Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (of order \(6\), degree \(2\), not 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.32905425960566784.37 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 849.5 | ||
Root | \(4.06501i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.849 |
Dual form | 1400.2.bh.i.249.5 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 2.23800 | − | 1.29211i | 1.29211 | − | 0.746002i | 0.313084 | − | 0.949725i | \(-0.398638\pi\) |
0.979028 | + | 0.203724i | \(0.0653044\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62958 | + | 0.292113i | −0.993886 | + | 0.110408i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.83911 | − | 3.18543i | 0.613037 | − | 1.06181i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.839111 | − | 1.45338i | −0.253001 | − | 0.438211i | 0.711349 | − | 0.702839i | \(-0.248084\pi\) |
−0.964351 | + | 0.264627i | \(0.914751\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.84667i | − | 1.34422i | −0.740449 | − | 0.672112i | \(-0.765387\pi\) | ||
0.740449 | − | 0.672112i | \(-0.234613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.73205 | + | 1.00000i | −0.420084 | + | 0.242536i | −0.695113 | − | 0.718900i | \(-0.744646\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42334 | − | 5.92939i | 0.785367 | − | 1.36030i | −0.143412 | − | 0.989663i | \(-0.545808\pi\) |
0.928779 | − | 0.370633i | \(-0.120859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.50756 | + | 4.05146i | −1.20185 | + | 0.884101i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.95934 | + | 1.13122i | 0.408550 | + | 0.235876i | 0.690166 | − | 0.723651i | \(-0.257537\pi\) |
−0.281617 | + | 0.959527i | \(0.590871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.75268i | − | 0.337303i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.32178 | −0.616839 | −0.308419 | − | 0.951250i | \(-0.599800\pi\) | ||||
−0.308419 | + | 0.951250i | \(0.599800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58423 | − | 7.94011i | −0.823351 | − | 1.42609i | −0.903173 | − | 0.429277i | \(-0.858768\pi\) |
0.0798217 | − | 0.996809i | \(-0.474565\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.75587 | − | 2.16845i | −0.653813 | − | 0.377479i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.46529 | − | 1.42334i | −0.405291 | − | 0.233995i | 0.283473 | − | 0.958980i | \(-0.408513\pi\) |
−0.688765 | + | 0.724985i | \(0.741847\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 6.58423i | 1.00408i | 0.864843 | + | 0.502042i | \(0.167418\pi\) | ||||
−0.864843 | + | 0.502042i | \(0.832582\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5682 | − | 6.10156i | −1.54153 | − | 0.890004i | −0.998742 | − | 0.0501344i | \(-0.984035\pi\) |
−0.542789 | − | 0.839869i | \(-0.682632\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | 6.48673 | − | 3.74511i | 0.891021 | − | 0.514431i | 0.0167445 | − | 0.999860i | \(-0.494670\pi\) |
0.874276 | + | 0.485429i | \(0.161336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 17.6933i | − | 2.34354i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | + | 6.92820i | 0.520756 | + | 0.901975i | 0.999709 | + | 0.0241347i | \(0.00768307\pi\) |
−0.478953 | + | 0.877841i | \(0.658984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24511 | − | 5.62070i | 0.415494 | − | 0.719657i | −0.579986 | − | 0.814627i | \(-0.696942\pi\) |
0.995480 | + | 0.0949692i | \(0.0302753\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.90558 | + | 8.91357i | −0.492056 | + | 1.12300i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.98196 | − | 2.87634i | 0.608644 | − | 0.351401i | −0.163791 | − | 0.986495i | \(-0.552372\pi\) |
0.772434 | + | 0.635094i | \(0.219039\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −10.1267 | + | 5.84667i | −1.18524 | + | 0.684301i | −0.957222 | − | 0.289355i | \(-0.906559\pi\) |
−0.228022 | + | 0.973656i | \(0.573226\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.63106 | + | 3.57666i | 0.299837 | + | 0.407599i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.84667 | − | 4.93058i | 0.320276 | − | 0.554734i | −0.660269 | − | 0.751029i | \(-0.729558\pi\) |
0.980545 | + | 0.196295i | \(0.0628911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.25268 | + | 5.63380i | 0.361408 | + | 0.625978i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.5842i | − | 1.38130i | −0.723190 | − | 0.690649i | \(-0.757325\pi\) | ||
0.723190 | − | 0.690649i | \(-0.242675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.43416 | + | 4.29211i | −0.797025 | + | 0.460163i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.92334 | + | 5.06337i | −0.309873 | + | 0.536716i | −0.978334 | − | 0.207031i | \(-0.933620\pi\) |
0.668461 | + | 0.743747i | \(0.266953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.41577 | + | 12.7447i | 0.148414 | + | 1.33601i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.5190 | − | 11.8467i | −2.12773 | − | 1.22844i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.17287 | −0.620397 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.50756 | + | 14.7355i | 0.846534 | + | 1.46624i | 0.884282 | + | 0.466953i | \(0.154648\pi\) |
−0.0377483 | + | 0.999287i | \(0.512019\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.15668 | − | 3.55456i | −0.606635 | − | 0.350241i | 0.165012 | − | 0.986292i | \(-0.447234\pi\) |
−0.771648 | + | 0.636050i | \(0.780567\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.51786 | − | 0.876338i | −0.146737 | − | 0.0847188i | 0.424834 | − | 0.905271i | \(-0.360333\pi\) |
−0.571571 | + | 0.820553i | \(0.693666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.77001 | + | 16.9222i | 0.935797 | + | 1.62085i | 0.773206 | + | 0.634154i | \(0.218652\pi\) |
0.162591 | + | 0.986694i | \(0.448015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.35644 | −0.698243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3369i | 0.972414i | 0.873844 | + | 0.486207i | \(0.161620\pi\) | ||||
