Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,2,Mod(16,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.g (of order \(5\), degree \(4\), 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: | \(0.598878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-2.17386 + 1.57940i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.31 |
Dual form | 75.2.g.c.46.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.830342 | − | 2.55553i | −0.587140 | − | 1.80703i | −0.590500 | − | 0.807038i | \(-0.701069\pi\) |
0.00335992 | − | 0.999994i | \(-0.498931\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | −4.22323 | + | 3.06835i | −2.11161 | + | 1.53418i | ||||
\(5\) | −1.34843 | − | 1.78375i | −0.603034 | − | 0.797715i | ||||
\(6\) | −2.17386 | − | 1.57940i | −0.887476 | − | 0.644789i | ||||
\(7\) | 1.68704 | 0.637642 | 0.318821 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(8\) | 7.00026 | + | 5.08599i | 2.47497 | + | 1.79817i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | −3.43876 | + | 4.92706i | −1.08743 | + | 1.55807i | ||||
\(11\) | 0.333373 | + | 1.02602i | 0.100516 | + | 0.309356i | 0.988652 | − | 0.150225i | \(-0.0479998\pi\) |
−0.888136 | + | 0.459581i | \(0.848000\pi\) | |||||||
\(12\) | −1.61313 | + | 4.96470i | −0.465670 | + | 1.43319i | ||||
\(13\) | 0.827310 | − | 2.54620i | 0.229455 | − | 0.706189i | −0.768354 | − | 0.640025i | \(-0.778924\pi\) |
0.997809 | − | 0.0661638i | \(-0.0210760\pi\) | |||||||
\(14\) | −1.40082 | − | 4.31129i | −0.374385 | − | 1.15224i | ||||
\(15\) | −2.13936 | − | 0.650495i | −0.552380 | − | 0.167957i | ||||
\(16\) | 3.95852 | − | 12.1831i | 0.989631 | − | 3.04577i | ||||
\(17\) | 3.18079 | + | 2.31098i | 0.771454 | + | 0.560494i | 0.902402 | − | 0.430895i | \(-0.141802\pi\) |
−0.130948 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(18\) | −2.68704 | −0.633342 | ||||||||
\(19\) | 0.952655 | + | 0.692144i | 0.218554 | + | 0.158789i | 0.691676 | − | 0.722208i | \(-0.256873\pi\) |
−0.473121 | + | 0.880997i | \(0.656873\pi\) | |||||||
\(20\) | 11.1679 | + | 3.39571i | 2.49721 | + | 0.759305i | ||||
\(21\) | 1.36485 | − | 0.991619i | 0.297834 | − | 0.216389i | ||||
\(22\) | 2.34520 | − | 1.70389i | 0.499999 | − | 0.363270i | ||||
\(23\) | −1.25552 | − | 3.86409i | −0.261794 | − | 0.805719i | −0.992415 | − | 0.122935i | \(-0.960769\pi\) |
0.730621 | − | 0.682783i | \(-0.239231\pi\) | |||||||
\(24\) | 8.65280 | 1.76625 | ||||||||
\(25\) | −1.36350 | + | 4.81050i | −0.272699 | + | 0.962099i | ||||
\(26\) | −7.19384 | −1.41083 | ||||||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | −7.12476 | + | 5.17644i | −1.34645 | + | 0.978256i | ||||
\(29\) | −4.81846 | + | 3.50082i | −0.894766 | + | 0.650086i | −0.937116 | − | 0.349017i | \(-0.886516\pi\) |
0.0423500 | + | 0.999103i | \(0.486516\pi\) | |||||||
\(30\) | 0.114039 | + | 6.00733i | 0.0208205 | + | 1.09678i | ||||
\(31\) | 5.74653 | + | 4.17510i | 1.03211 | + | 0.749870i | 0.968729 | − | 0.248120i | \(-0.0798128\pi\) |
0.0633776 | + | 0.997990i | \(0.479813\pi\) | |||||||
\(32\) | −17.1155 | −3.02563 | ||||||||
\(33\) | 0.872782 | + | 0.634113i | 0.151932 | + | 0.110385i | ||||
\(34\) | 3.26463 | − | 10.0475i | 0.559879 | − | 1.72313i | ||||
\(35\) | −2.27485 | − | 3.00925i | −0.384520 | − | 0.508657i | ||||
\(36\) | 1.61313 | + | 4.96470i | 0.268855 | + | 0.827450i | ||||
\(37\) | −1.41587 | + | 4.35761i | −0.232768 | + | 0.716387i | 0.764641 | + | 0.644456i | \(0.222916\pi\) |
−0.997410 | + | 0.0719311i | \(0.977084\pi\) | |||||||
\(38\) | 0.977766 | − | 3.00925i | 0.158615 | − | 0.488165i | ||||
\(39\) | −0.827310 | − | 2.54620i | −0.132476 | − | 0.407718i | ||||
\(40\) | −0.367227 | − | 19.3448i | −0.0580637 | − | 3.05868i | ||||
\(41\) | −3.47998 | + | 10.7103i | −0.543481 | + | 1.67266i | 0.181093 | + | 0.983466i | \(0.442037\pi\) |
−0.724574 | + | 0.689197i | \(0.757963\pi\) | |||||||
\(42\) | −3.66740 | − | 2.66452i | −0.565892 | − | 0.411144i | ||||
\(43\) | 2.58587 | 0.394342 | 0.197171 | − | 0.980369i | \(-0.436825\pi\) | ||||
0.197171 | + | 0.980369i | \(0.436825\pi\) | |||||||
\(44\) | −4.55609 | − | 3.31019i | −0.686857 | − | 0.499031i | ||||
\(45\) | −2.11313 | + | 0.731222i | −0.315007 | + | 0.109004i | ||||
\(46\) | −8.83229 | + | 6.41703i | −1.30225 | + | 0.946140i | ||||
\(47\) | 1.55155 | − | 1.12727i | 0.226317 | − | 0.164429i | −0.468849 | − | 0.883278i | \(-0.655331\pi\) |
0.695166 | + | 0.718850i | \(0.255331\pi\) | |||||||
\(48\) | −3.95852 | − | 12.1831i | −0.571364 | − | 1.75848i | ||||
\(49\) | −4.15389 | −0.593413 | ||||||||
\(50\) | 13.4255 | − | 0.509905i | 1.89866 | − | 0.0721114i | ||||
\(51\) | 3.93167 | 0.550544 | ||||||||
\(52\) | 4.31872 | + | 13.2917i | 0.598899 | + | 1.84322i | ||||
\(53\) | 2.06187 | − | 1.49803i | 0.283219 | − | 0.205771i | −0.437101 | − | 0.899412i | \(-0.643995\pi\) |
0.720320 | + | 0.693642i | \(0.243995\pi\) | |||||||
\(54\) | −2.17386 | + | 1.57940i | −0.295825 | + | 0.214930i | ||||
\(55\) | 1.38062 | − | 1.97816i | 0.186163 | − | 0.266735i | ||||
\(56\) | 11.8097 | + | 8.58028i | 1.57814 | + | 1.14659i | ||||
\(57\) | 1.17755 | 0.155970 | ||||||||
\(58\) | 12.9474 | + | 9.40685i | 1.70008 | + | 1.23518i | ||||
\(59\) | 0.412843 | − | 1.27060i | 0.0537476 | − | 0.165418i | −0.920579 | − | 0.390555i | \(-0.872283\pi\) |
0.974327 | + | 0.225137i | \(0.0722830\pi\) | |||||||
\(60\) | 11.0309 | − | 3.81712i | 1.42409 | − | 0.492788i | ||||
\(61\) | −2.24997 | − | 6.92470i | −0.288079 | − | 0.886617i | −0.985459 | − | 0.169915i | \(-0.945651\pi\) |
0.697379 | − | 0.716702i | \(-0.254349\pi\) | |||||||
\(62\) | 5.89800 | − | 18.1522i | 0.749047 | − | 2.30533i | ||||
\(63\) | 0.521325 | − | 1.60447i | 0.0656807 | − | 0.202145i | ||||
\(64\) | 6.29470 | + | 19.3731i | 0.786838 | + | 2.42164i | ||||
\(65\) | −5.65734 | + | 1.95765i | −0.701706 | + | 0.242817i | ||||
\(66\) | 0.895787 | − | 2.75695i | 0.110264 | − | 0.339357i | ||||
\(67\) | −10.0683 | − | 7.31502i | −1.23003 | − | 0.893672i | −0.233141 | − | 0.972443i | \(-0.574900\pi\) |
−0.996893 | + | 0.0787711i | \(0.974900\pi\) | |||||||
\(68\) | −20.5241 | −2.48891 | ||||||||
\(69\) | −3.28699 | − | 2.38814i | −0.395707 | − | 0.287498i | ||||
\(70\) | −5.80133 | + | 8.31216i | −0.693392 | + | 0.993493i | ||||
\(71\) | 4.84181 | − | 3.51778i | 0.574617 | − | 0.417484i | −0.262162 | − | 0.965024i | \(-0.584436\pi\) |
0.836779 | + | 0.547540i | \(0.184436\pi\) | |||||||
\(72\) | 7.00026 | − | 5.08599i | 0.824989 | − | 0.599390i | ||||
\(73\) | −1.01996 | − | 3.13911i | −0.119377 | − | 0.367405i | 0.873458 | − | 0.486900i | \(-0.161872\pi\) |
−0.992835 | + | 0.119495i | \(0.961872\pi\) | |||||||
\(74\) | 12.3117 | 1.43120 | ||||||||
\(75\) | 1.72445 | + | 4.69322i | 0.199122 | + | 0.541926i | ||||
\(76\) | −6.14702 | −0.705112 | ||||||||
\(77\) | 0.562414 | + | 1.73093i | 0.0640931 | + | 0.197258i | ||||
\(78\) | −5.81994 | + | 4.22843i | −0.658978 | + | 0.478776i | ||||
\(79\) | 3.23934 | − | 2.35351i | 0.364454 | − | 0.264791i | −0.390454 | − | 0.920623i | \(-0.627682\pi\) |
0.754907 | + | 0.655831i | \(0.227682\pi\) | |||||||
\(80\) | −27.0693 | + | 9.36699i | −3.02644 | + | 1.04726i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 30.2600 | 3.34166 | ||||||||
\(83\) | −7.17988 | − | 5.21649i | −0.788094 | − | 0.572584i | 0.119303 | − | 0.992858i | \(-0.461934\pi\) |
−0.907397 | + | 0.420274i | \(0.861934\pi\) | |||||||
\(84\) | −2.72142 | + | 8.37566i | −0.296931 | + | 0.913859i | ||||
\(85\) | −0.166861 | − | 8.78989i | −0.0180986 | − | 0.953398i | ||||
\(86\) | −2.14716 | − | 6.60827i | −0.231534 | − | 0.712588i | ||||
\(87\) | −1.84049 | + | 5.66445i | −0.197321 | + | 0.607292i | ||||
\(88\) | −2.88461 | + | 8.87792i | −0.307501 | + | 0.946389i | ||||
\(89\) | 4.77234 | + | 14.6877i | 0.505867 | + | 1.55690i | 0.799309 | + | 0.600920i | \(0.205199\pi\) |
−0.293442 | + | 0.955977i | \(0.594801\pi\) | |||||||
\(90\) | 3.62328 | + | 4.79300i | 0.381927 | + | 0.505226i | ||||
\(91\) | 1.39571 | − | 4.29555i | 0.146310 | − | 0.450296i | ||||
\(92\) | 17.1587 | + | 12.4666i | 1.78892 | + | 1.29973i | ||||
\(93\) | 7.10310 | 0.736557 | ||||||||
\(94\) | −4.16908 | − | 3.02901i | −0.430008 | − | 0.312419i | ||||
\(95\) | −0.0499753 | − | 2.63260i | −0.00512736 | − | 0.270099i | ||||
\(96\) | −13.8468 | + | 10.0603i | −1.41323 | + | 1.02677i | ||||
\(97\) | −8.71166 | + | 6.32939i | −0.884535 | + | 0.642652i | −0.934447 | − | 0.356101i | \(-0.884106\pi\) |
0.0499122 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(98\) | 3.44915 | + | 10.6154i | 0.348416 | + | 1.07232i | ||||
\(99\) | 1.07882 | 0.108425 | ||||||||
\(100\) | −9.00196 | − | 24.4995i | −0.900196 | − | 2.44995i | ||||
\(101\) | −13.5654 | −1.34981 | −0.674905 | − | 0.737905i | \(-0.735815\pi\) | ||||
−0.674905 | + | 0.737905i | \(0.735815\pi\) | |||||||
\(102\) | −3.26463 | − | 10.0475i | −0.323246 | − | 0.994850i | ||||
\(103\) | −1.10757 | + | 0.804700i | −0.109133 | + | 0.0792894i | −0.641013 | − | 0.767530i | \(-0.721486\pi\) |
0.531880 | + | 0.846819i | \(0.321486\pi\) | |||||||
\(104\) | 18.7413 | − | 13.6164i | 1.83774 | − | 1.33520i | ||||
\(105\) | −3.60919 | − | 1.09741i | −0.352221 | − | 0.107097i | ||||
\(106\) | −5.54032 | − | 4.02528i | −0.538124 | − | 0.390970i | ||||
\(107\) | 11.0115 | 1.06452 | 0.532262 | − | 0.846579i | \(-0.321342\pi\) | ||||
0.532262 | + | 0.846579i | \(0.321342\pi\) | |||||||
\(108\) | 4.22323 | + | 3.06835i | 0.406380 | + | 0.295253i | ||||
\(109\) | 1.06577 | − | 3.28010i | 0.102082 | − | 0.314176i | −0.886952 | − | 0.461861i | \(-0.847182\pi\) |
0.989035 | + | 0.147684i | \(0.0471820\pi\) | |||||||
\(110\) | −6.20163 | − | 1.88568i | −0.591303 | − | 0.179792i | ||||
\(111\) | 1.41587 | + | 4.35761i | 0.134389 | + | 0.413606i | ||||
\(112\) | 6.67820 | − | 20.5534i | 0.631030 | − | 1.94211i | ||||
\(113\) | 1.87015 | − | 5.75574i | 0.175929 | − | 0.541455i | −0.823745 | − | 0.566960i | \(-0.808119\pi\) |
0.999675 | + | 0.0255053i | \(0.00811946\pi\) | |||||||
\(114\) | −0.977766 | − | 3.00925i | −0.0915762 | − | 0.281842i | ||||
\(115\) | −5.19958 | + | 7.44997i | −0.484863 | + | 0.694713i | ||||
