Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (of order \(4\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 497.4 | ||
Root | \(2.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.f.683.4 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.292893 | + | 1.70711i | 0.169102 | + | 0.985599i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.23483 | − | 0.0743018i | 0.999448 | − | 0.0332288i | ||||
\(6\) | 1.41421 | + | 1.00000i | 0.577350 | + | 0.408248i | ||||
\(7\) | 0.218591 | + | 0.218591i | 0.0826198 | + | 0.0826198i | 0.747209 | − | 0.664589i | \(-0.231393\pi\) |
−0.664589 | + | 0.747209i | \(0.731393\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | 1.52773 | − | 1.63280i | 0.483109 | − | 0.516338i | ||||
\(11\) | − | 0.894921i | − | 0.269829i | −0.990857 | − | 0.134914i | \(-0.956924\pi\) | ||
0.990857 | − | 0.134914i | \(-0.0430760\pi\) | |||||||
\(12\) | 1.70711 | − | 0.292893i | 0.492799 | − | 0.0845510i | ||||
\(13\) | 3.57474 | − | 3.57474i | 0.991456 | − | 0.991456i | −0.00850795 | − | 0.999964i | \(-0.502708\pi\) |
0.999964 | + | 0.00850795i | \(0.00270820\pi\) | |||||||
\(14\) | 0.309135 | 0.0826198 | ||||||||
\(15\) | 0.781409 | + | 3.79334i | 0.201759 | + | 0.979435i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.36459 | − | 4.36459i | 1.05857 | − | 1.05857i | 0.0603934 | − | 0.998175i | \(-0.480764\pi\) |
0.998175 | − | 0.0603934i | \(-0.0192355\pi\) | |||||||
\(18\) | −1.29289 | + | 2.70711i | −0.304738 | + | 0.638071i | ||||
\(19\) | 6.55178i | 1.50308i | 0.659687 | + | 0.751540i | \(0.270689\pi\) | ||||
−0.659687 | + | 0.751540i | \(0.729311\pi\) | |||||||
\(20\) | −0.0743018 | − | 2.23483i | −0.0166144 | − | 0.499724i | ||||
\(21\) | −0.309135 | + | 0.437183i | −0.0674588 | + | 0.0954011i | ||||
\(22\) | −0.632805 | − | 0.632805i | −0.134914 | − | 0.134914i | ||||
\(23\) | 3.19562 | + | 3.19562i | 0.666333 | + | 0.666333i | 0.956865 | − | 0.290532i | \(-0.0938323\pi\) |
−0.290532 | + | 0.956865i | \(0.593832\pi\) | |||||||
\(24\) | 1.00000 | − | 1.41421i | 0.204124 | − | 0.288675i | ||||
\(25\) | 4.98896 | − | 0.332104i | 0.997792 | − | 0.0664208i | ||||
\(26\) | − | 5.05545i | − | 0.991456i | ||||||
\(27\) | −2.53553 | − | 4.53553i | −0.487964 | − | 0.872864i | ||||
\(28\) | 0.218591 | − | 0.218591i | 0.0413099 | − | 0.0413099i | ||||
\(29\) | −2.39124 | −0.444043 | −0.222021 | − | 0.975042i | \(-0.571266\pi\) | ||||
−0.222021 | + | 0.975042i | \(0.571266\pi\) | |||||||
\(30\) | 3.23483 | + | 2.12975i | 0.590597 | + | 0.388838i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.52773 | − | 0.262116i | 0.265943 | − | 0.0456286i | ||||
\(34\) | − | 6.17246i | − | 1.05857i | ||||||
\(35\) | 0.504757 | + | 0.472274i | 0.0853195 | + | 0.0798288i | ||||
\(36\) | 1.00000 | + | 2.82843i | 0.166667 | + | 0.471405i | ||||
\(37\) | −2.00000 | − | 2.00000i | −0.328798 | − | 0.328798i | 0.523331 | − | 0.852129i | \(-0.324689\pi\) |
−0.852129 | + | 0.523331i | \(0.824689\pi\) | |||||||
\(38\) | 4.63280 | + | 4.63280i | 0.751540 | + | 0.751540i | ||||
\(39\) | 7.14949 | + | 5.05545i | 1.14483 | + | 0.809520i | ||||
\(40\) | −1.63280 | − | 1.52773i | −0.258169 | − | 0.241555i | ||||
\(41\) | 4.71231i | 0.735939i | 0.929838 | + | 0.367969i | \(0.119947\pi\) | ||||
−0.929838 | + | 0.367969i | \(0.880053\pi\) | |||||||
\(42\) | 0.0905435 | + | 0.527726i | 0.0139712 | + | 0.0814299i | ||||
\(43\) | −3.37912 | + | 3.37912i | −0.515311 | + | 0.515311i | −0.916149 | − | 0.400838i | \(-0.868719\pi\) |
0.400838 | + | 0.916149i | \(0.368719\pi\) | |||||||
\(44\) | −0.894921 | −0.134914 | ||||||||
\(45\) | −6.24676 | + | 2.44499i | −0.931212 | + | 0.364478i | ||||
\(46\) | 4.51929 | 0.666333 | ||||||||
\(47\) | −8.98896 | + | 8.98896i | −1.31117 | + | 1.31117i | −0.390624 | + | 0.920550i | \(0.627741\pi\) |
−0.920550 | + | 0.390624i | \(0.872259\pi\) | |||||||
\(48\) | −0.292893 | − | 1.70711i | −0.0422755 | − | 0.246400i | ||||
\(49\) | − | 6.90444i | − | 0.986348i | ||||||
\(50\) | 3.29289 | − | 3.76256i | 0.465685 | − | 0.532106i | ||||
\(51\) | 8.72918 | + | 6.17246i | 1.22233 | + | 0.864317i | ||||
\(52\) | −3.57474 | − | 3.57474i | −0.495728 | − | 0.495728i | ||||
\(53\) | 10.1579 | + | 10.1579i | 1.39530 | + | 1.39530i | 0.812913 | + | 0.582385i | \(0.197880\pi\) |
0.582385 | + | 0.812913i | \(0.302120\pi\) | |||||||
\(54\) | −5.00000 | − | 1.41421i | −0.680414 | − | 0.192450i | ||||
\(55\) | −0.0664943 | − | 2.00000i | −0.00896609 | − | 0.269680i | ||||
\(56\) | − | 0.309135i | − | 0.0413099i | ||||||
\(57\) | −11.1846 | + | 1.91897i | −1.48143 | + | 0.254174i | ||||
\(58\) | −1.69087 | + | 1.69087i | −0.222021 | + | 0.222021i | ||||
\(59\) | 6.79073 | 0.884078 | 0.442039 | − | 0.896996i | \(-0.354255\pi\) | ||||
0.442039 | + | 0.896996i | \(0.354255\pi\) | |||||||
\(60\) | 3.79334 | − | 0.781409i | 0.489718 | − | 0.100879i | ||||
\(61\) | −5.61916 | −0.719459 | −0.359730 | − | 0.933057i | \(-0.617131\pi\) | ||||
−0.359730 | + | 0.933057i | \(0.617131\pi\) | |||||||
\(62\) | 0.707107 | − | 0.707107i | 0.0898027 | − | 0.0898027i | ||||
\(63\) | −0.836861 | − | 0.399678i | −0.105435 | − | 0.0503548i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 7.72335 | − | 8.25457i | 0.957963 | − | 1.02385i | ||||
\(66\) | 0.894921 | − | 1.26561i | 0.110157 | − | 0.155786i | ||||
\(67\) | −9.52512 | − | 9.52512i | −1.16368 | − | 1.16368i | −0.983664 | − | 0.180015i | \(-0.942386\pi\) |
−0.180015 | − | 0.983664i | \(-0.557614\pi\) | |||||||
\(68\) | −4.36459 | − | 4.36459i | −0.529284 | − | 0.529284i | ||||
\(69\) | −4.51929 | + | 6.39124i | −0.544059 | + | 0.769415i | ||||
\(70\) | 0.690865 | − | 0.0229693i | 0.0825742 | − | 0.00274535i | ||||
\(71\) | − | 12.5518i | − | 1.48962i | −0.667276 | − | 0.744811i | \(-0.732540\pi\) | ||
0.667276 | − | 0.744811i | \(-0.267460\pi\) | |||||||
\(72\) | 2.70711 | + | 1.29289i | 0.319036 | + | 0.152369i | ||||
\(73\) | −7.83686 | + | 7.83686i | −0.917235 | + | 0.917235i | −0.996828 | − | 0.0795923i | \(-0.974638\pi\) |
0.0795923 | + | 0.996828i | \(0.474638\pi\) | |||||||
\(74\) | −2.82843 | −0.328798 | ||||||||
\(75\) | 2.02817 | + | 8.41941i | 0.234193 | + | 0.972190i | ||||
\(76\) | 6.55178 | 0.751540 | ||||||||
\(77\) | 0.195622 | − | 0.195622i | 0.0222932 | − | 0.0222932i | ||||
\(78\) | 8.63020 | − | 1.48071i | 0.977177 | − | 0.167657i | ||||
\(79\) | − | 13.0830i | − | 1.47195i | −0.677008 | − | 0.735976i | \(-0.736724\pi\) | ||
0.677008 | − | 0.735976i | \(-0.263276\pi\) | |||||||
\(80\) | −2.23483 | + | 0.0743018i | −0.249862 | + | 0.00830719i | ||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 3.33210 | + | 3.33210i | 0.367969 | + | 0.367969i | ||||
\(83\) | 1.55913 | + | 1.55913i | 0.171137 | + | 0.171137i | 0.787479 | − | 0.616342i | \(-0.211386\pi\) |
−0.616342 | + | 0.787479i | \(0.711386\pi\) | |||||||
\(84\) | 0.437183 | + | 0.309135i | 0.0477006 | + | 0.0337294i | ||||
\(85\) | 9.42983 | − | 10.0784i | 1.02281 | − | 1.09316i | ||||
\(86\) | 4.77880i | 0.515311i | ||||||||
\(87\) | −0.700379 | − | 4.08211i | −0.0750885 | − | 0.437648i | ||||
\(88\) | −0.632805 | + | 0.632805i | −0.0674572 | + | 0.0674572i | ||||
\(89\) | −1.83947 | −0.194983 | −0.0974916 | − | 0.995236i | \(-0.531082\pi\) | ||||
−0.0974916 | + | 0.995236i | \(0.531082\pi\) | |||||||
\(90\) | −2.68826 | + | 6.14600i | −0.283367 | + | 0.647845i | ||||
\(91\) | 1.56282 | 0.163828 | ||||||||
\(92\) | 3.19562 | − | 3.19562i | 0.333167 | − | 0.333167i | ||||
\(93\) | 0.292893 | + | 1.70711i | 0.0303716 | + | 0.177019i | ||||
\(94\) | 12.7123i | 1.31117i | ||||||||
\(95\) | 0.486809 | + | 14.6421i | 0.0499455 | + | 1.50225i | ||||
\(96\) | −1.41421 | − | 1.00000i | −0.144338 | − | 0.102062i | ||||
\(97\) | −6.81739 | − | 6.81739i | −0.692201 | − | 0.692201i | 0.270515 | − | 0.962716i | \(-0.412806\pi\) |
−0.962716 | + | 0.270515i | \(0.912806\pi\) | |||||||
\(98\) | −4.88217 | − | 4.88217i | −0.493174 | − | 0.493174i | ||||
\(99\) | 0.894921 | + | 2.53122i | 0.0899430 | + | 0.254397i | ||||
\(100\) | −0.332104 | − | 4.98896i | −0.0332104 | − | 0.498896i | ||||
\(101\) | 9.43477i | 0.938795i | 0.882987 | + | 0.469397i | \(0.155529\pi\) | ||||
−0.882987 | + | 0.469397i | \(0.844471\pi\) | |||||||
\(102\) | 10.5370 | − | 1.80787i | 1.04332 | − | 0.179006i | ||||
\(103\) | −5.08211 | + | 5.08211i | −0.500755 | + | 0.500755i | −0.911673 | − | 0.410917i | \(-0.865208\pi\) |
0.410917 | + | 0.911673i | \(0.365208\pi\) | |||||||
\(104\) | −5.05545 | −0.495728 | ||||||||
\(105\) | −0.658382 | + | 1.00000i | −0.0642515 | + | 0.0975900i | ||||
\(106\) | 14.3655 | 1.39530 | ||||||||
\(107\) | 3.16897 | − | 3.16897i | 0.306355 | − | 0.306355i | −0.537139 | − | 0.843494i | \(-0.680495\pi\) |
0.843494 | + | 0.537139i | \(0.180495\pi\) | |||||||
\(108\) | −4.53553 | + | 2.53553i | −0.436432 | + | 0.243982i | ||||
\(109\) | − | 17.8618i | − | 1.71085i | −0.517927 | − | 0.855425i | \(-0.673296\pi\) | ||
0.517927 | − | 0.855425i | \(-0.326704\pi\) | |||||||
\(110\) | −1.46123 | − | 1.36720i | −0.139323 | − | 0.130357i | ||||
\(111\) | 2.82843 | − | 4.00000i | 0.268462 | − | 0.379663i | ||||
\(112\) | −0.218591 | − | 0.218591i | −0.0206549 | − | 0.0206549i | ||||
\(113\) | −0.0470185 | − | 0.0470185i | −0.00442313 | − | 0.00442313i | 0.704892 | − | 0.709315i | \(-0.250996\pi\) |
−0.709315 | + | 0.704892i | \(0.750996\pi\) | |||||||
\(114\) | −6.55178 | + | 9.26561i | −0.613630 | + | 0.867804i | ||||
\(115\) | 7.37912 | + | 6.90424i | 0.688107 | + | 0.643824i | ||||
\(116\) | 2.39124i | 0.222021i | ||||||||
\(117\) | −6.53616 | + | 13.6857i | −0.604268 | + | 1.26524i | ||||
\(118\) | 4.80177 | − | 4.80177i | 0.442039 | − | 0.442039i | ||||
\(119\) | 1.90812 | 0.174917 | ||||||||
