Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 571.33 | ||
Character | \(\chi\) | \(=\) | 585.571 |
Dual form | 585.2.bt.b.376.33 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.569525 | − | 0.328815i | 0.402715 | − | 0.232507i | −0.284940 | − | 0.958545i | \(-0.591974\pi\) |
0.687655 | + | 0.726038i | \(0.258640\pi\) | |||||||
\(3\) | 1.49163 | − | 0.880367i | 0.861192 | − | 0.508280i | ||||
\(4\) | −0.783761 | + | 1.35751i | −0.391881 | + | 0.678757i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 0.560040 | − | 0.991861i | 0.228636 | − | 0.404925i | ||||
\(7\) | 0.282702 | − | 0.163218i | 0.106851 | − | 0.0616905i | −0.445622 | − | 0.895221i | \(-0.647017\pi\) |
0.552473 | + | 0.833531i | \(0.313684\pi\) | |||||||
\(8\) | 2.34611i | 0.829475i | ||||||||
\(9\) | 1.44991 | − | 2.62636i | 0.483302 | − | 0.875454i | ||||
\(10\) | 0.657630 | 0.207961 | ||||||||
\(11\) | −1.86962 | + | 1.07943i | −0.563713 | + | 0.325460i | −0.754634 | − | 0.656146i | \(-0.772186\pi\) |
0.190922 | + | 0.981605i | \(0.438852\pi\) | |||||||
\(12\) | 0.0260313 | + | 2.71490i | 0.00751460 | + | 0.783725i | ||||
\(13\) | 3.53934 | + | 0.687825i | 0.981635 | + | 0.190768i | ||||
\(14\) | 0.107337 | − | 0.185913i | 0.0286870 | − | 0.0496874i | ||||
\(15\) | 1.73197 | − | 0.0166067i | 0.447193 | − | 0.00428783i | ||||
\(16\) | −0.796086 | − | 1.37886i | −0.199021 | − | 0.344715i | ||||
\(17\) | 7.02806 | 1.70455 | 0.852277 | − | 0.523090i | \(-0.175221\pi\) | ||||
0.852277 | + | 0.523090i | \(0.175221\pi\) | |||||||
\(18\) | −0.0378299 | − | 1.97253i | −0.00891659 | − | 0.464929i | ||||
\(19\) | 1.98213i | 0.454732i | 0.973809 | + | 0.227366i | \(0.0730114\pi\) | ||||
−0.973809 | + | 0.227366i | \(0.926989\pi\) | |||||||
\(20\) | −1.35751 | + | 0.783761i | −0.303549 | + | 0.175254i | ||||
\(21\) | 0.277994 | − | 0.492341i | 0.0606632 | − | 0.107438i | ||||
\(22\) | −0.709864 | + | 1.22952i | −0.151344 | + | 0.262135i | ||||
\(23\) | 1.07152 | − | 1.85592i | 0.223426 | − | 0.386986i | −0.732420 | − | 0.680853i | \(-0.761609\pi\) |
0.955846 | + | 0.293867i | \(0.0949424\pi\) | |||||||
\(24\) | 2.06544 | + | 3.49952i | 0.421606 | + | 0.714337i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 2.24191 | − | 0.772054i | 0.439674 | − | 0.151412i | ||||
\(27\) | −0.149442 | − | 5.19400i | −0.0287601 | − | 0.999586i | ||||
\(28\) | 0.511695i | 0.0967013i | ||||||||
\(29\) | 1.80200 | + | 3.12115i | 0.334623 | + | 0.579583i | 0.983412 | − | 0.181384i | \(-0.0580578\pi\) |
−0.648790 | + | 0.760968i | \(0.724724\pi\) | |||||||
\(30\) | 0.980940 | − | 0.578956i | 0.179094 | − | 0.105702i | ||||
\(31\) | −6.45532 | − | 3.72698i | −1.15941 | − | 0.669386i | −0.208247 | − | 0.978076i | \(-0.566776\pi\) |
−0.951163 | + | 0.308691i | \(0.900109\pi\) | |||||||
\(32\) | −4.97036 | − | 2.86964i | −0.878644 | − | 0.507286i | ||||
\(33\) | −1.83849 | + | 3.25606i | −0.320040 | + | 0.566807i | ||||
\(34\) | 4.00265 | − | 2.31093i | 0.686449 | − | 0.396322i | ||||
\(35\) | 0.326436 | 0.0551777 | ||||||||
\(36\) | 2.42894 | + | 4.02671i | 0.404824 | + | 0.671118i | ||||
\(37\) | 7.86547i | 1.29308i | 0.762882 | + | 0.646538i | \(0.223784\pi\) | ||||
−0.762882 | + | 0.646538i | \(0.776216\pi\) | |||||||
\(38\) | 0.651755 | + | 1.12887i | 0.105729 | + | 0.183127i | ||||
\(39\) | 5.88491 | − | 2.08994i | 0.942340 | − | 0.334658i | ||||
\(40\) | −1.17306 | + | 2.03179i | −0.185476 | + | 0.321254i | ||||
\(41\) | −3.36407 | − | 1.94224i | −0.525379 | − | 0.303328i | 0.213754 | − | 0.976888i | \(-0.431431\pi\) |
−0.739133 | + | 0.673560i | \(0.764764\pi\) | |||||||
\(42\) | −0.00356502 | − | 0.371809i | −0.000550095 | − | 0.0573714i | ||||
\(43\) | −2.83158 | − | 4.90444i | −0.431812 | − | 0.747920i | 0.565217 | − | 0.824942i | \(-0.308792\pi\) |
−0.997029 | + | 0.0770217i | \(0.975459\pi\) | |||||||
\(44\) | − | 3.38405i | − | 0.510165i | ||||||
\(45\) | 2.56884 | − | 1.54954i | 0.382939 | − | 0.230992i | ||||
\(46\) | − | 1.40932i | − | 0.207793i | ||||||
\(47\) | 0.0831560 | − | 0.0480102i | 0.0121296 | − | 0.00700300i | −0.493923 | − | 0.869506i | \(-0.664438\pi\) |
0.506053 | + | 0.862503i | \(0.331104\pi\) | |||||||
\(48\) | −2.40137 | − | 1.35590i | −0.346608 | − | 0.195707i | ||||
\(49\) | −3.44672 | + | 5.96989i | −0.492389 | + | 0.852842i | ||||
\(50\) | 0.569525 | + | 0.328815i | 0.0805429 | + | 0.0465015i | ||||
\(51\) | 10.4832 | − | 6.18727i | 1.46795 | − | 0.866391i | ||||
\(52\) | −3.70773 | + | 4.26561i | −0.514169 | + | 0.591533i | ||||
\(53\) | −2.33484 | −0.320715 | −0.160358 | − | 0.987059i | \(-0.551265\pi\) | ||||
−0.160358 | + | 0.987059i | \(0.551265\pi\) | |||||||
\(54\) | −1.79298 | − | 2.90897i | −0.243993 | − | 0.395861i | ||||
\(55\) | −2.15885 | −0.291100 | ||||||||
\(56\) | 0.382927 | + | 0.663249i | 0.0511708 | + | 0.0886304i | ||||
\(57\) | 1.74500 | + | 2.95660i | 0.231131 | + | 0.391612i | ||||
\(58\) | 2.05256 | + | 1.18505i | 0.269515 | + | 0.155604i | ||||
\(59\) | 8.49087 | + | 4.90221i | 1.10542 | + | 0.638213i | 0.937638 | − | 0.347612i | \(-0.113007\pi\) |
0.167778 | + | 0.985825i | \(0.446341\pi\) | |||||||
\(60\) | −1.33491 | + | 2.36419i | −0.172336 | + | 0.305216i | ||||
\(61\) | −7.60709 | − | 13.1759i | −0.973989 | − | 1.68700i | −0.683233 | − | 0.730201i | \(-0.739427\pi\) |
−0.290756 | − | 0.956797i | \(-0.593907\pi\) | |||||||
\(62\) | −4.90195 | −0.622548 | ||||||||
\(63\) | −0.0187781 | − | 0.979127i | −0.00236581 | − | 0.123358i | ||||
\(64\) | −0.589982 | −0.0737478 | ||||||||
\(65\) | 2.72124 | + | 2.36534i | 0.337529 | + | 0.293385i | ||||
\(66\) | 0.0235770 | + | 2.45893i | 0.00290212 | + | 0.302673i | ||||
\(67\) | −4.62569 | − | 2.67064i | −0.565118 | − | 0.326271i | 0.190079 | − | 0.981769i | \(-0.439125\pi\) |
−0.755197 | + | 0.655498i | \(0.772459\pi\) | |||||||
\(68\) | −5.50832 | + | 9.54069i | −0.667982 | + | 1.15698i | ||||
\(69\) | −0.0355886 | − | 3.71167i | −0.00428437 | − | 0.446832i | ||||
\(70\) | 0.185913 | − | 0.107337i | 0.0222209 | − | 0.0128292i | ||||
\(71\) | − | 11.6852i | − | 1.38678i | −0.720562 | − | 0.693390i | \(-0.756116\pi\) | ||
0.720562 | − | 0.693390i | \(-0.243884\pi\) | |||||||
\(72\) | 6.16173 | + | 3.40164i | 0.726167 | + | 0.400887i | ||||
\(73\) | − | 12.1088i | − | 1.41723i | −0.705596 | − | 0.708614i | \(-0.749321\pi\) | ||
0.705596 | − | 0.708614i | \(-0.250679\pi\) | |||||||
\(74\) | 2.58629 | + | 4.47958i | 0.300650 | + | 0.520740i | ||||
\(75\) | 1.50823 | + | 0.851604i | 0.174156 | + | 0.0983347i | ||||
\(76\) | −2.69077 | − | 1.55352i | −0.308653 | − | 0.178201i | ||||
\(77\) | −0.352364 | + | 0.610312i | −0.0401556 | + | 0.0695515i | ||||
\(78\) | 2.66440 | − | 3.12532i | 0.301684 | − | 0.353873i | ||||
\(79\) | −5.54372 | − | 9.60200i | −0.623717 | − | 1.08031i | −0.988787 | − | 0.149330i | \(-0.952288\pi\) |
0.365070 | − | 0.930980i | \(-0.381045\pi\) | |||||||
\(80\) | − | 1.59217i | − | 0.178010i | ||||||
\(81\) | −4.79554 | − | 7.61596i | −0.532838 | − | 0.846217i | ||||
\(82\) | −2.55456 | −0.282104 | ||||||||
\(83\) | −13.8398 | + | 7.99043i | −1.51912 | + | 0.877063i | −0.519372 | + | 0.854548i | \(0.673834\pi\) |
−0.999747 | + | 0.0225150i | \(0.992833\pi\) | |||||||
\(84\) | 0.450480 | + | 0.763259i | 0.0491514 | + | 0.0832783i | ||||
\(85\) | 6.08648 | + | 3.51403i | 0.660171 | + | 0.381150i | ||||
\(86\) | −3.22531 | − | 1.86213i | −0.347794 | − | 0.200799i | ||||
\(87\) | 5.43567 | + | 3.06918i | 0.582765 | + | 0.329050i | ||||
\(88\) | −2.53246 | − | 4.38634i | −0.269961 | − | 0.467586i | ||||
\(89\) | 7.29707i | 0.773488i | 0.922187 | + | 0.386744i | \(0.126400\pi\) | ||||
−0.922187 | + | 0.386744i | \(0.873600\pi\) | |||||||
\(90\) | 0.953502 | − | 1.72717i | 0.100508 | − | 0.182060i | ||||
\(91\) | 1.11284 | − | 0.383233i | 0.116657 | − | 0.0401738i | ||||
\(92\) | 1.67962 | + | 2.90920i | 0.175113 | + | 0.303305i | ||||
\(93\) | −12.9100 | + | 0.123786i | −1.33871 | + | 0.0128360i | ||||
\(94\) | 0.0315729 | − | 0.0546859i | 0.00325650 | − | 0.00564042i | ||||
\(95\) | −0.991066 | + | 1.71658i | −0.101681 | + | 0.176117i | ||||
\(96\) | −9.94027 | + | 0.0953104i | −1.01452 | + | 0.00972758i | ||||
\(97\) | 1.55370 | − | 0.897027i | 0.157754 | − | 0.0910793i | −0.419045 | − | 0.907966i | \(-0.637635\pi\) |
0.576799 | + | 0.816886i | \(0.304302\pi\) | |||||||
\(98\) | 4.53333i | 0.457936i | ||||||||
\(99\) | 0.124187 | + | 6.47537i | 0.0124813 | + | 0.650800i | ||||
\(100\) | −1.56752 | −0.156752 | ||||||||
\(101\) | 5.13309 | + | 8.89076i | 0.510761 | + | 0.884664i | 0.999922 | + | 0.0124707i | \(0.00396965\pi\) |
−0.489161 | + | 0.872193i | \(0.662697\pi\) | |||||||
\(102\) | 3.93600 | − | 6.97085i | 0.389722 | − | 0.690217i | ||||
\(103\) | −6.44957 | + | 11.1710i | −0.635495 | + | 1.10071i | 0.350916 | + | 0.936407i | \(0.385870\pi\) |
−0.986410 | + | 0.164302i | \(0.947463\pi\) | |||||||
\(104\) | −1.61371 | + | 8.30367i | −0.158238 | + | 0.814242i | ||||
\(105\) | 0.486920 | − | 0.287383i | 0.0475186 | − | 0.0280457i | ||||
\(106\) | −1.32975 | + | 0.767731i | −0.129157 | + | 0.0745687i | ||||
\(107\) | 10.6783 | 1.03231 | 0.516157 | − | 0.856494i | \(-0.327362\pi\) | ||||
0.516157 | + | 0.856494i | \(0.327362\pi\) | |||||||
\(108\) | 7.16806 | + | 3.86799i | 0.689747 | + | 0.372197i | ||||
\(109\) | − | 13.2609i | − | 1.27017i | −0.772444 | − | 0.635083i | \(-0.780966\pi\) | ||
0.772444 | − | 0.635083i | \(-0.219034\pi\) | |||||||
\(110\) | −1.22952 | + | 0.709864i | −0.117230 | + | 0.0676829i | ||||
\(111\) | 6.92450 | + | 11.7324i | 0.657245 | + | 1.11359i | ||||
\(112\) | −0.450109 | − | 0.259871i | −0.0425313 | − | 0.0245555i | ||||
\(113\) | 3.73784 | − | 6.47413i | 0.351626 | − | 0.609035i | −0.634908 | − | 0.772588i | \(-0.718962\pi\) |
0.986535 | + | 0.163553i | \(0.0522954\pi\) | |||||||
\(114\) | 1.96600 | + | 1.11007i | 0.184133 | + | 0.103968i | ||||
\(115\) | 1.85592 | − | 1.07152i | 0.173065 | − | 0.0999194i | ||||
\(116\) | −5.64935 | −0.524529 | ||||||||
\(117\) | 6.93818 | − | 8.29829i | 0.641435 | − | 0.767177i | ||||