−0.873844 | + | 0.486207i | \(0.838380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.4387 | − | 8.91357i | −1.42731 | − | 0.824059i | ||||
\(118\) | 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 | ||||||||
\(123\) | 21.3168 | − | 12.3072i | 1.92207 | − | 1.10971i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1836i | 1.70227i | 0.524949 | + | 0.851133i | \(0.324084\pi\) | ||||
−0.524949 | + | 0.851133i | \(0.675916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.50756 | + | 14.7355i | 0.749049 | + | 1.29739i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.91357 | − | 15.4387i | 0.778782 | − | 1.34889i | −0.153862 | − | 0.988092i | \(-0.549171\pi\) |
0.932644 | − | 0.360797i | \(-0.117495\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.26987 | + | 16.5918i | −0.630378 | + | 1.43869i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.46410 | + | 2.00000i | −0.295958 | + | 0.170872i | −0.640626 | − | 0.767853i | \(-0.721325\pi\) |
0.344668 | + | 0.938725i | \(0.387992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.16845 | 0.438382 | 0.219191 | − | 0.975682i | \(-0.429658\pi\) | ||||
0.219191 | + | 0.975682i | \(0.429658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.5356 | −2.65578 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.04407 | + | 4.06689i | −0.589054 | + | 0.340091i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.2991 | − | 12.2624i | 1.09689 | − | 1.01139i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.398443 | − | 0.690123i | 0.0326417 | − | 0.0565371i | −0.849243 | − | 0.528002i | \(-0.822941\pi\) |
0.881885 | + | 0.471465i | \(0.156275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.26245 | + | 14.3110i | 0.672388 | + | 1.16461i | 0.977225 | + | 0.212206i | \(0.0680648\pi\) |
−0.304837 | + | 0.952405i | \(0.598602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.35644i | 0.594733i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.10411 | + | 4.10156i | −0.566969 | + | 0.327340i | −0.755938 | − | 0.654643i | \(-0.772819\pi\) |
0.188969 | + | 0.981983i | \(0.439486\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −3.19853 | − | 1.84667i | −0.250528 | − | 0.144643i | 0.369478 | − | 0.929240i | \(-0.379537\pi\) |
−0.620006 | + | 0.784597i | \(0.712870\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.262447i | 0.0203087i | 0.999948 | + | 0.0101544i | \(0.00323229\pi\) | ||||
−0.999948 | + | 0.0101544i | \(0.996768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4902 | −0.806941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.5918 | − | 21.8096i | −0.962918 | − | 1.66782i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.3217 | + | 9.42334i | 1.24092 | + | 0.716443i | 0.969281 | − | 0.245957i | \(-0.0791023\pi\) |
0.271635 | + | 0.962400i | \(0.412436\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.9040 | + | 10.3369i | 1.34575 | + | 0.776969i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00756 | − | 10.4054i | −0.449026 | − | 0.777736i | 0.549297 | − | 0.835627i | \(-0.314896\pi\) |
−0.998323 | + | 0.0578912i | \(0.981562\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.03466 | −0.448553 | −0.224276 | − | 0.974526i | \(-0.572002\pi\) | ||||
−0.224276 | + | 0.974526i | \(0.572002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 16.7722i | − | 1.23984i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.90676 | + | 1.67822i | 0.212564 | + | 0.122724i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.511979 | + | 4.60880i | 0.0372410 | + | 0.335241i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41577 | + | 2.45219i | −0.102442 | + | 0.177434i | −0.912690 | − | 0.408652i | \(-0.865999\pi\) |
0.810248 | + | 0.586087i | \(0.199332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2414 | − | 6.49023i | 0.809174 | − | 0.467177i | −0.0374948 | − | 0.999297i | \(-0.511938\pi\) |
0.846669 | + | 0.532120i | \(0.178604\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.84667i | 0.345311i | 0.984982 | + | 0.172656i | \(0.0552347\pi\) | ||||
−0.984982 | + | 0.172656i | \(0.944765\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.69334 | − | 13.3253i | −0.545367 | − | 0.944603i | −0.998584 | − | 0.0532026i | \(-0.983057\pi\) |
0.453217 | − | 0.891400i | \(-0.350276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.43311 | − | 12.8745i | 0.524291 | − | 0.908098i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.73487 | − | 0.970334i | 0.613068 | − | 0.0681041i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.20687 | − | 4.16089i | 0.500912 | − | 0.289202i | ||||
\(208\) | 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 | ||||||||
\(217\) | 14.3740 | + | 19.5400i | 0.975769 | + | 1.32646i | ||||
\(218\) | 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 | ||||||||
\(223\) | − | 12.9805i | − | 0.869236i | −0.900615 | − | 0.434618i | \(-0.856883\pi\) | ||
0.900615 | − | 0.434618i | \(-0.143117\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0788 | − | 11.0151i | 1.26630 | − | 0.731099i | 0.292015 | − | 0.956414i | \(-0.405674\pi\) |
0.974286 | + | 0.225314i | \(0.0723409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.15333 | − | 3.72967i | 0.142296 | − | 0.246464i | −0.786065 | − | 0.618144i | \(-0.787885\pi\) |
0.928361 | + | 0.371680i | \(0.121218\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.5098 | + | 4.60497i | 0.691492 | + | 0.302985i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5885 | − | 9.00000i | −1.02123 | − | 0.589610i | −0.106773 | − | 0.994283i | \(-0.534052\pi\) |
−0.914461 | + | 0.404674i | \(0.867385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 14.7129i | − | 0.955705i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.8618 | −0.702591 | −0.351296 | − | 0.936265i | \(-0.614259\pi\) | ||||
