Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 311.4 | ||
Character | \(\chi\) | \(=\) | 630.311 |
Dual form | 630.2.t.c.551.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.423533 | + | 1.67947i | −0.244527 | + | 0.969643i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.20653 | − | 1.24270i | 0.492562 | − | 0.507329i | ||||
\(7\) | 2.20024 | − | 1.46933i | 0.831614 | − | 0.555354i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.64124 | − | 1.42262i | −0.880413 | − | 0.474207i | ||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | − | 4.43825i | − | 1.33818i | −0.743181 | − | 0.669091i | \(-0.766684\pi\) | ||
0.743181 | − | 0.669091i | \(-0.233316\pi\) | |||||||
\(12\) | −1.66623 | + | 0.472945i | −0.480999 | + | 0.136527i | ||||
\(13\) | −4.51990 | − | 2.60957i | −1.25360 | − | 0.723763i | −0.281773 | − | 0.959481i | \(-0.590923\pi\) |
−0.971822 | + | 0.235717i | \(0.924256\pi\) | |||||||
\(14\) | −2.64013 | + | 0.172355i | −0.705605 | + | 0.0460638i | ||||
\(15\) | −0.423533 | + | 1.67947i | −0.109356 | + | 0.433637i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.46981 | − | 6.00989i | 0.841552 | − | 1.45761i | −0.0470295 | − | 0.998894i | \(-0.514975\pi\) |
0.888582 | − | 0.458718i | \(-0.151691\pi\) | |||||||
\(18\) | 1.57607 | + | 2.55265i | 0.371483 | + | 0.601664i | ||||
\(19\) | −2.43077 | + | 1.40341i | −0.557657 | + | 0.321963i | −0.752204 | − | 0.658930i | \(-0.771009\pi\) |
0.194548 | + | 0.980893i | \(0.437676\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | 1.53582 | + | 4.31755i | 0.335143 | + | 0.942167i | ||||
\(22\) | −2.21912 | + | 3.84363i | −0.473119 | + | 0.819466i | ||||
\(23\) | − | 3.48491i | − | 0.726653i | −0.931662 | − | 0.363326i | \(-0.881641\pi\) | ||
0.931662 | − | 0.363326i | \(-0.118359\pi\) | |||||||
\(24\) | 1.67947 | + | 0.423533i | 0.342820 | + | 0.0864533i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.60957 | + | 4.51990i | 0.511778 | + | 0.886426i | ||||
\(27\) | 3.50790 | − | 3.83336i | 0.675096 | − | 0.737730i | ||||
\(28\) | 2.37260 | + | 1.17080i | 0.448379 | + | 0.221261i | ||||
\(29\) | −6.40344 | + | 3.69703i | −1.18909 | + | 0.686521i | −0.958100 | − | 0.286435i | \(-0.907530\pi\) |
−0.230990 | + | 0.972956i | \(0.574196\pi\) | |||||||
\(30\) | 1.20653 | − | 1.24270i | 0.220280 | − | 0.226884i | ||||
\(31\) | −1.82054 | + | 1.05109i | −0.326979 | + | 0.188781i | −0.654499 | − | 0.756063i | \(-0.727120\pi\) |
0.327520 | + | 0.944844i | \(0.393787\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 7.45390 | + | 1.87974i | 1.29756 | + | 0.327221i | ||||
\(34\) | −6.00989 | + | 3.46981i | −1.03069 | + | 0.595067i | ||||
\(35\) | 2.20024 | − | 1.46933i | 0.371909 | − | 0.248362i | ||||
\(36\) | −0.0885938 | − | 2.99869i | −0.0147656 | − | 0.499782i | ||||
\(37\) | 4.36995 | + | 7.56898i | 0.718416 | + | 1.24433i | 0.961627 | + | 0.274359i | \(0.0884658\pi\) |
−0.243211 | + | 0.969973i | \(0.578201\pi\) | |||||||
\(38\) | 2.80681 | 0.455325 | ||||||||
\(39\) | 6.29702 | − | 6.48580i | 1.00833 | − | 1.03856i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 2.90122 | − | 5.02506i | 0.453094 | − | 0.784782i | −0.545482 | − | 0.838122i | \(-0.683653\pi\) |
0.998576 | + | 0.0533403i | \(0.0169868\pi\) | |||||||
\(42\) | 0.828717 | − | 4.50702i | 0.127874 | − | 0.695448i | ||||
\(43\) | −1.02568 | − | 1.77653i | −0.156415 | − | 0.270919i | 0.777158 | − | 0.629305i | \(-0.216660\pi\) |
−0.933573 | + | 0.358386i | \(0.883327\pi\) | |||||||
\(44\) | 3.84363 | − | 2.21912i | 0.579450 | − | 0.334545i | ||||
\(45\) | −2.64124 | − | 1.42262i | −0.393733 | − | 0.212072i | ||||
\(46\) | −1.74245 | + | 3.01802i | −0.256911 | + | 0.444982i | ||||
\(47\) | 5.16742 | − | 8.95023i | 0.753745 | − | 1.30552i | −0.192251 | − | 0.981346i | \(-0.561579\pi\) |
0.945996 | − | 0.324179i | \(-0.105088\pi\) | |||||||
\(48\) | −1.24270 | − | 1.20653i | −0.179368 | − | 0.174147i | ||||
\(49\) | 2.68214 | − | 6.46576i | 0.383163 | − | 0.923681i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 8.62385 | + | 8.37283i | 1.20758 | + | 1.17243i | ||||
\(52\) | − | 5.21913i | − | 0.723763i | ||||||
\(53\) | −4.60281 | − | 2.65743i | −0.632245 | − | 0.365027i | 0.149376 | − | 0.988780i | \(-0.452273\pi\) |
−0.781621 | + | 0.623754i | \(0.785607\pi\) | |||||||
\(54\) | −4.95461 | + | 1.56583i | −0.674237 | + | 0.213083i | ||||
\(55\) | − | 4.43825i | − | 0.598453i | ||||||
\(56\) | −1.46933 | − | 2.20024i | −0.196347 | − | 0.294020i | ||||
\(57\) | −1.32747 | − | 4.67679i | −0.175827 | − | 0.619456i | ||||
\(58\) | 7.39406 | 0.970887 | ||||||||
\(59\) | −0.534861 | − | 0.926406i | −0.0696329 | − | 0.120608i | 0.829107 | − | 0.559090i | \(-0.188849\pi\) |
−0.898740 | + | 0.438482i | \(0.855516\pi\) | |||||||
\(60\) | −1.66623 | + | 0.472945i | −0.215109 | + | 0.0610569i | ||||
\(61\) | 5.23536 | + | 3.02264i | 0.670319 | + | 0.387009i | 0.796198 | − | 0.605037i | \(-0.206842\pi\) |
−0.125878 | + | 0.992046i | \(0.540175\pi\) | |||||||
\(62\) | 2.10218 | 0.266977 | ||||||||
\(63\) | −7.90167 | + | 0.750738i | −0.995517 | + | 0.0945842i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.51990 | − | 2.60957i | −0.560625 | − | 0.323677i | ||||
\(66\) | −5.51540 | − | 5.35486i | −0.678899 | − | 0.659137i | ||||
\(67\) | −2.46400 | − | 4.26778i | −0.301026 | − | 0.521392i | 0.675343 | − | 0.737504i | \(-0.263996\pi\) |
−0.976369 | + | 0.216112i | \(0.930662\pi\) | |||||||
\(68\) | 6.93962 | 0.841552 | ||||||||
\(69\) | 5.85279 | + | 1.47597i | 0.704594 | + | 0.177686i | ||||
\(70\) | −2.64013 | + | 0.172355i | −0.315556 | + | 0.0206004i | ||||
\(71\) | 11.5388i | 1.36940i | 0.728825 | + | 0.684700i | \(0.240067\pi\) | ||||
−0.728825 | + | 0.684700i | \(0.759933\pi\) | |||||||
\(72\) | −1.42262 | + | 2.64124i | −0.167658 | + | 0.311273i | ||||
\(73\) | 13.1874 | + | 7.61374i | 1.54347 | + | 0.891121i | 0.998616 | + | 0.0525873i | \(0.0167468\pi\) |
0.544850 | + | 0.838533i | \(0.316587\pi\) | |||||||
\(74\) | − | 8.73991i | − | 1.01599i | ||||||
\(75\) | −0.423533 | + | 1.67947i | −0.0489054 | + | 0.193929i | ||||
\(76\) | −2.43077 | − | 1.40341i | −0.278828 | − | 0.160982i | ||||
\(77\) | −6.52125 | − | 9.76522i | −0.743165 | − | 1.11285i | ||||
\(78\) | −8.69628 | + | 2.46836i | −0.984659 | + | 0.279487i | ||||
\(79\) | −3.88551 | + | 6.72991i | −0.437155 | + | 0.757174i | −0.997469 | − | 0.0711063i | \(-0.977347\pi\) |
0.560314 | + | 0.828280i | \(0.310680\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | 4.95230 | + | 7.51497i | 0.550255 | + | 0.834997i | ||||
\(82\) | −5.02506 | + | 2.90122i | −0.554925 | + | 0.320386i | ||||
\(83\) | −2.84720 | − | 4.93150i | −0.312521 | − | 0.541302i | 0.666387 | − | 0.745606i | \(-0.267840\pi\) |
−0.978907 | + | 0.204304i | \(0.934507\pi\) | |||||||
\(84\) | −2.97120 | + | 3.48884i | −0.324185 | + | 0.380663i | ||||
\(85\) | 3.46981 | − | 6.00989i | 0.376354 | − | 0.651864i | ||||
\(86\) | 2.05136i | 0.221204i | ||||||||
\(87\) | −3.49698 | − | 12.3202i | −0.374916 | − | 1.32086i | ||||
\(88\) | −4.43825 | −0.473119 | ||||||||
\(89\) | 4.16961 | + | 7.22198i | 0.441978 | + | 0.765528i | 0.997836 | − | 0.0657488i | \(-0.0209436\pi\) |
−0.555858 | + | 0.831277i | \(0.687610\pi\) | |||||||
\(90\) | 1.57607 | + | 2.55265i | 0.166132 | + | 0.269073i | ||||
\(91\) | −13.7792 | + | 0.899543i | −1.44445 | + | 0.0942977i | ||||
\(92\) | 3.01802 | − | 1.74245i | 0.314650 | − | 0.181663i | ||||
\(93\) | −0.994216 | − | 3.50272i | −0.103095 | − | 0.363215i | ||||
\(94\) | −8.95023 | + | 5.16742i | −0.923145 | + | 0.532978i | ||||
\(95\) | −2.43077 | + | 1.40341i | −0.249392 | + | 0.143986i | ||||
\(96\) | 0.472945 | + | 1.66623i | 0.0482697 | + | 0.170059i | ||||
\(97\) | −11.4765 | + | 6.62595i | −1.16526 | + | 0.672763i | −0.952559 | − | 0.304354i | \(-0.901559\pi\) |
−0.212701 | + | 0.977117i | \(0.568226\pi\) | |||||||
\(98\) | −5.55569 | + | 4.25845i | −0.561209 | + | 0.430168i | ||||
\(99\) | −6.31395 | + | 11.7225i | −0.634575 | + | 1.17815i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 18.1043 | 1.80144 | 0.900721 | − | 0.434399i | \(-0.143039\pi\) | ||||
0.900721 | + | 0.434399i | \(0.143039\pi\) | |||||||
\(102\) | −3.28206 | − | 11.5630i | −0.324972 | − | 1.14491i | ||||
\(103\) | − | 9.83724i | − | 0.969292i | −0.874710 | − | 0.484646i | \(-0.838948\pi\) | ||
0.874710 | − | 0.484646i | \(-0.161052\pi\) | |||||||
\(104\) | −2.60957 | + | 4.51990i | −0.255889 | + | 0.443213i | ||||
\(105\) | 1.53582 | + | 4.31755i | 0.149881 | + | 0.421350i | ||||
\(106\) | 2.65743 | + | 4.60281i | 0.258113 | + | 0.447064i | ||||
\(107\) | 10.4663 | − | 6.04270i | 1.01181 | − | 0.584170i | 0.100090 | − | 0.994978i | \(-0.468087\pi\) |
0.911722 | + | 0.410809i | \(0.134754\pi\) | |||||||
\(108\) | 5.07374 | + | 1.12125i | 0.488220 | + | 0.107893i | ||||
\(109\) | −1.65320 | + | 2.86343i | −0.158348 | + | 0.274267i | −0.934273 | − | 0.356558i | \(-0.883950\pi\) |
0.775925 | + | 0.630825i | \(0.217283\pi\) | |||||||
\(110\) | −2.21912 | + | 3.84363i | −0.211585 | + | 0.366476i | ||||
\(111\) | −14.5627 | + | 4.13349i | −1.38223 | + | 0.392334i | ||||
\(112\) | 0.172355 | + | 2.64013i | 0.0162860 | + | 0.249469i | ||||
\(113\) | 2.79421 | + | 1.61324i | 0.262857 | + | 0.151760i | 0.625637 | − | 0.780114i | \(-0.284839\pi\) |
−0.362780 | + | 0.931875i | \(0.618172\pi\) | |||||||
\(114\) | −1.18878 | + | 4.71395i | −0.111339 | + | 0.441502i | ||||
\(115\) | − | 3.48491i | − | 0.324969i | ||||||
\(116\) | −6.40344 | − | 3.69703i | −0.594545 | − | 0.343260i | ||||
\(117\) | 8.22572 | + | 13.3226i | 0.760468 | + | 1.23167i | ||||
\(118\) | 1.06972i | 0.0984758i | ||||||||
\(119\) | −1.19608 | − | 18.3215i | −0.109644 | − | 1.67953i | ||||
\(120\) | 1.67947 | + | 0.423533i | 0.153314 | + | 0.0386631i | ||||
\(121\) | −8.69804 | −0.790731 | ||||||||
\(122\) | −3.02264 | − | 5.23536i | −0.273657 | − | 0.473987i | ||||
\(123\) | 7.21067 | + | 7.00079i | 0.650164 | + | 0.631240i | ||||