\(118\) | 6.44768 | 0.593557 | ||||||||
\(119\) | 1.98684 | − | 1.14710i | 0.182134 | − | 0.105155i | ||||
\(120\) | 0.0389611 | + | 4.06340i | 0.00355665 | + | 0.370936i | ||||
\(121\) | −3.16967 | + | 5.49003i | −0.288152 | + | 0.499094i | ||||
\(122\) | −8.66485 | − | 5.00266i | −0.784479 | − | 0.452919i | ||||
\(123\) | −6.72782 | + | 0.0645085i | −0.606627 | + | 0.00581653i | ||||
\(124\) | 10.1189 | − | 5.84213i | 0.908701 | − | 0.524639i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −0.332646 | − | 0.551462i | −0.0296345 | − | 0.0491282i | ||||
\(127\) | −11.9857 | −1.06355 | −0.531777 | − | 0.846884i | \(-0.678476\pi\) | ||||
−0.531777 | + | 0.846884i | \(0.678476\pi\) | |||||||
\(128\) | 9.60472 | − | 5.54529i | 0.848945 | − | 0.490139i | ||||
\(129\) | −8.54137 | − | 4.82277i | −0.752026 | − | 0.424621i | ||||
\(130\) | 2.32757 | + | 0.452335i | 0.204142 | + | 0.0396724i | ||||
\(131\) | −9.46251 | + | 16.3895i | −0.826743 | + | 1.43196i | 0.0738364 | + | 0.997270i | \(0.476476\pi\) |
−0.900580 | + | 0.434691i | \(0.856858\pi\) | |||||||
\(132\) | −2.97921 | − | 5.04775i | −0.259307 | − | 0.439350i | ||||
\(133\) | 0.323519 | + | 0.560352i | 0.0280527 | + | 0.0485887i | ||||
\(134\) | −3.51259 | −0.303441 | ||||||||
\(135\) | 2.46758 | − | 4.57286i | 0.212376 | − | 0.393569i | ||||
\(136\) | 16.4886i | 1.41389i | ||||||||
\(137\) | −7.06326 | + | 4.07797i | −0.603455 | + | 0.348405i | −0.770399 | − | 0.637562i | \(-0.779943\pi\) |
0.166945 | + | 0.985966i | \(0.446610\pi\) | |||||||
\(138\) | −1.24072 | − | 2.10218i | −0.105617 | − | 0.178950i | ||||
\(139\) | −2.58206 | + | 4.47226i | −0.219008 | + | 0.379333i | −0.954505 | − | 0.298195i | \(-0.903615\pi\) |
0.735497 | + | 0.677528i | \(0.236949\pi\) | |||||||
\(140\) | −0.255848 | + | 0.443141i | −0.0216231 | + | 0.0374522i | ||||
\(141\) | 0.0817713 | − | 0.144821i | 0.00688638 | − | 0.0121961i | ||||
\(142\) | −3.84228 | − | 6.65502i | −0.322437 | − | 0.558477i | ||||
\(143\) | −7.35968 | + | 2.53448i | −0.615447 | + | 0.211944i | ||||
\(144\) | −4.77564 | + | 0.0915890i | −0.397970 | + | 0.00763242i | ||||
\(145\) | 3.60400i | 0.299296i | ||||||||
\(146\) | −3.98156 | − | 6.89626i | −0.329516 | − | 0.570739i | ||||
\(147\) | 0.114477 | + | 11.9392i | 0.00944192 | + | 0.984732i | ||||
\(148\) | −10.6775 | − | 6.16465i | −0.877684 | − | 0.506731i | ||||
\(149\) | 18.7254 | + | 10.8111i | 1.53404 | + | 0.885680i | 0.999169 | + | 0.0407488i | \(0.0129743\pi\) |
0.534874 | + | 0.844932i | \(0.320359\pi\) | |||||||
\(150\) | 1.13900 | − | 0.0109211i | 0.0929987 | − | 0.000891700i | ||||
\(151\) | 10.6056 | − | 6.12314i | 0.863071 | − | 0.498294i | −0.00196859 | − | 0.999998i | \(-0.500627\pi\) |
0.865039 | + | 0.501704i | \(0.167293\pi\) | |||||||
\(152\) | −4.65030 | −0.377189 | ||||||||
\(153\) | 10.1900 | − | 18.4582i | 0.823815 | − | 1.49226i | ||||
\(154\) | 0.463450i | 0.0373459i | ||||||||
\(155\) | −3.72698 | − | 6.45532i | −0.299358 | − | 0.518504i | ||||
\(156\) | −1.77525 | + | 9.62686i | −0.142133 | + | 0.770766i | ||||
\(157\) | −1.42241 | + | 2.46369i | −0.113521 | + | 0.196624i | −0.917188 | − | 0.398456i | \(-0.869546\pi\) |
0.803667 | + | 0.595080i | \(0.202880\pi\) | |||||||
\(158\) | −6.31457 | − | 3.64572i | −0.502360 | − | 0.290038i | ||||
\(159\) | −3.48271 | + | 2.05552i | −0.276197 | + | 0.163013i | ||||
\(160\) | −2.86964 | − | 4.97036i | −0.226865 | − | 0.392942i | ||||
\(161\) | − | 0.699562i | − | 0.0551332i | ||||||
\(162\) | −5.23542 | − | 2.76063i | −0.411333 | − | 0.216895i | ||||
\(163\) | 0.319490i | 0.0250244i | 0.999922 | + | 0.0125122i | \(0.00398286\pi\) | ||||
−0.999922 | + | 0.0125122i | \(0.996017\pi\) | |||||||
\(164\) | 5.27325 | − | 3.04451i | 0.411772 | − | 0.237736i | ||||
\(165\) | −3.22021 | + | 1.90059i | −0.250693 | + | 0.147960i | ||||
\(166\) | −5.25475 | + | 9.10149i | −0.407847 | + | 0.706413i | ||||
\(167\) | −13.8413 | − | 7.99125i | −1.07107 | − | 0.618382i | −0.142596 | − | 0.989781i | \(-0.545545\pi\) |
−0.928473 | + | 0.371399i | \(0.878878\pi\) | |||||||
\(168\) | 1.15509 | + | 0.652204i | 0.0891169 | + | 0.0503186i | ||||
\(169\) | 12.0538 | + | 4.86889i | 0.927215 | + | 0.374530i | ||||
\(170\) | 4.62186 | 0.354481 | ||||||||
\(171\) | 5.20579 | + | 2.87391i | 0.398097 | + | 0.219773i | ||||
\(172\) | 8.87713 | 0.676875 | ||||||||
\(173\) | 0.891038 | + | 1.54332i | 0.0677443 | + | 0.117337i | 0.897908 | − | 0.440183i | \(-0.145086\pi\) |
−0.830164 | + | 0.557520i | \(0.811753\pi\) | |||||||
\(174\) | 4.10494 | − | 0.0393594i | 0.311195 | − | 0.00298383i | ||||
\(175\) | 0.282702 | + | 0.163218i | 0.0213702 | + | 0.0123381i | ||||
\(176\) | 2.97676 | + | 1.71863i | 0.224382 | + | 0.129547i | ||||
\(177\) | 16.9810 | − | 0.162819i | 1.27637 | − | 0.0122382i | ||||
\(178\) | 2.39939 | + | 4.15586i | 0.179842 | + | 0.311495i | ||||
\(179\) | 2.89894 | 0.216677 | 0.108338 | − | 0.994114i | \(-0.465447\pi\) | ||||
0.108338 | + | 0.994114i | \(0.465447\pi\) | |||||||
\(180\) | 0.0901711 | + | 4.70170i | 0.00672096 | + | 0.350444i | ||||
\(181\) | 1.44881 | 0.107689 | 0.0538445 | − | 0.998549i | \(-0.482852\pi\) | ||||
0.0538445 | + | 0.998549i | \(0.482852\pi\) | |||||||
\(182\) | 0.507777 | − | 0.584180i | 0.0376390 | − | 0.0433023i | ||||
\(183\) | −22.9466 | − | 12.9565i | −1.69626 | − | 0.957769i | ||||
\(184\) | 4.35419 | + | 2.51389i | 0.320995 | + | 0.185327i | ||||
\(185\) | −3.93273 | + | 6.81170i | −0.289140 | + | 0.500806i | ||||
\(186\) | −7.31189 | + | 4.31552i | −0.536134 | + | 0.316429i | ||||
\(187\) | −13.1398 | + | 7.58628i | −0.960879 | + | 0.554764i | ||||
\(188\) | 0.150514i | 0.0109774i | ||||||||
\(189\) | −0.890001 | − | 1.44396i | −0.0647381 | − | 0.105033i | ||||
\(190\) | 1.30351i | 0.0945666i | ||||||||
\(191\) | −1.55424 | − | 2.69202i | −0.112461 | − | 0.194788i | 0.804301 | − | 0.594222i | \(-0.202540\pi\) |
−0.916762 | + | 0.399434i | \(0.869207\pi\) | |||||||
\(192\) | −0.880034 | + | 0.519401i | −0.0635110 | + | 0.0374845i | ||||
\(193\) | −15.9475 | − | 9.20727i | −1.14792 | − | 0.662754i | −0.199543 | − | 0.979889i | \(-0.563946\pi\) |
−0.948380 | + | 0.317136i | \(0.897279\pi\) | |||||||
\(194\) | 0.589912 | − | 1.02176i | 0.0423532 | − | 0.0733580i | ||||
\(195\) | 6.14145 | + | 1.13252i | 0.439798 | + | 0.0811012i | ||||
\(196\) | −5.40281 | − | 9.35794i | −0.385915 | − | 0.668424i | ||||
\(197\) | − | 9.35543i | − | 0.666546i | −0.942830 | − | 0.333273i | \(-0.891847\pi\) | ||
0.942830 | − | 0.333273i | \(-0.108153\pi\) | |||||||
\(198\) | 2.19993 | + | 3.64705i | 0.156342 | + | 0.259185i | ||||
\(199\) | 1.93111 | 0.136893 | 0.0684463 | − | 0.997655i | \(-0.478196\pi\) | ||||
0.0684463 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(200\) | −2.03179 | + | 1.17306i | −0.143669 | + | 0.0829475i | ||||
\(201\) | −9.25095 | + | 0.0887010i | −0.652512 | + | 0.00625648i | ||||
\(202\) | 5.84684 | + | 3.37567i | 0.411382 | + | 0.237511i | ||||
\(203\) | 1.01886 | + | 0.588236i | 0.0715096 | + | 0.0412861i | ||||
\(204\) | 0.182950 | + | 19.0805i | 0.0128090 | + | 1.33590i | ||||
\(205\) | −1.94224 | − | 3.36407i | −0.135652 | − | 0.234957i | ||||
\(206\) | 8.48286i | 0.591029i | ||||||||
\(207\) | −3.32072 | − | 5.50510i | −0.230806 | − | 0.382631i | ||||
\(208\) | −1.86920 | − | 5.42782i | −0.129606 | − | 0.376352i | ||||
\(209\) | −2.13957 | − | 3.70584i | −0.147997 | − | 0.256338i | ||||
\(210\) | 0.182817 | − | 0.323779i | 0.0126156 | − | 0.0223428i | ||||
\(211\) | 1.33361 | − | 2.30988i | 0.0918095 | − | 0.159019i | −0.816463 | − | 0.577398i | \(-0.804068\pi\) |
0.908273 | + | 0.418379i | \(0.137402\pi\) | |||||||
\(212\) | 1.82996 | − | 3.16958i | 0.125682 | − | 0.217688i | ||||
\(213\) | −10.2873 | − | 17.4300i | −0.704873 | − | 1.19428i | ||||
\(214\) | 6.08158 | − | 3.51120i | 0.415728 | − | 0.240021i | ||||
\(215\) | − | 5.66316i | − | 0.386224i | ||||||
\(216\) | 12.1857 | − | 0.350607i | 0.829132 | − | 0.0238558i | ||||
\(217\) | −2.43324 | −0.165179 | ||||||||
\(218\) | −4.36039 | − | 7.55242i | −0.295323 | − | 0.511514i | ||||
\(219\) | −10.6602 | − | 18.0618i | −0.720349 | − | 1.22051i | ||||
\(220\) | 1.69203 | − | 2.93068i | 0.114076 | − | 0.197586i | ||||
\(221\) | 24.8747 | + | 4.83408i | 1.67325 | + | 0.325175i | ||||
\(222\) | 7.80145 | + | 4.40498i | 0.523599 | + | 0.295643i | ||||
\(223\) | 3.70928 | − | 2.14155i | 0.248392 | − | 0.143409i | −0.370636 | − | 0.928778i | \(-0.620860\pi\) |
0.619028 | + | 0.785369i | \(0.287527\pi\) | |||||||
\(224\) | −1.87351 | −0.125179 | ||||||||
\(225\) | 2.99945 | − | 0.0575246i | 0.199963 | − | 0.00383497i | ||||
\(226\) | − | 4.91623i | − | 0.327023i | ||||||
\(227\) | 21.5080 | − | 12.4176i | 1.42753 | − | 0.824187i | 0.430608 | − | 0.902539i | \(-0.358299\pi\) |
0.996926 | + | 0.0783523i | \(0.0249659\pi\) | |||||||
\(228\) | −5.38130 | + | 0.0515976i | −0.356385 | + | 0.00341713i | ||||
\(229\) | −3.19530 | − | 1.84480i | −0.211151 | − | 0.121908i | 0.390695 | − | 0.920520i | \(-0.372235\pi\) |
−0.601846 | + | 0.798612i | \(0.705568\pi\) | |||||||
\(230\) | 0.704661 | − | 1.22051i | 0.0464640 | − | 0.0804780i | ||||
\(231\) | 0.0117032 | + | 1.22057i | 0.000770013 | + | 0.0803074i | ||||
\(232\) | −7.32257 | + | 4.22769i | −0.480750 | + | 0.277561i | ||||
\(233\) | 11.0442 | 0.723531 | 0.361766 | − | 0.932269i | \(-0.382174\pi\) | ||||
0.361766 | + | 0.932269i | \(0.382174\pi\) | |||||||
\(234\) | 1.22286 | − | 7.00746i | 0.0799410 | − | 0.458092i | ||||
\(235\) | 0.0960203 | 0.00626367 | ||||||||
\(236\) | −13.3096 | + | 7.68432i | −0.866383 | + | 0.500206i | ||||
\(237\) | −16.7225 | − | 9.44210i | −1.08624 | − | 0.613330i | ||||
\(238\) | 0.754370 | − | 1.30661i | 0.0488986 | − | 0.0846948i | ||||
\(239\) | 4.39448 | + | 2.53715i | 0.284255 | + | 0.164115i | 0.635348 | − | 0.772226i | \(-0.280857\pi\) |
−0.351093 | + | 0.936341i | \(0.614190\pi\) | |||||||
\(240\) | −1.40170 | − | 2.37493i | −0.0904791 | − | 0.153301i | ||||