\(116\) | 9.60772 | − | 29.5695i | 0.892054 | − | 2.74546i | ||||
\(117\) | −2.16593 | − | 1.57364i | −0.200240 | − | 0.145483i | ||||
\(118\) | −3.58986 | −0.330473 | ||||||||
\(119\) | 5.36612 | + | 3.89872i | 0.491912 | + | 0.357395i | ||||
\(120\) | −11.6677 | − | 15.4344i | −1.06511 | − | 1.40896i | ||||
\(121\) | 7.95761 | − | 5.78155i | 0.723419 | − | 0.525595i | ||||
\(122\) | −15.8280 | + | 11.4997i | −1.43300 | + | 1.04114i | ||||
\(123\) | 3.47998 | + | 10.7103i | 0.313779 | + | 0.965713i | ||||
\(124\) | −37.0796 | −3.32984 | ||||||||
\(125\) | 10.4193 | − | 4.05447i | 0.931928 | − | 0.362643i | ||||
\(126\) | −4.53315 | −0.403845 | ||||||||
\(127\) | −6.25332 | − | 19.2457i | −0.554893 | − | 1.70778i | −0.696227 | − | 0.717822i | \(-0.745139\pi\) |
0.141334 | − | 0.989962i | \(-0.454861\pi\) | |||||||
\(128\) | 16.5882 | − | 12.0521i | 1.46621 | − | 1.06526i | ||||
\(129\) | 2.09201 | − | 1.51994i | 0.184192 | − | 0.133823i | ||||
\(130\) | 9.70036 | + | 12.8320i | 0.850778 | + | 1.12544i | ||||
\(131\) | 2.46759 | + | 1.79281i | 0.215595 | + | 0.156639i | 0.690341 | − | 0.723484i | \(-0.257460\pi\) |
−0.474747 | + | 0.880122i | \(0.657460\pi\) | |||||||
\(132\) | −5.63164 | −0.490171 | ||||||||
\(133\) | 1.60717 | + | 1.16768i | 0.139359 | + | 0.101250i | ||||
\(134\) | −10.3336 | + | 31.8037i | −0.892691 | + | 2.74742i | ||||
\(135\) | −1.27976 | + | 1.83364i | −0.110144 | + | 0.157814i | ||||
\(136\) | 10.5127 | + | 32.3549i | 0.901460 | + | 2.77441i | ||||
\(137\) | −6.33795 | + | 19.5062i | −0.541487 | + | 1.66653i | 0.187711 | + | 0.982224i | \(0.439893\pi\) |
−0.729199 | + | 0.684302i | \(0.760107\pi\) | |||||||
\(138\) | −3.37363 | + | 10.3830i | −0.287183 | + | 0.883858i | ||||
\(139\) | 5.66068 | + | 17.4218i | 0.480133 | + | 1.47770i | 0.838908 | + | 0.544273i | \(0.183194\pi\) |
−0.358775 | + | 0.933424i | \(0.616806\pi\) | |||||||
\(140\) | 18.8407 | + | 5.72871i | 1.59233 | + | 0.484165i | ||||
\(141\) | 0.592639 | − | 1.82396i | 0.0499092 | − | 0.153605i | ||||
\(142\) | −13.0101 | − | 9.45242i | −1.09179 | − | 0.793230i | ||||
\(143\) | 2.88825 | 0.241527 | ||||||||
\(144\) | −10.3635 | − | 7.52956i | −0.863629 | − | 0.627463i | ||||
\(145\) | 12.7419 | + | 3.87432i | 1.05816 | + | 0.321745i | ||||
\(146\) | −7.17517 | + | 5.21306i | −0.593821 | + | 0.431436i | ||||
\(147\) | −3.36057 | + | 2.44159i | −0.277175 | + | 0.201379i | ||||
\(148\) | −7.39114 | − | 22.7476i | −0.607548 | − | 1.86984i | ||||
\(149\) | 0.705938 | 0.0578327 | 0.0289163 | − | 0.999582i | \(-0.490794\pi\) | ||||
0.0289163 | + | 0.999582i | \(0.490794\pi\) | |||||||
\(150\) | 10.5618 | − | 8.30385i | 0.862365 | − | 0.678007i | ||||
\(151\) | 7.04538 | 0.573345 | 0.286673 | − | 0.958029i | \(-0.407451\pi\) | ||||
0.286673 | + | 0.958029i | \(0.407451\pi\) | |||||||
\(152\) | 3.14860 | + | 9.69039i | 0.255385 | + | 0.785994i | ||||
\(153\) | 3.18079 | − | 2.31098i | 0.257151 | − | 0.186831i | ||||
\(154\) | 3.95645 | − | 2.87453i | 0.318820 | − | 0.231636i | ||||
\(155\) | −0.301457 | − | 15.8802i | −0.0242136 | − | 1.27552i | ||||
\(156\) | 11.3066 | + | 8.21470i | 0.905249 | + | 0.657702i | ||||
\(157\) | −5.12880 | −0.409323 | −0.204662 | − | 0.978833i | \(-0.565609\pi\) | ||||
−0.204662 | + | 0.978833i | \(0.565609\pi\) | |||||||
\(158\) | −8.70423 | − | 6.32399i | −0.692471 | − | 0.503110i | ||||
\(159\) | 0.787563 | − | 2.42387i | 0.0624578 | − | 0.192225i | ||||
\(160\) | 23.0790 | + | 30.5298i | 1.82456 | + | 2.41359i | ||||
\(161\) | −2.11811 | − | 6.51888i | −0.166931 | − | 0.513760i | ||||
\(162\) | −0.830342 | + | 2.55553i | −0.0652378 | + | 0.200781i | ||||
\(163\) | −7.49715 | + | 23.0739i | −0.587222 | + | 1.80728i | 0.00293441 | + | 0.999996i | \(0.499066\pi\) |
−0.590157 | + | 0.807289i | \(0.700934\pi\) | |||||||
\(164\) | −18.1662 | − | 55.9097i | −1.41854 | − | 4.36581i | ||||
\(165\) | −0.0457853 | − | 2.41188i | −0.00356438 | − | 0.187764i | ||||
\(166\) | −7.36913 | + | 22.6799i | −0.571955 | + | 1.76030i | ||||
\(167\) | −3.68013 | − | 2.67377i | −0.284777 | − | 0.206903i | 0.436221 | − | 0.899840i | \(-0.356317\pi\) |
−0.720998 | + | 0.692937i | \(0.756317\pi\) | |||||||
\(168\) | 14.5976 | 1.12623 | ||||||||
\(169\) | 4.71853 | + | 3.42821i | 0.362964 | + | 0.263709i | ||||
\(170\) | −22.3243 | + | 7.72503i | −1.71219 | + | 0.592483i | ||||
\(171\) | 0.952655 | − | 0.692144i | 0.0728513 | − | 0.0529296i | ||||
\(172\) | −10.9207 | + | 7.93437i | −0.832697 | + | 0.604990i | ||||
\(173\) | −0.827327 | − | 2.54625i | −0.0629005 | − | 0.193588i | 0.914668 | − | 0.404206i | \(-0.132452\pi\) |
−0.977568 | + | 0.210618i | \(0.932452\pi\) | |||||||
\(174\) | 16.0039 | 1.21325 | ||||||||
\(175\) | −2.30027 | + | 8.11551i | −0.173884 | + | 0.613475i | ||||
\(176\) | 13.8197 | 1.04170 | ||||||||
\(177\) | −0.412843 | − | 1.27060i | −0.0310312 | − | 0.0955042i | ||||
\(178\) | 33.5723 | − | 24.3917i | 2.51635 | − | 1.82823i | ||||
\(179\) | 12.6422 | − | 9.18511i | 0.944924 | − | 0.686528i | −0.00467674 | − | 0.999989i | \(-0.501489\pi\) |
0.949601 | + | 0.313461i | \(0.101489\pi\) | |||||||
\(180\) | 6.68058 | − | 9.57194i | 0.497941 | − | 0.713451i | ||||
\(181\) | −0.164103 | − | 0.119228i | −0.0121977 | − | 0.00886215i | 0.581670 | − | 0.813425i | \(-0.302400\pi\) |
−0.593867 | + | 0.804563i | \(0.702400\pi\) | |||||||
\(182\) | −12.1363 | −0.899603 | ||||||||
\(183\) | −5.89050 | − | 4.27970i | −0.435439 | − | 0.316365i | ||||
\(184\) | 10.8638 | − | 33.4352i | 0.800887 | − | 2.46488i | ||||
\(185\) | 9.68207 | − | 3.35036i | 0.711840 | − | 0.246323i | ||||
\(186\) | −5.89800 | − | 18.1522i | −0.432462 | − | 1.33098i | ||||
\(187\) | −1.31071 | + | 4.03396i | −0.0958488 | + | 0.294992i | ||||
\(188\) | −3.09369 | + | 9.52141i | −0.225631 | + | 0.694420i | ||||
\(189\) | −0.521325 | − | 1.60447i | −0.0379208 | − | 0.116708i | ||||
\(190\) | −6.68619 | + | 2.31367i | −0.485067 | + | 0.167851i | ||||
\(191\) | −2.44734 | + | 7.53213i | −0.177083 | + | 0.545006i | −0.999722 | − | 0.0235578i | \(-0.992501\pi\) |
0.822639 | + | 0.568563i | \(0.192501\pi\) | |||||||
\(192\) | 16.4798 | + | 11.9732i | 1.18932 | + | 0.864094i | ||||
\(193\) | −16.4269 | −1.18243 | −0.591216 | − | 0.806513i | \(-0.701352\pi\) | ||||
−0.591216 | + | 0.806513i | \(0.701352\pi\) | |||||||
\(194\) | 23.4086 | + | 17.0073i | 1.68064 | + | 1.22106i | ||||
\(195\) | −3.42620 | + | 4.90907i | −0.245356 | + | 0.351546i | ||||
\(196\) | 17.5428 | − | 12.7456i | 1.25306 | − | 0.910400i | ||||
\(197\) | 13.8640 | − | 10.0728i | 0.987770 | − | 0.717657i | 0.0283382 | − | 0.999598i | \(-0.490978\pi\) |
0.959432 | + | 0.281942i | \(0.0909785\pi\) | |||||||
\(198\) | −0.895787 | − | 2.75695i | −0.0636608 | − | 0.195928i | ||||
\(199\) | −2.01848 | −0.143086 | −0.0715430 | − | 0.997438i | \(-0.522792\pi\) | ||||
−0.0715430 | + | 0.997438i | \(0.522792\pi\) | |||||||
\(200\) | −34.0110 | + | 26.7400i | −2.40494 | + | 1.89081i | ||||
\(201\) | −12.4451 | −0.877806 | ||||||||
\(202\) | 11.2639 | + | 34.6668i | 0.792528 | + | 2.43915i | ||||
\(203\) | −8.12895 | + | 5.90603i | −0.570541 | + | 0.414522i | ||||
\(204\) | −16.6043 | + | 12.0638i | −1.16254 | + | 0.844632i | ||||
\(205\) | 23.7969 | − | 8.23461i | 1.66205 | − | 0.575130i | ||||
\(206\) | 2.97610 | + | 2.16226i | 0.207355 | + | 0.150652i | ||||
\(207\) | −4.06295 | −0.282394 | ||||||||
\(208\) | −27.7456 | − | 20.1584i | −1.92381 | − | 1.39773i | ||||
\(209\) | −0.392562 | + | 1.20818i | −0.0271541 | + | 0.0835717i | ||||
\(210\) | 0.192388 | + | 10.1346i | 0.0132760 | + | 0.699355i | ||||
\(211\) | −7.36119 | − | 22.6554i | −0.506765 | − | 1.55966i | −0.797783 | − | 0.602945i | \(-0.793994\pi\) |
0.291018 | − | 0.956718i | \(-0.406006\pi\) | |||||||
\(212\) | −4.11123 | + | 12.6531i | −0.282361 | + | 0.869017i | ||||
\(213\) | 1.84941 | − | 5.69189i | 0.126719 | − | 0.390002i | ||||
\(214\) | −9.14333 | − | 28.1403i | −0.625025 | − | 1.92363i | ||||
\(215\) | −3.48686 | − | 4.61254i | −0.237802 | − | 0.314572i | ||||
\(216\) | 2.67386 | − | 8.22930i | 0.181933 | − | 0.559933i | ||||
\(217\) | 9.69463 | + | 7.04356i | 0.658115 | + | 0.478148i | ||||
\(218\) | −9.26733 | −0.627663 | ||||||||
\(219\) | −2.67028 | − | 1.94007i | −0.180441 | − | 0.131098i | ||||
\(220\) | 0.239008 | + | 12.5905i | 0.0161139 | + | 0.848849i | ||||
\(221\) | 8.51571 | − | 6.18702i | 0.572828 | − | 0.416184i | ||||
\(222\) | 9.96035 | − | 7.23662i | 0.668495 | − | 0.485690i | ||||
\(223\) | 4.05158 | + | 12.4695i | 0.271314 | + | 0.835017i | 0.990171 | + | 0.139860i | \(0.0446653\pi\) |
−0.718858 | + | 0.695157i | \(0.755335\pi\) | |||||||
\(224\) | −28.8746 | −1.92927 | ||||||||
\(225\) | 4.15371 | + | 2.78329i | 0.276914 | + | 0.185552i | ||||
\(226\) | −16.2618 | −1.08172 | ||||||||
\(227\) | −8.12118 | − | 24.9944i | −0.539022 | − | 1.65894i | −0.734795 | − | 0.678289i | \(-0.762722\pi\) |
0.195774 | − | 0.980649i | \(-0.437278\pi\) | |||||||
\(228\) | −4.97305 | + | 3.61313i | −0.329348 | + | 0.239285i | ||||
\(229\) | −1.61484 | + | 1.17325i | −0.106711 | + | 0.0775304i | −0.639861 | − | 0.768490i | \(-0.721008\pi\) |
0.533150 | + | 0.846021i | \(0.321008\pi\) | |||||||
\(230\) | 23.3560 | + | 7.10166i | 1.54005 | + | 0.468269i | ||||
\(231\) | 1.47242 | + | 1.06978i | 0.0968781 | + | 0.0703861i | ||||
\(232\) | −51.5357 | −3.38348 | ||||||||
\(233\) | 0.425178 | + | 0.308910i | 0.0278543 | + | 0.0202373i | 0.601625 | − | 0.798778i | \(-0.294520\pi\) |
−0.573771 | + | 0.819016i | \(0.694520\pi\) | |||||||
\(234\) | −2.22302 | + | 6.84175i | −0.145323 | + | 0.447259i | ||||
\(235\) | −4.10291 | − | 1.24753i | −0.267644 | − | 0.0813801i | ||||
\(236\) | 2.15512 | + | 6.63278i | 0.140286 | + | 0.431757i | ||||
\(237\) | 1.23732 | − | 3.80807i | 0.0803723 | − | 0.247361i | ||||
\(238\) | 5.50757 | − | 16.9505i | 0.357002 | − | 1.09874i | ||||
\(239\) | −2.16612 | − | 6.66663i | −0.140115 | − | 0.431229i | 0.856236 | − | 0.516585i | \(-0.172797\pi\) |
−0.996350 | + | 0.0853565i | \(0.972797\pi\) | |||||||
\(240\) | −16.3937 | + | 23.4890i | −1.05821 | + | 1.51621i | ||||
\(241\) | 0.715542 | − | 2.20221i | 0.0460921 | − | 0.141857i | −0.925362 | − | 0.379085i | \(-0.876239\pi\) |