\(124\) | −1.82054 | − | 1.05109i | −0.163489 | − | 0.0943907i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 7.21842 | + | 3.30068i | 0.643068 | + | 0.294048i | ||||
\(127\) | 4.10553 | 0.364307 | 0.182154 | − | 0.983270i | \(-0.441693\pi\) | ||||
0.182154 | + | 0.983270i | \(0.441693\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 3.41805 | − | 0.970182i | 0.300942 | − | 0.0854198i | ||||
\(130\) | 2.60957 | + | 4.51990i | 0.228874 | + | 0.396422i | ||||
\(131\) | −19.4136 | −1.69618 | −0.848089 | − | 0.529854i | \(-0.822247\pi\) | ||||
−0.848089 | + | 0.529854i | \(0.822247\pi\) | |||||||
\(132\) | 2.09905 | + | 7.39514i | 0.182699 | + | 0.643664i | ||||
\(133\) | −3.28622 | + | 6.65943i | −0.284951 | + | 0.577446i | ||||
\(134\) | 4.92801i | 0.425715i | ||||||||
\(135\) | 3.50790 | − | 3.83336i | 0.301912 | − | 0.329923i | ||||
\(136\) | −6.00989 | − | 3.46981i | −0.515343 | − | 0.297534i | ||||
\(137\) | 9.19632i | 0.785695i | 0.919604 | + | 0.392847i | \(0.128510\pi\) | ||||
−0.919604 | + | 0.392847i | \(0.871490\pi\) | |||||||
\(138\) | −4.33068 | − | 4.20463i | −0.368652 | − | 0.357922i | ||||
\(139\) | −8.90078 | − | 5.13887i | −0.754954 | − | 0.435873i | 0.0725271 | − | 0.997366i | \(-0.476894\pi\) |
−0.827481 | + | 0.561494i | \(0.810227\pi\) | |||||||
\(140\) | 2.37260 | + | 1.17080i | 0.200521 | + | 0.0989508i | ||||
\(141\) | 12.8431 | + | 12.4692i | 1.08158 | + | 1.05010i | ||||
\(142\) | 5.76938 | − | 9.99286i | 0.484156 | − | 0.838582i | ||||
\(143\) | −11.5819 | + | 20.0604i | −0.968527 | + | 1.67754i | ||||
\(144\) | 2.55265 | − | 1.57607i | 0.212721 | − | 0.131339i | ||||
\(145\) | −6.40344 | + | 3.69703i | −0.531777 | + | 0.307021i | ||||
\(146\) | −7.61374 | − | 13.1874i | −0.630118 | − | 1.09140i | ||||
\(147\) | 9.72308 | + | 7.24304i | 0.801946 | + | 0.597396i | ||||
\(148\) | −4.36995 | + | 7.56898i | −0.359208 | + | 0.622166i | ||||
\(149\) | 15.3288i | 1.25578i | 0.778302 | + | 0.627890i | \(0.216081\pi\) | ||||
−0.778302 | + | 0.627890i | \(0.783919\pi\) | |||||||
\(150\) | 1.20653 | − | 1.24270i | 0.0985124 | − | 0.101466i | ||||
\(151\) | 5.74675 | 0.467664 | 0.233832 | − | 0.972277i | \(-0.424873\pi\) | ||||
0.233832 | + | 0.972277i | \(0.424873\pi\) | |||||||
\(152\) | 1.40341 | + | 2.43077i | 0.113831 | + | 0.197161i | ||||
\(153\) | −17.7144 | + | 10.9373i | −1.43212 | + | 0.884230i | ||||
\(154\) | 0.764954 | + | 11.7176i | 0.0616417 | + | 0.944228i | ||||
\(155\) | −1.82054 | + | 1.05109i | −0.146229 | + | 0.0844256i | ||||
\(156\) | 8.76538 | + | 2.21047i | 0.701792 | + | 0.176980i | ||||
\(157\) | 6.17457 | − | 3.56489i | 0.492784 | − | 0.284509i | −0.232945 | − | 0.972490i | \(-0.574836\pi\) |
0.725729 | + | 0.687981i | \(0.241503\pi\) | |||||||
\(158\) | 6.72991 | − | 3.88551i | 0.535403 | − | 0.309115i | ||||
\(159\) | 6.41252 | − | 6.60477i | 0.508546 | − | 0.523792i | ||||
\(160\) | 0.866025 | − | 0.500000i | 0.0684653 | − | 0.0395285i | ||||
\(161\) | −5.12047 | − | 7.66764i | −0.403550 | − | 0.604295i | ||||
\(162\) | −0.531331 | − | 8.98430i | −0.0417453 | − | 0.705873i | ||||
\(163\) | −1.11012 | − | 1.92279i | −0.0869517 | − | 0.150605i | 0.819270 | − | 0.573409i | \(-0.194379\pi\) |
−0.906221 | + | 0.422804i | \(0.861046\pi\) | |||||||
\(164\) | 5.80244 | 0.453094 | ||||||||
\(165\) | 7.45390 | + | 1.87974i | 0.580286 | + | 0.146338i | ||||
\(166\) | 5.69440i | 0.441971i | ||||||||
\(167\) | 7.27271 | − | 12.5967i | 0.562779 | − | 0.974762i | −0.434473 | − | 0.900685i | \(-0.643065\pi\) |
0.997252 | − | 0.0740777i | \(-0.0236013\pi\) | |||||||
\(168\) | 4.31755 | − | 1.53582i | 0.333106 | − | 0.118491i | ||||
\(169\) | 7.11967 | + | 12.3316i | 0.547667 | + | 0.948587i | ||||
\(170\) | −6.00989 | + | 3.46981i | −0.460937 | + | 0.266122i | ||||
\(171\) | 8.41676 | − | 0.248666i | 0.643646 | − | 0.0190160i | ||||
\(172\) | 1.02568 | − | 1.77653i | 0.0782075 | − | 0.135459i | ||||
\(173\) | −1.25357 | + | 2.17125i | −0.0953073 | + | 0.165077i | −0.909737 | − | 0.415185i | \(-0.863717\pi\) |
0.814430 | + | 0.580262i | \(0.197050\pi\) | |||||||
\(174\) | −3.13163 | + | 12.4181i | −0.237408 | + | 0.941414i | ||||
\(175\) | 2.20024 | − | 1.46933i | 0.166323 | − | 0.111071i | ||||
\(176\) | 3.84363 | + | 2.21912i | 0.289725 | + | 0.167273i | ||||
\(177\) | 1.78240 | − | 0.505919i | 0.133974 | − | 0.0380272i | ||||
\(178\) | − | 8.33922i | − | 0.625051i | ||||||
\(179\) | 6.45012 | + | 3.72398i | 0.482105 | + | 0.278343i | 0.721293 | − | 0.692630i | \(-0.243548\pi\) |
−0.239188 | + | 0.970973i | \(0.576881\pi\) | |||||||
\(180\) | −0.0885938 | − | 2.99869i | −0.00660339 | − | 0.223509i | ||||
\(181\) | − | 6.18571i | − | 0.459780i | −0.973217 | − | 0.229890i | \(-0.926163\pi\) | ||
0.973217 | − | 0.229890i | \(-0.0738367\pi\) | |||||||
\(182\) | 12.3829 | + | 6.11057i | 0.917882 | + | 0.452946i | ||||
\(183\) | −7.29377 | + | 7.51244i | −0.539171 | + | 0.555336i | ||||
\(184\) | −3.48491 | −0.256911 | ||||||||
\(185\) | 4.36995 | + | 7.56898i | 0.321285 | + | 0.556482i | ||||
\(186\) | −0.890342 | + | 3.53055i | −0.0652831 | + | 0.258872i | ||||
\(187\) | −26.6734 | − | 15.3999i | −1.95055 | − | 1.12615i | ||||
\(188\) | 10.3348 | 0.753745 | ||||||||
\(189\) | 2.08577 | − | 13.5886i | 0.151718 | − | 0.988424i | ||||
\(190\) | 2.80681 | 0.203627 | ||||||||
\(191\) | −19.9088 | − | 11.4944i | −1.44055 | − | 0.831704i | −0.442667 | − | 0.896686i | \(-0.645968\pi\) |
−0.997886 | + | 0.0649822i | \(0.979301\pi\) | |||||||
\(192\) | 0.423533 | − | 1.67947i | 0.0305658 | − | 0.121205i | ||||
\(193\) | 5.44323 | + | 9.42795i | 0.391812 | + | 0.678638i | 0.992689 | − | 0.120703i | \(-0.0385150\pi\) |
−0.600877 | + | 0.799342i | \(0.705182\pi\) | |||||||
\(194\) | 13.2519 | 0.951431 | ||||||||
\(195\) | 6.29702 | − | 6.48580i | 0.450939 | − | 0.464458i | ||||
\(196\) | 6.94059 | − | 0.910079i | 0.495756 | − | 0.0650057i | ||||
\(197\) | 7.07434i | 0.504026i | 0.967724 | + | 0.252013i | \(0.0810926\pi\) | ||||
−0.967724 | + | 0.252013i | \(0.918907\pi\) | |||||||
\(198\) | 11.3293 | − | 6.99499i | 0.805137 | − | 0.497112i | ||||
\(199\) | 15.9968 | + | 9.23577i | 1.13398 | + | 0.654706i | 0.944934 | − | 0.327261i | \(-0.106126\pi\) |
0.189051 | + | 0.981967i | \(0.439459\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 8.21120 | − | 2.33068i | 0.579173 | − | 0.164393i | ||||
\(202\) | −15.6788 | − | 9.05213i | −1.10315 | − | 0.636906i | ||||
\(203\) | −8.65698 | + | 17.5431i | −0.607601 | + | 1.23129i | ||||
\(204\) | −2.93916 | + | 11.6549i | −0.205782 | + | 0.816005i | ||||
\(205\) | 2.90122 | − | 5.02506i | 0.202630 | − | 0.350965i | ||||
\(206\) | −4.91862 | + | 8.51930i | −0.342697 | + | 0.593568i | ||||
\(207\) | −4.95770 | + | 9.20447i | −0.344584 | + | 0.639755i | ||||
\(208\) | 4.51990 | − | 2.60957i | 0.313399 | − | 0.180941i | ||||
\(209\) | 6.22866 | + | 10.7884i | 0.430845 | + | 0.746246i | ||||
\(210\) | 0.828717 | − | 4.50702i | 0.0571869 | − | 0.311014i | ||||
\(211\) | −3.88575 | + | 6.73032i | −0.267506 | + | 0.463334i | −0.968217 | − | 0.250111i | \(-0.919533\pi\) |
0.700711 | + | 0.713445i | \(0.252866\pi\) | |||||||
\(212\) | − | 5.31487i | − | 0.365027i | ||||||
\(213\) | −19.3790 | − | 4.88704i | −1.32783 | − | 0.334855i | ||||
\(214\) | −12.0854 | −0.826141 | ||||||||
\(215\) | −1.02568 | − | 1.77653i | −0.0699509 | − | 0.121159i | ||||
\(216\) | −3.83336 | − | 3.50790i | −0.260827 | − | 0.238682i | ||||
\(217\) | −2.46124 | + | 4.98763i | −0.167080 | + | 0.338582i | ||||
\(218\) | 2.86343 | − | 1.65320i | 0.193936 | − | 0.111969i | ||||
\(219\) | −18.3723 | + | 18.9231i | −1.24149 | + | 1.27871i | ||||
\(220\) | 3.84363 | − | 2.21912i | 0.259138 | − | 0.149613i | ||||
\(221\) | −31.3664 | + | 18.1094i | −2.10993 | + | 1.21817i | ||||
\(222\) | 14.6784 | + | 3.70164i | 0.985150 | + | 0.248438i | ||||
\(223\) | 1.25245 | − | 0.723100i | 0.0838699 | − | 0.0484223i | −0.457479 | − | 0.889221i | \(-0.651247\pi\) |
0.541348 | + | 0.840798i | \(0.317914\pi\) | |||||||
\(224\) | 1.17080 | − | 2.37260i | 0.0782275 | − | 0.158526i | ||||
\(225\) | −2.64124 | − | 1.42262i | −0.176083 | − | 0.0948414i | ||||
\(226\) | −1.61324 | − | 2.79421i | −0.107311 | − | 0.185868i | ||||
\(227\) | −8.46455 | −0.561812 | −0.280906 | − | 0.959735i | \(-0.590635\pi\) | ||||
−0.280906 | + | 0.959735i | \(0.590635\pi\) | |||||||
\(228\) | 3.38649 | − | 3.48802i | 0.224276 | − | 0.230999i | ||||
\(229\) | − | 13.7837i | − | 0.910853i | −0.890273 | − | 0.455427i | \(-0.849487\pi\) | ||
0.890273 | − | 0.455427i | \(-0.150513\pi\) | |||||||
\(230\) | −1.74245 | + | 3.01802i | −0.114894 | + | 0.199002i | ||||
\(231\) | 19.1624 | − | 6.81635i | 1.26079 | − | 0.448483i | ||||
\(232\) | 3.69703 | + | 6.40344i | 0.242722 | + | 0.420406i | ||||
\(233\) | 16.7359 | − | 9.66250i | 1.09641 | − | 0.633011i | 0.161133 | − | 0.986933i | \(-0.448485\pi\) |
0.935275 | + | 0.353921i | \(0.115152\pi\) | |||||||
\(234\) | −0.462383 | − | 15.6506i | −0.0302269 | − | 1.02311i | ||||
\(235\) | 5.16742 | − | 8.95023i | 0.337085 | − | 0.583848i | ||||
\(236\) | 0.534861 | − | 0.926406i | 0.0348165 | − | 0.0603039i | ||||
\(237\) | −9.65704 | − | 9.37594i | −0.627292 | − | 0.609033i | ||||
\(238\) | −8.12492 | + | 16.4649i | −0.526660 | + | 1.06726i | ||||
\(239\) | −7.14170 | − | 4.12327i | −0.461958 | − | 0.266712i | 0.250909 | − | 0.968011i | \(-0.419271\pi\) |
−0.712867 | + | 0.701299i | \(0.752604\pi\) | |||||||
\(240\) | −1.24270 | − | 1.20653i | −0.0802158 | − | 0.0778809i | ||||
\(241\) | − | 23.9106i | − | 1.54022i | −0.637914 | − | 0.770108i | \(-0.720203\pi\) | ||
0.637914 | − | 0.770108i | \(-0.279797\pi\) | |||||||
\(242\) | 7.53272 | + | 4.34902i | 0.484222 | + | 0.279566i | ||||
\(243\) | −14.7186 | + | 5.13440i | −0.944200 | + | 0.329372i | ||||
\(244\) | 6.04527i | 0.387009i | ||||||||
\(245\) | 2.68214 | − | 6.46576i | 0.171356 | − | 0.413083i | ||||
