.0000i | 0.0227790i | 0.999935 | + | 0.0113895i | \(0.00362548\pi\) | ||||
−0.999935 | + | 0.0113895i | \(0.996375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00000 | 0.0136054 | ||||||||
\(442\) | 242.499 | + | 242.499i | 0.548641 | + | 0.548641i | ||||
\(443\) | 86.9569 | − | 86.9569i | 0.196291 | − | 0.196291i | −0.602117 | − | 0.798408i | \(-0.705676\pi\) |
0.798408 | + | 0.602117i | \(0.205676\pi\) | |||||||
\(444\) | 48.0000i | 0.108108i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 492.000 | 1.10314 | ||||||||
\(447\) | −183.712 | − | 183.712i | −0.410988 | − | 0.410988i | ||||
\(448\) | 347.828 | − | 347.828i | 0.776401 | − | 0.776401i | ||||
\(449\) | − | 75.0000i | − | 0.167038i | −0.996506 | − | 0.0835189i | \(-0.973384\pi\) | ||
0.996506 | − | 0.0835189i | \(-0.0266159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −171.000 | −0.379157 | ||||||||
\(452\) | 84.5074 | + | 84.5074i | 0.186963 | + | 0.186963i | ||||
\(453\) | 63.6867 | − | 63.6867i | 0.140589 | − | 0.140589i | ||||
\(454\) | − | 672.000i | − | 1.48018i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −75.0000 | −0.164474 | ||||||||
\(457\) | −209.431 | − | 209.431i | −0.458274 | − | 0.458274i | 0.439814 | − | 0.898089i | \(-0.355044\pi\) |
−0.898089 | + | 0.439814i | \(0.855044\pi\) | |||||||
\(458\) | 24.4949 | − | 24.4949i | 0.0534823 | − | 0.0534823i | ||||
\(459\) | − | 495.000i | − | 1.07843i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −228.000 | −0.494577 | −0.247289 | − | 0.968942i | \(-0.579540\pi\) | ||||
−0.247289 | + | 0.968942i | \(0.579540\pi\) | |||||||
\(462\) | 44.0908 | + | 44.0908i | 0.0954347 | + | 0.0954347i | ||||
\(463\) | 436.009 | − | 436.009i | 0.941704 | − | 0.941704i | −0.0566875 | − | 0.998392i | \(-0.518054\pi\) |
0.998392 | + | 0.0566875i | \(0.0180539\pi\) | |||||||
\(464\) | − | 330.000i | − | 0.711207i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 252.000 | 0.540773 | ||||||||
\(467\) | −533.989 | − | 533.989i | −1.14344 | − | 1.14344i | −0.987816 | − | 0.155629i | \(-0.950259\pi\) |
−0.155629 | − | 0.987816i | \(-0.549741\pi\) | |||||||
\(468\) | 44.0908 | − | 44.0908i | 0.0942111 | − | 0.0942111i | ||||
\(469\) | 468.000i | 0.997868i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 462.000 | 0.980892 | ||||||||
\(472\) | −551.135 | − | 551.135i | −1.16766 | − | 1.16766i | ||||
\(473\) | 14.6969 | − | 14.6969i | 0.0310718 | − | 0.0310718i | ||||
\(474\) | 240.000i | 0.506329i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −132.000 | −0.277311 | ||||||||
\(477\) | 191.060 | + | 191.060i | 0.400545 | + | 0.400545i | ||||
\(478\) | 257.196 | − | 257.196i | 0.538068 | − | 0.538068i | ||||
\(479\) | 270.000i | 0.563674i | 0.959462 | + | 0.281837i | \(0.0909438\pi\) | ||||
−0.959462 | + | 0.281837i | \(0.909056\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −288.000 | −0.598753 | ||||||||
\(482\) | 52.6640 | + | 52.6640i | 0.109261 | + | 0.109261i | ||||
\(483\) | −205.757 | + | 205.757i | −0.425998 | + | 0.425998i | ||||
\(484\) | 112.000i | 0.231405i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 432.000 | 0.888889 | ||||||||
\(487\) | −80.8332 | − | 80.8332i | −0.165982 | − | 0.165982i | 0.619229 | − | 0.785211i | \(-0.287445\pi\) |
−0.785211 | + | 0.619229i | \(0.787445\pi\) | |||||||
\(488\) | 171.464 | − | 171.464i | 0.351361 | − | 0.351361i | ||||
\(489\) | − | 243.000i | − | 0.496933i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 582.000 | 1.18534 | 0.592668 | − | 0.805447i | \(-0.298075\pi\) | ||||
0.592668 | + | 0.805447i | \(0.298075\pi\) | |||||||
\(492\) | −69.8105 | − | 69.8105i | −0.141891 | − | 0.141891i | ||||
\(493\) | −404.166 | + | 404.166i | −0.819809 | + | 0.819809i | ||||
\(494\) | − | 90.0000i | − | 0.182186i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −418.000 | −0.842742 | ||||||||
\(497\) | 205.757 | + | 205.757i | 0.413998 | + | 0.413998i | ||||
\(498\) | −334.355 | + | 334.355i | −0.671396 | + | 0.671396i | ||||
\(499\) | 250.000i | 0.501002i | 0.968116 | + | 0.250501i | \(0.0805953\pi\) | ||||
−0.968116 | + | 0.250501i | \(0.919405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.0000 | 0.0838323 | ||||||||
\(502\) | 150.644 | + | 150.644i | 0.300087 | + | 0.300087i | ||||
\(503\) | 460.504 | − | 460.504i | 0.915515 | − | 0.915515i | −0.0811841 | − | 0.996699i | \(-0.525870\pi\) |
0.996699 | + | 0.0811841i | \(0.0258702\pi\) | |||||||
\(504\) | − | 360.000i | − | 0.714286i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −126.000 | −0.249012 | ||||||||
\(507\) | 74.7094 | + | 74.7094i | 0.147356 | + | 0.147356i | ||||
\(508\) | −154.318 | + | 154.318i | −0.303775 | + | 0.303775i | ||||
