Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(230,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.230");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.p (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 230.15 | ||
Character | \(\chi\) | \(=\) | 429.230 |
Dual form | 429.2.p.b.263.15 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.642823 | + | 1.11340i | −0.454544 | + | 0.787294i | −0.998662 | − | 0.0517150i | \(-0.983531\pi\) |
0.544117 | + | 0.839009i | \(0.316865\pi\) | |||||||
\(3\) | −1.71725 | + | 0.225956i | −0.991454 | + | 0.130456i | ||||
\(4\) | 0.173557 | + | 0.300610i | 0.0867787 | + | 0.150305i | ||||
\(5\) | − | 1.88239i | − | 0.841831i | −0.907100 | − | 0.420916i | \(-0.861709\pi\) | ||
0.907100 | − | 0.420916i | \(-0.138291\pi\) | |||||||
\(6\) | 0.852307 | − | 2.05724i | 0.347953 | − | 0.839864i | ||||
\(7\) | 0.680391 | − | 0.392824i | 0.257164 | − | 0.148473i | −0.365876 | − | 0.930663i | \(-0.619231\pi\) |
0.623040 | + | 0.782190i | \(0.285897\pi\) | |||||||
\(8\) | −3.01756 | −1.06687 | ||||||||
\(9\) | 2.89789 | − | 0.776047i | 0.965962 | − | 0.258682i | ||||
\(10\) | 2.09586 | + | 1.21004i | 0.662769 | + | 0.382650i | ||||
\(11\) | 3.12491 | + | 1.11127i | 0.942197 | + | 0.335059i | ||||
\(12\) | −0.365966 | − | 0.477006i | −0.105645 | − | 0.137700i | ||||
\(13\) | −0.275603 | + | 3.59500i | −0.0764385 | + | 0.997074i | ||||
\(14\) | 1.01006i | 0.269951i | ||||||||
\(15\) | 0.425339 | + | 3.23254i | 0.109822 | + | 0.834637i | ||||
\(16\) | 1.59264 | − | 2.75854i | 0.398160 | − | 0.689634i | ||||
\(17\) | 2.60948 | + | 4.51975i | 0.632891 | + | 1.09620i | 0.986958 | + | 0.160979i | \(0.0514653\pi\) |
−0.354067 | + | 0.935220i | \(0.615201\pi\) | |||||||
\(18\) | −0.998776 | + | 3.72537i | −0.235414 | + | 0.878079i | ||||
\(19\) | −1.34814 | + | 0.778347i | −0.309284 | + | 0.178565i | −0.646606 | − | 0.762824i | \(-0.723812\pi\) |
0.337322 | + | 0.941389i | \(0.390479\pi\) | |||||||
\(20\) | 0.565866 | − | 0.326703i | 0.126532 | − | 0.0730530i | ||||
\(21\) | −1.07964 | + | 0.828315i | −0.235597 | + | 0.180753i | ||||
\(22\) | −3.24605 | + | 2.76494i | −0.692061 | + | 0.589487i | ||||
\(23\) | −4.08474 | − | 2.35833i | −0.851727 | − | 0.491745i | 0.00950587 | − | 0.999955i | \(-0.496974\pi\) |
−0.861233 | + | 0.508210i | \(0.830307\pi\) | |||||||
\(24\) | 5.18190 | − | 0.681837i | 1.05775 | − | 0.139179i | ||||
\(25\) | 1.45660 | 0.291320 | ||||||||
\(26\) | −3.82552 | − | 2.61781i | −0.750246 | − | 0.513394i | ||||
\(27\) | −4.80104 | + | 1.98746i | −0.923961 | + | 0.382487i | ||||
\(28\) | 0.236174 | + | 0.136355i | 0.0446326 | + | 0.0257687i | ||||
\(29\) | −4.75033 | + | 8.22781i | −0.882114 | + | 1.52787i | −0.0331271 | + | 0.999451i | \(0.510547\pi\) |
−0.848987 | + | 0.528414i | \(0.822787\pi\) | |||||||
\(30\) | −3.87253 | − | 1.60438i | −0.707024 | − | 0.292918i | ||||
\(31\) | 7.47016 | 1.34168 | 0.670840 | − | 0.741602i | \(-0.265934\pi\) | ||||
0.670840 | + | 0.741602i | \(0.265934\pi\) | |||||||
\(32\) | −0.969986 | − | 1.68007i | −0.171471 | − | 0.296996i | ||||
\(33\) | −5.61735 | − | 1.20223i | −0.977856 | − | 0.209281i | ||||
\(34\) | −6.70973 | −1.15071 | ||||||||
\(35\) | −0.739449 | − | 1.28076i | −0.124990 | − | 0.216488i | ||||
\(36\) | 0.736237 | + | 0.736446i | 0.122706 | + | 0.122741i | ||||
\(37\) | −1.51663 | + | 2.62688i | −0.249333 | + | 0.431857i | −0.963341 | − | 0.268281i | \(-0.913545\pi\) |
0.714008 | + | 0.700137i | \(0.246878\pi\) | |||||||
\(38\) | − | 2.00136i | − | 0.324663i | ||||||
\(39\) | −0.339035 | − | 6.23579i | −0.0542891 | − | 0.998525i | ||||
\(40\) | 5.68023i | 0.898123i | ||||||||
\(41\) | −0.941201 | + | 1.63021i | −0.146991 | + | 0.254596i | −0.930114 | − | 0.367271i | \(-0.880292\pi\) |
0.783123 | + | 0.621867i | \(0.213625\pi\) | |||||||
\(42\) | −0.228231 | − | 1.73453i | −0.0352167 | − | 0.267644i | ||||
\(43\) | 1.13181 | − | 0.653451i | 0.172600 | − | 0.0996504i | −0.411212 | − | 0.911540i | \(-0.634894\pi\) |
0.583811 | + | 0.811890i | \(0.301561\pi\) | |||||||
\(44\) | 0.208294 | + | 1.13225i | 0.0314015 | + | 0.170693i | ||||
\(45\) | −1.46082 | − | 5.45496i | −0.217767 | − | 0.813178i | ||||
\(46\) | 5.25153 | − | 3.03197i | 0.774296 | − | 0.447040i | ||||
\(47\) | 2.92720i | 0.426976i | 0.976946 | + | 0.213488i | \(0.0684825\pi\) | ||||
−0.976946 | + | 0.213488i | \(0.931518\pi\) | |||||||
\(48\) | −2.11165 | + | 5.09696i | −0.304791 | + | 0.735683i | ||||
\(49\) | −3.19138 | + | 5.52763i | −0.455911 | + | 0.789661i | ||||
\(50\) | −0.936335 | + | 1.62178i | −0.132418 | + | 0.229354i | ||||
\(51\) | −5.50239 | − | 7.17190i | −0.770488 | − | 1.00427i | ||||
\(52\) | −1.12853 | + | 0.541090i | −0.156499 | + | 0.0750357i | ||||
\(53\) | 11.0997i | 1.52466i | 0.647186 | + | 0.762332i | \(0.275946\pi\) | ||||
−0.647186 | + | 0.762332i | \(0.724054\pi\) | |||||||
\(54\) | 0.873375 | − | 6.62307i | 0.118851 | − | 0.901286i | ||||
\(55\) | 2.09184 | − | 5.88231i | 0.282063 | − | 0.793171i | ||||
\(56\) | −2.05312 | + | 1.18537i | −0.274360 | + | 0.158402i | ||||
\(57\) | 2.13921 | − | 1.64124i | 0.283346 | − | 0.217387i | ||||
\(58\) | −6.10724 | − | 10.5780i | −0.801920 | − | 1.38897i | ||||
\(59\) | 1.42241 | − | 0.821229i | 0.185182 | − | 0.106915i | −0.404543 | − | 0.914519i | \(-0.632569\pi\) |
0.589725 | + | 0.807604i | \(0.299236\pi\) | |||||||
\(60\) | −0.897913 | + | 0.688892i | −0.115920 | + | 0.0889355i | ||||
\(61\) | 7.20945 | − | 4.16238i | 0.923076 | − | 0.532938i | 0.0384608 | − | 0.999260i | \(-0.487755\pi\) |
0.884615 | + | 0.466322i | \(0.154421\pi\) | |||||||
\(62\) | −4.80199 | + | 8.31729i | −0.609853 | + | 1.05630i | ||||
\(63\) | 1.66685 | − | 1.66637i | 0.210003 | − | 0.209943i | ||||
\(64\) | 8.86468 | 1.10809 | ||||||||
\(65\) | 6.76721 | + | 0.518793i | 0.839369 | + | 0.0643483i | ||||
\(66\) | 4.94952 | − | 5.48155i | 0.609244 | − | 0.674733i | ||||
\(67\) | −2.32003 | + | 4.01840i | −0.283436 | + | 0.490926i | −0.972229 | − | 0.234032i | \(-0.924808\pi\) |
0.688792 | + | 0.724959i | \(0.258141\pi\) | |||||||
\(68\) | −0.905788 | + | 1.56887i | −0.109843 | + | 0.190254i | ||||
\(69\) | 7.54740 | + | 3.12686i | 0.908600 | + | 0.376430i | ||||
\(70\) | 1.90134 | 0.227253 | ||||||||
\(71\) | 5.68912 | − | 3.28461i | 0.675174 | − | 0.389812i | −0.122860 | − | 0.992424i | \(-0.539207\pi\) |
0.798034 | + | 0.602612i | \(0.205873\pi\) | |||||||
\(72\) | −8.74454 | + | 2.34177i | −1.03055 | + | 0.275980i | ||||
\(73\) | − | 2.77489i | − | 0.324776i | −0.986727 | − | 0.162388i | \(-0.948080\pi\) | ||
0.986727 | − | 0.162388i | \(-0.0519196\pi\) | |||||||
\(74\) | −1.94985 | − | 3.37724i | −0.226665 | − | 0.392596i | ||||
\(75\) | −2.50134 | + | 0.329128i | −0.288830 | + | 0.0380044i | ||||
\(76\) | −0.467958 | − | 0.270176i | −0.0536785 | − | 0.0309913i | ||||
\(77\) | 2.56269 | − | 0.471445i | 0.292046 | − | 0.0537262i | ||||
\(78\) | 7.16088 | + | 3.63103i | 0.810810 | + | 0.411133i | ||||
\(79\) | − | 8.07992i | − | 0.909062i | −0.890731 | − | 0.454531i | \(-0.849807\pi\) | ||
0.890731 | − | 0.454531i | \(-0.150193\pi\) | |||||||
\(80\) | −5.19265 | − | 2.99798i | −0.580555 | − | 0.335184i | ||||
\(81\) | 7.79550 | − | 4.49779i | 0.866167 | − | 0.499755i | ||||
\(82\) | −1.21005 | − | 2.09587i | −0.133628 | − | 0.231450i | ||||
\(83\) | 14.1307 | 1.55105 | 0.775523 | − | 0.631319i | \(-0.217486\pi\) | ||||
0.775523 | + | 0.631319i | \(0.217486\pi\) | |||||||
\(84\) | −0.436379 | − | 0.180790i | −0.0476129 | − | 0.0197258i | ||||
\(85\) | 8.50794 | − | 4.91206i | 0.922815 | − | 0.532788i | ||||
\(86\) | 1.68021i | 0.181182i | ||||||||
\(87\) | 6.29837 | − | 15.2026i | 0.675256 | − | 1.62989i | ||||
\(88\) | −9.42961 | − | 3.35331i | −1.00520 | − | 0.357464i | ||||
\(89\) | −0.306119 | − | 0.176738i | −0.0324485 | − | 0.0187342i | 0.483688 | − | 0.875240i | \(-0.339297\pi\) |
−0.516137 | + | 0.856506i | \(0.672630\pi\) | |||||||
\(90\) | 7.01262 | + | 1.88009i | 0.739195 | + | 0.198179i | ||||
\(91\) | 1.22468 | + | 2.55427i | 0.128382 | + | 0.267760i | ||||
\(92\) | − | 1.63722i | − | 0.170692i | ||||||
\(93\) | −12.8281 | + | 1.68793i | −1.33021 | + | 0.175030i | ||||
\(94\) | −3.25915 | − | 1.88167i | −0.336156 | − | 0.194080i | ||||
\(95\) | 1.46515 | + | 2.53772i | 0.150322 | + | 0.260365i | ||||
\(96\) | 2.04533 | + | 2.66592i | 0.208751 | + | 0.272089i | ||||
\(97\) | −2.19788 | − | 3.80684i | −0.223161 | − | 0.386526i | 0.732605 | − | 0.680654i | \(-0.238304\pi\) |
−0.955766 | + | 0.294128i | \(0.904971\pi\) | |||||||
\(98\) | −4.10298 | − | 7.10658i | −0.414464 | − | 0.717873i | ||||
\(99\) | 9.91804 | + | 0.795244i | 0.996801 | + | 0.0799250i | ||||
\(100\) | 0.252803 | + | 0.437868i | 0.0252803 | + | 0.0437868i | ||||
\(101\) | 5.97069 | − | 10.3415i | 0.594105 | − | 1.02902i | −0.399567 | − | 0.916704i | \(-0.630839\pi\) |
0.993672 | − | 0.112317i | \(-0.0358272\pi\) | |||||||
\(102\) | 11.5223 | − | 1.51611i | 1.14087 | − | 0.150117i | ||||
\(103\) | 4.50179 | 0.443574 | 0.221787 | − | 0.975095i | \(-0.428811\pi\) | ||||
0.221787 | + | 0.975095i | \(0.428811\pi\) | |||||||
\(104\) | 0.831648 | − | 10.8481i | 0.0815498 | − | 1.06375i | ||||
\(105\) | 1.55921 | + | 2.03230i | 0.152164 | + | 0.198333i | ||||
\(106\) | −12.3585 | − | 7.13516i | −1.20036 | − | 0.693028i | ||||
\(107\) | −2.93693 | + | 5.08692i | −0.283924 | + | 0.491771i | −0.972348 | − | 0.233538i | \(-0.924970\pi\) |
0.688424 | + | 0.725309i | \(0.258303\pi\) | |||||||
\(108\) | −1.43071 | − | 1.09830i | −0.137670 | − | 0.105684i | ||||
\(109\) | 10.0278i | 0.960492i | 0.877134 | + | 0.480246i | \(0.159453\pi\) | ||||
−0.877134 | + | 0.480246i | \(0.840547\pi\) | |||||||
\(110\) | 5.20470 | + | 6.11034i | 0.496249 | + | 0.582598i | ||||
\(111\) | 2.01087 | − | 4.85370i | 0.190863 | − | 0.460693i | ||||
\(112\) | − | 2.50251i | − | 0.236465i | ||||||
\(113\) | −4.56474 | + | 2.63545i | −0.429414 | + | 0.247922i | −0.699097 | − | 0.715027i | \(-0.746414\pi\) |
0.269683 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(114\) | 0.452220 | + | 3.43683i | 0.0423542 | + | 0.321888i | ||||
