Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 619.2 | ||
Character | \(\chi\) | \(=\) | 1110.619 |
Dual form | 1110.2.ba.a.529.2 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.648845 | + | 2.13986i | −0.290172 | + | 0.956974i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 1.49882 | − | 0.865342i | 0.566499 | − | 0.327069i | −0.189251 | − | 0.981929i | \(-0.560606\pi\) |
0.755750 | + | 0.654860i | \(0.227273\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.52875 | − | 1.63185i | −0.483433 | − | 0.516035i | ||||
\(11\) | −1.54769 | −0.466645 | −0.233323 | − | 0.972399i | \(-0.574960\pi\) | ||||
−0.233323 | + | 0.972399i | \(0.574960\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −1.64535 | − | 2.84982i | −0.456337 | − | 0.790398i | 0.542427 | − | 0.840103i | \(-0.317505\pi\) |
−0.998764 | + | 0.0497044i | \(0.984172\pi\) | |||||||
\(14\) | 1.73068i | 0.462545i | ||||||||
\(15\) | −0.508014 | − | 2.17760i | −0.131169 | − | 0.562253i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.18797 | − | 5.52173i | 0.773197 | − | 1.33922i | −0.162606 | − | 0.986691i | \(-0.551990\pi\) |
0.935802 | − | 0.352525i | \(-0.114677\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −3.40218 | + | 1.96425i | −0.780513 | + | 0.450629i | −0.836612 | − | 0.547796i | \(-0.815467\pi\) |
0.0560991 | + | 0.998425i | \(0.482134\pi\) | |||||||
\(20\) | 2.17760 | − | 0.508014i | 0.486925 | − | 0.113595i | ||||
\(21\) | −0.865342 | + | 1.49882i | −0.188833 | + | 0.327069i | ||||
\(22\) | 0.773843 | − | 1.34034i | 0.164984 | − | 0.285761i | ||||
\(23\) | 5.76456 | 1.20199 | 0.600997 | − | 0.799251i | \(-0.294770\pi\) | ||||
0.600997 | + | 0.799251i | \(0.294770\pi\) | |||||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | −4.15800 | − | 2.77687i | −0.831600 | − | 0.555375i | ||||
\(26\) | 3.29069 | 0.645358 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.49882 | − | 0.865342i | −0.283250 | − | 0.163534i | ||||
\(29\) | − | 0.719561i | − | 0.133619i | −0.997766 | − | 0.0668096i | \(-0.978718\pi\) | ||
0.997766 | − | 0.0668096i | \(-0.0212820\pi\) | |||||||
\(30\) | 2.13986 | + | 0.648845i | 0.390683 | + | 0.118462i | ||||
\(31\) | − | 9.04219i | − | 1.62403i | −0.583639 | − | 0.812013i | \(-0.698372\pi\) | ||
0.583639 | − | 0.812013i | \(-0.301628\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 1.34034 | − | 0.773843i | 0.233323 | − | 0.134709i | ||||
\(34\) | 3.18797 | + | 5.52173i | 0.546733 | + | 0.946969i | ||||
\(35\) | 0.879211 | + | 3.76873i | 0.148614 | + | 0.637032i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −5.20707 | − | 3.14427i | −0.856037 | − | 0.516915i | ||||
\(38\) | − | 3.92850i | − | 0.637286i | ||||||
\(39\) | 2.84982 | + | 1.64535i | 0.456337 | + | 0.263466i | ||||
\(40\) | −0.648845 | + | 2.13986i | −0.102591 | + | 0.338342i | ||||
\(41\) | 0.726915 | + | 1.25905i | 0.113525 | + | 0.196631i | 0.917189 | − | 0.398452i | \(-0.130452\pi\) |
−0.803664 | + | 0.595083i | \(0.797119\pi\) | |||||||
\(42\) | −0.865342 | − | 1.49882i | −0.133525 | − | 0.231272i | ||||
\(43\) | 0.853321 | 0.130130 | 0.0650651 | − | 0.997881i | \(-0.479274\pi\) | ||||
0.0650651 | + | 0.997881i | \(0.479274\pi\) | |||||||
\(44\) | 0.773843 | + | 1.34034i | 0.116661 | + | 0.202063i | ||||
\(45\) | 1.52875 | + | 1.63185i | 0.227893 | + | 0.243261i | ||||
\(46\) | −2.88228 | + | 4.99226i | −0.424969 | + | 0.736068i | ||||
\(47\) | − | 8.07046i | − | 1.17720i | −0.808425 | − | 0.588599i | \(-0.799680\pi\) | ||
0.808425 | − | 0.588599i | \(-0.200320\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −2.00237 | + | 3.46820i | −0.286052 | + | 0.495457i | ||||
\(50\) | 4.48384 | − | 2.21250i | 0.634111 | − | 0.312894i | ||||
\(51\) | 6.37594i | 0.892811i | ||||||||
\(52\) | −1.64535 | + | 2.84982i | −0.228168 | + | 0.395199i | ||||
\(53\) | 9.03833 | + | 5.21828i | 1.24151 | + | 0.716786i | 0.969402 | − | 0.245481i | \(-0.0789457\pi\) |
0.272108 | + | 0.962267i | \(0.412279\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 1.00421 | − | 3.31183i | 0.135407 | − | 0.446567i | ||||
\(56\) | 1.49882 | − | 0.865342i | 0.200288 | − | 0.115636i | ||||
\(57\) | 1.96425 | − | 3.40218i | 0.260171 | − | 0.450629i | ||||
\(58\) | 0.623158 | + | 0.359780i | 0.0818247 | + | 0.0472415i | ||||
\(59\) | 3.25086 | + | 1.87689i | 0.423226 | + | 0.244350i | 0.696457 | − | 0.717599i | \(-0.254759\pi\) |
−0.273230 | + | 0.961949i | \(0.588092\pi\) | |||||||
\(60\) | −1.63185 | + | 1.52875i | −0.210670 | + | 0.197361i | ||||
\(61\) | −0.355641 | + | 0.205329i | −0.0455352 | + | 0.0262897i | −0.522595 | − | 0.852581i | \(-0.675036\pi\) |
0.477060 | + | 0.878871i | \(0.341703\pi\) | |||||||
\(62\) | 7.83077 | + | 4.52110i | 0.994509 | + | 0.574180i | ||||
\(63\) | − | 1.73068i | − | 0.218046i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.16579 | − | 1.67172i | 0.888807 | − | 0.207351i | ||||
\(66\) | 1.54769i | 0.190507i | ||||||||
\(67\) | 7.11411 | − | 4.10733i | 0.869127 | − | 0.501791i | 0.00206895 | − | 0.999998i | \(-0.499341\pi\) |
0.867058 | + | 0.498207i | \(0.166008\pi\) | |||||||
\(68\) | −6.37594 | −0.773197 | ||||||||
\(69\) | −4.99226 | + | 2.88228i | −0.600997 | + | 0.346986i | ||||
\(70\) | −3.70342 | − | 1.12295i | −0.442643 | − | 0.134218i | ||||
\(71\) | 2.29731 | + | 3.97906i | 0.272641 | + | 0.472228i | 0.969537 | − | 0.244944i | \(-0.0787696\pi\) |
−0.696896 | + | 0.717172i | \(0.745436\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | − | 5.50667i | − | 0.644507i | −0.946653 | − | 0.322254i | \(-0.895560\pi\) | ||
0.946653 | − | 0.322254i | \(-0.104440\pi\) | |||||||
\(74\) | 5.32655 | − | 2.93732i | 0.619199 | − | 0.341457i | ||||
\(75\) | 4.98937 | + | 0.325844i | 0.576123 | + | 0.0376252i | ||||
\(76\) | 3.40218 | + | 1.96425i | 0.390256 | + | 0.225315i | ||||
\(77\) | −2.31970 | + | 1.33928i | −0.264354 | + | 0.152625i | ||||
\(78\) | −2.84982 | + | 1.64535i | −0.322679 | + | 0.186299i | ||||
\(79\) | 10.5472 | − | 6.08942i | 1.18665 | − | 0.685113i | 0.229107 | − | 0.973401i | \(-0.426419\pi\) |
0.957544 | + | 0.288288i | \(0.0930860\pi\) | |||||||
\(80\) | −1.52875 | − | 1.63185i | −0.170919 | − | 0.182446i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.45383 | −0.160549 | ||||||||
\(83\) | 10.2377 | + | 5.91076i | 1.12374 | + | 0.648790i | 0.942352 | − | 0.334622i | \(-0.108609\pi\) |
0.181385 | + | 0.983412i | \(0.441942\pi\) | |||||||
\(84\) | 1.73068 | 0.188833 | ||||||||
\(85\) | 9.74723 | + | 10.4046i | 1.05724 | + | 1.12853i | ||||
\(86\) | −0.426660 | + | 0.738998i | −0.0460080 | + | 0.0796882i | ||||
\(87\) | 0.359780 | + | 0.623158i | 0.0385725 | + | 0.0668096i | ||||
\(88\) | −1.54769 | −0.164984 | ||||||||
\(89\) | −8.13018 | − | 4.69396i | −0.861798 | − | 0.497559i | 0.00281612 | − | 0.999996i | \(-0.499104\pi\) |
−0.864614 | + | 0.502437i | \(0.832437\pi\) | |||||||
\(90\) | −2.17760 | + | 0.508014i | −0.229539 | + | 0.0535493i | ||||
\(91\) | −4.93214 | − | 2.84757i | −0.517029 | − | 0.298507i | ||||
\(92\) | −2.88228 | − | 4.99226i | −0.300499 | − | 0.520479i | ||||
\(93\) | 4.52110 | + | 7.83077i | 0.468816 | + | 0.812013i | ||||
\(94\) | 6.98922 | + | 4.03523i | 0.720883 | + | 0.416202i | ||||
\(95\) | −1.99573 | − | 8.55467i | −0.204757 | − | 0.877691i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 16.6738 | 1.69296 | 0.846482 | − | 0.532417i | \(-0.178716\pi\) | ||||
0.846482 | + | 0.532417i | \(0.178716\pi\) | |||||||
\(98\) | −2.00237 | − | 3.46820i | −0.202270 | − | 0.350341i | ||||
\(99\) | −0.773843 | + | 1.34034i | −0.0777742 | + | 0.134709i | ||||
\(100\) | −0.325844 | + | 4.98937i | −0.0325844 | + | 0.498937i | ||||
\(101\) | 2.56090 | 0.254819 | 0.127410 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127410 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(102\) | −5.52173 | − | 3.18797i | −0.546733 | − | 0.315656i | ||||
\(103\) | 3.81879 | 0.376276 | 0.188138 | − | 0.982143i | \(-0.439755\pi\) | ||||
0.188138 | + | 0.982143i | \(0.439755\pi\) | |||||||
\(104\) | −1.64535 | − | 2.84982i | −0.161339 | − | 0.279448i | ||||
\(105\) | −2.64578 | − | 2.82421i | −0.258202 | − | 0.275615i | ||||
\(106\) | −9.03833 | + | 5.21828i | −0.877880 | + | 0.506844i | ||||
\(107\) | 12.8377 | − | 7.41182i | 1.24106 | − | 0.716528i | 0.271752 | − | 0.962367i | \(-0.412397\pi\) |
0.969311 | + | 0.245839i | \(0.0790635\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 1.92541 | + | 1.11164i | 0.184421 | + | 0.106475i | 0.589368 | − | 0.807865i | \(-0.299377\pi\) |
−0.404947 | + | 0.914340i | \(0.632710\pi\) | |||||||
\(110\) | 2.36603 | + | 2.52559i | 0.225592 | + | 0.240805i | ||||
\(111\) | 6.08159 | + | 0.119482i | 0.577239 | + | 0.0113407i | ||||
\(112\) | 1.73068i | 0.163534i | ||||||||
\(113\) | −9.77887 | + | 16.9375i | −0.919918 | + | 1.59335i | −0.120382 | + | 0.992728i | \(0.538412\pi\) |
−0.799536 | + | 0.600618i | \(0.794921\pi\) | |||||||
\(114\) | 1.96425 | + | 3.40218i | 0.183969 | + | 0.318643i | ||||
\(115\) | −3.74031 | + | 12.3354i | −0.348785 | + | 1.15028i | ||||
\(116\) | −0.623158 | + | 0.359780i | −0.0578588 | + | 0.0334048i | ||||
\(117\) | −3.29069 | −0.304224 | ||||||||
\(118\) | −3.25086 | + | 1.87689i | −0.299266 | + | 0.172781i | ||||
\(119\) | − | 11.0347i | − | 1.01155i | ||||||
\(120\) | −0.508014 | − | 2.17760i | −0.0463751 | − | 0.198786i | ||||
\(121\) | −8.60467 | −0.782242 | ||||||||
\(122\) | − | 0.410659i | − | 0.0371793i | ||||||
\(123\) | −1.25905 | − | 0.726915i | −0.113525 | − | 0.0655437i | ||||
\(124\) | −7.83077 | + | 4.52110i | −0.703224 | + | 0.406006i | ||||
\(125\) | 8.64002 | − | 7.09578i | 0.772787 | − | 0.634666i | ||||
