Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(401,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.q (of order \(3\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.11337408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 18x^{4} + 81x^{2} + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.3 | ||
Root | \(0.391571i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.1201 |
Dual form | 1400.2.q.j.401.3 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.29211 | − | 2.23800i | 0.746002 | − | 1.29211i | −0.203724 | − | 0.979028i | \(-0.565304\pi\) |
0.949725 | − | 0.313084i | \(-0.101362\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.292113 | − | 2.62958i | 0.110408 | − | 0.993886i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.83911 | − | 3.18543i | −0.613037 | − | 1.06181i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.839111 | + | 1.45338i | −0.253001 | + | 0.438211i | −0.964351 | − | 0.264627i | \(-0.914751\pi\) |
0.711349 | + | 0.702839i | \(0.248084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.84667 | 1.34422 | 0.672112 | − | 0.740449i | \(-0.265387\pi\) | ||||
0.672112 | + | 0.740449i | \(0.265387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.42334 | − | 5.92939i | −0.785367 | − | 1.36030i | −0.928779 | − | 0.370633i | \(-0.879141\pi\) |
0.143412 | − | 0.989663i | \(-0.454192\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.50756 | − | 4.05146i | −1.20185 | − | 0.884101i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.13122 | − | 1.95934i | −0.235876 | − | 0.408550i | 0.723651 | − | 0.690166i | \(-0.242463\pi\) |
−0.959527 | + | 0.281617i | \(0.909129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.75268 | −0.337303 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.32178 | 0.616839 | 0.308419 | − | 0.951250i | \(-0.400200\pi\) | ||||
0.308419 | + | 0.951250i | \(0.400200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58423 | + | 7.94011i | −0.823351 | + | 1.42609i | 0.0798217 | + | 0.996809i | \(0.474565\pi\) |
−0.903173 | + | 0.429277i | \(0.858768\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.16845 | + | 3.75587i | 0.377479 | + | 0.653813i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.42334 | − | 2.46529i | −0.233995 | − | 0.405291i | 0.724985 | − | 0.688765i | \(-0.241847\pi\) |
−0.958980 | + | 0.283473i | \(0.908513\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.26245 | − | 10.8469i | 1.00279 | − | 1.73689i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.52489 | 1.48754 | 0.743769 | − | 0.668437i | \(-0.233036\pi\) | ||||
0.743769 | + | 0.668437i | \(0.233036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.58423 | −1.00408 | −0.502042 | − | 0.864843i | \(-0.667418\pi\) | ||||
−0.502042 | + | 0.864843i | \(0.667418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.10156 | − | 10.5682i | −0.890004 | − | 1.54153i | −0.839869 | − | 0.542789i | \(-0.817368\pi\) |
−0.0501344 | − | 0.998742i | \(-0.515965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82934 | − | 1.53627i | −0.975620 | − | 0.219466i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.58423 | − | 4.47601i | −0.361864 | − | 0.626767i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.74511 | − | 6.48673i | 0.514431 | − | 0.891021i | −0.485429 | − | 0.874276i | \(-0.661336\pi\) |
0.999860 | − | 0.0167445i | \(-0.00533020\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.6933 | −2.34354 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | + | 6.92820i | −0.520756 | + | 0.901975i | 0.478953 | + | 0.877841i | \(0.341016\pi\) |
−0.999709 | + | 0.0241347i | \(0.992317\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24511 | + | 5.62070i | 0.415494 | + | 0.719657i | 0.995480 | − | 0.0949692i | \(-0.0302753\pi\) |
−0.579986 | + | 0.814627i | \(0.696942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.91357 | + | 3.90558i | −1.12300 | + | 0.492056i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.87634 | + | 4.98196i | −0.351401 | + | 0.608644i | −0.986495 | − | 0.163791i | \(-0.947628\pi\) |
0.635094 | + | 0.772434i | \(0.280961\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.84667 | −0.703857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.84667 | + | 10.1267i | −0.684301 | + | 1.18524i | 0.289355 | + | 0.957222i | \(0.406559\pi\) |
−0.973656 | + | 0.228022i | \(0.926774\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.57666 | + | 2.63106i | 0.407599 | + | 0.299837i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.84667 | − | 4.93058i | −0.320276 | − | 0.554734i | 0.660269 | − | 0.751029i | \(-0.270442\pi\) |
−0.980545 | + | 0.196295i | \(0.937109\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.25268 | − | 5.63380i | 0.361408 | − | 0.625978i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5842 | 1.38130 | 0.690649 | − | 0.723190i | \(-0.257325\pi\) | ||||
0.690649 | + | 0.723190i | \(0.257325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.29211 | − | 7.43416i | 0.460163 | − | 0.797025i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.92334 | + | 5.06337i | 0.309873 | + | 0.536716i | 0.978334 | − | 0.207031i | \(-0.0663801\pi\) |
−0.668461 | + | 0.743747i | \(0.733047\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.41577 | − | 12.7447i | 0.148414 | − | 1.33601i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.8467 | + | 20.5190i | 1.22844 | + | 2.12773i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.17287 | 0.620397 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.50756 | − | 14.7355i | 0.846534 | − | 1.46624i | −0.0377483 | − | 0.999287i | \(-0.512019\pi\) |
0.884282 | − | 0.466953i | \(-0.154648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.55456 | + | 6.15668i | 0.350241 | + | 0.606635i | 0.986292 | − | 0.165012i | \(-0.0527663\pi\) |
−0.636050 | + | 0.771648i | \(0.719433\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.876338 | − | 1.51786i | −0.0847188 | − | 0.146737i | 0.820553 | − | 0.571571i | \(-0.193666\pi\) |
−0.905271 | + | 0.424834i | \(0.860333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.77001 | + | 16.9222i | −0.935797 | + | 1.62085i | −0.162591 | + | 0.986694i | \(0.551985\pi\) |
−0.773206 | + | 0.634154i | \(0.781348\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.35644 | −0.698243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.3369 | −0.972414 | −0.486207 | − | 0.873844i | \(-0.661620\pi\) | ||||