\(115\) | −4.43930 | + | 7.68909i | −0.413966 | + | 0.717011i | ||||
\(116\) | −3.29782 | −0.306195 | ||||||||
\(117\) | 1.99122 | + | 10.6318i | 0.184089 | + | 0.982910i | ||||
\(118\) | 2.11162i | 0.194390i | ||||||||
\(119\) | 3.55093 | + | 2.05013i | 0.325513 | + | 0.187935i | ||||
\(120\) | −1.28348 | − | 9.75437i | −0.117166 | − | 0.890448i | ||||
\(121\) | 8.53018 | + | 6.94522i | 0.775471 | + | 0.631384i | ||||
\(122\) | 10.7027i | 0.968976i | ||||||||
\(123\) | 1.24792 | − | 3.01214i | 0.112521 | − | 0.271596i | ||||
\(124\) | 1.29650 | + | 2.24561i | 0.116429 | + | 0.201661i | ||||
\(125\) | − | 12.1539i | − | 1.08707i | ||||||
\(126\) | 0.783858 | + | 2.92705i | 0.0698316 | + | 0.260763i | ||||
\(127\) | −17.9506 | − | 10.3638i | −1.59285 | − | 0.919635i | −0.992814 | − | 0.119665i | \(-0.961818\pi\) |
−0.600040 | − | 0.799970i | \(-0.704849\pi\) | |||||||
\(128\) | −3.75845 | + | 6.50982i | −0.332203 | + | 0.575392i | ||||
\(129\) | −1.79595 | + | 1.37788i | −0.158124 | + | 0.121315i | ||||
\(130\) | −4.92774 | + | 7.20113i | −0.432191 | + | 0.631581i | ||||
\(131\) | 5.41086 | 0.472749 | 0.236374 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236374 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(132\) | −0.613532 | − | 1.89729i | −0.0534011 | − | 0.165138i | ||||
\(133\) | −0.611506 | + | 1.05916i | −0.0530243 | + | 0.0918408i | ||||
\(134\) | −2.98273 | − | 5.16624i | −0.257669 | − | 0.446295i | ||||
\(135\) | 3.74118 | + | 9.03744i | 0.321990 | + | 0.777819i | ||||
\(136\) | −7.87425 | − | 13.6386i | −0.675211 | − | 1.16950i | ||||
\(137\) | −2.75131 | + | 1.58847i | −0.235060 | + | 0.135712i | −0.612904 | − | 0.790157i | \(-0.709999\pi\) |
0.377844 | + | 0.925869i | \(0.376666\pi\) | |||||||
\(138\) | −8.33309 | + | 6.39327i | −0.709360 | + | 0.544231i | ||||
\(139\) | −14.4845 | + | 8.36262i | −1.22856 | + | 0.709308i | −0.966728 | − | 0.255806i | \(-0.917659\pi\) |
−0.261829 | + | 0.965114i | \(0.584326\pi\) | |||||||
\(140\) | 0.256673 | − | 0.444571i | 0.0216929 | − | 0.0375731i | ||||
\(141\) | −0.661420 | − | 5.02673i | −0.0557016 | − | 0.423327i | ||||
\(142\) | 8.44570i | 0.708747i | ||||||||
\(143\) | −4.85624 | + | 10.9278i | −0.406099 | + | 0.913829i | ||||
\(144\) | 2.47454 | − | 9.22989i | 0.206212 | − | 0.769157i | ||||
\(145\) | 15.4880 | + | 8.94198i | 1.28621 | + | 0.742591i | ||||
\(146\) | 3.08956 | + | 1.78376i | 0.255694 | + | 0.147625i | ||||
\(147\) | 4.23139 | − | 10.2134i | 0.348999 | − | 0.842389i | ||||
\(148\) | −1.05289 | −0.0865470 | ||||||||
\(149\) | 6.91283 | + | 11.9734i | 0.566321 | + | 0.980896i | 0.996925 | + | 0.0783558i | \(0.0249670\pi\) |
−0.430605 | + | 0.902541i | \(0.641700\pi\) | |||||||
\(150\) | 1.24147 | − | 2.99657i | 0.101366 | − | 0.244669i | ||||
\(151\) | − | 16.0553i | − | 1.30656i | −0.757116 | − | 0.653281i | \(-0.773392\pi\) | ||
0.757116 | − | 0.653281i | \(-0.226608\pi\) | |||||||
\(152\) | 4.06808 | − | 2.34871i | 0.329965 | − | 0.190505i | ||||
\(153\) | 11.0695 | + | 11.0726i | 0.894917 | + | 0.895170i | ||||
\(154\) | −1.12245 | + | 3.15637i | −0.0904496 | + | 0.254347i | ||||
\(155\) | − | 14.0618i | − | 1.12947i | ||||||
\(156\) | 1.81570 | − | 1.18418i | 0.145372 | − | 0.0948106i | ||||
\(157\) | 19.6793 | 1.57058 | 0.785291 | − | 0.619127i | \(-0.212513\pi\) | ||||
0.785291 | + | 0.619127i | \(0.212513\pi\) | |||||||
\(158\) | 8.99620 | + | 5.19396i | 0.715699 | + | 0.413209i | ||||
\(159\) | −2.50806 | − | 19.0610i | −0.198902 | − | 1.51164i | ||||
\(160\) | −3.16254 | + | 1.82589i | −0.250021 | + | 0.144350i | ||||
\(161\) | −3.70563 | −0.292044 | ||||||||
\(162\) | −0.00327593 | + | 11.5708i | −0.000257381 | + | 0.909089i | ||||
\(163\) | −9.30375 | − | 16.1146i | −0.728726 | − | 1.26219i | −0.957422 | − | 0.288692i | \(-0.906780\pi\) |
0.228696 | − | 0.973498i | \(-0.426554\pi\) | |||||||
\(164\) | −0.653409 | −0.0510227 | ||||||||
\(165\) | −2.26306 | + | 10.5741i | −0.176179 | + | 0.823190i | ||||
\(166\) | −9.08354 | + | 15.7332i | −0.705020 | + | 1.22113i | ||||
\(167\) | 12.6522 | − | 21.9142i | 0.979053 | − | 1.69577i | 0.313199 | − | 0.949688i | \(-0.398599\pi\) |
0.665854 | − | 0.746082i | \(-0.268067\pi\) | |||||||
\(168\) | 3.25787 | − | 2.49949i | 0.251350 | − | 0.192840i | ||||
\(169\) | −12.8481 | − | 1.98159i | −0.988314 | − | 0.152430i | ||||
\(170\) | 12.6303i | 0.968703i | ||||||||
\(171\) | −3.30271 | + | 3.30178i | −0.252565 | + | 0.252493i | ||||
\(172\) | 0.392868 | + | 0.226823i | 0.0299559 | + | 0.0172951i | ||||
\(173\) | −6.35468 | − | 11.0066i | −0.483137 | − | 0.836818i | 0.516675 | − | 0.856181i | \(-0.327169\pi\) |
−0.999813 | + | 0.0193632i | \(0.993836\pi\) | |||||||
\(174\) | 12.8778 | + | 16.7852i | 0.976266 | + | 1.27248i | ||||
\(175\) | 0.991057 | − | 0.572187i | 0.0749168 | − | 0.0432533i | ||||
\(176\) | 8.04233 | − | 6.85034i | 0.606214 | − | 0.516364i | ||||
\(177\) | −2.25707 | + | 1.73166i | −0.169652 | + | 0.130159i | ||||
\(178\) | 0.393560 | − | 0.227222i | 0.0294986 | − | 0.0170310i | ||||
\(179\) | −6.16640 | − | 3.56017i | −0.460899 | − | 0.266100i | 0.251523 | − | 0.967851i | \(-0.419068\pi\) |
−0.712422 | + | 0.701751i | \(0.752402\pi\) | |||||||
\(180\) | 1.38628 | − | 1.38589i | 0.103327 | − | 0.103298i | ||||
\(181\) | −20.2885 | −1.50803 | −0.754016 | − | 0.656856i | \(-0.771886\pi\) | ||||
−0.754016 | + | 0.656856i | \(0.771886\pi\) | |||||||
\(182\) | −3.63118 | − | 0.278377i | −0.269161 | − | 0.0206347i | ||||
\(183\) | −11.4399 | + | 8.77686i | −0.845662 | + | 0.648804i | ||||
\(184\) | 12.3259 | + | 7.11639i | 0.908681 | + | 0.524627i | ||||
\(185\) | 4.94482 | + | 2.85489i | 0.363551 | + | 0.209896i | ||||
\(186\) | 6.36687 | − | 15.3679i | 0.466841 | − | 1.12683i | ||||
\(187\) | 3.13175 | + | 17.0236i | 0.229016 | + | 1.24489i | ||||
\(188\) | −0.879947 | + | 0.508037i | −0.0641767 | + | 0.0370524i | ||||
\(189\) | −2.48586 | + | 3.23821i | −0.180820 | + | 0.235545i | ||||
\(190\) | −3.76734 | −0.273312 | ||||||||
\(191\) | −19.2669 | + | 11.1238i | −1.39411 | + | 0.804888i | −0.993767 | − | 0.111478i | \(-0.964442\pi\) |
−0.400341 | + | 0.916366i | \(0.631108\pi\) | |||||||
\(192\) | −15.2229 | + | 2.00303i | −1.09862 | + | 0.144556i | ||||
\(193\) | 13.6059 | + | 7.85538i | 0.979376 | + | 0.565443i | 0.902082 | − | 0.431565i | \(-0.142039\pi\) |
0.0772942 | + | 0.997008i | \(0.475372\pi\) | |||||||
\(194\) | 5.65139 | 0.405746 | ||||||||
\(195\) | −11.7382 | + | 0.638197i | −0.840590 | + | 0.0457023i | ||||
\(196\) | −2.21555 | −0.158254 | ||||||||
\(197\) | 4.12726 | − | 7.14862i | 0.294055 | − | 0.509318i | −0.680710 | − | 0.732553i | \(-0.738329\pi\) |
0.974765 | + | 0.223235i | \(0.0716619\pi\) | |||||||
\(198\) | −7.26097 | + | 10.5316i | −0.516015 | + | 0.748446i | ||||
\(199\) | −2.45861 | − | 4.25843i | −0.174286 | − | 0.301872i | 0.765628 | − | 0.643284i | \(-0.222428\pi\) |
−0.939914 | + | 0.341411i | \(0.889095\pi\) | |||||||
\(200\) | −4.39537 | −0.310800 | ||||||||
\(201\) | 3.07608 | − | 7.42482i | 0.216970 | − | 0.523707i | ||||
\(202\) | 7.67619 | + | 13.2955i | 0.540095 | + | 0.935471i | ||||
\(203\) | 7.46417i | 0.523882i | ||||||||
\(204\) | 1.20097 | − | 2.89881i | 0.0840845 | − | 0.202957i | ||||
\(205\) | 3.06869 | + | 1.77171i | 0.214327 | + | 0.123742i | ||||
\(206\) | −2.89385 | + | 5.01230i | −0.201624 | + | 0.349223i | ||||
\(207\) | −13.6673 | − | 3.66421i | −0.949943 | − | 0.254680i | ||||
\(208\) | 9.47800 | + | 6.48581i | 0.657181 | + | 0.449710i | ||||
\(209\) | −5.07776 | + | 0.934129i | −0.351236 | + | 0.0646151i | ||||
\(210\) | −3.26507 | + | 0.429620i | −0.225311 | + | 0.0296466i | ||||
\(211\) | −8.67850 | − | 5.01053i | −0.597452 | − | 0.344939i | 0.170586 | − | 0.985343i | \(-0.445434\pi\) |
−0.768039 | + | 0.640403i | \(0.778767\pi\) | |||||||
\(212\) | −3.33669 | + | 1.92644i | −0.229165 | + | 0.132308i | ||||
\(213\) | −9.02745 | + | 6.92599i | −0.618550 | + | 0.474561i | ||||
\(214\) | −3.77586 | − | 6.53998i | −0.258112 | − | 0.447064i | ||||
\(215\) | −1.23005 | − | 2.13051i | −0.0838888 | − | 0.145300i | ||||
\(216\) | 14.4874 | − | 5.99728i | 0.985744 | − | 0.408063i | ||||
\(217\) | 5.08263 | − | 2.93446i | 0.345031 | − | 0.199204i | ||||
\(218\) | −11.1650 | − | 6.44612i | −0.756190 | − | 0.436586i | ||||
\(219\) | 0.627003 | + | 4.76517i | 0.0423690 | + | 0.322000i | ||||
\(220\) | 2.13134 | − | 0.392091i | 0.143695 | − | 0.0264348i | ||||
\(221\) | −16.9677 | + | 8.13542i | −1.14137 | + | 0.547248i | ||||
\(222\) | 4.11149 | + | 5.35898i | 0.275945 | + | 0.359671i | ||||
\(223\) | −6.85404 | + | 11.8715i | −0.458980 | + | 0.794977i | −0.998907 | − | 0.0467345i | \(-0.985119\pi\) |
0.539927 | + | 0.841712i | \(0.318452\pi\) | |||||||
\(224\) | −1.31994 | − | 0.762067i | −0.0881921 | − | 0.0509178i | ||||
\(225\) | 4.22106 | − | 1.13039i | 0.281404 | − | 0.0753593i | ||||
\(226\) | − | 6.77651i | − | 0.450767i | ||||||
\(227\) | −0.452628 | − | 0.783975i | −0.0300420 | − | 0.0520342i | 0.850614 | − | 0.525791i | \(-0.176231\pi\) |
−0.880656 | + | 0.473757i | \(0.842897\pi\) | |||||||
\(228\) | 0.864648 | + | 0.358221i | 0.0572627 | + | 0.0237238i | ||||
\(229\) | 16.1366 | 1.06634 | 0.533170 | − | 0.846008i | \(-0.321001\pi\) | ||||
0.533170 | + | 0.846008i | \(0.321001\pi\) | |||||||
\(230\) | −5.70736 | − | 9.88544i | −0.376332 | − | 0.651827i | ||||
\(231\) | −4.29426 | + | 1.38865i | −0.282541 | + | 0.0913662i | ||||
\(232\) | 14.3344 | − | 24.8279i | 0.941099 | − | 1.63003i | ||||
\(233\) | −26.1727 | −1.71463 | −0.857317 | − | 0.514789i | \(-0.827870\pi\) | ||||
−0.857317 | + | 0.514789i | \(0.827870\pi\) | |||||||
\(234\) | −13.1175 | − | 4.61733i | −0.857515 | − | 0.301844i | ||||
\(235\) | 5.51014 | 0.359442 | ||||||||
\(236\) | 0.493740 | + | 0.285061i | 0.0321397 | + | 0.0185559i | ||||
\(237\) | 1.82571 | + | 13.8752i | 0.118593 | + | 0.901293i | ||||
\(238\) | −4.56524 | + | 2.63574i | −0.295920 | + | 0.170850i | ||||
\(239\) | 12.0333 | 0.778372 | 0.389186 | − | 0.921159i | \(-0.372756\pi\) | ||||
0.389186 | + | 0.921159i | \(0.372756\pi\) | |||||||
