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 | 16.1 | ||
Root | \(-0.667650 - 2.05481i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.16 |
Dual form | 75.2.g.c.61.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.74793 | − | 1.26995i | −1.23597 | − | 0.897987i | −0.238650 | − | 0.971106i | \(-0.576705\pi\) |
−0.997323 | + | 0.0731189i | \(0.976705\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | 0.824463 | + | 2.53744i | 0.412232 | + | 1.26872i | ||||
\(5\) | −0.460159 | − | 2.18821i | −0.205789 | − | 0.978596i | ||||
\(6\) | −0.667650 | + | 2.05481i | −0.272567 | + | 0.838875i | ||||
\(7\) | −3.16056 | −1.19458 | −0.597290 | − | 0.802026i | \(-0.703756\pi\) | ||||
−0.597290 | + | 0.802026i | \(0.703756\pi\) | |||||||
\(8\) | 0.446002 | − | 1.37265i | 0.157686 | − | 0.485307i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −1.97458 | + | 4.40921i | −0.624417 | + | 1.39431i | ||||
\(11\) | −1.24455 | − | 0.904220i | −0.375247 | − | 0.272633i | 0.384137 | − | 0.923276i | \(-0.374499\pi\) |
−0.759383 | + | 0.650644i | \(0.774499\pi\) | |||||||
\(12\) | 2.15847 | − | 1.56822i | 0.623097 | − | 0.452707i | ||||
\(13\) | 4.24041 | − | 3.08084i | 1.17608 | − | 0.854471i | 0.184355 | − | 0.982860i | \(-0.440981\pi\) |
0.991724 | + | 0.128389i | \(0.0409805\pi\) | |||||||
\(14\) | 5.52444 | + | 4.01374i | 1.47647 | + | 1.07272i | ||||
\(15\) | −1.93891 | + | 1.11383i | −0.500625 | + | 0.287590i | ||||
\(16\) | 1.79417 | − | 1.30354i | 0.448542 | − | 0.325885i | ||||
\(17\) | 0.398843 | − | 1.22751i | 0.0967337 | − | 0.297716i | −0.890968 | − | 0.454066i | \(-0.849973\pi\) |
0.987702 | + | 0.156351i | \(0.0499730\pi\) | |||||||
\(18\) | 2.16056 | 0.509249 | ||||||||
\(19\) | 1.68287 | − | 5.17933i | 0.386076 | − | 1.18822i | −0.549620 | − | 0.835415i | \(-0.685228\pi\) |
0.935696 | − | 0.352806i | \(-0.114772\pi\) | |||||||
\(20\) | 5.17306 | − | 2.97172i | 1.15673 | − | 0.664497i | ||||
\(21\) | 0.976667 | + | 3.00587i | 0.213126 | + | 0.655935i | ||||
\(22\) | 1.02708 | + | 3.16103i | 0.218974 | + | 0.673933i | ||||
\(23\) | 5.21204 | + | 3.78677i | 1.08679 | + | 0.789596i | 0.978854 | − | 0.204562i | \(-0.0655770\pi\) |
0.107932 | + | 0.994158i | \(0.465577\pi\) | |||||||
\(24\) | −1.44329 | −0.294611 | ||||||||
\(25\) | −4.57651 | + | 2.01385i | −0.915302 | + | 0.402769i | ||||
\(26\) | −11.3244 | −2.22090 | ||||||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | −2.60577 | − | 8.01972i | −0.492443 | − | 1.51558i | ||||
\(29\) | −0.730396 | − | 2.24793i | −0.135631 | − | 0.417430i | 0.860056 | − | 0.510199i | \(-0.170428\pi\) |
−0.995688 | + | 0.0927690i | \(0.970428\pi\) | |||||||
\(30\) | 4.80359 | + | 0.515416i | 0.877011 | + | 0.0941016i | ||||
\(31\) | −1.37989 | + | 4.24687i | −0.247836 | + | 0.762760i | 0.747321 | + | 0.664463i | \(0.231340\pi\) |
−0.995157 | + | 0.0982974i | \(0.968660\pi\) | |||||||
\(32\) | −7.67809 | −1.35731 | ||||||||
\(33\) | −0.475377 | + | 1.46306i | −0.0827525 | + | 0.254686i | ||||
\(34\) | −2.25602 | + | 1.63910i | −0.386905 | + | 0.281103i | ||||
\(35\) | 1.45436 | + | 6.91596i | 0.245831 | + | 1.16901i | ||||
\(36\) | −2.15847 | − | 1.56822i | −0.359745 | − | 0.261370i | ||||
\(37\) | 4.81973 | − | 3.50174i | 0.792358 | − | 0.575682i | −0.116304 | − | 0.993214i | \(-0.537105\pi\) |
0.908662 | + | 0.417532i | \(0.137105\pi\) | |||||||
\(38\) | −9.51901 | + | 6.91596i | −1.54419 | + | 1.12192i | ||||
\(39\) | −4.24041 | − | 3.08084i | −0.679009 | − | 0.493329i | ||||
\(40\) | −3.20889 | − | 0.344307i | −0.507369 | − | 0.0544398i | ||||
\(41\) | 6.90269 | − | 5.01510i | 1.07802 | − | 0.783227i | 0.100683 | − | 0.994919i | \(-0.467897\pi\) |
0.977336 | + | 0.211692i | \(0.0678974\pi\) | |||||||
\(42\) | 2.11015 | − | 6.49436i | 0.325603 | − | 1.00210i | ||||
\(43\) | −8.48426 | −1.29384 | −0.646919 | − | 0.762559i | \(-0.723943\pi\) | ||||
−0.646919 | + | 0.762559i | \(0.723943\pi\) | |||||||
\(44\) | 1.26831 | − | 3.90347i | 0.191206 | − | 0.588470i | ||||
\(45\) | 1.65847 | + | 1.49982i | 0.247230 | + | 0.223580i | ||||
\(46\) | −4.30129 | − | 13.2380i | −0.634191 | − | 1.95184i | ||||
\(47\) | 0.232712 | + | 0.716212i | 0.0339445 | + | 0.104470i | 0.966593 | − | 0.256315i | \(-0.0825086\pi\) |
−0.932649 | + | 0.360786i | \(0.882509\pi\) | |||||||
\(48\) | −1.79417 | − | 1.30354i | −0.258966 | − | 0.188150i | ||||
\(49\) | 2.98914 | 0.427020 | ||||||||
\(50\) | 10.5569 | + | 2.29185i | 1.49297 | + | 0.324117i | ||||
\(51\) | −1.29068 | −0.180732 | ||||||||
\(52\) | 11.3135 | + | 8.21974i | 1.56890 | + | 1.13987i | ||||
\(53\) | 3.01289 | + | 9.27271i | 0.413852 | + | 1.27371i | 0.913274 | + | 0.407346i | \(0.133546\pi\) |
−0.499422 | + | 0.866359i | \(0.666454\pi\) | |||||||
\(54\) | −0.667650 | − | 2.05481i | −0.0908556 | − | 0.279625i | ||||
\(55\) | −1.40593 | + | 3.13942i | −0.189576 | + | 0.423320i | ||||
\(56\) | −1.40962 | + | 4.33836i | −0.188368 | + | 0.579737i | ||||
\(57\) | −5.44587 | −0.721324 | ||||||||
\(58\) | −1.57806 | + | 4.85678i | −0.207210 | + | 0.637727i | ||||
\(59\) | −3.32724 | + | 2.41738i | −0.433170 | + | 0.314717i | −0.782915 | − | 0.622128i | \(-0.786268\pi\) |
0.349745 | + | 0.936845i | \(0.386268\pi\) | |||||||
\(60\) | −4.42484 | − | 4.00156i | −0.571244 | − | 0.516599i | ||||
\(61\) | 8.65159 | + | 6.28574i | 1.10772 | + | 0.804807i | 0.982303 | − | 0.187297i | \(-0.0599726\pi\) |
0.125419 | + | 0.992104i | \(0.459973\pi\) | |||||||
\(62\) | 7.80525 | − | 5.67084i | 0.991267 | − | 0.720198i | ||||
\(63\) | 2.55695 | − | 1.85773i | 0.322145 | − | 0.234052i | ||||
\(64\) | 9.83243 | + | 7.14368i | 1.22905 | + | 0.892960i | ||||
\(65\) | −8.69278 | − | 7.86123i | −1.07821 | − | 0.975065i | ||||
\(66\) | 2.68893 | − | 1.95362i | 0.330984 | − | 0.240474i | ||||
\(67\) | −0.586713 | + | 1.80572i | −0.0716785 | + | 0.220604i | −0.980478 | − | 0.196630i | \(-0.937000\pi\) |
0.908799 | + | 0.417233i | \(0.137000\pi\) | |||||||
\(68\) | 3.44357 | 0.417594 | ||||||||
\(69\) | 1.99082 | − | 6.12712i | 0.239667 | − | 0.737619i | ||||
\(70\) | 6.24078 | − | 13.9356i | 0.745915 | − | 1.66562i | ||||
\(71\) | −0.0219023 | − | 0.0674084i | −0.00259933 | − | 0.00799990i | 0.949748 | − | 0.313014i | \(-0.101339\pi\) |
−0.952348 | + | 0.305014i | \(0.901339\pi\) | |||||||
\(72\) | 0.446002 | + | 1.37265i | 0.0525619 | + | 0.161769i | ||||
\(73\) | −3.24515 | − | 2.35774i | −0.379816 | − | 0.275952i | 0.381454 | − | 0.924388i | \(-0.375424\pi\) |
−0.761270 | + | 0.648436i | \(0.775424\pi\) | |||||||
\(74\) | −12.8716 | −1.49629 | ||||||||
\(75\) | 3.32950 | + | 3.73021i | 0.384457 | + | 0.430727i | ||||
\(76\) | 14.5297 | 1.66667 | ||||||||
\(77\) | 3.93348 | + | 2.85784i | 0.448262 | + | 0.325681i | ||||
\(78\) | 3.49944 | + | 10.7702i | 0.396234 | + | 1.21948i | ||||
\(79\) | 0.500141 | + | 1.53928i | 0.0562703 | + | 0.173182i | 0.975242 | − | 0.221143i | \(-0.0709786\pi\) |
−0.918971 | + | 0.394325i | \(0.870979\pi\) | |||||||
\(80\) | −3.67802 | − | 3.32618i | −0.411215 | − | 0.371878i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −18.4343 | −2.03573 | ||||||||
\(83\) | 4.06322 | − | 12.5053i | 0.445996 | − | 1.37263i | −0.435392 | − | 0.900241i | \(-0.643390\pi\) |
0.881388 | − | 0.472393i | \(-0.156610\pi\) | |||||||
\(84\) | −6.82198 | + | 4.95646i | −0.744339 | + | 0.540794i | ||||
\(85\) | −2.86958 | − | 0.307901i | −0.311250 | − | 0.0333966i | ||||
\(86\) | 14.8299 | + | 10.7745i | 1.59915 | + | 1.16185i | ||||
\(87\) | −1.91220 | + | 1.38930i | −0.205010 | + | 0.148948i | ||||
\(88\) | −1.79626 | + | 1.30506i | −0.191481 | + | 0.139119i | ||||
\(89\) | −5.88638 | − | 4.27671i | −0.623955 | − | 0.453330i | 0.230345 | − | 0.973109i | \(-0.426014\pi\) |
−0.854301 | + | 0.519779i | \(0.826014\pi\) | |||||||
\(90\) | −0.994200 | − | 4.72775i | −0.104798 | − | 0.498349i | ||||
\(91\) | −13.4021 | + | 9.73718i | −1.40492 | + | 1.02073i | ||||
\(92\) | −5.31155 | + | 16.3473i | −0.553768 | + | 1.70432i | ||||
\(93\) | 4.46542 | 0.463043 | ||||||||
\(94\) | 0.502787 | − | 1.54742i | 0.0518585 | − | 0.159604i | ||||
\(95\) | −12.1078 | − | 1.29915i | −1.24224 | − | 0.133290i | ||||
\(96\) | 2.37266 | + | 7.30230i | 0.242159 | + | 0.745288i | ||||
\(97\) | 3.15009 | + | 9.69499i | 0.319843 | + | 0.984377i | 0.973715 | + | 0.227771i | \(0.0731438\pi\) |
−0.653871 | + | 0.756606i | \(0.726856\pi\) | |||||||
\(98\) | −5.22480 | − | 3.79604i | −0.527785 | − | 0.383458i | ||||
\(99\) | 1.53835 | 0.154610 | ||||||||
\(100\) | −8.88317 | − | 9.95226i | −0.888317 | − | 0.995226i | ||||
\(101\) | 1.08759 | 0.108219 | 0.0541096 | − | 0.998535i | \(-0.482768\pi\) | ||||
0.0541096 | + | 0.998535i | \(0.482768\pi\) | |||||||
\(102\) | 2.25602 | + | 1.63910i | 0.223380 | + | 0.162295i | ||||
\(103\) | −1.52579 | − | 4.69590i | −0.150341 | − | 0.462701i | 0.847319 | − | 0.531085i | \(-0.178216\pi\) |
−0.997659 | + | 0.0683845i | \(0.978216\pi\) | |||||||
\(104\) | −2.33769 | − | 7.19468i | −0.229230 | − | 0.705497i | ||||
\(105\) | 6.12805 | − | 3.52033i | 0.598036 | − | 0.343549i | ||||
\(106\) | 6.50952 | − | 20.0343i | 0.632261 | − | 1.94590i | ||||
\(107\) | 15.3059 | 1.47967 | 0.739837 | − | 0.672786i | \(-0.234902\pi\) | ||||
0.739837 | + | 0.672786i | \(0.234902\pi\) | |||||||
\(108\) | −0.824463 | + | 2.53744i | −0.0793340 | + | 0.244165i | ||||
\(109\) | −5.38724 | + | 3.91406i | −0.516004 | + | 0.374899i | −0.815097 | − | 0.579325i | \(-0.803316\pi\) |
0.299092 | + | 0.954224i | \(0.403316\pi\) | |||||||
\(110\) | 6.44436 | − | 3.70204i | 0.614446 | − | 0.352975i | ||||
\(111\) | −4.81973 | − | 3.50174i | −0.457468 | − | 0.332370i | ||||
\(112\) | −5.67058 | + | 4.11991i | −0.535819 | + | 0.389295i | ||||
\(113\) | 7.25804 | − | 5.27328i | 0.682779 | − | 0.496068i | −0.191499 | − | 0.981493i | \(-0.561335\pi\) |
0.874278 | + | 0.485425i | \(0.161335\pi\) | |||||||
\(114\) | 9.51901 | + | 6.91596i | 0.891537 | + | 0.647739i | ||||
\(115\) | 5.88787 | − | 13.1475i | 0.549047 | − | 1.22601i | ||||
\(116\) | 5.10179 | − | 3.70667i | 0.473689 | − | 0.344155i | ||||
\(117\) | −1.61969 | + | 4.98490i | −0.149741 | + | 0.460854i | ||||
\(118\) | 8.88573 | 0.817998 | ||||||||
