Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} + 18 x^{14} - 35 x^{13} + 89 x^{12} - 185 x^{11} + 837 x^{10} - 1660 x^{9} + 4196 x^{8} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 71.4 | ||
Root | \(-2.05435 + 1.49258i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.71 |
Dual form | 770.2.n.k.141.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | 2.05435 | + | 1.49258i | 1.18608 | + | 0.861739i | 0.992845 | − | 0.119413i | \(-0.0381014\pi\) |
0.193237 | + | 0.981152i | \(0.438101\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | −0.784693 | + | 2.41504i | −0.320350 | + | 0.985935i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 1.06554 | + | 3.27939i | 0.355179 | + | 1.09313i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.57392 | + | 2.91938i | 0.474554 | + | 0.880227i | ||||
\(12\) | −2.53932 | −0.733039 | ||||||||
\(13\) | −1.27148 | − | 3.91321i | −0.352645 | − | 1.08533i | −0.957363 | − | 0.288889i | \(-0.906714\pi\) |
0.604718 | − | 0.796440i | \(-0.293286\pi\) | |||||||
\(14\) | 0.809017 | + | 0.587785i | 0.216219 | + | 0.157092i | ||||
\(15\) | −2.05435 | + | 1.49258i | −0.530432 | + | 0.385381i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −2.11624 | + | 6.51311i | −0.513263 | + | 1.57966i | 0.273157 | + | 0.961970i | \(0.411932\pi\) |
−0.786420 | + | 0.617692i | \(0.788068\pi\) | |||||||
\(18\) | −2.78961 | + | 2.02677i | −0.657518 | + | 0.477715i | ||||
\(19\) | 5.35695 | + | 3.89205i | 1.22897 | + | 0.892898i | 0.996812 | − | 0.0797809i | \(-0.0254221\pi\) |
0.232156 | + | 0.972679i | \(0.425422\pi\) | |||||||
\(20\) | −0.309017 | − | 0.951057i | −0.0690983 | − | 0.212663i | ||||
\(21\) | 2.53932 | 0.554125 | ||||||||
\(22\) | −2.29013 | + | 2.39902i | −0.488257 | + | 0.511473i | ||||
\(23\) | −3.13877 | −0.654479 | −0.327240 | − | 0.944941i | \(-0.606118\pi\) | ||||
−0.327240 | + | 0.944941i | \(0.606118\pi\) | |||||||
\(24\) | −0.784693 | − | 2.41504i | −0.160175 | − | 0.492967i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 3.32878 | − | 2.41850i | 0.652827 | − | 0.474306i | ||||
\(27\) | −0.351660 | + | 1.08230i | −0.0676770 | + | 0.208288i | ||||
\(28\) | −0.309017 | + | 0.951057i | −0.0583987 | + | 0.179733i | ||||
\(29\) | −4.44605 | + | 3.23024i | −0.825610 | + | 0.599841i | −0.918314 | − | 0.395853i | \(-0.870449\pi\) |
0.0927040 | + | 0.995694i | \(0.470449\pi\) | |||||||
\(30\) | −2.05435 | − | 1.49258i | −0.375072 | − | 0.272506i | ||||
\(31\) | −1.72249 | − | 5.30127i | −0.309368 | − | 0.952137i | −0.978011 | − | 0.208553i | \(-0.933125\pi\) |
0.668643 | − | 0.743583i | \(-0.266875\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.12402 | + | 8.34663i | −0.195666 | + | 1.45296i | ||||
\(34\) | −6.84829 | −1.17447 | ||||||||
\(35\) | 0.309017 | + | 0.951057i | 0.0522334 | + | 0.160758i | ||||
\(36\) | −2.78961 | − | 2.02677i | −0.464935 | − | 0.337795i | ||||
\(37\) | 6.29838 | − | 4.57604i | 1.03545 | − | 0.752296i | 0.0660556 | − | 0.997816i | \(-0.478959\pi\) |
0.969392 | + | 0.245519i | \(0.0789585\pi\) | |||||||
\(38\) | −2.04617 | + | 6.29747i | −0.331933 | + | 1.02158i | ||||
\(39\) | 3.22869 | − | 9.93689i | 0.517005 | − | 1.59118i | ||||
\(40\) | 0.809017 | − | 0.587785i | 0.127917 | − | 0.0929370i | ||||
\(41\) | −2.35226 | − | 1.70902i | −0.367361 | − | 0.266904i | 0.388755 | − | 0.921341i | \(-0.372905\pi\) |
−0.756116 | + | 0.654438i | \(0.772905\pi\) | |||||||
\(42\) | 0.784693 | + | 2.41504i | 0.121081 | + | 0.372648i | ||||
\(43\) | 3.23479 | 0.493301 | 0.246651 | − | 0.969104i | \(-0.420670\pi\) | ||||
0.246651 | + | 0.969104i | \(0.420670\pi\) | |||||||
\(44\) | −2.98929 | − | 1.43670i | −0.450653 | − | 0.216591i | ||||
\(45\) | −3.44815 | −0.514020 | ||||||||
\(46\) | −0.969934 | − | 2.98515i | −0.143009 | − | 0.440136i | ||||
\(47\) | 1.21343 | + | 0.881607i | 0.176997 | + | 0.128596i | 0.672756 | − | 0.739864i | \(-0.265110\pi\) |
−0.495760 | + | 0.868460i | \(0.665110\pi\) | |||||||
\(48\) | 2.05435 | − | 1.49258i | 0.296520 | − | 0.215435i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 0.309017 | − | 0.951057i | 0.0437016 | − | 0.134500i | ||||
\(51\) | −14.0688 | + | 10.2216i | −1.97003 | + | 1.43131i | ||||
\(52\) | 3.32878 | + | 2.41850i | 0.461618 | + | 0.335385i | ||||
\(53\) | −3.43975 | − | 10.5865i | −0.472486 | − | 1.45416i | −0.849318 | − | 0.527881i | \(-0.822987\pi\) |
0.376832 | − | 0.926282i | \(-0.377013\pi\) | |||||||
\(54\) | −1.13800 | −0.154862 | ||||||||
\(55\) | −3.26286 | + | 0.594745i | −0.439964 | + | 0.0801954i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 5.19589 | + | 15.9913i | 0.688212 | + | 2.11810i | ||||
\(58\) | −4.44605 | − | 3.23024i | −0.583794 | − | 0.424151i | ||||
\(59\) | 6.00637 | − | 4.36389i | 0.781963 | − | 0.568129i | −0.123604 | − | 0.992332i | \(-0.539445\pi\) |
0.905568 | + | 0.424202i | \(0.139445\pi\) | |||||||
\(60\) | 0.784693 | − | 2.41504i | 0.101303 | − | 0.311780i | ||||
\(61\) | −0.705073 | + | 2.16999i | −0.0902753 | + | 0.277839i | −0.985994 | − | 0.166783i | \(-0.946662\pi\) |
0.895718 | + | 0.444622i | \(0.146662\pi\) | |||||||
\(62\) | 4.50953 | − | 3.27637i | 0.572711 | − | 0.416099i | ||||
\(63\) | 2.78961 | + | 2.02677i | 0.351458 | + | 0.255349i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 4.11459 | 0.510352 | ||||||||
\(66\) | −8.28546 | + | 1.51025i | −1.01987 | + | 0.185899i | ||||
\(67\) | 14.1969 | 1.73442 | 0.867212 | − | 0.497939i | \(-0.165910\pi\) | ||||
0.867212 | + | 0.497939i | \(0.165910\pi\) | |||||||
\(68\) | −2.11624 | − | 6.51311i | −0.256632 | − | 0.789831i | ||||
\(69\) | −6.44815 | − | 4.68485i | −0.776266 | − | 0.563990i | ||||
\(70\) | −0.809017 | + | 0.587785i | −0.0966960 | + | 0.0702538i | ||||
\(71\) | 0.0188133 | − | 0.0579014i | 0.00223273 | − | 0.00687163i | −0.949934 | − | 0.312451i | \(-0.898850\pi\) |
0.952167 | + | 0.305579i | \(0.0988501\pi\) | |||||||
\(72\) | 1.06554 | − | 3.27939i | 0.125575 | − | 0.386479i | ||||
\(73\) | 3.16555 | − | 2.29991i | 0.370500 | − | 0.269184i | −0.386918 | − | 0.922114i | \(-0.626460\pi\) |
0.757418 | + | 0.652930i | \(0.226460\pi\) | |||||||
\(74\) | 6.29838 | + | 4.57604i | 0.732172 | + | 0.531954i | ||||
\(75\) | −0.784693 | − | 2.41504i | −0.0906086 | − | 0.278865i | ||||
\(76\) | −6.62155 | −0.759544 | ||||||||
\(77\) | 2.98929 | + | 1.43670i | 0.340662 | + | 0.163728i | ||||
\(78\) | 10.4483 | 1.18303 | ||||||||
\(79\) | −1.31018 | − | 4.03232i | −0.147407 | − | 0.453671i | 0.849906 | − | 0.526934i | \(-0.176659\pi\) |
−0.997313 | + | 0.0732634i | \(0.976659\pi\) | |||||||
\(80\) | 0.809017 | + | 0.587785i | 0.0904508 | + | 0.0657164i | ||||
\(81\) | 6.03099 | − | 4.38177i | 0.670110 | − | 0.486863i | ||||
\(82\) | 0.898483 | − | 2.76525i | 0.0992209 | − | 0.305371i | ||||
\(83\) | 3.16642 | − | 9.74525i | 0.347560 | − | 1.06968i | −0.612639 | − | 0.790363i | \(-0.709892\pi\) |
0.960199 | − | 0.279317i | \(-0.0901081\pi\) | |||||||
\(84\) | −2.05435 | + | 1.49258i | −0.224148 | + | 0.162853i | ||||
\(85\) | −5.54038 | − | 4.02533i | −0.600939 | − | 0.436608i | ||||
\(86\) | 0.999606 | + | 3.07647i | 0.107790 | + | 0.331744i | ||||
\(87\) | −13.9551 | −1.49615 | ||||||||
\(88\) | 0.442644 | − | 3.28695i | 0.0471861 | − | 0.350390i | ||||
\(89\) | −6.54394 | −0.693656 | −0.346828 | − | 0.937929i | \(-0.612741\pi\) | ||||
−0.346828 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(90\) | −1.06554 | − | 3.27939i | −0.112317 | − | 0.345678i | ||||
\(91\) | −3.32878 | − | 2.41850i | −0.348950 | − | 0.253527i | ||||
\(92\) | 2.53932 | − | 1.84492i | 0.264742 | − | 0.192347i | ||||
\(93\) | 4.37395 | − | 13.4616i | 0.453557 | − | 1.39591i | ||||
\(94\) | −0.463488 | + | 1.42647i | −0.0478052 | + | 0.147129i | ||||
\(95\) | −5.35695 | + | 3.89205i | −0.549611 | + | 0.399316i | ||||
\(96\) | 2.05435 | + | 1.49258i | 0.209672 | + | 0.152335i | ||||
\(97\) | −0.213537 | − | 0.657198i | −0.0216814 | − | 0.0667284i | 0.939630 | − | 0.342191i | \(-0.111169\pi\) |
−0.961312 | + | 0.275463i | \(0.911169\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −7.89671 | + | 8.27219i | −0.793649 | + | 0.831386i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.51753 | + | 13.9035i | 0.449511 | + | 1.38345i | 0.877460 | + | 0.479649i | \(0.159236\pi\) |
−0.427949 | + | 0.903803i | \(0.640764\pi\) | |||||||
\(102\) | −14.0688 | − | 10.2216i | −1.39302 | − | 1.01209i | ||||
\(103\) | −0.868543 | + | 0.631033i | −0.0855800 | + | 0.0621775i | −0.629753 | − | 0.776796i | \(-0.716844\pi\) |
0.544172 | + | 0.838973i | \(0.316844\pi\) | |||||||
\(104\) | −1.27148 | + | 3.91321i | −0.124679 | + | 0.383722i | ||||
\(105\) | −0.784693 | + | 2.41504i | −0.0765782 | + | 0.235684i | ||||
\(106\) | 9.00539 | − | 6.54280i | 0.874680 | − | 0.635493i | ||||
\(107\) | 15.2727 | + | 11.0963i | 1.47647 | + | 1.07272i | 0.978674 | + | 0.205420i | \(0.0658559\pi\) |
0.497793 | + | 0.867296i | \(0.334144\pi\) | |||||||
\(108\) | −0.351660 | − | 1.08230i | −0.0338385 | − | 0.104144i | ||||
\(109\) | 4.22315 | 0.404504 | 0.202252 | − | 0.979333i | \(-0.435174\pi\) | ||||
0.202252 | + | 0.979333i | \(0.435174\pi\) | |||||||
\(110\) | −1.57392 | − | 2.91938i | −0.150067 | − | 0.278352i | ||||
\(111\) | 19.7692 | 1.87641 | ||||||||
\(112\) | −0.309017 | − | 0.951057i | −0.0291994 | − | 0.0898664i | ||||
\(113\) | −5.95877 | − | 4.32930i | −0.560554 | − | 0.407267i | 0.271107 | − | 0.962549i | \(-0.412610\pi\) |
−0.831662 | + | 0.555283i | \(0.812610\pi\) | |||||||
\(114\) | −13.6030 | + | 9.88317i | −1.27404 | + | 0.925643i | ||||
\(115\) | 0.969934 | − | 2.98515i | 0.0904468 | − | 0.278367i | ||||
\(116\) | 1.69824 | − | 5.22664i | 0.157677 | − | 0.485281i | ||||
\(117\) | 11.4781 | − | 8.33934i | 1.06115 | − | 0.770972i | ||||
\(118\) | 6.00637 | + | 4.36389i | 0.552931 | + | 0.401728i | ||||
\(119\) | 2.11624 | + | 6.51311i | 0.193995 | + | 0.597056i | ||||
\(120\) | 2.53932 | 0.231807 | ||||||||
