Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([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("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.159390625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 729.2 | ||
Root | \(-0.628998 + 0.456994i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.p.323.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.628998 | − | 0.456994i | 0.444769 | − | 0.323143i | −0.342758 | − | 0.939424i | \(-0.611361\pi\) |
0.787527 | + | 0.616280i | \(0.211361\pi\) | |||||||
\(3\) | 0.190983 | + | 0.587785i | 0.110264 | + | 0.339358i | 0.990930 | − | 0.134380i | \(-0.0429043\pi\) |
−0.880666 | + | 0.473738i | \(0.842904\pi\) | |||||||
\(4\) | −0.431239 | + | 1.32722i | −0.215619 | + | 0.663608i | ||||
\(5\) | 0.180019 | + | 0.130791i | 0.0805070 | + | 0.0584917i | 0.627311 | − | 0.778769i | \(-0.284156\pi\) |
−0.546804 | + | 0.837261i | \(0.684156\pi\) | |||||||
\(6\) | 0.388742 | + | 0.282438i | 0.158703 | + | 0.115305i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | 0.815793 | + | 2.51075i | 0.288426 | + | 0.887685i | ||||
\(9\) | 2.11803 | − | 1.53884i | 0.706011 | − | 0.512947i | ||||
\(10\) | 0.173002 | 0.0547082 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.862478 | −0.248976 | ||||||||
\(13\) | −5.28251 | + | 3.83797i | −1.46511 | + | 1.06446i | −0.483109 | + | 0.875560i | \(0.660493\pi\) |
−0.981996 | + | 0.188901i | \(0.939507\pi\) | |||||||
\(14\) | 0.240256 | + | 0.739431i | 0.0642111 | + | 0.197621i | ||||
\(15\) | −0.0424967 | + | 0.130791i | −0.0109726 | + | 0.0337702i | ||||
\(16\) | −0.597465 | − | 0.434084i | −0.149366 | − | 0.108521i | ||||
\(17\) | 3.50678 | + | 2.54782i | 0.850518 | + | 0.617938i | 0.925289 | − | 0.379263i | \(-0.123822\pi\) |
−0.0747707 | + | 0.997201i | \(0.523822\pi\) | |||||||
\(18\) | 0.628998 | − | 1.93586i | 0.148256 | − | 0.456286i | ||||
\(19\) | 0.900787 | + | 2.77234i | 0.206655 | + | 0.636017i | 0.999641 | + | 0.0267786i | \(0.00852493\pi\) |
−0.792987 | + | 0.609239i | \(0.791475\pi\) | |||||||
\(20\) | −0.251220 | + | 0.182522i | −0.0561745 | + | 0.0408131i | ||||
\(21\) | −0.618034 | −0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.89796 | −0.812780 | −0.406390 | − | 0.913700i | \(-0.633213\pi\) | ||||
−0.406390 | + | 0.913700i | \(0.633213\pi\) | |||||||
\(24\) | −1.31998 | + | 0.959022i | −0.269440 | + | 0.195760i | ||||
\(25\) | −1.52978 | − | 4.70819i | −0.305957 | − | 0.941639i | ||||
\(26\) | −1.56876 | + | 4.82815i | −0.307659 | + | 0.946878i | ||||
\(27\) | 2.80902 | + | 2.04087i | 0.540596 | + | 0.392766i | ||||
\(28\) | −1.12900 | − | 0.820265i | −0.213361 | − | 0.155016i | ||||
\(29\) | −1.16623 | + | 3.58928i | −0.216563 | + | 0.666512i | 0.782476 | + | 0.622681i | \(0.213956\pi\) |
−0.999039 | + | 0.0438312i | \(0.986044\pi\) | |||||||
\(30\) | 0.0330405 | + | 0.101688i | 0.00603235 | + | 0.0185657i | ||||
\(31\) | 5.57379 | − | 4.04959i | 1.00108 | − | 0.727329i | 0.0387621 | − | 0.999248i | \(-0.487659\pi\) |
0.962320 | + | 0.271920i | \(0.0876585\pi\) | |||||||
\(32\) | −5.85410 | −1.03487 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.37009 | 0.577966 | ||||||||
\(35\) | −0.180019 | + | 0.130791i | −0.0304288 | + | 0.0221078i | ||||
\(36\) | 1.12900 | + | 3.47470i | 0.188166 | + | 0.579116i | ||||
\(37\) | −1.74703 | + | 5.37681i | −0.287210 | + | 0.883942i | 0.698517 | + | 0.715593i | \(0.253844\pi\) |
−0.985727 | + | 0.168349i | \(0.946156\pi\) | |||||||
\(38\) | 1.83353 | + | 1.33214i | 0.297438 | + | 0.216102i | ||||
\(39\) | −3.26477 | − | 2.37200i | −0.522782 | − | 0.379823i | ||||
\(40\) | −0.181527 | + | 0.558682i | −0.0287019 | + | 0.0883354i | ||||
\(41\) | 0.413499 | + | 1.27262i | 0.0645777 | + | 0.198750i | 0.978139 | − | 0.207951i | \(-0.0666793\pi\) |
−0.913562 | + | 0.406700i | \(0.866679\pi\) | |||||||
\(42\) | −0.388742 | + | 0.282438i | −0.0599842 | + | 0.0435811i | ||||
\(43\) | −4.70820 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.582554 | 0.0868420 | ||||||||
\(46\) | −2.45181 | + | 1.78134i | −0.361499 | + | 0.262645i | ||||
\(47\) | 1.86817 | + | 5.74965i | 0.272501 | + | 0.838672i | 0.989870 | + | 0.141978i | \(0.0453463\pi\) |
−0.717369 | + | 0.696694i | \(0.754654\pi\) | |||||||
\(48\) | 0.141042 | − | 0.434084i | 0.0203577 | − | 0.0626546i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | −3.11385 | − | 2.26234i | −0.440364 | − | 0.319943i | ||||
\(51\) | −0.827838 | + | 2.54782i | −0.115920 | + | 0.356766i | ||||
\(52\) | −2.81579 | − | 8.66612i | −0.390480 | − | 1.20177i | ||||
\(53\) | 1.38982 | − | 1.00977i | 0.190907 | − | 0.138702i | −0.488226 | − | 0.872717i | \(-0.662356\pi\) |
0.679133 | + | 0.734015i | \(0.262356\pi\) | |||||||
\(54\) | 2.69953 | 0.367360 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.63996 | −0.352780 | ||||||||
\(57\) | −1.45750 | + | 1.05894i | −0.193051 | + | 0.140260i | ||||
\(58\) | 0.906723 | + | 2.79061i | 0.119059 | + | 0.366424i | ||||
\(59\) | −2.94587 | + | 9.06646i | −0.383520 | + | 1.18035i | 0.554029 | + | 0.832498i | \(0.313090\pi\) |
−0.937548 | + | 0.347855i | \(0.886910\pi\) | |||||||
\(60\) | −0.155262 | − | 0.112805i | −0.0200443 | − | 0.0145630i | ||||
\(61\) | 7.79037 | + | 5.66003i | 0.997455 | + | 0.724693i | 0.961541 | − | 0.274662i | \(-0.0885659\pi\) |
0.0359136 | + | 0.999355i | \(0.488566\pi\) | |||||||
\(62\) | 1.65526 | − | 5.09437i | 0.210219 | − | 0.646986i | ||||
\(63\) | 0.809017 | + | 2.48990i | 0.101927 | + | 0.313698i | ||||
\(64\) | −2.48729 | + | 1.80712i | −0.310911 | + | 0.225890i | ||||
\(65\) | −1.45293 | −0.180213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.27155 | 0.155344 | 0.0776722 | − | 0.996979i | \(-0.475251\pi\) | ||||
0.0776722 | + | 0.996979i | \(0.475251\pi\) | |||||||
\(68\) | −4.89377 | + | 3.55553i | −0.593457 | + | 0.431172i | ||||
\(69\) | −0.744444 | − | 2.29116i | −0.0896205 | − | 0.275824i | ||||
\(70\) | −0.0534607 | + | 0.164535i | −0.00638978 | + | 0.0196657i | ||||
\(71\) | 7.53129 | + | 5.47180i | 0.893800 | + | 0.649384i | 0.936866 | − | 0.349689i | \(-0.113713\pi\) |
−0.0430661 | + | 0.999072i | \(0.513713\pi\) | |||||||
\(72\) | 5.59153 | + | 4.06248i | 0.658968 | + | 0.478768i | ||||
\(73\) | 1.72713 | − | 5.31556i | 0.202145 | − | 0.622140i | −0.797673 | − | 0.603090i | \(-0.793936\pi\) |
0.999819 | − | 0.0190495i | \(-0.00606402\pi\) | |||||||
\(74\) | 1.35829 | + | 4.18039i | 0.157898 | + | 0.485960i | ||||
\(75\) | 2.47524 | − | 1.79837i | 0.285816 | − | 0.207658i | ||||
\(76\) | −4.06794 | −0.466625 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.13752 | −0.355254 | ||||||||
\(79\) | 3.66448 | − | 2.66240i | 0.412286 | − | 0.299543i | −0.362241 | − | 0.932085i | \(-0.617988\pi\) |
0.774527 | + | 0.632541i | \(0.217988\pi\) | |||||||
\(80\) | −0.0507806 | − | 0.156287i | −0.00567745 | − | 0.0174734i | ||||
\(81\) | 1.76393 | − | 5.42882i | 0.195992 | − | 0.603203i | ||||
\(82\) | 0.841669 | + | 0.611508i | 0.0929467 | + | 0.0675298i | ||||
\(83\) | −9.12876 | − | 6.63243i | −1.00201 | − | 0.728004i | −0.0394928 | − | 0.999220i | \(-0.512574\pi\) |
−0.962519 | + | 0.271216i | \(0.912574\pi\) | |||||||
\(84\) | 0.266520 | − | 0.820265i | 0.0290797 | − | 0.0894983i | ||||
\(85\) | 0.298053 | + | 0.917313i | 0.0323284 | + | 0.0994965i | ||||
\(86\) | −2.96145 | + | 2.15162i | −0.319341 | + | 0.232015i | ||||
\(87\) | −2.33245 | −0.250065 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.92157 | 0.839684 | 0.419842 | − | 0.907597i | \(-0.362085\pi\) | ||||
0.419842 | + | 0.907597i | \(0.362085\pi\) | |||||||
\(90\) | 0.366425 | − | 0.266223i | 0.0386246 | − | 0.0280624i | ||||
\(91\) | −2.01774 | − | 6.20997i | −0.211517 | − | 0.650981i | ||||
\(92\) | 1.68095 | − | 5.17343i | 0.175251 | − | 0.539368i | ||||
\(93\) | 3.44479 | + | 2.50279i | 0.357208 | + | 0.259527i | ||||
\(94\) | 3.80263 | + | 2.76277i | 0.392211 | + | 0.284958i | ||||
\(95\) | −0.200439 | + | 0.616888i | −0.0205646 | + | 0.0632914i | ||||
\(96\) | −1.11803 | − | 3.44095i | −0.114109 | − | 0.351191i | ||||
\(97\) | 7.32477 | − | 5.32176i | 0.743718 | − | 0.540342i | −0.150156 | − | 0.988662i | \(-0.547977\pi\) |