\(240\) | 9.59448 | + | 3.97496i | 0.619321 | + | 0.256582i | ||||
\(241\) | 17.0159 | − | 9.82411i | 1.09609 | − | 0.632826i | 0.160897 | − | 0.986971i | \(-0.448561\pi\) |
0.935191 | + | 0.354145i | \(0.115228\pi\) | |||||||
\(242\) | −13.2162 | + | 5.03297i | −0.849571 | + | 0.323531i | ||||
\(243\) | −12.3705 | + | 9.48527i | −0.793569 | + | 0.608481i | ||||
\(244\) | 2.50251 | + | 1.44482i | 0.160207 | + | 0.0924953i | ||||
\(245\) | 10.4052 | + | 6.00743i | 0.664762 | + | 0.383800i | ||||
\(246\) | 2.55153 | + | 3.32571i | 0.162680 | + | 0.212040i | ||||
\(247\) | −2.42661 | − | 5.06107i | −0.154401 | − | 0.322028i | ||||
\(248\) | −22.5416 | −1.43140 | ||||||||
\(249\) | −24.2659 | + | 3.19292i | −1.53779 | + | 0.202343i | ||||
\(250\) | 13.5321 | + | 7.81278i | 0.855847 | + | 0.494123i | ||||
\(251\) | 2.91807 | − | 1.68475i | 0.184187 | − | 0.106340i | −0.405071 | − | 0.914285i | \(-0.632753\pi\) |
0.589258 | + | 0.807945i | \(0.299420\pi\) | |||||||
\(252\) | 0.790222 | + | 0.211859i | 0.0497793 | + | 0.0133459i | ||||
\(253\) | −10.1437 | − | 11.9088i | −0.637731 | − | 0.748700i | ||||
\(254\) | 23.0781 | − | 13.3241i | 1.44805 | − | 0.836030i | ||||
\(255\) | −13.5003 | + | 10.3577i | −0.845424 | + | 0.648621i | ||||
\(256\) | 4.03265 | + | 6.98475i | 0.252040 | + | 0.436547i | ||||
\(257\) | −13.2127 | − | 7.62835i | −0.824185 | − | 0.475843i | 0.0276725 | − | 0.999617i | \(-0.491190\pi\) |
−0.851858 | + | 0.523774i | \(0.824524\pi\) | |||||||
\(258\) | −0.379655 | − | 2.88534i | −0.0236363 | − | 0.179634i | ||||
\(259\) | 2.38307i | 0.148077i | ||||||||
\(260\) | 1.01854 | + | 2.12433i | 0.0631674 | + | 0.131745i | ||||
\(261\) | −7.38075 | + | 27.5297i | −0.456857 | + | 1.70405i | ||||
\(262\) | −3.47822 | + | 6.02446i | −0.214885 | + | 0.372192i | ||||
\(263\) | 9.11114 | − | 15.7810i | 0.561817 | − | 0.973095i | −0.435521 | − | 0.900178i | \(-0.643436\pi\) |
0.997338 | − | 0.0729167i | \(-0.0232307\pi\) | |||||||
\(264\) | 16.9507 | + | 3.62779i | 1.04324 | + | 0.223275i | ||||
\(265\) | 20.8940 | 1.28351 | ||||||||
\(266\) | −0.786181 | − | 1.36171i | −0.0482038 | − | 0.0834915i | ||||
\(267\) | 0.565617 | + | 0.234333i | 0.0346152 | + | 0.0143410i | ||||
\(268\) | −1.61063 | −0.0983849 | ||||||||
\(269\) | 23.0909 | − | 13.3316i | 1.40788 | − | 0.812839i | 0.412696 | − | 0.910869i | \(-0.364587\pi\) |
0.995183 | + | 0.0980297i | \(0.0312540\pi\) | |||||||
\(270\) | −12.4672 | − | 1.64403i | −0.758731 | − | 0.100053i | ||||
\(271\) | −19.4676 | − | 11.2396i | −1.18257 | − | 0.682758i | −0.225964 | − | 0.974136i | \(-0.572553\pi\) |
−0.956608 | + | 0.291378i | \(0.905886\pi\) | |||||||
\(272\) | 16.6238 | 1.00797 | ||||||||
\(273\) | −2.68024 | − | 4.10959i | −0.162216 | − | 0.248724i | ||||
\(274\) | − | 4.08442i | − | 0.246749i | ||||||
\(275\) | 4.55175 | + | 1.61867i | 0.274481 | + | 0.0976094i | ||||
\(276\) | 0.369940 | + | 2.81151i | 0.0222678 | + | 0.169233i | ||||
\(277\) | −11.7472 | + | 6.78225i | −0.705821 | + | 0.407506i | −0.809512 | − | 0.587103i | \(-0.800268\pi\) |
0.103691 | + | 0.994610i | \(0.466935\pi\) | |||||||
\(278\) | − | 21.5027i | − | 1.28965i | ||||||
\(279\) | 21.6477 | − | 5.79719i | 1.29601 | − | 0.347069i | ||||
\(280\) | 2.23133 | + | 3.86478i | 0.133347 | + | 0.230964i | ||||
\(281\) | 14.3432 | 0.855645 | 0.427822 | − | 0.903863i | \(-0.359281\pi\) | ||||
0.427822 | + | 0.903863i | \(0.359281\pi\) | |||||||
\(282\) | 6.02195 | + | 2.49487i | 0.358602 | + | 0.148568i | ||||
\(283\) | 9.84173 | + | 5.68212i | 0.585030 | + | 0.337767i | 0.763130 | − | 0.646245i | \(-0.223662\pi\) |
−0.178100 | + | 0.984012i | \(0.556995\pi\) | |||||||
\(284\) | 1.97478 | + | 1.14014i | 0.117181 | + | 0.0676547i | ||||
\(285\) | −3.08945 | − | 4.02684i | −0.183003 | − | 0.238529i | ||||
\(286\) | −9.04534 | − | 12.4316i | −0.534862 | − | 0.735095i | ||||
\(287\) | 1.47890i | 0.0872969i | ||||||||
\(288\) | −4.11472 | − | 4.11588i | −0.242462 | − | 0.242531i | ||||
\(289\) | −5.11874 | + | 8.86592i | −0.301102 | + | 0.521525i | ||||
\(290\) | −19.9120 | + | 11.4962i | −1.16928 | + | 0.675081i | ||||
\(291\) | 4.63449 | + | 6.04067i | 0.271678 | + | 0.354110i | ||||
\(292\) | 0.834159 | − | 0.481602i | 0.0488155 | − | 0.0281836i | ||||
\(293\) | 1.03335 | + | 1.78981i | 0.0603690 | + | 0.104562i | 0.894630 | − | 0.446807i | \(-0.147439\pi\) |
−0.834261 | + | 0.551369i | \(0.814106\pi\) | |||||||
\(294\) | 8.65162 | + | 11.2767i | 0.504573 | + | 0.657668i | ||||
\(295\) | −1.54588 | − | 2.67754i | −0.0900044 | − | 0.155892i | ||||
\(296\) | 4.57652 | − | 7.92677i | 0.266005 | − | 0.460734i | ||||
\(297\) | −17.2114 | + | 0.875414i | −0.998709 | + | 0.0507967i | ||||
\(298\) | −17.7749 | −1.02967 | ||||||||
\(299\) | 9.60396 | − | 14.0347i | 0.555411 | − | 0.811647i | ||||
\(300\) | −0.533066 | − | 0.694807i | −0.0307766 | − | 0.0401147i | ||||
\(301\) | 0.513382 | − | 0.889204i | 0.0295909 | − | 0.0512529i | ||||
\(302\) | 17.8760 | + | 10.3207i | 1.02865 | + | 0.593890i | ||||
\(303\) | −7.91642 | + | 19.1081i | −0.454786 | + | 1.09773i | ||||
\(304\) | 4.95851i | 0.284390i | ||||||||
\(305\) | −7.83523 | − | 13.5710i | −0.448644 | − | 0.777074i | ||||
\(306\) | −19.4440 | + | 5.20706i | −1.11154 | + | 0.297668i | ||||
\(307\) | 19.6728i | 1.12279i | 0.827548 | + | 0.561394i | \(0.189735\pi\) | ||||
−0.827548 | + | 0.561394i | \(0.810265\pi\) | |||||||
\(308\) | 0.586496 | + | 0.688549i | 0.0334187 | + | 0.0392337i | ||||
\(309\) | −7.73069 | + | 1.01721i | −0.439784 | + | 0.0578669i | ||||
\(310\) | 15.6564 | + | 9.03923i | 0.889224 | + | 0.513394i | ||||
\(311\) | 5.91130i | 0.335199i | 0.985855 | + | 0.167600i | \(0.0536016\pi\) | ||||
−0.985855 | + | 0.167600i | \(0.946398\pi\) | |||||||
\(312\) | 1.02306 | + | 18.8169i | 0.0579193 | + | 1.06529i | ||||
\(313\) | 29.3849 | 1.66093 | 0.830465 | − | 0.557071i | \(-0.188075\pi\) | ||||
0.830465 | + | 0.557071i | \(0.188075\pi\) | |||||||
\(314\) | −12.6503 | + | 21.9110i | −0.713900 | + | 1.23651i | ||||
\(315\) | −3.13677 | − | 3.13766i | −0.176737 | − | 0.176787i | ||||
\(316\) | 2.42891 | − | 1.40233i | 0.136637 | − | 0.0788872i | ||||
\(317\) | − | 6.52763i | − | 0.366628i | −0.983054 | − | 0.183314i | \(-0.941317\pi\) | ||
0.983054 | − | 0.183314i | \(-0.0586825\pi\) | |||||||
\(318\) | 22.8348 | + | 9.46037i | 1.28051 | + | 0.530511i | ||||
\(319\) | −23.9876 | + | 20.4323i | −1.34305 | + | 1.14399i | ||||
\(320\) | − | 16.6868i | − | 0.932821i | ||||||
\(321\) | 3.89403 | − | 9.39913i | 0.217343 | − | 0.524608i | ||||
\(322\) | 2.38206 | − | 4.12585i | 0.132747 | − | 0.229925i | ||||
\(323\) | −7.03586 | − | 4.06216i | −0.391486 | − | 0.226025i | ||||
\(324\) | 2.70505 | + | 1.56278i | 0.150281 | + | 0.0868212i | ||||
\(325\) | −0.401443 | + | 5.23648i | −0.0222680 | + | 0.290467i | ||||
\(326\) | 23.9226 | 1.32495 | ||||||||
\(327\) | −2.26585 | − | 17.2203i | −0.125302 | − | 0.952284i | ||||
\(328\) | 2.84013 | − | 4.91925i | 0.156820 | − | 0.271620i | ||||
\(329\) | 1.14987 | + | 1.99164i | 0.0633946 | + | 0.109803i | ||||
\(330\) | −10.3184 | − | 9.31695i | −0.568011 | − | 0.512881i | ||||
\(331\) | 5.63726 | + | 9.76403i | 0.309852 | + | 0.536680i | 0.978330 | − | 0.207053i | \(-0.0663871\pi\) |
−0.668478 | + | 0.743732i | \(0.733054\pi\) | |||||||
\(332\) | 2.45249 | + | 4.24783i | 0.134598 | + | 0.233130i | ||||
\(333\) | −2.35644 | + | 8.78938i | −0.129132 | + | 0.481655i | ||||
\(334\) | 16.2662 | + | 28.1739i | 0.890046 | + | 1.54161i | ||||
\(335\) | 7.56421 | + | 4.36720i | 0.413277 | + | 0.238606i | ||||
\(336\) | 0.565458 | + | 4.29743i | 0.0308483 | + | 0.234444i | ||||
\(337\) | − | 23.6987i | − | 1.29095i | −0.763782 | − | 0.645475i | \(-0.776660\pi\) | ||
0.763782 | − | 0.645475i | \(-0.223340\pi\) | |||||||
\(338\) | 10.4653 | − | 13.0313i | 0.569240 | − | 0.708808i | ||||
\(339\) | 7.24329 | − | 5.55716i | 0.393402 | − | 0.301823i | ||||
\(340\) | 2.95323 | + | 1.70505i | 0.160161 | + | 0.0924692i | ||||
\(341\) | 23.3436 | + | 8.30133i | 1.26413 | + | 0.449542i | ||||
\(342\) | −1.55315 | − | 5.79971i | −0.0839846 | − | 0.313612i | ||||
\(343\) | 10.5141i | 0.567710i | ||||||||
\(344\) | −3.41530 | + | 1.97183i | −0.184141 | + | 0.106314i | ||||
\(345\) | 5.88598 | − | 14.2072i | 0.316890 | − | 0.764888i | ||||
\(346\) | 16.3397 | 0.878429 | ||||||||
\(347\) | −3.80572 | − | 6.59170i | −0.204302 | − | 0.353861i | 0.745608 | − | 0.666385i | \(-0.232159\pi\) |
−0.949910 | + | 0.312523i | \(0.898826\pi\) | |||||||
\(348\) | 5.66317 | − | 0.745163i | 0.303578 | − | 0.0399449i | ||||
\(349\) | −19.0165 | − | 10.9792i | −1.01793 | − | 0.587703i | −0.104427 | − | 0.994533i | \(-0.533301\pi\) |
−0.913504 | + | 0.406830i | \(0.866634\pi\) | |||||||
\(350\) | 1.47126i | 0.0786421i | ||||||||
\(351\) | −5.82175 | − | 17.8075i | −0.310742 | − | 0.950494i | ||||
\(352\) | −1.16412 | − | 6.32797i | −0.0620480 | − | 0.337282i | ||||
\(353\) | 17.8147 | + | 10.2853i | 0.948183 | + | 0.547434i | 0.892516 | − | 0.451016i | \(-0.148938\pi\) |
0.0556668 | + | 0.998449i | \(0.482272\pi\) | |||||||
\(354\) | −0.477134 | − | 3.62618i | −0.0253594 | − | 0.192729i | ||||
\(355\) | −6.18293 | − | 10.7091i | −0.328156 | − | 0.568383i | ||||
\(356\) | − | 0.122696i | − | 0.00650290i | ||||||
\(357\) | −6.56107 | − | 2.71823i | −0.347249 | − | 0.143864i | ||||
\(358\) | 7.92781 | − | 4.57712i | 0.418998 | − | 0.241909i | ||||
\(359\) | −1.30326 | −0.0687833 | −0.0343917 | − | 0.999408i | \(-0.510949\pi\) | ||||
−0.0343917 | + | 0.999408i | \(0.510949\pi\) | |||||||
\(360\) | 4.40812 | + | 16.4607i | 0.232329 | + | 0.867553i | ||||
\(361\) | −8.28835 | + | 14.3558i | −0.436229 | + | 0.755571i | ||||
\(362\) | 13.0419 | − | 22.5893i | 0.685468 | − | 1.18727i | ||||
\(363\) | −16.2178 | − | 9.99923i | −0.851211 | − | 0.524823i | ||||
\(364\) | −0.555286 | + | 0.811465i | −0.0291049 | + | 0.0425323i | ||||
\(365\) | −5.22342 | −0.273406 | ||||||||
\(366\) | −2.41834 | − | 18.3792i | −0.126409 | − | 0.960695i | ||||
\(367\) | 3.17542 | − | 5.49999i | 0.165756 | − | 0.287097i | −0.771168 | − | 0.636632i | \(-0.780327\pi\) |
