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: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.26265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(-1.21700 - 0.720348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.31 |
Dual form | 75.2.g.b.46.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.655837 | + | 2.01846i | 0.463747 | + | 1.42727i | 0.860552 | + | 0.509363i | \(0.170119\pi\) |
−0.396805 | + | 0.917903i | \(0.629881\pi\) | |||||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −2.02602 | + | 1.47199i | −1.01301 | + | 0.735995i | ||||
\(5\) | −2.21700 | − | 0.291365i | −0.991474 | − | 0.130303i | ||||
\(6\) | −1.71700 | − | 1.24748i | −0.700964 | − | 0.509280i | ||||
\(7\) | 4.35840 | 1.64732 | 0.823660 | − | 0.567083i | \(-0.191928\pi\) | ||||
0.823660 | + | 0.567083i | \(0.191928\pi\) | |||||||
\(8\) | −0.865884 | − | 0.629102i | −0.306136 | − | 0.222421i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | −0.865884 | − | 4.66602i | −0.273817 | − | 1.47553i | ||||
\(11\) | −0.488218 | − | 1.50258i | −0.147203 | − | 0.453045i | 0.850085 | − | 0.526646i | \(-0.176551\pi\) |
−0.997288 | + | 0.0736014i | \(0.976551\pi\) | |||||||
\(12\) | 0.773871 | − | 2.38173i | 0.223397 | − | 0.687546i | ||||
\(13\) | 0.370184 | − | 1.13931i | 0.102670 | − | 0.315987i | −0.886506 | − | 0.462717i | \(-0.846875\pi\) |
0.989177 | + | 0.146729i | \(0.0468747\pi\) | |||||||
\(14\) | 2.85840 | + | 8.79726i | 0.763940 | + | 2.35117i | ||||
\(15\) | 1.96485 | − | 1.06740i | 0.507323 | − | 0.275602i | ||||
\(16\) | −0.845805 | + | 2.60312i | −0.211451 | + | 0.650780i | ||||
\(17\) | 0.907987 | + | 0.659691i | 0.220219 | + | 0.159999i | 0.692425 | − | 0.721490i | \(-0.256542\pi\) |
−0.472206 | + | 0.881488i | \(0.656542\pi\) | |||||||
\(18\) | 2.12233 | 0.500239 | ||||||||
\(19\) | −6.21218 | − | 4.51341i | −1.42517 | − | 1.03545i | −0.990890 | − | 0.134670i | \(-0.957002\pi\) |
−0.434281 | − | 0.900777i | \(-0.642998\pi\) | |||||||
\(20\) | 4.92058 | − | 2.67310i | 1.10028 | − | 0.597722i | ||||
\(21\) | −3.52602 | + | 2.56180i | −0.769441 | + | 0.559031i | ||||
\(22\) | 2.71270 | − | 1.97090i | 0.578351 | − | 0.420196i | ||||
\(23\) | −0.717004 | − | 2.20671i | −0.149506 | − | 0.460131i | 0.848057 | − | 0.529905i | \(-0.177772\pi\) |
−0.997563 | + | 0.0697736i | \(0.977772\pi\) | |||||||
\(24\) | 1.07029 | 0.218472 | ||||||||
\(25\) | 4.83021 | + | 1.29192i | 0.966042 | + | 0.258383i | ||||
\(26\) | 2.54243 | 0.498611 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | −8.83021 | + | 6.41552i | −1.66875 | + | 1.21242i | ||||
\(29\) | 4.45307 | − | 3.23535i | 0.826915 | − | 0.600789i | −0.0917701 | − | 0.995780i | \(-0.529252\pi\) |
0.918685 | + | 0.394992i | \(0.129252\pi\) | |||||||
\(30\) | 3.44313 | + | 3.26594i | 0.628627 | + | 0.596276i | ||||
\(31\) | −3.88495 | − | 2.82258i | −0.697757 | − | 0.506950i | 0.181444 | − | 0.983401i | \(-0.441923\pi\) |
−0.879201 | + | 0.476451i | \(0.841923\pi\) | |||||||
\(32\) | −7.94959 | −1.40530 | ||||||||
\(33\) | 1.27817 | + | 0.928645i | 0.222501 | + | 0.161656i | ||||
\(34\) | −0.736068 | + | 2.26538i | −0.126235 | + | 0.388510i | ||||
\(35\) | −9.66259 | − | 1.26989i | −1.63328 | − | 0.214650i | ||||
\(36\) | 0.773871 | + | 2.38173i | 0.128979 | + | 0.396955i | ||||
\(37\) | −1.96915 | + | 6.06043i | −0.323727 | + | 0.996329i | 0.648285 | + | 0.761398i | \(0.275486\pi\) |
−0.972012 | + | 0.234931i | \(0.924514\pi\) | |||||||
\(38\) | 5.03596 | − | 15.4991i | 0.816941 | − | 2.51428i | ||||
\(39\) | 0.370184 | + | 1.13931i | 0.0592768 | + | 0.182435i | ||||
\(40\) | 1.73637 | + | 1.64701i | 0.274544 | + | 0.260415i | ||||
\(41\) | −2.30902 | + | 7.10642i | −0.360608 | + | 1.10984i | 0.592078 | + | 0.805881i | \(0.298308\pi\) |
−0.952686 | + | 0.303956i | \(0.901692\pi\) | |||||||
\(42\) | −7.48339 | − | 5.43700i | −1.15471 | − | 0.838948i | ||||
\(43\) | −1.24998 | −0.190620 | −0.0953102 | − | 0.995448i | \(-0.530384\pi\) | ||||
−0.0953102 | + | 0.995448i | \(0.530384\pi\) | |||||||
\(44\) | 3.20092 | + | 2.32561i | 0.482557 | + | 0.350598i | ||||
\(45\) | −0.962197 | + | 2.01846i | −0.143436 | + | 0.300894i | ||||
\(46\) | 3.98392 | − | 2.89449i | 0.587397 | − | 0.426769i | ||||
\(47\) | −3.33934 | + | 2.42617i | −0.487092 | + | 0.353893i | −0.804065 | − | 0.594541i | \(-0.797334\pi\) |
0.316973 | + | 0.948435i | \(0.397334\pi\) | |||||||
\(48\) | −0.845805 | − | 2.60312i | −0.122081 | − | 0.375728i | ||||
\(49\) | 11.9957 | 1.71367 | ||||||||
\(50\) | 0.560152 | + | 10.5969i | 0.0792174 | + | 1.49862i | ||||
\(51\) | −1.12233 | −0.157158 | ||||||||
\(52\) | 0.927051 | + | 2.85317i | 0.128559 | + | 0.395663i | ||||
\(53\) | −3.03032 | + | 2.20166i | −0.416247 | + | 0.302421i | −0.776126 | − | 0.630578i | \(-0.782818\pi\) |
0.359879 | + | 0.932999i | \(0.382818\pi\) | |||||||
\(54\) | −1.71700 | + | 1.24748i | −0.233655 | + | 0.169760i | ||||
\(55\) | 0.644581 | + | 3.47347i | 0.0869153 | + | 0.468363i | ||||
\(56\) | −3.77387 | − | 2.74188i | −0.504305 | − | 0.366399i | ||||
\(57\) | 7.67867 | 1.01707 | ||||||||
\(58\) | 9.45090 | + | 6.86648i | 1.24096 | + | 0.901613i | ||||
\(59\) | 2.82940 | − | 8.70799i | 0.368356 | − | 1.13368i | −0.579496 | − | 0.814975i | \(-0.696751\pi\) |
0.947853 | − | 0.318709i | \(-0.103249\pi\) | |||||||
\(60\) | −2.40963 | + | 5.05483i | −0.311082 | + | 0.652575i | ||||
\(61\) | 0.431351 | + | 1.32756i | 0.0552288 | + | 0.169977i | 0.974866 | − | 0.222792i | \(-0.0715172\pi\) |
−0.919637 | + | 0.392769i | \(0.871517\pi\) | |||||||
\(62\) | 3.14937 | − | 9.69276i | 0.399970 | − | 1.23098i | ||||
\(63\) | 1.34682 | − | 4.14509i | 0.169683 | − | 0.522232i | ||||
\(64\) | −3.52202 | − | 10.8397i | −0.440253 | − | 1.35496i | ||||
\(65\) | −1.15265 | + | 2.41799i | −0.142969 | + | 0.299915i | ||||
\(66\) | −1.03616 | + | 3.18898i | −0.127543 | + | 0.392536i | ||||
\(67\) | 3.12499 | + | 2.27044i | 0.381778 | + | 0.277378i | 0.762078 | − | 0.647485i | \(-0.224179\pi\) |
−0.380300 | + | 0.924863i | \(0.624179\pi\) | |||||||
\(68\) | −2.81066 | −0.340843 | ||||||||
\(69\) | 1.87714 | + | 1.36382i | 0.225981 | + | 0.164185i | ||||
\(70\) | −3.77387 | − | 20.3364i | −0.451064 | − | 2.43066i | ||||
\(71\) | 8.57970 | − | 6.23352i | 1.01822 | − | 0.739783i | 0.0523057 | − | 0.998631i | \(-0.483343\pi\) |
0.965918 | + | 0.258848i | \(0.0833430\pi\) | |||||||
\(72\) | −0.865884 | + | 0.629102i | −0.102045 | + | 0.0741403i | ||||
\(73\) | 1.54407 | + | 4.75216i | 0.180720 | + | 0.556198i | 0.999848 | − | 0.0174117i | \(-0.00554259\pi\) |
−0.819129 | + | 0.573610i | \(0.805543\pi\) | |||||||
\(74\) | −13.5242 | −1.57215 | ||||||||
\(75\) | −4.66709 | + | 1.79395i | −0.538910 | + | 0.207147i | ||||
\(76\) | 19.2297 | 2.20580 | ||||||||
\(77\) | −2.12785 | − | 6.54885i | −0.242491 | − | 0.746310i | ||||
\(78\) | −2.05687 | + | 1.49440i | −0.232894 | + | 0.169208i | ||||
\(79\) | −11.7737 | + | 8.55407i | −1.32464 | + | 0.962408i | −0.324779 | + | 0.945790i | \(0.605290\pi\) |
−0.999862 | + | 0.0166185i | \(0.994710\pi\) | |||||||
\(80\) | 2.63361 | − | 5.52469i | 0.294447 | − | 0.617679i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −15.8584 | −1.75126 | ||||||||
\(83\) | 7.06760 | + | 5.13491i | 0.775770 | + | 0.563630i | 0.903706 | − | 0.428153i | \(-0.140835\pi\) |
−0.127937 | + | 0.991782i | \(0.540835\pi\) | |||||||
\(84\) | 3.37284 | − | 10.3805i | 0.368007 | − | 1.13261i | ||||
\(85\) | −1.82080 | − | 1.72709i | −0.197493 | − | 0.187330i | ||||
\(86\) | −0.819784 | − | 2.52304i | −0.0883996 | − | 0.272066i | ||||
\(87\) | −1.70092 | + | 5.23490i | −0.182358 | + | 0.561240i | ||||
\(88\) | −0.522535 | + | 1.60820i | −0.0557025 | + | 0.171435i | ||||
\(89\) | −3.10195 | − | 9.54683i | −0.328806 | − | 1.01196i | −0.969693 | − | 0.244326i | \(-0.921433\pi\) |
0.640887 | − | 0.767635i | \(-0.278567\pi\) | |||||||
\(90\) | −4.70522 | − | 0.618375i | −0.495974 | − | 0.0651824i | ||||
\(91\) | 1.61341 | − | 4.96556i | 0.169131 | − | 0.520532i | ||||
\(92\) | 4.70092 | + | 3.41542i | 0.490105 | + | 0.356082i | ||||
\(93\) | 4.80206 | 0.497950 | ||||||||
\(94\) | −7.08719 | − | 5.14914i | −0.730988 | − | 0.531094i | ||||
\(95\) | 12.4574 | + | 11.8163i | 1.27810 | + | 1.21232i | ||||
\(96\) | 6.43135 | − | 4.67265i | 0.656397 | − | 0.476900i | ||||
\(97\) | 6.06760 | − | 4.40837i | 0.616071 | − | 0.447602i | −0.235476 | − | 0.971880i | \(-0.575665\pi\) |
0.851547 | + | 0.524278i | \(0.175665\pi\) | |||||||
\(98\) | 7.86720 | + | 24.2128i | 0.794707 | + | 2.44586i | ||||
\(99\) | −1.57991 | −0.158787 | ||||||||
\(100\) | −11.6878 | + | 4.49258i | −1.16878 | + | 0.449258i | ||||
\(101\) | −6.51821 | −0.648586 | −0.324293 | − | 0.945957i | \(-0.605126\pi\) | ||||
−0.324293 | + | 0.945957i | \(0.605126\pi\) | |||||||
\(102\) | −0.736068 | − | 2.26538i | −0.0728816 | − | 0.224306i | ||||
\(103\) | −6.51158 | + | 4.73094i | −0.641605 | + | 0.466153i | −0.860401 | − | 0.509617i | \(-0.829787\pi\) |
0.218796 | + | 0.975771i | \(0.429787\pi\) | |||||||
\(104\) | −1.03728 | + | 0.753626i | −0.101713 | + | 0.0738991i | ||||
\(105\) | 8.56362 | − | 4.65217i | 0.835724 | − | 0.454005i | ||||
\(106\) | −6.43135 | − | 4.67265i | −0.624668 | − | 0.453848i | ||||
\(107\) | 9.47745 | 0.916220 | 0.458110 | − | 0.888896i | \(-0.348527\pi\) | ||||
0.458110 | + | 0.888896i | \(0.348527\pi\) | |||||||
\(108\) | −2.02602 | − | 1.47199i | −0.194954 | − | 0.141642i | ||||
\(109\) | −3.60491 | + | 11.0948i | −0.345288 | + | 1.06269i | 0.616142 | + | 0.787635i | \(0.288695\pi\) |
−0.961429 | + | 0.275052i | \(0.911305\pi\) | |||||||
\(110\) | −6.58833 | + | 3.57909i | −0.628172 | + | 0.341253i | ||||
\(111\) | −1.96915 | − | 6.06043i | −0.186904 | − | 0.575231i | ||||
\(112\) | −3.68636 | + | 11.3454i | −0.348328 | + | 1.07204i | ||||
\(113\) | −4.61219 | + | 14.1949i | −0.433879 | + | 1.33534i | 0.460353 | + | 0.887736i | \(0.347723\pi\) |
−0.894231 | + | 0.447605i | \(0.852277\pi\) | |||||||
\(114\) | 5.03596 | + | 15.4991i | 0.471661 | + | 1.45162i | ||||
\(115\) | 0.946641 | + | 5.10120i | 0.0882747 | + | 0.475689i | ||||
\(116\) | −4.25962 | + | 13.1098i | −0.395496 | + | 1.21721i | ||||