\(126\) | 1.49882 | + | 0.865342i | 0.133525 | + | 0.0770908i | ||||
\(127\) | −8.57640 | − | 4.95159i | −0.761033 | − | 0.439382i | 0.0686338 | − | 0.997642i | \(-0.478136\pi\) |
−0.829666 | + | 0.558260i | \(0.811469\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −0.738998 | + | 0.426660i | −0.0650651 | + | 0.0375654i | ||||
\(130\) | −2.13515 | + | 7.04162i | −0.187265 | + | 0.617591i | ||||
\(131\) | −10.8086 | − | 6.24033i | −0.944349 | − | 0.545220i | −0.0530283 | − | 0.998593i | \(-0.516887\pi\) |
−0.891321 | + | 0.453373i | \(0.850221\pi\) | |||||||
\(132\) | −1.34034 | − | 0.773843i | −0.116661 | − | 0.0673544i | ||||
\(133\) | −3.39949 | + | 5.88809i | −0.294773 | + | 0.510562i | ||||
\(134\) | 8.21467i | 0.709639i | ||||||||
\(135\) | −2.13986 | − | 0.648845i | −0.184170 | − | 0.0558437i | ||||
\(136\) | 3.18797 | − | 5.52173i | 0.273366 | − | 0.473484i | ||||
\(137\) | − | 11.5585i | − | 0.987508i | −0.869602 | − | 0.493754i | \(-0.835624\pi\) | ||
0.869602 | − | 0.493754i | \(-0.164376\pi\) | |||||||
\(138\) | − | 5.76456i | − | 0.490712i | ||||||
\(139\) | 1.25720 | − | 2.17753i | 0.106634 | − | 0.184696i | −0.807771 | − | 0.589497i | \(-0.799326\pi\) |
0.914405 | + | 0.404801i | \(0.132659\pi\) | |||||||
\(140\) | 2.82421 | − | 2.64578i | 0.238689 | − | 0.223610i | ||||
\(141\) | 4.03523 | + | 6.98922i | 0.339828 | + | 0.588599i | ||||
\(142\) | −4.59462 | −0.385572 | ||||||||
\(143\) | 2.54648 | + | 4.41063i | 0.212947 | + | 0.368835i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 1.53976 | + | 0.466884i | 0.127870 | + | 0.0387726i | ||||
\(146\) | 4.76892 | + | 2.75334i | 0.394678 | + | 0.227868i | ||||
\(147\) | − | 4.00473i | − | 0.330305i | ||||||
\(148\) | −0.119482 | + | 6.08159i | −0.00982137 | + | 0.499904i | ||||
\(149\) | −12.5220 | −1.02584 | −0.512920 | − | 0.858436i | \(-0.671436\pi\) | ||||
−0.512920 | + | 0.858436i | \(0.671436\pi\) | |||||||
\(150\) | −2.77687 | + | 4.15800i | −0.226731 | + | 0.339499i | ||||
\(151\) | −9.02188 | − | 15.6264i | −0.734191 | − | 1.27166i | −0.955078 | − | 0.296356i | \(-0.904229\pi\) |
0.220887 | − | 0.975299i | \(-0.429105\pi\) | |||||||
\(152\) | −3.40218 | + | 1.96425i | −0.275953 | + | 0.159322i | ||||
\(153\) | −3.18797 | − | 5.52173i | −0.257732 | − | 0.446405i | ||||
\(154\) | − | 2.67856i | − | 0.215844i | ||||||
\(155\) | 19.3490 | + | 5.86698i | 1.55415 | + | 0.471247i | ||||
\(156\) | − | 3.29069i | − | 0.263466i | ||||||
\(157\) | −19.0331 | − | 10.9888i | −1.51901 | − | 0.876999i | −0.999750 | − | 0.0223804i | \(-0.992875\pi\) |
−0.519257 | − | 0.854618i | \(-0.673791\pi\) | |||||||
\(158\) | 12.1788i | 0.968897i | ||||||||
\(159\) | −10.4366 | −0.827673 | ||||||||
\(160\) | 2.17760 | − | 0.508014i | 0.172154 | − | 0.0401620i | ||||
\(161\) | 8.64002 | − | 4.98832i | 0.680929 | − | 0.393135i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −6.27827 | + | 10.8743i | −0.491752 | + | 0.851739i | −0.999955 | − | 0.00949793i | \(-0.996977\pi\) |
0.508203 | + | 0.861237i | \(0.330310\pi\) | |||||||
\(164\) | 0.726915 | − | 1.25905i | 0.0567625 | − | 0.0983156i | ||||
\(165\) | 0.786246 | + | 3.37024i | 0.0612092 | + | 0.262372i | ||||
\(166\) | −10.2377 | + | 5.91076i | −0.794602 | + | 0.458764i | ||||
\(167\) | 3.34316 | + | 5.79053i | 0.258702 | + | 0.448085i | 0.965894 | − | 0.258936i | \(-0.0833720\pi\) |
−0.707193 | + | 0.707021i | \(0.750039\pi\) | |||||||
\(168\) | −0.865342 | + | 1.49882i | −0.0667626 | + | 0.115636i | ||||
\(169\) | 1.08568 | − | 1.88045i | 0.0835137 | − | 0.144650i | ||||
\(170\) | −13.8842 | + | 3.23907i | −1.06487 | + | 0.248425i | ||||
\(171\) | 3.92850i | 0.300420i | ||||||||
\(172\) | −0.426660 | − | 0.738998i | −0.0325326 | − | 0.0563480i | ||||
\(173\) | −3.16647 | − | 1.82816i | −0.240742 | − | 0.138993i | 0.374776 | − | 0.927116i | \(-0.377720\pi\) |
−0.615518 | + | 0.788123i | \(0.711053\pi\) | |||||||
\(174\) | −0.719561 | −0.0545498 | ||||||||
\(175\) | −8.63502 | − | 0.563933i | −0.652747 | − | 0.0426293i | ||||
\(176\) | 0.773843 | − | 1.34034i | 0.0583306 | − | 0.101032i | ||||
\(177\) | −3.75377 | −0.282151 | ||||||||
\(178\) | 8.13018 | − | 4.69396i | 0.609383 | − | 0.351827i | ||||
\(179\) | − | 22.2334i | − | 1.66180i | −0.556422 | − | 0.830900i | \(-0.687826\pi\) | ||
0.556422 | − | 0.830900i | \(-0.312174\pi\) | |||||||
\(180\) | 0.648845 | − | 2.13986i | 0.0483621 | − | 0.159496i | ||||
\(181\) | 4.97146 | + | 8.61082i | 0.369526 | + | 0.640037i | 0.989491 | − | 0.144591i | \(-0.0461868\pi\) |
−0.619966 | + | 0.784629i | \(0.712853\pi\) | |||||||
\(182\) | 4.93214 | − | 2.84757i | 0.365595 | − | 0.211076i | ||||
\(183\) | 0.205329 | − | 0.355641i | 0.0151784 | − | 0.0262897i | ||||
\(184\) | 5.76456 | 0.424969 | ||||||||
\(185\) | 10.1069 | − | 9.10226i | 0.743072 | − | 0.669211i | ||||
\(186\) | −9.04219 | −0.663006 | ||||||||
\(187\) | −4.93398 | + | 8.54591i | −0.360808 | + | 0.624939i | ||||
\(188\) | −6.98922 | + | 4.03523i | −0.509741 | + | 0.294299i | ||||
\(189\) | 0.865342 | + | 1.49882i | 0.0629444 | + | 0.109023i | ||||
\(190\) | 8.40643 | + | 2.54898i | 0.609866 | + | 0.184923i | ||||
\(191\) | 12.7228i | 0.920592i | 0.887766 | + | 0.460296i | \(0.152257\pi\) | ||||
−0.887766 | + | 0.460296i | \(0.847743\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −7.19149 | −0.517655 | −0.258827 | − | 0.965924i | \(-0.583336\pi\) | ||||
−0.258827 | + | 0.965924i | \(0.583336\pi\) | |||||||
\(194\) | −8.33688 | + | 14.4399i | −0.598553 | + | 1.03672i | ||||
\(195\) | −5.36990 | + | 5.03064i | −0.384547 | + | 0.360252i | ||||
\(196\) | 4.00473 | 0.286052 | ||||||||
\(197\) | 4.31757 | + | 2.49275i | 0.307614 | + | 0.177601i | 0.645858 | − | 0.763457i | \(-0.276500\pi\) |
−0.338244 | + | 0.941058i | \(0.609833\pi\) | |||||||
\(198\) | −0.773843 | − | 1.34034i | −0.0549947 | − | 0.0952535i | ||||
\(199\) | 7.94025i | 0.562870i | 0.959580 | + | 0.281435i | \(0.0908103\pi\) | ||||
−0.959580 | + | 0.281435i | \(0.909190\pi\) | |||||||
\(200\) | −4.15800 | − | 2.77687i | −0.294015 | − | 0.196355i | ||||
\(201\) | −4.10733 | + | 7.11411i | −0.289709 | + | 0.501791i | ||||
\(202\) | −1.28045 | + | 2.21781i | −0.0900922 | + | 0.156044i | ||||
\(203\) | −0.622666 | − | 1.07849i | −0.0437026 | − | 0.0756951i | ||||
\(204\) | 5.52173 | − | 3.18797i | 0.386598 | − | 0.223203i | ||||
\(205\) | −3.16585 | + | 0.738566i | −0.221113 | + | 0.0515837i | ||||
\(206\) | −1.90939 | + | 3.30717i | −0.133034 | + | 0.230421i | ||||
\(207\) | 2.88228 | − | 4.99226i | 0.200332 | − | 0.346986i | ||||
\(208\) | 3.29069 | 0.228168 | ||||||||
\(209\) | 5.26550 | − | 3.04004i | 0.364223 | − | 0.210284i | ||||
\(210\) | 3.76873 | − | 0.879211i | 0.260067 | − | 0.0606713i | ||||
\(211\) | 11.7676 | 0.810112 | 0.405056 | − | 0.914292i | \(-0.367252\pi\) | ||||
0.405056 | + | 0.914292i | \(0.367252\pi\) | |||||||
\(212\) | − | 10.4366i | − | 0.716786i | ||||||
\(213\) | −3.97906 | − | 2.29731i | −0.272641 | − | 0.157409i | ||||
\(214\) | 14.8236i | 1.01332i | ||||||||
\(215\) | −0.553673 | + | 1.82599i | −0.0377602 | + | 0.124531i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −7.82459 | − | 13.5526i | −0.531168 | − | 0.920010i | ||||
\(218\) | −1.92541 | + | 1.11164i | −0.130405 | + | 0.0752894i | ||||
\(219\) | 2.75334 | + | 4.76892i | 0.186053 | + | 0.322254i | ||||
\(220\) | −3.37024 | + | 0.786246i | −0.227221 | + | 0.0530087i | ||||
\(221\) | −20.9813 | −1.41135 | ||||||||
\(222\) | −3.14427 | + | 5.20707i | −0.211030 | + | 0.349476i | ||||
\(223\) | − | 16.7406i | − | 1.12103i | −0.828143 | − | 0.560517i | \(-0.810602\pi\) | ||
0.828143 | − | 0.560517i | \(-0.189398\pi\) | |||||||
\(224\) | −1.49882 | − | 0.865342i | −0.100144 | − | 0.0578181i | ||||
\(225\) | −4.48384 | + | 2.21250i | −0.298923 | + | 0.147500i | ||||
\(226\) | −9.77887 | − | 16.9375i | −0.650481 | − | 1.12667i | ||||
\(227\) | 1.51026 | + | 2.61584i | 0.100239 | + | 0.173620i | 0.911783 | − | 0.410672i | \(-0.134706\pi\) |
−0.811544 | + | 0.584291i | \(0.801372\pi\) | |||||||
\(228\) | −3.92850 | −0.260171 | ||||||||
\(229\) | 0.284128 | + | 0.492123i | 0.0187757 | + | 0.0325204i | 0.875261 | − | 0.483652i | \(-0.160690\pi\) |
−0.856485 | + | 0.516172i | \(0.827356\pi\) | |||||||
\(230\) | −8.81258 | − | 9.40688i | −0.581084 | − | 0.620271i | ||||
\(231\) | 1.33928 | − | 2.31970i | 0.0881180 | − | 0.152625i | ||||
\(232\) | − | 0.719561i | − | 0.0472415i | ||||||
\(233\) | − | 5.62242i | − | 0.368337i | −0.982895 | − | 0.184169i | \(-0.941041\pi\) | ||
0.982895 | − | 0.184169i | \(-0.0589592\pi\) | |||||||
\(234\) | 1.64535 | − | 2.84982i | 0.107560 | − | 0.186299i | ||||
\(235\) | 17.2696 | + | 5.23648i | 1.12655 | + | 0.341590i | ||||
\(236\) | − | 3.75377i | − | 0.244350i | ||||||
\(237\) | −6.08942 | + | 10.5472i | −0.395550 | + | 0.685113i | ||||
\(238\) | 9.55637 | + | 5.51737i | 0.619447 | + | 0.357638i | ||||
\(239\) | 21.1400 | + | 12.2052i | 1.36743 | + | 0.789487i | 0.990600 | − | 0.136794i | \(-0.0436799\pi\) |
0.376833 | + | 0.926281i | \(0.377013\pi\) | |||||||
\(240\) | 2.13986 | + | 0.648845i | 0.138127 | + | 0.0418828i | ||||
\(241\) | −10.2774 | + | 5.93368i | −0.662027 | + | 0.382222i | −0.793049 | − | 0.609158i | \(-0.791508\pi\) |
0.131022 | + | 0.991379i | \(0.458174\pi\) | |||||||
\(242\) | 4.30233 | − | 7.45186i | 0.276564 | − | 0.479024i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0.355641 | + | 0.205329i | 0.0227676 | + | 0.0131449i | ||||
\(245\) | −6.12224 | − | 6.53511i | −0.391135 | − | 0.417513i | ||||
\(246\) | 1.25905 | − | 0.726915i | 0.0802744 | − | 0.0463464i | ||||
\(247\) | 11.1955 | + | 6.46373i | 0.712353 | + | 0.411277i | ||||