0.936923 | + | 0.349535i | \(0.113660\pi\) | |||||||
\(368\) | −13.0111 | + | 7.51193i | −0.678248 | + | 0.391587i | ||||
\(369\) | −1.46238 | + | 5.45457i | −0.0761283 | + | 0.283954i | ||||
\(370\) | −6.35729 | + | 3.67038i | −0.330500 | + | 0.190814i | ||||
\(371\) | 4.36024 | + | 7.55215i | 0.226372 | + | 0.392088i | ||||
\(372\) | −2.73382 | − | 3.56331i | −0.141742 | − | 0.184749i | ||||
\(373\) | −26.6370 | + | 15.3789i | −1.37921 | + | 0.796288i | −0.992064 | − | 0.125731i | \(-0.959872\pi\) |
−0.387146 | + | 0.922018i | \(0.626539\pi\) | |||||||
\(374\) | −20.9673 | − | 7.45629i | −1.08419 | − | 0.385556i | ||||
\(375\) | 2.74624 | + | 20.8712i | 0.141815 | + | 1.07778i | ||||
\(376\) | − | 8.83300i | − | 0.455527i | ||||||
\(377\) | −28.2698 | − | 19.3450i | −1.45597 | − | 0.996321i | ||||
\(378\) | −2.00747 | − | 4.84936i | −0.103253 | − | 0.249424i | ||||
\(379\) | 4.51316 | − | 7.81702i | 0.231825 | − | 0.401533i | −0.726520 | − | 0.687145i | \(-0.758864\pi\) |
0.958345 | + | 0.285612i | \(0.0921969\pi\) | |||||||
\(380\) | −0.508577 | + | 0.880881i | −0.0260894 | + | 0.0451882i | ||||
\(381\) | 33.1673 | + | 13.7411i | 1.69921 | + | 0.703978i | ||||
\(382\) | − | 28.6025i | − | 1.46343i | ||||||
\(383\) | 22.5219 | − | 13.0030i | 1.15081 | − | 0.664423i | 0.201729 | − | 0.979441i | \(-0.435344\pi\) |
0.949086 | + | 0.315019i | \(0.102011\pi\) | |||||||
\(384\) | 4.98325 | − | 12.0282i | 0.254301 | − | 0.613813i | ||||
\(385\) | −0.887445 | − | 4.82400i | −0.0452284 | − | 0.245854i | ||||
\(386\) | −17.4924 | + | 10.0992i | −0.890340 | + | 0.514038i | ||||
\(387\) | 2.77275 | − | 2.77197i | 0.140947 | − | 0.140907i | ||||
\(388\) | 0.762917 | − | 1.32141i | 0.0387312 | − | 0.0670844i | ||||
\(389\) | 2.46705i | 0.125084i | 0.998042 | + | 0.0625422i | \(0.0199208\pi\) | ||||
−0.998042 | + | 0.0625422i | \(0.980079\pi\) | |||||||
\(390\) | 6.83501 | − | 13.4796i | 0.346104 | − | 0.682565i | ||||
\(391\) | − | 24.6160i | − | 1.24488i | ||||||
\(392\) | 9.63017 | − | 16.6799i | 0.486397 | − | 0.842465i | ||||
\(393\) | −9.29179 | + | 1.22262i | −0.468709 | + | 0.0616729i | ||||
\(394\) | 5.30619 | + | 9.19059i | 0.267322 | + | 0.463015i | ||||
\(395\) | −15.2096 | −0.765277 | ||||||||
\(396\) | 1.48229 | + | 3.11949i | 0.0744879 | + | 0.156760i | ||||
\(397\) | −6.99348 | − | 12.1131i | −0.350993 | − | 0.607937i | 0.635431 | − | 0.772158i | \(-0.280822\pi\) |
−0.986424 | + | 0.164221i | \(0.947489\pi\) | |||||||
\(398\) | 6.32180 | 0.316883 | ||||||||
\(399\) | 0.810785 | − | 1.95702i | 0.0405900 | − | 0.0979733i | ||||
\(400\) | 2.31984 | − | 4.01808i | 0.115992 | − | 0.200904i | ||||
\(401\) | 2.77462 | + | 1.60193i | 0.138558 | + | 0.0799966i | 0.567677 | − | 0.823252i | \(-0.307842\pi\) |
−0.429119 | + | 0.903248i | \(0.641176\pi\) | |||||||
\(402\) | 6.28944 | + | 8.19776i | 0.313689 | + | 0.408867i | ||||
\(403\) | −2.05880 | + | 26.8552i | −0.102556 | + | 1.33775i | ||||
\(404\) | 4.14503 | 0.206223 | ||||||||
\(405\) | −8.46661 | − | 14.6742i | −0.420709 | − | 0.729167i | ||||
\(406\) | −8.31062 | − | 4.79814i | −0.412449 | − | 0.238128i | ||||
\(407\) | −7.65850 | + | 6.52340i | −0.379618 | + | 0.323353i | ||||
\(408\) | 16.6038 | + | 21.6416i | 0.822009 | + | 1.07142i | ||||
\(409\) | 24.4146 | − | 14.0958i | 1.20723 | − | 0.696992i | 0.245074 | − | 0.969504i | \(-0.421188\pi\) |
0.962152 | + | 0.272512i | \(0.0878545\pi\) | |||||||
\(410\) | −3.94525 | + | 2.27779i | −0.194842 | + | 0.112492i | ||||
\(411\) | 4.36576 | − | 3.34947i | 0.215347 | − | 0.165217i | ||||
\(412\) | 0.781318 | + | 1.35328i | 0.0384928 | + | 0.0666715i | ||||
\(413\) | 0.645197 | − | 1.11751i | 0.0317481 | − | 0.0549893i | ||||
\(414\) | 12.8654 | − | 12.8617i | 0.632300 | − | 0.632121i | ||||
\(415\) | − | 26.5995i | − | 1.30572i | ||||||
\(416\) | 6.30717 | − | 3.02407i | 0.309234 | − | 0.148267i | ||||
\(417\) | 22.9839 | − | 17.6336i | 1.12552 | − | 0.863519i | ||||
\(418\) | 2.22404 | − | 6.25407i | 0.108781 | − | 0.305897i | ||||
\(419\) | 10.9461 | + | 6.31973i | 0.534752 | + | 0.308739i | 0.742949 | − | 0.669348i | \(-0.233426\pi\) |
−0.208198 | + | 0.978087i | \(0.566760\pi\) | |||||||
\(420\) | −0.340318 | + | 0.821437i | −0.0166058 | + | 0.0400820i | ||||
\(421\) | 0.782107 | 0.0381176 | 0.0190588 | − | 0.999818i | \(-0.493933\pi\) | ||||
0.0190588 | + | 0.999818i | \(0.493933\pi\) | |||||||
\(422\) | 11.1575 | − | 6.44177i | 0.543137 | − | 0.313580i | ||||
\(423\) | 2.27165 | + | 8.48270i | 0.110451 | + | 0.412443i | ||||
\(424\) | − | 33.4941i | − | 1.62662i | ||||||
\(425\) | 3.80096 | + | 6.58346i | 0.184374 | + | 0.319345i | ||||
\(426\) | −1.90836 | − | 14.5034i | −0.0924603 | − | 0.702690i | ||||
\(427\) | 3.27016 | − | 5.66409i | 0.158254 | − | 0.274104i | ||||
\(428\) | −2.03891 | −0.0985543 | ||||||||
\(429\) | 5.87016 | − | 19.8631i | 0.283414 | − | 0.958998i | ||||
\(430\) | 3.16282 | 0.152525 | ||||||||
\(431\) | 5.74017 | − | 9.94227i | 0.276494 | − | 0.478903i | −0.694017 | − | 0.719959i | \(-0.744161\pi\) |
0.970511 | + | 0.241056i | \(0.0774939\pi\) | |||||||
\(432\) | −2.16385 | + | 16.4092i | −0.104108 | + | 0.789486i | ||||
\(433\) | −6.36473 | − | 11.0240i | −0.305869 | − | 0.529781i | 0.671585 | − | 0.740927i | \(-0.265614\pi\) |
−0.977454 | + | 0.211146i | \(0.932280\pi\) | |||||||
\(434\) | 7.54534i | 0.362188i | ||||||||
\(435\) | −28.6172 | − | 11.8560i | −1.37209 | − | 0.568452i | ||||
\(436\) | −3.01447 | + | 1.74040i | −0.144367 | + | 0.0833502i | ||||
\(437\) | 7.34239 | 0.351234 | ||||||||
\(438\) | −5.70860 | − | 2.36505i | −0.272768 | − | 0.113007i | ||||
\(439\) | 1.54489 | + | 0.891944i | 0.0737337 | + | 0.0425702i | 0.536414 | − | 0.843955i | \(-0.319779\pi\) |
−0.462680 | + | 0.886525i | \(0.653112\pi\) | |||||||
\(440\) | −6.31225 | + | 17.7502i | −0.300924 | + | 0.846209i | ||||
\(441\) | −4.95856 | + | 18.4951i | −0.236122 | + | 0.880720i | ||||
\(442\) | 1.84922 | − | 24.1215i | 0.0879584 | − | 1.14734i | ||||
\(443\) | 32.6843i | 1.55288i | 0.630193 | + | 0.776439i | \(0.282976\pi\) | ||||
−0.630193 | + | 0.776439i | \(0.717024\pi\) | |||||||
\(444\) | 1.80807 | − | 0.237907i | 0.0858074 | − | 0.0112906i | ||||
\(445\) | −0.332690 | + | 0.576235i | −0.0157710 | + | 0.0273162i | ||||
\(446\) | −8.81187 | − | 15.2626i | −0.417254 | − | 0.722705i | ||||
\(447\) | −14.5765 | − | 18.9993i | −0.689445 | − | 0.898634i | ||||
\(448\) | 6.03145 | − | 3.48226i | 0.284959 | − | 0.164521i | ||||
\(449\) | 11.2128 | − | 6.47370i | 0.529163 | − | 0.305513i | −0.211512 | − | 0.977375i | \(-0.567839\pi\) |
0.740676 | + | 0.671863i | \(0.234506\pi\) | |||||||
\(450\) | −1.45482 | + | 5.42638i | −0.0685807 | + | 0.255802i | ||||
\(451\) | −4.75277 | + | 4.04833i | −0.223799 | + | 0.190629i | ||||
\(452\) | −1.58449 | − | 0.914804i | −0.0745280 | − | 0.0430288i | ||||
\(453\) | 3.62780 | + | 27.5709i | 0.170449 | + | 1.29540i | ||||
\(454\) | 1.16384 | 0.0546217 | ||||||||
\(455\) | 4.80814 | − | 2.30534i | 0.225409 | − | 0.108076i | ||||
\(456\) | −6.45520 | + | 4.95252i | −0.302293 | + | 0.231923i | ||||
\(457\) | 21.4498 | + | 12.3840i | 1.00338 | + | 0.579300i | 0.909246 | − | 0.416260i | \(-0.136659\pi\) |
0.0941315 | + | 0.995560i | \(0.469993\pi\) | |||||||
\(458\) | −10.3730 | + | 17.9666i | −0.484699 | + | 0.839523i | ||||
\(459\) | −21.5110 | − | 16.5133i | −1.00405 | − | 0.770773i | ||||
\(460\) | −3.08189 | −0.143694 | ||||||||
\(461\) | −10.2211 | − | 17.7035i | −0.476046 | − | 0.824536i | 0.523577 | − | 0.851978i | \(-0.324597\pi\) |
−0.999623 | + | 0.0274423i | \(0.991264\pi\) | |||||||
\(462\) | 1.21433 | − | 5.67389i | 0.0564955 | − | 0.263973i | ||||
\(463\) | 6.99131 | 0.324914 | 0.162457 | − | 0.986716i | \(-0.448058\pi\) | ||||
0.162457 | + | 0.986716i | \(0.448058\pi\) | |||||||
\(464\) | 15.1311 | + | 26.2079i | 0.702445 | + | 1.21667i | ||||
\(465\) | 3.17735 | + | 24.1476i | 0.147346 | + | 1.11982i | ||||
\(466\) | 16.8244 | − | 29.1408i | 0.779377 | − | 1.34992i | ||||
\(467\) | − | 12.4446i | − | 0.575867i | −0.957650 | − | 0.287934i | \(-0.907032\pi\) | ||
0.957650 | − | 0.287934i | \(-0.0929682\pi\) | |||||||
\(468\) | −2.85043 | + | 2.44381i | −0.131761 | + | 0.112965i | ||||
\(469\) | 3.64545i | 0.168331i | ||||||||
\(470\) | −3.54205 | + | 6.13500i | −0.163382 | + | 0.282987i | ||||
\(471\) | −33.7943 | + | 4.44667i | −1.55716 | + | 0.204892i | ||||
\(472\) | −4.29221 | + | 2.47811i | −0.197565 | + | 0.114064i | ||||
\(473\) | 4.26297 | − | 0.784236i | 0.196012 | − | 0.0360592i | ||||
\(474\) | −16.6223 | − | 6.88657i | −0.763488 | − | 0.316311i | ||||
\(475\) | −1.96369 | + | 1.13374i | −0.0901005 | + | 0.0520195i | ||||
\(476\) | 1.42326i | 0.0652350i | ||||||||
\(477\) | 8.61391 | + | 32.1658i | 0.394404 | + | 1.47277i | ||||
\(478\) | −7.73530 | + | 13.3979i | −0.353805 | + | 0.612807i | ||||
\(479\) | −3.11718 | + | 5.39911i | −0.142428 | + | 0.246692i | −0.928410 | − | 0.371557i | \(-0.878824\pi\) |
0.785983 | + | 0.618249i | \(0.212157\pi\) | |||||||
\(480\) | 5.01830 | − | 3.85011i | 0.229053 | − | 0.175733i | ||||
\(481\) | −9.02566 | − | 6.17627i | −0.411535 | − | 0.281614i | ||||
\(482\) | 25.2606i | 1.15059i | ||||||||
\(483\) | 6.36348 | − | 0.837310i | 0.289549 | − | 0.0380989i | ||||
\(484\) | −0.607329 | + | 3.76965i | −0.0276059 | + | 0.171348i | ||||
\(485\) | −7.16597 | + | 4.13727i | −0.325390 | + | 0.187864i | ||||
\(486\) | −2.60887 | − | 19.8707i | −0.118341 | − | 0.901353i | ||||
\(487\) | −3.02035 | − | 5.23140i | −0.136865 | − | 0.237057i | 0.789443 | − | 0.613823i | \(-0.210369\pi\) |
−0.926308 | + | 0.376766i | \(0.877036\pi\) | |||||||
\(488\) | −21.7549 | + | 12.5602i | −0.984800 | + | 0.568575i | ||||
\(489\) | 19.6180 | + | 25.5705i | 0.887158 | + | 1.15634i | ||||
\(490\) | −13.3774 | + | 7.72342i | −0.604328 | + | 0.348909i | ||||
\(491\) | 13.6385 | − | 23.6226i | 0.615498 | − | 1.06607i | −0.374799 | − | 0.927106i | \(-0.622288\pi\) |
0.990297 | − | 0.138967i | \(-0.0443782\pi\) | |||||||
\(492\) | 1.12207 | − | 0.147642i | 0.0505867 | − | 0.00665622i | ||||
\(493\) | −49.5835 | −2.23313 | ||||||||