\(117\) | −0.969154 | − | 0.704131i | −0.0895983 | − | 0.0650970i | ||||
\(118\) | 19.4324 | 1.78889 | ||||||||
\(119\) | 3.95737 | + | 2.87520i | 0.362772 | + | 0.263569i | ||||
\(120\) | −2.37284 | − | 0.311846i | −0.216610 | − | 0.0284675i | ||||
\(121\) | 6.87980 | − | 4.99847i | 0.625436 | − | 0.454406i | ||||
\(122\) | −2.39673 | + | 1.74133i | −0.216990 | + | 0.157652i | ||||
\(123\) | −2.30902 | − | 7.10642i | −0.208197 | − | 0.640765i | ||||
\(124\) | 12.0258 | 1.07995 | ||||||||
\(125\) | −10.3322 | − | 4.27154i | −0.924138 | − | 0.382058i | ||||
\(126\) | 9.24998 | 0.824054 | ||||||||
\(127\) | −5.25195 | − | 16.1638i | −0.466035 | − | 1.43431i | −0.857676 | − | 0.514190i | \(-0.828092\pi\) |
0.391641 | − | 0.920118i | \(-0.371908\pi\) | |||||||
\(128\) | 6.70686 | − | 4.87282i | 0.592809 | − | 0.430701i | ||||
\(129\) | 1.01126 | − | 0.734721i | 0.0890362 | − | 0.0646886i | ||||
\(130\) | −5.63657 | − | 0.740776i | −0.494360 | − | 0.0649703i | ||||
\(131\) | 0.266063 | + | 0.193306i | 0.0232461 | + | 0.0168892i | 0.599348 | − | 0.800489i | \(-0.295427\pi\) |
−0.576102 | + | 0.817378i | \(0.695427\pi\) | |||||||
\(132\) | −3.95656 | −0.344374 | ||||||||
\(133\) | −27.0752 | − | 19.6713i | −2.34771 | − | 1.70571i | ||||
\(134\) | −2.53330 | + | 7.79670i | −0.218844 | + | 0.673533i | ||||
\(135\) | −0.407987 | − | 2.19853i | −0.0351139 | − | 0.189220i | ||||
\(136\) | −0.371199 | − | 1.14243i | −0.0318300 | − | 0.0979628i | ||||
\(137\) | 1.40995 | − | 4.33939i | 0.120461 | − | 0.370739i | −0.872586 | − | 0.488460i | \(-0.837559\pi\) |
0.993047 | + | 0.117721i | \(0.0375588\pi\) | |||||||
\(138\) | −1.52172 | + | 4.68338i | −0.129538 | + | 0.398676i | ||||
\(139\) | −1.46289 | − | 4.50230i | −0.124080 | − | 0.381880i | 0.869652 | − | 0.493665i | \(-0.164343\pi\) |
−0.993732 | + | 0.111785i | \(0.964343\pi\) | |||||||
\(140\) | 21.4459 | − | 11.6504i | 1.81251 | − | 0.984641i | ||||
\(141\) | 1.27551 | − | 3.92563i | 0.107418 | − | 0.330597i | ||||
\(142\) | 18.2090 | + | 13.2296i | 1.52806 | + | 1.11020i | ||||
\(143\) | −1.89263 | −0.158270 | ||||||||
\(144\) | 2.21435 | + | 1.60882i | 0.184529 | + | 0.134068i | ||||
\(145\) | −10.8151 | + | 5.87530i | −0.898149 | + | 0.487917i | ||||
\(146\) | −8.57938 | + | 6.23328i | −0.710035 | + | 0.515870i | ||||
\(147\) | −9.70470 | + | 7.05087i | −0.800430 | + | 0.581546i | ||||
\(148\) | −4.93135 | − | 15.1771i | −0.405355 | − | 1.24755i | ||||
\(149\) | 4.67644 | 0.383109 | 0.191555 | − | 0.981482i | \(-0.438647\pi\) | ||||
0.191555 | + | 0.981482i | \(0.438647\pi\) | |||||||
\(150\) | −6.68186 | − | 8.24380i | −0.545571 | − | 0.673104i | ||||
\(151\) | −6.54178 | −0.532362 | −0.266181 | − | 0.963923i | \(-0.585762\pi\) | ||||
−0.266181 | + | 0.963923i | \(0.585762\pi\) | |||||||
\(152\) | 2.53963 | + | 7.81618i | 0.205991 | + | 0.633976i | ||||
\(153\) | 0.907987 | − | 0.659691i | 0.0734064 | − | 0.0533329i | ||||
\(154\) | 11.8231 | − | 8.58995i | 0.952729 | − | 0.692198i | ||||
\(155\) | 7.79054 | + | 7.38961i | 0.625751 | + | 0.593548i | ||||
\(156\) | −2.42705 | − | 1.76336i | −0.194320 | − | 0.141181i | ||||
\(157\) | 3.99404 | 0.318759 | 0.159379 | − | 0.987217i | \(-0.449051\pi\) | ||||
0.159379 | + | 0.987217i | \(0.449051\pi\) | |||||||
\(158\) | −24.9877 | − | 18.1546i | −1.98791 | − | 1.44430i | ||||
\(159\) | 1.15748 | − | 3.56236i | 0.0917941 | − | 0.282513i | ||||
\(160\) | 17.6243 | + | 2.31623i | 1.39332 | + | 0.183114i | ||||
\(161\) | −3.12499 | − | 9.61773i | −0.246284 | − | 0.757984i | ||||
\(162\) | 0.655837 | − | 2.01846i | 0.0515274 | − | 0.158585i | ||||
\(163\) | 1.48372 | − | 4.56641i | 0.116214 | − | 0.357669i | −0.875985 | − | 0.482339i | \(-0.839787\pi\) |
0.992198 | + | 0.124670i | \(0.0397873\pi\) | |||||||
\(164\) | −5.78247 | − | 17.7966i | −0.451535 | − | 1.38968i | ||||
\(165\) | −2.56313 | − | 2.43123i | −0.199540 | − | 0.189271i | ||||
\(166\) | −5.72941 | + | 17.6333i | −0.444689 | + | 1.36861i | ||||
\(167\) | −19.1414 | − | 13.9070i | −1.48120 | − | 1.07616i | −0.977167 | − | 0.212474i | \(-0.931848\pi\) |
−0.504036 | − | 0.863682i | \(-0.668152\pi\) | |||||||
\(168\) | 4.66476 | 0.359894 | ||||||||
\(169\) | 9.35623 | + | 6.79770i | 0.719710 | + | 0.522900i | ||||
\(170\) | 2.29192 | − | 4.80790i | 0.175782 | − | 0.368749i | ||||
\(171\) | −6.21218 | + | 4.51341i | −0.475057 | + | 0.345149i | ||||
\(172\) | 2.53249 | − | 1.83996i | 0.193100 | − | 0.140296i | ||||
\(173\) | 4.48208 | + | 13.7944i | 0.340766 | + | 1.04877i | 0.963812 | + | 0.266584i | \(0.0858950\pi\) |
−0.623046 | + | 0.782185i | \(0.714105\pi\) | |||||||
\(174\) | −11.6820 | −0.885607 | ||||||||
\(175\) | 21.0520 | + | 5.63069i | 1.59138 | + | 0.425640i | ||||
\(176\) | 4.32433 | 0.325959 | ||||||||
\(177\) | 2.82940 | + | 8.70799i | 0.212671 | + | 0.654533i | ||||
\(178\) | 17.2355 | − | 12.5223i | 1.29186 | − | 0.938588i | ||||
\(179\) | −0.644581 | + | 0.468315i | −0.0481782 | + | 0.0350035i | −0.611614 | − | 0.791157i | \(-0.709479\pi\) |
0.563436 | + | 0.826160i | \(0.309479\pi\) | |||||||
\(180\) | −1.02172 | − | 5.50578i | −0.0761546 | − | 0.410377i | ||||
\(181\) | 11.5030 | + | 8.35741i | 0.855010 | + | 0.621201i | 0.926523 | − | 0.376239i | \(-0.122783\pi\) |
−0.0715129 | + | 0.997440i | \(0.522783\pi\) | |||||||
\(182\) | 11.0809 | 0.821372 | ||||||||
\(183\) | −1.12929 | − | 0.820477i | −0.0834795 | − | 0.0606514i | ||||
\(184\) | −0.767403 | + | 2.36182i | −0.0565737 | + | 0.174116i | ||||
\(185\) | 6.13142 | − | 12.8623i | 0.450791 | − | 0.945652i | ||||
\(186\) | 3.14937 | + | 9.69276i | 0.230923 | + | 0.710708i | ||||
\(187\) | 0.547943 | − | 1.68640i | 0.0400696 | − | 0.123321i | ||||
\(188\) | 3.19427 | − | 9.83094i | 0.232966 | − | 0.716995i | ||||
\(189\) | 1.34682 | + | 4.14509i | 0.0979667 | + | 0.301511i | ||||
\(190\) | −15.6806 | + | 32.8942i | −1.13759 | + | 2.38640i | ||||
\(191\) | −3.20441 | + | 9.86215i | −0.231863 | + | 0.713600i | 0.765659 | + | 0.643246i | \(0.222413\pi\) |
−0.997522 | + | 0.0703540i | \(0.977587\pi\) | |||||||
\(192\) | 9.22078 | + | 6.69929i | 0.665452 | + | 0.483479i | ||||
\(193\) | 4.34712 | 0.312913 | 0.156456 | − | 0.987685i | \(-0.449993\pi\) | ||||
0.156456 | + | 0.987685i | \(0.449993\pi\) | |||||||
\(194\) | 12.8775 | + | 9.35603i | 0.924548 | + | 0.671724i | ||||
\(195\) | −0.488744 | − | 2.63371i | −0.0349997 | − | 0.188604i | ||||
\(196\) | −24.3035 | + | 17.6575i | −1.73596 | + | 1.26125i | ||||
\(197\) | −1.52087 | + | 1.10498i | −0.108358 | + | 0.0787263i | −0.640644 | − | 0.767838i | \(-0.721333\pi\) |
0.532287 | + | 0.846564i | \(0.321333\pi\) | |||||||
\(198\) | −1.03616 | − | 3.18898i | −0.0736367 | − | 0.226631i | ||||
\(199\) | 4.26028 | 0.302003 | 0.151002 | − | 0.988534i | \(-0.451750\pi\) | ||||
0.151002 | + | 0.988534i | \(0.451750\pi\) | |||||||
\(200\) | −3.36966 | − | 4.15735i | −0.238271 | − | 0.293969i | ||||
\(201\) | −3.86270 | −0.272454 | ||||||||
\(202\) | −4.27489 | − | 13.1567i | −0.300780 | − | 0.925705i | ||||
\(203\) | 19.4083 | − | 14.1009i | 1.36219 | − | 0.989692i | ||||
\(204\) | 2.27387 | − | 1.65206i | 0.159203 | − | 0.115668i | ||||
\(205\) | 7.18967 | − | 15.0822i | 0.502148 | − | 1.05339i | ||||
\(206\) | −13.8197 | − | 10.0406i | −0.962867 | − | 0.699564i | ||||
\(207\) | −2.32027 | −0.161270 | ||||||||
\(208\) | 2.65265 | + | 1.92727i | 0.183928 | + | 0.133632i | ||||
\(209\) | −3.74887 | + | 11.5378i | −0.259314 | + | 0.798088i | ||||
\(210\) | 15.0066 | + | 14.2343i | 1.03555 | + | 0.982257i | ||||
\(211\) | −2.87284 | − | 8.84170i | −0.197775 | − | 0.608687i | −0.999933 | − | 0.0115762i | \(-0.996315\pi\) |
0.802158 | − | 0.597111i | \(-0.203685\pi\) | |||||||
\(212\) | 2.89868 | − | 8.92120i | 0.199082 | − | 0.612711i | ||||
\(213\) | −3.27716 | + | 10.0860i | −0.224547 | + | 0.691085i | ||||
\(214\) | 6.21566 | + | 19.1298i | 0.424894 | + | 1.30769i | ||||
\(215\) | 2.77121 | + | 0.364201i | 0.188995 | + | 0.0248383i | ||||
\(216\) | 0.330738 | − | 1.01791i | 0.0225039 | − | 0.0692599i | ||||
\(217\) | −16.9322 | − | 12.3019i | −1.14943 | − | 0.835110i | ||||
\(218\) | −24.7586 | −1.67686 | ||||||||
\(219\) | −4.04243 | − | 2.93700i | −0.273162 | − | 0.198464i | ||||
\(220\) | −6.41886 | − | 6.08852i | −0.432759 | − | 0.410488i | ||||
\(221\) | 1.08771 | − | 0.790270i | 0.0731675 | − | 0.0531593i | ||||
\(222\) | 10.9413 | − | 7.94931i | 0.734331 | − | 0.533523i | ||||
\(223\) | −1.04991 | − | 3.23129i | −0.0703072 | − | 0.216383i | 0.909729 | − | 0.415203i | \(-0.136289\pi\) |
−0.980036 | + | 0.198819i | \(0.936289\pi\) | |||||||
\(224\) | −34.6475 | −2.31498 | ||||||||
\(225\) | 2.72130 | − | 4.19458i | 0.181420 | − | 0.279639i | ||||
\(226\) | −31.6766 | −2.10710 | ||||||||
\(227\) | 8.28083 | + | 25.4858i | 0.549618 | + | 1.69155i | 0.709750 | + | 0.704454i | \(0.248808\pi\) |
−0.160132 | + | 0.987096i | \(0.551192\pi\) | |||||||
\(228\) | −15.5572 | + | 11.3029i | −1.03030 | + | 0.748555i | ||||
\(229\) | 0.956255 | − | 0.694760i | 0.0631911 | − | 0.0459110i | −0.555741 | − | 0.831355i | \(-0.687565\pi\) |
0.618932 | + | 0.785444i | \(0.287565\pi\) | |||||||
\(230\) | −9.67572 | + | 5.25631i | −0.637998 | + | 0.346591i | ||||
\(231\) | 5.57078 | + | 4.04741i | 0.366530 | + | 0.266300i | ||||
\(232\) | −5.89121 | −0.386777 | ||||||||
\(233\) | −5.73984 | − | 4.17024i | −0.376030 | − | 0.273201i | 0.383677 | − | 0.923467i | \(-0.374658\pi\) |
−0.759707 | + | 0.650266i | \(0.774658\pi\) | |||||||
\(234\) | 0.785653 | − | 2.41799i | 0.0513598 | − | 0.158069i | ||||
\(235\) | 8.11023 | − | 4.40586i | 0.529053 | − | 0.287407i | ||||
\(236\) | 7.08566 | + | 21.8074i | 0.461237 | + | 1.41954i | ||||
\(237\) | 4.49714 | − | 13.8408i | 0.292121 | − | 0.899055i | ||||
\(238\) | −3.20808 | + | 9.87345i | −0.207949 | + | 0.640001i | ||||
\(239\) | 0.0132236 | + | 0.0406981i | 0.000855365 | + | 0.00263254i | 0.951483 | − | 0.307700i | \(-0.0995595\pi\) |
−0.950628 | + | 0.310333i | \(0.899559\pi\) | |||||||
\(240\) | 1.11669 | + | 6.01757i | 0.0720823 | + | 0.388432i | ||||
\(241\) | −3.63746 | + | 11.1950i | −0.234310 | + | 0.721131i | 0.762903 | + | 0.646513i | \(0.223774\pi\) |