\(248\) | − | 9.04219i | − | 0.574180i | ||||||
\(249\) | −11.8215 | −0.749158 | ||||||||
\(250\) | 1.82511 | + | 11.0304i | 0.115430 | + | 0.697622i | ||||
\(251\) | − | 11.7493i | − | 0.741611i | −0.928710 | − | 0.370806i | \(-0.879082\pi\) | ||
0.928710 | − | 0.370806i | \(-0.120918\pi\) | |||||||
\(252\) | −1.49882 | + | 0.865342i | −0.0944166 | + | 0.0545114i | ||||
\(253\) | −8.92174 | −0.560905 | ||||||||
\(254\) | 8.57640 | − | 4.95159i | 0.538131 | − | 0.310690i | ||||
\(255\) | −13.6436 | − | 4.13700i | −0.854397 | − | 0.259069i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.56386 | − | 13.1010i | 0.471820 | − | 0.817217i | −0.527660 | − | 0.849456i | \(-0.676930\pi\) |
0.999480 | + | 0.0322389i | \(0.0102637\pi\) | |||||||
\(258\) | − | 0.853321i | − | 0.0531254i | ||||||
\(259\) | −10.5253 | − | 0.206786i | −0.654011 | − | 0.0128490i | ||||
\(260\) | −5.03064 | − | 5.36990i | −0.311987 | − | 0.333027i | ||||
\(261\) | −0.623158 | − | 0.359780i | −0.0385725 | − | 0.0222699i | ||||
\(262\) | 10.8086 | − | 6.24033i | 0.667756 | − | 0.385529i | ||||
\(263\) | −12.4096 | + | 7.16469i | −0.765209 | + | 0.441794i | −0.831163 | − | 0.556029i | \(-0.812324\pi\) |
0.0659538 | + | 0.997823i | \(0.478991\pi\) | |||||||
\(264\) | 1.34034 | − | 0.773843i | 0.0824920 | − | 0.0476268i | ||||
\(265\) | −17.0309 | + | 15.9549i | −1.04620 | + | 0.980102i | ||||
\(266\) | −3.39949 | − | 5.88809i | −0.208436 | − | 0.361022i | ||||
\(267\) | 9.38793 | 0.574532 | ||||||||
\(268\) | −7.11411 | − | 4.10733i | −0.434563 | − | 0.250895i | ||||
\(269\) | −4.81724 | −0.293713 | −0.146856 | − | 0.989158i | \(-0.546915\pi\) | ||||
−0.146856 | + | 0.989158i | \(0.546915\pi\) | |||||||
\(270\) | 1.63185 | − | 1.52875i | 0.0993110 | − | 0.0930368i | ||||
\(271\) | 3.92526 | − | 6.79875i | 0.238443 | − | 0.412995i | −0.721825 | − | 0.692076i | \(-0.756696\pi\) |
0.960268 | + | 0.279081i | \(0.0900298\pi\) | |||||||
\(272\) | 3.18797 | + | 5.52173i | 0.193299 | + | 0.334804i | ||||
\(273\) | 5.69515 | 0.344686 | ||||||||
\(274\) | 10.0099 | + | 5.77924i | 0.604723 | + | 0.349137i | ||||
\(275\) | 6.43528 | + | 4.29773i | 0.388062 | + | 0.259163i | ||||
\(276\) | 4.99226 | + | 2.88228i | 0.300499 | + | 0.173493i | ||||
\(277\) | −4.07494 | − | 7.05800i | −0.244839 | − | 0.424074i | 0.717247 | − | 0.696819i | \(-0.245402\pi\) |
−0.962086 | + | 0.272745i | \(0.912069\pi\) | |||||||
\(278\) | 1.25720 | + | 2.17753i | 0.0754017 | + | 0.130600i | ||||
\(279\) | −7.83077 | − | 4.52110i | −0.468816 | − | 0.270671i | ||||
\(280\) | 0.879211 | + | 3.76873i | 0.0525429 | + | 0.225225i | ||||
\(281\) | −26.6881 | − | 15.4084i | −1.59208 | − | 0.919188i | −0.992950 | − | 0.118537i | \(-0.962179\pi\) |
−0.599131 | − | 0.800651i | \(-0.704487\pi\) | |||||||
\(282\) | −8.07046 | −0.480589 | ||||||||
\(283\) | 3.63012 | + | 6.28756i | 0.215789 | + | 0.373757i | 0.953516 | − | 0.301342i | \(-0.0974345\pi\) |
−0.737728 | + | 0.675098i | \(0.764101\pi\) | |||||||
\(284\) | 2.29731 | − | 3.97906i | 0.136320 | − | 0.236114i | ||||
\(285\) | 6.00569 | + | 6.41070i | 0.355746 | + | 0.379737i | ||||
\(286\) | −5.09296 | −0.301153 | ||||||||
\(287\) | 2.17903 | + | 1.25806i | 0.128624 | + | 0.0742610i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −11.8263 | − | 20.4838i | −0.695667 | − | 1.20493i | ||||
\(290\) | −1.17421 | + | 1.10003i | −0.0689522 | + | 0.0645959i | ||||
\(291\) | −14.4399 | + | 8.33688i | −0.846482 | + | 0.488717i | ||||
\(292\) | −4.76892 | + | 2.75334i | −0.279080 | + | 0.161127i | ||||
\(293\) | −27.1811 | + | 15.6930i | −1.58794 | + | 0.916796i | −0.594291 | + | 0.804250i | \(0.702567\pi\) |
−0.993646 | + | 0.112546i | \(0.964099\pi\) | |||||||
\(294\) | 3.46820 | + | 2.00237i | 0.202270 | + | 0.116780i | ||||
\(295\) | −6.12558 | + | 5.73858i | −0.356645 | + | 0.334113i | ||||
\(296\) | −5.20707 | − | 3.14427i | −0.302655 | − | 0.182757i | ||||
\(297\) | − | 1.54769i | − | 0.0898059i | ||||||
\(298\) | 6.26099 | − | 10.8444i | 0.362689 | − | 0.628196i | ||||
\(299\) | −9.48470 | − | 16.4280i | −0.548514 | − | 0.950054i | ||||
\(300\) | −2.21250 | − | 4.48384i | −0.127739 | − | 0.258875i | ||||
\(301\) | 1.27897 | − | 0.738414i | 0.0737187 | − | 0.0425615i | ||||
\(302\) | 18.0438 | 1.03830 | ||||||||
\(303\) | −2.21781 | + | 1.28045i | −0.127410 | + | 0.0735600i | ||||
\(304\) | − | 3.92850i | − | 0.225315i | ||||||
\(305\) | −0.208620 | − | 0.894249i | −0.0119456 | − | 0.0512045i | ||||
\(306\) | 6.37594 | 0.364488 | ||||||||
\(307\) | − | 19.2087i | − | 1.09630i | −0.836381 | − | 0.548149i | \(-0.815333\pi\) | ||
0.836381 | − | 0.548149i | \(-0.184667\pi\) | |||||||
\(308\) | 2.31970 | + | 1.33928i | 0.132177 | + | 0.0763125i | ||||
\(309\) | −3.30717 | + | 1.90939i | −0.188138 | + | 0.108622i | ||||
\(310\) | −14.7555 | + | 13.8233i | −0.838054 | + | 0.785108i | ||||
\(311\) | 15.8871 | + | 9.17242i | 0.900875 | + | 0.520120i | 0.877484 | − | 0.479606i | \(-0.159220\pi\) |
0.0233910 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(312\) | 2.84982 | + | 1.64535i | 0.161339 | + | 0.0931493i | ||||
\(313\) | 13.4284 | − | 23.2587i | 0.759018 | − | 1.31466i | −0.184334 | − | 0.982864i | \(-0.559013\pi\) |
0.943352 | − | 0.331794i | \(-0.107654\pi\) | |||||||
\(314\) | 19.0331 | − | 10.9888i | 1.07410 | − | 0.620132i | ||||
\(315\) | 3.70342 | + | 1.12295i | 0.208664 | + | 0.0632708i | ||||
\(316\) | −10.5472 | − | 6.08942i | −0.593326 | − | 0.342557i | ||||
\(317\) | −19.7427 | − | 11.3984i | −1.10886 | − | 0.640200i | −0.170325 | − | 0.985388i | \(-0.554482\pi\) |
−0.938534 | + | 0.345188i | \(0.887815\pi\) | |||||||
\(318\) | 5.21828 | − | 9.03833i | 0.292627 | − | 0.506844i | ||||
\(319\) | 1.11365i | 0.0623527i | ||||||||
\(320\) | −0.648845 | + | 2.13986i | −0.0362715 | + | 0.119622i | ||||
\(321\) | −7.41182 | + | 12.8377i | −0.413688 | + | 0.716528i | ||||
\(322\) | 9.97664i | 0.555976i | ||||||||
\(323\) | 25.0479i | 1.39370i | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −1.07225 | + | 16.4185i | −0.0594778 | + | 0.910733i | ||||
\(326\) | −6.27827 | − | 10.8743i | −0.347721 | − | 0.602271i | ||||
\(327\) | −2.22327 | −0.122947 | ||||||||
\(328\) | 0.726915 | + | 1.25905i | 0.0401372 | + | 0.0695196i | ||||
\(329\) | −6.98371 | − | 12.0961i | −0.385024 | − | 0.666881i | ||||
\(330\) | −3.31183 | − | 1.00421i | −0.182310 | − | 0.0552799i | ||||
\(331\) | −0.719083 | − | 0.415163i | −0.0395244 | − | 0.0228194i | 0.480108 | − | 0.877210i | \(-0.340598\pi\) |
−0.519632 | + | 0.854390i | \(0.673931\pi\) | |||||||
\(332\) | − | 11.8215i | − | 0.648790i | ||||||
\(333\) | −5.32655 | + | 2.93732i | −0.291893 | + | 0.160964i | ||||
\(334\) | −6.68633 | −0.365859 | ||||||||
\(335\) | 4.17316 | + | 17.8882i | 0.228004 | + | 0.977338i | ||||
\(336\) | −0.865342 | − | 1.49882i | −0.0472083 | − | 0.0817671i | ||||
\(337\) | −25.7764 | + | 14.8820i | −1.40413 | + | 0.810674i | −0.994813 | − | 0.101719i | \(-0.967566\pi\) |
−0.409315 | + | 0.912393i | \(0.634232\pi\) | |||||||
\(338\) | 1.08568 | + | 1.88045i | 0.0590531 | + | 0.102283i | ||||
\(339\) | − | 19.5577i | − | 1.06223i | ||||||
\(340\) | 4.13700 | − | 13.6436i | 0.224360 | − | 0.739930i | ||||
\(341\) | 13.9945i | 0.757844i | ||||||||
\(342\) | −3.40218 | − | 1.96425i | −0.183969 | − | 0.106214i | ||||
\(343\) | 19.0457i | 1.02837i | ||||||||
\(344\) | 0.853321 | 0.0460080 | ||||||||
\(345\) | −2.92848 | − | 12.5529i | −0.157664 | − | 0.675825i | ||||
\(346\) | 3.16647 | − | 1.82816i | 0.170230 | − | 0.0982826i | ||||
\(347\) | 6.26127 | 0.336123 | 0.168061 | − | 0.985777i | \(-0.446249\pi\) | ||||
0.168061 | + | 0.985777i | \(0.446249\pi\) | |||||||
\(348\) | 0.359780 | − | 0.623158i | 0.0192863 | − | 0.0334048i | ||||
\(349\) | 10.1013 | − | 17.4960i | 0.540712 | − | 0.936540i | −0.458152 | − | 0.888874i | \(-0.651488\pi\) |
0.998863 | − | 0.0476661i | \(-0.0151783\pi\) | |||||||
\(350\) | 4.80589 | − | 7.19618i | 0.256886 | − | 0.384652i | ||||
\(351\) | 2.84982 | − | 1.64535i | 0.152112 | − | 0.0878220i | ||||
\(352\) | 0.773843 | + | 1.34034i | 0.0412460 | + | 0.0714401i | ||||
\(353\) | 4.65889 | − | 8.06944i | 0.247968 | − | 0.429493i | −0.714994 | − | 0.699131i | \(-0.753571\pi\) |
0.962962 | + | 0.269638i | \(0.0869039\pi\) | |||||||
\(354\) | 1.87689 | − | 3.25086i | 0.0997554 | − | 0.172781i | ||||
\(355\) | −10.0052 | + | 2.33413i | −0.531023 | + | 0.123883i | ||||
\(356\) | 9.38793i | 0.497559i | ||||||||
\(357\) | 5.51737 | + | 9.55637i | 0.292010 | + | 0.505777i | ||||
\(358\) | 19.2547 | + | 11.1167i | 1.01764 | + | 0.587535i | ||||
\(359\) | −17.3408 | −0.915214 | −0.457607 | − | 0.889154i | \(-0.651293\pi\) | ||||
−0.457607 | + | 0.889154i | \(0.651293\pi\) | |||||||
\(360\) | 1.52875 | + | 1.63185i | 0.0805722 | + | 0.0860058i | ||||
\(361\) | −1.78346 | + | 3.08905i | −0.0938664 | + | 0.162581i | ||||
\(362\) | −9.94292 | −0.522588 | ||||||||
\(363\) | 7.45186 | − | 4.30233i | 0.391121 | − | 0.225814i | ||||
\(364\) | 5.69515i | 0.298507i | ||||||||
\(365\) | 11.7835 | + | 3.57298i | 0.616777 | + | 0.187018i | ||||
\(366\) | 0.205329 | + | 0.355641i | 0.0107327 | + | 0.0185896i | ||||
\(367\) | 24.1739 | − | 13.9568i | 1.26187 | − | 0.728540i | 0.288432 | − | 0.957500i | \(-0.406866\pi\) |
0.973436 | + | 0.228960i | \(0.0735326\pi\) | |||||||
\(368\) | −2.88228 | + | 4.99226i | −0.150249 | + | 0.260239i | ||||
\(369\) | 1.45383 | 0.0756834 | ||||||||
\(370\) | 2.82935 | + | 13.3039i | 0.147091 | + | 0.691639i | ||||
\(371\) | 18.0624 | 0.937753 | ||||||||
\(372\) | 4.52110 | − | 7.83077i | 0.234408 | − | 0.406006i | ||||