0.971454 | + | 0.237228i | \(0.0762388\pi\) | |||||||
\(242\) | −21.3824 | − | 15.5353i | −1.37452 | − | 0.998644i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 30.7496 | + | 22.3409i | 1.96854 | + | 1.43023i | ||||
\(245\) | 5.60121 | + | 7.40948i | 0.357848 | + | 0.473374i | ||||
\(246\) | 24.4808 | − | 17.7864i | 1.56084 | − | 1.13402i | ||||
\(247\) | 2.55048 | − | 1.85303i | 0.162283 | − | 0.117906i | ||||
\(248\) | 18.9927 | + | 58.4536i | 1.20604 | + | 3.71180i | ||||
\(249\) | −8.87482 | −0.562419 | ||||||||
\(250\) | −19.0129 | − | 23.2602i | −1.20248 | − | 1.47110i | ||||
\(251\) | −6.17885 | −0.390005 | −0.195003 | − | 0.980803i | \(-0.562472\pi\) | ||||
−0.195003 | + | 0.980803i | \(0.562472\pi\) | |||||||
\(252\) | 2.72142 | + | 8.37566i | 0.171433 | + | 0.527617i | ||||
\(253\) | 3.54607 | − | 2.57637i | 0.222939 | − | 0.161975i | ||||
\(254\) | −43.9907 | + | 31.9611i | −2.76022 | + | 2.00542i | ||||
\(255\) | −5.30156 | − | 7.01310i | −0.331997 | − | 0.439177i | ||||
\(256\) | −11.6138 | − | 8.43794i | −0.725864 | − | 0.527371i | ||||
\(257\) | 13.2239 | 0.824882 | 0.412441 | − | 0.910984i | \(-0.364676\pi\) | ||||
0.412441 | + | 0.910984i | \(0.364676\pi\) | |||||||
\(258\) | −5.62133 | − | 4.08413i | −0.349969 | − | 0.254267i | ||||
\(259\) | −2.38864 | + | 7.35148i | −0.148423 | + | 0.456799i | ||||
\(260\) | 17.8855 | − | 25.6263i | 1.10921 | − | 1.58928i | ||||
\(261\) | 1.84049 | + | 5.66445i | 0.113923 | + | 0.350620i | ||||
\(262\) | 2.53264 | − | 7.79465i | 0.156467 | − | 0.481555i | ||||
\(263\) | −2.15583 | + | 6.63498i | −0.132934 | + | 0.409130i | −0.995263 | − | 0.0972190i | \(-0.969005\pi\) |
0.862329 | + | 0.506349i | \(0.169005\pi\) | |||||||
\(264\) | 2.88461 | + | 8.87792i | 0.177536 | + | 0.546398i | ||||
\(265\) | −5.45239 | − | 1.65786i | −0.334937 | − | 0.101841i | ||||
\(266\) | 1.64953 | − | 5.07674i | 0.101139 | − | 0.311275i | ||||
\(267\) | 12.4941 | + | 9.07752i | 0.764629 | + | 0.555535i | ||||
\(268\) | 64.9656 | 3.96841 | ||||||||
\(269\) | −19.1898 | − | 13.9422i | −1.17002 | − | 0.850070i | −0.179010 | − | 0.983847i | \(-0.557289\pi\) |
−0.991011 | + | 0.133777i | \(0.957289\pi\) | |||||||
\(270\) | 5.74855 | + | 1.74791i | 0.349845 | + | 0.106374i | ||||
\(271\) | −23.4542 | + | 17.0405i | −1.42474 | + | 1.03514i | −0.433775 | + | 0.901021i | \(0.642819\pi\) |
−0.990966 | + | 0.134114i | \(0.957181\pi\) | |||||||
\(272\) | 40.7460 | − | 29.6037i | 2.47059 | − | 1.79499i | ||||
\(273\) | −1.39571 | − | 4.29555i | −0.0844721 | − | 0.259978i | ||||
\(274\) | 55.1113 | 3.32940 | ||||||||
\(275\) | −5.39020 | + | 0.204721i | −0.325041 | + | 0.0123451i | ||||
\(276\) | 21.2094 | 1.27665 | ||||||||
\(277\) | −2.65343 | − | 8.16641i | −0.159429 | − | 0.490672i | 0.839154 | − | 0.543894i | \(-0.183051\pi\) |
−0.998583 | + | 0.0532223i | \(0.983051\pi\) | |||||||
\(278\) | 39.8216 | − | 28.9321i | 2.38834 | − | 1.73523i | ||||
\(279\) | 5.74653 | − | 4.17510i | 0.344036 | − | 0.249957i | ||||
\(280\) | −0.619527 | − | 32.6354i | −0.0370238 | − | 1.95034i | ||||
\(281\) | −13.8877 | − | 10.0900i | −0.828471 | − | 0.601919i | 0.0906557 | − | 0.995882i | \(-0.471104\pi\) |
−0.919126 | + | 0.393963i | \(0.871104\pi\) | |||||||
\(282\) | −5.15327 | −0.306872 | ||||||||
\(283\) | 7.78278 | + | 5.65452i | 0.462638 | + | 0.336126i | 0.794565 | − | 0.607179i | \(-0.207699\pi\) |
−0.331927 | + | 0.943305i | \(0.607699\pi\) | |||||||
\(284\) | −9.65426 | + | 29.7128i | −0.572875 | + | 1.76313i | ||||
\(285\) | −1.58783 | − | 2.10044i | −0.0940552 | − | 0.124419i | ||||
\(286\) | −2.39823 | − | 7.38100i | −0.141810 | − | 0.436447i | ||||
\(287\) | −5.87087 | + | 18.0687i | −0.346546 | + | 1.06656i | ||||
\(288\) | −5.28899 | + | 16.2779i | −0.311657 | + | 0.959182i | ||||
\(289\) | −0.476498 | − | 1.46651i | −0.0280293 | − | 0.0862654i | ||||
\(290\) | −0.679209 | − | 35.7793i | −0.0398845 | − | 2.10104i | ||||
\(291\) | −3.32756 | + | 10.2412i | −0.195065 | + | 0.600348i | ||||
\(292\) | 13.9394 | + | 10.1276i | 0.815742 | + | 0.592671i | ||||
\(293\) | 16.8202 | 0.982649 | 0.491324 | − | 0.870977i | \(-0.336513\pi\) | ||||
0.491324 | + | 0.870977i | \(0.336513\pi\) | |||||||
\(294\) | 9.02998 | + | 6.56067i | 0.526639 | + | 0.382626i | ||||
\(295\) | −2.82312 | + | 0.976903i | −0.164368 | + | 0.0568775i | ||||
\(296\) | −32.0743 | + | 23.3033i | −1.86428 | + | 1.35448i | ||||
\(297\) | 0.872782 | − | 0.634113i | 0.0506439 | − | 0.0367950i | ||||
\(298\) | −0.586170 | − | 1.80404i | −0.0339559 | − | 0.104505i | ||||
\(299\) | −10.8775 | −0.629059 | ||||||||
\(300\) | −21.6832 | − | 14.5293i | −1.25188 | − | 0.838849i | ||||
\(301\) | 4.36247 | 0.251449 | ||||||||
\(302\) | −5.85008 | − | 18.0047i | −0.336634 | − | 1.03605i | ||||
\(303\) | −10.9747 | + | 7.97356i | −0.630478 | + | 0.458069i | ||||
\(304\) | 12.2036 | − | 8.86641i | 0.699922 | − | 0.508523i | ||||
\(305\) | −9.31799 | + | 13.3508i | −0.533546 | + | 0.764466i | ||||
\(306\) | −8.54691 | − | 6.20969i | −0.488594 | − | 0.354984i | ||||
\(307\) | 11.3212 | 0.646134 | 0.323067 | − | 0.946376i | \(-0.395286\pi\) | ||||
0.323067 | + | 0.946376i | \(0.395286\pi\) | |||||||
\(308\) | −7.68632 | − | 5.58444i | −0.437969 | − | 0.318203i | ||||
\(309\) | −0.423056 | + | 1.30203i | −0.0240668 | + | 0.0740700i | ||||
\(310\) | −40.3319 | + | 13.9563i | −2.29070 | + | 0.792667i | ||||
\(311\) | 5.73642 | + | 17.6549i | 0.325283 | + | 1.00112i | 0.971313 | + | 0.237805i | \(0.0764280\pi\) |
−0.646030 | + | 0.763312i | \(0.723572\pi\) | |||||||
\(312\) | 7.15855 | − | 22.0318i | 0.405273 | − | 1.24730i | ||||
\(313\) | −2.99731 | + | 9.22478i | −0.169418 | + | 0.521416i | −0.999335 | − | 0.0364720i | \(-0.988388\pi\) |
0.829916 | + | 0.557888i | \(0.188388\pi\) | |||||||
\(314\) | 4.25866 | + | 13.1068i | 0.240330 | + | 0.739660i | ||||
\(315\) | −3.56494 | + | 1.23360i | −0.200862 | + | 0.0695056i | ||||
\(316\) | −6.45903 | + | 19.8789i | −0.363349 | + | 1.11827i | ||||
\(317\) | −6.04859 | − | 4.39456i | −0.339723 | − | 0.246823i | 0.404822 | − | 0.914395i | \(-0.367333\pi\) |
−0.744545 | + | 0.667573i | \(0.767333\pi\) | |||||||
\(318\) | −6.84822 | −0.384029 | ||||||||
\(319\) | −5.19825 | − | 3.77675i | −0.291046 | − | 0.211457i | ||||
\(320\) | 26.0688 | − | 37.3514i | 1.45729 | − | 2.08800i | ||||
\(321\) | 8.90851 | − | 6.47241i | 0.497225 | − | 0.361255i | ||||
\(322\) | −14.9004 | + | 10.8258i | −0.830369 | + | 0.603298i | ||||
\(323\) | 1.43066 | + | 4.40313i | 0.0796042 | + | 0.244997i | ||||
\(324\) | 5.22020 | 0.290011 | ||||||||
\(325\) | 11.1205 | + | 7.45150i | 0.616852 | + | 0.413335i | ||||
\(326\) | 65.1911 | 3.61060 | ||||||||
\(327\) | −1.06577 | − | 3.28010i | −0.0589371 | − | 0.181390i | ||||
\(328\) | −78.8331 | + | 57.2756i | −4.35283 | + | 3.16252i | ||||
\(329\) | 2.61753 | − | 1.90175i | 0.144309 | − | 0.104847i | ||||
\(330\) | −6.12560 | + | 2.11969i | −0.337203 | + | 0.116685i | ||||
\(331\) | 20.4333 | + | 14.8457i | 1.12312 | + | 0.815993i | 0.984679 | − | 0.174378i | \(-0.0557914\pi\) |
0.138439 | + | 0.990371i | \(0.455791\pi\) | |||||||
\(332\) | 46.3283 | 2.54259 | ||||||||
\(333\) | 3.70681 | + | 2.69315i | 0.203132 | + | 0.147584i | ||||
\(334\) | −3.77714 | + | 11.6248i | −0.206676 | + | 0.636083i | ||||
\(335\) | 0.528171 | + | 27.8230i | 0.0288571 | + | 1.52013i | ||||
\(336\) | −6.67820 | − | 20.5534i | −0.364325 | − | 1.12128i | ||||
\(337\) | −4.02464 | + | 12.3866i | −0.219236 | + | 0.674739i | 0.779590 | + | 0.626291i | \(0.215428\pi\) |
−0.998826 | + | 0.0484485i | \(0.984572\pi\) | |||||||
\(338\) | 4.84291 | − | 14.9049i | 0.263419 | − | 0.810721i | ||||
\(339\) | −1.87015 | − | 5.75574i | −0.101573 | − | 0.312609i | ||||
\(340\) | 27.6752 | + | 36.6097i | 1.50090 | + | 1.98544i | ||||
\(341\) | −2.36798 | + | 7.28790i | −0.128233 | + | 0.394662i | ||||
\(342\) | −2.55982 | − | 1.85982i | −0.138419 | − | 0.100568i | ||||
\(343\) | −18.8171 | −1.01603 | ||||||||
\(344\) | 18.1018 | + | 13.1517i | 0.975983 | + | 0.709093i | ||||
\(345\) | 0.172432 | + | 9.08339i | 0.00928344 | + | 0.489033i | ||||
\(346\) | −5.82005 | + | 4.22852i | −0.312888 | + | 0.227326i | ||||
\(347\) | 4.85531 | − | 3.52759i | 0.260647 | − | 0.189371i | −0.449785 | − | 0.893137i | \(-0.648500\pi\) |
0.710432 | + | 0.703766i | \(0.248500\pi\) | |||||||
\(348\) | −9.60772 | − | 29.5695i | −0.515028 | − | 1.58509i | ||||
\(349\) | −22.7183 | −1.21608 | −0.608042 | − | 0.793905i | \(-0.708045\pi\) | ||||
−0.608042 | + | 0.793905i | \(0.708045\pi\) | |||||||
\(350\) | 22.6494 | − | 0.860231i | 1.21066 | − | 0.0459813i | ||||
\(351\) | −2.67723 | −0.142900 | ||||||||
\(352\) | −5.70586 | − | 17.5608i | −0.304123 | − | 0.935996i | ||||
\(353\) | 3.92772 | − | 2.85366i | 0.209052 | − | 0.151885i | −0.478333 | − | 0.878179i | \(-0.658759\pi\) |
0.687385 | + | 0.726294i | \(0.258759\pi\) | |||||||
\(354\) | −2.90425 | + | 2.11006i | −0.154359 | + | 0.112149i | ||||
\(355\) | −12.8036 | − | 3.89309i | −0.679547 | − | 0.206624i | ||||
\(356\) | −65.2218 | − | 47.3864i | −3.45675 | − | 2.51148i | ||||
\(357\) | 6.63289 | 0.351050 | ||||||||
\(358\) | −33.9702 | − | 24.6808i | −1.79538 | − | 1.30442i | ||||
\(359\) | 8.92780 | − | 27.4769i | 0.471191 | − | 1.45018i | −0.379835 | − | 0.925054i | \(-0.624019\pi\) |
0.851026 | − | 0.525123i | \(-0.175981\pi\) | |||||||
\(360\) | −18.5114 | − | 5.62861i | −0.975639 | − | 0.296654i | ||||
\(361\) | −5.44284 | − | 16.7513i | −0.286465 | − | 0.881649i | ||||
\(362\) | −0.168429 | + | 0.518371i | −0.00885242 | + | 0.0272450i | ||||
\(363\) | 3.03954 | − | 9.35474i | 0.159534 | − | 0.490996i | ||||
\(364\) | 7.28587 | + | 22.4236i | 0.381883 | + | 1.17532i | ||||
\(365\) | −4.22403 | + | 6.05220i | −0.221096 | + | 0.316787i | ||||
\(366\) | −6.04577 | + | 18.6070i | −0.316018 | + | 0.972602i | ||||
\(367\) | 11.8998 | + | 8.64570i | 0.621163 | + | 0.451302i | 0.853328 | − | 0.521375i | \(-0.174581\pi\) |
−0.232164 | + | 0.972677i | \(0.574581\pi\) | |||||||
\(368\) | −52.0465 | −2.71311 | ||||||||
\(369\) | 9.11070 | + | 6.61931i | 0.474284 | + | 0.344588i | ||||