\(121\) | −6.04558 | + | 9.18972i | −0.549598 | + | 0.835429i | ||||
\(122\) | −2.28166 | −0.206572 | ||||||||
\(123\) | −2.28154 | − | 7.02185i | −0.205719 | − | 0.633139i | ||||
\(124\) | 4.50953 | + | 3.27637i | 0.404968 | + | 0.294226i | ||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | −1.06554 | + | 3.27939i | −0.0949256 | + | 0.292151i | ||||
\(127\) | −4.63622 | + | 14.2688i | −0.411398 | + | 1.26615i | 0.504035 | + | 0.863683i | \(0.331848\pi\) |
−0.915433 | + | 0.402470i | \(0.868152\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | 6.64541 | + | 4.82817i | 0.585096 | + | 0.425097i | ||||
\(130\) | 1.27148 | + | 3.91321i | 0.111516 | + | 0.343211i | ||||
\(131\) | −6.77296 | −0.591757 | −0.295878 | − | 0.955226i | \(-0.595612\pi\) | ||||
−0.295878 | + | 0.955226i | \(0.595612\pi\) | |||||||
\(132\) | −3.99668 | − | 7.41325i | −0.347866 | − | 0.645240i | ||||
\(133\) | 6.62155 | 0.574161 | ||||||||
\(134\) | 4.38707 | + | 13.5020i | 0.378986 | + | 1.16640i | ||||
\(135\) | −0.920658 | − | 0.668897i | −0.0792376 | − | 0.0575695i | ||||
\(136\) | 5.54038 | − | 4.02533i | 0.475084 | − | 0.345169i | ||||
\(137\) | −2.82781 | + | 8.70311i | −0.241596 | + | 0.743557i | 0.754581 | + | 0.656207i | \(0.227840\pi\) |
−0.996178 | + | 0.0873506i | \(0.972160\pi\) | |||||||
\(138\) | 2.46297 | − | 7.58025i | 0.209662 | − | 0.645274i | ||||
\(139\) | −12.8740 | + | 9.35348i | −1.09195 | + | 0.793352i | −0.979728 | − | 0.200331i | \(-0.935798\pi\) |
−0.112227 | + | 0.993683i | \(0.535798\pi\) | |||||||
\(140\) | −0.809017 | − | 0.587785i | −0.0683744 | − | 0.0496769i | ||||
\(141\) | 1.17695 | + | 3.62227i | 0.0991167 | + | 0.305050i | ||||
\(142\) | 0.0608812 | 0.00510903 | ||||||||
\(143\) | 9.42295 | − | 9.87100i | 0.787987 | − | 0.825454i | ||||
\(144\) | 3.44815 | 0.287346 | ||||||||
\(145\) | −1.69824 | − | 5.22664i | −0.141031 | − | 0.434049i | ||||
\(146\) | 3.16555 | + | 2.29991i | 0.261983 | + | 0.190342i | ||||
\(147\) | 2.05435 | − | 1.49258i | 0.169440 | − | 0.123106i | ||||
\(148\) | −2.40577 | + | 7.40419i | −0.197753 | + | 0.608621i | ||||
\(149\) | 2.97604 | − | 9.15932i | 0.243807 | − | 0.750361i | −0.752023 | − | 0.659137i | \(-0.770922\pi\) |
0.995830 | − | 0.0912245i | \(-0.0290781\pi\) | |||||||
\(150\) | 2.05435 | − | 1.49258i | 0.167737 | − | 0.121868i | ||||
\(151\) | −16.4670 | − | 11.9640i | −1.34006 | − | 0.973613i | −0.999442 | − | 0.0334132i | \(-0.989362\pi\) |
−0.340622 | − | 0.940200i | \(-0.610638\pi\) | |||||||
\(152\) | −2.04617 | − | 6.29747i | −0.165966 | − | 0.510792i | ||||
\(153\) | −23.6139 | −1.90907 | ||||||||
\(154\) | −0.442644 | + | 3.28695i | −0.0356693 | + | 0.264870i | ||||
\(155\) | 5.57409 | 0.447721 | ||||||||
\(156\) | 3.22869 | + | 9.93689i | 0.258502 | + | 0.795588i | ||||
\(157\) | 4.86753 | + | 3.53647i | 0.388472 | + | 0.282241i | 0.764829 | − | 0.644233i | \(-0.222823\pi\) |
−0.376357 | + | 0.926475i | \(0.622823\pi\) | |||||||
\(158\) | 3.43009 | − | 2.49211i | 0.272884 | − | 0.198261i | ||||
\(159\) | 8.73463 | − | 26.8824i | 0.692701 | − | 2.13192i | ||||
\(160\) | −0.309017 | + | 0.951057i | −0.0244299 | + | 0.0751876i | ||||
\(161\) | −2.53932 | + | 1.84492i | −0.200127 | + | 0.145400i | ||||
\(162\) | 6.03099 | + | 4.38177i | 0.473839 | + | 0.344264i | ||||
\(163\) | −2.66203 | − | 8.19288i | −0.208506 | − | 0.641716i | −0.999551 | − | 0.0299581i | \(-0.990463\pi\) |
0.791045 | − | 0.611758i | \(-0.209537\pi\) | |||||||
\(164\) | 2.90755 | 0.227042 | ||||||||
\(165\) | −7.59078 | − | 3.64825i | −0.590941 | − | 0.284016i | ||||
\(166\) | 10.2468 | 0.795303 | ||||||||
\(167\) | −2.78607 | − | 8.57463i | −0.215592 | − | 0.663525i | −0.999111 | − | 0.0421565i | \(-0.986577\pi\) |
0.783519 | − | 0.621368i | \(-0.213423\pi\) | |||||||
\(168\) | −2.05435 | − | 1.49258i | −0.158497 | − | 0.115155i | ||||
\(169\) | −3.17933 | + | 2.30992i | −0.244564 | + | 0.177686i | ||||
\(170\) | 2.11624 | − | 6.51311i | 0.162308 | − | 0.499533i | ||||
\(171\) | −7.05551 | + | 21.7146i | −0.539548 | + | 1.66056i | ||||
\(172\) | −2.61700 | + | 1.90136i | −0.199545 | + | 0.144978i | ||||
\(173\) | 10.4677 | + | 7.60521i | 0.795842 | + | 0.578213i | 0.909691 | − | 0.415285i | \(-0.136318\pi\) |
−0.113849 | + | 0.993498i | \(0.536318\pi\) | |||||||
\(174\) | −4.31237 | − | 13.2721i | −0.326920 | − | 1.00616i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 3.26286 | − | 0.594745i | 0.245948 | − | 0.0448306i | ||||
\(177\) | 18.8526 | 1.41705 | ||||||||
\(178\) | −2.02219 | − | 6.22365i | −0.151569 | − | 0.466483i | ||||
\(179\) | −12.7503 | − | 9.26363i | −0.953002 | − | 0.692396i | −0.00148685 | − | 0.999999i | \(-0.500473\pi\) |
−0.951515 | + | 0.307603i | \(0.900473\pi\) | |||||||
\(180\) | 2.78961 | − | 2.02677i | 0.207925 | − | 0.151067i | ||||
\(181\) | −4.51455 | + | 13.8943i | −0.335564 | + | 1.03276i | 0.630880 | + | 0.775880i | \(0.282694\pi\) |
−0.966444 | + | 0.256878i | \(0.917306\pi\) | |||||||
\(182\) | 1.27148 | − | 3.91321i | 0.0942483 | − | 0.290066i | ||||
\(183\) | −4.68734 | + | 3.40555i | −0.346498 | + | 0.251746i | ||||
\(184\) | 2.53932 | + | 1.84492i | 0.187201 | + | 0.136010i | ||||
\(185\) | 2.40577 | + | 7.40419i | 0.176876 | + | 0.544367i | ||||
\(186\) | 14.1544 | 1.03785 | ||||||||
\(187\) | −22.3450 | + | 4.07299i | −1.63403 | + | 0.297846i | ||||
\(188\) | −1.49988 | −0.109390 | ||||||||
\(189\) | 0.351660 | + | 1.08230i | 0.0255795 | + | 0.0787256i | ||||
\(190\) | −5.35695 | − | 3.89205i | −0.388634 | − | 0.282359i | ||||
\(191\) | 14.5352 | − | 10.5604i | 1.05173 | − | 0.764125i | 0.0791880 | − | 0.996860i | \(-0.474767\pi\) |
0.972540 | + | 0.232734i | \(0.0747673\pi\) | |||||||
\(192\) | −0.784693 | + | 2.41504i | −0.0566304 | + | 0.174290i | ||||
\(193\) | 7.36017 | − | 22.6523i | 0.529797 | − | 1.63055i | −0.224833 | − | 0.974397i | \(-0.572184\pi\) |
0.754630 | − | 0.656150i | \(-0.227816\pi\) | |||||||
\(194\) | 0.559046 | − | 0.406171i | 0.0401372 | − | 0.0291614i | ||||
\(195\) | 8.45283 | + | 6.14134i | 0.605320 | + | 0.439790i | ||||
\(196\) | 0.309017 | + | 0.951057i | 0.0220726 | + | 0.0679326i | ||||
\(197\) | −1.85551 | −0.132200 | −0.0660998 | − | 0.997813i | \(-0.521056\pi\) | ||||
−0.0660998 | + | 0.997813i | \(0.521056\pi\) | |||||||
\(198\) | −10.3075 | − | 4.95397i | −0.732525 | − | 0.352063i | ||||
\(199\) | 21.8206 | 1.54682 | 0.773411 | − | 0.633905i | \(-0.218549\pi\) | ||||
0.773411 | + | 0.633905i | \(0.218549\pi\) | |||||||
\(200\) | 0.309017 | + | 0.951057i | 0.0218508 | + | 0.0672499i | ||||
\(201\) | 29.1654 | + | 21.1899i | 2.05717 | + | 1.49462i | ||||
\(202\) | −11.8270 | + | 8.59285i | −0.832148 | + | 0.604591i | ||||
\(203\) | −1.69824 | + | 5.22664i | −0.119193 | + | 0.366838i | ||||
\(204\) | 5.37381 | − | 16.5389i | 0.376242 | − | 1.15795i | ||||
\(205\) | 2.35226 | − | 1.70902i | 0.164289 | − | 0.119363i | ||||
\(206\) | −0.868543 | − | 0.631033i | −0.0605142 | − | 0.0439662i | ||||
\(207\) | −3.34448 | − | 10.2932i | −0.232457 | − | 0.715430i | ||||
\(208\) | −4.11459 | −0.285296 | ||||||||
\(209\) | −2.93099 | + | 21.7647i | −0.202741 | + | 1.50550i | ||||
\(210\) | −2.53932 | −0.175230 | ||||||||
\(211\) | −8.21125 | − | 25.2716i | −0.565286 | − | 1.73977i | −0.667102 | − | 0.744967i | \(-0.732465\pi\) |
0.101816 | − | 0.994803i | \(-0.467535\pi\) | |||||||
\(212\) | 9.00539 | + | 6.54280i | 0.618492 | + | 0.449361i | ||||
\(213\) | 0.125071 | − | 0.0908697i | 0.00856975 | − | 0.00622629i | ||||
\(214\) | −5.83365 | + | 17.9541i | −0.398780 | + | 1.22732i | ||||
\(215\) | −0.999606 | + | 3.07647i | −0.0681726 | + | 0.209814i | ||||
\(216\) | 0.920658 | − | 0.668897i | 0.0626428 | − | 0.0455127i | ||||
\(217\) | −4.50953 | − | 3.27637i | −0.306127 | − | 0.222414i | ||||
\(218\) | 1.30502 | + | 4.01645i | 0.0883874 | + | 0.272029i | ||||
\(219\) | 9.93595 | 0.671409 | ||||||||
\(220\) | 2.29013 | − | 2.39902i | 0.154401 | − | 0.161742i | ||||
\(221\) | 28.1779 | 1.89545 | ||||||||
\(222\) | 6.10901 | + | 18.8016i | 0.410010 | + | 1.26188i | ||||
\(223\) | 8.00306 | + | 5.81457i | 0.535925 | + | 0.389372i | 0.822569 | − | 0.568665i | \(-0.192540\pi\) |
−0.286645 | + | 0.958037i | \(0.592540\pi\) | |||||||
\(224\) | 0.809017 | − | 0.587785i | 0.0540547 | − | 0.0392731i | ||||
\(225\) | 1.06554 | − | 3.27939i | 0.0710358 | − | 0.218626i | ||||
\(226\) | 2.27605 | − | 7.00496i | 0.151401 | − | 0.465963i | ||||
\(227\) | −11.2696 | + | 8.18782i | −0.747987 | + | 0.543445i | −0.895202 | − | 0.445660i | \(-0.852969\pi\) |
0.147215 | + | 0.989105i | \(0.452969\pi\) | |||||||
\(228\) | −13.6030 | − | 9.88317i | −0.900881 | − | 0.654529i | ||||
\(229\) | −3.14980 | − | 9.69409i | −0.208145 | − | 0.640604i | −0.999570 | − | 0.0293371i | \(-0.990660\pi\) |
0.791425 | − | 0.611266i | \(-0.209340\pi\) | |||||||
\(230\) | 3.13877 | 0.206965 | ||||||||
\(231\) | 3.99668 | + | 7.41325i | 0.262962 | + | 0.487756i | ||||
\(232\) | 5.49561 | 0.360805 | ||||||||
\(233\) | −4.08277 | − | 12.5655i | −0.267471 | − | 0.823191i | −0.991114 | − | 0.133016i | \(-0.957534\pi\) |
0.723643 | − | 0.690175i | \(-0.242466\pi\) | |||||||
\(234\) | 11.4781 | + | 8.33934i | 0.750348 | + | 0.545160i | ||||
\(235\) | −1.21343 | + | 0.881607i | −0.0791553 | + | 0.0575097i | ||||
\(236\) | −2.29423 | + | 7.06091i | −0.149342 | + | 0.459626i | ||||
\(237\) | 3.32696 | − | 10.2393i | 0.216110 | − | 0.665117i | ||||
\(238\) | −5.54038 | + | 4.02533i | −0.359130 | + | 0.260923i | ||||
\(239\) | −4.12702 | − | 2.99846i | −0.266955 | − | 0.193954i | 0.446253 | − | 0.894907i | \(-0.352758\pi\) |
−0.713208 | + | 0.700953i | \(0.752758\pi\) | |||||||
\(240\) | 0.784693 | + | 2.41504i | 0.0506517 | + | 0.155890i | ||||
\(241\) | 24.0075 | 1.54646 | 0.773229 | − | 0.634127i | \(-0.218640\pi\) | ||||
0.773229 | + | 0.634127i | \(0.218640\pi\) | |||||||
\(242\) | −10.6081 | − | 2.90990i | −0.681917 | − | 0.187056i | ||||