\(509\) | 390.000i | 0.766208i | 0.923705 | + | 0.383104i | \(0.125145\pi\) | ||||
−0.923705 | + | 0.383104i | \(0.874855\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 132.000 | 0.258317 | ||||||||
\(512\) | 390.694 | + | 390.694i | 0.763073 | + | 0.763073i | ||||
\(513\) | −91.8559 | + | 91.8559i | −0.179056 | + | 0.179056i | ||||
\(514\) | − | 12.0000i | − | 0.0233463i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.0000 | 0.0232558 | ||||||||
\(517\) | 22.0454 | + | 22.0454i | 0.0426410 | + | 0.0426410i | ||||
\(518\) | −235.151 | + | 235.151i | −0.453959 | + | 0.453959i | ||||
\(519\) | 192.000i | 0.369942i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −183.000 | −0.351248 | −0.175624 | − | 0.984457i | \(-0.556194\pi\) | ||||
−0.175624 | + | 0.984457i | \(0.556194\pi\) | |||||||
\(522\) | −220.454 | − | 220.454i | −0.422326 | − | 0.422326i | ||||
\(523\) | −476.426 | + | 476.426i | −0.910948 | + | 0.910948i | −0.996347 | − | 0.0853989i | \(-0.972784\pi\) |
0.0853989 | + | 0.996347i | \(0.472784\pi\) | |||||||
\(524\) | − | 162.000i | − | 0.309160i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0000 | −0.0342205 | ||||||||
\(527\) | 511.943 | + | 511.943i | 0.971430 | + | 0.971430i | ||||
\(528\) | −40.4166 | + | 40.4166i | −0.0765466 | + | 0.0765466i | ||||
\(529\) | − | 59.0000i | − | 0.111531i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −540.000 | −1.01695 | ||||||||
\(532\) | 24.4949 | + | 24.4949i | 0.0460430 | + | 0.0460430i | ||||
\(533\) | 418.863 | − | 418.863i | 0.785859 | − | 0.785859i | ||||
\(534\) | 45.0000i | 0.0842697i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −585.000 | −1.09142 | ||||||||
\(537\) | 238.825 | + | 238.825i | 0.444740 | + | 0.444740i | ||||
\(538\) | −146.969 | + | 146.969i | −0.273177 | + | 0.273177i | ||||
\(539\) | 3.00000i | 0.00556586i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −568.000 | −1.04991 | −0.524954 | − | 0.851131i | \(-0.675917\pi\) | ||||
−0.524954 | + | 0.851131i | \(0.675917\pi\) | |||||||
\(542\) | 71.0352 | + | 71.0352i | 0.131061 | + | 0.131061i | ||||
\(543\) | 320.883 | − | 320.883i | 0.590945 | − | 0.590945i | ||||
\(544\) | − | 297.000i | − | 0.545956i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −216.000 | −0.395604 | ||||||||
\(547\) | −160.442 | − | 160.442i | −0.293312 | − | 0.293312i | 0.545075 | − | 0.838387i | \(-0.316501\pi\) |
−0.838387 | + | 0.545075i | \(0.816501\pi\) | |||||||
\(548\) | −50.2145 | + | 50.2145i | −0.0916324 | + | 0.0916324i | ||||
\(549\) | − | 168.000i | − | 0.306011i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 150.000 | 0.272232 | ||||||||
\(552\) | −257.196 | − | 257.196i | −0.465936 | − | 0.465936i | ||||
\(553\) | 391.918 | − | 391.918i | 0.708713 | − | 0.708713i | ||||
\(554\) | 678.000i | 1.22383i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 185.000 | 0.332734 | ||||||||
\(557\) | 66.1362 | + | 66.1362i | 0.118736 | + | 0.118736i | 0.763978 | − | 0.645242i | \(-0.223243\pi\) |
−0.645242 | + | 0.763978i | \(0.723243\pi\) | |||||||
\(558\) | −279.242 | + | 279.242i | −0.500433 | + | 0.500433i | ||||
\(559\) | 72.0000i | 0.128801i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 99.0000 | 0.176471 | ||||||||
\(562\) | −565.832 | − | 565.832i | −1.00682 | − | 1.00682i | ||||
\(563\) | 191.060 | − | 191.060i | 0.339361 | − | 0.339361i | −0.516766 | − | 0.856127i | \(-0.672864\pi\) |
0.856127 | + | 0.516766i | \(0.172864\pi\) | |||||||
\(564\) | 18.0000i | 0.0319149i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 177.000 | 0.312721 | ||||||||
\(567\) | −44.0908 | − | 44.0908i | −0.0777616 | − | 0.0777616i | ||||
\(568\) | −257.196 | + | 257.196i | −0.452811 | + | 0.452811i | ||||
\(569\) | − | 45.0000i | − | 0.0790861i | −0.999218 | − | 0.0395431i | \(-0.987410\pi\) | ||
0.999218 | − | 0.0395431i | \(-0.0125902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 542.000 | 0.949212 | 0.474606 | − | 0.880198i | \(-0.342591\pi\) | ||||
0.474606 | + | 0.880198i | \(0.342591\pi\) | |||||||
\(572\) | 22.0454 | + | 22.0454i | 0.0385409 | + | 0.0385409i | ||||
\(573\) | −22.0454 | + | 22.0454i | −0.0384737 | + | 0.0384737i | ||||
\(574\) | − | 684.000i | − | 1.19164i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 426.000 | 0.739583 | ||||||||
\(577\) | 549.910 | + | 549.910i | 0.953051 | + | 0.953051i | 0.998946 | − | 0.0458952i | \(-0.0146140\pi\) |
−0.0458952 | + | 0.998946i | \(0.514614\pi\) | |||||||
\(578\) | 90.6311 | − | 90.6311i | 0.156801 | − | 0.156801i | ||||
\(579\) | − | 213.000i | − | 0.367876i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1092.00 | 1.87952 | ||||||||
\(582\) | −161.666 | − | 161.666i | −0.277777 | − | 0.277777i | ||||