\(119\) | −1.26057 | + | 3.87963i | −0.115556 | + | 0.355645i | ||||
\(120\) | 0.664144 | + | 3.15823i | 0.0606278 | + | 0.288305i | ||||
\(121\) | −2.66789 | − | 8.21092i | −0.242536 | − | 0.746448i | ||||
\(122\) | −7.13981 | − | 21.9741i | −0.646408 | − | 1.98944i | ||||
\(123\) | −6.90269 | − | 5.01510i | −0.622395 | − | 0.452196i | ||||
\(124\) | −11.9138 | −1.06989 | ||||||||
\(125\) | 6.51263 | + | 9.08766i | 0.582508 | + | 0.812825i | ||||
\(126\) | −6.82858 | −0.608338 | ||||||||
\(127\) | −8.10511 | − | 5.88870i | −0.719212 | − | 0.522538i | 0.166920 | − | 0.985970i | \(-0.446618\pi\) |
−0.886132 | + | 0.463432i | \(0.846618\pi\) | |||||||
\(128\) | −3.36899 | − | 10.3687i | −0.297780 | − | 0.916471i | ||||
\(129\) | 2.62178 | + | 8.06901i | 0.230835 | + | 0.710437i | ||||
\(130\) | 5.21104 | + | 24.7802i | 0.457038 | + | 2.17337i | ||||
\(131\) | −1.97111 | + | 6.06645i | −0.172217 | + | 0.530029i | −0.999495 | − | 0.0317631i | \(-0.989888\pi\) |
0.827279 | + | 0.561792i | \(0.189888\pi\) | |||||||
\(132\) | −4.10435 | −0.357238 | ||||||||
\(133\) | −5.31880 | + | 16.3696i | −0.461199 | + | 1.41942i | ||||
\(134\) | 3.31870 | − | 2.41117i | 0.286692 | − | 0.208294i | ||||
\(135\) | 0.913920 | − | 2.04077i | 0.0786577 | − | 0.175642i | ||||
\(136\) | −1.50707 | − | 1.09495i | −0.129230 | − | 0.0938910i | ||||
\(137\) | 7.42461 | − | 5.39429i | 0.634327 | − | 0.460866i | −0.223570 | − | 0.974688i | \(-0.571771\pi\) |
0.857897 | + | 0.513822i | \(0.171771\pi\) | |||||||
\(138\) | −11.2609 | + | 8.18154i | −0.958594 | + | 0.696459i | ||||
\(139\) | 7.49586 | + | 5.44606i | 0.635790 | + | 0.461929i | 0.858401 | − | 0.512979i | \(-0.171458\pi\) |
−0.222611 | + | 0.974907i | \(0.571458\pi\) | |||||||
\(140\) | −16.3498 | + | 9.39230i | −1.38181 | + | 0.793794i | ||||
\(141\) | 0.609247 | − | 0.442644i | 0.0513078 | − | 0.0372773i | ||||
\(142\) | −0.0473213 | + | 0.145640i | −0.00397111 | + | 0.0122218i | ||||
\(143\) | −8.06317 | −0.674276 | ||||||||
\(144\) | −0.685311 | + | 2.10917i | −0.0571093 | + | 0.175764i | ||||
\(145\) | −4.58284 | + | 2.63266i | −0.380584 | + | 0.218631i | ||||
\(146\) | 2.67809 | + | 8.24232i | 0.221641 | + | 0.682140i | ||||
\(147\) | −0.923695 | − | 2.84284i | −0.0761850 | − | 0.234473i | ||||
\(148\) | 12.8591 | + | 9.34270i | 1.05701 | + | 0.767965i | ||||
\(149\) | −10.0817 | −0.825928 | −0.412964 | − | 0.910747i | \(-0.635506\pi\) | ||||
−0.412964 | + | 0.910747i | \(0.635506\pi\) | |||||||
\(150\) | −1.08257 | − | 10.7484i | −0.0883918 | − | 0.877605i | ||||
\(151\) | 10.7375 | 0.873804 | 0.436902 | − | 0.899509i | \(-0.356076\pi\) | ||||
0.436902 | + | 0.899509i | \(0.356076\pi\) | |||||||
\(152\) | −6.35887 | − | 4.61999i | −0.515773 | − | 0.374731i | ||||
\(153\) | 0.398843 | + | 1.22751i | 0.0322446 | + | 0.0992385i | ||||
\(154\) | −3.24615 | − | 9.99061i | −0.261582 | − | 0.805067i | ||||
\(155\) | 9.92800 | + | 1.06526i | 0.797436 | + | 0.0855634i | ||||
\(156\) | 4.32137 | − | 13.2998i | 0.345987 | − | 1.06484i | ||||
\(157\) | 17.4417 | 1.39200 | 0.696001 | − | 0.718041i | \(-0.254961\pi\) | ||||
0.696001 | + | 0.718041i | \(0.254961\pi\) | |||||||
\(158\) | 1.08058 | − | 3.32570i | 0.0859667 | − | 0.264578i | ||||
\(159\) | 7.88784 | − | 5.73085i | 0.625546 | − | 0.454486i | ||||
\(160\) | 3.53314 | + | 16.8013i | 0.279319 | + | 1.32826i | ||||
\(161\) | −16.4730 | − | 11.9683i | −1.29825 | − | 0.943235i | ||||
\(162\) | −1.74793 | + | 1.26995i | −0.137330 | + | 0.0997763i | ||||
\(163\) | 13.1525 | − | 9.55586i | 1.03018 | − | 0.748473i | 0.0618392 | − | 0.998086i | \(-0.480303\pi\) |
0.968346 | + | 0.249613i | \(0.0803034\pi\) | |||||||
\(164\) | 18.4165 | + | 13.3804i | 1.43809 | + | 1.04483i | ||||
\(165\) | 3.42023 | + | 0.366984i | 0.266264 | + | 0.0285697i | ||||
\(166\) | −22.9832 | + | 16.6983i | −1.78385 | + | 1.29604i | ||||
\(167\) | −3.51989 | + | 10.8331i | −0.272377 | + | 0.838290i | 0.717525 | + | 0.696533i | \(0.245275\pi\) |
−0.989902 | + | 0.141757i | \(0.954725\pi\) | |||||||
\(168\) | 4.56162 | 0.351936 | ||||||||
\(169\) | 4.47230 | − | 13.7643i | 0.344023 | − | 1.05879i | ||||
\(170\) | 4.62481 | + | 4.18240i | 0.354707 | + | 0.320776i | ||||
\(171\) | 1.68287 | + | 5.17933i | 0.128692 | + | 0.396074i | ||||
\(172\) | −6.99496 | − | 21.5283i | −0.533361 | − | 1.64152i | ||||
\(173\) | −7.65205 | − | 5.55954i | −0.581775 | − | 0.422684i | 0.257589 | − | 0.966255i | \(-0.417072\pi\) |
−0.839363 | + | 0.543571i | \(0.817072\pi\) | |||||||
\(174\) | 5.10672 | 0.387140 | ||||||||
\(175\) | 14.4643 | − | 6.36488i | 1.09340 | − | 0.481140i | ||||
\(176\) | −3.41162 | −0.257161 | ||||||||
\(177\) | 3.32724 | + | 2.41738i | 0.250091 | + | 0.181702i | ||||
\(178\) | 4.85780 | + | 14.9508i | 0.364107 | + | 1.12061i | ||||
\(179\) | 1.26001 | + | 3.87790i | 0.0941773 | + | 0.289848i | 0.987038 | − | 0.160484i | \(-0.0513056\pi\) |
−0.892861 | + | 0.450332i | \(0.851306\pi\) | |||||||
\(180\) | −2.43836 | + | 5.44482i | −0.181744 | + | 0.405833i | ||||
\(181\) | −3.43633 | + | 10.5759i | −0.255421 | + | 0.786104i | 0.738326 | + | 0.674444i | \(0.235617\pi\) |
−0.993747 | + | 0.111660i | \(0.964383\pi\) | |||||||
\(182\) | 35.7916 | 2.65305 | ||||||||
\(183\) | 3.30461 | − | 10.1705i | 0.244284 | − | 0.751829i | ||||
\(184\) | 7.52251 | − | 5.46542i | 0.554567 | − | 0.402916i | ||||
\(185\) | −9.88036 | − | 8.93521i | −0.726419 | − | 0.656930i | ||||
\(186\) | −7.80525 | − | 5.67084i | −0.572308 | − | 0.415806i | ||||
\(187\) | −1.60632 | + | 1.16706i | −0.117466 | + | 0.0853440i | ||||
\(188\) | −1.62548 | + | 1.18098i | −0.118550 | + | 0.0861319i | ||||
\(189\) | −2.55695 | − | 1.85773i | −0.185990 | − | 0.135130i | ||||
\(190\) | 19.5138 | + | 17.6471i | 1.41568 | + | 1.28026i | ||||
\(191\) | −2.92164 | + | 2.12270i | −0.211403 | + | 0.153593i | −0.688448 | − | 0.725286i | \(-0.741708\pi\) |
0.477046 | + | 0.878879i | \(0.341708\pi\) | |||||||
\(192\) | 3.75565 | − | 11.5587i | 0.271041 | − | 0.834178i | ||||
\(193\) | −17.0562 | −1.22774 | −0.613868 | − | 0.789409i | \(-0.710387\pi\) | ||||
−0.613868 | + | 0.789409i | \(0.710387\pi\) | |||||||
\(194\) | 6.80596 | − | 20.9466i | 0.488640 | − | 1.50388i | ||||
\(195\) | −4.79026 | + | 10.6966i | −0.343037 | + | 0.765998i | ||||
\(196\) | 2.46443 | + | 7.58475i | 0.176031 | + | 0.541768i | ||||
\(197\) | −1.36129 | − | 4.18963i | −0.0969880 | − | 0.298498i | 0.890779 | − | 0.454437i | \(-0.150160\pi\) |
−0.987767 | + | 0.155939i | \(0.950160\pi\) | |||||||
\(198\) | −2.68893 | − | 1.95362i | −0.191094 | − | 0.138838i | ||||
\(199\) | 16.5956 | 1.17643 | 0.588214 | − | 0.808705i | \(-0.299831\pi\) | ||||
0.588214 | + | 0.808705i | \(0.299831\pi\) | |||||||
\(200\) | 0.723180 | + | 7.18014i | 0.0511365 | + | 0.507713i | ||||
\(201\) | 1.89864 | 0.133920 | ||||||||
\(202\) | −1.90103 | − | 1.38118i | −0.133756 | − | 0.0971795i | ||||
\(203\) | 2.30846 | + | 7.10471i | 0.162022 | + | 0.498653i | ||||
\(204\) | −1.06412 | − | 3.27503i | −0.0745034 | − | 0.229298i | ||||
\(205\) | −14.1504 | − | 12.7968i | −0.988307 | − | 0.893766i | ||||
\(206\) | −3.29656 | + | 10.1458i | −0.229682 | + | 0.706889i | ||||
\(207\) | −6.44244 | −0.447780 | ||||||||
\(208\) | 3.59202 | − | 11.0551i | 0.249061 | − | 0.766532i | ||||
\(209\) | −6.77768 | + | 4.92427i | −0.468822 | + | 0.340619i | ||||
\(210\) | −15.1820 | − | 1.62900i | −1.04766 | − | 0.112412i | ||||
\(211\) | −15.0035 | − | 10.9007i | −1.03288 | − | 0.750434i | −0.0640001 | − | 0.997950i | \(-0.520386\pi\) |
−0.968884 | + | 0.247516i | \(0.920386\pi\) | |||||||
\(212\) | −21.0449 | + | 15.2900i | −1.44537 | + | 1.05012i | ||||
\(213\) | −0.0573410 | + | 0.0416607i | −0.00392894 | + | 0.00285454i | ||||
\(214\) | −26.7536 | − | 19.4376i | −1.82884 | − | 1.32873i | ||||
\(215\) | 3.90410 | + | 18.5653i | 0.266258 | + | 1.26614i | ||||
\(216\) | 1.16765 | − | 0.848347i | 0.0794485 | − | 0.0577227i | ||||
\(217\) | 4.36123 | − | 13.4225i | 0.296060 | − | 0.911178i | ||||
\(218\) | 14.3872 | 0.974422 | ||||||||
\(219\) | −1.23954 | + | 3.81490i | −0.0837601 | + | 0.257787i | ||||
\(220\) | −9.12523 | − | 0.979120i | −0.615223 | − | 0.0660122i | ||||
\(221\) | −2.09051 | − | 6.43393i | −0.140623 | − | 0.432793i | ||||
\(222\) | 3.97753 | + | 12.2416i | 0.266954 | + | 0.821601i | ||||
\(223\) | 0.624203 | + | 0.453510i | 0.0417997 | + | 0.0303693i | 0.608489 | − | 0.793562i | \(-0.291776\pi\) |
−0.566689 | + | 0.823932i | \(0.691776\pi\) | |||||||
\(224\) | 24.2671 | 1.62141 | ||||||||
\(225\) | 2.51876 | − | 4.31924i | 0.167918 | − | 0.287949i | ||||
\(226\) | −19.3833 | −1.28936 | ||||||||
\(227\) | −9.24817 | − | 6.71919i | −0.613823 | − | 0.445968i | 0.236936 | − | 0.971525i | \(-0.423857\pi\) |
−0.850758 | + | 0.525557i | \(0.823857\pi\) | |||||||
\(228\) | −4.48992 | − | 13.8186i | −0.297352 | − | 0.915157i | ||||
\(229\) | 3.15962 | + | 9.72432i | 0.208794 | + | 0.642601i | 0.999536 | + | 0.0304520i | \(0.00969467\pi\) |
−0.790743 | + | 0.612149i | \(0.790305\pi\) | |||||||
\(230\) | −26.9883 | + | 15.5037i | −1.77955 | + | 1.02228i | ||||
\(231\) | 1.50246 | − | 4.62409i | 0.0988544 | − | 0.304242i | ||||
\(232\) | −3.41139 | −0.223969 | ||||||||
\(233\) | −6.95997 | + | 21.4206i | −0.455963 | + | 1.40331i | 0.414038 | + | 0.910260i | \(0.364118\pi\) |
−0.870001 | + | 0.493050i | \(0.835882\pi\) | |||||||
\(234\) | 9.16166 | − | 6.65634i | 0.598917 | − | 0.435138i | ||||
\(235\) | 1.46014 | − | 0.838793i | 0.0952489 | − | 0.0547168i | ||||
\(236\) | −8.87715 | − | 6.44963i | −0.577853 | − | 0.419835i | ||||
\(237\) | 1.30939 | − | 0.951325i | 0.0850538 | − | 0.0617952i | ||||
\(238\) | 7.13030 | − | 5.18047i | 0.462189 | − | 0.335800i | ||||
\(239\) | 0.476571 | + | 0.346249i | 0.0308268 | + | 0.0223970i | 0.603092 | − | 0.797672i | \(-0.293935\pi\) |
−0.572265 | + | 0.820069i | \(0.693935\pi\) | |||||||
\(240\) | −2.02681 | + | 4.52585i | −0.130830 | + | 0.292142i | ||||
\(241\) | −1.22110 | + | 0.887185i | −0.0786583 | + | 0.0571486i | −0.626419 | − | 0.779486i | \(-0.715480\pi\) |
0.547761 | + | 0.836635i | \(0.315480\pi\) | |||||||