−0.351296 | + | 0.936265i | \(0.614259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.101557 | − | 0.175902i | −0.00654187 | − | 0.0113309i | 0.862736 | − | 0.505655i | \(-0.168749\pi\) |
−0.869278 | + | 0.494324i | \(0.835416\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.1126 | + | 11.0347i | 1.22607 | + | 0.707874i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.7378 | − | 16.5918i | −1.82854 | − | 1.05571i | ||||
\(248\) | 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 | ||||||||
\(253\) | − | 3.79689i | − | 0.238708i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2535 | + | 11.6933i | 1.26338 | + | 0.729411i | 0.973726 | − | 0.227722i | \(-0.0731277\pi\) |
0.289650 | + | 0.957133i | \(0.406461\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 23.4772 | − | 13.5546i | 1.44767 | − | 0.835810i | 0.449323 | − | 0.893369i | \(-0.351665\pi\) |
0.998342 | + | 0.0575594i | \(0.0183318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.1091i | 0.924663i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.24511 | + | 5.62070i | 0.197858 | + | 0.342700i | 0.947834 | − | 0.318765i | \(-0.103268\pi\) |
−0.749976 | + | 0.661466i | \(0.769935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6933 | − | 20.2535i | 0.710320 | − | 1.23031i | −0.254417 | − | 0.967095i | \(-0.581884\pi\) |
0.964737 | − | 0.263216i | \(-0.0847831\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.6361 | + | 26.6933i | 1.18843 | + | 1.61555i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.17234 | + | 1.83155i | −0.190607 | + | 0.110047i | −0.592267 | − | 0.805742i | \(-0.701767\pi\) |
0.401660 | + | 0.915789i | \(0.368434\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −17.6123 | + | 10.1685i | −1.04694 | + | 0.604452i | −0.921791 | − | 0.387686i | \(-0.873274\pi\) |
−0.125150 | + | 0.992138i | \(0.539941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.0464 | + | 2.78234i | −1.47844 | + | 0.164236i | ||||
\(288\) | 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 | ||||||||
\(293\) | 18.8467i | 1.10103i | 0.834824 | + | 0.550517i | \(0.185569\pi\) | ||||
−0.834824 | + | 0.550517i | \(0.814431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.54731 | + | 1.47069i | −0.147810 | + | 0.0853380i | ||||
\(298\) | 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 | ||||||||
\(303\) | 38.0799 | + | 21.9855i | 2.18763 | + | 1.26303i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.39623i | 0.136760i | 0.997659 | + | 0.0683802i | \(0.0217831\pi\) | ||||
−0.997659 | + | 0.0683802i | \(0.978217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.3716 | −1.04512 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.83155 | + | 4.90439i | 0.160562 | + | 0.278102i | 0.935071 | − | 0.354462i | \(-0.115336\pi\) |
−0.774508 | + | 0.632564i | \(0.782003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.7414 | − | 14.8618i | −1.45499 | − | 0.840038i | −0.456231 | − | 0.889861i | \(-0.650801\pi\) |
−0.998758 | + | 0.0498231i | \(0.984134\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.4976 | + | 9.52489i | 0.926597 | + | 0.534971i | 0.885734 | − | 0.464193i | \(-0.153656\pi\) |
0.0408636 | + | 0.999165i | \(0.486989\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.78734 | + | 4.82781i | 0.156061 | + | 0.270306i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.52931 | −0.252801 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6933i | 0.761918i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43.7307 | + | 25.2479i | 2.41831 | + | 1.39621i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.5722 | + | 12.9574i | 1.63037 | + | 0.714365i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.16089 | + | 2.01072i | −0.0638083 | + | 0.110519i | −0.896165 | − | 0.443722i | \(-0.853658\pi\) |
0.832356 | + | 0.554241i | \(0.186991\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.06788 | + | 5.23534i | −0.496917 | + | 0.286895i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4062i | 0.893704i | 0.894608 | + | 0.446852i | \(0.147455\pi\) | ||||
−0.894608 | + | 0.446852i | \(0.852545\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | −17.5095 | + | 6.03466i | −0.945425 | + | 0.325841i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.97006 | + | 2.29211i | −0.213124 | + | 0.123047i | −0.602762 | − | 0.797921i | \(-0.705933\pi\) |
0.389639 | + | 0.920968i | \(0.372600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3716 | −0.662235 | −0.331117 | − | 0.943590i | \(-0.607426\pi\) | ||||
−0.331117 | + | 0.943590i | \(0.607426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.49465 | −0.453411 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.7894 | − | 9.69334i | 0.893608 | − | 0.515925i | 0.0184869 | − | 0.999829i | \(-0.494115\pi\) |
0.875121 | + | 0.483904i | \(0.160782\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.48792 | − | 12.5249i | 0.290451 | − | 0.662888i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.90600 | + | 8.49745i | −0.258929 | + | 0.448478i | −0.965955 | − | 0.258709i | \(-0.916703\pi\) |
0.707026 | + | 0.707187i | \(0.250036\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9385 | − | 24.1421i | −0.733603 | − | 1.27064i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 21.1482i | − | 1.10999i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0141 | − | 6.35901i | 0.574933 | − | 0.331937i | −0.184184 | − | 0.982892i | \(-0.558964\pi\) |
0.759117 | + | 0.650954i | \(0.225631\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 14.2082 | + | 8.20311i | 0.735673 | + | 0.424741i | 0.820494 | − | 0.571655i | \(-0.193698\pi\) |
−0.0848208 | + | 0.996396i | \(0.527032\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0996i | 0.829170i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.4707 | −0.743309 | −0.371655 | − | 0.928371i | \(-0.621209\pi\) | ||||