\(373\) | 3.32576 | − | 1.92013i | 0.172202 | − | 0.0994206i | −0.411422 | − | 0.911445i | \(-0.634968\pi\) |
0.583624 | + | 0.812024i | \(0.301634\pi\) | |||||||
\(374\) | −4.93398 | − | 8.54591i | −0.255130 | − | 0.441898i | ||||
\(375\) | −3.93459 | + | 10.4651i | −0.203181 | + | 0.540417i | ||||
\(376\) | − | 8.07046i | − | 0.416202i | ||||||
\(377\) | −2.05062 | + | 1.18393i | −0.105612 | + | 0.0609753i | ||||
\(378\) | −1.73068 | −0.0890168 | ||||||||
\(379\) | −9.96232 | + | 17.2553i | −0.511730 | + | 0.886343i | 0.488177 | + | 0.872744i | \(0.337662\pi\) |
−0.999908 | + | 0.0135983i | \(0.995671\pi\) | |||||||
\(380\) | −6.41070 | + | 6.00569i | −0.328862 | + | 0.308085i | ||||
\(381\) | 9.90318 | 0.507355 | ||||||||
\(382\) | −11.0183 | − | 6.36142i | −0.563745 | − | 0.325478i | ||||
\(383\) | 8.99091 | + | 15.5727i | 0.459414 | + | 0.795728i | 0.998930 | − | 0.0462470i | \(-0.0147261\pi\) |
−0.539516 | + | 0.841975i | \(0.681393\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −1.36074 | − | 5.83281i | −0.0693499 | − | 0.297268i | ||||
\(386\) | 3.59574 | − | 6.22801i | 0.183019 | − | 0.316997i | ||||
\(387\) | 0.426660 | − | 0.738998i | 0.0216884 | − | 0.0375654i | ||||
\(388\) | −8.33688 | − | 14.4399i | −0.423241 | − | 0.733075i | ||||
\(389\) | 1.27239 | − | 0.734617i | 0.0645129 | − | 0.0372465i | −0.467397 | − | 0.884048i | \(-0.654808\pi\) |
0.531910 | + | 0.846801i | \(0.321475\pi\) | |||||||
\(390\) | −1.67172 | − | 7.16579i | −0.0846506 | − | 0.362854i | ||||
\(391\) | 18.3773 | − | 31.8304i | 0.929378 | − | 1.60973i | ||||
\(392\) | −2.00237 | + | 3.46820i | −0.101135 | + | 0.175171i | ||||
\(393\) | 12.4807 | 0.629566 | ||||||||
\(394\) | −4.31757 | + | 2.49275i | −0.217516 | + | 0.125583i | ||||
\(395\) | 6.18702 | + | 26.5206i | 0.311303 | + | 1.33440i | ||||
\(396\) | 1.54769 | 0.0777742 | ||||||||
\(397\) | − | 30.5115i | − | 1.53133i | −0.643242 | − | 0.765663i | \(-0.722411\pi\) | ||
0.643242 | − | 0.765663i | \(-0.277589\pi\) | |||||||
\(398\) | −6.87646 | − | 3.97013i | −0.344686 | − | 0.199004i | ||||
\(399\) | − | 6.79898i | − | 0.340375i | ||||||
\(400\) | 4.48384 | − | 2.21250i | 0.224192 | − | 0.110625i | ||||
\(401\) | 21.3954i | 1.06844i | 0.845347 | + | 0.534218i | \(0.179394\pi\) | ||||
−0.845347 | + | 0.534218i | \(0.820606\pi\) | |||||||
\(402\) | −4.10733 | − | 7.11411i | −0.204855 | − | 0.354820i | ||||
\(403\) | −25.7686 | + | 14.8775i | −1.28363 | + | 0.741103i | ||||
\(404\) | −1.28045 | − | 2.21781i | −0.0637048 | − | 0.110340i | ||||
\(405\) | 2.17760 | − | 0.508014i | 0.108206 | − | 0.0252434i | ||||
\(406\) | 1.24533 | 0.0618048 | ||||||||
\(407\) | 8.05891 | + | 4.86634i | 0.399465 | + | 0.241216i | ||||
\(408\) | 6.37594i | 0.315656i | ||||||||
\(409\) | 29.3220 | + | 16.9291i | 1.44988 | + | 0.837089i | 0.998474 | − | 0.0552285i | \(-0.0175887\pi\) |
0.451408 | + | 0.892318i | \(0.350922\pi\) | |||||||
\(410\) | 0.943311 | − | 3.11099i | 0.0465868 | − | 0.153641i | ||||
\(411\) | 5.77924 | + | 10.0099i | 0.285069 | + | 0.493754i | ||||
\(412\) | −1.90939 | − | 3.30717i | −0.0940691 | − | 0.162932i | ||||
\(413\) | 6.49659 | 0.319676 | ||||||||
\(414\) | 2.88228 | + | 4.99226i | 0.141656 | + | 0.245356i | ||||
\(415\) | −19.2909 | + | 18.0721i | −0.946953 | + | 0.887127i | ||||
\(416\) | −1.64535 | + | 2.84982i | −0.0806697 | + | 0.139724i | ||||
\(417\) | 2.51440i | 0.123130i | ||||||||
\(418\) | 6.08008i | 0.297386i | ||||||||
\(419\) | 5.34770 | − | 9.26250i | 0.261252 | − | 0.452503i | −0.705323 | − | 0.708887i | \(-0.749198\pi\) |
0.966575 | + | 0.256384i | \(0.0825312\pi\) | |||||||
\(420\) | −1.12295 | + | 3.70342i | −0.0547941 | + | 0.180708i | ||||
\(421\) | − | 5.00935i | − | 0.244141i | −0.992521 | − | 0.122070i | \(-0.961047\pi\) | ||
0.992521 | − | 0.122070i | \(-0.0389534\pi\) | |||||||
\(422\) | −5.88378 | + | 10.1910i | −0.286418 | + | 0.496090i | ||||
\(423\) | −6.98922 | − | 4.03523i | −0.339828 | − | 0.196200i | ||||
\(424\) | 9.03833 | + | 5.21828i | 0.438940 | + | 0.253422i | ||||
\(425\) | −28.5887 | + | 14.1068i | −1.38676 | + | 0.684278i | ||||
\(426\) | 3.97906 | − | 2.29731i | 0.192786 | − | 0.111305i | ||||
\(427\) | −0.355360 | + | 0.615502i | −0.0171971 | + | 0.0297862i | ||||
\(428\) | −12.8377 | − | 7.41182i | −0.620532 | − | 0.358264i | ||||
\(429\) | −4.41063 | − | 2.54648i | −0.212947 | − | 0.122945i | ||||
\(430\) | −1.30451 | − | 1.39249i | −0.0629093 | − | 0.0671518i | ||||
\(431\) | 17.0851 | − | 9.86409i | 0.822960 | − | 0.475136i | −0.0284759 | − | 0.999594i | \(-0.509065\pi\) |
0.851436 | + | 0.524458i | \(0.175732\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 36.6203i | − | 1.75986i | −0.475102 | − | 0.879931i | \(-0.657589\pi\) | ||
0.475102 | − | 0.879931i | \(-0.342411\pi\) | |||||||
\(434\) | 15.6492 | 0.751185 | ||||||||
\(435\) | −1.56691 | + | 0.365547i | −0.0751277 | + | 0.0175266i | ||||
\(436\) | − | 2.22327i | − | 0.106475i | ||||||
\(437\) | −19.6121 | + | 11.3230i | −0.938172 | + | 0.541654i | ||||
\(438\) | −5.50667 | −0.263119 | ||||||||
\(439\) | −3.37908 | + | 1.95091i | −0.161275 | + | 0.0931119i | −0.578465 | − | 0.815707i | \(-0.696348\pi\) |
0.417191 | + | 0.908819i | \(0.363015\pi\) | |||||||
\(440\) | 1.00421 | − | 3.31183i | 0.0478738 | − | 0.157885i | ||||
\(441\) | 2.00237 | + | 3.46820i | 0.0953508 | + | 0.165152i | ||||
\(442\) | 10.4906 | − | 18.1703i | 0.498988 | − | 0.864273i | ||||
\(443\) | − | 8.30484i | − | 0.394575i | −0.980346 | − | 0.197287i | \(-0.936787\pi\) | ||
0.980346 | − | 0.197287i | \(-0.0632132\pi\) | |||||||
\(444\) | −2.93732 | − | 5.32655i | −0.139399 | − | 0.252787i | ||||
\(445\) | 15.3197 | − | 14.3518i | 0.726221 | − | 0.680341i | ||||
\(446\) | 14.4978 | + | 8.37030i | 0.686490 | + | 0.396345i | ||||
\(447\) | 10.8444 | − | 6.26099i | 0.512920 | − | 0.296135i | ||||
\(448\) | 1.49882 | − | 0.865342i | 0.0708124 | − | 0.0408836i | ||||
\(449\) | −28.5245 | + | 16.4687i | −1.34616 | + | 0.777204i | −0.987703 | − | 0.156344i | \(-0.950029\pi\) |
−0.358454 | + | 0.933548i | \(0.616696\pi\) | |||||||
\(450\) | 0.325844 | − | 4.98937i | 0.0153604 | − | 0.235201i | ||||
\(451\) | −1.12504 | − | 1.94862i | −0.0529759 | − | 0.0917570i | ||||
\(452\) | 19.5577 | 0.919918 | ||||||||
\(453\) | 15.6264 | + | 9.02188i | 0.734191 | + | 0.423885i | ||||
\(454\) | −3.02052 | −0.141760 | ||||||||
\(455\) | 9.29360 | − | 8.70646i | 0.435691 | − | 0.408165i | ||||
\(456\) | 1.96425 | − | 3.40218i | 0.0919843 | − | 0.159322i | ||||
\(457\) | 14.5444 | + | 25.1916i | 0.680359 | + | 1.17842i | 0.974871 | + | 0.222768i | \(0.0715093\pi\) |
−0.294513 | + | 0.955647i | \(0.595157\pi\) | |||||||
\(458\) | −0.568255 | −0.0265528 | ||||||||
\(459\) | 5.52173 | + | 3.18797i | 0.257732 | + | 0.148802i | ||||
\(460\) | 12.5529 | − | 2.92848i | 0.585281 | − | 0.136541i | ||||
\(461\) | 21.8552 | + | 12.6181i | 1.01790 | + | 0.587684i | 0.913495 | − | 0.406851i | \(-0.133373\pi\) |
0.104404 | + | 0.994535i | \(0.466706\pi\) | |||||||
\(462\) | 1.33928 | + | 2.31970i | 0.0623089 | + | 0.107922i | ||||
\(463\) | 10.2575 | + | 17.7665i | 0.476707 | + | 0.825680i | 0.999644 | − | 0.0266912i | \(-0.00849707\pi\) |
−0.522937 | + | 0.852371i | \(0.675164\pi\) | |||||||
\(464\) | 0.623158 | + | 0.359780i | 0.0289294 | + | 0.0167024i | ||||
\(465\) | −19.6902 | + | 4.59356i | −0.913113 | + | 0.213021i | ||||
\(466\) | 4.86916 | + | 2.81121i | 0.225559 | + | 0.130227i | ||||
\(467\) | 10.1214 | 0.468362 | 0.234181 | − | 0.972193i | \(-0.424759\pi\) | ||||
0.234181 | + | 0.972193i | \(0.424759\pi\) | |||||||
\(468\) | 1.64535 | + | 2.84982i | 0.0760561 | + | 0.131733i | ||||
\(469\) | 7.10850 | − | 12.3123i | 0.328240 | − | 0.568528i | ||||
\(470\) | −13.1697 | + | 12.3377i | −0.607475 | + | 0.569096i | ||||
\(471\) | 21.9775 | 1.01267 | ||||||||
\(472\) | 3.25086 | + | 1.87689i | 0.149633 | + | 0.0863907i | ||||
\(473\) | −1.32067 | −0.0607246 | ||||||||
\(474\) | −6.08942 | − | 10.5472i | −0.279696 | − | 0.484448i | ||||
\(475\) | 19.6007 | + | 1.28008i | 0.899343 | + | 0.0587340i | ||||
\(476\) | −9.55637 | + | 5.51737i | −0.438015 | + | 0.252888i | ||||
\(477\) | 9.03833 | − | 5.21828i | 0.413837 | − | 0.238929i | ||||
\(478\) | −21.1400 | + | 12.2052i | −0.966921 | + | 0.558252i | ||||
\(479\) | 12.1338 | + | 7.00544i | 0.554407 | + | 0.320087i | 0.750897 | − | 0.660419i | \(-0.229621\pi\) |
−0.196491 | + | 0.980506i | \(0.562955\pi\) | |||||||
\(480\) | −1.63185 | + | 1.52875i | −0.0744832 | + | 0.0697776i | ||||
\(481\) | −0.393178 | + | 20.0126i | −0.0179274 | + | 0.912497i | ||||
\(482\) | − | 11.8674i | − | 0.540543i | ||||||
\(483\) | −4.98832 | + | 8.64002i | −0.226976 | + | 0.393135i | ||||
\(484\) | 4.30233 | + | 7.45186i | 0.195561 | + | 0.338721i | ||||
\(485\) | −10.8187 | + | 35.6795i | −0.491251 | + | 1.62012i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 22.1521 | 1.00381 | 0.501903 | − | 0.864924i | \(-0.332633\pi\) | ||||
0.501903 | + | 0.864924i | \(0.332633\pi\) | |||||||
\(488\) | −0.355641 | + | 0.205329i | −0.0160991 | + | 0.00929482i | ||||
\(489\) | − | 12.5565i | − | 0.567826i | ||||||
\(490\) | 8.72069 | − | 2.03446i | 0.393961 | − | 0.0919075i | ||||
\(491\) | 17.8500 | 0.805561 | 0.402780 | − | 0.915297i | \(-0.368044\pi\) | ||||
0.402780 | + | 0.915297i | \(0.368044\pi\) | |||||||
\(492\) | 1.45383i | 0.0655437i | ||||||||
\(493\) | −3.97322 | − | 2.29394i | −0.178945 | − | 0.103314i | ||||
\(494\) | −11.1955 | + | 6.46373i | −0.503710 | + | 0.290817i | ||||
\(495\) | −2.36603 | − | 2.52559i | −0.106345 | − | 0.113517i | ||||
\(496\) | 7.83077 | + | 4.52110i | 0.351612 | + | 0.203003i | ||||