\(120\) | 2.12975 | − | 3.23483i | 0.194419 | − | 0.295299i | ||||
\(121\) | 10.1991 | 0.927192 | ||||||||
\(122\) | −3.97334 | + | 3.97334i | −0.359730 | + | 0.359730i | ||||
\(123\) | −8.04441 | + | 1.38020i | −0.725340 | + | 0.124449i | ||||
\(124\) | − | 1.00000i | − | 0.0898027i | ||||||
\(125\) | 11.1248 | − | 1.11289i | 0.995034 | − | 0.0995396i | ||||
\(126\) | −0.874366 | + | 0.309135i | −0.0778947 | + | 0.0275399i | ||||
\(127\) | 6.40811 | + | 6.40811i | 0.568628 | + | 0.568628i | 0.931744 | − | 0.363116i | \(-0.118287\pi\) |
−0.363116 | + | 0.931744i | \(0.618287\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −6.75825 | − | 4.77880i | −0.595030 | − | 0.420750i | ||||
\(130\) | −0.375629 | − | 11.2981i | −0.0329449 | − | 0.990908i | ||||
\(131\) | − | 13.7521i | − | 1.20153i | −0.799426 | − | 0.600765i | \(-0.794863\pi\) | ||
0.799426 | − | 0.600765i | \(-0.205137\pi\) | |||||||
\(132\) | −0.262116 | − | 1.52773i | −0.0228143 | − | 0.132972i | ||||
\(133\) | −1.43216 | + | 1.43216i | −0.124184 | + | 0.124184i | ||||
\(134\) | −13.4706 | −1.16368 | ||||||||
\(135\) | −6.00349 | − | 9.94777i | −0.516698 | − | 0.856167i | ||||
\(136\) | −6.17246 | −0.529284 | ||||||||
\(137\) | −3.81650 | + | 3.81650i | −0.326066 | + | 0.326066i | −0.851088 | − | 0.525023i | \(-0.824057\pi\) |
0.525023 | + | 0.851088i | \(0.324057\pi\) | |||||||
\(138\) | 1.32367 | + | 7.71491i | 0.112678 | + | 0.656737i | ||||
\(139\) | 11.2279i | 0.952339i | 0.879354 | + | 0.476170i | \(0.157975\pi\) | ||||
−0.879354 | + | 0.476170i | \(0.842025\pi\) | |||||||
\(140\) | 0.472274 | − | 0.504757i | 0.0399144 | − | 0.0426598i | ||||
\(141\) | −17.9779 | − | 12.7123i | −1.51401 | − | 1.07057i | ||||
\(142\) | −8.87545 | − | 8.87545i | −0.744811 | − | 0.744811i | ||||
\(143\) | −3.19912 | − | 3.19912i | −0.267523 | − | 0.267523i | ||||
\(144\) | 2.82843 | − | 1.00000i | 0.235702 | − | 0.0833333i | ||||
\(145\) | −5.34403 | + | 0.177674i | −0.443798 | + | 0.0147550i | ||||
\(146\) | 11.0830i | 0.917235i | ||||||||
\(147\) | 11.7866 | − | 2.02226i | 0.972143 | − | 0.166793i | ||||
\(148\) | −2.00000 | + | 2.00000i | −0.164399 | + | 0.164399i | ||||
\(149\) | −17.1853 | −1.40787 | −0.703936 | − | 0.710263i | \(-0.748576\pi\) | ||||
−0.703936 | + | 0.710263i | \(0.748576\pi\) | |||||||
\(150\) | 7.38756 | + | 4.51929i | 0.603192 | + | 0.368999i | ||||
\(151\) | −19.3474 | −1.57447 | −0.787236 | − | 0.616651i | \(-0.788489\pi\) | ||||
−0.787236 | + | 0.616651i | \(0.788489\pi\) | |||||||
\(152\) | 4.63280 | − | 4.63280i | 0.375770 | − | 0.375770i | ||||
\(153\) | −7.98033 | + | 16.7095i | −0.645171 | + | 1.35088i | ||||
\(154\) | − | 0.276651i | − | 0.0222932i | ||||||
\(155\) | 2.23483 | − | 0.0743018i | 0.179506 | − | 0.00596806i | ||||
\(156\) | 5.05545 | − | 7.14949i | 0.404760 | − | 0.572417i | ||||
\(157\) | −12.6276 | − | 12.6276i | −1.00779 | − | 1.00779i | −0.999969 | − | 0.00782202i | \(-0.997510\pi\) |
−0.00782202 | − | 0.999969i | \(-0.502490\pi\) | |||||||
\(158\) | −9.25107 | − | 9.25107i | −0.735976 | − | 0.735976i | ||||
\(159\) | −14.3655 | + | 20.3158i | −1.13926 | + | 1.61115i | ||||
\(160\) | −1.52773 | + | 1.63280i | −0.120777 | + | 0.129085i | ||||
\(161\) | 1.39707i | 0.110105i | ||||||||
\(162\) | 0.949747 | − | 8.94975i | 0.0746192 | − | 0.703159i | ||||
\(163\) | −2.30913 | + | 2.30913i | −0.180865 | + | 0.180865i | −0.791733 | − | 0.610867i | \(-0.790821\pi\) |
0.610867 | + | 0.791733i | \(0.290821\pi\) | |||||||
\(164\) | 4.71231 | 0.367969 | ||||||||
\(165\) | 3.39474 | − | 0.699299i | 0.264280 | − | 0.0544404i | ||||
\(166\) | 2.20494 | 0.171137 | ||||||||
\(167\) | −5.07950 | + | 5.07950i | −0.393064 | + | 0.393064i | −0.875778 | − | 0.482714i | \(-0.839651\pi\) |
0.482714 | + | 0.875778i | \(0.339651\pi\) | |||||||
\(168\) | 0.527726 | − | 0.0905435i | 0.0407150 | − | 0.00698559i | ||||
\(169\) | − | 12.5576i | − | 0.965969i | ||||||
\(170\) | −0.458625 | − | 13.7944i | −0.0351749 | − | 1.05798i | ||||
\(171\) | −6.55178 | − | 18.5312i | −0.501027 | − | 1.41712i | ||||
\(172\) | 3.37912 | + | 3.37912i | 0.257656 | + | 0.257656i | ||||
\(173\) | −11.9402 | − | 11.9402i | −0.907798 | − | 0.907798i | 0.0882962 | − | 0.996094i | \(-0.471858\pi\) |
−0.996094 | + | 0.0882962i | \(0.971858\pi\) | |||||||
\(174\) | −3.38173 | − | 2.39124i | −0.256368 | − | 0.181280i | ||||
\(175\) | 1.16314 | + | 1.01795i | 0.0879250 | + | 0.0769497i | ||||
\(176\) | 0.894921i | 0.0674572i | ||||||||
\(177\) | 1.98896 | + | 11.5925i | 0.149499 | + | 0.871346i | ||||
\(178\) | −1.30070 | + | 1.30070i | −0.0974916 | + | 0.0974916i | ||||
\(179\) | 9.77996 | 0.730989 | 0.365494 | − | 0.930814i | \(-0.380900\pi\) | ||||
0.365494 | + | 0.930814i | \(0.380900\pi\) | |||||||
\(180\) | 2.44499 | + | 6.24676i | 0.182239 | + | 0.465606i | ||||
\(181\) | −17.2485 | −1.28207 | −0.641034 | − | 0.767512i | \(-0.721494\pi\) | ||||
−0.641034 | + | 0.767512i | \(0.721494\pi\) | |||||||
\(182\) | 1.10508 | − | 1.10508i | 0.0819139 | − | 0.0819139i | ||||
\(183\) | −1.64581 | − | 9.59250i | −0.121662 | − | 0.709098i | ||||
\(184\) | − | 4.51929i | − | 0.333167i | ||||||
\(185\) | −4.61827 | − | 4.32106i | −0.339542 | − | 0.317691i | ||||
\(186\) | 1.41421 | + | 1.00000i | 0.103695 | + | 0.0733236i | ||||
\(187\) | −3.90596 | − | 3.90596i | −0.285632 | − | 0.285632i | ||||
\(188\) | 8.98896 | + | 8.98896i | 0.655587 | + | 0.655587i | ||||
\(189\) | 0.437183 | − | 1.54567i | 0.0318004 | − | 0.112431i | ||||
\(190\) | 10.6978 | + | 10.0093i | 0.776098 | + | 0.726152i | ||||
\(191\) | 24.0429i | 1.73968i | 0.493332 | + | 0.869841i | \(0.335779\pi\) | ||||
−0.493332 | + | 0.869841i | \(0.664221\pi\) | |||||||
\(192\) | −1.70711 | + | 0.292893i | −0.123200 | + | 0.0211377i | ||||
\(193\) | 6.53705 | − | 6.53705i | 0.470547 | − | 0.470547i | −0.431545 | − | 0.902092i | \(-0.642031\pi\) |
0.902092 | + | 0.431545i | \(0.142031\pi\) | |||||||
\(194\) | −9.64124 | −0.692201 | ||||||||
\(195\) | 16.3535 | + | 10.7669i | 1.17110 | + | 0.771032i | ||||
\(196\) | −6.90444 | −0.493174 | ||||||||
\(197\) | −6.26650 | + | 6.26650i | −0.446469 | + | 0.446469i | −0.894179 | − | 0.447710i | \(-0.852240\pi\) |
0.447710 | + | 0.894179i | \(0.352240\pi\) | |||||||
\(198\) | 2.42265 | + | 1.15704i | 0.172170 | + | 0.0822271i | ||||
\(199\) | 10.7497i | 0.762028i | 0.924569 | + | 0.381014i | \(0.124425\pi\) | ||||
−0.924569 | + | 0.381014i | \(0.875575\pi\) | |||||||
\(200\) | −3.76256 | − | 3.29289i | −0.266053 | − | 0.232843i | ||||
\(201\) | 13.4706 | − | 19.0502i | 0.950140 | − | 1.34370i | ||||
\(202\) | 6.67139 | + | 6.67139i | 0.469397 | + | 0.469397i | ||||
\(203\) | −0.522705 | − | 0.522705i | −0.0366867 | − | 0.0366867i | ||||
\(204\) | 6.17246 | − | 8.72918i | 0.432159 | − | 0.611165i | ||||
\(205\) | 0.350133 | + | 10.5312i | 0.0244543 | + | 0.735532i | ||||
\(206\) | 7.18719i | 0.500755i | ||||||||
\(207\) | −12.2342 | − | 5.84296i | −0.850336 | − | 0.406114i | ||||
\(208\) | −3.57474 | + | 3.57474i | −0.247864 | + | 0.247864i | ||||
\(209\) | 5.86332 | 0.405575 | ||||||||
\(210\) | 0.241561 | + | 1.17265i | 0.0166693 | + | 0.0809207i | ||||
\(211\) | −2.91700 | −0.200815 | −0.100407 | − | 0.994946i | \(-0.532015\pi\) | ||||
−0.100407 | + | 0.994946i | \(0.532015\pi\) | |||||||
\(212\) | 10.1579 | − | 10.1579i | 0.697649 | − | 0.697649i | ||||
\(213\) | 21.4272 | − | 3.67633i | 1.46817 | − | 0.251898i | ||||
\(214\) | − | 4.48159i | − | 0.306355i | ||||||
\(215\) | −7.30070 | + | 7.80285i | −0.497904 | + | 0.532150i | ||||
\(216\) | −1.41421 | + | 5.00000i | −0.0962250 | + | 0.340207i | ||||
\(217\) | 0.218591 | + | 0.218591i | 0.0148390 | + | 0.0148390i | ||||
\(218\) | −12.6302 | − | 12.6302i | −0.855425 | − | 0.855425i | ||||
\(219\) | −15.6737 | − | 11.0830i | −1.05913 | − | 0.748919i | ||||
\(220\) | −2.00000 | + | 0.0664943i | −0.134840 | + | 0.00448304i | ||||
\(221\) | − | 31.2046i | − | 2.09905i | ||||||
\(222\) | −0.828427 | − | 4.82843i | −0.0556004 | − | 0.324063i | ||||
\(223\) | −13.7181 | + | 13.7181i | −0.918634 | + | 0.918634i | −0.996930 | − | 0.0782960i | \(-0.975052\pi\) |
0.0782960 | + | 0.996930i | \(0.475052\pi\) | |||||||
\(224\) | −0.309135 | −0.0206549 | ||||||||
\(225\) | −13.7788 | + | 5.92829i | −0.918587 | + | 0.395219i | ||||
\(226\) | −0.0664943 | −0.00442313 | ||||||||
\(227\) | 7.35704 | − | 7.35704i | 0.488304 | − | 0.488304i | −0.419467 | − | 0.907771i | \(-0.637783\pi\) |
0.907771 | + | 0.419467i | \(0.137783\pi\) | |||||||
\(228\) | 1.91897 | + | 11.1846i | 0.127087 | + | 0.740717i | ||||
\(229\) | − | 15.6228i | − | 1.03239i | −0.856472 | − | 0.516193i | \(-0.827349\pi\) | ||
0.856472 | − | 0.516193i | \(-0.172651\pi\) | |||||||
\(230\) | 10.0999 | − | 0.335792i | 0.665965 | − | 0.0221414i | ||||
\(231\) | 0.391244 | + | 0.276651i | 0.0257420 | + | 0.0182023i | ||||
\(232\) | 1.69087 | + | 1.69087i | 0.111011 | + | 0.111011i | ||||
\(233\) | −1.35857 | − | 1.35857i | −0.0890027 | − | 0.0890027i | 0.661204 | − | 0.750206i | \(-0.270046\pi\) |
−0.750206 | + | 0.661204i | \(0.770046\pi\) | |||||||
\(234\) | 5.05545 | + | 14.2990i | 0.330485 | + | 0.934754i | ||||
\(235\) | −19.4209 | + | 20.7567i | −1.26688 | + | 1.35402i | ||||
\(236\) | − | 6.79073i | − | 0.442039i | ||||||
\(237\) | 22.3341 | − | 3.83192i | 1.45075 | − | 0.248910i | ||||
\(238\) | 1.34925 | − | 1.34925i | 0.0874587 | − | 0.0874587i | ||||
\(239\) | −4.09226 | −0.264707 | −0.132353 | − | 0.991203i | \(-0.542253\pi\) | ||||
−0.132353 | + | 0.991203i | \(0.542253\pi\) | |||||||
\(240\) | −0.781409 | − | 3.79334i | −0.0504397 | − | 0.244859i | ||||
\(241\) | −2.94455 | −0.189675 | −0.0948375 | − | 0.995493i | \(-0.530233\pi\) | ||||
−0.0948375 | + | 0.995493i | \(0.530233\pi\) | |||||||