−0.371655 | + | 0.928371i | \(0.621209\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.7873 | + | 42.9329i | 1.26989 | + | 2.19952i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.07401 | + | 1.77478i | 0.157075 | + | 0.0906871i | 0.576477 | − | 0.817113i | \(-0.304427\pi\) |
−0.419402 | + | 0.907800i | \(0.637760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.9736 | + | 12.1091i | 1.06615 | + | 0.615541i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.49023 | + | 7.77731i | 0.227664 | + | 0.394325i | 0.957115 | − | 0.289707i | \(-0.0935580\pi\) |
−0.729452 | + | 0.684032i | \(0.760225\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.52489 | −0.228834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 46.0693i | − | 2.32389i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.3349 | − | 14.0498i | −1.22134 | − | 0.705139i | −0.256133 | − | 0.966642i | \(-0.582449\pi\) |
−0.965203 | + | 0.261503i | \(0.915782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.16845 | + | 46.5260i | 0.258746 | + | 2.32921i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3467 | − | 23.1171i | 0.666501 | − | 1.15441i | −0.312375 | − | 0.949959i | \(-0.601125\pi\) |
0.978876 | − | 0.204455i | \(-0.0655421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.4831 | + | 22.2182i | −1.91698 | + | 1.10677i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.77735i | 0.236804i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0325 | + | 24.3049i | 0.693860 | + | 1.20180i | 0.970563 | + | 0.240846i | \(0.0774248\pi\) |
−0.276703 | + | 0.960955i | \(0.589242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.16845 | + | 8.95202i | −0.254941 | + | 0.441571i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.5421 | − | 17.0498i | −0.617157 | − | 0.838965i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.5670 | − | 6.67822i | 0.566439 | − | 0.327034i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8769 | 0.922198 | 0.461099 | − | 0.887349i | \(-0.347455\pi\) | ||||
0.461099 | + | 0.887349i | \(0.347455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.1836 | −1.37358 | −0.686792 | − | 0.726854i | \(-0.740982\pi\) | ||||
−0.686792 | + | 0.726854i | \(0.740982\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −38.8722 | + | 22.4429i | −1.89003 | + | 1.09121i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.89140 | + | 15.7280i | −0.333498 | + | 0.761132i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.5098 | + | 18.2035i | −0.507416 | + | 0.878871i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.41577 | − | 2.45219i | −0.0681955 | − | 0.118118i | 0.829912 | − | 0.557895i | \(-0.188391\pi\) |
−0.898107 | + | 0.439777i | \(0.855057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.33690i | − | 0.112304i | −0.998422 | − | 0.0561522i | \(-0.982117\pi\) | ||
0.998422 | − | 0.0561522i | \(-0.0178832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.4149 | − | 7.74511i | 0.641723 | − | 0.370499i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.03466 | + | 5.25619i | −0.144837 | + | 0.250864i | −0.929312 | − | 0.369296i | \(-0.879599\pi\) |
0.784475 | + | 0.620160i | \(0.212932\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.66624 | − | 24.5798i | 0.365059 | − | 1.17047i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0492 | − | 5.80188i | −0.477450 | − | 0.275656i | 0.241903 | − | 0.970300i | \(-0.422228\pi\) |
−0.719353 | + | 0.694645i | \(0.755562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.05933i | − | 0.0974031i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.13821 | −0.195294 | −0.0976470 | − | 0.995221i | \(-0.531132\pi\) | ||||
−0.0976470 | + | 0.995221i | \(0.531132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.99244 | − | 13.8433i | −0.376349 | − | 0.651856i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 36.9828 | + | 21.3520i | 1.73760 | + | 1.00321i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.9496 | − | 6.32178i | −0.512203 | − | 0.295720i | 0.221536 | − | 0.975152i | \(-0.428893\pi\) |
−0.733739 | + | 0.679432i | \(0.762226\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | − | 16.3811i | − | 0.761295i | −0.924720 | − | 0.380647i | \(-0.875701\pi\) | ||
0.924720 | − | 0.380647i | \(-0.124299\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.49167 | − | 0.861215i | −0.0690262 | − | 0.0398523i | 0.465090 | − | 0.885264i | \(-0.346022\pi\) |
−0.534116 | + | 0.845411i | \(0.679355\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | 9.56940 | − | 5.52489i | 0.440001 | − | 0.254035i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 27.5507i | − | 1.26146i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.890881 | − | 1.54305i | −0.0407054 | − | 0.0705038i | 0.844955 | − | 0.534838i | \(-0.179627\pi\) |
−0.885660 | + | 0.464334i | \(0.846294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.89844 | + | 11.9485i | −0.314542 | + | 0.544803i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.3743 | + | 1.70789i | −0.699553 | + | 0.0777116i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.54320 | − | 5.50977i | 0.432444 | − | 0.249672i | −0.267943 | − | 0.963435i | \(-0.586344\pi\) |
0.700387 | + | 0.713763i | \(0.253011\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 5.75349 | − | 3.32178i | 0.259124 | − | 0.149605i | ||||
\(494\) | 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 | \(-0.887062\pi\) |
0.769721 | + | 0.638380i | \(0.220395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.339111 | + | 0.587357i | 0.0151503 | + | 0.0262412i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.5842i | 0.917805i | 0.888487 | + | 0.458903i | \(0.151757\pi\) | ||||