0.893873 | + | 0.448320i | \(0.147977\pi\) | |||||||
\(98\) | −0.777484 | −0.0785378 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.90849 | 0.690849 | ||||||||
\(101\) | 15.5413 | − | 11.2915i | 1.54642 | − | 1.12354i | 0.600280 | − | 0.799790i | \(-0.295056\pi\) |
0.946142 | − | 0.323751i | \(-0.104944\pi\) | |||||||
\(102\) | 0.643631 | + | 1.98089i | 0.0637289 | + | 0.196137i | ||||
\(103\) | 5.01791 | − | 15.4435i | 0.494430 | − | 1.52170i | −0.323414 | − | 0.946258i | \(-0.604831\pi\) |
0.817844 | − | 0.575440i | \(-0.195169\pi\) | |||||||
\(104\) | −13.9456 | − | 10.1321i | −1.36748 | − | 0.993534i | ||||
\(105\) | −0.111258 | − | 0.0808336i | −0.0108577 | − | 0.00788855i | ||||
\(106\) | 0.412739 | − | 1.27028i | 0.0400888 | − | 0.123381i | ||||
\(107\) | −1.66664 | − | 5.12939i | −0.161120 | − | 0.495877i | 0.837609 | − | 0.546270i | \(-0.183953\pi\) |
−0.998729 | + | 0.0503930i | \(0.983953\pi\) | |||||||
\(108\) | −3.92003 | + | 2.84807i | −0.377205 | + | 0.274056i | ||||
\(109\) | 5.39901 | 0.517132 | 0.258566 | − | 0.965994i | \(-0.416750\pi\) | ||||
0.258566 | + | 0.965994i | \(0.416750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.49406 | −0.331642 | ||||||||
\(112\) | 0.597465 | − | 0.434084i | 0.0564552 | − | 0.0410171i | ||||
\(113\) | −5.09761 | − | 15.6888i | −0.479543 | − | 1.47588i | −0.839731 | − | 0.543002i | \(-0.817287\pi\) |
0.360188 | − | 0.932880i | \(-0.382713\pi\) | |||||||
\(114\) | −0.432838 | + | 1.33214i | −0.0405390 | + | 0.124766i | ||||
\(115\) | −0.701707 | − | 0.509820i | −0.0654345 | − | 0.0475409i | ||||
\(116\) | −4.26082 | − | 3.09567i | −0.395608 | − | 0.287426i | ||||
\(117\) | −5.28251 | + | 16.2579i | −0.488368 | + | 1.50304i | ||||
\(118\) | 2.29037 | + | 7.04903i | 0.210846 | + | 0.648916i | ||||
\(119\) | −3.50678 | + | 2.54782i | −0.321466 | + | 0.233558i | ||||
\(120\) | −0.363054 | −0.0331421 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 7.48673 | 0.677816 | ||||||||
\(123\) | −0.669055 | + | 0.486097i | −0.0603267 | + | 0.0438299i | ||||
\(124\) | 2.97106 | + | 9.14397i | 0.266809 | + | 0.821153i | ||||
\(125\) | 0.684207 | − | 2.10577i | 0.0611973 | − | 0.188346i | ||||
\(126\) | 1.64674 | + | 1.19643i | 0.146703 | + | 0.106586i | ||||
\(127\) | −1.61583 | − | 1.17397i | −0.143382 | − | 0.104173i | 0.513782 | − | 0.857921i | \(-0.328244\pi\) |
−0.657164 | + | 0.753748i | \(0.728244\pi\) | |||||||
\(128\) | 2.87938 | − | 8.86181i | 0.254503 | − | 0.783281i | ||||
\(129\) | −0.899187 | − | 2.76741i | −0.0791690 | − | 0.243657i | ||||
\(130\) | −0.913888 | + | 0.663978i | −0.0801533 | + | 0.0582348i | ||||
\(131\) | 1.37009 | 0.119706 | 0.0598528 | − | 0.998207i | \(-0.480937\pi\) | ||||
0.0598528 | + | 0.998207i | \(0.480937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.91501 | −0.252763 | ||||||||
\(134\) | 0.799801 | − | 0.581090i | 0.0690923 | − | 0.0501985i | ||||
\(135\) | 0.238748 | + | 0.734791i | 0.0205482 | + | 0.0632407i | ||||
\(136\) | −3.53615 | + | 10.8831i | −0.303222 | + | 0.933222i | ||||
\(137\) | −2.02193 | − | 1.46902i | −0.172745 | − | 0.125507i | 0.498053 | − | 0.867146i | \(-0.334048\pi\) |
−0.670798 | + | 0.741640i | \(0.734048\pi\) | |||||||
\(138\) | −1.51530 | − | 1.10093i | −0.128991 | − | 0.0937174i | ||||
\(139\) | −1.47172 | + | 4.52950i | −0.124830 | + | 0.384187i | −0.993870 | − | 0.110555i | \(-0.964737\pi\) |
0.869040 | + | 0.494742i | \(0.164737\pi\) | |||||||
\(140\) | −0.0959574 | − | 0.295327i | −0.00810988 | − | 0.0249597i | ||||
\(141\) | −3.02277 | + | 2.19617i | −0.254563 | + | 0.184951i | ||||
\(142\) | 7.23775 | 0.607378 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.93344 | −0.161120 | ||||||||
\(145\) | −0.679390 | + | 0.493605i | −0.0564202 | + | 0.0409917i | ||||
\(146\) | −1.34282 | − | 4.13277i | −0.111132 | − | 0.342030i | ||||
\(147\) | 0.190983 | − | 0.587785i | 0.0157520 | − | 0.0484797i | ||||
\(148\) | −6.38281 | − | 4.63738i | −0.524663 | − | 0.381190i | ||||
\(149\) | 5.84907 | + | 4.24960i | 0.479175 | + | 0.348141i | 0.801006 | − | 0.598656i | \(-0.204298\pi\) |
−0.321831 | + | 0.946797i | \(0.604298\pi\) | |||||||
\(150\) | 0.735079 | − | 2.26234i | 0.0600190 | − | 0.184719i | ||||
\(151\) | 2.51530 | + | 7.74130i | 0.204692 | + | 0.629978i | 0.999726 | + | 0.0234126i | \(0.00745315\pi\) |
−0.795034 | + | 0.606565i | \(0.792547\pi\) | |||||||
\(152\) | −6.22580 | + | 4.52331i | −0.504979 | + | 0.366888i | ||||
\(153\) | 11.3482 | 0.917445 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.53304 | 0.123137 | ||||||||
\(156\) | 4.55605 | − | 3.31016i | 0.364776 | − | 0.265025i | ||||
\(157\) | 6.22713 | + | 19.1651i | 0.496979 | + | 1.52954i | 0.813850 | + | 0.581076i | \(0.197368\pi\) |
−0.316870 | + | 0.948469i | \(0.602632\pi\) | |||||||
\(158\) | 1.08825 | − | 3.34929i | 0.0865765 | − | 0.266455i | ||||
\(159\) | 0.858958 | + | 0.624069i | 0.0681198 | + | 0.0494919i | ||||
\(160\) | −1.05385 | − | 0.765667i | −0.0833141 | − | 0.0605313i | ||||
\(161\) | 1.20454 | − | 3.70718i | 0.0949307 | − | 0.292167i | ||||
\(162\) | −1.37143 | − | 4.22083i | −0.107750 | − | 0.331619i | ||||
\(163\) | −6.01463 | + | 4.36989i | −0.471102 | + | 0.342276i | −0.797871 | − | 0.602829i | \(-0.794040\pi\) |
0.326768 | + | 0.945104i | \(0.394040\pi\) | |||||||
\(164\) | −1.86736 | −0.145816 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.77295 | −0.680913 | ||||||||
\(167\) | 1.78884 | − | 1.29967i | 0.138424 | − | 0.100571i | −0.516418 | − | 0.856337i | \(-0.672735\pi\) |
0.654843 | + | 0.755765i | \(0.272735\pi\) | |||||||
\(168\) | −0.504188 | − | 1.55173i | −0.0388989 | − | 0.119719i | ||||
\(169\) | 9.15770 | − | 28.1845i | 0.704439 | − | 2.16804i | ||||
\(170\) | 0.606681 | + | 0.440780i | 0.0465303 | + | 0.0338062i | ||||
\(171\) | 6.17408 | + | 4.48573i | 0.472144 | + | 0.343033i | ||||
\(172\) | 2.03036 | − | 6.24881i | 0.154814 | − | 0.476467i | ||||
\(173\) | −3.20210 | − | 9.85504i | −0.243451 | − | 0.749265i | −0.995887 | − | 0.0905998i | \(-0.971122\pi\) |
0.752437 | − | 0.658665i | \(-0.228878\pi\) | |||||||
\(174\) | −1.46711 | + | 1.06592i | −0.111221 | + | 0.0808069i | ||||
\(175\) | 4.95049 | 0.374222 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.89174 | −0.442851 | ||||||||
\(178\) | 4.98265 | − | 3.62011i | 0.373465 | − | 0.271338i | ||||
\(179\) | −7.23391 | − | 22.2637i | −0.540688 | − | 1.66407i | −0.731028 | − | 0.682347i | \(-0.760959\pi\) |
0.190341 | − | 0.981718i | \(-0.439041\pi\) | |||||||
\(180\) | −0.251220 | + | 0.773175i | −0.0187248 | + | 0.0576291i | ||||
\(181\) | 11.0966 | + | 8.06212i | 0.824801 | + | 0.599253i | 0.918084 | − | 0.396387i | \(-0.129736\pi\) |
−0.0932830 | + | 0.995640i | \(0.529736\pi\) | |||||||
\(182\) | −4.10707 | − | 2.98396i | −0.304436 | − | 0.221186i | ||||
\(183\) | −1.83906 | + | 5.66003i | −0.135947 | + | 0.418402i | ||||
\(184\) | −3.17993 | − | 9.78681i | −0.234427 | − | 0.721493i | ||||
\(185\) | −1.01774 | + | 0.739431i | −0.0748257 | + | 0.0543641i | ||||
\(186\) | 3.31052 | 0.242739 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.43666 | −0.615306 | ||||||||
\(189\) | −2.80902 | + | 2.04087i | −0.204326 | + | 0.148451i | ||||
\(190\) | 0.155838 | + | 0.479621i | 0.0113057 | + | 0.0347954i | ||||
\(191\) | −3.71591 | + | 11.4364i | −0.268874 | + | 0.827509i | 0.721902 | + | 0.691996i | \(0.243268\pi\) |
−0.990776 | + | 0.135513i | \(0.956732\pi\) | |||||||
\(192\) | −1.53723 | − | 1.11686i | −0.110940 | − | 0.0806026i | ||||
\(193\) | −12.8504 | − | 9.33634i | −0.924990 | − | 0.672044i | 0.0197714 | − | 0.999805i | \(-0.493706\pi\) |
−0.944761 | + | 0.327760i | \(0.893706\pi\) | |||||||
\(194\) | 2.17526 | − | 6.69475i | 0.156174 | − | 0.480655i | ||||
\(195\) | −0.277484 | − | 0.854009i | −0.0198711 | − | 0.0611568i | ||||
\(196\) | 1.12900 | − | 0.820265i | 0.0806427 | − | 0.0585904i | ||||
\(197\) | 12.3035 | 0.876590 | 0.438295 | − | 0.898831i | \(-0.355582\pi\) | ||||
0.438295 | + | 0.898831i | \(0.355582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2615 | 1.08186 | 0.540929 | − | 0.841068i | \(-0.318073\pi\) | ||||