\(242\) | 7.21186 | − | 7.21186i | 0.463596 | − | 0.463596i | ||||
\(243\) | 11.7071 | + | 10.2929i | 0.751011 | + | 0.660289i | ||||
\(244\) | 5.61916i | 0.359730i | ||||||||
\(245\) | −0.513012 | − | 15.4303i | −0.0327751 | − | 0.985803i | ||||
\(246\) | −4.71231 | + | 6.66421i | −0.300446 | + | 0.424894i | ||||
\(247\) | 23.4209 | + | 23.4209i | 1.49024 | + | 1.49024i | ||||
\(248\) | −0.707107 | − | 0.707107i | −0.0449013 | − | 0.0449013i | ||||
\(249\) | −2.20494 | + | 3.11826i | −0.139733 | + | 0.197612i | ||||
\(250\) | 7.07950 | − | 8.65336i | 0.447747 | − | 0.547287i | ||||
\(251\) | 20.9870i | 1.32469i | 0.749199 | + | 0.662345i | \(0.230439\pi\) | ||||
−0.749199 | + | 0.662345i | \(0.769561\pi\) | |||||||
\(252\) | −0.399678 | + | 0.836861i | −0.0251774 | + | 0.0527173i | ||||
\(253\) | 2.85983 | − | 2.85983i | 0.179796 | − | 0.179796i | ||||
\(254\) | 9.06244 | 0.568628 | ||||||||
\(255\) | 19.9669 | + | 13.1458i | 1.25037 | + | 0.823223i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.75234 | + | 8.75234i | −0.545956 | + | 0.545956i | −0.925269 | − | 0.379313i | \(-0.876160\pi\) |
0.379313 | + | 0.925269i | \(0.376160\pi\) | |||||||
\(258\) | −8.15792 | + | 1.39968i | −0.507890 | + | 0.0871402i | ||||
\(259\) | − | 0.874366i | − | 0.0543304i | ||||||
\(260\) | −8.25457 | − | 7.72335i | −0.511927 | − | 0.478982i | ||||
\(261\) | 6.76346 | − | 2.39124i | 0.418648 | − | 0.148014i | ||||
\(262\) | −9.72423 | − | 9.72423i | −0.600765 | − | 0.600765i | ||||
\(263\) | −7.25457 | − | 7.25457i | −0.447336 | − | 0.447336i | 0.447132 | − | 0.894468i | \(-0.352445\pi\) |
−0.894468 | + | 0.447132i | \(0.852445\pi\) | |||||||
\(264\) | −1.26561 | − | 0.894921i | −0.0778929 | − | 0.0550786i | ||||
\(265\) | 23.4560 | + | 21.9465i | 1.44089 | + | 1.34816i | ||||
\(266\) | 2.02538i | 0.124184i | ||||||||
\(267\) | −0.538768 | − | 3.14017i | −0.0329721 | − | 0.192175i | ||||
\(268\) | −9.52512 | + | 9.52512i | −0.581839 | + | 0.581839i | ||||
\(269\) | 23.1274 | 1.41010 | 0.705051 | − | 0.709156i | \(-0.250924\pi\) | ||||
0.705051 | + | 0.709156i | \(0.250924\pi\) | |||||||
\(270\) | −11.2792 | − | 2.78902i | −0.686433 | − | 0.169734i | ||||
\(271\) | 12.0132 | 0.729749 | 0.364874 | − | 0.931057i | \(-0.381112\pi\) | ||||
0.364874 | + | 0.931057i | \(0.381112\pi\) | |||||||
\(272\) | −4.36459 | + | 4.36459i | −0.264642 | + | 0.264642i | ||||
\(273\) | 0.457739 | + | 2.66790i | 0.0277036 | + | 0.161468i | ||||
\(274\) | 5.39735i | 0.326066i | ||||||||
\(275\) | −0.297207 | − | 4.46473i | −0.0179223 | − | 0.269233i | ||||
\(276\) | 6.39124 | + | 4.51929i | 0.384708 | + | 0.272029i | ||||
\(277\) | −8.31612 | − | 8.31612i | −0.499667 | − | 0.499667i | 0.411667 | − | 0.911334i | \(-0.364947\pi\) |
−0.911334 | + | 0.411667i | \(0.864947\pi\) | |||||||
\(278\) | 7.93933 | + | 7.93933i | 0.476170 | + | 0.476170i | ||||
\(279\) | −2.82843 | + | 1.00000i | −0.169334 | + | 0.0598684i | ||||
\(280\) | −0.0229693 | − | 0.690865i | −0.00137268 | − | 0.0412871i | ||||
\(281\) | 18.1759i | 1.08428i | 0.840288 | + | 0.542141i | \(0.182386\pi\) | ||||
−0.840288 | + | 0.542141i | \(0.817614\pi\) | |||||||
\(282\) | −21.7013 | + | 3.72335i | −1.29229 | + | 0.221722i | ||||
\(283\) | −2.79442 | + | 2.79442i | −0.166111 | + | 0.166111i | −0.785267 | − | 0.619157i | \(-0.787475\pi\) |
0.619157 | + | 0.785267i | \(0.287475\pi\) | |||||||
\(284\) | −12.5518 | −0.744811 | ||||||||
\(285\) | −24.8531 | + | 5.11961i | −1.47217 | + | 0.303260i | ||||
\(286\) | −4.52423 | −0.267523 | ||||||||
\(287\) | −1.03007 | + | 1.03007i | −0.0608031 | + | 0.0608031i | ||||
\(288\) | 1.29289 | − | 2.70711i | 0.0761845 | − | 0.159518i | ||||
\(289\) | − | 21.0993i | − | 1.24113i | ||||||
\(290\) | −3.65317 | + | 3.90444i | −0.214521 | + | 0.229276i | ||||
\(291\) | 9.64124 | − | 13.6348i | 0.565179 | − | 0.799284i | ||||
\(292\) | 7.83686 | + | 7.83686i | 0.458618 | + | 0.458618i | ||||
\(293\) | 8.65774 | + | 8.65774i | 0.505791 | + | 0.505791i | 0.913232 | − | 0.407441i | \(-0.133579\pi\) |
−0.407441 | + | 0.913232i | \(0.633579\pi\) | |||||||
\(294\) | 6.90444 | − | 9.76435i | 0.402675 | − | 0.569468i | ||||
\(295\) | 15.1761 | − | 0.504563i | 0.883589 | − | 0.0293768i | ||||
\(296\) | 2.82843i | 0.164399i | ||||||||
\(297\) | −4.05895 | + | 2.26910i | −0.235524 | + | 0.131667i | ||||
\(298\) | −12.1518 | + | 12.1518i | −0.703936 | + | 0.703936i | ||||
\(299\) | 22.8471 | 1.32128 | ||||||||
\(300\) | 8.41941 | − | 2.02817i | 0.486095 | − | 0.117096i | ||||
\(301\) | −1.47729 | −0.0851498 | ||||||||
\(302\) | −13.6807 | + | 13.6807i | −0.787236 | + | 0.787236i | ||||
\(303\) | −16.1062 | + | 2.76338i | −0.925275 | + | 0.158752i | ||||
\(304\) | − | 6.55178i | − | 0.375770i | ||||||
\(305\) | −12.5579 | + | 0.417513i | −0.719062 | + | 0.0239067i | ||||
\(306\) | 6.17246 | + | 17.4584i | 0.352856 | + | 0.998027i | ||||
\(307\) | −9.70621 | − | 9.70621i | −0.553962 | − | 0.553962i | 0.373620 | − | 0.927582i | \(-0.378117\pi\) |
−0.927582 | + | 0.373620i | \(0.878117\pi\) | |||||||
\(308\) | −0.195622 | − | 0.195622i | −0.0111466 | − | 0.0111466i | ||||
\(309\) | −10.1642 | − | 7.18719i | −0.578222 | − | 0.408865i | ||||
\(310\) | 1.52773 | − | 1.63280i | 0.0867690 | − | 0.0927371i | ||||
\(311\) | − | 26.1226i | − | 1.48127i | −0.671905 | − | 0.740637i | \(-0.734524\pi\) | ||
0.671905 | − | 0.740637i | \(-0.265476\pi\) | |||||||
\(312\) | −1.48071 | − | 8.63020i | −0.0838286 | − | 0.488589i | ||||
\(313\) | 6.78374 | − | 6.78374i | 0.383440 | − | 0.383440i | −0.488900 | − | 0.872340i | \(-0.662602\pi\) |
0.872340 | + | 0.488900i | \(0.162602\pi\) | |||||||
\(314\) | −17.8581 | −1.00779 | ||||||||
\(315\) | −1.89994 | − | 0.831034i | −0.107050 | − | 0.0468235i | ||||
\(316\) | −13.0830 | −0.735976 | ||||||||
\(317\) | −12.3863 | + | 12.3863i | −0.695684 | + | 0.695684i | −0.963477 | − | 0.267792i | \(-0.913706\pi\) |
0.267792 | + | 0.963477i | \(0.413706\pi\) | |||||||
\(318\) | 4.20755 | + | 24.5234i | 0.235948 | + | 1.37520i | ||||
\(319\) | 2.13998i | 0.119816i | ||||||||
\(320\) | 0.0743018 | + | 2.23483i | 0.00415360 | + | 0.124931i | ||||
\(321\) | 6.33793 | + | 4.48159i | 0.353749 | + | 0.250138i | ||||
\(322\) | 0.987879 | + | 0.987879i | 0.0550523 | + | 0.0550523i | ||||
\(323\) | 28.5958 | + | 28.5958i | 1.59111 | + | 1.59111i | ||||
\(324\) | −5.65685 | − | 7.00000i | −0.314270 | − | 0.388889i | ||||
\(325\) | 16.6471 | − | 19.0214i | 0.923413 | − | 1.05512i | ||||
\(326\) | 3.26561i | 0.180865i | ||||||||
\(327\) | 30.4920 | − | 5.23160i | 1.68621 | − | 0.289308i | ||||
\(328\) | 3.33210 | − | 3.33210i | 0.183985 | − | 0.183985i | ||||
\(329\) | −3.92982 | −0.216658 | ||||||||
\(330\) | 1.90596 | − | 2.89492i | 0.104920 | − | 0.159360i | ||||
\(331\) | 7.16510 | 0.393830 | 0.196915 | − | 0.980421i | \(-0.436908\pi\) | ||||
0.196915 | + | 0.980421i | \(0.436908\pi\) | |||||||
\(332\) | 1.55913 | − | 1.55913i | 0.0855684 | − | 0.0855684i | ||||
\(333\) | 7.65685 | + | 3.65685i | 0.419593 | + | 0.200394i | ||||
\(334\) | 7.18350i | 0.393064i | ||||||||
\(335\) | −21.9948 | − | 20.5793i | −1.20170 | − | 1.12437i | ||||
\(336\) | 0.309135 | − | 0.437183i | 0.0168647 | − | 0.0238503i | ||||
\(337\) | 19.8293 | + | 19.8293i | 1.08017 | + | 1.08017i | 0.996493 | + | 0.0836787i | \(0.0266670\pi\) |
0.0836787 | + | 0.996493i | \(0.473333\pi\) | |||||||
\(338\) | −8.87957 | − | 8.87957i | −0.482985 | − | 0.482985i | ||||
\(339\) | 0.0664943 | − | 0.0940371i | 0.00361147 | − | 0.00510739i | ||||
\(340\) | −10.0784 | − | 9.42983i | −0.546579 | − | 0.511404i | ||||
\(341\) | − | 0.894921i | − | 0.0484627i | ||||||
\(342\) | −17.7364 | − | 8.47075i | −0.959072 | − | 0.458046i | ||||
\(343\) | 3.03939 | − | 3.03939i | 0.164112 | − | 0.164112i | ||||
\(344\) | 4.77880 | 0.257656 | ||||||||
\(345\) | −9.62498 | + | 14.6192i | −0.518192 | + | 0.787069i | ||||
\(346\) | −16.8860 | −0.907798 | ||||||||
\(347\) | −2.61458 | + | 2.61458i | −0.140358 | + | 0.140358i | −0.773795 | − | 0.633437i | \(-0.781644\pi\) |
0.633437 | + | 0.773795i | \(0.281644\pi\) | |||||||
\(348\) | −4.08211 | + | 0.700379i | −0.218824 | + | 0.0375443i | ||||
\(349\) | 5.15937i | 0.276175i | 0.990420 | + | 0.138087i | \(0.0440955\pi\) | ||||
−0.990420 | + | 0.138087i | \(0.955905\pi\) | |||||||
\(350\) | 1.54226 | − | 0.102665i | 0.0824373 | − | 0.00548768i | ||||
\(351\) | −25.2773 | − | 7.14949i | −1.34920 | − | 0.381612i | ||||
\(352\) | 0.632805 | + | 0.632805i | 0.0337286 | + | 0.0337286i | ||||
\(353\) | 5.67982 | + | 5.67982i | 0.302307 | + | 0.302307i | 0.841916 | − | 0.539609i | \(-0.181428\pi\) |
−0.539609 | + | 0.841916i | \(0.681428\pi\) | |||||||
\(354\) | 9.60354 | + | 6.79073i | 0.510422 | + | 0.360923i | ||||
\(355\) | −0.932619 | − | 28.0511i | −0.0494983 | − | 1.48880i | ||||
\(356\) | 1.83947i | 0.0974916i | ||||||||
\(357\) | 0.558876 | + | 3.25737i | 0.0295789 | + | 0.172398i | ||||
\(358\) | 6.91548 | − | 6.91548i | 0.365494 | − | 0.365494i | ||||
\(359\) | 8.87284 | 0.468290 | 0.234145 | − | 0.972202i | \(-0.424771\pi\) | ||||
0.234145 | + | 0.972202i | \(0.424771\pi\) | |||||||
\(360\) | 6.14600 | + | 2.68826i | 0.323922 | + | 0.141684i | ||||
\(361\) | −23.9258 | −1.25925 | ||||||||
\(362\) | −12.1965 | + | 12.1965i | −0.641034 | + | 0.641034i | ||||
\(363\) | 2.98725 | + | 17.4110i | 0.156790 | + | 0.913839i | ||||
\(364\) | − | 1.56282i | − | 0.0819139i | ||||||
\(365\) | −16.9318 | + | 18.0964i | −0.886250 | + | 0.947207i | ||||
\(366\) | −7.94669 | − | 5.61916i | −0.415380 | − | 0.293718i | ||||
\(367\) | 7.33579 | + | 7.33579i | 0.382925 | + | 0.382925i | 0.872155 | − | 0.489230i | \(-0.162722\pi\) |
−0.489230 | + | 0.872155i | \(0.662722\pi\) | |||||||
