Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(196,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.196");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 196.8 | ||
Root | \(1.79305 + 1.53983i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.196 |
Dual form | 585.2.i.e.391.8 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29305 | − | 2.23963i | 0.914326 | − | 1.58366i | 0.106440 | − | 0.994319i | \(-0.466055\pi\) |
0.807885 | − | 0.589340i | \(-0.200612\pi\) | |||||||
\(3\) | 1.68259 | + | 0.410979i | 0.971442 | + | 0.237279i | ||||
\(4\) | −2.34397 | − | 4.05987i | −1.17198 | − | 2.02993i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 3.09611 | − | 3.23696i | 1.26398 | − | 1.32148i | ||||
\(7\) | 2.13745 | − | 3.70217i | 0.807879 | − | 1.39929i | −0.106451 | − | 0.994318i | \(-0.533949\pi\) |
0.914330 | − | 0.404969i | \(-0.132718\pi\) | |||||||
\(8\) | −6.95128 | −2.45765 | ||||||||
\(9\) | 2.66219 | + | 1.38302i | 0.887397 | + | 0.461006i | ||||
\(10\) | 2.58610 | 0.817798 | ||||||||
\(11\) | −2.19223 | + | 3.79706i | −0.660983 | + | 1.14486i | 0.319375 | + | 0.947628i | \(0.396527\pi\) |
−0.980358 | + | 0.197227i | \(0.936806\pi\) | |||||||
\(12\) | −2.27540 | − | 7.79440i | −0.656852 | − | 2.25005i | ||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | ||||
\(14\) | −5.52766 | − | 9.57419i | −1.47733 | − | 2.55881i | ||||
\(15\) | 0.485374 | + | 1.66265i | 0.125323 | + | 0.429295i | ||||
\(16\) | −4.30043 | + | 7.44856i | −1.07511 | + | 1.86214i | ||||
\(17\) | 0.619151 | 0.150166 | 0.0750831 | − | 0.997177i | \(-0.476078\pi\) | ||||
0.0750831 | + | 0.997177i | \(0.476078\pi\) | |||||||
\(18\) | 6.53980 | − | 4.17402i | 1.54145 | − | 0.983825i | ||||
\(19\) | −2.61288 | −0.599435 | −0.299718 | − | 0.954028i | \(-0.596892\pi\) | ||||
−0.299718 | + | 0.954028i | \(0.596892\pi\) | |||||||
\(20\) | 2.34397 | − | 4.05987i | 0.524127 | − | 0.907814i | ||||
\(21\) | 5.11795 | − | 5.35077i | 1.11683 | − | 1.16763i | ||||
\(22\) | 5.66934 | + | 9.81959i | 1.20871 | + | 2.09354i | ||||
\(23\) | −2.71443 | − | 4.70154i | −0.565998 | − | 0.980338i | −0.996956 | − | 0.0779658i | \(-0.975157\pi\) |
0.430958 | − | 0.902372i | \(-0.358176\pi\) | |||||||
\(24\) | −11.6961 | − | 2.85683i | −2.38746 | − | 0.583148i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.58610 | 0.507177 | ||||||||
\(27\) | 3.91098 | + | 3.42115i | 0.752668 | + | 0.658401i | ||||
\(28\) | −20.0404 | −3.78728 | ||||||||
\(29\) | −3.47887 | + | 6.02558i | −0.646010 | + | 1.11892i | 0.338057 | + | 0.941125i | \(0.390230\pi\) |
−0.984067 | + | 0.177796i | \(0.943103\pi\) | |||||||
\(30\) | 4.35134 | + | 1.06284i | 0.794443 | + | 0.194046i | ||||
\(31\) | 3.44304 | + | 5.96353i | 0.618389 | + | 1.07108i | 0.989780 | + | 0.142605i | \(0.0455477\pi\) |
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(32\) | 4.17008 | + | 7.22278i | 0.737172 | + | 1.27682i | ||||
\(33\) | −5.24913 | + | 5.48791i | −0.913757 | + | 0.955323i | ||||
\(34\) | 0.800595 | − | 1.38667i | 0.137301 | − | 0.237812i | ||||
\(35\) | 4.27489 | 0.722589 | ||||||||
\(36\) | −0.625222 | − | 14.0499i | −0.104204 | − | 2.34165i | ||||
\(37\) | −4.02164 | −0.661154 | −0.330577 | − | 0.943779i | \(-0.607243\pi\) | ||||
−0.330577 | + | 0.943779i | \(0.607243\pi\) | |||||||
\(38\) | −3.37859 | + | 5.85188i | −0.548079 | + | 0.949301i | ||||
\(39\) | 0.485374 | + | 1.66265i | 0.0777221 | + | 0.266237i | ||||
\(40\) | −3.47564 | − | 6.01998i | −0.549547 | − | 0.951843i | ||||
\(41\) | 2.03714 | + | 3.52842i | 0.318147 | + | 0.551047i | 0.980101 | − | 0.198497i | \(-0.0636060\pi\) |
−0.661954 | + | 0.749544i | \(0.730273\pi\) | |||||||
\(42\) | −5.36597 | − | 18.3811i | −0.827987 | − | 2.83627i | ||||
\(43\) | 5.01845 | − | 8.69221i | 0.765307 | − | 1.32555i | −0.174778 | − | 0.984608i | \(-0.555921\pi\) |
0.940084 | − | 0.340942i | \(-0.110746\pi\) | |||||||
\(44\) | 20.5541 | 3.09864 | ||||||||
\(45\) | 0.133368 | + | 2.99703i | 0.0198814 | + | 0.446771i | ||||
\(46\) | −14.0396 | −2.07003 | ||||||||
\(47\) | 0.202993 | − | 0.351595i | 0.0296096 | − | 0.0512854i | −0.850841 | − | 0.525423i | \(-0.823907\pi\) |
0.880450 | + | 0.474138i | \(0.157240\pi\) | |||||||
\(48\) | −10.2970 | + | 10.7655i | −1.48625 | + | 1.55386i | ||||
\(49\) | −5.63736 | − | 9.76419i | −0.805337 | − | 1.39488i | ||||
\(50\) | 1.29305 | + | 2.23963i | 0.182865 | + | 0.316732i | ||||
\(51\) | 1.04178 | + | 0.254458i | 0.145878 | + | 0.0356313i | ||||
\(52\) | 2.34397 | − | 4.05987i | 0.325050 | − | 0.563003i | ||||
\(53\) | −8.71205 | −1.19669 | −0.598346 | − | 0.801238i | \(-0.704175\pi\) | ||||
−0.598346 | + | 0.801238i | \(0.704175\pi\) | |||||||
\(54\) | 12.7192 | − | 4.33542i | 1.73087 | − | 0.589976i | ||||
\(55\) | −4.38446 | −0.591201 | ||||||||
\(56\) | −14.8580 | + | 25.7348i | −1.98548 | + | 3.43895i | ||||
\(57\) | −4.39639 | − | 1.07384i | −0.582316 | − | 0.142233i | ||||
\(58\) | 8.99672 | + | 15.5828i | 1.18133 | + | 2.04612i | ||||
\(59\) | 5.36073 | + | 9.28505i | 0.697907 | + | 1.20881i | 0.969191 | + | 0.246311i | \(0.0792185\pi\) |
−0.271284 | + | 0.962499i | \(0.587448\pi\) | |||||||
\(60\) | 5.61245 | − | 5.86776i | 0.724564 | − | 0.757524i | ||||
\(61\) | −2.53609 | + | 4.39263i | −0.324713 | + | 0.562419i | −0.981454 | − | 0.191697i | \(-0.938601\pi\) |
0.656742 | + | 0.754116i | \(0.271934\pi\) | |||||||
\(62\) | 17.8081 | 2.26164 | ||||||||
\(63\) | 10.8105 | − | 6.89975i | 1.36199 | − | 0.869287i | ||||
\(64\) | 4.36679 | 0.545849 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 5.50350 | + | 18.8523i | 0.677435 | + | 2.32056i | ||||
\(67\) | −7.27894 | − | 12.6075i | −0.889264 | − | 1.54025i | −0.840747 | − | 0.541428i | \(-0.817884\pi\) |
−0.0485164 | − | 0.998822i | \(-0.515449\pi\) | |||||||
\(68\) | −1.45127 | − | 2.51367i | −0.175992 | − | 0.304828i | ||||
\(69\) | −2.63503 | − | 9.02632i | −0.317221 | − | 1.08664i | ||||
\(70\) | 5.52766 | − | 9.57419i | 0.660682 | − | 1.14433i | ||||
\(71\) | 6.57523 | 0.780336 | 0.390168 | − | 0.920744i | \(-0.372417\pi\) | ||||
0.390168 | + | 0.920744i | \(0.372417\pi\) | |||||||
\(72\) | −18.5056 | − | 9.61373i | −2.18091 | − | 1.13299i | ||||
\(73\) | 16.7313 | 1.95825 | 0.979125 | − | 0.203257i | \(-0.0651527\pi\) | ||||
0.979125 | + | 0.203257i | \(0.0651527\pi\) | |||||||
\(74\) | −5.20019 | + | 9.00700i | −0.604510 | + | 1.04704i | ||||
\(75\) | −1.19721 | + | 1.25167i | −0.138242 | + | 0.144531i | ||||
\(76\) | 6.12450 | + | 10.6079i | 0.702528 | + | 1.21681i | ||||
\(77\) | 9.37156 | + | 16.2320i | 1.06799 | + | 1.84981i | ||||
\(78\) | 4.35134 | + | 1.06284i | 0.492693 | + | 0.120342i | ||||
\(79\) | −7.27288 | + | 12.5970i | −0.818263 | + | 1.41727i | 0.0886982 | + | 0.996059i | \(0.471729\pi\) |
−0.906961 | + | 0.421214i | \(0.861604\pi\) | |||||||
\(80\) | −8.60086 | −0.961605 | ||||||||
\(81\) | 5.17453 | + | 7.36371i | 0.574948 | + | 0.818190i | ||||
\(82\) | 10.5365 | 1.16356 | ||||||||
\(83\) | 1.52057 | − | 2.63370i | 0.166904 | − | 0.289086i | −0.770426 | − | 0.637530i | \(-0.779956\pi\) |
0.937330 | + | 0.348444i | \(0.113290\pi\) | |||||||
\(84\) | −33.7197 | − | 8.23620i | −3.67912 | − | 0.898643i | ||||
\(85\) | 0.309576 | + | 0.536201i | 0.0335782 | + | 0.0581591i | ||||
\(86\) | −12.9782 | − | 22.4790i | −1.39948 | − | 2.42397i | ||||
\(87\) | −8.32989 | + | 8.70881i | −0.893058 | + | 0.933682i | ||||
\(88\) | 15.2388 | − | 26.3944i | 1.62446 | − | 2.81365i | ||||
\(89\) | 7.27070 | 0.770693 | 0.385347 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385347 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(90\) | 6.88470 | + | 3.57663i | 0.725712 | + | 0.377009i | ||||
\(91\) | 4.27489 | 0.448131 | ||||||||
\(92\) | −12.7251 | + | 22.0405i | −1.32668 | + | 2.29788i | ||||
\(93\) | 3.34233 | + | 11.4492i | 0.346584 | + | 1.18722i | ||||
\(94\) | −0.524962 | − | 0.909260i | −0.0541457 | − | 0.0937830i | ||||
\(95\) | −1.30644 | − | 2.26282i | −0.134038 | − | 0.232160i | ||||
\(96\) | 4.04810 | + | 13.8668i | 0.413157 | + | 1.41527i | ||||
\(97\) | 4.81738 | − | 8.34394i | 0.489130 | − | 0.847199i | −0.510791 | − | 0.859705i | \(-0.670648\pi\) |
0.999922 | + | 0.0125059i | \(0.00398085\pi\) | |||||||
\(98\) | −29.1576 | −2.94536 | ||||||||
\(99\) | −11.0875 | + | 7.07660i | −1.11434 | + | 0.711225i | ||||
\(100\) | 4.68793 | 0.468793 | ||||||||
\(101\) | −3.89976 | + | 6.75458i | −0.388041 | + | 0.672106i | −0.992186 | − | 0.124768i | \(-0.960181\pi\) |
0.604145 | + | 0.796874i | \(0.293515\pi\) | |||||||
\(102\) | 1.91696 | − | 2.00417i | 0.189808 | − | 0.198442i | ||||
\(103\) | −0.496621 | − | 0.860172i | −0.0489335 | − | 0.0847553i | 0.840521 | − | 0.541779i | \(-0.182249\pi\) |
−0.889455 | + | 0.457023i | \(0.848916\pi\) | |||||||
\(104\) | −3.47564 | − | 6.01998i | −0.340814 | − | 0.590308i | ||||
\(105\) | 7.19288 | + | 1.75689i | 0.701953 | + | 0.171455i | ||||
\(106\) | −11.2651 | + | 19.5118i | −1.09417 | + | 1.89515i | ||||
\(107\) | 4.24171 | 0.410062 | 0.205031 | − | 0.978755i | \(-0.434270\pi\) | ||||
0.205031 | + | 0.978755i | \(0.434270\pi\) | |||||||
\(108\) | 4.72223 | − | 23.8971i | 0.454397 | − | 2.29950i | ||||
\(109\) | 4.72247 | 0.452330 | 0.226165 | − | 0.974089i | \(-0.427381\pi\) | ||||
0.226165 | + | 0.974089i | \(0.427381\pi\) | |||||||
\(110\) | −5.66934 | + | 9.81959i | −0.540550 | + | 0.936261i | ||||
\(111\) | −6.76676 | − | 1.65281i | −0.642272 | − | 0.156878i | ||||
\(112\) | 18.3839 | + | 31.8418i | 1.73711 | + | 3.00877i | ||||
\(113\) | 1.77704 | + | 3.07792i | 0.167170 | + | 0.289546i | 0.937424 | − | 0.348191i | \(-0.113204\pi\) |
−0.770254 | + | 0.637737i | \(0.779871\pi\) | |||||||
\(114\) | −8.08977 | + | 8.45777i | −0.757676 | + | 0.792143i | ||||
\(115\) | 2.71443 | − | 4.70154i | 0.253122 | − | 0.438420i | ||||