\(243\) | 22.3439 | 1.43336 | ||||||||
\(244\) | −0.705073 | − | 2.16999i | −0.0451377 | − | 0.138919i | ||||
\(245\) | 0.809017 | + | 0.587785i | 0.0516862 | + | 0.0375522i | ||||
\(246\) | 5.97314 | − | 4.33974i | 0.380834 | − | 0.276692i | ||||
\(247\) | 8.41916 | − | 25.9115i | 0.535699 | − | 1.64871i | ||||
\(248\) | −1.72249 | + | 5.30127i | −0.109378 | + | 0.336631i | ||||
\(249\) | 21.0505 | − | 15.2941i | 1.33402 | − | 0.969222i | ||||
\(250\) | 0.809017 | + | 0.587785i | 0.0511667 | + | 0.0371748i | ||||
\(251\) | 4.78873 | + | 14.7382i | 0.302262 | + | 0.930267i | 0.980685 | + | 0.195595i | \(0.0626638\pi\) |
−0.678423 | + | 0.734672i | \(0.737336\pi\) | |||||||
\(252\) | −3.44815 | −0.217213 | ||||||||
\(253\) | −4.94017 | − | 9.16328i | −0.310586 | − | 0.576090i | ||||
\(254\) | −15.0031 | −0.941380 | ||||||||
\(255\) | −5.37381 | − | 16.5389i | −0.336521 | − | 1.03571i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 3.33705 | − | 2.42451i | 0.208159 | − | 0.151237i | −0.478821 | − | 0.877912i | \(-0.658936\pi\) |
0.686980 | + | 0.726676i | \(0.258936\pi\) | |||||||
\(258\) | −2.53832 | + | 7.81215i | −0.158029 | + | 0.486363i | ||||
\(259\) | 2.40577 | − | 7.40419i | 0.149487 | − | 0.460074i | ||||
\(260\) | −3.32878 | + | 2.41850i | −0.206442 | + | 0.149989i | ||||
\(261\) | −15.3306 | − | 11.1384i | −0.948942 | − | 0.689447i | ||||
\(262\) | −2.09296 | − | 6.44147i | −0.129304 | − | 0.397955i | ||||
\(263\) | 0.308382 | 0.0190156 | 0.00950781 | − | 0.999955i | \(-0.496974\pi\) | ||||
0.00950781 | + | 0.999955i | \(0.496974\pi\) | |||||||
\(264\) | 5.81537 | − | 6.09189i | 0.357912 | − | 0.374930i | ||||
\(265\) | 11.1313 | 0.683788 | ||||||||
\(266\) | 2.04617 | + | 6.29747i | 0.125459 | + | 0.386123i | ||||
\(267\) | −13.4436 | − | 9.76732i | −0.822733 | − | 0.597750i | ||||
\(268\) | −11.4855 | + | 8.34471i | −0.701589 | + | 0.509734i | ||||
\(269\) | −5.29707 | + | 16.3027i | −0.322968 | + | 0.993993i | 0.649382 | + | 0.760463i | \(0.275028\pi\) |
−0.972350 | + | 0.233530i | \(0.924972\pi\) | |||||||
\(270\) | 0.351660 | − | 1.08230i | 0.0214013 | − | 0.0658666i | ||||
\(271\) | −21.5407 | + | 15.6502i | −1.30850 | + | 0.950684i | −1.00000 | 0.000538195i | \(-0.999829\pi\) | |
−0.308505 | + | 0.951223i | \(0.599829\pi\) | |||||||
\(272\) | 5.54038 | + | 4.02533i | 0.335935 | + | 0.244071i | ||||
\(273\) | −3.22869 | − | 9.93689i | −0.195409 | − | 0.601408i | ||||
\(274\) | −9.15100 | −0.552832 | ||||||||
\(275\) | 0.442644 | − | 3.28695i | 0.0266925 | − | 0.198211i | ||||
\(276\) | 7.97035 | 0.479759 | ||||||||
\(277\) | −4.85556 | − | 14.9439i | −0.291742 | − | 0.897891i | −0.984296 | − | 0.176525i | \(-0.943515\pi\) |
0.692554 | − | 0.721366i | \(-0.256485\pi\) | |||||||
\(278\) | −12.8740 | − | 9.35348i | −0.772129 | − | 0.560984i | ||||
\(279\) | 15.5495 | − | 11.2974i | 0.930927 | − | 0.676358i | ||||
\(280\) | 0.309017 | − | 0.951057i | 0.0184673 | − | 0.0568365i | ||||
\(281\) | −5.38747 | + | 16.5809i | −0.321390 | + | 0.989136i | 0.651654 | + | 0.758516i | \(0.274075\pi\) |
−0.973044 | + | 0.230620i | \(0.925925\pi\) | |||||||
\(282\) | −3.08128 | + | 2.23868i | −0.183488 | + | 0.133312i | ||||
\(283\) | −12.1510 | − | 8.82821i | −0.722302 | − | 0.524783i | 0.164817 | − | 0.986324i | \(-0.447297\pi\) |
−0.887119 | + | 0.461541i | \(0.847297\pi\) | |||||||
\(284\) | 0.0188133 | + | 0.0579014i | 0.00111636 | + | 0.00343582i | ||||
\(285\) | −16.8142 | −0.995990 | ||||||||
\(286\) | 12.2997 | + | 5.91145i | 0.727298 | + | 0.349552i | ||||
\(287\) | −2.90755 | −0.171627 | ||||||||
\(288\) | 1.06554 | + | 3.27939i | 0.0627874 | + | 0.193240i | ||||
\(289\) | −24.1889 | − | 17.5743i | −1.42288 | − | 1.03378i | ||||
\(290\) | 4.44605 | − | 3.23024i | 0.261081 | − | 0.189686i | ||||
\(291\) | 0.542238 | − | 1.66884i | 0.0317866 | − | 0.0978290i | ||||
\(292\) | −1.20913 | + | 3.72133i | −0.0707592 | + | 0.217774i | ||||
\(293\) | −6.07302 | + | 4.41231i | −0.354790 | + | 0.257770i | −0.750876 | − | 0.660444i | \(-0.770368\pi\) |
0.396086 | + | 0.918213i | \(0.370368\pi\) | |||||||
\(294\) | 2.05435 | + | 1.49258i | 0.119812 | + | 0.0870488i | ||||
\(295\) | 2.29423 | + | 7.06091i | 0.133575 | + | 0.411102i | ||||
\(296\) | −7.78523 | −0.452507 | ||||||||
\(297\) | −3.71312 | + | 0.676817i | −0.215457 | + | 0.0392729i | ||||
\(298\) | 9.63068 | 0.557891 | ||||||||
\(299\) | 3.99088 | + | 12.2827i | 0.230799 | + | 0.710326i | ||||
\(300\) | 2.05435 | + | 1.49258i | 0.118608 | + | 0.0861739i | ||||
\(301\) | 2.61700 | − | 1.90136i | 0.150842 | − | 0.109593i | ||||
\(302\) | 6.28983 | − | 19.3581i | 0.361939 | − | 1.11393i | ||||
\(303\) | −11.4715 | + | 35.3055i | −0.659018 | + | 2.02825i | ||||
\(304\) | 5.35695 | − | 3.89205i | 0.307242 | − | 0.223224i | ||||
\(305\) | −1.84590 | − | 1.34113i | −0.105696 | − | 0.0767928i | ||||
\(306\) | −7.29711 | − | 22.4582i | −0.417148 | − | 1.28385i | ||||
\(307\) | −5.08116 | −0.289997 | −0.144998 | − | 0.989432i | \(-0.546318\pi\) | ||||
−0.144998 | + | 0.989432i | \(0.546318\pi\) | |||||||
\(308\) | −3.26286 | + | 0.594745i | −0.185919 | + | 0.0338887i | ||||
\(309\) | −2.72616 | −0.155086 | ||||||||
\(310\) | 1.72249 | + | 5.30127i | 0.0978307 | + | 0.301092i | ||||
\(311\) | −8.77265 | − | 6.37370i | −0.497451 | − | 0.361420i | 0.310591 | − | 0.950544i | \(-0.399473\pi\) |
−0.808043 | + | 0.589124i | \(0.799473\pi\) | |||||||
\(312\) | −8.45283 | + | 6.14134i | −0.478547 | + | 0.347685i | ||||
\(313\) | 10.3225 | − | 31.7695i | 0.583463 | − | 1.79572i | −0.0218922 | − | 0.999760i | \(-0.506969\pi\) |
0.605356 | − | 0.795955i | \(-0.293031\pi\) | |||||||
\(314\) | −1.85923 | + | 5.72213i | −0.104923 | + | 0.322918i | ||||
\(315\) | −2.78961 | + | 2.02677i | −0.157177 | + | 0.114196i | ||||
\(316\) | 3.43009 | + | 2.49211i | 0.192958 | + | 0.140192i | ||||
\(317\) | −8.55999 | − | 26.3450i | −0.480777 | − | 1.47968i | −0.838005 | − | 0.545663i | \(-0.816278\pi\) |
0.357228 | − | 0.934017i | \(-0.383722\pi\) | |||||||
\(318\) | 28.2659 | 1.58507 | ||||||||
\(319\) | −16.4280 | − | 7.89557i | −0.919792 | − | 0.442067i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 14.8135 | + | 45.5913i | 0.826809 | + | 2.54466i | ||||
\(322\) | −2.53932 | − | 1.84492i | −0.141511 | − | 0.102814i | ||||
\(323\) | −36.6860 | + | 26.6539i | −2.04126 | + | 1.48306i | ||||
\(324\) | −2.30363 | + | 7.08985i | −0.127980 | + | 0.393881i | ||||
\(325\) | −1.27148 | + | 3.91321i | −0.0705290 | + | 0.217066i | ||||
\(326\) | 6.96928 | − | 5.06348i | 0.385993 | − | 0.280440i | ||||
\(327\) | 8.67584 | + | 6.30337i | 0.479775 | + | 0.348577i | ||||
\(328\) | 0.898483 | + | 2.76525i | 0.0496105 | + | 0.152685i | ||||
\(329\) | 1.49988 | 0.0826911 | ||||||||
\(330\) | 1.12402 | − | 8.34663i | 0.0618751 | − | 0.459467i | ||||
\(331\) | −28.8317 | −1.58473 | −0.792367 | − | 0.610045i | \(-0.791152\pi\) | ||||
−0.792367 | + | 0.610045i | \(0.791152\pi\) | |||||||
\(332\) | 3.16642 | + | 9.74525i | 0.173780 | + | 0.534840i | ||||
\(333\) | 21.7178 | + | 15.7789i | 1.19013 | + | 0.864677i | ||||
\(334\) | 7.29401 | − | 5.29941i | 0.399111 | − | 0.289971i | ||||
\(335\) | −4.38707 | + | 13.5020i | −0.239691 | + | 0.737695i | ||||
\(336\) | 0.784693 | − | 2.41504i | 0.0428085 | − | 0.131751i | ||||
\(337\) | 13.7314 | − | 9.97646i | 0.747998 | − | 0.543453i | −0.147207 | − | 0.989106i | \(-0.547028\pi\) |
0.895206 | + | 0.445653i | \(0.147028\pi\) | |||||||
\(338\) | −3.17933 | − | 2.30992i | −0.172933 | − | 0.125643i | ||||
\(339\) | −5.77962 | − | 17.7878i | −0.313906 | − | 0.966103i | ||||
\(340\) | 6.84829 | 0.371401 | ||||||||
\(341\) | 12.7654 | − | 13.3724i | 0.691284 | − | 0.724154i | ||||
\(342\) | −22.8321 | −1.23462 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | −2.61700 | − | 1.90136i | −0.141099 | − | 0.102515i | ||||
\(345\) | 6.44815 | − | 4.68485i | 0.347157 | − | 0.252224i | ||||
\(346\) | −3.99829 | + | 12.3055i | −0.214950 | + | 0.661547i | ||||
\(347\) | 7.05990 | − | 21.7281i | 0.378995 | − | 1.16643i | −0.561749 | − | 0.827308i | \(-0.689871\pi\) |
0.940744 | − | 0.339119i | \(-0.110129\pi\) | |||||||
\(348\) | 11.2899 | − | 8.20262i | 0.605204 | − | 0.439707i | ||||
\(349\) | 12.2502 | + | 8.90032i | 0.655741 | + | 0.476423i | 0.865222 | − | 0.501389i | \(-0.167178\pi\) |
−0.209481 | + | 0.977813i | \(0.567178\pi\) | |||||||
\(350\) | −0.309017 | − | 0.951057i | −0.0165177 | − | 0.0508361i | ||||
\(351\) | 4.68239 | 0.249927 | ||||||||
\(352\) | 1.57392 | + | 2.91938i | 0.0838900 | + | 0.155604i | ||||
\(353\) | −9.01014 | −0.479561 | −0.239781 | − | 0.970827i | \(-0.577076\pi\) | ||||
−0.239781 | + | 0.970827i | \(0.577076\pi\) | |||||||
\(354\) | 5.82579 | + | 17.9299i | 0.309637 | + | 0.952965i | ||||
\(355\) | 0.0492539 | + | 0.0357850i | 0.00261412 | + | 0.00189927i | ||||
\(356\) | 5.29416 | − | 3.84643i | 0.280590 | − | 0.203860i | ||||
\(357\) | −5.37381 | + | 16.5389i | −0.284412 | + | 0.875330i | ||||
\(358\) | 4.87018 | − | 14.9889i | 0.257397 | − | 0.792186i | ||||
\(359\) | −29.8470 | + | 21.6851i | −1.57526 | + | 1.14450i | −0.653377 | + | 0.757033i | \(0.726648\pi\) |
−0.921886 | + | 0.387462i | \(0.873352\pi\) | |||||||
\(360\) | 2.78961 | + | 2.02677i | 0.147025 | + | 0.106820i | ||||
\(361\) | 7.67751 | + | 23.6290i | 0.404080 | + | 1.24363i | ||||
\(362\) | −14.6094 | −0.767852 | ||||||||
\(363\) | −26.1361 | + | 9.85546i | −1.37179 | + | 0.517278i | ||||
\(364\) | 4.11459 | 0.215663 | ||||||||
\(365\) | 1.20913 | + | 3.72133i | 0.0632889 | + | 0.194783i | ||||
\(366\) | −4.68734 | − | 3.40555i | −0.245011 | − | 0.178011i | ||||
\(367\) | −27.9176 | + | 20.2834i | −1.45729 | + | 1.05878i | −0.473230 | + | 0.880939i | \(0.656912\pi\) |
−0.984059 | + | 0.177844i | \(0.943088\pi\) | |||||||
\(368\) | −0.969934 | + | 2.98515i | −0.0505613 | + | 0.155612i | ||||
\(369\) | 3.09811 | − | 9.53499i | 0.161281 | − | 0.496372i | ||||