0.540929 | + | 0.841068i | \(0.318073\pi\) | |||||||
\(200\) | 10.5731 | − | 7.68182i | 0.747633 | − | 0.543187i | ||||
\(201\) | 0.242844 | + | 0.747397i | 0.0171289 | + | 0.0527173i | ||||
\(202\) | 4.61535 | − | 14.2046i | 0.324735 | − | 0.999432i | ||||
\(203\) | −3.05322 | − | 2.21829i | −0.214294 | − | 0.155694i | ||||
\(204\) | −3.02452 | − | 2.19744i | −0.211758 | − | 0.153852i | ||||
\(205\) | −0.0920100 | + | 0.283178i | −0.00642626 | + | 0.0197780i | ||||
\(206\) | −3.90135 | − | 12.0071i | −0.271820 | − | 0.836575i | ||||
\(207\) | −8.25601 | + | 5.99834i | −0.573832 | + | 0.416913i | ||||
\(208\) | 4.82212 | 0.334354 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.106921 | −0.00737828 | ||||||||
\(211\) | −7.22730 | + | 5.25094i | −0.497548 | + | 0.361490i | −0.808080 | − | 0.589073i | \(-0.799493\pi\) |
0.310532 | + | 0.950563i | \(0.399493\pi\) | |||||||
\(212\) | 0.740832 | + | 2.28005i | 0.0508805 | + | 0.156594i | ||||
\(213\) | −1.77790 | + | 5.47180i | −0.121819 | + | 0.374922i | ||||
\(214\) | −3.39241 | − | 2.46473i | −0.231900 | − | 0.168486i | ||||
\(215\) | −0.847566 | − | 0.615793i | −0.0578035 | − | 0.0419967i | ||||
\(216\) | −2.83254 | + | 8.71768i | −0.192730 | + | 0.593163i | ||||
\(217\) | 2.12900 | + | 6.55238i | 0.144526 | + | 0.444805i | ||||
\(218\) | 3.39597 | − | 2.46732i | 0.230004 | − | 0.167108i | ||||
\(219\) | 3.45426 | 0.233417 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.3031 | −1.90387 | ||||||||
\(222\) | −2.19776 | + | 1.59677i | −0.147504 | + | 0.107168i | ||||
\(223\) | 0.221023 | + | 0.680238i | 0.0148008 | + | 0.0455521i | 0.958184 | − | 0.286152i | \(-0.0923763\pi\) |
−0.943383 | + | 0.331704i | \(0.892376\pi\) | |||||||
\(224\) | 1.80902 | − | 5.56758i | 0.120870 | − | 0.372000i | ||||
\(225\) | −10.4853 | − | 7.61802i | −0.699020 | − | 0.507868i | ||||
\(226\) | −10.3761 | − | 7.53867i | −0.690207 | − | 0.501465i | ||||
\(227\) | −1.64447 | + | 5.06116i | −0.109147 | + | 0.335921i | −0.990681 | − | 0.136199i | \(-0.956511\pi\) |
0.881534 | + | 0.472120i | \(0.156511\pi\) | |||||||
\(228\) | −0.776908 | − | 2.39108i | −0.0514520 | − | 0.158353i | ||||
\(229\) | 5.34625 | − | 3.88427i | 0.353290 | − | 0.256680i | −0.396958 | − | 0.917837i | \(-0.629934\pi\) |
0.750248 | + | 0.661157i | \(0.229934\pi\) | |||||||
\(230\) | −0.674356 | −0.0444657 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.96318 | −0.654115 | ||||||||
\(233\) | 7.73188 | − | 5.61754i | 0.506532 | − | 0.368017i | −0.304974 | − | 0.952361i | \(-0.598648\pi\) |
0.811507 | + | 0.584343i | \(0.198648\pi\) | |||||||
\(234\) | 4.10707 | + | 12.6403i | 0.268488 | + | 0.826320i | ||||
\(235\) | −0.415698 | + | 1.27939i | −0.0271171 | + | 0.0834580i | ||||
\(236\) | −10.7628 | − | 7.81962i | −0.700598 | − | 0.509014i | ||||
\(237\) | 2.26477 | + | 1.64545i | 0.147113 | + | 0.106884i | ||||
\(238\) | −1.04142 | + | 3.20515i | −0.0675050 | + | 0.207759i | ||||
\(239\) | 8.29606 | + | 25.5327i | 0.536628 | + | 1.65157i | 0.740105 | + | 0.672491i | \(0.234776\pi\) |
−0.203478 | + | 0.979080i | \(0.565224\pi\) | |||||||
\(240\) | 0.0821648 | − | 0.0596962i | 0.00530371 | − | 0.00385337i | ||||
\(241\) | 18.8663 | 1.21529 | 0.607643 | − | 0.794210i | \(-0.292115\pi\) | ||||
0.607643 | + | 0.794210i | \(0.292115\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | −10.8716 | + | 7.89868i | −0.695983 | + | 0.505661i | ||||
\(245\) | −0.0687611 | − | 0.211625i | −0.00439299 | − | 0.0135202i | ||||
\(246\) | −0.198691 | + | 0.611508i | −0.0126681 | + | 0.0389883i | ||||
\(247\) | −15.3986 | − | 11.1877i | −0.979787 | − | 0.711857i | ||||
\(248\) | 14.7146 | + | 10.6908i | 0.934377 | + | 0.678865i | ||||
\(249\) | 2.15501 | − | 6.63243i | 0.136568 | − | 0.420313i | ||||
\(250\) | −0.531960 | − | 1.63720i | −0.0336441 | − | 0.103546i | ||||
\(251\) | −23.7634 | + | 17.2651i | −1.49993 | + | 1.08976i | −0.529523 | + | 0.848296i | \(0.677629\pi\) |
−0.970409 | + | 0.241468i | \(0.922371\pi\) | |||||||
\(252\) | −3.65351 | −0.230150 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.55285 | −0.0974348 | ||||||||
\(255\) | −0.482260 | + | 0.350382i | −0.0302003 | + | 0.0219418i | ||||
\(256\) | −4.13879 | − | 12.7379i | −0.258674 | − | 0.796118i | ||||
\(257\) | −5.22745 | + | 16.0884i | −0.326079 | + | 1.00357i | 0.644872 | + | 0.764291i | \(0.276911\pi\) |
−0.970951 | + | 0.239278i | \(0.923089\pi\) | |||||||
\(258\) | −1.83028 | − | 1.32977i | −0.113948 | − | 0.0827881i | ||||
\(259\) | −4.57379 | − | 3.32305i | −0.284201 | − | 0.206484i | ||||
\(260\) | 0.626558 | − | 1.92835i | 0.0388575 | − | 0.119591i | ||||
\(261\) | 3.05322 | + | 9.39685i | 0.188990 | + | 0.581650i | ||||
\(262\) | 0.861786 | − | 0.626124i | 0.0532413 | − | 0.0386821i | ||||
\(263\) | −8.18034 | −0.504421 | −0.252211 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252211 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.382263 | 0.0234822 | ||||||||
\(266\) | −1.83353 | + | 1.33214i | −0.112421 | + | 0.0816787i | ||||
\(267\) | 1.51288 | + | 4.65618i | 0.0925870 | + | 0.284954i | ||||
\(268\) | −0.548341 | + | 1.68762i | −0.0334953 | + | 0.103088i | ||||
\(269\) | 5.05406 | + | 3.67199i | 0.308151 | + | 0.223885i | 0.731103 | − | 0.682267i | \(-0.239006\pi\) |
−0.422951 | + | 0.906152i | \(0.639006\pi\) | |||||||
\(270\) | 0.485967 | + | 0.353076i | 0.0295750 | + | 0.0214875i | ||||
\(271\) | 2.43100 | − | 7.48184i | 0.147673 | − | 0.454490i | −0.849672 | − | 0.527311i | \(-0.823200\pi\) |
0.997345 | + | 0.0728213i | \(0.0232003\pi\) | |||||||
\(272\) | −0.989208 | − | 3.04447i | −0.0599796 | − | 0.184598i | ||||
\(273\) | 3.26477 | − | 2.37200i | 0.197593 | − | 0.143560i | ||||
\(274\) | −1.94312 | −0.117388 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.36190 | 0.202363 | ||||||||
\(277\) | −9.74675 | + | 7.08143i | −0.585626 | + | 0.425482i | −0.840748 | − | 0.541427i | \(-0.817884\pi\) |
0.255122 | + | 0.966909i | \(0.417884\pi\) | |||||||
\(278\) | 1.14424 | + | 3.52161i | 0.0686271 | + | 0.211212i | ||||
\(279\) | 5.57379 | − | 17.1544i | 0.333694 | − | 1.02700i | ||||
\(280\) | −0.475243 | − | 0.345285i | −0.0284012 | − | 0.0206347i | ||||
\(281\) | −17.1147 | − | 12.4345i | −1.02098 | − | 0.741783i | −0.0544937 | − | 0.998514i | \(-0.517354\pi\) |
−0.966483 | + | 0.256731i | \(0.917354\pi\) | |||||||
\(282\) | −0.897679 | + | 2.76277i | −0.0534560 | + | 0.164521i | ||||
\(283\) | −7.72646 | − | 23.7796i | −0.459291 | − | 1.41355i | −0.866023 | − | 0.500004i | \(-0.833332\pi\) |
0.406733 | − | 0.913547i | \(-0.366668\pi\) | |||||||
\(284\) | −10.5101 | + | 7.63600i | −0.623657 | + | 0.453113i | ||||
\(285\) | −0.400878 | −0.0237460 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.33811 | −0.0789861 | ||||||||
\(288\) | −12.3992 | + | 9.00854i | −0.730629 | + | 0.530833i | ||||
\(289\) | 0.552793 | + | 1.70132i | 0.0325172 | + | 0.100078i | ||||
\(290\) | −0.201760 | + | 0.620954i | −0.0118478 | + | 0.0364637i | ||||
\(291\) | 4.52696 | + | 3.28903i | 0.265375 | + | 0.192806i | ||||
\(292\) | 6.31010 | + | 4.58455i | 0.369271 | + | 0.268291i | ||||
\(293\) | −0.140630 | + | 0.432814i | −0.00821568 | + | 0.0252852i | −0.955080 | − | 0.296347i | \(-0.904231\pi\) |
0.946865 | + | 0.321632i | \(0.104231\pi\) | |||||||
\(294\) | −0.148486 | − | 0.456994i | −0.00865990 | − | 0.0266524i | ||||
\(295\) | −1.71613 | + | 1.24684i | −0.0999169 | + | 0.0725939i | ||||
\(296\) | −14.9251 | −0.867502 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.62110 | 0.325621 | ||||||||
\(299\) | 20.5910 | − | 14.9602i | 1.19081 | − | 0.865173i | ||||
\(300\) | 1.31941 | + | 4.06071i | 0.0761759 | + | 0.234445i | ||||
\(301\) | 1.45492 | − | 4.47777i | 0.0838599 | − | 0.258094i | ||||
\(302\) | 5.11984 | + | 3.71978i | 0.294614 | + | 0.214050i | ||||
\(303\) | 9.60508 | + | 6.97850i | 0.551798 | + | 0.400904i | ||||
\(304\) | 0.665238 | − | 2.04739i | 0.0381540 | − | 0.117426i | ||||
\(305\) | 0.662130 | + | 2.03783i | 0.0379135 | + | 0.116686i | ||||
\(306\) | 7.13797 | − | 5.18604i | 0.408051 | − | 0.296466i | ||||
\(307\) | −8.03578 | −0.458626 | −0.229313 | − | 0.973353i | \(-0.573648\pi\) | ||||