−0.486207 | + | 0.873844i | \(0.661620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.91357 | − | 15.4387i | −0.824059 | − | 1.42731i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.26245 | − | 3.13553i | −0.390738 | − | 0.287434i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.09179 | + | 7.08718i | 0.371981 | + | 0.644289i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.3072 | − | 21.3168i | 1.10971 | − | 1.92207i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1836 | 1.70227 | 0.851133 | − | 0.524949i | \(-0.175916\pi\) | ||||
0.851133 | + | 0.524949i | \(0.175916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.50756 | + | 14.7355i | −0.749049 | + | 1.29739i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.91357 | + | 15.4387i | 0.778782 | + | 1.34889i | 0.932644 | + | 0.360797i | \(0.117495\pi\) |
−0.153862 | + | 0.988092i | \(0.549171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.5918 | + | 7.26987i | −1.43869 | + | 0.630378i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | − | 3.46410i | 0.170872 | − | 0.295958i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) |
0.938725 | + | 0.344668i | \(0.112008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.16845 | −0.438382 | −0.219191 | − | 0.975682i | \(-0.570342\pi\) | ||||
−0.219191 | + | 0.975682i | \(0.570342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.5356 | −2.65578 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.06689 | + | 7.04407i | −0.340091 | + | 0.589054i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.2624 | + | 13.2991i | −1.01139 | + | 1.09689i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.398443 | − | 0.690123i | −0.0326417 | − | 0.0565371i | 0.849243 | − | 0.528002i | \(-0.177059\pi\) |
−0.881885 | + | 0.471465i | \(0.843725\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.26245 | − | 14.3110i | 0.672388 | − | 1.16461i | −0.304837 | − | 0.952405i | \(-0.598602\pi\) |
0.977225 | − | 0.212206i | \(-0.0680648\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.35644 | −0.594733 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.10156 | − | 7.10411i | 0.327340 | − | 0.566969i | −0.654643 | − | 0.755938i | \(-0.727181\pi\) |
0.981983 | + | 0.188969i | \(0.0605145\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.67822 | − | 16.7632i | −0.767533 | − | 1.32941i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.48267 | + | 2.40229i | −0.432095 | + | 0.189327i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.84667 | + | 3.19853i | 0.144643 | + | 0.250528i | 0.929240 | − | 0.369478i | \(-0.120463\pi\) |
−0.784597 | + | 0.620006i | \(0.787130\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.262447 | 0.0203087 | 0.0101544 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101544 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4902 | 0.806941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.5918 | + | 21.8096i | −0.962918 | + | 1.66782i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.42334 | − | 16.3217i | −0.716443 | − | 1.24092i | −0.962400 | − | 0.271635i | \(-0.912436\pi\) |
0.245957 | − | 0.969281i | \(-0.420898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3369 | + | 17.9040i | 0.776969 | + | 1.34575i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00756 | − | 10.4054i | 0.449026 | − | 0.777736i | −0.549297 | − | 0.835627i | \(-0.685104\pi\) |
0.998323 | + | 0.0578912i | \(0.0184376\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.03466 | −0.448553 | −0.224276 | − | 0.974526i | \(-0.572002\pi\) | ||||
−0.224276 | + | 0.974526i | \(0.572002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.7722 | 1.23984 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.67822 | + | 2.90676i | 0.122724 | + | 0.212564i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.511979 | + | 4.60880i | −0.0372410 | + | 0.335241i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41577 | − | 2.45219i | −0.102442 | − | 0.177434i | 0.810248 | − | 0.586087i | \(-0.199332\pi\) |
−0.912690 | + | 0.408652i | \(0.865999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.49023 | − | 11.2414i | 0.467177 | − | 0.809174i | −0.532120 | − | 0.846669i | \(-0.678604\pi\) |
0.999297 | + | 0.0374948i | \(0.0119378\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.84667 | 0.345311 | 0.172656 | − | 0.984982i | \(-0.444765\pi\) | ||||
0.172656 | + | 0.984982i | \(0.444765\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.69334 | − | 13.3253i | 0.545367 | − | 0.944603i | −0.453217 | − | 0.891400i | \(-0.649724\pi\) |
0.998584 | − | 0.0532026i | \(-0.0169429\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.43311 | + | 12.8745i | 0.524291 | + | 0.908098i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.970334 | − | 8.73487i | 0.0681041 | − | 0.613068i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.16089 | + | 7.20687i | −0.289202 | + | 0.500912i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.4902 | 0.794796 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.18357 | 0.632223 | 0.316112 | − | 0.948722i | \(-0.397623\pi\) | ||||
0.316112 | + | 0.948722i | \(0.397623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.5400 | + | 14.3740i | 1.32646 | + | 0.975769i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.1091 | + | 26.1698i | 1.02098 | + | 1.76839i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.84667 | − | 8.39468i | 0.326022 | − | 0.564687i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9805 | 0.869236 | 0.434618 | − | 0.900615i | \(-0.356883\pi\) | ||||
0.434618 | + | 0.900615i | \(0.356883\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0151 | + | 19.0788i | −0.731099 | + | 1.26630i | 0.225314 | + | 0.974286i | \(0.427659\pi\) |
−0.956414 | + | 0.292015i | \(0.905674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.15333 | − | 3.72967i | −0.142296 | − | 0.246464i | 0.786065 | − | 0.618144i | \(-0.212115\pi\) |
−0.928361 | + | 0.371680i | \(0.878782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.5098 | − | 4.60497i | 0.691492 | − | 0.302985i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.00000 | + | 15.5885i | 0.589610 | + | 1.02123i | 0.994283 | + | 0.106773i | \(0.0340517\pi\) |
−0.404674 | + | 0.914461i | \(0.632615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7129 | −0.955705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8618 | 0.702591 | 0.351296 | − | 0.936265i | \(-0.385741\pi\) | ||||
0.351296 | + | 0.936265i | \(0.385741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.101557 | + | 0.175902i | −0.00654187 | + | 0.0113309i | −0.869278 | − | 0.494324i | \(-0.835416\pi\) |