\(370\) | −16.6014 | − | 21.9609i | −0.863064 | − | 1.14169i | ||||
\(371\) | 3.47846 | − | 2.52725i | 0.180592 | − | 0.131208i | ||||
\(372\) | −29.9980 | + | 21.7948i | −1.55532 | + | 1.13001i | ||||
\(373\) | −10.2096 | − | 31.4220i | −0.528635 | − | 1.62697i | −0.757013 | − | 0.653399i | \(-0.773342\pi\) |
0.228378 | − | 0.973572i | \(-0.426658\pi\) | |||||||
\(374\) | 11.3972 | 0.589337 | ||||||||
\(375\) | 6.04621 | − | 9.40443i | 0.312225 | − | 0.485643i | ||||
\(376\) | 16.5945 | 0.855797 | ||||||||
\(377\) | 4.92742 | + | 15.1650i | 0.253775 | + | 0.781039i | ||||
\(378\) | −3.66740 | + | 2.66452i | −0.188631 | + | 0.137048i | ||||
\(379\) | 12.2612 | − | 8.90826i | 0.629814 | − | 0.457587i | −0.226522 | − | 0.974006i | \(-0.572735\pi\) |
0.856336 | + | 0.516419i | \(0.172735\pi\) | |||||||
\(380\) | 8.28880 | + | 10.9647i | 0.425207 | + | 0.562478i | ||||
\(381\) | −16.3714 | − | 11.8945i | −0.838733 | − | 0.609375i | ||||
\(382\) | 21.2807 | 1.08882 | ||||||||
\(383\) | 6.47870 | + | 4.70705i | 0.331046 | + | 0.240519i | 0.740874 | − | 0.671644i | \(-0.234411\pi\) |
−0.409828 | + | 0.912163i | \(0.634411\pi\) | |||||||
\(384\) | 6.33615 | − | 19.5007i | 0.323340 | − | 0.995139i | ||||
\(385\) | 2.32917 | − | 3.33724i | 0.118706 | − | 0.170081i | ||||
\(386\) | 13.6399 | + | 41.9793i | 0.694253 | + | 2.13669i | ||||
\(387\) | 0.799078 | − | 2.45931i | 0.0406194 | − | 0.125014i | ||||
\(388\) | 17.3705 | − | 53.4609i | 0.881854 | − | 2.71407i | ||||
\(389\) | 0.332078 | + | 1.02203i | 0.0168370 | + | 0.0518191i | 0.959122 | − | 0.282993i | \(-0.0913272\pi\) |
−0.942285 | + | 0.334812i | \(0.891327\pi\) | |||||||
\(390\) | 15.3902 | + | 4.67956i | 0.779313 | + | 0.236959i | ||||
\(391\) | 4.93629 | − | 15.1923i | 0.249639 | − | 0.768309i | ||||
\(392\) | −29.0783 | − | 21.1266i | −1.46868 | − | 1.06706i | ||||
\(393\) | 3.05011 | 0.153858 | ||||||||
\(394\) | −37.2532 | − | 27.0660i | −1.87679 | − | 1.36357i | ||||
\(395\) | −8.56607 | − | 2.60461i | −0.431006 | − | 0.131052i | ||||
\(396\) | −4.55609 | + | 3.31019i | −0.228952 | + | 0.166344i | ||||
\(397\) | 19.5894 | − | 14.2326i | 0.983166 | − | 0.714312i | 0.0247517 | − | 0.999694i | \(-0.492120\pi\) |
0.958414 | + | 0.285382i | \(0.0921205\pi\) | |||||||
\(398\) | 1.67603 | + | 5.15828i | 0.0840116 | + | 0.258561i | ||||
\(399\) | 1.98657 | 0.0994529 | ||||||||
\(400\) | 53.2093 | + | 35.6540i | 2.66046 | + | 1.78270i | ||||
\(401\) | −1.99317 | −0.0995340 | −0.0497670 | − | 0.998761i | \(-0.515848\pi\) | ||||
−0.0497670 | + | 0.998761i | \(0.515848\pi\) | |||||||
\(402\) | 10.3336 | + | 31.8037i | 0.515395 | + | 1.58622i | ||||
\(403\) | 15.3848 | − | 11.1777i | 0.766371 | − | 0.556801i | ||||
\(404\) | 57.2899 | − | 41.6235i | 2.85028 | − | 2.07085i | ||||
\(405\) | 0.0424402 | + | 2.23567i | 0.00210887 | + | 0.111091i | ||||
\(406\) | 21.8428 | + | 15.8698i | 1.08404 | + | 0.787603i | ||||
\(407\) | −4.94300 | −0.245015 | ||||||||
\(408\) | 27.5227 | + | 19.9964i | 1.36258 | + | 0.989971i | ||||
\(409\) | 2.05953 | − | 6.33858i | 0.101837 | − | 0.313423i | −0.887138 | − | 0.461504i | \(-0.847310\pi\) |
0.988975 | + | 0.148082i | \(0.0473098\pi\) | |||||||
\(410\) | −40.8033 | − | 53.9761i | −2.01513 | − | 2.66569i | ||||
\(411\) | 6.33795 | + | 19.5062i | 0.312628 | + | 0.962169i | ||||
\(412\) | 2.20843 | − | 6.79686i | 0.108802 | − | 0.334857i | ||||
\(413\) | 0.696484 | − | 2.14356i | 0.0342717 | − | 0.105477i | ||||
\(414\) | 3.37363 | + | 10.3830i | 0.165805 | + | 0.510295i | ||||
\(415\) | 0.376649 | + | 19.8411i | 0.0184890 | + | 0.973962i | ||||
\(416\) | −14.1599 | + | 43.5796i | −0.694245 | + | 2.13667i | ||||
\(417\) | 14.8199 | + | 10.7673i | 0.725732 | + | 0.527275i | ||||
\(418\) | 3.41351 | 0.166960 | ||||||||
\(419\) | −17.2758 | − | 12.5516i | −0.843977 | − | 0.613185i | 0.0795021 | − | 0.996835i | \(-0.474667\pi\) |
−0.923479 | + | 0.383650i | \(0.874667\pi\) | |||||||
\(420\) | 18.6097 | − | 6.43964i | 0.908059 | − | 0.314222i | ||||
\(421\) | −18.0708 | + | 13.1292i | −0.880717 | + | 0.639878i | −0.933441 | − | 0.358731i | \(-0.883210\pi\) |
0.0527243 | + | 0.998609i | \(0.483210\pi\) | |||||||
\(422\) | −51.7842 | + | 37.6235i | −2.52082 | + | 1.83148i | ||||
\(423\) | −0.592639 | − | 1.82396i | −0.0288151 | − | 0.0886838i | ||||
\(424\) | 22.0526 | 1.07097 | ||||||||
\(425\) | −15.4539 | + | 12.1502i | −0.749626 | + | 0.589369i | ||||
\(426\) | −16.0814 | −0.779147 | ||||||||
\(427\) | −3.79580 | − | 11.6823i | −0.183692 | − | 0.565344i | ||||
\(428\) | −46.5042 | + | 33.7873i | −2.24786 | + | 1.63317i | ||||
\(429\) | 2.33664 | − | 1.69767i | 0.112814 | − | 0.0819642i | ||||
\(430\) | −8.89219 | + | 12.7407i | −0.428819 | + | 0.614413i | ||||
\(431\) | 24.6046 | + | 17.8763i | 1.18516 | + | 0.861070i | 0.992744 | − | 0.120244i | \(-0.0383677\pi\) |
0.192416 | + | 0.981313i | \(0.438368\pi\) | |||||||
\(432\) | −12.8101 | −0.616324 | ||||||||
\(433\) | −0.466511 | − | 0.338940i | −0.0224191 | − | 0.0162884i | 0.576519 | − | 0.817084i | \(-0.304411\pi\) |
−0.598938 | + | 0.800795i | \(0.704411\pi\) | |||||||
\(434\) | 9.95017 | − | 30.6235i | 0.477624 | − | 1.46997i | ||||
\(435\) | 12.5857 | − | 4.35512i | 0.603438 | − | 0.208812i | ||||
\(436\) | 5.56352 | + | 17.1227i | 0.266444 | + | 0.820031i | ||||
\(437\) | 1.47843 | − | 4.55015i | 0.0707230 | − | 0.217663i | ||||
\(438\) | −2.74067 | + | 8.43491i | −0.130954 | + | 0.403036i | ||||
\(439\) | 3.95681 | + | 12.1778i | 0.188848 | + | 0.581215i | 0.999993 | − | 0.00363006i | \(-0.00115549\pi\) |
−0.811145 | + | 0.584845i | \(0.801155\pi\) | |||||||
\(440\) | 19.7256 | − | 6.82580i | 0.940383 | − | 0.325407i | ||||
\(441\) | −1.28362 | + | 3.95058i | −0.0611249 | + | 0.188123i | ||||
\(442\) | −22.8821 | − | 16.6248i | −1.08839 | − | 0.790761i | ||||
\(443\) | 14.3147 | 0.680110 | 0.340055 | − | 0.940405i | \(-0.389554\pi\) | ||||
0.340055 | + | 0.940405i | \(0.389554\pi\) | |||||||
\(444\) | −19.3503 | − | 14.0588i | −0.918323 | − | 0.667200i | ||||
\(445\) | 19.7640 | − | 28.3180i | 0.936906 | − | 1.34240i | ||||
\(446\) | 28.5019 | − | 20.7078i | 1.34960 | − | 0.980545i | ||||
\(447\) | 0.571116 | − | 0.414940i | 0.0270128 | − | 0.0196260i | ||||
\(448\) | 10.6194 | + | 32.6833i | 0.501721 | + | 1.54414i | ||||
\(449\) | −11.9663 | −0.564724 | −0.282362 | − | 0.959308i | \(-0.591118\pi\) | ||||
−0.282362 | + | 0.959308i | \(0.591118\pi\) | |||||||
\(450\) | 3.66377 | − | 12.9260i | 0.172712 | − | 0.609338i | ||||
\(451\) | −12.1490 | −0.572076 | ||||||||
\(452\) | 9.76257 | + | 30.0461i | 0.459193 | + | 1.41325i | ||||
\(453\) | 5.69983 | − | 4.14117i | 0.267802 | − | 0.194569i | ||||
\(454\) | −57.1306 | + | 41.5078i | −2.68127 | + | 1.94806i | ||||
\(455\) | −9.54417 | + | 3.30264i | −0.447438 | + | 0.154830i | ||||
\(456\) | 8.24313 | + | 5.98899i | 0.386020 | + | 0.280460i | ||||
\(457\) | −8.22154 | −0.384587 | −0.192294 | − | 0.981337i | \(-0.561593\pi\) | ||||
−0.192294 | + | 0.981337i | \(0.561593\pi\) | |||||||
\(458\) | 4.33913 | + | 3.15257i | 0.202754 | + | 0.147310i | ||||
\(459\) | 1.21495 | − | 3.73924i | 0.0567091 | − | 0.174533i | ||||
\(460\) | −0.900131 | − | 47.4171i | −0.0419688 | − | 2.21083i | ||||
\(461\) | 0.393120 | + | 1.20990i | 0.0183094 | + | 0.0563506i | 0.959794 | − | 0.280706i | \(-0.0905686\pi\) |
−0.941484 | + | 0.337057i | \(0.890569\pi\) | |||||||
\(462\) | 1.51123 | − | 4.65109i | 0.0703088 | − | 0.216388i | ||||
\(463\) | 10.0976 | − | 31.0771i | 0.469273 | − | 1.44428i | −0.384254 | − | 0.923227i | \(-0.625541\pi\) |
0.853527 | − | 0.521048i | \(-0.174459\pi\) | |||||||
\(464\) | 23.5768 | + | 72.5618i | 1.09452 | + | 3.36860i | ||||
\(465\) | −9.57800 | − | 12.6701i | −0.444169 | − | 0.587563i | ||||
\(466\) | 0.436385 | − | 1.34305i | 0.0202151 | − | 0.0622158i | ||||
\(467\) | −11.6779 | − | 8.48450i | −0.540389 | − | 0.392616i | 0.283840 | − | 0.958872i | \(-0.408391\pi\) |
−0.824230 | + | 0.566256i | \(0.808391\pi\) | |||||||
\(468\) | 13.9757 | 0.646026 | ||||||||
\(469\) | −16.9856 | − | 12.3407i | −0.784321 | − | 0.569843i | ||||
\(470\) | 0.218706 | + | 11.5210i | 0.0100881 | + | 0.531423i | ||||
\(471\) | −4.14929 | + | 3.01464i | −0.191189 | + | 0.138907i | ||||
\(472\) | 9.35227 | − | 6.79482i | 0.430473 | − | 0.312757i | ||||
\(473\) | 0.862060 | + | 2.65315i | 0.0396375 | + | 0.121992i | ||||
\(474\) | −10.7590 | −0.494178 | ||||||||
\(475\) | −4.62850 | + | 3.63901i | −0.212370 | + | 0.166969i | ||||
\(476\) | −34.6250 | −1.58703 | ||||||||
\(477\) | −0.787563 | − | 2.42387i | −0.0360600 | − | 0.110981i | ||||
\(478\) | −15.2382 | + | 11.0712i | −0.696977 | + | 0.506383i | ||||
\(479\) | 13.6415 | − | 9.91113i | 0.623296 | − | 0.452851i | −0.230775 | − | 0.973007i | \(-0.574126\pi\) |
0.854071 | + | 0.520156i | \(0.174126\pi\) | |||||||
\(480\) | 36.6163 | + | 11.1336i | 1.67130 | + | 0.508176i | ||||
\(481\) | 9.92398 | + | 7.21020i | 0.452495 | + | 0.328757i | ||||
\(482\) | −6.22196 | −0.283403 | ||||||||
\(483\) | −5.54529 | − | 4.02889i | −0.252320 | − | 0.183321i | ||||
\(484\) | −15.8670 | + | 48.8336i | −0.721227 | + | 2.21971i | ||||
\(485\) | 23.0371 | + | 7.00467i | 1.04606 | + | 0.318066i | ||||
\(486\) | 0.830342 | + | 2.55553i | 0.0376651 | + | 0.115921i | ||||
\(487\) | 12.3061 | − | 37.8744i | 0.557644 | − | 1.71625i | −0.131212 | − | 0.991354i | \(-0.541887\pi\) |
0.688856 | − | 0.724898i | \(-0.258113\pi\) | |||||||
\(488\) | 19.4686 | − | 59.9181i | 0.881301 | − | 2.71236i | ||||
\(489\) | 7.49715 | + | 23.0739i | 0.339033 | + | 1.04344i | ||||
\(490\) | 14.2842 | − | 20.4665i | 0.645295 | − | 0.924580i | ||||
\(491\) | 4.33411 | − | 13.3390i | 0.195596 | − | 0.601981i | −0.804374 | − | 0.594124i | \(-0.797499\pi\) |
0.999969 | − | 0.00785739i | \(-0.00250111\pi\) | |||||||
\(492\) | −47.5596 | − | 34.5541i | −2.14415 | − | 1.55782i | ||||
\(493\) | −23.4168 | −1.05464 | ||||||||
\(494\) | −6.85324 | − | 4.97917i | −0.308342 | − | 0.224024i | ||||
\(495\) | −1.45471 | − | 1.92434i | −0.0653842 | − | 0.0864925i | ||||
\(496\) | 73.6133 | − | 53.4832i | 3.30534 | − | 2.40147i | ||||