\(246\) | −2.74423 | − | 9.66820i | −0.174966 | − | 0.616422i | ||||
\(247\) | 14.6491 | 0.932101 | ||||||||
\(248\) | 1.05109 | + | 1.82054i | 0.0667443 | + | 0.115605i | ||||
\(249\) | 9.48818 | − | 2.69314i | 0.601289 | − | 0.170671i | ||||
\(250\) | −0.866025 | − | 0.500000i | −0.0547723 | − | 0.0316228i | ||||
\(251\) | −21.8070 | −1.37644 | −0.688222 | − | 0.725500i | \(-0.741609\pi\) | ||||
−0.688222 | + | 0.725500i | \(0.741609\pi\) | |||||||
\(252\) | −4.60099 | − | 6.46768i | −0.289835 | − | 0.407425i | ||||
\(253\) | −15.4669 | −0.972394 | ||||||||
\(254\) | −3.55550 | − | 2.05277i | −0.223092 | − | 0.128802i | ||||
\(255\) | 8.62385 | + | 8.37283i | 0.540046 | + | 0.524327i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.0751 | −0.628471 | −0.314235 | − | 0.949345i | \(-0.601748\pi\) | ||||
−0.314235 | + | 0.949345i | \(0.601748\pi\) | |||||||
\(258\) | −3.44521 | − | 0.868820i | −0.214489 | − | 0.0540904i | ||||
\(259\) | 20.7363 | + | 10.2327i | 1.28849 | + | 0.635829i | ||||
\(260\) | − | 5.21913i | − | 0.323677i | ||||||
\(261\) | 22.1725 | − | 0.655068i | 1.37244 | − | 0.0405477i | ||||
\(262\) | 16.8127 | + | 9.70682i | 1.03869 | + | 0.599690i | ||||
\(263\) | − | 1.97563i | − | 0.121823i | −0.998143 | − | 0.0609113i | \(-0.980599\pi\) | ||
0.998143 | − | 0.0609113i | \(-0.0194007\pi\) | |||||||
\(264\) | 1.87974 | − | 7.45390i | 0.115690 | − | 0.458756i | ||||
\(265\) | −4.60281 | − | 2.65743i | −0.282748 | − | 0.163245i | ||||
\(266\) | 6.17567 | − | 4.12413i | 0.378654 | − | 0.252867i | ||||
\(267\) | −13.8951 | + | 3.94399i | −0.850364 | + | 0.241368i | ||||
\(268\) | 2.46400 | − | 4.26778i | 0.150513 | − | 0.260696i | ||||
\(269\) | 4.12540 | − | 7.14541i | 0.251530 | − | 0.435663i | −0.712417 | − | 0.701756i | \(-0.752400\pi\) |
0.963947 | + | 0.266093i | \(0.0857329\pi\) | |||||||
\(270\) | −4.95461 | + | 1.56583i | −0.301528 | + | 0.0952936i | ||||
\(271\) | 24.8880 | − | 14.3691i | 1.51184 | − | 0.872859i | 0.511932 | − | 0.859026i | \(-0.328930\pi\) |
0.999904 | − | 0.0138328i | \(-0.00440326\pi\) | |||||||
\(272\) | 3.46981 | + | 6.00989i | 0.210388 | + | 0.364403i | ||||
\(273\) | 4.32519 | − | 23.5227i | 0.261772 | − | 1.42366i | ||||
\(274\) | 4.59816 | − | 7.96425i | 0.277785 | − | 0.481138i | ||||
\(275\) | − | 4.43825i | − | 0.267636i | ||||||
\(276\) | 1.64817 | + | 5.80665i | 0.0992081 | + | 0.349520i | ||||
\(277\) | 20.4226 | 1.22707 | 0.613537 | − | 0.789666i | \(-0.289746\pi\) | ||||
0.613537 | + | 0.789666i | \(0.289746\pi\) | |||||||
\(278\) | 5.13887 | + | 8.90078i | 0.308209 | + | 0.533833i | ||||
\(279\) | 6.30379 | − | 0.186240i | 0.377398 | − | 0.0111499i | ||||
\(280\) | −1.46933 | − | 2.20024i | −0.0878092 | − | 0.131490i | ||||
\(281\) | −1.53417 | + | 0.885754i | −0.0915209 | + | 0.0528396i | −0.545062 | − | 0.838396i | \(-0.683494\pi\) |
0.453541 | + | 0.891235i | \(0.350161\pi\) | |||||||
\(282\) | −4.88781 | − | 17.2202i | −0.291065 | − | 1.02545i | ||||
\(283\) | 2.09766 | − | 1.21108i | 0.124693 | − | 0.0719915i | −0.436356 | − | 0.899774i | \(-0.643731\pi\) |
0.561049 | + | 0.827783i | \(0.310398\pi\) | |||||||
\(284\) | −9.99286 | + | 5.76938i | −0.592967 | + | 0.342350i | ||||
\(285\) | −1.32747 | − | 4.67679i | −0.0786323 | − | 0.277029i | ||||
\(286\) | 20.0604 | − | 11.5819i | 1.18620 | − | 0.684852i | ||||
\(287\) | −1.00008 | − | 15.3192i | −0.0590328 | − | 0.904263i | ||||
\(288\) | −2.99869 | + | 0.0885938i | −0.176700 | + | 0.00522044i | ||||
\(289\) | −15.5792 | − | 26.9839i | −0.916421 | − | 1.58729i | ||||
\(290\) | 7.39406 | 0.434194 | ||||||||
\(291\) | −6.26742 | − | 22.0807i | −0.367403 | − | 1.29439i | ||||
\(292\) | 15.2275i | 0.891121i | ||||||||
\(293\) | −5.58519 | + | 9.67384i | −0.326290 | + | 0.565152i | −0.981773 | − | 0.190059i | \(-0.939132\pi\) |
0.655482 | + | 0.755211i | \(0.272465\pi\) | |||||||
\(294\) | −4.79892 | − | 11.1342i | −0.279879 | − | 0.649360i | ||||
\(295\) | −0.534861 | − | 0.926406i | −0.0311408 | − | 0.0539374i | ||||
\(296\) | 7.56898 | − | 4.36995i | 0.439938 | − | 0.253998i | ||||
\(297\) | −17.0134 | − | 15.5689i | −0.987217 | − | 0.903401i | ||||
\(298\) | 7.66438 | − | 13.2751i | 0.443985 | − | 0.769005i | ||||
\(299\) | −9.09409 | + | 15.7514i | −0.525925 | + | 0.910929i | ||||
\(300\) | −1.66623 | + | 0.472945i | −0.0961998 | + | 0.0273055i | ||||
\(301\) | −4.86706 | − | 2.40174i | −0.280533 | − | 0.138434i | ||||
\(302\) | −4.97683 | − | 2.87338i | −0.286384 | − | 0.165344i | ||||
\(303\) | −7.66775 | + | 30.4056i | −0.440501 | + | 1.74675i | ||||
\(304\) | − | 2.80681i | − | 0.160982i | ||||||
\(305\) | 5.23536 | + | 3.02264i | 0.299776 | + | 0.173076i | ||||
\(306\) | 20.8098 | − | 0.614807i | 1.18962 | − | 0.0351462i | ||||
\(307\) | 2.48600i | 0.141884i | 0.997480 | + | 0.0709419i | \(0.0226005\pi\) | ||||
−0.997480 | + | 0.0709419i | \(0.977400\pi\) | |||||||
\(308\) | 5.19631 | − | 10.5302i | 0.296087 | − | 0.600013i | ||||
\(309\) | 16.5214 | + | 4.16640i | 0.939867 | + | 0.237018i | ||||
\(310\) | 2.10218 | 0.119396 | ||||||||
\(311\) | −3.31033 | − | 5.73365i | −0.187711 | − | 0.325126i | 0.756775 | − | 0.653675i | \(-0.226774\pi\) |
−0.944487 | + | 0.328549i | \(0.893440\pi\) | |||||||
\(312\) | −6.48580 | − | 6.29702i | −0.367186 | − | 0.356498i | ||||
\(313\) | −22.1815 | − | 12.8065i | −1.25377 | − | 0.723866i | −0.281916 | − | 0.959439i | \(-0.590970\pi\) |
−0.971857 | + | 0.235573i | \(0.924303\pi\) | |||||||
\(314\) | −7.12978 | −0.402357 | ||||||||
\(315\) | −7.90167 | + | 0.750738i | −0.445209 | + | 0.0422993i | ||||
\(316\) | −7.77103 | −0.437155 | ||||||||
\(317\) | −16.9737 | − | 9.79975i | −0.953336 | − | 0.550409i | −0.0592204 | − | 0.998245i | \(-0.518861\pi\) |
−0.894116 | + | 0.447836i | \(0.852195\pi\) | |||||||
\(318\) | −8.85579 | + | 2.51364i | −0.496608 | + | 0.140958i | ||||
\(319\) | 16.4083 | + | 28.4201i | 0.918690 | + | 1.59122i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 5.71573 | + | 20.1371i | 0.319021 | + | 1.12394i | ||||
\(322\) | 0.600641 | + | 9.20061i | 0.0334724 | + | 0.512730i | ||||
\(323\) | 19.4782i | 1.08380i | ||||||||
\(324\) | −4.03201 | + | 8.04630i | −0.224000 | + | 0.447017i | ||||
\(325\) | −4.51990 | − | 2.60957i | −0.250719 | − | 0.144753i | ||||
\(326\) | 2.22025i | 0.122968i | ||||||||
\(327\) | −4.10886 | − | 3.98926i | −0.227220 | − | 0.220606i | ||||
\(328\) | −5.02506 | − | 2.90122i | −0.277462 | − | 0.160193i | ||||
\(329\) | −1.78126 | − | 27.2853i | −0.0982040 | − | 1.50429i | ||||
\(330\) | −5.51540 | − | 5.35486i | −0.303613 | − | 0.294775i | ||||
\(331\) | 11.3343 | − | 19.6316i | 0.622991 | − | 1.07905i | −0.365934 | − | 0.930641i | \(-0.619251\pi\) |
0.988926 | − | 0.148412i | \(-0.0474161\pi\) | |||||||
\(332\) | 2.84720 | − | 4.93150i | 0.156260 | − | 0.270651i | ||||
\(333\) | −0.774301 | − | 26.2083i | −0.0424315 | − | 1.43620i | ||||
\(334\) | −12.5967 | + | 7.27271i | −0.689261 | + | 0.397945i | ||||
\(335\) | −2.46400 | − | 4.26778i | −0.134623 | − | 0.233174i | ||||
\(336\) | −4.50702 | − | 0.828717i | −0.245878 | − | 0.0452102i | ||||
\(337\) | −9.56790 | + | 16.5721i | −0.521196 | + | 0.902739i | 0.478500 | + | 0.878088i | \(0.341181\pi\) |
−0.999696 | + | 0.0246511i | \(0.992153\pi\) | |||||||
\(338\) | − | 14.2393i | − | 0.774518i | ||||||
\(339\) | −3.89282 | + | 4.00953i | −0.211429 | + | 0.217768i | ||||
\(340\) | 6.93962 | 0.376354 | ||||||||
\(341\) | 4.66500 | + | 8.08001i | 0.252624 | + | 0.437557i | ||||
\(342\) | −7.41346 | − | 3.99303i | −0.400874 | − | 0.215918i | ||||
\(343\) | −3.59897 | − | 18.1672i | −0.194326 | − | 0.980937i | ||||
\(344\) | −1.77653 | + | 1.02568i | −0.0957843 | + | 0.0553011i | ||||
\(345\) | 5.85279 | + | 1.47597i | 0.315104 | + | 0.0794636i | ||||
\(346\) | 2.17125 | − | 1.25357i | 0.116727 | − | 0.0673924i | ||||
\(347\) | 0.443672 | − | 0.256154i | 0.0238176 | − | 0.0137511i | −0.488044 | − | 0.872819i | \(-0.662289\pi\) |
0.511862 | + | 0.859068i | \(0.328956\pi\) | |||||||
\(348\) | 8.92112 | − | 9.18858i | 0.478222 | − | 0.492559i | ||||
\(349\) | −1.14174 | + | 0.659186i | −0.0611161 | + | 0.0352854i | −0.530247 | − | 0.847843i | \(-0.677901\pi\) |
0.469131 | + | 0.883129i | \(0.344567\pi\) | |||||||
\(350\) | −2.64013 | + | 0.172355i | −0.141121 | + | 0.00921276i | ||||
\(351\) | −25.8588 | + | 8.17229i | −1.38024 | + | 0.436205i | ||||
\(352\) | −2.21912 | − | 3.84363i | −0.118280 | − | 0.204866i | ||||
\(353\) | 12.3002 | 0.654672 | 0.327336 | − | 0.944908i | \(-0.393849\pi\) | ||||
0.327336 | + | 0.944908i | \(0.393849\pi\) | |||||||
\(354\) | −1.79656 | − | 0.453062i | −0.0954864 | − | 0.0240800i | ||||
\(355\) | 11.5388i | 0.612414i | ||||||||
\(356\) | −4.16961 | + | 7.22198i | −0.220989 | + | 0.382764i | ||||
\(357\) | 31.2770 | + | 5.75098i | 1.65535 | + | 0.304374i | ||||
\(358\) | −3.72398 | − | 6.45012i | −0.196819 | − | 0.340900i | ||||
\(359\) | 20.6370 | − | 11.9148i | 1.08918 | − | 0.628837i | 0.155820 | − | 0.987785i | \(-0.450198\pi\) |
0.933357 | + | 0.358948i | \(0.116865\pi\) | |||||||
\(360\) | −1.42262 | + | 2.64124i | −0.0749787 | + | 0.139206i | ||||
\(361\) | −5.56091 | + | 9.63178i | −0.292679 | + | 0.506936i | ||||
\(362\) | −3.09285 | + | 5.35698i | −0.162557 | + | 0.281557i | ||||
\(363\) | 3.68390 | − | 14.6081i | 0.193355 | − | 0.766726i | ||||
\(364\) | −7.66863 | − | 11.4834i | −0.401945 | − | 0.601892i | ||||
\(365\) | 13.1874 | + | 7.61374i | 0.690259 | + | 0.398521i | ||||
\(366\) | 10.0728 | − | 2.85908i | 0.526514 | − | 0.149447i | ||||
\(367\) | 30.1194i | 1.57222i | 0.618087 | + | 0.786110i | \(0.287908\pi\) | ||||
−0.618087 | + | 0.786110i | \(0.712092\pi\) | |||||||
\(368\) | 3.01802 | + | 1.74245i | 0.157325 | + | 0.0908316i | ||||
\(369\) | −14.8116 | + | 9.14505i | −0.771059 | + | 0.476072i | ||||
\(370\) | − | 8.73991i | − | 0.454366i | ||||||
\(371\) | −14.0319 | + | 0.916043i | −0.728502 | + | 0.0475586i | ||||
\(372\) | 2.53633 | − | 2.61237i | 0.131503 | − | 0.135445i | ||||