\(494\) | 7.19488 | + | 0.551580i | 0.323713 | + | 0.0248167i | ||||
\(495\) | 1.49696 | − | 18.6696i | 0.0672834 | − | 0.839138i | ||||
\(496\) | 11.8973 | − | 20.6067i | 0.534204 | − | 0.925268i | ||||
\(497\) | 2.58055 | − | 4.46964i | 0.115753 | − | 0.200491i | ||||
\(498\) | 12.0437 | − | 29.0702i | 0.539691 | − | 1.30267i | ||||
\(499\) | −24.4043 | −1.09249 | −0.546244 | − | 0.837626i | \(-0.683943\pi\) | ||||
−0.546244 | + | 0.837626i | \(0.683943\pi\) | |||||||
\(500\) | 3.65357 | − | 2.10939i | 0.163393 | − | 0.0943348i | ||||
\(501\) | −16.7752 | + | 40.4909i | −0.749463 | + | 1.80900i | ||||
\(502\) | 4.33198i | 0.193346i | ||||||||
\(503\) | −2.96644 | − | 5.13803i | −0.132267 | − | 0.229093i | 0.792283 | − | 0.610154i | \(-0.208892\pi\) |
−0.924550 | + | 0.381060i | \(0.875559\pi\) | |||||||
\(504\) | −5.02981 | + | 5.02838i | −0.224045 | + | 0.223982i | ||||
\(505\) | −19.4668 | − | 11.2392i | −0.866262 | − | 0.500137i | ||||
\(506\) | 19.7799 | − | 3.63881i | 0.879324 | − | 0.161765i | ||||
\(507\) | 22.5111 | + | 0.499768i | 0.999754 | + | 0.0221955i | ||||
\(508\) | − | 7.19483i | − | 0.319219i | ||||||
\(509\) | −25.5552 | − | 14.7543i | −1.13271 | − | 0.653972i | −0.188097 | − | 0.982150i | \(-0.560232\pi\) |
−0.944616 | + | 0.328179i | \(0.893565\pi\) | |||||||
\(510\) | −2.85391 | − | 21.6894i | −0.126373 | − | 0.960424i | ||||
\(511\) | −1.09004 | − | 1.88801i | −0.0482206 | − | 0.0835205i | ||||
\(512\) | −25.4029 | −1.12266 | ||||||||
\(513\) | 4.92552 | − | 6.41625i | 0.217467 | − | 0.283284i | ||||
\(514\) | 16.9868 | − | 9.80736i | 0.749257 | − | 0.432584i | ||||
\(515\) | − | 8.47413i | − | 0.373415i | ||||||
\(516\) | −0.725904 | − | 0.300740i | −0.0319562 | − | 0.0132393i | ||||
\(517\) | −3.25290 | + | 9.14725i | −0.143062 | + | 0.402296i | ||||
\(518\) | −2.65332 | − | 1.53189i | −0.116580 | − | 0.0673076i | ||||
\(519\) | 13.3996 | + | 17.4652i | 0.588176 | + | 0.766639i | ||||
\(520\) | −20.4204 | − | 1.56549i | −0.895495 | − | 0.0686512i | ||||
\(521\) | 10.6312i | 0.465763i | 0.972505 | + | 0.232882i | \(0.0748154\pi\) | ||||
−0.972505 | + | 0.232882i | \(0.925185\pi\) | |||||||
\(522\) | −25.9072 | − | 25.9145i | −1.13393 | − | 1.13425i | ||||
\(523\) | 37.9756 | + | 21.9252i | 1.66056 | + | 0.958723i | 0.972449 | + | 0.233114i | \(0.0748916\pi\) |
0.688108 | + | 0.725609i | \(0.258442\pi\) | |||||||
\(524\) | 0.939094 | + | 1.62656i | 0.0410245 | + | 0.0710565i | ||||
\(525\) | −1.57260 | + | 1.20652i | −0.0686340 | + | 0.0526570i | ||||
\(526\) | 11.7137 | + | 20.2887i | 0.510741 | + | 0.884630i | ||||
\(527\) | 19.4932 | + | 33.7632i | 0.849137 | + | 1.47075i | ||||
\(528\) | −12.2628 | + | 13.5810i | −0.533670 | + | 0.591035i | ||||
\(529\) | −0.376592 | − | 0.652276i | −0.0163736 | − | 0.0283598i | ||||
\(530\) | −13.4312 | + | 23.2635i | −0.583413 | + | 1.01050i | ||||
\(531\) | 3.48467 | − | 3.48369i | 0.151222 | − | 0.151179i | ||||
\(532\) | −0.424526 | −0.0184055 | ||||||||
\(533\) | −5.60120 | − | 3.83291i | −0.242615 | − | 0.166022i | ||||
\(534\) | −0.624498 | + | 0.479124i | −0.0270247 | + | 0.0207337i | ||||
\(535\) | 9.57558 | + | 5.52846i | 0.413988 | + | 0.239016i | ||||
\(536\) | 7.00081 | − | 12.1258i | 0.302389 | − | 0.523753i | ||||
\(537\) | 11.3937 | + | 4.72037i | 0.491674 | + | 0.203699i | ||||
\(538\) | 34.2793i | 1.47789i | ||||||||
\(539\) | −16.1155 | + | 13.7269i | −0.694142 | + | 0.591259i | ||||
\(540\) | −2.06744 | + | 2.69315i | −0.0889683 | + | 0.115895i | ||||
\(541\) | 23.7234i | 1.01995i | 0.860189 | + | 0.509975i | \(0.170345\pi\) | ||||
−0.860189 | + | 0.509975i | \(0.829655\pi\) | |||||||
\(542\) | 25.0284 | − | 14.4502i | 1.07506 | − | 0.620688i | ||||
\(543\) | 34.8404 | − | 4.58432i | 1.49515 | − | 0.196732i | ||||
\(544\) | 5.06231 | − | 8.76818i | 0.217045 | − | 0.375933i | ||||
\(545\) | 18.8763 | 0.808572 | ||||||||
\(546\) | 6.29855 | − | 0.342448i | 0.269553 | − | 0.0146554i | ||||
\(547\) | 5.58737i | 0.238899i | 0.992840 | + | 0.119449i | \(0.0381129\pi\) | ||||
−0.992840 | + | 0.119449i | \(0.961887\pi\) | |||||||
\(548\) | −0.955020 | − | 0.551381i | −0.0407964 | − | 0.0235538i | ||||
\(549\) | 17.6620 | − | 17.6570i | 0.753795 | − | 0.753582i | ||||
\(550\) | −4.72820 | + | 4.02741i | −0.201611 | + | 0.171729i | ||||
\(551\) | − | 14.7896i | − | 0.630059i | ||||||
\(552\) | −22.7747 | − | 9.43548i | −0.969356 | − | 0.401601i | ||||
\(553\) | −3.17398 | − | 5.49750i | −0.134972 | − | 0.233778i | ||||
\(554\) | − | 17.4392i | − | 0.740919i | ||||||
\(555\) | −9.13657 | − | 3.78525i | −0.387826 | − | 0.160675i | ||||
\(556\) | −5.02777 | − | 2.90279i | −0.213225 | − | 0.123106i | ||||
\(557\) | −18.3115 | + | 31.7164i | −0.775882 | + | 1.34387i | 0.158415 | + | 0.987373i | \(0.449362\pi\) |
−0.934297 | + | 0.356495i | \(0.883972\pi\) | |||||||
\(558\) | −7.46102 | + | 27.8291i | −0.315850 | + | 1.17810i | ||||
\(559\) | 2.03723 | + | 4.24896i | 0.0861656 | + | 0.179712i | ||||
\(560\) | −4.71070 | −0.199064 | ||||||||
\(561\) | −9.22460 | − | 28.5262i | −0.389463 | − | 1.20438i | ||||
\(562\) | −9.22015 | + | 15.9698i | −0.388929 | + | 0.673644i | ||||
\(563\) | 5.20356 | + | 9.01282i | 0.219304 | + | 0.379845i | 0.954595 | − | 0.297906i | \(-0.0962881\pi\) |
−0.735292 | + | 0.677751i | \(0.762955\pi\) | |||||||
\(564\) | 1.39629 | − | 1.07126i | 0.0587945 | − | 0.0451080i | ||||
\(565\) | 4.96095 | + | 8.59262i | 0.208709 | + | 0.361494i | ||||
\(566\) | −12.6530 | + | 7.30520i | −0.531844 | + | 0.307060i | ||||
\(567\) | 3.53715 | − | 6.12252i | 0.148546 | − | 0.257121i | ||||
\(568\) | −17.1672 | + | 9.91151i | −0.720321 | + | 0.415878i | ||||
\(569\) | −4.33236 | + | 7.50387i | −0.181622 | + | 0.314579i | −0.942433 | − | 0.334395i | \(-0.891468\pi\) |
0.760811 | + | 0.648973i | \(0.224801\pi\) | |||||||
\(570\) | 6.46946 | − | 0.851255i | 0.270976 | − | 0.0356551i | ||||
\(571\) | 25.4592i | 1.06543i | 0.846294 | + | 0.532717i | \(0.178829\pi\) | ||||
−0.846294 | + | 0.532717i | \(0.821171\pi\) | |||||||
\(572\) | −4.12785 | + | 0.436766i | −0.172594 | + | 0.0182621i | ||||
\(573\) | 30.5727 | − | 23.4558i | 1.27719 | − | 0.979880i | ||||
\(574\) | −1.64661 | − | 0.950673i | −0.0687284 | − | 0.0396803i | ||||
\(575\) | −5.94983 | − | 3.43514i | −0.248125 | − | 0.143255i | ||||
\(576\) | 25.6888 | − | 6.87941i | 1.07037 | − | 0.286642i | ||||
\(577\) | 14.7178 | 0.612711 | 0.306356 | − | 0.951917i | \(-0.400890\pi\) | ||||
0.306356 | + | 0.951917i | \(0.400890\pi\) | |||||||
\(578\) | −6.58089 | − | 11.3984i | −0.273729 | − | 0.474112i | ||||
\(579\) | −25.1397 | − | 10.4153i | −1.04477 | − | 0.432845i | ||||
\(580\) | 6.20779i | 0.257764i | ||||||||
\(581\) | 9.61440 | − | 5.55088i | 0.398873 | − | 0.230289i | ||||
\(582\) | −9.70484 | + | 1.27697i | −0.402279 | + | 0.0529320i | ||||
\(583\) | −12.3348 | + | 34.6857i | −0.510853 | + | 1.43653i | ||||
\(584\) | 8.37338i | 0.346493i | ||||||||
\(585\) | 20.0132 | − | 3.74827i | 0.827444 | − | 0.154972i | ||||
\(586\) | −2.65704 | −0.109762 | ||||||||
\(587\) | 7.41690 | + | 4.28215i | 0.306128 | + | 0.176743i | 0.645193 | − | 0.764020i | \(-0.276777\pi\) |
−0.339064 | + | 0.940763i | \(0.610110\pi\) | |||||||
\(588\) | 3.80465 | − | 0.500618i | 0.156901 | − | 0.0206451i | ||||
\(589\) | −10.0708 | + | 5.81438i | −0.414960 | + | 0.239577i | ||||
\(590\) | 3.97490 | 0.163644 | ||||||||
\(591\) | −5.47225 | + | 13.2085i | −0.225098 | + | 0.543326i | ||||
\(592\) | 4.83090 | + | 8.36736i | 0.198549 | + | 0.343896i | ||||
\(593\) | −41.1367 | −1.68928 | −0.844641 | − | 0.535334i | \(-0.820186\pi\) | ||||
−0.844641 | + | 0.535334i | \(0.820186\pi\) | |||||||
\(594\) | 10.0892 | − | 19.7260i | 0.413966 | − | 0.809367i | ||||
\(595\) | 3.85915 | − | 6.68424i | 0.158210 | − | 0.274027i | ||||
\(596\) | −2.39954 | + | 4.15613i | −0.0982891 | + | 0.170242i | ||||
\(597\) | 5.18426 | + | 6.75725i | 0.212178 | + | 0.276556i | ||||
\(598\) | 9.45261 | + | 19.7149i | 0.386546 | + | 0.806202i | ||||
\(599\) | 19.6210i | 0.801694i | 0.916145 | + | 0.400847i | \(0.131284\pi\) | ||||
−0.916145 | + | 0.400847i | \(0.868716\pi\) | |||||||
\(600\) | 7.54795 | − | 0.993163i | 0.308144 | − | 0.0405457i | ||||
\(601\) | 11.3439 | + | 6.54940i | 0.462727 | + | 0.267156i | 0.713190 | − | 0.700970i | \(-0.247250\pi\) |
−0.250463 | + | 0.968126i | \(0.580583\pi\) | |||||||
\(602\) | 0.660028 | + | 1.14320i | 0.0269007 | + | 0.0465934i | ||||
\(603\) | −3.60471 | + | 13.4453i | −0.146795 | + | 0.547536i | ||||
\(604\) | 4.82639 | − | 2.78652i | 0.196383 | − | 0.113382i | ||||
\(605\) | 13.0736 | − | 16.0571i | 0.531519 | − | 0.652815i | ||||
\(606\) | −16.1861 | − | 21.0973i | −0.657517 | − | 0.857018i | ||||
\(607\) | −1.35973 | + | 0.785041i | −0.0551898 | + | 0.0318638i | −0.527341 | − | 0.849654i | \(-0.676811\pi\) |
0.472151 | + | 0.881518i | \(0.343478\pi\) | |||||||
\(608\) | 2.61535 | + | 1.50997i | 0.106066 | + | 0.0612374i | ||||
\(609\) | −1.68658 | − | 12.8178i | −0.0683435 | − | 0.519405i | ||||
\(610\) | 20.1467 | 0.815715 | ||||||||
\(611\) | −10.5233 | − | 0.806745i | −0.425727 | − | 0.0326374i | ||||
\(612\) | −1.40735 | + | 5.24934i | −0.0568889 | + | 0.212192i | ||||
\(613\) | 13.4805 | + | 7.78299i | 0.544474 | + | 0.314352i | 0.746890 | − | 0.664947i | \(-0.231546\pi\) |
−0.202416 | + | 0.979300i | \(0.564879\pi\) | |||||||
\(614\) | −21.9038 | − | 12.6462i | −0.883965 | − | 0.510357i | ||||
\(615\) | −5.67003 | − | 2.34907i | −0.228638 | − | 0.0947238i | ||||
\(616\) | −7.73308 | + | 1.42261i | −0.311575 | + | 0.0573188i | ||||
\(617\) | 0.866000 | − | 0.499986i | 0.0348639 | − | 0.0201287i | −0.482467 | − | 0.875914i | \(-0.660259\pi\) |
0.517331 | + | 0.855786i | \(0.326926\pi\) | |||||||
\(618\) | 3.83690 | − | 9.26125i | 0.154343 | − | 0.372542i | ||||
\(619\) | −13.3439 | −0.536335 | −0.268168 | − | 0.963372i | \(-0.586418\pi\) | ||||
−0.268168 | + | 0.963372i | \(0.586418\pi\) | |||||||
\(620\) | 4.22711 | − | 2.44052i | 0.169765 | − | 0.0980138i | ||||
\(621\) | 24.2981 | + | 3.20415i | 0.975049 | + | 0.128578i | ||||