\(497\) | 8.16834 | − | 5.93464i | 0.366400 | − | 0.266205i | ||||
\(498\) | 7.36913 | + | 22.6799i | 0.330219 | + | 1.01631i | ||||
\(499\) | 15.2315 | 0.681857 | 0.340929 | − | 0.940089i | \(-0.389259\pi\) | ||||
0.340929 | + | 0.940089i | \(0.389259\pi\) | |||||||
\(500\) | −31.5624 | + | 49.0930i | −1.41151 | + | 2.19550i | ||||
\(501\) | −4.54890 | −0.203230 | ||||||||
\(502\) | 5.13055 | + | 15.7902i | 0.228988 | + | 0.704752i | ||||
\(503\) | −19.2004 | + | 13.9499i | −0.856104 | + | 0.621996i | −0.926822 | − | 0.375501i | \(-0.877471\pi\) |
0.0707185 | + | 0.997496i | \(0.477471\pi\) | |||||||
\(504\) | 11.8097 | − | 8.58028i | 0.526048 | − | 0.382196i | ||||
\(505\) | 18.2920 | + | 24.1973i | 0.813982 | + | 1.07676i | ||||
\(506\) | −9.52843 | − | 6.92281i | −0.423590 | − | 0.307756i | ||||
\(507\) | 5.83243 | 0.259027 | ||||||||
\(508\) | 85.4620 | + | 62.0918i | 3.79176 | + | 2.75488i | ||||
\(509\) | −3.86570 | + | 11.8974i | −0.171344 | + | 0.527343i | −0.999448 | − | 0.0332320i | \(-0.989420\pi\) |
0.828103 | + | 0.560575i | \(0.189420\pi\) | |||||||
\(510\) | −13.5201 | + | 19.3716i | −0.598678 | + | 0.857787i | ||||
\(511\) | −1.72071 | − | 5.29581i | −0.0761198 | − | 0.234273i | ||||
\(512\) | 0.752345 | − | 2.31548i | 0.0332493 | − | 0.102331i | ||||
\(513\) | 0.363882 | − | 1.11991i | 0.0160658 | − | 0.0494454i | ||||
\(514\) | −10.9803 | − | 33.7940i | −0.484321 | − | 1.49059i | ||||
\(515\) | 2.92886 | + | 0.890552i | 0.129061 | + | 0.0392424i | ||||
\(516\) | −4.17134 | + | 12.8381i | −0.183633 | + | 0.565165i | ||||
\(517\) | 1.67384 | + | 1.21612i | 0.0736154 | + | 0.0534847i | ||||
\(518\) | 20.7703 | 0.912595 | ||||||||
\(519\) | −2.16597 | − | 1.57367i | −0.0950755 | − | 0.0690764i | ||||
\(520\) | −49.5594 | − | 15.0691i | −2.17333 | − | 0.660823i | ||||
\(521\) | 22.6232 | − | 16.4367i | 0.991141 | − | 0.720106i | 0.0309702 | − | 0.999520i | \(-0.490140\pi\) |
0.960171 | + | 0.279414i | \(0.0901403\pi\) | |||||||
\(522\) | 12.9474 | − | 9.40685i | 0.566693 | − | 0.411727i | ||||
\(523\) | 4.85196 | + | 14.9328i | 0.212162 | + | 0.652966i | 0.999343 | + | 0.0362446i | \(0.0115395\pi\) |
−0.787181 | + | 0.616722i | \(0.788460\pi\) | |||||||
\(524\) | −15.9222 | −0.695564 | ||||||||
\(525\) | 2.90922 | + | 7.91765i | 0.126969 | + | 0.345555i | ||||
\(526\) | 18.7460 | 0.817362 | ||||||||
\(527\) | 8.62993 | + | 26.5602i | 0.375926 | + | 1.15698i | ||||
\(528\) | 11.1804 | − | 8.12302i | 0.486564 | − | 0.353509i | ||||
\(529\) | 5.25252 | − | 3.81618i | 0.228370 | − | 0.165921i | ||||
\(530\) | 0.290640 | + | 15.3103i | 0.0126246 | + | 0.665038i | ||||
\(531\) | −1.08084 | − | 0.785274i | −0.0469043 | − | 0.0340780i | ||||
\(532\) | −10.3703 | −0.449609 | ||||||||
\(533\) | 24.3915 | + | 17.7214i | 1.05651 | + | 0.767601i | ||||
\(534\) | 12.8235 | − | 39.4666i | 0.554926 | − | 1.70789i | ||||
\(535\) | −14.8482 | − | 19.6418i | −0.641945 | − | 0.849187i | ||||
\(536\) | −33.2764 | − | 102.414i | −1.43732 | − | 4.42362i | ||||
\(537\) | 4.82890 | − | 14.8618i | 0.208382 | − | 0.641335i | ||||
\(538\) | −19.6956 | + | 60.6168i | −0.849137 | + | 2.61338i | ||||
\(539\) | −1.38479 | − | 4.26196i | −0.0596473 | − | 0.183576i | ||||
\(540\) | −0.221546 | − | 11.6706i | −0.00953383 | − | 0.502223i | ||||
\(541\) | −7.40971 | + | 22.8048i | −0.318569 | + | 0.980453i | 0.655692 | + | 0.755028i | \(0.272377\pi\) |
−0.974261 | + | 0.225425i | \(0.927623\pi\) | |||||||
\(542\) | 63.0224 | + | 45.7885i | 2.70705 | + | 1.96678i | ||||
\(543\) | −0.202843 | −0.00870482 | ||||||||
\(544\) | −54.4409 | − | 39.5536i | −2.33413 | − | 1.69585i | ||||
\(545\) | −7.28796 | + | 2.52191i | −0.312182 | + | 0.108027i | ||||
\(546\) | −9.81848 | + | 7.13354i | −0.420192 | + | 0.305287i | ||||
\(547\) | 4.55219 | − | 3.30736i | 0.194637 | − | 0.141412i | −0.486198 | − | 0.873848i | \(-0.661617\pi\) |
0.680836 | + | 0.732436i | \(0.261617\pi\) | |||||||
\(548\) | −33.0853 | − | 101.826i | −1.41333 | − | 4.34980i | ||||
\(549\) | −7.28106 | −0.310748 | ||||||||
\(550\) | 4.99888 | + | 13.6048i | 0.213153 | + | 0.580112i | ||||
\(551\) | −7.01341 | −0.298781 | ||||||||
\(552\) | −10.8638 | − | 33.4352i | −0.462392 | − | 1.42310i | ||||
\(553\) | 5.46490 | − | 3.97048i | 0.232391 | − | 0.168842i | ||||
\(554\) | −18.6663 | + | 13.5618i | −0.793053 | + | 0.576187i | ||||
\(555\) | 5.86367 | − | 8.40148i | 0.248899 | − | 0.356623i | ||||
\(556\) | −77.3626 | − | 56.2072i | −3.28090 | − | 2.38372i | ||||
\(557\) | −42.4247 | −1.79759 | −0.898796 | − | 0.438366i | \(-0.855557\pi\) | ||||
−0.898796 | + | 0.438366i | \(0.855557\pi\) | |||||||
\(558\) | −15.4412 | − | 11.2187i | −0.653677 | − | 0.474924i | ||||
\(559\) | 2.13932 | − | 6.58414i | 0.0904835 | − | 0.278480i | ||||
\(560\) | −45.6670 | + | 15.8025i | −1.92978 | + | 0.667778i | ||||
\(561\) | 1.31071 | + | 4.03396i | 0.0553383 | + | 0.170314i | ||||
\(562\) | −14.2538 | + | 43.8686i | −0.601259 | + | 1.85048i | ||||
\(563\) | 1.78796 | − | 5.50279i | 0.0753537 | − | 0.231915i | −0.906284 | − | 0.422669i | \(-0.861093\pi\) |
0.981638 | + | 0.190754i | \(0.0610933\pi\) | |||||||
\(564\) | 3.09369 | + | 9.52141i | 0.130268 | + | 0.400924i | ||||
\(565\) | −12.7885 | + | 4.42531i | −0.538018 | + | 0.186174i | ||||
\(566\) | 7.98793 | − | 24.5843i | 0.335758 | − | 1.03336i | ||||
\(567\) | −1.36485 | − | 0.991619i | −0.0573181 | − | 0.0416441i | ||||
\(568\) | 51.7853 | 2.17286 | ||||||||
\(569\) | 17.8029 | + | 12.9346i | 0.746336 | + | 0.542245i | 0.894689 | − | 0.446690i | \(-0.147397\pi\) |
−0.148353 | + | 0.988934i | \(0.547397\pi\) | |||||||
\(570\) | −4.04930 | + | 5.80184i | −0.169606 | + | 0.243012i | ||||
\(571\) | −27.1946 | + | 19.7580i | −1.13806 | + | 0.826847i | −0.986847 | − | 0.161654i | \(-0.948317\pi\) |
−0.151210 | + | 0.988502i | \(0.548317\pi\) | |||||||
\(572\) | −12.1977 | + | 8.86216i | −0.510012 | + | 0.370546i | ||||
\(573\) | 2.44734 | + | 7.53213i | 0.102239 | + | 0.314659i | ||||
\(574\) | 51.0499 | 2.13078 | ||||||||
\(575\) | 20.3001 | − | 0.771002i | 0.846572 | − | 0.0321530i | ||||
\(576\) | 20.3701 | 0.848754 | ||||||||
\(577\) | 12.4333 | + | 38.2658i | 0.517605 | + | 1.59303i | 0.778491 | + | 0.627656i | \(0.215985\pi\) |
−0.260886 | + | 0.965370i | \(0.584015\pi\) | |||||||
\(578\) | −3.35205 | + | 2.43541i | −0.139427 | + | 0.101300i | ||||
\(579\) | −13.2896 | + | 9.65547i | −0.552297 | + | 0.401268i | ||||
\(580\) | −65.6998 | + | 22.7346i | −2.72803 | + | 0.944002i | ||||
\(581\) | −12.1128 | − | 8.80043i | −0.502522 | − | 0.365103i | ||||
\(582\) | 28.9346 | 1.19938 | ||||||||
\(583\) | 2.22438 | + | 1.61611i | 0.0921243 | + | 0.0669323i | ||||
\(584\) | 8.82549 | − | 27.1621i | 0.365201 | − | 1.12397i | ||||
\(585\) | 0.113622 | + | 5.98540i | 0.00469771 | + | 0.247466i | ||||
\(586\) | −13.9665 | − | 42.9846i | −0.576952 | − | 1.77568i | ||||
\(587\) | −0.872353 | + | 2.68483i | −0.0360059 | + | 0.110815i | −0.967444 | − | 0.253085i | \(-0.918555\pi\) |
0.931438 | + | 0.363899i | \(0.118555\pi\) | |||||||
\(588\) | 6.70076 | − | 20.6228i | 0.276335 | − | 0.850471i | ||||
\(589\) | 2.58469 | + | 7.95485i | 0.106500 | + | 0.327774i | ||||
\(590\) | 4.84066 | + | 6.40339i | 0.199287 | + | 0.263623i | ||||
\(591\) | 5.29558 | − | 16.2981i | 0.217831 | − | 0.670415i | ||||
\(592\) | 47.4844 | + | 34.4994i | 1.95160 | + | 1.41792i | ||||
\(593\) | −24.6805 | −1.01351 | −0.506754 | − | 0.862091i | \(-0.669155\pi\) | ||||
−0.506754 | + | 0.862091i | \(0.669155\pi\) | |||||||
\(594\) | −2.34520 | − | 1.70389i | −0.0962248 | − | 0.0699114i | ||||
\(595\) | −0.281501 | − | 14.8289i | −0.0115404 | − | 0.607927i | ||||
\(596\) | −2.98134 | + | 2.16607i | −0.122120 | + | 0.0887256i | ||||
\(597\) | −1.63298 | + | 1.18643i | −0.0668335 | + | 0.0485574i | ||||
\(598\) | 9.03200 | + | 27.7976i | 0.369346 | + | 1.13673i | ||||
\(599\) | −7.71547 | −0.315245 | −0.157623 | − | 0.987499i | \(-0.550383\pi\) | ||||
−0.157623 | + | 0.987499i | \(0.550383\pi\) | |||||||
\(600\) | −11.7981 | + | 41.6243i | −0.481654 | + | 1.69930i | ||||
\(601\) | 22.6506 | 0.923938 | 0.461969 | − | 0.886896i | \(-0.347143\pi\) | ||||
0.461969 | + | 0.886896i | \(0.347143\pi\) | |||||||
\(602\) | −3.62234 | − | 11.1484i | −0.147636 | − | 0.454376i | ||||
\(603\) | −10.0683 | + | 7.31502i | −0.410011 | + | 0.297891i | ||||
\(604\) | −29.7543 | + | 21.6177i | −1.21068 | + | 0.879613i | ||||
\(605\) | −21.0431 | − | 6.39837i | −0.855522 | − | 0.260131i | ||||
\(606\) | 29.4894 | + | 21.4253i | 1.19792 | + | 0.870343i | ||||
\(607\) | −24.6423 | −1.00020 | −0.500099 | − | 0.865968i | \(-0.666703\pi\) | ||||
−0.500099 | + | 0.865968i | \(0.666703\pi\) | |||||||
\(608\) | −16.3052 | − | 11.8464i | −0.661264 | − | 0.480436i | ||||
\(609\) | −3.10498 | + | 9.55616i | −0.125820 | + | 0.387235i | ||||
\(610\) | 41.8555 | + | 12.7266i | 1.69468 | + | 0.515286i | ||||
\(611\) | −1.58663 | − | 4.88315i | −0.0641883 | − | 0.197551i | ||||
\(612\) | −6.34229 | + | 19.5196i | −0.256372 | + | 0.789031i | ||||
\(613\) | −12.9180 | + | 39.7574i | −0.521751 | + | 1.60579i | 0.248901 | + | 0.968529i | \(0.419931\pi\) |
−0.770652 | + | 0.637256i | \(0.780069\pi\) | |||||||
\(614\) | −9.40045 | − | 28.9316i | −0.379371 | − | 1.16758i | ||||
\(615\) | 14.4119 | − | 20.6494i | 0.581144 | − | 0.832664i | ||||
\(616\) | −4.86646 | + | 14.9774i | −0.196075 | + | 0.603458i | ||||
\(617\) | −12.8949 | − | 9.36871i | −0.519130 | − | 0.377170i | 0.297146 | − | 0.954832i | \(-0.403965\pi\) |
−0.816276 | + | 0.577662i | \(0.803965\pi\) | |||||||
\(618\) | 3.67866 | 0.147977 | ||||||||
\(619\) | 38.1613 | + | 27.7258i | 1.53383 | + | 1.11440i | 0.954059 | + | 0.299619i | \(0.0968595\pi\) |
0.579775 | + | 0.814777i | \(0.303141\pi\) | |||||||
\(620\) | 49.9990 | + | 66.1405i | 2.00801 | + | 2.65627i | ||||
\(621\) | −3.28699 | + | 2.38814i | −0.131902 | + | 0.0958327i | ||||
\(622\) | 40.3544 | − | 29.3192i | 1.61806 | − | 1.17559i | ||||
\(623\) | 8.05113 | + | 24.7788i | 0.322562 | + | 0.992743i | ||||
\(624\) | −34.2955 | −1.37292 | ||||||||
\(625\) | −21.2818 | − | 13.1182i | −0.851270 | − | 0.524727i | ||||
\(626\) | 26.0630 | 1.04169 | ||||||||
