Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.9 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.p.765.9 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.646444 | − | 1.25782i | −0.457105 | − | 0.889413i | ||||
\(3\) | −0.729365 | − | 2.72203i | −0.421099 | − | 1.57156i | −0.772297 | − | 0.635262i | \(-0.780892\pi\) |
0.351198 | − | 0.936301i | \(-0.385775\pi\) | |||||||
\(4\) | −1.16422 | + | 1.62622i | −0.582110 | + | 0.813110i | ||||
\(5\) | −0.691444 | + | 2.58050i | −0.309223 | + | 1.15404i | 0.620026 | + | 0.784581i | \(0.287122\pi\) |
−0.929249 | + | 0.369454i | \(0.879545\pi\) | |||||||
\(6\) | −2.95233 | + | 2.67705i | −1.20528 | + | 1.09290i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.79809 | + | 0.413120i | 0.989276 | + | 0.146060i | ||||
\(9\) | −4.27938 | + | 2.47070i | −1.42646 | + | 0.823568i | ||||
\(10\) | 3.69279 | − | 0.798439i | 1.16776 | − | 0.252489i | ||||
\(11\) | 5.36650 | − | 1.43795i | 1.61806 | − | 0.433558i | 0.667629 | − | 0.744494i | \(-0.267309\pi\) |
0.950431 | + | 0.310936i | \(0.100642\pi\) | |||||||
\(12\) | 5.27576 | + | 1.98293i | 1.52298 | + | 0.572423i | ||||
\(13\) | 3.30151 | − | 3.30151i | 0.915674 | − | 0.915674i | −0.0810367 | − | 0.996711i | \(-0.525823\pi\) |
0.996711 | + | 0.0810367i | \(0.0258231\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.52851 | 1.94385 | ||||||||
\(16\) | −1.28918 | − | 3.78656i | −0.322295 | − | 0.946639i | ||||
\(17\) | −2.63692 | + | 4.56728i | −0.639547 | + | 1.10773i | 0.345985 | + | 0.938240i | \(0.387545\pi\) |
−0.985532 | + | 0.169488i | \(0.945789\pi\) | |||||||
\(18\) | 5.87408 | + | 3.78552i | 1.38453 | + | 0.892256i | ||||
\(19\) | −2.19147 | − | 0.587201i | −0.502757 | − | 0.134713i | −0.00147756 | − | 0.999999i | \(-0.500470\pi\) |
−0.501279 | + | 0.865286i | \(0.667137\pi\) | |||||||
\(20\) | −3.39147 | − | 4.12871i | −0.758356 | − | 0.923208i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.27782 | − | 5.82053i | −1.12524 | − | 1.24094i | ||||
\(23\) | 3.73587 | − | 2.15691i | 0.778984 | − | 0.449746i | −0.0570864 | − | 0.998369i | \(-0.518181\pi\) |
0.836070 | + | 0.548623i | \(0.184848\pi\) | |||||||
\(24\) | −0.916309 | − | 7.91781i | −0.187041 | − | 1.61622i | ||||
\(25\) | −1.85077 | − | 1.06854i | −0.370155 | − | 0.213709i | ||||
\(26\) | −6.28695 | − | 2.01846i | −1.23297 | − | 0.395853i | ||||
\(27\) | 3.86857 | + | 3.86857i | 0.744507 | + | 0.744507i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.07893 | − | 1.07893i | 0.200353 | − | 0.200353i | −0.599798 | − | 0.800151i | \(-0.704753\pi\) |
0.800151 | + | 0.599798i | \(0.204753\pi\) | |||||||
\(30\) | −4.86676 | − | 9.46951i | −0.888545 | − | 1.72889i | ||||
\(31\) | 2.24040 | − | 3.88049i | 0.402388 | − | 0.696957i | −0.591625 | − | 0.806213i | \(-0.701514\pi\) |
0.994014 | + | 0.109256i | \(0.0348469\pi\) | |||||||
\(32\) | −3.92942 | + | 4.06935i | −0.694630 | + | 0.719367i | ||||
\(33\) | −7.82827 | − | 13.5590i | −1.36273 | − | 2.36031i | ||||
\(34\) | 7.44943 | + | 0.364280i | 1.27757 | + | 0.0624735i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.964240 | − | 9.83566i | 0.160707 | − | 1.63928i | ||||
\(37\) | −0.143285 | + | 0.534749i | −0.0235560 | + | 0.0879121i | −0.976703 | − | 0.214595i | \(-0.931157\pi\) |
0.953147 | + | 0.302507i | \(0.0978236\pi\) | |||||||
\(38\) | 0.678066 | + | 3.13606i | 0.109997 | + | 0.508736i | ||||
\(39\) | −11.3948 | − | 6.57880i | −1.82463 | − | 1.05345i | ||||
\(40\) | −3.00078 | + | 6.93484i | −0.474465 | + | 1.09649i | ||||
\(41\) | − | 7.35196i | − | 1.14818i | −0.818791 | − | 0.574091i | \(-0.805355\pi\) | ||
0.818791 | − | 0.574091i | \(-0.194645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.67142 | + | 1.67142i | 0.254889 | + | 0.254889i | 0.822972 | − | 0.568082i | \(-0.192314\pi\) |
−0.568082 | + | 0.822972i | \(0.692314\pi\) | |||||||
\(44\) | −3.90937 | + | 10.4012i | −0.589359 | + | 1.56804i | ||||
\(45\) | −3.41670 | − | 12.7513i | −0.509332 | − | 1.90085i | ||||
\(46\) | −5.12803 | − | 3.30474i | −0.756087 | − | 0.487257i | ||||
\(47\) | −0.245394 | − | 0.425035i | −0.0357944 | − | 0.0619978i | 0.847573 | − | 0.530678i | \(-0.178063\pi\) |
−0.883368 | + | 0.468681i | \(0.844729\pi\) | |||||||
\(48\) | −9.36683 | + | 6.27097i | −1.35199 | + | 0.905136i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.147615 | + | 3.01869i | −0.0208759 | + | 0.426908i | ||||
\(51\) | 14.3555 | + | 3.84655i | 2.01018 | + | 0.538625i | ||||
\(52\) | 1.52530 | + | 9.21267i | 0.211520 | + | 1.27757i | ||||
\(53\) | 7.90260 | − | 2.11750i | 1.08551 | − | 0.290860i | 0.328656 | − | 0.944450i | \(-0.393404\pi\) |
0.756849 | + | 0.653589i | \(0.226738\pi\) | |||||||
\(54\) | 2.36515 | − | 7.36678i | 0.321856 | − | 1.00249i | ||||
\(55\) | 14.8425i | 2.00137i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.39351i | 0.846842i | ||||||||
\(58\) | −2.05457 | − | 0.659634i | −0.269779 | − | 0.0866142i | ||||
\(59\) | 3.53183 | − | 0.946351i | 0.459805 | − | 0.123204i | −0.0214786 | − | 0.999769i | \(-0.506837\pi\) |
0.481284 | + | 0.876565i | \(0.340171\pi\) | |||||||
\(60\) | −8.76485 | + | 12.2430i | −1.13154 | + | 1.58057i | ||||
\(61\) | −7.30218 | − | 1.95661i | −0.934949 | − | 0.250519i | −0.240985 | − | 0.970529i | \(-0.577470\pi\) |
−0.693964 | + | 0.720010i | \(0.744137\pi\) | |||||||
\(62\) | −6.32925 | − | 0.309503i | −0.803816 | − | 0.0393069i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.65866 | + | 2.31190i | 0.957333 | + | 0.288987i | ||||
\(65\) | 6.23675 | + | 10.8024i | 0.773574 | + | 1.33987i | ||||
\(66\) | −11.9942 | + | 18.6117i | −1.47638 | + | 2.29094i | ||||
\(67\) | 3.33541 | + | 12.4479i | 0.407485 | + | 1.52076i | 0.799425 | + | 0.600766i | \(0.205137\pi\) |
−0.391940 | + | 0.919991i | \(0.628196\pi\) | |||||||
\(68\) | −4.35744 | − | 9.60553i | −0.528418 | − | 1.16484i | ||||
\(69\) | −8.59598 | − | 8.59598i | −1.03483 | − | 1.03483i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.2570i | − | 1.92935i | −0.263442 | − | 0.964675i | \(-0.584858\pi\) | ||
0.263442 | − | 0.964675i | \(-0.415142\pi\) | |||||||
\(72\) | −12.9948 | + | 5.14536i | −1.53145 | + | 0.606387i | ||||
\(73\) | −6.89278 | − | 3.97955i | −0.806739 | − | 0.465771i | 0.0390832 | − | 0.999236i | \(-0.487556\pi\) |
−0.845822 | + | 0.533465i | \(0.820890\pi\) | |||||||
\(74\) | 0.765243 | − | 0.165458i | 0.0889577 | − | 0.0192341i | ||||
\(75\) | −1.55872 | + | 5.81721i | −0.179985 | + | 0.671714i | ||||
\(76\) | 3.50627 | − | 2.88017i | 0.402196 | − | 0.330378i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.908834 | + | 18.5854i | −0.102905 | + | 2.10439i | ||||
\(79\) | −1.10561 | − | 1.91497i | −0.124390 | − | 0.215451i | 0.797104 | − | 0.603842i | \(-0.206364\pi\) |
−0.921494 | + | 0.388391i | \(0.873031\pi\) | |||||||
\(80\) | 10.6626 | − | 0.708545i | 1.19212 | − | 0.0792177i | ||||
\(81\) | 0.296643 | − | 0.513800i | 0.0329603 | − | 0.0570889i | ||||
\(82\) | −9.24743 | + | 4.75263i | −1.02121 | + | 0.524840i | ||||
\(83\) | −3.81693 | + | 3.81693i | −0.418963 | + | 0.418963i | −0.884846 | − | 0.465883i | \(-0.845737\pi\) |
0.465883 | + | 0.884846i | \(0.345737\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.96259 | − | 9.96259i | −1.08060 | − | 1.08060i | ||||
\(86\) | 1.02187 | − | 3.18283i | 0.110191 | − | 0.343213i | ||||
\(87\) | −3.72382 | − | 2.14995i | −0.399236 | − | 0.230499i | ||||
\(88\) | 15.6100 | − | 1.80651i | 1.66403 | − | 0.192575i | ||||
\(89\) | 9.66675 | − | 5.58110i | 1.02467 | − | 0.591596i | 0.109219 | − | 0.994018i | \(-0.465165\pi\) |
0.915454 | + | 0.402422i | \(0.131832\pi\) | |||||||
\(90\) | −13.8301 | + | 12.5406i | −1.45783 | + | 1.32190i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.841775 | + | 8.58647i | −0.0877611 | + | 0.895201i | ||||
\(93\) | −12.1969 | − | 3.26814i | −1.26476 | − | 0.338891i | ||||
\(94\) | −0.375984 | + | 0.583423i | −0.0387798 | + | 0.0601755i | ||||
\(95\) | 3.03055 | − | 5.24907i | 0.310928 | − | 0.538543i | ||||
\(96\) | 13.9429 | + | 7.72795i | 1.42304 | + | 0.788731i | ||||
\(97\) | 2.26374 | 0.229848 | 0.114924 | − | 0.993374i | \(-0.463338\pi\) | ||||
0.114924 | + | 0.993374i | \(0.463338\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19.4126 | + | 19.4126i | −1.95104 | + | 1.95104i | ||||
\(100\) | 3.89240 | − | 1.76574i | 0.389240 | − | 0.176574i | ||||
\(101\) | 12.2544 | − | 3.28356i | 1.21936 | − | 0.326727i | 0.408932 | − | 0.912565i | \(-0.365901\pi\) |
0.810428 | + | 0.585838i | \(0.199235\pi\) | |||||||
\(102\) | −4.44178 | − | 20.5433i | −0.439802 | − | 2.03409i | ||||
\(103\) | 3.23781 | − | 1.86935i | 0.319031 | − | 0.184193i | −0.331930 | − | 0.943304i | \(-0.607700\pi\) |
0.650961 | + | 0.759112i | \(0.274366\pi\) | |||||||
\(104\) | 10.6019 | − | 7.87402i | 1.03960 | − | 0.772111i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.77201 | − | 8.57120i | −0.754885 | − | 0.832509i | ||||
\(107\) | 2.13890 | − | 7.98249i | 0.206775 | − | 0.771697i | −0.782126 | − | 0.623121i | \(-0.785864\pi\) |
0.988901 | − | 0.148576i | \(-0.0474689\pi\) | |||||||
\(108\) | −10.7950 | + | 1.78728i | −1.03875 | + | 0.171981i | ||||
\(109\) | −3.54589 | − | 13.2335i | −0.339635 | − | 1.26753i | −0.898756 | − | 0.438449i | \(-0.855528\pi\) |
0.559121 | − | 0.829086i | \(-0.311139\pi\) | |||||||
\(110\) | 18.6692 | − | 9.59486i | 1.78004 | − | 0.914834i | ||||
\(111\) | 1.56011 | 0.148079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.11093 | −0.763012 | −0.381506 | − | 0.924366i | \(-0.624594\pi\) | ||||
−0.381506 | + | 0.924366i | \(0.624594\pi\) | |||||||
\(114\) | 8.04189 | − | 4.13305i | 0.753192 | − | 0.387095i | ||||
\(115\) | 2.98276 | + | 11.1318i | 0.278144 | + | 1.03805i | ||||
\(116\) | 0.498467 | + | 3.01070i | 0.0462815 | + | 0.279537i | ||||