\(241\) | −11.7182 | + | 6.76552i | −0.754837 | + | 0.435805i | −0.827439 | − | 0.561556i | \(-0.810203\pi\) |
0.0726019 | + | 0.997361i | \(0.476870\pi\) | |||||||
\(242\) | 4.16895i | 0.267990i | ||||||||
\(243\) | −13.8580 | − | 7.13833i | −0.888991 | − | 0.457924i | ||||
\(244\) | 23.8486 | 1.52675 | ||||||||
\(245\) | −5.96989 | + | 3.44672i | −0.381403 | + | 0.220203i | ||||
\(246\) | −3.81045 | + | 2.24895i | −0.242945 | + | 0.143388i | ||||
\(247\) | −1.36336 | + | 7.01543i | −0.0867485 | + | 0.446381i | ||||
\(248\) | 8.74391 | − | 15.1449i | 0.555239 | − | 0.961702i | ||||
\(249\) | −13.6094 | + | 24.1029i | −0.862458 | + | 1.52746i | ||||
\(250\) | 0.328815 | + | 0.569525i | 0.0207961 | + | 0.0360199i | ||||
\(251\) | 14.9804 | 0.945554 | 0.472777 | − | 0.881182i | \(-0.343252\pi\) | ||||
0.472777 | + | 0.881182i | \(0.343252\pi\) | |||||||
\(252\) | 1.34390 | + | 0.741910i | 0.0846575 | + | 0.0467359i | ||||
\(253\) | 4.62649i | 0.290865i | ||||||||
\(254\) | −6.82612 | + | 3.94106i | −0.428309 | + | 0.247284i | ||||
\(255\) | 12.1724 | − | 0.116713i | 0.762265 | − | 0.00730883i | ||||
\(256\) | 4.23673 | − | 7.33823i | 0.264796 | − | 0.458639i | ||||
\(257\) | 10.6951 | − | 18.5244i | 0.667141 | − | 1.15552i | −0.311559 | − | 0.950227i | \(-0.600851\pi\) |
0.978700 | − | 0.205295i | \(-0.0658155\pi\) | |||||||
\(258\) | −6.45032 | + | 0.0618477i | −0.401579 | + | 0.00385047i | ||||
\(259\) | 1.28378 | + | 2.22358i | 0.0797705 | + | 0.138167i | ||||
\(260\) | −5.34379 | + | 1.84026i | −0.331408 | + | 0.114128i | ||||
\(261\) | 10.8100 | − | 0.207318i | 0.669122 | − | 0.0128327i | ||||
\(262\) | 12.4457i | 0.768896i | ||||||||
\(263\) | 7.48463 | + | 12.9638i | 0.461522 | + | 0.799380i | 0.999037 | − | 0.0438743i | \(-0.0139701\pi\) |
−0.537515 | + | 0.843254i | \(0.680637\pi\) | |||||||
\(264\) | −7.63908 | − | 4.31330i | −0.470153 | − | 0.265465i | ||||
\(265\) | −2.02203 | − | 1.16742i | −0.124212 | − | 0.0717141i | ||||
\(266\) | 0.368504 | + | 0.212756i | 0.0225944 | + | 0.0130449i | ||||
\(267\) | 6.42410 | + | 10.8845i | 0.393149 | + | 0.666122i | ||||
\(268\) | 7.25087 | − | 4.18629i | 0.442917 | − | 0.255718i | ||||
\(269\) | 4.48895 | 0.273696 | 0.136848 | − | 0.990592i | \(-0.456303\pi\) | ||||
0.136848 | + | 0.990592i | \(0.456303\pi\) | |||||||
\(270\) | −0.0982775 | − | 3.41573i | −0.00598098 | − | 0.207875i | ||||
\(271\) | − | 19.1023i | − | 1.16038i | −0.814481 | − | 0.580190i | \(-0.802978\pi\) | ||
0.814481 | − | 0.580190i | \(-0.197022\pi\) | |||||||
\(272\) | −5.59494 | − | 9.69071i | −0.339243 | − | 0.587586i | ||||
\(273\) | 1.32256 | − | 1.55135i | 0.0800449 | − | 0.0938920i | ||||
\(274\) | −2.68180 | + | 4.64501i | −0.162013 | + | 0.280615i | ||||
\(275\) | −1.86962 | − | 1.07943i | −0.112743 | − | 0.0650919i | ||||
\(276\) | 5.06654 | + | 2.86075i | 0.304970 | + | 0.172197i | ||||
\(277\) | 9.77781 | + | 16.9357i | 0.587492 | + | 1.01757i | 0.994560 | + | 0.104168i | \(0.0332179\pi\) |
−0.407068 | + | 0.913398i | \(0.633449\pi\) | |||||||
\(278\) | 3.39609i | 0.203684i | ||||||||
\(279\) | −19.1480 | + | 11.5502i | −1.14636 | + | 0.691494i | ||||
\(280\) | 0.765854i | 0.0457685i | ||||||||
\(281\) | −0.681142 | + | 0.393257i | −0.0406335 | + | 0.0234598i | −0.520179 | − | 0.854057i | \(-0.674135\pi\) |
0.479546 | + | 0.877517i | \(0.340801\pi\) | |||||||
\(282\) | −0.00104864 | − | 0.109367i | −6.24458e−5 | − | 0.00651270i | ||||
\(283\) | 9.11042 | − | 15.7797i | 0.541558 | − | 0.938007i | −0.457256 | − | 0.889335i | \(-0.651168\pi\) |
0.998815 | − | 0.0486719i | \(-0.0154989\pi\) | |||||||
\(284\) | 15.8629 | + | 9.15842i | 0.941287 | + | 0.543452i | ||||
\(285\) | 0.0329166 | + | 3.43300i | 0.00194981 | + | 0.203353i | ||||
\(286\) | −3.35814 | + | 3.86342i | −0.198571 | + | 0.228449i | ||||
\(287\) | −1.26804 | −0.0748498 | ||||||||
\(288\) | −14.7433 | + | 8.89326i | −0.868756 | + | 0.524040i | ||||
\(289\) | 32.3936 | 1.90551 | ||||||||
\(290\) | 1.18505 | + | 2.05256i | 0.0695884 | + | 0.120531i | ||||
\(291\) | 1.52782 | − | 2.70585i | 0.0895626 | − | 0.158620i | ||||
\(292\) | 16.4379 | + | 9.49041i | 0.961954 | + | 0.555384i | ||||
\(293\) | −10.6694 | − | 6.16000i | −0.623315 | − | 0.359871i | 0.154844 | − | 0.987939i | \(-0.450513\pi\) |
−0.778158 | + | 0.628068i | \(0.783846\pi\) | |||||||
\(294\) | 3.99100 | + | 6.76205i | 0.232760 | + | 0.394371i | ||||
\(295\) | 4.90221 | + | 8.49087i | 0.285417 | + | 0.494358i | ||||
\(296\) | −18.4533 | −1.07257 | ||||||||
\(297\) | 5.88595 | + | 9.54952i | 0.341537 | + | 0.554119i | ||||
\(298\) | 14.2194 | 0.823709 | ||||||||
\(299\) | 5.06900 | − | 5.83171i | 0.293148 | − | 0.337256i | ||||
\(300\) | −2.33816 | + | 1.38000i | −0.134994 | + | 0.0796741i | ||||
\(301\) | −1.60098 | − | 0.924329i | −0.0922792 | − | 0.0532774i | ||||
\(302\) | 4.02676 | − | 6.97456i | 0.231714 | − | 0.401341i | ||||
\(303\) | 15.4838 | + | 8.74271i | 0.889521 | + | 0.502256i | ||||
\(304\) | 2.73308 | − | 1.57795i | 0.156753 | − | 0.0905015i | ||||
\(305\) | − | 15.2142i | − | 0.871162i | ||||||
\(306\) | −0.265871 | − | 13.8630i | −0.0151988 | − | 0.792497i | ||||
\(307\) | 34.9414i | 1.99421i | 0.0760427 | + | 0.997105i | \(0.475771\pi\) | ||||
−0.0760427 | + | 0.997105i | \(0.524229\pi\) | |||||||
\(308\) | −0.552338 | − | 0.956677i | −0.0314724 | − | 0.0545117i | ||||
\(309\) | 0.214212 | + | 22.3409i | 0.0121861 | + | 1.27093i | ||||
\(310\) | −4.24521 | − | 2.45098i | −0.241112 | − | 0.139206i | ||||
\(311\) | −1.64637 | + | 2.85160i | −0.0933571 | + | 0.161699i | −0.908922 | − | 0.416967i | \(-0.863093\pi\) |
0.815565 | + | 0.578666i | \(0.196427\pi\) | |||||||
\(312\) | 4.90322 | + | 13.8067i | 0.277590 | + | 0.781648i | ||||
\(313\) | 13.3187 | + | 23.0687i | 0.752819 | + | 1.30392i | 0.946451 | + | 0.322846i | \(0.104640\pi\) |
−0.193633 | + | 0.981074i | \(0.562027\pi\) | |||||||
\(314\) | 1.87085i | 0.105578i | ||||||||
\(315\) | 0.473301 | − | 0.857338i | 0.0266675 | − | 0.0483055i | ||||
\(316\) | 17.3798 | 0.977690 | ||||||||
\(317\) | −20.0163 | + | 11.5564i | −1.12422 | + | 0.649071i | −0.942476 | − | 0.334274i | \(-0.891509\pi\) |
−0.181749 | + | 0.983345i | \(0.558176\pi\) | |||||||
\(318\) | −1.30761 | + | 2.31584i | −0.0733269 | + | 0.129866i | ||||
\(319\) | −6.73812 | − | 3.89025i | −0.377262 | − | 0.217812i | ||||
\(320\) | −0.510939 | − | 0.294991i | −0.0285624 | − | 0.0164905i | ||||
\(321\) | 15.9281 | − | 9.40087i | 0.889021 | − | 0.524705i | ||||
\(322\) | −0.230026 | − | 0.398418i | −0.0128189 | − | 0.0222029i | ||||
\(323\) | 13.9305i | 0.775116i | ||||||||
\(324\) | 14.0973 | − | 0.540927i | 0.783185 | − | 0.0300515i | ||||
\(325\) | 1.17399 | + | 3.40907i | 0.0651215 | + | 0.189101i | ||||
\(326\) | 0.105053 | + | 0.181957i | 0.00581835 | + | 0.0100777i | ||||
\(327\) | −11.6745 | − | 19.7804i | −0.645600 | − | 1.09386i | ||||
\(328\) | 4.55672 | − | 7.89247i | 0.251603 | − | 0.435789i | ||||
\(329\) | 0.0156722 | − | 0.0271451i | 0.000864038 | − | 0.00149656i | ||||
\(330\) | −1.20905 | + | 2.14128i | −0.0665558 | + | 0.117874i | ||||
\(331\) | 16.3568 | − | 9.44361i | 0.899052 | − | 0.519068i | 0.0221596 | − | 0.999754i | \(-0.492946\pi\) |
0.876893 | + | 0.480686i | \(0.159612\pi\) | |||||||
\(332\) | − | 25.0503i | − | 1.37482i | ||||||
\(333\) | 20.6576 | + | 11.4042i | 1.13203 | + | 0.624946i | ||||
\(334\) | −10.5106 | −0.575113 | ||||||||
\(335\) | −2.67064 | − | 4.62569i | −0.145913 | − | 0.252728i | ||||
\(336\) | −0.900177 | + | 0.00863118i | −0.0491087 | + | 0.000470869i | ||||
\(337\) | −3.75322 | + | 6.50077i | −0.204451 | + | 0.354120i | −0.949958 | − | 0.312379i | \(-0.898874\pi\) |
0.745507 | + | 0.666498i | \(0.232208\pi\) | |||||||
\(338\) | 8.46589 | − | 1.19052i | 0.460484 | − | 0.0647557i | ||||
\(339\) | −0.124146 | − | 12.9477i | −0.00674270 | − | 0.703220i | ||||
\(340\) | −9.54069 | + | 5.50832i | −0.517416 | + | 0.298731i | ||||
\(341\) | 16.0920 | 0.871432 | ||||||||
\(342\) | 3.90981 | − | 0.0749839i | 0.211418 | − | 0.00405466i | ||||
\(343\) | 4.53531i | 0.244884i | ||||||||
\(344\) | 11.5064 | − | 6.64320i | 0.620382 | − | 0.358177i | ||||
\(345\) | 1.82501 | − | 3.23219i | 0.0982554 | − | 0.174015i | ||||
\(346\) | 1.01494 | + | 0.585973i | 0.0545633 | + | 0.0315021i | ||||
\(347\) | 7.31677 | − | 12.6730i | 0.392785 | − | 0.680324i | −0.600031 | − | 0.799977i | \(-0.704845\pi\) |
0.992816 | + | 0.119653i | \(0.0381783\pi\) | |||||||
\(348\) | −8.42672 | + | 4.97350i | −0.451720 | + | 0.266608i | ||||
\(349\) | −10.8180 | + | 6.24575i | −0.579072 | + | 0.334327i | −0.760764 | − | 0.649028i | \(-0.775176\pi\) |
0.181693 | + | 0.983355i | \(0.441842\pi\) | |||||||
\(350\) | 0.214674 | 0.0114748 | ||||||||
\(351\) | 3.04364 | − | 18.4861i | 0.162458 | − | 0.986716i | ||||
\(352\) | 12.3903 | 0.660404 | ||||||||
\(353\) | 16.2880 | − | 9.40390i | 0.866925 | − | 0.500519i | 0.000599592 | − | 1.00000i | \(-0.499809\pi\) |
0.866325 | + | 0.499481i | \(0.166476\pi\) | |||||||
\(354\) | 9.61753 | − | 5.67632i | 0.511166 | − | 0.301693i | ||||
\(355\) | 5.84261 | − | 10.1197i | 0.310094 | − | 0.537098i | ||||
\(356\) | −9.90588 | − | 5.71916i | −0.525011 | − | 0.303115i | ||||
\(357\) | 1.95376 | − | 3.46020i | 0.103404 | − | 0.183133i | ||||
\(358\) | 1.65102 | − | 0.953214i | 0.0872589 | − | 0.0503789i | ||||
\(359\) | 16.0915i | 0.849279i | 0.905363 | + | 0.424639i | \(0.139599\pi\) | ||||
−0.905363 | + | 0.424639i | \(0.860401\pi\) | |||||||
\(360\) | 3.63540 | + | 6.02677i | 0.191602 | + | 0.317639i | ||||
\(361\) | 15.0712 | 0.793219 | ||||||||
\(362\) | 0.825132 | − | 0.476390i | 0.0433680 | − | 0.0250385i | ||||
\(363\) | 0.105275 | + | 10.9796i | 0.00552553 | + | 0.576278i | ||||
\(364\) | −0.351957 | + | 1.81106i | −0.0184475 | + | 0.0949254i | ||||
\(365\) | 6.05440 | − | 10.4865i | 0.316902 | − | 0.548890i | ||||
\(366\) | −17.3289 | + | 0.166155i | −0.905797 | + | 0.00868506i | ||||
\(367\) | −13.3103 | − | 23.0540i | −0.694790 | − | 1.20341i | −0.970252 | − | 0.242099i | \(-0.922164\pi\) |