−0.997212 | + | 0.0746174i | \(0.976226\pi\) | |||||||
\(242\) | 14.6012 | + | 10.6084i | 0.938602 | + | 0.681934i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.82808 | − | 2.05472i | −0.181049 | − | 0.131540i | ||||
\(245\) | −26.5944 | − | 3.49512i | −1.69906 | − | 0.223295i | ||||
\(246\) | 12.8297 | − | 9.32131i | 0.817991 | − | 0.594305i | ||||
\(247\) | −7.44182 | + | 5.40680i | −0.473511 | + | 0.344026i | ||||
\(248\) | 1.58823 | + | 4.88806i | 0.100852 | + | 0.310392i | ||||
\(249\) | −8.73603 | −0.553623 | ||||||||
\(250\) | 1.84570 | − | 23.6565i | 0.116733 | − | 1.49617i | ||||
\(251\) | 17.4764 | 1.10310 | 0.551550 | − | 0.834142i | \(-0.314036\pi\) | ||||
0.551550 | + | 0.834142i | \(0.314036\pi\) | |||||||
\(252\) | 3.37284 | + | 10.3805i | 0.212469 | + | 0.653912i | ||||
\(253\) | −2.96571 | + | 2.15471i | −0.186452 | + | 0.135466i | ||||
\(254\) | 29.1816 | − | 21.2017i | 1.83102 | − | 1.33031i | ||||
\(255\) | 2.48822 | + | 0.327009i | 0.155818 | + | 0.0204781i | ||||
\(256\) | −4.20735 | − | 3.05682i | −0.262960 | − | 0.191051i | ||||
\(257\) | 15.4671 | 0.964814 | 0.482407 | − | 0.875947i | \(-0.339763\pi\) | ||||
0.482407 | + | 0.875947i | \(0.339763\pi\) | |||||||
\(258\) | 2.14622 | + | 1.55932i | 0.133618 | + | 0.0970792i | ||||
\(259\) | −8.58236 | + | 26.4138i | −0.533282 | + | 1.64127i | ||||
\(260\) | −1.22396 | − | 6.59560i | −0.0759068 | − | 0.409042i | ||||
\(261\) | −1.70092 | − | 5.23490i | −0.105284 | − | 0.324032i | ||||
\(262\) | −0.215687 | + | 0.663815i | −0.0133252 | + | 0.0410106i | ||||
\(263\) | 0.447331 | − | 1.37674i | 0.0275836 | − | 0.0848936i | −0.936317 | − | 0.351156i | \(-0.885789\pi\) |
0.963901 | + | 0.266262i | \(0.0857887\pi\) | |||||||
\(264\) | −0.522535 | − | 1.60820i | −0.0321598 | − | 0.0989778i | ||||
\(265\) | 7.35972 | − | 3.99815i | 0.452104 | − | 0.245604i | ||||
\(266\) | 21.9487 | − | 67.5513i | 1.34576 | − | 4.14183i | ||||
\(267\) | 8.12102 | + | 5.90026i | 0.496998 | + | 0.361090i | ||||
\(268\) | −9.67336 | −0.590895 | ||||||||
\(269\) | 7.04344 | + | 5.11736i | 0.429446 | + | 0.312011i | 0.781427 | − | 0.623996i | \(-0.214492\pi\) |
−0.351981 | + | 0.936007i | \(0.614492\pi\) | |||||||
\(270\) | 4.17008 | − | 2.26538i | 0.253783 | − | 0.137867i | ||||
\(271\) | 23.1652 | − | 16.8305i | 1.40719 | − | 1.02238i | 0.413462 | − | 0.910521i | \(-0.364319\pi\) |
0.993724 | − | 0.111860i | \(-0.0356807\pi\) | |||||||
\(272\) | −2.48524 | + | 1.80563i | −0.150690 | + | 0.109482i | ||||
\(273\) | 1.61341 | + | 4.96556i | 0.0976480 | + | 0.300530i | ||||
\(274\) | 9.68359 | 0.585007 | ||||||||
\(275\) | −0.416988 | − | 7.88852i | −0.0251453 | − | 0.475695i | ||||
\(276\) | −5.81066 | −0.349761 | ||||||||
\(277\) | 1.63844 | + | 5.04259i | 0.0984442 | + | 0.302980i | 0.988136 | − | 0.153582i | \(-0.0490808\pi\) |
−0.889692 | + | 0.456562i | \(0.849081\pi\) | |||||||
\(278\) | 8.12830 | − | 5.90555i | 0.487503 | − | 0.354192i | ||||
\(279\) | −3.88495 | + | 2.82258i | −0.232586 | + | 0.168983i | ||||
\(280\) | 7.56780 | + | 7.17833i | 0.452262 | + | 0.428987i | ||||
\(281\) | 19.4837 | + | 14.1557i | 1.16230 | + | 0.844461i | 0.990067 | − | 0.140595i | \(-0.0449015\pi\) |
0.172234 | + | 0.985056i | \(0.444902\pi\) | |||||||
\(282\) | 8.76025 | 0.521665 | ||||||||
\(283\) | 21.9359 | + | 15.9374i | 1.30396 | + | 0.947380i | 0.999986 | − | 0.00530192i | \(-0.00168766\pi\) |
0.303970 | + | 0.952682i | \(0.401688\pi\) | |||||||
\(284\) | −8.20698 | + | 25.2585i | −0.486995 | + | 1.49882i | ||||
\(285\) | −17.0237 | − | 2.23730i | −1.00839 | − | 0.132526i | ||||
\(286\) | −1.24126 | − | 3.82020i | −0.0733971 | − | 0.225893i | ||||
\(287\) | −10.0636 | + | 30.9726i | −0.594037 | + | 1.82826i | ||||
\(288\) | −2.45656 | + | 7.56051i | −0.144754 | + | 0.445507i | ||||
\(289\) | −4.86404 | − | 14.9700i | −0.286120 | − | 0.880587i | ||||
\(290\) | −18.9520 | − | 17.9767i | −1.11290 | − | 1.05563i | ||||
\(291\) | −2.31762 | + | 7.13289i | −0.135861 | + | 0.418137i | ||||
\(292\) | −10.1234 | − | 7.35512i | −0.592430 | − | 0.430426i | ||||
\(293\) | −20.3016 | −1.18603 | −0.593017 | − | 0.805190i | \(-0.702063\pi\) | ||||
−0.593017 | + | 0.805190i | \(0.702063\pi\) | |||||||
\(294\) | −20.5966 | − | 14.9643i | −1.20122 | − | 0.872736i | ||||
\(295\) | −8.81000 | + | 18.4813i | −0.512938 | + | 1.07602i | ||||
\(296\) | 5.51769 | − | 4.00883i | 0.320709 | − | 0.233009i | ||||
\(297\) | 1.27817 | − | 0.928645i | 0.0741670 | − | 0.0538855i | ||||
\(298\) | 3.06698 | + | 9.43921i | 0.177666 | + | 0.546799i | ||||
\(299\) | −2.77955 | −0.160745 | ||||||||
\(300\) | 6.81496 | − | 10.5045i | 0.393462 | − | 0.606477i | ||||
\(301\) | −5.44792 | −0.314013 | ||||||||
\(302\) | −4.29034 | − | 13.2043i | −0.246881 | − | 0.759823i | ||||
\(303\) | 5.27335 | − | 3.83131i | 0.302946 | − | 0.220103i | ||||
\(304\) | 17.0032 | − | 12.3536i | 0.975203 | − | 0.708527i | ||||
\(305\) | −0.569501 | − | 3.06889i | −0.0326095 | − | 0.175724i | ||||
\(306\) | 1.92705 | + | 1.40008i | 0.110162 | + | 0.0800375i | ||||
\(307\) | −2.51330 | −0.143442 | −0.0717208 | − | 0.997425i | \(-0.522849\pi\) | ||||
−0.0717208 | + | 0.997425i | \(0.522849\pi\) | |||||||
\(308\) | 13.9509 | + | 10.1359i | 0.794927 | + | 0.577548i | ||||
\(309\) | 2.48720 | − | 7.65482i | 0.141492 | − | 0.435468i | ||||
\(310\) | −9.80630 | + | 20.5713i | −0.556960 | + | 1.16837i | ||||
\(311\) | 1.49075 | + | 4.58806i | 0.0845327 | + | 0.260165i | 0.984385 | − | 0.176030i | \(-0.0563257\pi\) |
−0.899852 | + | 0.436195i | \(0.856326\pi\) | |||||||
\(312\) | 0.396205 | − | 1.21939i | 0.0224307 | − | 0.0690345i | ||||
\(313\) | −1.85043 | + | 5.69504i | −0.104592 | + | 0.321903i | −0.989635 | − | 0.143608i | \(-0.954129\pi\) |
0.885042 | + | 0.465511i | \(0.154129\pi\) | |||||||
\(314\) | 2.61944 | + | 8.06180i | 0.147823 | + | 0.454954i | ||||
\(315\) | −4.19364 | + | 8.79726i | −0.236285 | + | 0.495669i | ||||
\(316\) | 11.2622 | − | 34.6615i | 0.633548 | − | 1.94986i | ||||
\(317\) | −14.0389 | − | 10.1999i | −0.788506 | − | 0.572883i | 0.119014 | − | 0.992893i | \(-0.462027\pi\) |
−0.907520 | + | 0.420010i | \(0.862027\pi\) | |||||||
\(318\) | 7.94959 | 0.445791 | ||||||||
\(319\) | −7.03543 | − | 5.11154i | −0.393909 | − | 0.286191i | ||||
\(320\) | 4.65003 | + | 25.0578i | 0.259945 | + | 1.40077i | ||||
\(321\) | −7.66742 | + | 5.57071i | −0.427954 | + | 0.310926i | ||||
\(322\) | 17.3635 | − | 12.6153i | 0.967631 | − | 0.703025i | ||||
\(323\) | −2.66312 | − | 8.19624i | −0.148180 | − | 0.456051i | ||||
\(324\) | 2.50430 | 0.139128 | ||||||||
\(325\) | 3.25996 | − | 5.02486i | 0.180830 | − | 0.278729i | ||||
\(326\) | 10.1902 | 0.564383 | ||||||||
\(327\) | −3.60491 | − | 11.0948i | −0.199352 | − | 0.613543i | ||||
\(328\) | 6.47000 | − | 4.70073i | 0.357246 | − | 0.259555i | ||||
\(329\) | −14.5542 | + | 10.5742i | −0.802398 | + | 0.582976i | ||||
\(330\) | 3.22633 | − | 6.76807i | 0.177604 | − | 0.372570i | ||||
\(331\) | −16.4518 | − | 11.9529i | −0.904270 | − | 0.656991i | 0.0352890 | − | 0.999377i | \(-0.488765\pi\) |
−0.939559 | + | 0.342386i | \(0.888765\pi\) | |||||||
\(332\) | −21.8776 | −1.20069 | ||||||||
\(333\) | 5.15531 | + | 3.74555i | 0.282509 | + | 0.205255i | ||||
\(334\) | 15.5171 | − | 47.7568i | 0.849059 | − | 2.61314i | ||||
\(335\) | −6.26659 | − | 5.94409i | −0.342380 | − | 0.324760i | ||||
\(336\) | −3.68636 | − | 11.3454i | −0.201107 | − | 0.618945i | ||||
\(337\) | 10.5860 | − | 32.5805i | 0.576658 | − | 1.77477i | −0.0538048 | − | 0.998551i | \(-0.517135\pi\) |
0.630463 | − | 0.776219i | \(-0.282865\pi\) | |||||||
\(338\) | −7.58472 | + | 23.3434i | −0.412554 | + | 1.26971i | ||||
\(339\) | −4.61219 | − | 14.1949i | −0.250500 | − | 0.770960i | ||||
\(340\) | 6.23124 | + | 0.818929i | 0.337937 | + | 0.0444127i | ||||
\(341\) | −2.34445 | + | 7.21548i | −0.126959 | + | 0.390740i | ||||
\(342\) | −13.1843 | − | 9.57897i | −0.712926 | − | 0.517971i | ||||
\(343\) | 21.7731 | 1.17564 | ||||||||
\(344\) | 1.08234 | + | 0.786366i | 0.0583558 | + | 0.0423980i | ||||
\(345\) | −3.76426 | − | 3.57053i | −0.202661 | − | 0.192231i | ||||
\(346\) | −24.9039 | + | 18.0938i | −1.33884 | + | 0.972727i | ||||
\(347\) | 0.0399344 | − | 0.0290140i | 0.00214379 | − | 0.00155756i | −0.586713 | − | 0.809795i | \(-0.699578\pi\) |
0.588857 | + | 0.808238i | \(0.299578\pi\) | |||||||
\(348\) | −4.25962 | − | 13.1098i | −0.228340 | − | 0.702757i | ||||
\(349\) | −7.47437 | −0.400094 | −0.200047 | − | 0.979786i | \(-0.564109\pi\) | ||||
−0.200047 | + | 0.979786i | \(0.564109\pi\) | |||||||
\(350\) | 2.44137 | + | 46.1854i | 0.130497 | + | 2.46871i | ||||
\(351\) | 1.19794 | 0.0639413 | ||||||||
\(352\) | 3.88113 | + | 11.9449i | 0.206865 | + | 0.636665i | ||||
\(353\) | 15.0194 | − | 10.9122i | 0.799401 | − | 0.580799i | −0.111337 | − | 0.993783i | \(-0.535513\pi\) |
0.910738 | + | 0.412984i | \(0.135513\pi\) | |||||||
\(354\) | −15.7211 | + | 11.4220i | −0.835567 | + | 0.607075i | ||||
\(355\) | −20.8375 | + | 11.3199i | −1.10594 | + | 0.600798i | ||||
\(356\) | 20.3375 | + | 14.7760i | 1.07788 | + | 0.783128i | ||||
\(357\) | −4.89158 | −0.258890 | ||||||||
\(358\) | −1.36802 | − | 0.993921i | −0.0723019 | − | 0.0525304i | ||||
\(359\) | 3.27695 | − | 10.0854i | 0.172951 | − | 0.532289i | −0.826583 | − | 0.562815i | \(-0.809718\pi\) |
0.999534 | + | 0.0305264i | \(0.00971835\pi\) | |||||||
\(360\) | 2.10297 | − | 1.14243i | 0.110836 | − | 0.0602115i | ||||
\(361\) | 12.3490 | + | 38.0062i | 0.649945 | + | 2.00032i | ||||
\(362\) | −9.32500 | + | 28.6994i | −0.490111 | + | 1.50841i | ||||
\(363\) | −2.62785 | + | 8.08769i | −0.137926 | + | 0.424493i | ||||
\(364\) | 4.04046 | + | 12.4353i | 0.211778 | + | 0.651785i | ||||
\(365\) | −2.03859 | − | 10.9854i | −0.106705 | − | 0.575004i | ||||
\(366\) | 0.915470 | − | 2.81753i | 0.0478524 | − | 0.147274i | ||||
\(367\) | 9.39886 | + | 6.82867i | 0.490617 | + | 0.356454i | 0.805421 | − | 0.592703i | \(-0.201939\pi\) |
−0.314805 | + | 0.949156i | \(0.601939\pi\) | |||||||
\(368\) | 6.35078 | 0.331057 | ||||||||
\(369\) | 6.04508 | + | 4.39201i | 0.314695 | + | 0.228639i | ||||
\(370\) | 29.9832 | + | 3.94048i | 1.55875 | + | 0.204856i | ||||