\(627\) | 0.392562 | + | 1.20818i | 0.0156774 | + | 0.0482501i | ||||
\(628\) | 21.6601 | − | 15.7370i | 0.864332 | − | 0.627974i | ||||
\(629\) | −14.5739 | + | 10.5886i | −0.581101 | + | 0.422195i | ||||
\(630\) | 6.11262 | + | 8.08599i | 0.243533 | + | 0.322154i | ||||
\(631\) | −26.1825 | − | 19.0227i | −1.04231 | − | 0.757282i | −0.0715741 | − | 0.997435i | \(-0.522802\pi\) |
−0.970735 | + | 0.240153i | \(0.922802\pi\) | |||||||
\(632\) | 34.6462 | 1.37815 | ||||||||
\(633\) | −19.2718 | − | 14.0018i | −0.765987 | − | 0.556522i | ||||
\(634\) | −6.20802 | + | 19.1063i | −0.246552 | + | 0.758809i | ||||
\(635\) | −25.8974 | + | 37.1058i | −1.02771 | + | 1.47250i | ||||
\(636\) | 4.11123 | + | 12.6531i | 0.163021 | + | 0.501727i | ||||
\(637\) | −3.43656 | + | 10.5766i | −0.136161 | + | 0.419061i | ||||
\(638\) | −5.33526 | + | 16.4203i | −0.211225 | + | 0.650084i | ||||
\(639\) | −1.84941 | − | 5.69189i | −0.0731614 | − | 0.225168i | ||||
\(640\) | −43.8658 | − | 13.3379i | −1.73395 | − | 0.527226i | ||||
\(641\) | 5.56360 | − | 17.1230i | 0.219749 | − | 0.676317i | −0.779033 | − | 0.626982i | \(-0.784290\pi\) |
0.998782 | − | 0.0493350i | \(-0.0157102\pi\) | |||||||
\(642\) | −23.9376 | − | 17.3916i | −0.944740 | − | 0.686394i | ||||
\(643\) | 21.8891 | 0.863224 | 0.431612 | − | 0.902059i | \(-0.357945\pi\) | ||||
0.431612 | + | 0.902059i | \(0.357945\pi\) | |||||||
\(644\) | 28.9475 | + | 21.0316i | 1.14069 | + | 0.828761i | ||||
\(645\) | −5.53211 | − | 1.68210i | −0.217826 | − | 0.0662325i | ||||
\(646\) | 10.0644 | − | 7.31220i | 0.395978 | − | 0.287695i | ||||
\(647\) | −15.3926 | + | 11.1834i | −0.605147 | + | 0.439665i | −0.847702 | − | 0.530473i | \(-0.822015\pi\) |
0.242555 | + | 0.970138i | \(0.422015\pi\) | |||||||
\(648\) | −2.67386 | − | 8.22930i | −0.105039 | − | 0.323278i | ||||
\(649\) | 1.44129 | 0.0565755 | ||||||||
\(650\) | 9.80876 | − | 34.6059i | 0.384731 | − | 1.35736i | ||||
\(651\) | 11.9832 | 0.469660 | ||||||||
\(652\) | −39.1366 | − | 120.450i | −1.53271 | − | 4.71719i | ||||
\(653\) | 1.87669 | − | 1.36349i | 0.0734405 | − | 0.0533576i | −0.550459 | − | 0.834862i | \(-0.685547\pi\) |
0.623900 | + | 0.781504i | \(0.285547\pi\) | |||||||
\(654\) | −7.49743 | + | 5.44720i | −0.293173 | + | 0.213002i | ||||
\(655\) | −0.129447 | − | 6.81903i | −0.00505793 | − | 0.266442i | ||||
\(656\) | 116.709 | + | 84.7937i | 4.55670 | + | 3.31064i | ||||
\(657\) | −3.30065 | −0.128771 | ||||||||
\(658\) | −7.03341 | − | 5.11007i | −0.274191 | − | 0.199211i | ||||
\(659\) | 2.22239 | − | 6.83980i | 0.0865719 | − | 0.266441i | −0.898394 | − | 0.439191i | \(-0.855265\pi\) |
0.984966 | + | 0.172750i | \(0.0552652\pi\) | |||||||
\(660\) | 7.59385 | + | 10.0454i | 0.295590 | + | 0.391017i | ||||
\(661\) | 13.2943 | + | 40.9158i | 0.517090 | + | 1.59144i | 0.779447 | + | 0.626468i | \(0.215500\pi\) |
−0.262358 | + | 0.964971i | \(0.584500\pi\) | |||||||
\(662\) | 20.9719 | − | 64.5450i | 0.815098 | − | 2.50861i | ||||
\(663\) | 3.25271 | − | 10.0108i | 0.126325 | − | 0.388788i | ||||
\(664\) | −23.7300 | − | 73.0336i | −0.920904 | − | 2.83425i | ||||
\(665\) | −0.0843105 | − | 4.44131i | −0.00326942 | − | 0.172226i | ||||
\(666\) | 3.80451 | − | 11.7091i | 0.147422 | − | 0.453718i | ||||
\(667\) | 19.5772 | + | 14.2236i | 0.758031 | + | 0.550742i | ||||
\(668\) | 23.7461 | 0.918765 | ||||||||
\(669\) | 10.6072 | + | 7.70656i | 0.410097 | + | 0.297953i | ||||
\(670\) | 70.6639 | − | 24.4523i | 2.72998 | − | 0.944676i | ||||
\(671\) | 6.35478 | − | 4.61702i | 0.245324 | − | 0.178238i | ||||
\(672\) | −23.3601 | + | 16.9721i | −0.901135 | + | 0.654713i | ||||
\(673\) | −9.20966 | − | 28.3444i | −0.355006 | − | 1.09260i | −0.956006 | − | 0.293348i | \(-0.905231\pi\) |
0.600999 | − | 0.799250i | \(-0.294769\pi\) | |||||||
\(674\) | 34.9961 | 1.34800 | ||||||||
\(675\) | 4.99640 | − | 0.189764i | 0.192311 | − | 0.00730403i | ||||
\(676\) | −30.4464 | −1.17102 | ||||||||
\(677\) | −8.26144 | − | 25.4261i | −0.317513 | − | 0.977204i | −0.974708 | − | 0.223483i | \(-0.928257\pi\) |
0.657195 | − | 0.753721i | \(-0.271743\pi\) | |||||||
\(678\) | −13.1561 | + | 9.55846i | −0.505257 | + | 0.367091i | ||||
\(679\) | −14.6969 | + | 10.6780i | −0.564017 | + | 0.409782i | ||||
\(680\) | 43.5372 | − | 62.3802i | 1.66958 | − | 2.39217i | ||||
\(681\) | −21.2615 | − | 15.4474i | −0.814743 | − | 0.591946i | ||||
\(682\) | 20.5907 | 0.788457 | ||||||||
\(683\) | −23.0529 | − | 16.7489i | −0.882096 | − | 0.640880i | 0.0517093 | − | 0.998662i | \(-0.483533\pi\) |
−0.933805 | + | 0.357782i | \(0.883533\pi\) | |||||||
\(684\) | −1.89953 | + | 5.84617i | −0.0726305 | + | 0.223534i | ||||
\(685\) | 43.3403 | − | 14.9974i | 1.65595 | − | 0.573020i | ||||
\(686\) | 15.6246 | + | 48.0876i | 0.596550 | + | 1.83599i | ||||
\(687\) | −0.616813 | + | 1.89835i | −0.0235329 | + | 0.0724267i | ||||
\(688\) | 10.2362 | − | 31.5039i | 0.390253 | − | 1.20107i | ||||
\(689\) | −2.10849 | − | 6.48926i | −0.0803270 | − | 0.247221i | ||||
\(690\) | 23.0697 | − | 7.98297i | 0.878248 | − | 0.303906i | ||||
\(691\) | 10.7065 | − | 32.9512i | 0.407294 | − | 1.25352i | −0.511671 | − | 0.859182i | \(-0.670973\pi\) |
0.918965 | − | 0.394340i | \(-0.129027\pi\) | |||||||
\(692\) | 11.3068 | + | 8.21486i | 0.429820 | + | 0.312282i | ||||
\(693\) | 1.82001 | 0.0691365 | ||||||||
\(694\) | −13.0464 | − | 9.47878i | −0.495235 | − | 0.359810i | ||||
\(695\) | 23.4430 | − | 33.5892i | 0.889245 | − | 1.27411i | ||||
\(696\) | −41.6932 | + | 30.2919i | −1.58038 | + | 1.14821i | ||||
\(697\) | −35.8203 | + | 26.0249i | −1.35679 | + | 0.985765i | ||||
\(698\) | 18.8640 | + | 58.0574i | 0.714012 | + | 2.19750i | ||||
\(699\) | 0.525548 | 0.0198781 | ||||||||
\(700\) | −15.1867 | − | 41.3317i | −0.574003 | − | 1.56219i | ||||
\(701\) | 0.973305 | 0.0367612 | 0.0183806 | − | 0.999831i | \(-0.494149\pi\) | ||||
0.0183806 | + | 0.999831i | \(0.494149\pi\) | |||||||
\(702\) | 2.22302 | + | 6.84175i | 0.0839024 | + | 0.258225i | ||||
\(703\) | −4.36494 | + | 3.17131i | −0.164627 | + | 0.119608i | ||||
\(704\) | −17.7786 | + | 12.9169i | −0.670058 | + | 0.486826i | ||||
\(705\) | −4.05260 | + | 1.40235i | −0.152630 | + | 0.0528156i | ||||
\(706\) | −10.5540 | − | 7.66790i | −0.397204 | − | 0.288585i | ||||
\(707\) | −22.8854 | −0.860696 | ||||||||
\(708\) | 5.64218 | + | 4.09928i | 0.212046 | + | 0.154061i | ||||
\(709\) | −3.49938 | + | 10.7700i | −0.131422 | + | 0.404475i | −0.995016 | − | 0.0997119i | \(-0.968208\pi\) |
0.863594 | + | 0.504187i | \(0.168208\pi\) | |||||||
\(710\) | 0.682499 | + | 35.9527i | 0.0256137 | + | 1.34928i | ||||
\(711\) | −1.23732 | − | 3.80807i | −0.0464030 | − | 0.142814i | ||||
\(712\) | −41.2941 | + | 127.090i | −1.54756 | + | 4.76290i | ||||
\(713\) | 8.91808 | − | 27.4470i | 0.333985 | − | 1.02790i | ||||
\(714\) | −5.50757 | − | 16.9505i | −0.206115 | − | 0.634358i | ||||
\(715\) | −3.89459 | − | 5.15190i | −0.145649 | − | 0.192670i | ||||
\(716\) | −25.2078 | + | 77.5816i | −0.942060 | + | 2.89936i | ||||
\(717\) | −5.67098 | − | 4.12021i | −0.211787 | − | 0.153872i | ||||
\(718\) | −77.6312 | −2.89717 | ||||||||
\(719\) | 24.8627 | + | 18.0638i | 0.927224 | + | 0.673667i | 0.945311 | − | 0.326169i | \(-0.105758\pi\) |
−0.0180878 | + | 0.999836i | \(0.505758\pi\) | |||||||
\(720\) | 0.543662 | + | 28.6390i | 0.0202611 | + | 1.06731i | ||||
\(721\) | −1.86852 | + | 1.35756i | −0.0695875 | + | 0.0505583i | ||||
\(722\) | −38.2891 | + | 27.8186i | −1.42497 | + | 1.03530i | ||||
\(723\) | −0.715542 | − | 2.20221i | −0.0266113 | − | 0.0819011i | ||||
\(724\) | 1.05888 | 0.0393529 | ||||||||
\(725\) | −10.2707 | − | 27.9526i | −0.381445 | − | 1.03813i | ||||
\(726\) | −26.4302 | −0.980915 | ||||||||
\(727\) | −2.02973 | − | 6.24688i | −0.0752787 | − | 0.231684i | 0.906336 | − | 0.422558i | \(-0.138868\pi\) |
−0.981615 | + | 0.190874i | \(0.938868\pi\) | |||||||
\(728\) | 31.6174 | − | 22.9714i | 1.17182 | − | 0.851377i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 18.9740 | + | 5.76924i | 0.702258 | + | 0.213529i | ||||
\(731\) | 8.22510 | + | 5.97589i | 0.304216 | + | 0.221026i | ||||
\(732\) | 38.0086 | 1.40484 | ||||||||
\(733\) | 25.8300 | + | 18.7666i | 0.954051 | + | 0.693159i | 0.951762 | − | 0.306838i | \(-0.0992711\pi\) |
0.00228977 | + | 0.999997i | \(0.499271\pi\) | |||||||
\(734\) | 12.2134 | − | 37.5891i | 0.450806 | − | 1.38744i | ||||
\(735\) | 8.88666 | + | 2.70209i | 0.327789 | + | 0.0996679i | ||||
\(736\) | 21.4889 | + | 66.1360i | 0.792091 | + | 2.43781i | ||||
\(737\) | 4.14885 | − | 12.7688i | 0.152825 | − | 0.470346i | ||||
\(738\) | 9.35085 | − | 28.7789i | 0.344209 | − | 1.05937i | ||||
\(739\) | −4.73017 | − | 14.5580i | −0.174002 | − | 0.535524i | 0.825584 | − | 0.564279i | \(-0.190846\pi\) |
−0.999586 | + | 0.0287550i | \(0.990846\pi\) | |||||||
\(740\) | −30.6095 | + | 43.8574i | −1.12523 | + | 1.61223i | ||||
\(741\) | 0.974196 | − | 2.99827i | 0.0357880 | − | 0.110144i | ||||
\(742\) | −9.34676 | − | 6.79082i | −0.343130 | − | 0.249299i | ||||
\(743\) | 16.5455 | 0.606995 | 0.303498 | − | 0.952832i | \(-0.401846\pi\) | ||||
0.303498 | + | 0.952832i | \(0.401846\pi\) | |||||||
\(744\) | 49.7236 | + | 36.1263i | 1.82295 | + | 1.32445i | ||||
\(745\) | −0.951905 | − | 1.25921i | −0.0348751 | − | 0.0461340i | ||||
\(746\) | −71.8225 | + | 52.1821i | −2.62961 | + | 1.91052i | ||||
\(747\) | −7.17988 | + | 5.21649i | −0.262698 | + | 0.190861i | ||||
\(748\) | −6.84217 | − | 21.0580i | −0.250175 | − | 0.769959i | ||||
\(749\) | 18.5769 | 0.678786 | ||||||||
\(750\) | −29.0537 | − | 7.64238i | −1.06089 | − | 0.279060i | ||||
\(751\) | 46.0279 | 1.67958 | 0.839791 | − | 0.542911i | \(-0.182678\pi\) | ||||
0.839791 | + | 0.542911i | \(0.182678\pi\) | |||||||
\(752\) | −7.59174 | − | 23.3650i | −0.276842 | − | 0.852033i | ||||
\(753\) | −4.99879 | + | 3.63184i | −0.182166 | + | 0.132351i | ||||
\(754\) | 34.6632 | − | 25.1843i | 1.26236 | − | 0.917159i | ||||
\(755\) | −9.50018 | − | 12.5672i | −0.345747 | − | 0.457366i | ||||
\(756\) | 7.12476 | + | 5.17644i | 0.259125 | + | 0.188265i | ||||