\(368\) | −3.19562 | − | 3.19562i | −0.166583 | − | 0.166583i | ||||
\(369\) | −4.71231 | − | 13.3284i | −0.245313 | − | 0.693850i | ||||
\(370\) | −6.32106 | + | 0.210157i | −0.328616 | + | 0.0109256i | ||||
\(371\) | 4.44087i | 0.230558i | ||||||||
\(372\) | 1.70711 | − | 0.292893i | 0.0885094 | − | 0.0151858i | ||||
\(373\) | −11.2342 | + | 11.2342i | −0.581685 | + | 0.581685i | −0.935366 | − | 0.353681i | \(-0.884930\pi\) |
0.353681 | + | 0.935366i | \(0.384930\pi\) | |||||||
\(374\) | −5.52387 | −0.285632 | ||||||||
\(375\) | 5.15820 | + | 18.6653i | 0.266368 | + | 0.963871i | ||||
\(376\) | 12.7123 | 0.655587 | ||||||||
\(377\) | −8.54809 | + | 8.54809i | −0.440249 | + | 0.440249i | ||||
\(378\) | −0.783822 | − | 1.40209i | −0.0403155 | − | 0.0721158i | ||||
\(379\) | − | 16.6939i | − | 0.857509i | −0.903421 | − | 0.428754i | \(-0.858953\pi\) | ||
0.903421 | − | 0.428754i | \(-0.141047\pi\) | |||||||
\(380\) | 14.6421 | − | 0.486809i | 0.751125 | − | 0.0249728i | ||||
\(381\) | −9.06244 | + | 12.8162i | −0.464283 | + | 0.656595i | ||||
\(382\) | 17.0009 | + | 17.0009i | 0.869841 | + | 0.869841i | ||||
\(383\) | 4.38542 | + | 4.38542i | 0.224084 | + | 0.224084i | 0.810216 | − | 0.586132i | \(-0.199350\pi\) |
−0.586132 | + | 0.810216i | \(0.699350\pi\) | |||||||
\(384\) | −1.00000 | + | 1.41421i | −0.0510310 | + | 0.0721688i | ||||
\(385\) | 0.422648 | − | 0.451718i | 0.0215401 | − | 0.0230217i | ||||
\(386\) | − | 9.24478i | − | 0.470547i | ||||||
\(387\) | 6.17848 | − | 12.9367i | 0.314070 | − | 0.657611i | ||||
\(388\) | −6.81739 | + | 6.81739i | −0.346100 | + | 0.346100i | ||||
\(389\) | −0.173712 | −0.00880757 | −0.00440379 | − | 0.999990i | \(-0.501402\pi\) | ||||
−0.00440379 | + | 0.999990i | \(0.501402\pi\) | |||||||
\(390\) | 19.1770 | − | 3.95037i | 0.971067 | − | 0.200035i | ||||
\(391\) | 27.8951 | 1.41072 | ||||||||
\(392\) | −4.88217 | + | 4.88217i | −0.246587 | + | 0.246587i | ||||
\(393\) | 23.4764 | − | 4.02791i | 1.18423 | − | 0.203181i | ||||
\(394\) | 8.86216i | 0.446469i | ||||||||
\(395\) | −0.972090 | − | 29.2383i | −0.0489112 | − | 1.47114i | ||||
\(396\) | 2.53122 | − | 0.894921i | 0.127199 | − | 0.0449715i | ||||
\(397\) | 10.7268 | + | 10.7268i | 0.538365 | + | 0.538365i | 0.923048 | − | 0.384684i | \(-0.125689\pi\) |
−0.384684 | + | 0.923048i | \(0.625689\pi\) | |||||||
\(398\) | 7.60121 | + | 7.60121i | 0.381014 | + | 0.381014i | ||||
\(399\) | −2.86432 | − | 2.02538i | −0.143396 | − | 0.101396i | ||||
\(400\) | −4.98896 | + | 0.332104i | −0.249448 | + | 0.0166052i | ||||
\(401\) | − | 6.81309i | − | 0.340229i | −0.985424 | − | 0.170115i | \(-0.945586\pi\) | ||
0.985424 | − | 0.170115i | \(-0.0544138\pi\) | |||||||
\(402\) | −3.94543 | − | 22.9957i | −0.196780 | − | 1.14692i | ||||
\(403\) | 3.57474 | − | 3.57474i | 0.178071 | − | 0.178071i | ||||
\(404\) | 9.43477 | 0.469397 | ||||||||
\(405\) | 15.2235 | − | 13.1622i | 0.756463 | − | 0.654037i | ||||
\(406\) | −0.739217 | −0.0366867 | ||||||||
\(407\) | −1.78984 | + | 1.78984i | −0.0887192 | + | 0.0887192i | ||||
\(408\) | −1.80787 | − | 10.5370i | −0.0895030 | − | 0.521662i | ||||
\(409\) | − | 13.8327i | − | 0.683984i | −0.939703 | − | 0.341992i | \(-0.888898\pi\) | ||
0.939703 | − | 0.341992i | \(-0.111102\pi\) | |||||||
\(410\) | 7.69428 | + | 7.19912i | 0.379993 | + | 0.355539i | ||||
\(411\) | −7.63300 | − | 5.39735i | −0.376508 | − | 0.266231i | ||||
\(412\) | 5.08211 | + | 5.08211i | 0.250378 | + | 0.250378i | ||||
\(413\) | 1.48440 | + | 1.48440i | 0.0730423 | + | 0.0730423i | ||||
\(414\) | −12.7825 | + | 4.51929i | −0.628225 | + | 0.222111i | ||||
\(415\) | 3.60024 | + | 3.36855i | 0.176729 | + | 0.165356i | ||||
\(416\) | 5.05545i | 0.247864i | ||||||||
\(417\) | −19.1672 | + | 3.28858i | −0.938624 | + | 0.161042i | ||||
\(418\) | 4.14600 | − | 4.14600i | 0.202787 | − | 0.202787i | ||||
\(419\) | 14.3518 | 0.701130 | 0.350565 | − | 0.936538i | \(-0.385990\pi\) | ||||
0.350565 | + | 0.936538i | \(0.385990\pi\) | |||||||
\(420\) | 1.00000 | + | 0.658382i | 0.0487950 | + | 0.0321257i | ||||
\(421\) | 23.1036 | 1.12600 | 0.562999 | − | 0.826458i | \(-0.309647\pi\) | ||||
0.562999 | + | 0.826458i | \(0.309647\pi\) | |||||||
\(422\) | −2.06263 | + | 2.06263i | −0.100407 | + | 0.100407i | ||||
\(423\) | 16.4357 | − | 34.4136i | 0.799129 | − | 1.67325i | ||||
\(424\) | − | 14.3655i | − | 0.697649i | ||||||
\(425\) | 20.3252 | − | 23.2242i | 0.985919 | − | 1.12654i | ||||
\(426\) | 12.5518 | − | 17.7509i | 0.608136 | − | 0.860033i | ||||
\(427\) | −1.22830 | − | 1.22830i | −0.0594416 | − | 0.0594416i | ||||
\(428\) | −3.16897 | − | 3.16897i | −0.153178 | − | 0.153178i | ||||
\(429\) | 4.52423 | − | 6.39823i | 0.218432 | − | 0.308910i | ||||
\(430\) | 0.355074 | + | 10.6798i | 0.0171232 | + | 0.515027i | ||||
\(431\) | − | 15.4008i | − | 0.741828i | −0.928667 | − | 0.370914i | \(-0.879044\pi\) | ||
0.928667 | − | 0.370914i | \(-0.120956\pi\) | |||||||
\(432\) | 2.53553 | + | 4.53553i | 0.121991 | + | 0.218216i | ||||
\(433\) | 5.07340 | − | 5.07340i | 0.243812 | − | 0.243812i | −0.574613 | − | 0.818425i | \(-0.694847\pi\) |
0.818425 | + | 0.574613i | \(0.194847\pi\) | |||||||
\(434\) | 0.309135 | 0.0148390 | ||||||||
\(435\) | −1.86854 | − | 9.07079i | −0.0895896 | − | 0.434911i | ||||
\(436\) | −17.8618 | −0.855425 | ||||||||
\(437\) | −20.9370 | + | 20.9370i | −1.00155 | + | 1.00155i | ||||
\(438\) | −18.9199 | + | 3.24613i | −0.904026 | + | 0.155106i | ||||
\(439\) | 8.76562i | 0.418360i | 0.977877 | + | 0.209180i | \(0.0670795\pi\) | ||||
−0.977877 | + | 0.209180i | \(0.932921\pi\) | |||||||
\(440\) | −1.36720 | + | 1.46123i | −0.0651785 | + | 0.0696615i | ||||
\(441\) | 6.90444 | + | 19.5287i | 0.328783 | + | 0.929938i | ||||
\(442\) | −22.0650 | − | 22.0650i | −1.04952 | − | 1.04952i | ||||
\(443\) | 21.1417 | + | 21.1417i | 1.00447 | + | 1.00447i | 0.999990 | + | 0.00448100i | \(0.00142635\pi\) |
0.00448100 | + | 0.999990i | \(0.498574\pi\) | |||||||
\(444\) | −4.00000 | − | 2.82843i | −0.189832 | − | 0.134231i | ||||
\(445\) | −4.11091 | + | 0.136676i | −0.194876 | + | 0.00647906i | ||||
\(446\) | 19.4004i | 0.918634i | ||||||||
\(447\) | −5.03345 | − | 29.3371i | −0.238074 | − | 1.38760i | ||||
\(448\) | −0.218591 | + | 0.218591i | −0.0103275 | + | 0.0103275i | ||||
\(449\) | −9.58146 | −0.452177 | −0.226088 | − | 0.974107i | \(-0.572594\pi\) | ||||
−0.226088 | + | 0.974107i | \(0.572594\pi\) | |||||||
\(450\) | −5.55115 | + | 13.9350i | −0.261684 | + | 0.656903i | ||||
\(451\) | 4.21714 | 0.198578 | ||||||||
\(452\) | −0.0470185 | + | 0.0470185i | −0.00221157 | + | 0.00221157i | ||||
\(453\) | −5.66674 | − | 33.0282i | −0.266246 | − | 1.55180i | ||||
\(454\) | − | 10.4044i | − | 0.488304i | ||||||
\(455\) | 3.49264 | − | 0.116120i | 0.163737 | − | 0.00544380i | ||||
\(456\) | 9.26561 | + | 6.55178i | 0.433902 | + | 0.306815i | ||||
\(457\) | −8.63350 | − | 8.63350i | −0.403858 | − | 0.403858i | 0.475732 | − | 0.879590i | \(-0.342183\pi\) |
−0.879590 | + | 0.475732i | \(0.842183\pi\) | |||||||
\(458\) | −11.0470 | − | 11.0470i | −0.516193 | − | 0.516193i | ||||
\(459\) | −30.8623 | − | 8.72918i | −1.44053 | − | 0.407443i | ||||
\(460\) | 6.90424 | − | 7.37912i | 0.321912 | − | 0.344053i | ||||
\(461\) | − | 7.85481i | − | 0.365835i | −0.983128 | − | 0.182917i | \(-0.941446\pi\) | ||
0.983128 | − | 0.182917i | \(-0.0585541\pi\) | |||||||
\(462\) | 0.472274 | − | 0.0810293i | 0.0219722 | − | 0.00376983i | ||||
\(463\) | 21.6311 | − | 21.6311i | 1.00528 | − | 1.00528i | 0.00529575 | − | 0.999986i | \(-0.498314\pi\) |
0.999986 | − | 0.00529575i | \(-0.00168570\pi\) | |||||||
\(464\) | 2.39124 | 0.111011 | ||||||||
\(465\) | 0.781409 | + | 3.79334i | 0.0362370 | + | 0.175912i | ||||
\(466\) | −1.92130 | −0.0890027 | ||||||||
\(467\) | −2.83706 | + | 2.83706i | −0.131283 | + | 0.131283i | −0.769695 | − | 0.638412i | \(-0.779592\pi\) |
0.638412 | + | 0.769695i | \(0.279592\pi\) | |||||||
\(468\) | 13.6857 | + | 6.53616i | 0.632619 | + | 0.302134i | ||||
\(469\) | − | 4.16422i | − | 0.192286i | ||||||
\(470\) | 0.944547 | + | 28.4099i | 0.0435687 | + | 1.31045i | ||||
\(471\) | 17.8581 | − | 25.2552i | 0.822858 | − | 1.16370i | ||||
\(472\) | −4.80177 | − | 4.80177i | −0.221019 | − | 0.221019i | ||||
\(473\) | 3.02405 | + | 3.02405i | 0.139046 | + | 0.139046i | ||||
\(474\) | 13.0830 | − | 18.5021i | 0.600922 | − | 0.849832i | ||||
\(475\) | 2.17587 | + | 32.6865i | 0.0998359 | + | 1.49976i | ||||
\(476\) | − | 1.90812i | − | 0.0874587i | ||||||
\(477\) | −38.8889 | − | 18.5730i | −1.78060 | − | 0.850400i | ||||
\(478\) | −2.89367 | + | 2.89367i | −0.132353 | + | 0.132353i | ||||
\(479\) | 32.7974 | 1.49855 | 0.749277 | − | 0.662257i | \(-0.230401\pi\) | ||||
0.749277 | + | 0.662257i | \(0.230401\pi\) | |||||||
\(480\) | −3.23483 | − | 2.12975i | −0.147649 | − | 0.0972096i | ||||
\(481\) | −14.2990 | −0.651977 | ||||||||
\(482\) | −2.08211 | + | 2.08211i | −0.0948375 | + | 0.0948375i | ||||
\(483\) | −2.38495 | + | 0.409193i | −0.108519 | + | 0.0186189i | ||||
\(484\) | − | 10.1991i | − | 0.463596i | ||||||
\(485\) | −15.7423 | − | 14.7292i | −0.714819 | − | 0.668817i | ||||
\(486\) | 15.5563 | − | 1.00000i | 0.705650 | − | 0.0453609i | ||||
\(487\) | 5.36953 | + | 5.36953i | 0.243317 | + | 0.243317i | 0.818221 | − | 0.574904i | \(-0.194961\pi\) |
−0.574904 | + | 0.818221i | \(0.694961\pi\) | |||||||
\(488\) | 3.97334 | + | 3.97334i | 0.179865 | + | 0.179865i | ||||
\(489\) | −4.61827 | − | 3.26561i | −0.208845 | − | 0.147676i | ||||
\(490\) | −11.2736 | − | 10.5481i | −0.509289 | − | 0.476514i | ||||
\(491\) | 16.7932i | 0.757865i | 0.925424 | + | 0.378932i | \(0.123709\pi\) | ||||
−0.925424 | + | 0.378932i | \(0.876291\pi\) | |||||||