\(242\) | −5.76414 | + | 17.7402i | −0.370533 | + | 1.14038i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −8.81677 | + | 27.1352i | −0.564436 | + | 1.73715i | ||||
\(245\) | −1.37548 | − | 6.54086i | −0.0878760 | − | 0.417880i | ||||
\(246\) | 5.69652 | + | 17.5321i | 0.363197 | + | 1.11780i | ||||
\(247\) | −8.82065 | − | 27.1472i | −0.561244 | − | 1.72733i | ||||
\(248\) | 5.21405 | + | 3.78823i | 0.331093 | + | 0.240553i | ||||
\(249\) | −13.1488 | −0.833274 | ||||||||
\(250\) | 0.157212 | − | 24.1553i | 0.00994296 | − | 1.52771i | ||||
\(251\) | 11.8953 | 0.750823 | 0.375412 | − | 0.926858i | \(-0.377501\pi\) | ||||
0.375412 | + | 0.926858i | \(0.377501\pi\) | |||||||
\(252\) | 6.82198 | + | 4.95646i | 0.429744 | + | 0.312228i | ||||
\(253\) | −3.06258 | − | 9.42567i | −0.192543 | − | 0.592587i | ||||
\(254\) | 6.68882 | + | 20.5861i | 0.419694 | + | 1.29169i | ||||
\(255\) | 0.593919 | + | 2.82428i | 0.0371927 | + | 0.176864i | ||||
\(256\) | 0.232398 | − | 0.715248i | 0.0145249 | − | 0.0447030i | ||||
\(257\) | −18.0492 | −1.12588 | −0.562939 | − | 0.826498i | \(-0.690329\pi\) | ||||
−0.562939 | + | 0.826498i | \(0.690329\pi\) | |||||||
\(258\) | 5.66451 | − | 17.4336i | 0.352657 | − | 1.08537i | ||||
\(259\) | −15.2330 | + | 11.0674i | −0.946534 | + | 0.687698i | ||||
\(260\) | 12.7805 | − | 28.5387i | 0.792612 | − | 1.76989i | ||||
\(261\) | 1.91220 | + | 1.38930i | 0.118362 | + | 0.0859953i | ||||
\(262\) | 11.1494 | − | 8.10053i | 0.688814 | − | 0.500453i | ||||
\(263\) | 15.4576 | − | 11.2306i | 0.953157 | − | 0.692509i | 0.00160518 | − | 0.999999i | \(-0.499489\pi\) |
0.951551 | + | 0.307490i | \(0.0994891\pi\) | |||||||
\(264\) | 1.79626 | + | 1.30506i | 0.110552 | + | 0.0803206i | ||||
\(265\) | 18.9042 | − | 10.8597i | 1.16128 | − | 0.667109i | ||||
\(266\) | 30.0854 | − | 21.8583i | 1.84465 | − | 1.34022i | ||||
\(267\) | −2.24840 | + | 6.91986i | −0.137600 | + | 0.423489i | ||||
\(268\) | −5.06562 | −0.309432 | ||||||||
\(269\) | −6.86791 | + | 21.1372i | −0.418744 | + | 1.28876i | 0.490115 | + | 0.871658i | \(0.336955\pi\) |
−0.908859 | + | 0.417103i | \(0.863045\pi\) | |||||||
\(270\) | −4.18914 | + | 2.40650i | −0.254943 | + | 0.146455i | ||||
\(271\) | 6.24546 | + | 19.2216i | 0.379385 | + | 1.16763i | 0.940472 | + | 0.339870i | \(0.110383\pi\) |
−0.561088 | + | 0.827756i | \(0.689617\pi\) | |||||||
\(272\) | −0.884520 | − | 2.72227i | −0.0536319 | − | 0.165062i | ||||
\(273\) | 13.4021 | + | 9.73718i | 0.811130 | + | 0.589321i | ||||
\(274\) | −19.8281 | −1.19786 | ||||||||
\(275\) | 7.51666 | + | 1.63184i | 0.453272 | + | 0.0984034i | ||||
\(276\) | 17.1885 | 1.03463 | ||||||||
\(277\) | 12.9777 | + | 9.42882i | 0.779752 | + | 0.566523i | 0.904904 | − | 0.425615i | \(-0.139942\pi\) |
−0.125153 | + | 0.992137i | \(0.539942\pi\) | |||||||
\(278\) | −6.18604 | − | 19.0387i | −0.371014 | − | 1.14186i | ||||
\(279\) | −1.37989 | − | 4.24687i | −0.0826120 | − | 0.254253i | ||||
\(280\) | 10.1419 | + | 1.08820i | 0.606093 | + | 0.0650326i | ||||
\(281\) | 2.58742 | − | 7.96327i | 0.154353 | − | 0.475049i | −0.843742 | − | 0.536749i | \(-0.819652\pi\) |
0.998095 | + | 0.0617001i | \(0.0196522\pi\) | |||||||
\(282\) | −1.62705 | −0.0968896 | ||||||||
\(283\) | −0.349174 | + | 1.07465i | −0.0207562 | + | 0.0638811i | −0.960898 | − | 0.276902i | \(-0.910692\pi\) |
0.940142 | + | 0.340783i | \(0.110692\pi\) | |||||||
\(284\) | 0.152987 | − | 0.111151i | 0.00907810 | − | 0.00659563i | ||||
\(285\) | 2.50597 | + | 11.9167i | 0.148441 | + | 0.705885i | ||||
\(286\) | 14.0939 | + | 10.2398i | 0.833387 | + | 0.605491i | ||||
\(287\) | −21.8164 | + | 15.8505i | −1.28778 | + | 0.935626i | ||||
\(288\) | 6.21171 | − | 4.51307i | 0.366028 | − | 0.265935i | ||||
\(289\) | 12.4056 | + | 9.01318i | 0.729740 | + | 0.530187i | ||||
\(290\) | 11.3538 | + | 1.21824i | 0.666719 | + | 0.0715377i | ||||
\(291\) | 8.24705 | − | 5.99183i | 0.483451 | − | 0.351247i | ||||
\(292\) | 3.30711 | − | 10.1782i | 0.193534 | − | 0.595636i | ||||
\(293\) | −2.37857 | −0.138958 | −0.0694789 | − | 0.997583i | \(-0.522134\pi\) | ||||
−0.0694789 | + | 0.997583i | \(0.522134\pi\) | |||||||
\(294\) | −1.99570 | + | 6.14212i | −0.116391 | + | 0.358216i | ||||
\(295\) | 6.82080 | + | 6.16832i | 0.397122 | + | 0.359134i | ||||
\(296\) | −2.65706 | − | 8.17760i | −0.154439 | − | 0.475313i | ||||
\(297\) | −0.475377 | − | 1.46306i | −0.0275842 | − | 0.0848953i | ||||
\(298\) | 17.6222 | + | 12.8032i | 1.02082 | + | 0.741672i | ||||
\(299\) | 33.7676 | 1.95283 | ||||||||
\(300\) | −6.72011 | + | 11.5238i | −0.387986 | + | 0.665328i | ||||
\(301\) | 26.8150 | 1.54559 | ||||||||
\(302\) | −18.7684 | − | 13.6360i | −1.08000 | − | 0.784665i | ||||
\(303\) | −0.336084 | − | 1.03436i | −0.0193075 | − | 0.0594224i | ||||
\(304\) | −3.73212 | − | 11.4863i | −0.214052 | − | 0.658783i | ||||
\(305\) | 9.77342 | − | 21.8239i | 0.559624 | − | 1.24963i | ||||
\(306\) | 0.861724 | − | 2.65212i | 0.0492615 | − | 0.151611i | ||||
\(307\) | 2.89366 | 0.165150 | 0.0825748 | − | 0.996585i | \(-0.473686\pi\) | ||||
0.0825748 | + | 0.996585i | \(0.473686\pi\) | |||||||
\(308\) | −4.00858 | + | 12.3371i | −0.228410 | + | 0.702974i | ||||
\(309\) | −3.99457 | + | 2.90222i | −0.227243 | + | 0.165102i | ||||
\(310\) | −16.0006 | − | 14.4700i | −0.908775 | − | 0.821842i | ||||
\(311\) | 5.78079 | + | 4.19999i | 0.327799 | + | 0.238160i | 0.739496 | − | 0.673161i | \(-0.235064\pi\) |
−0.411697 | + | 0.911321i | \(0.635064\pi\) | |||||||
\(312\) | −6.12016 | + | 4.44656i | −0.346486 | + | 0.251737i | ||||
\(313\) | −18.6331 | + | 13.5378i | −1.05321 | + | 0.765200i | −0.972820 | − | 0.231563i | \(-0.925616\pi\) |
−0.0803879 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(314\) | −30.4869 | − | 22.1500i | −1.72048 | − | 1.25000i | ||||
\(315\) | −5.24170 | − | 4.74028i | −0.295336 | − | 0.267085i | ||||
\(316\) | −3.49347 | + | 2.53815i | −0.196523 | + | 0.142782i | ||||
\(317\) | −6.41981 | + | 19.7582i | −0.360573 | + | 1.10973i | 0.592135 | + | 0.805839i | \(0.298285\pi\) |
−0.952707 | + | 0.303890i | \(0.901715\pi\) | |||||||
\(318\) | −21.0653 | −1.18128 | ||||||||
\(319\) | −1.12361 | + | 3.45810i | −0.0629098 | + | 0.193617i | ||||
\(320\) | 11.1074 | − | 24.8026i | 0.620921 | − | 1.38651i | ||||
\(321\) | −4.72978 | − | 14.5568i | −0.263990 | − | 0.812479i | ||||
\(322\) | 13.5945 | + | 41.8395i | 0.757591 | + | 2.33163i | ||||
\(323\) | −5.68650 | − | 4.13148i | −0.316405 | − | 0.229882i | ||||
\(324\) | 2.66802 | 0.148223 | ||||||||
\(325\) | −13.2019 | + | 22.6390i | −0.732312 | + | 1.25579i | ||||
\(326\) | −35.1251 | −1.94540 | ||||||||
\(327\) | 5.38724 | + | 3.91406i | 0.297915 | + | 0.216448i | ||||
\(328\) | −3.80538 | − | 11.7118i | −0.210117 | − | 0.646673i | ||||
\(329\) | −0.735499 | − | 2.26363i | −0.0405494 | − | 0.124798i | ||||
\(330\) | −5.51226 | − | 4.98496i | −0.303440 | − | 0.274413i | ||||
\(331\) | −5.94869 | + | 18.3082i | −0.326969 | + | 1.00631i | 0.643574 | + | 0.765383i | \(0.277451\pi\) |
−0.970544 | + | 0.240925i | \(0.922549\pi\) | |||||||
\(332\) | 35.0814 | 1.92534 | ||||||||
\(333\) | −1.84097 | + | 5.66593i | −0.100885 | + | 0.310491i | ||||
\(334\) | 19.9099 | − | 14.4654i | 1.08942 | − | 0.791513i | ||||
\(335\) | 4.22127 | + | 0.452934i | 0.230633 | + | 0.0247464i | ||||
\(336\) | 5.67058 | + | 4.11991i | 0.309355 | + | 0.224760i | ||||
\(337\) | −17.5609 | + | 12.7587i | −0.956602 | + | 0.695012i | −0.952359 | − | 0.304979i | \(-0.901351\pi\) |
−0.00424305 | + | 0.999991i | \(0.501351\pi\) | |||||||
\(338\) | −25.2972 | + | 18.3795i | −1.37599 | + | 0.999712i | ||||
\(339\) | −7.25804 | − | 5.27328i | −0.394203 | − | 0.286405i | ||||
\(340\) | −1.58459 | − | 7.53524i | −0.0859363 | − | 0.408656i | ||||
\(341\) | 5.55745 | − | 4.03773i | 0.300953 | − | 0.218655i | ||||
\(342\) | 3.63594 | − | 11.1903i | 0.196609 | − | 0.605100i | ||||
\(343\) | 12.6766 | 0.684470 | ||||||||
\(344\) | −3.78400 | + | 11.6460i | −0.204020 | + | 0.627908i | ||||
\(345\) | −14.3235 | − | 1.53689i | −0.771152 | − | 0.0827432i | ||||
\(346\) | 6.31493 | + | 19.4354i | 0.339493 | + | 1.04485i | ||||
\(347\) | −0.529944 | − | 1.63100i | −0.0284489 | − | 0.0875567i | 0.935824 | − | 0.352468i | \(-0.114657\pi\) |
−0.964273 | + | 0.264911i | \(0.914657\pi\) | |||||||
\(348\) | −5.10179 | − | 3.70667i | −0.273485 | − | 0.198698i | ||||
\(349\) | −15.5553 | −0.832654 | −0.416327 | − | 0.909215i | \(-0.636683\pi\) | ||||
−0.416327 | + | 0.909215i | \(0.636683\pi\) | |||||||
\(350\) | −33.3657 | − | 7.24354i | −1.78347 | − | 0.387184i | ||||
\(351\) | 5.24144 | 0.279767 | ||||||||
\(352\) | 9.55579 | + | 6.94268i | 0.509325 | + | 0.370046i | ||||
\(353\) | 4.80632 | + | 14.7923i | 0.255814 | + | 0.787316i | 0.993668 | + | 0.112355i | \(0.0358394\pi\) |
−0.737854 | + | 0.674961i | \(0.764161\pi\) | |||||||
\(354\) | −2.74584 | − | 8.45083i | −0.145940 | − | 0.449157i | ||||
\(355\) | −0.137425 | + | 0.0789454i | −0.00729376 | + | 0.00418998i | ||||
\(356\) | 5.99877 | − | 18.4623i | 0.317934 | − | 0.978501i | ||||
\(357\) | 4.07928 | 0.215899 | ||||||||
\(358\) | 2.72232 | − | 8.37844i | 0.143879 | − | 0.442814i | ||||
\(359\) | 19.8509 | − | 14.4225i | 1.04769 | − | 0.761191i | 0.0759181 | − | 0.997114i | \(-0.475811\pi\) |
0.971772 | + | 0.235923i | \(0.0758112\pi\) | |||||||
\(360\) | 2.79842 | − | 1.60758i | 0.147490 | − | 0.0847272i | ||||
\(361\) | −8.62214 | − | 6.26435i | −0.453797 | − | 0.329703i | ||||
\(362\) | 19.4373 | − | 14.1221i | 1.02160 | − | 0.742239i | ||||
\(363\) | −6.98463 | + | 5.07463i | −0.366598 | + | 0.266349i | ||||
\(364\) | −35.7570 | − | 25.9790i | −1.87418 | − | 1.36167i | ||||
\(365\) | −3.66594 | + | 8.18600i | −0.191884 | + | 0.428475i | ||||
\(366\) | −18.6923 | + | 13.5807i | −0.977060 | + | 0.709876i | ||||
\(367\) | 8.68548 | − | 26.7311i | 0.453378 | − | 1.39535i | −0.419651 | − | 0.907686i | \(-0.637847\pi\) |
0.873029 | − | 0.487669i | \(-0.162153\pi\) | |||||||
\(368\) | 14.2875 | 0.744786 | ||||||||
\(369\) | −2.63659 | + | 8.11460i | −0.137256 | + | 0.422429i | ||||
\(370\) | 5.92296 | + | 28.1656i | 0.307920 | + | 1.46426i | ||||
\(371\) | −9.52241 | − | 29.3070i | −0.494379 | − | 1.52154i | ||||