\(583\) | −95.5301 | + | 95.5301i | −0.163860 | + | 0.163860i | ||||
\(584\) | 165.000i | 0.282534i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.0204778 | ||||||||
\(587\) | −417.638 | − | 417.638i | −0.711479 | − | 0.711479i | 0.255366 | − | 0.966845i | \(-0.417804\pi\) |
−0.966845 | + | 0.255366i | \(0.917804\pi\) | |||||||
\(588\) | −1.22474 | + | 1.22474i | −0.00208290 | + | 0.00208290i | ||||
\(589\) | − | 190.000i | − | 0.322581i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −318.000 | −0.538071 | ||||||||
\(592\) | −215.555 | − | 215.555i | −0.364113 | − | 0.364113i | ||||
\(593\) | 331.906 | − | 331.906i | 0.559706 | − | 0.559706i | −0.369517 | − | 0.929224i | \(-0.620477\pi\) |
0.929224 | + | 0.369517i | \(0.120477\pi\) | |||||||
\(594\) | 135.000i | 0.227273i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −150.000 | −0.251678 | ||||||||
\(597\) | −244.949 | − | 244.949i | −0.410300 | − | 0.410300i | ||||
\(598\) | 308.636 | − | 308.636i | 0.516113 | − | 0.516113i | ||||
\(599\) | 900.000i | 1.50250i | 0.660015 | + | 0.751252i | \(0.270550\pi\) | ||||
−0.660015 | + | 0.751252i | \(0.729450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 577.000 | 0.960067 | 0.480033 | − | 0.877250i | \(-0.340625\pi\) | ||||
0.480033 | + | 0.877250i | \(0.340625\pi\) | |||||||
\(602\) | 58.7878 | + | 58.7878i | 0.0976541 | + | 0.0976541i | ||||
\(603\) | −286.590 | + | 286.590i | −0.475274 | + | 0.475274i | ||||
\(604\) | − | 52.0000i | − | 0.0860927i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 144.000 | 0.237624 | ||||||||
\(607\) | 127.373 | + | 127.373i | 0.209841 | + | 0.209841i | 0.804200 | − | 0.594359i | \(-0.202594\pi\) |
−0.594359 | + | 0.804200i | \(0.702594\pi\) | |||||||
\(608\) | −55.1135 | + | 55.1135i | −0.0906472 | + | 0.0906472i | ||||
\(609\) | − | 360.000i | − | 0.591133i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −108.000 | −0.176759 | ||||||||
\(612\) | −80.8332 | − | 80.8332i | −0.132080 | − | 0.132080i | ||||
\(613\) | −237.601 | + | 237.601i | −0.387603 | + | 0.387603i | −0.873832 | − | 0.486229i | \(-0.838372\pi\) |
0.486229 | + | 0.873832i | \(0.338372\pi\) | |||||||
\(614\) | 213.000i | 0.346906i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 180.000 | 0.292208 | ||||||||
\(617\) | −656.463 | − | 656.463i | −1.06396 | − | 1.06396i | −0.997810 | − | 0.0661502i | \(-0.978928\pi\) |
−0.0661502 | − | 0.997810i | \(-0.521072\pi\) | |||||||
\(618\) | 271.893 | − | 271.893i | 0.439957 | − | 0.439957i | ||||
\(619\) | − | 470.000i | − | 0.759289i | −0.925132 | − | 0.379645i | \(-0.876046\pi\) | ||
0.925132 | − | 0.379645i | \(-0.123954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −630.000 | −1.01449 | ||||||||
\(622\) | 646.665 | + | 646.665i | 1.03965 | + | 1.03965i | ||||
\(623\) | 73.4847 | − | 73.4847i | 0.117953 | − | 0.117953i | ||||
\(624\) | − | 198.000i | − | 0.317308i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −468.000 | −0.747604 | ||||||||
\(627\) | −18.3712 | − | 18.3712i | −0.0293001 | − | 0.0293001i | ||||
\(628\) | 188.611 | − | 188.611i | 0.300336 | − | 0.300336i | ||||
\(629\) | 528.000i | 0.839428i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −838.000 | −1.32805 | −0.664025 | − | 0.747710i | \(-0.731153\pi\) | ||||
−0.664025 | + | 0.747710i | \(0.731153\pi\) | |||||||
\(632\) | 489.898 | + | 489.898i | 0.775155 | + | 0.775155i | ||||
\(633\) | −126.149 | + | 126.149i | −0.199287 | + | 0.199287i | ||||
\(634\) | − | 492.000i | − | 0.776025i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −78.0000 | −0.122642 | ||||||||
\(637\) | −7.34847 | − | 7.34847i | −0.0115361 | − | 0.0115361i | ||||
\(638\) | 110.227 | − | 110.227i | 0.172770 | − | 0.172770i | ||||
\(639\) | 252.000i | 0.394366i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −618.000 | −0.964119 | −0.482059 | − | 0.876139i | \(-0.660111\pi\) | ||||
−0.482059 | + | 0.876139i | \(0.660111\pi\) | |||||||
\(642\) | 77.1589 | + | 77.1589i | 0.120185 | + | 0.120185i | ||||
\(643\) | −249.848 | + | 249.848i | −0.388566 | + | 0.388566i | −0.874176 | − | 0.485610i | \(-0.838598\pi\) |
0.485610 | + | 0.874176i | \(0.338598\pi\) | |||||||
\(644\) | 168.000i | 0.260870i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −165.000 | −0.255418 | ||||||||
\(647\) | 421.312 | + | 421.312i | 0.651178 | + | 0.651178i | 0.953277 | − | 0.302099i | \(-0.0976872\pi\) |
−0.302099 | + | 0.953277i | \(0.597687\pi\) | |||||||
\(648\) | 55.1135 | − | 55.1135i | 0.0850517 | − | 0.0850517i | ||||
\(649\) | − | 270.000i | − | 0.416025i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −456.000 | −0.700461 | ||||||||
\(652\) | −99.2043 | − | 99.2043i | −0.152154 | − | 0.152154i | ||||