\(492\) | 1.38020 | + | 8.04441i | 0.0622243 | + | 0.362670i | ||||
\(493\) | −10.4368 | + | 10.4368i | −0.470050 | + | 0.470050i | ||||
\(494\) | 33.1222 | 1.49024 | ||||||||
\(495\) | 2.18807 | + | 5.59036i | 0.0983466 | + | 0.251268i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 2.74371 | − | 2.74371i | 0.123072 | − | 0.123072i | ||||
\(498\) | 0.645813 | + | 3.76407i | 0.0289396 | + | 0.168672i | ||||
\(499\) | − | 40.3002i | − | 1.80409i | −0.431646 | − | 0.902043i | \(-0.642067\pi\) | ||
0.431646 | − | 0.902043i | \(-0.357933\pi\) | |||||||
\(500\) | −1.11289 | − | 11.1248i | −0.0497698 | − | 0.497517i | ||||
\(501\) | −10.1590 | − | 7.18350i | −0.453871 | − | 0.320935i | ||||
\(502\) | 14.8401 | + | 14.8401i | 0.662345 | + | 0.662345i | ||||
\(503\) | −14.5686 | − | 14.5686i | −0.649584 | − | 0.649584i | 0.303309 | − | 0.952892i | \(-0.401909\pi\) |
−0.952892 | + | 0.303309i | \(0.901909\pi\) | |||||||
\(504\) | 0.309135 | + | 0.874366i | 0.0137700 | + | 0.0389473i | ||||
\(505\) | 0.701020 | + | 21.0851i | 0.0311950 | + | 0.938276i | ||||
\(506\) | − | 4.04441i | − | 0.179796i | ||||||
\(507\) | 21.4372 | − | 3.67804i | 0.952058 | − | 0.163347i | ||||
\(508\) | 6.40811 | − | 6.40811i | 0.284314 | − | 0.284314i | ||||
\(509\) | 27.4584 | 1.21707 | 0.608535 | − | 0.793527i | \(-0.291758\pi\) | ||||
0.608535 | + | 0.793527i | \(0.291758\pi\) | |||||||
\(510\) | 23.4142 | − | 4.82321i | 1.03680 | − | 0.213575i | ||||
\(511\) | −3.42614 | −0.151564 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 29.7158 | − | 16.6122i | 1.31198 | − | 0.733449i | ||||
\(514\) | 12.3777i | 0.545956i | ||||||||
\(515\) | −10.9801 | + | 11.7353i | −0.483839 | + | 0.517118i | ||||
\(516\) | −4.77880 | + | 6.75825i | −0.210375 | + | 0.297515i | ||||
\(517\) | 8.04441 | + | 8.04441i | 0.353793 | + | 0.353793i | ||||
\(518\) | −0.618270 | − | 0.618270i | −0.0271652 | − | 0.0271652i | ||||
\(519\) | 16.8860 | − | 23.8804i | 0.741214 | − | 1.04823i | ||||
\(520\) | −11.2981 | + | 0.375629i | −0.495454 | + | 0.0164724i | ||||
\(521\) | 1.83617i | 0.0804440i | 0.999191 | + | 0.0402220i | \(0.0128065\pi\) | ||||
−0.999191 | + | 0.0402220i | \(0.987193\pi\) | |||||||
\(522\) | 3.09162 | − | 6.47335i | 0.135317 | − | 0.283331i | ||||
\(523\) | −20.3678 | + | 20.3678i | −0.890622 | + | 0.890622i | −0.994582 | − | 0.103960i | \(-0.966849\pi\) |
0.103960 | + | 0.994582i | \(0.466849\pi\) | |||||||
\(524\) | −13.7521 | −0.600765 | ||||||||
\(525\) | −1.39707 | + | 2.28375i | −0.0609732 | + | 0.0996711i | ||||
\(526\) | −10.2595 | −0.447336 | ||||||||
\(527\) | 4.36459 | − | 4.36459i | 0.190124 | − | 0.190124i | ||||
\(528\) | −1.52773 | + | 0.262116i | −0.0664858 | + | 0.0114072i | ||||
\(529\) | − | 2.57600i | − | 0.112000i | ||||||
\(530\) | 32.1044 | − | 1.06738i | 1.39453 | − | 0.0463640i | ||||
\(531\) | −19.2071 | + | 6.79073i | −0.833516 | + | 0.294693i | ||||
\(532\) | 1.43216 | + | 1.43216i | 0.0620921 | + | 0.0620921i | ||||
\(533\) | 16.8453 | + | 16.8453i | 0.729651 | + | 0.729651i | ||||
\(534\) | −2.60140 | − | 1.83947i | −0.112574 | − | 0.0796016i | ||||
\(535\) | 6.84665 | − | 7.31757i | 0.296006 | − | 0.316366i | ||||
\(536\) | 13.4706i | 0.581839i | ||||||||
\(537\) | 2.86448 | + | 16.6954i | 0.123612 | + | 0.720461i | ||||
\(538\) | 16.3535 | − | 16.3535i | 0.705051 | − | 0.705051i | ||||
\(539\) | −6.17893 | −0.266145 | ||||||||
\(540\) | −9.94777 | + | 6.00349i | −0.428084 | + | 0.258349i | ||||
\(541\) | 14.4899 | 0.622972 | 0.311486 | − | 0.950251i | \(-0.399173\pi\) | ||||
0.311486 | + | 0.950251i | \(0.399173\pi\) | |||||||
\(542\) | 8.49460 | − | 8.49460i | 0.364874 | − | 0.364874i | ||||
\(543\) | −5.05196 | − | 29.4450i | −0.216800 | − | 1.26360i | ||||
\(544\) | 6.17246i | 0.264642i | ||||||||
\(545\) | −1.32716 | − | 39.9181i | −0.0568494 | − | 1.70991i | ||||
\(546\) | 2.21016 | + | 1.56282i | 0.0945860 | + | 0.0668824i | ||||
\(547\) | 5.73896 | + | 5.73896i | 0.245380 | + | 0.245380i | 0.819072 | − | 0.573691i | \(-0.194489\pi\) |
−0.573691 | + | 0.819072i | \(0.694489\pi\) | |||||||
\(548\) | 3.81650 | + | 3.81650i | 0.163033 | + | 0.163033i | ||||
\(549\) | 15.8934 | − | 5.61916i | 0.678313 | − | 0.239820i | ||||
\(550\) | −3.36720 | − | 2.94688i | −0.143578 | − | 0.125655i | ||||
\(551\) | − | 15.6669i | − | 0.667432i | ||||||
\(552\) | 7.71491 | − | 1.32367i | 0.328369 | − | 0.0563391i | ||||
\(553\) | 2.85983 | − | 2.85983i | 0.121612 | − | 0.121612i | ||||
\(554\) | −11.7608 | −0.499667 | ||||||||
\(555\) | 6.02386 | − | 9.14949i | 0.255698 | − | 0.388374i | ||||
\(556\) | 11.2279 | 0.476170 | ||||||||
\(557\) | 0.0691016 | − | 0.0691016i | 0.00292793 | − | 0.00292793i | −0.705641 | − | 0.708569i | \(-0.749341\pi\) |
0.708569 | + | 0.705641i | \(0.249341\pi\) | |||||||
\(558\) | −1.29289 | + | 2.70711i | −0.0547325 | + | 0.114601i | ||||
\(559\) | 24.1590i | 1.02182i | ||||||||
\(560\) | −0.504757 | − | 0.472274i | −0.0213299 | − | 0.0199572i | ||||
\(561\) | 5.52387 | − | 7.81193i | 0.233218 | − | 0.329820i | ||||
\(562\) | 12.8523 | + | 12.8523i | 0.542141 | + | 0.542141i | ||||
\(563\) | −24.3232 | − | 24.3232i | −1.02510 | − | 1.02510i | −0.999677 | − | 0.0254249i | \(-0.991906\pi\) |
−0.0254249 | − | 0.999677i | \(-0.508094\pi\) | |||||||
\(564\) | −12.7123 | + | 17.9779i | −0.535285 | + | 0.757007i | ||||
\(565\) | −0.108572 | − | 0.101585i | −0.00456767 | − | 0.00427371i | ||||
\(566\) | 3.95190i | 0.166111i | ||||||||
\(567\) | 2.76668 | + | 0.293600i | 0.116190 | + | 0.0123300i | ||||
\(568\) | −8.87545 | + | 8.87545i | −0.372405 | + | 0.372405i | ||||
\(569\) | 35.1115 | 1.47195 | 0.735976 | − | 0.677008i | \(-0.236724\pi\) | ||||
0.735976 | + | 0.677008i | \(0.236724\pi\) | |||||||
\(570\) | −13.9537 | + | 21.1939i | −0.584455 | + | 0.887715i | ||||
\(571\) | 6.21180 | 0.259956 | 0.129978 | − | 0.991517i | \(-0.458509\pi\) | ||||
0.129978 | + | 0.991517i | \(0.458509\pi\) | |||||||
\(572\) | −3.19912 | + | 3.19912i | −0.133762 | + | 0.133762i | ||||
\(573\) | −41.0438 | + | 7.04200i | −1.71463 | + | 0.294184i | ||||
\(574\) | 1.45674i | 0.0608031i | ||||||||
\(575\) | 17.0041 | + | 14.8815i | 0.709120 | + | 0.620603i | ||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | 23.7019 | + | 23.7019i | 0.986722 | + | 0.986722i | 0.999913 | − | 0.0131909i | \(-0.00419892\pi\) |
−0.0131909 | + | 0.999913i | \(0.504199\pi\) | |||||||
\(578\) | −14.9194 | − | 14.9194i | −0.620566 | − | 0.620566i | ||||
\(579\) | 13.0741 | + | 9.24478i | 0.543341 | + | 0.384200i | ||||
\(580\) | 0.177674 | + | 5.34403i | 0.00737750 | + | 0.221899i | ||||
\(581\) | 0.681625i | 0.0282786i | ||||||||
\(582\) | −2.82385 | − | 16.4586i | −0.117052 | − | 0.682232i | ||||
\(583\) | 9.09054 | − | 9.09054i | 0.376492 | − | 0.376492i | ||||
\(584\) | 11.0830 | 0.458618 | ||||||||
\(585\) | −13.5904 | + | 31.0708i | −0.561892 | + | 1.28462i | ||||
\(586\) | 12.2439 | 0.505791 | ||||||||
\(587\) | −16.7138 | + | 16.7138i | −0.689854 | + | 0.689854i | −0.962199 | − | 0.272346i | \(-0.912201\pi\) |
0.272346 | + | 0.962199i | \(0.412201\pi\) | |||||||
\(588\) | −2.02226 | − | 11.7866i | −0.0833967 | − | 0.486072i | ||||
\(589\) | 6.55178i | 0.269961i | ||||||||
\(590\) | 10.3744 | − | 11.0879i | 0.427106 | − | 0.456483i | ||||
\(591\) | −12.5330 | − | 8.86216i | −0.515538 | − | 0.364541i | ||||
\(592\) | 2.00000 | + | 2.00000i | 0.0821995 | + | 0.0821995i | ||||
\(593\) | −23.3939 | − | 23.3939i | −0.960672 | − | 0.960672i | 0.0385829 | − | 0.999255i | \(-0.487716\pi\) |
−0.999255 | + | 0.0385829i | \(0.987716\pi\) | |||||||
\(594\) | −1.26561 | + | 4.47461i | −0.0519286 | + | 0.183595i | ||||
\(595\) | 4.26434 | − | 0.141777i | 0.174821 | − | 0.00581229i | ||||
\(596\) | 17.1853i | 0.703936i | ||||||||
\(597\) | −18.3509 | + | 3.14852i | −0.751054 | + | 0.128860i | ||||
\(598\) | 16.1553 | − | 16.1553i | 0.660640 | − | 0.660640i | ||||
\(599\) | 21.9457 | 0.896677 | 0.448339 | − | 0.893864i | \(-0.352016\pi\) | ||||
0.448339 | + | 0.893864i | \(0.352016\pi\) | |||||||
\(600\) | 4.51929 | − | 7.38756i | 0.184499 | − | 0.301596i | ||||
\(601\) | 12.5120 | 0.510376 | 0.255188 | − | 0.966891i | \(-0.417863\pi\) | ||||
0.255188 | + | 0.966891i | \(0.417863\pi\) | |||||||
\(602\) | −1.04460 | + | 1.04460i | −0.0425749 | + | 0.0425749i | ||||
\(603\) | 36.4662 | + | 17.4160i | 1.48502 | + | 0.709234i | ||||
\(604\) | 19.3474i | 0.787236i | ||||||||
\(605\) | 22.7933 | − | 0.757813i | 0.926680 | − | 0.0308095i | ||||
\(606\) | −9.43477 | + | 13.3428i | −0.383261 | + | 0.542013i | ||||
\(607\) | 0.824660 | + | 0.824660i | 0.0334719 | + | 0.0334719i | 0.723645 | − | 0.690173i | \(-0.242465\pi\) |
−0.690173 | + | 0.723645i | \(0.742465\pi\) | |||||||
\(608\) | −4.63280 | − | 4.63280i | −0.187885 | − | 0.187885i | ||||
\(609\) | 0.739217 | − | 1.04541i | 0.0299546 | − | 0.0423622i | ||||
\(610\) | −8.58453 | + | 9.17499i | −0.347578 | + | 0.371484i | ||||
\(611\) | 64.2665i | 2.59994i | ||||||||
\(612\) | 16.7095 | + | 7.98033i | 0.675442 | + | 0.322586i | ||||
\(613\) | −30.7528 | + | 30.7528i | −1.24209 | + | 1.24209i | −0.282961 | + | 0.959132i | \(0.591317\pi\) |
−0.959132 | + | 0.282961i | \(0.908683\pi\) | |||||||
\(614\) | −13.7266 | −0.553962 | ||||||||
\(615\) | −17.8754 | + | 3.68224i | −0.720804 | + | 0.148482i | ||||
\(616\) | −0.276651 | −0.0111466 | ||||||||
\(617\) | −7.17227 | + | 7.17227i | −0.288745 | + | 0.288745i | −0.836584 | − | 0.547839i | \(-0.815451\pi\) |
0.547839 | + | 0.836584i | \(0.315451\pi\) | |||||||
\(618\) | −12.2693 | + | 2.10508i | −0.493544 | + | 0.0846787i | ||||
\(619\) | 29.0416i | 1.16728i | 0.812012 | + | 0.583640i | \(0.198372\pi\) | ||||
−0.812012 | + | 0.583640i | \(0.801628\pi\) | |||||||