\(117\) | −5.97138 | + | 22.2855i | −0.552054 | + | 2.06029i | ||||
\(118\) | −3.47347 | − | 3.83064i | −0.319759 | − | 0.352639i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 21.0655 | + | 3.11018i | 1.92301 | + | 0.283919i | ||||
\(121\) | 17.2053 | − | 9.93351i | 1.56412 | − | 0.903046i | ||||
\(122\) | 2.25938 | + | 10.4497i | 0.204555 | + | 0.946068i | ||||
\(123\) | −20.0122 | + | 5.36226i | −1.80444 | + | 0.483499i | ||||
\(124\) | 3.70221 | + | 8.16113i | 0.332468 | + | 0.732892i | ||||
\(125\) | −5.40821 | + | 5.40821i | −0.483725 | + | 0.483725i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.238096 | −0.0211276 | −0.0105638 | − | 0.999944i | \(-0.503363\pi\) | ||||
−0.0105638 | + | 0.999944i | \(0.503363\pi\) | |||||||
\(128\) | −2.04295 | − | 11.1277i | −0.180573 | − | 0.983562i | ||||
\(129\) | 3.33058 | − | 5.76873i | 0.293241 | − | 0.507909i | ||||
\(130\) | 9.55572 | − | 14.8278i | 0.838092 | − | 1.30049i | ||||
\(131\) | 0.624805 | + | 0.167416i | 0.0545895 | + | 0.0146272i | 0.286010 | − | 0.958227i | \(-0.407671\pi\) |
−0.231421 | + | 0.972854i | \(0.574337\pi\) | |||||||
\(132\) | 31.1637 | + | 3.05514i | 2.71245 | + | 0.265915i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.5011 | − | 12.2422i | 1.16632 | − | 1.05757i | ||||
\(135\) | −12.6578 | + | 7.30796i | −1.08941 | + | 0.628969i | ||||
\(136\) | −9.26518 | + | 11.6903i | −0.794483 | + | 1.00244i | ||||
\(137\) | 3.51539 | + | 2.02961i | 0.300340 | + | 0.173402i | 0.642596 | − | 0.766205i | \(-0.277857\pi\) |
−0.342255 | + | 0.939607i | \(0.611191\pi\) | |||||||
\(138\) | −5.25537 | + | 16.3690i | −0.447367 | + | 1.39342i | ||||
\(139\) | 6.00840 | + | 6.00840i | 0.509626 | + | 0.509626i | 0.914411 | − | 0.404786i | \(-0.132654\pi\) |
−0.404786 | + | 0.914411i | \(0.632654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.977976 | + | 0.977976i | −0.0823604 | + | 0.0823604i | ||||
\(142\) | −20.4484 | + | 10.5092i | −1.71599 | + | 0.881916i | ||||
\(143\) | 12.9702 | − | 22.4650i | 1.08462 | − | 1.87861i | ||||
\(144\) | 14.8724 | + | 13.0189i | 1.23936 | + | 1.08491i | ||||
\(145\) | 2.03817 | + | 3.53021i | 0.169261 | + | 0.293168i | ||||
\(146\) | −0.549758 | + | 11.2424i | −0.0454983 | + | 0.930430i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.702803 | − | 0.855579i | −0.0577700 | − | 0.0703281i | ||||
\(149\) | −0.773337 | + | 2.88613i | −0.0633542 | + | 0.236441i | −0.990341 | − | 0.138653i | \(-0.955723\pi\) |
0.926987 | + | 0.375094i | \(0.122390\pi\) | |||||||
\(150\) | 8.32463 | − | 1.79992i | 0.679703 | − | 0.146963i | ||||
\(151\) | −13.1296 | − | 7.58036i | −1.06847 | − | 0.616881i | −0.140706 | − | 0.990051i | \(-0.544937\pi\) |
−0.927763 | + | 0.373171i | \(0.878271\pi\) | |||||||
\(152\) | −5.88934 | − | 2.54838i | −0.477689 | − | 0.206701i | ||||
\(153\) | − | 26.0602i | − | 2.10684i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.46451 | + | 8.46451i | 0.679885 | + | 0.679885i | ||||
\(156\) | 23.9646 | − | 10.8713i | 1.91871 | − | 0.870400i | ||||
\(157\) | 2.72507 | + | 10.1701i | 0.217484 | + | 0.811661i | 0.985277 | + | 0.170964i | \(0.0546880\pi\) |
−0.767793 | + | 0.640697i | \(0.778645\pi\) | |||||||
\(158\) | −1.69397 | + | 2.62857i | −0.134765 | + | 0.209118i | ||||
\(159\) | −11.5278 | − | 19.9667i | −0.914211 | − | 1.58346i | ||||
\(160\) | −7.78401 | − | 12.9536i | −0.615380 | − | 1.02407i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.838030 | − | 0.0409800i | −0.0658419 | − | 0.00321969i | ||||
\(163\) | 6.46324 | + | 1.73182i | 0.506240 | + | 0.135647i | 0.502894 | − | 0.864348i | \(-0.332268\pi\) |
0.00334537 | + | 0.999994i | \(0.498935\pi\) | |||||||
\(164\) | 11.9559 | + | 8.55930i | 0.933599 | + | 0.668369i | ||||
\(165\) | 40.4018 | − | 10.8256i | 3.14527 | − | 0.842773i | ||||
\(166\) | 7.26844 | + | 2.33358i | 0.564141 | + | 0.181121i | ||||
\(167\) | − | 13.8640i | − | 1.07283i | −0.843955 | − | 0.536414i | \(-0.819779\pi\) | ||
0.843955 | − | 0.536414i | \(-0.180221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.79995i | − | 0.676919i | ||||||
\(170\) | −6.09089 | + | 18.9714i | −0.467150 | + | 1.45504i | ||||
\(171\) | 10.8289 | − | 2.90160i | 0.828108 | − | 0.221891i | ||||
\(172\) | −4.66400 | + | 0.772196i | −0.355627 | + | 0.0588794i | ||||
\(173\) | 23.2018 | + | 6.21690i | 1.76400 | + | 0.472662i | 0.987522 | − | 0.157483i | \(-0.0503380\pi\) |
0.776477 | + | 0.630145i | \(0.217005\pi\) | |||||||
\(174\) | −0.297007 | + | 6.07372i | −0.0225160 | + | 0.460448i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.3633 | − | 18.4668i | −0.931916 | − | 1.39199i | ||||
\(177\) | −5.15199 | − | 8.92350i | −0.387247 | − | 0.670732i | ||||
\(178\) | −13.2690 | − | 8.55116i | −0.994556 | − | 0.640937i | ||||
\(179\) | −4.96759 | − | 18.5393i | −0.371295 | − | 1.38569i | −0.858683 | − | 0.512506i | \(-0.828717\pi\) |
0.487389 | − | 0.873185i | \(-0.337950\pi\) | |||||||
\(180\) | 24.7142 | + | 9.28903i | 1.84209 | + | 0.692363i | ||||
\(181\) | 4.76859 | + | 4.76859i | 0.354446 | + | 0.354446i | 0.861761 | − | 0.507315i | \(-0.169362\pi\) |
−0.507315 | + | 0.861761i | \(0.669362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.3038i | 1.57482i | ||||||||
\(184\) | 11.3444 | − | 4.49187i | 0.836319 | − | 0.331145i | ||||
\(185\) | −1.28085 | − | 0.739497i | −0.0941697 | − | 0.0543689i | ||||
\(186\) | 3.77386 | + | 17.4541i | 0.276713 | + | 1.27980i | ||||
\(187\) | −7.58351 | + | 28.3021i | −0.554561 | + | 2.06965i | ||||
\(188\) | 0.976894 | + | 0.0957699i | 0.0712473 | + | 0.00698473i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.56146 | − | 0.418658i | −0.621113 | − | 0.0303726i | ||||
\(191\) | −1.71906 | − | 2.97750i | −0.124387 | − | 0.215444i | 0.797106 | − | 0.603839i | \(-0.206363\pi\) |
−0.921493 | + | 0.388395i | \(0.873030\pi\) | |||||||
\(192\) | 0.707080 | − | 22.5333i | 0.0510291 | − | 1.62620i | ||||
\(193\) | −11.0060 | + | 19.0629i | −0.792227 | + | 1.37218i | 0.132358 | + | 0.991202i | \(0.457745\pi\) |
−0.924585 | + | 0.380976i | \(0.875588\pi\) | |||||||
\(194\) | −1.46338 | − | 2.84737i | −0.105065 | − | 0.204430i | ||||
\(195\) | 24.8555 | − | 24.8555i | 1.77994 | − | 1.77994i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.02579 | − | 6.02579i | −0.429320 | − | 0.429320i | 0.459077 | − | 0.888397i | \(-0.348180\pi\) |
−0.888397 | + | 0.459077i | \(0.848180\pi\) | |||||||
\(198\) | 36.9666 | + | 11.8684i | 2.62710 | + | 0.843448i | ||||
\(199\) | −2.94240 | − | 1.69879i | −0.208581 | − | 0.120424i | 0.392071 | − | 0.919935i | \(-0.371759\pi\) |
−0.600652 | + | 0.799511i | \(0.705092\pi\) | |||||||
\(200\) | −4.73720 | − | 3.75448i | −0.334971 | − | 0.265482i | ||||
\(201\) | 31.4509 | − | 18.1582i | 2.21837 | − | 1.28078i | ||||
\(202\) | −12.0519 | − | 13.2912i | −0.847971 | − | 0.935167i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −22.9684 | + | 18.8670i | −1.60811 | + | 1.32096i | ||||
\(205\) | 18.9717 | + | 5.08346i | 1.32504 | + | 0.355044i | ||||
\(206\) | −4.44437 | − | 2.86415i | −0.309654 | − | 0.199555i | ||||
\(207\) | −10.6582 | + | 18.4605i | −0.740793 | + | 1.28309i | ||||
\(208\) | −16.7576 | − | 8.24511i | −1.16193 | − | 0.571696i | ||||
\(209\) | −12.6049 | −0.871897 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.23499 | + | 3.23499i | −0.222706 | + | 0.222706i | −0.809637 | − | 0.586931i | \(-0.800336\pi\) |
0.586931 | + | 0.809637i | \(0.300336\pi\) | |||||||
\(212\) | −5.75686 | + | 15.3166i | −0.395382 | + | 1.05195i | ||||
\(213\) | −44.2520 | + | 11.8573i | −3.03210 | + | 0.812448i | ||||
\(214\) | −11.4232 | + | 2.46988i | −0.780875 | + | 0.168838i | ||||
\(215\) | −5.46880 | + | 3.15742i | −0.372969 | + | 0.215334i | ||||
\(216\) | 9.22644 | + | 12.4228i | 0.627780 | + | 0.845265i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.3531 | + | 13.0148i | −0.972113 | + | 0.881472i | ||||
\(219\) | −5.80509 | + | 21.6649i | −0.392271 | + | 1.46398i | ||||
\(220\) | −24.1372 | − | 17.2800i | −1.62733 | − | 1.16502i | ||||
\(221\) | 6.37310 | + | 23.7847i | 0.428701 | + | 1.59993i | ||||
\(222\) | −1.00852 | − | 1.96233i | −0.0676876 | − | 0.131703i | ||||
\(223\) | −0.464368 | −0.0310964 | −0.0155482 | − | 0.999879i | \(-0.504949\pi\) | ||||
−0.0155482 | + | 0.999879i | \(0.504949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.5602 | 0.704015 | ||||||||
\(226\) | 5.24326 | + | 10.2021i | 0.348777 | + | 0.678633i | ||||
\(227\) | 5.02951 | + | 18.7704i | 0.333821 | + | 1.24584i | 0.905142 | + | 0.425109i | \(0.139764\pi\) |
−0.571322 | + | 0.820726i | \(0.693569\pi\) | |||||||
\(228\) | −10.3973 | − | 7.44346i | −0.688575 | − | 0.492955i | ||||
\(229\) | −0.288531 | + | 1.07681i | −0.0190667 | + | 0.0711578i | −0.974804 | − | 0.223065i | \(-0.928394\pi\) |
0.955737 | + | 0.294222i | \(0.0950606\pi\) | |||||||
\(230\) | 12.0736 | − | 10.9479i | 0.796111 | − | 0.721881i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.46469 | − | 2.57323i | 0.227468 | − | 0.168941i | ||||
\(233\) | −9.11534 | + | 5.26274i | −0.597166 | + | 0.344774i | −0.767926 | − | 0.640539i | \(-0.778711\pi\) |
0.170760 | + | 0.985313i | \(0.445378\pi\) | |||||||
\(234\) | 31.8913 | − | 6.89540i | 2.08480 | − | 0.450767i | ||||
\(235\) | 1.26648 | − | 0.339353i | 0.0826161 | − | 0.0221369i | ||||
\(236\) | −2.57285 | + | 6.84529i | −0.167479 | + | 0.445591i | ||||
\(237\) | −4.40620 | + | 4.40620i | −0.286213 | + | 0.286213i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0909 | 1.42894 | 0.714469 | − | 0.699667i | \(-0.246668\pi\) | ||||
0.714469 | + | 0.699667i | \(0.246668\pi\) | |||||||
\(240\) | −9.70562 | − | 28.5071i | −0.626495 | − | 1.84013i | ||||
\(241\) | −1.74230 | + | 3.01775i | −0.112231 | + | 0.194391i | −0.916670 | − | 0.399646i | \(-0.869133\pi\) |