0.275462 | − | 0.961312i | \(-0.411169\pi\) | |||||||
\(368\) | −3.41207 | −0.177867 | ||||||||
\(369\) | −9.97862 | + | 6.01918i | −0.519466 | + | 0.313346i | ||||
\(370\) | 5.17257i | 0.268909i | ||||||||
\(371\) | −0.660063 | + | 0.381088i | −0.0342688 | + | 0.0197851i | ||||
\(372\) | 9.95036 | − | 17.6226i | 0.515902 | − | 0.913689i | ||||
\(373\) | −7.45606 | + | 12.9143i | −0.386060 | + | 0.668676i | −0.991916 | − | 0.126899i | \(-0.959498\pi\) |
0.605855 | + | 0.795575i | \(0.292831\pi\) | |||||||
\(374\) | −4.98897 | + | 8.64114i | −0.257973 | + | 0.446823i | ||||
\(375\) | 0.880367 | + | 1.49163i | 0.0454620 | + | 0.0770273i | ||||
\(376\) | 0.112637 | + | 0.195093i | 0.00580882 | + | 0.0100612i | ||||
\(377\) | 4.23107 | + | 12.2863i | 0.217911 | + | 0.632775i | ||||
\(378\) | −0.981674 | − | 0.529725i | −0.0504918 | − | 0.0272461i | ||||
\(379\) | − | 11.1367i | − | 0.572052i | −0.958222 | − | 0.286026i | \(-0.907666\pi\) | ||
0.958222 | − | 0.286026i | \(-0.0923345\pi\) | |||||||
\(380\) | −1.55352 | − | 2.69077i | −0.0796938 | − | 0.138034i | ||||
\(381\) | −17.8781 | + | 10.5518i | −0.915925 | + | 0.540584i | ||||
\(382\) | −1.77036 | − | 1.02212i | −0.0905793 | − | 0.0522960i | ||||
\(383\) | 10.5980 | + | 6.11875i | 0.541532 | + | 0.312654i | 0.745700 | − | 0.666282i | \(-0.232115\pi\) |
−0.204167 | + | 0.978936i | \(0.565449\pi\) | |||||||
\(384\) | 9.44477 | − | 16.7272i | 0.481977 | − | 0.853606i | ||||
\(385\) | −0.610312 | + | 0.352364i | −0.0311044 | + | 0.0179581i | ||||
\(386\) | −12.1100 | −0.616380 | ||||||||
\(387\) | −16.9864 | + | 0.325771i | −0.863465 | + | 0.0165599i | ||||
\(388\) | 2.81222i | 0.142769i | ||||||||
\(389\) | −11.9098 | − | 20.6284i | −0.603851 | − | 1.04590i | −0.992232 | − | 0.124401i | \(-0.960299\pi\) |
0.388381 | − | 0.921499i | \(-0.373034\pi\) | |||||||
\(390\) | 3.87009 | − | 1.37441i | 0.195970 | − | 0.0695957i | ||||
\(391\) | 7.53067 | − | 13.0435i | 0.380843 | − | 0.659639i | ||||
\(392\) | −14.0060 | − | 8.08639i | −0.707411 | − | 0.408424i | ||||
\(393\) | 0.314282 | + | 32.7776i | 0.0158534 | + | 1.65341i | ||||
\(394\) | −3.07621 | − | 5.32814i | −0.154977 | − | 0.268428i | ||||
\(395\) | − | 11.0874i | − | 0.557869i | ||||||
\(396\) | −8.88775 | − | 4.90656i | −0.446626 | − | 0.246564i | ||||
\(397\) | − | 13.0095i | − | 0.652928i | −0.945210 | − | 0.326464i | \(-0.894143\pi\) | ||
0.945210 | − | 0.326464i | \(-0.105857\pi\) | |||||||
\(398\) | 1.09981 | − | 0.634978i | 0.0551287 | − | 0.0318286i | ||||
\(399\) | 0.975886 | + | 0.551020i | 0.0488554 | + | 0.0275855i | ||||
\(400\) | 0.796086 | − | 1.37886i | 0.0398043 | − | 0.0689431i | ||||
\(401\) | 3.74595 | + | 2.16272i | 0.187064 | + | 0.108001i | 0.590607 | − | 0.806959i | \(-0.298888\pi\) |
−0.403544 | + | 0.914960i | \(0.632222\pi\) | |||||||
\(402\) | −5.23948 | + | 3.09237i | −0.261321 | + | 0.154233i | ||||
\(403\) | −20.2840 | − | 17.6312i | −1.01042 | − | 0.878271i | ||||
\(404\) | −16.0925 | −0.800629 | ||||||||
\(405\) | −0.345084 | − | 8.99338i | −0.0171474 | − | 0.446885i | ||||
\(406\) | 0.773684 | 0.0383973 | ||||||||
\(407\) | −8.49020 | − | 14.7055i | −0.420844 | − | 0.728923i | ||||
\(408\) | 14.5160 | + | 24.5949i | 0.718650 | + | 1.21763i | ||||
\(409\) | 12.3517 | + | 7.13127i | 0.610753 | + | 0.352618i | 0.773260 | − | 0.634089i | \(-0.218625\pi\) |
−0.162507 | + | 0.986707i | \(0.551958\pi\) | |||||||
\(410\) | −2.21231 | − | 1.27728i | −0.109258 | − | 0.0630803i | ||||
\(411\) | −6.94563 | + | 12.3011i | −0.342603 | + | 0.606767i | ||||
\(412\) | −10.1098 | − | 17.5108i | −0.498076 | − | 0.862693i | ||||
\(413\) | 3.20051 | 0.157487 | ||||||||
\(414\) | −3.70139 | − | 2.04339i | −0.181913 | − | 0.100427i | ||||
\(415\) | −15.9809 | −0.784469 | ||||||||
\(416\) | −15.6180 | − | 13.5754i | −0.765734 | − | 0.665587i | ||||
\(417\) | 0.0857590 | + | 8.94412i | 0.00419964 | + | 0.437995i | ||||
\(418\) | −2.43707 | − | 1.40704i | −0.119201 | − | 0.0688208i | ||||
\(419\) | −7.23754 | + | 12.5358i | −0.353577 | + | 0.612413i | −0.986873 | − | 0.161496i | \(-0.948368\pi\) |
0.633297 | + | 0.773909i | \(0.281701\pi\) | |||||||
\(420\) | 0.00849756 | + | 0.886241i | 0.000414638 | + | 0.0432441i | ||||
\(421\) | −3.86957 | + | 2.23410i | −0.188591 | + | 0.108883i | −0.591323 | − | 0.806435i | \(-0.701394\pi\) |
0.402732 | + | 0.915318i | \(0.368061\pi\) | |||||||
\(422\) | − | 1.75404i | − | 0.0853855i | ||||||
\(423\) | −0.00552353 | − | 0.288008i | −0.000268563 | − | 0.0140034i | ||||
\(424\) | − | 5.47780i | − | 0.266025i | ||||||
\(425\) | 3.51403 | + | 6.08648i | 0.170455 | + | 0.295237i | ||||
\(426\) | −11.5901 | − | 6.54420i | −0.561543 | − | 0.317067i | ||||
\(427\) | −4.30107 | − | 2.48323i | −0.208144 | − | 0.120172i | ||||
\(428\) | −8.36927 | + | 14.4960i | −0.404544 | + | 0.700691i | ||||
\(429\) | −8.74663 | + | 10.2597i | −0.422291 | + | 0.495344i | ||||
\(430\) | −1.86213 | − | 3.22531i | −0.0898000 | − | 0.155538i | ||||
\(431\) | − | 19.8690i | − | 0.957057i | −0.878072 | − | 0.478529i | \(-0.841170\pi\) | ||
0.878072 | − | 0.478529i | \(-0.158830\pi\) | |||||||
\(432\) | −7.04284 | + | 4.34093i | −0.338849 | + | 0.208853i | ||||
\(433\) | −12.0708 | −0.580087 | −0.290044 | − | 0.957013i | \(-0.593670\pi\) | ||||
−0.290044 | + | 0.957013i | \(0.593670\pi\) | |||||||
\(434\) | −1.38579 | + | 0.800086i | −0.0665200 | + | 0.0384053i | ||||
\(435\) | 3.17284 | + | 5.37582i | 0.152126 | + | 0.257751i | ||||
\(436\) | 18.0019 | + | 10.3934i | 0.862134 | + | 0.497753i | ||||
\(437\) | 3.67868 | + | 2.12389i | 0.175975 | + | 0.101599i | ||||
\(438\) | −12.0102 | − | 6.78142i | −0.573872 | − | 0.324029i | ||||
\(439\) | 7.91595 | + | 13.7108i | 0.377808 | + | 0.654382i | 0.990743 | − | 0.135751i | \(-0.0433446\pi\) |
−0.612935 | + | 0.790133i | \(0.710011\pi\) | |||||||
\(440\) | − | 5.06491i | − | 0.241460i | ||||||
\(441\) | 10.6817 | + | 17.7081i | 0.508651 | + | 0.843244i | ||||
\(442\) | 15.7562 | − | 5.42604i | 0.749448 | − | 0.258090i | ||||
\(443\) | −0.0730197 | − | 0.126474i | −0.00346927 | − | 0.00600895i | 0.864286 | − | 0.503001i | \(-0.167771\pi\) |
−0.867755 | + | 0.496993i | \(0.834438\pi\) | |||||||
\(444\) | −21.3540 | + | 0.204749i | −1.01342 | + | 0.00971695i | ||||
\(445\) | −3.64854 | + | 6.31945i | −0.172957 | + | 0.299571i | ||||
\(446\) | 1.40835 | − | 2.43933i | 0.0666873 | − | 0.115506i | ||||
\(447\) | 37.4491 | − | 0.359073i | 1.77128 | − | 0.0169836i | ||||
\(448\) | −0.166789 | + | 0.0962956i | −0.00788003 | + | 0.00454954i | ||||
\(449\) | 1.68576i | 0.0795562i | 0.999209 | + | 0.0397781i | \(0.0126651\pi\) | ||||
−0.999209 | + | 0.0397781i | \(0.987335\pi\) | |||||||
\(450\) | 1.68934 | − | 1.01903i | 0.0796365 | − | 0.0480373i | ||||
\(451\) | 8.38605 | 0.394884 | ||||||||
\(452\) | 5.85915 | + | 10.1483i | 0.275591 | + | 0.477338i | ||||
\(453\) | 10.4290 | − | 18.4703i | 0.489996 | − | 0.867809i | ||||
\(454\) | 8.16621 | − | 14.1443i | 0.383259 | − | 0.663824i | ||||
\(455\) | 1.15537 | + | 0.224531i | 0.0541644 | + | 0.0105262i | ||||
\(456\) | −6.93652 | + | 4.09397i | −0.324832 | + | 0.191718i | ||||
\(457\) | −18.8050 | + | 10.8571i | −0.879662 | + | 0.507873i | −0.870547 | − | 0.492085i | \(-0.836235\pi\) |
−0.00911515 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(458\) | −2.42640 | −0.113378 | ||||||||
\(459\) | −1.05029 | − | 36.5038i | −0.0490231 | − | 1.70385i | ||||
\(460\) | 3.35925i | 0.156626i | ||||||||
\(461\) | 21.1304 | − | 12.1997i | 0.984142 | − | 0.568195i | 0.0806242 | − | 0.996745i | \(-0.474309\pi\) |
0.903518 | + | 0.428550i | \(0.140975\pi\) | |||||||
\(462\) | 0.408006 | + | 0.691295i | 0.0189822 | + | 0.0321619i | ||||
\(463\) | 19.2118 | + | 11.0919i | 0.892847 | + | 0.515486i | 0.874873 | − | 0.484353i | \(-0.160945\pi\) |
0.0179744 | + | 0.999838i | \(0.494278\pi\) | |||||||
\(464\) | 2.86909 | − | 4.96941i | 0.133194 | − | 0.230699i | ||||
\(465\) | −11.2423 | − | 6.34782i | −0.521350 | − | 0.294373i | ||||
\(466\) | 6.28996 | − | 3.63151i | 0.291377 | − | 0.168226i | ||||
\(467\) | −9.62358 | −0.445326 | −0.222663 | − | 0.974895i | \(-0.571475\pi\) | ||||
−0.222663 | + | 0.974895i | \(0.571475\pi\) | |||||||
\(468\) | 5.82717 | + | 15.9226i | 0.269361 | + | 0.736021i | ||||
\(469\) | −1.74358 | −0.0805113 | ||||||||
\(470\) | 0.0546859 | − | 0.0315729i | 0.00252247 | − | 0.00145635i | ||||
\(471\) | 0.0472432 | + | 4.92716i | 0.00217685 | + | 0.227032i | ||||
\(472\) | −11.5011 | + | 19.9205i | −0.529382 | + | 0.916916i | ||||
\(473\) | 10.5880 | + | 6.11297i | 0.486836 | + | 0.281075i | ||||
\(474\) | −12.6286 | + | 0.121087i | −0.580049 | + | 0.00556169i | ||||
\(475\) | −1.71658 | + | 0.991066i | −0.0787619 | + | 0.0454732i | ||||
\(476\) | 3.59622i | 0.164833i | ||||||||
\(477\) | −3.38530 | + | 6.13214i | −0.155002 | + | 0.280771i | ||||
\(478\) | 3.33702 | 0.152632 | ||||||||
\(479\) | −9.15602 | + | 5.28623i | −0.418349 | + | 0.241534i | −0.694371 | − | 0.719617i | \(-0.744317\pi\) |
0.276022 | + | 0.961151i | \(0.410984\pi\) | |||||||
\(480\) | −8.65618 | − | 4.88759i | −0.395099 | − | 0.223087i | ||||
\(481\) | −5.41007 | + | 27.8385i | −0.246678 | + | 1.26933i | ||||
\(482\) | −4.44921 | + | 7.70626i | −0.202656 | + | 0.351010i | ||||
\(483\) | −0.615871 | − | 1.04349i | −0.0280231 | − | 0.0474802i | ||||
\(484\) | −4.96853 | − | 8.60575i | −0.225842 | − | 0.391171i | ||||
\(485\) | 1.79405 | 0.0814638 | ||||||||
\(486\) | −10.2397 | + | 0.491267i | −0.464481 | + | 0.0222843i | ||||
\(487\) | 37.0636i | 1.67951i | 0.542964 | + | 0.839756i | \(0.317302\pi\) | ||||
−0.542964 | + | 0.839756i | \(0.682698\pi\) | |||||||
\(488\) | 30.9121 | − | 17.8471i | 1.39932 | − | 0.807900i | ||||
\(489\) | 0.281269 | + | 0.476560i | 0.0127194 | + | 0.0215508i | ||||
\(490\) | −2.26667 | + | 3.92598i | −0.102398 | + | 0.177358i | ||||
\(491\) | −4.25397 | + | 7.36810i | −0.191979 | + | 0.332517i | −0.945906 | − | 0.324441i | \(-0.894824\pi\) |
0.753927 | + | 0.656958i | \(0.228157\pi\) | |||||||