\(497\) | 6.88650 | + | 3.97592i | 0.308902 | + | 0.178344i | ||||
\(498\) | 5.91076 | − | 10.2377i | 0.264867 | − | 0.458764i | ||||
\(499\) | −6.41175 | + | 3.70182i | −0.287029 | + | 0.165716i | −0.636601 | − | 0.771193i | \(-0.719660\pi\) |
0.349572 | + | 0.936909i | \(0.386327\pi\) | |||||||
\(500\) | −10.4651 | − | 3.93459i | −0.468015 | − | 0.175960i | ||||
\(501\) | −5.79053 | − | 3.34316i | −0.258702 | − | 0.149362i | ||||
\(502\) | 10.1752 | + | 5.87467i | 0.454142 | + | 0.262199i | ||||
\(503\) | 5.60295 | − | 9.70459i | 0.249823 | − | 0.432706i | −0.713653 | − | 0.700499i | \(-0.752961\pi\) |
0.963477 | + | 0.267793i | \(0.0862942\pi\) | |||||||
\(504\) | − | 1.73068i | − | 0.0770908i | ||||||
\(505\) | −1.66163 | + | 5.47997i | −0.0739415 | + | 0.243855i | ||||
\(506\) | 4.46087 | − | 7.72645i | 0.198310 | − | 0.343483i | ||||
\(507\) | 2.17136i | 0.0964333i | ||||||||
\(508\) | 9.90318i | 0.439382i | ||||||||
\(509\) | −4.33262 | + | 7.50432i | −0.192040 | + | 0.332623i | −0.945926 | − | 0.324382i | \(-0.894844\pi\) |
0.753886 | + | 0.657005i | \(0.228177\pi\) | |||||||
\(510\) | 10.4046 | − | 9.74723i | 0.460722 | − | 0.431614i | ||||
\(511\) | −4.76515 | − | 8.25349i | −0.210798 | − | 0.365113i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.96425 | − | 3.40218i | −0.0867237 | − | 0.150210i | ||||
\(514\) | 7.56386 | + | 13.1010i | 0.333627 | + | 0.577860i | ||||
\(515\) | −2.47780 | + | 8.17167i | −0.109185 | + | 0.360087i | ||||
\(516\) | 0.738998 | + | 0.426660i | 0.0325326 | + | 0.0187827i | ||||
\(517\) | 12.4905i | 0.549333i | ||||||||
\(518\) | 5.44174 | − | 9.01179i | 0.239096 | − | 0.395955i | ||||
\(519\) | 3.65632 | 0.160495 | ||||||||
\(520\) | 7.16579 | − | 1.67172i | 0.314241 | − | 0.0733096i | ||||
\(521\) | 14.1102 | + | 24.4396i | 0.618180 | + | 1.07072i | 0.989818 | + | 0.142342i | \(0.0454632\pi\) |
−0.371637 | + | 0.928378i | \(0.621203\pi\) | |||||||
\(522\) | 0.623158 | − | 0.359780i | 0.0272749 | − | 0.0157472i | ||||
\(523\) | 16.0303 | + | 27.7652i | 0.700954 | + | 1.21409i | 0.968132 | + | 0.250441i | \(0.0805756\pi\) |
−0.267178 | + | 0.963647i | \(0.586091\pi\) | |||||||
\(524\) | 12.4807i | 0.545220i | ||||||||
\(525\) | 7.76012 | − | 3.82913i | 0.338679 | − | 0.167117i | ||||
\(526\) | − | 14.3294i | − | 0.624791i | ||||||
\(527\) | −49.9285 | − | 28.8263i | −2.17492 | − | 1.25569i | ||||
\(528\) | 1.54769i | 0.0673544i | ||||||||
\(529\) | 10.2302 | 0.444790 | ||||||||
\(530\) | −5.30192 | − | 22.7266i | −0.230301 | − | 0.987181i | ||||
\(531\) | 3.25086 | − | 1.87689i | 0.141075 | − | 0.0814499i | ||||
\(532\) | 6.79898 | 0.294773 | ||||||||
\(533\) | 2.39205 | − | 4.14316i | 0.103611 | − | 0.179460i | ||||
\(534\) | −4.69396 | + | 8.13018i | −0.203128 | + | 0.351827i | ||||
\(535\) | 7.53062 | + | 32.2799i | 0.325577 | + | 1.39558i | ||||
\(536\) | 7.11411 | − | 4.10733i | 0.307283 | − | 0.177410i | ||||
\(537\) | 11.1167 | + | 19.2547i | 0.479720 | + | 0.830900i | ||||
\(538\) | 2.40862 | − | 4.17186i | 0.103843 | − | 0.179861i | ||||
\(539\) | 3.09904 | − | 5.36769i | 0.133485 | − | 0.231203i | ||||
\(540\) | 0.508014 | + | 2.17760i | 0.0218614 | + | 0.0937088i | ||||
\(541\) | 34.9514i | 1.50268i | 0.659917 | + | 0.751339i | \(0.270592\pi\) | ||||
−0.659917 | + | 0.751339i | \(0.729408\pi\) | |||||||
\(542\) | 3.92526 | + | 6.79875i | 0.168604 | + | 0.292031i | ||||
\(543\) | −8.61082 | − | 4.97146i | −0.369526 | − | 0.213346i | ||||
\(544\) | −6.37594 | −0.273366 | ||||||||
\(545\) | −3.62804 | + | 3.39883i | −0.155408 | + | 0.145590i | ||||
\(546\) | −2.84757 | + | 4.93214i | −0.121865 | + | 0.211076i | ||||
\(547\) | −8.96803 | −0.383445 | −0.191723 | − | 0.981449i | \(-0.561407\pi\) | ||||
−0.191723 | + | 0.981449i | \(0.561407\pi\) | |||||||
\(548\) | −10.0099 | + | 5.77924i | −0.427603 | + | 0.246877i | ||||
\(549\) | 0.410659i | 0.0175265i | ||||||||
\(550\) | −6.93959 | + | 3.42425i | −0.295905 | + | 0.146011i | ||||
\(551\) | 1.41340 | + | 2.44807i | 0.0602127 | + | 0.104291i | ||||
\(552\) | −4.99226 | + | 2.88228i | −0.212485 | + | 0.122678i | ||||
\(553\) | 10.5389 | − | 18.2538i | 0.448158 | − | 0.776232i | ||||
\(554\) | 8.14988 | 0.346255 | ||||||||
\(555\) | −4.20168 | + | 12.9362i | −0.178352 | + | 0.549112i | ||||
\(556\) | −2.51440 | −0.106634 | ||||||||
\(557\) | 0.0853571 | − | 0.147843i | 0.00361670 | − | 0.00626430i | −0.864211 | − | 0.503129i | \(-0.832182\pi\) |
0.867828 | + | 0.496865i | \(0.165515\pi\) | |||||||
\(558\) | 7.83077 | − | 4.52110i | 0.331503 | − | 0.191393i | ||||
\(559\) | −1.40401 | − | 2.43181i | −0.0593832 | − | 0.102855i | ||||
\(560\) | −3.70342 | − | 1.12295i | −0.156498 | − | 0.0474531i | ||||
\(561\) | − | 9.86796i | − | 0.416626i | ||||||
\(562\) | 26.6881 | − | 15.4084i | 1.12577 | − | 0.649964i | ||||
\(563\) | −34.8483 | −1.46868 | −0.734340 | − | 0.678782i | \(-0.762508\pi\) | ||||
−0.734340 | + | 0.678782i | \(0.762508\pi\) | |||||||
\(564\) | 4.03523 | − | 6.98922i | 0.169914 | − | 0.294299i | ||||
\(565\) | −29.8989 | − | 31.9152i | −1.25786 | − | 1.34268i | ||||
\(566\) | −7.26025 | −0.305171 | ||||||||
\(567\) | −1.49882 | − | 0.865342i | −0.0629444 | − | 0.0363409i | ||||
\(568\) | 2.29731 | + | 3.97906i | 0.0963931 | + | 0.166958i | ||||
\(569\) | 33.1753i | 1.39078i | 0.718632 | + | 0.695391i | \(0.244769\pi\) | ||||
−0.718632 | + | 0.695391i | \(0.755231\pi\) | |||||||
\(570\) | −8.55467 | + | 1.99573i | −0.358316 | + | 0.0835919i | ||||
\(571\) | 11.2302 | − | 19.4512i | 0.469967 | − | 0.814007i | −0.529443 | − | 0.848346i | \(-0.677599\pi\) |
0.999410 | + | 0.0343382i | \(0.0109324\pi\) | |||||||
\(572\) | 2.54648 | − | 4.41063i | 0.106474 | − | 0.184418i | ||||
\(573\) | −6.36142 | − | 11.0183i | −0.265752 | − | 0.460296i | ||||
\(574\) | −2.17903 | + | 1.25806i | −0.0909507 | + | 0.0525104i | ||||
\(575\) | −23.9691 | − | 16.0075i | −0.999579 | − | 0.667558i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 18.1519 | − | 31.4399i | 0.755672 | − | 1.30886i | −0.189368 | − | 0.981906i | \(-0.560644\pi\) |
0.945040 | − | 0.326956i | \(-0.106023\pi\) | |||||||
\(578\) | 23.6527 | 0.983821 | ||||||||
\(579\) | 6.22801 | − | 3.59574i | 0.258827 | − | 0.149434i | ||||
\(580\) | −0.365547 | − | 1.56691i | −0.0151785 | − | 0.0650625i | ||||
\(581\) | 20.4593 | 0.848795 | ||||||||
\(582\) | − | 16.6738i | − | 0.691150i | ||||||
\(583\) | −13.9885 | − | 8.07626i | −0.579345 | − | 0.334485i | ||||
\(584\) | − | 5.50667i | − | 0.227868i | ||||||
\(585\) | 2.13515 | − | 7.04162i | 0.0882775 | − | 0.291135i | ||||
\(586\) | − | 31.3860i | − | 1.29655i | ||||||
\(587\) | −16.9255 | − | 29.3157i | −0.698588 | − | 1.20999i | −0.968956 | − | 0.247233i | \(-0.920479\pi\) |
0.270368 | − | 0.962757i | \(-0.412855\pi\) | |||||||
\(588\) | −3.46820 | + | 2.00237i | −0.143026 | + | 0.0825762i | ||||
\(589\) | 17.7611 | + | 30.7631i | 0.731834 | + | 1.26757i | ||||
\(590\) | −1.90697 | − | 8.17420i | −0.0785086 | − | 0.336526i | ||||
\(591\) | −4.98550 | −0.205076 | ||||||||
\(592\) | 5.32655 | − | 2.93732i | 0.218920 | − | 0.120723i | ||||
\(593\) | − | 29.3602i | − | 1.20568i | −0.797862 | − | 0.602840i | \(-0.794036\pi\) | ||
0.797862 | − | 0.602840i | \(-0.205964\pi\) | |||||||
\(594\) | 1.34034 | + | 0.773843i | 0.0549947 | + | 0.0317512i | ||||
\(595\) | 23.6128 | + | 7.15984i | 0.968031 | + | 0.293525i | ||||
\(596\) | 6.26099 | + | 10.8444i | 0.256460 | + | 0.444202i | ||||
\(597\) | −3.97013 | − | 6.87646i | −0.162486 | − | 0.281435i | ||||
\(598\) | 18.9694 | 0.775716 | ||||||||
\(599\) | 4.83015 | + | 8.36606i | 0.197354 | + | 0.341828i | 0.947670 | − | 0.319252i | \(-0.103432\pi\) |
−0.750315 | + | 0.661080i | \(0.770098\pi\) | |||||||
\(600\) | 4.98937 | + | 0.325844i | 0.203690 | + | 0.0133025i | ||||
\(601\) | 19.3609 | − | 33.5341i | 0.789748 | − | 1.36788i | −0.136373 | − | 0.990658i | \(-0.543544\pi\) |
0.926121 | − | 0.377226i | \(-0.123122\pi\) | |||||||
\(602\) | 1.47683i | 0.0601910i | ||||||||
\(603\) | − | 8.21467i | − | 0.334527i | ||||||
\(604\) | −9.02188 | + | 15.6264i | −0.367095 | + | 0.635828i | ||||
\(605\) | 5.58309 | − | 18.4128i | 0.226985 | − | 0.748586i | ||||
\(606\) | − | 2.56090i | − | 0.104030i | ||||||
\(607\) | −11.2085 | + | 19.4138i | −0.454941 | + | 0.787980i | −0.998685 | − | 0.0512708i | \(-0.983673\pi\) |
0.543744 | + | 0.839251i | \(0.317006\pi\) | |||||||
\(608\) | 3.40218 | + | 1.96425i | 0.137976 | + | 0.0796608i | ||||
\(609\) | 1.07849 | + | 0.622666i | 0.0437026 | + | 0.0252317i | ||||
\(610\) | 0.878752 | + | 0.266454i | 0.0355796 | + | 0.0107884i | ||||
\(611\) | −22.9994 | + | 13.2787i | −0.930455 | + | 0.537198i | ||||
\(612\) | −3.18797 | + | 5.52173i | −0.128866 | + | 0.223203i | ||||
\(613\) | 23.8394 | + | 13.7637i | 0.962863 | + | 0.555909i | 0.897053 | − | 0.441923i | \(-0.145703\pi\) |
0.0658102 | + | 0.997832i | \(0.479037\pi\) | |||||||
\(614\) | 16.6352 | + | 9.60435i | 0.671343 | + | 0.387600i | ||||
\(615\) | 2.37243 | − | 2.22254i | 0.0956655 | − | 0.0896216i | ||||
\(616\) | −2.31970 | + | 1.33928i | −0.0934633 | + | 0.0539611i | ||||
\(617\) | −12.3634 | − | 7.13803i | −0.497733 | − | 0.287366i | 0.230044 | − | 0.973180i | \(-0.426113\pi\) |
−0.727777 | + | 0.685814i | \(0.759446\pi\) | |||||||
\(618\) | − | 3.81879i | − | 0.153614i | ||||||
\(619\) | −13.8734 | −0.557618 | −0.278809 | − | 0.960347i | \(-0.589940\pi\) | ||||
−0.278809 | + | 0.960347i | \(0.589940\pi\) | |||||||
\(620\) | −4.59356 | − | 19.6902i | −0.184482 | − | 0.790779i | ||||
\(621\) | 5.76456i | 0.231324i | ||||||||
\(622\) | −15.8871 | + | 9.17242i | −0.637015 | + | 0.367781i | ||||
\(623\) | −16.2475 | −0.650944 | ||||||||