\(116\) | 32.6174 | 3.02845 | ||||||||
\(117\) | 0.133368 | + | 2.99703i | 0.0123299 | + | 0.277076i | ||||
\(118\) | 27.7268 | 2.55246 | ||||||||
\(119\) | 1.32340 | − | 2.29220i | 0.121316 | − | 0.210126i | ||||
\(120\) | −3.37397 | − | 11.5576i | −0.308000 | − | 1.05506i | ||||
\(121\) | −4.11176 | − | 7.12178i | −0.373797 | − | 0.647435i | ||||
\(122\) | 6.55858 | + | 11.3598i | 0.593786 | + | 1.02847i | ||||
\(123\) | 1.97755 | + | 6.77410i | 0.178309 | + | 0.610800i | ||||
\(124\) | 16.1408 | − | 27.9566i | 1.44948 | − | 2.51058i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.47443 | − | 33.1332i | −0.131353 | − | 2.95174i | ||||
\(127\) | −13.6413 | −1.21047 | −0.605234 | − | 0.796048i | \(-0.706920\pi\) | ||||
−0.605234 | + | 0.796048i | \(0.706920\pi\) | |||||||
\(128\) | −2.69366 | + | 4.66556i | −0.238088 | + | 0.412381i | ||||
\(129\) | 12.0163 | − | 12.5629i | 1.05798 | − | 1.10610i | ||||
\(130\) | 1.29305 | + | 2.23963i | 0.113408 | + | 0.196429i | ||||
\(131\) | −4.18118 | − | 7.24202i | −0.365312 | − | 0.632738i | 0.623514 | − | 0.781812i | \(-0.285704\pi\) |
−0.988826 | + | 0.149073i | \(0.952371\pi\) | |||||||
\(132\) | 34.5840 | + | 8.44730i | 3.01015 | + | 0.735244i | ||||
\(133\) | −5.58489 | + | 9.67331i | −0.484271 | + | 0.838782i | ||||
\(134\) | −37.6482 | −3.25231 | ||||||||
\(135\) | −1.00732 | + | 5.09758i | −0.0866960 | + | 0.438730i | ||||
\(136\) | −4.30389 | −0.369056 | ||||||||
\(137\) | 3.37544 | − | 5.84643i | 0.288383 | − | 0.499494i | −0.685041 | − | 0.728505i | \(-0.740216\pi\) |
0.973424 | + | 0.229010i | \(0.0735489\pi\) | |||||||
\(138\) | −23.6229 | − | 5.76999i | −2.01091 | − | 0.491174i | ||||
\(139\) | −1.75288 | − | 3.03608i | −0.148678 | − | 0.257517i | 0.782061 | − | 0.623201i | \(-0.214168\pi\) |
−0.930739 | + | 0.365684i | \(0.880835\pi\) | |||||||
\(140\) | −10.0202 | − | 17.3555i | −0.846862 | − | 1.46681i | ||||
\(141\) | 0.486052 | − | 0.508162i | 0.0409330 | − | 0.0427950i | ||||
\(142\) | 8.50211 | − | 14.7261i | 0.713481 | − | 1.23579i | ||||
\(143\) | −4.38446 | −0.366647 | ||||||||
\(144\) | −21.7500 | + | 13.8819i | −1.81250 | + | 1.15683i | ||||
\(145\) | −6.95774 | −0.577809 | ||||||||
\(146\) | 21.6344 | − | 37.4720i | 1.79048 | − | 3.10120i | ||||
\(147\) | −5.47246 | − | 18.7459i | −0.451361 | − | 1.54614i | ||||
\(148\) | 9.42660 | + | 16.3273i | 0.774861 | + | 1.34210i | ||||
\(149\) | −6.13951 | − | 10.6339i | −0.502968 | − | 0.871166i | −0.999994 | − | 0.00343063i | \(-0.998908\pi\) |
0.497026 | − | 0.867736i | \(-0.334425\pi\) | |||||||
\(150\) | 1.25523 | + | 4.29979i | 0.102489 | + | 0.351076i | ||||
\(151\) | 8.34821 | − | 14.4595i | 0.679367 | − | 1.17670i | −0.295804 | − | 0.955249i | \(-0.595588\pi\) |
0.975172 | − | 0.221450i | \(-0.0710791\pi\) | |||||||
\(152\) | 18.1628 | 1.47320 | ||||||||
\(153\) | 1.64830 | + | 0.856297i | 0.133257 | + | 0.0692275i | ||||
\(154\) | 48.4717 | 3.90596 | ||||||||
\(155\) | −3.44304 | + | 5.96353i | −0.276552 | + | 0.479002i | ||||
\(156\) | 5.61245 | − | 5.86776i | 0.449356 | − | 0.469797i | ||||
\(157\) | −3.99844 | − | 6.92550i | −0.319110 | − | 0.552715i | 0.661192 | − | 0.750216i | \(-0.270051\pi\) |
−0.980303 | + | 0.197501i | \(0.936717\pi\) | |||||||
\(158\) | 18.8084 | + | 32.5771i | 1.49632 | + | 2.59170i | ||||
\(159\) | −14.6588 | − | 3.58048i | −1.16252 | − | 0.283950i | ||||
\(160\) | −4.17008 | + | 7.22278i | −0.329674 | + | 0.571011i | ||||
\(161\) | −23.2078 | −1.82903 | ||||||||
\(162\) | 23.1829 | − | 2.06738i | 1.82142 | − | 0.162429i | ||||
\(163\) | −17.3723 | −1.36071 | −0.680353 | − | 0.732885i | \(-0.738173\pi\) | ||||
−0.680353 | + | 0.732885i | \(0.738173\pi\) | |||||||
\(164\) | 9.54996 | − | 16.5410i | 0.745727 | − | 1.29164i | ||||
\(165\) | −7.37724 | − | 1.80192i | −0.574317 | − | 0.140280i | ||||
\(166\) | −3.93234 | − | 6.81102i | −0.305209 | − | 0.528637i | ||||
\(167\) | −2.13795 | − | 3.70303i | −0.165439 | − | 0.286549i | 0.771372 | − | 0.636385i | \(-0.219571\pi\) |
−0.936811 | + | 0.349835i | \(0.886238\pi\) | |||||||
\(168\) | −35.5763 | + | 37.1947i | −2.74477 | + | 2.86963i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 1.60119 | 0.122806 | ||||||||
\(171\) | −6.95598 | − | 3.61365i | −0.531937 | − | 0.276343i | ||||
\(172\) | −47.0523 | −3.58771 | ||||||||
\(173\) | −6.47793 | + | 11.2201i | −0.492508 | + | 0.853049i | −0.999963 | − | 0.00862929i | \(-0.997253\pi\) |
0.507455 | + | 0.861679i | \(0.330587\pi\) | |||||||
\(174\) | 8.73355 | + | 29.9168i | 0.662089 | + | 2.26799i | ||||
\(175\) | 2.13745 | + | 3.70217i | 0.161576 | + | 0.279857i | ||||
\(176\) | −18.8551 | − | 32.6579i | −1.42125 | − | 2.46169i | ||||
\(177\) | 5.20392 | + | 17.8260i | 0.391150 | + | 1.33989i | ||||
\(178\) | 9.40140 | − | 16.2837i | 0.704665 | − | 1.22051i | ||||
\(179\) | 18.8530 | 1.40914 | 0.704571 | − | 0.709633i | \(-0.251139\pi\) | ||||
0.704571 | + | 0.709633i | \(0.251139\pi\) | |||||||
\(180\) | 11.8550 | − | 7.56641i | 0.883616 | − | 0.563967i | ||||
\(181\) | −21.2593 | −1.58019 | −0.790097 | − | 0.612982i | \(-0.789970\pi\) | ||||
−0.790097 | + | 0.612982i | \(0.789970\pi\) | |||||||
\(182\) | 5.52766 | − | 9.57419i | 0.409737 | − | 0.709686i | ||||
\(183\) | −6.07246 | + | 6.34870i | −0.448889 | + | 0.469309i | ||||
\(184\) | 18.8688 | + | 32.6817i | 1.39102 | + | 2.40933i | ||||
\(185\) | −2.01082 | − | 3.48284i | −0.147838 | − | 0.256064i | ||||
\(186\) | 29.9637 | + | 7.31878i | 2.19705 | + | 0.536639i | ||||
\(187\) | −1.35732 | + | 2.35095i | −0.0992573 | + | 0.171919i | ||||
\(188\) | −1.90324 | −0.138808 | ||||||||
\(189\) | 21.0252 | − | 7.16655i | 1.52936 | − | 0.521290i | ||||
\(190\) | −6.75717 | −0.490217 | ||||||||
\(191\) | 7.70849 | − | 13.3515i | 0.557767 | − | 0.966081i | −0.439916 | − | 0.898039i | \(-0.644992\pi\) |
0.997682 | − | 0.0680415i | \(-0.0216750\pi\) | |||||||
\(192\) | 7.34751 | + | 1.79466i | 0.530261 | + | 0.129519i | ||||
\(193\) | −0.944008 | − | 1.63507i | −0.0679512 | − | 0.117695i | 0.830048 | − | 0.557692i | \(-0.188313\pi\) |
−0.897999 | + | 0.439997i | \(0.854980\pi\) | |||||||
\(194\) | −12.4582 | − | 21.5783i | −0.894449 | − | 1.54923i | ||||
\(195\) | −1.19721 | + | 1.25167i | −0.0857341 | + | 0.0896341i | ||||
\(196\) | −26.4276 | + | 45.7739i | −1.88768 | + | 3.26956i | ||||
\(197\) | −10.8597 | −0.773723 | −0.386862 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386862 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(198\) | 1.51222 | + | 33.9824i | 0.107469 | + | 2.41502i | ||||
\(199\) | −1.20110 | −0.0851436 | −0.0425718 | − | 0.999093i | \(-0.513555\pi\) | ||||
−0.0425718 | + | 0.999093i | \(0.513555\pi\) | |||||||
\(200\) | 3.47564 | − | 6.01998i | 0.245765 | − | 0.425677i | ||||
\(201\) | −7.06602 | − | 24.2047i | −0.498399 | − | 1.70727i | ||||
\(202\) | 10.0852 | + | 17.4681i | 0.709591 | + | 1.22905i | ||||
\(203\) | 14.8718 | + | 25.7587i | 1.04380 | + | 1.80791i | ||||
\(204\) | −1.40882 | − | 4.82591i | −0.0986370 | − | 0.337882i | ||||
\(205\) | −2.03714 | + | 3.52842i | −0.142280 | + | 0.246436i | ||||
\(206\) | −2.56863 | −0.178965 | ||||||||
\(207\) | −0.724038 | − | 16.2705i | −0.0503241 | − | 1.13088i | ||||
\(208\) | −8.60086 | −0.596362 | ||||||||
\(209\) | 5.72803 | − | 9.92125i | 0.396216 | − | 0.686267i | ||||
\(210\) | 13.2356 | − | 13.8376i | 0.913340 | − | 0.954888i | ||||
\(211\) | 0.117606 | + | 0.203699i | 0.00809632 | + | 0.0140232i | 0.870045 | − | 0.492972i | \(-0.164089\pi\) |
−0.861949 | + | 0.506995i | \(0.830756\pi\) | |||||||
\(212\) | 20.4208 | + | 35.3698i | 1.40250 | + | 2.42921i | ||||
\(213\) | 11.0634 | + | 2.70228i | 0.758051 | + | 0.185157i | ||||
\(214\) | 5.48476 | − | 9.49988i | 0.374930 | − | 0.649398i | ||||
\(215\) | 10.0369 | 0.684511 | ||||||||
\(216\) | −27.1863 | − | 23.7814i | −1.84979 | − | 1.61812i | ||||
\(217\) | 29.4373 | 1.99833 | ||||||||
\(218\) | 6.10639 | − | 10.5766i | 0.413577 | − | 0.716337i | ||||
\(219\) | 28.1519 | + | 6.87622i | 1.90233 | + | 0.464652i | ||||
\(220\) | 10.2770 | + | 17.8004i | 0.692878 | + | 1.20010i | ||||
\(221\) | 0.309576 | + | 0.536201i | 0.0208243 | + | 0.0360688i | ||||
\(222\) | −12.4515 | + | 13.0179i | −0.835687 | + | 0.873703i | ||||
\(223\) | 8.37747 | − | 14.5102i | 0.560997 | − | 0.971675i | −0.436413 | − | 0.899747i | \(-0.643751\pi\) |
0.997410 | − | 0.0719287i | \(-0.0229154\pi\) | |||||||
\(224\) | 35.6533 | 2.38218 | ||||||||
\(225\) | −2.52882 | + | 1.61402i | −0.168588 | + | 0.107601i | ||||
\(226\) | 9.19121 | 0.611390 | ||||||||
\(227\) | −11.4002 | + | 19.7457i | −0.756656 | + | 1.31057i | 0.187891 | + | 0.982190i | \(0.439835\pi\) |
−0.944547 | + | 0.328377i | \(0.893498\pi\) | |||||||
\(228\) | 5.94535 | + | 20.3658i | 0.393740 | + | 1.34876i | ||||
\(229\) | 3.48739 | + | 6.04033i | 0.230453 | + | 0.399156i | 0.957942 | − | 0.286964i | \(-0.0926459\pi\) |
−0.727488 | + | 0.686120i | \(0.759313\pi\) | |||||||
\(230\) | −7.01981 | − | 12.1587i | −0.462872 | − | 0.801718i | ||||
\(231\) | 9.09743 | + | 31.1633i | 0.598567 | + | 2.05039i | ||||
\(232\) | 24.1826 | − | 41.8855i | 1.58766 | − | 2.74992i | ||||
\(233\) | −8.63201 | −0.565502 | −0.282751 | − | 0.959193i | \(-0.591247\pi\) | ||||
−0.282751 | + | 0.959193i | \(0.591247\pi\) | |||||||
\(234\) | 6.88470 | + | 3.57663i | 0.450067 | + | 0.233811i | ||||
\(235\) | 0.405987 | 0.0264836 | ||||||||
\(236\) | 25.1307 | − | 43.5277i | 1.63587 | − | 2.83341i | ||||
\(237\) | −17.4144 | + | 18.2065i | −1.13118 | + | 1.18264i | ||||
\(238\) | −3.42246 | − | 5.92787i | −0.221845 | − | 0.384247i | ||||
\(239\) | 1.53550 | + | 2.65957i | 0.0993235 | + | 0.172033i | 0.911405 | − | 0.411511i | \(-0.134999\pi\) |
−0.812081 | + | 0.583544i | \(0.801665\pi\) | |||||||
\(240\) | −14.4717 | − | 3.53478i | −0.934143 | − | 0.228169i | ||||