\(653\) | −519.292 | + | 519.292i | −0.795240 | + | 0.795240i | −0.982341 | − | 0.187101i | \(-0.940091\pi\) |
0.187101 | + | 0.982341i | \(0.440091\pi\) | |||||||
\(654\) | − | 120.000i | − | 0.183486i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 627.000 | 0.955793 | ||||||||
\(657\) | 80.8332 | + | 80.8332i | 0.123034 | + | 0.123034i | ||||
\(658\) | −88.1816 | + | 88.1816i | −0.134015 | + | 0.134015i | ||||
\(659\) | − | 885.000i | − | 1.34294i | −0.741030 | − | 0.671472i | \(-0.765662\pi\) | ||
0.741030 | − | 0.671472i | \(-0.234338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 922.000 | 1.39486 | 0.697428 | − | 0.716655i | \(-0.254328\pi\) | ||||
0.697428 | + | 0.716655i | \(0.254328\pi\) | |||||||
\(662\) | 383.345 | + | 383.345i | 0.579071 | + | 0.579071i | ||||
\(663\) | −242.499 | + | 242.499i | −0.365761 | + | 0.365761i | ||||
\(664\) | 1365.00i | 2.05572i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −288.000 | −0.432432 | ||||||||
\(667\) | 514.393 | + | 514.393i | 0.771204 | + | 0.771204i | ||||
\(668\) | 17.1464 | − | 17.1464i | 0.0256683 | − | 0.0256683i | ||||
\(669\) | 492.000i | 0.735426i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 84.0000 | 0.125186 | ||||||||
\(672\) | 132.272 | + | 132.272i | 0.196834 | + | 0.196834i | ||||
\(673\) | −78.3837 | + | 78.3837i | −0.116469 | + | 0.116469i | −0.762939 | − | 0.646470i | \(-0.776244\pi\) |
0.646470 | + | 0.762939i | \(0.276244\pi\) | |||||||
\(674\) | − | 477.000i | − | 0.707715i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 61.0000 | 0.0902367 | ||||||||
\(677\) | −705.453 | − | 705.453i | −1.04203 | − | 1.04203i | −0.999077 | − | 0.0429510i | \(-0.986324\pi\) |
−0.0429510 | − | 0.999077i | \(-0.513676\pi\) | |||||||
\(678\) | 253.522 | − | 253.522i | 0.373927 | − | 0.373927i | ||||
\(679\) | 528.000i | 0.777614i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 672.000 | 0.986784 | ||||||||
\(682\) | −139.621 | − | 139.621i | −0.204723 | − | 0.204723i | ||||
\(683\) | −133.497 | + | 133.497i | −0.195457 | + | 0.195457i | −0.798049 | − | 0.602592i | \(-0.794135\pi\) |
0.602592 | + | 0.798049i | \(0.294135\pi\) | |||||||
\(684\) | 30.0000i | 0.0438596i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −600.000 | −0.874636 | ||||||||
\(687\) | 24.4949 | + | 24.4949i | 0.0356549 | + | 0.0356549i | ||||
\(688\) | −53.8888 | + | 53.8888i | −0.0783267 | + | 0.0783267i | ||||
\(689\) | − | 468.000i | − | 0.679245i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −893.000 | −1.29233 | −0.646165 | − | 0.763198i | \(-0.723628\pi\) | ||||
−0.646165 | + | 0.763198i | \(0.723628\pi\) | |||||||
\(692\) | 78.3837 | + | 78.3837i | 0.113271 | + | 0.113271i | ||||
\(693\) | 88.1816 | − | 88.1816i | 0.127246 | − | 0.127246i | ||||
\(694\) | 243.000i | 0.350144i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 450.000 | 0.646552 | ||||||||
\(697\) | −767.915 | − | 767.915i | −1.10174 | − | 1.10174i | ||||
\(698\) | −122.474 | + | 122.474i | −0.175465 | + | 0.175465i | ||||
\(699\) | 252.000i | 0.360515i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 402.000 | 0.573466 | 0.286733 | − | 0.958010i | \(-0.407431\pi\) | ||||
0.286733 | + | 0.958010i | \(0.407431\pi\) | |||||||
\(702\) | −330.681 | − | 330.681i | −0.471056 | − | 0.471056i | ||||
\(703\) | 97.9796 | − | 97.9796i | 0.139374 | − | 0.139374i | ||||
\(704\) | 213.000i | 0.302557i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 972.000 | 1.37677 | ||||||||
\(707\) | −235.151 | − | 235.151i | −0.332604 | − | 0.332604i | ||||
\(708\) | 110.227 | − | 110.227i | 0.155688 | − | 0.155688i | ||||
\(709\) | − | 1060.00i | − | 1.49506i | −0.664226 | − | 0.747532i | \(-0.731239\pi\) | ||
0.664226 | − | 0.747532i | \(-0.268761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 480.000 | 0.675105 | ||||||||
\(712\) | 91.8559 | + | 91.8559i | 0.129011 | + | 0.129011i | ||||
\(713\) | 651.564 | − | 651.564i | 0.913835 | − | 0.913835i | ||||
\(714\) | 396.000i | 0.554622i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 195.000 | 0.272346 | ||||||||
\(717\) | 257.196 | + | 257.196i | 0.358712 | + | 0.358712i | ||||
\(718\) | 661.362 | − | 661.362i | 0.921117 | − | 0.921117i | ||||
\(719\) | − | 1320.00i | − | 1.83588i | −0.396716 | − | 0.917942i | \(-0.629850\pi\) | ||
0.396716 | − | 0.917942i | \(-0.370150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −888.000 | −1.23162 | ||||||||
\(722\) | −411.514 | − | 411.514i | −0.569964 | − | 0.569964i | ||||
\(723\) | −52.6640 | + | 52.6640i | −0.0728410 | + | 0.0728410i | ||||
\(724\) | − | 262.000i | − | 0.361878i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 336.000 | 0.462810 | ||||||||