0.804438 | + | 0.594036i | \(0.202466\pi\) | |||||||
\(242\) | −23.6168 | − | 15.2198i | −1.51815 | − | 0.978363i | ||||
\(243\) | 14.2388 | + | 3.81526i | 0.913417 | + | 0.244749i | ||||
\(244\) | 11.6832 | − | 9.59702i | 0.747942 | − | 0.614386i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.6815 | + | 21.7054i | 1.25485 | + | 1.38388i | ||||
\(247\) | −9.17380 | + | 5.29650i | −0.583715 | + | 0.337008i | ||||
\(248\) | 7.87197 | − | 9.93243i | 0.499870 | − | 0.630710i | ||||
\(249\) | 13.1737 | + | 7.60586i | 0.834851 | + | 0.482002i | ||||
\(250\) | 10.2987 | + | 3.30645i | 0.651344 | + | 0.209118i | ||||
\(251\) | 19.4610 | + | 19.4610i | 1.22837 | + | 1.22837i | 0.964582 | + | 0.263784i | \(0.0849707\pi\) |
0.263784 | + | 0.964582i | \(0.415029\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.9470 | − | 16.9470i | 1.06545 | − | 1.06545i | ||||
\(254\) | 0.153916 | + | 0.299482i | 0.00965753 | + | 0.0187912i | ||||
\(255\) | −19.8521 | + | 34.3848i | −1.24319 | + | 2.15326i | ||||
\(256\) | −12.6760 | + | 9.76312i | −0.792251 | + | 0.610195i | ||||
\(257\) | −10.9786 | − | 19.0155i | −0.684827 | − | 1.18615i | −0.973491 | − | 0.228724i | \(-0.926545\pi\) |
0.288664 | − | 0.957430i | \(-0.406789\pi\) | |||||||
\(258\) | −9.40906 | − | 0.460106i | −0.585783 | − | 0.0286450i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −24.8280 | − | 2.43401i | −1.53977 | − | 0.150951i | ||||
\(261\) | −1.95145 | + | 7.28290i | −0.120792 | + | 0.450800i | ||||
\(262\) | −0.193322 | − | 0.894118i | −0.0119435 | − | 0.0552388i | ||||
\(263\) | 13.6351 | + | 7.87225i | 0.840779 | + | 0.485424i | 0.857529 | − | 0.514436i | \(-0.171999\pi\) |
−0.0167499 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(264\) | −16.3028 | − | 41.1733i | −1.00337 | − | 2.53404i | ||||
\(265\) | 21.8568i | 1.34265i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.2425 | − | 22.2425i | −1.36122 | − | 1.36122i | ||||
\(268\) | −24.1262 | − | 9.06802i | −1.47374 | − | 0.553917i | ||||
\(269\) | −0.435915 | − | 1.62686i | −0.0265782 | − | 0.0991913i | 0.951363 | − | 0.308073i | \(-0.0996842\pi\) |
−0.977941 | + | 0.208882i | \(0.933018\pi\) | |||||||
\(270\) | 17.3746 | + | 11.1970i | 1.05739 | + | 0.681427i | ||||
\(271\) | 6.14352 | + | 10.6409i | 0.373192 | + | 0.646388i | 0.990055 | − | 0.140683i | \(-0.0449299\pi\) |
−0.616863 | + | 0.787071i | \(0.711597\pi\) | |||||||
\(272\) | 20.6937 | + | 4.09680i | 1.25474 | + | 0.248405i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.280383 | − | 5.73376i | 0.0169385 | − | 0.346389i | ||||
\(275\) | −11.4687 | − | 3.07302i | −0.691588 | − | 0.185310i | ||||
\(276\) | 23.9866 | − | 3.97134i | 1.44382 | − | 0.239046i | ||||
\(277\) | −29.8378 | + | 7.99501i | −1.79278 | + | 0.480374i | −0.992813 | − | 0.119673i | \(-0.961815\pi\) |
−0.799965 | + | 0.600046i | \(0.795149\pi\) | |||||||
\(278\) | 3.67339 | − | 11.4416i | 0.220315 | − | 0.686220i | ||||
\(279\) | 22.1415i | 1.32558i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.3934i | 1.27622i | 0.769944 | + | 0.638111i | \(0.220284\pi\) | ||||
−0.769944 | + | 0.638111i | \(0.779716\pi\) | |||||||
\(282\) | 1.86232 | + | 0.597911i | 0.110900 | + | 0.0356051i | ||||
\(283\) | −14.4807 | + | 3.88010i | −0.860790 | + | 0.230648i | −0.662101 | − | 0.749415i | \(-0.730335\pi\) |
−0.198689 | + | 0.980063i | \(0.563668\pi\) | |||||||
\(284\) | 26.4374 | + | 18.9267i | 1.56877 | + | 1.12309i | ||||
\(285\) | −16.4985 | − | 4.42075i | −0.977285 | − | 0.261863i | ||||
\(286\) | −36.6413 | − | 1.79177i | −2.16665 | − | 0.105950i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.76134 | − | 27.1228i | 0.398416 | − | 1.59822i | ||||
\(289\) | −5.40669 | − | 9.36467i | −0.318041 | − | 0.550863i | ||||
\(290\) | 3.12281 | − | 4.84574i | 0.183378 | − | 0.284551i | ||||
\(291\) | −1.65109 | − | 6.16196i | −0.0967887 | − | 0.361220i | ||||
\(292\) | 14.4963 | − | 6.57610i | 0.848334 | − | 0.384837i | ||||
\(293\) | 21.0093 | + | 21.0093i | 1.22738 | + | 1.22738i | 0.964952 | + | 0.262428i | \(0.0845231\pi\) |
0.262428 | + | 0.964952i | \(0.415477\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.76825i | 0.568729i | ||||||||
\(296\) | −0.621841 | + | 1.43708i | −0.0361438 | + | 0.0835287i | ||||
\(297\) | 26.3235 | + | 15.1979i | 1.52744 | + | 0.881870i | ||||
\(298\) | 4.13015 | − | 0.893005i | 0.239253 | − | 0.0517304i | ||||
\(299\) | 5.21297 | − | 19.4551i | 0.301474 | − | 1.12512i | ||||
\(300\) | −7.64538 | − | 9.30734i | −0.441406 | − | 0.537359i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.04720 | + | 21.4149i | −0.0602593 | + | 1.23229i | ||||
\(303\) | −17.8759 | − | 30.9620i | −1.02694 | − | 1.77872i | ||||
\(304\) | 0.601725 | + | 9.05512i | 0.0345113 | + | 0.519347i | ||||
\(305\) | 10.0981 | − | 17.4904i | 0.578215 | − | 1.00150i | ||||
\(306\) | −32.7790 | + | 16.8465i | −1.87385 | + | 0.963048i | ||||
\(307\) | −0.818174 | + | 0.818174i | −0.0466957 | + | 0.0466957i | −0.730069 | − | 0.683373i | \(-0.760512\pi\) |
0.683373 | + | 0.730069i | \(0.260512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.44997 | − | 7.44997i | −0.423814 | − | 0.423814i | ||||
\(310\) | 5.17499 | − | 16.1187i | 0.293920 | − | 0.915478i | ||||
\(311\) | 6.81671 | + | 3.93563i | 0.386540 | + | 0.223169i | 0.680660 | − | 0.732599i | \(-0.261693\pi\) |
−0.294120 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(312\) | −29.1659 | − | 23.1155i | −1.65120 | − | 1.30866i | ||||
\(313\) | −4.43539 | + | 2.56077i | −0.250703 | + | 0.144743i | −0.620086 | − | 0.784534i | \(-0.712902\pi\) |
0.369383 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(314\) | 11.0305 | − | 10.0020i | 0.622489 | − | 0.564447i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.40132 | + | 0.431484i | 0.247594 | + | 0.0242729i | ||||
\(317\) | 18.0167 | + | 4.82757i | 1.01192 | + | 0.271144i | 0.726432 | − | 0.687238i | \(-0.241177\pi\) |
0.285489 | + | 0.958382i | \(0.407844\pi\) | |||||||
\(318\) | −17.6624 | + | 27.4072i | −0.990459 | + | 1.53692i | ||||
\(319\) | 4.23865 | − | 7.34155i | 0.237319 | − | 0.411048i | ||||
\(320\) | −11.2614 | + | 18.1647i | −0.629531 | + | 1.01544i | ||||
\(321\) | −23.2886 | −1.29984 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.46063 | − | 8.46063i | 0.470762 | − | 0.470762i | ||||
\(324\) | 0.490194 | + | 1.08058i | 0.0272330 | + | 0.0600323i | ||||
\(325\) | −9.63816 | + | 2.58254i | −0.534629 | + | 0.143253i | ||||
\(326\) | −1.99980 | − | 9.24911i | −0.110759 | − | 0.512261i | ||||
\(327\) | −33.4356 | + | 19.3040i | −1.84899 | + | 1.06752i | ||||
\(328\) | 3.03724 | − | 20.5715i | 0.167703 | − | 1.13587i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −39.7342 | − | 43.8200i | −2.18729 | − | 2.41221i | ||||
\(331\) | 3.37401 | − | 12.5920i | 0.185453 | − | 0.692118i | −0.809081 | − | 0.587698i | \(-0.800034\pi\) |
0.994533 | − | 0.104421i | \(-0.0332989\pi\) | |||||||
\(332\) | −1.76342 | − | 10.6509i | −0.0967802 | − | 0.584545i | ||||
\(333\) | −0.708032 | − | 2.64241i | −0.0387999 | − | 0.144803i | ||||
\(334\) | −17.4384 | + | 8.96229i | −0.954186 | + | 0.490395i | ||||
\(335\) | −34.4282 | −1.88101 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5463 | 0.737913 | 0.368956 | − | 0.929447i | \(-0.379715\pi\) | ||||
0.368956 | + | 0.929447i | \(0.379715\pi\) | |||||||
\(338\) | −11.0687 | + | 5.68867i | −0.602061 | + | 0.309423i | ||||
\(339\) | 5.91583 | + | 22.0782i | 0.321304 | + | 1.19912i | ||||
\(340\) | 27.8000 | − | 4.60271i | 1.50767 | − | 0.249617i | ||||
\(341\) | 6.44317 | − | 24.0462i | 0.348917 | − | 1.30218i | ||||
\(342\) | −10.6500 | − | 11.7451i | −0.575885 | − | 0.635103i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.98630 | + | 5.36729i | 0.214927 | + | 0.289385i | ||||
\(345\) | 28.1256 | − | 16.2383i | 1.51423 | − | 0.874241i | ||||
\(346\) | −7.17891 | − | 33.2025i | −0.385941 | − | 1.78498i | ||||
\(347\) | 24.5626 | − | 6.58152i | 1.31859 | − | 0.353314i | 0.470139 | − | 0.882592i | \(-0.344204\pi\) |
0.848448 | + | 0.529278i | \(0.177537\pi\) | |||||||
\(348\) | 7.83165 | − | 3.55274i | 0.419820 | − | 0.190447i | ||||
\(349\) | 3.17376 | − | 3.17376i | 0.169887 | − | 0.169887i | −0.617043 | − | 0.786930i | \(-0.711669\pi\) |
0.786930 | + | 0.617043i | \(0.211669\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.5443 | 1.36345 | ||||||||
\(352\) | −15.2357 | + | 27.4885i | −0.812066 | + | 1.46514i | ||||
\(353\) | −3.29923 | + | 5.71444i | −0.175600 | + | 0.304149i | −0.940369 | − | 0.340156i | \(-0.889520\pi\) |
0.764769 | + | 0.644305i | \(0.222853\pi\) | |||||||
\(354\) | −7.89369 | + | 12.2488i | −0.419545 | + | 0.651017i | ||||
\(355\) | 41.9512 | + | 11.2408i | 2.22654 | + | 0.596600i | ||||
\(356\) | −2.17813 | + | 22.2179i | −0.115441 | + | 1.17755i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.1078 | + | 18.2329i | −1.06273 | + | 0.963641i | ||||
\(359\) | −7.68624 | + | 4.43765i | −0.405664 | + | 0.234210i | −0.688925 | − | 0.724833i | \(-0.741917\pi\) |
0.283261 | + | 0.959043i | \(0.408584\pi\) | |||||||
\(360\) | −4.29244 | − | 37.0909i | −0.226232 | − | 1.95486i | ||||
\(361\) | −11.9968 | − | 6.92634i | −0.631409 | − | 0.364544i | ||||
\(362\) | 2.91540 | − | 9.08064i | 0.153230 | − | 0.477268i | ||||
\(363\) | −39.5882 | − | 39.5882i | −2.07784 | − | 2.07784i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0352 | − | 15.0352i | 0.786979 | − | 0.786979i | ||||
\(366\) | 26.7964 | − | 13.7717i | 1.40067 | − | 0.719860i | ||||
\(367\) | 13.7984 | − | 23.8996i | 0.720273 | − | 1.24755i | −0.240618 | − | 0.970620i | \(-0.577350\pi\) |
0.960890 | − | 0.276929i | \(-0.0893167\pi\) | |||||||
\(368\) | −12.9835 | − | 11.3655i | −0.676810 | − | 0.592465i | ||||