\(372\) | 3.68158 | + | 11.3307i | 0.190881 | + | 0.587471i | ||||
\(373\) | 7.85414 | + | 5.70637i | 0.406672 | + | 0.295464i | 0.772253 | − | 0.635315i | \(-0.219130\pi\) |
−0.365581 | + | 0.930779i | \(0.619130\pi\) | |||||||
\(374\) | 4.28984 | 0.221823 | ||||||||
\(375\) | 6.63037 | − | 9.00212i | 0.342391 | − | 0.464868i | ||||
\(376\) | 1.08690 | 0.0560527 | ||||||||
\(377\) | −10.0227 | − | 7.28191i | −0.516195 | − | 0.375037i | ||||
\(378\) | 2.11015 | + | 6.49436i | 0.108534 | + | 0.334034i | ||||
\(379\) | −6.88071 | − | 21.1767i | −0.353438 | − | 1.08777i | −0.956909 | − | 0.290387i | \(-0.906216\pi\) |
0.603471 | − | 0.797385i | \(-0.293784\pi\) | |||||||
\(380\) | −6.68596 | − | 31.7940i | −0.342983 | − | 1.63100i | ||||
\(381\) | −3.09587 | + | 9.52812i | −0.158606 | + | 0.488141i | ||||
\(382\) | 7.80253 | 0.399212 | ||||||||
\(383\) | −4.21189 | + | 12.9628i | −0.215217 | + | 0.662371i | 0.783921 | + | 0.620861i | \(0.213217\pi\) |
−0.999138 | + | 0.0415099i | \(0.986783\pi\) | |||||||
\(384\) | −8.82014 | + | 6.40820i | −0.450101 | + | 0.327017i | ||||
\(385\) | 4.44353 | − | 9.92234i | 0.226463 | − | 0.505689i | ||||
\(386\) | 29.8131 | + | 21.6605i | 1.51745 | + | 1.10249i | ||||
\(387\) | 6.86391 | − | 4.98692i | 0.348912 | − | 0.253500i | ||||
\(388\) | −22.0033 | + | 15.9863i | −1.11705 | + | 0.811582i | ||||
\(389\) | −15.5577 | − | 11.3034i | −0.788808 | − | 0.573103i | 0.118801 | − | 0.992918i | \(-0.462095\pi\) |
−0.907610 | + | 0.419815i | \(0.862095\pi\) | |||||||
\(390\) | 21.9571 | − | 12.6135i | 1.11184 | − | 0.638709i | ||||
\(391\) | 6.72710 | − | 4.88752i | 0.340204 | − | 0.247173i | ||||
\(392\) | 1.33316 | − | 4.10305i | 0.0673349 | − | 0.207236i | ||||
\(393\) | 6.37865 | 0.321760 | ||||||||
\(394\) | −2.94115 | + | 9.05194i | −0.148173 | + | 0.456030i | ||||
\(395\) | 3.13811 | − | 1.80272i | 0.157895 | − | 0.0907049i | ||||
\(396\) | 1.26831 | + | 3.90347i | 0.0637352 | + | 0.196157i | ||||
\(397\) | 6.86887 | + | 21.1402i | 0.344739 | + | 1.06100i | 0.961723 | + | 0.274022i | \(0.0883541\pi\) |
−0.616984 | + | 0.786975i | \(0.711646\pi\) | |||||||
\(398\) | −29.0079 | − | 21.0755i | −1.45403 | − | 1.05642i | ||||
\(399\) | 17.2120 | 0.861678 | ||||||||
\(400\) | −5.58590 | + | 9.57884i | −0.279295 | + | 0.478942i | ||||
\(401\) | 4.71728 | 0.235570 | 0.117785 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117785 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(402\) | −3.31870 | − | 2.41117i | −0.165522 | − | 0.120258i | ||||
\(403\) | 7.23261 | + | 22.2597i | 0.360282 | + | 1.10883i | ||||
\(404\) | 0.896678 | + | 2.75969i | 0.0446114 | + | 0.137300i | ||||
\(405\) | −2.22331 | − | 0.238557i | −0.110477 | − | 0.0118540i | ||||
\(406\) | 4.98757 | − | 15.3502i | 0.247529 | − | 0.761815i | ||||
\(407\) | −9.16474 | −0.454279 | ||||||||
\(408\) | −0.575648 | + | 1.77166i | −0.0284988 | + | 0.0877104i | ||||
\(409\) | 10.0971 | − | 7.33597i | 0.499269 | − | 0.362740i | −0.309469 | − | 0.950910i | \(-0.600151\pi\) |
0.808738 | + | 0.588169i | \(0.200151\pi\) | |||||||
\(410\) | 8.48271 | + | 40.3381i | 0.418931 | + | 1.99216i | ||||
\(411\) | −7.42461 | − | 5.39429i | −0.366229 | − | 0.266081i | ||||
\(412\) | 10.6576 | − | 7.74319i | 0.525062 | − | 0.381480i | ||||
\(413\) | 10.5160 | − | 7.64029i | 0.517456 | − | 0.375954i | ||||
\(414\) | 11.2609 | + | 8.18154i | 0.553444 | + | 0.402101i | ||||
\(415\) | −29.2339 | − | 3.13674i | −1.43504 | − | 0.153977i | ||||
\(416\) | −32.5583 | + | 23.6550i | −1.59630 | + | 1.15978i | ||||
\(417\) | 2.86316 | − | 8.81191i | 0.140210 | − | 0.431521i | ||||
\(418\) | 18.1005 | 0.885322 | ||||||||
\(419\) | 10.7996 | − | 33.2379i | 0.527597 | − | 1.62378i | −0.231527 | − | 0.972829i | \(-0.574372\pi\) |
0.759123 | − | 0.650947i | \(-0.225628\pi\) | |||||||
\(420\) | 13.9850 | + | 12.6472i | 0.682396 | + | 0.617118i | ||||
\(421\) | −12.2247 | − | 37.6239i | −0.595797 | − | 1.83368i | −0.550717 | − | 0.834692i | \(-0.685646\pi\) |
−0.0450804 | − | 0.998983i | \(-0.514354\pi\) | |||||||
\(422\) | 12.3818 | + | 38.1073i | 0.602737 | + | 1.85503i | ||||
\(423\) | −0.609247 | − | 0.442644i | −0.0296226 | − | 0.0215221i | ||||
\(424\) | 14.0720 | 0.683396 | ||||||||
\(425\) | 0.646712 | + | 6.42093i | 0.0313702 | + | 0.311461i | ||||
\(426\) | 0.153135 | 0.00741940 | ||||||||
\(427\) | −27.3439 | − | 19.8665i | −1.32326 | − | 0.961406i | ||||
\(428\) | 12.6191 | + | 38.8377i | 0.609969 | + | 1.87729i | ||||
\(429\) | 2.49166 | + | 7.66853i | 0.120298 | + | 0.370240i | ||||
\(430\) | 16.7528 | − | 37.4089i | 0.807894 | − | 1.80402i | ||||
\(431\) | −4.34429 | + | 13.3703i | −0.209257 | + | 0.644027i | 0.790255 | + | 0.612778i | \(0.209948\pi\) |
−0.999512 | + | 0.0312481i | \(0.990052\pi\) | |||||||
\(432\) | 2.21771 | 0.106700 | ||||||||
\(433\) | −0.169860 | + | 0.522775i | −0.00816294 | + | 0.0251230i | −0.955055 | − | 0.296429i | \(-0.904204\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(434\) | −24.6689 | + | 17.9230i | −1.18415 | + | 0.860333i | ||||
\(435\) | 3.91998 | + | 3.54500i | 0.187949 | + | 0.169970i | ||||
\(436\) | −14.3733 | − | 10.4428i | −0.688355 | − | 0.500119i | ||||
\(437\) | 28.3841 | − | 20.6223i | 1.35780 | − | 0.986497i | ||||
\(438\) | 7.01134 | − | 5.09404i | 0.335015 | − | 0.243402i | ||||
\(439\) | 2.40583 | + | 1.74794i | 0.114824 | + | 0.0834245i | 0.643715 | − | 0.765265i | \(-0.277392\pi\) |
−0.528891 | + | 0.848690i | \(0.677392\pi\) | |||||||
\(440\) | 3.68230 | + | 3.33005i | 0.175547 | + | 0.158754i | ||||
\(441\) | −2.41826 | + | 1.75697i | −0.115155 | + | 0.0836653i | ||||
\(442\) | −4.51667 | + | 13.9009i | −0.214836 | + | 0.661198i | ||||
\(443\) | −36.6893 | −1.74316 | −0.871580 | − | 0.490253i | \(-0.836905\pi\) | ||||
−0.871580 | + | 0.490253i | \(0.836905\pi\) | |||||||
\(444\) | 4.91175 | − | 15.1168i | 0.233101 | − | 0.717412i | ||||
\(445\) | −6.64966 | + | 14.8486i | −0.315224 | + | 0.703891i | ||||
\(446\) | −0.515130 | − | 1.58541i | −0.0243921 | − | 0.0750712i | ||||
\(447\) | 3.11543 | + | 9.58830i | 0.147355 | + | 0.453511i | ||||
\(448\) | −31.0760 | − | 22.5780i | −1.46820 | − | 1.06671i | ||||
\(449\) | −17.8432 | −0.842071 | −0.421036 | − | 0.907044i | \(-0.638333\pi\) | ||||
−0.421036 | + | 0.907044i | \(0.638333\pi\) | |||||||
\(450\) | −9.88782 | + | 4.35103i | −0.466116 | + | 0.205110i | ||||
\(451\) | −13.1255 | −0.618056 | ||||||||
\(452\) | 19.3646 | + | 14.0692i | 0.910834 | + | 0.661759i | ||||
\(453\) | −3.31807 | − | 10.2120i | −0.155896 | − | 0.479800i | ||||
\(454\) | 7.63215 | + | 23.4893i | 0.358195 | + | 1.10241i | ||||
\(455\) | 27.4740 | + | 24.8459i | 1.28800 | + | 1.16479i | ||||
\(456\) | −2.42887 | + | 7.47530i | −0.113742 | + | 0.350063i | ||||
\(457\) | −24.1784 | −1.13102 | −0.565509 | − | 0.824742i | \(-0.691320\pi\) | ||||
−0.565509 | + | 0.824742i | \(0.691320\pi\) | |||||||
\(458\) | 6.82655 | − | 21.0100i | 0.318984 | − | 0.981731i | ||||
\(459\) | 1.04418 | − | 0.758645i | 0.0487384 | − | 0.0354105i | ||||
\(460\) | 38.2154 | + | 4.10044i | 1.78180 | + | 0.191184i | ||||
\(461\) | 30.2470 | + | 21.9757i | 1.40874 | + | 1.02351i | 0.993504 | + | 0.113800i | \(0.0363024\pi\) |
0.415240 | + | 0.909712i | \(0.363698\pi\) | |||||||
\(462\) | −8.49852 | + | 6.17454i | −0.395387 | + | 0.287266i | ||||
\(463\) | −16.5294 | + | 12.0093i | −0.768186 | + | 0.558120i | −0.901410 | − | 0.432966i | \(-0.857467\pi\) |
0.133224 | + | 0.991086i | \(0.457467\pi\) | |||||||
\(464\) | −4.24072 | − | 3.08106i | −0.196870 | − | 0.143035i | ||||
\(465\) | −2.05480 | − | 9.77127i | −0.0952892 | − | 0.453132i | ||||
\(466\) | 39.3685 | − | 28.6029i | 1.82371 | − | 1.32500i | ||||
\(467\) | 9.64517 | − | 29.6848i | 0.446325 | − | 1.37365i | −0.434699 | − | 0.900576i | \(-0.643145\pi\) |
0.881024 | − | 0.473072i | \(-0.156855\pi\) | |||||||
\(468\) | −13.9843 | −0.646422 | ||||||||
\(469\) | 1.85434 | − | 5.70708i | 0.0856256 | − | 0.263529i | ||||
\(470\) | −3.61744 | − | 0.388144i | −0.166860 | − | 0.0179038i | ||||
\(471\) | −5.38979 | − | 16.5881i | −0.248348 | − | 0.764338i | ||||
\(472\) | 1.83427 | + | 5.64532i | 0.0844293 | + | 0.259847i | ||||
\(473\) | 10.5591 | + | 7.67164i | 0.485508 | + | 0.352742i | ||||
\(474\) | −3.49684 | −0.160615 | ||||||||
\(475\) | 2.72872 | + | 27.0923i | 0.125202 | + | 1.24308i | ||||
\(476\) | −10.8836 | −0.498849 | ||||||||
\(477\) | −7.88784 | − | 5.73085i | −0.361159 | − | 0.262398i | ||||
\(478\) | −0.393295 | − | 1.21044i | −0.0179889 | − | 0.0553641i | ||||
\(479\) | 3.42915 | + | 10.5538i | 0.156682 | + | 0.482217i | 0.998327 | − | 0.0578133i | \(-0.0184128\pi\) |
−0.841646 | + | 0.540030i | \(0.818413\pi\) | |||||||
\(480\) | 14.8871 | − | 8.55209i | 0.679502 | − | 0.390348i | ||||
\(481\) | 9.64933 | − | 29.6976i | 0.439972 | − | 1.35409i | ||||
\(482\) | 3.26108 | 0.148538 | ||||||||
\(483\) | −6.29211 | + | 19.3651i | −0.286301 | + | 0.881144i | ||||
\(484\) | 18.6351 | − | 13.5392i | 0.847051 | − | 0.615418i | ||||
\(485\) | 19.7651 | − | 11.3543i | 0.897487 | − | 0.515572i | ||||
\(486\) | 1.74793 | + | 1.26995i | 0.0792877 | + | 0.0576059i | ||||
\(487\) | −5.77397 | + | 4.19504i | −0.261644 | + | 0.190095i | −0.710871 | − | 0.703322i | \(-0.751699\pi\) |
0.449228 | + | 0.893417i | \(0.351699\pi\) | |||||||
\(488\) | 12.4868 | − | 9.07218i | 0.565250 | − | 0.410678i | ||||
\(489\) | −13.1525 | − | 9.55586i | −0.594777 | − | 0.432131i | ||||
\(490\) | −5.90229 | + | 13.1797i | −0.266638 | + | 0.595400i | ||||
\(491\) | −5.85201 | + | 4.25173i | −0.264097 | + | 0.191878i | −0.711951 | − | 0.702229i | \(-0.752188\pi\) |
0.447854 | + | 0.894107i | \(0.352188\pi\) | |||||||
\(492\) | 7.03448 | − | 21.6499i | 0.317139 | − | 0.976053i | ||||
\(493\) | −3.05067 | −0.137395 | ||||||||
\(494\) | −19.0575 | + | 58.6531i | −0.857439 | + | 2.63893i | ||||
\(495\) | −0.707886 | − | 3.36623i | −0.0318171 | − | 0.151301i | ||||
\(496\) | 3.06020 | + | 9.41834i | 0.137407 | + | 0.422896i | ||||
\(497\) | 0.0692236 | + | 0.213048i | 0.00310510 | + | 0.00955652i | ||||
\(498\) | 22.9832 | + | 16.6983i | 1.02990 | + | 0.748269i | ||||