\(727\) | −31.8434 | − | 31.8434i | −0.0438011 | − | 0.0438011i | 0.684867 | − | 0.728668i | \(-0.259860\pi\) |
−0.728668 | + | 0.684867i | \(0.759860\pi\) | |||||||
\(728\) | −440.908 | + | 440.908i | −0.605643 | + | 0.605643i | ||||
\(729\) | 351.000i | 0.481481i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 132.000 | 0.180575 | ||||||||
\(732\) | 34.2929 | + | 34.2929i | 0.0468482 | + | 0.0468482i | ||||
\(733\) | 815.680 | − | 815.680i | 1.11280 | − | 1.11280i | 0.120026 | − | 0.992771i | \(-0.461702\pi\) |
0.992771 | − | 0.120026i | \(-0.0382978\pi\) | |||||||
\(734\) | 108.000i | 0.147139i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −378.000 | −0.513587 | ||||||||
\(737\) | −143.295 | − | 143.295i | −0.194430 | − | 0.194430i | ||||
\(738\) | 418.863 | − | 418.863i | 0.567565 | − | 0.567565i | ||||
\(739\) | 710.000i | 0.960758i | 0.877061 | + | 0.480379i | \(0.159501\pi\) | ||||
−0.877061 | + | 0.480379i | \(0.840499\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 90.0000 | 0.121457 | ||||||||
\(742\) | −382.120 | − | 382.120i | −0.514987 | − | 0.514987i | ||||
\(743\) | −800.983 | + | 800.983i | −1.07804 | + | 1.07804i | −0.0813540 | + | 0.996685i | \(0.525924\pi\) |
−0.996685 | + | 0.0813540i | \(0.974076\pi\) | |||||||
\(744\) | − | 570.000i | − | 0.766129i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −858.000 | −1.15013 | ||||||||
\(747\) | 668.711 | + | 668.711i | 0.895195 | + | 0.895195i | ||||
\(748\) | 40.4166 | − | 40.4166i | 0.0540329 | − | 0.0540329i | ||||
\(749\) | − | 252.000i | − | 0.336449i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 502.000 | 0.668442 | 0.334221 | − | 0.942495i | \(-0.391527\pi\) | ||||
0.334221 | + | 0.942495i | \(0.391527\pi\) | |||||||
\(752\) | −80.8332 | − | 80.8332i | −0.107491 | − | 0.107491i | ||||
\(753\) | −150.644 | + | 150.644i | −0.200058 | + | 0.200058i | ||||
\(754\) | 540.000i | 0.716180i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 180.000 | 0.238095 | ||||||||
\(757\) | 4.89898 | + | 4.89898i | 0.00647157 | + | 0.00647157i | 0.710335 | − | 0.703864i | \(-0.248543\pi\) |
−0.703864 | + | 0.710335i | \(0.748543\pi\) | |||||||
\(758\) | −618.496 | + | 618.496i | −0.815958 | + | 0.815958i | ||||
\(759\) | − | 126.000i | − | 0.166008i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 747.000 | 0.981603 | 0.490802 | − | 0.871271i | \(-0.336704\pi\) | ||||
0.490802 | + | 0.871271i | \(0.336704\pi\) | |||||||
\(762\) | 462.954 | + | 462.954i | 0.607551 | + | 0.607551i | ||||
\(763\) | −195.959 | + | 195.959i | −0.256827 | + | 0.256827i | ||||
\(764\) | 18.0000i | 0.0235602i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −348.000 | −0.454308 | ||||||||
\(767\) | 661.362 | + | 661.362i | 0.862271 | + | 0.862271i | ||||
\(768\) | −219.229 | + | 219.229i | −0.285455 | + | 0.285455i | ||||
\(769\) | 1255.00i | 1.63199i | 0.578059 | + | 0.815995i | \(0.303810\pi\) | ||||
−0.578059 | + | 0.815995i | \(0.696190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | 0.0155642 | ||||||||
\(772\) | −86.9569 | − | 86.9569i | −0.112638 | − | 0.112638i | ||||
\(773\) | −17.1464 | + | 17.1464i | −0.0221817 | + | 0.0221817i | −0.718111 | − | 0.695929i | \(-0.754993\pi\) |
0.695929 | + | 0.718111i | \(0.254993\pi\) | |||||||
\(774\) | 72.0000i | 0.0930233i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −660.000 | −0.850515 | ||||||||
\(777\) | −235.151 | − | 235.151i | −0.302640 | − | 0.302640i | ||||
\(778\) | −845.074 | + | 845.074i | −1.08621 | + | 1.08621i | ||||
\(779\) | 285.000i | 0.365854i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −126.000 | −0.161332 | ||||||||
\(782\) | −565.832 | − | 565.832i | −0.723570 | − | 0.723570i | ||||
\(783\) | 551.135 | − | 551.135i | 0.703876 | − | 0.703876i | ||||
\(784\) | − | 11.0000i | − | 0.0140306i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −486.000 | −0.618321 | ||||||||
\(787\) | 592.777 | + | 592.777i | 0.753210 | + | 0.753210i | 0.975077 | − | 0.221867i | \(-0.0712150\pi\) |
−0.221867 | + | 0.975077i | \(0.571215\pi\) | |||||||
\(788\) | −129.823 | + | 129.823i | −0.164750 | + | 0.164750i | ||||
\(789\) | − | 18.0000i | − | 0.0228137i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −828.000 | −1.04678 | ||||||||
\(792\) | 110.227 | + | 110.227i | 0.139176 | + | 0.139176i | ||||
\(793\) | −205.757 | + | 205.757i | −0.259467 | + | 0.259467i | ||||
\(794\) | − | 1032.00i | − | 1.29975i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −200.000 | −0.251256 | ||||||||
\(797\) | 605.024 | + | 605.024i | 0.759127 | + | 0.759127i | 0.976163 | − | 0.217037i | \(-0.0696391\pi\) |
−0.217037 | + | 0.976163i | \(0.569639\pi\) | |||||||
\(798\) | 73.4847 | − | 73.4847i | 0.0920861 | − | 0.0920861i | ||||