\(369\) | 18.1645 | + | 31.4618i | 0.945606 | + | 1.63784i | ||||
\(370\) | −0.102158 | + | 2.08912i | −0.00531097 | + | 0.108608i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 19.5146 | − | 16.0300i | 1.01178 | − | 0.831115i | ||||
\(373\) | −7.05779 | + | 26.3400i | −0.365439 | + | 1.36384i | 0.501387 | + | 0.865223i | \(0.332823\pi\) |
−0.866825 | + | 0.498612i | \(0.833843\pi\) | |||||||
\(374\) | 40.5012 | − | 8.75700i | 2.09427 | − | 0.452814i | ||||
\(375\) | 18.6659 | + | 10.7767i | 0.963901 | + | 0.556508i | ||||
\(376\) | −0.511046 | − | 1.29067i | −0.0263552 | − | 0.0665610i | ||||
\(377\) | − | 7.12422i | − | 0.366916i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.2102 | + | 16.2102i | 0.832663 | + | 0.832663i | 0.987880 | − | 0.155218i | \(-0.0496079\pi\) |
−0.155218 | + | 0.987880i | \(0.549608\pi\) | |||||||
\(380\) | 5.00791 | + | 11.0394i | 0.256900 | + | 0.566310i | ||||
\(381\) | 0.173659 | + | 0.648103i | 0.00889681 | + | 0.0332033i | ||||
\(382\) | −2.63388 | + | 4.08706i | −0.134761 | + | 0.209112i | ||||
\(383\) | −0.993740 | − | 1.72121i | −0.0507778 | − | 0.0879496i | 0.839519 | − | 0.543330i | \(-0.182837\pi\) |
−0.890297 | + | 0.455380i | \(0.849503\pi\) | |||||||
\(384\) | −28.7999 | + | 13.6771i | −1.46969 | + | 0.697959i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.0924 | + | 1.52043i | 1.58256 | + | 0.0773879i | ||||
\(387\) | −11.2822 | − | 3.02307i | −0.573509 | − | 0.153671i | ||||
\(388\) | −2.63549 | + | 3.68134i | −0.133797 | + | 0.186892i | ||||
\(389\) | −19.8389 | + | 5.31582i | −1.00587 | + | 0.269523i | −0.723904 | − | 0.689901i | \(-0.757654\pi\) |
−0.281969 | + | 0.959424i | \(0.590988\pi\) | |||||||
\(390\) | −47.3314 | − | 15.1960i | −2.39672 | − | 0.769481i | ||||
\(391\) | 22.7504i | 1.15054i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.82285i | − | 0.0919504i | ||||||
\(394\) | −3.68402 | + | 11.4747i | −0.185598 | + | 0.578087i | ||||
\(395\) | 5.70604 | − | 1.52893i | 0.287102 | − | 0.0769287i | ||||
\(396\) | −8.96859 | − | 54.1696i | −0.450689 | − | 2.72213i | ||||
\(397\) | −32.5487 | − | 8.72141i | −1.63357 | − | 0.437715i | −0.678625 | − | 0.734485i | \(-0.737424\pi\) |
−0.954949 | + | 0.296770i | \(0.904091\pi\) | |||||||
\(398\) | −0.234681 | + | 4.79918i | −0.0117635 | + | 0.240561i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.66012 | + | 8.38560i | −0.0830061 | + | 0.419280i | ||||
\(401\) | −11.5351 | − | 19.9794i | −0.576037 | − | 0.997726i | −0.995928 | − | 0.0901513i | \(-0.971265\pi\) |
0.419891 | − | 0.907575i | \(-0.362068\pi\) | |||||||
\(402\) | −43.1709 | − | 27.8213i | −2.15317 | − | 1.38760i | ||||
\(403\) | −5.41477 | − | 20.2082i | −0.269729 | − | 1.00664i | ||||
\(404\) | −8.92706 | + | 23.7512i | −0.444138 | + | 1.18167i | ||||
\(405\) | 1.12075 | + | 1.12075i | 0.0556905 | + | 0.0556905i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.07576i | 0.152460i | ||||||||
\(408\) | 38.5791 | + | 16.6936i | 1.90995 | + | 0.826455i | ||||
\(409\) | 21.6470 | + | 12.4979i | 1.07038 | + | 0.617982i | 0.928284 | − | 0.371872i | \(-0.121284\pi\) |
0.142092 | + | 0.989853i | \(0.454617\pi\) | |||||||
\(410\) | −5.87009 | − | 27.1492i | −0.289903 | − | 1.34080i | ||||
\(411\) | 2.96066 | − | 11.0493i | 0.146038 | − | 0.545023i | ||||
\(412\) | −0.729550 | + | 7.44173i | −0.0359424 | + | 0.366628i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 30.1099 | + | 1.47238i | 1.47982 | + | 0.0723636i | ||||
\(415\) | −7.21041 | − | 12.4888i | −0.353945 | − | 0.613051i | ||||
\(416\) | 0.461987 | + | 26.4080i | 0.0226508 | + | 1.29476i | ||||
\(417\) | 11.9727 | − | 20.7373i | 0.586306 | − | 1.01551i | ||||
\(418\) | 8.14834 | + | 15.8546i | 0.398548 | + | 0.775476i | ||||
\(419\) | −11.0926 | + | 11.0926i | −0.541911 | + | 0.541911i | −0.924089 | − | 0.382178i | \(-0.875174\pi\) |
0.382178 | + | 0.924089i | \(0.375174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.513978 | + | 0.513978i | 0.0250497 | + | 0.0250497i | 0.719521 | − | 0.694471i | \(-0.244362\pi\) |
−0.694471 | + | 0.719521i | \(0.744362\pi\) | |||||||
\(422\) | 6.16028 | + | 1.97779i | 0.299878 | + | 0.0962776i | ||||
\(423\) | 2.10027 | + | 1.21259i | 0.102119 | + | 0.0589583i | ||||
\(424\) | 22.9870 | − | 2.66023i | 1.11635 | − | 0.129192i | ||||
\(425\) | 9.76068 | − | 5.63533i | 0.473463 | − | 0.273354i | ||||
\(426\) | 43.5208 | + | 47.9960i | 2.10859 | + | 2.32541i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.4911 | + | 12.7717i | 0.507108 | + | 0.617344i | ||||
\(429\) | −70.6102 | − | 18.9200i | −3.40909 | − | 0.913464i | ||||
\(430\) | 7.50673 | + | 4.83768i | 0.362007 | + | 0.233293i | ||||
\(431\) | −15.8660 | + | 27.4807i | −0.764238 | + | 1.32370i | 0.176410 | + | 0.984317i | \(0.443552\pi\) |
−0.940648 | + | 0.339383i | \(0.889782\pi\) | |||||||
\(432\) | 9.66127 | − | 19.6358i | 0.464828 | − | 0.944730i | ||||
\(433\) | −18.4117 | −0.884808 | −0.442404 | − | 0.896816i | \(-0.645874\pi\) | ||||
−0.442404 | + | 0.896816i | \(0.645874\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.12277 | − | 8.12277i | 0.389457 | − | 0.389457i | ||||
\(436\) | 25.6487 | + | 9.64025i | 1.22835 | + | 0.461684i | ||||
\(437\) | −9.45358 | + | 2.53308i | −0.452226 | + | 0.121174i | ||||
\(438\) | 31.0032 | − | 6.70338i | 1.48139 | − | 0.320300i | ||||
\(439\) | −7.67855 | + | 4.43321i | −0.366477 | + | 0.211586i | −0.671918 | − | 0.740625i | \(-0.734529\pi\) |
0.305441 | + | 0.952211i | \(0.401196\pi\) | |||||||
\(440\) | −6.13174 | + | 41.5308i | −0.292319 | + | 1.97990i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.7971 | − | 23.3917i | 1.22704 | − | 1.11263i | ||||
\(443\) | −1.91253 | + | 7.13765i | −0.0908669 | + | 0.339120i | −0.996360 | − | 0.0852402i | \(-0.972834\pi\) |
0.905494 | + | 0.424360i | \(0.139501\pi\) | |||||||
\(444\) | −1.81631 | + | 2.53708i | −0.0861982 | + | 0.120404i | ||||
\(445\) | 7.71803 | + | 28.8041i | 0.365870 | + | 1.36545i | ||||
\(446\) | 0.300188 | + | 0.584091i | 0.0142143 | + | 0.0276575i | ||||
\(447\) | 8.42018 | 0.398261 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.5402 | −1.72444 | −0.862218 | − | 0.506537i | \(-0.830925\pi\) | ||||
−0.862218 | + | 0.506537i | \(0.830925\pi\) | |||||||
\(450\) | −6.82659 | − | 13.2829i | −0.321809 | − | 0.626160i | ||||
\(451\) | −10.5717 | − | 39.4543i | −0.497804 | − | 1.85783i | ||||
\(452\) | 9.44291 | − | 13.1902i | 0.444157 | − | 0.620413i | ||||
\(453\) | −11.0577 | + | 41.2679i | −0.519536 | + | 1.93893i | ||||
\(454\) | 20.3585 | − | 18.4602i | 0.955471 | − | 0.866382i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.64129 | + | 17.8897i | −0.123690 | + | 0.837760i | ||||
\(457\) | −13.7199 | + | 7.92121i | −0.641792 | + | 0.370539i | −0.785304 | − | 0.619110i | \(-0.787494\pi\) |
0.143513 | + | 0.989648i | \(0.454160\pi\) | |||||||
\(458\) | 1.54096 | − | 0.333179i | 0.0720041 | − | 0.0155684i | ||||
\(459\) | −27.8699 | + | 7.46773i | −1.30086 | + | 0.348564i | ||||
\(460\) | −21.5754 | − | 8.10926i | −1.00596 | − | 0.378096i | ||||
\(461\) | 3.07760 | − | 3.07760i | 0.143338 | − | 0.143338i | −0.631796 | − | 0.775134i | \(-0.717682\pi\) |
0.775134 | + | 0.631796i | \(0.217682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.2198 | −1.21854 | −0.609269 | − | 0.792964i | \(-0.708537\pi\) | ||||
−0.609269 | + | 0.792964i | \(0.708537\pi\) | |||||||
\(464\) | −5.47639 | − | 2.69450i | −0.254235 | − | 0.125089i | ||||
\(465\) | 16.8669 | − | 29.2143i | 0.782184 | − | 1.35478i | ||||
\(466\) | 12.5121 | + | 8.06339i | 0.579614 | + | 0.373529i | ||||
\(467\) | 1.33886 | + | 0.358746i | 0.0619549 | + | 0.0166008i | 0.289663 | − | 0.957129i | \(-0.406457\pi\) |
−0.227708 | + | 0.973729i | \(0.573123\pi\) | |||||||
\(468\) | −29.2891 | − | 35.6560i | −1.35389 | − | 1.64820i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.24555 | − | 1.37363i | −0.0574531 | − | 0.0633609i | ||||
\(471\) | 25.6957 | − | 14.8354i | 1.18399 | − | 0.683579i | ||||
\(472\) | 10.2734 | − | 1.18891i | 0.472869 | − | 0.0547241i | ||||
\(473\) | 11.3731 | + | 6.56627i | 0.522936 | + | 0.301917i | ||||
\(474\) | 8.39057 | + | 2.69384i | 0.385391 | + | 0.123732i | ||||
\(475\) | 3.42845 | + | 3.42845i | 0.157308 | + | 0.157308i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.5866 | + | 28.5866i | −1.30889 | + | 1.30889i | ||||
\(478\) | −14.2805 | − | 27.7863i | −0.653175 | − | 1.27092i | ||||
\(479\) | 3.71973 | − | 6.44276i | 0.169959 | − | 0.294377i | −0.768446 | − | 0.639914i | \(-0.778970\pi\) |
0.938405 | + | 0.345537i | \(0.112303\pi\) | |||||||
\(480\) | −29.5827 | + | 30.6362i | −1.35026 | + | 1.39834i | ||||
\(481\) | 1.29242 | + | 2.23854i | 0.0589293 | + | 0.102068i | ||||
\(482\) | 4.92209 | + | 0.240692i | 0.224195 | + | 0.0109632i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.87674 | + | 39.5444i | −0.176216 | + | 1.79747i | ||||
\(485\) | −1.56525 | + | 5.84158i | −0.0710742 | + | 0.265253i | ||||
\(486\) | −4.40564 | − | 20.3761i | −0.199844 | − | 0.924280i | ||||
\(487\) | 25.8498 | + | 14.9244i | 1.17137 | + | 0.676290i | 0.954002 | − | 0.299800i | \(-0.0969201\pi\) |
0.217366 | + | 0.976090i | \(0.430253\pi\) | |||||||
\(488\) | −19.6239 | − | 8.49146i | −0.888331 | − | 0.384390i | ||||
\(489\) | − | 18.8562i | − | 0.852708i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.1830 | − | 17.1830i | −0.775457 | − | 0.775457i | 0.203597 | − | 0.979055i | \(-0.434737\pi\) |
−0.979055 | + | 0.203597i | \(0.934737\pi\) | |||||||
\(492\) | 14.5784 | − | 38.7871i | 0.657246 | − | 1.74866i | ||||
\(493\) | 2.08273 | + | 7.77285i | 0.0938014 | + | 0.350072i | ||||
\(494\) | 12.5924 | + | 8.11510i | 0.566558 | + | 0.365115i | ||||
\(495\) | −36.6715 | − | 63.5169i | −1.64826 | − | 2.85487i | ||||