\(241\) | −2.91634 | + | 5.05125i | −0.187858 | + | 0.325379i | −0.944536 | − | 0.328408i | \(-0.893488\pi\) |
0.756678 | + | 0.653788i | \(0.226821\pi\) | |||||||
\(242\) | −21.2669 | −1.36709 | ||||||||
\(243\) | 5.68026 | + | 14.5167i | 0.364389 | + | 0.931247i | ||||
\(244\) | 23.7780 | 1.52223 | ||||||||
\(245\) | 5.63736 | − | 9.76419i | 0.360157 | − | 0.623811i | ||||
\(246\) | 17.7286 | + | 4.33028i | 1.13033 | + | 0.276089i | ||||
\(247\) | −1.30644 | − | 2.26282i | −0.0831267 | − | 0.143980i | ||||
\(248\) | −23.9336 | − | 41.4541i | −1.51978 | − | 2.63234i | ||||
\(249\) | 3.64088 | − | 3.80650i | 0.230731 | − | 0.241227i | ||||
\(250\) | −1.29305 | + | 2.23963i | −0.0817798 | + | 0.141647i | ||||
\(251\) | −23.7101 | −1.49657 | −0.748285 | − | 0.663378i | \(-0.769122\pi\) | ||||
−0.748285 | + | 0.663378i | \(0.769122\pi\) | |||||||
\(252\) | −53.3514 | − | 27.7162i | −3.36082 | − | 1.74596i | ||||
\(253\) | 23.8027 | 1.49646 | ||||||||
\(254\) | −17.6389 | + | 30.5514i | −1.10676 | + | 1.91697i | ||||
\(255\) | 0.300520 | + | 1.02943i | 0.0188193 | + | 0.0644656i | ||||
\(256\) | 11.3329 | + | 19.6291i | 0.708305 | + | 1.22682i | ||||
\(257\) | −9.65384 | − | 16.7209i | −0.602190 | − | 1.04302i | −0.992489 | − | 0.122335i | \(-0.960962\pi\) |
0.390299 | − | 0.920688i | \(-0.372372\pi\) | |||||||
\(258\) | −12.5986 | − | 43.1566i | −0.784355 | − | 2.68681i | ||||
\(259\) | −8.59604 | + | 14.8888i | −0.534132 | + | 0.925144i | ||||
\(260\) | 4.68793 | 0.290733 | ||||||||
\(261\) | −17.5949 | + | 11.2299i | −1.08910 | + | 0.695114i | ||||
\(262\) | −21.6260 | −1.33606 | ||||||||
\(263\) | 5.85985 | − | 10.1496i | 0.361334 | − | 0.625848i | −0.626847 | − | 0.779142i | \(-0.715655\pi\) |
0.988181 | + | 0.153294i | \(0.0489882\pi\) | |||||||
\(264\) | 36.4882 | − | 38.1480i | 2.24569 | − | 2.34785i | ||||
\(265\) | −4.35603 | − | 7.54486i | −0.267589 | − | 0.463477i | ||||
\(266\) | 14.4431 | + | 25.0162i | 0.885563 | + | 1.53384i | ||||
\(267\) | 12.2336 | + | 2.98811i | 0.748683 | + | 0.182869i | ||||
\(268\) | −34.1232 | + | 59.1031i | −2.08440 | + | 3.61029i | ||||
\(269\) | −17.0088 | −1.03705 | −0.518524 | − | 0.855063i | \(-0.673518\pi\) | ||||
−0.518524 | + | 0.855063i | \(0.673518\pi\) | |||||||
\(270\) | 10.1142 | + | 8.84745i | 0.615530 | + | 0.538439i | ||||
\(271\) | −12.4840 | −0.758348 | −0.379174 | − | 0.925325i | \(-0.623792\pi\) | ||||
−0.379174 | + | 0.925325i | \(0.623792\pi\) | |||||||
\(272\) | −2.66262 | + | 4.61179i | −0.161445 | + | 0.279631i | ||||
\(273\) | 7.19288 | + | 1.75689i | 0.435333 | + | 0.106332i | ||||
\(274\) | −8.72924 | − | 15.1195i | −0.527353 | − | 0.913401i | ||||
\(275\) | −2.19223 | − | 3.79706i | −0.132197 | − | 0.228971i | ||||
\(276\) | −30.4692 | + | 31.8553i | −1.83403 | + | 1.91746i | ||||
\(277\) | −10.1444 | + | 17.5705i | −0.609516 | + | 1.05571i | 0.381805 | + | 0.924243i | \(0.375303\pi\) |
−0.991320 | + | 0.131469i | \(0.958031\pi\) | |||||||
\(278\) | −9.06628 | −0.543759 | ||||||||
\(279\) | 0.918386 | + | 20.6378i | 0.0549823 | + | 1.23556i | ||||
\(280\) | −29.7160 | −1.77587 | ||||||||
\(281\) | 4.18725 | − | 7.25252i | 0.249790 | − | 0.432649i | −0.713677 | − | 0.700475i | \(-0.752972\pi\) |
0.963467 | + | 0.267825i | \(0.0863050\pi\) | |||||||
\(282\) | −0.509606 | − | 1.74566i | −0.0303466 | − | 0.103952i | ||||
\(283\) | 1.11281 | + | 1.92745i | 0.0661498 | + | 0.114575i | 0.897203 | − | 0.441617i | \(-0.145595\pi\) |
−0.831054 | + | 0.556192i | \(0.812262\pi\) | |||||||
\(284\) | −15.4121 | − | 26.6946i | −0.914541 | − | 1.58403i | ||||
\(285\) | −1.26822 | − | 4.34431i | −0.0751231 | − | 0.257335i | ||||
\(286\) | −5.66934 | + | 9.81959i | −0.335235 | + | 0.580644i | ||||
\(287\) | 17.4171 | 1.02810 | ||||||||
\(288\) | 1.11231 | + | 24.9957i | 0.0655436 | + | 1.47289i | ||||
\(289\) | −16.6167 | −0.977450 | ||||||||
\(290\) | −8.99672 | + | 15.5828i | −0.528305 | + | 0.915052i | ||||
\(291\) | 11.5348 | − | 12.0596i | 0.676184 | − | 0.706944i | ||||
\(292\) | −39.2176 | − | 67.9269i | −2.29504 | − | 3.97512i | ||||
\(293\) | 1.26944 | + | 2.19873i | 0.0741613 | + | 0.128451i | 0.900721 | − | 0.434398i | \(-0.143039\pi\) |
−0.826560 | + | 0.562849i | \(0.809705\pi\) | |||||||
\(294\) | −49.0601 | − | 11.9832i | −2.86125 | − | 0.698873i | ||||
\(295\) | −5.36073 | + | 9.28505i | −0.312114 | + | 0.540596i | ||||
\(296\) | 27.9555 | 1.62488 | ||||||||
\(297\) | −21.5641 | + | 7.35024i | −1.25127 | + | 0.426504i | ||||
\(298\) | −31.7548 | −1.83951 | ||||||||
\(299\) | 2.71443 | − | 4.70154i | 0.156980 | − | 0.271897i | ||||
\(300\) | 7.88785 | + | 1.92664i | 0.455405 | + | 0.111235i | ||||
\(301\) | −21.4533 | − | 37.1583i | −1.23655 | − | 2.14177i | ||||
\(302\) | −21.5893 | − | 37.3938i | −1.24233 | − | 2.15177i | ||||
\(303\) | −9.33768 | + | 9.76245i | −0.536436 | + | 0.560838i | ||||
\(304\) | 11.2365 | − | 19.4622i | 0.644457 | − | 1.11623i | ||||
\(305\) | −5.07217 | −0.290432 | ||||||||
\(306\) | 4.04913 | − | 2.58435i | 0.231473 | − | 0.147737i | ||||
\(307\) | 19.2343 | 1.09776 | 0.548881 | − | 0.835901i | \(-0.315054\pi\) | ||||
0.548881 | + | 0.835901i | \(0.315054\pi\) | |||||||
\(308\) | 43.9332 | − | 76.0946i | 2.50333 | − | 4.33589i | ||||
\(309\) | −0.482094 | − | 1.65141i | −0.0274254 | − | 0.0939457i | ||||
\(310\) | 8.90407 | + | 15.4223i | 0.505717 | + | 0.875928i | ||||
\(311\) | −4.38021 | − | 7.58674i | −0.248379 | − | 0.430205i | 0.714697 | − | 0.699434i | \(-0.246564\pi\) |
−0.963076 | + | 0.269229i | \(0.913231\pi\) | |||||||
\(312\) | −3.37397 | − | 11.5576i | −0.191014 | − | 0.654318i | ||||
\(313\) | 6.08910 | − | 10.5466i | 0.344176 | − | 0.596131i | −0.641027 | − | 0.767518i | \(-0.721491\pi\) |
0.985204 | + | 0.171387i | \(0.0548248\pi\) | |||||||
\(314\) | −20.6808 | −1.16708 | ||||||||
\(315\) | 11.3806 | + | 5.91225i | 0.641223 | + | 0.333117i | ||||
\(316\) | 68.1896 | 3.83596 | ||||||||
\(317\) | −8.66227 | + | 15.0035i | −0.486521 | + | 0.842680i | −0.999880 | − | 0.0154945i | \(-0.995068\pi\) |
0.513359 | + | 0.858174i | \(0.328401\pi\) | |||||||
\(318\) | −26.9735 | + | 28.2005i | −1.51260 | + | 1.58141i | ||||
\(319\) | −15.2530 | − | 26.4189i | −0.854003 | − | 1.47918i | ||||
\(320\) | 2.18340 | + | 3.78175i | 0.122056 | + | 0.211407i | ||||
\(321\) | 7.13705 | + | 1.74326i | 0.398351 | + | 0.0972992i | ||||
\(322\) | −30.0089 | + | 51.9770i | −1.67233 | + | 2.89656i | ||||
\(323\) | −1.61777 | −0.0900149 | ||||||||
\(324\) | 17.7668 | − | 38.2682i | 0.987043 | − | 2.12601i | ||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −22.4633 | + | 38.9076i | −1.24413 | + | 2.15489i | ||||
\(327\) | 7.94596 | + | 1.94084i | 0.439412 | + | 0.107329i | ||||
\(328\) | −14.1607 | − | 24.5270i | −0.781894 | − | 1.35428i | ||||
\(329\) | −0.867775 | − | 1.50303i | −0.0478420 | − | 0.0828647i | ||||
\(330\) | −13.5748 | + | 14.1923i | −0.747268 | + | 0.781261i | ||||
\(331\) | −1.23037 | + | 2.13106i | −0.0676272 | + | 0.117134i | −0.897856 | − | 0.440288i | \(-0.854876\pi\) |
0.830229 | + | 0.557422i | \(0.188210\pi\) | |||||||
\(332\) | −14.2566 | −0.782434 | ||||||||
\(333\) | −10.7064 | − | 5.56200i | −0.586706 | − | 0.304796i | ||||
\(334\) | −11.0579 | −0.605062 | ||||||||
\(335\) | 7.27894 | − | 12.6075i | 0.397691 | − | 0.688821i | ||||
\(336\) | 17.8461 | + | 61.1320i | 0.973586 | + | 3.33502i | ||||
\(337\) | −10.3743 | − | 17.9688i | −0.565123 | − | 0.978821i | −0.997038 | − | 0.0769073i | \(-0.975495\pi\) |
0.431915 | − | 0.901914i | \(-0.357838\pi\) | |||||||
\(338\) | 1.29305 | + | 2.23963i | 0.0703328 | + | 0.121820i | ||||
\(339\) | 1.72506 | + | 5.90919i | 0.0936922 | + | 0.320943i | ||||
\(340\) | 1.45127 | − | 2.51367i | 0.0787062 | − | 0.136323i | ||||
\(341\) | −30.1918 | −1.63498 | ||||||||
\(342\) | −17.0877 | + | 10.9062i | −0.923997 | + | 0.589739i | ||||
\(343\) | −18.2739 | −0.986700 | ||||||||
\(344\) | −34.8846 | + | 60.4220i | −1.88085 | + | 3.25773i | ||||
\(345\) | 6.49950 | − | 6.79516i | 0.349921 | − | 0.365839i | ||||
\(346\) | 16.7526 | + | 29.0164i | 0.900626 | + | 1.55993i | ||||
\(347\) | 6.29383 | + | 10.9012i | 0.337871 | + | 0.585209i | 0.984032 | − | 0.177992i | \(-0.0569601\pi\) |
−0.646161 | + | 0.763201i | \(0.723627\pi\) | |||||||
\(348\) | 54.8816 | + | 13.4051i | 2.94196 | + | 0.718588i | ||||
\(349\) | 9.98642 | − | 17.2970i | 0.534561 | − | 0.925887i | −0.464624 | − | 0.885508i | \(-0.653810\pi\) |
0.999184 | − | 0.0403782i | \(-0.0128563\pi\) | |||||||
\(350\) | 11.0553 | 0.590932 | ||||||||
\(351\) | −1.00732 | + | 5.09758i | −0.0537665 | + | 0.272089i | ||||
\(352\) | −36.5671 | −1.94903 | ||||||||
\(353\) | −2.94467 | + | 5.10031i | −0.156729 | + | 0.271462i | −0.933687 | − | 0.358090i | \(-0.883428\pi\) |
0.776958 | + | 0.629552i | \(0.216762\pi\) | |||||||
\(354\) | 46.6527 | + | 11.3951i | 2.47956 | + | 0.605645i | ||||
\(355\) | 3.28761 | + | 5.69431i | 0.174488 | + | 0.302223i | ||||
\(356\) | −17.0423 | − | 29.5181i | −0.903240 | − | 1.56446i | ||||
\(357\) | 3.16879 | − | 3.31293i | 0.167710 | − | 0.175339i | ||||
\(358\) | 24.3780 | − | 42.2239i | 1.28842 | − | 2.23160i | ||||
\(359\) | 17.8334 | 0.941209 | 0.470605 | − | 0.882344i | \(-0.344036\pi\) | ||||
0.470605 | + | 0.882344i | \(0.344036\pi\) | |||||||
\(360\) | −0.927080 | − | 20.8332i | −0.0488614 | − | 1.09801i | ||||
\(361\) | −12.1729 | −0.640677 | ||||||||
\(362\) | −27.4894 | + | 47.6131i | −1.44481 | + | 2.50249i | ||||
\(363\) | −3.99149 | − | 13.6729i | −0.209499 | − | 0.717639i | ||||
\(364\) | −10.0202 | − | 17.3555i | −0.525202 | − | 0.909676i | ||||
\(365\) | 8.36565 | + | 14.4897i | 0.437878 | + | 0.758427i | ||||
\(366\) | 6.36673 | + | 21.8093i | 0.332795 | + | 1.13999i | ||||