\(373\) | 36.8547 | 1.90826 | 0.954131 | − | 0.299389i | \(-0.0967829\pi\) | ||||
0.954131 | + | 0.299389i | \(0.0967829\pi\) | |||||||
\(374\) | 15.3999 | + | 26.6734i | 0.796308 | + | 1.37925i | ||||
\(375\) | −0.423533 | + | 1.67947i | −0.0218711 | + | 0.0867275i | ||||
\(376\) | −8.95023 | − | 5.16742i | −0.461573 | − | 0.266489i | ||||
\(377\) | 38.5906 | 1.98752 | ||||||||
\(378\) | −8.60062 | + | 10.7252i | −0.442368 | + | 0.551643i | ||||
\(379\) | −3.10706 | −0.159599 | −0.0797994 | − | 0.996811i | \(-0.525428\pi\) | ||||
−0.0797994 | + | 0.996811i | \(0.525428\pi\) | |||||||
\(380\) | −2.43077 | − | 1.40341i | −0.124696 | − | 0.0719932i | ||||
\(381\) | −1.73883 | + | 6.89512i | −0.0890828 | + | 0.353248i | ||||
\(382\) | 11.4944 | + | 19.9088i | 0.588103 | + | 1.01863i | ||||
\(383\) | −11.1938 | −0.571979 | −0.285990 | − | 0.958233i | \(-0.592322\pi\) | ||||
−0.285990 | + | 0.958233i | \(0.592322\pi\) | |||||||
\(384\) | −1.20653 | + | 1.24270i | −0.0615702 | + | 0.0634161i | ||||
\(385\) | −6.52125 | − | 9.76522i | −0.332354 | − | 0.497682i | ||||
\(386\) | − | 10.8865i | − | 0.554106i | ||||||
\(387\) | 0.181738 | + | 6.15141i | 0.00923827 | + | 0.312694i | ||||
\(388\) | −11.4765 | − | 6.62595i | −0.582630 | − | 0.336382i | ||||
\(389\) | 22.9992i | 1.16610i | 0.812435 | + | 0.583052i | \(0.198142\pi\) | ||||
−0.812435 | + | 0.583052i | \(0.801858\pi\) | |||||||
\(390\) | −8.69628 | + | 2.46836i | −0.440353 | + | 0.124990i | ||||
\(391\) | −20.9439 | − | 12.0920i | −1.05918 | − | 0.611517i | ||||
\(392\) | −6.46576 | − | 2.68214i | −0.326570 | − | 0.135469i | ||||
\(393\) | 8.22232 | − | 32.6046i | 0.414761 | − | 1.64469i | ||||
\(394\) | 3.53717 | − | 6.12656i | 0.178200 | − | 0.308652i | ||||
\(395\) | −3.88551 | + | 6.72991i | −0.195501 | + | 0.338618i | ||||
\(396\) | −13.3089 | + | 0.393201i | −0.668799 | + | 0.0197591i | ||||
\(397\) | −6.76832 | + | 3.90769i | −0.339692 | + | 0.196121i | −0.660136 | − | 0.751146i | \(-0.729501\pi\) |
0.320444 | + | 0.947268i | \(0.396168\pi\) | |||||||
\(398\) | −9.23577 | − | 15.9968i | −0.462947 | − | 0.801848i | ||||
\(399\) | −9.79250 | − | 8.33959i | −0.490238 | − | 0.417502i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 11.6348i | 0.581015i | 0.956873 | + | 0.290507i | \(0.0938241\pi\) | ||||
−0.956873 | + | 0.290507i | \(0.906176\pi\) | |||||||
\(402\) | −8.27644 | − | 2.08717i | −0.412791 | − | 0.104099i | ||||
\(403\) | 10.9716 | 0.546532 | ||||||||
\(404\) | 9.05213 | + | 15.6788i | 0.450360 | + | 0.780047i | ||||
\(405\) | 4.95230 | + | 7.51497i | 0.246082 | + | 0.373422i | ||||
\(406\) | 16.2687 | − | 10.8643i | 0.807403 | − | 0.539186i | ||||
\(407\) | 33.5930 | − | 19.3949i | 1.66514 | − | 0.961371i | ||||
\(408\) | 8.37283 | − | 8.62385i | 0.414517 | − | 0.426944i | ||||
\(409\) | 24.2276 | − | 13.9878i | 1.19798 | − | 0.691653i | 0.237874 | − | 0.971296i | \(-0.423549\pi\) |
0.960104 | + | 0.279643i | \(0.0902161\pi\) | |||||||
\(410\) | −5.02506 | + | 2.90122i | −0.248170 | + | 0.143281i | ||||
\(411\) | −15.4450 | − | 3.89494i | −0.761843 | − | 0.192123i | ||||
\(412\) | 8.51930 | − | 4.91862i | 0.419716 | − | 0.242323i | ||||
\(413\) | −2.53802 | − | 1.25243i | −0.124888 | − | 0.0616281i | ||||
\(414\) | 8.89573 | − | 5.49246i | 0.437201 | − | 0.269939i | ||||
\(415\) | −2.84720 | − | 4.93150i | −0.139764 | − | 0.242078i | ||||
\(416\) | −5.21913 | −0.255889 | ||||||||
\(417\) | 12.4003 | − | 12.7721i | 0.607247 | − | 0.625453i | ||||
\(418\) | − | 12.4573i | − | 0.609307i | ||||||
\(419\) | 1.60593 | − | 2.78155i | 0.0784549 | − | 0.135888i | −0.824129 | − | 0.566403i | \(-0.808335\pi\) |
0.902583 | + | 0.430515i | \(0.141668\pi\) | |||||||
\(420\) | −2.97120 | + | 3.48884i | −0.144980 | + | 0.170238i | ||||
\(421\) | 3.72961 | + | 6.45987i | 0.181770 | + | 0.314835i | 0.942483 | − | 0.334253i | \(-0.108484\pi\) |
−0.760713 | + | 0.649088i | \(0.775151\pi\) | |||||||
\(422\) | 6.73032 | − | 3.88575i | 0.327627 | − | 0.189155i | ||||
\(423\) | −26.3812 | + | 16.2884i | −1.28270 | + | 0.791970i | ||||
\(424\) | −2.65743 | + | 4.60281i | −0.129056 | + | 0.223532i | ||||
\(425\) | 3.46981 | − | 6.00989i | 0.168310 | − | 0.291522i | ||||
\(426\) | 14.3392 | + | 13.9218i | 0.694736 | + | 0.674514i | ||||
\(427\) | 15.9603 | − | 1.04193i | 0.772374 | − | 0.0504226i | ||||
\(428\) | 10.4663 | + | 6.04270i | 0.505906 | + | 0.292085i | ||||
\(429\) | −28.7856 | − | 27.9477i | −1.38978 | − | 1.34933i | ||||
\(430\) | 2.05136i | 0.0989256i | ||||||||
\(431\) | −12.2228 | − | 7.05686i | −0.588753 | − | 0.339917i | 0.175851 | − | 0.984417i | \(-0.443732\pi\) |
−0.764604 | + | 0.644500i | \(0.777066\pi\) | |||||||
\(432\) | 1.56583 | + | 4.95461i | 0.0753362 | + | 0.238379i | ||||
\(433\) | 17.9235i | 0.861348i | 0.902508 | + | 0.430674i | \(0.141724\pi\) | ||||
−0.902508 | + | 0.430674i | \(0.858276\pi\) | |||||||
\(434\) | 4.62531 | − | 3.08880i | 0.222022 | − | 0.148267i | ||||
\(435\) | −3.49698 | − | 12.3202i | −0.167667 | − | 0.590708i | ||||
\(436\) | −3.30640 | −0.158348 | ||||||||
\(437\) | 4.89073 | + | 8.47100i | 0.233956 | + | 0.405223i | ||||
\(438\) | 25.3725 | − | 7.20176i | 1.21234 | − | 0.344113i | ||||
\(439\) | 33.6745 | + | 19.4420i | 1.60719 | + | 0.927914i | 0.989994 | + | 0.141109i | \(0.0450667\pi\) |
0.617201 | + | 0.786806i | \(0.288267\pi\) | |||||||
\(440\) | −4.43825 | −0.211585 | ||||||||
\(441\) | −16.2825 | + | 13.2620i | −0.775358 | + | 0.631522i | ||||
\(442\) | 36.2188 | 1.72275 | ||||||||
\(443\) | 23.5754 | + | 13.6113i | 1.12010 | + | 0.646692i | 0.941427 | − | 0.337216i | \(-0.109485\pi\) |
0.178676 | + | 0.983908i | \(0.442819\pi\) | |||||||
\(444\) | −10.8611 | − | 10.5449i | −0.515443 | − | 0.500440i | ||||
\(445\) | 4.16961 | + | 7.22198i | 0.197659 | + | 0.342355i | ||||
\(446\) | −1.44620 | −0.0684795 | ||||||||
\(447\) | −25.7442 | − | 6.49223i | −1.21766 | − | 0.307072i | ||||
\(448\) | −2.20024 | + | 1.46933i | −0.103952 | + | 0.0694193i | ||||
\(449\) | − | 16.5846i | − | 0.782674i | −0.920248 | − | 0.391337i | \(-0.872013\pi\) | ||
0.920248 | − | 0.391337i | \(-0.127987\pi\) | |||||||
\(450\) | 1.57607 | + | 2.55265i | 0.0742967 | + | 0.120333i | ||||
\(451\) | −22.3024 | − | 12.8763i | −1.05018 | − | 0.606322i | ||||
\(452\) | 3.22647i | 0.151760i | ||||||||
\(453\) | −2.43394 | + | 9.65150i | −0.114356 | + | 0.453467i | ||||
\(454\) | 7.33052 | + | 4.23228i | 0.344038 | + | 0.198631i | ||||
\(455\) | −13.7792 | + | 0.899543i | −0.645979 | + | 0.0421712i | ||||
\(456\) | −4.67679 | + | 1.32747i | −0.219011 | + | 0.0621643i | ||||
\(457\) | −8.76829 | + | 15.1871i | −0.410163 | + | 0.710424i | −0.994907 | − | 0.100794i | \(-0.967862\pi\) |
0.584744 | + | 0.811218i | \(0.301195\pi\) | |||||||
\(458\) | −6.89186 | + | 11.9370i | −0.322035 | + | 0.557782i | ||||
\(459\) | −10.8663 | − | 34.3831i | −0.507195 | − | 1.60487i | ||||
\(460\) | 3.01802 | − | 1.74245i | 0.140716 | − | 0.0812423i | ||||
\(461\) | 17.8733 | + | 30.9575i | 0.832444 | + | 1.44184i | 0.896095 | + | 0.443863i | \(0.146392\pi\) |
−0.0636506 | + | 0.997972i | \(0.520274\pi\) | |||||||
\(462\) | −20.0033 | − | 3.67805i | −0.930636 | − | 0.171118i | ||||
\(463\) | 10.2703 | − | 17.7886i | 0.477299 | − | 0.826707i | −0.522362 | − | 0.852724i | \(-0.674949\pi\) |
0.999661 | + | 0.0260170i | \(0.00828242\pi\) | |||||||
\(464\) | − | 7.39406i | − | 0.343260i | ||||||
\(465\) | −0.994216 | − | 3.50272i | −0.0461056 | − | 0.162435i | ||||
\(466\) | −19.3250 | −0.895213 | ||||||||
\(467\) | 3.54772 | + | 6.14483i | 0.164169 | + | 0.284349i | 0.936360 | − | 0.351042i | \(-0.114173\pi\) |
−0.772191 | + | 0.635390i | \(0.780839\pi\) | |||||||
\(468\) | −7.42485 | + | 13.7850i | −0.343214 | + | 0.637211i | ||||
\(469\) | −11.6922 | − | 5.76972i | −0.539895 | − | 0.266421i | ||||
\(470\) | −8.95023 | + | 5.16742i | −0.412843 | + | 0.238355i | ||||
\(471\) | 3.37199 | + | 11.8799i | 0.155373 | + | 0.547395i | ||||
\(472\) | −0.926406 | + | 0.534861i | −0.0426413 | + | 0.0246190i | ||||
\(473\) | −7.88470 | + | 4.55223i | −0.362539 | + | 0.209312i | ||||
\(474\) | 3.67527 | + | 12.9483i | 0.168811 | + | 0.594736i | ||||
\(475\) | −2.43077 | + | 1.40341i | −0.111531 | + | 0.0643926i | ||||
\(476\) | 15.2689 | − | 10.1966i | 0.699847 | − | 0.467360i | ||||
\(477\) | 8.37660 | + | 13.5670i | 0.383538 | + | 0.621189i | ||||
\(478\) | 4.12327 | + | 7.14170i | 0.188594 | + | 0.326654i | ||||
\(479\) | 17.3106 | 0.790942 | 0.395471 | − | 0.918478i | \(-0.370581\pi\) | ||||
0.395471 | + | 0.918478i | \(0.370581\pi\) | |||||||
\(480\) | 0.472945 | + | 1.66623i | 0.0215869 | + | 0.0760527i | ||||
\(481\) | − | 45.6147i | − | 2.07985i | ||||||
\(482\) | −11.9553 | + | 20.7072i | −0.544548 | + | 0.943185i | ||||
\(483\) | 15.0463 | − | 5.35219i | 0.684629 | − | 0.243533i | ||||
\(484\) | −4.34902 | − | 7.53272i | −0.197683 | − | 0.342396i | ||||
\(485\) | −11.4765 | + | 6.62595i | −0.521120 | + | 0.300869i | ||||
\(486\) | 15.3139 | + | 2.91279i | 0.694653 | + | 0.132127i | ||||
\(487\) | −17.8900 | + | 30.9864i | −0.810675 | + | 1.40413i | 0.101718 | + | 0.994813i | \(0.467566\pi\) |
−0.912393 | + | 0.409316i | \(0.865767\pi\) | |||||||
\(488\) | 3.02264 | − | 5.23536i | 0.136828 | − | 0.236994i | ||||
\(489\) | 3.69945 | − | 1.05006i | 0.167295 | − | 0.0474852i | ||||
\(490\) | −5.55569 | + | 4.25845i | −0.250980 | + | 0.192377i | ||||
\(491\) | 24.0944 | + | 13.9109i | 1.08736 | + | 0.627789i | 0.932873 | − | 0.360205i | \(-0.117293\pi\) |
0.154490 | + | 0.987994i | \(0.450627\pi\) | |||||||
\(492\) | −2.45752 | + | 9.74502i | −0.110794 | + | 0.439339i | ||||
\(493\) | 51.3119i | 2.31097i | ||||||||
\(494\) | −12.6865 | − | 7.32456i | −0.570793 | − | 0.329547i | ||||
\(495\) | −6.31395 | + | 11.7225i | −0.283791 | + | 0.526886i | ||||
\(496\) | − | 2.10218i | − | 0.0943907i | ||||||
\(497\) | 16.9542 | + | 25.3881i | 0.760502 | + | 1.13881i | ||||