\(496\) | −17.5820 | − | 3.48076i | −0.789454 | − | 0.156291i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.05072 | − | 21.4869i | 0.0470838 | − | 0.962853i | ||||
\(499\) | 11.6949 | + | 3.13364i | 0.523536 | + | 0.140281i | 0.510902 | − | 0.859639i | \(-0.329312\pi\) |
0.0126341 | + | 0.999920i | \(0.495978\pi\) | |||||||
\(500\) | −2.49859 | − | 15.0913i | −0.111740 | − | 0.674903i | ||||
\(501\) | −37.7381 | + | 10.1119i | −1.68602 | + | 0.451767i | ||||
\(502\) | 11.8980 | − | 37.0588i | 0.531032 | − | 1.65402i | ||||
\(503\) | − | 16.3203i | − | 0.727686i | −0.931460 | − | 0.363843i | \(-0.881465\pi\) | ||
0.931460 | − | 0.363843i | \(-0.118535\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.8930i | 1.50822i | ||||||||
\(506\) | −32.2716 | − | 10.3610i | −1.43465 | − | 0.460603i | ||||
\(507\) | −23.9537 | + | 6.41838i | −1.06382 | + | 0.285050i | ||||
\(508\) | 0.277196 | − | 0.387196i | 0.0122986 | − | 0.0171791i | ||||
\(509\) | −3.29918 | − | 0.884013i | −0.146234 | − | 0.0391832i | 0.184960 | − | 0.982746i | \(-0.440785\pi\) |
−0.331193 | + | 0.943563i | \(0.607451\pi\) | |||||||
\(510\) | 56.0832 | + | 2.74249i | 2.48340 | + | 0.121439i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.4746 | + | 9.63285i | 0.904857 | + | 0.425716i | ||||
\(513\) | −6.20621 | − | 10.7495i | −0.274011 | − | 0.474601i | ||||
\(514\) | −16.8210 | + | 26.1016i | −0.741944 | + | 1.15129i | ||||
\(515\) | 2.58510 | + | 9.64773i | 0.113913 | + | 0.425130i | ||||
\(516\) | 5.50370 | + | 12.1323i | 0.242287 | + | 0.534096i | ||||
\(517\) | −1.92809 | − | 1.92809i | −0.0847972 | − | 0.0847972i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 67.6903i | − | 2.97127i | ||||||
\(520\) | 12.9883 | + | 32.8026i | 0.569577 | + | 1.43849i | ||||
\(521\) | −24.8133 | − | 14.3260i | −1.08709 | − | 0.627633i | −0.154291 | − | 0.988025i | \(-0.549309\pi\) |
−0.932801 | + | 0.360393i | \(0.882643\pi\) | |||||||
\(522\) | 10.4221 | − | 2.25342i | 0.456162 | − | 0.0986294i | ||||
\(523\) | 0.216091 | − | 0.806464i | 0.00944902 | − | 0.0352642i | −0.961040 | − | 0.276408i | \(-0.910856\pi\) |
0.970489 | + | 0.241144i | \(0.0775225\pi\) | |||||||
\(524\) | −0.999667 | + | 0.821162i | −0.0436706 | + | 0.0358726i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.08752 | − | 22.2395i | 0.0474181 | − | 0.969689i | ||||
\(527\) | 11.8155 | + | 20.4651i | 0.514692 | + | 0.891473i | ||||
\(528\) | −41.2497 | + | 47.1222i | −1.79516 | + | 2.05073i | ||||
\(529\) | −2.19550 | + | 3.80271i | −0.0954564 | + | 0.165335i | ||||
\(530\) | 27.4919 | − | 14.1292i | 1.19417 | − | 0.613733i | ||||
\(531\) | −12.7759 | + | 12.7759i | −0.554427 | + | 0.554427i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.2726 | − | 24.2726i | −1.05136 | − | 1.05136i | ||||
\(534\) | −13.5985 | + | 42.3556i | −0.588466 | + | 1.83291i | ||||
\(535\) | 19.1199 | + | 11.0389i | 0.826626 | + | 0.477253i | ||||
\(536\) | 4.19032 | + | 36.2084i | 0.180994 | + | 1.56396i | ||||
\(537\) | −46.8413 | + | 27.0438i | −2.02135 | + | 1.16703i | ||||
\(538\) | −1.76450 | + | 1.59998i | −0.0760730 | + | 0.0689799i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.85207 | − | 29.0924i | 0.122734 | − | 1.25194i | ||||
\(541\) | −12.2532 | − | 3.28325i | −0.526808 | − | 0.141158i | −0.0143942 | − | 0.999896i | \(-0.504582\pi\) |
−0.512414 | + | 0.858739i | \(0.671249\pi\) | |||||||
\(542\) | 9.41287 | − | 14.6062i | 0.404318 | − | 0.627389i | ||||
\(543\) | 9.50218 | − | 16.4583i | 0.407778 | − | 0.706292i | ||||
\(544\) | −8.22430 | − | 28.6773i | −0.352614 | − | 1.22953i | ||||
\(545\) | 36.6007 | 1.56780 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6827 | + | 15.6827i | −0.670546 | + | 0.670546i | −0.957842 | − | 0.287296i | \(-0.907244\pi\) |
0.287296 | + | 0.957842i | \(0.407244\pi\) | |||||||
\(548\) | −7.39329 | + | 3.35388i | −0.315826 | + | 0.143271i | ||||
\(549\) | 36.0831 | − | 9.66842i | 1.53999 | − | 0.412638i | ||||
\(550\) | 3.54855 | + | 16.4121i | 0.151311 | + | 0.699813i | ||||
\(551\) | −2.99800 | + | 1.73089i | −0.127719 | + | 0.0737386i | ||||
\(552\) | −20.5012 | − | 27.6035i | −0.872589 | − | 1.17488i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 29.3447 | + | 32.3622i | 1.24674 | + | 1.37494i | ||||
\(555\) | −1.07873 | + | 4.02586i | −0.0457894 | + | 0.170888i | ||||
\(556\) | −16.7661 | + | 2.77587i | −0.711040 | + | 0.117723i | ||||
\(557\) | −4.28460 | − | 15.9904i | −0.181544 | − | 0.677533i | −0.995344 | − | 0.0963873i | \(-0.969271\pi\) |
0.813799 | − | 0.581146i | \(-0.197395\pi\) | |||||||
\(558\) | 27.8500 | − | 14.3132i | 1.17898 | − | 0.605927i | ||||
\(559\) | 11.0364 | 0.466792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 82.5701 | 3.48611 | ||||||||
\(562\) | 26.9090 | − | 13.8296i | 1.13509 | − | 0.583367i | ||||
\(563\) | −5.52415 | − | 20.6164i | −0.232815 | − | 0.868878i | −0.979122 | − | 0.203275i | \(-0.934841\pi\) |
0.746306 | − | 0.665602i | \(-0.231825\pi\) | |||||||
\(564\) | −0.451824 | − | 2.72898i | −0.0190252 | − | 0.114911i | ||||
\(565\) | 5.60825 | − | 20.9303i | 0.235941 | − | 0.880544i | ||||
\(566\) | 14.2414 | + | 15.7059i | 0.598613 | + | 0.660168i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.71608 | − | 45.4886i | 0.281801 | − | 1.90866i | ||||
\(569\) | −23.3737 | + | 13.4948i | −0.979875 | + | 0.565731i | −0.902232 | − | 0.431250i | \(-0.858073\pi\) |
−0.0776423 | + | 0.996981i | \(0.524739\pi\) | |||||||
\(570\) | 5.10483 | + | 23.6099i | 0.213818 | + | 0.988909i | ||||
\(571\) | −8.98941 | + | 2.40871i | −0.376195 | + | 0.100801i | −0.441962 | − | 0.897034i | \(-0.645717\pi\) |
0.0657667 | + | 0.997835i | \(0.479051\pi\) | |||||||
\(572\) | 21.4328 | + | 47.2465i | 0.896152 | + | 1.97547i | ||||
\(573\) | −6.85102 | + | 6.85102i | −0.286205 | + | 0.286205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.21901 | −0.384459 | ||||||||
\(576\) | −38.4864 | + | 9.02880i | −1.60360 | + | 0.376200i | ||||
\(577\) | 0.726967 | − | 1.25914i | 0.0302640 | − | 0.0524188i | −0.850497 | − | 0.525980i | \(-0.823699\pi\) |
0.880761 | + | 0.473562i | \(0.157032\pi\) | |||||||
\(578\) | −8.28394 | + | 12.8544i | −0.344566 | + | 0.534672i | ||||
\(579\) | 59.9171 | + | 16.0547i | 2.49007 | + | 0.667212i | ||||
\(580\) | −8.11378 | − | 0.795435i | −0.336906 | − | 0.0330287i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.68329 | + | 6.06014i | −0.277031 | + | 0.251201i | ||||
\(583\) | 39.3644 | − | 22.7271i | 1.63031 | − | 0.941259i | ||||
\(584\) | −17.6426 | − | 13.9827i | −0.730057 | − | 0.578608i | ||||
\(585\) | −53.3789 | − | 30.8183i | −2.20695 | − | 1.27418i | ||||
\(586\) | 12.8446 | − | 40.0073i | 0.530606 | − | 1.65269i | ||||
\(587\) | 10.3785 | + | 10.3785i | 0.428367 | + | 0.428367i | 0.888072 | − | 0.459705i | \(-0.152045\pi\) |
−0.459705 | + | 0.888072i | \(0.652045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.18839 | + | 7.18839i | −0.296193 | + | 0.296193i | ||||
\(590\) | 12.2867 | − | 6.31462i | 0.505835 | − | 0.259969i | ||||
\(591\) | −12.0074 | + | 20.7974i | −0.493917 | + | 0.855489i | ||||
\(592\) | 2.20958 | − | 0.146829i | 0.0908130 | − | 0.00603465i | ||||
\(593\) | 4.32233 | + | 7.48650i | 0.177497 | + | 0.307434i | 0.941023 | − | 0.338344i | \(-0.109867\pi\) |
−0.763526 | + | 0.645777i | \(0.776533\pi\) | |||||||
\(594\) | 2.09952 | − | 42.9348i | 0.0861445 | − | 1.76163i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.79315 | − | 4.61771i | −0.155374 | − | 0.189149i | ||||
\(597\) | −2.47808 | + | 9.24833i | −0.101421 | + | 0.378509i | ||||
\(598\) | −27.8409 | + | 6.01964i | −1.13850 | + | 0.246161i | ||||
\(599\) | 25.5370 | + | 14.7438i | 1.04341 | + | 0.602415i | 0.920798 | − | 0.390039i | \(-0.127539\pi\) |
0.122615 | + | 0.992454i | \(0.460872\pi\) | |||||||
\(600\) | −6.76464 | + | 15.6332i | −0.276165 | + | 0.638222i | ||||
\(601\) | 21.8149i | 0.889849i | 0.895568 | + | 0.444925i | \(0.146769\pi\) | ||||
−0.895568 | + | 0.444925i | \(0.853231\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −45.0287 | − | 45.0287i | −1.83371 | − | 1.83371i | ||||
\(604\) | 27.6130 | − | 12.5263i | 1.12356 | − | 0.509690i | ||||
\(605\) | 13.7369 | + | 51.2669i | 0.558485 | + | 2.08429i | ||||
\(606\) | −27.3888 | + | 42.4998i | −1.11259 | + | 1.72644i | ||||
\(607\) | 7.17791 | + | 12.4325i | 0.291342 | + | 0.504620i | 0.974127 | − | 0.225999i | \(-0.0725648\pi\) |
−0.682785 | + | 0.730619i | \(0.739231\pi\) | |||||||
\(608\) | 11.0007 | − | 6.61049i | 0.446138 | − | 0.268091i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.5276 | − | 1.39501i | −1.15505 | − | 0.0564823i | ||||
\(611\) | −2.21343 | − | 0.593087i | −0.0895458 | − | 0.0239937i | ||||
\(612\) | 42.3796 | + | 30.3398i | 1.71309 | + | 1.22641i | ||||
\(613\) | −3.04073 | + | 0.814761i | −0.122814 | + | 0.0329079i | −0.319702 | − | 0.947518i | \(-0.603583\pi\) |
0.196889 | + | 0.980426i | \(0.436916\pi\) | |||||||
\(614\) | 1.55802 | + | 0.500212i | 0.0628765 | + | 0.0201869i | ||||
\(615\) | − | 55.3493i | − | 2.23190i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.3166i | 1.42179i | 0.703296 | + | 0.710897i | \(0.251711\pi\) | ||||
−0.703296 | + | 0.710897i | \(0.748289\pi\) | |||||||
\(618\) | −4.55473 | + | 14.1867i | −0.183218 | + | 0.570673i | ||||
\(619\) | −32.0875 | + | 8.59783i | −1.28971 | + | 0.345576i | −0.837549 | − | 0.546362i | \(-0.816012\pi\) |
−0.452158 | + | 0.891938i | \(0.649346\pi\) | |||||||
\(620\) | −23.6197 | + | 3.91060i | −0.948590 | + | 0.157053i | ||||
\(621\) | 22.7966 | + | 6.10834i | 0.914798 | + | 0.245119i | ||||
\(622\) | 0.543692 | − | 11.1184i | 0.0218000 | − | 0.445806i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10.2210 | + | 51.6284i | −0.409168 | + | 2.06679i | ||||
\(625\) | −15.5591 | − | 26.9492i | −0.622366 | − | 1.07797i | ||||