\(367\) | 14.9165 | − | 25.8361i | 0.778633 | − | 1.34863i | −0.154097 | − | 0.988056i | \(-0.549247\pi\) |
0.932730 | − | 0.360576i | \(-0.117420\pi\) | |||||||
\(368\) | 46.6929 | 2.43404 | ||||||||
\(369\) | 0.543379 | + | 12.2107i | 0.0282872 | + | 0.635665i | ||||
\(370\) | −10.4004 | −0.540690 | ||||||||
\(371\) | −18.6215 | + | 32.2535i | −0.966783 | + | 1.67452i | ||||
\(372\) | 38.6478 | − | 40.4059i | 2.00380 | − | 2.09495i | ||||
\(373\) | 7.28970 | + | 12.6261i | 0.377446 | + | 0.653756i | 0.990690 | − | 0.136138i | \(-0.0434690\pi\) |
−0.613244 | + | 0.789894i | \(0.710136\pi\) | |||||||
\(374\) | 3.51018 | + | 6.07981i | 0.181507 | + | 0.314379i | ||||
\(375\) | −1.68259 | − | 0.410979i | −0.0868884 | − | 0.0212229i | ||||
\(376\) | −1.41106 | + | 2.44403i | −0.0727700 | + | 0.126041i | ||||
\(377\) | −6.95774 | −0.358342 | ||||||||
\(378\) | 11.1362 | − | 56.3554i | 0.572784 | − | 2.89861i | ||||
\(379\) | 20.7048 | 1.06353 | 0.531766 | − | 0.846891i | \(-0.321529\pi\) | ||||
0.531766 | + | 0.846891i | \(0.321529\pi\) | |||||||
\(380\) | −6.12450 | + | 10.6079i | −0.314180 | + | 0.544176i | ||||
\(381\) | −22.9526 | − | 5.60628i | −1.17590 | − | 0.287219i | ||||
\(382\) | −19.9350 | − | 34.5284i | −1.01996 | − | 1.76663i | ||||
\(383\) | 12.7832 | + | 22.1412i | 0.653193 | + | 1.13136i | 0.982344 | + | 0.187086i | \(0.0599043\pi\) |
−0.329150 | + | 0.944277i | \(0.606762\pi\) | |||||||
\(384\) | −6.44977 | + | 6.74317i | −0.329138 | + | 0.344111i | ||||
\(385\) | −9.37156 | + | 16.2320i | −0.477619 | + | 0.827260i | ||||
\(386\) | −4.88260 | −0.248518 | ||||||||
\(387\) | 25.3816 | − | 16.1997i | 1.29022 | − | 0.823479i | ||||
\(388\) | −45.1671 | −2.29301 | ||||||||
\(389\) | 8.56520 | − | 14.8354i | 0.434273 | − | 0.752183i | −0.562963 | − | 0.826482i | \(-0.690339\pi\) |
0.997236 | + | 0.0742992i | \(0.0236720\pi\) | |||||||
\(390\) | 1.25523 | + | 4.29979i | 0.0635610 | + | 0.217728i | ||||
\(391\) | −1.68064 | − | 2.91096i | −0.0849939 | − | 0.147214i | ||||
\(392\) | 39.1868 | + | 67.8736i | 1.97923 | + | 3.42813i | ||||
\(393\) | −4.05888 | − | 13.9037i | −0.204743 | − | 0.701349i | ||||
\(394\) | −14.0422 | + | 24.3218i | −0.707435 | + | 1.22531i | ||||
\(395\) | −14.5458 | −0.731877 | ||||||||
\(396\) | 54.7189 | + | 28.4266i | 2.74973 | + | 1.42849i | ||||
\(397\) | −15.8337 | −0.794669 | −0.397334 | − | 0.917674i | \(-0.630065\pi\) | ||||
−0.397334 | + | 0.917674i | \(0.630065\pi\) | |||||||
\(398\) | −1.55308 | + | 2.69002i | −0.0778490 | + | 0.134838i | ||||
\(399\) | −13.3726 | + | 13.9809i | −0.669467 | + | 0.699920i | ||||
\(400\) | −4.30043 | − | 7.44856i | −0.215021 | − | 0.372428i | ||||
\(401\) | 17.0554 | + | 29.5408i | 0.851706 | + | 1.47520i | 0.879668 | + | 0.475588i | \(0.157765\pi\) |
−0.0279624 | + | 0.999609i | \(0.508902\pi\) | |||||||
\(402\) | −63.3463 | − | 15.4726i | −3.15943 | − | 0.771705i | ||||
\(403\) | −3.44304 | + | 5.96353i | −0.171510 | + | 0.297065i | ||||
\(404\) | 36.5636 | 1.81911 | ||||||||
\(405\) | −3.78990 | + | 8.16313i | −0.188321 | + | 0.405629i | ||||
\(406\) | 76.9200 | 3.81748 | ||||||||
\(407\) | 8.81637 | − | 15.2704i | 0.437011 | − | 0.756926i | ||||
\(408\) | −7.24167 | − | 1.76881i | −0.358516 | − | 0.0875692i | ||||
\(409\) | 9.57264 | + | 16.5803i | 0.473336 | + | 0.819843i | 0.999534 | − | 0.0305196i | \(-0.00971618\pi\) |
−0.526198 | + | 0.850362i | \(0.676383\pi\) | |||||||
\(410\) | 5.26825 | + | 9.12487i | 0.260180 | + | 0.450645i | ||||
\(411\) | 8.08223 | − | 8.44989i | 0.398667 | − | 0.416802i | ||||
\(412\) | −2.32812 | + | 4.03243i | −0.114698 | + | 0.198664i | ||||
\(413\) | 45.8331 | 2.25530 | ||||||||
\(414\) | −37.3761 | − | 19.4170i | −1.83694 | − | 0.954294i | ||||
\(415\) | 3.04113 | 0.149283 | ||||||||
\(416\) | −4.17008 | + | 7.22278i | −0.204455 | + | 0.354126i | ||||
\(417\) | −1.70161 | − | 5.82887i | −0.0833282 | − | 0.285441i | ||||
\(418\) | −14.8133 | − | 25.6574i | −0.724542 | − | 1.25494i | ||||
\(419\) | −3.56749 | − | 6.17908i | −0.174284 | − | 0.301868i | 0.765630 | − | 0.643282i | \(-0.222428\pi\) |
−0.939913 | + | 0.341414i | \(0.889094\pi\) | |||||||
\(420\) | −9.72710 | − | 33.3202i | −0.474634 | − | 1.62586i | ||||
\(421\) | 13.0809 | − | 22.6568i | 0.637524 | − | 1.10422i | −0.348451 | − | 0.937327i | \(-0.613292\pi\) |
0.985974 | − | 0.166896i | \(-0.0533745\pi\) | |||||||
\(422\) | 0.608282 | 0.0296107 | ||||||||
\(423\) | 1.02667 | − | 0.655269i | 0.0499183 | − | 0.0318603i | ||||
\(424\) | 60.5599 | 2.94105 | ||||||||
\(425\) | −0.309576 | + | 0.536201i | −0.0150166 | + | 0.0260096i | ||||
\(426\) | 20.3577 | − | 21.2837i | 0.986332 | − | 1.03120i | ||||
\(427\) | 10.8415 | + | 18.7780i | 0.524657 | + | 0.908732i | ||||
\(428\) | −9.94244 | − | 17.2208i | −0.480586 | − | 0.832399i | ||||
\(429\) | −7.37724 | − | 1.80192i | −0.356176 | − | 0.0869978i | ||||
\(430\) | 12.9782 | − | 22.4790i | 0.625866 | − | 1.08403i | ||||
\(431\) | −12.4211 | −0.598302 | −0.299151 | − | 0.954206i | \(-0.596703\pi\) | ||||
−0.299151 | + | 0.954206i | \(0.596703\pi\) | |||||||
\(432\) | −42.3015 | + | 14.4187i | −2.03523 | + | 0.693721i | ||||
\(433\) | −6.04541 | −0.290524 | −0.145262 | − | 0.989393i | \(-0.546402\pi\) | ||||
−0.145262 | + | 0.989393i | \(0.546402\pi\) | |||||||
\(434\) | 38.0640 | − | 65.9287i | 1.82713 | − | 3.16468i | ||||
\(435\) | −11.7070 | − | 2.85949i | −0.561307 | − | 0.137102i | ||||
\(436\) | −11.0693 | − | 19.1726i | −0.530124 | − | 0.918201i | ||||
\(437\) | 7.09248 | + | 12.2845i | 0.339279 | + | 0.587649i | ||||
\(438\) | 51.8020 | − | 54.1585i | 2.47520 | − | 2.58779i | ||||
\(439\) | 14.3382 | − | 24.8345i | 0.684326 | − | 1.18529i | −0.289323 | − | 0.957232i | \(-0.593430\pi\) |
0.973648 | − | 0.228055i | \(-0.0732366\pi\) | |||||||
\(440\) | 30.4776 | 1.45296 | ||||||||
\(441\) | −1.50369 | − | 33.7907i | −0.0716042 | − | 1.60908i | ||||
\(442\) | 1.60119 | 0.0761608 | ||||||||
\(443\) | 4.57498 | − | 7.92410i | 0.217364 | − | 0.376485i | −0.736637 | − | 0.676288i | \(-0.763588\pi\) |
0.954001 | + | 0.299803i | \(0.0969209\pi\) | |||||||
\(444\) | 9.15086 | + | 31.3463i | 0.434280 | + | 1.48763i | ||||
\(445\) | 3.63535 | + | 6.29661i | 0.172332 | + | 0.298488i | ||||
\(446\) | −21.6650 | − | 37.5249i | −1.02587 | − | 1.77686i | ||||
\(447\) | −5.95992 | − | 20.4157i | −0.281895 | − | 0.965631i | ||||
\(448\) | 9.33379 | − | 16.1666i | 0.440980 | − | 0.763800i | ||||
\(449\) | 35.4645 | 1.67367 | 0.836837 | − | 0.547452i | \(-0.184402\pi\) | ||||
0.836837 | + | 0.547452i | \(0.184402\pi\) | |||||||
\(450\) | 0.344904 | + | 7.75064i | 0.0162589 | + | 0.365369i | ||||
\(451\) | −17.8635 | −0.841160 | ||||||||
\(452\) | 8.33064 | − | 14.4291i | 0.391840 | − | 0.678687i | ||||
\(453\) | 19.9891 | − | 20.8984i | 0.939172 | − | 0.981895i | ||||
\(454\) | 29.4820 | + | 51.0644i | 1.38366 | + | 2.39657i | ||||
\(455\) | 2.13745 | + | 3.70217i | 0.100205 | + | 0.173560i | ||||
\(456\) | 30.5605 | + | 7.46455i | 1.43113 | + | 0.349560i | ||||
\(457\) | −4.70631 | + | 8.15156i | −0.220152 | + | 0.381314i | −0.954854 | − | 0.297076i | \(-0.903989\pi\) |
0.734702 | + | 0.678390i | \(0.237322\pi\) | |||||||
\(458\) | 18.0375 | 0.842837 | ||||||||
\(459\) | 2.42149 | + | 2.11821i | 0.113025 | + | 0.0988696i | ||||
\(460\) | −25.4502 | −1.18662 | ||||||||
\(461\) | 10.2513 | − | 17.7557i | 0.477450 | − | 0.826967i | −0.522216 | − | 0.852813i | \(-0.674895\pi\) |
0.999666 | + | 0.0258461i | \(0.00822797\pi\) | |||||||
\(462\) | 81.5577 | + | 19.9209i | 3.79441 | + | 0.926802i | ||||
\(463\) | 18.8916 | + | 32.7211i | 0.877965 | + | 1.52068i | 0.853570 | + | 0.520978i | \(0.174433\pi\) |
0.0243951 | + | 0.999702i | \(0.492234\pi\) | |||||||
\(464\) | −29.9213 | − | 51.8251i | −1.38906 | − | 2.40592i | ||||
\(465\) | −8.24411 | + | 8.61913i | −0.382311 | + | 0.399703i | ||||
\(466\) | −11.1616 | + | 19.3325i | −0.517053 | + | 0.895562i | ||||
\(467\) | −12.8882 | −0.596394 | −0.298197 | − | 0.954504i | \(-0.596385\pi\) | ||||
−0.298197 | + | 0.954504i | \(0.596385\pi\) | |||||||
\(468\) | 11.8550 | − | 7.56641i | 0.547996 | − | 0.349757i | ||||
\(469\) | −62.2334 | −2.87367 | ||||||||
\(470\) | 0.524962 | − | 0.909260i | 0.0242147 | − | 0.0419411i | ||||
\(471\) | −3.88148 | − | 13.2960i | −0.178849 | − | 0.612649i | ||||
\(472\) | −37.2639 | − | 64.5429i | −1.71521 | − | 2.97083i | ||||
\(473\) | 22.0032 | + | 38.1107i | 1.01171 | + | 1.75233i | ||||
\(474\) | 18.2583 | + | 62.5437i | 0.838629 | + | 2.87273i | ||||
\(475\) | 1.30644 | − | 2.26282i | 0.0599435 | − | 0.103825i | ||||
\(476\) | −12.4080 | −0.568722 | ||||||||
\(477\) | −23.1932 | − | 12.0489i | −1.06194 | − | 0.551682i | ||||
\(478\) | 7.94194 | 0.363256 | ||||||||
\(479\) | −10.0940 | + | 17.4833i | −0.461207 | + | 0.798835i | −0.999021 | − | 0.0442289i | \(-0.985917\pi\) |
0.537814 | + | 0.843063i | \(0.319250\pi\) | |||||||
\(480\) | −9.98493 | + | 10.4391i | −0.455748 | + | 0.476479i | ||||
\(481\) | −2.01082 | − | 3.48284i | −0.0916855 | − | 0.158804i | ||||
\(482\) | 7.54195 | + | 13.0630i | 0.343527 | + | 0.595006i | ||||
\(483\) | −39.0492 | − | 9.53794i | −1.77680 | − | 0.433991i | ||||
\(484\) | −19.2757 | + | 33.3865i | −0.876167 | + | 1.51757i | ||||
\(485\) | 9.63475 | 0.437492 | ||||||||
\(486\) | 39.8569 | + | 6.04917i | 1.80795 | + | 0.274396i | ||||
\(487\) | 15.1480 | 0.686423 | 0.343212 | − | 0.939258i | \(-0.388485\pi\) | ||||
0.343212 | + | 0.939258i | \(0.388485\pi\) | |||||||
\(488\) | 17.6290 | − | 30.5344i | 0.798029 | − | 1.38223i | ||||
\(489\) | −29.2304 | − | 7.13967i | −1.32185 | − | 0.322867i | ||||
\(490\) | −14.5788 | − | 25.2512i | −0.658603 | − | 1.14073i | ||||
\(491\) | 5.74374 | + | 9.94845i | 0.259211 | + | 0.448967i | 0.966031 | − | 0.258427i | \(-0.0832040\pi\) |
−0.706820 | + | 0.707394i | \(0.749871\pi\) | |||||||