\(622\) | −6.58165 | − | 3.79992i | −0.263900 | − | 0.152363i | ||||
\(623\) | −0.277707 | −0.0111261 | ||||||||
\(624\) | −17.7416 | − | 8.99613i | −0.710232 | − | 0.360133i | ||||
\(625\) | −15.5953 | −0.623813 | ||||||||
\(626\) | −18.8893 | + | 32.7172i | −0.754967 | + | 1.30764i | ||||
\(627\) | 8.50871 | − | 2.75149i | 0.339805 | − | 0.109884i | ||||
\(628\) | 3.41549 | + | 5.91581i | 0.136293 | + | 0.236067i | ||||
\(629\) | −15.8305 | −0.631201 | ||||||||
\(630\) | 5.50986 | − | 1.47553i | 0.219518 | − | 0.0587864i | ||||
\(631\) | −10.0481 | − | 17.4037i | −0.400007 | − | 0.692832i | 0.593719 | − | 0.804672i | \(-0.297659\pi\) |
−0.993726 | + | 0.111840i | \(0.964326\pi\) | |||||||
\(632\) | 24.3816i | 0.969849i | ||||||||
\(633\) | 16.0353 | + | 6.64337i | 0.637346 | + | 0.264050i | ||||
\(634\) | 7.26787 | + | 4.19611i | 0.288644 | + | 0.166649i | ||||
\(635\) | −19.5087 | + | 33.7900i | −0.774178 | + | 1.34091i | ||||
\(636\) | 5.29464 | − | 4.06212i | 0.209946 | − | 0.161074i | ||||
\(637\) | −18.9923 | − | 12.9964i | −0.752502 | − | 0.514938i | ||||
\(638\) | −7.32957 | − | 39.8423i | −0.290180 | − | 1.57737i | ||||
\(639\) | 13.9374 | − | 13.9335i | 0.551355 | − | 0.551199i | ||||
\(640\) | 12.2540 | + | 7.07487i | 0.484384 | + | 0.279659i | ||||
\(641\) | 23.8108 | − | 13.7472i | 0.940469 | − | 0.542980i | 0.0503617 | − | 0.998731i | \(-0.483963\pi\) |
0.890107 | + | 0.455751i | \(0.150629\pi\) | |||||||
\(642\) | 7.96184 | + | 10.3776i | 0.314229 | + | 0.409571i | ||||
\(643\) | 9.09258 | + | 15.7488i | 0.358576 | + | 0.621072i | 0.987723 | − | 0.156214i | \(-0.0499289\pi\) |
−0.629147 | + | 0.777286i | \(0.716596\pi\) | |||||||
\(644\) | −0.643139 | − | 1.11395i | −0.0253432 | − | 0.0438957i | ||||
\(645\) | 2.59371 | + | 3.38068i | 0.102127 | + | 0.133114i | ||||
\(646\) | 9.04563 | − | 5.22250i | 0.355896 | − | 0.205476i | ||||
\(647\) | −0.273139 | − | 0.157697i | −0.0107382 | − | 0.00619970i | 0.494621 | − | 0.869109i | \(-0.335307\pi\) |
−0.505359 | + | 0.862909i | \(0.668640\pi\) | |||||||
\(648\) | −23.5234 | + | 13.5724i | −0.924086 | + | 0.533172i | ||||
\(649\) | 5.35752 | − | 0.985594i | 0.210301 | − | 0.0386880i | ||||
\(650\) | −5.57225 | − | 3.81309i | −0.218562 | − | 0.149562i | ||||
\(651\) | −8.06508 | + | 6.18764i | −0.316095 | + | 0.242513i | ||||
\(652\) | 3.22947 | − | 5.59360i | 0.126476 | − | 0.219062i | ||||
\(653\) | 10.1817 | + | 5.87839i | 0.398439 | + | 0.230039i | 0.685810 | − | 0.727780i | \(-0.259448\pi\) |
−0.287371 | + | 0.957819i | \(0.592781\pi\) | |||||||
\(654\) | 20.6296 | + | 8.54679i | 0.806683 | + | 0.334206i | ||||
\(655\) | − | 10.1854i | − | 0.397975i | ||||||
\(656\) | 2.99799 | + | 5.19267i | 0.117052 | + | 0.202740i | ||||
\(657\) | −2.15344 | − | 8.04131i | −0.0840138 | − | 0.313721i | ||||
\(658\) | −2.95666 | −0.115263 | ||||||||
\(659\) | 12.1807 | + | 21.0976i | 0.474493 | + | 0.821846i | 0.999573 | − | 0.0292066i | \(-0.00929806\pi\) |
−0.525080 | + | 0.851053i | \(0.675965\pi\) | |||||||
\(660\) | −3.57144 | + | 1.15491i | −0.139018 | + | 0.0449547i | ||||
\(661\) | −8.76690 | + | 15.1847i | −0.340993 | + | 0.590617i | −0.984617 | − | 0.174724i | \(-0.944097\pi\) |
0.643624 | + | 0.765342i | \(0.277430\pi\) | |||||||
\(662\) | −14.4951 | −0.563366 | ||||||||
\(663\) | 27.2995 | − | 17.8045i | 1.06022 | − | 0.691470i | ||||
\(664\) | −42.6402 | −1.65476 | ||||||||
\(665\) | 1.99376 | + | 1.15110i | 0.0773145 | + | 0.0446376i | ||||
\(666\) | −8.27134 | − | 8.27368i | −0.320508 | − | 0.320599i | ||||
\(667\) | 38.8077 | − | 22.4056i | 1.50264 | − | 0.867550i | ||||
\(668\) | 8.78350 | 0.339844 | ||||||||
\(669\) | 9.08764 | − | 21.9351i | 0.351348 | − | 0.848060i | ||||
\(670\) | −9.72490 | + | 5.61467i | −0.375706 | + | 0.216914i | ||||
\(671\) | 27.1544 | − | 4.99546i | 1.04829 | − | 0.192848i | ||||
\(672\) | 2.43886 | + | 1.01041i | 0.0940810 | + | 0.0389774i | ||||
\(673\) | 3.21516 | + | 1.85627i | 0.123935 | + | 0.0715540i | 0.560686 | − | 0.828029i | \(-0.310538\pi\) |
−0.436751 | + | 0.899583i | \(0.643871\pi\) | |||||||
\(674\) | 26.3862 | + | 15.2341i | 1.01636 | + | 0.586794i | ||||
\(675\) | −6.99319 | + | 2.89494i | −0.269168 | + | 0.111426i | ||||
\(676\) | −1.63420 | − | 4.20618i | −0.0628537 | − | 0.161776i | ||||
\(677\) | 4.42978 | 0.170250 | 0.0851251 | − | 0.996370i | \(-0.472871\pi\) | ||||
0.0851251 | + | 0.996370i | \(0.472871\pi\) | |||||||
\(678\) | 1.53120 | + | 11.6370i | 0.0588053 | + | 0.446915i | ||||
\(679\) | −2.99083 | − | 1.72676i | −0.114778 | − | 0.0662669i | ||||
\(680\) | −25.6732 | + | 14.8224i | −0.984522 | + | 0.568414i | ||||
\(681\) | 0.954419 | + | 1.24401i | 0.0365734 | + | 0.0476704i | ||||
\(682\) | −24.2485 | + | 20.6545i | −0.928524 | + | 0.790903i | ||||
\(683\) | 7.50519 | − | 4.33312i | 0.287178 | − | 0.165802i | −0.349491 | − | 0.936940i | \(-0.613645\pi\) |
0.636668 | + | 0.771138i | \(0.280312\pi\) | |||||||
\(684\) | −1.56576 | − | 0.419781i | −0.0598683 | − | 0.0160507i | ||||
\(685\) | 2.99012 | + | 5.17904i | 0.114247 | + | 0.197881i | ||||
\(686\) | −11.7065 | − | 6.75872i | −0.446955 | − | 0.258049i | ||||
\(687\) | −27.7106 | + | 3.64618i | −1.05723 | + | 0.139110i | ||||
\(688\) | − | 4.16285i | − | 0.158707i | ||||||
\(689\) | −39.9036 | − | 3.05912i | −1.52020 | − | 0.116543i | ||||
\(690\) | 12.0346 | + | 15.6861i | 0.458151 | + | 0.597161i | ||||
\(691\) | −13.7667 | + | 23.8446i | −0.523709 | + | 0.907091i | 0.475910 | + | 0.879494i | \(0.342119\pi\) |
−0.999619 | + | 0.0275970i | \(0.991214\pi\) | |||||||
\(692\) | 2.20580 | − | 3.82056i | 0.0838520 | − | 0.145236i | ||||
\(693\) | 7.06054 | − | 3.35497i | 0.268208 | − | 0.127445i | ||||
\(694\) | 9.78562 | 0.371457 | ||||||||
\(695\) | 15.7417 | + | 27.2655i | 0.597118 | + | 1.03424i | ||||
\(696\) | −19.0057 | + | 45.8746i | −0.720409 | + | 1.73887i | ||||
\(697\) | −9.82417 | −0.372117 | ||||||||
\(698\) | 24.4485 | − | 14.1154i | 0.925390 | − | 0.534274i | ||||
\(699\) | 44.9451 | − | 5.91390i | 1.69998 | − | 0.223684i | ||||
\(700\) | 0.344010 | + | 0.198614i | 0.0130024 | + | 0.00750692i | ||||
\(701\) | −25.6241 | −0.967811 | −0.483905 | − | 0.875120i | \(-0.660782\pi\) | ||||
−0.483905 | + | 0.875120i | \(0.660782\pi\) | |||||||
\(702\) | 23.5693 | + | 4.96512i | 0.889565 | + | 0.187397i | ||||
\(703\) | − | 4.72186i | − | 0.178088i | ||||||
\(704\) | 27.7014 | + | 9.85102i | 1.04403 | + | 0.371274i | ||||
\(705\) | −9.46228 | + | 1.24505i | −0.356370 | + | 0.0468914i | ||||
\(706\) | −22.9034 | + | 13.2233i | −0.861982 | + | 0.497666i | ||||
\(707\) | − | 9.38171i | − | 0.352836i | ||||||
\(708\) | −0.912285 | − | 0.377957i | −0.0342858 | − | 0.0142045i | ||||
\(709\) | −8.99200 | − | 15.5746i | −0.337702 | − | 0.584917i | 0.646298 | − | 0.763085i | \(-0.276316\pi\) |
−0.984000 | + | 0.178168i | \(0.942983\pi\) | |||||||
\(710\) | 15.8981 | 0.596646 | ||||||||
\(711\) | −6.27040 | − | 23.4147i | −0.235158 | − | 0.878120i | ||||
\(712\) | 0.923731 | + | 0.533316i | 0.0346183 | + | 0.0199869i | ||||
\(713\) | −30.5137 | − | 17.6171i | −1.14275 | − | 0.659765i | ||||
\(714\) | 7.24408 | − | 5.55777i | 0.271103 | − | 0.207994i | ||||
\(715\) | 20.5704 | + | 9.14135i | 0.769290 | + | 0.341867i | ||||
\(716\) | − | 2.47158i | − | 0.0923672i | ||||||
\(717\) | −20.6642 | + | 2.71901i | −0.771720 | + | 0.101543i | ||||
\(718\) | 0.837764 | − | 1.45105i | 0.0312651 | − | 0.0541527i | ||||
\(719\) | −19.1134 | + | 11.0351i | −0.712811 | + | 0.411542i | −0.812101 | − | 0.583517i | \(-0.801676\pi\) |
0.0992901 | + | 0.995059i | \(0.468343\pi\) | |||||||
\(720\) | −17.3743 | − | 4.65806i | −0.647501 | − | 0.173596i | ||||
\(721\) | 3.06298 | − | 1.76841i | 0.114071 | − | 0.0658590i | ||||
\(722\) | −10.6559 | − | 18.4565i | −0.396571 | − | 0.686881i | ||||
\(723\) | −27.0006 | + | 20.7153i | −1.00416 | + | 0.770410i | ||||
\(724\) | −3.52122 | − | 6.09893i | −0.130865 | − | 0.226665i | ||||
\(725\) | −6.91932 | + | 11.9846i | −0.256977 | + | 0.445098i | ||||
\(726\) | 21.5583 | − | 11.6291i | 0.800104 | − | 0.431598i | ||||
\(727\) | 29.5913 | 1.09748 | 0.548741 | − | 0.835993i | \(-0.315107\pi\) | ||||
0.548741 | + | 0.835993i | \(0.315107\pi\) | |||||||
\(728\) | −3.69556 | − | 7.70766i | −0.136966 | − | 0.285665i | ||||
\(729\) | 19.1000 | − | 19.0838i | 0.707407 | − | 0.706806i | ||||
\(730\) | 3.35774 | − | 5.81577i | 0.124275 | − | 0.215251i | ||||
\(731\) | 5.90687 | + | 3.41033i | 0.218473 | + | 0.126136i | ||||
\(732\) | −4.62389 | − | 1.91566i | −0.170904 | − | 0.0708050i | ||||
\(733\) | − | 25.9780i | − | 0.959518i | −0.877400 | − | 0.479759i | \(-0.840724\pi\) | ||
0.877400 | − | 0.479759i | \(-0.159276\pi\) | |||||||
\(734\) | 4.08247 | + | 7.07104i | 0.150687 | + | 0.260997i | ||||
\(735\) | −19.2257 | − | 7.96513i | −0.709150 | − | 0.293798i | ||||
\(736\) | 9.15018i | 0.337280i | ||||||||
\(737\) | −11.7154 | + | 9.97900i | −0.431542 | + | 0.367581i | ||||
\(738\) | −5.13308 | − | 5.13454i | −0.188951 | − | 0.189005i | ||||
\(739\) | −32.5554 | − | 18.7958i | −1.19757 | − | 0.691416i | −0.237556 | − | 0.971374i | \(-0.576346\pi\) |
−0.960012 | + | 0.279957i | \(0.909680\pi\) | |||||||
\(740\) | 1.98195i | 0.0728580i | ||||||||
\(741\) | 5.31067 | + | 8.14281i | 0.195092 | + | 0.299134i | ||||
\(742\) | −11.2114 | −0.411585 | ||||||||
\(743\) | 23.4658 | − | 40.6440i | 0.860877 | − | 1.49108i | −0.0102075 | − | 0.999948i | \(-0.503249\pi\) |
0.871084 | − | 0.491134i | \(-0.163417\pi\) | |||||||
\(744\) | 38.7096 | − | 5.09343i | 1.41916 | − | 0.186734i | ||||
\(745\) | 22.5386 | − | 13.0127i | 0.825749 | − | 0.476747i | ||||
\(746\) | − | 39.5436i | − | 1.44779i | ||||||
\(747\) | 40.9492 | − | 10.9661i | 1.49825 | − | 0.401228i | ||||
\(748\) | −4.57394 | + | 3.89601i | −0.167240 | + | 0.142452i | ||||
\(749\) | 4.61479i | 0.168621i | ||||||||
\(750\) | −25.0034 | − | 10.3588i | −0.912994 | − | 0.378250i | ||||
\(751\) | 9.74603 | − | 16.8806i | 0.355638 | − | 0.615983i | −0.631589 | − | 0.775303i | \(-0.717597\pi\) |
0.987227 | + | 0.159321i | \(0.0509303\pi\) | |||||||
\(752\) | 8.07479 | + | 4.66198i | 0.294457 | + | 0.170005i | ||||