\(371\) | −13.2074 | + | 9.59570i | −0.685692 | + | 0.498184i | ||||
\(372\) | −9.72907 | + | 7.06859i | −0.504429 | + | 0.366489i | ||||
\(373\) | −7.14671 | − | 21.9953i | −0.370043 | − | 1.13887i | −0.946763 | − | 0.321932i | \(-0.895668\pi\) |
0.576720 | − | 0.816942i | \(-0.304332\pi\) | |||||||
\(374\) | 3.76328 | 0.194595 | ||||||||
\(375\) | 10.8697 | − | 2.61735i | 0.561307 | − | 0.135160i | ||||
\(376\) | 4.41779 | 0.227830 | ||||||||
\(377\) | −2.03760 | − | 6.27109i | −0.104942 | − | 0.322978i | ||||
\(378\) | −7.48339 | + | 5.43700i | −0.384904 | + | 0.279649i | ||||
\(379\) | −20.1374 | + | 14.6307i | −1.03439 | + | 0.751527i | −0.969182 | − | 0.246345i | \(-0.920770\pi\) |
−0.0652058 | + | 0.997872i | \(0.520770\pi\) | |||||||
\(380\) | −42.6323 | − | 5.60287i | −2.18699 | − | 0.287421i | ||||
\(381\) | 13.7498 | + | 9.98980i | 0.704423 | + | 0.511793i | ||||
\(382\) | −22.0079 | −1.12602 | ||||||||
\(383\) | 12.7195 | + | 9.24123i | 0.649934 | + | 0.472205i | 0.863249 | − | 0.504779i | \(-0.168426\pi\) |
−0.213315 | + | 0.976984i | \(0.568426\pi\) | |||||||
\(384\) | −2.56179 | + | 7.88439i | −0.130731 | + | 0.402349i | ||||
\(385\) | 2.80934 | + | 15.1388i | 0.143177 | + | 0.771545i | ||||
\(386\) | 2.85100 | + | 8.77449i | 0.145112 | + | 0.446610i | ||||
\(387\) | −0.386266 | + | 1.18880i | −0.0196350 | + | 0.0604303i | ||||
\(388\) | −5.80400 | + | 17.8629i | −0.294654 | + | 0.906851i | ||||
\(389\) | −2.62860 | − | 8.09000i | −0.133275 | − | 0.410179i | 0.862042 | − | 0.506836i | \(-0.169185\pi\) |
−0.995318 | + | 0.0966568i | \(0.969185\pi\) | |||||||
\(390\) | 4.99550 | − | 2.71379i | 0.252957 | − | 0.137418i | ||||
\(391\) | 0.804717 | − | 2.47667i | 0.0406963 | − | 0.125250i | ||||
\(392\) | −10.3869 | − | 7.54649i | −0.524615 | − | 0.381155i | ||||
\(393\) | −0.328872 | −0.0165894 | ||||||||
\(394\) | −3.22779 | − | 2.34513i | −0.162614 | − | 0.118146i | ||||
\(395\) | 28.5946 | − | 15.5340i | 1.43875 | − | 0.781599i | ||||
\(396\) | 3.20092 | − | 2.32561i | 0.160852 | − | 0.116866i | ||||
\(397\) | −21.2407 | + | 15.4322i | −1.06604 | + | 0.774522i | −0.975196 | − | 0.221343i | \(-0.928956\pi\) |
−0.0908420 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(398\) | 2.79405 | + | 8.59921i | 0.140053 | + | 0.431039i | ||||
\(399\) | 33.4667 | 1.67543 | ||||||||
\(400\) | −7.44843 | + | 11.4809i | −0.372422 | + | 0.574046i | ||||
\(401\) | −25.2815 | −1.26250 | −0.631250 | − | 0.775579i | \(-0.717458\pi\) | ||||
−0.631250 | + | 0.775579i | \(0.717458\pi\) | |||||||
\(402\) | −2.53330 | − | 7.79670i | −0.126350 | − | 0.388864i | ||||
\(403\) | −4.65393 | + | 3.38128i | −0.231829 | + | 0.168434i | ||||
\(404\) | 13.2060 | − | 9.59475i | 0.657025 | − | 0.477356i | ||||
\(405\) | 1.62233 | + | 1.53884i | 0.0806144 | + | 0.0764657i | ||||
\(406\) | 41.1908 | + | 29.9269i | 2.04427 | + | 1.48525i | ||||
\(407\) | 10.0677 | 0.499035 | ||||||||
\(408\) | 0.971811 | + | 0.706062i | 0.0481118 | + | 0.0349553i | ||||
\(409\) | 10.4427 | − | 32.1392i | 0.516357 | − | 1.58918i | −0.264443 | − | 0.964401i | \(-0.585188\pi\) |
0.780800 | − | 0.624781i | \(-0.214812\pi\) | |||||||
\(410\) | 35.1581 | + | 4.62058i | 1.73633 | + | 0.228194i | ||||
\(411\) | 1.40995 | + | 4.33939i | 0.0695479 | + | 0.214046i | ||||
\(412\) | 6.22870 | − | 19.1700i | 0.306866 | − | 0.944437i | ||||
\(413\) | 12.3317 | − | 37.9529i | 0.606801 | − | 1.86754i | ||||
\(414\) | −1.52172 | − | 4.68338i | −0.0747885 | − | 0.230175i | ||||
\(415\) | −14.1728 | − | 13.4434i | −0.695713 | − | 0.659909i | ||||
\(416\) | −2.94281 | + | 9.05703i | −0.144283 | + | 0.444057i | ||||
\(417\) | 3.82989 | + | 2.78258i | 0.187550 | + | 0.136263i | ||||
\(418\) | −25.7473 | −1.25934 | ||||||||
\(419\) | −6.41819 | − | 4.66309i | −0.313549 | − | 0.227807i | 0.419869 | − | 0.907585i | \(-0.362076\pi\) |
−0.733418 | + | 0.679778i | \(0.762076\pi\) | |||||||
\(420\) | −10.5021 | + | 22.0310i | −0.512452 | + | 1.07500i | ||||
\(421\) | −6.05788 | + | 4.40131i | −0.295243 | + | 0.214507i | −0.725539 | − | 0.688181i | \(-0.758409\pi\) |
0.430296 | + | 0.902688i | \(0.358409\pi\) | |||||||
\(422\) | 15.9625 | − | 11.5974i | 0.777042 | − | 0.564554i | ||||
\(423\) | 1.27551 | + | 3.92563i | 0.0620176 | + | 0.190870i | ||||
\(424\) | 4.00897 | 0.194693 | ||||||||
\(425\) | 3.53350 | + | 4.35949i | 0.171400 | + | 0.211466i | ||||
\(426\) | −22.5076 | −1.09049 | ||||||||
\(427\) | 1.88000 | + | 5.78604i | 0.0909795 | + | 0.280006i | ||||
\(428\) | −19.2015 | + | 13.9507i | −0.928140 | + | 0.674333i | ||||
\(429\) | 1.53117 | − | 1.11246i | 0.0739257 | − | 0.0537101i | ||||
\(430\) | 1.08234 | + | 5.83244i | 0.0521950 | + | 0.281265i | ||||
\(431\) | −18.8882 | − | 13.7231i | −0.909811 | − | 0.661016i | 0.0311564 | − | 0.999515i | \(-0.490081\pi\) |
−0.940967 | + | 0.338498i | \(0.890081\pi\) | |||||||
\(432\) | −2.73708 | −0.131688 | ||||||||
\(433\) | 2.71569 | + | 1.97306i | 0.130508 | + | 0.0948193i | 0.651124 | − | 0.758971i | \(-0.274298\pi\) |
−0.520616 | + | 0.853791i | \(0.674298\pi\) | |||||||
\(434\) | 13.7262 | − | 42.2449i | 0.658879 | − | 2.02782i | ||||
\(435\) | 5.29622 | − | 11.1102i | 0.253934 | − | 0.532693i | ||||
\(436\) | −9.02778 | − | 27.7846i | −0.432352 | − | 1.33064i | ||||
\(437\) | −5.50564 | + | 16.9446i | −0.263370 | + | 0.810571i | ||||
\(438\) | 3.27703 | − | 10.0857i | 0.156583 | − | 0.481912i | ||||
\(439\) | −2.93072 | − | 9.01984i | −0.139876 | − | 0.430493i | 0.856441 | − | 0.516245i | \(-0.172671\pi\) |
−0.996317 | + | 0.0857520i | \(0.972671\pi\) | |||||||
\(440\) | 1.62704 | − | 3.41313i | 0.0775659 | − | 0.162715i | ||||
\(441\) | 3.70686 | − | 11.4086i | 0.176517 | − | 0.543264i | ||||
\(442\) | 2.30849 | + | 1.67722i | 0.109804 | + | 0.0797771i | ||||
\(443\) | 9.65446 | 0.458697 | 0.229349 | − | 0.973344i | \(-0.426340\pi\) | ||||
0.229349 | + | 0.973344i | \(0.426340\pi\) | |||||||
\(444\) | 12.9104 | + | 9.37999i | 0.612703 | + | 0.445154i | ||||
\(445\) | 4.09542 | + | 22.0692i | 0.194142 | + | 1.04618i | ||||
\(446\) | 5.83366 | − | 4.23840i | 0.276232 | − | 0.200694i | ||||
\(447\) | −3.78332 | + | 2.74874i | −0.178945 | + | 0.130011i | ||||
\(448\) | −15.3504 | − | 47.2437i | −0.725238 | − | 2.23205i | ||||
\(449\) | 31.5260 | 1.48780 | 0.743902 | − | 0.668289i | \(-0.232973\pi\) | ||||
0.743902 | + | 0.668289i | \(0.232973\pi\) | |||||||
\(450\) | 10.2513 | + | 2.74188i | 0.483252 | + | 0.129253i | ||||
\(451\) | 11.8053 | 0.555888 | ||||||||
\(452\) | −11.5503 | − | 35.5482i | −0.543281 | − | 1.67205i | ||||
\(453\) | 5.29241 | − | 3.84516i | 0.248659 | − | 0.180661i | ||||
\(454\) | −46.0111 | + | 33.4290i | −2.15941 | + | 1.56890i | ||||
\(455\) | −5.02373 | + | 10.5386i | −0.235516 | + | 0.494056i | ||||
\(456\) | −6.64884 | − | 4.83067i | −0.311361 | − | 0.226217i | ||||
\(457\) | −9.94467 | −0.465192 | −0.232596 | − | 0.972573i | \(-0.574722\pi\) | ||||
−0.232596 | + | 0.972573i | \(0.574722\pi\) | |||||||
\(458\) | 2.02949 | + | 1.47451i | 0.0948319 | + | 0.0688994i | ||||
\(459\) | −0.346820 | + | 1.06740i | −0.0161882 | + | 0.0498221i | ||||
\(460\) | −9.42683 | − | 8.94169i | −0.439528 | − | 0.416908i | ||||
\(461\) | −7.31863 | − | 22.5244i | −0.340863 | − | 1.04907i | −0.963762 | − | 0.266765i | \(-0.914045\pi\) |
0.622899 | − | 0.782302i | \(-0.285955\pi\) | |||||||
\(462\) | −4.51601 | + | 13.8988i | −0.210104 | + | 0.646632i | ||||
\(463\) | 8.54443 | − | 26.2971i | 0.397094 | − | 1.22213i | −0.530226 | − | 0.847857i | \(-0.677893\pi\) |
0.927319 | − | 0.374272i | \(-0.122107\pi\) | |||||||
\(464\) | 4.65556 | + | 14.3284i | 0.216129 | + | 0.665177i | ||||
\(465\) | −10.6462 | − | 1.39915i | −0.493705 | − | 0.0648842i | ||||
\(466\) | 4.65306 | − | 14.3206i | 0.215549 | − | 0.663391i | ||||
\(467\) | −3.52602 | − | 2.56180i | −0.163165 | − | 0.118546i | 0.503207 | − | 0.864166i | \(-0.332153\pi\) |
−0.666371 | + | 0.745620i | \(0.732153\pi\) | |||||||
\(468\) | 3.00000 | 0.138675 | ||||||||
\(469\) | 13.6200 | + | 9.89548i | 0.628912 | + | 0.456931i | ||||
\(470\) | 14.2120 | + | 13.4806i | 0.655553 | + | 0.621815i | ||||
\(471\) | −3.23124 | + | 2.34764i | −0.148888 | + | 0.108173i | ||||
\(472\) | −7.92814 | + | 5.76013i | −0.364922 | + | 0.265132i | ||||
\(473\) | 0.610263 | + | 1.87820i | 0.0280599 | + | 0.0863596i | ||||
\(474\) | 30.8864 | 1.41866 | ||||||||
\(475\) | −24.1752 | − | 29.8264i | −1.10923 | − | 1.36853i | ||||
\(476\) | −12.2500 | −0.561477 | ||||||||
\(477\) | 1.15748 | + | 3.56236i | 0.0529973 | + | 0.163109i | ||||
\(478\) | −0.0734750 | + | 0.0533827i | −0.00336067 | + | 0.00244167i | ||||
\(479\) | −10.3670 | + | 7.53204i | −0.473679 | + | 0.344148i | −0.798873 | − | 0.601499i | \(-0.794570\pi\) |
0.325195 | + | 0.945647i | \(0.394570\pi\) | |||||||
\(480\) | −15.6198 | + | 8.48541i | −0.712942 | + | 0.387304i | ||||
\(481\) | 6.17575 | + | 4.48695i | 0.281590 | + | 0.204587i | ||||
\(482\) | −24.9822 | −1.13791 | ||||||||
\(483\) | 8.18133 | + | 5.94409i | 0.372263 | + | 0.270465i | ||||
\(484\) | −6.58092 | + | 20.2540i | −0.299133 | + | 0.920636i | ||||
\(485\) | −14.7363 | + | 8.00548i | −0.669142 | + | 0.363510i | ||||
\(486\) | 0.655837 | + | 2.01846i | 0.0297494 | + | 0.0915592i | ||||
\(487\) | −2.13904 | + | 6.58330i | −0.0969293 | + | 0.298318i | −0.987752 | − | 0.156034i | \(-0.950129\pi\) |
0.890822 | + | 0.454352i | \(0.150129\pi\) | |||||||
\(488\) | 0.461671 | − | 1.42088i | 0.0208989 | − | 0.0643201i | ||||
\(489\) | 1.48372 | + | 4.56641i | 0.0670960 | + | 0.206500i | ||||
\(490\) | −10.3869 | − | 55.9720i | −0.469230 | − | 2.52856i | ||||
\(491\) | 8.28665 | − | 25.5037i | 0.373971 | − | 1.15096i | −0.570199 | − | 0.821507i | \(-0.693134\pi\) |
0.944170 | − | 0.329458i | \(-0.106866\pi\) | |||||||
\(492\) | 15.1387 | + | 10.9989i | 0.682505 | + | 0.495869i | ||||
\(493\) | 6.17766 | 0.278228 | ||||||||
\(494\) | −15.7940 | − | 11.4750i | −0.710606 | − | 0.516286i | ||||
\(495\) | 3.50266 | + | 0.460330i | 0.157433 | + | 0.0206903i | ||||
\(496\) | 10.6334 | − | 7.72564i | 0.477455 | − | 0.346891i | ||||
\(497\) | 37.3938 | − | 27.1682i | 1.67734 | − | 1.21866i | ||||