\(799\) | 198.000i | 0.247810i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 90.0000 | 0.112360 | ||||||||
\(802\) | 701.779 | + | 701.779i | 0.875036 | + | 0.875036i | ||||
\(803\) | −40.4166 | + | 40.4166i | −0.0503320 | + | 0.0503320i | ||||
\(804\) | − | 117.000i | − | 0.145522i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 684.000 | 0.848635 | ||||||||
\(807\) | −146.969 | − | 146.969i | −0.182118 | − | 0.182118i | ||||
\(808\) | 293.939 | − | 293.939i | 0.363786 | − | 0.363786i | ||||
\(809\) | 90.0000i | 0.111248i | 0.998452 | + | 0.0556242i | \(0.0177149\pi\) | ||||
−0.998452 | + | 0.0556242i | \(0.982285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −278.000 | −0.342787 | −0.171393 | − | 0.985203i | \(-0.554827\pi\) | ||||
−0.171393 | + | 0.985203i | \(0.554827\pi\) | |||||||
\(812\) | −146.969 | − | 146.969i | −0.180997 | − | 0.180997i | ||||
\(813\) | −71.0352 | + | 71.0352i | −0.0873742 | + | 0.0873742i | ||||
\(814\) | − | 144.000i | − | 0.176904i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −363.000 | −0.444853 | ||||||||
\(817\) | −24.4949 | − | 24.4949i | −0.0299815 | − | 0.0299815i | ||||
\(818\) | 447.032 | − | 447.032i | 0.546494 | − | 0.546494i | ||||
\(819\) | 432.000i | 0.527473i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.0000 | 0.0511571 | 0.0255786 | − | 0.999673i | \(-0.491857\pi\) | ||||
0.0255786 | + | 0.999673i | \(0.491857\pi\) | |||||||
\(822\) | 150.644 | + | 150.644i | 0.183265 | + | 0.183265i | ||||
\(823\) | 778.938 | − | 778.938i | 0.946461 | − | 0.946461i | −0.0521765 | − | 0.998638i | \(-0.516616\pi\) |
0.998638 | + | 0.0521765i | \(0.0166158\pi\) | |||||||
\(824\) | − | 1110.00i | − | 1.34709i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1080.00 | 1.30751 | ||||||||
\(827\) | −674.834 | − | 674.834i | −0.816003 | − | 0.816003i | 0.169523 | − | 0.985526i | \(-0.445777\pi\) |
−0.985526 | + | 0.169523i | \(0.945777\pi\) | |||||||
\(828\) | −102.879 | + | 102.879i | −0.124249 | + | 0.124249i | ||||
\(829\) | 170.000i | 0.205066i | 0.994730 | + | 0.102533i | \(0.0326948\pi\) | ||||
−0.994730 | + | 0.102533i | \(0.967305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −678.000 | −0.815884 | ||||||||
\(832\) | −521.741 | − | 521.741i | −0.627093 | − | 0.627093i | ||||
\(833\) | −13.4722 | + | 13.4722i | −0.0161731 | + | 0.0161731i | ||||
\(834\) | − | 555.000i | − | 0.665468i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.0000 | −0.0179426 | ||||||||
\(837\) | −698.105 | − | 698.105i | −0.834056 | − | 0.834056i | ||||
\(838\) | −789.960 | + | 789.960i | −0.942674 | + | 0.942674i | ||||
\(839\) | 360.000i | 0.429082i | 0.976715 | + | 0.214541i | \(0.0688256\pi\) | ||||
−0.976715 | + | 0.214541i | \(0.931174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −59.0000 | −0.0701546 | ||||||||
\(842\) | 9.79796 | + | 9.79796i | 0.0116365 | + | 0.0116365i | ||||
\(843\) | 565.832 | − | 565.832i | 0.671212 | − | 0.671212i | ||||
\(844\) | 103.000i | 0.122038i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −108.000 | −0.127660 | ||||||||
\(847\) | −548.686 | − | 548.686i | −0.647799 | − | 0.647799i | ||||
\(848\) | 350.277 | − | 350.277i | 0.413063 | − | 0.413063i | ||||
\(849\) | 177.000i | 0.208481i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 672.000 | 0.789659 | ||||||||
\(852\) | −51.4393 | − | 51.4393i | −0.0603747 | − | 0.0603747i | ||||
\(853\) | 521.741 | − | 521.741i | 0.611655 | − | 0.611655i | −0.331722 | − | 0.943377i | \(-0.607630\pi\) |
0.943377 | + | 0.331722i | \(0.107630\pi\) | |||||||
\(854\) | 336.000i | 0.393443i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 315.000 | 0.367991 | ||||||||
\(857\) | 280.467 | + | 280.467i | 0.327266 | + | 0.327266i | 0.851546 | − | 0.524280i | \(-0.175666\pi\) |
−0.524280 | + | 0.851546i | \(0.675666\pi\) | |||||||
\(858\) | 66.1362 | − | 66.1362i | 0.0770818 | − | 0.0770818i | ||||
\(859\) | − | 335.000i | − | 0.389988i | −0.980804 | − | 0.194994i | \(-0.937531\pi\) | ||
0.980804 | − | 0.194994i | \(-0.0624688\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 684.000 | 0.794425 | ||||||||
\(862\) | −14.6969 | − | 14.6969i | −0.0170498 | − | 0.0170498i | ||||
\(863\) | −849.973 | + | 849.973i | −0.984905 | + | 0.984905i | −0.999888 | − | 0.0149828i | \(-0.995231\pi\) |
0.0149828 | + | 0.999888i | \(0.495231\pi\) | |||||||
\(864\) | 405.000i | 0.468750i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1077.00 | 1.24365 | ||||||||
\(867\) | 90.6311 | + | 90.6311i | 0.104534 | + | 0.104534i | ||||
\(868\) | −186.161 | + | 186.161i | −0.214471 | + | 0.214471i | ||||
\(869\) | 240.000i | 0.276180i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 702.000 | 0.805970 | ||||||||