\(753\) | −4.63037 | + | 3.55249i | −0.168740 | + | 0.129460i | ||||
\(754\) | 39.7113 | − | 19.0402i | 1.44620 | − | 0.693403i | ||||
\(755\) | −30.2224 | −1.09990 | ||||||||
\(756\) | −1.40488 | − | 0.185259i | −0.0510950 | − | 0.00673782i | ||||
\(757\) | 22.9192 | − | 39.6973i | 0.833014 | − | 1.44282i | −0.0626239 | − | 0.998037i | \(-0.519947\pi\) |
0.895638 | − | 0.444785i | \(-0.146720\pi\) | |||||||
\(758\) | 5.80232 | + | 10.0499i | 0.210750 | + | 0.365029i | ||||
\(759\) | 20.1102 | + | 18.1583i | 0.729954 | + | 0.659106i | ||||
\(760\) | −4.42119 | − | 7.65772i | −0.160373 | − | 0.277775i | ||||
\(761\) | 15.2862 | + | 26.4765i | 0.554125 | + | 0.959772i | 0.997971 | + | 0.0636691i | \(0.0202802\pi\) |
−0.443847 | + | 0.896103i | \(0.646386\pi\) | |||||||
\(762\) | −36.6201 | + | 28.0955i | −1.32661 | + | 1.01779i | ||||
\(763\) | 3.93917 | + | 6.82284i | 0.142608 | + | 0.247004i | ||||
\(764\) | −6.68784 | − | 3.86123i | −0.241958 | − | 0.139694i | ||||
\(765\) | 20.8431 | − | 20.8372i | 0.753582 | − | 0.753369i | ||||
\(766\) | 33.4345i | 1.20804i | ||||||||
\(767\) | 2.56030 | + | 5.33990i | 0.0924471 | + | 0.192813i | ||||
\(768\) | −8.50331 | − | 11.0834i | −0.306837 | − | 0.399936i | ||||
\(769\) | −7.68447 | − | 4.43663i | −0.277109 | − | 0.159989i | 0.355005 | − | 0.934864i | \(-0.384479\pi\) |
−0.632114 | + | 0.774876i | \(0.717813\pi\) | |||||||
\(770\) | 5.94152 | + | 2.11289i | 0.214117 | + | 0.0761433i | ||||
\(771\) | 24.4132 | + | 10.1143i | 0.879218 | + | 0.364257i | ||||
\(772\) | 5.45344i | 0.196274i | ||||||||
\(773\) | −41.2712 | + | 23.8279i | −1.48442 | + | 0.857031i | −0.999843 | − | 0.0177177i | \(-0.994360\pi\) |
−0.484578 | + | 0.874748i | \(0.661027\pi\) | |||||||
\(774\) | 1.30392 | + | 4.86907i | 0.0468686 | + | 0.175015i | ||||
\(775\) | 10.8810 | 0.390858 | ||||||||
\(776\) | 6.63223 | + | 11.4874i | 0.238083 | + | 0.412372i | ||||
\(777\) | −0.538471 | − | 4.09233i | −0.0193175 | − | 0.146812i | ||||
\(778\) | −2.74682 | − | 1.58588i | −0.0984783 | − | 0.0568565i | ||||
\(779\) | − | 2.93032i | − | 0.104990i | ||||||
\(780\) | −2.22910 | − | 3.41786i | −0.0798146 | − | 0.122379i | ||||
\(781\) | 21.4281 | − | 3.94201i | 0.766757 | − | 0.141056i | ||||
\(782\) | 27.4075 | + | 15.8237i | 0.980090 | + | 0.565855i | ||||
\(783\) | 6.45406 | − | 48.9431i | 0.230649 | − | 1.74909i | ||||
\(784\) | 10.1654 | + | 17.6071i | 0.363051 | + | 0.628824i | ||||
\(785\) | − | 37.0442i | − | 1.32217i | ||||||
\(786\) | 4.61171 | − | 11.1314i | 0.164494 | − | 0.397045i | ||||
\(787\) | 9.27484 | − | 5.35483i | 0.330612 | − | 0.190879i | −0.325501 | − | 0.945542i | \(-0.605533\pi\) |
0.656113 | + | 0.754663i | \(0.272199\pi\) | |||||||
\(788\) | 2.86526 | 0.102071 | ||||||||
\(789\) | −12.0803 | + | 29.1585i | −0.430069 | + | 1.03807i | ||||
\(790\) | 9.77707 | − | 16.9344i | 0.347852 | − | 0.602498i | ||||
\(791\) | −2.07054 | + | 3.58627i | −0.0736198 | + | 0.127513i | ||||
\(792\) | −29.9283 | − | 2.39969i | −1.06345 | − | 0.0852694i | ||||
\(793\) | 12.9768 | + | 27.0652i | 0.460820 | + | 0.961112i | ||||
\(794\) | 17.9823 | 0.638167 | ||||||||
\(795\) | −35.8803 | + | 4.72114i | −1.27254 | + | 0.167442i | ||||
\(796\) | 0.853419 | − | 1.47816i | 0.0302486 | − | 0.0523922i | ||||
\(797\) | −11.2012 | + | 6.46704i | −0.396768 | + | 0.229074i | −0.685089 | − | 0.728460i | \(-0.740237\pi\) |
0.288320 | + | 0.957534i | \(0.406903\pi\) | |||||||
\(798\) | 1.65775 | + | 2.16074i | 0.0586839 | + | 0.0764895i | ||||
\(799\) | −13.2302 | + | 7.63847i | −0.468051 | + | 0.270229i | ||||
\(800\) | −1.41288 | − | 2.44718i | −0.0499529 | − | 0.0865209i | ||||
\(801\) | −1.02425 | − | 0.274603i | −0.0361902 | − | 0.00970263i | ||||
\(802\) | −3.56718 | + | 2.05951i | −0.125962 | + | 0.0727240i | ||||
\(803\) | 3.08364 | − | 8.67128i | 0.108819 | − | 0.306003i | ||||
\(804\) | 2.76585 | − | 0.363932i | 0.0975441 | − | 0.0128349i | ||||
\(805\) | 6.97544i | 0.245852i | ||||||||
\(806\) | −28.5772 | − | 19.5554i | −1.00659 | − | 0.688811i | ||||
\(807\) | −36.6405 | + | 28.1111i | −1.28981 | + | 0.989559i | ||||
\(808\) | −18.0169 | + | 31.2062i | −0.633832 | + | 1.09783i | ||||
\(809\) | −5.51808 | + | 9.55760i | −0.194005 | + | 0.336027i | −0.946574 | − | 0.322487i | \(-0.895481\pi\) |
0.752569 | + | 0.658514i | \(0.228815\pi\) | |||||||
\(810\) | 21.7808 | + | 0.00616659i | 0.765300 | + | 0.000216672i | ||||
\(811\) | − | 8.14284i | − | 0.285934i | −0.989727 | − | 0.142967i | \(-0.954336\pi\) | ||
0.989727 | − | 0.142967i | \(-0.0456643\pi\) | |||||||
\(812\) | −2.24380 | + | 1.29546i | −0.0787421 | + | 0.0454618i | ||||
\(813\) | 35.9704 | + | 14.9024i | 1.26154 | + | 0.522650i | ||||
\(814\) | −2.34010 | − | 12.7204i | −0.0820205 | − | 0.445849i | ||||
\(815\) | −30.3339 | + | 17.5133i | −1.06255 | + | 0.613464i | ||||
\(816\) | −28.5473 | + | 3.75626i | −0.999354 | + | 0.131496i | ||||
\(817\) | −1.01722 | + | 1.76188i | −0.0355881 | + | 0.0616405i | ||||
\(818\) | 36.2444i | 1.26726i | ||||||||
\(819\) | 5.53123 | + | 6.45157i | 0.193277 | + | 0.225436i | ||||
\(820\) | 1.22997i | 0.0429525i | ||||||||
\(821\) | 7.18822 | − | 12.4504i | 0.250871 | − | 0.434521i | −0.712895 | − | 0.701271i | \(-0.752616\pi\) |
0.963766 | + | 0.266750i | \(0.0859498\pi\) | |||||||
\(822\) | 0.922900 | + | 7.01396i | 0.0321898 | + | 0.244640i | ||||
\(823\) | −23.6086 | − | 40.8913i | −0.822944 | − | 1.42538i | −0.903480 | − | 0.428630i | \(-0.858996\pi\) |
0.0805358 | − | 0.996752i | \(-0.474337\pi\) | |||||||
\(824\) | −13.5844 | −0.473235 | ||||||||
\(825\) | −8.18223 | − | 1.75116i | −0.284869 | − | 0.0609676i | ||||
\(826\) | 0.829495 | + | 1.43673i | 0.0288618 | + | 0.0499901i | ||||
\(827\) | 30.7199 | 1.06824 | 0.534118 | − | 0.845410i | \(-0.320644\pi\) | ||||
0.534118 | + | 0.845410i | \(0.320644\pi\) | |||||||
\(828\) | −1.27056 | − | 4.74448i | −0.0441550 | − | 0.164882i | ||||
\(829\) | −0.323797 | + | 0.560833i | −0.0112459 | + | 0.0194785i | −0.871594 | − | 0.490229i | \(-0.836913\pi\) |
0.860348 | + | 0.509708i | \(0.170246\pi\) | |||||||
\(830\) | 29.6160 | + | 17.0988i | 1.02799 | + | 0.593508i | ||||
\(831\) | 18.6404 | − | 14.3012i | 0.646628 | − | 0.496102i | ||||
\(832\) | −2.44313 | + | 31.8686i | −0.0847003 | + | 1.10484i | ||||
\(833\) | −33.3113 | −1.15417 | ||||||||
\(834\) | 4.85868 | + | 36.9255i | 0.168242 | + | 1.27863i | ||||
\(835\) | −41.2511 | − | 23.8163i | −1.42755 | − | 0.824198i | ||||
\(836\) | −1.16209 | − | 1.36430i | −0.0401918 | − | 0.0471854i | ||||
\(837\) | −35.8645 | + | 14.8467i | −1.23966 | + | 0.513176i | ||||
\(838\) | −14.0728 | + | 8.12493i | −0.486137 | + | 0.280671i | ||||
\(839\) | −7.69113 | + | 4.44048i | −0.265527 | + | 0.153302i | −0.626853 | − | 0.779137i | \(-0.715657\pi\) |
0.361326 | + | 0.932440i | \(0.382324\pi\) | |||||||
\(840\) | −4.70502 | − | 6.13260i | −0.162339 | − | 0.211595i | ||||
\(841\) | −30.6312 | − | 53.0548i | −1.05625 | − | 1.82948i | ||||
\(842\) | −0.502757 | + | 0.870800i | −0.0173261 | + | 0.0300097i | ||||
\(843\) | −24.6309 | + | 3.24094i | −0.848333 | + | 0.111624i | ||||
\(844\) | − | 3.47846i | − | 0.119734i | ||||||
\(845\) | −3.73012 | + | 24.1851i | −0.128320 | + | 0.831994i | ||||
\(846\) | −10.9049 | − | 2.92362i | −0.374919 | − | 0.100516i | ||||
\(847\) | 8.53210 | + | 1.37461i | 0.293166 | + | 0.0472321i | ||||
\(848\) | 30.6190 | + | 17.6779i | 1.05146 | + | 0.607061i | ||||
\(849\) | −18.1846 | − | 7.53382i | −0.624094 | − | 0.258560i | ||||
\(850\) | −9.77338 | −0.335224 | ||||||||
\(851\) | 12.3901 | − | 7.15342i | 0.424727 | − | 0.245216i | ||||
\(852\) | −3.64880 | − | 1.51169i | −0.125006 | − | 0.0517895i | ||||
\(853\) | − | 18.2763i | − | 0.625767i | −0.949791 | − | 0.312884i | \(-0.898705\pi\) | ||
0.949791 | − | 0.312884i | \(-0.101295\pi\) | |||||||
\(854\) | 4.20427 | + | 7.28201i | 0.143867 | + | 0.249185i | ||||
\(855\) | 6.21524 | + | 6.21700i | 0.212557 | + | 0.212617i | ||||
\(856\) | 8.86237 | − | 15.3501i | 0.302910 | − | 0.524655i | ||||
\(857\) | 6.67213 | 0.227916 | 0.113958 | − | 0.993486i | \(-0.463647\pi\) | ||||
0.113958 | + | 0.993486i | \(0.463647\pi\) | |||||||
\(858\) | 18.3421 | + | 19.3043i | 0.626189 | + | 0.659037i | ||||
\(859\) | −30.6728 | −1.04654 | −0.523272 | − | 0.852166i | \(-0.675289\pi\) | ||||
−0.523272 | + | 0.852166i | \(0.675289\pi\) | |||||||
\(860\) | 0.426969 | − | 0.739532i | 0.0145595 | − | 0.0252178i | ||||
\(861\) | −0.334168 | − | 2.53965i | −0.0113884 | − | 0.0865509i | ||||
\(862\) | 7.37983 | + | 12.7822i | 0.251358 | + | 0.435365i | ||||
\(863\) | − | 38.0330i | − | 1.29466i | −0.762210 | − | 0.647330i | \(-0.775886\pi\) | ||
0.762210 | − | 0.647330i | \(-0.224114\pi\) | |||||||
\(864\) | 7.99601 | + | 6.13825i | 0.272030 | + | 0.208828i | ||||
\(865\) | −20.7188 | + | 11.9620i | −0.704460 | + | 0.406720i | ||||
\(866\) | 16.3656 | 0.556125 | ||||||||
\(867\) | 6.78684 | − | 16.3816i | 0.230493 | − | 0.556349i | ||||
\(868\) | 1.76425 | + | 1.01859i | 0.0598827 | + | 0.0345733i | ||||
\(869\) | 8.97894 | − | 25.2491i | 0.304590 | − | 0.856515i | ||||
\(870\) | 31.5963 | − | 24.2411i | 1.07121 | − | 0.821851i | ||||
\(871\) | −13.8068 | − | 9.44798i | −0.467824 | − | 0.320133i | ||||
\(872\) | − | 30.2596i | − | 1.02472i | ||||||
\(873\) | −9.32350 | − | 9.32614i | −0.315553 | − | 0.315642i | ||||
\(874\) | −4.71985 | + | 8.17503i | −0.159651 | + | 0.276524i | ||||
\(875\) | −4.77432 | − | 8.26937i | −0.161402 | − | 0.279556i | ||||
\(876\) | −1.32364 | + | 1.01551i | −0.0447216 | + | 0.0343110i | ||||
\(877\) | 32.8246 | − | 18.9513i | 1.10841 | − | 0.639939i | 0.169991 | − | 0.985446i | \(-0.445626\pi\) |
0.938416 | + | 0.345506i | \(0.112293\pi\) | |||||||
\(878\) | −1.98618 | + | 1.14672i | −0.0670305 | + | 0.0387001i | ||||
\(879\) | −2.17894 | − | 2.84007i | −0.0734938 | − | 0.0957930i | ||||
\(880\) | −12.8950 | − | 15.1388i | −0.434691 | − | 0.510330i | ||||
\(881\) | 14.3233 | + | 8.26957i | 0.482564 | + | 0.278609i | 0.721485 | − | 0.692430i | \(-0.243460\pi\) |