\(492\) | 22.8666 | − | 23.9068i | 1.03091 | − | 1.07780i | ||||
\(493\) | −2.15395 | + | 3.73074i | −0.0970089 | + | 0.168024i | ||||
\(494\) | −6.75717 | −0.304020 | ||||||||
\(495\) | −11.6723 | − | 6.06379i | −0.524630 | − | 0.272547i | ||||
\(496\) | −59.2263 | −2.65934 | ||||||||
\(497\) | 14.0542 | − | 24.3426i | 0.630417 | − | 1.09191i | ||||
\(498\) | −3.81732 | − | 13.0762i | −0.171058 | − | 0.585960i | ||||
\(499\) | 6.56005 | + | 11.3623i | 0.293668 | + | 0.508648i | 0.974674 | − | 0.223630i | \(-0.0717906\pi\) |
−0.681006 | + | 0.732278i | \(0.738457\pi\) | |||||||
\(500\) | 2.34397 | + | 4.05987i | 0.104825 | + | 0.181563i | ||||
\(501\) | −2.07541 | − | 7.10933i | −0.0927225 | − | 0.317621i | ||||
\(502\) | −30.6584 | + | 53.1019i | −1.36835 | + | 2.37006i | ||||
\(503\) | 7.80396 | 0.347961 | 0.173981 | − | 0.984749i | \(-0.444337\pi\) | ||||
0.173981 | + | 0.984749i | \(0.444337\pi\) | |||||||
\(504\) | −75.1464 | + | 47.9621i | −3.34729 | + | 2.13640i | ||||
\(505\) | −7.79952 | −0.347074 | ||||||||
\(506\) | 30.7781 | − | 53.3092i | 1.36825 | − | 2.36988i | ||||
\(507\) | −1.19721 | + | 1.25167i | −0.0531700 | + | 0.0555887i | ||||
\(508\) | 31.9747 | + | 55.3818i | 1.41865 | + | 2.45717i | ||||
\(509\) | −10.9919 | − | 19.0385i | −0.487205 | − | 0.843865i | 0.512686 | − | 0.858576i | \(-0.328650\pi\) |
−0.999892 | + | 0.0147114i | \(0.995317\pi\) | |||||||
\(510\) | 2.69414 | + | 0.658056i | 0.119298 | + | 0.0291392i | ||||
\(511\) | 35.7623 | − | 61.9421i | 1.58203 | − | 2.74016i | ||||
\(512\) | 47.8414 | 2.11431 | ||||||||
\(513\) | −10.2189 | − | 8.93905i | −0.451175 | − | 0.394669i | ||||
\(514\) | −49.9316 | −2.20239 | ||||||||
\(515\) | 0.496621 | − | 0.860172i | 0.0218837 | − | 0.0379037i | ||||
\(516\) | −79.1696 | − | 19.3375i | −3.48525 | − | 0.851288i | ||||
\(517\) | 0.890017 | + | 1.54155i | 0.0391429 | + | 0.0677975i | ||||
\(518\) | 22.2303 | + | 38.5039i | 0.976742 | + | 1.69177i | ||||
\(519\) | −15.5109 | + | 16.2165i | −0.680854 | + | 0.711826i | ||||
\(520\) | 3.47564 | − | 6.01998i | 0.152417 | − | 0.263994i | ||||
\(521\) | 12.1706 | 0.533205 | 0.266603 | − | 0.963807i | \(-0.414099\pi\) | ||||
0.266603 | + | 0.963807i | \(0.414099\pi\) | |||||||
\(522\) | 2.39975 | + | 53.9269i | 0.105034 | + | 2.36032i | ||||
\(523\) | 32.5468 | 1.42317 | 0.711587 | − | 0.702598i | \(-0.247977\pi\) | ||||
0.711587 | + | 0.702598i | \(0.247977\pi\) | |||||||
\(524\) | −19.6011 | + | 33.9501i | −0.856279 | + | 1.48312i | ||||
\(525\) | 2.07492 | + | 7.10766i | 0.0905571 | + | 0.310204i | ||||
\(526\) | −15.1542 | − | 26.2478i | −0.660753 | − | 1.14446i | ||||
\(527\) | 2.13177 | + | 3.69233i | 0.0928612 | + | 0.160840i | ||||
\(528\) | −18.3035 | − | 62.6988i | −0.796559 | − | 2.72862i | ||||
\(529\) | −3.23629 | + | 5.60543i | −0.140708 | + | 0.243714i | ||||
\(530\) | −22.5303 | −0.978653 | ||||||||
\(531\) | 1.42990 | + | 32.1326i | 0.0620524 | + | 1.39443i | ||||
\(532\) | 52.3632 | 2.27023 | ||||||||
\(533\) | −2.03714 | + | 3.52842i | −0.0882382 | + | 0.152833i | ||||
\(534\) | 22.5109 | − | 23.5349i | 0.974143 | − | 1.01846i | ||||
\(535\) | 2.12086 | + | 3.67343i | 0.0916927 | + | 0.158816i | ||||
\(536\) | 50.5979 | + | 87.6381i | 2.18550 | + | 3.78539i | ||||
\(537\) | 31.7219 | + | 7.74821i | 1.36890 | + | 0.334360i | ||||
\(538\) | −21.9933 | + | 38.0936i | −0.948199 | + | 1.64233i | ||||
\(539\) | 49.4336 | 2.12925 | ||||||||
\(540\) | 23.0566 | − | 7.85899i | 0.992199 | − | 0.338197i | ||||
\(541\) | −16.3865 | −0.704511 | −0.352256 | − | 0.935904i | \(-0.614585\pi\) | ||||
−0.352256 | + | 0.935904i | \(0.614585\pi\) | |||||||
\(542\) | −16.1424 | + | 27.9595i | −0.693378 | + | 1.20097i | ||||
\(543\) | −35.7707 | − | 8.73715i | −1.53507 | − | 0.374947i | ||||
\(544\) | 2.58191 | + | 4.47200i | 0.110698 | + | 0.191735i | ||||
\(545\) | 2.36123 | + | 4.08978i | 0.101144 | + | 0.175187i | ||||
\(546\) | 13.2356 | − | 13.8376i | 0.566430 | − | 0.592196i | ||||
\(547\) | −9.53335 | + | 16.5122i | −0.407616 | + | 0.706012i | −0.994622 | − | 0.103570i | \(-0.966973\pi\) |
0.587006 | + | 0.809583i | \(0.300307\pi\) | |||||||
\(548\) | −31.6477 | −1.35192 | ||||||||
\(549\) | −12.8266 | + | 8.18657i | −0.547427 | + | 0.349394i | ||||
\(550\) | −11.3387 | −0.483483 | ||||||||
\(551\) | 9.08986 | − | 15.7441i | 0.387241 | − | 0.670721i | ||||
\(552\) | 18.3168 | + | 62.7444i | 0.779616 | + | 2.67058i | ||||
\(553\) | 31.0908 | + | 53.8508i | 1.32211 | + | 2.28997i | ||||
\(554\) | 26.2344 | + | 45.4393i | 1.11459 | + | 1.93053i | ||||
\(555\) | −1.95200 | − | 6.68659i | −0.0828579 | − | 0.283830i | ||||
\(556\) | −8.21740 | + | 14.2330i | −0.348495 | + | 0.603612i | ||||
\(557\) | −38.2913 | −1.62245 | −0.811227 | − | 0.584732i | \(-0.801200\pi\) | ||||
−0.811227 | + | 0.584732i | \(0.801200\pi\) | |||||||
\(558\) | 47.4087 | + | 24.6290i | 2.00697 | + | 1.04263i | ||||
\(559\) | 10.0369 | 0.424516 | ||||||||
\(560\) | −18.3839 | + | 31.8418i | −0.776860 | + | 1.34556i | ||||
\(561\) | −3.25001 | + | 3.39785i | −0.137215 | + | 0.143457i | ||||
\(562\) | −10.8287 | − | 18.7558i | −0.456779 | − | 0.791165i | ||||
\(563\) | −5.17040 | − | 8.95540i | −0.217906 | − | 0.377425i | 0.736261 | − | 0.676697i | \(-0.236589\pi\) |
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(564\) | −3.20236 | − | 0.782192i | −0.134844 | − | 0.0329362i | ||||
\(565\) | −1.77704 | + | 3.07792i | −0.0747605 | + | 0.129489i | ||||
\(566\) | 5.75569 | 0.241930 | ||||||||
\(567\) | 38.3220 | − | 3.41743i | 1.60937 | − | 0.143518i | ||||
\(568\) | −45.7062 | −1.91779 | ||||||||
\(569\) | 13.0134 | − | 22.5398i | 0.545548 | − | 0.944917i | −0.453024 | − | 0.891498i | \(-0.649655\pi\) |
0.998572 | − | 0.0534187i | \(-0.0170118\pi\) | |||||||
\(570\) | −11.3695 | − | 2.77706i | −0.476217 | − | 0.116318i | ||||
\(571\) | 16.1620 | + | 27.9933i | 0.676357 | + | 1.17148i | 0.976070 | + | 0.217456i | \(0.0697757\pi\) |
−0.299713 | + | 0.954029i | \(0.596891\pi\) | |||||||
\(572\) | 10.2770 | + | 17.8004i | 0.429705 | + | 0.744270i | ||||
\(573\) | 18.4574 | − | 19.2970i | 0.771069 | − | 0.806144i | ||||
\(574\) | 22.5212 | − | 39.0078i | 0.940016 | − | 1.62816i | ||||
\(575\) | 5.42887 | 0.226399 | ||||||||
\(576\) | 11.6252 | + | 6.03935i | 0.484385 | + | 0.251640i | ||||
\(577\) | 12.4808 | 0.519581 | 0.259790 | − | 0.965665i | \(-0.416347\pi\) | ||||
0.259790 | + | 0.965665i | \(0.416347\pi\) | |||||||
\(578\) | −21.4862 | + | 37.2152i | −0.893708 | + | 1.54795i | ||||
\(579\) | −0.916394 | − | 3.13911i | −0.0380841 | − | 0.130457i | ||||
\(580\) | 16.3087 | + | 28.2475i | 0.677182 | + | 1.17291i | ||||
\(581\) | −6.50026 | − | 11.2588i | −0.269676 | − | 0.467093i | ||||
\(582\) | −12.0938 | − | 41.4274i | −0.501305 | − | 1.71722i | ||||
\(583\) | 19.0988 | − | 33.0802i | 0.790993 | − | 1.37004i | ||||
\(584\) | −116.304 | −4.81269 | ||||||||
\(585\) | −2.52882 | + | 1.61402i | −0.104554 | + | 0.0667314i | ||||
\(586\) | 6.56579 | 0.271230 | ||||||||
\(587\) | 12.5975 | − | 21.8195i | 0.519955 | − | 0.900588i | −0.479776 | − | 0.877391i | \(-0.659282\pi\) |
0.999731 | − | 0.0231969i | \(-0.00738446\pi\) | |||||||
\(588\) | −63.2788 | + | 66.1573i | −2.60957 | + | 2.72828i | ||||
\(589\) | −8.99625 | − | 15.5820i | −0.370684 | − | 0.642044i | ||||
\(590\) | 13.8634 | + | 24.0121i | 0.570747 | + | 0.988563i | ||||
\(591\) | −18.2724 | − | 4.46312i | −0.751627 | − | 0.183588i | ||||
\(592\) | 17.2948 | − | 29.9554i | 0.710811 | − | 1.23116i | ||||
\(593\) | −38.4456 | −1.57877 | −0.789385 | − | 0.613898i | \(-0.789601\pi\) | ||||
−0.789385 | + | 0.613898i | \(0.789601\pi\) | |||||||
\(594\) | −11.4216 | + | 57.7998i | −0.468635 | + | 2.37156i | ||||
\(595\) | 2.64681 | 0.108508 | ||||||||
\(596\) | −28.7816 | + | 49.8512i | −1.17894 | + | 2.04198i | ||||
\(597\) | −2.02095 | − | 0.493627i | −0.0827120 | − | 0.0202028i | ||||
\(598\) | −7.01981 | − | 12.1587i | −0.287061 | − | 0.497205i | ||||
\(599\) | 23.6618 | + | 40.9834i | 0.966795 | + | 1.67454i | 0.704713 | + | 0.709493i | \(0.251076\pi\) |
0.262082 | + | 0.965045i | \(0.415591\pi\) | |||||||
\(600\) | 8.32215 | − | 8.70072i | 0.339750 | − | 0.355205i | ||||
\(601\) | −20.0328 | + | 34.6979i | −0.817156 | + | 1.41536i | 0.0906140 | + | 0.995886i | \(0.471117\pi\) |
−0.907770 | + | 0.419469i | \(0.862216\pi\) | |||||||
\(602\) | −110.961 | −4.52244 | ||||||||
\(603\) | −1.94156 | − | 43.6304i | −0.0790664 | − | 1.77677i | ||||
\(604\) | −78.2717 | −3.18483 | ||||||||
\(605\) | 4.11176 | − | 7.12178i | 0.167167 | − | 0.289542i | ||||
\(606\) | 9.79018 | + | 33.5363i | 0.397699 | + | 1.36232i | ||||
\(607\) | −10.3060 | − | 17.8505i | −0.418306 | − | 0.724528i | 0.577463 | − | 0.816417i | \(-0.304043\pi\) |
−0.995769 | + | 0.0918893i | \(0.970709\pi\) | |||||||
\(608\) | −10.8959 | − | 18.8723i | −0.441887 | − | 0.765371i | ||||
\(609\) | 14.4368 | + | 49.4532i | 0.585008 | + | 2.00395i | ||||
\(610\) | −6.55858 | + | 11.3598i | −0.265549 | + | 0.459945i | ||||
\(611\) | 0.405987 | 0.0164245 | ||||||||
\(612\) | −0.387107 | − | 8.69901i | −0.0156479 | − | 0.351637i | ||||
\(613\) | −4.02465 | −0.162554 | −0.0812770 | − | 0.996692i | \(-0.525900\pi\) | ||||
−0.0812770 | + | 0.996692i | \(0.525900\pi\) | |||||||
\(614\) | 24.8710 | − | 43.0778i | 1.00371 | − | 1.73848i | ||||
\(615\) | −4.87777 | + | 5.09966i | −0.196691 | + | 0.205638i | ||||
\(616\) | −65.1443 | − | 112.833i | −2.62474 | − | 4.54618i | ||||
\(617\) | −14.9120 | − | 25.8283i | −0.600334 | − | 1.03981i | −0.992770 | − | 0.120030i | \(-0.961701\pi\) |
0.392436 | − | 0.919779i | \(-0.371632\pi\) | |||||||
\(618\) | −4.32193 | − | 1.05565i | −0.173854 | − | 0.0424646i | ||||
\(619\) | 23.7693 | − | 41.1696i | 0.955368 | − | 1.65475i | 0.221844 | − | 0.975082i | \(-0.428792\pi\) |