\(499\) | 16.0169 | 0.717014 | 0.358507 | − | 0.933527i | \(-0.383286\pi\) | ||||
0.358507 | + | 0.933527i | \(0.383286\pi\) | |||||||
\(500\) | −17.6899 | + | 24.0178i | −0.791118 | + | 1.07411i | ||||
\(501\) | 11.3906 | 0.508894 | ||||||||
\(502\) | −20.7921 | − | 15.1063i | −0.927997 | − | 0.674229i | ||||
\(503\) | −10.4436 | − | 32.1422i | −0.465659 | − | 1.43315i | −0.858152 | − | 0.513396i | \(-0.828387\pi\) |
0.392492 | − | 0.919755i | \(-0.371613\pi\) | |||||||
\(504\) | −1.40962 | − | 4.33836i | −0.0627894 | − | 0.193246i | ||||
\(505\) | −0.500464 | − | 2.37987i | −0.0222703 | − | 0.105903i | ||||
\(506\) | −6.61690 | + | 20.3647i | −0.294157 | + | 0.905322i | ||||
\(507\) | −14.4727 | −0.642753 | ||||||||
\(508\) | 8.25985 | − | 25.4212i | 0.366472 | − | 1.12788i | ||||
\(509\) | 29.4701 | − | 21.4113i | 1.30624 | − | 0.949038i | 0.306243 | − | 0.951953i | \(-0.400928\pi\) |
0.999996 | + | 0.00291563i | \(0.000928074\pi\) | |||||||
\(510\) | 2.54856 | − | 5.69089i | 0.112852 | − | 0.251997i | ||||
\(511\) | 10.2565 | + | 7.45178i | 0.453720 | + | 0.329647i | ||||
\(512\) | −18.9548 | + | 13.7715i | −0.837692 | + | 0.608619i | ||||
\(513\) | 4.40581 | − | 3.20100i | 0.194521 | − | 0.141328i | ||||
\(514\) | 31.5487 | + | 22.9215i | 1.39156 | + | 1.01102i | ||||
\(515\) | −9.57350 | + | 5.49960i | −0.421859 | + | 0.242341i | ||||
\(516\) | −18.3130 | + | 13.3052i | −0.806187 | + | 0.585729i | ||||
\(517\) | 0.357992 | − | 1.10179i | 0.0157445 | − | 0.0484565i | ||||
\(518\) | 40.6813 | 1.78743 | ||||||||
\(519\) | −2.92282 | + | 8.99552i | −0.128298 | + | 0.394860i | ||||
\(520\) | −14.6678 | + | 8.42606i | −0.643223 | + | 0.369507i | ||||
\(521\) | 7.87972 | + | 24.2513i | 0.345217 | + | 1.06247i | 0.961468 | + | 0.274918i | \(0.0886507\pi\) |
−0.616251 | + | 0.787550i | \(0.711349\pi\) | |||||||
\(522\) | −1.57806 | − | 4.85678i | −0.0690700 | − | 0.212576i | ||||
\(523\) | 5.68880 | + | 4.13315i | 0.248754 | + | 0.180730i | 0.705174 | − | 0.709034i | \(-0.250869\pi\) |
−0.456420 | + | 0.889764i | \(0.650869\pi\) | |||||||
\(524\) | −17.0184 | −0.743450 | ||||||||
\(525\) | −10.5231 | − | 11.7895i | −0.459265 | − | 0.514538i | ||||
\(526\) | −41.2811 | −1.79994 | ||||||||
\(527\) | 4.66273 | + | 3.38767i | 0.203112 | + | 0.147569i | ||||
\(528\) | 1.05425 | + | 3.24465i | 0.0458803 | + | 0.141205i | ||||
\(529\) | 5.71836 | + | 17.5993i | 0.248624 | + | 0.765187i | ||||
\(530\) | −46.8345 | − | 5.02526i | −2.03436 | − | 0.218283i | ||||
\(531\) | 1.27089 | − | 3.91141i | 0.0551521 | − | 0.169741i | ||||
\(532\) | −45.9220 | −1.99097 | ||||||||
\(533\) | 13.8195 | − | 42.5322i | 0.598590 | − | 1.84227i | ||||
\(534\) | 12.7179 | − | 9.24008i | 0.550357 | − | 0.399858i | ||||
\(535\) | −7.04313 | − | 33.4924i | −0.304501 | − | 1.44800i | ||||
\(536\) | 2.21695 | + | 1.61071i | 0.0957577 | + | 0.0695721i | ||||
\(537\) | 3.29874 | − | 2.39667i | 0.142351 | − | 0.103424i | ||||
\(538\) | 38.8478 | − | 28.2246i | 1.67485 | − | 1.21685i | ||||
\(539\) | −3.72014 | − | 2.70284i | −0.160238 | − | 0.116420i | ||||
\(540\) | 5.93182 | + | 0.636474i | 0.255265 | + | 0.0273895i | ||||
\(541\) | 21.9629 | − | 15.9570i | 0.944258 | − | 0.686044i | −0.00518365 | − | 0.999987i | \(-0.501650\pi\) |
0.949442 | + | 0.313943i | \(0.101650\pi\) | |||||||
\(542\) | 13.4937 | − | 41.5293i | 0.579604 | − | 1.78384i | ||||
\(543\) | 11.1202 | 0.477214 | ||||||||
\(544\) | −3.06235 | + | 9.42496i | −0.131297 | + | 0.404092i | ||||
\(545\) | 11.0438 | + | 9.98732i | 0.473063 | + | 0.427810i | ||||
\(546\) | −11.0602 | − | 34.0398i | −0.473333 | − | 1.45677i | ||||
\(547\) | 13.6205 | + | 41.9196i | 0.582371 | + | 1.79235i | 0.609582 | + | 0.792723i | \(0.291337\pi\) |
−0.0272113 | + | 0.999630i | \(0.508663\pi\) | |||||||
\(548\) | 19.8090 | + | 14.3921i | 0.846198 | + | 0.614799i | ||||
\(549\) | −10.6939 | −0.456407 | ||||||||
\(550\) | −11.0663 | − | 12.3981i | −0.471867 | − | 0.528656i | ||||
\(551\) | −12.8719 | −0.548363 | ||||||||
\(552\) | −7.52251 | − | 5.46542i | −0.320179 | − | 0.232624i | ||||
\(553\) | −1.58073 | − | 4.86497i | −0.0672193 | − | 0.206880i | ||||
\(554\) | −10.7099 | − | 32.9618i | −0.455022 | − | 1.40041i | ||||
\(555\) | −5.44469 | + | 12.1579i | −0.231114 | + | 0.516075i | ||||
\(556\) | −7.63897 | + | 23.5103i | −0.323965 | + | 0.997061i | ||||
\(557\) | −9.85667 | −0.417641 | −0.208820 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208820 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(558\) | −2.98134 | + | 9.17562i | −0.126210 | + | 0.388435i | ||||
\(559\) | −35.9768 | + | 26.1386i | −1.52165 | + | 1.10555i | ||||
\(560\) | 11.6246 | + | 10.5126i | 0.491229 | + | 0.444238i | ||||
\(561\) | 1.60632 | + | 1.16706i | 0.0678190 | + | 0.0492734i | ||||
\(562\) | −14.6356 | + | 10.6334i | −0.617363 | + | 0.448541i | ||||
\(563\) | 10.0251 | − | 7.28367i | 0.422508 | − | 0.306970i | −0.356138 | − | 0.934433i | \(-0.615907\pi\) |
0.778646 | + | 0.627463i | \(0.215907\pi\) | |||||||
\(564\) | 1.62548 | + | 1.18098i | 0.0684451 | + | 0.0497283i | ||||
\(565\) | −14.8789 | − | 13.4556i | −0.625959 | − | 0.566080i | ||||
\(566\) | 1.97507 | − | 1.43497i | 0.0830185 | − | 0.0603165i | ||||
\(567\) | −0.976667 | + | 3.00587i | −0.0410161 | + | 0.126235i | ||||
\(568\) | −0.102297 | −0.00429228 | ||||||||
\(569\) | −3.62037 | + | 11.1424i | −0.151774 | + | 0.467112i | −0.997820 | − | 0.0659983i | \(-0.978977\pi\) |
0.846046 | + | 0.533110i | \(0.178977\pi\) | |||||||
\(570\) | 10.7533 | − | 24.0120i | 0.450407 | − | 1.00575i | ||||
\(571\) | 8.95523 | + | 27.5614i | 0.374765 | + | 1.15341i | 0.943637 | + | 0.330982i | \(0.107380\pi\) |
−0.568872 | + | 0.822426i | \(0.692620\pi\) | |||||||
\(572\) | −6.64779 | − | 20.4598i | −0.277958 | − | 0.855467i | ||||
\(573\) | 2.92164 | + | 2.12270i | 0.122053 | + | 0.0886769i | ||||
\(574\) | 58.2628 | 2.43184 | ||||||||
\(575\) | −31.4789 | − | 6.83394i | −1.31276 | − | 0.284995i | ||||
\(576\) | −12.1535 | −0.506398 | ||||||||
\(577\) | 26.5377 | + | 19.2808i | 1.10478 | + | 0.802668i | 0.981833 | − | 0.189745i | \(-0.0607662\pi\) |
0.122945 | + | 0.992414i | \(0.460766\pi\) | |||||||
\(578\) | −10.2378 | − | 31.5088i | −0.425838 | − | 1.31059i | ||||
\(579\) | 5.27067 | + | 16.2215i | 0.219042 | + | 0.674141i | ||||
\(580\) | −10.4586 | − | 9.45812i | −0.434269 | − | 0.392727i | ||||
\(581\) | −12.8420 | + | 39.5237i | −0.532777 | + | 1.63972i | ||||
\(582\) | −22.0246 | −0.912947 | ||||||||
\(583\) | 4.63488 | − | 14.2647i | 0.191957 | − | 0.590783i | ||||
\(584\) | −4.68371 | + | 3.40291i | −0.193813 | + | 0.140813i | ||||
\(585\) | 11.6533 | + | 1.25038i | 0.481805 | + | 0.0516968i | ||||
\(586\) | 4.15758 | + | 3.02066i | 0.171748 | + | 0.124782i | ||||
\(587\) | −15.0797 | + | 10.9560i | −0.622405 | + | 0.452203i | −0.853761 | − | 0.520666i | \(-0.825684\pi\) |
0.231356 | + | 0.972869i | \(0.425684\pi\) | |||||||
\(588\) | 6.45197 | − | 4.68763i | 0.266075 | − | 0.193315i | ||||
\(589\) | 19.6738 | + | 14.2938i | 0.810644 | + | 0.588967i | ||||
\(590\) | −4.08885 | − | 19.4438i | −0.168335 | − | 0.800490i | ||||
\(591\) | −3.56391 | + | 2.58933i | −0.146600 | + | 0.106511i | ||||
\(592\) | 4.08275 | − | 12.5654i | 0.167800 | − | 0.516435i | ||||
\(593\) | 1.55882 | 0.0640129 | 0.0320064 | − | 0.999488i | \(-0.489810\pi\) | ||||
0.0320064 | + | 0.999488i | \(0.489810\pi\) | |||||||
\(594\) | −1.02708 | + | 3.16103i | −0.0421416 | + | 0.129698i | ||||
\(595\) | 9.06949 | + | 0.973140i | 0.371813 | + | 0.0398948i | ||||
\(596\) | −8.31202 | − | 25.5818i | −0.340474 | − | 1.04787i | ||||
\(597\) | −5.12831 | − | 15.7833i | −0.209888 | − | 0.645969i | ||||
\(598\) | −59.0234 | − | 42.8830i | −2.41365 | − | 1.75362i | ||||
\(599\) | −31.5470 | −1.28898 | −0.644489 | − | 0.764614i | \(-0.722930\pi\) | ||||
−0.644489 | + | 0.764614i | \(0.722930\pi\) | |||||||
\(600\) | 6.60525 | − | 2.90657i | 0.269658 | − | 0.118660i | ||||
\(601\) | −32.3999 | −1.32162 | −0.660809 | − | 0.750554i | \(-0.729787\pi\) | ||||
−0.660809 | + | 0.750554i | \(0.729787\pi\) | |||||||
\(602\) | −46.8707 | − | 34.0536i | −1.91031 | − | 1.38792i | ||||
\(603\) | −0.586713 | − | 1.80572i | −0.0238928 | − | 0.0735345i | ||||
\(604\) | 8.85266 | + | 27.2457i | 0.360210 | + | 1.10861i | ||||
\(605\) | −16.7396 | + | 9.61623i | −0.680560 | + | 0.390955i | ||||
\(606\) | −0.726129 | + | 2.23480i | −0.0294970 | + | 0.0907824i | ||||
\(607\) | 24.8410 | 1.00827 | 0.504133 | − | 0.863626i | \(-0.331812\pi\) | ||||
0.504133 | + | 0.863626i | \(0.331812\pi\) | |||||||
\(608\) | −12.9212 | + | 39.7674i | −0.524024 | + | 1.61278i | ||||
\(609\) | 6.04363 | − | 4.39095i | 0.244900 | − | 0.177930i | ||||
\(610\) | −44.7984 | + | 25.7350i | −1.81383 | + | 1.04198i | ||||
\(611\) | 3.19333 | + | 2.32009i | 0.129188 | + | 0.0938607i | ||||
\(612\) | −2.78590 | + | 2.02408i | −0.112614 | + | 0.0818185i | ||||
\(613\) | 3.19204 | − | 2.31915i | 0.128925 | − | 0.0936697i | −0.521454 | − | 0.853280i | \(-0.674610\pi\) |
0.650379 | + | 0.759610i | \(0.274610\pi\) | |||||||
\(614\) | −5.05791 | − | 3.67478i | −0.204120 | − | 0.148302i | ||||
\(615\) | −7.79774 | + | 17.4123i | −0.314435 | + | 0.702130i | ||||
\(616\) | 5.67717 | − | 4.12471i | 0.228740 | − | 0.166189i | ||||
\(617\) | −5.40225 | + | 16.6264i | −0.217486 | + | 0.669354i | 0.781481 | + | 0.623929i | \(0.214464\pi\) |
−0.998968 | + | 0.0454257i | \(0.985536\pi\) | |||||||
\(618\) | 10.6679 | 0.429126 | ||||||||
\(619\) | −4.44581 | + | 13.6828i | −0.178692 | + | 0.549958i | −0.999783 | − | 0.0208398i | \(-0.993366\pi\) |
0.821091 | + | 0.570798i | \(0.193366\pi\) | |||||||
\(620\) | 5.48225 | + | 26.0699i | 0.220173 | + | 1.04699i | ||||
\(621\) | 1.99082 | + | 6.12712i | 0.0798890 | + | 0.245873i | ||||
\(622\) | −4.77066 | − | 14.6826i | −0.191286 | − | 0.588718i | ||||
\(623\) | 18.6043 | + | 13.5168i | 0.745364 | + | 0.541539i | ||||
\(624\) | −11.6240 | −0.465333 | ||||||||
\(625\) | 16.8889 | − | 18.4328i | 0.675554 | − | 0.737310i | ||||
\(626\) | 49.7617 | 1.98888 | ||||||||
\(627\) | 6.77768 | + | 4.92427i | 0.270674 | + | 0.196656i | ||||