\(872\) | −244.949 | − | 244.949i | −0.280905 | − | 0.280905i | ||||
\(873\) | −323.333 | + | 323.333i | −0.370370 | + | 0.370370i | ||||
\(874\) | 210.000i | 0.240275i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.0000 | −0.0376712 | ||||||||
\(877\) | 151.868 | + | 151.868i | 0.173168 | + | 0.173168i | 0.788370 | − | 0.615202i | \(-0.210925\pi\) |
−0.615202 | + | 0.788370i | \(0.710925\pi\) | |||||||
\(878\) | 12.2474 | − | 12.2474i | 0.0139493 | − | 0.0139493i | ||||
\(879\) | 12.0000i | 0.0136519i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 162.000 | 0.183882 | 0.0919410 | − | 0.995764i | \(-0.470693\pi\) | ||||
0.0919410 | + | 0.995764i | \(0.470693\pi\) | |||||||
\(882\) | −7.34847 | − | 7.34847i | −0.00833160 | − | 0.00833160i | ||||
\(883\) | 295.164 | − | 295.164i | 0.334274 | − | 0.334274i | −0.519933 | − | 0.854207i | \(-0.674043\pi\) |
0.854207 | + | 0.519933i | \(0.174043\pi\) | |||||||
\(884\) | 198.000i | 0.223982i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −213.000 | −0.240406 | ||||||||
\(887\) | −509.494 | − | 509.494i | −0.574401 | − | 0.574401i | 0.358954 | − | 0.933355i | \(-0.383133\pi\) |
−0.933355 | + | 0.358954i | \(0.883133\pi\) | |||||||
\(888\) | 293.939 | − | 293.939i | 0.331012 | − | 0.331012i | ||||
\(889\) | − | 1512.00i | − | 1.70079i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | 0.0303030 | ||||||||
\(892\) | 200.858 | + | 200.858i | 0.225177 | + | 0.225177i | ||||
\(893\) | 36.7423 | − | 36.7423i | 0.0411448 | − | 0.0411448i | ||||
\(894\) | 450.000i | 0.503356i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −420.000 | −0.468750 | ||||||||
\(897\) | 308.636 | + | 308.636i | 0.344075 | + | 0.344075i | ||||
\(898\) | −91.8559 | + | 91.8559i | −0.102289 | + | 0.102289i | ||||
\(899\) | 1140.00i | 1.26808i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −858.000 | −0.952275 | ||||||||
\(902\) | 209.431 | + | 209.431i | 0.232186 | + | 0.232186i | ||||
\(903\) | −58.7878 | + | 58.7878i | −0.0651027 | + | 0.0651027i | ||||
\(904\) | − | 1035.00i | − | 1.14491i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −156.000 | −0.172185 | ||||||||
\(907\) | 494.797 | + | 494.797i | 0.545531 | + | 0.545531i | 0.925145 | − | 0.379614i | \(-0.123943\pi\) |
−0.379614 | + | 0.925145i | \(0.623943\pi\) | |||||||
\(908\) | 274.343 | − | 274.343i | 0.302140 | − | 0.302140i | ||||
\(909\) | − | 288.000i | − | 0.316832i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −828.000 | −0.908891 | −0.454446 | − | 0.890774i | \(-0.650163\pi\) | ||||
−0.454446 | + | 0.890774i | \(0.650163\pi\) | |||||||
\(912\) | 67.3610 | + | 67.3610i | 0.0738607 | + | 0.0738607i | ||||
\(913\) | −334.355 | + | 334.355i | −0.366216 | + | 0.366216i | ||||
\(914\) | 513.000i | 0.561269i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.0218341 | ||||||||
\(917\) | 793.635 | + | 793.635i | 0.865469 | + | 0.865469i | ||||
\(918\) | −606.249 | + | 606.249i | −0.660402 | + | 0.660402i | ||||
\(919\) | − | 1270.00i | − | 1.38194i | −0.722885 | − | 0.690968i | \(-0.757184\pi\) | ||
0.722885 | − | 0.690968i | \(-0.242816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −213.000 | −0.231270 | ||||||||
\(922\) | 279.242 | + | 279.242i | 0.302865 | + | 0.302865i | ||||
\(923\) | 308.636 | − | 308.636i | 0.334383 | − | 0.334383i | ||||
\(924\) | 36.0000i | 0.0389610i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1068.00 | −1.15335 | ||||||||
\(927\) | −543.787 | − | 543.787i | −0.586609 | − | 0.586609i | ||||
\(928\) | 330.681 | − | 330.681i | 0.356337 | − | 0.356337i | ||||
\(929\) | 570.000i | 0.613563i | 0.951780 | + | 0.306781i | \(0.0992521\pi\) | ||||
−0.951780 | + | 0.306781i | \(0.900748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | 0.00537057 | ||||||||
\(932\) | 102.879 | + | 102.879i | 0.110385 | + | 0.110385i | ||||
\(933\) | −646.665 | + | 646.665i | −0.693103 | + | 0.693103i | ||||
\(934\) | 1308.00i | 1.40043i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −540.000 | −0.576923 | ||||||||
\(937\) | 317.209 | + | 317.209i | 0.338537 | + | 0.338537i | 0.855816 | − | 0.517280i | \(-0.173055\pi\) |
−0.517280 | + | 0.855816i | \(0.673055\pi\) | |||||||
\(938\) | 573.181 | − | 573.181i | 0.611067 | − | 0.611067i | ||||
\(939\) | − | 468.000i | − | 0.498403i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1518.00 | −1.61318 | −0.806589 | − | 0.591113i | \(-0.798689\pi\) | ||||
−0.806589 | + | 0.591113i | \(0.798689\pi\) | |||||||
\(942\) | −565.832 | − | 565.832i | −0.600671 | − | 0.600671i | ||||
\(943\) | −977.346 | + | 977.346i | −1.03642 | + | 1.03642i | ||||
\(944\) | 990.000i | 1.04873i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.0000 | −0.0380550 | ||||||||