\(626\) | 6.08822 | + | 3.92352i | 0.243334 | + | 0.156815i | ||||
\(627\) | 9.19355 | + | 34.3108i | 0.367155 | + | 1.37024i | ||||
\(628\) | −19.7114 | − | 7.40866i | −0.786569 | − | 0.295638i | ||||
\(629\) | −2.06451 | − | 2.06451i | −0.0823175 | − | 0.0823175i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7508i | 0.666841i | 0.942778 | + | 0.333420i | \(0.108203\pi\) | ||||
−0.942778 | + | 0.333420i | \(0.891797\pi\) | |||||||
\(632\) | −2.30248 | − | 5.81500i | −0.0915878 | − | 0.231308i | ||||
\(633\) | 11.1652 | + | 6.44625i | 0.443778 | + | 0.256215i | ||||
\(634\) | −5.57460 | − | 25.7826i | −0.221396 | − | 1.02396i | ||||
\(635\) | 0.164630 | − | 0.614407i | 0.00653314 | − | 0.0243820i | ||||
\(636\) | 45.8910 | + | 4.49893i | 1.81970 | + | 0.178394i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.9744 | − | 0.585552i | −0.474071 | − | 0.0231822i | ||||
\(639\) | 40.1662 | + | 69.5699i | 1.58895 | + | 2.75214i | ||||
\(640\) | 30.1277 | + | 2.42236i | 1.19090 | + | 0.0957522i | ||||
\(641\) | −11.6917 | + | 20.2506i | −0.461795 | + | 0.799852i | −0.999050 | − | 0.0435673i | \(-0.986128\pi\) |
0.537256 | + | 0.843419i | \(0.319461\pi\) | |||||||
\(642\) | 15.0548 | + | 29.2929i | 0.594165 | + | 1.15610i | ||||
\(643\) | −2.10371 | + | 2.10371i | −0.0829620 | + | 0.0829620i | −0.747370 | − | 0.664408i | \(-0.768684\pi\) |
0.664408 | + | 0.747370i | \(0.268684\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.5833 | + | 12.5833i | 0.495468 | + | 0.495468i | ||||
\(646\) | −16.1113 | − | 5.17262i | −0.633889 | − | 0.203514i | ||||
\(647\) | −5.68625 | − | 3.28296i | −0.223550 | − | 0.129066i | 0.384043 | − | 0.923315i | \(-0.374531\pi\) |
−0.607593 | + | 0.794249i | \(0.707865\pi\) | |||||||
\(648\) | 1.04229 | − | 1.31511i | 0.0409452 | − | 0.0516625i | ||||
\(649\) | 17.5928 | − | 10.1572i | 0.690576 | − | 0.398704i | ||||
\(650\) | 9.47889 | + | 10.4536i | 0.371793 | + | 0.410024i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.3410 | + | 8.49442i | −0.404983 | + | 0.332667i | ||||
\(653\) | 37.3783 | + | 10.0155i | 1.46273 | + | 0.391936i | 0.900430 | − | 0.435000i | \(-0.143252\pi\) |
0.562295 | + | 0.826937i | \(0.309918\pi\) | |||||||
\(654\) | 45.8952 | + | 29.5769i | 1.79464 | + | 1.15655i | ||||
\(655\) | −0.864035 | + | 1.49655i | −0.0337607 | + | 0.0584752i | ||||
\(656\) | −27.8386 | + | 9.47800i | −1.08691 | + | 0.370054i | ||||
\(657\) | 39.3291 | 1.53438 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7559 | − | 20.7559i | 0.808533 | − | 0.808533i | −0.175879 | − | 0.984412i | \(-0.556277\pi\) |
0.984412 | + | 0.175879i | \(0.0562766\pi\) | |||||||
\(660\) | −29.4317 | + | 78.3056i | −1.14563 | + | 3.04804i | ||||
\(661\) | 42.5471 | − | 11.4005i | 1.65489 | − | 0.443426i | 0.693913 | − | 0.720059i | \(-0.255885\pi\) |
0.960976 | + | 0.276632i | \(0.0892184\pi\) | |||||||
\(662\) | −18.0196 | + | 3.89612i | −0.700350 | + | 0.151427i | ||||
\(663\) | 60.0944 | − | 34.6955i | 2.33387 | − | 1.34746i | ||||
\(664\) | −12.2570 | + | 9.10329i | −0.475663 | + | 0.353276i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.86597 | + | 2.59875i | −0.111054 | + | 0.100699i | ||||
\(667\) | 1.70360 | − | 6.35792i | 0.0659637 | − | 0.246180i | ||||
\(668\) | 22.5459 | + | 16.1407i | 0.872326 | + | 0.624504i | ||||
\(669\) | 0.338694 | + | 1.26402i | 0.0130947 | + | 0.0488699i | ||||
\(670\) | 22.2559 | + | 43.3044i | 0.859819 | + | 1.67300i | ||||
\(671\) | −42.0007 | −1.62142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.5908 | 1.02500 | 0.512500 | − | 0.858687i | \(-0.328720\pi\) | ||||
0.512500 | + | 0.858687i | \(0.328720\pi\) | |||||||
\(674\) | −8.75691 | − | 17.0388i | −0.337304 | − | 0.656309i | ||||
\(675\) | −3.02611 | − | 11.2936i | −0.116475 | − | 0.434690i | ||||
\(676\) | 14.3107 | + | 10.2451i | 0.550410 | + | 0.394042i | ||||
\(677\) | −8.26024 | + | 30.8276i | −0.317467 | + | 1.18480i | 0.604204 | + | 0.796830i | \(0.293491\pi\) |
−0.921671 | + | 0.387973i | \(0.873175\pi\) | |||||||
\(678\) | 23.9461 | − | 21.7134i | 0.919645 | − | 0.833896i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −23.7605 | − | 31.9920i | −0.911175 | − | 1.22684i | ||||
\(681\) | 47.4252 | − | 27.3810i | 1.81734 | − | 1.04924i | ||||
\(682\) | −34.4110 | + | 7.44020i | −1.31766 | + | 0.284900i | ||||
\(683\) | 24.5538 | − | 6.57917i | 0.939525 | − | 0.251745i | 0.243614 | − | 0.969872i | \(-0.421667\pi\) |
0.695912 | + | 0.718127i | \(0.255000\pi\) | |||||||
\(684\) | −7.88861 | + | 20.9883i | −0.301629 | + | 0.802508i | ||||
\(685\) | −7.66812 | + | 7.66812i | −0.292984 | + | 0.292984i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.14156 | 0.119858 | ||||||||
\(688\) | 4.17417 | − | 8.48370i | 0.159139 | − | 0.323438i | ||||
\(689\) | 19.0996 | − | 33.0815i | 0.727636 | − | 1.26030i | ||||
\(690\) | −38.6065 | − | 24.8798i | −1.46972 | − | 0.947156i | ||||
\(691\) | −33.4013 | − | 8.94986i | −1.27065 | − | 0.340469i | −0.440368 | − | 0.897817i | \(-0.645152\pi\) |
−0.830279 | + | 0.557349i | \(0.811819\pi\) | |||||||
\(692\) | −37.1220 | + | 30.4934i | −1.41117 | + | 1.15918i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.1567 | − | 26.6407i | −0.916975 | − | 1.01127i | ||||
\(695\) | −19.6591 | + | 11.3502i | −0.745714 | + | 0.430538i | ||||
\(696\) | −9.53143 | − | 7.55415i | −0.361288 | − | 0.286339i | ||||
\(697\) | 33.5784 | + | 19.3865i | 1.27187 | + | 0.734317i | ||||
\(698\) | −6.04367 | − | 1.94036i | −0.228756 | − | 0.0734436i | ||||
\(699\) | 20.9737 | + | 20.9737i | 0.793300 | + | 0.793300i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.0840 | + | 31.0840i | −1.17403 | + | 1.17403i | −0.192785 | + | 0.981241i | \(0.561752\pi\) |
−0.981241 | + | 0.192785i | \(0.938248\pi\) | |||||||
\(702\) | −16.5129 | − | 32.1301i | −0.623240 | − | 1.21267i | ||||
\(703\) | 0.628010 | − | 1.08775i | 0.0236858 | − | 0.0410251i | ||||
\(704\) | 44.4246 | + | 1.39401i | 1.67432 | + | 0.0525389i | ||||
\(705\) | −1.84745 | − | 3.19988i | −0.0695791 | − | 0.120515i | ||||
\(706\) | 9.32050 | + | 0.455775i | 0.350782 | + | 0.0171533i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20.5096 | + | 2.01066i | 0.770799 | + | 0.0755653i | ||||
\(709\) | 10.1162 | − | 37.7540i | 0.379921 | − | 1.41788i | −0.466100 | − | 0.884732i | \(-0.654341\pi\) |
0.846020 | − | 0.533151i | \(-0.178992\pi\) | |||||||
\(710\) | −12.9802 | − | 60.0336i | −0.487139 | − | 2.25302i | ||||
\(711\) | 9.46263 | + | 5.46325i | 0.354876 | + | 0.204888i | ||||
\(712\) | 29.3541 | − | 11.6229i | 1.10009 | − | 0.435588i | ||||
\(713\) | − | 19.3294i | − | 0.723891i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 49.0028 | + | 49.0028i | 1.83260 | + | 1.83260i | ||||
\(716\) | 35.9323 | + | 13.5054i | 1.34285 | + | 0.504722i | ||||
\(717\) | −16.1123 | − | 60.1319i | −0.601725 | − | 2.24567i | ||||
\(718\) | 10.5505 | + | 6.79921i | 0.393741 | + | 0.253744i | ||||
\(719\) | 1.34884 | + | 2.33625i | 0.0503031 | + | 0.0871276i | 0.890081 | − | 0.455803i | \(-0.150648\pi\) |
−0.839777 | + | 0.542931i | \(0.817315\pi\) | |||||||
\(720\) | −43.8788 | + | 29.3763i | −1.63527 | + | 1.09479i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.956845 | + | 19.5673i | −0.0356101 | + | 0.728218i | ||||
\(723\) | 9.48518 | + | 2.54155i | 0.352758 | + | 0.0945211i | ||||
\(724\) | −13.3065 | + | 2.20308i | −0.494530 | + | 0.0818769i | ||||
\(725\) | −3.14975 | + | 0.843973i | −0.116979 | + | 0.0313444i | ||||
\(726\) | −24.2033 | + | 75.3865i | −0.898269 | + | 2.79785i | ||||
\(727\) | − | 29.4609i | − | 1.09264i | −0.837576 | − | 0.546321i | \(-0.816028\pi\) | ||
0.837576 | − | 0.546321i | \(-0.183972\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 43.3209i | − | 1.60448i | ||||||
\(730\) | −28.6310 | − | 9.19216i | −1.05968 | − | 0.340217i | ||||
\(731\) | −12.0413 | + | 3.22645i | −0.445362 | + | 0.119334i | ||||
\(732\) | −34.6447 | − | 24.8023i | −1.28050 | − | 0.916721i | ||||
\(733\) | −22.6627 | − | 6.07246i | −0.837067 | − | 0.224291i | −0.185273 | − | 0.982687i | \(-0.559317\pi\) |
−0.651794 | + | 0.758396i | \(0.725984\pi\) | |||||||
\(734\) | −38.9813 | − | 1.90620i | −1.43883 | − | 0.0703591i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.90260 | + | 23.6780i | −0.217573 | + | 0.872783i | ||||
\(737\) | 35.7990 | + | 62.0056i | 1.31867 | + | 2.28401i | ||||
\(738\) | 27.8310 | − | 43.1860i | 1.02447 | − | 1.58970i | ||||
\(739\) | −11.0520 | − | 41.2466i | −0.406555 | − | 1.51728i | −0.801171 | − | 0.598436i | \(-0.795789\pi\) |
0.394616 | − | 0.918846i | \(-0.370878\pi\) | |||||||
\(740\) | 2.69377 | − | 1.22200i | 0.0990250 | − | 0.0449216i | ||||
\(741\) | 21.1083 | + | 21.1083i | 0.775431 | + | 0.775431i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 15.9080i | − | 0.583606i | −0.956478 | − | 0.291803i | \(-0.905745\pi\) | ||
0.956478 | − | 0.291803i | \(-0.0942552\pi\) | |||||||
\(744\) | −32.7779 | − | 14.1833i | −1.20170 | − | 0.519986i | ||||
\(745\) | −6.91296 | − | 3.99120i | −0.253271 | − | 0.146226i | ||||
\(746\) | 37.6935 | − | 8.14993i | 1.38006 | − | 0.298390i | ||||
\(747\) | 6.90361 | − | 25.7646i | 0.252590 | − | 0.942678i | ||||
\(748\) | −37.1965 | − | 45.2823i | −1.36004 | − | 1.65568i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.48876 | − | 30.4448i | 0.0543619 | − | 1.11169i | ||||
\(751\) | −17.0414 | − | 29.5165i | −0.621848 | − | 1.07707i | −0.989141 | − | 0.146967i | \(-0.953049\pi\) |
0.367294 | − | 0.930105i | \(-0.380284\pi\) | |||||||
\(752\) | −1.29306 | + | 1.47715i | −0.0471531 | + | 0.0538660i | ||||
\(753\) | 38.7792 | − | 67.1675i | 1.41319 | − | 2.44772i | ||||
\(754\) | −8.96099 | + | 4.60541i | −0.326340 | + | 0.167719i | ||||
