Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1273.5 | ||
Root | \(-1.07534 - 1.96052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1273 |
Dual form | 1470.2.m.c.97.5 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.22280 | + | 0.243230i | −0.994066 | + | 0.108776i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.39977 | + | 1.74375i | −0.442645 | + | 0.551421i | ||||
\(11\) | −5.33525 | −1.60864 | −0.804319 | − | 0.594197i | \(-0.797470\pi\) | ||||
−0.804319 | + | 0.594197i | \(0.797470\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | −3.82733 | + | 3.82733i | −1.06151 | + | 1.06151i | −0.0635301 | + | 0.997980i | \(0.520236\pi\) |
−0.997980 | + | 0.0635301i | \(0.979764\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.39977 | + | 1.74375i | −0.361418 | + | 0.450233i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 5.19896 | + | 5.19896i | 1.26093 | + | 1.26093i | 0.950641 | + | 0.310293i | \(0.100427\pi\) |
0.310293 | + | 0.950641i | \(0.399573\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | 3.04189 | 0.697858 | 0.348929 | − | 0.937149i | \(-0.386545\pi\) | ||||
0.348929 | + | 0.937149i | \(0.386545\pi\) | |||||||
\(20\) | 0.243230 | + | 2.22280i | 0.0543879 | + | 0.497033i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.77259 | + | 3.77259i | −0.804319 | + | 0.804319i | ||||
\(23\) | −1.63559 | − | 1.63559i | −0.341044 | − | 0.341044i | 0.515716 | − | 0.856760i | \(-0.327526\pi\) |
−0.856760 | + | 0.515716i | \(0.827526\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.88168 | − | 1.08130i | 0.976336 | − | 0.216261i | ||||
\(26\) | 5.41266i | 1.06151i | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.97911i | 0.924598i | 0.886724 | + | 0.462299i | \(0.152975\pi\) | ||||
−0.886724 | + | 0.462299i | \(0.847025\pi\) | |||||||
\(30\) | 0.243230 | + | 2.22280i | 0.0444075 | + | 0.405826i | ||||
\(31\) | 6.37678i | 1.14530i | 0.819799 | + | 0.572652i | \(0.194085\pi\) | ||||
−0.819799 | + | 0.572652i | \(0.805915\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.77259 | + | 3.77259i | −0.656724 | + | 0.656724i | ||||
\(34\) | 7.35245 | 1.26093 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.11124 | − | 2.11124i | 0.347086 | − | 0.347086i | −0.511937 | − | 0.859023i | \(-0.671072\pi\) |
0.859023 | + | 0.511937i | \(0.171072\pi\) | |||||||
\(38\) | 2.15094 | − | 2.15094i | 0.348929 | − | 0.348929i | ||||
\(39\) | 5.41266i | 0.866719i | ||||||||
\(40\) | 1.74375 | + | 1.39977i | 0.275711 | + | 0.221323i | ||||
\(41\) | 10.4281i | 1.62860i | 0.580442 | + | 0.814301i | \(0.302880\pi\) | ||||
−0.580442 | + | 0.814301i | \(0.697120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.27961 | + | 1.27961i | 0.195139 | + | 0.195139i | 0.797912 | − | 0.602774i | \(-0.205938\pi\) |
−0.602774 | + | 0.797912i | \(0.705938\pi\) | |||||||
\(44\) | 5.33525i | 0.804319i | ||||||||
\(45\) | 0.243230 | + | 2.22280i | 0.0362586 | + | 0.331355i | ||||
\(46\) | −2.31307 | −0.341044 | ||||||||
\(47\) | −8.75513 | − | 8.75513i | −1.27707 | − | 1.27707i | −0.942301 | − | 0.334766i | \(-0.891343\pi\) |
−0.334766 | − | 0.942301i | \(-0.608657\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.68727 | − | 4.21646i | 0.380038 | − | 0.596298i | ||||
\(51\) | 7.35245 | 1.02955 | ||||||||
\(52\) | 3.82733 | + | 3.82733i | 0.530755 | + | 0.530755i | ||||
\(53\) | −4.91277 | − | 4.91277i | −0.674820 | − | 0.674820i | 0.284003 | − | 0.958823i | \(-0.408337\pi\) |
−0.958823 | + | 0.284003i | \(0.908337\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 11.8592 | − | 1.29769i | 1.59909 | − | 0.174981i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.15094 | − | 2.15094i | 0.284899 | − | 0.284899i | ||||
\(58\) | 3.52077 | + | 3.52077i | 0.462299 | + | 0.462299i | ||||
\(59\) | −6.15893 | −0.801824 | −0.400912 | − | 0.916117i | \(-0.631307\pi\) | ||||
−0.400912 | + | 0.916117i | \(0.631307\pi\) | |||||||
\(60\) | 1.74375 | + | 1.39977i | 0.225117 | + | 0.180709i | ||||
\(61\) | − | 0.777764i | − | 0.0995824i | −0.998760 | − | 0.0497912i | \(-0.984144\pi\) | ||
0.998760 | − | 0.0497912i | \(-0.0158556\pi\) | |||||||
\(62\) | 4.50907 | + | 4.50907i | 0.572652 | + | 0.572652i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 7.57646 | − | 9.43831i | 0.939745 | − | 1.17068i | ||||
\(66\) | 5.33525i | 0.656724i | ||||||||
\(67\) | −5.72162 | + | 5.72162i | −0.699007 | + | 0.699007i | −0.964196 | − | 0.265189i | \(-0.914566\pi\) |
0.265189 | + | 0.964196i | \(0.414566\pi\) | |||||||
\(68\) | 5.19896 | − | 5.19896i | 0.630467 | − | 0.630467i | ||||
\(69\) | −2.31307 | −0.278461 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.85378 | −0.694715 | −0.347358 | − | 0.937733i | \(-0.612921\pi\) | ||||
−0.347358 | + | 0.937733i | \(0.612921\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −5.03959 | + | 5.03959i | −0.589840 | + | 0.589840i | −0.937588 | − | 0.347748i | \(-0.886946\pi\) |
0.347748 | + | 0.937588i | \(0.386946\pi\) | |||||||
\(74\) | − | 2.98575i | − | 0.347086i | ||||||
\(75\) | 2.68727 | − | 4.21646i | 0.310299 | − | 0.486875i | ||||
\(76\) | − | 3.04189i | − | 0.348929i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.82733 | + | 3.82733i | 0.433360 | + | 0.433360i | ||||
\(79\) | − | 11.3463i | − | 1.27656i | −0.769805 | − | 0.638279i | \(-0.779647\pi\) | ||
0.769805 | − | 0.638279i | \(-0.220353\pi\) | |||||||
\(80\) | 2.22280 | − | 0.243230i | 0.248517 | − | 0.0271939i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 7.37381 | + | 7.37381i | 0.814301 | + | 0.814301i | ||||
\(83\) | −2.41890 | + | 2.41890i | −0.265509 | + | 0.265509i | −0.827288 | − | 0.561779i | \(-0.810117\pi\) |
0.561779 | + | 0.827288i | \(0.310117\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.8208 | − | 10.2917i | −1.39061 | − | 1.11629i | ||||
\(86\) | 1.80964 | 0.195139 | ||||||||
\(87\) | 3.52077 | + | 3.52077i | 0.377466 | + | 0.377466i | ||||
\(88\) | 3.77259 | + | 3.77259i | 0.402160 | + | 0.402160i | ||||
\(89\) | −3.19810 | −0.338998 | −0.169499 | − | 0.985530i | \(-0.554215\pi\) | ||||
−0.169499 | + | 0.985530i | \(0.554215\pi\) | |||||||
\(90\) | 1.74375 | + | 1.39977i | 0.183807 | + | 0.147548i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.63559 | + | 1.63559i | −0.170522 | + | 0.170522i | ||||
\(93\) | 4.50907 | + | 4.50907i | 0.467568 | + | 0.467568i | ||||
\(94\) | −12.3816 | −1.27707 | ||||||||
\(95\) | −6.76152 | + | 0.739880i | −0.693717 | + | 0.0759101i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 4.72414 | + | 4.72414i | 0.479664 | + | 0.479664i | 0.905024 | − | 0.425360i | \(-0.139853\pi\) |
−0.425360 | + | 0.905024i | \(0.639853\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.33525i | 0.536213i | ||||||||
\(100\) | −1.08130 | − | 4.88168i | −0.108130 | − | 0.488168i | ||||
\(101\) | − | 10.2204i | − | 1.01697i | −0.861072 | − | 0.508483i | \(-0.830206\pi\) | ||
0.861072 | − | 0.508483i | \(-0.169794\pi\) | |||||||
\(102\) | 5.19896 | − | 5.19896i | 0.514774 | − | 0.514774i | ||||
\(103\) | −0.809817 | + | 0.809817i | −0.0797936 | + | 0.0797936i | −0.745877 | − | 0.666084i | \(-0.767969\pi\) |
0.666084 | + | 0.745877i | \(0.267969\pi\) | |||||||
\(104\) | 5.41266 | 0.530755 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.94770 | −0.674820 | ||||||||
\(107\) | −10.1474 | + | 10.1474i | −0.980991 | + | 0.980991i | −0.999823 | − | 0.0188320i | \(-0.994005\pi\) |
0.0188320 | + | 0.999823i | \(0.494005\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 2.97059i | 0.284531i | 0.989829 | + | 0.142265i | \(0.0454386\pi\) | ||||
−0.989829 | + | 0.142265i | \(0.954561\pi\) | |||||||
\(110\) | 7.46811 | − | 9.30333i | 0.712056 | − | 0.887037i | ||||
\(111\) | − | 2.98575i | − | 0.283395i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.14988 | + | 5.14988i | 0.484460 | + | 0.484460i | 0.906553 | − | 0.422093i | \(-0.138704\pi\) |
−0.422093 | + | 0.906553i | \(0.638704\pi\) | |||||||
\(114\) | − | 3.04189i | − | 0.284899i | ||||||
\(115\) | 4.03342 | + | 3.23777i | 0.376118 | + | 0.301923i | ||||
\(116\) | 4.97911 | 0.462299 | ||||||||
\(117\) | 3.82733 | + | 3.82733i | 0.353837 | + | 0.353837i | ||||
\(118\) | −4.35502 | + | 4.35502i | −0.400912 | + | 0.400912i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.22280 | − | 0.243230i | 0.202913 | − | 0.0222038i | ||||
\(121\) | 17.4649 | 1.58772 | ||||||||
\(122\) | −0.549962 | − | 0.549962i | −0.0497912 | − | 0.0497912i | ||||
\(123\) | 7.37381 | + | 7.37381i | 0.664874 | + | 0.664874i | ||||
\(124\) | 6.37678 | 0.572652 | ||||||||