\(498\) | −5.72941 | − | 17.6333i | −0.256741 | − | 0.790168i | ||||
\(499\) | 2.75460 | 0.123313 | 0.0616565 | − | 0.998097i | \(-0.480362\pi\) | ||||
0.0616565 | + | 0.998097i | \(0.480362\pi\) | |||||||
\(500\) | 27.2209 | − | 6.55464i | 1.21735 | − | 0.293132i | ||||
\(501\) | 23.6600 | 1.05705 | ||||||||
\(502\) | 11.4617 | + | 35.2754i | 0.511559 | + | 1.57442i | ||||
\(503\) | −12.7098 | + | 9.23422i | −0.566702 | + | 0.411733i | −0.833906 | − | 0.551907i | \(-0.813900\pi\) |
0.267203 | + | 0.963640i | \(0.413900\pi\) | |||||||
\(504\) | −3.77387 | + | 2.74188i | −0.168102 | + | 0.122133i | ||||
\(505\) | 14.4509 | + | 1.89918i | 0.643057 | + | 0.0845125i | ||||
\(506\) | −6.29422 | − | 4.57302i | −0.279812 | − | 0.203295i | ||||
\(507\) | −11.5649 | −0.513617 | ||||||||
\(508\) | 34.4336 | + | 25.0175i | 1.52774 | + | 1.10997i | ||||
\(509\) | −12.6970 | + | 39.0774i | −0.562785 | + | 1.73207i | 0.111657 | + | 0.993747i | \(0.464384\pi\) |
−0.674442 | + | 0.738328i | \(0.735616\pi\) | |||||||
\(510\) | 0.971811 | + | 5.23683i | 0.0430325 | + | 0.231891i | ||||
\(511\) | 6.72968 | + | 20.7118i | 0.297703 | + | 0.916237i | ||||
\(512\) | 8.53432 | − | 26.2659i | 0.377167 | − | 1.16080i | ||||
\(513\) | 2.37284 | − | 7.30285i | 0.104763 | − | 0.322429i | ||||
\(514\) | 10.1439 | + | 31.2198i | 0.447430 | + | 1.37705i | ||||
\(515\) | 15.8146 | − | 8.59126i | 0.696876 | − | 0.378576i | ||||
\(516\) | −0.967325 | + | 2.97712i | −0.0425841 | + | 0.131060i | ||||
\(517\) | 5.27584 | + | 3.83312i | 0.232031 | + | 0.168580i | ||||
\(518\) | −58.9438 | −2.58984 | ||||||||
\(519\) | −11.7342 | − | 8.52541i | −0.515075 | − | 0.374224i | ||||
\(520\) | 2.51923 | − | 1.36856i | 0.110475 | − | 0.0600155i | ||||
\(521\) | −29.2630 | + | 21.2608i | −1.28203 | + | 0.931452i | −0.999612 | − | 0.0278383i | \(-0.991138\pi\) |
−0.282421 | + | 0.959290i | \(0.591138\pi\) | |||||||
\(522\) | 9.45090 | − | 6.86648i | 0.413655 | − | 0.300538i | ||||
\(523\) | 8.66761 | + | 26.6761i | 0.379008 | + | 1.16647i | 0.940735 | + | 0.339144i | \(0.110137\pi\) |
−0.561727 | + | 0.827323i | \(0.689863\pi\) | |||||||
\(524\) | −0.823595 | −0.0359789 | ||||||||
\(525\) | −20.3411 | + | 7.81873i | −0.887757 | + | 0.341237i | ||||
\(526\) | 3.07228 | 0.133958 | ||||||||
\(527\) | −1.66545 | − | 5.12573i | −0.0725482 | − | 0.223280i | ||||
\(528\) | −3.49846 | + | 2.54178i | −0.152251 | + | 0.110617i | ||||
\(529\) | 14.2519 | − | 10.3546i | 0.619648 | − | 0.450201i | ||||
\(530\) | 12.8969 | + | 12.2332i | 0.560205 | + | 0.531374i | ||||
\(531\) | −7.40746 | − | 5.38184i | −0.321456 | − | 0.233552i | ||||
\(532\) | 83.8108 | 3.63366 | ||||||||
\(533\) | 7.24165 | + | 5.26137i | 0.313671 | + | 0.227895i | ||||
\(534\) | −6.58338 | + | 20.2616i | −0.284891 | + | 0.876803i | ||||
\(535\) | −21.0115 | − | 2.76140i | −0.908408 | − | 0.119386i | ||||
\(536\) | −1.27754 | − | 3.93187i | −0.0551815 | − | 0.169831i | ||||
\(537\) | 0.246208 | − | 0.757750i | 0.0106247 | − | 0.0326993i | ||||
\(538\) | −5.70983 | + | 17.5731i | −0.246168 | + | 0.757628i | ||||
\(539\) | −5.85650 | − | 18.0244i | −0.252257 | − | 0.776368i | ||||
\(540\) | 4.06281 | + | 3.85372i | 0.174835 | + | 0.165838i | ||||
\(541\) | 1.06865 | − | 3.28896i | 0.0459448 | − | 0.141404i | −0.925452 | − | 0.378864i | \(-0.876315\pi\) |
0.971397 | + | 0.237460i | \(0.0763149\pi\) | |||||||
\(542\) | 49.1643 | + | 35.7200i | 2.11179 | + | 1.53430i | ||||
\(543\) | −14.2185 | −0.610173 | ||||||||
\(544\) | −7.21812 | − | 5.24427i | −0.309474 | − | 0.224846i | ||||
\(545\) | 11.2247 | − | 23.5468i | 0.480815 | − | 1.00863i | ||||
\(546\) | −8.96465 | + | 6.51320i | −0.383652 | + | 0.278739i | ||||
\(547\) | −11.2967 | + | 8.20751i | −0.483011 | + | 0.350928i | −0.802490 | − | 0.596665i | \(-0.796492\pi\) |
0.319479 | + | 0.947593i | \(0.396492\pi\) | |||||||
\(548\) | 3.53095 | + | 10.8671i | 0.150835 | + | 0.464221i | ||||
\(549\) | 1.39588 | 0.0595747 | ||||||||
\(550\) | 15.6492 | − | 6.01525i | 0.667283 | − | 0.256491i | ||||
\(551\) | −42.2657 | −1.80058 | ||||||||
\(552\) | −0.767403 | − | 2.36182i | −0.0326629 | − | 0.100526i | ||||
\(553\) | −51.3144 | + | 37.2821i | −2.18211 | + | 1.58540i | ||||
\(554\) | −9.10372 | + | 6.61424i | −0.386780 | + | 0.281012i | ||||
\(555\) | 2.59982 | + | 14.0097i | 0.110356 | + | 0.594681i | ||||
\(556\) | 9.59118 | + | 6.96840i | 0.406757 | + | 0.295526i | ||||
\(557\) | −6.59585 | −0.279475 | −0.139738 | − | 0.990189i | \(-0.544626\pi\) | ||||
−0.139738 | + | 0.990189i | \(0.544626\pi\) | |||||||
\(558\) | −8.24516 | − | 5.99046i | −0.349045 | − | 0.253596i | ||||
\(559\) | −0.462723 | + | 1.42411i | −0.0195711 | + | 0.0602336i | ||||
\(560\) | 11.4783 | − | 24.0788i | 0.485048 | − | 1.01752i | ||||
\(561\) | 0.547943 | + | 1.68640i | 0.0231342 | + | 0.0711997i | ||||
\(562\) | −15.7947 | + | 48.6110i | −0.666257 | + | 2.05053i | ||||
\(563\) | −4.95100 | + | 15.2376i | −0.208660 | + | 0.642189i | 0.790883 | + | 0.611967i | \(0.209621\pi\) |
−0.999543 | + | 0.0302222i | \(0.990379\pi\) | |||||||
\(564\) | 3.19427 | + | 9.83094i | 0.134503 | + | 0.413957i | ||||
\(565\) | 14.3611 | − | 30.1263i | 0.604178 | − | 1.26742i | ||||
\(566\) | −17.7826 | + | 54.7291i | −0.747457 | + | 2.30044i | ||||
\(567\) | −3.52602 | − | 2.56180i | −0.148079 | − | 0.107586i | ||||
\(568\) | −11.3505 | −0.476258 | ||||||||
\(569\) | −18.6813 | − | 13.5728i | −0.783162 | − | 0.569001i | 0.122764 | − | 0.992436i | \(-0.460824\pi\) |
−0.905926 | + | 0.423435i | \(0.860824\pi\) | |||||||
\(570\) | −6.64884 | − | 35.8288i | −0.278489 | − | 1.50071i | ||||
\(571\) | 27.5148 | − | 19.9907i | 1.15146 | − | 0.836583i | 0.162784 | − | 0.986662i | \(-0.447953\pi\) |
0.988674 | + | 0.150078i | \(0.0479526\pi\) | |||||||
\(572\) | 3.83451 | − | 2.78594i | 0.160329 | − | 0.116486i | ||||
\(573\) | −3.20441 | − | 9.86215i | −0.133866 | − | 0.411997i | ||||
\(574\) | −69.1171 | −2.88489 | ||||||||
\(575\) | −0.612394 | − | 11.5852i | −0.0255386 | − | 0.483136i | ||||
\(576\) | −11.3975 | −0.474896 | ||||||||
\(577\) | −1.99850 | − | 6.15074i | −0.0831985 | − | 0.256059i | 0.900800 | − | 0.434233i | \(-0.142981\pi\) |
−0.983999 | + | 0.178175i | \(0.942981\pi\) | |||||||
\(578\) | 27.0263 | − | 19.6357i | 1.12414 | − | 0.816739i | ||||
\(579\) | −3.51690 | + | 2.55517i | −0.146157 | + | 0.106189i | ||||
\(580\) | 13.2633 | − | 27.8233i | 0.550729 | − | 1.15530i | ||||
\(581\) | 30.8034 | + | 22.3800i | 1.27794 | + | 0.928479i | ||||
\(582\) | −15.9174 | −0.659798 | ||||||||
\(583\) | 4.78762 | + | 3.47841i | 0.198283 | + | 0.144061i | ||||
\(584\) | 1.65261 | − | 5.08620i | 0.0683853 | − | 0.210468i | ||||
\(585\) | 1.94346 | + | 1.84344i | 0.0803521 | + | 0.0762169i | ||||
\(586\) | −13.3146 | − | 40.9780i | −0.550019 | − | 1.69279i | ||||
\(587\) | 11.8975 | − | 36.6168i | 0.491063 | − | 1.51134i | −0.331940 | − | 0.943301i | \(-0.607703\pi\) |
0.823003 | − | 0.568037i | \(-0.192297\pi\) | |||||||
\(588\) | 9.28310 | − | 28.5704i | 0.382828 | − | 1.17822i | ||||
\(589\) | 11.3945 | + | 35.0687i | 0.469503 | + | 1.44498i | ||||
\(590\) | −43.0816 | − | 5.66192i | −1.77364 | − | 0.233097i | ||||
\(591\) | 0.580921 | − | 1.78789i | 0.0238959 | − | 0.0735440i | ||||
\(592\) | −14.1105 | − | 10.2519i | −0.579939 | − | 0.421350i | ||||
\(593\) | 4.93069 | 0.202479 | 0.101240 | − | 0.994862i | \(-0.467719\pi\) | ||||
0.101240 | + | 0.994862i | \(0.467719\pi\) | |||||||
\(594\) | 2.71270 | + | 1.97090i | 0.111304 | + | 0.0808668i | ||||
\(595\) | −7.93577 | − | 7.52737i | −0.325335 | − | 0.308592i | ||||
\(596\) | −9.47457 | + | 6.88368i | −0.388093 | + | 0.281966i | ||||
\(597\) | −3.44664 | + | 2.50413i | −0.141062 | + | 0.102487i | ||||
\(598\) | −1.82293 | − | 5.61040i | −0.0745452 | − | 0.229426i | ||||
\(599\) | −35.0268 | −1.43116 | −0.715578 | − | 0.698533i | \(-0.753836\pi\) | ||||
−0.715578 | + | 0.698533i | \(0.753836\pi\) | |||||||
\(600\) | 5.16974 | + | 1.38273i | 0.211054 | + | 0.0564496i | ||||
\(601\) | −4.90570 | −0.200108 | −0.100054 | − | 0.994982i | \(-0.531901\pi\) | ||||
−0.100054 | + | 0.994982i | \(0.531901\pi\) | |||||||
\(602\) | −3.57295 | − | 10.9964i | −0.145623 | − | 0.448180i | ||||
\(603\) | 3.12499 | − | 2.27044i | 0.127259 | − | 0.0924594i | ||||
\(604\) | 13.2538 | − | 9.62943i | 0.539289 | − | 0.391816i | ||||
\(605\) | −16.7089 | + | 9.07708i | −0.679314 | + | 0.369036i | ||||
\(606\) | 11.1918 | + | 8.13132i | 0.454636 | + | 0.330312i | ||||
\(607\) | 48.6955 | 1.97649 | 0.988244 | − | 0.152884i | \(-0.0488562\pi\) | ||||
0.988244 | + | 0.152884i | \(0.0488562\pi\) | |||||||
\(608\) | 49.3842 | + | 35.8798i | 2.00280 | + | 1.45512i | ||||
\(609\) | −7.41330 | + | 22.8158i | −0.300402 | + | 0.924543i | ||||
\(610\) | 5.82092 | − | 3.16220i | 0.235682 | − | 0.128034i | ||||
\(611\) | 1.52799 | + | 4.70266i | 0.0618158 | + | 0.190249i | ||||
\(612\) | −0.868541 | + | 2.67310i | −0.0351087 | + | 0.108053i | ||||
\(613\) | 5.31938 | − | 16.3714i | 0.214848 | − | 0.661234i | −0.784317 | − | 0.620361i | \(-0.786986\pi\) |
0.999164 | − | 0.0408728i | \(-0.0130138\pi\) | |||||||
\(614\) | −1.64832 | − | 5.07299i | −0.0665206 | − | 0.204729i | ||||
\(615\) | 3.04853 | + | 16.4277i | 0.122929 | + | 0.662430i | ||||
\(616\) | −2.27742 | + | 7.00918i | −0.0917598 | + | 0.282408i | ||||
\(617\) | 25.5723 | + | 18.5794i | 1.02950 | + | 0.747978i | 0.968209 | − | 0.250141i | \(-0.0804771\pi\) |
0.0612947 | + | 0.998120i | \(0.480477\pi\) | |||||||
\(618\) | 17.0821 | 0.687145 | ||||||||
\(619\) | 18.4615 | + | 13.4130i | 0.742029 | + | 0.539116i | 0.893346 | − | 0.449370i | \(-0.148351\pi\) |
−0.151317 | + | 0.988485i | \(0.548351\pi\) | |||||||
\(620\) | −26.6612 | − | 3.50390i | −1.07074 | − | 0.140720i | ||||
\(621\) | 1.87714 | − | 1.36382i | 0.0753271 | − | 0.0547283i | ||||
\(622\) | −8.28312 | + | 6.01804i | −0.332123 | + | 0.241301i | ||||
\(623\) | −13.5196 | − | 41.6089i | −0.541649 | − | 1.66703i | ||||
\(624\) | −3.27886 | −0.131259 | ||||||||
\(625\) | 21.6619 | + | 12.4805i | 0.866476 | + | 0.499219i | ||||
\(626\) | −12.7088 | −0.507945 | ||||||||