\(370\) | −6.29838 | + | 4.57604i | −0.327437 | + | 0.237897i | ||||
\(371\) | −9.00539 | − | 6.54280i | −0.467536 | − | 0.339685i | ||||
\(372\) | 4.37395 | + | 13.4616i | 0.226779 | + | 0.697953i | ||||
\(373\) | 2.31601 | 0.119918 | 0.0599592 | − | 0.998201i | \(-0.480903\pi\) | ||||
0.0599592 | + | 0.998201i | \(0.480903\pi\) | |||||||
\(374\) | −10.7786 | − | 19.9928i | −0.557350 | − | 1.03380i | ||||
\(375\) | 2.53932 | 0.131130 | ||||||||
\(376\) | −0.463488 | − | 1.42647i | −0.0239026 | − | 0.0735646i | ||||
\(377\) | 18.2937 | + | 13.2911i | 0.942172 | + | 0.684528i | ||||
\(378\) | −0.920658 | + | 0.668897i | −0.0473535 | + | 0.0344043i | ||||
\(379\) | −2.44863 | + | 7.53611i | −0.125778 | + | 0.387104i | −0.994042 | − | 0.108998i | \(-0.965236\pi\) |
0.868264 | + | 0.496102i | \(0.165236\pi\) | |||||||
\(380\) | 2.04617 | − | 6.29747i | 0.104966 | − | 0.323053i | ||||
\(381\) | −30.8217 | + | 22.3933i | −1.57904 | + | 1.14724i | ||||
\(382\) | 14.5352 | + | 10.5604i | 0.743684 | + | 0.540318i | ||||
\(383\) | 5.93452 | + | 18.2646i | 0.303240 | + | 0.933275i | 0.980328 | + | 0.197374i | \(0.0632413\pi\) |
−0.677089 | + | 0.735901i | \(0.736759\pi\) | |||||||
\(384\) | −2.53932 | −0.129584 | ||||||||
\(385\) | −2.29013 | + | 2.39902i | −0.116716 | + | 0.122265i | ||||
\(386\) | 23.8180 | 1.21231 | ||||||||
\(387\) | 3.44679 | + | 10.6081i | 0.175210 | + | 0.539242i | ||||
\(388\) | 0.559046 | + | 0.406171i | 0.0283813 | + | 0.0206202i | ||||
\(389\) | 6.19652 | − | 4.50204i | 0.314176 | − | 0.228262i | −0.419510 | − | 0.907751i | \(-0.637798\pi\) |
0.733686 | + | 0.679488i | \(0.237798\pi\) | |||||||
\(390\) | −3.22869 | + | 9.93689i | −0.163491 | + | 0.503174i | ||||
\(391\) | 6.64239 | − | 20.4432i | 0.335920 | − | 1.03386i | ||||
\(392\) | −0.809017 | + | 0.587785i | −0.0408615 | + | 0.0296876i | ||||
\(393\) | −13.9141 | − | 10.1092i | −0.701872 | − | 0.509940i | ||||
\(394\) | −0.573384 | − | 1.76470i | −0.0288867 | − | 0.0889041i | ||||
\(395\) | 4.23983 | 0.213329 | ||||||||
\(396\) | 1.52630 | − | 11.3339i | 0.0766997 | − | 0.569550i | ||||
\(397\) | −20.0239 | −1.00497 | −0.502486 | − | 0.864585i | \(-0.667581\pi\) | ||||
−0.502486 | + | 0.864585i | \(0.667581\pi\) | |||||||
\(398\) | 6.74294 | + | 20.7526i | 0.337993 | + | 1.04024i | ||||
\(399\) | 13.6030 | + | 9.88317i | 0.681002 | + | 0.494777i | ||||
\(400\) | −0.809017 | + | 0.587785i | −0.0404508 | + | 0.0293893i | ||||
\(401\) | 6.41401 | − | 19.7403i | 0.320301 | − | 0.985784i | −0.653217 | − | 0.757171i | \(-0.726581\pi\) |
0.973517 | − | 0.228613i | \(-0.0734190\pi\) | |||||||
\(402\) | −11.1402 | + | 34.2860i | −0.555622 | + | 1.71003i | ||||
\(403\) | −18.5549 | + | 13.4809i | −0.924285 | + | 0.671532i | ||||
\(404\) | −11.8270 | − | 8.59285i | −0.588417 | − | 0.427510i | ||||
\(405\) | 2.30363 | + | 7.08985i | 0.114468 | + | 0.352298i | ||||
\(406\) | −5.49561 | −0.272743 | ||||||||
\(407\) | 23.2723 | + | 11.1851i | 1.15357 | + | 0.554423i | ||||
\(408\) | 17.3900 | 0.860934 | ||||||||
\(409\) | 10.1528 | + | 31.2472i | 0.502026 | + | 1.54508i | 0.805714 | + | 0.592305i | \(0.201782\pi\) |
−0.303688 | + | 0.952772i | \(0.598218\pi\) | |||||||
\(410\) | 2.35226 | + | 1.70902i | 0.116170 | + | 0.0844023i | ||||
\(411\) | −18.7994 | + | 13.6586i | −0.927305 | + | 0.673727i | ||||
\(412\) | 0.331754 | − | 1.02103i | 0.0163443 | − | 0.0503027i | ||||
\(413\) | 2.29423 | − | 7.06091i | 0.112892 | − | 0.347445i | ||||
\(414\) | 8.75596 | − | 6.36158i | 0.430332 | − | 0.312654i | ||||
\(415\) | 8.28981 | + | 6.02290i | 0.406931 | + | 0.295652i | ||||
\(416\) | −1.27148 | − | 3.91321i | −0.0623394 | − | 0.191861i | ||||
\(417\) | −40.4084 | −1.97881 | ||||||||
\(418\) | −21.6052 | + | 3.93813i | −1.05675 | + | 0.192620i | ||||
\(419\) | −16.3625 | −0.799361 | −0.399680 | − | 0.916655i | \(-0.630879\pi\) | ||||
−0.399680 | + | 0.916655i | \(0.630879\pi\) | |||||||
\(420\) | −0.784693 | − | 2.41504i | −0.0382891 | − | 0.117842i | ||||
\(421\) | −21.0726 | − | 15.3102i | −1.02702 | − | 0.746171i | −0.0593072 | − | 0.998240i | \(-0.518889\pi\) |
−0.967709 | + | 0.252069i | \(0.918889\pi\) | |||||||
\(422\) | 21.4973 | − | 15.6187i | 1.04647 | − | 0.760307i | ||||
\(423\) | −1.59818 | + | 4.91868i | −0.0777060 | + | 0.239155i | ||||
\(424\) | −3.43975 | + | 10.5865i | −0.167049 | + | 0.514124i | ||||
\(425\) | 5.54038 | − | 4.02533i | 0.268748 | − | 0.195257i | ||||
\(426\) | 0.125071 | + | 0.0908697i | 0.00605973 | + | 0.00440265i | ||||
\(427\) | 0.705073 | + | 2.16999i | 0.0341209 | + | 0.105013i | ||||
\(428\) | −18.8781 | −0.912507 | ||||||||
\(429\) | 34.0913 | − | 6.21405i | 1.64594 | − | 0.300017i | ||||
\(430\) | −3.23479 | −0.155996 | ||||||||
\(431\) | 5.64188 | + | 17.3639i | 0.271760 | + | 0.836390i | 0.990059 | + | 0.140656i | \(0.0449211\pi\) |
−0.718299 | + | 0.695735i | \(0.755079\pi\) | |||||||
\(432\) | 0.920658 | + | 0.668897i | 0.0442952 | + | 0.0321823i | ||||
\(433\) | −26.3818 | + | 19.1675i | −1.26783 | + | 0.921130i | −0.999114 | − | 0.0420905i | \(-0.986598\pi\) |
−0.268713 | + | 0.963220i | \(0.586598\pi\) | |||||||
\(434\) | 1.72249 | − | 5.30127i | 0.0826821 | − | 0.254469i | ||||
\(435\) | 4.31237 | − | 13.2721i | 0.206762 | − | 0.636349i | ||||
\(436\) | −3.41660 | + | 2.48230i | −0.163625 | + | 0.118881i | ||||
\(437\) | −16.8142 | − | 12.2163i | −0.804334 | − | 0.584383i | ||||
\(438\) | 3.07038 | + | 9.44965i | 0.146708 | + | 0.451522i | ||||
\(439\) | −29.2540 | −1.39622 | −0.698108 | − | 0.715993i | \(-0.745974\pi\) | ||||
−0.698108 | + | 0.715993i | \(0.745974\pi\) | |||||||
\(440\) | 2.98929 | + | 1.43670i | 0.142509 | + | 0.0684922i | ||||
\(441\) | 3.44815 | 0.164198 | ||||||||
\(442\) | 8.70746 | + | 26.7988i | 0.414172 | + | 1.27469i | ||||
\(443\) | −9.23016 | − | 6.70611i | −0.438538 | − | 0.318617i | 0.346516 | − | 0.938044i | \(-0.387365\pi\) |
−0.785054 | + | 0.619427i | \(0.787365\pi\) | |||||||
\(444\) | −15.9936 | + | 11.6200i | −0.759023 | + | 0.551462i | ||||
\(445\) | 2.02219 | − | 6.22365i | 0.0958609 | − | 0.295029i | ||||
\(446\) | −3.05690 | + | 9.40817i | −0.144748 | + | 0.445490i | ||||
\(447\) | 19.7848 | − | 14.3745i | 0.935790 | − | 0.679891i | ||||
\(448\) | 0.809017 | + | 0.587785i | 0.0382225 | + | 0.0277702i | ||||
\(449\) | 4.21238 | + | 12.9644i | 0.198794 | + | 0.611826i | 0.999911 | + | 0.0133185i | \(0.00423952\pi\) |
−0.801117 | + | 0.598508i | \(0.795760\pi\) | |||||||
\(450\) | 3.44815 | 0.162547 | ||||||||
\(451\) | 1.28701 | − | 9.55699i | 0.0606031 | − | 0.450021i | ||||
\(452\) | 7.36545 | 0.346442 | ||||||||
\(453\) | −15.9719 | − | 49.1564i | −0.750425 | − | 2.30957i | ||||
\(454\) | −11.2696 | − | 8.18782i | −0.528907 | − | 0.384273i | ||||
\(455\) | 3.32878 | − | 2.41850i | 0.156055 | − | 0.113381i | ||||
\(456\) | 5.19589 | − | 15.9913i | 0.243320 | − | 0.748861i | ||||
\(457\) | −2.05915 | + | 6.33743i | −0.0963232 | + | 0.296452i | −0.987596 | − | 0.157015i | \(-0.949813\pi\) |
0.891273 | + | 0.453467i | \(0.149813\pi\) | |||||||
\(458\) | 8.24629 | − | 5.99128i | 0.385324 | − | 0.279954i | ||||
\(459\) | −6.30493 | − | 4.58080i | −0.294289 | − | 0.213814i | ||||
\(460\) | 0.969934 | + | 2.98515i | 0.0452234 | + | 0.139183i | ||||
\(461\) | 18.1977 | 0.847553 | 0.423776 | − | 0.905767i | \(-0.360704\pi\) | ||||
0.423776 | + | 0.905767i | \(0.360704\pi\) | |||||||
\(462\) | −5.81537 | + | 6.09189i | −0.270556 | + | 0.283420i | ||||
\(463\) | 11.3971 | 0.529666 | 0.264833 | − | 0.964294i | \(-0.414683\pi\) | ||||
0.264833 | + | 0.964294i | \(0.414683\pi\) | |||||||
\(464\) | 1.69824 | + | 5.22664i | 0.0788387 | + | 0.242641i | ||||
\(465\) | 11.4511 | + | 8.31975i | 0.531034 | + | 0.385819i | ||||
\(466\) | 10.6888 | − | 7.76588i | 0.495150 | − | 0.359748i | ||||
\(467\) | 7.10101 | − | 21.8547i | 0.328595 | − | 1.01131i | −0.641196 | − | 0.767377i | \(-0.721561\pi\) |
0.969791 | − | 0.243936i | \(-0.0784386\pi\) | |||||||
\(468\) | −4.38425 | + | 13.4933i | −0.202662 | + | 0.623730i | ||||
\(469\) | 11.4855 | − | 8.34471i | 0.530352 | − | 0.385323i | ||||
\(470\) | −1.21343 | − | 0.881607i | −0.0559713 | − | 0.0406655i | ||||
\(471\) | 4.72119 | + | 14.5303i | 0.217541 | + | 0.669522i | ||||
\(472\) | −7.42428 | −0.341730 | ||||||||
\(473\) | 5.09129 | + | 9.44359i | 0.234098 | + | 0.434217i | ||||
\(474\) | 10.7663 | 0.494512 | ||||||||
\(475\) | −2.04617 | − | 6.29747i | −0.0938848 | − | 0.288948i | ||||
\(476\) | −5.54038 | − | 4.02533i | −0.253943 | − | 0.184500i | ||||
\(477\) | 31.0519 | − | 22.5605i | 1.42177 | − | 1.03298i | ||||
\(478\) | 1.57638 | − | 4.85161i | 0.0721021 | − | 0.221907i | ||||
\(479\) | 0.422409 | − | 1.30004i | 0.0193004 | − | 0.0594004i | −0.940942 | − | 0.338566i | \(-0.890058\pi\) |
0.960243 | + | 0.279166i | \(0.0900580\pi\) | |||||||
\(480\) | −2.05435 | + | 1.49258i | −0.0937680 | + | 0.0681264i | ||||
\(481\) | −25.9153 | − | 18.8285i | −1.18163 | − | 0.858508i | ||||
\(482\) | 7.41872 | + | 22.8325i | 0.337913 | + | 1.03999i | ||||
\(483\) | −7.97035 | −0.362664 | ||||||||
\(484\) | −0.510610 | − | 10.9881i | −0.0232095 | − | 0.499461i | ||||
\(485\) | 0.691019 | 0.0313776 | ||||||||
\(486\) | 6.90464 | + | 21.2503i | 0.313201 | + | 0.963933i | ||||
\(487\) | 9.87790 | + | 7.17671i | 0.447610 | + | 0.325208i | 0.788651 | − | 0.614840i | \(-0.210780\pi\) |
−0.341041 | + | 0.940048i | \(0.610780\pi\) | |||||||
\(488\) | 1.84590 | − | 1.34113i | 0.0835602 | − | 0.0607100i | ||||
\(489\) | 6.75975 | − | 20.8044i | 0.305686 | − | 0.940806i | ||||
\(490\) | −0.309017 | + | 0.951057i | −0.0139600 | + | 0.0429644i | ||||
\(491\) | −32.2431 | + | 23.4260i | −1.45511 | + | 1.05720i | −0.470506 | + | 0.882397i | \(0.655928\pi\) |
−0.984604 | + | 0.174802i | \(0.944072\pi\) | |||||||
\(492\) | 5.97314 | + | 4.33974i | 0.269290 | + | 0.195651i | ||||
\(493\) | −11.6300 | − | 35.7936i | −0.523790 | − | 1.61206i | ||||
\(494\) | 27.2450 | 1.22581 | ||||||||