−0.888487 | + | 0.458903i | \(0.848243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.4772 | + | 13.5546i | −1.04266 | + | 0.601979i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.82934 | − | 11.8288i | 0.302705 | − | 0.524301i | −0.674043 | − | 0.738693i | \(-0.735444\pi\) |
0.976748 | + | 0.214392i | \(0.0687769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9211 | − | 18.3324i | 1.10245 | − | 0.810978i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.3923 | − | 6.00000i | −0.458831 | − | 0.264906i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.4795i | 0.900688i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.7040 | 2.13787 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0820 | + | 36.5151i | 0.923620 | + | 1.59976i | 0.793766 | + | 0.608224i | \(0.208118\pi\) |
0.129854 | + | 0.991533i | \(0.458549\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.5381 | + | 15.3218i | 1.16043 | + | 0.669975i | 0.951407 | − | 0.307936i | \(-0.0996383\pi\) |
0.209023 | + | 0.977911i | \(0.432972\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.8802 | + | 9.16845i | 0.691753 | + | 0.399384i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.94067 | − | 15.4857i | −0.388725 | − | 0.673291i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.4258 | 1.27697 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 46.1640i | − | 1.99959i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.8899 | − | 15.5249i | −1.16038 | − | 0.669949i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.96335 | − | 8.63654i | −0.343006 | − | 0.372002i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.8445 | − | 29.1755i | 0.724200 | − | 1.25435i | −0.235102 | − | 0.971971i | \(-0.575543\pi\) |
0.959302 | − | 0.282381i | \(-0.0911241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5056 | + | 7.79747i | −0.579581 | + | 0.334621i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.03979i | 0.129972i | 0.997886 | + | 0.0649861i | \(0.0207003\pi\) | ||||
−0.997886 | + | 0.0649861i | \(0.979300\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | −6.04526 | + | 13.7969i | −0.257070 | + | 0.586703i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.7305 | + | 9.08202i | −0.666523 | + | 0.384817i | −0.794758 | − | 0.606926i | \(-0.792402\pi\) |
0.128235 | + | 0.991744i | \(0.459069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.9116 | 1.34972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.67380 | 0.366208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.0347 | + | 18.4952i | −1.35010 | + | 0.779481i | −0.988263 | − | 0.152760i | \(-0.951184\pi\) |
−0.361837 | + | 0.932241i | \(0.617850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.1989 | − | 13.8644i | −0.428312 | − | 0.582248i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.3047 | − | 28.2405i | 0.683527 | − | 1.18390i | −0.290370 | − | 0.956915i | \(-0.593778\pi\) |
0.973897 | − | 0.226990i | \(-0.0728884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2182 | − | 35.0190i | −0.846107 | − | 1.46550i | −0.884656 | − | 0.466243i | \(-0.845607\pi\) |
0.0385496 | − | 0.999257i | \(-0.487726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.31736i | 0.305687i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.9352 | − | 19.0151i | 1.37111 | − | 0.791610i | 0.380041 | − | 0.924970i | \(-0.375910\pi\) |
0.991068 | + | 0.133360i | \(0.0425766\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −10.8862 | − | 6.28513i | −0.450859 | − | 0.260304i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 34.0302i | − | 1.40458i | −0.711892 | − | 0.702289i | \(-0.752161\pi\) | ||
0.711892 | − | 0.702289i | \(-0.247839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −62.7734 | −2.58653 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.26245 | + | 10.8469i | 0.257603 | + | 0.446181i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.2055 | + | 16.8618i | 1.19933 | + | 0.692431i | 0.960405 | − | 0.278608i | \(-0.0898731\pi\) |
0.238921 | + | 0.971039i | \(0.423206\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.4355 | − | 19.8813i | −1.40935 | − | 0.813689i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.15333 | + | 5.46172i | 0.128841 | + | 0.223160i | 0.923228 | − | 0.384253i | \(-0.125541\pi\) |
−0.794387 | + | 0.607413i | \(0.792207\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2871 | −0.460411 | −0.230206 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230206 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 21.1596i | − | 0.861686i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3897 | − | 7.73057i | −0.543473 | − | 0.313774i | 0.203012 | − | 0.979176i | \(-0.434927\pi\) |
−0.746485 | + | 0.665402i | \(0.768260\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | −19.1946 | + | 11.0820i | −0.775263 | + | 0.447598i | −0.834749 | − | 0.550631i | \(-0.814387\pi\) |
0.0594857 | + | 0.998229i | \(0.481054\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.9805i | 0.603091i | 0.953452 | + | 0.301545i | \(0.0975024\pi\) | ||||
−0.953452 | + | 0.301545i | \(0.902498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8196 | + | 20.4721i | 0.475069 | + | 0.822843i | 0.999592 | − | 0.0285529i | \(-0.00908990\pi\) |
−0.524524 | + | 0.851396i | \(0.675757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.98267 | − | 3.43408i | 0.0795617 | − | 0.137805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.20806 | − | 14.1685i | 0.248721 | − | 0.567647i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.7152 | + | 14.8467i | −1.02697 | + | 0.592919i | ||||
\(628\) | 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 | ||||||||
\(633\) | 20.5529 | − | 11.8662i | 0.816904 | − | 0.471640i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.44577 | − | 33.0996i | −0.295012 | − | 1.31145i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9309 | − | 37.9854i | −0.866218 | − | 1.50033i | −0.865832 | − | 0.500334i | \(-0.833210\pi\) |