\(627\) | −3.74887 | − | 11.5378i | −0.149715 | − | 0.460776i | ||||
\(628\) | −8.09200 | + | 5.87918i | −0.322906 | + | 0.234605i | ||||
\(629\) | −5.78598 | + | 4.20376i | −0.230702 | + | 0.167615i | ||||
\(630\) | −20.5072 | − | 2.69512i | −0.817028 | − | 0.107376i | ||||
\(631\) | −30.7830 | − | 22.3652i | −1.22545 | − | 0.890344i | −0.228913 | − | 0.973447i | \(-0.573517\pi\) |
−0.996541 | + | 0.0831027i | \(0.973517\pi\) | |||||||
\(632\) | 15.5760 | 0.619581 | ||||||||
\(633\) | 7.52120 | + | 5.46447i | 0.298941 | + | 0.217193i | ||||
\(634\) | 11.3808 | − | 35.0265i | 0.451989 | − | 1.39108i | ||||
\(635\) | 6.93401 | + | 37.3655i | 0.275168 | + | 1.48281i | ||||
\(636\) | 2.89868 | + | 8.92120i | 0.114940 | + | 0.353749i | ||||
\(637\) | 4.44060 | − | 13.6668i | 0.175943 | − | 0.541497i | ||||
\(638\) | 5.70334 | − | 17.5531i | 0.225797 | − | 0.694933i | ||||
\(639\) | −3.27716 | − | 10.0860i | −0.129642 | − | 0.398998i | ||||
\(640\) | −16.2889 | + | 8.84892i | −0.643876 | + | 0.349784i | ||||
\(641\) | 8.19229 | − | 25.2133i | 0.323576 | − | 0.995864i | −0.648504 | − | 0.761212i | \(-0.724605\pi\) |
0.972079 | − | 0.234652i | \(-0.0753952\pi\) | |||||||
\(642\) | −16.2728 | − | 11.8229i | −0.642237 | − | 0.466612i | ||||
\(643\) | −36.0014 | −1.41976 | −0.709879 | − | 0.704324i | \(-0.751250\pi\) | ||||
−0.709879 | + | 0.704324i | \(0.751250\pi\) | |||||||
\(644\) | 20.4885 | + | 14.8858i | 0.807360 | + | 0.586582i | ||||
\(645\) | −2.45603 | + | 1.33423i | −0.0967061 | + | 0.0525354i | ||||
\(646\) | 14.7972 | − | 10.7508i | 0.582188 | − | 0.422984i | ||||
\(647\) | −33.8040 | + | 24.5600i | −1.32897 | + | 0.965554i | −0.329197 | + | 0.944261i | \(0.606778\pi\) |
−0.999773 | + | 0.0212924i | \(0.993222\pi\) | |||||||
\(648\) | 0.330738 | + | 1.01791i | 0.0129926 | + | 0.0399872i | ||||
\(649\) | −14.4658 | −0.567833 | ||||||||
\(650\) | 12.2805 | + | 3.28460i | 0.481679 | + | 0.128833i | ||||
\(651\) | 20.9293 | 0.820284 | ||||||||
\(652\) | 3.71567 | + | 11.4357i | 0.145517 | + | 0.447855i | ||||
\(653\) | −17.3456 | + | 12.6023i | −0.678787 | + | 0.493168i | −0.872955 | − | 0.487801i | \(-0.837799\pi\) |
0.194168 | + | 0.980968i | \(0.437799\pi\) | |||||||
\(654\) | 20.0301 | − | 14.5527i | 0.783240 | − | 0.569057i | ||||
\(655\) | −0.533541 | − | 0.506082i | −0.0208472 | − | 0.0197743i | ||||
\(656\) | −16.5459 | − | 12.0213i | −0.646009 | − | 0.469353i | ||||
\(657\) | 4.99672 | 0.194940 | ||||||||
\(658\) | −30.8888 | − | 22.4420i | −1.20417 | − | 0.874882i | ||||
\(659\) | −5.20135 | + | 16.0081i | −0.202616 | + | 0.623587i | 0.797187 | + | 0.603732i | \(0.206320\pi\) |
−0.999803 | + | 0.0198549i | \(0.993680\pi\) | |||||||
\(660\) | 8.77170 | + | 1.15280i | 0.341438 | + | 0.0448728i | ||||
\(661\) | 0.629918 | + | 1.93869i | 0.0245010 | + | 0.0754062i | 0.962559 | − | 0.271071i | \(-0.0873778\pi\) |
−0.938058 | + | 0.346477i | \(0.887378\pi\) | |||||||
\(662\) | 13.3368 | − | 41.0463i | 0.518348 | − | 1.59531i | ||||
\(663\) | −0.415470 | + | 1.27868i | −0.0161355 | + | 0.0496600i | ||||
\(664\) | −2.88934 | − | 8.89248i | −0.112128 | − | 0.345095i | ||||
\(665\) | 54.2942 | + | 51.5000i | 2.10544 | + | 1.99709i | ||||
\(666\) | −4.17920 | + | 12.8623i | −0.161941 | + | 0.498402i | ||||
\(667\) | −10.3323 | − | 7.50689i | −0.400070 | − | 0.290668i | ||||
\(668\) | 59.2518 | 2.29252 | ||||||||
\(669\) | 2.74870 | + | 1.99705i | 0.106271 | + | 0.0772104i | ||||
\(670\) | 7.88803 | − | 16.5472i | 0.304741 | − | 0.639274i | ||||
\(671\) | 1.78417 | − | 1.29628i | 0.0688772 | − | 0.0500422i | ||||
\(672\) | 28.0304 | − | 20.3653i | 1.08130 | − | 0.785608i | ||||
\(673\) | 10.9323 | + | 33.6461i | 0.421409 | + | 1.29696i | 0.906391 | + | 0.422439i | \(0.138826\pi\) |
−0.484983 | + | 0.874524i | \(0.661174\pi\) | |||||||
\(674\) | 72.7050 | 2.80049 | ||||||||
\(675\) | 0.263932 | + | 4.99303i | 0.0101587 | + | 0.192182i | ||||
\(676\) | −28.9621 | −1.11393 | ||||||||
\(677\) | 13.7257 | + | 42.2434i | 0.527522 | + | 1.62354i | 0.759275 | + | 0.650770i | \(0.225554\pi\) |
−0.231753 | + | 0.972775i | \(0.574446\pi\) | |||||||
\(678\) | 25.6269 | − | 18.6190i | 0.984196 | − | 0.715060i | ||||
\(679\) | 26.4450 | − | 19.2134i | 1.01487 | − | 0.737344i | ||||
\(680\) | 0.490084 | + | 2.64093i | 0.0187939 | + | 0.101275i | ||||
\(681\) | −21.6795 | − | 15.7511i | −0.830760 | − | 0.603582i | ||||
\(682\) | −16.1017 | −0.616567 | ||||||||
\(683\) | −34.3793 | − | 24.9780i | −1.31549 | − | 0.955758i | −0.999977 | − | 0.00683639i | \(-0.997824\pi\) |
−0.315512 | − | 0.948922i | \(-0.602176\pi\) | |||||||
\(684\) | 5.94230 | − | 18.2885i | 0.227210 | − | 0.699280i | ||||
\(685\) | −4.39022 | + | 9.20964i | −0.167742 | + | 0.351882i | ||||
\(686\) | 14.2796 | + | 43.9481i | 0.545198 | + | 1.67795i | ||||
\(687\) | −0.365257 | + | 1.12415i | −0.0139354 | + | 0.0428888i | ||||
\(688\) | 1.05724 | − | 3.25385i | 0.0403069 | − | 0.124052i | ||||
\(689\) | 1.38659 | + | 4.26749i | 0.0528249 | + | 0.162578i | ||||
\(690\) | 4.73824 | − | 9.93969i | 0.180382 | − | 0.378397i | ||||
\(691\) | 8.67746 | − | 26.7065i | 0.330106 | − | 1.01596i | −0.638977 | − | 0.769226i | \(-0.720642\pi\) |
0.969083 | − | 0.246736i | \(-0.0793580\pi\) | |||||||
\(692\) | −29.3860 | − | 21.3502i | −1.11709 | − | 0.811612i | ||||
\(693\) | −6.88586 | −0.261572 | ||||||||
\(694\) | 0.0847541 | + | 0.0615775i | 0.00321722 | + | 0.00233745i | ||||
\(695\) | 1.93141 | + | 10.4079i | 0.0732626 | + | 0.394793i | ||||
\(696\) | 4.76609 | − | 3.46276i | 0.180658 | − | 0.131256i | ||||
\(697\) | −6.78460 | + | 4.92930i | −0.256985 | + | 0.186711i | ||||
\(698\) | −4.90197 | − | 15.0867i | −0.185542 | − | 0.571040i | ||||
\(699\) | 7.09483 | 0.268351 | ||||||||
\(700\) | −50.9401 | + | 19.5804i | −1.92536 | + | 0.740071i | ||||
\(701\) | 46.4314 | 1.75369 | 0.876845 | − | 0.480772i | \(-0.159644\pi\) | ||||
0.876845 | + | 0.480772i | \(0.159644\pi\) | |||||||
\(702\) | 0.785653 | + | 2.41799i | 0.0296526 | + | 0.0912612i | ||||
\(703\) | 39.5860 | − | 28.7609i | 1.49301 | − | 1.08474i | ||||
\(704\) | −14.5680 | + | 10.5842i | −0.549051 | + | 0.398909i | ||||
\(705\) | −3.97161 | + | 8.33149i | −0.149579 | + | 0.313782i | ||||
\(706\) | 31.8762 | + | 23.1594i | 1.19967 | + | 0.871615i | ||||
\(707\) | −28.4090 | −1.06843 | ||||||||
\(708\) | −18.5505 | − | 13.4777i | −0.697171 | − | 0.506524i | ||||
\(709\) | 15.0285 | − | 46.2529i | 0.564406 | − | 1.73706i | −0.105305 | − | 0.994440i | \(-0.533582\pi\) |
0.669710 | − | 0.742622i | \(-0.266418\pi\) | |||||||
\(710\) | −36.5148 | − | 34.6356i | −1.37037 | − | 1.29985i | ||||
\(711\) | 4.49714 | + | 13.8408i | 0.168656 | + | 0.519070i | ||||
\(712\) | −3.31999 | + | 10.2179i | −0.124422 | + | 0.382932i | ||||
\(713\) | −3.44310 | + | 10.5968i | −0.128945 | + | 0.396852i | ||||
\(714\) | −3.20808 | − | 9.87345i | −0.120059 | − | 0.369505i | ||||
\(715\) | 4.19597 | + | 0.551448i | 0.156920 | + | 0.0206230i | ||||
\(716\) | 0.616579 | − | 1.89763i | 0.0230426 | − | 0.0709179i | ||||
\(717\) | −0.0346199 | − | 0.0251528i | −0.00129290 | − | 0.000939350i | ||||
\(718\) | 22.5062 | 0.839923 | ||||||||
\(719\) | 17.1475 | + | 12.4584i | 0.639493 | + | 0.464619i | 0.859676 | − | 0.510840i | \(-0.170666\pi\) |
−0.220183 | + | 0.975459i | \(0.570666\pi\) | |||||||
\(720\) | −4.44046 | − | 4.21194i | −0.165486 | − | 0.156970i | ||||
\(721\) | −28.3801 | + | 20.6193i | −1.05693 | + | 0.767904i | ||||
\(722\) | −68.6150 | + | 49.8517i | −2.55359 | + | 1.85529i | ||||
\(723\) | −3.63746 | − | 11.1950i | −0.135279 | − | 0.416345i | ||||
\(724\) | −35.6073 | −1.32333 | ||||||||
\(725\) | 25.6891 | − | 9.87441i | 0.954068 | − | 0.366726i | ||||
\(726\) | −18.0481 | −0.669828 | ||||||||
\(727\) | 4.19988 | + | 12.9259i | 0.155765 | + | 0.479396i | 0.998238 | − | 0.0593437i | \(-0.0189008\pi\) |
−0.842473 | + | 0.538739i | \(0.818901\pi\) | |||||||
\(728\) | −4.52087 | + | 3.28460i | −0.167555 | + | 0.121736i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 20.8367 | − | 11.3195i | 0.771200 | − | 0.418953i | ||||
\(731\) | −1.13497 | − | 0.824602i | −0.0419783 | − | 0.0304990i | ||||
\(732\) | 3.49570 | 0.129205 | ||||||||
\(733\) | −15.0907 | − | 10.9640i | −0.557386 | − | 0.404965i | 0.273115 | − | 0.961981i | \(-0.411946\pi\) |
−0.830501 | + | 0.557017i | \(0.811946\pi\) | |||||||
\(734\) | −7.61927 | + | 23.4497i | −0.281233 | + | 0.865545i | ||||
\(735\) | 23.5697 | − | 12.8042i | 0.869383 | − | 0.472290i | ||||
\(736\) | 5.69988 | + | 17.5424i | 0.210101 | + | 0.646623i | ||||
\(737\) | 1.88584 | − | 5.80402i | 0.0694658 | − | 0.213794i | ||||
\(738\) | −4.90050 | + | 15.0822i | −0.180390 | + | 0.555183i | ||||
\(739\) | 8.17202 | + | 25.1509i | 0.300613 | + | 0.925191i | 0.981278 | + | 0.192596i | \(0.0616907\pi\) |
−0.680665 | + | 0.732594i | \(0.738309\pi\) | |||||||
\(740\) | 6.51073 | + | 35.0846i | 0.239339 | + | 1.28974i | ||||
\(741\) | 2.84252 | − | 8.74838i | 0.104423 | − | 0.321380i | ||||
\(742\) | −28.0304 | − | 20.3653i | −1.02903 | − | 0.747633i | ||||
\(743\) | −29.0191 | −1.06461 | −0.532304 | − | 0.846553i | \(-0.678674\pi\) | ||||
−0.532304 | + | 0.846553i | \(0.678674\pi\) | |||||||
\(744\) | −4.15803 | − | 3.02098i | −0.152441 | − | 0.110755i | ||||
\(745\) | −10.3677 | − | 1.36255i | −0.379843 | − | 0.0499201i | ||||
\(746\) | 39.7096 | − | 28.8507i | 1.45387 | − | 1.05630i | ||||
\(747\) | 7.06760 | − | 5.13491i | 0.258590 | − | 0.187877i | ||||
\(748\) | 1.37221 | + | 4.22324i | 0.0501731 | + | 0.154417i | ||||
\(749\) | 41.3065 | 1.50931 | ||||||||
\(750\) | 12.4117 | + | 20.2234i | 0.453213 | + | 0.738454i | ||||
\(751\) | 15.9489 | 0.581985 | 0.290992 | − | 0.956725i | \(-0.406015\pi\) | ||||
0.290992 | + | 0.956725i | \(0.406015\pi\) | |||||||
\(752\) | −3.49119 | − | 10.7448i | −0.127310 | − | 0.391821i | ||||
\(753\) | −14.1387 | + | 10.2724i | −0.515243 | + | 0.374346i | ||||
\(754\) | 11.3216 | − | 8.22563i | 0.412309 | − | 0.299560i | ||||
\(755\) | 14.5031 | + | 1.90605i | 0.527824 | + | 0.0693682i | ||||
\(756\) | −8.83021 | − | 6.41552i | −0.321152 | − | 0.233330i | ||||