\(125\) | −10.5880 | + | 3.59089i | −0.947018 | + | 0.321179i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.20668 | + | 1.20668i | −0.107075 | + | 0.107075i | −0.758615 | − | 0.651539i | \(-0.774124\pi\) |
0.651539 | + | 0.758615i | \(0.274124\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 1.80964 | 0.159330 | ||||||||
\(130\) | −1.31652 | − | 12.0313i | −0.115467 | − | 1.05521i | ||||
\(131\) | 19.4185i | 1.69660i | 0.529516 | + | 0.848300i | \(0.322374\pi\) | ||||
−0.529516 | + | 0.848300i | \(0.677626\pi\) | |||||||
\(132\) | 3.77259 | + | 3.77259i | 0.328362 | + | 0.328362i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.09159i | 0.699007i | ||||||||
\(135\) | 1.74375 | + | 1.39977i | 0.150078 | + | 0.120473i | ||||
\(136\) | − | 7.35245i | − | 0.630467i | ||||||
\(137\) | −7.80852 | + | 7.80852i | −0.667127 | + | 0.667127i | −0.957050 | − | 0.289923i | \(-0.906370\pi\) |
0.289923 | + | 0.957050i | \(0.406370\pi\) | |||||||
\(138\) | −1.63559 | + | 1.63559i | −0.139231 | + | 0.139231i | ||||
\(139\) | −11.7913 | −1.00013 | −0.500064 | − | 0.865989i | \(-0.666690\pi\) | ||||
−0.500064 | + | 0.865989i | \(0.666690\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.3816 | −1.04272 | ||||||||
\(142\) | −4.13924 | + | 4.13924i | −0.347358 | + | 0.347358i | ||||
\(143\) | 20.4198 | − | 20.4198i | 1.70759 | − | 1.70759i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −1.21107 | − | 11.0676i | −0.100574 | − | 0.919112i | ||||
\(146\) | 7.12706i | 0.589840i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.11124 | − | 2.11124i | −0.173543 | − | 0.173543i | ||||
\(149\) | − | 21.3443i | − | 1.74860i | −0.485390 | − | 0.874298i | \(-0.661322\pi\) | ||
0.485390 | − | 0.874298i | \(-0.338678\pi\) | |||||||
\(150\) | −1.08130 | − | 4.88168i | −0.0882880 | − | 0.398587i | ||||
\(151\) | 6.89343 | 0.560980 | 0.280490 | − | 0.959857i | \(-0.409503\pi\) | ||||
0.280490 | + | 0.959857i | \(0.409503\pi\) | |||||||
\(152\) | −2.15094 | − | 2.15094i | −0.174465 | − | 0.174465i | ||||
\(153\) | 5.19896 | − | 5.19896i | 0.420311 | − | 0.420311i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.55103 | − | 14.1743i | −0.124581 | − | 1.13851i | ||||
\(156\) | 5.41266 | 0.433360 | ||||||||
\(157\) | 5.07142 | + | 5.07142i | 0.404744 | + | 0.404744i | 0.879901 | − | 0.475157i | \(-0.157609\pi\) |
−0.475157 | + | 0.879901i | \(0.657609\pi\) | |||||||
\(158\) | −8.02304 | − | 8.02304i | −0.638279 | − | 0.638279i | ||||
\(159\) | −6.94770 | −0.550988 | ||||||||
\(160\) | 1.39977 | − | 1.74375i | 0.110661 | − | 0.137855i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −3.30725 | − | 3.30725i | −0.259044 | − | 0.259044i | 0.565621 | − | 0.824665i | \(-0.308636\pi\) |
−0.824665 | + | 0.565621i | \(0.808636\pi\) | |||||||
\(164\) | 10.4281 | 0.814301 | ||||||||
\(165\) | 7.46811 | − | 9.30333i | 0.581392 | − | 0.724263i | ||||
\(166\) | 3.42085i | 0.265509i | ||||||||
\(167\) | 5.19936 | + | 5.19936i | 0.402338 | + | 0.402338i | 0.879056 | − | 0.476718i | \(-0.158174\pi\) |
−0.476718 | + | 0.879056i | \(0.658174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 16.2969i | − | 1.25361i | ||||||
\(170\) | −16.3430 | + | 1.78834i | −1.25345 | + | 0.137159i | ||||
\(171\) | − | 3.04189i | − | 0.232619i | ||||||
\(172\) | 1.27961 | − | 1.27961i | 0.0975693 | − | 0.0975693i | ||||
\(173\) | 9.04482 | − | 9.04482i | 0.687665 | − | 0.687665i | −0.274050 | − | 0.961715i | \(-0.588363\pi\) |
0.961715 | + | 0.274050i | \(0.0883635\pi\) | |||||||
\(174\) | 4.97911 | 0.377466 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.33525 | 0.402160 | ||||||||
\(177\) | −4.35502 | + | 4.35502i | −0.327343 | + | 0.327343i | ||||
\(178\) | −2.26140 | + | 2.26140i | −0.169499 | + | 0.169499i | ||||
\(179\) | − | 9.80725i | − | 0.733028i | −0.930412 | − | 0.366514i | \(-0.880551\pi\) | ||
0.930412 | − | 0.366514i | \(-0.119449\pi\) | |||||||
\(180\) | 2.22280 | − | 0.243230i | 0.165678 | − | 0.0181293i | ||||
\(181\) | − | 14.3346i | − | 1.06548i | −0.846278 | − | 0.532741i | \(-0.821162\pi\) | ||
0.846278 | − | 0.532741i | \(-0.178838\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.549962 | − | 0.549962i | −0.0406544 | − | 0.0406544i | ||||
\(184\) | 2.31307i | 0.170522i | ||||||||
\(185\) | −4.17935 | + | 5.20639i | −0.307272 | + | 0.382781i | ||||
\(186\) | 6.37678 | 0.467568 | ||||||||
\(187\) | −27.7378 | − | 27.7378i | −2.02839 | − | 2.02839i | ||||
\(188\) | −8.75513 | + | 8.75513i | −0.638534 | + | 0.638534i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.25794 | + | 5.30429i | −0.308904 | + | 0.384814i | ||||
\(191\) | −6.50768 | −0.470879 | −0.235439 | − | 0.971889i | \(-0.575653\pi\) | ||||
−0.235439 | + | 0.971889i | \(0.575653\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 16.0866 | + | 16.0866i | 1.15794 | + | 1.15794i | 0.984919 | + | 0.173019i | \(0.0553521\pi\) |
0.173019 | + | 0.984919i | \(0.444648\pi\) | |||||||
\(194\) | 6.68094 | 0.479664 | ||||||||
\(195\) | −1.31652 | − | 12.0313i | −0.0942781 | − | 0.861576i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.52204 | + | 8.52204i | −0.607170 | + | 0.607170i | −0.942206 | − | 0.335035i | \(-0.891252\pi\) |
0.335035 | + | 0.942206i | \(0.391252\pi\) | |||||||
\(198\) | 3.77259 | + | 3.77259i | 0.268106 | + | 0.268106i | ||||
\(199\) | −5.68230 | −0.402808 | −0.201404 | − | 0.979508i | \(-0.564550\pi\) | ||||
−0.201404 | + | 0.979508i | \(0.564550\pi\) | |||||||
\(200\) | −4.21646 | − | 2.68727i | −0.298149 | − | 0.190019i | ||||
\(201\) | 8.09159i | 0.570737i | ||||||||
\(202\) | −7.22690 | − | 7.22690i | −0.508483 | − | 0.508483i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 7.35245i | − | 0.514774i | ||||||
\(205\) | −2.53644 | − | 23.1797i | −0.177153 | − | 1.61894i | ||||
\(206\) | 1.14525i | 0.0797936i | ||||||||
\(207\) | −1.63559 | + | 1.63559i | −0.113681 | + | 0.113681i | ||||
\(208\) | 3.82733 | − | 3.82733i | 0.265378 | − | 0.265378i | ||||
\(209\) | −16.2293 | −1.12260 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.9905 | 1.92695 | 0.963474 | − | 0.267803i | \(-0.0862978\pi\) | ||||
0.963474 | + | 0.267803i | \(0.0862978\pi\) | |||||||
\(212\) | −4.91277 | + | 4.91277i | −0.337410 | + | 0.337410i | ||||
\(213\) | −4.13924 | + | 4.13924i | −0.283616 | + | 0.283616i | ||||
\(214\) | 14.3507i | 0.980991i | ||||||||
\(215\) | −3.15555 | − | 2.53308i | −0.215207 | − | 0.172754i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.10052 | + | 2.10052i | 0.142265 | + | 0.142265i | ||||
\(219\) | 7.12706i | 0.481602i | ||||||||
\(220\) | −1.29769 | − | 11.8592i | −0.0874905 | − | 0.799547i | ||||
\(221\) | −39.7963 | −2.67699 | ||||||||
\(222\) | −2.11124 | − | 2.11124i | −0.141697 | − | 0.141697i | ||||
\(223\) | 0.994508 | − | 0.994508i | 0.0665972 | − | 0.0665972i | −0.673024 | − | 0.739621i | \(-0.735005\pi\) |
0.739621 | + | 0.673024i | \(0.235005\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.08130 | − | 4.88168i | −0.0720869 | − | 0.325445i | ||||
\(226\) | 7.28303 | 0.484460 | ||||||||
\(227\) | −11.7968 | − | 11.7968i | −0.782980 | − | 0.782980i | 0.197352 | − | 0.980333i | \(-0.436766\pi\) |
−0.980333 | + | 0.197352i | \(0.936766\pi\) | |||||||
\(228\) | −2.15094 | − | 2.15094i | −0.142450 | − | 0.142450i | ||||
\(229\) | 0.535959 | 0.0354172 | 0.0177086 | − | 0.999843i | \(-0.494363\pi\) | ||||
0.0177086 | + | 0.999843i | \(0.494363\pi\) | |||||||
\(230\) | 5.14150 | − | 0.562609i | 0.339021 | − | 0.0370973i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.52077 | − | 3.52077i | 0.231150 | − | 0.231150i | ||||
\(233\) | 15.3761 | + | 15.3761i | 1.00732 | + | 1.00732i | 0.999973 | + | 0.00734582i | \(0.00233827\pi\) |
0.00734582 | + | 0.999973i | \(0.497662\pi\) | |||||||
\(234\) | 5.41266 | 0.353837 | ||||||||
\(235\) | 21.5904 | + | 17.3314i | 1.40840 | + | 1.13058i | ||||
\(236\) | 6.15893i | 0.400912i | ||||||||
\(237\) | −8.02304 | − | 8.02304i | −0.521153 | − | 0.521153i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.25205i | 0.210357i | 0.994453 | + | 0.105179i | \(0.0335415\pi\) | ||||
−0.994453 | + | 0.105179i | \(0.966459\pi\) | |||||||
\(240\) | 1.39977 | − | 1.74375i | 0.0903546 | − | 0.112558i | ||||
\(241\) | − | 13.7283i | − | 0.884316i | −0.896937 | − | 0.442158i | \(-0.854213\pi\) | ||
0.896937 | − | 0.442158i | \(-0.145787\pi\) | |||||||
\(242\) | 12.3496 | − | 12.3496i | 0.793860 | − | 0.793860i | ||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −0.777764 | −0.0497912 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4281 | 0.664874 | ||||||||
\(247\) | −11.6423 | + | 11.6423i | −0.740783 | + | 0.740783i | ||||
\(248\) | 4.50907 | − | 4.50907i | 0.286326 | − | 0.286326i | ||||