−0.229313 | + | 0.973353i | \(0.573648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0358 | 0.570918 | ||||||||
\(310\) | 0.964279 | − | 0.700590i | 0.0547674 | − | 0.0397908i | ||||
\(311\) | 0.0423244 | + | 0.130261i | 0.00240000 | + | 0.00738644i | 0.952249 | − | 0.305321i | \(-0.0987639\pi\) |
−0.949849 | + | 0.312708i | \(0.898764\pi\) | |||||||
\(312\) | 3.29212 | − | 10.1321i | 0.186379 | − | 0.573617i | ||||
\(313\) | 12.3698 | + | 8.98720i | 0.699183 | + | 0.507986i | 0.879666 | − | 0.475592i | \(-0.157766\pi\) |
−0.180483 | + | 0.983578i | \(0.557766\pi\) | |||||||
\(314\) | 12.6752 | + | 9.20907i | 0.715303 | + | 0.519698i | ||||
\(315\) | −0.180019 | + | 0.554042i | −0.0101429 | + | 0.0312167i | ||||
\(316\) | 1.95332 | + | 6.01169i | 0.109883 | + | 0.338184i | ||||
\(317\) | 26.6915 | − | 19.3925i | 1.49914 | − | 1.08919i | 0.528424 | − | 0.848980i | \(-0.322783\pi\) |
0.970720 | − | 0.240212i | \(-0.0772170\pi\) | |||||||
\(318\) | 0.825478 | 0.0462905 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.684115 | −0.0382432 | ||||||||
\(321\) | 2.69668 | − | 1.95925i | 0.150514 | − | 0.109355i | ||||
\(322\) | −0.936507 | − | 2.88227i | −0.0521895 | − | 0.160623i | ||||
\(323\) | −3.90456 | + | 12.0170i | −0.217256 | + | 0.668644i | ||||
\(324\) | 6.44455 | + | 4.68224i | 0.358031 | + | 0.260124i | ||||
\(325\) | 26.1510 | + | 18.9998i | 1.45060 | + | 1.05392i | ||||
\(326\) | −1.78618 | + | 5.49730i | −0.0989274 | + | 0.304467i | ||||
\(327\) | 1.03112 | + | 3.17346i | 0.0570211 | + | 0.175493i | ||||
\(328\) | −2.85790 | + | 2.07639i | −0.157801 | + | 0.114649i | ||||
\(329\) | −6.04554 | −0.333301 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5335 | 1.62331 | 0.811653 | − | 0.584140i | \(-0.198568\pi\) | ||||
0.811653 | + | 0.584140i | \(0.198568\pi\) | |||||||
\(332\) | 12.7393 | − | 9.25568i | 0.699163 | − | 0.507971i | ||||
\(333\) | 4.57379 | + | 14.0767i | 0.250642 | + | 0.771397i | ||||
\(334\) | 0.531236 | − | 1.63497i | 0.0290679 | − | 0.0894619i | ||||
\(335\) | 0.228903 | + | 0.166308i | 0.0125063 | + | 0.00908636i | ||||
\(336\) | 0.369254 | + | 0.268279i | 0.0201444 | + | 0.0146358i | ||||
\(337\) | 1.73984 | − | 5.35469i | 0.0947753 | − | 0.291688i | −0.892420 | − | 0.451206i | \(-0.850994\pi\) |
0.987195 | + | 0.159518i | \(0.0509939\pi\) | |||||||
\(338\) | −7.11997 | − | 21.9130i | −0.387275 | − | 1.19191i | ||||
\(339\) | 8.24811 | − | 5.99260i | 0.447976 | − | 0.325474i | ||||
\(340\) | −1.34600 | −0.0729974 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.93344 | 0.320844 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | −3.84092 | − | 11.8211i | −0.207089 | − | 0.637353i | ||||
\(345\) | 0.165650 | − | 0.509820i | 0.00891832 | − | 0.0274478i | ||||
\(346\) | −6.51780 | − | 4.73546i | −0.350399 | − | 0.254580i | ||||
\(347\) | −7.06321 | − | 5.13173i | −0.379173 | − | 0.275485i | 0.381831 | − | 0.924232i | \(-0.375294\pi\) |
−0.761005 | + | 0.648747i | \(0.775294\pi\) | |||||||
\(348\) | 1.00584 | − | 3.09567i | 0.0539189 | − | 0.165945i | ||||
\(349\) | 5.70660 | + | 17.5631i | 0.305468 | + | 0.940132i | 0.979502 | + | 0.201433i | \(0.0645598\pi\) |
−0.674035 | + | 0.738700i | \(0.735440\pi\) | |||||||
\(350\) | 3.11385 | − | 2.26234i | 0.166442 | − | 0.120927i | ||||
\(351\) | −22.6715 | −1.21011 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.4857 | −1.25002 | −0.625009 | − | 0.780618i | \(-0.714905\pi\) | ||||
−0.625009 | + | 0.780618i | \(0.714905\pi\) | |||||||
\(354\) | −3.70589 | + | 2.69249i | −0.196966 | + | 0.143104i | ||||
\(355\) | 0.640111 | + | 1.97006i | 0.0339735 | + | 0.104560i | ||||
\(356\) | −3.41609 | + | 10.5136i | −0.181052 | + | 0.557222i | ||||
\(357\) | −2.16731 | − | 1.57464i | −0.114706 | − | 0.0833388i | ||||
\(358\) | −14.7245 | − | 10.6980i | −0.778213 | − | 0.565405i | ||||
\(359\) | 4.59855 | − | 14.1529i | 0.242702 | − | 0.746960i | −0.753304 | − | 0.657673i | \(-0.771541\pi\) |
0.996006 | − | 0.0892873i | \(-0.0284589\pi\) | |||||||
\(360\) | 0.475243 | + | 1.46265i | 0.0250475 | + | 0.0770884i | ||||
\(361\) | 8.49689 | − | 6.17335i | 0.447205 | − | 0.324913i | ||||
\(362\) | 10.6641 | 0.560490 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.11210 | 0.477604 | ||||||||
\(365\) | 1.00615 | − | 0.731008i | 0.0526641 | − | 0.0382627i | ||||
\(366\) | 1.42984 | + | 4.40059i | 0.0747388 | + | 0.230022i | ||||
\(367\) | −10.5764 | + | 32.5508i | −0.552083 | + | 1.69914i | 0.151441 | + | 0.988466i | \(0.451609\pi\) |
−0.703524 | + | 0.710671i | \(0.748391\pi\) | |||||||
\(368\) | 2.32889 | + | 1.69204i | 0.121402 | + | 0.0882037i | ||||
\(369\) | 2.83416 | + | 2.05914i | 0.147541 | + | 0.107195i | ||||
\(370\) | −0.302241 | + | 0.930202i | −0.0157128 | + | 0.0483589i | ||||
\(371\) | 0.530865 | + | 1.63383i | 0.0275611 | + | 0.0848245i | ||||
\(372\) | −4.80727 | + | 3.49269i | −0.249245 | + | 0.181087i | ||||
\(373\) | 3.01739 | 0.156235 | 0.0781173 | − | 0.996944i | \(-0.475109\pi\) | ||||
0.0781173 | + | 0.996944i | \(0.475109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.36841 | 0.0706646 | ||||||||
\(376\) | −12.9119 | + | 9.38104i | −0.665880 | + | 0.483790i | ||||
\(377\) | −7.61493 | − | 23.4363i | −0.392189 | − | 1.20703i | ||||
\(378\) | −0.834201 | + | 2.56741i | −0.0429067 | + | 0.132053i | ||||
\(379\) | 4.95467 | + | 3.59978i | 0.254505 | + | 0.184908i | 0.707721 | − | 0.706492i | \(-0.249723\pi\) |
−0.453216 | + | 0.891401i | \(0.649723\pi\) | |||||||
\(380\) | −0.732307 | − | 0.532053i | −0.0375666 | − | 0.0272937i | ||||
\(381\) | 0.381447 | − | 1.17397i | 0.0195421 | − | 0.0601444i | ||||
\(382\) | 2.88906 | + | 8.89162i | 0.147817 | + | 0.454935i | ||||
\(383\) | −3.55238 | + | 2.58096i | −0.181518 | + | 0.131881i | −0.674834 | − | 0.737970i | \(-0.735785\pi\) |
0.493316 | + | 0.869850i | \(0.335785\pi\) | |||||||
\(384\) | 5.75876 | 0.293875 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.3495 | −0.628573 | ||||||||
\(387\) | −9.97214 | + | 7.24518i | −0.506912 | + | 0.368293i | ||||
\(388\) | 3.90440 | + | 12.0165i | 0.198216 | + | 0.610046i | ||||
\(389\) | 3.24344 | − | 9.98229i | 0.164449 | − | 0.506122i | −0.834546 | − | 0.550938i | \(-0.814270\pi\) |
0.998995 | + | 0.0448157i | \(0.0142701\pi\) | |||||||
\(390\) | −0.564814 | − | 0.410361i | −0.0286005 | − | 0.0207794i | ||||
\(391\) | −13.6693 | − | 9.93130i | −0.691284 | − | 0.502248i | ||||
\(392\) | 0.815793 | − | 2.51075i | 0.0412038 | − | 0.126812i | ||||
\(393\) | 0.261665 | + | 0.805321i | 0.0131992 | + | 0.0406231i | ||||
\(394\) | 7.73890 | − | 5.62264i | 0.389880 | − | 0.283264i | ||||
\(395\) | 1.00789 | 0.0507127 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3888 | 0.571589 | 0.285794 | − | 0.958291i | \(-0.407743\pi\) | ||||
0.285794 | + | 0.958291i | \(0.407743\pi\) | |||||||
\(398\) | 9.59945 | − | 6.97441i | 0.481177 | − | 0.349595i | ||||
\(399\) | −0.556717 | − | 1.71340i | −0.0278707 | − | 0.0857772i | ||||
\(400\) | −1.12976 | + | 3.47704i | −0.0564879 | + | 0.173852i | ||||
\(401\) | 3.82257 | + | 2.77726i | 0.190890 | + | 0.138690i | 0.679125 | − | 0.734022i | \(-0.262359\pi\) |
−0.488235 | + | 0.872712i | \(0.662359\pi\) | |||||||
\(402\) | 0.494304 | + | 0.359133i | 0.0246537 | + | 0.0179119i | ||||
\(403\) | −13.9014 | + | 42.7841i | −0.692477 | + | 2.13123i | ||||
\(404\) | 8.28417 | + | 25.4960i | 0.412153 | + | 1.26848i | ||||
\(405\) | 1.02759 | − | 0.746584i | 0.0510611 | − | 0.0370981i | ||||
\(406\) | −2.93422 | −0.145623 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.07230 | −0.350131 | ||||||||
\(409\) | −1.99458 | + | 1.44915i | −0.0986258 | + | 0.0716558i | −0.636005 | − | 0.771685i | \(-0.719414\pi\) |
0.537379 | + | 0.843341i | \(0.319414\pi\) | |||||||
\(410\) | 0.0715363 | + | 0.220166i | 0.00353293 | + | 0.0108732i | ||||
\(411\) | 0.477312 | − | 1.46902i | 0.0235441 | − | 0.0724612i | ||||
\(412\) | 18.3330 | + | 13.3197i | 0.903203 | + | 0.656215i | ||||
\(413\) | −7.71239 | − | 5.60338i | −0.379502 | − | 0.275724i | ||||
\(414\) | −2.45181 | + | 7.54589i | −0.120500 | + | 0.370860i | ||||