\(757\) | −26.5282 | −0.964184 | −0.482092 | − | 0.876121i | \(-0.660123\pi\) | ||||
−0.482092 | + | 0.876121i | \(0.660123\pi\) | |||||||
\(758\) | −32.9463 | − | 23.9369i | −1.19666 | − | 0.869427i | ||||
\(759\) | 1.35448 | − | 4.16865i | 0.0491644 | − | 0.151312i | ||||
\(760\) | 13.0395 | − | 18.6831i | 0.472994 | − | 0.677706i | ||||
\(761\) | −8.78353 | − | 27.0329i | −0.318403 | − | 0.979943i | −0.974331 | − | 0.225120i | \(-0.927723\pi\) |
0.655928 | − | 0.754823i | \(-0.272277\pi\) | |||||||
\(762\) | −16.8029 | + | 51.7141i | −0.608706 | + | 1.87341i | ||||
\(763\) | 1.79800 | − | 5.53366i | 0.0650918 | − | 0.200332i | ||||
\(764\) | −12.7756 | − | 39.3192i | −0.462204 | − | 1.42252i | ||||
\(765\) | −8.41125 | − | 2.55753i | −0.304109 | − | 0.0924678i | ||||
\(766\) | 6.64947 | − | 20.4650i | 0.240255 | − | 0.739429i | ||||
\(767\) | −2.89365 | − | 2.10236i | −0.104484 | − | 0.0759119i | ||||
\(768\) | −14.3555 | −0.518009 | ||||||||
\(769\) | 7.24841 | + | 5.26628i | 0.261384 | + | 0.189907i | 0.710757 | − | 0.703438i | \(-0.248353\pi\) |
−0.449373 | + | 0.893344i | \(0.648353\pi\) | |||||||
\(770\) | −10.4624 | − | 3.18121i | −0.377039 | − | 0.114643i | ||||
\(771\) | 10.6983 | − | 7.77279i | 0.385291 | − | 0.279930i | ||||
\(772\) | 69.3744 | − | 50.4034i | 2.49684 | − | 1.81406i | ||||
\(773\) | 7.13959 | + | 21.9734i | 0.256793 | + | 0.790329i | 0.993471 | + | 0.114085i | \(0.0363935\pi\) |
−0.736678 | + | 0.676244i | \(0.763607\pi\) | |||||||
\(774\) | −6.94834 | −0.249753 | ||||||||
\(775\) | −27.9197 | + | 21.9509i | −1.00290 | + | 0.788501i | ||||
\(776\) | −93.1752 | −3.34479 | ||||||||
\(777\) | 2.38864 | + | 7.35148i | 0.0856920 | + | 0.263733i | ||||
\(778\) | 2.33609 | − | 1.69727i | 0.0837530 | − | 0.0608501i | ||||
\(779\) | −10.7283 | + | 7.79455i | −0.384380 | + | 0.279269i | ||||
\(780\) | −0.593131 | − | 31.2449i | −0.0212375 | − | 1.11875i | ||||
\(781\) | 5.22343 | + | 3.79504i | 0.186909 | + | 0.135797i | ||||
\(782\) | −42.9232 | −1.53493 | ||||||||
\(783\) | 4.81846 | + | 3.50082i | 0.172198 | + | 0.125109i | ||||
\(784\) | −16.4433 | + | 50.6072i | −0.587260 | + | 1.80740i | ||||
\(785\) | 6.91581 | + | 9.14848i | 0.246836 | + | 0.326523i | ||||
\(786\) | −2.53264 | − | 7.79465i | −0.0903361 | − | 0.278026i | ||||
\(787\) | −0.628511 | + | 1.93436i | −0.0224040 | + | 0.0689524i | −0.961633 | − | 0.274338i | \(-0.911541\pi\) |
0.939229 | + | 0.343290i | \(0.111541\pi\) | |||||||
\(788\) | −27.6440 | + | 85.0794i | −0.984776 | + | 3.03083i | ||||
\(789\) | 2.15583 | + | 6.63498i | 0.0767497 | + | 0.236211i | ||||
\(790\) | 0.456615 | + | 24.0536i | 0.0162456 | + | 0.855788i | ||||
\(791\) | 3.15503 | − | 9.71018i | 0.112180 | − | 0.345254i | ||||
\(792\) | 7.55201 | + | 5.48686i | 0.268349 | + | 0.194967i | ||||
\(793\) | −19.4931 | −0.692220 | ||||||||
\(794\) | −52.6376 | − | 38.2435i | −1.86804 | − | 1.35721i | ||||
\(795\) | −5.38554 | + | 1.86360i | −0.191005 | + | 0.0660950i | ||||
\(796\) | 8.52449 | − | 6.19340i | 0.302142 | − | 0.219519i | ||||
\(797\) | 9.86379 | − | 7.16646i | 0.349393 | − | 0.253849i | −0.399221 | − | 0.916855i | \(-0.630719\pi\) |
0.748614 | + | 0.663006i | \(0.230719\pi\) | |||||||
\(798\) | −1.64953 | − | 5.07674i | −0.0583928 | − | 0.179715i | ||||
\(799\) | 7.54024 | 0.266754 | ||||||||
\(800\) | 23.3370 | − | 82.3343i | 0.825086 | − | 2.91096i | ||||
\(801\) | 15.4436 | 0.545673 | ||||||||
\(802\) | 1.65501 | + | 5.09359i | 0.0584404 | + | 0.179861i | ||||
\(803\) | 2.88075 | − | 2.09299i | 0.101659 | − | 0.0738599i | ||||
\(804\) | 52.5583 | − | 38.1858i | 1.85359 | − | 1.34671i | ||||
\(805\) | −8.77191 | + | 12.5684i | −0.309169 | + | 0.442978i | ||||
\(806\) | −41.3396 | − | 30.0350i | −1.45612 | − | 1.05794i | ||||
\(807\) | −23.7199 | −0.834979 | ||||||||
\(808\) | −94.9616 | − | 68.9936i | −3.34074 | − | 2.42719i | ||||
\(809\) | 2.72972 | − | 8.40121i | 0.0959718 | − | 0.295371i | −0.891534 | − | 0.452954i | \(-0.850370\pi\) |
0.987506 | + | 0.157583i | \(0.0503702\pi\) | |||||||
\(810\) | 5.67807 | − | 1.96482i | 0.199507 | − | 0.0690369i | ||||
\(811\) | −4.30102 | − | 13.2372i | −0.151029 | − | 0.464820i | 0.846708 | − | 0.532058i | \(-0.178581\pi\) |
−0.997737 | + | 0.0672381i | \(0.978581\pi\) | |||||||
\(812\) | 16.2086 | − | 49.8850i | 0.568811 | − | 1.75062i | ||||
\(813\) | −8.95871 | + | 27.5721i | −0.314196 | + | 0.966995i | ||||
\(814\) | 4.10438 | + | 12.6320i | 0.143858 | + | 0.442750i | ||||
\(815\) | 51.2673 | − | 17.7404i | 1.79581 | − | 0.621419i | ||||
\(816\) | 15.5636 | − | 47.8998i | 0.544835 | − | 1.67683i | ||||
\(817\) | 2.46344 | + | 1.78980i | 0.0861850 | + | 0.0626170i | ||||
\(818\) | −17.9085 | −0.626158 | ||||||||
\(819\) | −3.65401 | − | 2.65479i | −0.127681 | − | 0.0927660i | ||||
\(820\) | −75.2330 | + | 107.794i | −2.62725 | + | 3.76433i | ||||
\(821\) | 23.8603 | − | 17.3355i | 0.832731 | − | 0.605015i | −0.0875994 | − | 0.996156i | \(-0.527920\pi\) |
0.920331 | + | 0.391141i | \(0.127920\pi\) | |||||||
\(822\) | 44.5860 | − | 32.3936i | 1.55511 | − | 1.12986i | ||||
\(823\) | −12.9682 | − | 39.9121i | −0.452044 | − | 1.39125i | −0.874571 | − | 0.484898i | \(-0.838857\pi\) |
0.422527 | − | 0.906350i | \(-0.361143\pi\) | |||||||
\(824\) | −11.8460 | −0.412675 | ||||||||
\(825\) | −4.24043 | + | 3.33390i | −0.147633 | + | 0.116072i | ||||
\(826\) | −6.05624 | −0.210724 | ||||||||
\(827\) | 11.5781 | + | 35.6336i | 0.402609 | + | 1.23910i | 0.922875 | + | 0.385099i | \(0.125833\pi\) |
−0.520266 | + | 0.854004i | \(0.674167\pi\) | |||||||
\(828\) | 17.1587 | − | 12.4666i | 0.596307 | − | 0.433243i | ||||
\(829\) | 7.73108 | − | 5.61696i | 0.268512 | − | 0.195085i | −0.445379 | − | 0.895342i | \(-0.646931\pi\) |
0.713891 | + | 0.700257i | \(0.246931\pi\) | |||||||
\(830\) | 50.3918 | − | 17.4374i | 1.74913 | − | 0.605263i | ||||
\(831\) | −6.94677 | − | 5.04712i | −0.240981 | − | 0.175083i | ||||
\(832\) | 54.5355 | 1.89068 | ||||||||
\(833\) | −13.2126 | − | 9.59954i | −0.457791 | − | 0.332604i | ||||
\(834\) | 15.2105 | − | 46.8131i | 0.526696 | − | 1.62100i | ||||
\(835\) | 0.193056 | + | 10.1698i | 0.00668099 | + | 0.351941i | ||||
\(836\) | −2.04925 | − | 6.30695i | −0.0708748 | − | 0.218130i | ||||
\(837\) | 2.19498 | − | 6.75545i | 0.0758695 | − | 0.233502i | ||||
\(838\) | −17.7311 | + | 54.5708i | −0.612512 | + | 1.88512i | ||||
\(839\) | 16.9128 | + | 52.0522i | 0.583895 | + | 1.79704i | 0.603665 | + | 0.797238i | \(0.293707\pi\) |
−0.0197702 | + | 0.999805i | \(0.506293\pi\) | |||||||
\(840\) | −19.6838 | − | 26.0385i | −0.679157 | − | 0.898413i | ||||
\(841\) | 2.00037 | − | 6.15651i | 0.0689783 | − | 0.212294i | ||||
\(842\) | 48.5570 | + | 35.2787i | 1.67338 | + | 1.21579i | ||||
\(843\) | −17.1661 | −0.591233 | ||||||||
\(844\) | 100.603 | + | 73.0922i | 3.46289 | + | 2.51594i | ||||
\(845\) | −0.247529 | − | 13.0394i | −0.00851527 | − | 0.448567i | ||||
\(846\) | −4.16908 | + | 3.02901i | −0.143336 | + | 0.104140i | ||||
\(847\) | 13.4248 | − | 9.75371i | 0.461283 | − | 0.335141i | ||||
\(848\) | −10.0887 | − | 31.0499i | −0.346448 | − | 1.06626i | ||||
\(849\) | 9.62005 | 0.330159 | ||||||||
\(850\) | 43.8821 | + | 29.4042i | 1.50514 | + | 1.00856i | ||||
\(851\) | 18.6159 | 0.638144 | ||||||||
\(852\) | 9.65426 | + | 29.7128i | 0.330750 | + | 1.01794i | ||||
\(853\) | 12.3834 | − | 8.99706i | 0.423999 | − | 0.308053i | −0.355246 | − | 0.934773i | \(-0.615603\pi\) |
0.779245 | + | 0.626720i | \(0.215603\pi\) | |||||||
\(854\) | −26.7026 | + | 19.4005i | −0.913743 | + | 0.663873i | ||||
\(855\) | −2.51919 | − | 0.765989i | −0.0861546 | − | 0.0261963i | ||||
\(856\) | 77.0836 | + | 56.0045i | 2.63466 | + | 1.91419i | ||||
\(857\) | −8.66910 | −0.296131 | −0.148065 | − | 0.988978i | \(-0.547305\pi\) | ||||
−0.148065 | + | 0.988978i | \(0.547305\pi\) | |||||||
\(858\) | −6.27865 | − | 4.56171i | −0.214350 | − | 0.155734i | ||||
\(859\) | −9.39653 | + | 28.9195i | −0.320605 | + | 0.986722i | 0.652780 | + | 0.757547i | \(0.273603\pi\) |
−0.973385 | + | 0.229174i | \(0.926397\pi\) | |||||||
\(860\) | 28.8787 | + | 8.78088i | 0.984755 | + | 0.299425i | ||||
\(861\) | 5.87087 | + | 18.0687i | 0.200079 | + | 0.615779i | ||||
\(862\) | 25.2531 | − | 77.7211i | 0.860125 | − | 2.64719i | ||||
\(863\) | −5.57545 | + | 17.1595i | −0.189791 | + | 0.584115i | −0.999998 | − | 0.00202803i | \(-0.999354\pi\) |
0.810207 | + | 0.586143i | \(0.199354\pi\) | |||||||
\(864\) | 5.28899 | + | 16.2779i | 0.179935 | + | 0.553784i | ||||
\(865\) | −3.42627 | + | 4.90917i | −0.116497 | + | 0.166917i | ||||
\(866\) | −0.478808 | + | 1.47362i | −0.0162706 | + | 0.0500756i | ||||
\(867\) | −1.24749 | − | 0.906354i | −0.0423669 | − | 0.0307814i | ||||
\(868\) | −62.5548 | −2.12325 | ||||||||
\(869\) | 3.49465 | + | 2.53901i | 0.118548 | + | 0.0861301i | ||||
\(870\) | −21.5801 | − | 28.5469i | −0.731632 | − | 0.967829i | ||||
\(871\) | −26.9551 | + | 19.5840i | −0.913338 | + | 0.663579i | ||||
\(872\) | 24.1432 | − | 17.5411i | 0.817591 | − | 0.594015i | ||||
\(873\) | 3.32756 | + | 10.2412i | 0.112621 | + | 0.346611i | ||||
\(874\) | −12.8556 | −0.434848 | ||||||||
\(875\) | 17.5778 | − | 6.84006i | 0.594237 | − | 0.231236i | ||||
\(876\) | 17.2301 | 0.582149 | ||||||||
\(877\) | 6.89285 | + | 21.2140i | 0.232755 | + | 0.716346i | 0.997411 | + | 0.0719076i | \(0.0229087\pi\) |
−0.764656 | + | 0.644438i | \(0.777091\pi\) | |||||||
\(878\) | 27.8352 | − | 20.2235i | 0.939393 | − | 0.682509i | ||||
\(879\) | 13.6079 | − | 9.88669i | 0.458982 | − | 0.333470i | ||||
\(880\) | −18.6349 | − | 24.6508i | −0.628181 | − | 0.830980i | ||||
\(881\) | −6.27761 | − | 4.56095i | −0.211498 | − | 0.153662i | 0.476993 | − | 0.878907i | \(-0.341727\pi\) |
−0.688491 | + | 0.725245i | \(0.741727\pi\) | |||||||
\(882\) | 11.1617 | 0.375833 | ||||||||
\(883\) | 16.1421 | + | 11.7279i | 0.543224 | + | 0.394675i | 0.825281 | − | 0.564722i | \(-0.191017\pi\) |
−0.282057 | + | 0.959398i | \(0.591017\pi\) | |||||||
\(884\) | −16.9798 | + | 52.2584i | −0.571092 | + | 1.75764i | ||||
\(885\) | −1.70974 | + | 2.44972i | −0.0574722 | + | 0.0823463i | ||||
\(886\) | −11.8861 | − | 36.5816i | −0.399320 | − | 1.22898i | ||||