\(249\) | 3.42085i | 0.216787i | ||||||||
\(250\) | −4.94769 | + | 10.0260i | −0.312920 | + | 0.634099i | ||||
\(251\) | − | 10.6569i | − | 0.672656i | −0.941745 | − | 0.336328i | \(-0.890815\pi\) | ||
0.941745 | − | 0.336328i | \(-0.109185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.72629 | + | 8.72629i | 0.548617 | + | 0.548617i | ||||
\(254\) | 1.70650i | 0.107075i | ||||||||
\(255\) | −16.3430 | + | 1.78834i | −1.02344 | + | 0.111990i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.53556 | + | 1.53556i | 0.0957858 | + | 0.0957858i | 0.753376 | − | 0.657590i | \(-0.228424\pi\) |
−0.657590 | + | 0.753376i | \(0.728424\pi\) | |||||||
\(258\) | 1.27961 | − | 1.27961i | 0.0796650 | − | 0.0796650i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.43831 | − | 7.57646i | −0.585339 | − | 0.469872i | ||||
\(261\) | 4.97911 | 0.308199 | ||||||||
\(262\) | 13.7309 | + | 13.7309i | 0.848300 | + | 0.848300i | ||||
\(263\) | 13.9959 | + | 13.9959i | 0.863025 | + | 0.863025i | 0.991688 | − | 0.128664i | \(-0.0410687\pi\) |
−0.128664 | + | 0.991688i | \(0.541069\pi\) | |||||||
\(264\) | 5.33525 | 0.328362 | ||||||||
\(265\) | 12.1150 | + | 9.72516i | 0.744220 | + | 0.597412i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.26140 | + | 2.26140i | −0.138395 | + | 0.138395i | ||||
\(268\) | 5.72162 | + | 5.72162i | 0.349504 | + | 0.349504i | ||||
\(269\) | −11.6671 | −0.711353 | −0.355677 | − | 0.934609i | \(-0.615750\pi\) | ||||
−0.355677 | + | 0.934609i | \(0.615750\pi\) | |||||||
\(270\) | 2.22280 | − | 0.243230i | 0.135275 | − | 0.0148025i | ||||
\(271\) | 11.2204i | 0.681588i | 0.940138 | + | 0.340794i | \(0.110696\pi\) | ||||
−0.940138 | + | 0.340794i | \(0.889304\pi\) | |||||||
\(272\) | −5.19896 | − | 5.19896i | −0.315234 | − | 0.315234i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.0429i | 0.667127i | ||||||||
\(275\) | −26.0450 | + | 5.76903i | −1.57057 | + | 0.347885i | ||||
\(276\) | 2.31307i | 0.139231i | ||||||||
\(277\) | 14.5443 | − | 14.5443i | 0.873881 | − | 0.873881i | −0.119012 | − | 0.992893i | \(-0.537973\pi\) |
0.992893 | + | 0.119012i | \(0.0379726\pi\) | |||||||
\(278\) | −8.33773 | + | 8.33773i | −0.500064 | + | 0.500064i | ||||
\(279\) | 6.37678 | 0.381768 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.810507 | 0.0483508 | 0.0241754 | − | 0.999708i | \(-0.492304\pi\) | ||||
0.0241754 | + | 0.999708i | \(0.492304\pi\) | |||||||
\(282\) | −8.75513 | + | 8.75513i | −0.521361 | + | 0.521361i | ||||
\(283\) | −2.35075 | + | 2.35075i | −0.139738 | + | 0.139738i | −0.773515 | − | 0.633778i | \(-0.781503\pi\) |
0.633778 | + | 0.773515i | \(0.281503\pi\) | |||||||
\(284\) | 5.85378i | 0.347358i | ||||||||
\(285\) | −4.25794 | + | 5.30429i | −0.252219 | + | 0.314199i | ||||
\(286\) | − | 28.8779i | − | 1.70759i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 37.0585i | 2.17991i | ||||||||
\(290\) | −8.68231 | − | 6.96960i | −0.509843 | − | 0.409269i | ||||
\(291\) | 6.68094 | 0.391644 | ||||||||
\(292\) | 5.03959 | + | 5.03959i | 0.294920 | + | 0.294920i | ||||
\(293\) | −5.05031 | + | 5.05031i | −0.295042 | + | 0.295042i | −0.839068 | − | 0.544026i | \(-0.816899\pi\) |
0.544026 | + | 0.839068i | \(0.316899\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6901 | − | 1.49804i | 0.797066 | − | 0.0872190i | ||||
\(296\) | −2.98575 | −0.173543 | ||||||||
\(297\) | 3.77259 | + | 3.77259i | 0.218908 | + | 0.218908i | ||||
\(298\) | −15.0927 | − | 15.0927i | −0.874298 | − | 0.874298i | ||||
\(299\) | 12.5199 | 0.724044 | ||||||||
\(300\) | −4.21646 | − | 2.68727i | −0.243438 | − | 0.155150i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.87439 | − | 4.87439i | 0.280490 | − | 0.280490i | ||||
\(303\) | −7.22690 | − | 7.22690i | −0.415175 | − | 0.415175i | ||||
\(304\) | −3.04189 | −0.174465 | ||||||||
\(305\) | 0.189175 | + | 1.72881i | 0.0108322 | + | 0.0989916i | ||||
\(306\) | − | 7.35245i | − | 0.420311i | ||||||
\(307\) | −19.1533 | − | 19.1533i | −1.09314 | − | 1.09314i | −0.995192 | − | 0.0979470i | \(-0.968772\pi\) |
−0.0979470 | − | 0.995192i | \(-0.531228\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.14525i | 0.0651512i | ||||||||
\(310\) | −11.1195 | − | 8.92601i | −0.631545 | − | 0.506963i | ||||
\(311\) | − | 16.8569i | − | 0.955868i | −0.878396 | − | 0.477934i | \(-0.841386\pi\) | ||
0.878396 | − | 0.477934i | \(-0.158614\pi\) | |||||||
\(312\) | 3.82733 | − | 3.82733i | 0.216680 | − | 0.216680i | ||||
\(313\) | −19.5236 | + | 19.5236i | −1.10354 | + | 1.10354i | −0.109558 | + | 0.993980i | \(0.534944\pi\) |
−0.993980 | + | 0.109558i | \(0.965056\pi\) | |||||||
\(314\) | 7.17208 | 0.404744 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3463 | −0.638279 | ||||||||
\(317\) | −20.6732 | + | 20.6732i | −1.16112 | + | 1.16112i | −0.176892 | + | 0.984230i | \(0.556604\pi\) |
−0.984230 | + | 0.176892i | \(0.943396\pi\) | |||||||
\(318\) | −4.91277 | + | 4.91277i | −0.275494 | + | 0.275494i | ||||
\(319\) | − | 26.5648i | − | 1.48735i | ||||||
\(320\) | −0.243230 | − | 2.22280i | −0.0135970 | − | 0.124258i | ||||
\(321\) | 14.3507i | 0.800976i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.8147 | + | 15.8147i | 0.879953 | + | 0.879953i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −14.5453 | + | 22.8223i | −0.806827 | + | 1.26595i | ||||
\(326\) | −4.67716 | −0.259044 | ||||||||
\(327\) | 2.10052 | + | 2.10052i | 0.116159 | + | 0.116159i | ||||
\(328\) | 7.37381 | − | 7.37381i | 0.407151 | − | 0.407151i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.29769 | − | 11.8592i | −0.0714357 | − | 0.652827i | ||||
\(331\) | −18.3302 | −1.00752 | −0.503759 | − | 0.863844i | \(-0.668050\pi\) | ||||
−0.503759 | + | 0.863844i | \(0.668050\pi\) | |||||||
\(332\) | 2.41890 | + | 2.41890i | 0.132755 | + | 0.132755i | ||||
\(333\) | −2.11124 | − | 2.11124i | −0.115695 | − | 0.115695i | ||||
\(334\) | 7.35300 | 0.402338 | ||||||||
\(335\) | 11.3263 | − | 14.1097i | 0.618824 | − | 0.770894i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8410 | − | 11.8410i | 0.645021 | − | 0.645021i | −0.306765 | − | 0.951785i | \(-0.599246\pi\) |
0.951785 | + | 0.306765i | \(0.0992465\pi\) | |||||||
\(338\) | −11.5236 | − | 11.5236i | −0.626804 | − | 0.626804i | ||||
\(339\) | 7.28303 | 0.395560 | ||||||||
\(340\) | −10.2917 | + | 12.8208i | −0.558146 | + | 0.695306i | ||||
\(341\) | − | 34.0217i | − | 1.84238i | ||||||
\(342\) | −2.15094 | − | 2.15094i | −0.116310 | − | 0.116310i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1.80964i | − | 0.0975693i | ||||||
\(345\) | 5.14150 | − | 0.562609i | 0.276809 | − | 0.0302899i | ||||
\(346\) | − | 12.7913i | − | 0.687665i | ||||||
\(347\) | 3.71384 | − | 3.71384i | 0.199370 | − | 0.199370i | −0.600360 | − | 0.799730i | \(-0.704976\pi\) |
0.799730 | + | 0.600360i | \(0.204976\pi\) | |||||||
\(348\) | 3.52077 | − | 3.52077i | 0.188733 | − | 0.188733i | ||||
\(349\) | 0.367827 | 0.0196893 | 0.00984466 | − | 0.999952i | \(-0.496866\pi\) | ||||
0.00984466 | + | 0.999952i | \(0.496866\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.41266 | 0.288906 | ||||||||
\(352\) | 3.77259 | − | 3.77259i | 0.201080 | − | 0.201080i | ||||
\(353\) | 19.3859 | − | 19.3859i | 1.03181 | − | 1.03181i | 0.0323299 | − | 0.999477i | \(-0.489707\pi\) |
0.999477 | − | 0.0323299i | \(-0.0102927\pi\) | |||||||
\(354\) | 6.15893i | 0.327343i | ||||||||
\(355\) | 13.0118 | − | 1.42381i | 0.690593 | − | 0.0755682i | ||||
\(356\) | 3.19810i | 0.169499i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.93477 | − | 6.93477i | −0.366514 | − | 0.366514i | ||||
\(359\) | − | 32.5796i | − | 1.71948i | −0.510728 | − | 0.859742i | \(-0.670624\pi\) | ||
0.510728 | − | 0.859742i | \(-0.329376\pi\) | |||||||
\(360\) | 1.39977 | − | 1.74375i | 0.0737742 | − | 0.0919035i | ||||
\(361\) | −9.74689 | −0.512994 | ||||||||
\(362\) | −10.1361 | − | 10.1361i | −0.532741 | − | 0.532741i | ||||
\(363\) | 12.3496 | − | 12.3496i | 0.648184 | − | 0.648184i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.97623 | − | 12.4278i | 0.522180 | − | 0.650500i | ||||
\(366\) | −0.777764 | −0.0406544 | ||||||||
\(367\) | 11.4724 | + | 11.4724i | 0.598852 | + | 0.598852i | 0.940007 | − | 0.341155i | \(-0.110818\pi\) |
−0.341155 | + | 0.940007i | \(0.610818\pi\) | |||||||
\(368\) | 1.63559 | + | 1.63559i | 0.0852611 | + | 0.0852611i | ||||
\(369\) | 10.4281 | 0.542868 | ||||||||
\(370\) | 0.726223 | + | 6.63672i | 0.0377546 | + | 0.345027i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.50907 | − | 4.50907i | 0.233784 | − | 0.233784i | ||||
\(373\) | 27.2609 | + | 27.2609i | 1.41151 | + | 1.41151i | 0.749422 | + | 0.662093i | \(0.230332\pi\) |