0.862736 | + | 0.505655i | \(0.168749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0347 | − | 19.1126i | −0.707874 | − | 1.22607i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.5918 | − | 28.7378i | −1.05571 | − | 1.82854i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.2602 | − | 28.1636i | 1.03045 | − | 1.78479i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.03466 | 0.317785 | 0.158893 | − | 0.987296i | \(-0.449208\pi\) | ||||
0.158893 | + | 0.987296i | \(0.449208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.79689 | 0.238708 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6933 | + | 20.2535i | 0.729411 | + | 1.26338i | 0.957133 | + | 0.289650i | \(0.0935390\pi\) |
−0.227722 | + | 0.973726i | \(0.573128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.89844 | + | 3.02263i | −0.428648 | + | 0.187817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.10912 | − | 10.5813i | −0.378145 | − | 0.654966i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5546 | − | 23.4772i | 0.835810 | − | 1.44767i | −0.0575594 | − | 0.998342i | \(-0.518332\pi\) |
0.893369 | − | 0.449323i | \(-0.148335\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.1091 | 0.924663 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.24511 | + | 5.62070i | −0.197858 | + | 0.342700i | −0.947834 | − | 0.318765i | \(-0.896732\pi\) |
0.749976 | + | 0.661466i | \(0.230065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6933 | + | 20.2535i | 0.710320 | + | 1.23031i | 0.964737 | + | 0.263216i | \(0.0847831\pi\) |
−0.254417 | + | 0.967095i | \(0.581884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.6933 | − | 19.6361i | −1.61555 | − | 1.18843i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.83155 | − | 3.17234i | 0.110047 | − | 0.190607i | −0.805742 | − | 0.592267i | \(-0.798233\pi\) |
0.915789 | + | 0.401660i | \(0.131566\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.7236 | 2.01898 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8965 | 0.828993 | 0.414497 | − | 0.910051i | \(-0.363958\pi\) | ||||
0.414497 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.1685 | + | 17.6123i | −0.604452 | + | 1.04694i | 0.387686 | + | 0.921791i | \(0.373274\pi\) |
−0.992138 | + | 0.125150i | \(0.960059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.78234 | − | 25.0464i | 0.164236 | − | 1.47844i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.58423 | − | 4.47601i | 0.151490 | − | 0.262388i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.8467 | −1.10103 | −0.550517 | − | 0.834824i | \(-0.685569\pi\) | ||||
−0.550517 | + | 0.834824i | \(0.685569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.47069 | − | 2.54731i | 0.0853380 | − | 0.147810i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.48267 | − | 9.49626i | −0.317071 | − | 0.549183i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.92334 | + | 17.3137i | −0.110859 | + | 0.997946i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.9855 | − | 38.0799i | −1.26303 | − | 2.18763i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.39623 | 0.136760 | 0.0683802 | − | 0.997659i | \(-0.478217\pi\) | ||||
0.0683802 | + | 0.997659i | \(0.478217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.3716 | 1.04512 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.83155 | − | 4.90439i | 0.160562 | − | 0.278102i | −0.774508 | − | 0.632564i | \(-0.782003\pi\) |
0.935071 | + | 0.354462i | \(0.115336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.8618 | + | 25.7414i | 0.840038 | + | 1.45499i | 0.889861 | + | 0.456231i | \(0.150801\pi\) |
−0.0498231 | + | 0.998758i | \(0.515866\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.52489 | + | 16.4976i | 0.534971 | + | 0.926597i | 0.999165 | + | 0.0408636i | \(0.0130109\pi\) |
−0.464193 | + | 0.885734i | \(0.653656\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.78734 | + | 4.82781i | −0.156061 | + | 0.270306i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.52931 | −0.252801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.6933 | −0.761918 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.2479 | + | 43.7307i | 1.39621 | + | 2.41831i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.5722 | + | 12.9574i | −1.63037 | + | 0.714365i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.16089 | − | 2.01072i | −0.0638083 | − | 0.110519i | 0.832356 | − | 0.554241i | \(-0.186991\pi\) |
−0.896165 | + | 0.443722i | \(0.853658\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.23534 | + | 9.06788i | −0.286895 | + | 0.496917i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4062 | 0.893704 | 0.446852 | − | 0.894608i | \(-0.352545\pi\) | ||||
0.446852 | + | 0.894608i | \(0.352545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.3564 | + | 23.1340i | −0.725422 | + | 1.25647i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.69334 | − | 13.3253i | −0.416618 | − | 0.721603i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.03466 | + | 17.5095i | −0.325841 | + | 0.945425i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.29211 | − | 3.97006i | 0.123047 | − | 0.213124i | −0.797921 | − | 0.602762i | \(-0.794067\pi\) |
0.920968 | + | 0.389639i | \(0.127400\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3716 | 0.662235 | 0.331117 | − | 0.943590i | \(-0.392574\pi\) | ||||
0.331117 | + | 0.943590i | \(0.392574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.49465 | −0.453411 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.69334 | − | 16.7894i | 0.515925 | − | 0.893608i | −0.483904 | − | 0.875121i | \(-0.660782\pi\) |
0.999829 | − | 0.0184869i | \(-0.00588489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.5249 | + | 5.48792i | −0.662888 | + | 0.290451i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.90600 | + | 8.49745i | 0.258929 | + | 0.448478i | 0.965955 | − | 0.258709i | \(-0.0832971\pi\) |
−0.707026 | + | 0.707187i | \(0.749964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9385 | + | 24.1421i | −0.733603 | + | 1.27064i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.1482 | 1.10999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.35901 | + | 11.0141i | −0.331937 | + | 0.574933i | −0.982892 | − | 0.184184i | \(-0.941036\pi\) |
0.650954 | + | 0.759117i | \(0.274369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.5173 | − | 30.3409i | −0.911916 | − | 1.57948i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.9634 | − | 11.7429i | −0.828776 | − | 0.609662i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.20311 | − | 14.2082i | −0.424741 | − | 0.735673i | 0.571655 | − | 0.820494i | \(-0.306302\pi\) |