\(628\) | 14.3801 | + | 44.2573i | 0.573827 | + | 1.76606i | ||||
\(629\) | −2.37611 | − | 7.31292i | −0.0947418 | − | 0.291585i | ||||
\(630\) | 3.14223 | + | 14.9423i | 0.125189 | + | 0.595317i | ||||
\(631\) | −5.46214 | + | 16.8107i | −0.217444 | + | 0.669225i | 0.781527 | + | 0.623872i | \(0.214441\pi\) |
−0.998971 | + | 0.0453529i | \(0.985559\pi\) | |||||||
\(632\) | 2.33596 | 0.0929194 | ||||||||
\(633\) | −5.73083 | + | 17.6377i | −0.227780 | + | 0.701035i | ||||
\(634\) | 36.3132 | − | 26.3831i | 1.44218 | − | 1.04781i | ||||
\(635\) | −9.15608 | + | 20.4454i | −0.363348 | + | 0.811351i | ||||
\(636\) | 21.0449 | + | 15.2900i | 0.834485 | + | 0.606289i | ||||
\(637\) | 12.6752 | − | 9.20905i | 0.502209 | − | 0.364876i | ||||
\(638\) | 6.35559 | − | 4.61760i | 0.251620 | − | 0.182813i | ||||
\(639\) | 0.0573410 | + | 0.0416607i | 0.00226837 | + | 0.00164807i | ||||
\(640\) | −21.1386 | + | 12.1433i | −0.835576 | + | 0.480006i | ||||
\(641\) | 2.21774 | − | 1.61128i | 0.0875954 | − | 0.0636417i | −0.543126 | − | 0.839651i | \(-0.682759\pi\) |
0.630721 | + | 0.776010i | \(0.282759\pi\) | |||||||
\(642\) | −10.2190 | + | 31.4507i | −0.403310 | + | 1.24126i | ||||
\(643\) | 20.9276 | 0.825303 | 0.412651 | − | 0.910889i | \(-0.364603\pi\) | ||||
0.412651 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(644\) | 16.7875 | − | 51.6665i | 0.661519 | − | 2.03595i | ||||
\(645\) | 16.4502 | − | 9.45003i | 0.647727 | − | 0.372094i | ||||
\(646\) | 4.69284 | + | 14.4431i | 0.184637 | + | 0.568256i | ||||
\(647\) | −0.570653 | − | 1.75629i | −0.0224347 | − | 0.0690469i | 0.939212 | − | 0.343337i | \(-0.111557\pi\) |
−0.961647 | + | 0.274290i | \(0.911557\pi\) | |||||||
\(648\) | −1.16765 | − | 0.848347i | −0.0458696 | − | 0.0333262i | ||||
\(649\) | 6.32678 | 0.248348 | ||||||||
\(650\) | 51.8264 | − | 22.8057i | 2.03280 | − | 0.894512i | ||||
\(651\) | −14.1132 | −0.553141 | ||||||||
\(652\) | 35.0912 | + | 25.4952i | 1.37428 | + | 0.998470i | ||||
\(653\) | −5.69002 | − | 17.5121i | −0.222667 | − | 0.685300i | −0.998520 | − | 0.0543858i | \(-0.982680\pi\) |
0.775853 | − | 0.630914i | \(-0.217320\pi\) | |||||||
\(654\) | −4.44588 | − | 13.6830i | −0.173848 | − | 0.535048i | ||||
\(655\) | 14.1817 | + | 1.52167i | 0.554124 | + | 0.0594565i | ||||
\(656\) | 5.84721 | − | 17.9959i | 0.228295 | − | 0.702620i | ||||
\(657\) | 4.01123 | 0.156493 | ||||||||
\(658\) | −1.58909 | + | 4.89071i | −0.0619491 | + | 0.190660i | ||||
\(659\) | 10.8246 | − | 7.86455i | 0.421668 | − | 0.306360i | −0.356641 | − | 0.934242i | \(-0.616078\pi\) |
0.778308 | + | 0.627882i | \(0.216078\pi\) | |||||||
\(660\) | 1.88865 | + | 8.98117i | 0.0735157 | + | 0.349592i | ||||
\(661\) | −31.7001 | − | 23.0315i | −1.23299 | − | 0.895820i | −0.235879 | − | 0.971782i | \(-0.575797\pi\) |
−0.997111 | + | 0.0759628i | \(0.975797\pi\) | |||||||
\(662\) | 33.6483 | − | 24.4469i | 1.30778 | − | 0.950155i | ||||
\(663\) | −5.47303 | + | 3.97639i | −0.212555 | + | 0.154430i | ||||
\(664\) | −15.3532 | − | 11.1548i | −0.595821 | − | 0.432890i | ||||
\(665\) | 38.2676 | + | 4.10604i | 1.48395 | + | 0.159225i | ||||
\(666\) | 10.4133 | − | 7.56571i | 0.403507 | − | 0.293165i | ||||
\(667\) | 4.70553 | − | 14.4821i | 0.182199 | − | 0.560751i | ||||
\(668\) | −30.3903 | −1.17584 | ||||||||
\(669\) | 0.238424 | − | 0.733794i | 0.00921801 | − | 0.0283701i | ||||
\(670\) | −6.80328 | − | 6.15248i | −0.262834 | − | 0.237691i | ||||
\(671\) | −5.08365 | − | 15.6459i | −0.196252 | − | 0.604002i | ||||
\(672\) | −7.49894 | − | 23.0794i | −0.289278 | − | 0.890305i | ||||
\(673\) | −15.6877 | − | 11.3978i | −0.604718 | − | 0.439353i | 0.242832 | − | 0.970068i | \(-0.421923\pi\) |
−0.847550 | + | 0.530715i | \(0.821923\pi\) | |||||||
\(674\) | 46.8981 | 1.80645 | ||||||||
\(675\) | −4.88618 | − | 1.06077i | −0.188069 | − | 0.0408290i | ||||
\(676\) | 38.6133 | 1.48513 | ||||||||
\(677\) | 36.9588 | + | 26.8522i | 1.42044 | + | 1.03201i | 0.991698 | + | 0.128587i | \(0.0410443\pi\) |
0.428746 | + | 0.903425i | \(0.358956\pi\) | |||||||
\(678\) | 5.98977 | + | 18.4346i | 0.230036 | + | 0.707978i | ||||
\(679\) | −9.95606 | − | 30.6416i | −0.382078 | − | 1.17592i | ||||
\(680\) | −1.70248 | + | 3.80162i | −0.0652873 | + | 0.145786i | ||||
\(681\) | −3.53249 | + | 10.8719i | −0.135365 | + | 0.416611i | ||||
\(682\) | −14.8417 | −0.568319 | ||||||||
\(683\) | 3.58128 | − | 11.0220i | 0.137034 | − | 0.421747i | −0.858867 | − | 0.512199i | \(-0.828831\pi\) |
0.995901 | + | 0.0904520i | \(0.0288312\pi\) | |||||||
\(684\) | −11.7548 | + | 8.54034i | −0.449455 | + | 0.326548i | ||||
\(685\) | −15.2203 | − | 13.7644i | −0.581539 | − | 0.525909i | ||||
\(686\) | −22.1577 | − | 16.0985i | −0.845987 | − | 0.614645i | ||||
\(687\) | 8.27200 | − | 6.00996i | 0.315596 | − | 0.229294i | ||||
\(688\) | −15.2222 | + | 11.0596i | −0.580340 | + | 0.421642i | ||||
\(689\) | 41.3436 | + | 30.0379i | 1.57507 | + | 1.14435i | ||||
\(690\) | 23.0847 | + | 20.8764i | 0.878821 | + | 0.794753i | ||||
\(691\) | 17.5091 | − | 12.7211i | 0.666077 | − | 0.483934i | −0.202632 | − | 0.979255i | \(-0.564950\pi\) |
0.868710 | + | 0.495321i | \(0.164950\pi\) | |||||||
\(692\) | 7.79815 | − | 24.0002i | 0.296441 | − | 0.912352i | ||||
\(693\) | −4.86205 | −0.184694 | ||||||||
\(694\) | −1.14498 | + | 3.52388i | −0.0434627 | + | 0.133764i | ||||
\(695\) | 8.46783 | − | 18.9086i | 0.321203 | − | 0.717242i | ||||
\(696\) | 1.05418 | + | 3.24442i | 0.0399585 | + | 0.122980i | ||||
\(697\) | −3.40301 | − | 10.4734i | −0.128898 | − | 0.396707i | ||||
\(698\) | 27.1895 | + | 19.7543i | 1.02914 | + | 0.747713i | ||||
\(699\) | 22.5229 | 0.851896 | ||||||||
\(700\) | 28.0758 | + | 31.4547i | 1.06116 | + | 1.18888i | ||||
\(701\) | −8.61904 | −0.325537 | −0.162768 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162768 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(702\) | −9.16166 | − | 6.65634i | −0.345785 | − | 0.251227i | ||||
\(703\) | −10.0257 | − | 30.8559i | −0.378126 | − | 1.16375i | ||||
\(704\) | −5.77751 | − | 17.7814i | −0.217748 | − | 0.670160i | ||||
\(705\) | −1.24895 | − | 1.12947i | −0.0470380 | − | 0.0425384i | ||||
\(706\) | 10.3843 | − | 31.9597i | 0.390820 | − | 1.20282i | ||||
\(707\) | −3.43739 | −0.129276 | ||||||||
\(708\) | −3.39077 | + | 10.4357i | −0.127433 | + | 0.392198i | ||||
\(709\) | −12.9443 | + | 9.40460i | −0.486134 | + | 0.353197i | −0.803696 | − | 0.595041i | \(-0.797136\pi\) |
0.317562 | + | 0.948238i | \(0.397136\pi\) | |||||||
\(710\) | 0.340466 | + | 0.0365313i | 0.0127774 | + | 0.00137100i | ||||
\(711\) | −1.30939 | − | 0.951325i | −0.0491058 | − | 0.0356775i | ||||
\(712\) | −8.49579 | + | 6.17255i | −0.318393 | + | 0.231326i | ||||
\(713\) | −23.2740 | + | 16.9095i | −0.871617 | + | 0.633267i | ||||
\(714\) | −7.13030 | − | 5.18047i | −0.266845 | − | 0.193874i | ||||
\(715\) | 3.71034 | + | 17.6439i | 0.138759 | + | 0.659844i | ||||
\(716\) | −8.80110 | + | 6.39437i | −0.328913 | + | 0.238969i | ||||
\(717\) | 0.182034 | − | 0.560243i | 0.00679818 | − | 0.0209226i | ||||
\(718\) | −53.0138 | −1.97846 | ||||||||
\(719\) | −15.0132 | + | 46.2060i | −0.559899 | + | 1.72319i | 0.122743 | + | 0.992438i | \(0.460831\pi\) |
−0.682642 | + | 0.730753i | \(0.739169\pi\) | |||||||
\(720\) | 4.93066 | + | 0.529050i | 0.183755 | + | 0.0197165i | ||||
\(721\) | 4.82235 | + | 14.8417i | 0.179594 | + | 0.552733i | ||||
\(722\) | 7.11551 | + | 21.8993i | 0.264812 | + | 0.815007i | ||||
\(723\) | 1.22110 | + | 0.887185i | 0.0454134 | + | 0.0329948i | ||||
\(724\) | −29.6689 | −1.10264 | ||||||||
\(725\) | 7.86964 | + | 8.81676i | 0.292271 | + | 0.327446i | ||||
\(726\) | 18.6531 | 0.692283 | ||||||||
\(727\) | −20.5756 | − | 14.9490i | −0.763106 | − | 0.554429i | 0.136755 | − | 0.990605i | \(-0.456333\pi\) |
−0.899861 | + | 0.436176i | \(0.856333\pi\) | |||||||
\(728\) | 7.38842 | + | 22.7392i | 0.273833 | + | 0.842772i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 16.8036 | − | 9.65300i | 0.621928 | − | 0.357274i | ||||
\(731\) | −3.38389 | + | 10.4145i | −0.125158 | + | 0.385196i | ||||
\(732\) | 28.5317 | 1.05456 | ||||||||
\(733\) | −5.75358 | + | 17.7077i | −0.212513 | + | 0.654049i | 0.786807 | + | 0.617199i | \(0.211733\pi\) |
−0.999321 | + | 0.0368505i | \(0.988267\pi\) | |||||||
\(734\) | −49.1287 | + | 35.6941i | −1.81337 | + | 1.31749i | ||||
\(735\) | −5.79568 | + | 3.32939i | −0.213777 | + | 0.122807i | ||||
\(736\) | −40.0185 | − | 29.0752i | −1.47510 | − | 1.07172i | ||||
\(737\) | 2.36296 | − | 1.71679i | 0.0870408 | − | 0.0632389i | ||||
\(738\) | 14.9137 | − | 10.8354i | 0.548980 | − | 0.398857i | ||||
\(739\) | −37.9326 | − | 27.5596i | −1.39537 | − | 1.01380i | −0.995252 | − | 0.0973351i | \(-0.968968\pi\) |
−0.400121 | − | 0.916462i | \(-0.631032\pi\) | |||||||
\(740\) | 14.5265 | − | 32.4375i | 0.534006 | − | 1.19243i | ||||
\(741\) | −23.0927 | + | 16.7779i | −0.848333 | + | 0.616350i | ||||
\(742\) | −20.5737 | + | 63.3194i | −0.755286 | + | 2.32453i | ||||
\(743\) | −42.7061 | −1.56674 | −0.783368 | − | 0.621558i | \(-0.786500\pi\) | ||||
−0.783368 | + | 0.621558i | \(0.786500\pi\) | |||||||
\(744\) | 1.99159 | − | 6.12948i | 0.0730152 | − | 0.224718i | ||||
\(745\) | 4.63920 | + | 22.0609i | 0.169967 | + | 0.808250i | ||||
\(746\) | −6.48171 | − | 19.9487i | −0.237312 | − | 0.730372i | ||||
\(747\) | 4.06322 | + | 12.5053i | 0.148665 | + | 0.457545i | ||||
\(748\) | −4.28570 | − | 3.11374i | −0.156701 | − | 0.113850i | ||||
\(749\) | −48.3751 | −1.76759 | ||||||||
\(750\) | −23.0216 | + | 7.31487i | −0.840631 | + | 0.267101i | ||||
\(751\) | −2.64893 | −0.0966608 | −0.0483304 | − | 0.998831i | \(-0.515390\pi\) | ||||
−0.0483304 | + | 0.998831i | \(0.515390\pi\) | |||||||
\(752\) | 1.35113 | + | 0.981657i | 0.0492708 | + | 0.0357973i | ||||
\(753\) | −3.67584 | − | 11.3131i | −0.133955 | − | 0.412272i | ||||
\(754\) | 8.27133 | + | 25.4565i | 0.301224 | + | 0.927072i | ||||
\(755\) | −4.94095 | − | 23.4959i | −0.179819 | − | 0.855102i | ||||
\(756\) | 2.60577 | − | 8.01972i | 0.0947708 | − | 0.291674i | ||||
\(757\) | 52.9153 | 1.92324 | 0.961620 | − | 0.274383i | \(-0.0884737\pi\) | ||||