\(757\) | −16.4183 | −0.596734 | −0.298367 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298367 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(758\) | −42.7382 | − | 31.0512i | −1.55232 | − | 1.12783i | ||||
\(759\) | 1.13280 | − | 3.48640i | 0.0411180 | − | 0.126548i | ||||
\(760\) | −3.35301 | − | 18.0685i | −0.121626 | − | 0.655412i | ||||
\(761\) | −15.2257 | − | 46.8600i | −0.551932 | − | 1.69867i | −0.703910 | − | 0.710289i | \(-0.748564\pi\) |
0.151978 | − | 0.988384i | \(-0.451436\pi\) | |||||||
\(762\) | −11.1464 | + | 34.3051i | −0.403791 | + | 1.24274i | ||||
\(763\) | −15.7117 | + | 48.3555i | −0.568800 | + | 1.75059i | ||||
\(764\) | −8.02480 | − | 24.6978i | −0.290327 | − | 0.893534i | ||||
\(765\) | −2.20522 | + | 1.19798i | −0.0797300 | + | 0.0433131i | ||||
\(766\) | −10.3111 | + | 31.7345i | −0.372557 | + | 1.14661i | ||||
\(767\) | −8.87369 | − | 6.44711i | −0.320410 | − | 0.232792i | ||||
\(768\) | 5.20057 | 0.187660 | ||||||||
\(769\) | −39.9845 | − | 29.0504i | −1.44188 | − | 1.04759i | −0.987646 | − | 0.156702i | \(-0.949914\pi\) |
−0.454232 | − | 0.890884i | \(-0.650086\pi\) | |||||||
\(770\) | −28.7146 | + | 15.5991i | −1.03480 | + | 0.562154i | ||||
\(771\) | −12.5132 | + | 9.09136i | −0.450651 | + | 0.327417i | ||||
\(772\) | −8.80736 | + | 6.39892i | −0.316984 | + | 0.230302i | ||||
\(773\) | 8.00613 | + | 24.6403i | 0.287960 | + | 0.886251i | 0.985496 | + | 0.169701i | \(0.0542801\pi\) |
−0.697535 | + | 0.716550i | \(0.745720\pi\) | |||||||
\(774\) | −2.65288 | −0.0953557 | ||||||||
\(775\) | −15.1186 | − | 18.6527i | −0.543076 | − | 0.670024i | ||||
\(776\) | −8.02715 | −0.288158 | ||||||||
\(777\) | −8.58236 | − | 26.4138i | −0.307891 | − | 0.947590i | ||||
\(778\) | 14.6054 | − | 10.6114i | 0.523629 | − | 0.380439i | ||||
\(779\) | 46.4182 | − | 33.7248i | 1.66311 | − | 1.20832i | ||||
\(780\) | 4.86700 | + | 4.61653i | 0.174267 | + | 0.165298i | ||||
\(781\) | −13.5551 | − | 9.84838i | −0.485041 | − | 0.352403i | ||||
\(782\) | 5.52681 | 0.197638 | ||||||||
\(783\) | 4.45307 | + | 3.23535i | 0.159140 | + | 0.115622i | ||||
\(784\) | −10.1460 | + | 31.2262i | −0.362357 | + | 1.11522i | ||||
\(785\) | −8.85479 | − | 1.16372i | −0.316041 | − | 0.0415351i | ||||
\(786\) | −0.215687 | − | 0.663815i | −0.00769329 | − | 0.0236775i | ||||
\(787\) | 9.49160 | − | 29.2122i | 0.338339 | − | 1.04130i | −0.626715 | − | 0.779249i | \(-0.715601\pi\) |
0.965054 | − | 0.262052i | \(-0.0843992\pi\) | |||||||
\(788\) | 1.45480 | − | 4.47741i | 0.0518251 | − | 0.159501i | ||||
\(789\) | 0.447331 | + | 1.37674i | 0.0159254 | + | 0.0490134i | ||||
\(790\) | 50.1081 | + | 47.5293i | 1.78277 | + | 1.69102i | ||||
\(791\) | −20.1018 | + | 61.8670i | −0.714737 | + | 2.19974i | ||||
\(792\) | 1.36802 | + | 0.993921i | 0.0486103 | + | 0.0353175i | ||||
\(793\) | 1.67218 | 0.0593808 | ||||||||
\(794\) | −45.0798 | − | 32.7524i | −1.59982 | − | 1.16234i | ||||
\(795\) | −3.60408 | + | 7.56051i | −0.127824 | + | 0.268144i | ||||
\(796\) | −8.63142 | + | 6.27109i | −0.305933 | + | 0.222273i | ||||
\(797\) | 27.2753 | − | 19.8166i | 0.966140 | − | 0.701942i | 0.0115713 | − | 0.999933i | \(-0.496317\pi\) |
0.954569 | + | 0.297991i | \(0.0963167\pi\) | |||||||
\(798\) | 21.9487 | + | 67.5513i | 0.776977 | + | 2.39129i | ||||
\(799\) | −4.63260 | −0.163890 | ||||||||
\(800\) | −38.3982 | − | 10.2702i | −1.35758 | − | 0.363106i | ||||
\(801\) | −10.0381 | −0.354680 | ||||||||
\(802\) | −16.5806 | − | 51.0298i | −0.585480 | − | 1.80192i | ||||
\(803\) | 6.38665 | − | 4.64018i | 0.225380 | − | 0.163748i | ||||
\(804\) | 7.82591 | − | 5.68586i | 0.275999 | − | 0.200525i | ||||
\(805\) | 4.12584 | + | 22.2331i | 0.145417 | + | 0.783613i | ||||
\(806\) | −9.87720 | − | 7.17621i | −0.347910 | − | 0.252771i | ||||
\(807\) | −8.70617 | −0.306472 | ||||||||
\(808\) | 5.64402 | + | 4.10062i | 0.198556 | + | 0.144259i | ||||
\(809\) | −0.285227 | + | 0.877838i | −0.0100280 | + | 0.0308632i | −0.955945 | − | 0.293545i | \(-0.905165\pi\) |
0.945917 | + | 0.324408i | \(0.105165\pi\) | |||||||
\(810\) | −2.04210 | + | 4.28384i | −0.0717522 | + | 0.150519i | ||||
\(811\) | 8.27593 | + | 25.4707i | 0.290607 | + | 0.894397i | 0.984662 | + | 0.174474i | \(0.0558226\pi\) |
−0.694055 | + | 0.719922i | \(0.744177\pi\) | |||||||
\(812\) | −18.5651 | + | 57.1376i | −0.651508 | + | 2.00514i | ||||
\(813\) | −8.84832 | + | 27.2323i | −0.310324 | + | 0.955080i | ||||
\(814\) | 6.60274 | + | 20.3212i | 0.231426 | + | 0.712256i | ||||
\(815\) | −4.61990 | + | 9.69145i | −0.161828 | + | 0.339477i | ||||
\(816\) | 0.949275 | − | 2.92157i | 0.0332313 | − | 0.102275i | ||||
\(817\) | 7.76511 | + | 5.64168i | 0.271667 | + | 0.197377i | ||||
\(818\) | 71.7204 | 2.50765 | ||||||||
\(819\) | −4.22396 | − | 3.06889i | −0.147597 | − | 0.107236i | ||||
\(820\) | 7.63444 | + | 41.1400i | 0.266606 | + | 1.43667i | ||||
\(821\) | 29.8114 | − | 21.6592i | 1.04042 | − | 0.755912i | 0.0700559 | − | 0.997543i | \(-0.477682\pi\) |
0.970368 | + | 0.241631i | \(0.0776822\pi\) | |||||||
\(822\) | −7.83419 | + | 5.69187i | −0.273249 | + | 0.198527i | ||||
\(823\) | 6.31204 | + | 19.4265i | 0.220024 | + | 0.677164i | 0.998759 | + | 0.0498106i | \(0.0158618\pi\) |
−0.778735 | + | 0.627353i | \(0.784138\pi\) | |||||||
\(824\) | 8.61452 | 0.300101 | ||||||||
\(825\) | 4.97410 | + | 6.13684i | 0.173176 | + | 0.213657i | ||||
\(826\) | 84.6940 | 2.94688 | ||||||||
\(827\) | 1.33810 | + | 4.11824i | 0.0465302 | + | 0.143205i | 0.971622 | − | 0.236537i | \(-0.0760126\pi\) |
−0.925092 | + | 0.379743i | \(0.876013\pi\) | |||||||
\(828\) | 4.70092 | − | 3.41542i | 0.163368 | − | 0.118694i | ||||
\(829\) | 0.497018 | − | 0.361104i | 0.0172621 | − | 0.0125417i | −0.579121 | − | 0.815242i | \(-0.696604\pi\) |
0.596383 | + | 0.802700i | \(0.296604\pi\) | |||||||
\(830\) | 17.8399 | − | 37.4238i | 0.619231 | − | 1.29900i | ||||
\(831\) | −4.28949 | − | 3.11649i | −0.148801 | − | 0.108110i | ||||
\(832\) | −13.6535 | −0.473351 | ||||||||
\(833\) | 10.8919 | + | 7.91343i | 0.377382 | + | 0.274184i | ||||
\(834\) | −3.10473 | + | 9.55539i | −0.107508 | + | 0.330876i | ||||
\(835\) | 38.3844 | + | 36.4090i | 1.32835 | + | 1.25999i | ||||
\(836\) | −9.38828 | − | 28.8942i | −0.324701 | − | 0.999325i | ||||
\(837\) | 1.48392 | − | 4.56703i | 0.0512917 | − | 0.157860i | ||||
\(838\) | 5.20297 | − | 16.0131i | 0.179733 | − | 0.553163i | ||||
\(839\) | 1.66863 | + | 5.13553i | 0.0576077 | + | 0.177298i | 0.975720 | − | 0.219023i | \(-0.0702868\pi\) |
−0.918112 | + | 0.396321i | \(0.870287\pi\) | |||||||
\(840\) | −10.3418 | − | 1.35915i | −0.356826 | − | 0.0468951i | ||||
\(841\) | 0.400892 | − | 1.23382i | 0.0138239 | − | 0.0425455i | ||||
\(842\) | −12.8568 | − | 9.34105i | −0.443076 | − | 0.321914i | ||||
\(843\) | −24.0832 | −0.829469 | ||||||||
\(844\) | 18.8353 | + | 13.6847i | 0.648339 | + | 0.471046i | ||||
\(845\) | −18.7622 | − | 17.7966i | −0.645439 | − | 0.612222i | ||||
\(846\) | −7.08719 | + | 5.14914i | −0.243663 | + | 0.177031i | ||||
\(847\) | 29.9849 | − | 21.7853i | 1.03029 | − | 0.748552i | ||||
\(848\) | −3.16812 | − | 9.75046i | −0.108794 | − | 0.334832i | ||||
\(849\) | −27.1143 | −0.930561 | ||||||||
\(850\) | −6.48205 | + | 9.99135i | −0.222333 | + | 0.342700i | ||||
\(851\) | 14.7855 | 0.506841 | ||||||||
\(852\) | −8.20698 | − | 25.2585i | −0.281166 | − | 0.865341i | ||||
\(853\) | 32.1936 | − | 23.3900i | 1.10229 | − | 0.800860i | 0.120857 | − | 0.992670i | \(-0.461436\pi\) |
0.981432 | + | 0.191810i | \(0.0614358\pi\) | |||||||
\(854\) | −10.4459 | + | 7.58940i | −0.357452 | + | 0.259704i | ||||
\(855\) | 15.0875 | − | 8.19624i | 0.515981 | − | 0.280305i | ||||
\(856\) | −8.20637 | − | 5.96228i | −0.280488 | − | 0.203787i | ||||
\(857\) | −42.8643 | −1.46422 | −0.732109 | − | 0.681188i | \(-0.761464\pi\) | ||||
−0.732109 | + | 0.681188i | \(0.761464\pi\) | |||||||
\(858\) | 3.24966 | + | 2.36101i | 0.110941 | + | 0.0806037i | ||||
\(859\) | −1.41064 | + | 4.34152i | −0.0481306 | + | 0.148131i | −0.972233 | − | 0.234013i | \(-0.924814\pi\) |
0.924103 | + | 0.382144i | \(0.124814\pi\) | |||||||
\(860\) | −6.15064 | + | 3.34132i | −0.209735 | + | 0.113938i | ||||
\(861\) | −10.0636 | − | 30.9726i | −0.342967 | − | 1.05554i | ||||
\(862\) | 15.3119 | − | 47.1251i | 0.521524 | − | 1.60509i | ||||
\(863\) | −11.6275 | + | 35.7857i | −0.395804 | + | 1.21816i | 0.532530 | + | 0.846411i | \(0.321241\pi\) |
−0.928334 | + | 0.371747i | \(0.878759\pi\) | |||||||
\(864\) | −2.45656 | − | 7.56051i | −0.0835738 | − | 0.257214i | ||||
\(865\) | −5.91756 | − | 31.8882i | −0.201203 | − | 1.08423i | ||||
\(866\) | −2.20150 | + | 6.77551i | −0.0748099 | + | 0.230241i | ||||
\(867\) | 12.7342 | + | 9.25196i | 0.432477 | + | 0.314213i | ||||
\(868\) | 52.4133 | 1.77902 | ||||||||
\(869\) | 18.6013 | + | 13.5146i | 0.631006 | + | 0.458452i | ||||
\(870\) | 25.8989 | + | 3.40372i | 0.878057 | + | 0.115397i | ||||
\(871\) | 3.74355 | − | 2.71985i | 0.126845 | − | 0.0921586i | ||||
\(872\) | 10.1012 | − | 7.33894i | 0.342069 | − | 0.248528i | ||||
\(873\) | −2.31762 | − | 7.13289i | −0.0784394 | − | 0.241412i | ||||
\(874\) | −37.8128 | −1.27904 | ||||||||
\(875\) | −45.0318 | − | 18.6171i | −1.52235 | − | 0.629373i | ||||
\(876\) | 12.5133 | 0.422784 | ||||||||
\(877\) | 16.1938 | + | 49.8393i | 0.546825 | + | 1.68295i | 0.716612 | + | 0.697472i | \(0.245692\pi\) |
−0.169787 | + | 0.985481i | \(0.554308\pi\) | |||||||
\(878\) | 16.2841 | − | 11.8311i | 0.549562 | − | 0.399280i | ||||
\(879\) | 16.4244 | − | 11.9330i | 0.553980 | − | 0.402490i | ||||
\(880\) | −9.58706 | − | 1.25996i | −0.323180 | − | 0.0424733i | ||||
\(881\) | 6.42180 | + | 4.66571i | 0.216356 | + | 0.157192i | 0.690685 | − | 0.723156i | \(-0.257309\pi\) |
−0.474329 | + | 0.880348i | \(0.657309\pi\) | |||||||
\(882\) | 25.4588 | 0.857242 | ||||||||
\(883\) | −25.6393 | − | 18.6280i | −0.862831 | − | 0.626883i | 0.0658227 | − | 0.997831i | \(-0.479033\pi\) |
−0.928654 | + | 0.370948i | \(0.879033\pi\) | |||||||
\(884\) | −1.04046 | + | 3.20221i | −0.0349945 | + | 0.107702i | ||||
\(885\) | −3.73558 | − | 20.1300i | −0.125570 | − | 0.676664i | ||||
\(886\) | 6.33175 | + | 19.4871i | 0.212719 | + | 0.654683i | ||||