−0.996396 | + | 0.0848208i | \(0.972968\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0996 | 0.829170 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4707 | 0.743309 | 0.371655 | − | 0.928371i | \(-0.378791\pi\) | ||||
0.371655 | + | 0.928371i | \(0.378791\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.7873 | − | 42.9329i | 1.26989 | − | 2.19952i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.77478 | − | 3.07401i | −0.0906871 | − | 0.157075i | 0.817113 | − | 0.576477i | \(-0.195573\pi\) |
−0.907800 | + | 0.419402i | \(0.862240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.1091 | + | 20.9736i | 0.615541 | + | 1.06615i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.49023 | + | 7.77731i | −0.227664 | + | 0.394325i | −0.957115 | − | 0.289707i | \(-0.906442\pi\) |
0.729452 | + | 0.684032i | \(0.239775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.52489 | −0.228834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 46.0693 | 2.32389 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0498 | − | 24.3349i | −0.705139 | − | 1.22134i | −0.966642 | − | 0.256133i | \(-0.917551\pi\) |
0.261503 | − | 0.965203i | \(-0.415782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.16845 | + | 46.5260i | −0.258746 | + | 2.32921i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3467 | + | 23.1171i | 0.666501 | + | 1.15441i | 0.978876 | + | 0.204455i | \(0.0655421\pi\) |
−0.312375 | + | 0.949959i | \(0.601125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.2182 | + | 38.4831i | −1.10677 | + | 1.91698i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.77735 | 0.236804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0325 | + | 24.3049i | −0.693860 | + | 1.20180i | 0.276703 | + | 0.960955i | \(0.410758\pi\) |
−0.970563 | + | 0.240846i | \(0.922575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.16845 | − | 8.95202i | −0.254941 | − | 0.441571i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.0498 | + | 12.5421i | 0.838965 | + | 0.617157i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.67822 | + | 11.5670i | −0.327034 | + | 0.566439i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.8769 | −0.922198 | −0.461099 | − | 0.887349i | \(-0.652545\pi\) | ||||
−0.461099 | + | 0.887349i | \(0.652545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.1836 | −1.37358 | −0.686792 | − | 0.726854i | \(-0.740982\pi\) | ||||
−0.686792 | + | 0.726854i | \(0.740982\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.4429 | + | 38.8722i | −1.09121 | + | 1.89003i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.7280 | − | 6.89140i | 0.761132 | − | 0.333498i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.5098 | + | 18.2035i | 0.507416 | + | 0.878871i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.41577 | + | 2.45219i | −0.0681955 | + | 0.118118i | −0.898107 | − | 0.439777i | \(-0.855057\pi\) |
0.829912 | + | 0.557895i | \(0.188391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.33690 | 0.112304 | 0.0561522 | − | 0.998422i | \(-0.482117\pi\) | ||||
0.0561522 | + | 0.998422i | \(0.482117\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.74511 | + | 13.4149i | −0.370499 | + | 0.641723i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.03466 | + | 5.25619i | 0.144837 | + | 0.250864i | 0.929312 | − | 0.369296i | \(-0.120401\pi\) |
−0.784475 | + | 0.620160i | \(0.787068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.66624 | + | 24.5798i | 0.365059 | + | 1.17047i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.80188 | + | 10.0492i | 0.275656 | + | 0.477450i | 0.970300 | − | 0.241903i | \(-0.0777717\pi\) |
−0.694645 | + | 0.719353i | \(0.744438\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.05933 | −0.0974031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.13821 | 0.195294 | 0.0976470 | − | 0.995221i | \(-0.468868\pi\) | ||||
0.0976470 | + | 0.995221i | \(0.468868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.99244 | + | 13.8433i | −0.376349 | + | 0.651856i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.3520 | − | 36.9828i | −1.00321 | − | 1.73760i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.32178 | − | 10.9496i | −0.295720 | − | 0.512203i | 0.679432 | − | 0.733739i | \(-0.262226\pi\) |
−0.975152 | + | 0.221536i | \(0.928893\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.75268 | + | 3.03572i | −0.0818079 | + | 0.141695i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.7129 | 0.964695 | 0.482348 | − | 0.875980i | \(-0.339784\pi\) | ||||
0.482348 | + | 0.875980i | \(0.339784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.3811 | 0.761295 | 0.380647 | − | 0.924720i | \(-0.375701\pi\) | ||||
0.380647 | + | 0.924720i | \(0.375701\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.861215 | − | 1.49167i | −0.0398523 | − | 0.0690262i | 0.845411 | − | 0.534116i | \(-0.179355\pi\) |
−0.885264 | + | 0.465090i | \(0.846022\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.2602 | + | 9.01884i | 0.566125 | + | 0.416452i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5993 | − | 18.3586i | −0.488392 | − | 0.845920i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.52489 | − | 9.56940i | 0.254035 | − | 0.440001i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.5507 | −1.26146 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.890881 | − | 1.54305i | 0.0407054 | − | 0.0705038i | −0.844955 | − | 0.534838i | \(-0.820373\pi\) |
0.885660 | + | 0.464334i | \(0.153706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.89844 | − | 11.9485i | −0.314542 | − | 0.544803i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.70789 | + | 15.3743i | −0.0777116 | + | 0.699553i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.50977 | + | 9.54320i | −0.249672 | + | 0.432444i | −0.963435 | − | 0.267943i | \(-0.913656\pi\) |
0.713763 | + | 0.700387i | \(0.246989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.54443 | 0.431614 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9311 | −0.944608 | −0.472304 | − | 0.881436i | \(-0.656578\pi\) | ||||
−0.472304 | + | 0.881436i | \(0.656578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.32178 | − | 5.75349i | 0.149605 | − | 0.259124i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.75268 | + | 6.49983i | 0.167993 | + | 0.290972i | 0.937714 | − | 0.347408i | \(-0.112938\pi\) |
−0.769721 | + | 0.638380i | \(0.779605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.339111 | − | 0.587357i | 0.0151503 | − | 0.0262412i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5842 | −0.917805 | −0.458903 | − | 0.888487i | \(-0.651757\pi\) | ||||