\(755\) | 28.6395 | − | 28.6395i | 1.04230 | − | 1.04230i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8161 | + | 15.8161i | 0.574845 | + | 0.574845i | 0.933478 | − | 0.358634i | \(-0.116757\pi\) |
−0.358634 | + | 0.933478i | \(0.616757\pi\) | |||||||
\(758\) | 9.91053 | − | 30.8685i | 0.359967 | − | 1.12119i | ||||
\(759\) | −58.4909 | − | 33.7697i | −2.12308 | − | 1.22576i | ||||
\(760\) | 10.6483 | − | 13.4354i | 0.386253 | − | 0.487353i | ||||
\(761\) | −14.7507 | + | 8.51630i | −0.534711 | + | 0.308716i | −0.742933 | − | 0.669366i | \(-0.766566\pi\) |
0.208222 | + | 0.978082i | \(0.433232\pi\) | |||||||
\(762\) | 0.702937 | − | 0.637394i | 0.0254647 | − | 0.0230903i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.84344 | + | 0.670897i | 0.247587 | + | 0.0242722i | ||||
\(765\) | 67.2484 | + | 18.0192i | 2.43137 | + | 0.651484i | ||||
\(766\) | −1.52257 | + | 2.36261i | −0.0550128 | + | 0.0853646i | ||||
\(767\) | 8.53599 | − | 14.7848i | 0.308217 | − | 0.533847i | ||||
\(768\) | 35.8209 | + | 27.3836i | 1.29258 | + | 0.988121i | ||||
\(769\) | 29.7823 | 1.07398 | 0.536989 | − | 0.843590i | \(-0.319562\pi\) | ||||
0.536989 | + | 0.843590i | \(0.319562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.7533 | + | 43.7533i | −1.57574 | + | 1.57574i | ||||
\(772\) | −18.1871 | − | 40.0915i | −0.654568 | − | 1.44293i | ||||
\(773\) | −50.1642 | + | 13.4415i | −1.80428 | + | 0.483456i | −0.994634 | − | 0.103459i | \(-0.967009\pi\) |
−0.809649 | + | 0.586915i | \(0.800342\pi\) | |||||||
\(774\) | 3.49086 | + | 16.1453i | 0.125477 | + | 0.580330i | ||||
\(775\) | −8.29295 | + | 4.78794i | −0.297892 | + | 0.171988i | ||||
\(776\) | 6.33415 | + | 0.935195i | 0.227383 | + | 0.0335715i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.5111 | + | 21.5174i | 0.699507 | + | 0.771436i | ||||
\(779\) | −4.31708 | + | 16.1116i | −0.154675 | + | 0.577256i | ||||
\(780\) | 11.4832 | + | 69.3577i | 0.411165 | + | 2.48340i | ||||
\(781\) | −23.3767 | − | 87.2432i | −0.836485 | − | 3.12181i | ||||
\(782\) | 28.6159 | − | 14.7068i | 1.02330 | − | 0.525916i | ||||
\(783\) | 8.34786 | 0.298328 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.1282 | −1.00394 | ||||||||
\(786\) | −2.29281 | + | 1.17837i | −0.0817818 | + | 0.0420310i | ||||
\(787\) | 4.56538 | + | 17.0382i | 0.162738 | + | 0.607347i | 0.998318 | + | 0.0579780i | \(0.0184653\pi\) |
−0.835580 | + | 0.549369i | \(0.814868\pi\) | |||||||
\(788\) | 16.8146 | − | 2.78391i | 0.598996 | − | 0.0991727i | ||||
\(789\) | 11.4835 | − | 42.8570i | 0.408823 | − | 1.52575i | ||||
\(790\) | −5.61175 | − | 6.18880i | −0.199657 | − | 0.220188i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −62.3379 | + | 46.2985i | −2.21508 | + | 1.64514i | ||||
\(793\) | −30.5680 | + | 17.6485i | −1.08550 | + | 0.626715i | ||||
\(794\) | 10.0710 | + | 46.5783i | 0.357406 | + | 1.65300i | ||||
\(795\) | 59.4948 | − | 15.9416i | 2.11006 | − | 0.565390i | ||||
\(796\) | 6.18821 | − | 2.80721i | 0.219335 | − | 0.0994990i | ||||
\(797\) | 22.0887 | − | 22.0887i | 0.782423 | − | 0.782423i | −0.197816 | − | 0.980239i | \(-0.563385\pi\) |
0.980239 | + | 0.197816i | \(0.0633850\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.58834 | 0.0915689 | ||||||||
\(800\) | 11.6208 | − | 3.33269i | 0.410856 | − | 0.117828i | ||||
\(801\) | −27.5785 | + | 47.7674i | −0.974438 | + | 1.68778i | ||||
\(802\) | −17.6737 | + | 27.4247i | −0.624081 | + | 0.968400i | ||||
\(803\) | −42.7125 | − | 11.4448i | −1.50729 | − | 0.403877i | ||||
\(804\) | −7.08658 | + | 72.2861i | −0.249924 | + | 2.54934i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.9179 | + | 19.8743i | −0.772026 | + | 0.700041i | ||||
\(807\) | −4.11041 | + | 2.37315i | −0.144693 | + | 0.0835388i | ||||
\(808\) | 35.6455 | − | 4.12518i | 1.25401 | − | 0.145123i | ||||
\(809\) | −13.6366 | − | 7.87312i | −0.479439 | − | 0.276804i | 0.240744 | − | 0.970589i | \(-0.422609\pi\) |
−0.720183 | + | 0.693785i | \(0.755942\pi\) | |||||||
\(810\) | 0.685200 | − | 2.13420i | 0.0240755 | − | 0.0749883i | ||||
\(811\) | −6.94480 | − | 6.94480i | −0.243865 | − | 0.243865i | 0.574582 | − | 0.818447i | \(-0.305165\pi\) |
−0.818447 | + | 0.574582i | \(0.805165\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.4839 | − | 24.4839i | 0.858688 | − | 0.858688i | ||||
\(814\) | 3.86876 | − | 1.98831i | 0.135600 | − | 0.0696902i | ||||
\(815\) | −8.93793 | + | 15.4809i | −0.313082 | + | 0.542274i | ||||
\(816\) | −3.94169 | − | 59.3170i | −0.137987 | − | 2.07651i | ||||
\(817\) | −2.68140 | − | 4.64433i | −0.0938104 | − | 0.162484i | ||||
\(818\) | 1.72654 | − | 35.3072i | 0.0603669 | − | 1.23449i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −30.3541 | + | 24.9339i | −1.06001 | + | 0.870731i | ||||
\(821\) | −2.42598 | + | 9.05390i | −0.0846674 | + | 0.315983i | −0.995251 | − | 0.0973418i | \(-0.968966\pi\) |
0.910584 | + | 0.413325i | \(0.135633\pi\) | |||||||
\(822\) | −15.8120 | + | 3.41880i | −0.551505 | + | 0.119244i | ||||
\(823\) | −28.2638 | − | 16.3181i | −0.985213 | − | 0.568813i | −0.0813732 | − | 0.996684i | \(-0.525931\pi\) |
−0.903840 | + | 0.427871i | \(0.859264\pi\) | |||||||
\(824\) | 9.83196 | − | 3.89302i | 0.342513 | − | 0.135620i | ||||
\(825\) | 33.4594i | 1.16491i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.84782 | + | 4.84782i | 0.168575 | + | 0.168575i | 0.786353 | − | 0.617778i | \(-0.211967\pi\) |
−0.617778 | + | 0.786353i | \(0.711967\pi\) | |||||||
\(828\) | −17.6123 | − | 38.8246i | −0.612071 | − | 1.34925i | ||||
\(829\) | −13.3049 | − | 49.6545i | −0.462098 | − | 1.72457i | −0.666336 | − | 0.745652i | \(-0.732138\pi\) |
0.204238 | − | 0.978921i | \(-0.434528\pi\) | |||||||
\(830\) | −11.0475 | + | 17.1427i | −0.383465 | + | 0.595032i | ||||
\(831\) | 43.5253 | + | 75.3880i | 1.50988 | + | 2.61518i | ||||
\(832\) | 32.9179 | − | 17.6524i | 1.14122 | − | 0.611987i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −33.8235 | − | 1.65398i | −1.17121 | − | 0.0572727i | ||||
\(835\) | 35.7760 | + | 9.58616i | 1.23808 | + | 0.331743i | ||||
\(836\) | 14.6748 | − | 20.4983i | 0.507540 | − | 0.708948i | ||||
\(837\) | 23.6791 | − | 6.34480i | 0.818470 | − | 0.219308i | ||||
\(838\) | 21.1233 | + | 6.78177i | 0.729693 | + | 0.234272i | ||||
\(839\) | 28.0971i | 0.970020i | 0.874509 | + | 0.485010i | \(0.161184\pi\) | ||||
−0.874509 | + | 0.485010i | \(0.838816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6718i | 0.919717i | ||||||||
\(842\) | 0.314233 | − | 0.978749i | 0.0108292 | − | 0.0337299i | ||||
\(843\) | 58.2334 | − | 15.6036i | 2.00566 | − | 0.537416i | ||||
\(844\) | −1.49456 | − | 9.02705i | −0.0514450 | − | 0.310724i | ||||
\(845\) | 22.7083 | + | 6.08467i | 0.781189 | + | 0.209319i | ||||
\(846\) | 0.167515 | − | 3.42564i | 0.00575928 | − | 0.117776i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.2059 | − | 27.1938i | −0.625193 | − | 0.933839i | ||||
\(849\) | 21.1235 | + | 36.5869i | 0.724956 | + | 1.25566i | ||||
\(850\) | −13.3980 | − | 8.63425i | −0.459546 | − | 0.296152i | ||||
\(851\) | 0.618107 | + | 2.30681i | 0.0211884 | + | 0.0790763i | ||||
\(852\) | 32.2365 | − | 85.7680i | 1.10441 | − | 2.93836i | ||||
\(853\) | 20.9925 | + | 20.9925i | 0.718769 | + | 0.718769i | 0.968353 | − | 0.249584i | \(-0.0802940\pi\) |
−0.249584 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.9504i | 1.02428i | ||||||||
\(856\) | 9.28257 | − | 21.4521i | 0.317272 | − | 0.733219i | ||||
\(857\) | 15.6359 | + | 9.02739i | 0.534112 | + | 0.308370i | 0.742689 | − | 0.669636i | \(-0.233550\pi\) |
−0.208577 | + | 0.978006i | \(0.566883\pi\) | |||||||
\(858\) | 21.8477 | + | 101.046i | 0.745867 | + | 3.44964i | ||||
\(859\) | −3.85776 | + | 14.3973i | −0.131625 | + | 0.491231i | −0.999989 | − | 0.00469633i | \(-0.998505\pi\) |
0.868364 | + | 0.495927i | \(0.165172\pi\) | |||||||
\(860\) | 1.23224 | − | 12.5694i | 0.0420191 | − | 0.428613i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 44.8223 | + | 2.19182i | 1.52665 | + | 0.0746538i | ||||
\(863\) | −19.4024 | − | 33.6060i | −0.660467 | − | 1.14396i | −0.980493 | − | 0.196554i | \(-0.937025\pi\) |
0.320026 | − | 0.947409i | \(-0.396308\pi\) | |||||||
\(864\) | −30.9438 | + | 0.541336i | −1.05273 | + | 0.0184166i | ||||
\(865\) | −32.0854 | + | 55.5736i | −1.09094 | + | 1.88956i | ||||
\(866\) | 11.9021 | + | 23.1585i | 0.404450 | + | 0.786959i | ||||
\(867\) | −21.5474 | + | 21.5474i | −0.731789 | + | 0.731789i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.68686 | − | 8.68686i | −0.294681 | − | 0.294681i | ||||
\(870\) | −15.4679 | − | 4.96606i | −0.524411 | − | 0.168365i | ||||
\(871\) | 52.1089 | + | 30.0851i | 1.76564 | + | 1.01939i | ||||
\(872\) | −4.45474 | − | 38.4933i | −0.150857 | − | 1.30355i | ||||
\(873\) | −9.68741 | + | 5.59303i | −0.327869 | + | 0.189295i | ||||
\(874\) | 9.29736 | + | 10.2534i | 0.314488 | + | 0.346827i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −28.4735 | − | 34.6630i | −0.962029 | − | 1.17116i | ||||
\(877\) | −1.32758 | − | 0.355724i | −0.0448291 | − | 0.0120119i | 0.236335 | − | 0.971672i | \(-0.424054\pi\) |
−0.281164 | + | 0.959660i | \(0.590720\pi\) | |||||||
\(878\) | 10.5399 | + | 6.79241i | 0.355706 | + | 0.229233i | ||||
\(879\) | 41.8645 | − | 72.5115i | 1.41206 | − | 2.44575i | ||||
\(880\) | 56.2021 | − | 19.1347i | 1.89457 | − | 0.645031i | ||||
\(881\) | 13.5748 | 0.457347 | 0.228673 | − | 0.973503i | \(-0.426561\pi\) | ||||
0.228673 | + | 0.973503i | \(0.426561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1719 | − | 15.1719i | 0.510576 | − | 0.510576i | −0.404127 | − | 0.914703i | \(-0.632425\pi\) |
0.914703 | + | 0.404127i | \(0.132425\pi\) | |||||||
\(884\) | −46.0989 | − | 17.3266i | −1.55047 | − | 0.582757i | ||||
\(885\) | 26.5894 | − | 7.12462i | 0.893794 | − | 0.239491i | ||||