0.662093 | + | 0.749422i | \(0.269668\pi\) | |||||||
\(374\) | −39.2272 | −2.02839 | ||||||||
\(375\) | −4.94769 | + | 10.0260i | −0.255498 | + | 0.517739i | ||||
\(376\) | 12.3816i | 0.638534i | ||||||||
\(377\) | −19.0567 | − | 19.0567i | −0.981471 | − | 0.981471i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.65378i | − | 0.495881i | −0.968775 | − | 0.247941i | \(-0.920246\pi\) | ||
0.968775 | − | 0.247941i | \(-0.0797538\pi\) | |||||||
\(380\) | 0.739880 | + | 6.76152i | 0.0379550 | + | 0.346859i | ||||
\(381\) | 1.70650i | 0.0874266i | ||||||||
\(382\) | −4.60162 | + | 4.60162i | −0.235439 | + | 0.235439i | ||||
\(383\) | −6.93385 | + | 6.93385i | −0.354303 | + | 0.354303i | −0.861708 | − | 0.507405i | \(-0.830605\pi\) |
0.507405 | + | 0.861708i | \(0.330605\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.7499 | 1.15794 | ||||||||
\(387\) | 1.27961 | − | 1.27961i | 0.0650462 | − | 0.0650462i | ||||
\(388\) | 4.72414 | − | 4.72414i | 0.239832 | − | 0.239832i | ||||
\(389\) | − | 4.84222i | − | 0.245510i | −0.992437 | − | 0.122755i | \(-0.960827\pi\) | ||
0.992437 | − | 0.122755i | \(-0.0391730\pi\) | |||||||
\(390\) | −9.43831 | − | 7.57646i | −0.477927 | − | 0.383649i | ||||
\(391\) | − | 17.0068i | − | 0.860069i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.7309 | + | 13.7309i | 0.692634 | + | 0.692634i | ||||
\(394\) | 12.0520i | 0.607170i | ||||||||
\(395\) | 2.75976 | + | 25.2206i | 0.138859 | + | 1.26898i | ||||
\(396\) | 5.33525 | 0.268106 | ||||||||
\(397\) | −0.741854 | − | 0.741854i | −0.0372326 | − | 0.0372326i | 0.688245 | − | 0.725478i | \(-0.258381\pi\) |
−0.725478 | + | 0.688245i | \(0.758381\pi\) | |||||||
\(398\) | −4.01799 | + | 4.01799i | −0.201404 | + | 0.201404i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.88168 | + | 1.08130i | −0.244084 | + | 0.0540652i | ||||
\(401\) | 8.86775 | 0.442834 | 0.221417 | − | 0.975179i | \(-0.428932\pi\) | ||||
0.221417 | + | 0.975179i | \(0.428932\pi\) | |||||||
\(402\) | 5.72162 | + | 5.72162i | 0.285368 | + | 0.285368i | ||||
\(403\) | −24.4060 | − | 24.4060i | −1.21575 | − | 1.21575i | ||||
\(404\) | −10.2204 | −0.508483 | ||||||||
\(405\) | 2.22280 | − | 0.243230i | 0.110452 | − | 0.0120862i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.2640 | + | 11.2640i | −0.558336 | + | 0.558336i | ||||
\(408\) | −5.19896 | − | 5.19896i | −0.257387 | − | 0.257387i | ||||
\(409\) | −2.81754 | −0.139318 | −0.0696592 | − | 0.997571i | \(-0.522191\pi\) | ||||
−0.0696592 | + | 0.997571i | \(0.522191\pi\) | |||||||
\(410\) | −18.1840 | − | 14.5970i | −0.898046 | − | 0.720893i | ||||
\(411\) | 11.0429i | 0.544707i | ||||||||
\(412\) | 0.809817 | + | 0.809817i | 0.0398968 | + | 0.0398968i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.31307i | 0.113681i | ||||||||
\(415\) | 4.78839 | − | 5.96509i | 0.235053 | − | 0.292815i | ||||
\(416\) | − | 5.41266i | − | 0.265378i | ||||||
\(417\) | −8.33773 | + | 8.33773i | −0.408300 | + | 0.408300i | ||||
\(418\) | −11.4758 | + | 11.4758i | −0.561301 | + | 0.561301i | ||||
\(419\) | −14.8943 | −0.727633 | −0.363817 | − | 0.931471i | \(-0.618527\pi\) | ||||
−0.363817 | + | 0.931471i | \(0.618527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.95472 | 0.485163 | 0.242582 | − | 0.970131i | \(-0.422006\pi\) | ||||
0.242582 | + | 0.970131i | \(0.422006\pi\) | |||||||
\(422\) | 19.7923 | − | 19.7923i | 0.963474 | − | 0.963474i | ||||
\(423\) | −8.75513 | + | 8.75513i | −0.425689 | + | 0.425689i | ||||
\(424\) | 6.94770i | 0.337410i | ||||||||
\(425\) | 31.0013 | + | 19.7580i | 1.50379 | + | 0.958404i | ||||
\(426\) | 5.85378i | 0.283616i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.1474 | + | 10.1474i | 0.490495 | + | 0.490495i | ||||
\(429\) | − | 28.8779i | − | 1.39424i | ||||||
\(430\) | −4.02247 | + | 0.440159i | −0.193981 | + | 0.0212263i | ||||
\(431\) | −9.34070 | −0.449926 | −0.224963 | − | 0.974367i | \(-0.572226\pi\) | ||||
−0.224963 | + | 0.974367i | \(0.572226\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −13.5192 | + | 13.5192i | −0.649693 | + | 0.649693i | −0.952919 | − | 0.303226i | \(-0.901936\pi\) |
0.303226 | + | 0.952919i | \(0.401936\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.68231 | − | 6.96960i | −0.416285 | − | 0.334167i | ||||
\(436\) | 2.97059 | 0.142265 | ||||||||
\(437\) | −4.97529 | − | 4.97529i | −0.238000 | − | 0.238000i | ||||
\(438\) | 5.03959 | + | 5.03959i | 0.240801 | + | 0.240801i | ||||
\(439\) | 29.1942 | 1.39337 | 0.696683 | − | 0.717380i | \(-0.254659\pi\) | ||||
0.696683 | + | 0.717380i | \(0.254659\pi\) | |||||||
\(440\) | −9.30333 | − | 7.46811i | −0.443519 | − | 0.356028i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28.1402 | + | 28.1402i | −1.33849 | + | 1.33849i | ||||
\(443\) | −18.2503 | − | 18.2503i | −0.867098 | − | 0.867098i | 0.125052 | − | 0.992150i | \(-0.460090\pi\) |
−0.992150 | + | 0.125052i | \(0.960090\pi\) | |||||||
\(444\) | −2.98575 | −0.141697 | ||||||||
\(445\) | 7.10874 | − | 0.777874i | 0.336986 | − | 0.0368748i | ||||
\(446\) | − | 1.40645i | − | 0.0665972i | ||||||
\(447\) | −15.0927 | − | 15.0927i | −0.713861 | − | 0.713861i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 28.0929i | − | 1.32579i | −0.748714 | − | 0.662893i | \(-0.769328\pi\) | ||
0.748714 | − | 0.662893i | \(-0.230672\pi\) | |||||||
\(450\) | −4.21646 | − | 2.68727i | −0.198766 | − | 0.126679i | ||||
\(451\) | − | 55.6368i | − | 2.61983i | ||||||
\(452\) | 5.14988 | − | 5.14988i | 0.242230 | − | 0.242230i | ||||
\(453\) | 4.87439 | − | 4.87439i | 0.229019 | − | 0.229019i | ||||
\(454\) | −16.6832 | −0.782980 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.04189 | −0.142450 | ||||||||
\(457\) | −13.0173 | + | 13.0173i | −0.608922 | + | 0.608922i | −0.942664 | − | 0.333742i | \(-0.891688\pi\) |
0.333742 | + | 0.942664i | \(0.391688\pi\) | |||||||
\(458\) | 0.378980 | − | 0.378980i | 0.0177086 | − | 0.0177086i | ||||
\(459\) | − | 7.35245i | − | 0.343183i | ||||||
\(460\) | 3.23777 | − | 4.03342i | 0.150962 | − | 0.188059i | ||||
\(461\) | 33.1391i | 1.54344i | 0.635962 | + | 0.771720i | \(0.280604\pi\) | ||||
−0.635962 | + | 0.771720i | \(0.719396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.6083 | + | 11.6083i | 0.539484 | + | 0.539484i | 0.923377 | − | 0.383893i | \(-0.125417\pi\) |
−0.383893 | + | 0.923377i | \(0.625417\pi\) | |||||||
\(464\) | − | 4.97911i | − | 0.231150i | ||||||
\(465\) | −11.1195 | − | 8.92601i | −0.515654 | − | 0.413934i | ||||
\(466\) | 21.7450 | 1.00732 | ||||||||
\(467\) | 17.7072 | + | 17.7072i | 0.819394 | + | 0.819394i | 0.986020 | − | 0.166626i | \(-0.0532874\pi\) |
−0.166626 | + | 0.986020i | \(0.553287\pi\) | |||||||
\(468\) | 3.82733 | − | 3.82733i | 0.176918 | − | 0.176918i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 27.5219 | − | 3.01158i | 1.26949 | − | 0.138914i | ||||
\(471\) | 7.17208 | 0.330472 | ||||||||
\(472\) | 4.35502 | + | 4.35502i | 0.200456 | + | 0.200456i | ||||
\(473\) | −6.82704 | − | 6.82704i | −0.313907 | − | 0.313907i | ||||
\(474\) | −11.3463 | −0.521153 | ||||||||
\(475\) | 14.8495 | − | 3.28921i | 0.681344 | − | 0.150919i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.91277 | + | 4.91277i | −0.224940 | + | 0.224940i | ||||
\(478\) | 2.29954 | + | 2.29954i | 0.105179 | + | 0.105179i | ||||
\(479\) | 22.1797 | 1.01341 | 0.506707 | − | 0.862118i | \(-0.330863\pi\) | ||||
0.506707 | + | 0.862118i | \(0.330863\pi\) | |||||||
\(480\) | −0.243230 | − | 2.22280i | −0.0111019 | − | 0.101456i | ||||
\(481\) | 16.1608i | 0.736871i | ||||||||
\(482\) | −9.70736 | − | 9.70736i | −0.442158 | − | 0.442158i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 17.4649i | − | 0.793860i | ||||||
\(485\) | −11.6499 | − | 9.35176i | −0.528993 | − | 0.424642i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 8.53994 | − | 8.53994i | 0.386982 | − | 0.386982i | −0.486628 | − | 0.873609i | \(-0.661773\pi\) |
0.873609 | + | 0.486628i | \(0.161773\pi\) | |||||||
\(488\) | −0.549962 | + | 0.549962i | −0.0248956 | + | 0.0248956i | ||||
\(489\) | −4.67716 | −0.211508 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4241 | 0.650953 | 0.325476 | − | 0.945550i | \(-0.394475\pi\) | ||||
0.325476 | + | 0.945550i | \(0.394475\pi\) | |||||||
\(492\) | 7.37381 | − | 7.37381i | 0.332437 | − | 0.332437i | ||||
\(493\) | −25.8862 | + | 25.8862i | −1.16586 | + | 1.16586i | ||||
\(494\) | 16.4647i | 0.740783i | ||||||||
\(495\) | −1.29769 | − | 11.8592i | −0.0583270 | − | 0.533031i | ||||
\(496\) | − | 6.37678i | − | 0.286326i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.41890 | + | 2.41890i | 0.108394 | + | 0.108394i | ||||