0.961620 | + | 0.274383i | \(0.0884737\pi\) | |||||||
\(758\) | −14.8662 | + | 45.7534i | −0.539964 | + | 1.66184i | ||||
\(759\) | −8.01795 | + | 5.82538i | −0.291033 | + | 0.211448i | ||||
\(760\) | −7.18341 | + | 16.0405i | −0.260570 | + | 0.581849i | ||||
\(761\) | −41.0808 | − | 29.8470i | −1.48918 | − | 1.08195i | −0.974451 | − | 0.224598i | \(-0.927893\pi\) |
−0.514728 | − | 0.857354i | \(-0.672107\pi\) | |||||||
\(762\) | 17.5116 | − | 12.7229i | 0.634377 | − | 0.460902i | ||||
\(763\) | 17.0267 | − | 12.3706i | 0.616408 | − | 0.447847i | ||||
\(764\) | −7.79499 | − | 5.66339i | −0.282013 | − | 0.204894i | ||||
\(765\) | 2.50252 | − | 1.43760i | 0.0904789 | − | 0.0519766i | ||||
\(766\) | 23.8242 | − | 17.3093i | 0.860803 | − | 0.625410i | ||||
\(767\) | −6.66131 | + | 20.5014i | −0.240526 | + | 0.740263i | ||||
\(768\) | −0.752056 | −0.0271375 | ||||||||
\(769\) | 7.59580 | − | 23.3775i | 0.273912 | − | 0.843013i | −0.715594 | − | 0.698517i | \(-0.753844\pi\) |
0.989505 | − | 0.144496i | \(-0.0461562\pi\) | |||||||
\(770\) | −20.3678 | + | 11.7005i | −0.734004 | + | 0.421657i | ||||
\(771\) | 5.57751 | + | 17.1658i | 0.200869 | + | 0.618212i | ||||
\(772\) | −14.0622 | − | 43.2791i | −0.506111 | − | 1.55765i | ||||
\(773\) | 16.1894 | + | 11.7623i | 0.582293 | + | 0.423061i | 0.839550 | − | 0.543282i | \(-0.182819\pi\) |
−0.257257 | + | 0.966343i | \(0.582819\pi\) | |||||||
\(774\) | −18.3308 | −0.658885 | ||||||||
\(775\) | −2.23745 | − | 22.2147i | −0.0803717 | − | 0.797976i | ||||
\(776\) | 14.7128 | 0.528159 | ||||||||
\(777\) | 15.2330 | + | 11.0674i | 0.546482 | + | 0.397042i | ||||
\(778\) | 12.8392 | + | 39.5149i | 0.460307 | + | 1.41668i | ||||
\(779\) | −14.3586 | − | 44.1911i | −0.514449 | − | 1.58331i | ||||
\(780\) | −31.0913 | − | 3.33604i | −1.11325 | − | 0.119449i | ||||
\(781\) | −0.0336934 | + | 0.103698i | −0.00120565 | + | 0.00371060i | ||||
\(782\) | −17.9654 | −0.642441 | ||||||||
\(783\) | 0.730396 | − | 2.24793i | 0.0261022 | − | 0.0803344i | ||||
\(784\) | 5.36302 | − | 3.89646i | 0.191536 | − | 0.139159i | ||||
\(785\) | −8.02596 | − | 38.1661i | −0.286459 | − | 1.36221i | ||||
\(786\) | −11.1494 | − | 8.10053i | −0.397687 | − | 0.288936i | ||||
\(787\) | −7.27526 | + | 5.28579i | −0.259335 | + | 0.188418i | −0.709854 | − | 0.704349i | \(-0.751239\pi\) |
0.450519 | + | 0.892767i | \(0.351239\pi\) | |||||||
\(788\) | 9.50857 | − | 6.90838i | 0.338729 | − | 0.246101i | ||||
\(789\) | −15.4576 | − | 11.2306i | −0.550305 | − | 0.399820i | ||||
\(790\) | −7.77456 | − | 0.834195i | −0.276606 | − | 0.0296793i | ||||
\(791\) | −22.9395 | + | 16.6665i | −0.815634 | + | 0.592593i | ||||
\(792\) | 0.686108 | − | 2.11162i | 0.0243798 | − | 0.0750333i | ||||
\(793\) | 56.0517 | 1.99045 | ||||||||
\(794\) | 14.8406 | − | 45.6747i | 0.526674 | − | 1.62093i | ||||
\(795\) | −16.1700 | − | 14.6231i | −0.573489 | − | 0.518629i | ||||
\(796\) | 13.6824 | + | 42.1102i | 0.484961 | + | 1.49256i | ||||
\(797\) | −11.6674 | − | 35.9084i | −0.413279 | − | 1.27194i | −0.913781 | − | 0.406207i | \(-0.866851\pi\) |
0.500502 | − | 0.865735i | \(-0.333149\pi\) | |||||||
\(798\) | −30.0854 | − | 21.8583i | −1.06501 | − | 0.773776i | ||||
\(799\) | 0.971976 | 0.0343860 | ||||||||
\(800\) | 35.1388 | − | 15.4625i | 1.24235 | − | 0.546682i | ||||
\(801\) | 7.27597 | 0.257084 | ||||||||
\(802\) | −8.24547 | − | 5.99069i | −0.291158 | − | 0.211538i | ||||
\(803\) | 1.90684 | + | 5.86866i | 0.0672910 | + | 0.207100i | ||||
\(804\) | 1.56536 | + | 4.81769i | 0.0552061 | + | 0.169907i | ||||
\(805\) | −18.6090 | + | 41.5536i | −0.655880 | + | 1.46457i | ||||
\(806\) | 15.6265 | − | 48.0934i | 0.550420 | − | 1.69402i | ||||
\(807\) | 22.2250 | 0.782358 | ||||||||
\(808\) | 0.485068 | − | 1.49289i | 0.0170646 | − | 0.0525195i | ||||
\(809\) | 39.5610 | − | 28.7428i | 1.39089 | − | 1.01054i | 0.395124 | − | 0.918628i | \(-0.370702\pi\) |
0.995767 | − | 0.0919140i | \(-0.0292985\pi\) | |||||||
\(810\) | 3.58323 | + | 3.24046i | 0.125902 | + | 0.113858i | ||||
\(811\) | 14.6069 | + | 10.6125i | 0.512916 | + | 0.372655i | 0.813929 | − | 0.580965i | \(-0.197325\pi\) |
−0.301013 | + | 0.953620i | \(0.597325\pi\) | |||||||
\(812\) | −16.1245 | + | 11.7151i | −0.565860 | + | 0.411121i | ||||
\(813\) | 16.3508 | − | 11.8796i | 0.573449 | − | 0.416635i | ||||
\(814\) | 16.0193 | + | 11.6387i | 0.561477 | + | 0.407937i | ||||
\(815\) | −26.9625 | − | 24.3832i | −0.944454 | − | 0.854107i | ||||
\(816\) | −2.31570 | + | 1.68246i | −0.0810658 | + | 0.0588978i | ||||
\(817\) | −14.2779 | + | 43.9428i | −0.499520 | + | 1.53736i | ||||
\(818\) | −26.9653 | −0.942819 | ||||||||
\(819\) | 5.11914 | − | 15.7551i | 0.178877 | − | 0.550527i | ||||
\(820\) | 20.8045 | − | 46.4562i | 0.726526 | − | 1.62232i | ||||
\(821\) | 15.6393 | + | 48.1327i | 0.545814 | + | 1.67984i | 0.719046 | + | 0.694962i | \(0.244579\pi\) |
−0.173232 | + | 0.984881i | \(0.555421\pi\) | |||||||
\(822\) | 6.12723 | + | 18.8577i | 0.213712 | + | 0.657737i | ||||
\(823\) | 21.6873 | + | 15.7568i | 0.755972 | + | 0.549246i | 0.897672 | − | 0.440664i | \(-0.145257\pi\) |
−0.141700 | + | 0.989910i | \(0.545257\pi\) | |||||||
\(824\) | −7.12635 | −0.248258 | ||||||||
\(825\) | −0.770809 | − | 7.65304i | −0.0268361 | − | 0.266445i | ||||
\(826\) | −28.0839 | −0.977163 | ||||||||
\(827\) | 17.2845 | + | 12.5580i | 0.601042 | + | 0.436683i | 0.846249 | − | 0.532788i | \(-0.178856\pi\) |
−0.245206 | + | 0.969471i | \(0.578856\pi\) | |||||||
\(828\) | −5.31155 | − | 16.3473i | −0.184589 | − | 0.568107i | ||||
\(829\) | −14.8675 | − | 45.7575i | −0.516370 | − | 1.58922i | −0.780775 | − | 0.624812i | \(-0.785176\pi\) |
0.264405 | − | 0.964412i | \(-0.414824\pi\) | |||||||
\(830\) | 47.1153 | + | 42.6083i | 1.63540 | + | 1.47895i | ||||
\(831\) | 4.95702 | − | 15.2561i | 0.171957 | − | 0.529230i | ||||
\(832\) | 63.7021 | 2.20847 | ||||||||
\(833\) | 1.19220 | − | 3.66921i | 0.0413072 | − | 0.127130i | ||||
\(834\) | −16.1953 | + | 11.7665i | −0.560796 | + | 0.407442i | ||||
\(835\) | 25.3248 | + | 2.71730i | 0.876400 | + | 0.0940361i | ||||
\(836\) | −18.0830 | − | 13.1380i | −0.625412 | − | 0.454389i | ||||
\(837\) | −3.61260 | + | 2.62471i | −0.124870 | + | 0.0907232i | ||||
\(838\) | −61.0873 | + | 44.3825i | −2.11022 | + | 1.53317i | ||||
\(839\) | 33.8606 | + | 24.6012i | 1.16900 | + | 0.849327i | 0.990889 | − | 0.134684i | \(-0.0430018\pi\) |
0.178110 | + | 0.984011i | \(0.443002\pi\) | |||||||
\(840\) | −2.09907 | − | 9.98177i | −0.0724247 | − | 0.344404i | ||||
\(841\) | 18.9418 | − | 13.7620i | 0.653165 | − | 0.474552i | ||||
\(842\) | −26.4123 | + | 81.2886i | −0.910227 | + | 2.80139i | ||||
\(843\) | −8.37308 | −0.288384 | ||||||||
\(844\) | 15.2900 | − | 47.0577i | 0.526302 | − | 1.61979i | ||||
\(845\) | −32.1772 | − | 3.45255i | −1.10693 | − | 0.118771i | ||||
\(846\) | 0.502787 | + | 1.54742i | 0.0172862 | + | 0.0532014i | ||||
\(847\) | 8.43203 | + | 25.9511i | 0.289728 | + | 0.891691i | ||||
\(848\) | 17.4930 | + | 12.7094i | 0.600711 | + | 0.436442i | ||||
\(849\) | 1.12995 | 0.0387798 | ||||||||
\(850\) | 7.02382 | − | 12.0446i | 0.240915 | − | 0.413127i | ||||
\(851\) | 38.3809 | 1.31568 | ||||||||
\(852\) | −0.152987 | − | 0.111151i | −0.00524124 | − | 0.00380799i | ||||
\(853\) | −17.9855 | − | 55.3537i | −0.615812 | − | 1.89527i | −0.388485 | − | 0.921455i | \(-0.627002\pi\) |
−0.227327 | − | 0.973819i | \(-0.572998\pi\) | |||||||
\(854\) | 22.5658 | + | 69.4504i | 0.772186 | + | 2.37654i | ||||
\(855\) | 10.5591 | − | 6.06578i | 0.361113 | − | 0.207445i | ||||
\(856\) | 6.82646 | − | 21.0097i | 0.233324 | − | 0.718096i | ||||
\(857\) | −3.22045 | −0.110008 | −0.0550042 | − | 0.998486i | \(-0.517517\pi\) | ||||
−0.0550042 | + | 0.998486i | \(0.517517\pi\) | |||||||
\(858\) | 5.38337 | − | 16.5683i | 0.183785 | − | 0.565633i | ||||
\(859\) | −40.0003 | + | 29.0619i | −1.36479 | + | 0.991580i | −0.366669 | + | 0.930351i | \(0.619502\pi\) |
−0.998124 | + | 0.0612288i | \(0.980498\pi\) | |||||||
\(860\) | −43.8895 | + | 25.2128i | −1.49662 | + | 0.859751i | ||||
\(861\) | 21.8164 | + | 15.8505i | 0.743500 | + | 0.540184i | ||||
\(862\) | 24.5731 | − | 17.8534i | 0.836963 | − | 0.608089i | ||||
\(863\) | −17.3878 | + | 12.6329i | −0.591886 | + | 0.430030i | −0.842990 | − | 0.537930i | \(-0.819207\pi\) |
0.251104 | + | 0.967960i | \(0.419207\pi\) | |||||||
\(864\) | −6.21171 | − | 4.51307i | −0.211327 | − | 0.153538i | ||||
\(865\) | −8.64427 | + | 19.3025i | −0.293914 | + | 0.656306i | ||||
\(866\) | 0.960798 | − | 0.698061i | 0.0326493 | − | 0.0237211i | ||||
\(867\) | 4.73851 | − | 14.5836i | 0.160928 | − | 0.495286i | ||||
\(868\) | 37.6544 | 1.27807 | ||||||||
\(869\) | 0.769392 | − | 2.36795i | 0.0260999 | − | 0.0803271i | ||||
\(870\) | −2.34990 | − | 11.1746i | −0.0796692 | − | 0.378854i | ||||
\(871\) | 3.07522 | + | 9.46456i | 0.104200 | + | 0.320694i | ||||
\(872\) | 2.96993 | + | 9.14051i | 0.100575 | + | 0.309537i | ||||
\(873\) | −8.24705 | − | 5.99183i | −0.279120 | − | 0.202793i | ||||
\(874\) | −75.8026 | −2.56406 | ||||||||
\(875\) | −20.5836 | − | 28.7221i | −0.695851 | − | 0.970984i | ||||
\(876\) | −10.7020 | −0.361588 | ||||||||
\(877\) | −12.4421 | − | 9.03971i | −0.420140 | − | 0.305249i | 0.357554 | − | 0.933892i | \(-0.383611\pi\) |
−0.777694 | + | 0.628643i | \(0.783611\pi\) | |||||||
\(878\) | −1.98544 | − | 6.11054i | −0.0670052 | − | 0.206221i | ||||
\(879\) | 0.735020 | + | 2.26216i | 0.0247916 | + | 0.0763007i | ||||
\(880\) | 1.56989 | + | 7.46534i | 0.0529209 | + | 0.251657i | ||||
\(881\) | 5.84891 | − | 18.0011i | 0.197055 | − | 0.606472i | −0.802892 | − | 0.596125i | \(-0.796706\pi\) |
0.999946 | − | 0.0103472i | \(-0.00329367\pi\) | |||||||
\(882\) | 6.45821 | 0.217459 | ||||||||
\(883\) | 1.95208 | − | 6.00790i | 0.0656928 | − | 0.202182i | −0.912822 | − | 0.408357i | \(-0.866102\pi\) |
0.978515 | + | 0.206175i | \(0.0661018\pi\) | |||||||
\(884\) | 14.6021 | − | 10.6091i | 0.491123 | − | 0.356822i | ||||
\(885\) | 3.75868 | − | 8.39308i | 0.126347 | − | 0.282130i | ||||
\(886\) | 64.1303 | + | 46.5934i | 2.15450 | + | 1.56534i | ||||