\(498\) | −9.56358 | − | 2.41177i | −0.428554 | − | 0.108074i | ||||
\(499\) | −10.7082 | −0.479365 | −0.239683 | − | 0.970851i | \(-0.577043\pi\) | ||||
−0.239683 | + | 0.970851i | \(0.577043\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 18.0756 | + | 17.5494i | 0.807557 | + | 0.784050i | ||||
\(502\) | 18.8854 | + | 10.9035i | 0.842897 | + | 0.486647i | ||||
\(503\) | 26.8197 | 1.19583 | 0.597916 | − | 0.801559i | \(-0.295996\pi\) | ||||
0.597916 | + | 0.801559i | \(0.295996\pi\) | |||||||
\(504\) | 0.750738 | + | 7.90167i | 0.0334406 | + | 0.351968i | ||||
\(505\) | 18.1043 | 0.805629 | ||||||||
\(506\) | 13.3947 | + | 7.73344i | 0.595467 | + | 0.343793i | ||||
\(507\) | −23.7260 | + | 6.73443i | −1.05371 | + | 0.299086i | ||||
\(508\) | 2.05277 | + | 3.55550i | 0.0910768 | + | 0.157750i | ||||
\(509\) | −10.7357 | −0.475852 | −0.237926 | − | 0.971283i | \(-0.576468\pi\) | ||||
−0.237926 | + | 0.971283i | \(0.576468\pi\) | |||||||
\(510\) | −3.28206 | − | 11.5630i | −0.145332 | − | 0.512018i | ||||
\(511\) | 40.2025 | − | 2.62453i | 1.77846 | − | 0.116102i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −3.14715 | + | 14.2410i | −0.138950 | + | 0.628756i | ||||
\(514\) | 8.72534 | + | 5.03757i | 0.384858 | + | 0.222198i | ||||
\(515\) | − | 9.83724i | − | 0.433481i | ||||||
\(516\) | 2.54923 | + | 2.47502i | 0.112223 | + | 0.108957i | ||||
\(517\) | −39.7233 | − | 22.9343i | −1.74703 | − | 1.00865i | ||||
\(518\) | −12.8418 | − | 19.2299i | −0.564236 | − | 0.844914i | ||||
\(519\) | −3.11562 | − | 3.02493i | −0.136761 | − | 0.132780i | ||||
\(520\) | −2.60957 | + | 4.51990i | −0.114437 | + | 0.198211i | ||||
\(521\) | −3.27417 | + | 5.67102i | −0.143444 | + | 0.248452i | −0.928791 | − | 0.370603i | \(-0.879151\pi\) |
0.785347 | + | 0.619055i | \(0.212484\pi\) | |||||||
\(522\) | −19.5295 | − | 10.5189i | −0.854782 | − | 0.460402i | ||||
\(523\) | 27.2374 | − | 15.7255i | 1.19101 | − | 0.687628i | 0.232472 | − | 0.972603i | \(-0.425319\pi\) |
0.958535 | + | 0.284975i | \(0.0919853\pi\) | |||||||
\(524\) | −9.70682 | − | 16.8127i | −0.424045 | − | 0.734467i | ||||
\(525\) | 1.53582 | + | 4.31755i | 0.0670287 | + | 0.188433i | ||||
\(526\) | −0.987816 | + | 1.71095i | −0.0430708 | + | 0.0746008i | ||||
\(527\) | 14.5883i | 0.635478i | ||||||||
\(528\) | −5.35486 | + | 5.51540i | −0.233040 | + | 0.240027i | ||||
\(529\) | 10.8554 | 0.471975 | ||||||||
\(530\) | 2.65743 | + | 4.60281i | 0.115432 | + | 0.199933i | ||||
\(531\) | 0.0947707 | + | 3.20776i | 0.00411270 | + | 0.139205i | ||||
\(532\) | −7.41035 | + | 0.483768i | −0.321279 | + | 0.0209740i | ||||
\(533\) | −26.2264 | + | 15.1418i | −1.13599 | + | 0.655866i | ||||
\(534\) | 14.0055 | + | 3.53193i | 0.606076 | + | 0.152842i | ||||
\(535\) | 10.4663 | − | 6.04270i | 0.452496 | − | 0.261249i | ||||
\(536\) | −4.26778 | + | 2.46400i | −0.184340 | + | 0.106429i | ||||
\(537\) | −8.98615 | + | 9.25556i | −0.387781 | + | 0.399407i | ||||
\(538\) | −7.14541 | + | 4.12540i | −0.308060 | + | 0.177859i | ||||
\(539\) | −28.6967 | − | 11.9040i | −1.23605 | − | 0.512742i | ||||
\(540\) | 5.07374 | + | 1.12125i | 0.218339 | + | 0.0482511i | ||||
\(541\) | 3.61196 | + | 6.25610i | 0.155290 | + | 0.268971i | 0.933165 | − | 0.359449i | \(-0.117035\pi\) |
−0.777874 | + | 0.628420i | \(0.783702\pi\) | |||||||
\(542\) | −28.7381 | −1.23441 | ||||||||
\(543\) | 10.3887 | + | 2.61985i | 0.445822 | + | 0.112429i | ||||
\(544\) | − | 6.93962i | − | 0.297534i | ||||||
\(545\) | −1.65320 | + | 2.86343i | −0.0708153 | + | 0.122656i | ||||
\(546\) | −15.5071 | + | 18.2087i | −0.663642 | + | 0.779260i | ||||
\(547\) | −3.09371 | − | 5.35846i | −0.132277 | − | 0.229111i | 0.792277 | − | 0.610162i | \(-0.208896\pi\) |
−0.924554 | + | 0.381051i | \(0.875562\pi\) | |||||||
\(548\) | −7.96425 | + | 4.59816i | −0.340216 | + | 0.196424i | ||||
\(549\) | −9.52777 | − | 15.4314i | −0.406635 | − | 0.658598i | ||||
\(550\) | −2.21912 | + | 3.84363i | −0.0946237 | + | 0.163893i | ||||
\(551\) | 10.3769 | − | 17.9732i | 0.442069 | − | 0.765686i | ||||
\(552\) | 1.47597 | − | 5.85279i | 0.0628215 | − | 0.249111i | ||||
\(553\) | 1.33937 | + | 20.5165i | 0.0569560 | + | 0.872452i | ||||
\(554\) | −17.6865 | − | 10.2113i | −0.751427 | − | 0.433837i | ||||
\(555\) | −14.5627 | + | 4.13349i | −0.618152 | + | 0.175457i | ||||
\(556\) | − | 10.2777i | − | 0.435873i | ||||||
\(557\) | 3.23352 | + | 1.86687i | 0.137009 | + | 0.0791020i | 0.566938 | − | 0.823761i | \(-0.308128\pi\) |
−0.429929 | + | 0.902863i | \(0.641461\pi\) | |||||||
\(558\) | −5.55236 | − | 2.99061i | −0.235050 | − | 0.126602i | ||||
\(559\) | 10.7063i | 0.452830i | ||||||||
\(560\) | 0.172355 | + | 2.64013i | 0.00728332 | + | 0.111566i | ||||
\(561\) | 37.1607 | − | 38.2748i | 1.56892 | − | 1.61596i | ||||
\(562\) | 1.77151 | 0.0747265 | ||||||||
\(563\) | −2.05579 | − | 3.56073i | −0.0866411 | − | 0.150067i | 0.819448 | − | 0.573153i | \(-0.194280\pi\) |
−0.906089 | + | 0.423086i | \(0.860947\pi\) | |||||||
\(564\) | −4.37714 | + | 17.3570i | −0.184311 | + | 0.730863i | ||||
\(565\) | 2.79421 | + | 1.61324i | 0.117553 | + | 0.0678693i | ||||
\(566\) | −2.42217 | −0.101811 | ||||||||
\(567\) | 21.9382 | + | 9.25820i | 0.921319 | + | 0.388808i | ||||
\(568\) | 11.5388 | 0.484156 | ||||||||
\(569\) | −17.0126 | − | 9.82222i | −0.713205 | − | 0.411769i | 0.0990419 | − | 0.995083i | \(-0.468422\pi\) |
−0.812246 | + | 0.583314i | \(0.801756\pi\) | |||||||
\(570\) | −1.18878 | + | 4.71395i | −0.0497924 | + | 0.197446i | ||||
\(571\) | 21.3658 | + | 37.0067i | 0.894132 | + | 1.54868i | 0.834875 | + | 0.550440i | \(0.185540\pi\) |
0.0592571 | + | 0.998243i | \(0.481127\pi\) | |||||||
\(572\) | −23.1638 | −0.968527 | ||||||||
\(573\) | 27.7365 | − | 28.5681i | 1.15871 | − | 1.19345i | ||||
\(574\) | −6.79350 | + | 13.7669i | −0.283555 | + | 0.574617i | ||||
\(575\) | − | 3.48491i | − | 0.145331i | ||||||
\(576\) | 2.64124 | + | 1.42262i | 0.110052 | + | 0.0592759i | ||||
\(577\) | −18.1866 | − | 10.5000i | −0.757117 | − | 0.437122i | 0.0711425 | − | 0.997466i | \(-0.477335\pi\) |
−0.828260 | + | 0.560344i | \(0.810669\pi\) | |||||||
\(578\) | 31.1583i | 1.29601i | ||||||||
\(579\) | −18.1393 | + | 5.14869i | −0.753845 | + | 0.213972i | ||||
\(580\) | −6.40344 | − | 3.69703i | −0.265888 | − | 0.153511i | ||||
\(581\) | −13.5105 | − | 6.66702i | −0.560511 | − | 0.276594i | ||||
\(582\) | −5.61261 | + | 22.2562i | −0.232650 | + | 0.922548i | ||||
\(583\) | −11.7943 | + | 20.4284i | −0.488472 | + | 0.846058i | ||||
\(584\) | 7.61374 | − | 13.1874i | 0.315059 | − | 0.545698i | ||||
\(585\) | 8.22572 | + | 13.3226i | 0.340092 | + | 0.550822i | ||||
\(586\) | 9.67384 | − | 5.58519i | 0.399623 | − | 0.230722i | ||||
\(587\) | −0.432150 | − | 0.748507i | −0.0178368 | − | 0.0308942i | 0.856969 | − | 0.515368i | \(-0.172345\pi\) |
−0.874806 | + | 0.484473i | \(0.839011\pi\) | |||||||
\(588\) | −1.41112 | + | 12.0420i | −0.0581934 | + | 0.496602i | ||||
\(589\) | 2.95021 | − | 5.10991i | 0.121561 | − | 0.210550i | ||||
\(590\) | 1.06972i | 0.0440397i | ||||||||
\(591\) | −11.8812 | − | 2.99622i | −0.488725 | − | 0.123248i | ||||
\(592\) | −8.73991 | −0.359208 | ||||||||
\(593\) | −0.642454 | − | 1.11276i | −0.0263824 | − | 0.0456957i | 0.852533 | − | 0.522674i | \(-0.175065\pi\) |
−0.878915 | + | 0.476978i | \(0.841732\pi\) | |||||||
\(594\) | 6.94956 | + | 21.9898i | 0.285144 | + | 0.902252i | ||||
\(595\) | −1.19608 | − | 18.3215i | −0.0490344 | − | 0.751109i | ||||
\(596\) | −13.2751 | + | 7.66438i | −0.543769 | + | 0.313945i | ||||
\(597\) | −22.2864 | + | 22.9545i | −0.912121 | + | 0.939467i | ||||
\(598\) | 15.7514 | − | 9.09409i | 0.644124 | − | 0.371885i | ||||
\(599\) | −0.953971 | + | 0.550775i | −0.0389782 | + | 0.0225041i | −0.519362 | − | 0.854554i | \(-0.673831\pi\) |
0.480384 | + | 0.877058i | \(0.340497\pi\) | |||||||
\(600\) | 1.67947 | + | 0.423533i | 0.0685641 | + | 0.0172907i | ||||
\(601\) | 0.162569 | − | 0.0938594i | 0.00663134 | − | 0.00382860i | −0.496681 | − | 0.867933i | \(-0.665448\pi\) |
0.503312 | + | 0.864105i | \(0.332115\pi\) | |||||||
\(602\) | 3.01413 | + | 4.51350i | 0.122847 | + | 0.183957i | ||||
\(603\) | 0.436591 | + | 14.7776i | 0.0177794 | + | 0.601789i | ||||
\(604\) | 2.87338 | + | 4.97683i | 0.116916 | + | 0.202504i | ||||
\(605\) | −8.69804 | −0.353626 | ||||||||
\(606\) | 21.8432 | − | 22.4981i | 0.887321 | − | 0.913924i | ||||
\(607\) | 2.78981i | 0.113235i | 0.998396 | + | 0.0566175i | \(0.0180315\pi\) | ||||
−0.998396 | + | 0.0566175i | \(0.981968\pi\) | |||||||
\(608\) | −1.40341 | + | 2.43077i | −0.0569156 | + | 0.0985807i | ||||
\(609\) | −25.7966 | − | 21.9692i | −1.04533 | − | 0.890238i | ||||
\(610\) | −3.02264 | − | 5.23536i | −0.122383 | − | 0.211973i | ||||
\(611\) | −46.7124 | + | 26.9694i | −1.88978 | + | 1.09107i | ||||
\(612\) | −18.3292 | − | 9.87245i | −0.740914 | − | 0.399070i | ||||
\(613\) | 15.0929 | − | 26.1417i | 0.609598 | − | 1.05586i | −0.381708 | − | 0.924283i | \(-0.624664\pi\) |
0.991307 | − | 0.131572i | \(-0.0420026\pi\) | |||||||
\(614\) | 1.24300 | − | 2.15294i | 0.0501635 | − | 0.0868857i | ||||
\(615\) | 7.21067 | + | 7.00079i | 0.290762 | + | 0.282299i | ||||
\(616\) | −9.76522 | + | 6.52125i | −0.393452 | + | 0.262749i | ||||
\(617\) | 18.6357 | + | 10.7593i | 0.750246 | + | 0.433155i | 0.825783 | − | 0.563988i | \(-0.190734\pi\) |
−0.0755367 | + | 0.997143i | \(0.524067\pi\) | |||||||
\(618\) | −12.2247 | − | 11.8689i | −0.491750 | − | 0.477437i | ||||
\(619\) | − | 26.6566i | − | 1.07142i | −0.844402 | − | 0.535710i | \(-0.820044\pi\) | ||
0.844402 | − | 0.535710i | \(-0.179956\pi\) | |||||||
\(620\) | −1.82054 | − | 1.05109i | −0.0731147 | − | 0.0422128i | ||||
\(621\) | −13.3589 | − | 12.2247i | −0.536074 | − | 0.490561i | ||||
\(622\) | 6.62065i | 0.265464i | ||||||||
\(623\) | 19.7856 | + | 9.76358i | 0.792694 | + | 0.391170i | ||||