−0.000386062 | − | 1.00000i | \(-0.500123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.04979i | 0.278016i | 0.990291 | + | 0.139008i | \(0.0443914\pi\) | ||||
−0.990291 | + | 0.139008i | \(0.955609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2009 | − | 12.2403i | 0.833493 | − | 0.481217i | −0.0215540 | − | 0.999768i | \(-0.506861\pi\) |
0.855047 | + | 0.518550i | \(0.173528\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | −0.707046 | − | 0.408213i | −0.0276688 | − | 0.0159746i | 0.486102 | − | 0.873902i | \(-0.338418\pi\) |
−0.513771 | + | 0.857928i | \(0.671752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 43.0107i | 1.67801i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.2871 | −0.829228 | −0.414614 | − | 0.909997i | \(-0.636083\pi\) | ||||
−0.414614 | + | 0.909997i | \(0.636083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.9731 | − | 22.4701i | −0.504596 | − | 0.873986i | −0.999986 | − | 0.00531513i | \(-0.998308\pi\) |
0.495390 | − | 0.868671i | \(-0.335025\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.6938 | + | 12.5249i | 0.842515 | + | 0.486427i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.50848 | − | 3.75767i | −0.252009 | − | 0.145498i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.7722 | − | 29.0503i | −0.648451 | − | 1.12315i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8920 | −0.420483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0693i | 0.850710i | 0.905027 | + | 0.425355i | \(0.139851\pi\) | ||||
−0.905027 | + | 0.425355i | \(0.860149\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.75468 | + | 2.74511i | 0.182737 | + | 0.105503i | 0.588578 | − | 0.808440i | \(-0.299688\pi\) |
−0.405841 | + | 0.913944i | \(0.633021\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 16.6517 | − | 9.61389i | 0.637161 | − | 0.367865i | −0.146359 | − | 0.989232i | \(-0.546755\pi\) |
0.783520 | + | 0.621366i | \(0.213422\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 11.1294i | − | 0.424612i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.1513 | − | 31.4390i | −0.691511 | − | 1.19773i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.10912 | + | 12.3134i | −0.270444 | + | 0.468422i | −0.968975 | − | 0.247157i | \(-0.920504\pi\) |
0.698532 | + | 0.715579i | \(0.253837\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.2320 | − | 1.80317i | 0.616604 | − | 0.0684969i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.4976 | + | 9.52489i | −0.624891 | + | 0.360781i | ||||
\(698\) | 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 | ||||||||
\(703\) | −16.8790 | + | 9.74511i | −0.636605 | + | 0.367544i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.6757 | − | 36.2630i | −1.00324 | − | 1.36381i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.52268 | − | 14.7617i | 0.320076 | − | 0.554388i | −0.660427 | − | 0.750890i | \(-0.729625\pi\) |
0.980503 | + | 0.196502i | \(0.0629582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.4707 | − | 18.1358i | −0.392682 | − | 0.680144i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20.7431i | − | 0.776836i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.3088 | + | 14.0347i | −0.907827 | + | 0.524134i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.75268 | + | 9.96393i | −0.214539 | + | 0.371592i | −0.953130 | − | 0.302562i | \(-0.902158\pi\) |
0.738591 | + | 0.674154i | \(0.235491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2278 | + | 7.54854i | 0.641596 | + | 0.281122i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.454571 | − | 0.262447i | −0.0169057 | − | 0.00976049i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.4114i | − | 0.608664i | −0.952566 | − | 0.304332i | \(-0.901567\pi\) | ||
0.952566 | − | 0.304332i | \(-0.0984331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 37.5161 | 1.38948 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.58423 | − | 11.4042i | −0.243526 | − | 0.421800i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.89317 | + | 4.55712i | 0.291541 | + | 0.168321i | 0.638637 | − | 0.769509i | \(-0.279499\pi\) |
−0.347096 | + | 0.937830i | \(0.612832\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.36084 | − | 4.82713i | −0.307975 | − | 0.177810i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.4978 | − | 30.3071i | −0.643667 | − | 1.11486i | −0.984608 | − | 0.174779i | \(-0.944079\pi\) |
0.340941 | − | 0.940085i | \(-0.389254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −85.7538 | −3.15025 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 43.5305i | − | 1.59698i | −0.602009 | − | 0.798489i | \(-0.705633\pi\) | ||
0.602009 | − | 0.798489i | \(-0.294367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40.0862 | − | 23.1438i | −1.46668 | − | 0.846787i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.24732 | + | 1.86101i | 0.155194 | + | 0.0679999i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.15333 | + | 5.46172i | −0.115067 | + | 0.199301i | −0.917806 | − | 0.397028i | \(-0.870041\pi\) |
0.802740 | + | 0.596329i | \(0.203375\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.2676 | − | 6.50535i | 0.410614 | − | 0.237068i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 24.3369i | − | 0.884540i | −0.896882 | − | 0.442270i | \(-0.854173\pi\) | ||
0.896882 | − | 0.442270i | \(-0.145827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.90600 | − | 8.49745i | −0.178077 | − | 0.308438i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1016 | − | 24.4246i | 0.511181 | − | 0.885392i | −0.488735 | − | 0.872432i | \(-0.662541\pi\) |
0.999916 | − | 0.0129592i | \(-0.00412517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.6342 | − | 41.6441i | −1.10903 | − | 1.50762i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.5787 | − | 19.3867i | 1.21246 | − | 0.700013i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.8965 | 1.51082 | 0.755412 | − | 0.655250i | \(-0.227437\pi\) | ||||