0.733524 | − | 0.679664i | \(-0.237874\pi\) | |||||||
\(620\) | 32.2815 | 1.29646 | ||||||||
\(621\) | 5.46858 | − | 27.6741i | 0.219447 | − | 1.11052i | ||||
\(622\) | −22.6554 | −0.908397 | ||||||||
\(623\) | 15.5407 | − | 26.9174i | 0.622627 | − | 1.07842i | ||||
\(624\) | −14.4717 | − | 3.53478i | −0.579331 | − | 0.141504i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −15.7471 | − | 27.2747i | −0.629379 | − | 1.09012i | ||||
\(627\) | 13.7153 | − | 14.3392i | 0.547738 | − | 0.572654i | ||||
\(628\) | −18.7444 | + | 32.4663i | −0.747984 | + | 1.29555i | ||||
\(629\) | −2.49000 | −0.0992830 | ||||||||
\(630\) | 27.9569 | − | 17.8435i | 1.11383 | − | 0.710901i | ||||
\(631\) | 32.2213 | 1.28271 | 0.641354 | − | 0.767245i | \(-0.278373\pi\) | ||||
0.641354 | + | 0.767245i | \(0.278373\pi\) | |||||||
\(632\) | 50.5558 | − | 87.5652i | 2.01100 | − | 3.48316i | ||||
\(633\) | 0.114166 | + | 0.391075i | 0.00453768 | + | 0.0155438i | ||||
\(634\) | 22.4015 | + | 38.8006i | 0.889678 | + | 1.54097i | ||||
\(635\) | −6.82064 | − | 11.8137i | −0.270669 | − | 0.468812i | ||||
\(636\) | 19.8234 | + | 67.9052i | 0.786050 | + | 2.69262i | ||||
\(637\) | 5.63736 | − | 9.76419i | 0.223360 | − | 0.386871i | ||||
\(638\) | −78.8916 | −3.12335 | ||||||||
\(639\) | 17.5045 | + | 9.09365i | 0.692468 | + | 0.359739i | ||||
\(640\) | −5.38732 | −0.212953 | ||||||||
\(641\) | −1.75107 | + | 3.03295i | −0.0691632 | + | 0.119794i | −0.898533 | − | 0.438906i | \(-0.855366\pi\) |
0.829370 | + | 0.558700i | \(0.188700\pi\) | |||||||
\(642\) | 13.1328 | − | 13.7302i | 0.518312 | − | 0.541889i | ||||
\(643\) | −0.0115697 | − | 0.0200394i | −0.000456266 | − | 0.000790276i | 0.865797 | − | 0.500395i | \(-0.166812\pi\) |
−0.866253 | + | 0.499605i | \(0.833479\pi\) | |||||||
\(644\) | 54.3984 | + | 94.2207i | 2.14360 | + | 3.71282i | ||||
\(645\) | 16.8880 | + | 4.12496i | 0.664963 | + | 0.162420i | ||||
\(646\) | −2.09186 | + | 3.62320i | −0.0823030 | + | 0.142553i | ||||
\(647\) | −20.8611 | −0.820136 | −0.410068 | − | 0.912055i | \(-0.634495\pi\) | ||||
−0.410068 | + | 0.912055i | \(0.634495\pi\) | |||||||
\(648\) | −35.9696 | − | 51.1872i | −1.41302 | − | 2.01082i | ||||
\(649\) | −47.0078 | −1.84522 | ||||||||
\(650\) | −1.29305 | + | 2.23963i | −0.0507177 | + | 0.0878456i | ||||
\(651\) | 49.5308 | + | 12.0981i | 1.94126 | + | 0.474163i | ||||
\(652\) | 40.7202 | + | 70.5294i | 1.59472 | + | 2.76214i | ||||
\(653\) | −5.47824 | − | 9.48859i | −0.214380 | − | 0.371317i | 0.738700 | − | 0.674034i | \(-0.235440\pi\) |
−0.953081 | + | 0.302716i | \(0.902106\pi\) | |||||||
\(654\) | 14.6213 | − | 15.2864i | 0.571738 | − | 0.597746i | ||||
\(655\) | 4.18118 | − | 7.24202i | 0.163372 | − | 0.282969i | ||||
\(656\) | −35.0422 | −1.36817 | ||||||||
\(657\) | 44.5419 | + | 23.1397i | 1.73775 | + | 0.902765i | ||||
\(658\) | −4.48831 | −0.174973 | ||||||||
\(659\) | 17.0546 | − | 29.5395i | 0.664354 | − | 1.15070i | −0.315106 | − | 0.949057i | \(-0.602040\pi\) |
0.979460 | − | 0.201639i | \(-0.0646267\pi\) | |||||||
\(660\) | 9.97642 | + | 34.1743i | 0.388332 | + | 1.33023i | ||||
\(661\) | 12.0901 | + | 20.9406i | 0.470249 | + | 0.814495i | 0.999421 | − | 0.0340194i | \(-0.0108308\pi\) |
−0.529172 | + | 0.848514i | \(0.677497\pi\) | |||||||
\(662\) | 3.18186 | + | 5.51115i | 0.123667 | + | 0.214197i | ||||
\(663\) | 0.300520 | + | 1.02943i | 0.0116712 | + | 0.0399799i | ||||
\(664\) | −10.5699 | + | 18.3076i | −0.410191 | + | 0.710471i | ||||
\(665\) | −11.1698 | −0.433145 | ||||||||
\(666\) | −26.3007 | + | 16.7864i | −1.01913 | + | 0.650460i | ||||
\(667\) | 37.7726 | 1.46256 | ||||||||
\(668\) | −10.0226 | + | 17.3596i | −0.387784 | + | 0.671662i | ||||
\(669\) | 20.0592 | − | 20.9717i | 0.775534 | − | 0.810813i | ||||
\(670\) | −18.8241 | − | 32.6043i | −0.727238 | − | 1.25961i | ||||
\(671\) | −11.1194 | − | 19.2593i | −0.429259 | − | 0.743498i | ||||
\(672\) | 59.9897 | + | 14.6528i | 2.31415 | + | 0.565243i | ||||
\(673\) | −9.66073 | + | 16.7329i | −0.372394 | + | 0.645005i | −0.989933 | − | 0.141535i | \(-0.954796\pi\) |
0.617539 | + | 0.786540i | \(0.288130\pi\) | |||||||
\(674\) | −53.6579 | −2.06683 | ||||||||
\(675\) | −4.91829 | + | 1.67643i | −0.189305 | + | 0.0645258i | ||||
\(676\) | 4.68793 | 0.180305 | ||||||||
\(677\) | 19.1367 | − | 33.1457i | 0.735483 | − | 1.27389i | −0.219028 | − | 0.975718i | \(-0.570289\pi\) |
0.954511 | − | 0.298175i | \(-0.0963779\pi\) | |||||||
\(678\) | 15.4650 | + | 3.77740i | 0.593930 | + | 0.145070i | ||||
\(679\) | −20.5938 | − | 35.6695i | −0.790316 | − | 1.36887i | ||||
\(680\) | −2.15195 | − | 3.72728i | −0.0825234 | − | 0.142935i | ||||
\(681\) | −27.2968 | + | 28.5386i | −1.04602 | + | 1.09360i | ||||
\(682\) | −39.0396 | + | 67.6185i | −1.49490 | + | 2.58925i | ||||
\(683\) | 0.692198 | 0.0264862 | 0.0132431 | − | 0.999912i | \(-0.495784\pi\) | ||||
0.0132431 | + | 0.999912i | \(0.495784\pi\) | |||||||
\(684\) | 1.63363 | + | 36.7107i | 0.0624633 | + | 1.40367i | ||||
\(685\) | 6.75088 | 0.257938 | ||||||||
\(686\) | −23.6292 | + | 40.9269i | −0.902165 | + | 1.56260i | ||||
\(687\) | 3.38538 | + | 11.5966i | 0.129160 | + | 0.442439i | ||||
\(688\) | 43.1630 | + | 74.7605i | 1.64557 | + | 2.85022i | ||||
\(689\) | −4.35603 | − | 7.54486i | −0.165951 | − | 0.287436i | ||||
\(690\) | −6.81447 | − | 23.3430i | −0.259422 | − | 0.888652i | ||||
\(691\) | 16.4956 | − | 28.5711i | 0.627520 | − | 1.08690i | −0.360527 | − | 0.932749i | \(-0.617403\pi\) |
0.988048 | − | 0.154148i | \(-0.0492634\pi\) | |||||||
\(692\) | 60.7363 | 2.30885 | ||||||||
\(693\) | 2.49974 | + | 56.1738i | 0.0949571 | + | 2.13386i | ||||
\(694\) | 32.5530 | 1.23569 | ||||||||
\(695\) | 1.75288 | − | 3.03608i | 0.0664907 | − | 0.115165i | ||||
\(696\) | 57.9033 | − | 60.5373i | 2.19482 | − | 2.29466i | ||||
\(697\) | 1.26130 | + | 2.18463i | 0.0477750 | + | 0.0827487i | ||||
\(698\) | −25.8259 | − | 44.7318i | −0.977526 | − | 1.69312i | ||||
\(699\) | −14.5241 | − | 3.54758i | −0.549352 | − | 0.134182i | ||||
\(700\) | 10.0202 | − | 17.3555i | 0.378728 | − | 0.655977i | ||||
\(701\) | −18.7776 | −0.709219 | −0.354610 | − | 0.935014i | \(-0.615386\pi\) | ||||
−0.354610 | + | 0.935014i | \(0.615386\pi\) | |||||||
\(702\) | 10.1142 | + | 8.84745i | 0.381735 | + | 0.333926i | ||||
\(703\) | 10.5081 | 0.396319 | ||||||||
\(704\) | −9.57303 | + | 16.5810i | −0.360797 | + | 0.624919i | ||||
\(705\) | 0.683107 | + | 0.166852i | 0.0257273 | + | 0.00628402i | ||||
\(706\) | 7.61522 | + | 13.1899i | 0.286603 | + | 0.496410i | ||||
\(707\) | 16.6711 | + | 28.8751i | 0.626980 | + | 1.08596i | ||||
\(708\) | 60.1736 | − | 62.9109i | 2.26146 | − | 2.36434i | ||||
\(709\) | −4.04721 | + | 7.00997i | −0.151996 | + | 0.263265i | −0.931961 | − | 0.362558i | \(-0.881903\pi\) |
0.779965 | + | 0.625823i | \(0.215237\pi\) | |||||||
\(710\) | 17.0042 | 0.638157 | ||||||||
\(711\) | −36.7837 | + | 23.4771i | −1.37949 | + | 0.880460i | ||||
\(712\) | −50.5407 | −1.89409 | ||||||||
\(713\) | 18.6918 | − | 32.3752i | 0.700014 | − | 1.21246i | ||||
\(714\) | −3.32235 | − | 11.3807i | −0.124336 | − | 0.425912i | ||||
\(715\) | −2.19223 | − | 3.79706i | −0.0819848 | − | 0.142002i | ||||
\(716\) | −44.1909 | − | 76.5409i | −1.65149 | − | 2.86047i | ||||
\(717\) | 1.49059 | + | 5.10602i | 0.0556670 | + | 0.190688i | ||||
\(718\) | 23.0595 | − | 39.9402i | 0.860572 | − | 1.49055i | ||||
\(719\) | 31.8467 | 1.18768 | 0.593840 | − | 0.804583i | \(-0.297611\pi\) | ||||
0.593840 | + | 0.804583i | \(0.297611\pi\) | |||||||
\(720\) | −22.8971 | − | 11.8951i | −0.853325 | − | 0.443305i | ||||
\(721\) | −4.24600 | −0.158129 | ||||||||
\(722\) | −15.7402 | + | 27.2627i | −0.585788 | + | 1.01461i | ||||
\(723\) | −6.98295 | + | 7.30060i | −0.259699 | + | 0.271512i | ||||
\(724\) | 49.8312 | + | 86.3101i | 1.85196 | + | 3.20769i | ||||
\(725\) | −3.47887 | − | 6.02558i | −0.129202 | − | 0.223784i | ||||
\(726\) | −35.7834 | − | 8.74026i | −1.32805 | − | 0.324381i | ||||
\(727\) | 10.1546 | − | 17.5883i | 0.376613 | − | 0.652313i | −0.613954 | − | 0.789342i | \(-0.710422\pi\) |
0.990567 | + | 0.137029i | \(0.0437552\pi\) | |||||||
\(728\) | −29.7160 | −1.10135 | ||||||||
\(729\) | 3.59145 | + | 26.7601i | 0.133017 | + | 0.991114i | ||||
\(730\) | 43.2689 | 1.60145 | ||||||||
\(731\) | 3.10718 | − | 5.38180i | 0.114923 | − | 0.199053i | ||||
\(732\) | 40.0085 | + | 9.77227i | 1.47876 | + | 0.361194i | ||||
\(733\) | 7.15966 | + | 12.4009i | 0.264448 | + | 0.458037i | 0.967419 | − | 0.253181i | \(-0.0814769\pi\) |
−0.702971 | + | 0.711219i | \(0.748144\pi\) | |||||||
\(734\) | −38.5755 | − | 66.8147i | −1.42385 | − | 2.46618i | ||||
\(735\) | 13.4982 | − | 14.1122i | 0.497889 | − | 0.520538i | ||||
\(736\) | 22.6388 | − | 39.2115i | 0.834477 | − | 1.44536i | ||||
\(737\) | 63.8285 | 2.35115 | ||||||||
\(738\) | 28.0502 | + | 14.5721i | 1.03254 | + | 0.536408i | ||||
\(739\) | −32.7316 | −1.20405 | −0.602025 | − | 0.798477i | \(-0.705639\pi\) | ||||
−0.602025 | + | 0.798477i | \(0.705639\pi\) | |||||||
\(740\) | −9.42660 | + | 16.3273i | −0.346529 | + | 0.600205i | ||||
\(741\) | −1.26822 | − | 4.34431i | −0.0465894 | − | 0.159592i | ||||
\(742\) | 48.1573 | + | 83.4108i | 1.76791 | + | 3.06211i | ||||
\(743\) | −19.4753 | − | 33.7323i | −0.714481 | − | 1.23752i | −0.963159 | − | 0.268931i | \(-0.913330\pi\) |
0.248678 | − | 0.968586i | \(-0.420004\pi\) | |||||||
\(744\) | −23.2335 | − | 79.5863i | −0.851780 | − | 2.91778i | ||||
\(745\) | 6.13951 | − | 10.6339i | 0.224934 | − | 0.389597i | ||||
\(746\) | 37.7038 | 1.38044 | ||||||||
\(747\) | 7.69049 | − | 4.90844i | 0.281380 | − | 0.179590i | ||||
\(748\) | 12.7261 | 0.465312 | ||||||||
\(749\) | 9.06644 | − | 15.7035i | 0.331280 | − | 0.573795i | ||||