−0.238920 | + | 0.971039i | \(0.576793\pi\) | |||||||
\(882\) | −17.4050 | − | 17.4099i | −0.586057 | − | 0.586223i | ||||
\(883\) | 29.9144 | 1.00670 | 0.503349 | − | 0.864083i | \(-0.332101\pi\) | ||||
0.503349 | + | 0.864083i | \(0.332101\pi\) | |||||||
\(884\) | −5.39046 | − | 3.68870i | −0.181301 | − | 0.124064i | ||||
\(885\) | 3.25966 | + | 4.24869i | 0.109572 | + | 0.142818i | ||||
\(886\) | −36.3907 | − | 21.0102i | −1.22257 | − | 0.705852i | ||||
\(887\) | 1.08541 | − | 1.87999i | 0.0364446 | − | 0.0631239i | −0.847228 | − | 0.531230i | \(-0.821730\pi\) |
0.883672 | + | 0.468106i | \(0.155063\pi\) | |||||||
\(888\) | −6.06792 | + | 14.6463i | −0.203626 | + | 0.491499i | ||||
\(889\) | −16.2845 | −0.546165 | ||||||||
\(890\) | −0.427721 | − | 0.740835i | −0.0143372 | − | 0.0248328i | ||||
\(891\) | 29.3585 | − | 5.39234i | 0.983547 | − | 0.180650i | ||||
\(892\) | −4.75828 | −0.159319 | ||||||||
\(893\) | −2.27838 | − | 3.94627i | −0.0762430 | − | 0.132057i | ||||
\(894\) | 30.5239 | − | 4.01635i | 1.02087 | − | 0.134327i | ||||
\(895\) | −6.70165 | + | 11.6076i | −0.224011 | + | 0.387999i | ||||
\(896\) | 5.90563i | 0.197293i | ||||||||
\(897\) | −13.3212 | + | 26.2711i | −0.444780 | + | 0.877168i | ||||
\(898\) | 16.6458i | 0.555476i | ||||||||
\(899\) | −35.4857 | + | 61.4630i | −1.18351 | + | 2.04991i | ||||
\(900\) | 1.07240 | + | 1.07271i | 0.0357468 | + | 0.0357569i | ||||
\(901\) | −50.1680 | + | 28.9645i | −1.67134 | + | 0.964947i | ||||
\(902\) | −1.45224 | − | 7.89410i | −0.0483542 | − | 0.262845i | ||||
\(903\) | −0.680684 | + | 1.64299i | −0.0226517 | + | 0.0546752i | ||||
\(904\) | 13.7744 | − | 7.95263i | 0.458128 | − | 0.264501i | ||||
\(905\) | 38.1909i | 1.26951i | ||||||||
\(906\) | −33.0296 | − | 13.6840i | −1.09733 | − | 0.454622i | ||||
\(907\) | 22.0087 | − | 38.1202i | 0.730787 | − | 1.26576i | −0.225761 | − | 0.974183i | \(-0.572487\pi\) |
0.956547 | − | 0.291577i | \(-0.0941798\pi\) | |||||||
\(908\) | 0.157114 | − | 0.272129i | 0.00521401 | − | 0.00903092i | ||||
\(909\) | 9.27686 | − | 34.6021i | 0.307694 | − | 1.14768i | ||||
\(910\) | −0.524014 | + | 6.83531i | −0.0173709 | + | 0.226588i | ||||
\(911\) | 55.2462i | 1.83039i | 0.403014 | + | 0.915194i | \(0.367963\pi\) | ||||
−0.403014 | + | 0.915194i | \(0.632037\pi\) | |||||||
\(912\) | −1.12041 | − | 8.51500i | −0.0371004 | − | 0.281960i | ||||
\(913\) | 44.1572 | + | 15.7030i | 1.46139 | + | 0.519693i | ||||
\(914\) | −27.5768 | + | 15.9215i | −0.912159 | + | 0.526635i | ||||
\(915\) | 16.5215 | + | 21.5344i | 0.546184 | + | 0.711905i | ||||
\(916\) | 2.80063 | + | 4.85084i | 0.0925356 | + | 0.160276i | ||||
\(917\) | 3.68150 | − | 2.12551i | 0.121574 | − | 0.0701906i | ||||
\(918\) | 32.2137 | − | 13.3353i | 1.06321 | − | 0.440131i | ||||
\(919\) | 14.7841 | − | 8.53559i | 0.487682 | − | 0.281563i | −0.235930 | − | 0.971770i | \(-0.575814\pi\) |
0.723612 | + | 0.690207i | \(0.242480\pi\) | |||||||
\(920\) | 13.3958 | − | 23.2023i | 0.441648 | − | 0.764956i | ||||
\(921\) | −4.44521 | − | 33.7832i | −0.146475 | − | 1.11319i | ||||
\(922\) | 26.2815 | 0.865536 | ||||||||
\(923\) | 10.2403 | + | 21.3576i | 0.337062 | + | 0.702995i | ||||
\(924\) | −1.16274 | − | 1.04989i | −0.0382514 | − | 0.0345388i | ||||
\(925\) | −2.20912 | + | 3.82631i | −0.0726355 | + | 0.125808i | ||||
\(926\) | −4.49417 | + | 7.78414i | −0.147688 | + | 0.255803i | ||||
\(927\) | 13.0457 | − | 3.49360i | 0.428476 | − | 0.114745i | ||||
\(928\) | 18.4310 | 0.605027 | ||||||||
\(929\) | −31.3257 | + | 18.0859i | −1.02776 | + | 0.593379i | −0.916343 | − | 0.400395i | \(-0.868873\pi\) |
−0.111419 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(930\) | −28.9284 | − | 11.9849i | −0.948600 | − | 0.393002i | ||||
\(931\) | − | 9.93600i | − | 0.325639i | ||||||
\(932\) | −4.54247 | − | 7.86779i | −0.148794 | − | 0.257718i | ||||
\(933\) | −1.33570 | − | 10.1512i | −0.0437287 | − | 0.332335i | ||||
\(934\) | 13.8558 | + | 7.99967i | 0.453377 | + | 0.261757i | ||||
\(935\) | 32.0452 | − | 5.89518i | 1.04799 | − | 0.192793i | ||||
\(936\) | −6.00864 | − | 32.0821i | −0.196398 | − | 1.04863i | ||||
\(937\) | − | 27.7950i | − | 0.908022i | −0.890996 | − | 0.454011i | \(-0.849993\pi\) | ||
0.890996 | − | 0.454011i | \(-0.150007\pi\) | |||||||
\(938\) | −4.05885 | − | 2.34338i | −0.132526 | − | 0.0765139i | ||||
\(939\) | −50.4611 | + | 6.63970i | −1.64674 | + | 0.216678i | ||||
\(940\) | 0.956326 | + | 1.65640i | 0.0311919 | + | 0.0540260i | ||||
\(941\) | 49.3053 | 1.60731 | 0.803653 | − | 0.595098i | \(-0.202887\pi\) | ||||
0.803653 | + | 0.595098i | \(0.202887\pi\) | |||||||
\(942\) | 16.7728 | − | 40.4851i | 0.546488 | − | 1.31908i | ||||
\(943\) | 7.68912 | − | 4.43932i | 0.250392 | − | 0.144564i | ||||
\(944\) | − | 5.23169i | − | 0.170277i | ||||||
\(945\) | 6.09559 | + | 4.67937i | 0.198290 | + | 0.152220i | ||||
\(946\) | −1.86716 | + | 5.25052i | −0.0607067 | + | 0.170709i | ||||
\(947\) | −42.0926 | − | 24.3022i | −1.36783 | − | 0.789714i | −0.377175 | − | 0.926142i | \(-0.623105\pi\) |
−0.990650 | + | 0.136427i | \(0.956438\pi\) | |||||||
\(948\) | −3.85417 | + | 2.95698i | −0.125178 | + | 0.0960381i | ||||
\(949\) | 9.97572 | + | 0.764766i | 0.323826 | + | 0.0248254i | ||||
\(950\) | − | 2.91518i | − | 0.0945808i | ||||||
\(951\) | 1.47496 | + | 11.2096i | 0.0478288 | + | 0.363495i | ||||
\(952\) | −10.7151 | − | 6.18639i | −0.347279 | − | 0.200502i | ||||
\(953\) | −10.9279 | − | 18.9277i | −0.353989 | − | 0.613127i | 0.632955 | − | 0.774188i | \(-0.281842\pi\) |
−0.986944 | + | 0.161061i | \(0.948508\pi\) | |||||||
\(954\) | −41.3506 | − | 11.0861i | −1.33878 | − | 0.358927i | ||||
\(955\) | 20.9393 | + | 36.2680i | 0.677580 | + | 1.17360i | ||||
\(956\) | 2.08847 | + | 3.61734i | 0.0675461 | + | 0.116993i | ||||
\(957\) | 36.5759 | − | 40.5075i | 1.18233 | − | 1.30942i | ||||
\(958\) | −4.00759 | − | 6.94135i | −0.129479 | − | 0.224265i | ||||
\(959\) | −1.24798 | + | 2.16156i | −0.0402993 | + | 0.0698004i | ||||
\(960\) | 3.77049 | + | 28.6554i | 0.121692 | + | 0.924849i | ||||
\(961\) | 24.8033 | 0.800105 | ||||||||
\(962\) | 12.6786 | − | 6.07894i | 0.408773 | − | 0.195993i | ||||
\(963\) | −4.56322 | + | 17.0205i | −0.147048 | + | 0.548479i | ||||
\(964\) | 5.90645 | + | 3.41009i | 0.190234 | + | 0.109832i | ||||
\(965\) | 14.7869 | − | 25.6117i | 0.476008 | − | 0.824469i | ||||
\(966\) | −3.15833 | + | 7.62336i | −0.101618 | + | 0.245278i | ||||
\(967\) | − | 55.8010i | − | 1.79444i | −0.441586 | − | 0.897219i | \(-0.645584\pi\) | ||
0.441586 | − | 0.897219i | \(-0.354416\pi\) | |||||||
\(968\) | −25.7403 | − | 20.9576i | −0.827325 | − | 0.673603i | ||||
\(969\) | 13.0002 | + | 5.38594i | 0.417627 | + | 0.173021i | ||||
\(970\) | − | 10.6381i | − | 0.341570i | ||||||
\(971\) | 37.0488 | − | 21.3901i | 1.18895 | − | 0.686442i | 0.230885 | − | 0.972981i | \(-0.425838\pi\) |
0.958069 | + | 0.286539i | \(0.0925047\pi\) | |||||||
\(972\) | −4.99836 | − | 2.07246i | −0.160323 | − | 0.0664743i | ||||
\(973\) | −6.57007 | + | 11.3797i | −0.210627 | + | 0.364816i | ||||
\(974\) | 7.76620 | 0.248845 | ||||||||
\(975\) | −0.493838 | − | 9.08304i | −0.0158155 | − | 0.290890i | ||||
\(976\) | − | 26.5167i | − | 0.848779i | ||||||
\(977\) | 35.2349 | + | 20.3429i | 1.12726 | + | 0.650826i | 0.943245 | − | 0.332097i | \(-0.107756\pi\) |
0.184018 | + | 0.982923i | \(0.441089\pi\) | |||||||
\(978\) | −41.0811 | + | 5.40548i | −1.31363 | + | 0.172848i | ||||
\(979\) | −0.760192 | − | 0.892469i | −0.0242958 | − | 0.0285234i | ||||
\(980\) | 4.17053i | 0.133223i | ||||||||
\(981\) | 7.78207 | + | 29.0595i | 0.248462 | + | 0.927799i | ||||
\(982\) | 17.5343 | + | 30.3703i | 0.559542 | + | 0.969155i | ||||
\(983\) | − | 60.5284i | − | 1.93056i | −0.261226 | − | 0.965278i | \(-0.584127\pi\) | ||
0.261226 | − | 0.965278i | \(-0.415873\pi\) | |||||||
\(984\) | −3.76567 | + | 9.08931i | −0.120045 | + | 0.289757i | ||||
\(985\) | −13.4565 | − | 7.76911i | −0.428760 | − | 0.247545i | ||||
\(986\) | 31.8734 | − | 55.2063i | 1.01506 | − | 1.75813i | ||||
\(987\) | −2.42464 | − | 3.16032i | −0.0771773 | − | 0.100594i | ||||
\(988\) | 1.10025 | − | 1.60785i | 0.0350037 | − | 0.0511525i | ||||
\(989\) | −6.16421 | −0.196010 | ||||||||
\(990\) | 19.8245 | + | 13.6680i | 0.630065 | + | 0.434397i | ||||
\(991\) | −1.58126 | + | 2.73883i | −0.0502305 | + | 0.0870017i | −0.890047 | − | 0.455868i | \(-0.849329\pi\) |
0.839817 | + | 0.542870i | \(0.182662\pi\) | |||||||
\(992\) | −7.24595 | − | 12.5504i | −0.230059 | − | 0.398474i | ||||
\(993\) | −11.8868 | − | 15.4935i | −0.377217 | − | 0.491671i | ||||
\(994\) | 3.31767 | + | 5.74637i | 0.105230 | + | 0.182264i | ||||
\(995\) | −8.01604 | + | 4.62806i | −0.254126 | + | 0.146719i | ||||
\(996\) | −5.17136 | − | 6.74043i | −0.163861 | − | 0.213579i | ||||
\(997\) | 25.9064 | − | 14.9571i | 0.820464 | − | 0.473695i | −0.0301122 | − | 0.999547i | \(-0.509586\pi\) |
0.850577 | + | 0.525851i | \(0.176253\pi\) | |||||||
\(998\) | 15.6877 | − | 27.1718i | 0.496584 | − | 0.860109i | ||||
\(999\) | 2.06058 | − | 15.6260i | 0.0651938 | − | 0.494385i |
(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 | 429.2.p.b.230.15 | ✓ | 96 | |
3.2 | odd | 2 | inner | 429.2.p.b.230.34 | yes | 96 | |
11.10 | odd | 2 | inner | 429.2.p.b.230.33 | yes | 96 | |
13.3 | even | 3 | inner | 429.2.p.b.263.16 | yes | 96 | |
33.32 | even | 2 | inner | 429.2.p.b.230.16 | yes | 96 | |
39.29 | odd | 6 | inner | 429.2.p.b.263.33 | yes | 96 | |
143.120 | odd | 6 | inner | 429.2.p.b.263.34 | yes | 96 | |
429.263 | even | 6 | inner | 429.2.p.b.263.15 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.p.b.230.15 | ✓ | 96 | 1.1 | even | 1 | trivial | |
429.2.p.b.230.16 | yes | 96 | 33.32 | even | 2 | inner | |
429.2.p.b.230.33 | yes | 96 | 11.10 | odd | 2 | inner | |
429.2.p.b.230.34 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.p.b.263.15 | yes | 96 | 429.263 | even | 6 | inner | |
429.2.p.b.263.16 | yes | 96 | 13.3 | even | 3 | inner | |
429.2.p.b.263.33 | yes | 96 | 39.29 | odd | 6 | inner | |
429.2.p.b.263.34 | yes | 96 | 143.120 | odd | 6 | inner |