\(624\) | 2.46836 | + | 8.69628i | 0.0988136 | + | 0.348130i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.8065 | + | 22.1815i | 0.511851 | + | 0.886551i | ||||
\(627\) | −20.7568 | + | 5.89163i | −0.828945 | + | 0.235289i | ||||
\(628\) | 6.17457 | + | 3.56489i | 0.246392 | + | 0.142255i | ||||
\(629\) | 60.6516 | 2.41834 | ||||||||
\(630\) | 7.21842 | + | 3.30068i | 0.287589 | + | 0.131502i | ||||
\(631\) | −12.9441 | −0.515297 | −0.257648 | − | 0.966239i | \(-0.582948\pi\) | ||||
−0.257648 | + | 0.966239i | \(0.582948\pi\) | |||||||
\(632\) | 6.72991 | + | 3.88551i | 0.267701 | + | 0.154557i | ||||
\(633\) | −9.65762 | − | 9.37651i | −0.383856 | − | 0.372683i | ||||
\(634\) | 9.79975 | + | 16.9737i | 0.389198 | + | 0.674110i | ||||
\(635\) | 4.10553 | 0.162923 | ||||||||
\(636\) | 8.92616 | + | 2.25102i | 0.353945 | + | 0.0892588i | ||||
\(637\) | −28.9959 | + | 22.2254i | −1.14886 | + | 0.880602i | ||||
\(638\) | − | 32.8167i | − | 1.29922i | ||||||
\(639\) | 16.4153 | − | 30.4766i | 0.649379 | − | 1.20564i | ||||
\(640\) | 0.866025 | + | 0.500000i | 0.0342327 | + | 0.0197642i | ||||
\(641\) | − | 50.1023i | − | 1.97892i | −0.144797 | − | 0.989461i | \(-0.546253\pi\) | ||
0.144797 | − | 0.989461i | \(-0.453747\pi\) | |||||||
\(642\) | 5.11856 | − | 20.2971i | 0.202014 | − | 0.801061i | ||||
\(643\) | 13.3473 | + | 7.70607i | 0.526366 | + | 0.303898i | 0.739535 | − | 0.673118i | \(-0.235045\pi\) |
−0.213169 | + | 0.977015i | \(0.568379\pi\) | |||||||
\(644\) | 4.08013 | − | 8.26828i | 0.160780 | − | 0.325816i | ||||
\(645\) | 3.41805 | − | 0.970182i | 0.134585 | − | 0.0382009i | ||||
\(646\) | 9.73910 | − | 16.8686i | 0.383180 | − | 0.663687i | ||||
\(647\) | −8.95179 | + | 15.5050i | −0.351931 | + | 0.609563i | −0.986588 | − | 0.163232i | \(-0.947808\pi\) |
0.634657 | + | 0.772794i | \(0.281142\pi\) | |||||||
\(648\) | 7.51497 | − | 4.95230i | 0.295216 | − | 0.194545i | ||||
\(649\) | −4.11162 | + | 2.37384i | −0.161395 | + | 0.0931815i | ||||
\(650\) | 2.60957 | + | 4.51990i | 0.102356 | + | 0.177285i | ||||
\(651\) | −7.33416 | − | 6.24600i | −0.287448 | − | 0.244800i | ||||
\(652\) | 1.11012 | − | 1.92279i | 0.0434758 | − | 0.0753024i | ||||
\(653\) | − | 0.406480i | − | 0.0159068i | −0.999968 | − | 0.00795339i | \(-0.997468\pi\) | ||
0.999968 | − | 0.00795339i | \(-0.00253167\pi\) | |||||||
\(654\) | 1.56375 | + | 5.50923i | 0.0611473 | + | 0.215428i | ||||
\(655\) | −19.4136 | −0.758554 | ||||||||
\(656\) | 2.90122 | + | 5.02506i | 0.113274 | + | 0.196196i | ||||
\(657\) | −23.9996 | − | 38.8704i | −0.936313 | − | 1.51648i | ||||
\(658\) | −12.1000 | + | 24.5204i | −0.471709 | + | 0.955905i | ||||
\(659\) | −17.3817 | + | 10.0353i | −0.677093 | + | 0.390920i | −0.798759 | − | 0.601651i | \(-0.794510\pi\) |
0.121666 | + | 0.992571i | \(0.461176\pi\) | |||||||
\(660\) | 2.09905 | + | 7.39514i | 0.0817053 | + | 0.287855i | ||||
\(661\) | −1.06654 | + | 0.615764i | −0.0414834 | + | 0.0239505i | −0.520598 | − | 0.853802i | \(-0.674291\pi\) |
0.479115 | + | 0.877752i | \(0.340958\pi\) | |||||||
\(662\) | −19.6316 | + | 11.3343i | −0.763005 | + | 0.440521i | ||||
\(663\) | −17.1295 | − | 60.3488i | −0.665254 | − | 2.34375i | ||||
\(664\) | −4.93150 | + | 2.84720i | −0.191379 | + | 0.110493i | ||||
\(665\) | −3.28622 | + | 6.65943i | −0.127434 | + | 0.258242i | ||||
\(666\) | −12.4336 | + | 23.0842i | −0.481791 | + | 0.894494i | ||||
\(667\) | 12.8838 | + | 22.3154i | 0.498862 | + | 0.864055i | ||||
\(668\) | 14.5454 | 0.562779 | ||||||||
\(669\) | 0.683973 | + | 2.40970i | 0.0264439 | + | 0.0931644i | ||||
\(670\) | 4.92801i | 0.190386i | ||||||||
\(671\) | 13.4152 | − | 23.2358i | 0.517888 | − | 0.897009i | ||||
\(672\) | 3.48884 | + | 2.97120i | 0.134585 | + | 0.114617i | ||||
\(673\) | −12.4710 | − | 21.6005i | −0.480723 | − | 0.832637i | 0.519032 | − | 0.854755i | \(-0.326293\pi\) |
−0.999755 | + | 0.0221176i | \(0.992959\pi\) | |||||||
\(674\) | 16.5721 | − | 9.56790i | 0.638333 | − | 0.368542i | ||||
\(675\) | 3.50790 | − | 3.83336i | 0.135019 | − | 0.147546i | ||||
\(676\) | −7.11967 | + | 12.3316i | −0.273834 | + | 0.474294i | ||||
\(677\) | 3.88825 | − | 6.73465i | 0.149438 | − | 0.258834i | −0.781582 | − | 0.623802i | \(-0.785587\pi\) |
0.931020 | + | 0.364969i | \(0.118920\pi\) | |||||||
\(678\) | 5.37604 | − | 1.52594i | 0.206466 | − | 0.0586035i | ||||
\(679\) | −15.5154 | + | 31.4414i | −0.595425 | + | 1.20661i | ||||
\(680\) | −6.00989 | − | 3.46981i | −0.230469 | − | 0.133061i | ||||
\(681\) | 3.58502 | − | 14.2160i | 0.137378 | − | 0.544757i | ||||
\(682\) | − | 9.33000i | − | 0.357264i | ||||||
\(683\) | −29.8265 | − | 17.2203i | −1.14128 | − | 0.658917i | −0.194532 | − | 0.980896i | \(-0.562319\pi\) |
−0.946747 | + | 0.321979i | \(0.895652\pi\) | |||||||
\(684\) | 4.42373 | + | 7.16479i | 0.169146 | + | 0.273953i | ||||
\(685\) | 9.19632i | 0.351373i | ||||||||
\(686\) | −5.96680 | + | 17.5327i | −0.227814 | + | 0.669403i | ||||
\(687\) | 23.1493 | + | 5.83785i | 0.883202 | + | 0.222728i | ||||
\(688\) | 2.05136 | 0.0782075 | ||||||||
\(689\) | 13.8695 | + | 24.0227i | 0.528386 | + | 0.915191i | ||||
\(690\) | −4.33068 | − | 4.20463i | −0.164866 | − | 0.160067i | ||||
\(691\) | −0.603200 | − | 0.348258i | −0.0229468 | − | 0.0132483i | 0.488483 | − | 0.872574i | \(-0.337551\pi\) |
−0.511430 | + | 0.859325i | \(0.670884\pi\) | |||||||
\(692\) | −2.50714 | −0.0953073 | ||||||||
\(693\) | 3.33196 | + | 35.0696i | 0.126571 | + | 1.33218i | ||||
\(694\) | −0.512308 | −0.0194470 | ||||||||
\(695\) | −8.90078 | − | 5.13887i | −0.337626 | − | 0.194928i | ||||
\(696\) | −12.3202 | + | 3.49698i | −0.466996 | + | 0.132553i | ||||
\(697\) | −20.1333 | − | 34.8720i | −0.762605 | − | 1.32087i | ||||
\(698\) | 1.31837 | 0.0499011 | ||||||||
\(699\) | 9.13966 | + | 32.1999i | 0.345694 | + | 1.21791i | ||||
\(700\) | 2.37260 | + | 1.17080i | 0.0896758 | + | 0.0442522i | ||||
\(701\) | 40.4903i | 1.52930i | 0.644447 | + | 0.764649i | \(0.277088\pi\) | ||||
−0.644447 | + | 0.764649i | \(0.722912\pi\) | |||||||
\(702\) | 26.4805 | + | 5.85197i | 0.999442 | + | 0.220868i | ||||
\(703\) | −21.2447 | − | 12.2656i | −0.801259 | − | 0.462607i | ||||
\(704\) | 4.43825i | 0.167273i | ||||||||
\(705\) | 12.8431 | + | 12.4692i | 0.483698 | + | 0.469619i | ||||
\(706\) | −10.6523 | − | 6.15009i | −0.400903 | − | 0.231462i | ||||
\(707\) | 39.8338 | − | 26.6011i | 1.49810 | − | 1.00044i | ||||
\(708\) | 1.32934 | + | 1.29065i | 0.0499597 | + | 0.0485054i | ||||
\(709\) | −17.9957 | + | 31.1695i | −0.675844 | + | 1.17060i | 0.300377 | + | 0.953820i | \(0.402887\pi\) |
−0.976221 | + | 0.216776i | \(0.930446\pi\) | |||||||
\(710\) | 5.76938 | − | 9.99286i | 0.216521 | − | 0.375025i | ||||
\(711\) | 19.8367 | − | 12.2477i | 0.743934 | − | 0.459324i | ||||
\(712\) | 7.22198 | − | 4.16961i | 0.270655 | − | 0.156263i | ||||
\(713\) | 3.66295 | + | 6.34442i | 0.137179 | + | 0.237600i | ||||
\(714\) | −24.2112 | − | 20.6190i | −0.906081 | − | 0.771647i | ||||
\(715\) | −11.5819 | + | 20.0604i | −0.433139 | + | 0.750218i | ||||
\(716\) | 7.44796i | 0.278343i | ||||||||
\(717\) | 9.94965 | − | 10.2479i | 0.371576 | − | 0.382716i | ||||
\(718\) | −23.8295 | −0.889310 | ||||||||
\(719\) | −2.71108 | − | 4.69573i | −0.101106 | − | 0.175121i | 0.811034 | − | 0.584998i | \(-0.198905\pi\) |
−0.912141 | + | 0.409877i | \(0.865572\pi\) | |||||||
\(720\) | 2.55265 | − | 1.57607i | 0.0951315 | − | 0.0587367i | ||||
\(721\) | −14.4542 | − | 21.6443i | −0.538301 | − | 0.806077i | ||||
\(722\) | 9.63178 | − | 5.56091i | 0.358458 | − | 0.206956i | ||||
\(723\) | 40.1571 | + | 10.1269i | 1.49346 | + | 0.376624i | ||||
\(724\) | 5.35698 | − | 3.09285i | 0.199091 | − | 0.114945i | ||||
\(725\) | −6.40344 | + | 3.69703i | −0.237818 | + | 0.137304i | ||||
\(726\) | −10.4944 | + | 10.8090i | −0.389484 | + | 0.401161i | ||||
\(727\) | −28.3952 | + | 16.3940i | −1.05312 | + | 0.608020i | −0.923522 | − | 0.383547i | \(-0.874703\pi\) |
−0.129600 | + | 0.991566i | \(0.541369\pi\) | |||||||
\(728\) | 0.899543 | + | 13.7792i | 0.0333393 | + | 0.510691i | ||||
\(729\) | −2.38925 | − | 26.8941i | −0.0884908 | − | 0.996077i | ||||
\(730\) | −7.61374 | − | 13.1874i | −0.281797 | − | 0.488087i | ||||
\(731\) | −14.2357 | −0.526526 | ||||||||
\(732\) | −10.1529 | − | 2.56037i | −0.375260 | − | 0.0946340i | ||||
\(733\) | 6.24073i | 0.230507i | 0.993336 | + | 0.115253i | \(0.0367680\pi\) | ||||
−0.993336 | + | 0.115253i | \(0.963232\pi\) | |||||||
\(734\) | 15.0597 | − | 26.0842i | 0.555864 | − | 0.962784i | ||||
\(735\) | 9.72308 | + | 7.24304i | 0.358641 | + | 0.267164i | ||||
\(736\) | −1.74245 | − | 3.01802i | −0.0642277 | − | 0.111246i | ||||
\(737\) | −18.9415 | + | 10.9359i | −0.697718 | + | 0.402828i | ||||
\(738\) | 17.3997 | − | 0.514060i | 0.640492 | − | 0.0189228i | ||||
\(739\) | 13.1808 | − | 22.8298i | 0.484864 | − | 0.839809i | −0.514985 | − | 0.857199i | \(-0.672202\pi\) |
0.999849 | + | 0.0173901i | \(0.00553572\pi\) | |||||||
\(740\) | −4.36995 | + | 7.56898i | −0.160643 | + | 0.278241i | ||||
\(741\) | −6.20438 | + | 24.6028i | −0.227924 | + | 0.903805i | ||||
\(742\) | 12.6100 | + | 6.22266i | 0.462929 | + | 0.228441i | ||||
\(743\) | −32.8093 | − | 18.9425i | −1.20366 | − | 0.694931i | −0.242290 | − | 0.970204i | \(-0.577899\pi\) |
−0.961366 | + | 0.275273i | \(0.911232\pi\) | |||||||
\(744\) | −3.50272 | + | 0.994216i | −0.128416 | + | 0.0364497i | ||||
\(745\) | 15.3288i | 0.561602i | ||||||||
\(746\) | −31.9171 | − | 18.4273i | −1.16857 | − | 0.674673i | ||||
\(747\) | 0.504489 | + | 17.0758i | 0.0184583 | + | 0.624769i | ||||
\(748\) | − | 30.7997i | − | 1.12615i | ||||||
\(749\) | 14.1496 | − | 28.6738i | 0.517015 | − | 1.04772i | ||||
\(750\) | 1.20653 | − | 1.24270i | 0.0440561 | − | 0.0453769i | ||||
\(751\) | 0.439573 | 0.0160402 | 0.00802012 | − | 0.999968i | \(-0.497447\pi\) | ||||
0.00802012 | + | 0.999968i | \(0.497447\pi\) | |||||||
\(752\) | 5.16742 | + | 8.95023i | 0.188436 | + | 0.326381i | ||||