\(750\) | −3.09611 | + | 3.23696i | −0.113054 | + | 0.118197i | ||||
\(751\) | 11.5075 | + | 19.9316i | 0.419916 | + | 0.727316i | 0.995931 | − | 0.0901237i | \(-0.0287263\pi\) |
−0.576015 | + | 0.817439i | \(0.695393\pi\) | |||||||
\(752\) | 1.74592 | + | 3.02401i | 0.0636670 | + | 0.110274i | ||||
\(753\) | −39.8943 | − | 9.74437i | −1.45383 | − | 0.355105i | ||||
\(754\) | −8.99672 | + | 15.5828i | −0.327641 | + | 0.567491i | ||||
\(755\) | 16.6964 | 0.607645 | ||||||||
\(756\) | −78.3776 | − | 68.5613i | −2.85056 | − | 2.49355i | ||||
\(757\) | 41.6474 | 1.51370 | 0.756850 | − | 0.653588i | \(-0.226737\pi\) | ||||
0.756850 | + | 0.653588i | \(0.226737\pi\) | |||||||
\(758\) | 26.7723 | − | 46.3710i | 0.972415 | − | 1.68427i | ||||
\(759\) | 40.0500 | + | 9.78241i | 1.45372 | + | 0.355079i | ||||
\(760\) | 9.08142 | + | 15.7295i | 0.329418 | + | 0.570568i | ||||
\(761\) | −3.44431 | − | 5.96571i | −0.124856 | − | 0.216257i | 0.796821 | − | 0.604216i | \(-0.206514\pi\) |
−0.921677 | + | 0.387959i | \(0.873180\pi\) | |||||||
\(762\) | −42.2349 | + | 44.1562i | −1.53001 | + | 1.59961i | ||||
\(763\) | 10.0940 | − | 17.4834i | 0.365428 | − | 0.632940i | ||||
\(764\) | −72.2738 | −2.61477 | ||||||||
\(765\) | 0.0825751 | + | 1.85562i | 0.00298551 | + | 0.0670900i | ||||
\(766\) | 66.1176 | 2.38893 | ||||||||
\(767\) | −5.36073 | + | 9.28505i | −0.193565 | + | 0.335264i | ||||
\(768\) | 11.0014 | + | 37.6853i | 0.396978 | + | 1.35985i | ||||
\(769\) | 4.78387 | + | 8.28591i | 0.172511 | + | 0.298797i | 0.939297 | − | 0.343105i | \(-0.111479\pi\) |
−0.766786 | + | 0.641903i | \(0.778145\pi\) | |||||||
\(770\) | 24.2358 | + | 41.9777i | 0.873399 | + | 1.51277i | ||||
\(771\) | −9.37145 | − | 32.1019i | −0.337504 | − | 1.15612i | ||||
\(772\) | −4.42545 | + | 7.66510i | −0.159275 | + | 0.275873i | ||||
\(773\) | −10.5131 | −0.378131 | −0.189066 | − | 0.981964i | \(-0.560546\pi\) | ||||
−0.189066 | + | 0.981964i | \(0.560546\pi\) | |||||||
\(774\) | −3.46177 | − | 77.7924i | −0.124431 | − | 2.79619i | ||||
\(775\) | −6.88609 | −0.247356 | ||||||||
\(776\) | −33.4869 | + | 58.0010i | −1.20211 | + | 2.08212i | ||||
\(777\) | −20.5826 | + | 21.5189i | −0.738396 | + | 0.771985i | ||||
\(778\) | −22.1505 | − | 38.3658i | −0.794134 | − | 1.37548i | ||||
\(779\) | −5.32279 | − | 9.21934i | −0.190709 | − | 0.330317i | ||||
\(780\) | 7.88785 | + | 1.92664i | 0.282430 | + | 0.0689849i | ||||
\(781\) | −14.4144 | + | 24.9665i | −0.515789 | + | 0.893372i | ||||
\(782\) | −8.69264 | −0.310848 | ||||||||
\(783\) | −34.2202 | + | 11.6642i | −1.22293 | + | 0.416843i | ||||
\(784\) | 96.9722 | 3.46329 | ||||||||
\(785\) | 3.99844 | − | 6.92550i | 0.142710 | − | 0.247182i | ||||
\(786\) | −36.3875 | − | 8.88782i | −1.29790 | − | 0.317018i | ||||
\(787\) | 18.0600 | + | 31.2808i | 0.643769 | + | 1.11504i | 0.984584 | + | 0.174910i | \(0.0559634\pi\) |
−0.340816 | + | 0.940130i | \(0.610703\pi\) | |||||||
\(788\) | 25.4548 | + | 44.0891i | 0.906791 | + | 1.57061i | ||||
\(789\) | 14.0310 | − | 14.6692i | 0.499515 | − | 0.522238i | ||||
\(790\) | −18.8084 | + | 32.5771i | −0.669174 | + | 1.15904i | ||||
\(791\) | 15.1933 | 0.540211 | ||||||||
\(792\) | 77.0725 | − | 49.1914i | 2.73865 | − | 1.74794i | ||||
\(793\) | −5.07217 | −0.180118 | ||||||||
\(794\) | −20.4738 | + | 35.4616i | −0.726586 | + | 1.25848i | ||||
\(795\) | −4.22861 | − | 14.4851i | −0.149973 | − | 0.513734i | ||||
\(796\) | 2.81533 | + | 4.87630i | 0.0997869 | + | 0.172836i | ||||
\(797\) | 7.37462 | + | 12.7732i | 0.261223 | + | 0.452451i | 0.966567 | − | 0.256414i | \(-0.0825410\pi\) |
−0.705344 | + | 0.708865i | \(0.749208\pi\) | |||||||
\(798\) | 14.0206 | + | 48.0277i | 0.496325 | + | 1.70016i | ||||
\(799\) | 0.125684 | − | 0.217690i | 0.00444636 | − | 0.00770133i | ||||
\(800\) | −8.34015 | −0.294869 | ||||||||
\(801\) | 19.3560 | + | 10.0555i | 0.683911 | + | 0.355294i | ||||
\(802\) | 88.2140 | 3.11495 | ||||||||
\(803\) | −36.6789 | + | 63.5297i | −1.29437 | + | 2.24192i | ||||
\(804\) | −81.7053 | + | 85.4221i | −2.88152 | + | 3.01260i | ||||
\(805\) | −11.6039 | − | 20.0986i | −0.408984 | − | 0.708381i | ||||
\(806\) | 8.90407 | + | 15.4223i | 0.313633 | + | 0.543227i | ||||
\(807\) | −28.6188 | − | 6.99029i | −1.00743 | − | 0.246070i | ||||
\(808\) | 27.1083 | − | 46.9530i | 0.953667 | − | 1.65180i | ||||
\(809\) | 1.81657 | 0.0638672 | 0.0319336 | − | 0.999490i | \(-0.489833\pi\) | ||||
0.0319336 | + | 0.999490i | \(0.489833\pi\) | |||||||
\(810\) | 13.3819 | + | 19.0433i | 0.470191 | + | 0.669114i | ||||
\(811\) | −33.3279 | −1.17030 | −0.585151 | − | 0.810924i | \(-0.698965\pi\) | ||||
−0.585151 | + | 0.810924i | \(0.698965\pi\) | |||||||
\(812\) | 69.7180 | − | 120.755i | 2.44662 | − | 4.23767i | ||||
\(813\) | −21.0054 | − | 5.13066i | −0.736691 | − | 0.179940i | ||||
\(814\) | −22.8001 | − | 39.4909i | −0.799142 | − | 1.38415i | ||||
\(815\) | −8.68616 | − | 15.0449i | −0.304263 | − | 0.526999i | ||||
\(816\) | −6.37543 | + | 6.66544i | −0.223185 | + | 0.233337i | ||||
\(817\) | −13.1126 | + | 22.7117i | −0.458752 | + | 0.794581i | ||||
\(818\) | 49.5117 | 1.73113 | ||||||||
\(819\) | 11.3806 | + | 5.91225i | 0.397670 | + | 0.206591i | ||||
\(820\) | 19.0999 | 0.666998 | ||||||||
\(821\) | −17.7439 | + | 30.7333i | −0.619266 | + | 1.07260i | 0.370354 | + | 0.928891i | \(0.379236\pi\) |
−0.989620 | + | 0.143709i | \(0.954097\pi\) | |||||||
\(822\) | −8.47390 | − | 29.0274i | −0.295561 | − | 1.01245i | ||||
\(823\) | 8.28999 | + | 14.3587i | 0.288971 | + | 0.500512i | 0.973564 | − | 0.228413i | \(-0.0733536\pi\) |
−0.684594 | + | 0.728925i | \(0.740020\pi\) | |||||||
\(824\) | 3.45215 | + | 5.97929i | 0.120261 | + | 0.208299i | ||||
\(825\) | −2.12811 | − | 7.28984i | −0.0740912 | − | 0.253800i | ||||
\(826\) | 59.2645 | − | 102.649i | 2.06208 | − | 3.57162i | ||||
\(827\) | 8.93071 | 0.310551 | 0.155276 | − | 0.987871i | \(-0.450373\pi\) | ||||
0.155276 | + | 0.987871i | \(0.450373\pi\) | |||||||
\(828\) | −64.3590 | + | 41.0770i | −2.23663 | + | 1.42752i | ||||
\(829\) | 12.9059 | 0.448240 | 0.224120 | − | 0.974562i | \(-0.428049\pi\) | ||||
0.224120 | + | 0.974562i | \(0.428049\pi\) | |||||||
\(830\) | 3.93234 | − | 6.81102i | 0.136494 | − | 0.236414i | ||||
\(831\) | −24.2899 | + | 25.3948i | −0.842607 | + | 0.880937i | ||||
\(832\) | 2.18340 | + | 3.78175i | 0.0756957 | + | 0.131109i | ||||
\(833\) | −3.49038 | − | 6.04551i | −0.120934 | − | 0.209464i | ||||
\(834\) | −15.2548 | − | 3.72605i | −0.528230 | − | 0.129023i | ||||
\(835\) | 2.13795 | − | 3.70303i | 0.0739867 | − | 0.128149i | ||||
\(836\) | −53.7053 | −1.85744 | ||||||||
\(837\) | −6.93647 | + | 35.1024i | −0.239759 | + | 1.21332i | ||||
\(838\) | −18.4518 | −0.637408 | ||||||||
\(839\) | −17.4959 | + | 30.3039i | −0.604027 | + | 1.04621i | 0.388178 | + | 0.921585i | \(0.373105\pi\) |
−0.992204 | + | 0.124621i | \(0.960229\pi\) | |||||||
\(840\) | −49.9997 | − | 12.2127i | −1.72515 | − | 0.421377i | ||||
\(841\) | −9.70506 | − | 16.8097i | −0.334657 | − | 0.579644i | ||||
\(842\) | −33.8286 | − | 58.5928i | −1.16581 | − | 2.01924i | ||||
\(843\) | 10.0260 | − | 10.4821i | 0.345315 | − | 0.361024i | ||||
\(844\) | 0.551328 | − | 0.954929i | 0.0189775 | − | 0.0328700i | ||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | −0.140026 | − | 3.14666i | −0.00481421 | − | 0.108184i | ||||
\(847\) | −35.1547 | −1.20793 | ||||||||
\(848\) | 37.4656 | − | 64.8922i | 1.28657 | − | 2.22841i | ||||
\(849\) | 1.08026 | + | 3.70044i | 0.0370744 | + | 0.126999i | ||||
\(850\) | 0.800595 | + | 1.38667i | 0.0274602 | + | 0.0475624i | ||||
\(851\) | 10.9165 | + | 18.9079i | 0.374212 | + | 0.648154i | ||||
\(852\) | −14.9613 | − | 51.2500i | −0.512565 | − | 1.75580i | ||||
\(853\) | 10.5784 | − | 18.3223i | 0.362198 | − | 0.627345i | −0.626125 | − | 0.779723i | \(-0.715360\pi\) |
0.988322 | + | 0.152378i | \(0.0486933\pi\) | |||||||
\(854\) | 56.0745 | 1.91883 | ||||||||
\(855\) | −0.348475 | − | 7.83088i | −0.0119176 | − | 0.267811i | ||||
\(856\) | −29.4853 | −1.00779 | ||||||||
\(857\) | 5.81524 | − | 10.0723i | 0.198645 | − | 0.344063i | −0.749444 | − | 0.662067i | \(-0.769679\pi\) |
0.948089 | + | 0.318004i | \(0.103013\pi\) | |||||||
\(858\) | −13.5748 | + | 14.1923i | −0.463436 | + | 0.484518i | ||||
\(859\) | −0.890335 | − | 1.54211i | −0.0303778 | − | 0.0526160i | 0.850437 | − | 0.526077i | \(-0.176338\pi\) |
−0.880815 | + | 0.473461i | \(0.843004\pi\) | |||||||
\(860\) | −23.5262 | − | 40.7485i | −0.802236 | − | 1.38951i | ||||
\(861\) | 29.3057 | + | 7.15806i | 0.998737 | + | 0.243946i | ||||
\(862\) | −16.0611 | + | 27.8186i | −0.547043 | + | 0.947506i | ||||
\(863\) | −7.65256 | −0.260496 | −0.130248 | − | 0.991481i | \(-0.541577\pi\) | ||||
−0.130248 | + | 0.991481i | \(0.541577\pi\) | |||||||
\(864\) | −8.40117 | + | 42.5146i | −0.285814 | + | 1.44638i | ||||
\(865\) | −12.9559 | −0.440513 | ||||||||
\(866\) | −7.81703 | + | 13.5395i | −0.265633 | + | 0.460091i | ||||
\(867\) | −27.9589 | − | 6.82910i | −0.949536 | − | 0.231928i | ||||
\(868\) | −69.0000 | − | 119.512i | −2.34201 | − | 4.05649i | ||||
\(869\) | −31.8877 | − | 55.2311i | −1.08172 | − | 1.87359i | ||||
\(870\) | −21.5420 | + | 22.5219i | −0.730341 | + | 0.763564i | ||||
\(871\) | 7.27894 | − | 12.6075i | 0.246637 | − | 0.427188i | ||||
\(872\) | −32.8272 | −1.11167 | ||||||||
\(873\) | 24.3646 | − | 15.5507i | 0.824616 | − | 0.526310i | ||||
\(874\) | 36.6838 | 1.24085 | ||||||||
\(875\) | −2.13745 | + | 3.70217i | −0.0722589 | + | 0.125156i | ||||
\(876\) | −38.0705 | − | 130.411i | −1.28628 | − | 4.40616i | ||||
\(877\) | −3.39612 | − | 5.88225i | −0.114679 | − | 0.198629i | 0.802973 | − | 0.596016i | \(-0.203251\pi\) |
−0.917651 | + | 0.397387i | \(0.869917\pi\) | |||||||
\(878\) | −37.0801 | − | 64.2246i | −1.25139 | − | 2.16748i | ||||