\(887\) | −0.0583776 | + | 0.0424138i | −0.00196013 | + | 0.00142412i | −0.588765 | − | 0.808304i | \(-0.700386\pi\) |
0.586805 | + | 0.809728i | \(0.300386\pi\) | |||||||
\(888\) | −6.95628 | + | 5.05404i | −0.233438 | + | 0.169602i | ||||
\(889\) | 25.6167 | + | 18.6116i | 0.859156 | + | 0.624213i | ||||
\(890\) | 30.4800 | − | 17.5096i | 1.02169 | − | 0.586923i | ||||
\(891\) | −1.24455 | + | 0.904220i | −0.0416941 | + | 0.0302925i | ||||
\(892\) | −0.636120 | + | 1.95778i | −0.0212989 | + | 0.0655512i | ||||
\(893\) | 4.10113 | 0.137239 | ||||||||
\(894\) | 6.73107 | − | 20.7161i | 0.225121 | − | 0.692850i | ||||
\(895\) | 7.90585 | − | 4.54161i | 0.264263 | − | 0.151809i | ||||
\(896\) | 10.6479 | + | 32.7709i | 0.355721 | + | 1.09480i | ||||
\(897\) | −10.4348 | − | 32.1149i | −0.348407 | − | 1.07229i | ||||
\(898\) | 31.1886 | + | 22.6599i | 1.04078 | + | 0.756169i | ||||
\(899\) | 10.5545 | 0.352013 | ||||||||
\(900\) | 13.0364 | + | 2.83015i | 0.434547 | + | 0.0943384i | ||||
\(901\) | 12.5840 | 0.419235 | ||||||||
\(902\) | 22.9425 | + | 16.6687i | 0.763901 | + | 0.555006i | ||||
\(903\) | −8.28629 | − | 25.5026i | −0.275751 | − | 0.848673i | ||||
\(904\) | −4.00128 | − | 12.3147i | −0.133081 | − | 0.409580i | ||||
\(905\) | 24.7236 | + | 2.65280i | 0.821841 | + | 0.0881820i | ||||
\(906\) | −7.16888 | + | 22.0635i | −0.238170 | + | 0.733012i | ||||
\(907\) | −25.4951 | −0.846550 | −0.423275 | − | 0.906001i | \(-0.639120\pi\) | ||||
−0.423275 | + | 0.906001i | \(0.639120\pi\) | |||||||
\(908\) | 9.42474 | − | 29.0064i | 0.312771 | − | 0.962610i | ||||
\(909\) | −0.879879 | + | 0.639269i | −0.0291837 | + | 0.0212032i | ||||
\(910\) | −16.4698 | − | 78.3194i | −0.545968 | − | 2.59626i | ||||
\(911\) | −2.87851 | − | 2.09136i | −0.0953692 | − | 0.0692898i | 0.539079 | − | 0.842255i | \(-0.318773\pi\) |
−0.634448 | + | 0.772966i | \(0.718773\pi\) | |||||||
\(912\) | −9.77081 | + | 7.09891i | −0.323544 | + | 0.235068i | ||||
\(913\) | −16.3644 | + | 11.8894i | −0.541583 | + | 0.393483i | ||||
\(914\) | 42.2621 | + | 30.7052i | 1.39791 | + | 1.01564i | ||||
\(915\) | −23.7759 | − | 2.55111i | −0.786008 | − | 0.0843372i | ||||
\(916\) | −22.0698 | + | 16.0347i | −0.729208 | + | 0.529801i | ||||
\(917\) | 6.22981 | − | 19.1734i | 0.205727 | − | 0.633161i | ||||
\(918\) | −2.78860 | −0.0920375 | ||||||||
\(919\) | 2.46277 | − | 7.57962i | 0.0812392 | − | 0.250029i | −0.902185 | − | 0.431350i | \(-0.858037\pi\) |
0.983424 | + | 0.181321i | \(0.0580374\pi\) | |||||||
\(920\) | −15.4210 | − | 13.9459i | −0.508416 | − | 0.459781i | ||||
\(921\) | −0.894189 | − | 2.75203i | −0.0294645 | − | 0.0906825i | ||||
\(922\) | −24.9617 | − | 76.8241i | −0.822068 | − | 2.53007i | ||||
\(923\) | −0.300549 | − | 0.218362i | −0.00989270 | − | 0.00718747i | ||||
\(924\) | 12.9720 | 0.426749 | ||||||||
\(925\) | −15.0056 | + | 25.7319i | −0.493380 | + | 0.846060i | ||||
\(926\) | 44.1434 | 1.45064 | ||||||||
\(927\) | 3.99457 | + | 2.90222i | 0.131199 | + | 0.0953216i | ||||
\(928\) | 5.60805 | + | 17.2598i | 0.184093 | + | 0.566581i | ||||
\(929\) | 15.0004 | + | 46.1666i | 0.492149 | + | 1.51468i | 0.821354 | + | 0.570419i | \(0.193219\pi\) |
−0.329205 | + | 0.944258i | \(0.606781\pi\) | |||||||
\(930\) | −8.81733 | + | 19.6890i | −0.289132 | + | 0.645627i | ||||
\(931\) | 5.03032 | − | 15.4817i | 0.164862 | − | 0.507394i | ||||
\(932\) | −60.0916 | −1.96837 | ||||||||
\(933\) | 2.20807 | − | 6.79573i | 0.0722888 | − | 0.222482i | ||||
\(934\) | −54.5571 | + | 39.6381i | −1.78516 | + | 1.29700i | ||||
\(935\) | 3.29294 | + | 2.97794i | 0.107691 | + | 0.0973889i | ||||
\(936\) | 6.12016 | + | 4.44656i | 0.200044 | + | 0.145340i | ||||
\(937\) | −25.6698 | + | 18.6502i | −0.838594 | + | 0.609274i | −0.921978 | − | 0.387243i | \(-0.873427\pi\) |
0.0833833 | + | 0.996518i | \(0.473427\pi\) | |||||||
\(938\) | −10.4889 | + | 7.62066i | −0.342476 | + | 0.248823i | ||||
\(939\) | 18.6331 | + | 13.5378i | 0.608070 | + | 0.441789i | ||||
\(940\) | 3.33221 | + | 3.01345i | 0.108685 | + | 0.0982880i | ||||
\(941\) | −33.1752 | + | 24.1032i | −1.08148 | + | 0.785742i | −0.977941 | − | 0.208883i | \(-0.933017\pi\) |
−0.103541 | + | 0.994625i | \(0.533017\pi\) | |||||||
\(942\) | −11.6450 | + | 35.8395i | −0.379414 | + | 1.16771i | ||||
\(943\) | 54.9681 | 1.79001 | ||||||||
\(944\) | −2.81848 | + | 8.67439i | −0.0917337 | + | 0.282327i | ||||
\(945\) | −2.88850 | + | 6.44998i | −0.0939629 | + | 0.209818i | ||||
\(946\) | −8.71401 | − | 26.8190i | −0.283317 | − | 0.871960i | ||||
\(947\) | −3.03389 | − | 9.33737i | −0.0985883 | − | 0.303424i | 0.889584 | − | 0.456772i | \(-0.150994\pi\) |
−0.988172 | + | 0.153348i | \(0.950994\pi\) | |||||||
\(948\) | 3.49347 | + | 2.53815i | 0.113463 | + | 0.0824353i | ||||
\(949\) | −21.0246 | −0.682487 | ||||||||
\(950\) | 29.6361 | − | 50.8208i | 0.961523 | − | 1.64884i | ||||
\(951\) | 20.7750 | 0.673674 | ||||||||
\(952\) | 4.76317 | + | 3.46065i | 0.154375 | + | 0.112160i | ||||
\(953\) | 16.4125 | + | 50.5123i | 0.531652 | + | 1.63626i | 0.750775 | + | 0.660558i | \(0.229680\pi\) |
−0.219123 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(954\) | 6.50952 | + | 20.0343i | 0.210754 | + | 0.648633i | ||||
\(955\) | 5.98932 | + | 5.41638i | 0.193810 | + | 0.175270i | ||||
\(956\) | −0.485670 | + | 1.49474i | −0.0157077 | + | 0.0483433i | ||||
\(957\) | 3.63606 | 0.117537 | ||||||||
\(958\) | 7.40888 | − | 22.8022i | 0.239370 | − | 0.736705i | ||||
\(959\) | −23.4659 | + | 17.0490i | −0.757754 | + | 0.550540i | ||||
\(960\) | −27.0211 | − | 2.89931i | −0.872101 | − | 0.0935748i | ||||
\(961\) | 8.94773 | + | 6.50090i | 0.288636 | + | 0.209707i | ||||
\(962\) | −54.5807 | + | 39.6552i | −1.75975 | + | 1.27853i | ||||
\(963\) | −12.3827 | + | 8.99657i | −0.399027 | + | 0.289910i | ||||
\(964\) | −3.25793 | − | 2.36703i | −0.104931 | − | 0.0762368i | ||||
\(965\) | 7.84858 | + | 37.3226i | 0.252655 | + | 1.20146i | ||||
\(966\) | 35.5908 | − | 25.8583i | 1.14512 | − | 0.831976i | ||||
\(967\) | −0.756262 | + | 2.32754i | −0.0243198 | + | 0.0748485i | −0.962480 | − | 0.271353i | \(-0.912529\pi\) |
0.938160 | + | 0.346202i | \(0.112529\pi\) | |||||||
\(968\) | −12.4606 | −0.400500 | ||||||||
\(969\) | −2.17205 | + | 6.68488i | −0.0697763 | + | 0.214749i | ||||
\(970\) | −48.9673 | − | 5.25410i | −1.57225 | − | 0.168699i | ||||
\(971\) | −14.8230 | − | 45.6205i | −0.475693 | − | 1.46403i | −0.845021 | − | 0.534734i | \(-0.820412\pi\) |
0.369328 | − | 0.929299i | \(-0.379588\pi\) | |||||||
\(972\) | −0.824463 | − | 2.53744i | −0.0264447 | − | 0.0813883i | ||||
\(973\) | −23.6911 | − | 17.2126i | −0.759502 | − | 0.551811i | ||||
\(974\) | 15.4200 | 0.494088 | ||||||||
\(975\) | 25.6106 | + | 5.55995i | 0.820196 | + | 0.178061i | ||||
\(976\) | 23.7161 | 0.759134 | ||||||||
\(977\) | −19.1696 | − | 13.9276i | −0.613291 | − | 0.445582i | 0.237280 | − | 0.971441i | \(-0.423744\pi\) |
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(978\) | 10.8543 | + | 33.4060i | 0.347081 | + | 1.06820i | ||||
\(979\) | 3.45883 | + | 10.6452i | 0.110545 | + | 0.340221i | ||||
\(980\) | 15.4630 | − | 8.88288i | 0.493947 | − | 0.283753i | ||||
\(981\) | 2.05774 | − | 6.33308i | 0.0656987 | − | 0.202200i | ||||
\(982\) | 15.6284 | 0.498721 | ||||||||
\(983\) | 4.00193 | − | 12.3167i | 0.127642 | − | 0.392841i | −0.866731 | − | 0.498775i | \(-0.833783\pi\) |
0.994373 | + | 0.105934i | \(0.0337833\pi\) | |||||||
\(984\) | −9.96261 | + | 7.23826i | −0.317597 | + | 0.230747i | ||||
\(985\) | −8.54136 | + | 4.90668i | −0.272150 | + | 0.156340i | ||||
\(986\) | 5.33236 | + | 3.87419i | 0.169817 | + | 0.123379i | ||||
\(987\) | −1.92556 | + | 1.39900i | −0.0612913 | + | 0.0445307i | ||||
\(988\) | 61.6119 | − | 44.7637i | 1.96014 | − | 1.42412i | ||||
\(989\) | −44.2203 | − | 32.1279i | −1.40612 | − | 1.02161i | ||||
\(990\) | −3.03760 | + | 6.78291i | −0.0965412 | + | 0.215575i | ||||
\(991\) | −35.9986 | + | 26.1545i | −1.14353 | + | 0.830826i | −0.987608 | − | 0.156943i | \(-0.949836\pi\) |
−0.155926 | + | 0.987769i | \(0.549836\pi\) | |||||||
\(992\) | 10.5949 | − | 32.6079i | 0.336389 | − | 1.03530i | ||||
\(993\) | 19.2504 | 0.610891 | ||||||||
\(994\) | 0.149562 | − | 0.460303i | 0.00474381 | − | 0.0145999i | ||||
\(995\) | −7.63660 | − | 36.3146i | −0.242096 | − | 1.15125i | ||||
\(996\) | −10.8407 | − | 33.3644i | −0.343502 | − | 1.05719i | ||||
\(997\) | −17.1663 | − | 52.8324i | −0.543662 | − | 1.67322i | −0.724150 | − | 0.689642i | \(-0.757768\pi\) |
0.180488 | − | 0.983577i | \(-0.442232\pi\) | |||||||
\(998\) | −27.9964 | − | 20.3406i | −0.886209 | − | 0.643869i | ||||
\(999\) | 5.95751 | 0.188487 |
(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.16.1 | ✓ | 12 | |
3.2 | odd | 2 | 225.2.h.d.91.3 | 12 | |||
5.2 | odd | 4 | 375.2.i.d.49.6 | 24 | |||
5.3 | odd | 4 | 375.2.i.d.49.1 | 24 | |||
5.4 | even | 2 | 375.2.g.c.76.3 | 12 | |||
25.2 | odd | 20 | 375.2.i.d.199.1 | 24 | |||
25.6 | even | 5 | 1875.2.a.j.1.5 | 6 | |||
25.8 | odd | 20 | 1875.2.b.f.1249.3 | 12 | |||
25.11 | even | 5 | inner | 75.2.g.c.61.1 | yes | 12 | |
25.14 | even | 10 | 375.2.g.c.301.3 | 12 | |||
25.17 | odd | 20 | 1875.2.b.f.1249.10 | 12 | |||
25.19 | even | 10 | 1875.2.a.k.1.2 | 6 | |||
25.23 | odd | 20 | 375.2.i.d.199.6 | 24 | |||
75.11 | odd | 10 | 225.2.h.d.136.3 | 12 | |||
75.44 | odd | 10 | 5625.2.a.q.1.5 | 6 | |||
75.56 | odd | 10 | 5625.2.a.p.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
75.2.g.c.61.1 | yes | 12 | 25.11 | even | 5 | inner | |
225.2.h.d.91.3 | 12 | 3.2 | odd | 2 | |||
225.2.h.d.136.3 | 12 | 75.11 | odd | 10 | |||
375.2.g.c.76.3 | 12 | 5.4 | even | 2 | |||
375.2.g.c.301.3 | 12 | 25.14 | even | 10 | |||
375.2.i.d.49.1 | 24 | 5.3 | odd | 4 | |||
375.2.i.d.49.6 | 24 | 5.2 | odd | 4 | |||
375.2.i.d.199.1 | 24 | 25.2 | odd | 20 | |||
375.2.i.d.199.6 | 24 | 25.23 | odd | 20 | |||
1875.2.a.j.1.5 | 6 | 25.6 | even | 5 | |||
1875.2.a.k.1.2 | 6 | 25.19 | even | 10 | |||
1875.2.b.f.1249.3 | 12 | 25.8 | odd | 20 | |||
1875.2.b.f.1249.10 | 12 | 25.17 | odd | 20 | |||
5625.2.a.p.1.2 | 6 | 75.56 | odd | 10 | |||
5625.2.a.q.1.5 | 6 | 75.44 | odd | 10 |