\(492\) | 5.18544 | − | 9.18368i | 0.233778 | − | 0.414032i | ||||
\(493\) | 12.6645 | + | 21.9356i | 0.570382 | + | 0.987931i | ||||
\(494\) | 1.53031 | + | 4.44375i | 0.0688520 | + | 0.199934i | ||||
\(495\) | −3.13014 | + | 5.66993i | −0.140689 | + | 0.254844i | ||||
\(496\) | 11.8680i | 0.532888i | ||||||||
\(497\) | −1.90724 | − | 3.30343i | −0.0855512 | − | 0.148179i | ||||
\(498\) | 0.174528 | + | 18.2021i | 0.00782078 | + | 0.815657i | ||||
\(499\) | −25.6678 | − | 14.8193i | −1.14905 | − | 0.663405i | −0.200395 | − | 0.979715i | \(-0.564222\pi\) |
−0.948656 | + | 0.316311i | \(0.897556\pi\) | |||||||
\(500\) | −1.35751 | − | 0.783761i | −0.0607099 | − | 0.0350509i | ||||
\(501\) | −27.6812 | + | 0.265416i | −1.23671 | + | 0.0118579i | ||||
\(502\) | 8.53170 | − | 4.92578i | 0.380788 | − | 0.219848i | ||||
\(503\) | −20.0429 | −0.893668 | −0.446834 | − | 0.894617i | \(-0.647448\pi\) | ||||
−0.446834 | + | 0.894617i | \(0.647448\pi\) | |||||||
\(504\) | 2.29714 | − | 0.0440554i | 0.102323 | − | 0.00196239i | ||||
\(505\) | 10.2662i | 0.456839i | ||||||||
\(506\) | 1.52126 | + | 2.63490i | 0.0676283 | + | 0.117136i | ||||
\(507\) | 22.2662 | − | 3.34920i | 0.988876 | − | 0.148743i | ||||
\(508\) | 9.39389 | − | 16.2707i | 0.416787 | − | 0.721895i | ||||
\(509\) | −30.7691 | − | 17.7645i | −1.36382 | − | 0.787400i | −0.373687 | − | 0.927555i | \(-0.621907\pi\) |
−0.990130 | + | 0.140155i | \(0.955240\pi\) | |||||||
\(510\) | 6.89410 | − | 4.06894i | 0.305276 | − | 0.180176i | ||||
\(511\) | −1.97637 | − | 3.42318i | −0.0874296 | − | 0.151432i | ||||
\(512\) | 16.6087i | 0.734010i | ||||||||
\(513\) | 10.2952 | − | 0.296213i | 0.454544 | − | 0.0130781i | ||||
\(514\) | − | 14.0668i | − | 0.620461i | ||||||
\(515\) | −11.1710 | + | 6.44957i | −0.492252 | + | 0.284202i | ||||
\(516\) | 13.2414 | − | 7.81514i | 0.582919 | − | 0.344042i | ||||
\(517\) | −0.103647 | + | 0.179522i | −0.00455839 | + | 0.00789536i | ||||
\(518\) | 1.46229 | + | 0.844256i | 0.0642495 | + | 0.0370945i | ||||
\(519\) | 2.68779 | + | 1.51762i | 0.117981 | + | 0.0666162i | ||||
\(520\) | −5.54935 | + | 6.38433i | −0.243355 | + | 0.279972i | ||||
\(521\) | −6.16502 | −0.270095 | −0.135047 | − | 0.990839i | \(-0.543119\pi\) | ||||
−0.135047 | + | 0.990839i | \(0.543119\pi\) | |||||||
\(522\) | 6.08839 | − | 3.67256i | 0.266482 | − | 0.160744i | ||||
\(523\) | −24.1503 | −1.05602 | −0.528010 | − | 0.849238i | \(-0.677062\pi\) | ||||
−0.528010 | + | 0.849238i | \(0.677062\pi\) | |||||||
\(524\) | −14.8327 | − | 25.6910i | −0.647969 | − | 1.12232i | ||||
\(525\) | 0.565377 | − | 0.00542101i | 0.0246751 | − | 0.000236592i | ||||
\(526\) | 8.52536 | + | 4.92212i | 0.371724 | + | 0.214615i | ||||
\(527\) | −45.3684 | − | 26.1934i | −1.97628 | − | 1.14100i | ||||
\(528\) | 5.95325 | − | 0.0570816i | 0.259082 | − | 0.00248416i | ||||
\(529\) | 9.20371 | + | 15.9413i | 0.400161 | + | 0.693100i | ||||
\(530\) | −1.53546 | −0.0666962 | ||||||||
\(531\) | 25.1859 | − | 15.1923i | 1.09298 | − | 0.659292i | ||||
\(532\) | −1.01425 | −0.0439732 | ||||||||
\(533\) | −10.5706 | − | 9.18815i | −0.457865 | − | 0.397983i | ||||
\(534\) | 7.23768 | + | 4.08666i | 0.313205 | + | 0.176847i | ||||
\(535\) | 9.24772 | + | 5.33917i | 0.399814 | + | 0.230833i | ||||
\(536\) | 6.26562 | − | 10.8524i | 0.270634 | − | 0.468751i | ||||
\(537\) | 4.32413 | − | 2.55213i | 0.186600 | − | 0.110133i | ||||
\(538\) | 2.55657 | − | 1.47603i | 0.110221 | − | 0.0636364i | ||||
\(539\) | − | 14.8819i | − | 0.641010i | ||||||
\(540\) | 4.27373 | + | 6.93381i | 0.183912 | + | 0.298384i | ||||
\(541\) | − | 13.4591i | − | 0.578650i | −0.957231 | − | 0.289325i | \(-0.906569\pi\) | ||
0.957231 | − | 0.289325i | \(-0.0934309\pi\) | |||||||
\(542\) | −6.28112 | − | 10.8792i | −0.269797 | − | 0.467302i | ||||
\(543\) | 2.16108 | − | 1.27548i | 0.0927409 | − | 0.0547362i | ||||
\(544\) | −34.9320 | − | 20.1680i | −1.49770 | − | 0.864696i | ||||
\(545\) | 6.63046 | − | 11.4843i | 0.284018 | − | 0.491933i | ||||
\(546\) | 0.243122 | − | 1.31841i | 0.0104047 | − | 0.0564227i | ||||
\(547\) | 6.88546 | + | 11.9260i | 0.294401 | + | 0.509918i | 0.974845 | − | 0.222882i | \(-0.0715465\pi\) |
−0.680444 | + | 0.732800i | \(0.738213\pi\) | |||||||
\(548\) | − | 12.7846i | − | 0.546132i | ||||||
\(549\) | −45.6342 | + | 0.875190i | −1.94762 | + | 0.0373522i | ||||
\(550\) | −1.41973 | −0.0605374 | ||||||||
\(551\) | −6.18654 | + | 3.57180i | −0.263555 | + | 0.152164i | ||||
\(552\) | 8.70799 | − | 0.0834949i | 0.370636 | − | 0.00355378i | ||||
\(553\) | −3.13443 | − | 1.80967i | −0.133290 | − | 0.0769549i | ||||
\(554\) | 11.1374 | + | 6.43018i | 0.473183 | + | 0.273192i | ||||
\(555\) | 0.130619 | + | 13.6228i | 0.00554448 | + | 0.578254i | ||||
\(556\) | −4.04744 | − | 7.01038i | −0.171650 | − | 0.297306i | ||||
\(557\) | 12.2312i | 0.518254i | 0.965843 | + | 0.259127i | \(0.0834348\pi\) | ||||
−0.965843 | + | 0.259127i | \(0.916565\pi\) | |||||||
\(558\) | −7.10737 | + | 12.8743i | −0.300879 | + | 0.545012i | ||||
\(559\) | −6.64852 | − | 19.3061i | −0.281202 | − | 0.816561i | ||||
\(560\) | −0.259871 | − | 0.450109i | −0.0109815 | − | 0.0190206i | ||||
\(561\) | −12.9210 | + | 22.8838i | −0.545525 | + | 0.966154i | ||||
\(562\) | −0.258618 | + | 0.447939i | −0.0109091 | + | 0.0188952i | ||||
\(563\) | −13.9445 | + | 24.1526i | −0.587691 | + | 1.01791i | 0.406843 | + | 0.913498i | \(0.366630\pi\) |
−0.994534 | + | 0.104413i | \(0.966704\pi\) | |||||||
\(564\) | 0.132508 | + | 0.224511i | 0.00557958 | + | 0.00945361i | ||||
\(565\) | 6.47413 | − | 3.73784i | 0.272369 | − | 0.157252i | ||||
\(566\) | − | 11.9826i | − | 0.503665i | ||||||
\(567\) | −2.59877 | − | 1.37032i | −0.109138 | − | 0.0575482i | ||||
\(568\) | 27.4148 | 1.15030 | ||||||||
\(569\) | 22.6269 | + | 39.1909i | 0.948567 | + | 1.64297i | 0.748446 | + | 0.663196i | \(0.230800\pi\) |
0.200121 | + | 0.979771i | \(0.435866\pi\) | |||||||
\(570\) | 1.14757 | + | 1.94435i | 0.0480663 | + | 0.0814399i | ||||
\(571\) | −15.4733 | + | 26.8006i | −0.647539 | + | 1.12157i | 0.336170 | + | 0.941801i | \(0.390868\pi\) |
−0.983709 | + | 0.179769i | \(0.942465\pi\) | |||||||
\(572\) | 2.32764 | − | 11.9773i | 0.0973234 | − | 0.500796i | ||||
\(573\) | −4.68832 | − | 2.64719i | −0.195857 | − | 0.110588i | ||||
\(574\) | −0.722177 | + | 0.416949i | −0.0301431 | + | 0.0174031i | ||||
\(575\) | 2.14303 | 0.0893706 | ||||||||
\(576\) | −0.855419 | + | 1.54951i | −0.0356424 | + | 0.0645627i | ||||
\(577\) | 9.66715i | 0.402449i | 0.979545 | + | 0.201224i | \(0.0644920\pi\) | ||||
−0.979545 | + | 0.201224i | \(0.935508\pi\) | |||||||
\(578\) | 18.4489 | − | 10.6515i | 0.767375 | − | 0.443044i | ||||
\(579\) | −31.8934 | + | 0.305804i | −1.32545 | + | 0.0127088i | ||||
\(580\) | −4.89248 | − | 2.82467i | −0.203149 | − | 0.117288i | ||||
\(581\) | −2.60836 | + | 4.51781i | −0.108213 | + | 0.187430i | ||||
\(582\) | −0.0195930 | − | 2.04342i | −0.000812155 | − | 0.0847026i | ||||
\(583\) | 4.36527 | − | 2.52029i | 0.180791 | − | 0.104380i | ||||
\(584\) | 28.4086 | 1.17556 | ||||||||
\(585\) | 10.1578 | − | 3.71744i | 0.419973 | − | 0.153697i | ||||
\(586\) | −8.10200 | −0.334691 | ||||||||
\(587\) | 6.08875 | − | 3.51534i | 0.251310 | − | 0.145094i | −0.369054 | − | 0.929408i | \(-0.620318\pi\) |
0.620364 | + | 0.784314i | \(0.286985\pi\) | |||||||
\(588\) | −16.2974 | − | 9.20211i | −0.672094 | − | 0.379489i | ||||
\(589\) | 7.38737 | − | 12.7953i | 0.304391 | − | 0.527221i | ||||
\(590\) | 5.58385 | + | 3.22384i | 0.229884 | + | 0.132723i | ||||
\(591\) | −8.23621 | − | 13.9548i | −0.338792 | − | 0.574024i | ||||
\(592\) | 10.8454 | − | 6.26159i | 0.445743 | − | 0.257350i | ||||
\(593\) | 5.93635i | 0.243777i | 0.992544 | + | 0.121888i | \(0.0388950\pi\) | ||||
−0.992544 | + | 0.121888i | \(0.961105\pi\) | |||||||
\(594\) | 6.49222 | + | 3.50329i | 0.266379 | + | 0.143742i | ||||
\(595\) | 2.29421 | 0.0940534 | ||||||||
\(596\) | −29.3525 | + | 16.9467i | −1.20232 | + | 0.694162i | ||||
\(597\) | 2.88050 | − | 1.70009i | 0.117891 | − | 0.0695799i | ||||
\(598\) | 0.969367 | − | 4.98806i | 0.0396404 | − | 0.203977i | ||||
\(599\) | 15.0613 | − | 26.0869i | 0.615387 | − | 1.06588i | −0.374930 | − | 0.927053i | \(-0.622333\pi\) |
0.990316 | − | 0.138828i | \(-0.0443336\pi\) | |||||||
\(600\) | −1.99796 | + | 3.53848i | −0.0815662 | + | 0.144458i | ||||
\(601\) | 7.99172 | + | 13.8421i | 0.325989 | + | 0.564630i | 0.981712 | − | 0.190372i | \(-0.0609693\pi\) |
−0.655723 | + | 0.755002i | \(0.727636\pi\) | |||||||
\(602\) | −1.21573 | −0.0495496 | ||||||||
\(603\) | −13.7209 | + | 8.27654i | −0.558757 | + | 0.337047i | ||||
\(604\) | 19.1963i | 0.781087i | ||||||||
\(605\) | −5.49003 | + | 3.16967i | −0.223202 | + | 0.128866i | ||||
\(606\) | 11.6931 | − | 0.112117i | 0.475001 | − | 0.00455446i | ||||
\(607\) | 1.38476 | − | 2.39848i | 0.0562057 | − | 0.0973512i | −0.836554 | − | 0.547885i | \(-0.815433\pi\) |
0.892759 | + | 0.450534i | \(0.148766\pi\) | |||||||
\(608\) | 5.68801 | − | 9.85192i | 0.230679 | − | 0.399548i | ||||
\(609\) | 2.03762 | − | 0.0195373i | 0.0825684 | − | 0.000791692i | ||||
\(610\) | −5.00266 | − | 8.66485i | −0.202552 | − | 0.350830i | ||||
\(611\) | 0.327340 | − | 0.112727i | 0.0132427 | − | 0.00456046i | ||||
\(612\) | 17.0707 | + | 28.2999i | 0.690044 | + | 1.14396i | ||||
\(613\) | 13.9203i | 0.562236i | 0.959673 | + | 0.281118i | \(0.0907053\pi\) | ||||
−0.959673 | + | 0.281118i | \(0.909295\pi\) | |||||||
\(614\) | 11.4892 | + | 19.9000i | 0.463668 | + | 0.803097i | ||||
\(615\) | −5.85872 | − | 3.30805i | −0.236246 | − | 0.133393i | ||||
\(616\) | −1.43186 | − | 0.826684i | −0.0576912 | − | 0.0333080i | ||||
\(617\) | −34.2279 | − | 19.7615i | −1.37796 | − | 0.795568i | −0.386050 | − | 0.922478i | \(-0.626161\pi\) |
−0.991914 | + | 0.126910i | \(0.959494\pi\) | |||||||
\(618\) | 7.46803 | + | 12.6533i | 0.300408 | + | 0.508989i | ||||
\(619\) | 32.2145 | − | 18.5990i | 1.29481 | − | 0.747559i | 0.315307 | − | 0.948990i | \(-0.397892\pi\) |