\(753\) | 9.23597 | − | 36.6242i | 0.336578 | − | 1.33466i | ||||
\(754\) | −33.4204 | − | 19.2953i | −1.21710 | − | 0.702693i | ||||
\(755\) | 5.74675 | 0.209146 | ||||||||
\(756\) | 12.8109 | − | 4.98796i | 0.465930 | − | 0.181410i | ||||
\(757\) | −5.35536 | −0.194644 | −0.0973220 | − | 0.995253i | \(-0.531028\pi\) | ||||
−0.0973220 | + | 0.995253i | \(0.531028\pi\) | |||||||
\(758\) | 2.69079 | + | 1.55353i | 0.0977339 | + | 0.0564267i | ||||
\(759\) | 6.55073 | − | 25.9761i | 0.237776 | − | 0.942874i | ||||
\(760\) | 1.40341 | + | 2.43077i | 0.0509069 | + | 0.0881733i | ||||
\(761\) | 1.19842 | 0.0434429 | 0.0217214 | − | 0.999764i | \(-0.493085\pi\) | ||||
0.0217214 | + | 0.999764i | \(0.493085\pi\) | |||||||
\(762\) | 4.95343 | − | 5.10193i | 0.179444 | − | 0.184824i | ||||
\(763\) | 0.569875 | + | 8.72933i | 0.0206308 | + | 0.316023i | ||||
\(764\) | − | 22.9888i | − | 0.831704i | ||||||
\(765\) | −17.7144 | + | 10.9373i | −0.640465 | + | 0.395440i | ||||
\(766\) | 9.69416 | + | 5.59692i | 0.350264 | + | 0.202225i | ||||
\(767\) | 5.58302i | 0.201591i | ||||||||
\(768\) | 1.66623 | − | 0.472945i | 0.0601249 | − | 0.0170659i | ||||
\(769\) | 37.0240 | + | 21.3758i | 1.33512 | + | 0.770831i | 0.986079 | − | 0.166277i | \(-0.0531745\pi\) |
0.349040 | + | 0.937108i | \(0.386508\pi\) | |||||||
\(770\) | 0.764954 | + | 11.7176i | 0.0275670 | + | 0.422271i | ||||
\(771\) | 4.26716 | − | 16.9209i | 0.153678 | − | 0.609392i | ||||
\(772\) | −5.44323 | + | 9.42795i | −0.195906 | + | 0.339319i | ||||
\(773\) | −11.5098 | + | 19.9356i | −0.413979 | + | 0.717032i | −0.995321 | − | 0.0966270i | \(-0.969195\pi\) |
0.581342 | + | 0.813659i | \(0.302528\pi\) | |||||||
\(774\) | 2.91831 | − | 5.41815i | 0.104897 | − | 0.194751i | ||||
\(775\) | −1.82054 | + | 1.05109i | −0.0653958 | + | 0.0377563i | ||||
\(776\) | 6.62595 | + | 11.4765i | 0.237858 | + | 0.411982i | ||||
\(777\) | −25.9680 | + | 30.4921i | −0.931597 | + | 1.09390i | ||||
\(778\) | 11.4996 | − | 19.9179i | 0.412280 | − | 0.714090i | ||||
\(779\) | 16.2863i | 0.583519i | ||||||||
\(780\) | 8.76538 | + | 2.21047i | 0.313851 | + | 0.0791477i | ||||
\(781\) | 51.2119 | 1.83251 | ||||||||
\(782\) | 12.0920 | + | 20.9439i | 0.432408 | + | 0.748952i | ||||
\(783\) | −8.29061 | + | 37.5155i | −0.296282 | + | 1.34069i | ||||
\(784\) | 4.25845 | + | 5.55569i | 0.152087 | + | 0.198417i | ||||
\(785\) | 6.17457 | − | 3.56489i | 0.220380 | − | 0.127236i | ||||
\(786\) | −23.4231 | + | 24.1253i | −0.835473 | + | 0.860521i | ||||
\(787\) | 45.4340 | − | 26.2313i | 1.61955 | − | 0.935046i | 0.632511 | − | 0.774552i | \(-0.282024\pi\) |
0.987037 | − | 0.160495i | \(-0.0513090\pi\) | |||||||
\(788\) | −6.12656 | + | 3.53717i | −0.218250 | + | 0.126007i | ||||
\(789\) | 3.31801 | + | 0.836745i | 0.118124 | + | 0.0297889i | ||||
\(790\) | 6.72991 | − | 3.88551i | 0.239439 | − | 0.138240i | ||||
\(791\) | 8.51831 | − | 0.556098i | 0.302876 | − | 0.0197726i | ||||
\(792\) | 11.7225 | + | 6.31395i | 0.416540 | + | 0.224356i | ||||
\(793\) | −15.7755 | − | 27.3240i | −0.560206 | − | 0.970305i | ||||
\(794\) | 7.81538 | 0.277358 | ||||||||
\(795\) | 6.41252 | − | 6.60477i | 0.227429 | − | 0.234247i | ||||
\(796\) | 18.4715i | 0.654706i | ||||||||
\(797\) | 23.0129 | − | 39.8595i | 0.815158 | − | 1.41190i | −0.0940562 | − | 0.995567i | \(-0.529983\pi\) |
0.909214 | − | 0.416328i | \(-0.136683\pi\) | |||||||
\(798\) | 4.31075 | + | 12.1185i | 0.152599 | + | 0.428992i | ||||
\(799\) | −35.8599 | − | 62.1112i | −1.26863 | − | 2.19734i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | −0.738803 | − | 25.0068i | −0.0261043 | − | 0.883570i | ||||
\(802\) | 5.81741 | − | 10.0760i | 0.205420 | − | 0.355797i | ||||
\(803\) | 33.7917 | − | 58.5289i | 1.19248 | − | 2.06544i | ||||
\(804\) | 6.12402 | + | 5.94577i | 0.215978 | + | 0.209691i | ||||
\(805\) | −5.12047 | − | 7.66764i | −0.180473 | − | 0.270249i | ||||
\(806\) | −9.50165 | − | 5.48578i | −0.334681 | − | 0.193228i | ||||
\(807\) | 10.2533 | + | 9.95480i | 0.360932 | + | 0.350426i | ||||
\(808\) | − | 18.1043i | − | 0.636906i | ||||||
\(809\) | 6.56411 | + | 3.78979i | 0.230782 | + | 0.133242i | 0.610933 | − | 0.791683i | \(-0.290795\pi\) |
−0.380151 | + | 0.924924i | \(0.624128\pi\) | |||||||
\(810\) | −0.531331 | − | 8.98430i | −0.0186691 | − | 0.315676i | ||||
\(811\) | 27.5654i | 0.967951i | 0.875081 | + | 0.483976i | \(0.160808\pi\) | ||||
−0.875081 | + | 0.483976i | \(0.839192\pi\) | |||||||
\(812\) | −19.5213 | + | 1.27440i | −0.685063 | + | 0.0447227i | ||||
\(813\) | 13.5916 | + | 47.8844i | 0.476677 | + | 1.67938i | ||||
\(814\) | −38.7899 | −1.35958 | ||||||||
\(815\) | −1.11012 | − | 1.92279i | −0.0388860 | − | 0.0673525i | ||||
\(816\) | −11.5630 | + | 3.28206i | −0.404786 | + | 0.114895i | ||||
\(817\) | 4.98639 | + | 2.87890i | 0.174452 | + | 0.100720i | ||||
\(818\) | −27.9756 | −0.978145 | ||||||||
\(819\) | 37.6739 | + | 17.2267i | 1.31643 | + | 0.601949i | ||||
\(820\) | 5.80244 | 0.202630 | ||||||||
\(821\) | 27.7304 | + | 16.0101i | 0.967796 | + | 0.558757i | 0.898564 | − | 0.438843i | \(-0.144612\pi\) |
0.0692324 | + | 0.997601i | \(0.477945\pi\) | |||||||
\(822\) | 11.4282 | + | 11.0956i | 0.398606 | + | 0.387003i | ||||
\(823\) | 16.9369 | + | 29.3356i | 0.590384 | + | 1.02258i | 0.994181 | + | 0.107727i | \(0.0343572\pi\) |
−0.403796 | + | 0.914849i | \(0.632309\pi\) | |||||||
\(824\) | −9.83724 | −0.342697 | ||||||||
\(825\) | 7.45390 | + | 1.87974i | 0.259512 | + | 0.0654443i | ||||
\(826\) | 1.57177 | + | 2.35365i | 0.0546890 | + | 0.0818939i | ||||
\(827\) | − | 49.6428i | − | 1.72625i | −0.504992 | − | 0.863124i | \(-0.668505\pi\) | ||
0.504992 | − | 0.863124i | \(-0.331495\pi\) | |||||||
\(828\) | −10.4502 | + | 0.308741i | −0.363168 | + | 0.0107295i | ||||
\(829\) | 23.6571 | + | 13.6584i | 0.821646 | + | 0.474378i | 0.850984 | − | 0.525192i | \(-0.176006\pi\) |
−0.0293377 | + | 0.999570i | \(0.509340\pi\) | |||||||
\(830\) | 5.69440i | 0.197656i | ||||||||
\(831\) | −8.64964 | + | 34.2991i | −0.300053 | + | 1.18982i | ||||
\(832\) | 4.51990 | + | 2.60957i | 0.156699 | + | 0.0904704i | ||||
\(833\) | −29.5520 | − | 38.5543i | −1.02392 | − | 1.33583i | ||||
\(834\) | −17.1251 | + | 4.86080i | −0.592993 | + | 0.168316i | ||||
\(835\) | 7.27271 | − | 12.5967i | 0.251683 | − | 0.435927i | ||||
\(836\) | −6.22866 | + | 10.7884i | −0.215423 | + | 0.373123i | ||||
\(837\) | −2.35708 | + | 10.6659i | −0.0814725 | + | 0.368668i | ||||
\(838\) | −2.78155 | + | 1.60593i | −0.0960872 | + | 0.0554760i | ||||
\(839\) | −15.8314 | − | 27.4209i | −0.546562 | − | 0.946673i | −0.998507 | − | 0.0546273i | \(-0.982603\pi\) |
0.451945 | − | 0.892046i | \(-0.350730\pi\) | |||||||
\(840\) | 4.31755 | − | 1.53582i | 0.148970 | − | 0.0529908i | ||||
\(841\) | 12.8360 | − | 22.2327i | 0.442622 | − | 0.766644i | ||||
\(842\) | − | 7.45922i | − | 0.257062i | ||||||
\(843\) | −0.837825 | − | 2.95174i | −0.0288562 | − | 0.101663i | ||||
\(844\) | −7.77150 | −0.267506 | ||||||||
\(845\) | 7.11967 | + | 12.3316i | 0.244924 | + | 0.424221i | ||||
\(846\) | 30.9910 | − | 0.915602i | 1.06549 | − | 0.0314790i | ||||
\(847\) | −19.1378 | + | 12.7803i | −0.657583 | + | 0.439136i | ||||
\(848\) | 4.60281 | − | 2.65743i | 0.158061 | − | 0.0912566i | ||||
\(849\) | 1.14555 | + | 4.03589i | 0.0393153 | + | 0.138511i | ||||
\(850\) | −6.00989 | + | 3.46981i | −0.206137 | + | 0.119013i | ||||
\(851\) | 26.3772 | − | 15.2289i | 0.904198 | − | 0.522039i | ||||
\(852\) | −5.45720 | − | 19.2262i | −0.186961 | − | 0.658680i | ||||
\(853\) | 8.23214 | − | 4.75283i | 0.281863 | − | 0.162734i | −0.352403 | − | 0.935848i | \(-0.614635\pi\) |
0.634267 | + | 0.773114i | \(0.281302\pi\) | |||||||
\(854\) | −14.3430 | − | 7.07782i | −0.490807 | − | 0.242198i | ||||
\(855\) | 8.41676 | − | 0.248666i | 0.287847 | − | 0.00850420i | ||||
\(856\) | −6.04270 | − | 10.4663i | −0.206535 | − | 0.357729i | ||||
\(857\) | −3.35621 | −0.114646 | −0.0573230 | − | 0.998356i | \(-0.518256\pi\) | ||||
−0.0573230 | + | 0.998356i | \(0.518256\pi\) | |||||||
\(858\) | 10.9552 | + | 38.5962i | 0.374004 | + | 1.31765i | ||||
\(859\) | 30.7525i | 1.04926i | 0.851330 | + | 0.524631i | \(0.175797\pi\) | ||||
−0.851330 | + | 0.524631i | \(0.824203\pi\) | |||||||
\(860\) | 1.02568 | − | 1.77653i | 0.0349755 | − | 0.0605793i | ||||
\(861\) | 26.1517 | + | 4.80858i | 0.891247 | + | 0.163876i | ||||
\(862\) | 7.05686 | + | 12.2228i | 0.240358 | + | 0.416312i | ||||
\(863\) | 46.5984 | − | 26.9036i | 1.58623 | − | 0.915809i | 0.592307 | − | 0.805712i | \(-0.298217\pi\) |
0.993921 | − | 0.110097i | \(-0.0351162\pi\) | |||||||
\(864\) | 1.12125 | − | 5.07374i | 0.0381458 | − | 0.172612i | ||||
\(865\) | −1.25357 | + | 2.17125i | −0.0426227 | + | 0.0738247i | ||||
\(866\) | 8.96174 | − | 15.5222i | 0.304532 | − | 0.527465i | ||||
\(867\) | 51.9169 | − | 14.7362i | 1.76319 | − | 0.500466i | ||||
\(868\) | −5.55003 | + | 0.362321i | −0.188380 | + | 0.0122980i | ||||
\(869\) | 29.8690 | + | 17.2449i | 1.01324 | + | 0.584992i | ||||
\(870\) | −3.13163 | + | 12.4181i | −0.106172 | + | 0.421013i | ||||
\(871\) | 25.7199i | 0.871487i | ||||||||
\(872\) | 2.86343 | + | 1.65320i | 0.0969679 | + | 0.0559844i | ||||
\(873\) | 39.7384 | − | 1.17404i | 1.34494 | − | 0.0397351i | ||||
\(874\) | − | 9.78147i | − | 0.330863i | ||||||
\(875\) | 2.20024 | − | 1.46933i | 0.0743818 | − | 0.0496724i | ||||
\(876\) | −25.5741 | − | 6.44934i | −0.864069 | − | 0.217903i | ||||
\(877\) | −50.5842 | −1.70811 | −0.854053 | − | 0.520186i | \(-0.825863\pi\) | ||||
−0.854053 | + | 0.520186i | \(0.825863\pi\) | |||||||
\(878\) | −19.4420 | − | 33.6745i | −0.656135 | − | 1.13646i | ||||
\(879\) | −13.8814 | − | 13.4774i | −0.468208 | − | 0.454580i | ||||
\(880\) | 3.84363 | + | 2.21912i | 0.129569 | + | 0.0748066i | ||||
\(881\) | −40.0580 | −1.34959 | −0.674793 | − | 0.738007i | \(-0.735767\pi\) | ||||
−0.674793 | + | 0.738007i | \(0.735767\pi\) | |||||||