\(415\) | −0.775885 | − | 2.38793i | −0.0380867 | − | 0.117219i | ||||
\(416\) | 30.9244 | − | 22.4679i | 1.51619 | − | 1.10158i | ||||
\(417\) | −2.94345 | −0.144141 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.3399 | −0.700548 | −0.350274 | − | 0.936647i | \(-0.613912\pi\) | ||||
−0.350274 | + | 0.936647i | \(0.613912\pi\) | |||||||
\(420\) | 0.155262 | − | 0.112805i | 0.00757603 | − | 0.00550431i | ||||
\(421\) | −5.35086 | − | 16.4683i | −0.260785 | − | 0.802614i | −0.992635 | − | 0.121147i | \(-0.961343\pi\) |
0.731850 | − | 0.681466i | \(-0.238657\pi\) | |||||||
\(422\) | −2.14631 | + | 6.60567i | −0.104481 | + | 0.321559i | ||||
\(423\) | 12.8047 | + | 9.30312i | 0.622583 | + | 0.452333i | ||||
\(424\) | 3.66908 | + | 2.66574i | 0.178186 | + | 0.129460i | ||||
\(425\) | 6.63102 | − | 20.4082i | 0.321652 | − | 0.989943i | ||||
\(426\) | 1.38229 | + | 4.25424i | 0.0669720 | + | 0.206119i | ||||
\(427\) | −7.79037 | + | 5.66003i | −0.377002 | + | 0.273908i | ||||
\(428\) | 7.52653 | 0.363808 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.814531 | −0.0392802 | ||||||||
\(431\) | −22.5653 | + | 16.3947i | −1.08693 | + | 0.789704i | −0.978879 | − | 0.204441i | \(-0.934462\pi\) |
−0.108055 | + | 0.994145i | \(0.534462\pi\) | |||||||
\(432\) | −0.792381 | − | 2.43870i | −0.0381235 | − | 0.117332i | ||||
\(433\) | −9.13053 | + | 28.1009i | −0.438785 | + | 1.35044i | 0.450372 | + | 0.892841i | \(0.351291\pi\) |
−0.889158 | + | 0.457601i | \(0.848709\pi\) | |||||||
\(434\) | 4.33353 | + | 3.14850i | 0.208016 | + | 0.151133i | ||||
\(435\) | −0.419886 | − | 0.305065i | −0.0201320 | − | 0.0146267i | ||||
\(436\) | −2.32826 | + | 7.16566i | −0.111504 | + | 0.343173i | ||||
\(437\) | −3.51123 | − | 10.8064i | −0.167965 | − | 0.516943i | ||||
\(438\) | 2.17272 | − | 1.57858i | 0.103817 | − | 0.0754273i | ||||
\(439\) | −33.6655 | −1.60677 | −0.803384 | − | 0.595461i | \(-0.796970\pi\) | ||||
−0.803384 | + | 0.595461i | \(0.796970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | −17.8026 | + | 12.9343i | −0.846782 | + | 0.615223i | ||||
\(443\) | 3.19113 | + | 9.82129i | 0.151615 | + | 0.466624i | 0.997802 | − | 0.0662624i | \(-0.0211074\pi\) |
−0.846187 | + | 0.532886i | \(0.821107\pi\) | |||||||
\(444\) | 1.50678 | − | 4.63738i | 0.0715084 | − | 0.220080i | ||||
\(445\) | 1.42603 | + | 1.03607i | 0.0676004 | + | 0.0491146i | ||||
\(446\) | 0.449887 | + | 0.326862i | 0.0213028 | + | 0.0154774i | ||||
\(447\) | −1.38078 | + | 4.24960i | −0.0653086 | + | 0.200999i | ||||
\(448\) | −0.950059 | − | 2.92398i | −0.0448861 | − | 0.138145i | ||||
\(449\) | 2.23115 | − | 1.62103i | 0.105294 | − | 0.0765009i | −0.533892 | − | 0.845553i | \(-0.679271\pi\) |
0.639187 | + | 0.769052i | \(0.279271\pi\) | |||||||
\(450\) | −10.0766 | −0.475016 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 23.0208 | 1.08281 | ||||||||
\(453\) | −4.06984 | + | 2.95691i | −0.191218 | + | 0.138928i | ||||
\(454\) | 1.27855 | + | 3.93497i | 0.0600053 | + | 0.184677i | ||||
\(455\) | 0.448979 | − | 1.38182i | 0.0210485 | − | 0.0647805i | ||||
\(456\) | −3.84775 | − | 2.79556i | −0.180188 | − | 0.130914i | ||||
\(457\) | 32.6281 | + | 23.7057i | 1.52628 | + | 1.10890i | 0.958264 | + | 0.285884i | \(0.0922874\pi\) |
0.568012 | + | 0.823020i | \(0.307713\pi\) | |||||||
\(458\) | 1.58769 | − | 4.88640i | 0.0741878 | − | 0.228327i | ||||
\(459\) | 4.65082 | + | 14.3138i | 0.217082 | + | 0.668109i | ||||
\(460\) | 0.979244 | − | 0.711463i | 0.0456575 | − | 0.0331721i | ||||
\(461\) | −34.2251 | −1.59402 | −0.797011 | − | 0.603965i | \(-0.793587\pi\) | ||||
−0.797011 | + | 0.603965i | \(0.793587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.707349 | 0.0328733 | 0.0164367 | − | 0.999865i | \(-0.494768\pi\) | ||||
0.0164367 | + | 0.999865i | \(0.494768\pi\) | |||||||
\(464\) | 2.25483 | − | 1.63823i | 0.104678 | − | 0.0760528i | ||||
\(465\) | 0.292785 | + | 0.901099i | 0.0135776 | + | 0.0417874i | ||||
\(466\) | 2.29616 | − | 7.06684i | 0.106367 | − | 0.327365i | ||||
\(467\) | 23.1318 | + | 16.8062i | 1.07041 | + | 0.777698i | 0.975986 | − | 0.217834i | \(-0.0698990\pi\) |
0.0944242 | + | 0.995532i | \(0.469899\pi\) | |||||||
\(468\) | −19.2997 | − | 14.0221i | −0.892130 | − | 0.648171i | ||||
\(469\) | −0.392930 | + | 1.20931i | −0.0181438 | + | 0.0558409i | ||||
\(470\) | 0.323199 | + | 0.994703i | 0.0149080 | + | 0.0458822i | ||||
\(471\) | −10.0757 | + | 7.32043i | −0.464264 | + | 0.337308i | ||||
\(472\) | −25.1669 | −1.15840 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.17650 | 0.0999699 | ||||||||
\(475\) | 11.6747 | − | 8.48215i | 0.535671 | − | 0.389188i | ||||
\(476\) | −1.86925 | − | 5.75297i | −0.0856771 | − | 0.263687i | ||||
\(477\) | 1.38982 | − | 4.27743i | 0.0636356 | − | 0.195850i | ||||
\(478\) | 16.8865 | + | 12.2687i | 0.772369 | + | 0.561159i | ||||
\(479\) | 4.12369 | + | 2.99604i | 0.188416 | + | 0.136892i | 0.677995 | − | 0.735067i | \(-0.262849\pi\) |
−0.489578 | + | 0.871959i | \(0.662849\pi\) | |||||||
\(480\) | 0.248780 | − | 0.765667i | 0.0113552 | − | 0.0349477i | ||||
\(481\) | −11.4073 | − | 35.1081i | −0.520129 | − | 1.60079i | ||||
\(482\) | 11.8669 | − | 8.62179i | 0.540521 | − | 0.392712i | ||||
\(483\) | 2.40907 | 0.109617 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.01464 | 0.0914800 | ||||||||
\(486\) | 8.77092 | − | 6.37245i | 0.397857 | − | 0.289060i | ||||
\(487\) | 9.01968 | + | 27.7597i | 0.408720 | + | 1.25791i | 0.917748 | + | 0.397162i | \(0.130005\pi\) |
−0.509028 | + | 0.860750i | \(0.669995\pi\) | |||||||
\(488\) | −7.85562 | + | 24.1771i | −0.355607 | + | 1.09445i | ||||
\(489\) | −3.71725 | − | 2.70074i | −0.168100 | − | 0.122132i | ||||
\(490\) | −0.139962 | − | 0.101688i | −0.00632284 | − | 0.00459381i | ||||
\(491\) | 9.31499 | − | 28.6686i | 0.420380 | − | 1.29380i | −0.486970 | − | 0.873419i | \(-0.661898\pi\) |
0.907350 | − | 0.420377i | \(-0.138102\pi\) | |||||||
\(492\) | −0.356633 | − | 1.09760i | −0.0160783 | − | 0.0494839i | ||||
\(493\) | −13.2345 | + | 9.61545i | −0.596053 | + | 0.433058i | ||||
\(494\) | −14.7984 | −0.665810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.08801 | −0.228458 | ||||||||
\(497\) | −7.53129 | + | 5.47180i | −0.337825 | + | 0.245444i | ||||
\(498\) | −1.67548 | − | 5.15661i | −0.0750802 | − | 0.231073i | ||||
\(499\) | 1.83897 | − | 5.65978i | 0.0823238 | − | 0.253367i | −0.901420 | − | 0.432947i | \(-0.857474\pi\) |
0.983743 | + | 0.179580i | \(0.0574739\pi\) | |||||||
\(500\) | 2.49976 | + | 1.81618i | 0.111793 | + | 0.0812221i | ||||
\(501\) | 1.10556 | + | 0.803238i | 0.0493929 | + | 0.0358860i | ||||
\(502\) | −7.05707 | + | 21.7194i | −0.314973 | + | 0.969386i | ||||
\(503\) | −1.53846 | − | 4.73489i | −0.0685964 | − | 0.211118i | 0.910882 | − | 0.412667i | \(-0.135403\pi\) |
−0.979479 | + | 0.201549i | \(0.935403\pi\) | |||||||
\(504\) | −5.59153 | + | 4.06248i | −0.249067 | + | 0.180957i | ||||
\(505\) | 4.27456 | 0.190216 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.3154 | 0.813416 | ||||||||
\(508\) | 2.25493 | − | 1.63830i | 0.100046 | − | 0.0726878i | ||||
\(509\) | −6.59088 | − | 20.2846i | −0.292135 | − | 0.899100i | −0.984169 | − | 0.177235i | \(-0.943285\pi\) |
0.692033 | − | 0.721866i | \(-0.256715\pi\) | |||||||
\(510\) | −0.143218 | + | 0.440780i | −0.00634180 | + | 0.0195180i | ||||
\(511\) | 4.52169 | + | 3.28520i | 0.200028 | + | 0.145329i | ||||
\(512\) | 6.65219 | + | 4.83310i | 0.293988 | + | 0.213595i | ||||
\(513\) | −3.12765 | + | 9.62593i | −0.138089 | + | 0.424995i | ||||
\(514\) | 4.06426 | + | 12.5085i | 0.179267 | + | 0.551727i | ||||
\(515\) | 2.92320 | − | 2.12383i | 0.128812 | − | 0.0935872i | ||||
\(516\) | 4.06072 | 0.178763 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.39552 | −0.193128 | ||||||||
\(519\) | 5.18110 | − | 3.76429i | 0.227425 | − | 0.165234i | ||||
\(520\) | −1.18529 | − | 3.64794i | −0.0519783 | − | 0.159973i | ||||
\(521\) | −6.84113 | + | 21.0548i | −0.299715 | + | 0.922428i | 0.681882 | + | 0.731463i | \(0.261162\pi\) |
−0.981597 | + | 0.190966i | \(0.938838\pi\) | |||||||
\(522\) | 6.21477 | + | 4.51529i | 0.272013 | + | 0.197629i | ||||