\(495\) | −5.42710 | − | 10.0665i | −0.243930 | − | 0.452454i | ||||
\(496\) | −5.57409 | −0.250284 | ||||||||
\(497\) | −0.0188133 | − | 0.0579014i | −0.000843892 | − | 0.00259723i | ||||
\(498\) | 21.0505 | + | 15.2941i | 0.943294 | + | 0.685343i | ||||
\(499\) | −29.7318 | + | 21.6014i | −1.33098 | + | 0.967011i | −0.331252 | + | 0.943542i | \(0.607471\pi\) |
−0.999725 | + | 0.0234691i | \(0.992529\pi\) | |||||||
\(500\) | −0.309017 | + | 0.951057i | −0.0138197 | + | 0.0425325i | ||||
\(501\) | 7.07471 | − | 21.7737i | 0.316075 | − | 0.972778i | ||||
\(502\) | −12.5371 | + | 9.10870i | −0.559556 | + | 0.406541i | ||||
\(503\) | −9.69056 | − | 7.04060i | −0.432081 | − | 0.313925i | 0.350400 | − | 0.936600i | \(-0.386046\pi\) |
−0.782480 | + | 0.622675i | \(0.786046\pi\) | |||||||
\(504\) | −1.06554 | − | 3.27939i | −0.0474628 | − | 0.146075i | ||||
\(505\) | −14.6190 | −0.650538 | ||||||||
\(506\) | 7.18820 | − | 7.52998i | 0.319554 | − | 0.334749i | ||||
\(507\) | −9.97920 | −0.443192 | ||||||||
\(508\) | −4.63622 | − | 14.2688i | −0.205699 | − | 0.633077i | ||||
\(509\) | 19.1420 | + | 13.9075i | 0.848455 | + | 0.616438i | 0.924720 | − | 0.380649i | \(-0.124299\pi\) |
−0.0762649 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(510\) | 14.0688 | − | 10.2216i | 0.622978 | − | 0.452620i | ||||
\(511\) | 1.20913 | − | 3.72133i | 0.0534889 | − | 0.164622i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | −6.09618 | + | 4.42914i | −0.269153 | + | 0.195551i | ||||
\(514\) | 3.33705 | + | 2.42451i | 0.147191 | + | 0.106940i | ||||
\(515\) | −0.331754 | − | 1.02103i | −0.0146188 | − | 0.0449921i | ||||
\(516\) | −8.21418 | −0.361609 | ||||||||
\(517\) | −0.663914 | + | 4.93004i | −0.0291989 | + | 0.216823i | ||||
\(518\) | 7.78523 | 0.342063 | ||||||||
\(519\) | 10.1530 | + | 31.2476i | 0.445665 | + | 1.37162i | ||||
\(520\) | −3.32878 | − | 2.41850i | −0.145976 | − | 0.106058i | ||||
\(521\) | 7.60910 | − | 5.52834i | 0.333361 | − | 0.242201i | −0.408494 | − | 0.912761i | \(-0.633946\pi\) |
0.741855 | + | 0.670560i | \(0.233946\pi\) | |||||||
\(522\) | 5.85578 | − | 18.0222i | 0.256301 | − | 0.788812i | ||||
\(523\) | −8.80500 | + | 27.0990i | −0.385016 | + | 1.18496i | 0.551453 | + | 0.834206i | \(0.314074\pi\) |
−0.936469 | + | 0.350751i | \(0.885926\pi\) | |||||||
\(524\) | 5.47944 | − | 3.98105i | 0.239371 | − | 0.173913i | ||||
\(525\) | −2.05435 | − | 1.49258i | −0.0896593 | − | 0.0651413i | ||||
\(526\) | 0.0952951 | + | 0.293288i | 0.00415507 | + | 0.0127880i | ||||
\(527\) | 38.1730 | 1.66284 | ||||||||
\(528\) | 7.59078 | + | 3.64825i | 0.330346 | + | 0.158770i | ||||
\(529\) | −13.1481 | −0.571657 | ||||||||
\(530\) | 3.43975 | + | 10.5865i | 0.149413 | + | 0.459847i | ||||
\(531\) | 20.7109 | + | 15.0473i | 0.898775 | + | 0.652998i | ||||
\(532\) | −5.35695 | + | 3.89205i | −0.232253 | + | 0.168742i | ||||
\(533\) | −3.69689 | + | 11.3779i | −0.160130 | + | 0.492830i | ||||
\(534\) | 5.13498 | − | 15.8039i | 0.222212 | − | 0.683900i | ||||
\(535\) | −15.2727 | + | 11.0963i | −0.660296 | + | 0.479733i | ||||
\(536\) | −11.4855 | − | 8.34471i | −0.496098 | − | 0.360437i | ||||
\(537\) | −12.3669 | − | 38.0615i | −0.533673 | − | 1.64248i | ||||
\(538\) | −17.1417 | −0.739030 | ||||||||
\(539\) | 3.26286 | − | 0.594745i | 0.140541 | − | 0.0256175i | ||||
\(540\) | 1.13800 | 0.0489715 | ||||||||
\(541\) | −0.740741 | − | 2.27977i | −0.0318469 | − | 0.0980148i | 0.933870 | − | 0.357614i | \(-0.116410\pi\) |
−0.965716 | + | 0.259599i | \(0.916410\pi\) | |||||||
\(542\) | −21.5407 | − | 15.6502i | −0.925253 | − | 0.672235i | ||||
\(543\) | −30.0128 | + | 21.8056i | −1.28797 | + | 0.935768i | ||||
\(544\) | −2.11624 | + | 6.51311i | −0.0907330 | + | 0.279247i | ||||
\(545\) | −1.30502 | + | 4.01645i | −0.0559011 | + | 0.172046i | ||||
\(546\) | 8.45283 | − | 6.14134i | 0.361748 | − | 0.262825i | ||||
\(547\) | −10.5441 | − | 7.66073i | −0.450832 | − | 0.327549i | 0.339092 | − | 0.940753i | \(-0.389880\pi\) |
−0.789924 | + | 0.613204i | \(0.789880\pi\) | |||||||
\(548\) | −2.82781 | − | 8.70311i | −0.120798 | − | 0.371779i | ||||
\(549\) | −7.86752 | −0.335777 | ||||||||
\(550\) | 3.26286 | − | 0.594745i | 0.139129 | − | 0.0253600i | ||||
\(551\) | −36.3895 | −1.55024 | ||||||||
\(552\) | 2.46297 | + | 7.58025i | 0.104831 | + | 0.322637i | ||||
\(553\) | −3.43009 | − | 2.49211i | −0.145862 | − | 0.105975i | ||||
\(554\) | 12.7120 | − | 9.23583i | 0.540082 | − | 0.392393i | ||||
\(555\) | −6.10901 | + | 18.8016i | −0.259313 | + | 0.798084i | ||||
\(556\) | 4.91741 | − | 15.1342i | 0.208545 | − | 0.641835i | ||||
\(557\) | −16.2894 | + | 11.8349i | −0.690203 | + | 0.501462i | −0.876727 | − | 0.480988i | \(-0.840278\pi\) |
0.186524 | + | 0.982450i | \(0.440278\pi\) | |||||||
\(558\) | 15.5495 | + | 11.2974i | 0.658264 | + | 0.478257i | ||||
\(559\) | −4.11297 | − | 12.6584i | −0.173960 | − | 0.535394i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −51.9839 | − | 24.9843i | −2.19476 | − | 1.05484i | ||||
\(562\) | −17.4342 | −0.735419 | ||||||||
\(563\) | 3.36541 | + | 10.3577i | 0.141835 | + | 0.436524i | 0.996590 | − | 0.0825073i | \(-0.0262928\pi\) |
−0.854755 | + | 0.519031i | \(0.826293\pi\) | |||||||
\(564\) | −3.08128 | − | 2.23868i | −0.129745 | − | 0.0942656i | ||||
\(565\) | 5.95877 | − | 4.32930i | 0.250688 | − | 0.182135i | ||||
\(566\) | 4.64127 | − | 14.2843i | 0.195087 | − | 0.600416i | ||||
\(567\) | 2.30363 | − | 7.08985i | 0.0967435 | − | 0.297746i | ||||
\(568\) | −0.0492539 | + | 0.0357850i | −0.00206665 | + | 0.00150151i | ||||
\(569\) | 18.2179 | + | 13.2361i | 0.763734 | + | 0.554885i | 0.900053 | − | 0.435780i | \(-0.143527\pi\) |
−0.136319 | + | 0.990665i | \(0.543527\pi\) | |||||||
\(570\) | −5.19589 | − | 15.9913i | −0.217632 | − | 0.669802i | ||||
\(571\) | 14.1198 | 0.590893 | 0.295447 | − | 0.955359i | \(-0.404532\pi\) | ||||
0.295447 | + | 0.955359i | \(0.404532\pi\) | |||||||
\(572\) | −1.82130 | + | 13.5245i | −0.0761524 | + | 0.565487i | ||||
\(573\) | 45.6226 | 1.90591 | ||||||||
\(574\) | −0.898483 | − | 2.76525i | −0.0375020 | − | 0.115419i | ||||
\(575\) | 2.53932 | + | 1.84492i | 0.105897 | + | 0.0769387i | ||||
\(576\) | −2.78961 | + | 2.02677i | −0.116234 | + | 0.0844488i | ||||
\(577\) | −3.89212 | + | 11.9787i | −0.162031 | + | 0.498681i | −0.998805 | − | 0.0488675i | \(-0.984439\pi\) |
0.836774 | + | 0.547548i | \(0.184439\pi\) | |||||||
\(578\) | 9.23933 | − | 28.4357i | 0.384306 | − | 1.18277i | ||||
\(579\) | 48.9306 | − | 35.5502i | 2.03349 | − | 1.47742i | ||||
\(580\) | 4.44605 | + | 3.23024i | 0.184612 | + | 0.134128i | ||||
\(581\) | −3.16642 | − | 9.74525i | −0.131365 | − | 0.404301i | ||||
\(582\) | 1.75472 | 0.0727355 | ||||||||
\(583\) | 25.4921 | − | 26.7042i | 1.05577 | − | 1.10597i | ||||
\(584\) | −3.91284 | −0.161914 | ||||||||
\(585\) | 4.38425 | + | 13.4933i | 0.181266 | + | 0.557881i | ||||
\(586\) | −6.07302 | − | 4.41231i | −0.250874 | − | 0.182271i | ||||
\(587\) | 12.4603 | − | 9.05296i | 0.514293 | − | 0.373656i | −0.300157 | − | 0.953890i | \(-0.597039\pi\) |
0.814450 | + | 0.580234i | \(0.197039\pi\) | |||||||
\(588\) | −0.784693 | + | 2.41504i | −0.0323602 | + | 0.0995945i | ||||
\(589\) | 11.4055 | − | 35.1027i | 0.469957 | − | 1.44638i | ||||
\(590\) | −6.00637 | + | 4.36389i | −0.247278 | + | 0.179658i | ||||
\(591\) | −3.81187 | − | 2.76949i | −0.156800 | − | 0.113922i | ||||
\(592\) | −2.40577 | − | 7.40419i | −0.0988764 | − | 0.304310i | ||||
\(593\) | 27.0005 | 1.10878 | 0.554389 | − | 0.832258i | \(-0.312952\pi\) | ||||
0.554389 | + | 0.832258i | \(0.312952\pi\) | |||||||
\(594\) | −1.79111 | − | 3.32224i | −0.0734901 | − | 0.136313i | ||||
\(595\) | −6.84829 | −0.280753 | ||||||||
\(596\) | 2.97604 | + | 9.15932i | 0.121904 | + | 0.375181i | ||||
\(597\) | 44.8273 | + | 32.5689i | 1.83466 | + | 1.33296i | ||||
\(598\) | −10.4483 | + | 7.59111i | −0.427262 | + | 0.310424i | ||||
\(599\) | 11.9064 | − | 36.6441i | 0.486482 | − | 1.49724i | −0.343340 | − | 0.939211i | \(-0.611558\pi\) |
0.829822 | − | 0.558028i | \(-0.188442\pi\) | |||||||
\(600\) | −0.784693 | + | 2.41504i | −0.0320350 | + | 0.0985935i | ||||
\(601\) | −12.8792 | + | 9.35726i | −0.525352 | + | 0.381691i | −0.818616 | − | 0.574341i | \(-0.805258\pi\) |
0.293264 | + | 0.956031i | \(0.405258\pi\) | |||||||
\(602\) | 2.61700 | + | 1.90136i | 0.106661 | + | 0.0774938i | ||||
\(603\) | 15.1273 | + | 46.5570i | 0.616031 | + | 1.89595i | ||||
\(604\) | 20.3543 | 0.828205 | ||||||||
\(605\) | −6.87176 | − | 8.58947i | −0.279377 | − | 0.349211i | ||||
\(606\) | −37.1224 | −1.50799 | ||||||||
\(607\) | 6.26206 | + | 19.2726i | 0.254169 | + | 0.782252i | 0.993992 | + | 0.109451i | \(0.0349092\pi\) |
−0.739823 | + | 0.672801i | \(0.765091\pi\) | |||||||
\(608\) | 5.35695 | + | 3.89205i | 0.217253 | + | 0.157844i | ||||
\(609\) | −11.2899 | + | 8.20262i | −0.457491 | + | 0.332387i | ||||
\(610\) | 0.705073 | − | 2.16999i | 0.0285476 | − | 0.0878604i | ||||
\(611\) | 1.90707 | − | 5.86934i | 0.0771516 | − | 0.237448i | ||||
\(612\) | 19.1041 | − | 13.8799i | 0.772236 | − | 0.561063i | ||||
\(613\) | 22.7035 | + | 16.4950i | 0.916985 | + | 0.666229i | 0.942772 | − | 0.333439i | \(-0.108209\pi\) |
−0.0257866 | + | 0.999667i | \(0.508209\pi\) | |||||||
\(614\) | −1.57016 | − | 4.83247i | −0.0633667 | − | 0.195023i | ||||
\(615\) | 7.38321 | 0.297720 | ||||||||
\(616\) | −1.57392 | − | 2.91938i | −0.0634149 | − | 0.117625i | ||||
\(617\) | 38.0285 | 1.53097 | 0.765484 | − | 0.643455i | \(-0.222500\pi\) | ||||
0.765484 | + | 0.643455i | \(0.222500\pi\) | |||||||
\(618\) | −0.842429 | − | 2.59273i | −0.0338875 | − | 0.104295i | ||||
\(619\) | 28.1504 | + | 20.4525i | 1.13146 | + | 0.822054i | 0.985907 | − | 0.167297i | \(-0.0535037\pi\) |
0.145553 | + | 0.989350i | \(0.453504\pi\) | |||||||
\(620\) | −4.50953 | + | 3.27637i | −0.181107 | + | 0.131582i | ||||