−0.458903 | + | 0.888487i | \(0.651757\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.5546 | − | 23.4772i | 0.601979 | − | 1.04266i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.82934 | − | 11.8288i | −0.302705 | − | 0.524301i | 0.674043 | − | 0.738693i | \(-0.264556\pi\) |
−0.976748 | + | 0.214392i | \(0.931223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9211 | + | 18.3324i | 1.10245 | + | 0.810978i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.00000 | + | 10.3923i | 0.264906 | + | 0.458831i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.4795 | 0.900688 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.7040 | −2.13787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0820 | − | 36.5151i | 0.923620 | − | 1.59976i | 0.129854 | − | 0.991533i | \(-0.458549\pi\) |
0.793766 | − | 0.608224i | \(-0.208118\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.3218 | − | 26.5381i | −0.669975 | − | 1.16043i | −0.977911 | − | 0.209023i | \(-0.932972\pi\) |
0.307936 | − | 0.951407i | \(-0.400362\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.16845 | + | 15.8802i | 0.399384 | + | 0.691753i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.94067 | − | 15.4857i | 0.388725 | − | 0.673291i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.4258 | 1.27697 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.1640 | 1.99959 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5249 | − | 26.8899i | −0.669949 | − | 1.16038i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.96335 | − | 8.63654i | 0.343006 | − | 0.372002i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.8445 | + | 29.1755i | 0.724200 | + | 1.25435i | 0.959302 | + | 0.282381i | \(0.0911241\pi\) |
−0.235102 | + | 0.971971i | \(0.575543\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.79747 | + | 13.5056i | −0.334621 | + | 0.579581i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.03979 | 0.129972 | 0.0649861 | − | 0.997886i | \(-0.479300\pi\) | ||||
0.0649861 | + | 0.997886i | \(0.479300\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.9363 | − | 20.6742i | 0.509427 | − | 0.882353i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3716 | − | 19.6961i | −0.484445 | − | 0.839083i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.7969 | + | 6.04526i | −0.586703 | + | 0.257070i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.08202 | − | 15.7305i | 0.384817 | − | 0.666523i | −0.606926 | − | 0.794758i | \(-0.707598\pi\) |
0.991744 | + | 0.128235i | \(0.0409311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.9116 | −1.34972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.67380 | 0.366208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4952 | + | 32.0347i | −0.779481 | + | 1.35010i | 0.152760 | + | 0.988263i | \(0.451184\pi\) |
−0.932241 | + | 0.361837i | \(0.882150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.8644 | − | 10.1989i | −0.582248 | − | 0.428312i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.3047 | − | 28.2405i | −0.683527 | − | 1.18390i | −0.973897 | − | 0.226990i | \(-0.927112\pi\) |
0.290370 | − | 0.956915i | \(-0.406222\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2182 | + | 35.0190i | −0.846107 | + | 1.46550i | 0.0385496 | + | 0.999257i | \(0.487726\pi\) |
−0.884656 | + | 0.466243i | \(0.845607\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.31736 | −0.305687 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0151 | + | 32.9352i | −0.791610 | + | 1.37111i | 0.133360 | + | 0.991068i | \(0.457423\pi\) |
−0.924970 | + | 0.380041i | \(0.875910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.7722 | − | 29.0503i | −0.697030 | − | 1.20729i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.67601 | − | 33.0912i | 0.152507 | − | 1.37285i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.28513 | + | 10.8862i | 0.260304 | + | 0.450859i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.0302 | −1.40458 | −0.702289 | − | 0.711892i | \(-0.747839\pi\) | ||||
−0.702289 | + | 0.711892i | \(0.747839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 62.7734 | 2.58653 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.26245 | − | 10.8469i | 0.257603 | − | 0.446181i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.8618 | − | 29.2055i | −0.692431 | − | 1.19933i | −0.971039 | − | 0.238921i | \(-0.923206\pi\) |
0.278608 | − | 0.960405i | \(-0.410127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.8813 | − | 34.4355i | −0.813689 | − | 1.40935i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.15333 | + | 5.46172i | −0.128841 | + | 0.223160i | −0.923228 | − | 0.384253i | \(-0.874459\pi\) |
0.794387 | + | 0.607413i | \(0.207793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2871 | −0.460411 | −0.230206 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230206 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.1596 | 0.861686 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.73057 | − | 13.3897i | −0.313774 | − | 0.543473i | 0.665402 | − | 0.746485i | \(-0.268260\pi\) |
−0.979176 | + | 0.203012i | \(0.934927\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.2949 | − | 13.4580i | −0.741347 | − | 0.545348i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.5722 | − | 51.2206i | −1.19637 | − | 2.07217i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0820 | + | 19.1946i | −0.447598 | + | 0.775263i | −0.998229 | − | 0.0594857i | \(-0.981054\pi\) |
0.550631 | + | 0.834749i | \(0.314387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.9805 | 0.603091 | 0.301545 | − | 0.953452i | \(-0.402498\pi\) | ||||
0.301545 | + | 0.953452i | \(0.402498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8196 | + | 20.4721i | −0.475069 | + | 0.822843i | −0.999592 | − | 0.0285529i | \(-0.990910\pi\) |
0.524524 | + | 0.851396i | \(0.324243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.98267 | + | 3.43408i | 0.0795617 | + | 0.137805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.1685 | − | 6.20806i | 0.567647 | − | 0.248721i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.8467 | − | 25.7152i | 0.592919 | − | 1.02697i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.69334 | −0.227008 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7818 | −0.548643 | −0.274322 | − | 0.961638i | \(-0.588453\pi\) | ||||
−0.274322 | + | 0.961638i | \(0.588453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.8662 | − | 20.5529i | 0.471640 | − | 0.816904i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.0996 | − | 7.44577i | −1.31145 | − | 0.295012i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9309 | + | 37.9854i | −0.866218 | + | 1.50033i | −0.000386062 | 1.00000i | \(0.500123\pi\) | |