\(624\) | −2.84982 | + | 1.64535i | −0.114084 | + | 0.0658665i | ||||
\(625\) | 9.57793 | + | 23.0925i | 0.383117 | + | 0.923700i | ||||
\(626\) | 13.4284 | + | 23.2587i | 0.536707 | + | 0.929603i | ||||
\(627\) | −3.04004 | + | 5.26550i | −0.121408 | + | 0.210284i | ||||
\(628\) | 21.9775i | 0.876999i | ||||||||
\(629\) | −33.9618 | + | 18.7282i | −1.35415 | + | 0.746742i | ||||
\(630\) | −2.82421 | + | 2.64578i | −0.112519 | + | 0.105411i | ||||
\(631\) | −20.7095 | − | 11.9566i | −0.824432 | − | 0.475986i | 0.0275102 | − | 0.999622i | \(-0.491242\pi\) |
−0.851943 | + | 0.523635i | \(0.824575\pi\) | |||||||
\(632\) | 10.5472 | − | 6.08942i | 0.419545 | − | 0.242224i | ||||
\(633\) | −10.1910 | + | 5.88378i | −0.405056 | + | 0.233859i | ||||
\(634\) | 19.7427 | − | 11.3984i | 0.784082 | − | 0.452690i | ||||
\(635\) | 16.1605 | − | 15.1395i | 0.641308 | − | 0.600792i | ||||
\(636\) | 5.21828 | + | 9.03833i | 0.206918 | + | 0.358393i | ||||
\(637\) | 13.1783 | 0.522145 | ||||||||
\(638\) | −0.964453 | − | 0.556827i | −0.0381831 | − | 0.0220450i | ||||
\(639\) | 4.59462 | 0.181761 | ||||||||
\(640\) | −1.52875 | − | 1.63185i | −0.0604292 | − | 0.0645044i | ||||
\(641\) | −6.76676 | + | 11.7204i | −0.267271 | + | 0.462927i | −0.968156 | − | 0.250347i | \(-0.919455\pi\) |
0.700885 | + | 0.713274i | \(0.252789\pi\) | |||||||
\(642\) | −7.41182 | − | 12.8377i | −0.292521 | − | 0.506662i | ||||
\(643\) | −29.4508 | −1.16143 | −0.580713 | − | 0.814108i | \(-0.697226\pi\) | ||||
−0.580713 | + | 0.814108i | \(0.697226\pi\) | |||||||
\(644\) | −8.64002 | − | 4.98832i | −0.340464 | − | 0.196567i | ||||
\(645\) | −0.433499 | − | 1.85819i | −0.0170690 | − | 0.0731661i | ||||
\(646\) | −21.6921 | − | 12.5239i | −0.853464 | − | 0.492748i | ||||
\(647\) | 22.4281 | + | 38.8466i | 0.881739 | + | 1.52722i | 0.849406 | + | 0.527740i | \(0.176960\pi\) |
0.0323330 | + | 0.999477i | \(0.489706\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −5.03132 | − | 2.90483i | −0.197496 | − | 0.114025i | ||||
\(650\) | −13.6827 | − | 9.13784i | −0.536679 | − | 0.358415i | ||||
\(651\) | 13.5526 | + | 7.82459i | 0.531168 | + | 0.306670i | ||||
\(652\) | 12.5565 | 0.491752 | ||||||||
\(653\) | 7.49053 | + | 12.9740i | 0.293127 | + | 0.507711i | 0.974547 | − | 0.224181i | \(-0.0719707\pi\) |
−0.681420 | + | 0.731892i | \(0.738637\pi\) | |||||||
\(654\) | 1.11164 | − | 1.92541i | 0.0434684 | − | 0.0752894i | ||||
\(655\) | 20.3665 | − | 19.0798i | 0.795786 | − | 0.745510i | ||||
\(656\) | −1.45383 | −0.0567625 | ||||||||
\(657\) | −4.76892 | − | 2.75334i | −0.186053 | − | 0.107418i | ||||
\(658\) | 13.9674 | 0.544506 | ||||||||
\(659\) | 17.7987 | + | 30.8282i | 0.693338 | + | 1.20090i | 0.970738 | + | 0.240142i | \(0.0771939\pi\) |
−0.277400 | + | 0.960754i | \(0.589473\pi\) | |||||||
\(660\) | 2.52559 | − | 2.36603i | 0.0983083 | − | 0.0920975i | ||||
\(661\) | −3.99182 | + | 2.30468i | −0.155264 | + | 0.0896417i | −0.575619 | − | 0.817718i | \(-0.695239\pi\) |
0.420355 | + | 0.907360i | \(0.361906\pi\) | |||||||
\(662\) | 0.719083 | − | 0.415163i | 0.0279480 | − | 0.0161358i | ||||
\(663\) | 18.1703 | − | 10.4906i | 0.705676 | − | 0.407422i | ||||
\(664\) | 10.2377 | + | 5.91076i | 0.397301 | + | 0.229382i | ||||
\(665\) | −10.3939 | − | 11.0949i | −0.403060 | − | 0.430242i | ||||
\(666\) | 0.119482 | − | 6.08159i | 0.00462984 | − | 0.235657i | ||||
\(667\) | − | 4.14795i | − | 0.160609i | ||||||
\(668\) | 3.34316 | − | 5.79053i | 0.129351 | − | 0.224042i | ||||
\(669\) | 8.37030 | + | 14.4978i | 0.323615 | + | 0.560517i | ||||
\(670\) | −17.5782 | − | 5.33005i | −0.679107 | − | 0.205918i | ||||
\(671\) | 0.550421 | − | 0.317786i | 0.0212488 | − | 0.0122680i | ||||
\(672\) | 1.73068 | 0.0667626 | ||||||||
\(673\) | 19.1175 | − | 11.0375i | 0.736926 | − | 0.425464i | −0.0840245 | − | 0.996464i | \(-0.526777\pi\) |
0.820951 | + | 0.570999i | \(0.193444\pi\) | |||||||
\(674\) | − | 29.7640i | − | 1.14647i | ||||||
\(675\) | 2.77687 | − | 4.15800i | 0.106882 | − | 0.160042i | ||||
\(676\) | −2.17136 | −0.0835137 | ||||||||
\(677\) | 16.0360i | 0.616312i | 0.951336 | + | 0.308156i | \(0.0997119\pi\) | ||||
−0.951336 | + | 0.308156i | \(0.900288\pi\) | |||||||
\(678\) | 16.9375 | + | 9.77887i | 0.650481 | + | 0.375555i | ||||
\(679\) | 24.9909 | − | 14.4285i | 0.959063 | − | 0.553715i | ||||
\(680\) | 9.74723 | + | 10.4046i | 0.373789 | + | 0.398997i | ||||
\(681\) | −2.61584 | − | 1.51026i | −0.100239 | − | 0.0578732i | ||||
\(682\) | −12.1196 | − | 6.99724i | −0.464083 | − | 0.267938i | ||||
\(683\) | 6.53813 | − | 11.3244i | 0.250175 | − | 0.433315i | −0.713399 | − | 0.700758i | \(-0.752845\pi\) |
0.963574 | + | 0.267443i | \(0.0861787\pi\) | |||||||
\(684\) | 3.40218 | − | 1.96425i | 0.130085 | − | 0.0751049i | ||||
\(685\) | 24.7335 | + | 7.49966i | 0.945020 | + | 0.286547i | ||||
\(686\) | −16.4941 | − | 9.52286i | −0.629747 | − | 0.363584i | ||||
\(687\) | −0.492123 | − | 0.284128i | −0.0187757 | − | 0.0108401i | ||||
\(688\) | −0.426660 | + | 0.738998i | −0.0162663 | + | 0.0281740i | ||||
\(689\) | − | 34.3435i | − | 1.30838i | ||||||
\(690\) | 12.3354 | + | 3.74031i | 0.469599 | + | 0.142391i | ||||
\(691\) | 21.9067 | − | 37.9435i | 0.833369 | − | 1.44344i | −0.0619818 | − | 0.998077i | \(-0.519742\pi\) |
0.895351 | − | 0.445361i | \(-0.146925\pi\) | |||||||
\(692\) | 3.65632i | 0.138993i | ||||||||
\(693\) | 2.67856i | 0.101750i | ||||||||
\(694\) | −3.13064 | + | 5.42242i | −0.118837 | + | 0.205832i | ||||
\(695\) | 3.84388 | + | 4.10311i | 0.145807 | + | 0.155640i | ||||
\(696\) | 0.359780 | + | 0.623158i | 0.0136374 | + | 0.0236207i | ||||
\(697\) | 9.26954 | 0.351109 | ||||||||
\(698\) | 10.1013 | + | 17.4960i | 0.382341 | + | 0.662234i | ||||
\(699\) | 2.81121 | + | 4.86916i | 0.106330 | + | 0.184169i | ||||
\(700\) | 3.82913 | + | 7.76012i | 0.144728 | + | 0.293305i | ||||
\(701\) | 7.54537 | + | 4.35632i | 0.284985 | + | 0.164536i | 0.635678 | − | 0.771954i | \(-0.280721\pi\) |
−0.350693 | + | 0.936490i | \(0.614054\pi\) | |||||||
\(702\) | 3.29069i | 0.124199i | ||||||||
\(703\) | 23.8915 | + | 0.469385i | 0.901085 | + | 0.0177032i | ||||
\(704\) | −1.54769 | −0.0583306 | ||||||||
\(705\) | −17.5742 | + | 4.09990i | −0.661882 | + | 0.154411i | ||||
\(706\) | 4.65889 | + | 8.06944i | 0.175340 | + | 0.303697i | ||||
\(707\) | 3.83832 | − | 2.21606i | 0.144355 | − | 0.0833434i | ||||
\(708\) | 1.87689 | + | 3.25086i | 0.0705377 | + | 0.122175i | ||||
\(709\) | − | 39.6479i | − | 1.48901i | −0.667618 | − | 0.744504i | \(-0.732686\pi\) | ||
0.667618 | − | 0.744504i | \(-0.267314\pi\) | |||||||
\(710\) | 2.98120 | − | 9.83185i | 0.111882 | − | 0.368983i | ||||
\(711\) | − | 12.1788i | − | 0.456742i | ||||||
\(712\) | −8.13018 | − | 4.69396i | −0.304692 | − | 0.175914i | ||||
\(713\) | − | 52.1243i | − | 1.95207i | ||||||
\(714\) | −11.0347 | −0.412965 | ||||||||
\(715\) | −11.0904 | + | 2.58729i | −0.414758 | + | 0.0967592i | ||||
\(716\) | −19.2547 | + | 11.1167i | −0.719581 | + | 0.415450i | ||||
\(717\) | −24.4104 | −0.911621 | ||||||||
\(718\) | 8.67042 | − | 15.0176i | 0.323577 | − | 0.560452i | ||||
\(719\) | 7.14786 | − | 12.3805i | 0.266570 | − | 0.461713i | −0.701404 | − | 0.712764i | \(-0.747443\pi\) |
0.967974 | + | 0.251051i | \(0.0807762\pi\) | |||||||
\(720\) | −2.17760 | + | 0.508014i | −0.0811542 | + | 0.0189326i | ||||
\(721\) | 5.72366 | − | 3.30456i | 0.213160 | − | 0.123068i | ||||
\(722\) | −1.78346 | − | 3.08905i | −0.0663736 | − | 0.114962i | ||||
\(723\) | 5.93368 | − | 10.2774i | 0.220676 | − | 0.382222i | ||||
\(724\) | 4.97146 | − | 8.61082i | 0.184763 | − | 0.320019i | ||||
\(725\) | −1.99813 | + | 2.99193i | −0.0742087 | + | 0.111118i | ||||
\(726\) | 8.60467i | 0.319349i | ||||||||
\(727\) | −12.5801 | − | 21.7894i | −0.466572 | − | 0.808126i | 0.532699 | − | 0.846305i | \(-0.321178\pi\) |
−0.999271 | + | 0.0381788i | \(0.987844\pi\) | |||||||
\(728\) | −4.93214 | − | 2.84757i | −0.182797 | − | 0.105538i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −8.98604 | + | 8.41833i | −0.332588 | + | 0.311576i | ||||
\(731\) | 2.72036 | − | 4.71181i | 0.100616 | − | 0.174272i | ||||
\(732\) | −0.410659 | −0.0151784 | ||||||||
\(733\) | −23.8349 | + | 13.7611i | −0.880364 | + | 0.508278i | −0.870778 | − | 0.491676i | \(-0.836385\pi\) |
−0.00958538 | + | 0.999954i | \(0.503051\pi\) | |||||||
\(734\) | 27.9136i | 1.03031i | ||||||||
\(735\) | 8.56957 | + | 2.59845i | 0.316093 | + | 0.0958453i | ||||
\(736\) | −2.88228 | − | 4.99226i | −0.106242 | − | 0.184017i | ||||
\(737\) | −11.0104 | + | 6.35687i | −0.405574 | + | 0.234158i | ||||
\(738\) | −0.726915 | + | 1.25905i | −0.0267581 | + | 0.0463464i | ||||
\(739\) | −36.0740 | −1.32700 | −0.663502 | − | 0.748174i | \(-0.730931\pi\) | ||||
−0.663502 | + | 0.748174i | \(0.730931\pi\) | |||||||
\(740\) | −12.9362 | − | 4.20168i | −0.475545 | − | 0.154457i | ||||
\(741\) | −12.9275 | −0.474902 | ||||||||
\(742\) | −9.03120 | + | 15.6425i | −0.331546 | + | 0.574254i | ||||
\(743\) | −1.98536 | + | 1.14625i | −0.0728357 | + | 0.0420517i | −0.535976 | − | 0.844234i | \(-0.680056\pi\) |
0.463140 | + | 0.886285i | \(0.346723\pi\) | |||||||
\(744\) | 4.52110 | + | 7.83077i | 0.165751 | + | 0.287090i | ||||
\(745\) | 8.12482 | − | 26.7953i | 0.297670 | − | 0.981703i | ||||
\(746\) | 3.84026i | 0.140602i | ||||||||
\(747\) | 10.2377 | − | 5.91076i | 0.374579 | − | 0.216263i | ||||
\(748\) | 9.86796 | 0.360808 | ||||||||
\(749\) | 12.8275 | − | 22.2179i | 0.468708 | − | 0.811825i | ||||
\(750\) | −7.09578 | − | 8.64002i | −0.259101 | − | 0.315489i | ||||