\(620\) | −0.0743018 | − | 2.23483i | −0.00298403 | − | 0.0897531i | ||||
\(621\) | 6.39124 | − | 22.5965i | 0.256472 | − | 0.906765i | ||||
\(622\) | −18.4714 | − | 18.4714i | −0.740637 | − | 0.740637i | ||||
\(623\) | −0.402092 | − | 0.402092i | −0.0161095 | − | 0.0161095i | ||||
\(624\) | −7.14949 | − | 5.05545i | −0.286209 | − | 0.202380i | ||||
\(625\) | 24.7794 | − | 3.31371i | 0.991177 | − | 0.132548i | ||||
\(626\) | − | 9.59366i | − | 0.383440i | ||||||
\(627\) | 1.71733 | + | 10.0093i | 0.0685835 | + | 0.399734i | ||||
\(628\) | −12.6276 | + | 12.6276i | −0.503896 | + | 0.503896i | ||||
\(629\) | −17.4584 | −0.696110 | ||||||||
\(630\) | −1.93109 | + | 0.755832i | −0.0769366 | + | 0.0301131i | ||||
\(631\) | −29.2810 | −1.16566 | −0.582828 | − | 0.812595i | \(-0.698054\pi\) | ||||
−0.582828 | + | 0.812595i | \(0.698054\pi\) | |||||||
\(632\) | −9.25107 | + | 9.25107i | −0.367988 | + | 0.367988i | ||||
\(633\) | −0.854371 | − | 4.97964i | −0.0339582 | − | 0.197923i | ||||
\(634\) | 17.5169i | 0.695684i | ||||||||
\(635\) | 14.7972 | + | 13.8449i | 0.587209 | + | 0.549419i | ||||
\(636\) | 20.3158 | + | 14.3655i | 0.805576 | + | 0.569628i | ||||
\(637\) | −24.6816 | − | 24.6816i | −0.977920 | − | 0.977920i | ||||
\(638\) | 1.51319 | + | 1.51319i | 0.0599078 | + | 0.0599078i | ||||
\(639\) | 12.5518 | + | 35.5018i | 0.496541 | + | 1.40443i | ||||
\(640\) | 1.63280 | + | 1.52773i | 0.0645423 | + | 0.0603887i | ||||
\(641\) | 48.2990i | 1.90770i | 0.300291 | + | 0.953848i | \(0.402916\pi\) | ||||
−0.300291 | + | 0.953848i | \(0.597084\pi\) | |||||||
\(642\) | 7.65056 | − | 1.31263i | 0.301944 | − | 0.0518053i | ||||
\(643\) | −12.7695 | + | 12.7695i | −0.503579 | + | 0.503579i | −0.912548 | − | 0.408969i | \(-0.865888\pi\) |
0.408969 | + | 0.912548i | \(0.365888\pi\) | |||||||
\(644\) | 1.39707 | 0.0550523 | ||||||||
\(645\) | −15.4586 | − | 10.1777i | −0.608683 | − | 0.400746i | ||||
\(646\) | 40.4406 | 1.59111 | ||||||||
\(647\) | −5.60373 | + | 5.60373i | −0.220306 | + | 0.220306i | −0.808627 | − | 0.588322i | \(-0.799789\pi\) |
0.588322 | + | 0.808627i | \(0.299789\pi\) | |||||||
\(648\) | −8.94975 | − | 0.949747i | −0.351579 | − | 0.0373096i | ||||
\(649\) | − | 6.07717i | − | 0.238550i | ||||||
\(650\) | −1.67894 | − | 25.2214i | −0.0658533 | − | 0.989266i | ||||
\(651\) | −0.309135 | + | 0.437183i | −0.0121160 | + | 0.0171345i | ||||
\(652\) | 2.30913 | + | 2.30913i | 0.0904327 | + | 0.0904327i | ||||
\(653\) | 5.29935 | + | 5.29935i | 0.207379 | + | 0.207379i | 0.803153 | − | 0.595773i | \(-0.203154\pi\) |
−0.595773 | + | 0.803153i | \(0.703154\pi\) | |||||||
\(654\) | 17.8618 | − | 25.2604i | 0.698452 | − | 0.987760i | ||||
\(655\) | −1.02181 | − | 30.7337i | −0.0399254 | − | 1.20087i | ||||
\(656\) | − | 4.71231i | − | 0.183985i | ||||||
\(657\) | 14.3291 | − | 30.0029i | 0.559033 | − | 1.17052i | ||||
\(658\) | −2.77880 | + | 2.77880i | −0.108329 | + | 0.108329i | ||||
\(659\) | −40.4185 | −1.57448 | −0.787241 | − | 0.616646i | \(-0.788491\pi\) | ||||
−0.787241 | + | 0.616646i | \(0.788491\pi\) | |||||||
\(660\) | −0.699299 | − | 3.39474i | −0.0272202 | − | 0.132140i | ||||
\(661\) | 8.54986 | 0.332551 | 0.166276 | − | 0.986079i | \(-0.446826\pi\) | ||||
0.166276 | + | 0.986079i | \(0.446826\pi\) | |||||||
\(662\) | 5.06649 | − | 5.06649i | 0.196915 | − | 0.196915i | ||||
\(663\) | 53.2695 | − | 9.13961i | 2.06882 | − | 0.354953i | ||||
\(664\) | − | 2.20494i | − | 0.0855684i | ||||||
\(665\) | −3.09423 | + | 3.30706i | −0.119989 | + | 0.128242i | ||||
\(666\) | 8.00000 | − | 2.82843i | 0.309994 | − | 0.109599i | ||||
\(667\) | −7.64151 | − | 7.64151i | −0.295881 | − | 0.295881i | ||||
\(668\) | 5.07950 | + | 5.07950i | 0.196532 | + | 0.196532i | ||||
\(669\) | −27.4363 | − | 19.4004i | −1.06075 | − | 0.750062i | ||||
\(670\) | −30.1044 | + | 1.00089i | −1.16304 | + | 0.0386676i | ||||
\(671\) | 5.02870i | 0.194131i | ||||||||
\(672\) | −0.0905435 | − | 0.527726i | −0.00349279 | − | 0.0203575i | ||||
\(673\) | −25.2231 | + | 25.2231i | −0.972278 | + | 0.972278i | −0.999626 | − | 0.0273475i | \(-0.991294\pi\) |
0.0273475 | + | 0.999626i | \(0.491294\pi\) | |||||||
\(674\) | 28.0429 | 1.08017 | ||||||||
\(675\) | −14.1559 | − | 21.7855i | −0.544863 | − | 0.838525i | ||||
\(676\) | −12.5576 | −0.482985 | ||||||||
\(677\) | 32.2155 | − | 32.2155i | 1.23814 | − | 1.23814i | 0.277384 | − | 0.960759i | \(-0.410533\pi\) |
0.960759 | − | 0.277384i | \(-0.0894673\pi\) | |||||||
\(678\) | −0.0194757 | − | 0.113513i | −0.000747961 | − | 0.00435943i | ||||
\(679\) | − | 2.98044i | − | 0.114379i | ||||||
\(680\) | −13.7944 | + | 0.458625i | −0.528992 | + | 0.0175875i | ||||
\(681\) | 14.7141 | + | 10.4044i | 0.563845 | + | 0.398698i | ||||
\(682\) | −0.632805 | − | 0.632805i | −0.0242314 | − | 0.0242314i | ||||
\(683\) | −6.13560 | − | 6.13560i | −0.234772 | − | 0.234772i | 0.579909 | − | 0.814681i | \(-0.303088\pi\) |
−0.814681 | + | 0.579909i | \(0.803088\pi\) | |||||||
\(684\) | −18.5312 | + | 6.55178i | −0.708559 | + | 0.250513i | ||||
\(685\) | −8.24567 | + | 8.81281i | −0.315051 | + | 0.336720i | ||||
\(686\) | − | 4.29835i | − | 0.164112i | ||||||
\(687\) | 26.6699 | − | 4.57582i | 1.01752 | − | 0.174579i | ||||
\(688\) | 3.37912 | − | 3.37912i | 0.128828 | − | 0.128828i | ||||
\(689\) | 72.6240 | 2.76675 | ||||||||
\(690\) | 3.53141 | + | 17.1432i | 0.134439 | + | 0.652630i | ||||
\(691\) | −26.6510 | −1.01385 | −0.506926 | − | 0.861989i | \(-0.669218\pi\) | ||||
−0.506926 | + | 0.861989i | \(0.669218\pi\) | |||||||
\(692\) | −11.9402 | + | 11.9402i | −0.453899 | + | 0.453899i | ||||
\(693\) | −0.357681 | + | 0.748925i | −0.0135872 | + | 0.0284493i | ||||
\(694\) | 3.69758i | 0.140358i | ||||||||
\(695\) | 0.834254 | + | 25.0925i | 0.0316451 | + | 0.951813i | ||||
\(696\) | −2.39124 | + | 3.38173i | −0.0906399 | + | 0.128184i | ||||
\(697\) | 20.5673 | + | 20.5673i | 0.779041 | + | 0.779041i | ||||
\(698\) | 3.64823 | + | 3.64823i | 0.138087 | + | 0.138087i | ||||
\(699\) | 1.92130 | − | 2.71713i | 0.0726704 | − | 0.102771i | ||||
\(700\) | 1.01795 | − | 1.16314i | 0.0384748 | − | 0.0439625i | ||||
\(701\) | − | 50.7429i | − | 1.91653i | −0.285878 | − | 0.958266i | \(-0.592285\pi\) | ||
0.285878 | − | 0.958266i | \(-0.407715\pi\) | |||||||
\(702\) | −22.9292 | + | 12.8183i | −0.865406 | + | 0.483794i | ||||
\(703\) | 13.1036 | − | 13.1036i | 0.494210 | − | 0.494210i | ||||
\(704\) | 0.894921 | 0.0337286 | ||||||||
\(705\) | −41.1222 | − | 27.0741i | −1.54875 | − | 1.01967i | ||||
\(706\) | 8.03248 | 0.302307 | ||||||||
\(707\) | −2.06236 | + | 2.06236i | −0.0775630 | + | 0.0775630i | ||||
\(708\) | 11.5925 | − | 1.98896i | 0.435673 | − | 0.0747496i | ||||
\(709\) | 12.7840i | 0.480113i | 0.970759 | + | 0.240056i | \(0.0771659\pi\) | ||||
−0.970759 | + | 0.240056i | \(0.922834\pi\) | |||||||
\(710\) | −20.4946 | − | 19.1757i | −0.769149 | − | 0.719650i | ||||
\(711\) | 13.0830 | + | 37.0043i | 0.490651 | + | 1.38777i | ||||
\(712\) | 1.30070 | + | 1.30070i | 0.0487458 | + | 0.0487458i | ||||
\(713\) | 3.19562 | + | 3.19562i | 0.119677 | + | 0.119677i | ||||
\(714\) | 2.69849 | + | 1.90812i | 0.100989 | + | 0.0714097i | ||||
\(715\) | −7.38719 | − | 6.91179i | −0.276265 | − | 0.258486i | ||||
\(716\) | − | 9.77996i | − | 0.365494i | ||||||
\(717\) | −1.19860 | − | 6.98593i | −0.0447624 | − | 0.260894i | ||||
\(718\) | 6.27404 | − | 6.27404i | 0.234145 | − | 0.234145i | ||||
\(719\) | −37.4700 | −1.39740 | −0.698698 | − | 0.715417i | \(-0.746237\pi\) | ||||
−0.698698 | + | 0.715417i | \(0.746237\pi\) | |||||||
\(720\) | 6.24676 | − | 2.44499i | 0.232803 | − | 0.0911194i | ||||
\(721\) | −2.22181 | −0.0827446 | ||||||||
\(722\) | −16.9181 | + | 16.9181i | −0.629625 | + | 0.629625i | ||||
\(723\) | −0.862438 | − | 5.02666i | −0.0320744 | − | 0.186943i | ||||
\(724\) | 17.2485i | 0.641034i | ||||||||
\(725\) | −11.9298 | + | 0.794142i | −0.443062 | + | 0.0294937i | ||||
\(726\) | 14.4237 | + | 10.1991i | 0.535315 | + | 0.378525i | ||||
\(727\) | 14.9790 | + | 14.9790i | 0.555540 | + | 0.555540i | 0.928034 | − | 0.372494i | \(-0.121497\pi\) |
−0.372494 | + | 0.928034i | \(0.621497\pi\) | |||||||
\(728\) | −1.10508 | − | 1.10508i | −0.0409569 | − | 0.0409569i | ||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | 0.823486 | + | 24.7686i | 0.0304786 | + | 0.916729i | ||||
\(731\) | 29.4970i | 1.09098i | ||||||||
\(732\) | −9.59250 | + | 1.64581i | −0.354549 | + | 0.0608310i | ||||
\(733\) | 12.0888 | − | 12.0888i | 0.446511 | − | 0.446511i | −0.447682 | − | 0.894193i | \(-0.647750\pi\) |
0.894193 | + | 0.447682i | \(0.147750\pi\) | |||||||
\(734\) | 10.3744 | 0.382925 | ||||||||
\(735\) | 26.1908 | − | 5.39519i | 0.966064 | − | 0.199004i | ||||
\(736\) | −4.51929 | −0.166583 | ||||||||
\(737\) | −8.52423 | + | 8.52423i | −0.313994 | + | 0.313994i | ||||
\(738\) | −12.7567 | − | 6.09251i | −0.469581 | − | 0.224268i | ||||
\(739\) | 6.73275i | 0.247668i | 0.992303 | + | 0.123834i | \(0.0395191\pi\) | ||||
−0.992303 | + | 0.123834i | \(0.960481\pi\) | |||||||
\(740\) | −4.32106 | + | 4.61827i | −0.158845 | + | 0.169771i | ||||
\(741\) | −33.1222 | + | 46.8419i | −1.21677 | + | 1.72078i | ||||
\(742\) | 3.14017 | + | 3.14017i | 0.115279 | + | 0.115279i | ||||
\(743\) | 15.0314 | + | 15.0314i | 0.551449 | + | 0.551449i | 0.926859 | − | 0.375410i | \(-0.122498\pi\) |
−0.375410 | + | 0.926859i | \(0.622498\pi\) | |||||||
\(744\) | 1.00000 | − | 1.41421i | 0.0366618 | − | 0.0518476i | ||||
\(745\) | −38.4062 | + | 1.27690i | −1.40709 | + | 0.0467819i | ||||
\(746\) | 15.8876i | 0.581685i | ||||||||
\(747\) | −5.96902 | − | 2.85076i | −0.218395 | − | 0.104304i | ||||
\(748\) | −3.90596 | + | 3.90596i | −0.142816 | + | 0.142816i | ||||