0.979503 | + | 0.201431i | \(0.0645591\pi\) | |||||||
\(620\) | 11.6843 | 0.469251 | ||||||||
\(621\) | −9.79978 | − | 5.28810i | −0.393252 | − | 0.212204i | ||||
\(622\) | 2.16541i | 0.0868249i | ||||||||
\(623\) | 1.19101 | + | 2.06289i | 0.0477169 | + | 0.0826481i | ||||
\(624\) | −7.56663 | − | 6.45070i | −0.302907 | − | 0.258235i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 15.1707 | + | 8.75879i | 0.606342 | + | 0.350072i | ||||
\(627\) | −6.45394 | − | 3.64413i | −0.257746 | − | 0.145532i | ||||
\(628\) | −2.22967 | − | 3.86190i | −0.0889734 | − | 0.154106i | ||||
\(629\) | 55.2790i | 2.20412i | ||||||||
\(630\) | −0.0123490 | − | 0.643903i | −0.000491997 | − | 0.0256537i | ||||
\(631\) | − | 0.503852i | − | 0.0200580i | −0.999950 | − | 0.0100290i | \(-0.996808\pi\) | ||
0.999950 | − | 0.0100290i | \(-0.00319239\pi\) | |||||||
\(632\) | 22.5274 | − | 13.0062i | 0.896090 | − | 0.517358i | ||||
\(633\) | −0.0442937 | − | 4.61955i | −0.00176051 | − | 0.183611i | ||||
\(634\) | −7.59983 | + | 13.1633i | −0.301828 | + | 0.522781i | ||||
\(635\) | −10.3799 | − | 5.99283i | −0.411913 | − | 0.237818i | ||||
\(636\) | −0.0607791 | − | 6.33887i | −0.00241005 | − | 0.251353i | ||||
\(637\) | −16.3053 | + | 18.7587i | −0.646041 | + | 0.743247i | ||||
\(638\) | −5.11670 | −0.202572 | ||||||||
\(639\) | −30.6896 | − | 16.9425i | −1.21406 | − | 0.670234i | ||||
\(640\) | 11.0906 | 0.438393 | ||||||||
\(641\) | 5.12505 | + | 8.87684i | 0.202427 | + | 0.350614i | 0.949310 | − | 0.314342i | \(-0.101784\pi\) |
−0.746883 | + | 0.664956i | \(0.768450\pi\) | |||||||
\(642\) | 5.98030 | − | 10.5914i | 0.236024 | − | 0.418010i | ||||
\(643\) | 32.0632 | + | 18.5117i | 1.26445 | + | 0.730029i | 0.973932 | − | 0.226841i | \(-0.0728397\pi\) |
0.290516 | + | 0.956870i | \(0.406173\pi\) | |||||||
\(644\) | 0.949665 | + | 0.548289i | 0.0374220 | + | 0.0216056i | ||||
\(645\) | −4.98566 | − | 8.44733i | −0.196310 | − | 0.332613i | ||||
\(646\) | 4.58057 | + | 7.93378i | 0.180220 | + | 0.312151i | ||||
\(647\) | −34.5539 | −1.35845 | −0.679227 | − | 0.733928i | \(-0.737685\pi\) | ||||
−0.679227 | + | 0.733928i | \(0.737685\pi\) | |||||||
\(648\) | 17.8679 | − | 11.2509i | 0.701916 | − | 0.441976i | ||||
\(649\) | −21.1663 | −0.830850 | ||||||||
\(650\) | 1.78957 | + | 1.55552i | 0.0701928 | + | 0.0610125i | ||||
\(651\) | −3.62949 | + | 2.14214i | −0.142251 | + | 0.0839572i | ||||
\(652\) | −0.433712 | − | 0.250404i | −0.0169855 | − | 0.00980657i | ||||
\(653\) | 7.50748 | − | 13.0033i | 0.293790 | − | 0.508860i | −0.680912 | − | 0.732365i | \(-0.738417\pi\) |
0.974703 | + | 0.223505i | \(0.0717499\pi\) | |||||||
\(654\) | −13.1530 | − | 7.42665i | −0.514322 | − | 0.290405i | ||||
\(655\) | −16.3895 | + | 9.46251i | −0.640393 | + | 0.369731i | ||||
\(656\) | 6.18477i | 0.241475i | ||||||||
\(657\) | −31.8021 | − | 17.5566i | −1.24072 | − | 0.684949i | ||||
\(658\) | − | 0.0206131i | − | 0.000803581i | ||||||
\(659\) | −3.24346 | − | 5.61783i | −0.126347 | − | 0.218840i | 0.795912 | − | 0.605413i | \(-0.206992\pi\) |
−0.922259 | + | 0.386573i | \(0.873659\pi\) | |||||||
\(660\) | −0.0561979 | − | 5.86108i | −0.00218750 | − | 0.228142i | ||||
\(661\) | −34.5991 | − | 19.9758i | −1.34575 | − | 0.776968i | −0.358104 | − | 0.933682i | \(-0.616577\pi\) |
−0.987644 | + | 0.156713i | \(0.949910\pi\) | |||||||
\(662\) | 6.21041 | − | 10.7567i | 0.241374 | − | 0.418073i | ||||
\(663\) | 41.3595 | − | 14.6882i | 1.60627 | − | 0.570442i | ||||
\(664\) | −18.7464 | − | 32.4698i | −0.727502 | − | 1.26007i | ||||
\(665\) | 0.647038i | 0.0250911i | ||||||||
\(666\) | 15.5149 | − | 0.297550i | 0.601189 | − | 0.0115298i | ||||
\(667\) | 7.72348 | 0.299054 | ||||||||
\(668\) | 21.6965 | − | 12.5265i | 0.839462 | − | 0.484664i | ||||
\(669\) | 3.64751 | − | 6.45993i | 0.141021 | − | 0.249755i | ||||
\(670\) | −3.04199 | − | 1.75629i | −0.117522 | − | 0.0678516i | ||||
\(671\) | 28.4448 | + | 16.4226i | 1.09810 | + | 0.633988i | ||||
\(672\) | −2.79457 | + | 1.64937i | −0.107803 | + | 0.0636260i | ||||
\(673\) | 3.38993 | + | 5.87154i | 0.130672 | + | 0.226331i | 0.923936 | − | 0.382547i | \(-0.124953\pi\) |
−0.793264 | + | 0.608878i | \(0.791620\pi\) | |||||||
\(674\) | 4.93647i | 0.190146i | ||||||||
\(675\) | 4.42342 | − | 2.72642i | 0.170257 | − | 0.104940i | ||||
\(676\) | −16.0569 | + | 12.5471i | −0.617572 | + | 0.482583i | ||||
\(677\) | 25.0490 | + | 43.3861i | 0.962711 | + | 1.66746i | 0.715642 | + | 0.698467i | \(0.246134\pi\) |
0.247069 | + | 0.968998i | \(0.420533\pi\) | |||||||
\(678\) | −4.32809 | − | 7.33319i | −0.166219 | − | 0.281629i | ||||
\(679\) | 0.292822 | − | 0.507182i | 0.0112375 | − | 0.0194639i | ||||
\(680\) | −8.24430 | + | 14.2795i | −0.316154 | + | 0.547596i | ||||
\(681\) | 21.1498 | − | 37.4574i | 0.810462 | − | 1.43537i | ||||
\(682\) | 9.16480 | − | 5.29130i | 0.350938 | − | 0.202614i | ||||
\(683\) | 35.7445i | 1.36773i | 0.729611 | + | 0.683863i | \(0.239701\pi\) | ||||
−0.729611 | + | 0.683863i | \(0.760299\pi\) | |||||||
\(684\) | −7.98147 | + | 4.81448i | −0.305179 | + | 0.184086i | ||||
\(685\) | −8.15595 | −0.311623 | ||||||||
\(686\) | 1.49128 | + | 2.58297i | 0.0569373 | + | 0.0986183i | ||||
\(687\) | −6.39030 | + | 0.0612722i | −0.243805 | + | 0.00233768i | ||||
\(688\) | −4.50836 | + | 7.80871i | −0.171880 | + | 0.297704i | ||||
\(689\) | −8.26379 | − | 1.60596i | −0.314825 | − | 0.0611823i | ||||
\(690\) | −0.0234042 | − | 2.44091i | −0.000890981 | − | 0.0929237i | ||||
\(691\) | 31.3027 | − | 18.0726i | 1.19081 | − | 0.687514i | 0.232319 | − | 0.972640i | \(-0.425369\pi\) |
0.958490 | + | 0.285125i | \(0.0920352\pi\) | |||||||
\(692\) | −2.79344 | −0.106191 | ||||||||
\(693\) | 1.09200 | + | 1.81033i | 0.0414818 | + | 0.0687687i | ||||
\(694\) | − | 9.62346i | − | 0.365302i | ||||||
\(695\) | −4.47226 | + | 2.58206i | −0.169643 | + | 0.0979432i | ||||
\(696\) | −7.20063 | + | 12.7527i | −0.272939 | + | 0.483389i | ||||
\(697\) | −23.6429 | − | 13.6502i | −0.895537 | − | 0.517039i | ||||
\(698\) | −4.10739 | + | 7.11421i | −0.155467 | + | 0.269277i | ||||
\(699\) | 16.4739 | − | 9.72297i | 0.623099 | − | 0.367757i | ||||
\(700\) | −0.443141 | + | 0.255848i | −0.0167492 | + | 0.00967013i | ||||
\(701\) | −8.46862 | −0.319856 | −0.159928 | − | 0.987129i | \(-0.551126\pi\) | ||||
−0.159928 | + | 0.987129i | \(0.551126\pi\) | |||||||
\(702\) | −4.34508 | − | 11.5291i | −0.163995 | − | 0.435137i | ||||
\(703\) | −15.5904 | −0.588003 | ||||||||
\(704\) | 1.10304 | − | 0.636843i | 0.0415725 | − | 0.0240019i | ||||
\(705\) | 0.143227 | − | 0.0845331i | 0.00539422 | − | 0.00318370i | ||||
\(706\) | 6.18429 | − | 10.7115i | 0.232749 | − | 0.403133i | ||||
\(707\) | 2.90226 | + | 1.67562i | 0.109151 | + | 0.0630182i | ||||
\(708\) | −13.0880 | + | 23.1795i | −0.491877 | + | 0.871139i | ||||
\(709\) | −39.3782 | + | 22.7350i | −1.47888 | + | 0.853832i | −0.999715 | − | 0.0238931i | \(-0.992394\pi\) |
−0.479165 | + | 0.877725i | \(0.659061\pi\) | |||||||
\(710\) | − | 7.68455i | − | 0.288396i | ||||||
\(711\) | −33.2562 | + | 0.637800i | −1.24720 | + | 0.0239194i | ||||
\(712\) | −17.1197 | −0.641589 | ||||||||
\(713\) | −13.8340 | + | 7.98704i | −0.518086 | + | 0.299117i | ||||
\(714\) | −0.0250552 | − | 2.61310i | −0.000937666 | − | 0.0977926i | ||||
\(715\) | −7.64091 | − | 1.48491i | −0.285754 | − | 0.0555327i | ||||
\(716\) | −2.27207 | + | 3.93535i | −0.0849114 | + | 0.147071i | ||||
\(717\) | 8.78856 | − | 0.0842674i | 0.328215 | − | 0.00314703i | ||||
\(718\) | 5.29114 | + | 9.16452i | 0.197464 | + | 0.342017i | ||||
\(719\) | −34.7901 | −1.29745 | −0.648725 | − | 0.761023i | \(-0.724697\pi\) | ||||
−0.648725 | + | 0.761023i | \(0.724697\pi\) | |||||||
\(720\) | −4.18162 | − | 2.30850i | −0.155840 | − | 0.0860327i | ||||
\(721\) | 4.21074i | 0.156816i | ||||||||
\(722\) | 8.58339 | − | 4.95562i | 0.319441 | − | 0.184429i | ||||
\(723\) | −11.5231 | + | 20.4080i | −0.428548 | + | 0.758981i | ||||
\(724\) | −1.13552 | + | 1.96678i | −0.0422012 | + | 0.0730947i | ||||
\(725\) | −1.80200 | + | 3.12115i | −0.0669245 | + | 0.115917i | ||||
\(726\) | 3.67020 | + | 6.21851i | 0.136214 | + | 0.230791i | ||||
\(727\) | −19.5971 | − | 33.9432i | −0.726817 | − | 1.25888i | −0.958222 | − | 0.286026i | \(-0.907666\pi\) |
0.231405 | − | 0.972857i | \(-0.425668\pi\) | |||||||
\(728\) | 0.899108 | + | 2.61085i | 0.0333232 | + | 0.0967645i | ||||
\(729\) | −26.9553 | + | 1.55240i | −0.998346 | + | 0.0574964i | ||||
\(730\) | − | 7.96312i | − | 0.294728i | ||||||
\(731\) | −19.9005 | − | 34.4687i | −0.736047 | − | 1.27487i | ||||
\(732\) | 35.5732 | − | 20.9955i | 1.31482 | − | 0.776017i | ||||
\(733\) | 3.42447 | + | 1.97712i | 0.126486 | + | 0.0730266i | 0.561908 | − | 0.827200i | \(-0.310068\pi\) |
−0.435422 | + | 0.900226i | \(0.643401\pi\) | |||||||
\(734\) | −15.1610 | − | 8.75323i | −0.559604 | − | 0.323087i | ||||
\(735\) | −5.87048 | + | 10.3969i | −0.216536 | + | 0.383496i | ||||
\(736\) | −10.6516 | + | 6.14973i | −0.392625 | + | 0.226682i | ||||
\(737\) | 11.5311 | 0.424752 | ||||||||
\(738\) | −3.70387 | + | 6.70919i | −0.136341 | + | 0.246969i | ||||
\(739\) | − | 33.3471i | − | 1.22669i | −0.789814 | − | 0.613347i | \(-0.789823\pi\) | ||
0.789814 | − | 0.613347i | \(-0.210177\pi\) | |||||||
\(740\) | −6.16465 | − | 10.6775i | −0.226617 | − | 0.392512i | ||||
\(741\) | 4.14253 | + | 11.6647i | 0.152180 | + | 0.428512i | ||||
\(742\) | −0.250615 | + | 0.434078i | −0.00920036 | + | 0.0159355i | ||||
\(743\) | −5.97731 | − | 3.45100i | −0.219286 | − | 0.126605i | 0.386333 | − | 0.922359i | \(-0.373741\pi\) |
−0.605620 | + | 0.795754i | \(0.707075\pi\) | |||||||
\(744\) | −0.290415 | − | 30.2884i | −0.0106471 | − | 1.11043i | ||||
\(745\) | 10.8111 | + | 18.7254i | 0.396088 | + | 0.686045i | ||||
\(746\) | 9.80666i | 0.359047i | ||||||||
\(747\) | 0.919292 | + | 47.9338i | 0.0336351 | + | 1.75380i | ||||
\(748\) | − | 23.7833i | − | 0.869604i | ||||||