0.755412 | + | 0.655250i | \(0.227437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.4365 | 2.17657 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.5175 | − | 19.9287i | 1.24151 | − | 0.716785i | 0.272107 | − | 0.962267i | \(-0.412280\pi\) |
0.969401 | + | 0.245482i | \(0.0789462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.3443 | − | 2.14891i | 0.693974 | − | 0.0770917i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.6069 | − | 56.4768i | 1.16826 | − | 2.02349i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.82200i | 0.208061i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.5944 | + | 17.6637i | −1.09057 | + | 0.629642i | −0.933729 | − | 0.357981i | \(-0.883465\pi\) |
−0.156843 | + | 0.987623i | \(0.550132\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −27.2417 | − | 15.7280i | −0.967381 | − | 0.558518i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 29.6933i | − | 1.05179i | −0.850549 | − | 0.525896i | \(-0.823730\pi\) | ||
0.850549 | − | 0.525896i | \(-0.176270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.4062 | 0.863430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.7527 | + | 18.6242i | 0.379927 | + | 0.658053i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9949 | + | 9.81201i | 0.599737 | + | 0.346258i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.5252 | + | 8.38611i | 0.511310 | + | 0.295205i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.82178 | − | 17.0118i | −0.345315 | − | 0.598104i | 0.640096 | − | 0.768295i | \(-0.278895\pi\) |
−0.985411 | + | 0.170191i | \(0.945561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.252452 | 0.00886479 | 0.00443239 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443239 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 60.4365i | − | 2.11960i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.0405 | + | 22.5400i | 1.36585 | + | 0.788575i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 43.2011 | + | 18.9290i | 1.50957 | + | 0.661434i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3867 | + | 38.7749i | −0.781301 | + | 1.35325i | 0.149883 | + | 0.988704i | \(0.452110\pi\) |
−0.931184 | + | 0.364549i | \(0.881223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.85538 | − | 1.64856i | 0.0995323 | − | 0.0574650i | −0.449408 | − | 0.893327i | \(-0.648365\pi\) |
0.548940 | + | 0.835862i | \(0.315032\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.41577i | − | 0.327419i | −0.986509 | − | 0.163709i | \(-0.947654\pi\) | ||
0.986509 | − | 0.163709i | \(-0.0523459\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.35644 | − | 4.08148i | −0.0818426 | − | 0.141756i | 0.822199 | − | 0.569200i | \(-0.192747\pi\) |
−0.904041 | + | 0.427445i | \(0.859414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.73314 | + | 8.19803i | −0.164191 | + | 0.284387i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.2925 | + | 9.49023i | −0.356614 | + | 0.328817i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.9164 | + | 8.03466i | −0.481023 | + | 0.277719i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1880 | −0.766015 | −0.383007 | − | 0.923745i | \(-0.625112\pi\) | ||||
−0.383007 | + | 0.923745i | \(0.625112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9658 | −0.619510 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.1003 | − | 17.9558i | 1.07115 | − | 0.618430i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.68941 | + | 19.8315i | −0.298572 | + | 0.681420i | ||||
\(848\) | 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 | ||||||||
\(853\) | 39.9267i | 1.36706i | 0.729920 | + | 0.683532i | \(0.239557\pi\) | ||||
−0.729920 | + | 0.683532i | \(0.760443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.40644 | − | 0.812009i | 0.0480431 | − | 0.0277377i | −0.475786 | − | 0.879561i | \(-0.657836\pi\) |
0.523829 | + | 0.851823i | \(0.324503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | − | 6.92820i | 0.136478 | − | 0.236387i | −0.789683 | − | 0.613515i | \(-0.789755\pi\) |
0.926161 | + | 0.377128i | \(0.123088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −52.4589 | + | 38.5897i | −1.78780 | + | 1.31513i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.7819 | − | 9.11168i | −0.537222 | − | 0.310165i | 0.206730 | − | 0.978398i | \(-0.433718\pi\) |
−0.743952 | + | 0.668233i | \(0.767051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.5949i | 1.14094i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.55469 | −0.324121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.9407 | − | 24.1459i | −0.472362 | − | 0.818154i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.37087 | + | 3.67822i | 0.215621 | + | 0.124489i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.0607 | − | 25.4385i | −1.48782 | − | 0.858996i | −0.487921 | − | 0.872888i | \(-0.662244\pi\) |
−0.999903 | + | 0.0138922i | \(0.995578\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 39.3174i | 1.32313i | 0.749886 | + | 0.661567i | \(0.230108\pi\) | ||||
−0.749886 | + | 0.661567i | \(0.769892\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.4171 | + | 13.5199i | 0.786271 | + | 0.453954i | 0.838648 | − | 0.544674i | \(-0.183346\pi\) |
−0.0523772 | + | 0.998627i | \(0.516680\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −72.3570 | + | 41.7754i | −2.42134 | + | 1.39796i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 28.3369i | − | 0.946142i | ||||||
\(898\) | 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 | ||||||||
\(903\) | −26.6757 | − | 36.2630i | −0.887712 | − | 1.20676i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.4078 | + | 16.4012i | −0.943264 | + | 0.544594i | −0.890982 | − | 0.454038i | \(-0.849983\pi\) |