\(499\) | − | 26.3989i | − | 1.18178i | −0.806753 | − | 0.590889i | \(-0.798777\pi\) | ||
0.806753 | − | 0.590889i | \(-0.201223\pi\) | |||||||
\(500\) | 3.59089 | + | 10.5880i | 0.160590 | + | 0.473509i | ||||
\(501\) | 7.35300 | 0.328508 | ||||||||
\(502\) | −7.53555 | − | 7.53555i | −0.336328 | − | 0.336328i | ||||
\(503\) | 28.1311 | − | 28.1311i | 1.25430 | − | 1.25430i | 0.300529 | − | 0.953773i | \(-0.402837\pi\) |
0.953773 | − | 0.300529i | \(-0.0971633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.48590 | + | 22.7179i | 0.110621 | + | 1.01093i | ||||
\(506\) | 12.3408 | 0.548617 | ||||||||
\(507\) | −11.5236 | − | 11.5236i | −0.511783 | − | 0.511783i | ||||
\(508\) | 1.20668 | + | 1.20668i | 0.0535377 | + | 0.0535377i | ||||
\(509\) | −25.6304 | −1.13605 | −0.568024 | − | 0.823012i | \(-0.692292\pi\) | ||||
−0.568024 | + | 0.823012i | \(0.692292\pi\) | |||||||
\(510\) | −10.2917 | + | 12.8208i | −0.455725 | + | 0.567715i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.15094 | − | 2.15094i | −0.0949665 | − | 0.0949665i | ||||
\(514\) | 2.17162 | 0.0957858 | ||||||||
\(515\) | 1.60309 | − | 1.99703i | 0.0706405 | − | 0.0879998i | ||||
\(516\) | − | 1.80964i | − | 0.0796650i | ||||||
\(517\) | 46.7108 | + | 46.7108i | 2.05434 | + | 2.05434i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.7913i | − | 0.561476i | ||||||
\(520\) | −12.0313 | + | 1.31652i | −0.527606 | + | 0.0577333i | ||||
\(521\) | 24.5533i | 1.07570i | 0.843041 | + | 0.537849i | \(0.180763\pi\) | ||||
−0.843041 | + | 0.537849i | \(0.819237\pi\) | |||||||
\(522\) | 3.52077 | − | 3.52077i | 0.154100 | − | 0.154100i | ||||
\(523\) | −2.18151 | + | 2.18151i | −0.0953909 | + | 0.0953909i | −0.753192 | − | 0.657801i | \(-0.771487\pi\) |
0.657801 | + | 0.753192i | \(0.271487\pi\) | |||||||
\(524\) | 19.4185 | 0.848300 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.7932 | 0.863025 | ||||||||
\(527\) | −33.1527 | + | 33.1527i | −1.44415 | + | 1.44415i | ||||
\(528\) | 3.77259 | − | 3.77259i | 0.164181 | − | 0.164181i | ||||
\(529\) | − | 17.6497i | − | 0.767378i | ||||||
\(530\) | 15.4433 | − | 1.68989i | 0.670816 | − | 0.0734041i | ||||
\(531\) | 6.15893i | 0.267275i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.9119 | − | 39.9119i | −1.72878 | − | 1.72878i | ||||
\(534\) | 3.19810i | 0.138395i | ||||||||
\(535\) | 20.0876 | − | 25.0239i | 0.868462 | − | 1.08188i | ||||
\(536\) | 8.09159 | 0.349504 | ||||||||
\(537\) | −6.93477 | − | 6.93477i | −0.299258 | − | 0.299258i | ||||
\(538\) | −8.24986 | + | 8.24986i | −0.355677 | + | 0.355677i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.39977 | − | 1.74375i | 0.0602364 | − | 0.0750389i | ||||
\(541\) | −32.9933 | −1.41849 | −0.709247 | − | 0.704961i | \(-0.750965\pi\) | ||||
−0.709247 | + | 0.704961i | \(0.750965\pi\) | |||||||
\(542\) | 7.93399 | + | 7.93399i | 0.340794 | + | 0.340794i | ||||
\(543\) | −10.1361 | − | 10.1361i | −0.434981 | − | 0.434981i | ||||
\(544\) | −7.35245 | −0.315234 | ||||||||
\(545\) | −0.722536 | − | 6.60302i | −0.0309500 | − | 0.282842i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.66749 | + | 3.66749i | −0.156811 | + | 0.156811i | −0.781152 | − | 0.624341i | \(-0.785368\pi\) |
0.624341 | + | 0.781152i | \(0.285368\pi\) | |||||||
\(548\) | 7.80852 | + | 7.80852i | 0.333563 | + | 0.333563i | ||||
\(549\) | −0.777764 | −0.0331941 | ||||||||
\(550\) | −14.3373 | + | 22.4959i | −0.611343 | + | 0.959228i | ||||
\(551\) | 15.1459i | 0.645239i | ||||||||
\(552\) | 1.63559 | + | 1.63559i | 0.0696154 | + | 0.0696154i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 20.5687i | − | 0.873881i | ||||||
\(555\) | 0.726223 | + | 6.63672i | 0.0308265 | + | 0.281713i | ||||
\(556\) | 11.7913i | 0.500064i | ||||||||
\(557\) | 11.5358 | − | 11.5358i | 0.488786 | − | 0.488786i | −0.419137 | − | 0.907923i | \(-0.637667\pi\) |
0.907923 | + | 0.419137i | \(0.137667\pi\) | |||||||
\(558\) | 4.50907 | − | 4.50907i | 0.190884 | − | 0.190884i | ||||
\(559\) | −9.79497 | −0.414283 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.2272 | −1.65617 | ||||||||
\(562\) | 0.573115 | − | 0.573115i | 0.0241754 | − | 0.0241754i | ||||
\(563\) | −10.8772 | + | 10.8772i | −0.458419 | + | 0.458419i | −0.898136 | − | 0.439717i | \(-0.855079\pi\) |
0.439717 | + | 0.898136i | \(0.355079\pi\) | |||||||
\(564\) | 12.3816i | 0.521361i | ||||||||
\(565\) | −12.6998 | − | 10.1945i | −0.534283 | − | 0.428888i | ||||
\(566\) | 3.32447i | 0.139738i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.13924 | + | 4.13924i | 0.173679 | + | 0.173679i | ||||
\(569\) | − | 3.64304i | − | 0.152724i | −0.997080 | − | 0.0763620i | \(-0.975670\pi\) | ||
0.997080 | − | 0.0763620i | \(-0.0243305\pi\) | |||||||
\(570\) | 0.739880 | + | 6.76152i | 0.0309902 | + | 0.283209i | ||||
\(571\) | 23.8194 | 0.996810 | 0.498405 | − | 0.866944i | \(-0.333919\pi\) | ||||
0.498405 | + | 0.866944i | \(0.333919\pi\) | |||||||
\(572\) | −20.4198 | − | 20.4198i | −0.853793 | − | 0.853793i | ||||
\(573\) | −4.60162 | + | 4.60162i | −0.192236 | + | 0.192236i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.75300 | − | 6.21586i | −0.406728 | − | 0.259219i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 7.24788 | + | 7.24788i | 0.301733 | + | 0.301733i | 0.841692 | − | 0.539959i | \(-0.181560\pi\) |
−0.539959 | + | 0.841692i | \(0.681560\pi\) | |||||||
\(578\) | 26.2043 | + | 26.2043i | 1.08995 | + | 1.08995i | ||||
\(579\) | 22.7499 | 0.945452 | ||||||||
\(580\) | −11.0676 | + | 1.21107i | −0.459556 | + | 0.0502870i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.72414 | − | 4.72414i | 0.195822 | − | 0.195822i | ||||
\(583\) | 26.2108 | + | 26.2108i | 1.08554 | + | 1.08554i | ||||
\(584\) | 7.12706 | 0.294920 | ||||||||
\(585\) | −9.43831 | − | 7.57646i | −0.390226 | − | 0.313248i | ||||
\(586\) | 7.14222i | 0.295042i | ||||||||
\(587\) | 11.2912 | + | 11.2912i | 0.466037 | + | 0.466037i | 0.900628 | − | 0.434591i | \(-0.143107\pi\) |
−0.434591 | + | 0.900628i | \(0.643107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.3975i | 0.799260i | ||||||||
\(590\) | 8.62106 | − | 10.7396i | 0.354923 | − | 0.442142i | ||||
\(591\) | 12.0520i | 0.495753i | ||||||||
\(592\) | −2.11124 | + | 2.11124i | −0.0867715 | + | 0.0867715i | ||||
\(593\) | −3.12947 | + | 3.12947i | −0.128512 | + | 0.128512i | −0.768437 | − | 0.639925i | \(-0.778965\pi\) |
0.639925 | + | 0.768437i | \(0.278965\pi\) | |||||||
\(594\) | 5.33525 | 0.218908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.3443 | −0.874298 | ||||||||
\(597\) | −4.01799 | + | 4.01799i | −0.164445 | + | 0.164445i | ||||
\(598\) | 8.85290 | − | 8.85290i | 0.362022 | − | 0.362022i | ||||
\(599\) | 6.34083i | 0.259079i | 0.991574 | + | 0.129540i | \(0.0413499\pi\) | ||||
−0.991574 | + | 0.129540i | \(0.958650\pi\) | |||||||
\(600\) | −4.88168 | + | 1.08130i | −0.199294 | + | 0.0441440i | ||||
\(601\) | 44.8871i | 1.83098i | 0.402338 | + | 0.915491i | \(0.368198\pi\) | ||||
−0.402338 | + | 0.915491i | \(0.631802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.72162 | + | 5.72162i | 0.233002 | + | 0.233002i | ||||
\(604\) | − | 6.89343i | − | 0.280490i | ||||||
\(605\) | −38.8210 | + | 4.24799i | −1.57830 | + | 0.172705i | ||||
\(606\) | −10.2204 | −0.415175 | ||||||||
\(607\) | −15.6974 | − | 15.6974i | −0.637139 | − | 0.637139i | 0.312710 | − | 0.949849i | \(-0.398763\pi\) |
−0.949849 | + | 0.312710i | \(0.898763\pi\) | |||||||
\(608\) | −2.15094 | + | 2.15094i | −0.0872323 | + | 0.0872323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.35622 | + | 1.08869i | 0.0549119 | + | 0.0440797i | ||||
\(611\) | 67.0176 | 2.71124 | ||||||||
\(612\) | −5.19896 | − | 5.19896i | −0.210156 | − | 0.210156i | ||||
\(613\) | 20.9439 | + | 20.9439i | 0.845918 | + | 0.845918i | 0.989621 | − | 0.143703i | \(-0.0459009\pi\) |
−0.143703 | + | 0.989621i | \(0.545901\pi\) | |||||||
\(614\) | −27.0869 | −1.09314 | ||||||||
\(615\) | −18.1840 | − | 14.5970i | −0.733251 | − | 0.588607i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.6484 | + | 19.6484i | −0.791014 | + | 0.791014i | −0.981659 | − | 0.190645i | \(-0.938942\pi\) |
0.190645 | + | 0.981659i | \(0.438942\pi\) | |||||||
\(618\) | 0.809817 | + | 0.809817i | 0.0325756 | + | 0.0325756i | ||||
\(619\) | 45.4316 | 1.82605 | 0.913026 | − | 0.407902i | \(-0.133740\pi\) | ||||
0.913026 | + | 0.407902i | \(0.133740\pi\) | |||||||
\(620\) | −14.1743 | + | 1.55103i | −0.569254 | + | 0.0622907i | ||||
\(621\) | 2.31307i | 0.0928205i | ||||||||