\(749\) | 3.01878 | − | 1.74290i | 0.110304 | − | 0.0636840i | ||||
\(750\) | 0.991861 | + | 0.560040i | 0.0362176 | + | 0.0204498i | ||||
\(751\) | 11.5467 | − | 19.9994i | 0.421344 | − | 0.729789i | −0.574727 | − | 0.818345i | \(-0.694892\pi\) |
0.996071 | + | 0.0885558i | \(0.0282252\pi\) | |||||||
\(752\) | −0.132399 | − | 0.0764404i | −0.00482808 | − | 0.00278749i | ||||
\(753\) | 22.3452 | − | 13.1882i | 0.814303 | − | 0.480606i | ||||
\(754\) | 6.44961 | + | 5.60609i | 0.234881 | + | 0.204162i | ||||
\(755\) | 12.2463 | 0.445688 | ||||||||
\(756\) | 2.65775 | − | 0.0764686i | 0.0966613 | − | 0.00278114i | ||||
\(757\) | −12.6259 | −0.458894 | −0.229447 | − | 0.973321i | \(-0.573692\pi\) | ||||
−0.229447 | + | 0.973321i | \(0.573692\pi\) | |||||||
\(758\) | −3.66191 | − | 6.34261i | −0.133006 | − | 0.230374i | ||||
\(759\) | 4.07301 | + | 6.90101i | 0.147841 | + | 0.250491i | ||||
\(760\) | −4.02728 | − | 2.32515i | −0.146085 | − | 0.0843421i | ||||
\(761\) | 35.4456 | + | 20.4645i | 1.28490 | + | 0.741838i | 0.977740 | − | 0.209820i | \(-0.0672877\pi\) |
0.307161 | + | 0.951658i | \(0.400621\pi\) | |||||||
\(762\) | −6.71245 | + | 11.8881i | −0.243166 | + | 0.430660i | ||||
\(763\) | −2.16442 | − | 3.74888i | −0.0783572 | − | 0.135719i | ||||
\(764\) | 4.87261 | 0.176285 | ||||||||
\(765\) | 18.0539 | − | 10.8903i | 0.652741 | − | 0.393739i | ||||
\(766\) | 8.04776 | 0.290777 | ||||||||
\(767\) | 26.6802 | + | 23.1908i | 0.963365 | + | 0.837371i | ||||
\(768\) | −0.140716 | − | 14.6758i | −0.00507765 | − | 0.529567i | ||||
\(769\) | 24.5247 | + | 14.1593i | 0.884382 | + | 0.510598i | 0.872101 | − | 0.489327i | \(-0.162757\pi\) |
0.0122811 | + | 0.999925i | \(0.496091\pi\) | |||||||
\(770\) | −0.231725 | + | 0.401359i | −0.00835079 | + | 0.0144640i | ||||
\(771\) | −0.355220 | − | 37.0472i | −0.0127929 | − | 1.33422i | ||||
\(772\) | 24.9980 | − | 14.4326i | 0.899697 | − | 0.519441i | ||||
\(773\) | − | 37.9270i | − | 1.36414i | −0.731286 | − | 0.682071i | \(-0.761080\pi\) | ||
0.731286 | − | 0.682071i | \(-0.238920\pi\) | |||||||
\(774\) | −9.56703 | + | 5.77091i | −0.343880 | + | 0.207431i | ||||
\(775\) | − | 7.45396i | − | 0.267754i | ||||||
\(776\) | 2.10453 | + | 3.64514i | 0.0755481 | + | 0.130853i | ||||
\(777\) | 3.87250 | + | 2.18655i | 0.138925 | + | 0.0784421i | ||||
\(778\) | −13.5658 | − | 7.83224i | −0.486359 | − | 0.280799i | ||||
\(779\) | 3.84979 | − | 6.66802i | 0.137933 | − | 0.238907i | ||||
\(780\) | −6.35084 | + | 7.44948i | −0.227396 | + | 0.266734i | ||||
\(781\) | 12.6133 | + | 21.8470i | 0.451341 | + | 0.781746i | ||||
\(782\) | − | 9.90480i | − | 0.354195i | ||||||
\(783\) | 15.9420 | − | 9.82601i | 0.569720 | − | 0.351153i | ||||
\(784\) | 10.9755 | 0.391984 | ||||||||
\(785\) | −2.46369 | + | 1.42241i | −0.0879330 | + | 0.0507682i | ||||
\(786\) | 10.9568 | + | 18.5643i | 0.390815 | + | 0.662167i | ||||
\(787\) | 28.2750 | + | 16.3246i | 1.00790 | + | 0.581909i | 0.910575 | − | 0.413344i | \(-0.135639\pi\) |
0.0973205 | + | 0.995253i | \(0.468973\pi\) | |||||||
\(788\) | 12.7001 | + | 7.33242i | 0.452423 | + | 0.261207i | ||||
\(789\) | 22.5772 | + | 12.7479i | 0.803768 | + | 0.453837i | ||||
\(790\) | −3.64572 | − | 6.31457i | −0.129709 | − | 0.224662i | ||||
\(791\) | − | 2.44033i | − | 0.0867681i | ||||||
\(792\) | −15.1919 | + | 0.291357i | −0.539822 | + | 0.0103529i | ||||
\(793\) | −17.8614 | − | 51.8662i | −0.634276 | − | 1.84182i | ||||
\(794\) | −4.27772 | − | 7.40923i | −0.151811 | − | 0.262944i | ||||
\(795\) | −4.04388 | + | 0.0387740i | −0.143422 | + | 0.00137517i | ||||
\(796\) | −1.51353 | + | 2.62151i | −0.0536456 | + | 0.0929169i | ||||
\(797\) | 7.91250 | − | 13.7048i | 0.280275 | − | 0.485451i | −0.691177 | − | 0.722685i | \(-0.742908\pi\) |
0.971452 | + | 0.237235i | \(0.0762410\pi\) | |||||||
\(798\) | 0.736975 | − | 0.00706634i | 0.0260886 | − | 0.000250146i | ||||
\(799\) | 0.584425 | − | 0.337418i | 0.0206755 | − | 0.0119370i | ||||
\(800\) | − | 5.73928i | − | 0.202914i | ||||||
\(801\) | 19.1647 | + | 10.5801i | 0.677153 | + | 0.373828i | ||||
\(802\) | 2.84455 | 0.100444 | ||||||||
\(803\) | 13.0706 | + | 22.6389i | 0.461251 | + | 0.798909i | ||||
\(804\) | 7.13012 | − | 12.6278i | 0.251460 | − | 0.445349i | ||||
\(805\) | 0.349781 | − | 0.605838i | 0.0123282 | − | 0.0213530i | ||||
\(806\) | −17.3497 | − | 3.37169i | −0.611115 | − | 0.118763i | ||||
\(807\) | 6.69584 | − | 3.95192i | 0.235705 | − | 0.139114i | ||||
\(808\) | −20.8587 | + | 12.0428i | −0.733807 | + | 0.423664i | ||||
\(809\) | 6.20843 | 0.218277 | 0.109138 | − | 0.994027i | \(-0.465191\pi\) | ||||
0.109138 | + | 0.994027i | \(0.465191\pi\) | |||||||
\(810\) | −3.15369 | − | 5.00848i | −0.110810 | − | 0.175980i | ||||
\(811\) | − | 18.5979i | − | 0.653060i | −0.945187 | − | 0.326530i | \(-0.894121\pi\) | ||
0.945187 | − | 0.326530i | \(-0.105879\pi\) | |||||||
\(812\) | −1.59708 | + | 0.922074i | −0.0560465 | + | 0.0323584i | ||||
\(813\) | −16.8170 | − | 28.4935i | −0.589799 | − | 0.999310i | ||||
\(814\) | −9.67076 | − | 5.58341i | −0.338960 | − | 0.195699i | ||||
\(815\) | −0.159745 | + | 0.276686i | −0.00559562 | + | 0.00969190i | ||||
\(816\) | −16.8770 | − | 9.52934i | −0.590811 | − | 0.333594i | ||||
\(817\) | 9.72125 | − | 5.61257i | 0.340104 | − | 0.196359i | ||||
\(818\) | 9.37947 | 0.327946 | ||||||||
\(819\) | 0.607006 | − | 3.47837i | 0.0212105 | − | 0.121544i | ||||
\(820\) | 6.08902 | 0.212638 | ||||||||
\(821\) | −7.08387 | + | 4.08987i | −0.247229 | + | 0.142738i | −0.618495 | − | 0.785789i | \(-0.712257\pi\) |
0.371266 | + | 0.928527i | \(0.378924\pi\) | |||||||
\(822\) | 0.0890715 | + | 9.28959i | 0.00310673 | + | 0.324012i | ||||
\(823\) | −13.0281 | + | 22.5654i | −0.454133 | + | 0.786581i | −0.998638 | − | 0.0521766i | \(-0.983384\pi\) |
0.544505 | + | 0.838757i | \(0.316717\pi\) | |||||||
\(824\) | −26.2083 | − | 15.1314i | −0.913011 | − | 0.527127i | ||||
\(825\) | −3.73907 | + | 0.0358514i | −0.130178 | + | 0.00124819i | ||||
\(826\) | 1.82277 | − | 1.05238i | 0.0634222 | − | 0.0366168i | ||||
\(827\) | 6.63409i | 0.230690i | 0.993325 | + | 0.115345i | \(0.0367974\pi\) | ||||
−0.993325 | + | 0.115345i | \(0.963203\pi\) | |||||||
\(828\) | 10.0759 | − | 0.193239i | 0.350162 | − | 0.00671554i | ||||
\(829\) | −3.16728 | −0.110004 | −0.0550021 | − | 0.998486i | \(-0.517517\pi\) | ||||
−0.0550021 | + | 0.998486i | \(0.517517\pi\) | |||||||
\(830\) | −9.10149 | + | 5.25475i | −0.315917 | + | 0.182395i | ||||
\(831\) | 29.4945 | + | 16.6536i | 1.02315 | + | 0.577708i | ||||
\(832\) | −2.08814 | − | 0.405805i | −0.0723934 | − | 0.0140687i | ||||
\(833\) | −24.2237 | + | 41.9568i | −0.839303 | + | 1.45372i | ||||
\(834\) | 2.98980 | + | 5.06570i | 0.103528 | + | 0.175411i | ||||
\(835\) | −7.99125 | − | 13.8413i | −0.276549 | − | 0.478997i | ||||
\(836\) | 6.70764 | 0.231989 | ||||||||
\(837\) | −18.3933 | + | 34.0859i | −0.635764 | + | 1.17818i | ||||
\(838\) | 9.51925i | 0.328837i | ||||||||
\(839\) | 29.8526 | − | 17.2354i | 1.03063 | − | 0.595032i | 0.113462 | − | 0.993542i | \(-0.463806\pi\) |
0.917164 | + | 0.398510i | \(0.130473\pi\) | |||||||
\(840\) | 0.674233 | + | 1.14237i | 0.0232632 | + | 0.0394155i | ||||
\(841\) | 8.00561 | − | 13.8661i | 0.276055 | − | 0.478142i | ||||
\(842\) | −1.46921 | + | 2.54475i | −0.0506324 | + | 0.0876978i | ||||
\(843\) | −0.669799 | + | 1.18625i | −0.0230691 | + | 0.0408566i | ||||
\(844\) | 2.09046 | + | 3.62079i | 0.0719567 | + | 0.124633i | ||||
\(845\) | 8.00445 | + | 10.2435i | 0.275361 | + | 0.352386i | ||||
\(846\) | −0.0978472 | − | 0.162211i | −0.00336405 | − | 0.00557694i | ||||
\(847\) | 2.06939i | 0.0711050i | ||||||||
\(848\) | 1.85873 | + | 3.21942i | 0.0638292 | + | 0.110555i | ||||
\(849\) | −0.302588 | − | 31.5580i | −0.0103848 | − | 1.08307i | ||||
\(850\) | 4.00265 | + | 2.31093i | 0.137290 | + | 0.0792643i | ||||
\(851\) | 14.5977 | + | 8.42797i | 0.500402 | + | 0.288907i | ||||
\(852\) | 31.7243 | − | 0.304182i | 1.08685 | − | 0.0104211i | ||||
\(853\) | 18.1118 | − | 10.4568i | 0.620135 | − | 0.358035i | −0.156786 | − | 0.987633i | \(-0.550113\pi\) |
0.776922 | + | 0.629597i | \(0.216780\pi\) | |||||||
\(854\) | −3.26609 | −0.111763 | ||||||||
\(855\) | 3.07140 | + | 5.09177i | 0.105040 | + | 0.174135i | ||||
\(856\) | 25.0526i | 0.856280i | ||||||||
\(857\) | 11.8102 | + | 20.4558i | 0.403427 | + | 0.698757i | 0.994137 | − | 0.108127i | \(-0.0344855\pi\) |
−0.590710 | + | 0.806884i | \(0.701152\pi\) | |||||||
\(858\) | −1.60787 | + | 8.71919i | −0.0548916 | + | 0.297668i | ||||
\(859\) | 1.47856 | − | 2.56094i | 0.0504478 | − | 0.0873781i | −0.839699 | − | 0.543052i | \(-0.817268\pi\) |
0.890147 | + | 0.455674i | \(0.150602\pi\) | |||||||
\(860\) | 7.68782 | + | 4.43857i | 0.262153 | + | 0.151354i | ||||
\(861\) | −1.89144 | + | 1.11634i | −0.0644600 | + | 0.0380447i | ||||
\(862\) | −6.53324 | − | 11.3159i | −0.222523 | − | 0.385421i | ||||
\(863\) | 0.569343i | 0.0193807i | 0.999953 | + | 0.00969033i | \(0.00308458\pi\) | ||||
−0.999953 | + | 0.00969033i | \(0.996915\pi\) | |||||||
\(864\) | −14.1621 | + | 26.2449i | −0.481806 | + | 0.892871i | ||||
\(865\) | 1.78208i | 0.0605924i | ||||||||
\(866\) | −6.87463 | + | 3.96907i | −0.233610 | + | 0.134875i | ||||
\(867\) | 48.3192 | − | 28.5183i | 1.64101 | − | 0.968531i | ||||
\(868\) | 1.90708 | − | 3.30316i | 0.0647305 | − | 0.112116i | ||||
\(869\) | 20.7293 | + | 11.9681i | 0.703194 | + | 0.405989i | ||||
\(870\) | 3.57466 | + | 2.01838i | 0.121192 | + | 0.0684296i | ||||
\(871\) | −14.5349 | − | 12.6340i | −0.492497 | − | 0.428085i | ||||
\(872\) | 31.1116 | 1.05357 | ||||||||
\(873\) | −0.103202 | − | 5.38117i | −0.00349287 | − | 0.182125i | ||||
\(874\) | 2.79346 | 0.0944903 | ||||||||
\(875\) | 0.163218 | + | 0.282702i | 0.00551777 | + | 0.00955706i | ||||
\(876\) | 32.8742 | − | 0.315208i | 1.11072 | − | 0.0106499i | ||||
\(877\) | 32.2837 | + | 18.6390i | 1.09014 | + | 0.629395i | 0.933615 | − | 0.358279i | \(-0.116636\pi\) |