−0.865832 | + | 0.500334i | \(0.833210\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.04979 | −0.278016 | −0.139008 | − | 0.990291i | \(-0.544391\pi\) | ||||
−0.139008 | + | 0.990291i | \(0.544391\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.2403 | + | 21.2009i | −0.481217 | + | 0.833493i | −0.999768 | − | 0.0215540i | \(-0.993139\pi\) |
0.518550 | + | 0.855047i | \(0.326472\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.71288 | − | 11.6271i | −0.263504 | − | 0.456402i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 57.4169 | − | 25.1579i | 2.25035 | − | 0.986014i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.408213 | + | 0.707046i | 0.0159746 | + | 0.0276688i | 0.873902 | − | 0.486102i | \(-0.161582\pi\) |
−0.857928 | + | 0.513771i | \(0.828248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 43.0107 | 1.67801 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.2871 | 0.829228 | 0.414614 | − | 0.909997i | \(-0.363917\pi\) | ||||
0.414614 | + | 0.909997i | \(0.363917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.9731 | + | 22.4701i | −0.504596 | + | 0.873986i | 0.495390 | + | 0.868671i | \(0.335025\pi\) |
−0.999986 | + | 0.00531513i | \(0.998308\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.5249 | − | 21.6938i | −0.486427 | − | 0.842515i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.75767 | − | 6.50848i | −0.145498 | − | 0.252009i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.7722 | − | 29.0503i | 0.648451 | − | 1.12315i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8920 | −0.420483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0693 | −0.850710 | −0.425355 | − | 0.905027i | \(-0.639851\pi\) | ||||
−0.425355 | + | 0.905027i | \(0.639851\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.74511 | + | 4.75468i | 0.105503 | + | 0.182737i | 0.913944 | − | 0.405841i | \(-0.133021\pi\) |
−0.808440 | + | 0.588578i | \(0.799688\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.584225 | − | 5.25915i | 0.0224205 | − | 0.201828i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.4656 | + | 49.3038i | 1.09080 | + | 1.88933i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.61389 | − | 16.6517i | 0.367865 | − | 0.637161i | −0.621366 | − | 0.783520i | \(-0.713422\pi\) |
0.989232 | + | 0.146359i | \(0.0467554\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.1294 | −0.424612 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.1513 | − | 31.4390i | 0.691511 | − | 1.19773i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.10912 | − | 12.3134i | −0.270444 | − | 0.468422i | 0.698532 | − | 0.715579i | \(-0.253837\pi\) |
−0.968975 | + | 0.247157i | \(0.920504\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.80317 | − | 16.2320i | 0.0684969 | − | 0.616604i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.52489 | − | 16.4976i | 0.360781 | − | 0.624891i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.5161 | 1.75940 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.1533 | 0.534564 | 0.267282 | − | 0.963618i | \(-0.413875\pi\) | ||||
0.267282 | + | 0.963618i | \(0.413875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.74511 | + | 16.8790i | −0.367544 | + | 0.636605i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.2630 | − | 26.6757i | −1.36381 | − | 1.00324i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.52268 | − | 14.7617i | −0.320076 | − | 0.554388i | 0.660427 | − | 0.750890i | \(-0.270375\pi\) |
−0.980503 | + | 0.196502i | \(0.937042\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.4707 | + | 18.1358i | −0.392682 | + | 0.680144i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7431 | 0.776836 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.0347 | − | 24.3088i | 0.524134 | − | 0.907827i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.75268 | + | 9.96393i | 0.214539 | + | 0.371592i | 0.953130 | − | 0.302562i | \(-0.0978419\pi\) |
−0.738591 | + | 0.674154i | \(0.764509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2278 | − | 7.54854i | 0.641596 | − | 0.281122i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.262447 | + | 0.454571i | 0.00976049 | + | 0.0169057i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4114 | −0.608664 | −0.304332 | − | 0.952566i | \(-0.598433\pi\) | ||||
−0.304332 | + | 0.952566i | \(0.598433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.5161 | −1.38948 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.58423 | + | 11.4042i | −0.243526 | + | 0.421800i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.55712 | − | 7.89317i | −0.168321 | − | 0.291541i | 0.769509 | − | 0.638637i | \(-0.220501\pi\) |
−0.937830 | + | 0.347096i | \(0.887168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.82713 | − | 8.36084i | −0.177810 | − | 0.307975i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.4978 | − | 30.3071i | 0.643667 | − | 1.11486i | −0.340941 | − | 0.940085i | \(-0.610746\pi\) |
0.984608 | − | 0.174779i | \(-0.0559210\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −85.7538 | −3.15025 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.5305 | 1.59698 | 0.798489 | − | 0.602009i | \(-0.205633\pi\) | ||||
0.798489 | + | 0.602009i | \(0.205633\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.1438 | − | 40.0862i | −0.846787 | − | 1.46668i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.24732 | + | 1.86101i | −0.155194 | + | 0.0679999i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.15333 | − | 5.46172i | −0.115067 | − | 0.199301i | 0.802740 | − | 0.596329i | \(-0.203375\pi\) |
−0.917806 | + | 0.397028i | \(0.870041\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.50535 | − | 11.2676i | 0.237068 | − | 0.410614i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.3369 | −0.884540 | −0.442270 | − | 0.896882i | \(-0.645827\pi\) | ||||
−0.442270 | + | 0.896882i | \(0.645827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.90600 | − | 8.49745i | 0.178077 | − | 0.308438i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1016 | + | 24.4246i | 0.511181 | + | 0.885392i | 0.999916 | + | 0.0129592i | \(0.00412517\pi\) |
−0.488735 | + | 0.872432i | \(0.662541\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.6441 | + | 30.6342i | 1.50762 | + | 1.10903i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.3867 | + | 33.5787i | −0.700013 | + | 1.21246i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.8965 | −1.51082 | −0.755412 | − | 0.655250i | \(-0.772563\pi\) | ||||