\(882\) | 20.7321 | − | 3.34394i | 0.698085 | − | 0.112596i | ||||
\(883\) | −20.3605 | −0.685187 | −0.342593 | − | 0.939484i | \(-0.611305\pi\) | ||||
−0.342593 | + | 0.939484i | \(0.611305\pi\) | |||||||
\(884\) | −31.3664 | − | 18.1094i | −1.05497 | − | 0.609085i | ||||
\(885\) | 1.78240 | − | 0.505919i | 0.0599148 | − | 0.0170063i | ||||
\(886\) | −13.6113 | − | 23.5754i | −0.457280 | − | 0.792032i | ||||
\(887\) | 25.8585 | 0.868245 | 0.434122 | − | 0.900854i | \(-0.357059\pi\) | ||||
0.434122 | + | 0.900854i | \(0.357059\pi\) | |||||||
\(888\) | 4.13349 | + | 14.5627i | 0.138711 | + | 0.488692i | ||||
\(889\) | 9.03317 | − | 6.03238i | 0.302963 | − | 0.202320i | ||||
\(890\) | − | 8.33922i | − | 0.279531i | ||||||
\(891\) | 33.3533 | − | 21.9795i | 1.11738 | − | 0.736342i | ||||
\(892\) | 1.25245 | + | 0.723100i | 0.0419350 | + | 0.0242112i | ||||
\(893\) | 29.0079i | 0.970713i | ||||||||
\(894\) | 19.0490 | + | 18.4945i | 0.637094 | + | 0.618549i | ||||
\(895\) | 6.45012 | + | 3.72398i | 0.215604 | + | 0.124479i | ||||
\(896\) | 2.64013 | − | 0.172355i | 0.0882006 | − | 0.00575797i | ||||
\(897\) | −22.6024 | − | 21.9445i | −0.754672 | − | 0.732706i | ||||
\(898\) | −8.29228 | + | 14.3626i | −0.276717 | + | 0.479288i | ||||
\(899\) | 7.77182 | − | 13.4612i | 0.259205 | − | 0.448956i | ||||
\(900\) | −0.0885938 | − | 2.99869i | −0.00295313 | − | 0.0999564i | ||||
\(901\) | −31.9417 | + | 18.4416i | −1.06413 | + | 0.614378i | ||||
\(902\) | 12.8763 | + | 22.3024i | 0.428735 | + | 0.742590i | ||||
\(903\) | 6.09501 | − | 7.15687i | 0.202829 | − | 0.238166i | ||||
\(904\) | 1.61324 | − | 2.79421i | 0.0536554 | − | 0.0929339i | ||||
\(905\) | − | 6.18571i | − | 0.205620i | ||||||
\(906\) | 6.93360 | − | 7.14147i | 0.230353 | − | 0.237260i | ||||
\(907\) | 37.0791 | 1.23119 | 0.615595 | − | 0.788062i | \(-0.288916\pi\) | ||||
0.615595 | + | 0.788062i | \(0.288916\pi\) | |||||||
\(908\) | −4.23228 | − | 7.33052i | −0.140453 | − | 0.243272i | ||||
\(909\) | −47.8177 | − | 25.7555i | −1.58601 | − | 0.854256i | ||||
\(910\) | 12.3829 | + | 6.11057i | 0.410489 | + | 0.202563i | ||||
\(911\) | −18.8303 | + | 10.8717i | −0.623874 | + | 0.360194i | −0.778376 | − | 0.627799i | \(-0.783956\pi\) |
0.154502 | + | 0.987993i | \(0.450623\pi\) | |||||||
\(912\) | 4.71395 | + | 1.18878i | 0.156095 | + | 0.0393643i | ||||
\(913\) | −21.8872 | + | 12.6366i | −0.724360 | + | 0.418210i | ||||
\(914\) | 15.1871 | − | 8.76829i | 0.502345 | − | 0.290029i | ||||
\(915\) | −7.29377 | + | 7.51244i | −0.241125 | + | 0.248354i | ||||
\(916\) | 11.9370 | − | 6.89186i | 0.394411 | − | 0.227713i | ||||
\(917\) | −42.7148 | + | 28.5250i | −1.41057 | + | 0.941980i | ||||
\(918\) | −7.78107 | + | 35.2098i | −0.256814 | + | 1.16210i | ||||
\(919\) | 9.93377 | + | 17.2058i | 0.327685 | + | 0.567567i | 0.982052 | − | 0.188610i | \(-0.0603983\pi\) |
−0.654367 | + | 0.756177i | \(0.727065\pi\) | |||||||
\(920\) | −3.48491 | −0.114894 | ||||||||
\(921\) | −4.17517 | − | 1.05290i | −0.137577 | − | 0.0346944i | ||||
\(922\) | − | 35.7467i | − | 1.17725i | ||||||
\(923\) | 30.1112 | − | 52.1541i | 0.991121 | − | 1.71667i | ||||
\(924\) | 15.4843 | + | 13.1869i | 0.509396 | + | 0.433818i | ||||
\(925\) | 4.36995 | + | 7.56898i | 0.143683 | + | 0.248867i | ||||
\(926\) | −17.7886 | + | 10.2703i | −0.584570 | + | 0.337502i | ||||
\(927\) | −13.9947 | + | 25.9825i | −0.459645 | + | 0.853378i | ||||
\(928\) | −3.69703 | + | 6.40344i | −0.121361 | + | 0.210203i | ||||
\(929\) | −9.12389 | + | 15.8030i | −0.299345 | + | 0.518481i | −0.975986 | − | 0.217832i | \(-0.930102\pi\) |
0.676641 | + | 0.736313i | \(0.263435\pi\) | |||||||
\(930\) | −0.890342 | + | 3.53055i | −0.0291955 | + | 0.115771i | ||||
\(931\) | 2.55442 | + | 19.4809i | 0.0837177 | + | 0.638461i | ||||
\(932\) | 16.7359 | + | 9.66250i | 0.548204 | + | 0.316506i | ||||
\(933\) | 11.0315 | − | 3.13120i | 0.361156 | − | 0.102511i | ||||
\(934\) | − | 7.09543i | − | 0.232170i | ||||||
\(935\) | −26.6734 | − | 15.3999i | −0.872312 | − | 0.503630i | ||||
\(936\) | 13.3226 | − | 8.22572i | 0.435463 | − | 0.268866i | ||||
\(937\) | 33.7791i | 1.10351i | 0.834005 | + | 0.551757i | \(0.186043\pi\) | ||||
−0.834005 | + | 0.551757i | \(0.813957\pi\) | |||||||
\(938\) | 7.24087 | + | 10.8428i | 0.236423 | + | 0.354031i | ||||
\(939\) | 30.9027 | − | 31.8292i | 1.00847 | − | 1.03871i | ||||
\(940\) | 10.3348 | 0.337085 | ||||||||
\(941\) | 4.40857 | + | 7.63587i | 0.143715 | + | 0.248922i | 0.928893 | − | 0.370348i | \(-0.120762\pi\) |
−0.785178 | + | 0.619271i | \(0.787428\pi\) | |||||||
\(942\) | 3.01969 | − | 11.9743i | 0.0983870 | − | 0.390142i | ||||
\(943\) | −17.5118 | − | 10.1105i | −0.570264 | − | 0.329242i | ||||
\(944\) | 1.06972 | 0.0348165 | ||||||||
\(945\) | 2.08577 | − | 13.5886i | 0.0678502 | − | 0.442037i | ||||
\(946\) | 9.10446 | 0.296012 | ||||||||
\(947\) | −28.6235 | − | 16.5258i | −0.930140 | − | 0.537017i | −0.0432843 | − | 0.999063i | \(-0.513782\pi\) |
−0.886856 | + | 0.462046i | \(0.847115\pi\) | |||||||
\(948\) | 3.29129 | − | 13.0512i | 0.106896 | − | 0.423884i | ||||
\(949\) | −39.7371 | − | 68.8267i | −1.28992 | − | 2.23421i | ||||
\(950\) | 2.80681 | 0.0910649 | ||||||||
\(951\) | 23.6473 | − | 24.3562i | 0.766816 | − | 0.789805i | ||||
\(952\) | −18.3215 | + | 1.19608i | −0.593803 | + | 0.0387651i | ||||
\(953\) | − | 8.17464i | − | 0.264803i | −0.991196 | − | 0.132401i | \(-0.957731\pi\) | ||
0.991196 | − | 0.132401i | \(-0.0422688\pi\) | |||||||
\(954\) | −0.470864 | − | 15.9376i | −0.0152448 | − | 0.516000i | ||||
\(955\) | −19.9088 | − | 11.4944i | −0.644235 | − | 0.371949i | ||||
\(956\) | − | 8.24653i | − | 0.266712i | ||||||
\(957\) | −54.6801 | + | 15.5205i | −1.76756 | + | 0.501706i | ||||
\(958\) | −14.9914 | − | 8.65531i | −0.484351 | − | 0.279640i | ||||
\(959\) | 13.5124 | + | 20.2342i | 0.436339 | + | 0.653395i | ||||
\(960\) | 0.423533 | − | 1.67947i | 0.0136695 | − | 0.0542047i | ||||
\(961\) | −13.2904 | + | 23.0197i | −0.428723 | + | 0.742570i | ||||
\(962\) | −22.8074 | + | 39.5035i | −0.735339 | + | 1.27364i | ||||
\(963\) | −36.2404 | + | 1.07069i | −1.16783 | + | 0.0345025i | ||||
\(964\) | 20.7072 | − | 11.9553i | 0.666933 | − | 0.385054i | ||||
\(965\) | 5.44323 | + | 9.42795i | 0.175224 | + | 0.303496i | ||||
\(966\) | −15.7065 | − | 2.88800i | −0.505350 | − | 0.0929199i | ||||
\(967\) | −16.5402 | + | 28.6485i | −0.531899 | + | 0.921275i | 0.467408 | + | 0.884042i | \(0.345188\pi\) |
−0.999307 | + | 0.0372336i | \(0.988145\pi\) | |||||||
\(968\) | 8.69804i | 0.279566i | ||||||||
\(969\) | −32.7130 | − | 8.24965i | −1.05089 | − | 0.265017i | ||||
\(970\) | 13.2519 | 0.425493 | ||||||||
\(971\) | 15.3895 | + | 26.6554i | 0.493873 | + | 0.855412i | 0.999975 | − | 0.00706089i | \(-0.00224757\pi\) |
−0.506102 | + | 0.862473i | \(0.668914\pi\) | |||||||
\(972\) | −11.8058 | − | 10.1795i | −0.378672 | − | 0.326508i | ||||
\(973\) | −27.1346 | + | 1.77142i | −0.869894 | + | 0.0567890i | ||||
\(974\) | 30.9864 | − | 17.8900i | 0.992870 | − | 0.573234i | ||||
\(975\) | 6.29702 | − | 6.48580i | 0.201666 | − | 0.207712i | ||||
\(976\) | −5.23536 | + | 3.02264i | −0.167580 | + | 0.0967522i | ||||
\(977\) | 33.0891 | − | 19.1040i | 1.05861 | − | 0.611190i | 0.133565 | − | 0.991040i | \(-0.457358\pi\) |
0.925048 | + | 0.379850i | \(0.124024\pi\) | |||||||
\(978\) | −3.72884 | − | 0.940349i | −0.119235 | − | 0.0300690i | ||||
\(979\) | 32.0529 | − | 18.5058i | 1.02442 | − | 0.591447i | ||||
\(980\) | 6.94059 | − | 0.910079i | 0.221709 | − | 0.0290714i | ||||
\(981\) | 8.44007 | − | 5.21112i | 0.269471 | − | 0.166378i | ||||
\(982\) | −13.9109 | − | 24.0944i | −0.443914 | − | 0.768882i | ||||
\(983\) | −26.4893 | −0.844877 | −0.422439 | − | 0.906391i | \(-0.638826\pi\) | ||||
−0.422439 | + | 0.906391i | \(0.638826\pi\) | |||||||
\(984\) | 7.00079 | − | 7.21067i | 0.223177 | − | 0.229868i | ||||
\(985\) | 7.07434i | 0.225407i | ||||||||
\(986\) | 25.6560 | − | 44.4374i | 0.817052 | − | 1.41518i | ||||
\(987\) | 46.5793 | + | 8.56465i | 1.48264 | + | 0.272616i | ||||
\(988\) | 7.32456 | + | 12.6865i | 0.233025 | + | 0.403612i | ||||
\(989\) | −6.19105 | + | 3.57441i | −0.196864 | + | 0.113659i | ||||
\(990\) | 11.3293 | − | 6.99499i | 0.360068 | − | 0.222315i | ||||
\(991\) | −19.0603 | + | 33.0135i | −0.605471 | + | 1.04871i | 0.386505 | + | 0.922287i | \(0.373682\pi\) |
−0.991977 | + | 0.126420i | \(0.959651\pi\) | |||||||
\(992\) | −1.05109 | + | 1.82054i | −0.0333721 | + | 0.0578023i | ||||
\(993\) | 28.1703 | + | 27.3503i | 0.893957 | + | 0.867936i | ||||
\(994\) | −1.98876 | − | 30.4639i | −0.0630797 | − | 0.966255i | ||||
\(995\) | 15.9968 | + | 9.23577i | 0.507133 | + | 0.292794i | ||||
\(996\) | 7.07642 | + | 6.87044i | 0.224225 | + | 0.217698i | ||||
\(997\) | − | 30.3486i | − | 0.961149i | −0.876954 | − | 0.480574i | \(-0.840428\pi\) | ||
0.876954 | − | 0.480574i | \(-0.159572\pi\) | |||||||
\(998\) | 9.27358 | + | 5.35410i | 0.293550 | + | 0.169481i | ||||
\(999\) | 44.3440 | + | 9.79965i | 1.40298 | + | 0.310047i |
(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 | 630.2.t.c.311.4 | ✓ | 32 | |
3.2 | odd | 2 | 1890.2.t.c.1151.16 | 32 | |||
7.5 | odd | 6 | 630.2.bk.c.131.14 | yes | 32 | ||
9.2 | odd | 6 | 630.2.bk.c.101.6 | yes | 32 | ||
9.7 | even | 3 | 1890.2.bk.c.521.5 | 32 | |||
21.5 | even | 6 | 1890.2.bk.c.341.5 | 32 | |||
63.47 | even | 6 | inner | 630.2.t.c.551.4 | yes | 32 | |
63.61 | odd | 6 | 1890.2.t.c.1601.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.c.311.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
630.2.t.c.551.4 | yes | 32 | 63.47 | even | 6 | inner | |
630.2.bk.c.101.6 | yes | 32 | 9.2 | odd | 6 | ||
630.2.bk.c.131.14 | yes | 32 | 7.5 | odd | 6 | ||
1890.2.t.c.1151.16 | 32 | 3.2 | odd | 2 | |||
1890.2.t.c.1601.16 | 32 | 63.61 | odd | 6 | |||
1890.2.bk.c.341.5 | 32 | 21.5 | even | 6 | |||
1890.2.bk.c.521.5 | 32 | 9.7 | even | 3 |