\(749\) | 1.38542 | 0.0506220 | ||||||||
\(750\) | 16.8457 | + | 9.55096i | 0.615120 | + | 0.348752i | ||||
\(751\) | 34.0716 | 1.24329 | 0.621645 | − | 0.783299i | \(-0.286465\pi\) | ||||
0.621645 | + | 0.783299i | \(0.286465\pi\) | |||||||
\(752\) | 8.98896 | − | 8.98896i | 0.327794 | − | 0.327794i | ||||
\(753\) | −35.8271 | + | 6.14696i | −1.30561 | + | 0.224008i | ||||
\(754\) | 12.0888i | 0.440249i | ||||||||
\(755\) | −43.2383 | + | 1.43755i | −1.57360 | + | 0.0523178i | ||||
\(756\) | −1.54567 | − | 0.437183i | −0.0562156 | − | 0.0159002i | ||||
\(757\) | −13.4109 | − | 13.4109i | −0.487428 | − | 0.487428i | 0.420066 | − | 0.907494i | \(-0.362007\pi\) |
−0.907494 | + | 0.420066i | \(0.862007\pi\) | |||||||
\(758\) | −11.8044 | − | 11.8044i | −0.428754 | − | 0.428754i | ||||
\(759\) | 5.71966 | + | 4.04441i | 0.207611 | + | 0.146803i | ||||
\(760\) | 10.0093 | − | 10.6978i | 0.363076 | − | 0.388049i | ||||
\(761\) | − | 51.2537i | − | 1.85794i | −0.370151 | − | 0.928972i | \(-0.620694\pi\) | ||
0.370151 | − | 0.928972i | \(-0.379306\pi\) | |||||||
\(762\) | 2.65433 | + | 15.4706i | 0.0961561 | + | 0.560439i | ||||
\(763\) | 3.90444 | − | 3.90444i | 0.141350 | − | 0.141350i | ||||
\(764\) | 24.0429 | 0.869841 | ||||||||
\(765\) | −16.5932 | + | 37.9359i | −0.599927 | + | 1.37158i | ||||
\(766\) | 6.20192 | 0.224084 | ||||||||
\(767\) | 24.2751 | − | 24.2751i | 0.876524 | − | 0.876524i | ||||
\(768\) | 0.292893 | + | 1.70711i | 0.0105689 | + | 0.0615999i | ||||
\(769\) | 21.1359i | 0.762181i | 0.924538 | + | 0.381090i | \(0.124451\pi\) | ||||
−0.924538 | + | 0.381090i | \(0.875549\pi\) | |||||||
\(770\) | −0.0205557 | − | 0.618270i | −0.000740776 | − | 0.0222809i | ||||
\(771\) | −17.5047 | − | 12.3777i | −0.630416 | − | 0.445771i | ||||
\(772\) | −6.53705 | − | 6.53705i | −0.235273 | − | 0.235273i | ||||
\(773\) | 5.10946 | + | 5.10946i | 0.183774 | + | 0.183774i | 0.792998 | − | 0.609224i | \(-0.208519\pi\) |
−0.609224 | + | 0.792998i | \(0.708519\pi\) | |||||||
\(774\) | −4.77880 | − | 13.5165i | −0.171770 | − | 0.485840i | ||||
\(775\) | 4.98896 | − | 0.332104i | 0.179209 | − | 0.0119295i | ||||
\(776\) | 9.64124i | 0.346100i | ||||||||
\(777\) | 1.49264 | − | 0.256096i | 0.0535480 | − | 0.00918738i | ||||
\(778\) | −0.122833 | + | 0.122833i | −0.00440379 | + | 0.00440379i | ||||
\(779\) | −30.8740 | −1.10618 | ||||||||
\(780\) | 10.7669 | − | 16.3535i | 0.385516 | − | 0.585551i | ||||
\(781\) | −11.2329 | −0.401943 | ||||||||
\(782\) | 19.7248 | − | 19.7248i | 0.705359 | − | 0.705359i | ||||
\(783\) | 6.06308 | + | 10.8456i | 0.216677 | + | 0.387589i | ||||
\(784\) | 6.90444i | 0.246587i | ||||||||
\(785\) | −29.1588 | − | 27.2823i | −1.04072 | − | 0.973747i | ||||
\(786\) | 13.7521 | − | 19.4485i | 0.490523 | − | 0.693704i | ||||
\(787\) | 5.33840 | + | 5.33840i | 0.190293 | + | 0.190293i | 0.795823 | − | 0.605529i | \(-0.207039\pi\) |
−0.605529 | + | 0.795823i | \(0.707039\pi\) | |||||||
\(788\) | 6.26650 | + | 6.26650i | 0.223235 | + | 0.223235i | ||||
\(789\) | 10.2595 | − | 14.5091i | 0.365248 | − | 0.516539i | ||||
\(790\) | −21.3620 | − | 19.9872i | −0.760025 | − | 0.711114i | ||||
\(791\) | − | 0.0205557i | − | 0.000730877i | ||||||
\(792\) | 1.15704 | − | 2.42265i | 0.0411135 | − | 0.0860850i | ||||
\(793\) | −20.0870 | + | 20.0870i | −0.713312 | + | 0.713312i | ||||
\(794\) | 15.1700 | 0.538365 | ||||||||
\(795\) | −30.5949 | + | 46.4699i | −1.08509 | + | 1.64812i | ||||
\(796\) | 10.7497 | 0.381014 | ||||||||
\(797\) | 2.18933 | − | 2.18933i | 0.0775500 | − | 0.0775500i | −0.667268 | − | 0.744818i | \(-0.732536\pi\) |
0.744818 | + | 0.667268i | \(0.232536\pi\) | |||||||
\(798\) | −3.45754 | + | 0.593221i | −0.122396 | + | 0.0209998i | ||||
\(799\) | 78.4662i | 2.77593i | ||||||||
\(800\) | −3.29289 | + | 3.76256i | −0.116421 | + | 0.133027i | ||||
\(801\) | 5.20280 | − | 1.83947i | 0.183832 | − | 0.0649944i | ||||
\(802\) | −4.81758 | − | 4.81758i | −0.170115 | − | 0.170115i | ||||
\(803\) | 7.01337 | + | 7.01337i | 0.247497 | + | 0.247497i | ||||
\(804\) | −19.0502 | − | 13.4706i | −0.671850 | − | 0.475070i | ||||
\(805\) | 0.103805 | + | 3.12222i | 0.00365864 | + | 0.110044i | ||||
\(806\) | − | 5.05545i | − | 0.178071i | ||||||
\(807\) | 6.77386 | + | 39.4810i | 0.238451 | + | 1.38980i | ||||
\(808\) | 6.67139 | − | 6.67139i | 0.234699 | − | 0.234699i | ||||
\(809\) | −2.54711 | −0.0895516 | −0.0447758 | − | 0.998997i | \(-0.514257\pi\) | ||||
−0.0447758 | + | 0.998997i | \(0.514257\pi\) | |||||||
\(810\) | 1.45754 | − | 20.0718i | 0.0512129 | − | 0.705250i | ||||
\(811\) | −5.43529 | −0.190859 | −0.0954294 | − | 0.995436i | \(-0.530422\pi\) | ||||
−0.0954294 | + | 0.995436i | \(0.530422\pi\) | |||||||
\(812\) | −0.522705 | + | 0.522705i | −0.0183434 | + | 0.0183434i | ||||
\(813\) | 3.51858 | + | 20.5078i | 0.123402 | + | 0.719239i | ||||
\(814\) | 2.53122i | 0.0887192i | ||||||||
\(815\) | −4.98896 | + | 5.33210i | −0.174756 | + | 0.186775i | ||||
\(816\) | −8.72918 | − | 6.17246i | −0.305582 | − | 0.216079i | ||||
\(817\) | −22.1393 | − | 22.1393i | −0.774554 | − | 0.774554i | ||||
\(818\) | −9.78121 | − | 9.78121i | −0.341992 | − | 0.341992i | ||||
\(819\) | −4.42031 | + | 1.56282i | −0.154458 | + | 0.0546093i | ||||
\(820\) | 10.5312 | − | 0.350133i | 0.367766 | − | 0.0122272i | ||||
\(821\) | − | 15.6179i | − | 0.545069i | −0.962146 | − | 0.272534i | \(-0.912138\pi\) | ||
0.962146 | − | 0.272534i | \(-0.0878618\pi\) | |||||||
\(822\) | −9.21384 | + | 1.58085i | −0.321370 | + | 0.0551383i | ||||
\(823\) | 24.6369 | − | 24.6369i | 0.858789 | − | 0.858789i | −0.132407 | − | 0.991195i | \(-0.542271\pi\) |
0.991195 | + | 0.132407i | \(0.0422705\pi\) | |||||||
\(824\) | 7.18719 | 0.250378 | ||||||||
\(825\) | 7.53471 | − | 1.81505i | 0.262325 | − | 0.0631920i | ||||
\(826\) | 2.09925 | 0.0730423 | ||||||||
\(827\) | 16.9360 | − | 16.9360i | 0.588924 | − | 0.588924i | −0.348416 | − | 0.937340i | \(-0.613280\pi\) |
0.937340 | + | 0.348416i | \(0.113280\pi\) | |||||||
\(828\) | −5.84296 | + | 12.2342i | −0.203057 | + | 0.425168i | ||||
\(829\) | 16.4317i | 0.570696i | 0.958424 | + | 0.285348i | \(0.0921092\pi\) | ||||
−0.958424 | + | 0.285348i | \(0.907891\pi\) | |||||||
\(830\) | 4.92768 | − | 0.163831i | 0.171042 | − | 0.00568666i | ||||
\(831\) | 11.7608 | − | 16.6322i | 0.407977 | − | 0.576966i | ||||
\(832\) | 3.57474 | + | 3.57474i | 0.123932 | + | 0.123932i | ||||
\(833\) | −30.1350 | − | 30.1350i | −1.04412 | − | 1.04412i | ||||
\(834\) | −11.2279 | + | 15.8787i | −0.388791 | + | 0.549833i | ||||
\(835\) | −10.9744 | + | 11.7293i | −0.379786 | + | 0.405908i | ||||
\(836\) | − | 5.86332i | − | 0.202787i | ||||||
\(837\) | −2.53553 | − | 4.53553i | −0.0876409 | − | 0.156771i | ||||
\(838\) | 10.1482 | − | 10.1482i | 0.350565 | − | 0.350565i | ||||
\(839\) | 35.2129 | 1.21569 | 0.607843 | − | 0.794057i | \(-0.292035\pi\) | ||||
0.607843 | + | 0.794057i | \(0.292035\pi\) | |||||||
\(840\) | 1.17265 | − | 0.241561i | 0.0404604 | − | 0.00833464i | ||||
\(841\) | −23.2820 | −0.802826 | ||||||||
\(842\) | 16.3367 | − | 16.3367i | 0.562999 | − | 0.562999i | ||||
\(843\) | −31.0282 | + | 5.32359i | −1.06867 | + | 0.183354i | ||||
\(844\) | 2.91700i | 0.100407i | ||||||||
\(845\) | −0.933052 | − | 28.0641i | −0.0320980 | − | 0.965436i | ||||
\(846\) | −12.7123 | − | 35.9558i | −0.437058 | − | 1.23619i | ||||
\(847\) | 2.22944 | + | 2.22944i | 0.0766044 | + | 0.0766044i | ||||
\(848\) | −10.1579 | − | 10.1579i | −0.348825 | − | 0.348825i | ||||
\(849\) | −5.58883 | − | 3.95190i | −0.191808 | − | 0.135629i | ||||
\(850\) | −2.04990 | − | 30.7941i | −0.0703110 | − | 1.05623i | ||||
\(851\) | − | 12.7825i | − | 0.438178i | ||||||
\(852\) | −3.67633 | − | 21.4272i | −0.125949 | − | 0.734085i | ||||
\(853\) | 14.1055 | − | 14.1055i | 0.482964 | − | 0.482964i | −0.423113 | − | 0.906077i | \(-0.639063\pi\) |
0.906077 | + | 0.423113i | \(0.139063\pi\) | |||||||
\(854\) | −1.73708 | −0.0594416 | ||||||||
\(855\) | −16.0190 | − | 40.9274i | −0.547839 | − | 1.39969i | ||||
\(856\) | −4.48159 | −0.153178 | ||||||||
\(857\) | 34.6304 | − | 34.6304i | 1.18295 | − | 1.18295i | 0.203978 | − | 0.978975i | \(-0.434613\pi\) |
0.978975 | − | 0.203978i | \(-0.0653871\pi\) | |||||||
\(858\) | −1.32512 | − | 7.72335i | −0.0452388 | − | 0.263671i | ||||
\(859\) | − | 11.2737i | − | 0.384653i | −0.981331 | − | 0.192327i | \(-0.938397\pi\) | ||
0.981331 | − | 0.192327i | \(-0.0616033\pi\) | |||||||
\(860\) | 7.80285 | + | 7.30070i | 0.266075 | + | 0.248952i | ||||
\(861\) | −2.06014 | − | 1.45674i | −0.0702094 | − | 0.0496455i | ||||
\(862\) | −10.8900 | − | 10.8900i | −0.370914 | − | 0.370914i | ||||
\(863\) | −24.7143 | − | 24.7143i | −0.841284 | − | 0.841284i | 0.147742 | − | 0.989026i | \(-0.452799\pi\) |
−0.989026 | + | 0.147742i | \(0.952799\pi\) | |||||||
\(864\) | 5.00000 | + | 1.41421i | 0.170103 | + | 0.0481125i | ||||
\(865\) | −27.5716 | − | 25.7972i | −0.937462 | − | 0.877132i | ||||
\(866\) | − | 7.17487i | − | 0.243812i | ||||||
\(867\) | 36.0187 | − | 6.17983i | 1.22326 | − | 0.209878i | ||||
\(868\) | 0.218591 | − | 0.218591i | 0.00741948 | − | 0.00741948i | ||||
\(869\) | −11.7083 | −0.397175 | ||||||||
\(870\) | −7.73528 | − | 5.09276i | −0.262250 | − | 0.172661i | ||||
\(871\) | −68.0997 | −2.30747 | ||||||||
\(872\) | −12.6302 | + | 12.6302i | −0.427712 | + | 0.427712i | ||||
\(873\) | 26.0999 | + | 12.4651i | 0.883347 | + | 0.421879i | ||||
\(874\) | 29.6094i | 1.00155i | ||||||||
\(875\) | 2.67506 | + | 2.18852i | 0.0904334 | + | 0.0739855i | ||||
\(876\) | −11.0830 | + | 15.6737i | −0.374460 | + | 0.529566i | ||||
\(877\) | −21.9874 | − | 21.9874i | −0.742462 | − | 0.742462i | 0.230589 | − | 0.973051i | \(-0.425935\pi\) |