\(523\) | −3.97346 | − | 2.88689i | −0.173747 | − | 0.126235i | 0.497513 | − | 0.867456i | \(-0.334247\pi\) |
−0.671260 | + | 0.741222i | \(0.734247\pi\) | |||||||
\(524\) | −0.590838 | + | 1.81841i | −0.0258109 | + | 0.0794377i | ||||
\(525\) | 0.945459 | + | 2.90982i | 0.0412632 | + | 0.126995i | ||||
\(526\) | −5.14542 | + | 3.73836i | −0.224351 | + | 0.163000i | ||||
\(527\) | 29.8637 | 1.30088 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.80592 | −0.339388 | ||||||||
\(530\) | 0.240443 | − | 0.174692i | 0.0104442 | − | 0.00758813i | ||||
\(531\) | 7.71239 | + | 23.7363i | 0.334689 | + | 1.03007i | ||||
\(532\) | 1.25706 | − | 3.86885i | 0.0545006 | − | 0.167736i | ||||
\(533\) | −7.06858 | − | 5.13563i | −0.306174 | − | 0.222449i | ||||
\(534\) | 3.07945 | + | 2.23735i | 0.133261 | + | 0.0968195i | ||||
\(535\) | 0.370853 | − | 1.14137i | 0.0160334 | − | 0.0493457i | ||||
\(536\) | 1.03732 | + | 3.19254i | 0.0448054 | + | 0.137897i | ||||
\(537\) | 11.7047 | − | 8.50397i | 0.505095 | − | 0.366973i | ||||
\(538\) | 4.85707 | 0.209403 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.07818 | −0.0463977 | ||||||||
\(541\) | −15.6824 | + | 11.3939i | −0.674238 | + | 0.489862i | −0.871441 | − | 0.490500i | \(-0.836814\pi\) |
0.197203 | + | 0.980363i | \(0.436814\pi\) | |||||||
\(542\) | −1.89006 | − | 5.81702i | −0.0811852 | − | 0.249862i | ||||
\(543\) | −2.61954 | + | 8.06212i | −0.112415 | + | 0.345979i | ||||
\(544\) | −20.5290 | − | 14.9152i | −0.880175 | − | 0.639484i | ||||
\(545\) | 0.971925 | + | 0.706145i | 0.0416327 | + | 0.0302479i | ||||
\(546\) | 0.969548 | − | 2.98396i | 0.0414928 | − | 0.127702i | ||||
\(547\) | 4.46532 | + | 13.7428i | 0.190923 | + | 0.587601i | 1.00000 | 0.000101747i | \(-3.23870e-5\pi\) | |
−0.809077 | + | 0.587703i | \(0.800032\pi\) | |||||||
\(548\) | 2.82164 | − | 2.05004i | 0.120534 | − | 0.0875733i | ||||
\(549\) | 25.2102 | 1.07594 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.0012 | −0.468667 | ||||||||
\(552\) | 5.14523 | − | 3.73823i | 0.218996 | − | 0.159110i | ||||
\(553\) | 1.39971 | + | 4.30785i | 0.0595216 | + | 0.183189i | ||||
\(554\) | −2.89452 | + | 8.90841i | −0.122976 | + | 0.378482i | ||||
\(555\) | −0.628998 | − | 0.456994i | −0.0266995 | − | 0.0193983i | ||||
\(556\) | −5.37696 | − | 3.90659i | −0.228034 | − | 0.165676i | ||||
\(557\) | 5.70780 | − | 17.5668i | 0.241847 | − | 0.744329i | −0.754292 | − | 0.656539i | \(-0.772020\pi\) |
0.996139 | − | 0.0877900i | \(-0.0279804\pi\) | |||||||
\(558\) | −4.33353 | − | 13.3372i | −0.183453 | − | 0.564611i | ||||
\(559\) | 24.8711 | − | 18.0699i | 1.05194 | − | 0.764277i | ||||
\(560\) | 0.164330 | 0.00694419 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.4476 | −0.693801 | ||||||||
\(563\) | −25.3092 | + | 18.3882i | −1.06665 | + | 0.774969i | −0.975308 | − | 0.220850i | \(-0.929117\pi\) |
−0.0913461 | + | 0.995819i | \(0.529117\pi\) | |||||||
\(564\) | −1.61126 | − | 4.95894i | −0.0678462 | − | 0.208809i | ||||
\(565\) | 1.13430 | − | 3.49101i | 0.0477203 | − | 0.146868i | ||||
\(566\) | −15.7271 | − | 11.4264i | −0.661058 | − | 0.480287i | ||||
\(567\) | 4.61803 | + | 3.35520i | 0.193939 | + | 0.140905i | ||||
\(568\) | −7.59437 | + | 23.3731i | −0.318653 | + | 0.980712i | ||||
\(569\) | 0.536469 | + | 1.65108i | 0.0224899 | + | 0.0692169i | 0.961672 | − | 0.274204i | \(-0.0884143\pi\) |
−0.939182 | + | 0.343421i | \(0.888414\pi\) | |||||||
\(570\) | −0.252152 | + | 0.183199i | −0.0105615 | + | 0.00767336i | ||||
\(571\) | 12.5309 | 0.524403 | 0.262201 | − | 0.965013i | \(-0.415551\pi\) | ||||
0.262201 | + | 0.965013i | \(0.415551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.43182 | −0.310469 | ||||||||
\(574\) | −0.841669 | + | 0.611508i | −0.0351306 | + | 0.0255238i | ||||
\(575\) | 5.96304 | + | 18.3523i | 0.248676 | + | 0.765345i | ||||
\(576\) | −2.48729 | + | 7.65508i | −0.103637 | + | 0.318962i | ||||
\(577\) | −16.3337 | − | 11.8672i | −0.679983 | − | 0.494036i | 0.193369 | − | 0.981126i | \(-0.438058\pi\) |
−0.873352 | + | 0.487090i | \(0.838058\pi\) | |||||||
\(578\) | 1.12520 | + | 0.817505i | 0.0468021 | + | 0.0340037i | ||||
\(579\) | 3.03356 | − | 9.33634i | 0.126070 | − | 0.388005i | ||||
\(580\) | −0.362142 | − | 1.11456i | −0.0150371 | − | 0.0462795i | ||||
\(581\) | 9.12876 | − | 6.63243i | 0.378725 | − | 0.275160i | ||||
\(582\) | 4.35051 | 0.180334 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.7550 | 0.610568 | ||||||||
\(585\) | −3.07735 | + | 2.23582i | −0.127233 | + | 0.0924399i | ||||
\(586\) | 0.109337 | + | 0.336506i | 0.00451669 | + | 0.0139009i | ||||
\(587\) | −0.00258825 | + | 0.00796580i | −0.000106828 | + | 0.000328784i | −0.951110 | − | 0.308853i | \(-0.900055\pi\) |
0.951003 | + | 0.309181i | \(0.100055\pi\) | |||||||
\(588\) | 0.697759 | + | 0.506952i | 0.0287751 | + | 0.0209063i | ||||
\(589\) | 16.2476 | + | 11.8046i | 0.669472 | + | 0.486400i | ||||
\(590\) | −0.509643 | + | 1.56852i | −0.0209817 | + | 0.0645750i | ||||
\(591\) | 2.34977 | + | 7.23183i | 0.0966564 | + | 0.297478i | ||||
\(592\) | 3.37778 | − | 2.45410i | 0.138826 | − | 0.100863i | ||||
\(593\) | −0.439298 | −0.0180398 | −0.00901989 | − | 0.999959i | \(-0.502871\pi\) | ||||
−0.00901989 | + | 0.999959i | \(0.502871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.964520 | −0.0395415 | ||||||||
\(596\) | −8.16249 | + | 5.93040i | −0.334349 | + | 0.242918i | ||||
\(597\) | 2.91469 | + | 8.97048i | 0.119290 | + | 0.367137i | ||||
\(598\) | 6.11496 | − | 18.8199i | 0.250060 | − | 0.769604i | ||||
\(599\) | −36.5403 | − | 26.5481i | −1.49300 | − | 1.08473i | −0.973068 | − | 0.230518i | \(-0.925958\pi\) |
−0.519930 | − | 0.854209i | \(-0.674042\pi\) | |||||||
\(600\) | 6.53455 | + | 4.74763i | 0.266772 | + | 0.193821i | ||||
\(601\) | 3.44358 | − | 10.5983i | 0.140467 | − | 0.432312i | −0.855934 | − | 0.517086i | \(-0.827017\pi\) |
0.996400 | + | 0.0847740i | \(0.0270168\pi\) | |||||||
\(602\) | −1.13117 | − | 3.48139i | −0.0461032 | − | 0.141891i | ||||
\(603\) | 2.69318 | − | 1.95671i | 0.109675 | − | 0.0796834i | ||||
\(604\) | −11.3591 | −0.462194 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.23071 | 0.374972 | ||||||||
\(607\) | 28.8817 | − | 20.9838i | 1.17227 | − | 0.851706i | 0.180994 | − | 0.983484i | \(-0.442069\pi\) |
0.991279 | + | 0.131778i | \(0.0420687\pi\) | |||||||
\(608\) | −5.27330 | − | 16.2295i | −0.213860 | − | 0.658195i | ||||
\(609\) | 0.720768 | − | 2.21829i | 0.0292070 | − | 0.0898898i | ||||
\(610\) | 1.34775 | + | 0.979200i | 0.0545689 | + | 0.0396466i | ||||
\(611\) | −31.9356 | − | 23.2026i | −1.29198 | − | 0.938676i | ||||
\(612\) | −4.89377 | + | 15.0615i | −0.197819 | + | 0.608824i | ||||
\(613\) | 5.31447 | + | 16.3563i | 0.214650 | + | 0.660623i | 0.999178 | + | 0.0405309i | \(0.0129049\pi\) |
−0.784529 | + | 0.620092i | \(0.787095\pi\) | |||||||
\(614\) | −5.05449 | + | 3.67230i | −0.203983 | + | 0.148202i | ||||
\(615\) | −0.184020 | −0.00742040 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8852 | −0.679774 | −0.339887 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339887 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(618\) | 6.31251 | − | 4.58631i | 0.253927 | − | 0.184488i | ||||
\(619\) | 9.60092 | + | 29.5486i | 0.385893 | + | 1.18766i | 0.935830 | + | 0.352452i | \(0.114652\pi\) |
−0.549937 | + | 0.835206i | \(0.685348\pi\) | |||||||
\(620\) | −0.661107 | + | 2.03468i | −0.0265507 | + | 0.0817146i | ||||
\(621\) | −10.9494 | − | 7.95523i | −0.439385 | − | 0.319232i | ||||
\(622\) | 0.0861506 | + | 0.0625921i | 0.00345432 | + | 0.00250971i | ||||
\(623\) | −2.44790 | + | 7.53386i | −0.0980730 | + | 0.301838i | ||||
\(624\) | 0.920943 | + | 2.83437i | 0.0368672 | + | 0.113466i | ||||
\(625\) | −19.6266 | + | 14.2595i | −0.785062 | + | 0.570381i | ||||
\(626\) | 11.8877 | 0.475127 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.1217 | −1.12218 | ||||||||
\(629\) | −19.8256 | + | 14.4041i | −0.790499 | + | 0.574331i | ||||
\(630\) | 0.139962 | + | 0.430759i | 0.00557622 | + | 0.0171618i | ||||