\(622\) | −11.9196 | − | 11.9196i | −0.477934 | − | 0.477934i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 5.41266i | − | 0.216680i | ||||||
\(625\) | 22.6616 | − | 10.5571i | 0.906463 | − | 0.422286i | ||||
\(626\) | 27.6105i | 1.10354i | ||||||||
\(627\) | −11.4758 | + | 11.4758i | −0.458300 | + | 0.458300i | ||||
\(628\) | 5.07142 | − | 5.07142i | 0.202372 | − | 0.202372i | ||||
\(629\) | 21.9525 | 0.875305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1912 | 1.24170 | 0.620851 | − | 0.783928i | \(-0.286787\pi\) | ||||
0.620851 | + | 0.783928i | \(0.286787\pi\) | |||||||
\(632\) | −8.02304 | + | 8.02304i | −0.319140 | + | 0.319140i | ||||
\(633\) | 19.7923 | − | 19.7923i | 0.786673 | − | 0.786673i | ||||
\(634\) | 29.2363i | 1.16112i | ||||||||
\(635\) | 2.38870 | − | 2.97570i | 0.0947928 | − | 0.118087i | ||||
\(636\) | 6.94770i | 0.275494i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.7842 | − | 18.7842i | −0.743673 | − | 0.743673i | ||||
\(639\) | 5.85378i | 0.231572i | ||||||||
\(640\) | −1.74375 | − | 1.39977i | −0.0689276 | − | 0.0553307i | ||||
\(641\) | 20.2641 | 0.800383 | 0.400191 | − | 0.916432i | \(-0.368944\pi\) | ||||
0.400191 | + | 0.916432i | \(0.368944\pi\) | |||||||
\(642\) | 10.1474 | + | 10.1474i | 0.400488 | + | 0.400488i | ||||
\(643\) | −2.85809 | + | 2.85809i | −0.112712 | + | 0.112712i | −0.761213 | − | 0.648501i | \(-0.775396\pi\) |
0.648501 | + | 0.761213i | \(0.275396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.02247 | + | 0.440159i | −0.158385 | + | 0.0173312i | ||||
\(646\) | 22.3654 | 0.879953 | ||||||||
\(647\) | −16.7153 | − | 16.7153i | −0.657147 | − | 0.657147i | 0.297557 | − | 0.954704i | \(-0.403828\pi\) |
−0.954704 | + | 0.297557i | \(0.903828\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 32.8594 | 1.28984 | ||||||||
\(650\) | 5.85273 | + | 26.4229i | 0.229563 | + | 1.03639i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.30725 | + | 3.30725i | −0.129522 | + | 0.129522i | ||||
\(653\) | 25.7755 | + | 25.7755i | 1.00867 | + | 1.00867i | 0.999962 | + | 0.00871283i | \(0.00277342\pi\) |
0.00871283 | + | 0.999962i | \(0.497227\pi\) | |||||||
\(654\) | 2.97059 | 0.116159 | ||||||||
\(655\) | −4.72316 | − | 43.1634i | −0.184549 | − | 1.68653i | ||||
\(656\) | − | 10.4281i | − | 0.407151i | ||||||
\(657\) | 5.03959 | + | 5.03959i | 0.196613 | + | 0.196613i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.0330i | 1.67633i | 0.545420 | + | 0.838163i | \(0.316370\pi\) | ||||
−0.545420 | + | 0.838163i | \(0.683630\pi\) | |||||||
\(660\) | −9.30333 | − | 7.46811i | −0.362131 | − | 0.290696i | ||||
\(661\) | − | 2.77875i | − | 0.108081i | −0.998539 | − | 0.0540404i | \(-0.982790\pi\) | ||
0.998539 | − | 0.0540404i | \(-0.0172100\pi\) | |||||||
\(662\) | −12.9614 | + | 12.9614i | −0.503759 | + | 0.503759i | ||||
\(663\) | −28.1402 | + | 28.1402i | −1.09288 | + | 1.09288i | ||||
\(664\) | 3.42085 | 0.132755 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.98575 | −0.115695 | ||||||||
\(667\) | 8.14379 | − | 8.14379i | 0.315329 | − | 0.315329i | ||||
\(668\) | 5.19936 | − | 5.19936i | 0.201169 | − | 0.201169i | ||||
\(669\) | − | 1.40645i | − | 0.0543764i | ||||||
\(670\) | −1.96812 | − | 17.9860i | −0.0760350 | − | 0.694859i | ||||
\(671\) | 4.14957i | 0.160192i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.5371 | − | 25.5371i | −0.984384 | − | 0.984384i | 0.0154963 | − | 0.999880i | \(-0.495067\pi\) |
−0.999880 | + | 0.0154963i | \(0.995067\pi\) | |||||||
\(674\) | − | 16.7457i | − | 0.645021i | ||||||
\(675\) | −4.21646 | − | 2.68727i | −0.162292 | − | 0.103433i | ||||
\(676\) | −16.2969 | −0.626804 | ||||||||
\(677\) | −13.3443 | − | 13.3443i | −0.512862 | − | 0.512862i | 0.402540 | − | 0.915402i | \(-0.368127\pi\) |
−0.915402 | + | 0.402540i | \(0.868127\pi\) | |||||||
\(678\) | 5.14988 | − | 5.14988i | 0.197780 | − | 0.197780i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.78834 | + | 16.3430i | 0.0685795 | + | 0.626726i | ||||
\(681\) | −16.6832 | −0.639301 | ||||||||
\(682\) | −24.0570 | − | 24.0570i | −0.921190 | − | 0.921190i | ||||
\(683\) | 20.7449 | + | 20.7449i | 0.793783 | + | 0.793783i | 0.982107 | − | 0.188324i | \(-0.0603055\pi\) |
−0.188324 | + | 0.982107i | \(0.560305\pi\) | |||||||
\(684\) | −3.04189 | −0.116310 | ||||||||
\(685\) | 15.4575 | − | 19.2560i | 0.590601 | − | 0.735736i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.378980 | − | 0.378980i | 0.0144590 | − | 0.0144590i | ||||
\(688\) | −1.27961 | − | 1.27961i | −0.0487846 | − | 0.0487846i | ||||
\(689\) | 37.6055 | 1.43266 | ||||||||
\(690\) | 3.23777 | − | 4.03342i | 0.123260 | − | 0.153549i | ||||
\(691\) | − | 41.1414i | − | 1.56509i | −0.622592 | − | 0.782546i | \(-0.713920\pi\) | ||
0.622592 | − | 0.782546i | \(-0.286080\pi\) | |||||||
\(692\) | −9.04482 | − | 9.04482i | −0.343833 | − | 0.343833i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 5.25217i | − | 0.199370i | ||||||
\(695\) | 26.2098 | − | 2.86801i | 0.994193 | − | 0.108790i | ||||
\(696\) | − | 4.97911i | − | 0.188733i | ||||||
\(697\) | −54.2156 | + | 54.2156i | −2.05356 | + | 2.05356i | ||||
\(698\) | 0.260093 | − | 0.260093i | 0.00984466 | − | 0.00984466i | ||||
\(699\) | 21.7450 | 0.822472 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.4144 | −0.884350 | −0.442175 | − | 0.896929i | \(-0.645793\pi\) | ||||
−0.442175 | + | 0.896929i | \(0.645793\pi\) | |||||||
\(702\) | 3.82733 | − | 3.82733i | 0.144453 | − | 0.144453i | ||||
\(703\) | 6.42217 | − | 6.42217i | 0.242217 | − | 0.242217i | ||||
\(704\) | − | 5.33525i | − | 0.201080i | ||||||
\(705\) | 27.5219 | − | 3.01158i | 1.03653 | − | 0.113423i | ||||
\(706\) | − | 27.4158i | − | 1.03181i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.35502 | + | 4.35502i | 0.163672 | + | 0.163672i | ||||
\(709\) | 37.4403i | 1.40610i | 0.711141 | + | 0.703049i | \(0.248179\pi\) | ||||
−0.711141 | + | 0.703049i | \(0.751821\pi\) | |||||||
\(710\) | 8.19392 | − | 10.2075i | 0.307512 | − | 0.383081i | ||||
\(711\) | −11.3463 | −0.425519 | ||||||||
\(712\) | 2.26140 | + | 2.26140i | 0.0847495 | + | 0.0847495i | ||||
\(713\) | 10.4298 | − | 10.4298i | 0.390599 | − | 0.390599i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.4223 | + | 50.3557i | −1.51171 | + | 1.88320i | ||||
\(716\) | −9.80725 | −0.366514 | ||||||||
\(717\) | 2.29954 | + | 2.29954i | 0.0858781 | + | 0.0858781i | ||||
\(718\) | −23.0372 | − | 23.0372i | −0.859742 | − | 0.859742i | ||||
\(719\) | 29.0630 | 1.08387 | 0.541934 | − | 0.840421i | \(-0.317692\pi\) | ||||
0.541934 | + | 0.840421i | \(0.317692\pi\) | |||||||
\(720\) | −0.243230 | − | 2.22280i | −0.00906465 | − | 0.0828389i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.89209 | + | 6.89209i | −0.256497 | + | 0.256497i | ||||
\(723\) | −9.70736 | − | 9.70736i | −0.361020 | − | 0.361020i | ||||
\(724\) | −14.3346 | −0.532741 | ||||||||
\(725\) | 5.38393 | + | 24.3064i | 0.199954 | + | 0.902718i | ||||
\(726\) | − | 17.4649i | − | 0.648184i | ||||||
\(727\) | 17.1526 | + | 17.1526i | 0.636155 | + | 0.636155i | 0.949605 | − | 0.313450i | \(-0.101485\pi\) |
−0.313450 | + | 0.949605i | \(0.601485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −1.73352 | − | 15.8420i | −0.0641603 | − | 0.586340i | ||||
\(731\) | 13.3053i | 0.492114i | ||||||||
\(732\) | −0.549962 | + | 0.549962i | −0.0203272 | + | 0.0203272i | ||||
\(733\) | −2.53448 | + | 2.53448i | −0.0936132 | + | 0.0936132i | −0.752362 | − | 0.658749i | \(-0.771086\pi\) |
0.658749 | + | 0.752362i | \(0.271086\pi\) | |||||||
\(734\) | 16.2244 | 0.598852 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.31307 | 0.0852611 | ||||||||
\(737\) | 30.5263 | − | 30.5263i | 1.12445 | − | 1.12445i | ||||
\(738\) | 7.37381 | − | 7.37381i | 0.271434 | − | 0.271434i | ||||
\(739\) | 5.57298i | 0.205006i | 0.994733 | + | 0.102503i | \(0.0326851\pi\) | ||||
−0.994733 | + | 0.102503i | \(0.967315\pi\) | |||||||
\(740\) | 5.20639 | + | 4.17935i | 0.191391 | + | 0.153636i | ||||
\(741\) | 16.4647i | 0.604847i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.16576 | + | 5.16576i | 0.189513 | + | 0.189513i | 0.795486 | − | 0.605972i | \(-0.207216\pi\) |
−0.605972 | + | 0.795486i | \(0.707216\pi\) | |||||||
\(744\) | − | 6.37678i | − | 0.233784i | ||||||
\(745\) | 5.19158 | + | 47.4442i | 0.190205 | + | 1.73822i | ||||
\(746\) | 38.5527 | 1.41151 | ||||||||
\(747\) | 2.41890 | + | 2.41890i | 0.0885031 | + | 0.0885031i | ||||
\(748\) | −27.7378 | + | 27.7378i | −1.01419 | + | 1.01419i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.59089 | + | 10.5880i | 0.131121 | + | 0.386619i | ||||
\(751\) | −27.2758 | −0.995308 | −0.497654 | − | 0.867376i | \(-0.665805\pi\) | ||||