−0.755412 | + | 0.655250i | \(0.772563\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.4365 | 2.17657 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.9287 | − | 34.5175i | 0.716785 | − | 1.24151i | −0.245482 | − | 0.969401i | \(-0.578946\pi\) |
0.962267 | − | 0.272107i | \(-0.0877205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.14891 | + | 19.3443i | −0.0770917 | + | 0.693974i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.6069 | − | 56.4768i | −1.16826 | − | 2.02349i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.82200 | −0.208061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.6637 | − | 30.5944i | 0.629642 | − | 1.09057i | −0.357981 | − | 0.933729i | \(-0.616535\pi\) |
0.987623 | − | 0.156843i | \(-0.0501318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35.0280 | − | 60.6703i | −1.24703 | − | 2.15992i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.01954 | + | 27.1817i | −0.107363 | + | 0.966469i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7280 | + | 27.2417i | 0.558518 | + | 0.967381i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.6933 | −1.05179 | −0.525896 | − | 0.850549i | \(-0.676270\pi\) | ||||
−0.525896 | + | 0.850549i | \(0.676270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.4062 | −0.863430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.7527 | − | 18.6242i | 0.379927 | − | 0.658053i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.81201 | − | 16.9949i | −0.346258 | − | 0.599737i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.38611 | + | 14.5252i | 0.295205 | + | 0.511310i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.82178 | − | 17.0118i | 0.345315 | − | 0.598104i | −0.640096 | − | 0.768295i | \(-0.721105\pi\) |
0.985411 | + | 0.170191i | \(0.0544386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.252452 | 0.00886479 | 0.00443239 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443239 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 60.4365 | 2.11960 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.5400 | + | 39.0405i | 0.788575 | + | 1.36585i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −43.2011 | + | 18.9290i | −1.50957 | + | 0.661434i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3867 | − | 38.7749i | −0.781301 | − | 1.35325i | −0.931184 | − | 0.364549i | \(-0.881223\pi\) |
0.149883 | − | 0.988704i | \(-0.452110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.64856 | − | 2.85538i | 0.0574650 | − | 0.0995323i | −0.835862 | − | 0.548940i | \(-0.815032\pi\) |
0.893327 | + | 0.449408i | \(0.148365\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.41577 | −0.327419 | −0.163709 | − | 0.986509i | \(-0.552346\pi\) | ||||
−0.163709 | + | 0.986509i | \(0.552346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.35644 | − | 4.08148i | 0.0818426 | − | 0.141756i | −0.822199 | − | 0.569200i | \(-0.807253\pi\) |
0.904041 | + | 0.427445i | \(0.140586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.73314 | − | 8.19803i | −0.164191 | − | 0.284387i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.49023 | + | 10.2925i | −0.328817 | + | 0.356614i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.03466 | − | 13.9164i | 0.277719 | − | 0.481023i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1880 | 0.766015 | 0.383007 | − | 0.923745i | \(-0.374888\pi\) | ||||
0.383007 | + | 0.923745i | \(0.374888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9658 | −0.619510 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.9558 | − | 31.1003i | 0.618430 | − | 1.07115i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.8315 | − | 8.68941i | 0.681420 | − | 0.298572i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.2776 | + | 45.5141i | 0.901844 | + | 1.56204i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.22022 | + | 5.57759i | −0.110388 | + | 0.191197i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.9267 | −1.36706 | −0.683532 | − | 0.729920i | \(-0.739557\pi\) | ||||
−0.683532 | + | 0.729920i | \(0.739557\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.812009 | + | 1.40644i | −0.0277377 | + | 0.0480431i | −0.879561 | − | 0.475786i | \(-0.842164\pi\) |
0.851823 | + | 0.523829i | \(0.175497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | − | 6.92820i | −0.136478 | − | 0.236387i | 0.789683 | − | 0.613515i | \(-0.210245\pi\) |
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −52.4589 | − | 38.5897i | −1.78780 | − | 1.31513i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.11168 | + | 15.7819i | 0.310165 | + | 0.537222i | 0.978398 | − | 0.206730i | \(-0.0662823\pi\) |
−0.668233 | + | 0.743952i | \(0.732949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.5949 | 1.14094 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.55469 | 0.324121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.9407 | + | 24.1459i | −0.472362 | + | 0.818154i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.67822 | − | 6.37087i | −0.124489 | − | 0.215621i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.4385 | − | 44.0607i | −0.858996 | − | 1.48782i | −0.872888 | − | 0.487921i | \(-0.837756\pi\) |
0.0138922 | − | 0.999903i | \(-0.495578\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.3520 | + | 42.1789i | −0.821373 | + | 1.42266i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.1187 | −0.644124 | −0.322062 | − | 0.946719i | \(-0.604376\pi\) | ||||
−0.322062 | + | 0.946719i | \(0.604376\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.3174 | −1.32313 | −0.661567 | − | 0.749886i | \(-0.730108\pi\) | ||||
−0.661567 | + | 0.749886i | \(0.730108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.5199 | + | 23.4171i | 0.453954 | + | 0.786271i | 0.998627 | − | 0.0523772i | \(-0.0166798\pi\) |
−0.544674 | + | 0.838648i | \(0.683346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.60377 | − | 50.4447i | 0.187944 | − | 1.69186i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.45871 | + | 9.45476i | 0.182874 | + | 0.316746i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.7754 | + | 72.3570i | −1.39796 | + | 2.42134i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.3369 | −0.946142 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.2278 | + | 26.3753i | −0.507875 | + | 0.879665i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.49023 | − | 12.9735i | −0.249536 | − | 0.432209i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.2630 | + | 26.6757i | 1.20676 | + | 0.887712i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4012 | − | 28.4078i | 0.544594 | − | 0.943264i | −0.454038 | − | 0.890982i | \(-0.650017\pi\) |