−0.973051 | + | 0.230589i | \(0.925935\pi\) | |||||||
\(878\) | 6.19823 | + | 6.19823i | 0.209180 | + | 0.209180i | ||||
\(879\) | −12.2439 | + | 17.3155i | −0.412976 | + | 0.584037i | ||||
\(880\) | 0.0664943 | + | 2.00000i | 0.00224152 | + | 0.0674200i | ||||
\(881\) | 50.8515i | 1.71323i | 0.515954 | + | 0.856616i | \(0.327437\pi\) | ||||
−0.515954 | + | 0.856616i | \(0.672563\pi\) | |||||||
\(882\) | 18.6910 | + | 8.92670i | 0.629360 | + | 0.300578i | ||||
\(883\) | −18.7011 | + | 18.7011i | −0.629341 | + | 0.629341i | −0.947902 | − | 0.318561i | \(-0.896800\pi\) |
0.318561 | + | 0.947902i | \(0.396800\pi\) | |||||||
\(884\) | −31.2046 | −1.04952 | ||||||||
\(885\) | 5.30633 | + | 25.7595i | 0.178370 | + | 0.865897i | ||||
\(886\) | 29.8988 | 1.00447 | ||||||||
\(887\) | 14.9041 | − | 14.9041i | 0.500430 | − | 0.500430i | −0.411142 | − | 0.911571i | \(-0.634870\pi\) |
0.911571 | + | 0.411142i | \(0.134870\pi\) | |||||||
\(888\) | −4.82843 | + | 0.828427i | −0.162031 | + | 0.0278002i | ||||
\(889\) | 2.80152i | 0.0939599i | ||||||||
\(890\) | −2.81020 | + | 3.00349i | −0.0941983 | + | 0.100677i | ||||
\(891\) | −5.06244 | − | 6.26445i | −0.169598 | − | 0.209867i | ||||
\(892\) | 13.7181 | + | 13.7181i | 0.459317 | + | 0.459317i | ||||
\(893\) | −58.8936 | − | 58.8936i | −1.97080 | − | 1.97080i | ||||
\(894\) | −24.3036 | − | 17.1853i | −0.812836 | − | 0.574762i | ||||
\(895\) | 21.8566 | − | 0.726669i | 0.730585 | − | 0.0242899i | ||||
\(896\) | 0.309135i | 0.0103275i | ||||||||
\(897\) | 6.69175 | + | 39.0024i | 0.223431 | + | 1.30225i | ||||
\(898\) | −6.77511 | + | 6.77511i | −0.226088 | + | 0.226088i | ||||
\(899\) | −2.39124 | −0.0797525 | ||||||||
\(900\) | 5.92829 | + | 13.7788i | 0.197610 | + | 0.459293i | ||||
\(901\) | 88.6703 | 2.95404 | ||||||||
\(902\) | 2.98197 | − | 2.98197i | 0.0992888 | − | 0.0992888i | ||||
\(903\) | −0.432690 | − | 2.52190i | −0.0143990 | − | 0.0839236i | ||||
\(904\) | 0.0664943i | 0.00221157i | ||||||||
\(905\) | −38.5474 | + | 1.28159i | −1.28136 | + | 0.0426016i | ||||
\(906\) | −27.3614 | − | 19.3474i | −0.909022 | − | 0.642776i | ||||
\(907\) | 28.6764 | + | 28.6764i | 0.952184 | + | 0.952184i | 0.998908 | − | 0.0467242i | \(-0.0148782\pi\) |
−0.0467242 | + | 0.998908i | \(0.514878\pi\) | |||||||
\(908\) | −7.35704 | − | 7.35704i | −0.244152 | − | 0.244152i | ||||
\(909\) | −9.43477 | − | 26.6856i | −0.312932 | − | 0.885104i | ||||
\(910\) | 2.38756 | − | 2.55178i | 0.0791467 | − | 0.0845905i | ||||
\(911\) | − | 31.2435i | − | 1.03514i | −0.855640 | − | 0.517572i | \(-0.826836\pi\) | ||
0.855640 | − | 0.517572i | \(-0.173164\pi\) | |||||||
\(912\) | 11.1846 | − | 1.91897i | 0.370358 | − | 0.0635435i | ||||
\(913\) | 1.39530 | − | 1.39530i | 0.0461776 | − | 0.0461776i | ||||
\(914\) | −12.2096 | −0.403858 | ||||||||
\(915\) | −4.39086 | − | 21.3153i | −0.145157 | − | 0.704664i | ||||
\(916\) | −15.6228 | −0.516193 | ||||||||
\(917\) | 3.00610 | − | 3.00610i | 0.0992702 | − | 0.0992702i | ||||
\(918\) | −27.9954 | + | 15.6505i | −0.923986 | + | 0.516543i | ||||
\(919\) | − | 35.4719i | − | 1.17011i | −0.810993 | − | 0.585056i | \(-0.801073\pi\) | ||
0.810993 | − | 0.585056i | \(-0.198927\pi\) | |||||||
\(920\) | −0.335792 | − | 10.0999i | −0.0110707 | − | 0.332983i | ||||
\(921\) | 13.7266 | − | 19.4124i | 0.452308 | − | 0.639661i | ||||
\(922\) | −5.55419 | − | 5.55419i | −0.182917 | − | 0.182917i | ||||
\(923\) | −44.8694 | − | 44.8694i | −1.47689 | − | 1.47689i | ||||
\(924\) | 0.276651 | − | 0.391244i | 0.00910117 | − | 0.0128710i | ||||
\(925\) | −10.6421 | − | 9.31371i | −0.349911 | − | 0.306233i | ||||
\(926\) | − | 30.5910i | − | 1.00528i | ||||||
\(927\) | 9.29227 | − | 19.4565i | 0.305198 | − | 0.639035i | ||||
\(928\) | 1.69087 | − | 1.69087i | 0.0555054 | − | 0.0555054i | ||||
\(929\) | 12.0618 | 0.395736 | 0.197868 | − | 0.980229i | \(-0.436598\pi\) | ||||
0.197868 | + | 0.980229i | \(0.436598\pi\) | |||||||
\(930\) | 3.23483 | + | 2.12975i | 0.106074 | + | 0.0698374i | ||||
\(931\) | 45.2363 | 1.48256 | ||||||||
\(932\) | −1.35857 | + | 1.35857i | −0.0445013 | + | 0.0445013i | ||||
\(933\) | 44.5940 | − | 7.65112i | 1.45994 | − | 0.250486i | ||||
\(934\) | 4.01220i | 0.131283i | ||||||||
\(935\) | −9.01940 | − | 8.43896i | −0.294966 | − | 0.275983i | ||||
\(936\) | 14.2990 | − | 5.05545i | 0.467377 | − | 0.165243i | ||||
\(937\) | 29.9584 | + | 29.9584i | 0.978697 | + | 0.978697i | 0.999778 | − | 0.0210808i | \(-0.00671072\pi\) |
−0.0210808 | + | 0.999778i | \(0.506711\pi\) | |||||||
\(938\) | −2.94455 | − | 2.94455i | −0.0961429 | − | 0.0961429i | ||||
\(939\) | 13.5675 | + | 9.59366i | 0.442758 | + | 0.313077i | ||||
\(940\) | 20.7567 | + | 19.4209i | 0.677010 | + | 0.633441i | ||||
\(941\) | 19.1066i | 0.622858i | 0.950269 | + | 0.311429i | \(0.100808\pi\) | ||||
−0.950269 | + | 0.311429i | \(0.899192\pi\) | |||||||
\(942\) | −5.23052 | − | 30.4857i | −0.170420 | − | 0.993278i | ||||
\(943\) | −15.0588 | + | 15.0588i | −0.490380 | + | 0.490380i | ||||
\(944\) | −6.79073 | −0.221019 | ||||||||
\(945\) | 0.862184 | − | 3.48681i | 0.0280469 | − | 0.113426i | ||||
\(946\) | 4.27665 | 0.139046 | ||||||||
\(947\) | 5.88211 | − | 5.88211i | 0.191143 | − | 0.191143i | −0.605047 | − | 0.796190i | \(-0.706846\pi\) |
0.796190 | + | 0.605047i | \(0.206846\pi\) | |||||||
\(948\) | −3.83192 | − | 22.3341i | −0.124455 | − | 0.725377i | ||||
\(949\) | 56.0296i | 1.81880i | ||||||||
\(950\) | 24.6514 | + | 21.5743i | 0.799799 | + | 0.699963i | ||||
\(951\) | −24.7726 | − | 17.5169i | −0.803307 | − | 0.568024i | ||||
\(952\) | −1.34925 | − | 1.34925i | −0.0437293 | − | 0.0437293i | ||||
\(953\) | 5.01193 | + | 5.01193i | 0.162352 | + | 0.162352i | 0.783608 | − | 0.621256i | \(-0.213377\pi\) |
−0.621256 | + | 0.783608i | \(0.713377\pi\) | |||||||
\(954\) | −40.6317 | + | 14.3655i | −1.31550 | + | 0.465099i | ||||
\(955\) | 1.78643 | + | 53.7318i | 0.0578075 | + | 1.73872i | ||||
\(956\) | 4.09226i | 0.132353i | ||||||||
\(957\) | −3.65317 | + | 0.626784i | −0.118090 | + | 0.0202611i | ||||
\(958\) | 23.1913 | − | 23.1913i | 0.749277 | − | 0.749277i | ||||
\(959\) | −1.66851 | −0.0538789 | ||||||||
\(960\) | −3.79334 | + | 0.781409i | −0.122429 | + | 0.0252199i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −10.1109 | + | 10.1109i | −0.325989 | + | 0.325989i | ||||
\(963\) | −5.79422 | + | 12.1322i | −0.186716 | + | 0.390953i | ||||
\(964\) | 2.94455i | 0.0948375i | ||||||||
\(965\) | 14.1235 | − | 15.0949i | 0.454651 | − | 0.485923i | ||||
\(966\) | −1.39707 | + | 1.97576i | −0.0449500 | + | 0.0635689i | ||||
\(967\) | −17.6499 | − | 17.6499i | −0.567581 | − | 0.567581i | 0.363869 | − | 0.931450i | \(-0.381456\pi\) |
−0.931450 | + | 0.363869i | \(0.881456\pi\) | |||||||
\(968\) | −7.21186 | − | 7.21186i | −0.231798 | − | 0.231798i | ||||
\(969\) | −40.4406 | + | 57.1916i | −1.29914 | + | 1.83726i | ||||
\(970\) | −21.5466 | + | 0.716361i | −0.691818 | + | 0.0230010i | ||||
\(971\) | − | 8.99838i | − | 0.288772i | −0.989521 | − | 0.144386i | \(-0.953879\pi\) | ||
0.989521 | − | 0.144386i | \(-0.0461207\pi\) | |||||||
\(972\) | 10.2929 | − | 11.7071i | 0.330145 | − | 0.375506i | ||||
\(973\) | −2.45433 | + | 2.45433i | −0.0786821 | + | 0.0786821i | ||||
\(974\) | 7.59366 | 0.243317 | ||||||||
\(975\) | 37.3474 | + | 22.8471i | 1.19608 | + | 0.731692i | ||||
\(976\) | 5.61916 | 0.179865 | ||||||||
\(977\) | −10.3778 | + | 10.3778i | −0.332015 | + | 0.332015i | −0.853351 | − | 0.521336i | \(-0.825434\pi\) |
0.521336 | + | 0.853351i | \(0.325434\pi\) | |||||||
\(978\) | −5.57474 | + | 0.956475i | −0.178261 | + | 0.0305847i | ||||
\(979\) | 1.64618i | 0.0526121i | ||||||||
\(980\) | −15.4303 | + | 0.513012i | −0.492902 | + | 0.0163876i | ||||
\(981\) | 17.8618 | + | 50.5208i | 0.570283 | + | 1.61300i | ||||
\(982\) | 11.8746 | + | 11.8746i | 0.378932 | + | 0.378932i | ||||
\(983\) | 28.4058 | + | 28.4058i | 0.906005 | + | 0.906005i | 0.995947 | − | 0.0899417i | \(-0.0286681\pi\) |
−0.0899417 | + | 0.995947i | \(0.528668\pi\) | |||||||
\(984\) | 6.66421 | + | 4.71231i | 0.212447 | + | 0.150223i | ||||
\(985\) | −13.5390 | + | 14.4702i | −0.431387 | + | 0.461058i | ||||
\(986\) | 14.7599i | 0.470050i | ||||||||
\(987\) | −1.15102 | − | 6.70862i | −0.0366373 | − | 0.213538i | ||||
\(988\) | 23.4209 | − | 23.4209i | 0.745119 | − | 0.745119i | ||||
\(989\) | −21.5968 | −0.686738 | ||||||||
\(990\) | 5.50018 | + | 2.40578i | 0.174807 | + | 0.0764607i | ||||
\(991\) | −22.2759 | −0.707618 | −0.353809 | − | 0.935318i | \(-0.615114\pi\) | ||||
−0.353809 | + | 0.935318i | \(0.615114\pi\) | |||||||
\(992\) | −0.707107 | + | 0.707107i | −0.0224507 | + | 0.0224507i | ||||
\(993\) | 2.09861 | + | 12.2316i | 0.0665974 | + | 0.388158i | ||||
\(994\) | − | 3.88019i | − | 0.123072i | ||||||
\(995\) | 0.798724 | + | 24.0239i | 0.0253213 | + | 0.761607i | ||||
\(996\) | 3.11826 | + | 2.20494i | 0.0988058 | + | 0.0698663i | ||||
\(997\) | 24.3930 | + | 24.3930i | 0.772535 | + | 0.772535i | 0.978549 | − | 0.206014i | \(-0.0660494\pi\) |
−0.206014 | + | 0.978549i | \(0.566049\pi\) | |||||||
\(998\) | −28.4966 | − | 28.4966i | −0.902043 | − | 0.902043i | ||||
\(999\) | −4.00000 | + | 14.1421i | −0.126554 | + | 0.447437i |
(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 | 930.2.j.f.497.4 | yes | 8 | |
3.2 | odd | 2 | 930.2.j.c.497.1 | ✓ | 8 | ||
5.3 | odd | 4 | 930.2.j.c.683.1 | yes | 8 | ||
15.8 | even | 4 | inner | 930.2.j.f.683.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.c.497.1 | ✓ | 8 | 3.2 | odd | 2 | ||
930.2.j.c.683.1 | yes | 8 | 5.3 | odd | 4 | ||
930.2.j.f.497.4 | yes | 8 | 1.1 | even | 1 | trivial | |
930.2.j.f.683.4 | yes | 8 | 15.8 | even | 4 | inner |