\(751\) | 11.1112 | 0.405453 | 0.202726 | − | 0.979235i | \(-0.435020\pi\) | ||||
0.202726 | + | 0.979235i | \(0.435020\pi\) | |||||||
\(752\) | 6.98922 | + | 4.03523i | 0.254871 | + | 0.147150i | ||||
\(753\) | 5.87467 | + | 10.1752i | 0.214085 | + | 0.370806i | ||||
\(754\) | − | 2.36785i | − | 0.0862321i | ||||||
\(755\) | 39.2920 | − | 9.16648i | 1.42998 | − | 0.333602i | ||||
\(756\) | 0.865342 | − | 1.49882i | 0.0314722 | − | 0.0545114i | ||||
\(757\) | −10.4100 | + | 18.0307i | −0.378359 | + | 0.655337i | −0.990824 | − | 0.135161i | \(-0.956845\pi\) |
0.612465 | + | 0.790498i | \(0.290178\pi\) | |||||||
\(758\) | −9.96232 | − | 17.2553i | −0.361848 | − | 0.626739i | ||||
\(759\) | 7.72645 | − | 4.46087i | 0.280452 | − | 0.161919i | ||||
\(760\) | −1.99573 | − | 8.55467i | −0.0723927 | − | 0.310311i | ||||
\(761\) | −21.8158 | + | 37.7861i | −0.790822 | + | 1.36974i | 0.134636 | + | 0.990895i | \(0.457013\pi\) |
−0.925458 | + | 0.378849i | \(0.876320\pi\) | |||||||
\(762\) | −4.95159 | + | 8.57640i | −0.179377 | + | 0.310690i | ||||
\(763\) | 3.84778 | 0.139299 | ||||||||
\(764\) | 11.0183 | − | 6.36142i | 0.398628 | − | 0.230148i | ||||
\(765\) | 13.8842 | − | 3.23907i | 0.501985 | − | 0.117109i | ||||
\(766\) | −17.9818 | −0.649709 | ||||||||
\(767\) | − | 12.3525i | − | 0.446023i | ||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 8.96772i | 0.323384i | 0.986841 | + | 0.161692i | \(0.0516951\pi\) | ||||
−0.986841 | + | 0.161692i | \(0.948305\pi\) | |||||||
\(770\) | 5.73174 | + | 1.73797i | 0.206557 | + | 0.0626320i | ||||
\(771\) | 15.1277i | 0.544811i | ||||||||
\(772\) | 3.59574 | + | 6.22801i | 0.129414 | + | 0.224151i | ||||
\(773\) | −20.2283 | + | 11.6788i | −0.727560 | + | 0.420057i | −0.817529 | − | 0.575887i | \(-0.804657\pi\) |
0.0899686 | + | 0.995945i | \(0.471323\pi\) | |||||||
\(774\) | 0.426660 | + | 0.738998i | 0.0153360 | + | 0.0265627i | ||||
\(775\) | −25.1090 | + | 37.5974i | −0.901943 | + | 1.35054i | ||||
\(776\) | 16.6738 | 0.598553 | ||||||||
\(777\) | 9.21858 | − | 5.08357i | 0.330715 | − | 0.182372i | ||||
\(778\) | 1.46923i | 0.0526746i | ||||||||
\(779\) | −4.94619 | − | 2.85568i | −0.177216 | − | 0.102315i | ||||
\(780\) | 7.04162 | + | 2.13515i | 0.252130 | + | 0.0764506i | ||||
\(781\) | −3.55552 | − | 6.15834i | −0.127226 | − | 0.220363i | ||||
\(782\) | 18.3773 | + | 31.8304i | 0.657170 | + | 1.13825i | ||||
\(783\) | 0.719561 | 0.0257150 | ||||||||
\(784\) | −2.00237 | − | 3.46820i | −0.0715131 | − | 0.123864i | ||||
\(785\) | 35.8639 | − | 33.5982i | 1.28004 | − | 1.19917i | ||||
\(786\) | −6.24033 | + | 10.8086i | −0.222585 | + | 0.385529i | ||||
\(787\) | 40.1034i | 1.42953i | 0.699364 | + | 0.714765i | \(0.253466\pi\) | ||||
−0.699364 | + | 0.714765i | \(0.746534\pi\) | |||||||
\(788\) | − | 4.98550i | − | 0.177601i | ||||||
\(789\) | 7.16469 | − | 12.4096i | 0.255070 | − | 0.441794i | ||||
\(790\) | −26.0610 | − | 7.90218i | −0.927209 | − | 0.281147i | ||||
\(791\) | 33.8483i | 1.20351i | ||||||||
\(792\) | −0.773843 | + | 1.34034i | −0.0274973 | + | 0.0476268i | ||||
\(793\) | 1.17030 | + | 0.675675i | 0.0415587 | + | 0.0239939i | ||||
\(794\) | 26.4237 | + | 15.2557i | 0.937742 | + | 0.541406i | ||||
\(795\) | 6.77171 | − | 22.3328i | 0.240168 | − | 0.792062i | ||||
\(796\) | 6.87646 | − | 3.97013i | 0.243730 | − | 0.140717i | ||||
\(797\) | −12.5578 | + | 21.7508i | −0.444821 | + | 0.770453i | −0.998040 | − | 0.0625830i | \(-0.980066\pi\) |
0.553218 | + | 0.833036i | \(0.313400\pi\) | |||||||
\(798\) | 5.88809 | + | 3.39949i | 0.208436 | + | 0.120341i | ||||
\(799\) | −44.5629 | − | 25.7284i | −1.57652 | − | 0.910205i | ||||
\(800\) | −0.325844 | + | 4.98937i | −0.0115203 | + | 0.176401i | ||||
\(801\) | −8.13018 | + | 4.69396i | −0.287266 | + | 0.165853i | ||||
\(802\) | −18.5290 | − | 10.6977i | −0.654281 | − | 0.377749i | ||||
\(803\) | 8.52260i | 0.300756i | ||||||||
\(804\) | 8.21467 | 0.289709 | ||||||||
\(805\) | 5.06827 | + | 21.7251i | 0.178633 | + | 0.765708i | ||||
\(806\) | − | 29.7551i | − | 1.04808i | ||||||
\(807\) | 4.17186 | − | 2.40862i | 0.146856 | − | 0.0847875i | ||||
\(808\) | 2.56090 | 0.0900922 | ||||||||
\(809\) | −30.4412 | + | 17.5752i | −1.07025 | + | 0.617912i | −0.928251 | − | 0.371954i | \(-0.878688\pi\) |
−0.142004 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(810\) | −0.648845 | + | 2.13986i | −0.0227981 | + | 0.0751870i | ||||
\(811\) | −14.0142 | − | 24.2733i | −0.492106 | − | 0.852352i | 0.507853 | − | 0.861444i | \(-0.330439\pi\) |
−0.999959 | + | 0.00909185i | \(0.997106\pi\) | |||||||
\(812\) | −0.622666 | + | 1.07849i | −0.0218513 | + | 0.0378476i | ||||
\(813\) | 7.85052i | 0.275330i | ||||||||
\(814\) | −8.24383 | + | 4.54605i | −0.288946 | + | 0.159339i | ||||
\(815\) | −19.1958 | − | 20.4903i | −0.672400 | − | 0.717745i | ||||
\(816\) | −5.52173 | − | 3.18797i | −0.193299 | − | 0.111601i | ||||
\(817\) | −2.90315 | + | 1.67613i | −0.101568 | + | 0.0586405i | ||||
\(818\) | −29.3220 | + | 16.9291i | −1.02522 | + | 0.591912i | ||||
\(819\) | −4.93214 | + | 2.84757i | −0.172343 | + | 0.0995022i | ||||
\(820\) | 2.22254 | + | 2.37243i | 0.0776146 | + | 0.0828488i | ||||
\(821\) | 10.0215 | + | 17.3577i | 0.349752 | + | 0.605788i | 0.986205 | − | 0.165527i | \(-0.0529326\pi\) |
−0.636453 | + | 0.771315i | \(0.719599\pi\) | |||||||
\(822\) | −11.5585 | −0.403148 | ||||||||
\(823\) | −13.6220 | − | 7.86465i | −0.474832 | − | 0.274144i | 0.243428 | − | 0.969919i | \(-0.421728\pi\) |
−0.718260 | + | 0.695775i | \(0.755061\pi\) | |||||||
\(824\) | 3.81879 | 0.133034 | ||||||||
\(825\) | −7.72198 | − | 0.504305i | −0.268845 | − | 0.0175576i | ||||
\(826\) | −3.24830 | + | 5.62621i | −0.113023 | + | 0.195761i | ||||
\(827\) | −3.63426 | − | 6.29472i | −0.126376 | − | 0.218889i | 0.795894 | − | 0.605436i | \(-0.207001\pi\) |
−0.922270 | + | 0.386547i | \(0.873668\pi\) | |||||||
\(828\) | −5.76456 | −0.200332 | ||||||||
\(829\) | −12.7848 | − | 7.38128i | −0.444033 | − | 0.256362i | 0.261274 | − | 0.965265i | \(-0.415857\pi\) |
−0.705307 | + | 0.708902i | \(0.749191\pi\) | |||||||
\(830\) | −6.00549 | − | 25.7425i | −0.208454 | − | 0.893534i | ||||
\(831\) | 7.05800 | + | 4.07494i | 0.244839 | + | 0.141358i | ||||
\(832\) | −1.64535 | − | 2.84982i | −0.0570421 | − | 0.0987998i | ||||
\(833\) | 12.7670 | + | 22.1131i | 0.442350 | + | 0.766172i | ||||
\(834\) | −2.17753 | − | 1.25720i | −0.0754017 | − | 0.0435332i | ||||
\(835\) | −14.5601 | + | 3.39674i | −0.503873 | + | 0.117549i | ||||
\(836\) | −5.26550 | − | 3.04004i | −0.182111 | − | 0.105142i | ||||
\(837\) | 9.04219 | 0.312544 | ||||||||
\(838\) | 5.34770 | + | 9.26250i | 0.184733 | + | 0.319968i | ||||
\(839\) | −22.4188 | + | 38.8305i | −0.773983 | + | 1.34058i | 0.161382 | + | 0.986892i | \(0.448405\pi\) |
−0.935365 | + | 0.353685i | \(0.884928\pi\) | |||||||
\(840\) | −2.64578 | − | 2.82421i | −0.0912882 | − | 0.0974445i | ||||
\(841\) | 28.4822 | 0.982146 | ||||||||
\(842\) | 4.33822 | + | 2.50468i | 0.149505 | + | 0.0863168i | ||||
\(843\) | 30.8168 | 1.06139 | ||||||||
\(844\) | −5.88378 | − | 10.1910i | −0.202528 | − | 0.350789i | ||||
\(845\) | 3.31946 | + | 3.54332i | 0.114193 | + | 0.121894i | ||||
\(846\) | 6.98922 | − | 4.03523i | 0.240294 | − | 0.138734i | ||||
\(847\) | −12.8968 | + | 7.44598i | −0.443140 | + | 0.255847i | ||||
\(848\) | −9.03833 | + | 5.21828i | −0.310377 | + | 0.179197i | ||||
\(849\) | −6.28756 | − | 3.63012i | −0.215789 | − | 0.124586i | ||||
\(850\) | 2.07756 | − | 31.8120i | 0.0712598 | − | 1.09114i | ||||
\(851\) | −30.0165 | − | 18.1253i | −1.02895 | − | 0.621328i | ||||
\(852\) | 4.59462i | 0.157409i | ||||||||
\(853\) | −5.10044 | + | 8.83422i | −0.174636 | + | 0.302478i | −0.940035 | − | 0.341078i | \(-0.889208\pi\) |
0.765399 | + | 0.643556i | \(0.222541\pi\) | |||||||
\(854\) | −0.355360 | − | 0.615502i | −0.0121602 | − | 0.0210620i | ||||
\(855\) | −8.40643 | − | 2.54898i | −0.287494 | − | 0.0871734i | ||||
\(856\) | 12.8377 | − | 7.41182i | 0.438782 | − | 0.253331i | ||||
\(857\) | −30.2272 | −1.03254 | −0.516271 | − | 0.856426i | \(-0.672680\pi\) | ||||
−0.516271 | + | 0.856426i | \(0.672680\pi\) | |||||||
\(858\) | 4.41063 | − | 2.54648i | 0.150576 | − | 0.0869354i | ||||
\(859\) | 40.3725i | 1.37749i | 0.725003 | + | 0.688746i | \(0.241839\pi\) | ||||
−0.725003 | + | 0.688746i | \(0.758161\pi\) | |||||||
\(860\) | 1.85819 | − | 0.433499i | 0.0633637 | − | 0.0147822i | ||||
\(861\) | −2.51612 | −0.0857492 | ||||||||
\(862\) | 19.7282i | 0.671944i | ||||||||
\(863\) | 14.0399 | + | 8.10594i | 0.477924 | + | 0.275929i | 0.719551 | − | 0.694440i | \(-0.244348\pi\) |
−0.241627 | + | 0.970369i | \(0.577681\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 5.96656 | − | 5.58961i | 0.202869 | − | 0.190052i | ||||
\(866\) | 31.7141 | + | 18.3102i | 1.07769 | + | 0.622205i | ||||
\(867\) | 20.4838 | + | 11.8263i | 0.695667 | + | 0.401643i | ||||
\(868\) | −7.82459 | + | 13.5526i | −0.265584 | + | 0.460005i | ||||
\(869\) | −16.3237 | + | 9.42452i | −0.553745 | + | 0.319705i | ||||
\(870\) | 0.466884 | − | 1.53976i | 0.0158288 | − | 0.0522027i | ||||
\(871\) | −23.4103 | − | 13.5160i | −0.793229 | − | 0.457971i | ||||
\(872\) | 1.92541 | + | 1.11164i | 0.0652026 | + | 0.0376447i | ||||
\(873\) | 8.33688 | − | 14.4399i | 0.282161 | − | 0.488717i | ||||
\(874\) | − | 22.6461i | − | 0.766014i | ||||||
\(875\) | 6.80953 | − | 18.1118i | 0.230204 | − | 0.612292i | ||||
\(876\) | 2.75334 | − | 4.76892i | 0.0930266 | − | 0.161127i | ||||
\(877\) | 15.8650i | 0.535724i | 0.963457 | + | 0.267862i | \(0.0863171\pi\) | ||||
−0.963457 | + | 0.267862i | \(0.913683\pi\) | |||||||