−0.0522823 | + | 0.998632i | \(0.516650\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −18.2897 | + | 10.5596i | −0.605300 | + | 0.349470i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.9290 | + | 43.2011i | −0.625092 | + | 1.42663i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.8965 | + | 41.3899i | −0.788271 | + | 1.36533i | 0.138754 | + | 0.990327i | \(0.455690\pi\) |
−0.927025 | + | 0.374999i | \(0.877643\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | −22.6456 | + | 13.0745i | −0.743780 | + | 0.429421i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.9309 | + | 34.5213i | −0.653912 | + | 1.13261i | 0.328254 | + | 0.944590i | \(0.393540\pi\) |
−0.982165 | + | 0.188018i | \(0.939794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.2700 | − | 45.7530i | 0.467681 | − | 1.49949i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.6740 | + | 7.31736i | 0.414929 | + | 0.239560i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.406229i | − | 0.0132709i | −0.999978 | − | 0.00663546i | \(-0.997888\pi\) | ||
0.999978 | − | 0.00663546i | \(-0.00211215\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −76.8125 | −2.50668 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.8271 | − | 29.1454i | −0.548549 | − | 0.950114i | −0.998374 | − | 0.0569979i | \(-0.981847\pi\) |
0.449825 | − | 0.893116i | \(-0.351486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.6625 | + | 10.7748i | 0.607734 | + | 0.350875i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.05854 | + | 2.92055i | 0.164380 | + | 0.0949050i | 0.579933 | − | 0.814664i | \(-0.303079\pi\) |
−0.415553 | + | 0.909569i | \(0.636412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.3369 | + | 49.0810i | 0.919855 | + | 1.59324i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.2289 | 1.59636 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0605i | 1.03854i | 0.854610 | + | 0.519271i | \(0.173796\pi\) | ||||
−0.854610 | + | 0.519271i | \(0.826204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.4762 | + | 7.20311i | 0.403297 | + | 0.232844i | ||||
\(958\) | 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 | ||||||||
\(963\) | −5.58303 | + | 3.22337i | −0.179911 | + | 0.103872i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.0896i | − | 0.774669i | −0.921939 | − | 0.387334i | \(-0.873396\pi\) | ||
0.921939 | − | 0.387334i | \(-0.126604\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.6933 | + | 30.6458i | 0.568392 | + | 0.984484i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.23534 | + | 15.9961i | −0.296376 | + | 0.513339i | −0.975304 | − | 0.220866i | \(-0.929112\pi\) |
0.678928 | + | 0.734205i | \(0.262445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.5908 | + | 1.50977i | −0.435702 | + | 0.0484010i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0764 | + | 12.1685i | −0.674293 | + | 0.389303i | −0.797701 | − | 0.603053i | \(-0.793951\pi\) |
0.123408 | + | 0.992356i | \(0.460618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.81201 | 0.313593 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 71.8725 | 2.29471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.50729 | − | 4.33434i | 0.239445 | − | 0.138244i | −0.375476 | − | 0.926832i | \(-0.622521\pi\) |
0.614922 | + | 0.788588i | \(0.289188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 82.9253 | − | 9.21195i | 2.63954 | − | 0.293220i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.44823 | + | 12.9007i | −0.236840 | + | 0.410219i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7527 | + | 48.0690i | 0.881593 | + | 1.52696i | 0.849570 | + | 0.527476i | \(0.176862\pi\) |
0.0320231 | + | 0.999487i | \(0.489805\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.00000i | 0.190404i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.4140 | − | 17.5596i | 0.963222 | − | 0.556117i | 0.0660591 | − | 0.997816i | \(-0.478957\pi\) |
0.897163 | + | 0.441699i | \(0.145624\pi\) | |||||||
\(998\) | 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.bh.i.849.5 | 12 | ||
5.2 | odd | 4 | 280.2.q.e.121.1 | yes | 6 | ||
5.3 | odd | 4 | 1400.2.q.j.401.3 | 6 | |||
5.4 | even | 2 | inner | 1400.2.bh.i.849.2 | 12 | ||
7.4 | even | 3 | inner | 1400.2.bh.i.249.2 | 12 | ||
15.2 | even | 4 | 2520.2.bi.q.1801.1 | 6 | |||
20.7 | even | 4 | 560.2.q.l.401.3 | 6 | |||
35.2 | odd | 12 | 1960.2.a.w.1.3 | 3 | |||
35.4 | even | 6 | inner | 1400.2.bh.i.249.5 | 12 | ||
35.12 | even | 12 | 1960.2.a.v.1.1 | 3 | |||
35.17 | even | 12 | 1960.2.q.w.361.3 | 6 | |||
35.18 | odd | 12 | 1400.2.q.j.1201.3 | 6 | |||
35.23 | odd | 12 | 9800.2.a.ce.1.1 | 3 | |||
35.27 | even | 4 | 1960.2.q.w.961.3 | 6 | |||
35.32 | odd | 12 | 280.2.q.e.81.1 | ✓ | 6 | ||
35.33 | even | 12 | 9800.2.a.cf.1.3 | 3 | |||
105.32 | even | 12 | 2520.2.bi.q.361.1 | 6 | |||
140.47 | odd | 12 | 3920.2.a.cb.1.3 | 3 | |||
140.67 | even | 12 | 560.2.q.l.81.3 | 6 | |||
140.107 | even | 12 | 3920.2.a.cc.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.e.81.1 | ✓ | 6 | 35.32 | odd | 12 | ||
280.2.q.e.121.1 | yes | 6 | 5.2 | odd | 4 | ||
560.2.q.l.81.3 | 6 | 140.67 | even | 12 | |||
560.2.q.l.401.3 | 6 | 20.7 | even | 4 | |||
1400.2.q.j.401.3 | 6 | 5.3 | odd | 4 | |||
1400.2.q.j.1201.3 | 6 | 35.18 | odd | 12 | |||
1400.2.bh.i.249.2 | 12 | 7.4 | even | 3 | inner | ||
1400.2.bh.i.249.5 | 12 | 35.4 | even | 6 | inner | ||
1400.2.bh.i.849.2 | 12 | 5.4 | even | 2 | inner | ||
1400.2.bh.i.849.5 | 12 | 1.1 | even | 1 | trivial | ||
1960.2.a.v.1.1 | 3 | 35.12 | even | 12 | |||
1960.2.a.w.1.3 | 3 | 35.2 | odd | 12 | |||
1960.2.q.w.361.3 | 6 | 35.17 | even | 12 | |||
1960.2.q.w.961.3 | 6 | 35.27 | even | 4 | |||
2520.2.bi.q.361.1 | 6 | 105.32 | even | 12 | |||
2520.2.bi.q.1801.1 | 6 | 15.2 | even | 4 | |||
3920.2.a.cb.1.3 | 3 | 140.47 | odd | 12 | |||
3920.2.a.cc.1.1 | 3 | 140.107 | even | 12 | |||
9800.2.a.ce.1.1 | 3 | 35.23 | odd | 12 | |||
9800.2.a.cf.1.3 | 3 | 35.33 | even | 12 |