\(887\) | 2.65844 | − | 8.18183i | 0.0892616 | − | 0.274719i | −0.896454 | − | 0.443137i | \(-0.853866\pi\) |
0.985716 | + | 0.168418i | \(0.0538657\pi\) | |||||||
\(888\) | −12.2513 | + | 37.7056i | −0.411126 | + | 1.26532i | ||||
\(889\) | −10.5496 | − | 32.4684i | −0.353823 | − | 1.08895i | ||||
\(890\) | −88.7783 | − | 26.9940i | −2.97585 | − | 0.904841i | ||||
\(891\) | 0.333373 | − | 1.02602i | 0.0111684 | − | 0.0343729i | ||||
\(892\) | −55.3715 | − | 40.2297i | −1.85397 | − | 1.34699i | ||||
\(893\) | 2.25832 | 0.0755719 | ||||||||
\(894\) | −1.53461 | − | 1.11496i | −0.0513251 | − | 0.0372899i | ||||
\(895\) | −33.4310 | − | 10.1651i | −1.11748 | − | 0.339781i | ||||
\(896\) | 27.9851 | − | 20.3323i | 0.934916 | − | 0.679256i | ||||
\(897\) | −8.80004 | + | 6.39360i | −0.293825 | + | 0.213476i | ||||
\(898\) | 9.93611 | + | 30.5802i | 0.331572 | + | 1.02047i | ||||
\(899\) | −42.3057 | −1.41097 | ||||||||
\(900\) | −26.0822 | + | 0.990607i | −0.869406 | + | 0.0330202i | ||||
\(901\) | 10.0203 | 0.333824 | ||||||||
\(902\) | 10.0879 | + | 31.0472i | 0.335889 | + | 1.03376i | ||||
\(903\) | 3.52932 | − | 2.56420i | 0.117448 | − | 0.0853312i | ||||
\(904\) | 42.3652 | − | 30.7801i | 1.40905 | − | 1.02373i | ||||
\(905\) | 0.00860869 | + | 0.453488i | 0.000286163 | + | 0.0150745i | ||||
\(906\) | −15.3157 | − | 11.1275i | −0.508830 | − | 0.369687i | ||||
\(907\) | 6.26125 | 0.207902 | 0.103951 | − | 0.994582i | \(-0.466852\pi\) | ||||
0.103951 | + | 0.994582i | \(0.466852\pi\) | |||||||
\(908\) | 110.989 | + | 80.6385i | 3.68331 | + | 2.67608i | ||||
\(909\) | −4.19195 | + | 12.9015i | −0.139038 | + | 0.427915i | ||||
\(910\) | 16.3649 | + | 21.6481i | 0.542491 | + | 0.717627i | ||||
\(911\) | 0.279838 | + | 0.861253i | 0.00927145 | + | 0.0285346i | 0.955585 | − | 0.294715i | \(-0.0952247\pi\) |
−0.946314 | + | 0.323250i | \(0.895225\pi\) | |||||||
\(912\) | 4.66135 | − | 14.3461i | 0.154353 | − | 0.475048i | ||||
\(913\) | 2.95862 | − | 9.10571i | 0.0979162 | − | 0.301355i | ||||
\(914\) | 6.82669 | + | 21.0104i | 0.225807 | + | 0.694962i | ||||
\(915\) | 0.309010 | + | 16.2780i | 0.0102156 | + | 0.538135i | ||||
\(916\) | 3.21988 | − | 9.90978i | 0.106388 | − | 0.327428i | ||||
\(917\) | 4.16293 | + | 3.02455i | 0.137472 | + | 0.0998794i | ||||
\(918\) | −10.5646 | −0.348682 | ||||||||
\(919\) | −35.5913 | − | 25.8586i | −1.17405 | − | 0.852997i | −0.182561 | − | 0.983194i | \(-0.558439\pi\) |
−0.991488 | + | 0.130198i | \(0.958439\pi\) | |||||||
\(920\) | −74.2889 | + | 25.7067i | −2.44923 | + | 0.847526i | ||||
\(921\) | 9.15903 | − | 6.65443i | 0.301800 | − | 0.219271i | ||||
\(922\) | 2.76551 | − | 2.00926i | 0.0910771 | − | 0.0661714i | ||||
\(923\) | −4.95129 | − | 15.2385i | −0.162974 | − | 0.501582i | ||||
\(924\) | −9.50081 | −0.312554 | ||||||||
\(925\) | −19.0317 | − | 12.7526i | −0.625760 | − | 0.419304i | ||||
\(926\) | −87.8029 | −2.88538 | ||||||||
\(927\) | 0.423056 | + | 1.30203i | 0.0138950 | + | 0.0427643i | ||||
\(928\) | 82.4707 | − | 59.9184i | 2.70723 | − | 1.96692i | ||||
\(929\) | 29.7271 | − | 21.5980i | 0.975313 | − | 0.708606i | 0.0186568 | − | 0.999826i | \(-0.494061\pi\) |
0.956656 | + | 0.291220i | \(0.0940610\pi\) | |||||||
\(930\) | −24.4258 | + | 34.9974i | −0.800955 | + | 1.14761i | ||||
\(931\) | −3.95722 | − | 2.87509i | −0.129693 | − | 0.0942273i | ||||
\(932\) | −2.74347 | −0.0898652 | ||||||||
\(933\) | 15.0181 | + | 10.9113i | 0.491672 | + | 0.357221i | ||||
\(934\) | −11.9857 | + | 36.8883i | −0.392185 | + | 1.20702i | ||||
\(935\) | 8.96295 | − | 3.10152i | 0.293120 | − | 0.101430i | ||||
\(936\) | −7.15855 | − | 22.0318i | −0.233985 | − | 0.720131i | ||||
\(937\) | 7.61696 | − | 23.4426i | 0.248835 | − | 0.765836i | −0.746147 | − | 0.665782i | \(-0.768098\pi\) |
0.994982 | − | 0.100055i | \(-0.0319017\pi\) | |||||||
\(938\) | −17.4333 | + | 53.6542i | −0.569217 | + | 1.75187i | ||||
\(939\) | 2.99731 | + | 9.22478i | 0.0978137 | + | 0.301039i | ||||
\(940\) | 21.1554 | − | 7.32055i | 0.690012 | − | 0.238770i | ||||
\(941\) | −18.2777 | + | 56.2530i | −0.595836 | + | 1.83379i | −0.0453159 | + | 0.998973i | \(0.514429\pi\) |
−0.550520 | + | 0.834822i | \(0.685571\pi\) | |||||||
\(942\) | 11.1493 | + | 8.10045i | 0.363264 | + | 0.263927i | ||||
\(943\) | 45.7546 | 1.48998 | ||||||||
\(944\) | −13.8456 | − | 10.0594i | −0.450635 | − | 0.327406i | ||||
\(945\) | −2.15900 | + | 3.09342i | −0.0702324 | + | 0.100629i | ||||
\(946\) | 6.06439 | − | 4.40604i | 0.197170 | − | 0.143253i | ||||
\(947\) | 24.3482 | − | 17.6900i | 0.791210 | − | 0.574848i | −0.117112 | − | 0.993119i | \(-0.537364\pi\) |
0.908322 | + | 0.418271i | \(0.137364\pi\) | |||||||
\(948\) | 6.45903 | + | 19.8789i | 0.209780 | + | 0.645635i | ||||
\(949\) | −8.83661 | −0.286849 | ||||||||
\(950\) | 13.1428 | + | 8.80664i | 0.426410 | + | 0.285725i | ||||
\(951\) | −7.47647 | −0.242441 | ||||||||
\(952\) | 17.7354 | + | 54.5841i | 0.574809 | + | 1.76908i | ||||
\(953\) | 16.6975 | − | 12.1315i | 0.540886 | − | 0.392977i | −0.283528 | − | 0.958964i | \(-0.591505\pi\) |
0.824414 | + | 0.565987i | \(0.191505\pi\) | |||||||
\(954\) | −5.54032 | + | 4.02528i | −0.179375 | + | 0.130323i | ||||
\(955\) | 16.7355 | − | 5.79109i | 0.541547 | − | 0.187395i | ||||
\(956\) | 29.6036 | + | 21.5083i | 0.957449 | + | 0.695628i | ||||
\(957\) | −6.42538 | −0.207703 | ||||||||
\(958\) | −36.6553 | − | 26.6316i | −1.18428 | − | 0.860429i | ||||
\(959\) | −10.6924 | + | 32.9078i | −0.345275 | + | 1.06265i | ||||
\(960\) | −0.864511 | − | 45.5407i | −0.0279020 | − | 1.46982i | ||||
\(961\) | 6.01162 | + | 18.5019i | 0.193923 | + | 0.596834i | ||||
\(962\) | 10.1856 | − | 31.3480i | 0.328396 | − | 1.01070i | ||||
\(963\) | 3.40275 | − | 10.4726i | 0.109652 | − | 0.337474i | ||||
\(964\) | 3.73527 | + | 11.4960i | 0.120305 | + | 0.370260i | ||||
\(965\) | 22.1504 | + | 29.3013i | 0.713047 | + | 0.943244i | ||||
\(966\) | −5.69146 | + | 17.5165i | −0.183120 | + | 0.563585i | ||||
\(967\) | 18.2850 | + | 13.2849i | 0.588007 | + | 0.427212i | 0.841602 | − | 0.540098i | \(-0.181613\pi\) |
−0.253595 | + | 0.967311i | \(0.581613\pi\) | |||||||
\(968\) | 85.1103 | 2.73555 | ||||||||
\(969\) | 3.74552 | + | 2.72128i | 0.120324 | + | 0.0874202i | ||||
\(970\) | −1.22799 | − | 64.6881i | −0.0394284 | − | 2.07701i | ||||
\(971\) | −19.5281 | + | 14.1880i | −0.626687 | + | 0.455315i | −0.855251 | − | 0.518214i | \(-0.826597\pi\) |
0.228564 | + | 0.973529i | \(0.426597\pi\) | |||||||
\(972\) | 4.22323 | − | 3.06835i | 0.135460 | − | 0.0984175i | ||||
\(973\) | 9.54981 | + | 29.3913i | 0.306153 | + | 0.942242i | ||||
\(974\) | −107.007 | −3.42874 | ||||||||
\(975\) | 13.3765 | − | 0.508043i | 0.428391 | − | 0.0162704i | ||||
\(976\) | −93.2708 | −2.98553 | ||||||||
\(977\) | 7.12302 | + | 21.9224i | 0.227886 | + | 0.701360i | 0.997986 | + | 0.0634371i | \(0.0202062\pi\) |
−0.770100 | + | 0.637923i | \(0.779794\pi\) | |||||||
\(978\) | 52.7407 | − | 38.3184i | 1.68646 | − | 1.22529i | ||||
\(979\) | −13.4789 | + | 9.79299i | −0.430787 | + | 0.312985i | ||||
\(980\) | −46.3901 | − | 14.1054i | −1.48188 | − | 0.450581i | ||||
\(981\) | −2.79022 | − | 2.02721i | −0.0890847 | − | 0.0647239i | ||||
\(982\) | −37.6870 | −1.20264 | ||||||||
\(983\) | −24.1664 | − | 17.5579i | −0.770787 | − | 0.560010i | 0.131413 | − | 0.991328i | \(-0.458049\pi\) |
−0.902200 | + | 0.431318i | \(0.858049\pi\) | |||||||
\(984\) | −30.1116 | + | 92.6738i | −0.959921 | + | 2.95433i | ||||
\(985\) | −36.6619 | − | 11.1474i | −1.16814 | − | 0.355187i | ||||
\(986\) | 19.4440 | + | 59.8424i | 0.619222 | + | 1.90577i | ||||
\(987\) | 0.999807 | − | 3.07709i | 0.0318242 | − | 0.0979449i | ||||
\(988\) | −5.08550 | + | 15.6515i | −0.161791 | + | 0.497942i | ||||
\(989\) | −3.24661 | − | 9.99204i | −0.103236 | − | 0.317728i | ||||
\(990\) | −3.70979 | + | 5.31540i | −0.117905 | + | 0.168934i | ||||
\(991\) | 5.14700 | − | 15.8408i | 0.163500 | − | 0.503201i | −0.835423 | − | 0.549608i | \(-0.814777\pi\) |
0.998923 | + | 0.0464072i | \(0.0147772\pi\) | |||||||
\(992\) | −98.3550 | − | 71.4591i | −3.12277 | − | 2.26883i | ||||
\(993\) | 25.2570 | 0.801507 | ||||||||
\(994\) | −21.9487 | − | 15.9466i | −0.696169 | − | 0.505797i | ||||
\(995\) | 2.72177 | + | 3.60045i | 0.0862858 | + | 0.114142i | ||||
\(996\) | 37.4804 | − | 27.2311i | 1.18761 | − | 0.862850i | ||||
\(997\) | −10.1074 | + | 7.34343i | −0.320103 | + | 0.232569i | −0.736220 | − | 0.676743i | \(-0.763391\pi\) |
0.416116 | + | 0.909311i | \(0.363391\pi\) | |||||||
\(998\) | −12.6474 | − | 38.9246i | −0.400346 | − | 1.23214i | ||||
\(999\) | 4.58187 | 0.144964 |
(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 | 75.2.g.c.31.1 | ✓ | 12 | |
3.2 | odd | 2 | 225.2.h.d.181.3 | 12 | |||
5.2 | odd | 4 | 375.2.i.d.349.6 | 24 | |||
5.3 | odd | 4 | 375.2.i.d.349.1 | 24 | |||
5.4 | even | 2 | 375.2.g.c.151.3 | 12 | |||
25.2 | odd | 20 | 1875.2.b.f.1249.1 | 12 | |||
25.3 | odd | 20 | 375.2.i.d.274.6 | 24 | |||
25.4 | even | 10 | 375.2.g.c.226.3 | 12 | |||
25.11 | even | 5 | 1875.2.a.j.1.1 | 6 | |||
25.14 | even | 10 | 1875.2.a.k.1.6 | 6 | |||
25.21 | even | 5 | inner | 75.2.g.c.46.1 | yes | 12 | |
25.22 | odd | 20 | 375.2.i.d.274.1 | 24 | |||
25.23 | odd | 20 | 1875.2.b.f.1249.12 | 12 | |||
75.11 | odd | 10 | 5625.2.a.p.1.6 | 6 | |||
75.14 | odd | 10 | 5625.2.a.q.1.1 | 6 | |||
75.71 | odd | 10 | 225.2.h.d.46.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
75.2.g.c.46.1 | yes | 12 | 25.21 | even | 5 | inner | |
225.2.h.d.46.3 | 12 | 75.71 | odd | 10 | |||
225.2.h.d.181.3 | 12 | 3.2 | odd | 2 | |||
375.2.g.c.151.3 | 12 | 5.4 | even | 2 | |||
375.2.g.c.226.3 | 12 | 25.4 | even | 10 | |||
375.2.i.d.274.1 | 24 | 25.22 | odd | 20 | |||
375.2.i.d.274.6 | 24 | 25.3 | odd | 20 | |||
375.2.i.d.349.1 | 24 | 5.3 | odd | 4 | |||
375.2.i.d.349.6 | 24 | 5.2 | odd | 4 | |||
1875.2.a.j.1.1 | 6 | 25.11 | even | 5 | |||
1875.2.a.k.1.6 | 6 | 25.14 | even | 10 | |||
1875.2.b.f.1249.1 | 12 | 25.2 | odd | 20 | |||
1875.2.b.f.1249.12 | 12 | 25.23 | odd | 20 | |||
5625.2.a.p.1.6 | 6 | 75.11 | odd | 10 | |||
5625.2.a.q.1.1 | 6 | 75.14 | odd | 10 |