−0.497654 | + | 0.867376i | \(0.665805\pi\) | |||||||
\(752\) | 8.75513 | + | 8.75513i | 0.319267 | + | 0.319267i | ||||
\(753\) | −7.53555 | − | 7.53555i | −0.274611 | − | 0.274611i | ||||
\(754\) | −26.9503 | −0.981471 | ||||||||
\(755\) | −15.3227 | + | 1.67669i | −0.557651 | + | 0.0610210i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.6453 | + | 27.6453i | −1.00479 | + | 1.00479i | −0.00479880 | + | 0.999988i | \(0.501528\pi\) |
−0.999988 | + | 0.00479880i | \(0.998472\pi\) | |||||||
\(758\) | −6.82625 | − | 6.82625i | −0.247941 | − | 0.247941i | ||||
\(759\) | 12.3408 | 0.447944 | ||||||||
\(760\) | 5.30429 | + | 4.25794i | 0.192407 | + | 0.154452i | ||||
\(761\) | 1.08093i | 0.0391837i | 0.999808 | + | 0.0195919i | \(0.00623668\pi\) | ||||
−0.999808 | + | 0.0195919i | \(0.993763\pi\) | |||||||
\(762\) | 1.20668 | + | 1.20668i | 0.0437133 | + | 0.0437133i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.50768i | 0.235439i | ||||||||
\(765\) | −10.2917 | + | 12.8208i | −0.372098 | + | 0.463537i | ||||
\(766\) | 9.80594i | 0.354303i | ||||||||
\(767\) | 23.5722 | − | 23.5722i | 0.851144 | − | 0.851144i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | −20.8561 | −0.752092 | −0.376046 | − | 0.926601i | \(-0.622717\pi\) | ||||
−0.376046 | + | 0.926601i | \(0.622717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.17162 | 0.0782088 | ||||||||
\(772\) | 16.0866 | − | 16.0866i | 0.578969 | − | 0.578969i | ||||
\(773\) | −4.97179 | + | 4.97179i | −0.178823 | + | 0.178823i | −0.790842 | − | 0.612020i | \(-0.790357\pi\) |
0.612020 | + | 0.790842i | \(0.290357\pi\) | |||||||
\(774\) | − | 1.80964i | − | 0.0650462i | ||||||
\(775\) | 6.89524 | + | 31.1294i | 0.247684 | + | 1.11820i | ||||
\(776\) | − | 6.68094i | − | 0.239832i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.42397 | − | 3.42397i | −0.122755 | − | 0.122755i | ||||
\(779\) | 31.7213i | 1.13653i | ||||||||
\(780\) | −12.0313 | + | 1.31652i | −0.430788 | + | 0.0471390i | ||||
\(781\) | 31.2314 | 1.11755 | ||||||||
\(782\) | −12.0256 | − | 12.0256i | −0.430034 | − | 0.430034i | ||||
\(783\) | 3.52077 | − | 3.52077i | 0.125822 | − | 0.125822i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.5063 | − | 10.0392i | −0.446368 | − | 0.358316i | ||||
\(786\) | 19.4185 | 0.692634 | ||||||||
\(787\) | 28.5800 | + | 28.5800i | 1.01877 | + | 1.01877i | 0.999820 | + | 0.0189465i | \(0.00603123\pi\) |
0.0189465 | + | 0.999820i | \(0.493969\pi\) | |||||||
\(788\) | 8.52204 | + | 8.52204i | 0.303585 | + | 0.303585i | ||||
\(789\) | 19.7932 | 0.704657 | ||||||||
\(790\) | 19.7851 | + | 15.8822i | 0.703921 | + | 0.565062i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.77259 | − | 3.77259i | 0.134053 | − | 0.134053i | ||||
\(793\) | 2.97676 | + | 2.97676i | 0.105708 | + | 0.105708i | ||||
\(794\) | −1.04914 | −0.0372326 | ||||||||
\(795\) | 15.4433 | − | 1.68989i | 0.547719 | − | 0.0599342i | ||||
\(796\) | 5.68230i | 0.201404i | ||||||||
\(797\) | 38.2383 | + | 38.2383i | 1.35447 | + | 1.35447i | 0.880589 | + | 0.473881i | \(0.157147\pi\) |
0.473881 | + | 0.880589i | \(0.342853\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 91.0353i | − | 3.22060i | ||||||
\(800\) | −2.68727 | + | 4.21646i | −0.0950094 | + | 0.149075i | ||||
\(801\) | 3.19810i | 0.112999i | ||||||||
\(802\) | 6.27044 | − | 6.27044i | 0.221417 | − | 0.221417i | ||||
\(803\) | 26.8875 | − | 26.8875i | 0.948839 | − | 0.948839i | ||||
\(804\) | 8.09159 | 0.285368 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −34.5154 | −1.21575 | ||||||||
\(807\) | −8.24986 | + | 8.24986i | −0.290409 | + | 0.290409i | ||||
\(808\) | −7.22690 | + | 7.22690i | −0.254241 | + | 0.254241i | ||||
\(809\) | − | 51.5137i | − | 1.81113i | −0.424212 | − | 0.905563i | \(-0.639449\pi\) | ||
0.424212 | − | 0.905563i | \(-0.360551\pi\) | |||||||
\(810\) | 1.39977 | − | 1.74375i | 0.0491828 | − | 0.0612690i | ||||
\(811\) | 23.8786i | 0.838490i | 0.907873 | + | 0.419245i | \(0.137705\pi\) | ||||
−0.907873 | + | 0.419245i | \(0.862295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.93399 | + | 7.93399i | 0.278257 | + | 0.278257i | ||||
\(814\) | 15.9297i | 0.558336i | ||||||||
\(815\) | 8.15578 | + | 6.54693i | 0.285684 | + | 0.229329i | ||||
\(816\) | −7.35245 | −0.257387 | ||||||||
\(817\) | 3.89243 | + | 3.89243i | 0.136179 | + | 0.136179i | ||||
\(818\) | −1.99230 | + | 1.99230i | −0.0696592 | + | 0.0696592i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.1797 | + | 2.53644i | −0.809470 | + | 0.0885763i | ||||
\(821\) | 12.9714 | 0.452703 | 0.226352 | − | 0.974046i | \(-0.427320\pi\) | ||||
0.226352 | + | 0.974046i | \(0.427320\pi\) | |||||||
\(822\) | 7.80852 | + | 7.80852i | 0.272353 | + | 0.272353i | ||||
\(823\) | −21.6334 | − | 21.6334i | −0.754092 | − | 0.754092i | 0.221148 | − | 0.975240i | \(-0.429019\pi\) |
−0.975240 | + | 0.221148i | \(0.929019\pi\) | |||||||
\(824\) | 1.14525 | 0.0398968 | ||||||||
\(825\) | −14.3373 | + | 22.4959i | −0.499160 | + | 0.783207i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.17418 | − | 8.17418i | 0.284244 | − | 0.284244i | −0.550555 | − | 0.834799i | \(-0.685584\pi\) |
0.834799 | + | 0.550555i | \(0.185584\pi\) | |||||||
\(828\) | 1.63559 | + | 1.63559i | 0.0568407 | + | 0.0568407i | ||||
\(829\) | −33.1649 | −1.15186 | −0.575932 | − | 0.817497i | \(-0.695361\pi\) | ||||
−0.575932 | + | 0.817497i | \(0.695361\pi\) | |||||||
\(830\) | −0.832052 | − | 7.60386i | −0.0288810 | − | 0.263934i | ||||
\(831\) | − | 20.5687i | − | 0.713521i | ||||||
\(832\) | −3.82733 | − | 3.82733i | −0.132689 | − | 0.132689i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.7913i | 0.408300i | ||||||||
\(835\) | −12.8218 | − | 10.2925i | −0.443715 | − | 0.356186i | ||||
\(836\) | 16.2293i | 0.561301i | ||||||||
\(837\) | 4.50907 | − | 4.50907i | 0.155856 | − | 0.155856i | ||||
\(838\) | −10.5318 | + | 10.5318i | −0.363817 | + | 0.363817i | ||||
\(839\) | 31.4195 | 1.08472 | 0.542360 | − | 0.840146i | \(-0.317531\pi\) | ||||
0.542360 | + | 0.840146i | \(0.317531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.20841 | 0.145118 | ||||||||
\(842\) | 7.03905 | − | 7.03905i | 0.242582 | − | 0.242582i | ||||
\(843\) | 0.573115 | − | 0.573115i | 0.0197391 | − | 0.0197391i | ||||
\(844\) | − | 27.9905i | − | 0.963474i | ||||||
\(845\) | 3.96389 | + | 36.2247i | 0.136362 | + | 1.24617i | ||||
\(846\) | 12.3816i | 0.425689i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.91277 | + | 4.91277i | 0.168705 | + | 0.168705i | ||||
\(849\) | 3.32447i | 0.114095i | ||||||||
\(850\) | 35.8923 | − | 7.95022i | 1.23109 | − | 0.272690i | ||||
\(851\) | −6.90626 | −0.236743 | ||||||||
\(852\) | 4.13924 | + | 4.13924i | 0.141808 | + | 0.141808i | ||||
\(853\) | −14.5233 | + | 14.5233i | −0.497267 | + | 0.497267i | −0.910586 | − | 0.413319i | \(-0.864369\pi\) |
0.413319 | + | 0.910586i | \(0.364369\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.739880 | + | 6.76152i | 0.0253034 | + | 0.231239i | ||||
\(856\) | 14.3507 | 0.490495 | ||||||||
\(857\) | 8.27080 | + | 8.27080i | 0.282525 | + | 0.282525i | 0.834115 | − | 0.551590i | \(-0.185979\pi\) |
−0.551590 | + | 0.834115i | \(0.685979\pi\) | |||||||
\(858\) | −20.4198 | − | 20.4198i | −0.697119 | − | 0.697119i | ||||
\(859\) | −36.0902 | −1.23138 | −0.615691 | − | 0.787988i | \(-0.711123\pi\) | ||||
−0.615691 | + | 0.787988i | \(0.711123\pi\) | |||||||
\(860\) | −2.53308 | + | 3.15555i | −0.0863772 | + | 0.107604i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.60487 | + | 6.60487i | −0.224963 | + | 0.224963i | ||||
\(863\) | −3.80716 | − | 3.80716i | −0.129597 | − | 0.129597i | 0.639333 | − | 0.768930i | \(-0.279211\pi\) |
−0.768930 | + | 0.639333i | \(0.779211\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −17.9049 | + | 22.3048i | −0.608783 | + | 0.758386i | ||||
\(866\) | 19.1191i | 0.649693i | ||||||||
\(867\) | 26.2043 | + | 26.2043i | 0.889944 | + | 0.889944i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.5354i | 2.05352i | ||||||||
\(870\) | −11.0676 | + | 1.21107i | −0.375226 | + | 0.0410591i | ||||
\(871\) | − | 43.7970i | − | 1.48401i | ||||||
\(872\) | 2.10052 | − | 2.10052i | 0.0711327 | − | 0.0711327i | ||||
\(873\) | 4.72414 | − | 4.72414i | 0.159888 | − | 0.159888i | ||||
\(874\) | −7.03613 | −0.238000 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.12706 | 0.240801 | ||||||||
\(877\) | 21.5744 | − | 21.5744i | 0.728515 | − | 0.728515i | −0.241809 | − | 0.970324i | \(-0.577741\pi\) |
0.970324 | + | 0.241809i | \(0.0777407\pi\) | |||||||
\(878\) | 20.6434 | − | 20.6434i | 0.696683 | − | 0.696683i | ||||