\(631\) | 2.24150 | − | 6.89863i | 0.0892327 | − | 0.274630i | −0.896475 | − | 0.443094i | \(-0.853881\pi\) |
0.985708 | + | 0.168464i | \(0.0538807\pi\) | |||||||
\(632\) | 9.67408 | + | 7.02863i | 0.384814 | + | 0.279584i | ||||
\(633\) | −4.46672 | − | 3.24526i | −0.177536 | − | 0.128988i | ||||
\(634\) | 7.92665 | − | 24.3957i | 0.314807 | − | 0.968877i | ||||
\(635\) | −0.137335 | − | 0.422675i | −0.00544999 | − | 0.0167733i | ||||
\(636\) | −1.19869 | + | 0.870900i | −0.0475312 | + | 0.0345334i | ||||
\(637\) | 6.52954 | 0.258710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.3718 | 0.964132 | ||||||||
\(640\) | 1.67739 | − | 1.21870i | 0.0663048 | − | 0.0481732i | ||||
\(641\) | −6.41207 | − | 19.7343i | −0.253262 | − | 0.779459i | −0.994167 | − | 0.107850i | \(-0.965603\pi\) |
0.740906 | − | 0.671609i | \(-0.234397\pi\) | |||||||
\(642\) | 0.800840 | − | 2.46473i | 0.0316066 | − | 0.0972752i | ||||
\(643\) | −5.75314 | − | 4.17990i | −0.226882 | − | 0.164839i | 0.468537 | − | 0.883444i | \(-0.344781\pi\) |
−0.695419 | + | 0.718605i | \(0.744781\pi\) | |||||||
\(644\) | 4.40079 | + | 3.19736i | 0.173415 | + | 0.125994i | ||||
\(645\) | 0.200083 | − | 0.615793i | 0.00787827 | − | 0.0242468i | ||||
\(646\) | 3.03574 | + | 9.34303i | 0.119439 | + | 0.367597i | ||||
\(647\) | −22.3118 | + | 16.2105i | −0.877166 | + | 0.637299i | −0.932500 | − | 0.361169i | \(-0.882378\pi\) |
0.0553338 | + | 0.998468i | \(0.482378\pi\) | |||||||
\(648\) | 15.0694 | 0.591984 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 25.1317 | 0.985748 | ||||||||
\(651\) | −3.44479 | + | 2.50279i | −0.135012 | + | 0.0980920i | ||||
\(652\) | −3.20604 | − | 9.86719i | −0.125558 | − | 0.386429i | ||||
\(653\) | 4.99190 | − | 15.3635i | 0.195348 | − | 0.601220i | −0.804624 | − | 0.593785i | \(-0.797633\pi\) |
0.999972 | − | 0.00743560i | \(-0.00236685\pi\) | |||||||
\(654\) | 2.09882 | + | 1.52489i | 0.0820705 | + | 0.0596277i | ||||
\(655\) | 0.246643 | + | 0.179197i | 0.00963714 | + | 0.00700179i | ||||
\(656\) | 0.305372 | − | 0.939838i | 0.0119228 | − | 0.0366945i | ||||
\(657\) | −4.52169 | − | 13.9163i | −0.176408 | − | 0.542927i | ||||
\(658\) | −3.80263 | + | 2.76277i | −0.148242 | + | 0.107704i | ||||
\(659\) | −13.2085 | −0.514531 | −0.257266 | − | 0.966341i | \(-0.582822\pi\) | ||||
−0.257266 | + | 0.966341i | \(0.582822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.90660 | −0.190845 | −0.0954223 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954223 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(662\) | 18.5765 | − | 13.4966i | 0.721996 | − | 0.524561i | ||||
\(663\) | −5.40540 | − | 16.6361i | −0.209928 | − | 0.646093i | ||||
\(664\) | 9.20522 | − | 28.3307i | 0.357232 | − | 1.09945i | ||||
\(665\) | −0.524757 | − | 0.381258i | −0.0203492 | − | 0.0147846i | ||||
\(666\) | 9.30986 | + | 6.76401i | 0.360750 | + | 0.262100i | ||||
\(667\) | 4.54590 | − | 13.9908i | 0.176018 | − | 0.541728i | ||||
\(668\) | 0.953523 | + | 2.93464i | 0.0368929 | + | 0.113545i | ||||
\(669\) | −0.357622 | + | 0.259828i | −0.0138265 | + | 0.0100455i | ||||
\(670\) | 0.219981 | 0.00849861 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.61803 | 0.139569 | ||||||||
\(673\) | 24.2601 | − | 17.6260i | 0.935159 | − | 0.679433i | −0.0120914 | − | 0.999927i | \(-0.503849\pi\) |
0.947251 | + | 0.320494i | \(0.103849\pi\) | |||||||
\(674\) | −1.35270 | − | 4.16318i | −0.0521041 | − | 0.160360i | ||||
\(675\) | 5.31162 | − | 16.3475i | 0.204444 | − | 0.629215i | ||||
\(676\) | 33.4578 | + | 24.3085i | 1.28684 | + | 0.934943i | ||||
\(677\) | −10.1847 | − | 7.39959i | −0.391428 | − | 0.284389i | 0.374612 | − | 0.927182i | \(-0.377776\pi\) |
−0.766040 | + | 0.642792i | \(0.777776\pi\) | |||||||
\(678\) | 2.44946 | − | 7.53867i | 0.0940711 | − | 0.289521i | ||||
\(679\) | 2.79781 | + | 8.61078i | 0.107370 | + | 0.330451i | ||||
\(680\) | −2.06000 | + | 1.49667i | −0.0789973 | + | 0.0573949i | ||||
\(681\) | −3.28894 | −0.126033 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.5342 | −1.09183 | −0.545916 | − | 0.837840i | \(-0.683818\pi\) | ||||
−0.545916 | + | 0.837840i | \(0.683818\pi\) | |||||||
\(684\) | −8.61605 | + | 6.25992i | −0.329443 | + | 0.239354i | ||||
\(685\) | −0.171851 | − | 0.528902i | −0.00656608 | − | 0.0202083i | ||||
\(686\) | 0.240256 | − | 0.739431i | 0.00917301 | − | 0.0282316i | ||||
\(687\) | 3.30416 | + | 2.40061i | 0.126062 | + | 0.0915891i | ||||
\(688\) | 2.81299 | + | 2.04376i | 0.107244 | + | 0.0779174i | ||||
\(689\) | −3.46631 | + | 10.6682i | −0.132056 | + | 0.406426i | ||||
\(690\) | −0.128791 | − | 0.396377i | −0.00490297 | − | 0.0150898i | ||||
\(691\) | −20.5282 | + | 14.9146i | −0.780929 | + | 0.567378i | −0.905258 | − | 0.424863i | \(-0.860322\pi\) |
0.124329 | + | 0.992241i | \(0.460322\pi\) | |||||||
\(692\) | 14.4606 | 0.549711 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.78791 | −0.257666 | ||||||||
\(695\) | −0.857358 | + | 0.622907i | −0.0325214 | + | 0.0236282i | ||||
\(696\) | −1.90280 | − | 5.85621i | −0.0721254 | − | 0.221979i | ||||
\(697\) | −1.79236 | + | 5.51631i | −0.0678904 | + | 0.208945i | ||||
\(698\) | 11.6157 | + | 8.43929i | 0.439660 | + | 0.319432i | ||||
\(699\) | 4.77856 | + | 3.47183i | 0.180742 | + | 0.131317i | ||||
\(700\) | −2.13484 | + | 6.57037i | −0.0806895 | + | 0.248337i | ||||
\(701\) | −14.1227 | − | 43.4653i | −0.533409 | − | 1.64166i | −0.747063 | − | 0.664753i | \(-0.768537\pi\) |
0.213654 | − | 0.976909i | \(-0.431463\pi\) | |||||||
\(702\) | −14.2603 | + | 10.3607i | −0.538221 | + | 0.391040i | ||||
\(703\) | −16.4800 | −0.621556 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.831396 | −0.0313122 | ||||||||
\(706\) | −14.7725 | + | 10.7328i | −0.555968 | + | 0.403935i | ||||
\(707\) | 5.93627 | + | 18.2700i | 0.223256 | + | 0.687112i | ||||
\(708\) | 2.54075 | − | 7.81962i | 0.0954872 | − | 0.293879i | ||||
\(709\) | −31.1717 | − | 22.6476i | −1.17068 | − | 0.850548i | −0.179589 | − | 0.983742i | \(-0.557477\pi\) |
−0.991090 | + | 0.133193i | \(0.957477\pi\) | |||||||
\(710\) | 1.30293 | + | 0.946636i | 0.0488982 | + | 0.0355266i | ||||
\(711\) | 3.66448 | − | 11.2781i | 0.137429 | − | 0.422962i | ||||
\(712\) | 6.46236 | + | 19.8891i | 0.242187 | + | 0.745375i | ||||
\(713\) | −21.7264 | + | 15.7851i | −0.813660 | + | 0.591159i | ||||
\(714\) | −2.08283 | −0.0779480 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.6683 | 1.22087 | ||||||||
\(717\) | −13.4233 | + | 9.75261i | −0.501303 | + | 0.364218i | ||||
\(718\) | −3.57530 | − | 11.0036i | −0.133429 | − | 0.410652i | ||||
\(719\) | 1.76205 | − | 5.42304i | 0.0657135 | − | 0.202245i | −0.912808 | − | 0.408388i | \(-0.866091\pi\) |
0.978522 | + | 0.206143i | \(0.0660911\pi\) | |||||||
\(720\) | −0.348056 | − | 0.252877i | −0.0129713 | − | 0.00942418i | ||||
\(721\) | 13.1371 | + | 9.54464i | 0.489250 | + | 0.355461i | ||||
\(722\) | 2.52334 | − | 7.76605i | 0.0939091 | − | 0.289023i | ||||
\(723\) | 3.60315 | + | 11.0893i | 0.134002 | + | 0.412417i | ||||
\(724\) | −15.4854 | + | 11.2508i | −0.575512 | + | 0.418134i | ||||
\(725\) | 18.6831 | 0.693872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.8221 | 0.438458 | 0.219229 | − | 0.975673i | \(-0.429646\pi\) | ||||
0.219229 | + | 0.975673i | \(0.429646\pi\) | |||||||
\(728\) | 13.9456 | − | 10.1321i | 0.516859 | − | 0.375520i | ||||
\(729\) | −2.62868 | − | 8.09024i | −0.0973584 | − | 0.299638i | ||||
\(730\) | 0.298798 | − | 0.919606i | 0.0110590 | − | 0.0340361i | ||||
\(731\) | −16.5106 | − | 11.9957i | −0.610667 | − | 0.443676i | ||||
\(732\) | −6.71902 | − | 4.88165i | −0.248342 | − | 0.180431i | ||||
\(733\) | 2.72303 | − | 8.38064i | 0.100578 | − | 0.309546i | −0.888089 | − | 0.459671i | \(-0.847967\pi\) |
0.988667 | + | 0.150125i | \(0.0479675\pi\) | |||||||
\(734\) | 8.22298 | + | 25.3077i | 0.303516 | + | 0.934125i | ||||
\(735\) | 0.111258 | − | 0.0808336i | 0.00410381 | − | 0.00298159i | ||||
\(736\) | 22.8190 | 0.841121 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.72370 | 0.100261 | ||||||||
\(739\) | −0.388983 | + | 0.282612i | −0.0143090 | + | 0.0103961i | −0.594917 | − | 0.803787i | \(-0.702815\pi\) |