\(947\) | −436.009 | − | 436.009i | −0.460411 | − | 0.460411i | 0.438379 | − | 0.898790i | \(-0.355553\pi\) |
−0.898790 | + | 0.438379i | \(0.855553\pi\) | |||||||
\(948\) | −97.9796 | + | 97.9796i | −0.103354 | + | 0.103354i | ||||
\(949\) | − | 198.000i | − | 0.208641i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 492.000 | 0.517350 | ||||||||
\(952\) | 808.332 | + | 808.332i | 0.849088 | + | 0.849088i | ||||
\(953\) | 429.885 | − | 429.885i | 0.451087 | − | 0.451087i | −0.444629 | − | 0.895715i | \(-0.646664\pi\) |
0.895715 | + | 0.444629i | \(0.146664\pi\) | |||||||
\(954\) | − | 468.000i | − | 0.490566i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 210.000 | 0.219665 | ||||||||
\(957\) | 110.227 | + | 110.227i | 0.115180 | + | 0.115180i | ||||
\(958\) | 330.681 | − | 330.681i | 0.345179 | − | 0.345179i | ||||
\(959\) | − | 492.000i | − | 0.513034i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 483.000 | 0.502601 | ||||||||
\(962\) | 352.727 | + | 352.727i | 0.366660 | + | 0.366660i | ||||
\(963\) | 154.318 | − | 154.318i | 0.160247 | − | 0.160247i | ||||
\(964\) | 43.0000i | 0.0446058i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 504.000 | 0.521739 | ||||||||
\(967\) | −533.989 | − | 533.989i | −0.552212 | − | 0.552212i | 0.374867 | − | 0.927079i | \(-0.377688\pi\) |
−0.927079 | + | 0.374867i | \(0.877688\pi\) | |||||||
\(968\) | 685.857 | − | 685.857i | 0.708530 | − | 0.708530i | ||||
\(969\) | − | 165.000i | − | 0.170279i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1467.00 | 1.51081 | 0.755407 | − | 0.655256i | \(-0.227439\pi\) | ||||
0.755407 | + | 0.655256i | \(0.227439\pi\) | |||||||
\(972\) | 176.363 | + | 176.363i | 0.181444 | + | 0.181444i | ||||
\(973\) | −906.311 | + | 906.311i | −0.931461 | + | 0.931461i | ||||
\(974\) | 198.000i | 0.203285i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −308.000 | −0.315574 | ||||||||
\(977\) | 1039.81 | + | 1039.81i | 1.06429 | + | 1.06429i | 0.997786 | + | 0.0665006i | \(0.0211834\pi\) |
0.0665006 | + | 0.997786i | \(0.478817\pi\) | |||||||
\(978\) | −297.613 | + | 297.613i | −0.304308 | + | 0.304308i | ||||
\(979\) | 45.0000i | 0.0459653i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −240.000 | −0.244648 | ||||||||
\(982\) | −712.802 | − | 712.802i | −0.725867 | − | 0.725867i | ||||
\(983\) | −715.251 | + | 715.251i | −0.727621 | + | 0.727621i | −0.970145 | − | 0.242525i | \(-0.922024\pi\) |
0.242525 | + | 0.970145i | \(0.422024\pi\) | |||||||
\(984\) | 855.000i | 0.868902i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 990.000 | 1.00406 | ||||||||
\(987\) | −88.1816 | − | 88.1816i | −0.0893431 | − | 0.0893431i | ||||
\(988\) | 36.7423 | − | 36.7423i | 0.0371886 | − | 0.0371886i | ||||
\(989\) | − | 168.000i | − | 0.169869i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1832.00 | 1.84864 | 0.924319 | − | 0.381621i | \(-0.124634\pi\) | ||||
0.924319 | + | 0.381621i | \(0.124634\pi\) | |||||||
\(992\) | −418.863 | − | 418.863i | −0.422241 | − | 0.422241i | ||||
\(993\) | −383.345 | + | 383.345i | −0.386047 | + | 0.386047i | ||||
\(994\) | − | 504.000i | − | 0.507042i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −273.000 | −0.274096 | ||||||||
\(997\) | −1293.33 | − | 1293.33i | −1.29722 | − | 1.29722i | −0.930220 | − | 0.367002i | \(-0.880384\pi\) |
−0.367002 | − | 0.930220i | \(-0.619616\pi\) | |||||||
\(998\) | 306.186 | − | 306.186i | 0.306800 | − | 0.306800i | ||||
\(999\) | − | 720.000i | − | 0.720721i |
(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 | 25.3.c.a.7.1 | ✓ | 4 | |
3.2 | odd | 2 | 225.3.g.e.82.2 | 4 | |||
4.3 | odd | 2 | 400.3.p.j.257.1 | 4 | |||
5.2 | odd | 4 | inner | 25.3.c.a.18.2 | yes | 4 | |
5.3 | odd | 4 | inner | 25.3.c.a.18.1 | yes | 4 | |
5.4 | even | 2 | inner | 25.3.c.a.7.2 | yes | 4 | |
15.2 | even | 4 | 225.3.g.e.118.1 | 4 | |||
15.8 | even | 4 | 225.3.g.e.118.2 | 4 | |||
15.14 | odd | 2 | 225.3.g.e.82.1 | 4 | |||
20.3 | even | 4 | 400.3.p.j.193.1 | 4 | |||
20.7 | even | 4 | 400.3.p.j.193.2 | 4 | |||
20.19 | odd | 2 | 400.3.p.j.257.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.3.c.a.7.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
25.3.c.a.7.2 | yes | 4 | 5.4 | even | 2 | inner | |
25.3.c.a.18.1 | yes | 4 | 5.3 | odd | 4 | inner | |
25.3.c.a.18.2 | yes | 4 | 5.2 | odd | 4 | inner | |
225.3.g.e.82.1 | 4 | 15.14 | odd | 2 | |||
225.3.g.e.82.2 | 4 | 3.2 | odd | 2 | |||
225.3.g.e.118.1 | 4 | 15.2 | even | 4 | |||
225.3.g.e.118.2 | 4 | 15.8 | even | 4 | |||
400.3.p.j.193.1 | 4 | 20.3 | even | 4 | |||
400.3.p.j.193.2 | 4 | 20.7 | even | 4 | |||
400.3.p.j.257.1 | 4 | 4.3 | odd | 2 | |||
400.3.p.j.257.2 | 4 | 20.19 | odd | 2 |