0.156529 | + | 0.987673i | \(0.449970\pi\) | |||||||
\(878\) | 9.01666 | + | 5.20577i | 0.304298 | + | 0.175686i | ||||
\(879\) | −21.3379 | + | 0.204594i | −0.719709 | + | 0.00690079i | ||||
\(880\) | 1.71863 | + | 2.97676i | 0.0579351 | + | 0.100347i | ||||
\(881\) | 53.2952 | 1.79556 | 0.897780 | − | 0.440443i | \(-0.145179\pi\) | ||||
0.897780 | + | 0.440443i | \(0.145179\pi\) | |||||||
\(882\) | 11.9062 | + | 6.57291i | 0.400902 | + | 0.221321i | ||||
\(883\) | 12.5410 | 0.422038 | 0.211019 | − | 0.977482i | \(-0.432322\pi\) | ||||
0.211019 | + | 0.977482i | \(0.432322\pi\) | |||||||
\(884\) | −26.0581 | + | 29.9789i | −0.876429 | + | 1.00830i | ||||
\(885\) | 14.7873 | + | 8.34947i | 0.497071 | + | 0.280664i | ||||
\(886\) | −0.0831730 | − | 0.0480200i | −0.00279425 | − | 0.00161326i | ||||
\(887\) | −28.7562 | + | 49.8072i | −0.965538 | + | 1.67236i | −0.257377 | + | 0.966311i | \(0.582858\pi\) |
−0.708162 | + | 0.706050i | \(0.750475\pi\) | |||||||
\(888\) | −27.5254 | + | 16.2456i | −0.923692 | + | 0.545168i | ||||
\(889\) | −3.38836 | + | 1.95627i | −0.113642 | + | 0.0656113i | ||||
\(890\) | 4.79878i | 0.160855i | ||||||||
\(891\) | 17.1867 | + | 9.06253i | 0.575777 | + | 0.303606i | ||||
\(892\) | 6.71386i | 0.224797i | ||||||||
\(893\) | 0.0951625 | + | 0.164826i | 0.00318449 | + | 0.00551570i | ||||
\(894\) | 21.2101 | − | 12.5183i | 0.709371 | − | 0.418675i | ||||
\(895\) | 2.51055 | + | 1.44947i | 0.0839185 | + | 0.0484504i | ||||
\(896\) | 1.81018 | − | 3.13532i | 0.0604738 | − | 0.104744i | ||||
\(897\) | 2.42702 | − | 13.1613i | 0.0810358 | − | 0.439444i | ||||
\(898\) | 0.554305 | + | 0.960084i | 0.0184974 | + | 0.0320384i | ||||
\(899\) | − | 26.8641i | − | 0.895966i | ||||||
\(900\) | −2.27276 | + | 4.11688i | −0.0757587 | + | 0.137229i | ||||
\(901\) | −16.4094 | −0.546676 | ||||||||
\(902\) | 4.77606 | − | 2.75746i | 0.159025 | − | 0.0918134i | ||||
\(903\) | −3.20182 | + | 0.0307001i | −0.106550 | + | 0.00102163i | ||||
\(904\) | 15.1890 | + | 8.76939i | 0.505179 | + | 0.291665i | ||||
\(905\) | 1.25470 | + | 0.724404i | 0.0417078 | + | 0.0240800i | ||||
\(906\) | −0.133742 | − | 13.9485i | −0.00444329 | − | 0.463407i | ||||
\(907\) | −19.6520 | − | 34.0383i | −0.652535 | − | 1.13022i | −0.982506 | − | 0.186232i | \(-0.940372\pi\) |
0.329971 | − | 0.943991i | \(-0.392961\pi\) | |||||||
\(908\) | 38.9298i | 1.29193i | ||||||||
\(909\) | 30.7928 | − | 0.590557i | 1.02133 | − | 0.0195875i | ||||
\(910\) | 0.731838 | − | 0.252026i | 0.0242602 | − | 0.00835457i | ||||
\(911\) | 17.0985 | + | 29.6154i | 0.566498 | + | 0.981203i | 0.996909 | + | 0.0785697i | \(0.0250353\pi\) |
−0.430411 | + | 0.902633i | \(0.641631\pi\) | |||||||
\(912\) | 2.68757 | − | 4.75983i | 0.0889944 | − | 0.157614i | ||||
\(913\) | 17.2502 | − | 29.8782i | 0.570897 | − | 0.988823i | ||||
\(914\) | −7.13995 | + | 12.3668i | −0.236169 | + | 0.409056i | ||||
\(915\) | −13.3941 | − | 22.6939i | −0.442795 | − | 0.750237i | ||||
\(916\) | 5.00870 | − | 2.89177i | 0.165492 | − | 0.0955469i | ||||
\(917\) | 6.17780i | 0.204009i | ||||||||
\(918\) | −12.6011 | − | 20.4444i | −0.415900 | − | 0.674767i | ||||
\(919\) | −25.6556 | −0.846301 | −0.423150 | − | 0.906059i | \(-0.639076\pi\) | ||||
−0.423150 | + | 0.906059i | \(0.639076\pi\) | |||||||
\(920\) | 2.51389 | + | 4.35419i | 0.0828806 | + | 0.143553i | ||||
\(921\) | 30.7612 | + | 52.1195i | 1.01362 | + | 1.71740i | ||||
\(922\) | 8.02287 | − | 13.8960i | 0.264219 | − | 0.457641i | ||||
\(923\) | 8.03739 | − | 41.3579i | 0.264554 | − | 1.36131i | ||||
\(924\) | −1.66611 | − | 0.940746i | −0.0548110 | − | 0.0309483i | ||||
\(925\) | −6.81170 | + | 3.93273i | −0.223967 | + | 0.129308i | ||||
\(926\) | 14.5888 | 0.479417 | ||||||||
\(927\) | 19.9877 | + | 33.1358i | 0.656484 | + | 1.08832i | ||||
\(928\) | − | 20.6843i | − | 0.678997i | ||||||
\(929\) | 4.22076 | − | 2.43686i | 0.138479 | − | 0.0799507i | −0.429160 | − | 0.903228i | \(-0.641190\pi\) |
0.567639 | + | 0.823278i | \(0.307857\pi\) | |||||||
\(930\) | −8.49004 | + | 0.0814051i | −0.278399 | + | 0.00266938i | ||||
\(931\) | −11.8331 | − | 6.83185i | −0.387815 | − | 0.223905i | ||||
\(932\) | −8.65603 | + | 14.9927i | −0.283538 | + | 0.491102i | ||||
\(933\) | 0.0546815 | + | 5.70293i | 0.00179019 | + | 0.186706i | ||||
\(934\) | −5.48086 | + | 3.16438i | −0.179339 | + | 0.103542i | ||||
\(935\) | −15.1726 | −0.496196 | ||||||||
\(936\) | 19.4687 | + | 16.2777i | 0.636355 | + | 0.532055i | ||||
\(937\) | 9.44461 | 0.308542 | 0.154271 | − | 0.988029i | \(-0.450697\pi\) | ||||
0.154271 | + | 0.988029i | \(0.450697\pi\) | |||||||
\(938\) | −0.993014 | + | 0.573317i | −0.0324231 | + | 0.0187195i | ||||
\(939\) | 40.1755 | + | 22.6845i | 1.31108 | + | 0.740282i | ||||
\(940\) | −0.0752570 | + | 0.130349i | −0.00245461 | + | 0.00425151i | ||||
\(941\) | 14.3094 | + | 8.26153i | 0.466473 | + | 0.269318i | 0.714762 | − | 0.699368i | \(-0.246535\pi\) |
−0.248289 | + | 0.968686i | \(0.579868\pi\) | |||||||
\(942\) | 1.64703 | + | 2.79061i | 0.0536632 | + | 0.0909229i | ||||
\(943\) | −7.20930 | + | 4.16229i | −0.234767 | + | 0.135543i | ||||
\(944\) | − | 15.6103i | − | 0.508072i | ||||||
\(945\) | −0.0487831 | − | 1.69551i | −0.00158692 | − | 0.0551549i | ||||
\(946\) | 8.04015 | 0.261408 | ||||||||
\(947\) | −11.6573 | + | 6.73036i | −0.378812 | + | 0.218707i | −0.677301 | − | 0.735706i | \(-0.736851\pi\) |
0.298489 | + | 0.954413i | \(0.403517\pi\) | |||||||
\(948\) | 25.9242 | − | 15.3006i | 0.841979 | − | 0.496941i | ||||
\(949\) | 8.32874 | − | 42.8571i | 0.270362 | − | 1.39120i | ||||
\(950\) | −0.651755 | + | 1.12887i | −0.0211457 | + | 0.0366255i | ||||
\(951\) | −19.6829 | + | 34.8595i | −0.638263 | + | 1.13040i | ||||
\(952\) | 2.69123 | + | 4.66135i | 0.0872234 | + | 0.151075i | ||||
\(953\) | 50.2664 | 1.62829 | 0.814144 | − | 0.580664i | \(-0.197207\pi\) | ||||
0.814144 | + | 0.580664i | \(0.197207\pi\) | |||||||
\(954\) | 0.0883268 | + | 4.60554i | 0.00285969 | + | 0.149110i | ||||
\(955\) | − | 3.10848i | − | 0.100588i | ||||||
\(956\) | −6.88845 | + | 3.97705i | −0.222788 | + | 0.128627i | ||||
\(957\) | −13.4756 | + | 0.129208i | −0.435605 | + | 0.00417671i | ||||
\(958\) | −3.47638 | + | 6.02127i | −0.112317 | + | 0.194539i | ||||
\(959\) | −1.33120 | + | 2.30570i | −0.0429865 | + | 0.0744549i | ||||
\(960\) | −1.02183 | + | 0.00979764i | −0.0329795 | + | 0.000316218i | ||||
\(961\) | 12.2808 | + | 21.2709i | 0.396154 | + | 0.686159i | ||||
\(962\) | 6.07257 | + | 17.6336i | 0.195787 | + | 0.568531i | ||||
\(963\) | 15.4826 | − | 28.0452i | 0.498920 | − | 0.903744i | ||||
\(964\) | − | 21.2102i | − | 0.683135i | ||||||
\(965\) | −9.20727 | − | 15.9475i | −0.296392 | − | 0.513367i | ||||
\(966\) | −0.693868 | − | 0.391783i | −0.0223248 | − | 0.0126054i | ||||
\(967\) | −42.3381 | − | 24.4439i | −1.36150 | − | 0.786063i | −0.371678 | − | 0.928362i | \(-0.621217\pi\) |
−0.989824 | + | 0.142299i | \(0.954551\pi\) | |||||||
\(968\) | −12.8802 | − | 7.43640i | −0.413986 | − | 0.239015i | ||||
\(969\) | 12.2640 | + | 20.7792i | 0.393976 | + | 0.667523i | ||||
\(970\) | 1.02176 | − | 0.589912i | 0.0328067 | − | 0.0189409i | ||||
\(971\) | 20.9990 | 0.673891 | 0.336945 | − | 0.941524i | \(-0.390606\pi\) | ||||
0.336945 | + | 0.941524i | \(0.390606\pi\) | |||||||
\(972\) | 20.5518 | − | 13.2177i | 0.659198 | − | 0.423958i | ||||
\(973\) | 1.68575i | 0.0540428i | ||||||||
\(974\) | 12.1871 | + | 21.1086i | 0.390499 | + | 0.676364i | ||||
\(975\) | 4.75239 | + | 4.05151i | 0.152198 | + | 0.129752i | ||||
\(976\) | −12.1118 | + | 20.9783i | −0.387689 | + | 0.671497i | ||||
\(977\) | 0.570511 | + | 0.329385i | 0.0182523 | + | 0.0105379i | 0.509098 | − | 0.860708i | \(-0.329979\pi\) |
−0.490846 | + | 0.871246i | \(0.663312\pi\) | |||||||
\(978\) | 0.316889 | + | 0.178927i | 0.0101330 | + | 0.00572146i | ||||
\(979\) | −7.87666 | − | 13.6428i | −0.251739 | − | 0.436025i | ||||
\(980\) | − | 10.8056i | − | 0.345173i | ||||||
\(981\) | −34.8280 | − | 19.2271i | −1.11197 | − | 0.613874i | ||||
\(982\) | 5.59508i | 0.178546i | ||||||||
\(983\) | −44.5459 | + | 25.7186i | −1.42079 | + | 0.820296i | −0.996367 | − | 0.0851662i | \(-0.972858\pi\) |
−0.424427 | + | 0.905462i | \(0.639525\pi\) | |||||||
\(984\) | −0.151344 | − | 15.7842i | −0.00482467 | − | 0.503183i | ||||
\(985\) | 4.67771 | − | 8.10204i | 0.149044 | − | 0.258152i | ||||
\(986\) | 14.4255 | + | 8.32859i | 0.459403 | + | 0.265236i | ||||
\(987\) | −0.000520527 | − | 0.0542877i | −1.65686e−5 | − | 0.00172800i | ||||
\(988\) | −8.45500 | − | 7.34920i | −0.268989 | − | 0.233809i | ||||
\(989\) | −12.1363 | −0.385913 | ||||||||
\(990\) | 0.0816693 | + | 4.25840i | 0.00259562 | + | 0.135341i | ||||
\(991\) | −56.2188 | −1.78585 | −0.892924 | − | 0.450208i | \(-0.851350\pi\) | ||||
−0.892924 | + | 0.450208i | \(0.851350\pi\) | |||||||
\(992\) | 21.3902 | + | 37.0489i | 0.679139 | + | 1.17630i | ||||
\(993\) | 16.0844 | − | 28.4864i | 0.510424 | − | 0.903988i | ||||
\(994\) | −2.17244 | − | 1.25426i | −0.0689055 | − | 0.0397826i | ||||
\(995\) | 1.67239 | + | 0.965555i | 0.0530183 | + | 0.0306101i | ||||
\(996\) | −22.0535 | − | 37.3658i | −0.698792 | − | 1.18398i | ||||
\(997\) | 19.3082 | + | 33.4428i | 0.611498 | + | 1.05915i | 0.990988 | + | 0.133950i | \(0.0427661\pi\) |
−0.379490 | + | 0.925196i | \(0.623901\pi\) | |||||||
\(998\) | −19.4913 | −0.616986 | ||||||||
\(999\) | 40.8533 | − | 1.17543i | 1.29254 | − | 0.0371890i |
(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 | 585.2.bt.b.571.33 | yes | 108 | |
9.7 | even | 3 | inner | 585.2.bt.b.376.22 | ✓ | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.571.22 | yes | 108 | |
117.25 | even | 6 | inner | 585.2.bt.b.376.33 | yes | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.22 | ✓ | 108 | 9.7 | even | 3 | inner | |
585.2.bt.b.376.33 | yes | 108 | 117.25 | even | 6 | inner | |
585.2.bt.b.571.22 | yes | 108 | 13.12 | even | 2 | inner | |
585.2.bt.b.571.33 | yes | 108 | 1.1 | even | 1 | trivial |