\(878\) | − | 3.90182i | − | 0.131680i | ||||||
\(879\) | 15.6930 | − | 27.1811i | 0.529313 | − | 0.916796i | ||||
\(880\) | 2.36603 | + | 2.52559i | 0.0797587 | + | 0.0851375i | ||||
\(881\) | 17.7662 | + | 30.7720i | 0.598559 | + | 1.03673i | 0.993034 | + | 0.117827i | \(0.0375930\pi\) |
−0.394475 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(882\) | −4.00473 | −0.134846 | ||||||||
\(883\) | −11.8068 | − | 20.4500i | −0.397331 | − | 0.688198i | 0.596064 | − | 0.802937i | \(-0.296730\pi\) |
−0.993396 | + | 0.114739i | \(0.963397\pi\) | |||||||
\(884\) | 10.4906 | + | 18.1703i | 0.352838 | + | 0.611133i | ||||
\(885\) | 2.43562 | − | 8.03255i | 0.0818723 | − | 0.270011i | ||||
\(886\) | 7.19220 | + | 4.15242i | 0.241627 | + | 0.139503i | ||||
\(887\) | − | 35.9203i | − | 1.20609i | −0.797709 | − | 0.603043i | \(-0.793955\pi\) | ||
0.797709 | − | 0.603043i | \(-0.206045\pi\) | |||||||
\(888\) | 6.08159 | + | 0.119482i | 0.204085 | + | 0.00400956i | ||||
\(889\) | −17.1393 | −0.574833 | ||||||||
\(890\) | 4.76920 | + | 20.4431i | 0.159864 | + | 0.685255i | ||||
\(891\) | 0.773843 | + | 1.34034i | 0.0259247 | + | 0.0449029i | ||||
\(892\) | −14.4978 | + | 8.37030i | −0.485422 | + | 0.280258i | ||||
\(893\) | 15.8524 | + | 27.4571i | 0.530480 | + | 0.918818i | ||||
\(894\) | 12.5220i | 0.418798i | ||||||||
\(895\) | 47.5763 | + | 14.4260i | 1.59030 | + | 0.482208i | ||||
\(896\) | 1.73068i | 0.0578181i | ||||||||
\(897\) | 16.4280 | + | 9.48470i | 0.548514 | + | 0.316685i | ||||
\(898\) | − | 32.9373i | − | 1.09913i | ||||||
\(899\) | −6.50641 | −0.217001 | ||||||||
\(900\) | 4.15800 | + | 2.77687i | 0.138600 | + | 0.0925625i | ||||
\(901\) | 57.6279 | − | 33.2715i | 1.91986 | − | 1.10843i | ||||
\(902\) | 2.25007 | 0.0749193 | ||||||||
\(903\) | −0.738414 | + | 1.27897i | −0.0245729 | + | 0.0425615i | ||||
\(904\) | −9.77887 | + | 16.9375i | −0.325240 | + | 0.563333i | ||||
\(905\) | −21.6517 | + | 5.05114i | −0.719726 | + | 0.167906i | ||||
\(906\) | −15.6264 | + | 9.02188i | −0.519151 | + | 0.299732i | ||||
\(907\) | 16.8837 | + | 29.2434i | 0.560614 | + | 0.971012i | 0.997443 | + | 0.0714676i | \(0.0227683\pi\) |
−0.436829 | + | 0.899545i | \(0.643898\pi\) | |||||||
\(908\) | 1.51026 | − | 2.61584i | 0.0501197 | − | 0.0868098i | ||||
\(909\) | 1.28045 | − | 2.21781i | 0.0424699 | − | 0.0735600i | ||||
\(910\) | 2.89321 | + | 12.4017i | 0.0959090 | + | 0.411113i | ||||
\(911\) | − | 23.5230i | − | 0.779353i | −0.920952 | − | 0.389676i | \(-0.872587\pi\) | ||
0.920952 | − | 0.389676i | \(-0.127413\pi\) | |||||||
\(912\) | 1.96425 | + | 3.40218i | 0.0650427 | + | 0.112657i | ||||
\(913\) | −15.8448 | − | 9.14800i | −0.524386 | − | 0.302755i | ||||
\(914\) | −29.0888 | −0.962172 | ||||||||
\(915\) | 0.627795 | + | 0.670132i | 0.0207543 | + | 0.0221539i | ||||
\(916\) | 0.284128 | − | 0.492123i | 0.00938784 | − | 0.0162602i | ||||
\(917\) | −21.6001 | −0.713298 | ||||||||
\(918\) | −5.52173 | + | 3.18797i | −0.182244 | + | 0.105219i | ||||
\(919\) | 0.790945i | 0.0260909i | 0.999915 | + | 0.0130454i | \(0.00415261\pi\) | ||||
−0.999915 | + | 0.0130454i | \(0.995847\pi\) | |||||||
\(920\) | −3.74031 | + | 12.3354i | −0.123314 | + | 0.406685i | ||||
\(921\) | 9.60435 | + | 16.6352i | 0.316474 | + | 0.548149i | ||||
\(922\) | −21.8552 | + | 12.6181i | −0.719763 | + | 0.415556i | ||||
\(923\) | 7.55974 | − | 13.0939i | 0.248832 | − | 0.430990i | ||||
\(924\) | −2.67856 | −0.0881180 | ||||||||
\(925\) | 12.9198 | + | 27.5333i | 0.424799 | + | 0.905288i | ||||
\(926\) | −20.5150 | −0.674165 | ||||||||
\(927\) | 1.90939 | − | 3.30717i | 0.0627127 | − | 0.108622i | ||||
\(928\) | −0.623158 | + | 0.359780i | −0.0204562 | + | 0.0118104i | ||||
\(929\) | −8.10742 | − | 14.0425i | −0.265996 | − | 0.460718i | 0.701828 | − | 0.712346i | \(-0.252367\pi\) |
−0.967824 | + | 0.251628i | \(0.919034\pi\) | |||||||
\(930\) | 5.86698 | − | 19.3490i | 0.192386 | − | 0.634480i | ||||
\(931\) | − | 15.7326i | − | 0.515614i | ||||||
\(932\) | −4.86916 | + | 2.81121i | −0.159495 | + | 0.0920843i | ||||
\(933\) | −18.3448 | −0.600583 | ||||||||
\(934\) | −5.06069 | + | 8.76537i | −0.165591 | + | 0.286812i | ||||
\(935\) | −15.0857 | − | 16.1030i | −0.493354 | − | 0.526624i | ||||
\(936\) | −3.29069 | −0.107560 | ||||||||
\(937\) | 36.9999 | + | 21.3619i | 1.20874 | + | 0.697864i | 0.962483 | − | 0.271342i | \(-0.0874675\pi\) |
0.246252 | + | 0.969206i | \(0.420801\pi\) | |||||||
\(938\) | 7.10850 | + | 12.3123i | 0.232101 | + | 0.402010i | ||||
\(939\) | 26.8568i | 0.876438i | ||||||||
\(940\) | −4.09990 | − | 17.5742i | −0.133724 | − | 0.573207i | ||||
\(941\) | −5.62000 | + | 9.73413i | −0.183207 | + | 0.317324i | −0.942971 | − | 0.332875i | \(-0.891981\pi\) |
0.759764 | + | 0.650199i | \(0.225314\pi\) | |||||||
\(942\) | −10.9888 | + | 19.0331i | −0.358033 | + | 0.620132i | ||||
\(943\) | 4.19035 | + | 7.25790i | 0.136457 | + | 0.236350i | ||||
\(944\) | −3.25086 | + | 1.87689i | −0.105807 | + | 0.0610874i | ||||
\(945\) | −3.76873 | + | 0.879211i | −0.122597 | + | 0.0286007i | ||||
\(946\) | 0.660337 | − | 1.14374i | 0.0214694 | − | 0.0371861i | ||||
\(947\) | 8.89604 | − | 15.4084i | 0.289083 | − | 0.500706i | −0.684508 | − | 0.729005i | \(-0.739983\pi\) |
0.973591 | + | 0.228299i | \(0.0733165\pi\) | |||||||
\(948\) | 12.1788 | 0.395550 | ||||||||
\(949\) | −15.6930 | + | 9.06038i | −0.509417 | + | 0.294112i | ||||
\(950\) | −10.9089 | + | 16.3347i | −0.353933 | + | 0.529967i | ||||
\(951\) | 22.7969 | 0.739239 | ||||||||
\(952\) | − | 11.0347i | − | 0.357638i | ||||||
\(953\) | −3.75265 | − | 2.16659i | −0.121560 | − | 0.0701828i | 0.437987 | − | 0.898981i | \(-0.355692\pi\) |
−0.559547 | + | 0.828799i | \(0.689025\pi\) | |||||||
\(954\) | 10.4366i | 0.337896i | ||||||||
\(955\) | −27.2251 | − | 8.25515i | −0.880983 | − | 0.267130i | ||||
\(956\) | − | 24.4104i | − | 0.789487i | ||||||
\(957\) | −0.556827 | − | 0.964453i | −0.0179997 | − | 0.0311764i | ||||
\(958\) | −12.1338 | + | 7.00544i | −0.392025 | + | 0.226336i | ||||
\(959\) | −10.0020 | − | 17.3240i | −0.322983 | − | 0.559423i | ||||
\(960\) | −0.508014 | − | 2.17760i | −0.0163961 | − | 0.0702816i | ||||
\(961\) | −50.7613 | −1.63746 | ||||||||
\(962\) | −17.1349 | − | 10.3468i | −0.552450 | − | 0.333595i | ||||
\(963\) | − | 14.8236i | − | 0.477685i | ||||||
\(964\) | 10.2774 | + | 5.93368i | 0.331014 | + | 0.191111i | ||||
\(965\) | 4.66616 | − | 15.3888i | 0.150209 | − | 0.495382i | ||||
\(966\) | −4.98832 | − | 8.64002i | −0.160497 | − | 0.277988i | ||||
\(967\) | 9.79037 | + | 16.9574i | 0.314837 | + | 0.545314i | 0.979403 | − | 0.201916i | \(-0.0647168\pi\) |
−0.664566 | + | 0.747230i | \(0.731383\pi\) | |||||||
\(968\) | −8.60467 | −0.276564 | ||||||||
\(969\) | −12.5239 | − | 21.6921i | −0.402327 | − | 0.696850i | ||||
\(970\) | −25.4900 | − | 27.2090i | −0.818435 | − | 0.873629i | ||||
\(971\) | −11.4170 | + | 19.7747i | −0.366388 | + | 0.634602i | −0.988998 | − | 0.147930i | \(-0.952739\pi\) |
0.622610 | + | 0.782532i | \(0.286072\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 4.35162i | − | 0.139507i | ||||||
\(974\) | −11.0760 | + | 19.1843i | −0.354899 | + | 0.614704i | ||||
\(975\) | −7.28064 | − | 14.7549i | −0.233167 | − | 0.472536i | ||||
\(976\) | − | 0.410659i | − | 0.0131449i | ||||||
\(977\) | −1.78574 | + | 3.09299i | −0.0571309 | + | 0.0989536i | −0.893176 | − | 0.449707i | \(-0.851529\pi\) |
0.836045 | + | 0.548660i | \(0.184862\pi\) | |||||||
\(978\) | 10.8743 | + | 6.27827i | 0.347721 | + | 0.200757i | ||||
\(979\) | 12.5830 | + | 7.26479i | 0.402154 | + | 0.232184i | ||||
\(980\) | −2.59845 | + | 8.56957i | −0.0830045 | + | 0.273745i | ||||
\(981\) | 1.92541 | − | 1.11164i | 0.0614736 | − | 0.0354918i | ||||
\(982\) | −8.92502 | + | 15.4586i | −0.284809 | + | 0.493303i | ||||
\(983\) | 15.7166 | + | 9.07399i | 0.501282 | + | 0.289415i | 0.729243 | − | 0.684255i | \(-0.239872\pi\) |
−0.227961 | + | 0.973670i | \(0.573206\pi\) | |||||||
\(984\) | −1.25905 | − | 0.726915i | −0.0401372 | − | 0.0231732i | ||||
\(985\) | −8.13557 | + | 7.62159i | −0.259221 | + | 0.242844i | ||||
\(986\) | 3.97322 | − | 2.29394i | 0.126533 | − | 0.0730539i | ||||
\(987\) | 12.0961 | + | 6.98371i | 0.385024 | + | 0.222294i | ||||
\(988\) | − | 12.9275i | − | 0.411277i | ||||||
\(989\) | 4.91902 | 0.156416 | ||||||||
\(990\) | 3.37024 | − | 0.786246i | 0.107113 | − | 0.0249885i | ||||
\(991\) | 8.13488i | 0.258413i | 0.991618 | + | 0.129207i | \(0.0412430\pi\) | ||||
−0.991618 | + | 0.129207i | \(0.958757\pi\) | |||||||
\(992\) | −7.83077 | + | 4.52110i | −0.248627 | + | 0.143545i | ||||
\(993\) | 0.830325 | 0.0263496 | ||||||||
\(994\) | −6.88650 | + | 3.97592i | −0.218426 | + | 0.126109i | ||||
\(995\) | −16.9910 | − | 5.15199i | −0.538652 | − | 0.163329i | ||||
\(996\) | 5.91076 | + | 10.2377i | 0.187290 | + | 0.324395i | ||||
\(997\) | 13.5553 | − | 23.4785i | 0.429301 | − | 0.743571i | −0.567510 | − | 0.823366i | \(-0.692093\pi\) |
0.996811 | + | 0.0797951i | \(0.0254266\pi\) | |||||||
\(998\) | − | 7.40365i | − | 0.234358i | ||||||
\(999\) | 3.14427 | − | 5.20707i | 0.0994803 | − | 0.164744i |
(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 | 1110.2.ba.a.619.2 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.b.619.17 | yes | 36 | ||
37.11 | even | 6 | 1110.2.ba.b.529.17 | yes | 36 | ||
185.159 | even | 6 | inner | 1110.2.ba.a.529.2 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.2 | ✓ | 36 | 185.159 | even | 6 | inner | |
1110.2.ba.a.619.2 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.529.17 | yes | 36 | 37.11 | even | 6 | ||
1110.2.ba.b.619.17 | yes | 36 | 5.4 | even | 2 |