\(621\) | 1.10378 | − | 3.39709i | 0.0442932 | − | 0.136320i | ||||
\(622\) | 3.35085 | − | 10.3129i | 0.134357 | − | 0.413508i | ||||
\(623\) | −5.29416 | + | 3.84643i | −0.212106 | + | 0.154104i | ||||
\(624\) | −8.45283 | − | 6.14134i | −0.338384 | − | 0.245850i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 33.4044 | 1.33511 | ||||||||
\(627\) | −38.5068 | + | 40.3377i | −1.53781 | + | 1.61093i | ||||
\(628\) | −6.01660 | −0.240089 | ||||||||
\(629\) | 16.4754 | + | 50.7061i | 0.656917 | + | 2.02178i | ||||
\(630\) | −2.78961 | − | 2.02677i | −0.111141 | − | 0.0807485i | ||||
\(631\) | 24.0948 | − | 17.5059i | 0.959199 | − | 0.696899i | 0.00623454 | − | 0.999981i | \(-0.498015\pi\) |
0.952965 | + | 0.303082i | \(0.0980155\pi\) | |||||||
\(632\) | −1.31018 | + | 4.03232i | −0.0521161 | + | 0.160397i | ||||
\(633\) | 20.8510 | − | 64.1727i | 0.828752 | − | 2.55064i | ||||
\(634\) | 22.4104 | − | 16.2821i | 0.890029 | − | 0.646644i | ||||
\(635\) | −12.1378 | − | 8.81862i | −0.481673 | − | 0.349956i | ||||
\(636\) | 8.73463 | + | 26.8824i | 0.346351 | + | 1.06596i | ||||
\(637\) | −4.11459 | −0.163026 | ||||||||
\(638\) | 2.43260 | − | 18.0638i | 0.0963077 | − | 0.715154i | ||||
\(639\) | 0.209927 | 0.00830460 | ||||||||
\(640\) | −0.309017 | − | 0.951057i | −0.0122150 | − | 0.0375938i | ||||
\(641\) | −0.469101 | − | 0.340822i | −0.0185284 | − | 0.0134617i | 0.578483 | − | 0.815695i | \(-0.303645\pi\) |
−0.597011 | + | 0.802233i | \(0.703645\pi\) | |||||||
\(642\) | −38.7823 | + | 28.1770i | −1.53061 | + | 1.11206i | ||||
\(643\) | 14.6711 | − | 45.1529i | 0.578571 | − | 1.78066i | −0.0451146 | − | 0.998982i | \(-0.514365\pi\) |
0.623685 | − | 0.781676i | \(-0.285635\pi\) | |||||||
\(644\) | 0.969934 | − | 2.98515i | 0.0382208 | − | 0.117631i | ||||
\(645\) | −6.64541 | + | 4.82817i | −0.261663 | + | 0.190109i | ||||
\(646\) | −36.6860 | − | 26.6539i | −1.44339 | − | 1.04868i | ||||
\(647\) | −12.8364 | − | 39.5064i | −0.504651 | − | 1.55316i | −0.801356 | − | 0.598188i | \(-0.795888\pi\) |
0.296704 | − | 0.954969i | \(-0.404112\pi\) | |||||||
\(648\) | −7.45471 | −0.292849 | ||||||||
\(649\) | 22.1934 | + | 10.6665i | 0.871166 | + | 0.418697i | ||||
\(650\) | −4.11459 | −0.161388 | ||||||||
\(651\) | −4.37395 | − | 13.4616i | −0.171429 | − | 0.527603i | ||||
\(652\) | 6.96928 | + | 5.06348i | 0.272938 | + | 0.198301i | ||||
\(653\) | 21.4334 | − | 15.5723i | 0.838753 | − | 0.609390i | −0.0832688 | − | 0.996527i | \(-0.526536\pi\) |
0.922022 | + | 0.387137i | \(0.126536\pi\) | |||||||
\(654\) | −3.31388 | + | 10.1991i | −0.129583 | + | 0.398815i | ||||
\(655\) | 2.09296 | − | 6.44147i | 0.0817788 | − | 0.251689i | ||||
\(656\) | −2.35226 | + | 1.70902i | −0.0918403 | + | 0.0667259i | ||||
\(657\) | 10.9153 | + | 7.93043i | 0.425846 | + | 0.309395i | ||||
\(658\) | 0.463488 | + | 1.42647i | 0.0180687 | + | 0.0556096i | ||||
\(659\) | −46.8092 | −1.82343 | −0.911713 | − | 0.410827i | \(-0.865240\pi\) | ||||
−0.911713 | + | 0.410827i | \(0.865240\pi\) | |||||||
\(660\) | 8.28546 | − | 1.51025i | 0.322511 | − | 0.0587863i | ||||
\(661\) | −35.7060 | −1.38880 | −0.694401 | − | 0.719588i | \(-0.744331\pi\) | ||||
−0.694401 | + | 0.719588i | \(0.744331\pi\) | |||||||
\(662\) | −8.90949 | − | 27.4206i | −0.346277 | − | 1.06573i | ||||
\(663\) | 57.8874 | + | 42.0577i | 2.24816 | + | 1.63339i | ||||
\(664\) | −8.28981 | + | 6.02290i | −0.321707 | + | 0.233734i | ||||
\(665\) | −2.04617 | + | 6.29747i | −0.0793472 | + | 0.244205i | ||||
\(666\) | −8.29544 | + | 25.5308i | −0.321442 | + | 0.989297i | ||||
\(667\) | 13.9551 | − | 10.1390i | 0.540345 | − | 0.392583i | ||||
\(668\) | 7.29401 | + | 5.29941i | 0.282214 | + | 0.205040i | ||||
\(669\) | 7.76244 | + | 23.8903i | 0.300113 | + | 0.923654i | ||||
\(670\) | −14.1969 | −0.548473 | ||||||||
\(671\) | −7.44476 | + | 1.35701i | −0.287402 | + | 0.0523867i | ||||
\(672\) | 2.53932 | 0.0979564 | ||||||||
\(673\) | 4.82817 | + | 14.8596i | 0.186112 | + | 0.572794i | 0.999966 | − | 0.00827564i | \(-0.00263425\pi\) |
−0.813854 | + | 0.581070i | \(0.802634\pi\) | |||||||
\(674\) | 13.7314 | + | 9.97646i | 0.528915 | + | 0.384279i | ||||
\(675\) | 0.920658 | − | 0.668897i | 0.0354361 | − | 0.0257459i | ||||
\(676\) | 1.21440 | − | 3.73753i | 0.0467076 | − | 0.143751i | ||||
\(677\) | 3.50218 | − | 10.7786i | 0.134600 | − | 0.414255i | −0.860928 | − | 0.508727i | \(-0.830116\pi\) |
0.995528 | + | 0.0944718i | \(0.0301162\pi\) | |||||||
\(678\) | 15.1312 | − | 10.9935i | 0.581112 | − | 0.422202i | ||||
\(679\) | −0.559046 | − | 0.406171i | −0.0214542 | − | 0.0155874i | ||||
\(680\) | 2.11624 | + | 6.51311i | 0.0811541 | + | 0.249766i | ||||
\(681\) | −35.3726 | −1.35548 | ||||||||
\(682\) | 16.6626 | + | 8.00832i | 0.638043 | + | 0.306654i | ||||
\(683\) | −12.5315 | −0.479504 | −0.239752 | − | 0.970834i | \(-0.577066\pi\) | ||||
−0.239752 | + | 0.970834i | \(0.577066\pi\) | |||||||
\(684\) | −7.05551 | − | 21.7146i | −0.269774 | − | 0.830279i | ||||
\(685\) | −7.40331 | − | 5.37882i | −0.282866 | − | 0.205514i | ||||
\(686\) | 0.809017 | − | 0.587785i | 0.0308884 | − | 0.0224417i | ||||
\(687\) | 7.99835 | − | 24.6164i | 0.305156 | − | 0.939174i | ||||
\(688\) | 0.999606 | − | 3.07647i | 0.0381096 | − | 0.117289i | ||||
\(689\) | −37.0535 | + | 26.9209i | −1.41163 | + | 1.02561i | ||||
\(690\) | 6.44815 | + | 4.68485i | 0.245477 | + | 0.178349i | ||||
\(691\) | 1.05531 | + | 3.24791i | 0.0401459 | + | 0.123556i | 0.969121 | − | 0.246586i | \(-0.0793088\pi\) |
−0.928975 | + | 0.370143i | \(0.879309\pi\) | |||||||
\(692\) | −12.9388 | −0.491858 | ||||||||
\(693\) | −1.52630 | + | 11.3339i | −0.0579795 | + | 0.430540i | ||||
\(694\) | 22.8463 | 0.867234 | ||||||||
\(695\) | −4.91741 | − | 15.1342i | −0.186528 | − | 0.574075i | ||||
\(696\) | 11.2899 | + | 8.20262i | 0.427944 | + | 0.310919i | ||||
\(697\) | 16.1090 | − | 11.7038i | 0.610171 | − | 0.443315i | ||||
\(698\) | −4.67918 | + | 14.4010i | −0.177109 | + | 0.545087i | ||||
\(699\) | 10.3675 | − | 31.9077i | 0.392133 | − | 1.20686i | ||||
\(700\) | 0.809017 | − | 0.587785i | 0.0305780 | − | 0.0222162i | ||||
\(701\) | −28.4015 | − | 20.6349i | −1.07271 | − | 0.779369i | −0.0963122 | − | 0.995351i | \(-0.530705\pi\) |
−0.976397 | + | 0.215982i | \(0.930705\pi\) | |||||||
\(702\) | 1.44694 | + | 4.45322i | 0.0546111 | + | 0.168076i | ||||
\(703\) | 51.5503 | 1.94426 | ||||||||
\(704\) | −2.29013 | + | 2.39902i | −0.0863125 | + | 0.0904165i | ||||
\(705\) | −3.80868 | −0.143443 | ||||||||
\(706\) | −2.78429 | − | 8.56915i | −0.104788 | − | 0.322504i | ||||
\(707\) | 11.8270 | + | 8.59285i | 0.444802 | + | 0.323167i | ||||
\(708\) | −15.2521 | + | 11.0813i | −0.573209 | + | 0.416461i | ||||
\(709\) | −8.94067 | + | 27.5165i | −0.335774 | + | 1.03341i | 0.630566 | + | 0.776136i | \(0.282823\pi\) |
−0.966340 | + | 0.257270i | \(0.917177\pi\) | |||||||
\(710\) | −0.0188133 | + | 0.0579014i | −0.000706051 | + | 0.00217300i | ||||
\(711\) | 11.8275 | − | 8.59316i | 0.443565 | − | 0.322269i | ||||
\(712\) | 5.29416 | + | 3.84643i | 0.198407 | + | 0.144151i | ||||
\(713\) | 5.40650 | + | 16.6395i | 0.202475 | + | 0.623154i | ||||
\(714\) | −17.3900 | −0.650805 | ||||||||
\(715\) | 6.47602 | + | 12.0121i | 0.242190 | + | 0.449226i | ||||
\(716\) | 15.7602 | 0.588987 | ||||||||
\(717\) | −4.00294 | − | 12.3198i | −0.149493 | − | 0.460091i | ||||
\(718\) | −29.8470 | − | 21.6851i | −1.11388 | − | 0.809280i | ||||
\(719\) | 5.71953 | − | 4.15548i | 0.213303 | − | 0.154973i | −0.476004 | − | 0.879443i | \(-0.657915\pi\) |
0.689307 | + | 0.724470i | \(0.257915\pi\) | |||||||
\(720\) | −1.06554 | + | 3.27939i | −0.0397102 | + | 0.122215i | ||||
\(721\) | −0.331754 | + | 1.02103i | −0.0123552 | + | 0.0380253i | ||||
\(722\) | −20.1000 | + | 14.6035i | −0.748044 | + | 0.543486i | ||||
\(723\) | 49.3198 | + | 35.8330i | 1.83422 | + | 1.33264i | ||||
\(724\) | −4.51455 | − | 13.8943i | −0.167782 | − | 0.516379i | ||||
\(725\) | 5.49561 | 0.204102 | ||||||||
\(726\) | −17.4496 | − | 21.8114i | −0.647615 | − | 0.809497i | ||||
\(727\) | −28.5131 | −1.05749 | −0.528747 | − | 0.848779i | \(-0.677338\pi\) | ||||
−0.528747 | + | 0.848779i | \(0.677338\pi\) | |||||||
\(728\) | 1.27148 | + | 3.91321i | 0.0471241 | + | 0.145033i | ||||
\(729\) | 27.8093 | + | 20.2046i | 1.02997 | + | 0.748320i | ||||
\(730\) | −3.16555 | + | 2.29991i | −0.117162 | + | 0.0851234i | ||||
\(731\) | −6.84559 | + | 21.0686i | −0.253193 | + | 0.779249i | ||||
\(732\) | 1.79041 | − | 5.51030i | 0.0661753 | − | 0.203667i | ||||
\(733\) | −32.4592 | + | 23.5830i | −1.19891 | + | 0.871059i | −0.994177 | − | 0.107759i | \(-0.965632\pi\) |
−0.204733 | + | 0.978818i | \(0.565632\pi\) | |||||||
\(734\) | −27.9176 | − | 20.2834i | −1.03046 | − | 0.748672i | ||||
\(735\) | 0.784693 | + | 2.41504i | 0.0289438 | + | 0.0890800i | ||||
\(736\) | −3.13877 | −0.115697 | ||||||||
\(737\) | 22.3447 | + | 41.4461i | 0.823077 | + | 1.52669i | ||||
\(738\) | 10.0257 | 0.369050 | ||||||||
\(739\) | −11.3005 | − | 34.7794i | −0.415696 | − | 1.27938i | −0.911627 | − | 0.411018i | \(-0.865173\pi\) |
0.495932 | − | 0.868362i | \(-0.334827\pi\) | |||||||
\(740\) | −6.29838 | − | 4.57604i | −0.231533 | − | 0.168219i | ||||
\(741\) | 55.9708 | − | 40.6652i | 2.05614 | − | 1.49387i | ||||
\(742\) | 3.43975 | − | 10.5865i | 0.126277 | − | 0.388641i | ||||
\(743\) | −0.0151877 | + | 0.0467431i | −0.000557184 | + | 0.00171484i | −0.951335 | − | 0.308159i | \(-0.900287\pi\) |
0.950778 | + | 0.309874i | \(0.100287\pi\) | |||||||
\(744\) | −11.4511 | + | 8.31975i | −0.419819 | + | 0.305017i | ||||
\(745\) | 7.79139 | + | 5.66077i | 0.285454 | + | 0.207395i | ||||
\(746\) | 0.715686 | + | 2.20265i | 0.0262031 | + | 0.0806449i | ||||
\(747\) | 35.3324 | 1.29274 | ||||||||
\(748\) | 15.6835 | − | 16.4292i | 0.573445 | − | 0.600711i | ||||
\(749\) | 18.8781 | 0.689790 | ||||||||