\(886\) | 10.2142 | − | 2.20847i | 0.343153 | − | 0.0741952i | ||||
\(887\) | −25.9694 | + | 14.9934i | −0.871966 | + | 0.503430i | −0.868001 | − | 0.496562i | \(-0.834595\pi\) |
−0.00396485 | + | 0.999992i | \(0.501262\pi\) | |||||||
\(888\) | 4.36533 | + | 0.644511i | 0.146491 | + | 0.0216284i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 31.2411 | − | 28.3281i | 1.04720 | − | 0.949561i | ||||
\(891\) | 0.853114 | − | 3.18386i | 0.0285804 | − | 0.106663i | ||||
\(892\) | 0.540627 | − | 0.755164i | 0.0181015 | − | 0.0252848i | ||||
\(893\) | 0.288192 | + | 1.07555i | 0.00964397 | + | 0.0359918i | ||||
\(894\) | −5.44317 | − | 10.5911i | −0.182047 | − | 0.354218i | ||||
\(895\) | 51.2755 | 1.71395 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −56.7594 | −1.89514 | ||||||||
\(898\) | 23.6212 | + | 45.9609i | 0.788248 | + | 1.53374i | ||||
\(899\) | −1.76955 | − | 6.60404i | −0.0590177 | − | 0.220257i | ||||
\(900\) | −12.2944 | + | 17.1732i | −0.409814 | + | 0.572442i | ||||
\(901\) | −11.1673 | + | 41.6770i | −0.372038 | + | 1.38846i | ||||
\(902\) | −42.7923 | + | 38.8023i | −1.42483 | + | 1.29198i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.6952 | − | 3.35078i | −0.754830 | − | 0.111445i | ||||
\(905\) | −15.6026 | + | 9.00814i | −0.518647 | + | 0.299441i | ||||
\(906\) | 59.0557 | − | 12.7688i | 1.96200 | − | 0.424214i | ||||
\(907\) | −20.5407 | + | 5.50387i | −0.682043 | + | 0.182753i | −0.583174 | − | 0.812347i | \(-0.698189\pi\) |
−0.0988696 | + | 0.995100i | \(0.531523\pi\) | |||||||
\(908\) | −36.3803 | − | 13.6738i | −1.20732 | − | 0.453781i | ||||
\(909\) | −44.3287 | + | 44.3287i | −1.47029 | + | 1.47029i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.3180 | 0.507506 | 0.253753 | − | 0.967269i | \(-0.418335\pi\) | ||||
0.253753 | + | 0.967269i | \(0.418335\pi\) | |||||||
\(912\) | 24.2094 | − | 8.24240i | 0.801653 | − | 0.272933i | ||||
\(913\) | −14.9950 | + | 25.9721i | −0.496262 | + | 0.859552i | ||||
\(914\) | 18.8326 | + | 12.1366i | 0.622928 | + | 0.401443i | ||||
\(915\) | −54.9746 | − | 14.7304i | −1.81740 | − | 0.486972i | ||||
\(916\) | −1.41522 | − | 1.72286i | −0.0467602 | − | 0.0569250i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 27.4094 | + | 30.2279i | 0.904645 | + | 0.997669i | ||||
\(919\) | −30.8775 | + | 17.8272i | −1.01856 | + | 0.588064i | −0.913685 | − | 0.406422i | \(-0.866776\pi\) |
−0.104871 | + | 0.994486i | \(0.533443\pi\) | |||||||
\(920\) | 3.74728 | + | 32.3801i | 0.123544 | + | 1.06754i | ||||
\(921\) | 2.82384 | + | 1.63035i | 0.0930487 | + | 0.0537217i | ||||
\(922\) | −5.86055 | − | 1.88157i | −0.193007 | − | 0.0619661i | ||||
\(923\) | −53.6727 | − | 53.6727i | −1.76666 | − | 1.76666i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.836591 | − | 0.836591i | 0.0275069 | − | 0.0275069i | ||||
\(926\) | 16.9496 | + | 32.9798i | 0.556999 | + | 1.08378i | ||||
\(927\) | −9.23722 | + | 15.9993i | −0.303390 | + | 0.525487i | ||||
\(928\) | 0.150977 | + | 8.63015i | 0.00495607 | + | 0.283299i | ||||
\(929\) | 12.6992 | + | 21.9956i | 0.416647 | + | 0.721653i | 0.995600 | − | 0.0937078i | \(-0.0298719\pi\) |
−0.578953 | + | 0.815361i | \(0.696539\pi\) | |||||||
\(930\) | −47.6499 | − | 2.33009i | −1.56250 | − | 0.0764068i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.05389 | − | 20.9505i | 0.0672773 | − | 0.686258i | ||||
\(933\) | 5.74103 | − | 21.4258i | 0.187953 | − | 0.701449i | ||||
\(934\) | −0.414259 | − | 1.91595i | −0.0135550 | − | 0.0626918i | ||||
\(935\) | −67.7900 | − | 39.1386i | −2.21697 | − | 1.27997i | ||||
\(936\) | −25.9151 | + | 59.8900i | −0.847060 | + | 1.95757i | ||||
\(937\) | 58.1917i | 1.90104i | 0.310664 | + | 0.950520i | \(0.399449\pi\) | ||||
−0.310664 | + | 0.950520i | \(0.600551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.2055 | + | 10.2055i | 0.333044 | + | 0.333044i | ||||
\(940\) | −0.922601 | + | 2.45466i | −0.0300919 | + | 0.0800621i | ||||
\(941\) | 10.4802 | + | 39.1126i | 0.341645 | + | 1.27504i | 0.896483 | + | 0.443078i | \(0.146113\pi\) |
−0.554838 | + | 0.831958i | \(0.687220\pi\) | |||||||
\(942\) | −35.2711 | − | 22.7303i | −1.14919 | − | 0.740592i | ||||
\(943\) | −15.8575 | − | 27.4660i | −0.516391 | − | 0.894415i | ||||
\(944\) | −8.13658 | − | 12.1535i | −0.264823 | − | 0.395561i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.907103 | − | 18.5500i | 0.0294925 | − | 0.603114i | ||||
\(947\) | −54.7515 | − | 14.6706i | −1.77918 | − | 0.476731i | −0.788750 | − | 0.614714i | \(-0.789271\pi\) |
−0.990435 | + | 0.137983i | \(0.955938\pi\) | |||||||
\(948\) | −2.03566 | − | 12.2952i | −0.0661152 | − | 0.399331i | ||||
\(949\) | −35.8951 | + | 9.61807i | −1.16520 | + | 0.312216i | ||||
\(950\) | 2.09607 | − | 6.52868i | 0.0680056 | − | 0.211818i | ||||
\(951\) | − | 52.5632i | − | 1.70448i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.65307i | 0.312694i | 0.987702 | + | 0.156347i | \(0.0499718\pi\) | ||||
−0.987702 | + | 0.156347i | \(0.950028\pi\) | |||||||
\(954\) | 54.4363 | + | 17.4771i | 1.76244 | + | 0.565843i | ||||
\(955\) | 8.87209 | − | 2.37727i | 0.287094 | − | 0.0769266i | ||||
\(956\) | −25.7186 | + | 35.9246i | −0.831800 | + | 1.16188i | ||||
\(957\) | −23.0754 | − | 6.18304i | −0.745922 | − | 0.199869i | ||||
\(958\) | −10.5084 | − | 0.513865i | −0.339512 | − | 0.0166022i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 57.6584 | + | 17.4051i | 1.86092 | + | 0.561748i | ||||
\(961\) | 5.46119 | + | 9.45906i | 0.176167 | + | 0.305131i | ||||
\(962\) | 1.98020 | − | 3.07272i | 0.0638442 | − | 0.0990684i | ||||
\(963\) | 10.5692 | + | 39.4447i | 0.340587 | + | 1.27109i | ||||
\(964\) | −2.87911 | − | 6.34669i | −0.0927298 | − | 0.204413i | ||||
\(965\) | −41.5819 | − | 41.5819i | −1.33857 | − | 1.33857i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29.5949i | − | 0.951706i | −0.879525 | − | 0.475853i | \(-0.842139\pi\) | ||
0.879525 | − | 0.475853i | \(-0.157861\pi\) | |||||||
\(968\) | 52.2459 | − | 20.6870i | 1.67925 | − | 0.664906i | ||||
\(969\) | −29.2010 | − | 16.8592i | −0.938070 | − | 0.541595i | ||||
\(970\) | 8.35950 | − | 1.80746i | 0.268407 | − | 0.0580339i | ||||
\(971\) | 10.3789 | − | 38.7346i | 0.333075 | − | 1.24305i | −0.572867 | − | 0.819648i | \(-0.694169\pi\) |
0.905942 | − | 0.423403i | \(-0.139164\pi\) | |||||||
\(972\) | −22.7815 | + | 18.7135i | −0.730717 | + | 0.600237i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.06175 | − | 42.1622i | 0.0660626 | − | 1.35097i | ||||
\(975\) | 14.0595 | + | 24.3517i | 0.450263 | + | 0.779879i | ||||
\(976\) | 2.00501 | + | 30.1726i | 0.0641787 | + | 0.965800i | ||||
\(977\) | −10.8910 | + | 18.8638i | −0.348434 | + | 0.603505i | −0.985971 | − | 0.166914i | \(-0.946620\pi\) |
0.637538 | + | 0.770419i | \(0.279953\pi\) | |||||||
\(978\) | −23.7177 | + | 12.1895i | −0.758410 | + | 0.389777i | ||||
\(979\) | 43.8513 | − | 43.8513i | 1.40149 | − | 1.40149i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.8702 | + | 47.8702i | 1.52838 | + | 1.52838i | ||||
\(982\) | −10.5053 | + | 32.7209i | −0.335236 | + | 1.04417i | ||||
\(983\) | −38.5006 | − | 22.2283i | −1.22798 | − | 0.708973i | −0.261371 | − | 0.965238i | \(-0.584175\pi\) |
−0.966607 | + | 0.256265i | \(0.917508\pi\) | |||||||
\(984\) | −58.2114 | + | 6.73667i | −1.85571 | + | 0.214757i | ||||
\(985\) | 19.7161 | − | 11.3831i | 0.628206 | − | 0.362695i | ||||
\(986\) | 8.43048 | − | 7.64441i | 0.268481 | − | 0.243448i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.06706 | − | 21.0849i | 0.0657619 | − | 0.670800i | ||||
\(989\) | 9.84933 | + | 2.63912i | 0.313190 | + | 0.0839191i | ||||
\(990\) | −56.1867 | + | 87.1862i | −1.78573 | + | 2.77096i | ||||
\(991\) | −13.3978 | + | 23.2057i | −0.425596 | + | 0.737154i | −0.996476 | − | 0.0838794i | \(-0.973269\pi\) |
0.570880 | + | 0.821034i | \(0.306602\pi\) | |||||||
\(992\) | 6.98760 | + | 24.3651i | 0.221857 | + | 0.773592i | ||||
\(993\) | −36.7366 | −1.16580 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.41824 | − | 6.41824i | 0.203472 | − | 0.203472i | ||||
\(996\) | −27.7059 | + | 12.5685i | −0.877896 | + | 0.398248i | ||||
\(997\) | 43.4209 | − | 11.6346i | 1.37515 | − | 0.368471i | 0.505795 | − | 0.862654i | \(-0.331199\pi\) |
0.869358 | + | 0.494183i | \(0.164533\pi\) | |||||||
\(998\) | −3.61854 | − | 16.7358i | −0.114543 | − | 0.529762i | ||||
\(999\) | −2.62302 | + | 1.51440i | −0.0829887 | + | 0.0479136i |
(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 | 784.2.x.p.165.9 | 96 | ||
7.2 | even | 3 | inner | 784.2.x.p.373.8 | 96 | ||
7.3 | odd | 6 | 784.2.m.l.197.24 | yes | 48 | ||
7.4 | even | 3 | 784.2.m.l.197.23 | ✓ | 48 | ||
7.5 | odd | 6 | inner | 784.2.x.p.373.7 | 96 | ||
7.6 | odd | 2 | inner | 784.2.x.p.165.10 | 96 | ||
16.13 | even | 4 | inner | 784.2.x.p.557.8 | 96 | ||
112.13 | odd | 4 | inner | 784.2.x.p.557.7 | 96 | ||
112.45 | odd | 12 | 784.2.m.l.589.24 | yes | 48 | ||
112.61 | odd | 12 | inner | 784.2.x.p.765.10 | 96 | ||
112.93 | even | 12 | inner | 784.2.x.p.765.9 | 96 | ||
112.109 | even | 12 | 784.2.m.l.589.23 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.m.l.197.23 | ✓ | 48 | 7.4 | even | 3 | ||
784.2.m.l.197.24 | yes | 48 | 7.3 | odd | 6 | ||
784.2.m.l.589.23 | yes | 48 | 112.109 | even | 12 | ||
784.2.m.l.589.24 | yes | 48 | 112.45 | odd | 12 | ||
784.2.x.p.165.9 | 96 | 1.1 | even | 1 | trivial | ||
784.2.x.p.165.10 | 96 | 7.6 | odd | 2 | inner | ||
784.2.x.p.373.7 | 96 | 7.5 | odd | 6 | inner | ||
784.2.x.p.373.8 | 96 | 7.2 | even | 3 | inner | ||
784.2.x.p.557.7 | 96 | 112.13 | odd | 4 | inner | ||
784.2.x.p.557.8 | 96 | 16.13 | even | 4 | inner | ||
784.2.x.p.765.9 | 96 | 112.93 | even | 12 | inner | ||
784.2.x.p.765.10 | 96 | 112.61 | odd | 12 | inner |