\(879\) | 1.23230 | + | 4.22127i | 0.0415646 | + | 0.142380i | ||||
\(880\) | 18.8551 | − | 32.6579i | 0.635604 | − | 1.10090i | ||||
\(881\) | 8.06104 | 0.271583 | 0.135792 | − | 0.990737i | \(-0.456642\pi\) | ||||
0.135792 | + | 0.990737i | \(0.456642\pi\) | |||||||
\(882\) | −77.6231 | − | 40.3254i | −2.61370 | − | 1.35783i | ||||
\(883\) | 15.7753 | 0.530882 | 0.265441 | − | 0.964127i | \(-0.414482\pi\) | ||||
0.265441 | + | 0.964127i | \(0.414482\pi\) | |||||||
\(884\) | 1.45127 | − | 2.51367i | 0.0488115 | − | 0.0845440i | ||||
\(885\) | −12.8358 | + | 13.4197i | −0.431472 | + | 0.451100i | ||||
\(886\) | −11.8314 | − | 20.4925i | −0.397483 | − | 0.688460i | ||||
\(887\) | 8.88157 | + | 15.3833i | 0.298214 | + | 0.516522i | 0.975727 | − | 0.218989i | \(-0.0702757\pi\) |
−0.677513 | + | 0.735510i | \(0.736942\pi\) | |||||||
\(888\) | 47.0376 | + | 11.4892i | 1.57848 | + | 0.385551i | ||||
\(889\) | −29.1575 | + | 50.5023i | −0.977911 | + | 1.69379i | ||||
\(890\) | 18.8028 | 0.630271 | ||||||||
\(891\) | −39.3042 | + | 3.50502i | −1.31674 | + | 0.117423i | ||||
\(892\) | −78.5461 | −2.62992 | ||||||||
\(893\) | −0.530397 | + | 0.918674i | −0.0177490 | + | 0.0307422i | ||||
\(894\) | −53.4302 | − | 13.0506i | −1.78697 | − | 0.436477i | ||||
\(895\) | 9.42652 | + | 16.3272i | 0.315094 | + | 0.545758i | ||||
\(896\) | 11.5151 | + | 19.9448i | 0.384693 | + | 0.666308i | ||||
\(897\) | 6.49950 | − | 6.79516i | 0.217012 | − | 0.226884i | ||||
\(898\) | 45.8575 | − | 79.4274i | 1.53028 | − | 2.65053i | ||||
\(899\) | −47.9116 | −1.59794 | ||||||||
\(900\) | 12.4802 | + | 6.48349i | 0.416006 | + | 0.216116i | ||||
\(901\) | −5.39408 | −0.179703 | ||||||||
\(902\) | −23.0984 | + | 40.0077i | −0.769094 | + | 1.33211i | ||||
\(903\) | −20.8258 | − | 71.3389i | −0.693039 | − | 2.37401i | ||||
\(904\) | −12.3527 | − | 21.3955i | −0.410844 | − | 0.711603i | ||||
\(905\) | −10.6297 | − | 18.4111i | −0.353342 | − | 0.612006i | ||||
\(906\) | −20.9578 | − | 71.7911i | −0.696277 | − | 2.38510i | ||||
\(907\) | −24.3180 | + | 42.1199i | −0.807464 | + | 1.39857i | 0.107150 | + | 0.994243i | \(0.465827\pi\) |
−0.914615 | + | 0.404327i | \(0.867506\pi\) | |||||||
\(908\) | 106.887 | 3.54715 | ||||||||
\(909\) | −19.7236 | + | 12.5886i | −0.654191 | + | 0.417536i | ||||
\(910\) | 11.0553 | 0.366480 | ||||||||
\(911\) | −9.32994 | + | 16.1599i | −0.309115 | + | 0.535402i | −0.978169 | − | 0.207811i | \(-0.933366\pi\) |
0.669054 | + | 0.743214i | \(0.266699\pi\) | |||||||
\(912\) | 26.9049 | − | 28.1288i | 0.890911 | − | 0.931438i | ||||
\(913\) | 6.66687 | + | 11.5474i | 0.220641 | + | 0.382162i | ||||
\(914\) | 12.1710 | + | 21.0808i | 0.402581 | + | 0.697290i | ||||
\(915\) | −8.53437 | − | 2.08456i | −0.282137 | − | 0.0689134i | ||||
\(916\) | 16.3486 | − | 28.3167i | 0.540174 | − | 0.935609i | ||||
\(917\) | −35.7482 | −1.18051 | ||||||||
\(918\) | 7.87512 | − | 2.68428i | 0.259918 | − | 0.0885944i | ||||
\(919\) | −13.8812 | −0.457898 | −0.228949 | − | 0.973438i | \(-0.573529\pi\) | ||||
−0.228949 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(920\) | −18.8688 | + | 32.6817i | −0.622085 | + | 1.07748i | ||||
\(921\) | 32.3634 | + | 7.90492i | 1.06641 | + | 0.260476i | ||||
\(922\) | −26.5109 | − | 45.9182i | −0.873089 | − | 1.51223i | ||||
\(923\) | 3.28761 | + | 5.69431i | 0.108213 | + | 0.187431i | ||||
\(924\) | 105.195 | − | 109.980i | 3.46065 | − | 3.61808i | ||||
\(925\) | 2.01082 | − | 3.48284i | 0.0661154 | − | 0.114515i | ||||
\(926\) | 97.7111 | 3.21099 | ||||||||
\(927\) | −0.132467 | − | 2.97678i | −0.00435078 | − | 0.0977702i | ||||
\(928\) | −58.0286 | −1.90488 | ||||||||
\(929\) | −8.83587 | + | 15.3042i | −0.289895 | + | 0.502114i | −0.973785 | − | 0.227472i | \(-0.926954\pi\) |
0.683889 | + | 0.729586i | \(0.260287\pi\) | |||||||
\(930\) | 8.64362 | + | 29.6087i | 0.283435 | + | 0.970909i | ||||
\(931\) | 14.7297 | + | 25.5126i | 0.482747 | + | 0.836143i | ||||
\(932\) | 20.2331 | + | 35.0448i | 0.662758 | + | 1.14793i | ||||
\(933\) | −4.25208 | − | 14.5655i | −0.139207 | − | 0.476854i | ||||
\(934\) | −16.6651 | + | 28.8648i | −0.545299 | + | 0.944485i | ||||
\(935\) | −2.71465 | −0.0887784 | ||||||||
\(936\) | −0.927080 | − | 20.8332i | −0.0303025 | − | 0.680955i | ||||
\(937\) | 33.4041 | 1.09126 | 0.545632 | − | 0.838025i | \(-0.316290\pi\) | ||||
0.545632 | + | 0.838025i | \(0.316290\pi\) | |||||||
\(938\) | −80.4710 | + | 139.380i | −2.62747 | + | 4.55091i | ||||
\(939\) | 14.5799 | − | 15.2431i | 0.475797 | − | 0.497441i | ||||
\(940\) | −0.951619 | − | 1.64825i | −0.0310384 | − | 0.0537601i | ||||
\(941\) | 28.9473 | + | 50.1383i | 0.943656 | + | 1.63446i | 0.758420 | + | 0.651766i | \(0.225972\pi\) |
0.185236 | + | 0.982694i | \(0.440695\pi\) | |||||||
\(942\) | −34.7972 | − | 8.49937i | −1.13375 | − | 0.276924i | ||||
\(943\) | 11.0593 | − | 19.1553i | 0.360142 | − | 0.623784i | ||||
\(944\) | −92.2136 | −3.00130 | ||||||||
\(945\) | 16.7190 | + | 14.6251i | 0.543869 | + | 0.475753i | ||||
\(946\) | 113.805 | 3.70013 | ||||||||
\(947\) | 27.3142 | − | 47.3096i | 0.887593 | − | 1.53736i | 0.0448808 | − | 0.998992i | \(-0.485709\pi\) |
0.842712 | − | 0.538364i | \(-0.180957\pi\) | |||||||
\(948\) | 114.735 | + | 28.0245i | 3.72641 | + | 0.910194i | ||||
\(949\) | 8.36565 | + | 14.4897i | 0.271561 | + | 0.470357i | ||||
\(950\) | −3.37859 | − | 5.85188i | −0.109616 | − | 0.189860i | ||||
\(951\) | −20.7411 | + | 21.6846i | −0.672577 | + | 0.703173i | ||||
\(952\) | −9.19934 | + | 15.9337i | −0.298152 | + | 0.516415i | ||||
\(953\) | 19.7207 | 0.638815 | 0.319407 | − | 0.947618i | \(-0.396516\pi\) | ||||
0.319407 | + | 0.947618i | \(0.396516\pi\) | |||||||
\(954\) | −56.9751 | + | 36.3643i | −1.84464 | + | 1.17734i | ||||
\(955\) | 15.4170 | 0.498882 | ||||||||
\(956\) | 7.19834 | − | 12.4679i | 0.232811 | − | 0.403240i | ||||
\(957\) | −14.8068 | − | 50.7208i | −0.478636 | − | 1.63957i | ||||
\(958\) | 26.1042 | + | 45.2138i | 0.843388 | + | 1.46079i | ||||
\(959\) | −14.4296 | − | 24.9929i | −0.465958 | − | 0.807062i | ||||
\(960\) | 2.11953 | + | 7.26046i | 0.0684075 | + | 0.234330i | ||||
\(961\) | −8.20911 | + | 14.2186i | −0.264810 | + | 0.458665i | ||||
\(962\) | −10.4004 | −0.335322 | ||||||||
\(963\) | 11.2923 | + | 5.86636i | 0.363888 | + | 0.189041i | ||||
\(964\) | 27.3432 | 0.880665 | ||||||||
\(965\) | 0.944008 | − | 1.63507i | 0.0303887 | − | 0.0526347i | ||||
\(966\) | −71.8541 | + | 75.1227i | −2.31187 | + | 2.41703i | ||||
\(967\) | 17.6087 | + | 30.4992i | 0.566259 | + | 0.980790i | 0.996931 | + | 0.0782812i | \(0.0249432\pi\) |
−0.430672 | + | 0.902508i | \(0.641723\pi\) | |||||||
\(968\) | 28.5820 | + | 49.5055i | 0.918661 | + | 1.59117i | ||||
\(969\) | −2.72203 | − | 0.664869i | −0.0874443 | − | 0.0213587i | ||||
\(970\) | 12.4582 | − | 21.5783i | 0.400010 | − | 0.692837i | ||||
\(971\) | −13.9711 | −0.448354 | −0.224177 | − | 0.974548i | \(-0.571969\pi\) | ||||
−0.224177 | + | 0.974548i | \(0.571969\pi\) | |||||||
\(972\) | 45.6216 | − | 57.0878i | 1.46331 | − | 1.83109i | ||||
\(973\) | −14.9868 | −0.480454 | ||||||||
\(974\) | 19.5872 | − | 33.9260i | 0.627614 | − | 1.08706i | ||||
\(975\) | −1.68259 | − | 0.410979i | −0.0538859 | − | 0.0131619i | ||||
\(976\) | −21.8125 | − | 37.7804i | −0.698201 | − | 1.20932i | ||||
\(977\) | −18.2453 | − | 31.6017i | −0.583718 | − | 1.01103i | −0.995034 | − | 0.0995362i | \(-0.968264\pi\) |
0.411316 | − | 0.911493i | \(-0.365069\pi\) | |||||||
\(978\) | −53.7867 | + | 56.2334i | −1.71991 | + | 1.79815i | ||||
\(979\) | −15.9391 | + | 27.6073i | −0.509415 | + | 0.882333i | ||||
\(980\) | −52.8551 | −1.68839 | ||||||||
\(981\) | 12.5721 | + | 6.53125i | 0.401397 | + | 0.208527i | ||||
\(982\) | 29.7078 | 0.948015 | ||||||||
\(983\) | 8.75026 | − | 15.1559i | 0.279090 | − | 0.483398i | −0.692069 | − | 0.721832i | \(-0.743301\pi\) |
0.971159 | + | 0.238433i | \(0.0766339\pi\) | |||||||
\(984\) | −13.7465 | − | 47.0886i | −0.438222 | − | 1.50113i | ||||
\(985\) | −5.42986 | − | 9.40480i | −0.173010 | − | 0.299662i | ||||
\(986\) | 5.57033 | + | 9.64809i | 0.177395 | + | 0.307258i | ||||
\(987\) | −0.842391 | − | 2.88561i | −0.0268136 | − | 0.0918501i | ||||
\(988\) | −6.12450 | + | 10.6079i | −0.194846 | + | 0.337484i | ||||
\(989\) | −54.4890 | −1.73265 | ||||||||
\(990\) | −28.6735 | + | 18.3008i | −0.911304 | + | 0.581638i | ||||
\(991\) | 18.8114 | 0.597565 | 0.298783 | − | 0.954321i | \(-0.403419\pi\) | ||||
0.298783 | + | 0.954321i | \(0.403419\pi\) | |||||||
\(992\) | −28.7155 | + | 49.7367i | −0.911719 | + | 1.57914i | ||||
\(993\) | −2.94603 | + | 3.08004i | −0.0934893 | + | 0.0977421i | ||||
\(994\) | −36.3456 | − | 62.9525i | −1.15281 | − | 1.99673i | ||||
\(995\) | −0.600549 | − | 1.04018i | −0.0190387 | − | 0.0329760i | ||||
\(996\) | −23.9880 | − | 5.85918i | −0.760089 | − | 0.185655i | ||||
\(997\) | −1.76712 | + | 3.06074i | −0.0559651 | + | 0.0969345i | −0.892651 | − | 0.450749i | \(-0.851157\pi\) |
0.836686 | + | 0.547684i | \(0.184490\pi\) | |||||||
\(998\) | 33.9299 | 1.07403 | ||||||||
\(999\) | −15.7285 | − | 13.7586i | −0.497629 | − | 0.435304i |
(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 | 585.2.i.e.196.8 | ✓ | 16 | |
3.2 | odd | 2 | 1755.2.i.f.586.1 | 16 | |||
9.2 | odd | 6 | 5265.2.a.ba.1.8 | 8 | |||
9.4 | even | 3 | inner | 585.2.i.e.391.8 | yes | 16 | |
9.5 | odd | 6 | 1755.2.i.f.1171.1 | 16 | |||
9.7 | even | 3 | 5265.2.a.bf.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.e.196.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
585.2.i.e.391.8 | yes | 16 | 9.4 | even | 3 | inner | |
1755.2.i.f.586.1 | 16 | 3.2 | odd | 2 | |||
1755.2.i.f.1171.1 | 16 | 9.5 | odd | 6 | |||
5265.2.a.ba.1.8 | 8 | 9.2 | odd | 6 | |||
5265.2.a.bf.1.1 | 8 | 9.7 | even | 3 |