\(750\) | 0.784693 | + | 2.41504i | 0.0286529 | + | 0.0881847i | ||||
\(751\) | −5.17702 | − | 3.76132i | −0.188912 | − | 0.137253i | 0.489309 | − | 0.872110i | \(-0.337249\pi\) |
−0.678221 | + | 0.734858i | \(0.737249\pi\) | |||||||
\(752\) | 1.21343 | − | 0.881607i | 0.0442492 | − | 0.0321489i | ||||
\(753\) | −12.1601 | + | 37.4250i | −0.443139 | + | 1.36384i | ||||
\(754\) | −6.98756 | + | 21.5055i | −0.254472 | + | 0.783184i | ||||
\(755\) | 16.4670 | − | 11.9640i | 0.599295 | − | 0.435413i | ||||
\(756\) | −0.920658 | − | 0.668897i | −0.0334840 | − | 0.0243275i | ||||
\(757\) | −5.93494 | − | 18.2659i | −0.215709 | − | 0.663885i | −0.999102 | − | 0.0423583i | \(-0.986513\pi\) |
0.783393 | − | 0.621526i | \(-0.213487\pi\) | |||||||
\(758\) | −7.92393 | −0.287810 | ||||||||
\(759\) | 3.52803 | − | 26.1982i | 0.128059 | − | 0.950934i | ||||
\(760\) | 6.62155 | 0.240189 | ||||||||
\(761\) | −0.888309 | − | 2.73394i | −0.0322012 | − | 0.0991051i | 0.933664 | − | 0.358150i | \(-0.116592\pi\) |
−0.965865 | + | 0.259045i | \(0.916592\pi\) | |||||||
\(762\) | −30.8217 | − | 22.3933i | −1.11655 | − | 0.811223i | ||||
\(763\) | 3.41660 | − | 2.48230i | 0.123689 | − | 0.0898655i | ||||
\(764\) | −5.55194 | + | 17.0871i | −0.200862 | + | 0.618190i | ||||
\(765\) | 7.29711 | − | 22.4582i | 0.263827 | − | 0.811978i | ||||
\(766\) | −15.5368 | + | 11.2881i | −0.561366 | + | 0.407856i | ||||
\(767\) | −24.7138 | − | 17.9556i | −0.892363 | − | 0.648339i | ||||
\(768\) | −0.784693 | − | 2.41504i | −0.0283152 | − | 0.0871452i | ||||
\(769\) | −35.4758 | −1.27929 | −0.639646 | − | 0.768670i | \(-0.720919\pi\) | ||||
−0.639646 | + | 0.768670i | \(0.720919\pi\) | |||||||
\(770\) | −2.98929 | − | 1.43670i | −0.107727 | − | 0.0517752i | ||||
\(771\) | 10.4742 | 0.377220 | ||||||||
\(772\) | 7.36017 | + | 22.6523i | 0.264898 | + | 0.815274i | ||||
\(773\) | 25.2909 | + | 18.3749i | 0.909650 | + | 0.660900i | 0.940926 | − | 0.338611i | \(-0.109957\pi\) |
−0.0312760 | + | 0.999511i | \(0.509957\pi\) | |||||||
\(774\) | −9.02382 | + | 6.55619i | −0.324354 | + | 0.235657i | ||||
\(775\) | −1.72249 | + | 5.30127i | −0.0618736 | + | 0.190427i | ||||
\(776\) | −0.213537 | + | 0.657198i | −0.00766552 | + | 0.0235921i | ||||
\(777\) | 15.9936 | − | 11.6200i | 0.573767 | − | 0.416866i | ||||
\(778\) | 6.19652 | + | 4.50204i | 0.222156 | + | 0.161406i | ||||
\(779\) | −5.94936 | − | 18.3102i | −0.213158 | − | 0.656032i | ||||
\(780\) | −10.4483 | −0.374108 | ||||||||
\(781\) | 0.198647 | − | 0.0362087i | 0.00710814 | − | 0.00129565i | ||||
\(782\) | 21.4952 | 0.768668 | ||||||||
\(783\) | −1.93259 | − | 5.94789i | −0.0690650 | − | 0.212560i | ||||
\(784\) | −0.809017 | − | 0.587785i | −0.0288935 | − | 0.0209923i | ||||
\(785\) | −4.86753 | + | 3.53647i | −0.173730 | + | 0.126222i | ||||
\(786\) | 5.31470 | − | 16.3570i | 0.189569 | − | 0.583434i | ||||
\(787\) | −3.99175 | + | 12.2853i | −0.142291 | + | 0.437925i | −0.996653 | − | 0.0817529i | \(-0.973948\pi\) |
0.854362 | + | 0.519678i | \(0.173948\pi\) | |||||||
\(788\) | 1.50114 | − | 1.09064i | 0.0534759 | − | 0.0388525i | ||||
\(789\) | 0.633525 | + | 0.460283i | 0.0225541 | + | 0.0163865i | ||||
\(790\) | 1.31018 | + | 4.03232i | 0.0466141 | + | 0.143463i | ||||
\(791\) | −7.36545 | −0.261885 | ||||||||
\(792\) | 11.2508 | − | 2.05077i | 0.399781 | − | 0.0728709i | ||||
\(793\) | 9.38812 | 0.333382 | ||||||||
\(794\) | −6.18773 | − | 19.0439i | −0.219594 | − | 0.675842i | ||||
\(795\) | 22.8676 | + | 16.6143i | 0.811029 | + | 0.589247i | ||||
\(796\) | −17.6533 | + | 12.8258i | −0.625703 | + | 0.454600i | ||||
\(797\) | 3.12420 | − | 9.61531i | 0.110665 | − | 0.340592i | −0.880353 | − | 0.474319i | \(-0.842694\pi\) |
0.991018 | + | 0.133727i | \(0.0426945\pi\) | |||||||
\(798\) | −5.19589 | + | 15.9913i | −0.183932 | + | 0.566086i | ||||
\(799\) | −8.30991 | + | 6.03750i | −0.293984 | + | 0.213592i | ||||
\(800\) | −0.809017 | − | 0.587785i | −0.0286031 | − | 0.0207813i | ||||
\(801\) | −6.97281 | − | 21.4601i | −0.246372 | − | 0.758255i | ||||
\(802\) | 20.7562 | 0.732926 | ||||||||
\(803\) | 11.6966 | + | 5.62159i | 0.412765 | + | 0.198382i | ||||
\(804\) | −36.0504 | −1.27140 | ||||||||
\(805\) | −0.969934 | − | 2.98515i | −0.0341857 | − | 0.105213i | ||||
\(806\) | −18.5549 | − | 13.4809i | −0.653568 | − | 0.474845i | ||||
\(807\) | −35.2151 | + | 25.5852i | −1.23963 | + | 0.900643i | ||||
\(808\) | 4.51753 | − | 13.9035i | 0.158926 | − | 0.489124i | ||||
\(809\) | 1.56498 | − | 4.81652i | 0.0550218 | − | 0.169340i | −0.919769 | − | 0.392460i | \(-0.871624\pi\) |
0.974791 | + | 0.223120i | \(0.0716242\pi\) | |||||||
\(810\) | −6.03099 | + | 4.38177i | −0.211907 | + | 0.153960i | ||||
\(811\) | 7.70306 | + | 5.59660i | 0.270491 | + | 0.196523i | 0.714759 | − | 0.699371i | \(-0.246536\pi\) |
−0.444268 | + | 0.895894i | \(0.646536\pi\) | |||||||
\(812\) | −1.69824 | − | 5.22664i | −0.0595965 | − | 0.183419i | ||||
\(813\) | −67.6114 | −2.37124 | ||||||||
\(814\) | −3.44609 | + | 25.5897i | −0.120785 | + | 0.896918i | ||||
\(815\) | 8.61451 | 0.301753 | ||||||||
\(816\) | 5.37381 | + | 16.5389i | 0.188121 | + | 0.578977i | ||||
\(817\) | 17.3286 | + | 12.5900i | 0.606252 | + | 0.440468i | ||||
\(818\) | −26.5805 | + | 19.3119i | −0.929365 | + | 0.675223i | ||||
\(819\) | 4.38425 | − | 13.4933i | 0.153198 | − | 0.471495i | ||||
\(820\) | −0.898483 | + | 2.76525i | −0.0313764 | + | 0.0965666i | ||||
\(821\) | −14.0774 | + | 10.2278i | −0.491305 | + | 0.356954i | −0.805686 | − | 0.592343i | \(-0.798203\pi\) |
0.314381 | + | 0.949297i | \(0.398203\pi\) | |||||||
\(822\) | −18.7994 | − | 13.6586i | −0.655704 | − | 0.476397i | ||||
\(823\) | 5.71246 | + | 17.5812i | 0.199124 | + | 0.612840i | 0.999904 | + | 0.0138814i | \(0.00441874\pi\) |
−0.800780 | + | 0.598959i | \(0.795581\pi\) | |||||||
\(824\) | 1.07358 | 0.0373998 | ||||||||
\(825\) | 5.81537 | − | 6.09189i | 0.202465 | − | 0.212092i | ||||
\(826\) | 7.42428 | 0.258324 | ||||||||
\(827\) | −17.0795 | − | 52.5652i | −0.593911 | − | 1.82787i | −0.560075 | − | 0.828442i | \(-0.689228\pi\) |
−0.0338362 | − | 0.999427i | \(-0.510772\pi\) | |||||||
\(828\) | 8.75596 | + | 6.36158i | 0.304291 | + | 0.221080i | ||||
\(829\) | 16.2367 | − | 11.7966i | 0.563922 | − | 0.409714i | −0.268970 | − | 0.963149i | \(-0.586683\pi\) |
0.832892 | + | 0.553435i | \(0.186683\pi\) | |||||||
\(830\) | −3.16642 | + | 9.74525i | −0.109908 | + | 0.338263i | ||||
\(831\) | 12.3298 | − | 37.9473i | 0.427717 | − | 1.31638i | ||||
\(832\) | 3.32878 | − | 2.41850i | 0.115405 | − | 0.0838463i | ||||
\(833\) | 5.54038 | + | 4.02533i | 0.191963 | + | 0.139469i | ||||
\(834\) | −12.4869 | − | 38.4307i | −0.432386 | − | 1.33075i | ||||
\(835\) | 9.01590 | 0.312008 | ||||||||
\(836\) | −10.4218 | − | 19.3308i | −0.360444 | − | 0.668571i | ||||
\(837\) | 6.34329 | 0.219256 | ||||||||
\(838\) | −5.05629 | − | 15.5617i | −0.174667 | − | 0.537569i | ||||
\(839\) | 8.70689 | + | 6.32593i | 0.300595 | + | 0.218395i | 0.727851 | − | 0.685736i | \(-0.240519\pi\) |
−0.427255 | + | 0.904131i | \(0.640519\pi\) | |||||||
\(840\) | 2.05435 | − | 1.49258i | 0.0708819 | − | 0.0514987i | ||||
\(841\) | 0.371371 | − | 1.14296i | 0.0128059 | − | 0.0394124i | ||||
\(842\) | 8.04902 | − | 24.7723i | 0.277388 | − | 0.853712i | ||||
\(843\) | −35.8161 | + | 26.0219i | −1.23357 | + | 0.896242i | ||||
\(844\) | 21.4973 | + | 15.6187i | 0.739968 | + | 0.537619i | ||||
\(845\) | −1.21440 | − | 3.73753i | −0.0417765 | − | 0.128575i | ||||
\(846\) | −5.17181 | −0.177811 | ||||||||
\(847\) | 0.510610 | + | 10.9881i | 0.0175448 | + | 0.377557i | ||||
\(848\) | −11.1313 | −0.382249 | ||||||||
\(849\) | −11.7857 | − | 36.2725i | −0.404483 | − | 1.24487i | ||||
\(850\) | 5.54038 | + | 4.02533i | 0.190034 | + | 0.138068i | ||||
\(851\) | −19.7692 | + | 14.3632i | −0.677679 | + | 0.492363i | ||||
\(852\) | −0.0477730 | + | 0.147030i | −0.00163668 | + | 0.00503717i | ||||
\(853\) | −4.52996 | + | 13.9418i | −0.155103 | + | 0.477358i | −0.998171 | − | 0.0604487i | \(-0.980747\pi\) |
0.843068 | + | 0.537806i | \(0.180747\pi\) | |||||||
\(854\) | −1.84590 | + | 1.34113i | −0.0631656 | + | 0.0458925i | ||||
\(855\) | −18.4716 | − | 13.4204i | −0.631714 | − | 0.458967i | ||||
\(856\) | −5.83365 | − | 17.9541i | −0.199390 | − | 0.613659i | ||||
\(857\) | 34.6532 | 1.18373 | 0.591865 | − | 0.806037i | \(-0.298392\pi\) | ||||
0.591865 | + | 0.806037i | \(0.298392\pi\) | |||||||
\(858\) | 16.4447 | + | 30.5025i | 0.561413 | + | 1.04134i | ||||
\(859\) | 9.13441 | 0.311662 | 0.155831 | − | 0.987784i | \(-0.450194\pi\) | ||||
0.155831 | + | 0.987784i | \(0.450194\pi\) | |||||||
\(860\) | −0.999606 | − | 3.07647i | −0.0340863 | − | 0.104907i | ||||
\(861\) | −5.97314 | − | 4.33974i | −0.203564 | − | 0.147898i | ||||
\(862\) | −14.7706 | + | 10.7315i | −0.503090 | + | 0.365516i | ||||
\(863\) | 7.24276 | − | 22.2909i | 0.246546 | − | 0.758792i | −0.748832 | − | 0.662760i | \(-0.769385\pi\) |
0.995378 | − | 0.0960319i | \(-0.0306151\pi\) | |||||||
\(864\) | −0.351660 | + | 1.08230i | −0.0119637 | + | 0.0368205i | ||||
\(865\) | −10.4677 | + | 7.60521i | −0.355911 | + | 0.258585i | ||||
\(866\) | −26.3818 | − | 19.1675i | −0.896489 | − | 0.651337i | ||||
\(867\) | −23.4616 | − | 72.2075i | −0.796799 | − | 2.45229i | ||||
\(868\) | 5.57409 | 0.189197 | ||||||||
\(869\) | 9.70976 | − | 10.1714i | 0.329381 | − | 0.345042i | ||||
\(870\) | 13.9551 | 0.473123 | ||||||||
\(871\) | −18.0510 | − | 55.5553i | −0.611636 | − | 1.88242i | ||||
\(872\) | −3.41660 | − | 2.48230i | −0.115701 | − | 0.0840614i | ||||
\(873\) | 1.92768 | − | 1.40054i | 0.0652419 | − | 0.0474010i | ||||
\(874\) | 6.42247 | − | 19.7663i | 0.217243 | − | 0.668606i | ||||
\(875\) | 0.309017 | − | 0.951057i | 0.0104467 | − | 0.0321516i | ||||
\(876\) | −8.03835 | + | 5.84020i | −0.271591 | + | 0.197322i | ||||
\(877\) | 41.2568 | + | 29.9748i | 1.39314 | + | 1.01218i | 0.995512 | + | 0.0946320i | \(0.0301675\pi\) |