\(879\) | 7.14222i | 0.240901i | ||||||||
\(880\) | −11.8592 | + | 1.29769i | −0.399773 | + | 0.0437452i | ||||
\(881\) | 3.63544i | 0.122481i | 0.998123 | + | 0.0612405i | \(0.0195057\pi\) | ||||
−0.998123 | + | 0.0612405i | \(0.980494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.17107 | − | 6.17107i | −0.207673 | − | 0.207673i | 0.595605 | − | 0.803278i | \(-0.296913\pi\) |
−0.803278 | + | 0.595605i | \(0.796913\pi\) | |||||||
\(884\) | 39.7963i | 1.33849i | ||||||||
\(885\) | 8.62106 | − | 10.7396i | 0.289794 | − | 0.361008i | ||||
\(886\) | −25.8098 | −0.867098 | ||||||||
\(887\) | 8.29549 | + | 8.29549i | 0.278535 | + | 0.278535i | 0.832524 | − | 0.553989i | \(-0.186895\pi\) |
−0.553989 | + | 0.832524i | \(0.686895\pi\) | |||||||
\(888\) | −2.11124 | + | 2.11124i | −0.0708487 | + | 0.0708487i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.47660 | − | 5.57668i | 0.150056 | − | 0.186931i | ||||
\(891\) | 5.33525 | 0.178738 | ||||||||
\(892\) | −0.994508 | − | 0.994508i | −0.0332986 | − | 0.0332986i | ||||
\(893\) | −26.6322 | − | 26.6322i | −0.891212 | − | 0.891212i | ||||
\(894\) | −21.3443 | −0.713861 | ||||||||
\(895\) | 2.38542 | + | 21.7996i | 0.0797357 | + | 0.728679i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.85290 | − | 8.85290i | 0.295590 | − | 0.295590i | ||||
\(898\) | −19.8647 | − | 19.8647i | −0.662893 | − | 0.662893i | ||||
\(899\) | −31.7507 | −1.05895 | ||||||||
\(900\) | −4.88168 | + | 1.08130i | −0.162723 | + | 0.0360434i | ||||
\(901\) | − | 51.0826i | − | 1.70181i | ||||||
\(902\) | −39.3411 | − | 39.3411i | −1.30992 | − | 1.30992i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.28303i | − | 0.242230i | ||||||
\(905\) | 3.48660 | + | 31.8629i | 0.115899 | + | 1.05916i | ||||
\(906\) | − | 6.89343i | − | 0.229019i | ||||||
\(907\) | −4.22039 | + | 4.22039i | −0.140136 | + | 0.140136i | −0.773695 | − | 0.633559i | \(-0.781593\pi\) |
0.633559 | + | 0.773695i | \(0.281593\pi\) | |||||||
\(908\) | −11.7968 | + | 11.7968i | −0.391490 | + | 0.391490i | ||||
\(909\) | −10.2204 | −0.338989 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.5780 | 1.17875 | 0.589376 | − | 0.807859i | \(-0.299374\pi\) | ||||
0.589376 | + | 0.807859i | \(0.299374\pi\) | |||||||
\(912\) | −2.15094 | + | 2.15094i | −0.0712248 | + | 0.0712248i | ||||
\(913\) | 12.9055 | − | 12.9055i | 0.427108 | − | 0.427108i | ||||
\(914\) | 18.4092i | 0.608922i | ||||||||
\(915\) | 1.35622 | + | 1.08869i | 0.0448353 | + | 0.0359909i | ||||
\(916\) | − | 0.535959i | − | 0.0177086i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.19896 | − | 5.19896i | −0.171591 | − | 0.171591i | ||||
\(919\) | − | 44.3793i | − | 1.46394i | −0.681338 | − | 0.731968i | \(-0.738602\pi\) | ||
0.681338 | − | 0.731968i | \(-0.261398\pi\) | |||||||
\(920\) | −0.562609 | − | 5.14150i | −0.0185487 | − | 0.169510i | ||||
\(921\) | −27.0869 | −0.892544 | ||||||||
\(922\) | 23.4329 | + | 23.4329i | 0.771720 | + | 0.771720i | ||||
\(923\) | 22.4043 | − | 22.4043i | 0.737447 | − | 0.737447i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.02351 | − | 12.5893i | 0.263811 | − | 0.413934i | ||||
\(926\) | 16.4166 | 0.539484 | ||||||||
\(927\) | 0.809817 | + | 0.809817i | 0.0265979 | + | 0.0265979i | ||||
\(928\) | −3.52077 | − | 3.52077i | −0.115575 | − | 0.115575i | ||||
\(929\) | −9.12123 | −0.299258 | −0.149629 | − | 0.988742i | \(-0.547808\pi\) | ||||
−0.149629 | + | 0.988742i | \(0.547808\pi\) | |||||||
\(930\) | −14.1743 | + | 1.55103i | −0.464794 | + | 0.0508601i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.3761 | − | 15.3761i | 0.503659 | − | 0.503659i | ||||
\(933\) | −11.9196 | − | 11.9196i | −0.390232 | − | 0.390232i | ||||
\(934\) | 25.0418 | 0.819394 | ||||||||
\(935\) | 68.4022 | + | 54.9089i | 2.23699 | + | 1.79571i | ||||
\(936\) | − | 5.41266i | − | 0.176918i | ||||||
\(937\) | −20.3769 | − | 20.3769i | −0.665686 | − | 0.665686i | 0.291028 | − | 0.956714i | \(-0.406003\pi\) |
−0.956714 | + | 0.291028i | \(0.906003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.6105i | 0.901035i | ||||||||
\(940\) | 17.3314 | − | 21.5904i | 0.565288 | − | 0.704202i | ||||
\(941\) | 36.1182i | 1.17742i | 0.808345 | + | 0.588709i | \(0.200364\pi\) | ||||
−0.808345 | + | 0.588709i | \(0.799636\pi\) | |||||||
\(942\) | 5.07142 | − | 5.07142i | 0.165236 | − | 0.165236i | ||||
\(943\) | 17.0562 | − | 17.0562i | 0.555426 | − | 0.555426i | ||||
\(944\) | 6.15893 | 0.200456 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.65489 | −0.313907 | ||||||||
\(947\) | 8.15755 | − | 8.15755i | 0.265085 | − | 0.265085i | −0.562031 | − | 0.827116i | \(-0.689980\pi\) |
0.827116 | + | 0.562031i | \(0.189980\pi\) | |||||||
\(948\) | −8.02304 | + | 8.02304i | −0.260576 | + | 0.260576i | ||||
\(949\) | − | 38.5764i | − | 1.25224i | ||||||
\(950\) | 8.17439 | − | 12.8260i | 0.265212 | − | 0.416132i | ||||
\(951\) | 29.2363i | 0.948053i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.8236 | + | 10.8236i | 0.350610 | + | 0.350610i | 0.860336 | − | 0.509727i | \(-0.170254\pi\) |
−0.509727 | + | 0.860336i | \(0.670254\pi\) | |||||||
\(954\) | 6.94770i | 0.224940i | ||||||||
\(955\) | 14.4653 | − | 1.58286i | 0.468085 | − | 0.0512202i | ||||
\(956\) | 3.25205 | 0.105179 | ||||||||
\(957\) | −18.7842 | − | 18.7842i | −0.607206 | − | 0.607206i | ||||
\(958\) | 15.6834 | − | 15.6834i | 0.506707 | − | 0.506707i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.74375 | − | 1.39977i | −0.0562792 | − | 0.0451773i | ||||
\(961\) | −9.66337 | −0.311722 | ||||||||
\(962\) | 11.4274 | + | 11.4274i | 0.368435 | + | 0.368435i | ||||
\(963\) | 10.1474 | + | 10.1474i | 0.326997 | + | 0.326997i | ||||
\(964\) | −13.7283 | −0.442158 | ||||||||
\(965\) | −39.6700 | − | 31.8445i | −1.27702 | − | 1.02511i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.2750 | + | 14.2750i | −0.459055 | + | 0.459055i | −0.898345 | − | 0.439290i | \(-0.855230\pi\) |
0.439290 | + | 0.898345i | \(0.355230\pi\) | |||||||
\(968\) | −12.3496 | − | 12.3496i | −0.396930 | − | 0.396930i | ||||
\(969\) | 22.3654 | 0.718479 | ||||||||
\(970\) | −14.8504 | + | 1.62501i | −0.476817 | + | 0.0521758i | ||||
\(971\) | 23.4515i | 0.752593i | 0.926499 | + | 0.376296i | \(0.122803\pi\) | ||||
−0.926499 | + | 0.376296i | \(0.877197\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 12.0773i | − | 0.386982i | ||||||
\(975\) | 5.85273 | + | 26.4229i | 0.187437 | + | 0.846209i | ||||
\(976\) | 0.777764i | 0.0248956i | ||||||||
\(977\) | −7.46754 | + | 7.46754i | −0.238908 | + | 0.238908i | −0.816398 | − | 0.577490i | \(-0.804032\pi\) |
0.577490 | + | 0.816398i | \(0.304032\pi\) | |||||||
\(978\) | −3.30725 | + | 3.30725i | −0.105754 | + | 0.105754i | ||||
\(979\) | 17.0627 | 0.545325 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.97059 | 0.0948435 | ||||||||
\(982\) | 10.1994 | − | 10.1994i | 0.325476 | − | 0.325476i | ||||
\(983\) | −43.8301 | + | 43.8301i | −1.39796 | + | 1.39796i | −0.592089 | + | 0.805873i | \(0.701697\pi\) |
−0.805873 | + | 0.592089i | \(0.798303\pi\) | |||||||
\(984\) | − | 10.4281i | − | 0.332437i | ||||||
\(985\) | 16.8700 | − | 21.0156i | 0.537522 | − | 0.669613i | ||||
\(986\) | 36.6087i | 1.16586i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.6423 | + | 11.6423i | 0.370392 | + | 0.370392i | ||||
\(989\) | − | 4.18583i | − | 0.133102i | ||||||
\(990\) | −9.30333 | − | 7.46811i | −0.295679 | − | 0.237352i | ||||
\(991\) | −32.0101 | −1.01684 | −0.508418 | − | 0.861110i | \(-0.669769\pi\) | ||||
−0.508418 | + | 0.861110i | \(0.669769\pi\) | |||||||
\(992\) | −4.50907 | − | 4.50907i | −0.143163 | − | 0.143163i | ||||
\(993\) | −12.9614 | + | 12.9614i | −0.411317 | + | 0.411317i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.6306 | − | 1.38211i | 0.400417 | − | 0.0438157i | ||||
\(996\) | 3.42085 | 0.108394 | ||||||||
\(997\) | −12.4334 | − | 12.4334i | −0.393768 | − | 0.393768i | 0.482260 | − | 0.876028i | \(-0.339816\pi\) |
−0.876028 | + | 0.482260i | \(0.839816\pi\) | |||||||
\(998\) | −18.6669 | − | 18.6669i | −0.590889 | − | 0.590889i | ||||
\(999\) | −2.98575 | −0.0944649 |
(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 | 1470.2.m.c.1273.5 | yes | 16 | |
5.2 | odd | 4 | 1470.2.m.f.97.8 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.f.1273.8 | yes | 16 | ||
35.27 | even | 4 | inner | 1470.2.m.c.97.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.m.c.97.5 | ✓ | 16 | 35.27 | even | 4 | inner | |
1470.2.m.c.1273.5 | yes | 16 | 1.1 | even | 1 | trivial | |
1470.2.m.f.97.8 | yes | 16 | 5.2 | odd | 4 | ||
1470.2.m.f.1273.8 | yes | 16 | 7.6 | odd | 2 |