0.998632 | − | 0.0522823i | \(-0.0166496\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −62.5854 | −2.07583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.18799 | 0.205017 | 0.102509 | − | 0.994732i | \(-0.467313\pi\) | ||||
0.102509 | + | 0.994732i | \(0.467313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5596 | + | 18.2897i | −0.349470 | + | 0.605300i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.2011 | − | 18.9290i | 1.42663 | − | 0.625092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.8965 | + | 41.3899i | 0.788271 | + | 1.36533i | 0.927025 | + | 0.374999i | \(0.122357\pi\) |
−0.138754 | + | 0.990327i | \(0.544310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.09620 | − | 5.36278i | 0.102023 | − | 0.176710i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0745 | − | 22.6456i | 0.429421 | − | 0.743780i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.9309 | + | 34.5213i | 0.653912 | + | 1.13261i | 0.982165 | + | 0.188018i | \(0.0602065\pi\) |
−0.328254 | + | 0.944590i | \(0.606460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.2700 | + | 45.7530i | 0.467681 | + | 1.49949i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.31736 | − | 12.6740i | −0.239560 | − | 0.414929i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.406229 | −0.0132709 | −0.00663546 | − | 0.999978i | \(-0.502112\pi\) | ||||
−0.00663546 | + | 0.999978i | \(0.502112\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 76.8125 | 2.50668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.8271 | + | 29.1454i | −0.548549 | + | 0.950114i | 0.449825 | + | 0.893116i | \(0.351486\pi\) |
−0.998374 | + | 0.0569979i | \(0.981847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.7748 | − | 18.6625i | −0.350875 | − | 0.607734i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.92055 | + | 5.05854i | 0.0949050 | + | 0.164380i | 0.909569 | − | 0.415553i | \(-0.136412\pi\) |
−0.814664 | + | 0.579933i | \(0.803079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.3369 | + | 49.0810i | −0.919855 | + | 1.59324i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.2289 | 1.59636 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.0605 | −1.03854 | −0.519271 | − | 0.854610i | \(-0.673796\pi\) | ||||
−0.519271 | + | 0.854610i | \(0.673796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.20311 | + | 12.4762i | 0.232844 | + | 0.403297i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.52489 | − | 6.27106i | −0.275283 | − | 0.202503i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5302 | − | 45.9517i | −0.855814 | − | 1.48231i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.22337 | + | 5.58303i | −0.103872 | + | 0.179911i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0896 | −0.774669 | −0.387334 | − | 0.921939i | \(-0.626604\pi\) | ||||
−0.387334 | + | 0.921939i | \(0.626604\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.6933 | + | 30.6458i | −0.568392 | + | 0.984484i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.23534 | − | 15.9961i | −0.296376 | − | 0.513339i | 0.678928 | − | 0.734205i | \(-0.262445\pi\) |
−0.975304 | + | 0.220866i | \(0.929112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.50977 | + | 13.5908i | −0.0484010 | + | 0.435702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.1685 | − | 21.0764i | 0.389303 | − | 0.674293i | −0.603053 | − | 0.797701i | \(-0.706049\pi\) |
0.992356 | + | 0.123408i | \(0.0393825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.81201 | −0.313593 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 71.8725 | 2.29471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.33434 | − | 7.50729i | 0.138244 | − | 0.239445i | −0.788588 | − | 0.614922i | \(-0.789188\pi\) |
0.926832 | + | 0.375476i | \(0.122521\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.21195 | + | 82.9253i | −0.293220 | + | 2.63954i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.44823 | + | 12.9007i | 0.236840 | + | 0.410219i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7527 | − | 48.0690i | 0.881593 | − | 1.52696i | 0.0320231 | − | 0.999487i | \(-0.489805\pi\) |
0.849570 | − | 0.527476i | \(-0.176862\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.00000 | −0.190404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.5596 | + | 30.4140i | −0.556117 | + | 0.963222i | 0.441699 | + | 0.897163i | \(0.354376\pi\) |
−0.997816 | + | 0.0660591i | \(0.978957\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.49465 | + | 4.32086i | 0.0789271 | + | 0.136706i |
(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 | 1400.2.q.j.1201.3 | 6 | ||
5.2 | odd | 4 | 1400.2.bh.i.249.2 | 12 | |||
5.3 | odd | 4 | 1400.2.bh.i.249.5 | 12 | |||
5.4 | even | 2 | 280.2.q.e.81.1 | ✓ | 6 | ||
7.2 | even | 3 | inner | 1400.2.q.j.401.3 | 6 | ||
7.3 | odd | 6 | 9800.2.a.cf.1.3 | 3 | |||
7.4 | even | 3 | 9800.2.a.ce.1.1 | 3 | |||
15.14 | odd | 2 | 2520.2.bi.q.361.1 | 6 | |||
20.19 | odd | 2 | 560.2.q.l.81.3 | 6 | |||
35.2 | odd | 12 | 1400.2.bh.i.849.5 | 12 | |||
35.4 | even | 6 | 1960.2.a.w.1.3 | 3 | |||
35.9 | even | 6 | 280.2.q.e.121.1 | yes | 6 | ||
35.19 | odd | 6 | 1960.2.q.w.961.3 | 6 | |||
35.23 | odd | 12 | 1400.2.bh.i.849.2 | 12 | |||
35.24 | odd | 6 | 1960.2.a.v.1.1 | 3 | |||
35.34 | odd | 2 | 1960.2.q.w.361.3 | 6 | |||
105.44 | odd | 6 | 2520.2.bi.q.1801.1 | 6 | |||
140.39 | odd | 6 | 3920.2.a.cc.1.1 | 3 | |||
140.59 | even | 6 | 3920.2.a.cb.1.3 | 3 | |||
140.79 | odd | 6 | 560.2.q.l.401.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.e.81.1 | ✓ | 6 | 5.4 | even | 2 | ||
280.2.q.e.121.1 | yes | 6 | 35.9 | even | 6 | ||
560.2.q.l.81.3 | 6 | 20.19 | odd | 2 | |||
560.2.q.l.401.3 | 6 | 140.79 | odd | 6 | |||
1400.2.q.j.401.3 | 6 | 7.2 | even | 3 | inner | ||
1400.2.q.j.1201.3 | 6 | 1.1 | even | 1 | trivial | ||
1400.2.bh.i.249.2 | 12 | 5.2 | odd | 4 | |||
1400.2.bh.i.249.5 | 12 | 5.3 | odd | 4 | |||
1400.2.bh.i.849.2 | 12 | 35.23 | odd | 12 | |||
1400.2.bh.i.849.5 | 12 | 35.2 | odd | 12 | |||
1960.2.a.v.1.1 | 3 | 35.24 | odd | 6 | |||
1960.2.a.w.1.3 | 3 | 35.4 | even | 6 | |||
1960.2.q.w.361.3 | 6 | 35.34 | odd | 2 | |||
1960.2.q.w.961.3 | 6 | 35.19 | odd | 6 | |||
2520.2.bi.q.361.1 | 6 | 15.14 | odd | 2 | |||
2520.2.bi.q.1801.1 | 6 | 105.44 | odd | 6 | |||
3920.2.a.cb.1.3 | 3 | 140.59 | even | 6 | |||
3920.2.a.cc.1.1 | 3 | 140.39 | odd | 6 | |||
9800.2.a.ce.1.1 | 3 | 7.4 | even | 3 | |||
9800.2.a.cf.1.3 | 3 | 7.3 | odd | 6 |