\(887\) | 0.871749 | − | 2.68297i | 0.0292705 | − | 0.0900853i | −0.935354 | − | 0.353713i | \(-0.884919\pi\) |
0.964625 | + | 0.263628i | \(0.0849190\pi\) | |||||||
\(888\) | −2.10757 | + | 6.48643i | −0.0707254 | + | 0.217670i | ||||
\(889\) | −22.8901 | − | 70.4485i | −0.767709 | − | 2.36277i | ||||
\(890\) | −41.8598 | + | 22.7402i | −1.40314 | + | 0.762254i | ||||
\(891\) | −0.488218 | + | 1.50258i | −0.0163559 | + | 0.0503383i | ||||
\(892\) | 6.88357 | + | 5.00121i | 0.230479 | + | 0.167453i | ||||
\(893\) | 31.6949 | 1.06063 | ||||||||
\(894\) | −8.02947 | − | 5.83375i | −0.268546 | − | 0.195110i | ||||
\(895\) | 1.56549 | − | 0.850448i | 0.0523285 | − | 0.0284274i | ||||
\(896\) | 29.2312 | − | 21.2377i | 0.976546 | − | 0.709502i | ||||
\(897\) | 2.24870 | − | 1.63378i | 0.0750820 | − | 0.0545502i | ||||
\(898\) | 20.6759 | + | 63.6340i | 0.689965 | + | 2.12349i | ||||
\(899\) | −26.4320 | −0.881556 | ||||||||
\(900\) | 0.660965 | + | 12.5040i | 0.0220322 | + | 0.416801i | ||||
\(901\) | −4.20390 | −0.140052 | ||||||||
\(902\) | 7.74233 | + | 23.8285i | 0.257792 | + | 0.793401i | ||||
\(903\) | 4.40746 | − | 3.20221i | 0.146671 | − | 0.106563i | ||||
\(904\) | 12.9236 | − | 9.38958i | 0.429834 | − | 0.312293i | ||||
\(905\) | −23.0671 | − | 21.8800i | −0.766776 | − | 0.727315i | ||||
\(906\) | 11.2323 | + | 8.16071i | 0.373167 | + | 0.271122i | ||||
\(907\) | −44.1799 | −1.46697 | −0.733485 | − | 0.679705i | \(-0.762108\pi\) | ||||
−0.733485 | + | 0.679705i | \(0.762108\pi\) | |||||||
\(908\) | −54.2919 | − | 39.4454i | −1.80174 | − | 1.30904i | ||||
\(909\) | −2.01424 | + | 6.19919i | −0.0668081 | + | 0.205614i | ||||
\(910\) | −24.5664 | − | 3.22860i | −0.814370 | − | 0.107027i | ||||
\(911\) | −10.6691 | − | 32.8362i | −0.353484 | − | 1.08791i | −0.956883 | − | 0.290472i | \(-0.906188\pi\) |
0.603400 | − | 0.797439i | \(-0.293812\pi\) | |||||||
\(912\) | −6.49466 | + | 19.9885i | −0.215060 | + | 0.661886i | ||||
\(913\) | 4.26509 | − | 13.1266i | 0.141154 | − | 0.434426i | ||||
\(914\) | −6.52209 | − | 20.0729i | −0.215731 | − | 0.663953i | ||||
\(915\) | 2.26458 | + | 2.14804i | 0.0748648 | + | 0.0710119i | ||||
\(916\) | −0.914713 | + | 2.81520i | −0.0302230 | + | 0.0930167i | ||||
\(917\) | 1.15961 | + | 0.842506i | 0.0382937 | + | 0.0278220i | ||||
\(918\) | −2.38197 | −0.0786166 | ||||||||
\(919\) | 0.429648 | + | 0.312158i | 0.0141728 | + | 0.0102971i | 0.594849 | − | 0.803837i | \(-0.297212\pi\) |
−0.580676 | + | 0.814135i | \(0.697212\pi\) | |||||||
\(920\) | 2.38949 | − | 5.01258i | 0.0787792 | − | 0.165260i | ||||
\(921\) | 2.03330 | − | 1.47728i | 0.0669996 | − | 0.0486781i | ||||
\(922\) | 40.6648 | − | 29.5447i | 1.33922 | − | 0.973003i | ||||
\(923\) | −3.92584 | − | 12.0825i | −0.129220 | − | 0.397700i | ||||
\(924\) | −17.2443 | −0.567295 | ||||||||
\(925\) | −17.3410 | + | 26.7292i | −0.570169 | + | 0.878850i | ||||
\(926\) | 58.6833 | 1.92845 | ||||||||
\(927\) | 2.48720 | + | 7.65482i | 0.0816905 | + | 0.251417i | ||||
\(928\) | −35.4001 | + | 25.7197i | −1.16206 | + | 0.844289i | ||||
\(929\) | −37.3735 | + | 27.1534i | −1.22618 | + | 0.890874i | −0.996598 | − | 0.0824143i | \(-0.973737\pi\) |
−0.229585 | + | 0.973289i | \(0.573737\pi\) | |||||||
\(930\) | −4.15803 | − | 22.4065i | −0.136347 | − | 0.734738i | ||||
\(931\) | −74.5192 | − | 54.1414i | −2.44227 | − | 1.77441i | ||||
\(932\) | 17.7676 | 0.581997 | ||||||||
\(933\) | −3.90284 | − | 2.83558i | −0.127773 | − | 0.0928326i | ||||
\(934\) | 2.85840 | − | 8.79726i | 0.0935298 | − | 0.287855i | ||||
\(935\) | −1.70615 | + | 3.57909i | −0.0557971 | + | 0.117049i | ||||
\(936\) | 0.396205 | + | 1.21939i | 0.0129504 | + | 0.0398571i | ||||
\(937\) | −9.30820 | + | 28.6477i | −0.304086 | + | 0.935880i | 0.675931 | + | 0.736965i | \(0.263742\pi\) |
−0.980017 | + | 0.198915i | \(0.936258\pi\) | |||||||
\(938\) | −11.0412 | + | 33.9812i | −0.360506 | + | 1.10952i | ||||
\(939\) | −1.85043 | − | 5.69504i | −0.0603865 | − | 0.185851i | ||||
\(940\) | −9.94610 | + | 20.8645i | −0.324406 | + | 0.680526i | ||||
\(941\) | 17.6382 | − | 54.2847i | 0.574988 | − | 1.76963i | −0.0612315 | − | 0.998124i | \(-0.519503\pi\) |
0.636220 | − | 0.771508i | \(-0.280497\pi\) | |||||||
\(942\) | −6.85777 | − | 4.98246i | −0.223438 | − | 0.162337i | ||||
\(943\) | 17.3374 | 0.564583 | ||||||||
\(944\) | 20.2748 | + | 14.7305i | 0.659890 | + | 0.479438i | ||||
\(945\) | −1.77817 | − | 9.58209i | −0.0578439 | − | 0.311705i | ||||
\(946\) | −3.39083 | + | 2.46358i | −0.110245 | + | 0.0800980i | ||||
\(947\) | 33.2708 | − | 24.1727i | 1.08116 | − | 0.785506i | 0.103273 | − | 0.994653i | \(-0.467069\pi\) |
0.977884 | + | 0.209147i | \(0.0670686\pi\) | |||||||
\(948\) | 11.2622 | + | 34.6615i | 0.365779 | + | 1.12575i | ||||
\(949\) | 5.98576 | 0.194306 | ||||||||
\(950\) | 44.3483 | − | 68.3579i | 1.43885 | − | 2.21782i | ||||
\(951\) | 17.3531 | 0.562712 | ||||||||
\(952\) | −1.61783 | − | 4.97918i | −0.0524343 | − | 0.161376i | ||||
\(953\) | −28.1654 | + | 20.4633i | −0.912366 | + | 0.662873i | −0.941612 | − | 0.336700i | \(-0.890689\pi\) |
0.0292462 | + | 0.999572i | \(0.490689\pi\) | |||||||
\(954\) | −6.43135 | + | 4.67265i | −0.208223 | + | 0.151283i | ||||
\(955\) | 9.97767 | − | 20.9308i | 0.322870 | − | 0.677304i | ||||
\(956\) | −0.0866986 | − | 0.0629902i | −0.00280403 | − | 0.00203725i | ||||
\(957\) | 8.69627 | 0.281111 | ||||||||
\(958\) | −22.0022 | − | 15.9855i | −0.710857 | − | 0.516468i | ||||
\(959\) | 6.14515 | − | 18.9128i | 0.198437 | − | 0.610727i | ||||
\(960\) | −18.4906 | − | 17.5390i | −0.596780 | − | 0.566068i | ||||
\(961\) | −2.45366 | − | 7.55160i | −0.0791504 | − | 0.243600i | ||||
\(962\) | −5.00643 | + | 15.4082i | −0.161414 | + | 0.496781i | ||||
\(963\) | 2.92869 | − | 9.01359i | 0.0943758 | − | 0.290459i | ||||
\(964\) | −9.10930 | − | 28.0355i | −0.293391 | − | 0.902964i | ||||
\(965\) | −9.63759 | − | 1.26660i | −0.310245 | − | 0.0407733i | ||||
\(966\) | −6.63227 | + | 20.4120i | −0.213390 | + | 0.656746i | ||||
\(967\) | 30.1519 | + | 21.9066i | 0.969618 | + | 0.704469i | 0.955365 | − | 0.295430i | \(-0.0954628\pi\) |
0.0142537 | + | 0.999898i | \(0.495463\pi\) | |||||||
\(968\) | −9.10165 | −0.292538 | ||||||||
\(969\) | 6.97214 | + | 5.06555i | 0.223977 | + | 0.162729i | ||||
\(970\) | −25.8234 | − | 24.4944i | −0.829138 | − | 0.786468i | ||||
\(971\) | 21.0419 | − | 15.2879i | 0.675267 | − | 0.490611i | −0.196517 | − | 0.980500i | \(-0.562963\pi\) |
0.871784 | + | 0.489890i | \(0.162963\pi\) | |||||||
\(972\) | −2.02602 | + | 1.47199i | −0.0649846 | + | 0.0472141i | ||||
\(973\) | −6.37585 | − | 19.6228i | −0.204400 | − | 0.629079i | ||||
\(974\) | −14.6910 | −0.470729 | ||||||||
\(975\) | 0.316175 | + | 5.98135i | 0.0101257 | + | 0.191556i | ||||
\(976\) | −3.82064 | −0.122296 | ||||||||
\(977\) | 0.141709 | + | 0.436134i | 0.00453366 | + | 0.0139532i | 0.953298 | − | 0.302032i | \(-0.0976650\pi\) |
−0.948764 | + | 0.315985i | \(0.897665\pi\) | |||||||
\(978\) | −8.24404 | + | 5.98965i | −0.263615 | + | 0.191528i | ||||
\(979\) | −12.8304 | + | 9.32186i | −0.410063 | + | 0.297928i | ||||
\(980\) | 59.0257 | − | 32.0656i | 1.88551 | − | 1.02430i | ||||
\(981\) | 9.43778 | + | 6.85695i | 0.301325 | + | 0.218926i | ||||
\(982\) | 56.9128 | 1.81616 | ||||||||
\(983\) | −7.23718 | − | 5.25812i | −0.230830 | − | 0.167708i | 0.466358 | − | 0.884596i | \(-0.345566\pi\) |
−0.697188 | + | 0.716888i | \(0.745566\pi\) | |||||||
\(984\) | −2.47132 | + | 7.60595i | −0.0787829 | + | 0.242469i | ||||
\(985\) | 3.69373 | − | 2.00661i | 0.117692 | − | 0.0639359i | ||||
\(986\) | 4.05154 | + | 12.4694i | 0.129027 | + | 0.397105i | ||||
\(987\) | 5.55920 | − | 17.1095i | 0.176951 | − | 0.544600i | ||||
\(988\) | 7.11852 | − | 21.9086i | 0.226470 | − | 0.697004i | ||||
\(989\) | 0.896242 | + | 2.75835i | 0.0284988 | + | 0.0877104i | ||||
\(990\) | 1.36802 | + | 7.37187i | 0.0434784 | + | 0.234293i | ||||
\(991\) | −17.4699 | + | 53.7667i | −0.554949 | + | 1.70796i | 0.141130 | + | 0.989991i | \(0.454926\pi\) |
−0.696079 | + | 0.717965i | \(0.745074\pi\) | |||||||
\(992\) | 30.8837 | + | 22.4383i | 0.980559 | + | 0.712418i | ||||
\(993\) | 20.3355 | 0.645327 | ||||||||
\(994\) | 79.3621 | + | 57.6599i | 2.51721 | + | 1.82886i | ||||
\(995\) | −9.44506 | − | 1.24130i | −0.299429 | − | 0.0393518i | ||||
\(996\) | 17.6994 | − | 12.8594i | 0.560826 | − | 0.407464i | ||||
\(997\) | −32.0463 | + | 23.2830i | −1.01492 | + | 0.737380i | −0.965235 | − | 0.261385i | \(-0.915821\pi\) |
−0.0496816 | + | 0.998765i | \(0.515821\pi\) | |||||||
\(998\) | 1.80657 | + | 5.56005i | 0.0571860 | + | 0.176000i | ||||
\(999\) | −6.37232 | −0.201611 |
(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.b.31.2 | ✓ | 8 | |
3.2 | odd | 2 | 225.2.h.c.181.1 | 8 | |||
5.2 | odd | 4 | 375.2.i.b.349.1 | 16 | |||
5.3 | odd | 4 | 375.2.i.b.349.4 | 16 | |||
5.4 | even | 2 | 375.2.g.b.151.1 | 8 | |||
25.2 | odd | 20 | 1875.2.b.c.1249.7 | 8 | |||
25.3 | odd | 20 | 375.2.i.b.274.1 | 16 | |||
25.4 | even | 10 | 375.2.g.b.226.1 | 8 | |||
25.11 | even | 5 | 1875.2.a.h.1.3 | 4 | |||
25.14 | even | 10 | 1875.2.a.e.1.2 | 4 | |||
25.21 | even | 5 | inner | 75.2.g.b.46.2 | yes | 8 | |
25.22 | odd | 20 | 375.2.i.b.274.4 | 16 | |||
25.23 | odd | 20 | 1875.2.b.c.1249.2 | 8 | |||
75.11 | odd | 10 | 5625.2.a.i.1.2 | 4 | |||
75.14 | odd | 10 | 5625.2.a.n.1.3 | 4 | |||
75.71 | odd | 10 | 225.2.h.c.46.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
75.2.g.b.46.2 | yes | 8 | 25.21 | even | 5 | inner | |
225.2.h.c.46.1 | 8 | 75.71 | odd | 10 | |||
225.2.h.c.181.1 | 8 | 3.2 | odd | 2 | |||
375.2.g.b.151.1 | 8 | 5.4 | even | 2 | |||
375.2.g.b.226.1 | 8 | 25.4 | even | 10 | |||
375.2.i.b.274.1 | 16 | 25.3 | odd | 20 | |||
375.2.i.b.274.4 | 16 | 25.22 | odd | 20 | |||
375.2.i.b.349.1 | 16 | 5.2 | odd | 4 | |||
375.2.i.b.349.4 | 16 | 5.3 | odd | 4 | |||
1875.2.a.e.1.2 | 4 | 25.14 | even | 10 | |||
1875.2.a.h.1.3 | 4 | 25.11 | even | 5 | |||
1875.2.b.c.1249.2 | 8 | 25.23 | odd | 20 | |||
1875.2.b.c.1249.7 | 8 | 25.2 | odd | 20 | |||
5625.2.a.i.1.2 | 4 | 75.11 | odd | 10 | |||
5625.2.a.n.1.3 | 4 | 75.14 | odd | 10 |