0.397631 | + | 0.917546i | \(0.369833\pi\) | |||||||
\(878\) | −9.03997 | − | 27.8222i | −0.305084 | − | 0.938953i | ||||
\(879\) | −19.0618 | −0.642940 | ||||||||
\(880\) | −0.442644 | + | 3.28695i | −0.0149215 | + | 0.110803i | ||||
\(881\) | −1.75183 | −0.0590207 | −0.0295103 | − | 0.999564i | \(-0.509395\pi\) | ||||
−0.0295103 | + | 0.999564i | \(0.509395\pi\) | |||||||
\(882\) | 1.06554 | + | 3.27939i | 0.0358785 | + | 0.110423i | ||||
\(883\) | 33.0611 | + | 24.0203i | 1.11259 | + | 0.808347i | 0.983070 | − | 0.183229i | \(-0.0586551\pi\) |
0.129524 | + | 0.991576i | \(0.458655\pi\) | |||||||
\(884\) | −22.7964 | + | 16.5626i | −0.766727 | + | 0.557060i | ||||
\(885\) | −5.82579 | + | 17.9299i | −0.195832 | + | 0.602708i | ||||
\(886\) | 3.52561 | − | 10.8507i | 0.118445 | − | 0.364537i | ||||
\(887\) | 19.0565 | − | 13.8454i | 0.639856 | − | 0.464883i | −0.219945 | − | 0.975512i | \(-0.570588\pi\) |
0.859801 | + | 0.510630i | \(0.170588\pi\) | |||||||
\(888\) | −15.9936 | − | 11.6200i | −0.536710 | − | 0.389943i | ||||
\(889\) | 4.63622 | + | 14.2688i | 0.155494 | + | 0.478561i | ||||
\(890\) | 6.54394 | 0.219353 | ||||||||
\(891\) | 22.2843 | + | 10.7102i | 0.746553 | + | 0.358806i | ||||
\(892\) | −9.89233 | −0.331220 | ||||||||
\(893\) | 3.06901 | + | 9.44545i | 0.102701 | + | 0.316080i | ||||
\(894\) | 19.7848 | + | 14.3745i | 0.661704 | + | 0.480756i | ||||
\(895\) | 12.7503 | − | 9.26363i | 0.426195 | − | 0.309649i | ||||
\(896\) | −0.309017 | + | 0.951057i | −0.0103235 | + | 0.0317726i | ||||
\(897\) | −10.1341 | + | 31.1897i | −0.338369 | + | 1.04139i | ||||
\(898\) | −11.0282 | + | 8.01242i | −0.368014 | + | 0.267378i | ||||
\(899\) | 24.7826 | + | 18.0056i | 0.826548 | + | 0.600522i | ||||
\(900\) | 1.06554 | + | 3.27939i | 0.0355179 | + | 0.109313i | ||||
\(901\) | 76.2302 | 2.53960 | ||||||||
\(902\) | 9.48695 | − | 1.72925i | 0.315881 | − | 0.0575778i | ||||
\(903\) | 8.21418 | 0.273351 | ||||||||
\(904\) | 2.27605 | + | 7.00496i | 0.0757003 | + | 0.232981i | ||||
\(905\) | −11.8192 | − | 8.58718i | −0.392885 | − | 0.285448i | ||||
\(906\) | 41.8149 | − | 30.3803i | 1.38921 | − | 1.00932i | ||||
\(907\) | −12.8016 | + | 39.3992i | −0.425069 | + | 1.30823i | 0.477859 | + | 0.878436i | \(0.341413\pi\) |
−0.902928 | + | 0.429791i | \(0.858587\pi\) | |||||||
\(908\) | 4.30459 | − | 13.2482i | 0.142853 | − | 0.439656i | ||||
\(909\) | −40.7814 | + | 29.6294i | −1.35263 | + | 0.982746i | ||||
\(910\) | 3.32878 | + | 2.41850i | 0.110348 | + | 0.0801724i | ||||
\(911\) | 13.9409 | + | 42.9058i | 0.461884 | + | 1.42153i | 0.862860 | + | 0.505444i | \(0.168671\pi\) |
−0.400976 | + | 0.916089i | \(0.631329\pi\) | |||||||
\(912\) | 16.8142 | 0.556775 | ||||||||
\(913\) | 33.4338 | − | 6.09421i | 1.10650 | − | 0.201689i | ||||
\(914\) | −6.66357 | −0.220411 | ||||||||
\(915\) | −1.79041 | − | 5.51030i | −0.0591890 | − | 0.182165i | ||||
\(916\) | 8.24629 | + | 5.99128i | 0.272465 | + | 0.197957i | ||||
\(917\) | −5.47944 | + | 3.98105i | −0.180947 | + | 0.131466i | ||||
\(918\) | 2.40827 | − | 7.41189i | 0.0794848 | − | 0.244629i | ||||
\(919\) | 1.82902 | − | 5.62913i | 0.0603336 | − | 0.185688i | −0.916347 | − | 0.400385i | \(-0.868876\pi\) |
0.976681 | + | 0.214697i | \(0.0688764\pi\) | |||||||
\(920\) | −2.53932 | + | 1.84492i | −0.0837189 | + | 0.0608254i | ||||
\(921\) | −10.4385 | − | 7.58401i | −0.343960 | − | 0.249902i | ||||
\(922\) | 5.62341 | + | 17.3071i | 0.185197 | + | 0.569978i | ||||
\(923\) | −0.250501 | −0.00824535 | ||||||||
\(924\) | −7.59078 | − | 3.64825i | −0.249718 | − | 0.120019i | ||||
\(925\) | −7.78523 | −0.255977 | ||||||||
\(926\) | 3.52189 | + | 10.8393i | 0.115736 | + | 0.356200i | ||||
\(927\) | −2.99486 | − | 2.17590i | −0.0983643 | − | 0.0714658i | ||||
\(928\) | −4.44605 | + | 3.23024i | −0.145949 | + | 0.106038i | ||||
\(929\) | −17.0796 | + | 52.5657i | −0.560365 | + | 1.72463i | 0.120972 | + | 0.992656i | \(0.461399\pi\) |
−0.681337 | + | 0.731970i | \(0.738601\pi\) | |||||||
\(930\) | −4.37395 | + | 13.4616i | −0.143427 | + | 0.441424i | ||||
\(931\) | 5.35695 | − | 3.89205i | 0.175567 | − | 0.127557i | ||||
\(932\) | 10.6888 | + | 7.76588i | 0.350124 | + | 0.254380i | ||||
\(933\) | −8.50889 | − | 26.1877i | −0.278569 | − | 0.857346i | ||||
\(934\) | 22.9793 | 0.751907 | ||||||||
\(935\) | 3.03136 | − | 22.5100i | 0.0991360 | − | 0.736156i | ||||
\(936\) | −14.1877 | −0.463740 | ||||||||
\(937\) | −4.97418 | − | 15.3090i | −0.162499 | − | 0.500122i | 0.836344 | − | 0.548205i | \(-0.184689\pi\) |
−0.998843 | + | 0.0480833i | \(0.984689\pi\) | |||||||
\(938\) | 11.4855 | + | 8.34471i | 0.375015 | + | 0.272464i | ||||
\(939\) | 68.6244 | − | 49.8585i | 2.23947 | − | 1.62707i | ||||
\(940\) | 0.463488 | − | 1.42647i | 0.0151173 | − | 0.0465263i | ||||
\(941\) | −15.4034 | + | 47.4068i | −0.502136 | + | 1.54542i | 0.303396 | + | 0.952865i | \(0.401880\pi\) |
−0.805532 | + | 0.592552i | \(0.798120\pi\) | |||||||
\(942\) | −12.3602 | + | 8.98023i | −0.402718 | + | 0.292592i | ||||
\(943\) | 7.38321 | + | 5.36422i | 0.240430 | + | 0.174683i | ||||
\(944\) | −2.29423 | − | 7.06091i | −0.0746708 | − | 0.229813i | ||||
\(945\) | −1.13800 | −0.0370190 | ||||||||
\(946\) | −7.40810 | + | 7.76034i | −0.240858 | + | 0.252310i | ||||
\(947\) | −31.1447 | −1.01207 | −0.506033 | − | 0.862514i | \(-0.668889\pi\) | ||||
−0.506033 | + | 0.862514i | \(0.668889\pi\) | |||||||
\(948\) | 3.32696 | + | 10.2393i | 0.108055 | + | 0.332558i | ||||
\(949\) | −13.0250 | − | 9.46319i | −0.422808 | − | 0.307188i | ||||
\(950\) | 5.35695 | − | 3.89205i | 0.173802 | − | 0.126275i | ||||
\(951\) | 21.7366 | − | 66.8983i | 0.704857 | − | 2.16933i | ||||
\(952\) | 2.11624 | − | 6.51311i | 0.0685877 | − | 0.211091i | ||||
\(953\) | 31.4130 | − | 22.8229i | 1.01757 | − | 0.739305i | 0.0517841 | − | 0.998658i | \(-0.483509\pi\) |
0.965783 | + | 0.259353i | \(0.0835092\pi\) | |||||||
\(954\) | 31.0519 | + | 22.5605i | 1.00534 | + | 0.730424i | ||||
\(955\) | 5.55194 | + | 17.0871i | 0.179657 | + | 0.552926i | ||||
\(956\) | 5.10128 | 0.164987 | ||||||||
\(957\) | −21.9642 | − | 40.7403i | −0.710002 | − | 1.31695i | ||||
\(958\) | 1.36694 | 0.0441640 | ||||||||
\(959\) | 2.82781 | + | 8.70311i | 0.0913149 | + | 0.281038i | ||||
\(960\) | −2.05435 | − | 1.49258i | −0.0663040 | − | 0.0481727i | ||||
\(961\) | −0.0569969 | + | 0.0414107i | −0.00183861 | + | 0.00133583i | ||||
\(962\) | 9.89875 | − | 30.4652i | 0.319149 | − | 0.982238i | ||||
\(963\) | −20.1153 | + | 61.9085i | −0.648206 | + | 1.99497i | ||||
\(964\) | −19.4225 | + | 14.1112i | −0.625555 | + | 0.454492i | ||||
\(965\) | 19.2692 | + | 13.9999i | 0.620297 | + | 0.450672i | ||||
\(966\) | −2.46297 | − | 7.58025i | −0.0792449 | − | 0.243891i | ||||
\(967\) | 18.4412 | 0.593030 | 0.296515 | − | 0.955028i | \(-0.404176\pi\) | ||||
0.296515 | + | 0.955028i | \(0.404176\pi\) | |||||||
\(968\) | 10.2926 | − | 3.88114i | 0.330815 | − | 0.124745i | ||||
\(969\) | −115.149 | −3.69911 | ||||||||
\(970\) | 0.213537 | + | 0.657198i | 0.00685625 | + | 0.0211014i | ||||
\(971\) | −5.24451 | − | 3.81036i | −0.168304 | − | 0.122280i | 0.500445 | − | 0.865769i | \(-0.333170\pi\) |
−0.668749 | + | 0.743488i | \(0.733170\pi\) | |||||||
\(972\) | −18.0766 | + | 13.1334i | −0.579807 | + | 0.421254i | ||||
\(973\) | −4.91741 | + | 15.1342i | −0.157645 | + | 0.485182i | ||||
\(974\) | −3.77302 | + | 11.6122i | −0.120895 | + | 0.372078i | ||||
\(975\) | −8.45283 | + | 6.14134i | −0.270707 | + | 0.196680i | ||||
\(976\) | 1.84590 | + | 1.34113i | 0.0590860 | + | 0.0429285i | ||||
\(977\) | −8.38820 | − | 25.8162i | −0.268362 | − | 0.825934i | −0.990900 | − | 0.134602i | \(-0.957024\pi\) |
0.722537 | − | 0.691332i | \(-0.242976\pi\) | |||||||
\(978\) | 21.8750 | 0.699485 | ||||||||
\(979\) | −10.2996 | − | 19.1042i | −0.329177 | − | 0.610574i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 4.49992 | + | 13.8493i | 0.143671 | + | 0.442175i | ||||
\(982\) | −32.2431 | − | 23.4260i | −1.02892 | − | 0.747552i | ||||
\(983\) | 8.01801 | − | 5.82543i | 0.255735 | − | 0.185802i | −0.452530 | − | 0.891749i | \(-0.649478\pi\) |
0.708265 | + | 0.705947i | \(0.249478\pi\) | |||||||
\(984\) | −2.28154 | + | 7.02185i | −0.0727328 | + | 0.223848i | ||||
\(985\) | 0.573384 | − | 1.76470i | 0.0182695 | − | 0.0562279i | ||||
\(986\) | 30.4478 | − | 22.1216i | 0.969656 | − | 0.704496i | ||||
\(987\) | 3.08128 | + | 2.23868i | 0.0980783 | + | 0.0712581i | ||||
\(988\) | 8.41916 | + | 25.9115i | 0.267849 | + | 0.824355i | ||||
\(989\) | −10.1533 | −0.322856 | ||||||||
\(990\) | 7.89671 | − | 8.27219i | 0.250974 | − | 0.262907i | ||||
\(991\) | 23.8739 | 0.758380 | 0.379190 | − | 0.925319i | \(-0.376203\pi\) | ||||
0.379190 | + | 0.925319i | \(0.376203\pi\) | |||||||
\(992\) | −1.72249 | − | 5.30127i | −0.0546890 | − | 0.168316i | ||||
\(993\) | −59.2305 | − | 43.0335i | −1.87962 | − | 1.36563i | ||||
\(994\) | 0.0492539 | − | 0.0357850i | 0.00156224 | − | 0.00113503i | ||||
\(995\) | −6.74294 | + | 20.7526i | −0.213766 | + | 0.657903i | ||||
\(996\) | −8.04057 | + | 24.7463i | −0.254775 | + | 0.784117i | ||||
\(997\) | 14.5272 | − | 10.5546i | 0.460080 | − | 0.334268i | −0.333482 | − | 0.942756i | \(-0.608224\pi\) |
0.793563 | + | 0.608488i | \(0.208224\pi\) | |||||||
\(998\) | −29.7318 | − | 21.6014i | −0.941143 | − | 0.683780i | ||||
\(999\) | 2.73775 | + | 8.42593i | 0.0866186 | + | 0.266585i |
(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 | 770.2.n.k.71.4 | ✓ | 16 | |
11.3 | even | 5 | 8470.2.a.dh.1.2 | 8 | |||
11.8 | odd | 10 | 8470.2.a.dg.1.2 | 8 | |||
11.9 | even | 5 | inner | 770.2.n.k.141.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.k.71.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
770.2.n.k.141.4 | yes | 16 | 11.9 | even | 5 | inner | |
8470.2.a.dg.1.2 | 8 | 11.8 | odd | 10 | |||
8470.2.a.dh.1.2 | 8 | 11.3 | even | 5 |