0.580608 | + | 0.814183i | \(0.302815\pi\) | |||||||
\(740\) | −0.542497 | − | 1.66963i | −0.0199426 | − | 0.0613769i | ||||
\(741\) | 3.63511 | − | 11.1877i | 0.133539 | − | 0.410991i | ||||
\(742\) | 1.08057 | + | 0.785077i | 0.0396688 | + | 0.0288211i | ||||
\(743\) | −26.8952 | − | 19.5405i | −0.986688 | − | 0.716871i | −0.0274948 | − | 0.999622i | \(-0.508753\pi\) |
−0.959193 | + | 0.282751i | \(0.908753\pi\) | |||||||
\(744\) | −3.47364 | + | 10.6908i | −0.127350 | + | 0.391943i | ||||
\(745\) | 0.497133 | + | 1.53002i | 0.0182135 | + | 0.0560555i | ||||
\(746\) | 1.89793 | − | 1.37893i | 0.0694883 | − | 0.0504862i | ||||
\(747\) | −29.5413 | −1.08086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.39336 | 0.197069 | ||||||||
\(750\) | 0.860729 | − | 0.625357i | 0.0314294 | − | 0.0228348i | ||||
\(751\) | 8.65453 | + | 26.6359i | 0.315808 | + | 0.971958i | 0.975421 | + | 0.220352i | \(0.0707205\pi\) |
−0.659612 | + | 0.751606i | \(0.729280\pi\) | |||||||
\(752\) | 1.37966 | − | 4.24616i | 0.0503110 | − | 0.154841i | ||||
\(753\) | −14.6866 | − | 10.6704i | −0.535209 | − | 0.388852i | ||||
\(754\) | −15.5000 | − | 11.2614i | −0.564478 | − | 0.410117i | ||||
\(755\) | −0.559694 | + | 1.72256i | −0.0203693 | + | 0.0626904i | ||||
\(756\) | −1.49732 | − | 4.60828i | −0.0544570 | − | 0.167601i | ||||
\(757\) | 17.9981 | − | 13.0764i | 0.654151 | − | 0.475269i | −0.210532 | − | 0.977587i | \(-0.567519\pi\) |
0.864683 | + | 0.502318i | \(0.167519\pi\) | |||||||
\(758\) | 4.76156 | 0.172948 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.71237 | −0.0621142 | ||||||||
\(761\) | 39.0152 | − | 28.3462i | 1.41430 | − | 1.02755i | 0.421619 | − | 0.906773i | \(-0.361462\pi\) |
0.992680 | − | 0.120775i | \(-0.0385379\pi\) | |||||||
\(762\) | −0.296569 | − | 0.912745i | −0.0107436 | − | 0.0330653i | ||||
\(763\) | −1.66839 | + | 5.13477i | −0.0603997 | + | 0.185891i | ||||
\(764\) | −13.5761 | − | 9.86364i | −0.491167 | − | 0.356854i | ||||
\(765\) | 2.04289 | + | 1.48424i | 0.0738607 | + | 0.0536629i | ||||
\(766\) | −1.05496 | + | 3.24683i | −0.0381172 | + | 0.117313i | ||||
\(767\) | −19.2352 | − | 59.1999i | −0.694543 | − | 2.13758i | ||||
\(768\) | 6.69670 | − | 4.86544i | 0.241646 | − | 0.175566i | ||||
\(769\) | 43.6883 | 1.57544 | 0.787721 | − | 0.616032i | \(-0.211261\pi\) | ||||
0.787721 | + | 0.616032i | \(0.211261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.4549 | −0.376524 | ||||||||
\(772\) | 17.9329 | − | 13.0290i | 0.645420 | − | 0.468925i | ||||
\(773\) | −0.180951 | − | 0.556910i | −0.00650835 | − | 0.0200306i | 0.947750 | − | 0.319015i | \(-0.103352\pi\) |
−0.954258 | + | 0.298985i | \(0.903352\pi\) | |||||||
\(774\) | −2.96145 | + | 9.11441i | −0.106447 | + | 0.327611i | ||||
\(775\) | −27.5930 | − | 20.0475i | −0.991169 | − | 0.720126i | ||||
\(776\) | 19.3371 | + | 14.0492i | 0.694162 | + | 0.504338i | ||||
\(777\) | 1.07973 | − | 3.32305i | 0.0387349 | − | 0.119214i | ||||
\(778\) | −2.52173 | − | 7.76108i | −0.0904083 | − | 0.278248i | ||||
\(779\) | −3.15565 | + | 2.29271i | −0.113063 | + | 0.0821450i | ||||
\(780\) | 1.25312 | 0.0448688 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −13.1365 | −0.469760 | ||||||||
\(783\) | −10.6012 | + | 7.70222i | −0.378856 | + | 0.275255i | ||||
\(784\) | 0.228211 | + | 0.702362i | 0.00815041 | + | 0.0250844i | ||||
\(785\) | −1.38563 | + | 4.26455i | −0.0494554 | + | 0.152208i | ||||
\(786\) | 0.532613 | + | 0.386966i | 0.0189977 | + | 0.0138026i | ||||
\(787\) | −24.8502 | − | 18.0548i | −0.885815 | − | 0.643582i | 0.0489683 | − | 0.998800i | \(-0.484407\pi\) |
−0.934784 | + | 0.355218i | \(0.884407\pi\) | |||||||
\(788\) | −5.30576 | + | 16.3295i | −0.189010 | + | 0.581713i | ||||
\(789\) | −1.56231 | − | 4.80828i | −0.0556196 | − | 0.171179i | ||||
\(790\) | 0.633964 | − | 0.460602i | 0.0225554 | − | 0.0163875i | ||||
\(791\) | 16.4962 | 0.586538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.8758 | −2.23278 | ||||||||
\(794\) | 7.16355 | − | 5.20462i | 0.254225 | − | 0.184705i | ||||
\(795\) | 0.0730058 | + | 0.224689i | 0.00258925 | + | 0.00796889i | ||||
\(796\) | −6.58135 | + | 20.2553i | −0.233270 | + | 0.717930i | ||||
\(797\) | 8.76431 | + | 6.36765i | 0.310448 | + | 0.225554i | 0.732089 | − | 0.681209i | \(-0.238546\pi\) |
−0.421641 | + | 0.906763i | \(0.638546\pi\) | |||||||
\(798\) | −1.13319 | − | 0.823308i | −0.0401143 | − | 0.0291448i | ||||
\(799\) | −8.09781 | + | 24.9225i | −0.286480 | + | 0.881695i | ||||
\(800\) | 8.95551 | + | 27.5622i | 0.316625 | + | 0.974472i | ||||
\(801\) | 16.7781 | − | 12.1900i | 0.592827 | − | 0.430714i | ||||
\(802\) | 3.67358 | 0.129719 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.09668 | −0.0386770 | ||||||||
\(805\) | 0.701707 | − | 0.509820i | 0.0247319 | − | 0.0179688i | ||||
\(806\) | 10.8081 | + | 33.2639i | 0.380699 | + | 1.17167i | ||||
\(807\) | −1.19310 | + | 3.67199i | −0.0419992 | + | 0.129260i | ||||
\(808\) | 41.0286 | + | 29.8090i | 1.44338 | + | 1.04868i | ||||
\(809\) | 31.2200 | + | 22.6827i | 1.09764 | + | 0.797480i | 0.980673 | − | 0.195656i | \(-0.0626836\pi\) |
0.116964 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(810\) | 0.305165 | − | 0.939200i | 0.0107224 | − | 0.0330001i | ||||
\(811\) | −15.7270 | − | 48.4026i | −0.552248 | − | 1.69964i | −0.703102 | − | 0.711089i | \(-0.748202\pi\) |
0.150854 | − | 0.988556i | \(-0.451798\pi\) | |||||||
\(812\) | 4.26082 | − | 3.09567i | 0.149526 | − | 0.108637i | ||||
\(813\) | 4.86200 | 0.170518 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.65429 | −0.0579473 | ||||||||
\(816\) | 1.60057 | − | 1.16288i | 0.0560312 | − | 0.0407091i | ||||
\(817\) | −4.24109 | − | 13.0527i | −0.148377 | − | 0.456657i | ||||
\(818\) | −0.592336 | + | 1.82302i | −0.0207106 | + | 0.0637405i | ||||
\(819\) | −13.8298 | − | 10.0479i | −0.483252 | − | 0.351103i | ||||
\(820\) | −0.336160 | − | 0.244234i | −0.0117392 | − | 0.00852903i | ||||
\(821\) | −12.4563 | + | 38.3365i | −0.434728 | + | 1.33795i | 0.458637 | + | 0.888623i | \(0.348338\pi\) |
−0.893365 | + | 0.449331i | \(0.851662\pi\) | |||||||
\(822\) | −0.371103 | − | 1.14214i | −0.0129437 | − | 0.0398366i | ||||
\(823\) | −20.7770 | + | 15.0953i | −0.724239 | + | 0.526191i | −0.887736 | − | 0.460353i | \(-0.847723\pi\) |
0.163496 | + | 0.986544i | \(0.447723\pi\) | |||||||
\(824\) | 42.8685 | 1.49340 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.41179 | −0.257889 | ||||||||
\(827\) | 25.8527 | − | 18.7831i | 0.898987 | − | 0.653152i | −0.0392187 | − | 0.999231i | \(-0.512487\pi\) |
0.938206 | + | 0.346078i | \(0.112487\pi\) | |||||||
\(828\) | −4.40079 | − | 13.5442i | −0.152938 | − | 0.470694i | ||||
\(829\) | 14.9565 | − | 46.0313i | 0.519460 | − | 1.59873i | −0.255557 | − | 0.966794i | \(-0.582259\pi\) |
0.775017 | − | 0.631940i | \(-0.217741\pi\) | |||||||
\(830\) | −1.57930 | − | 1.14743i | −0.0548182 | − | 0.0398278i | ||||
\(831\) | −6.02382 | − | 4.37656i | −0.208964 | − | 0.151821i | ||||
\(832\) | 6.20345 | − | 19.0923i | 0.215066 | − | 0.661905i | ||||
\(833\) | −1.33947 | − | 4.12246i | −0.0464099 | − | 0.142835i | ||||
\(834\) | −1.85142 | + | 1.34514i | −0.0641095 | + | 0.0465783i | ||||
\(835\) | 0.492010 | 0.0170267 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.9216 | 0.826850 | ||||||||
\(838\) | −9.01975 | + | 6.55323i | −0.311582 | + | 0.226378i | ||||
\(839\) | −11.6550 | − | 35.8705i | −0.402377 | − | 1.23839i | −0.923066 | − | 0.384642i | \(-0.874325\pi\) |
0.520689 | − | 0.853746i | \(-0.325675\pi\) | |||||||
\(840\) | 0.112190 | − | 0.345285i | 0.00387091 | − | 0.0119134i | ||||
\(841\) | 11.9387 | + | 8.67396i | 0.411679 | + | 0.299102i | ||||
\(842\) | −10.8916 | − | 7.91319i | −0.375348 | − | 0.272707i | ||||
\(843\) | 4.04023 | − | 12.4345i | 0.139153 | − | 0.428269i | ||||
\(844\) | −3.85245 | − | 11.8566i | −0.132607 | − | 0.408121i | ||||
\(845\) | 5.33485 | − | 3.87600i | 0.183525 | − | 0.133338i | ||||
\(846\) | 12.3056 | 0.423074 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.26869 | −0.0435671 | ||||||||
\(849\) | 12.5017 | − | 9.08300i | 0.429057 | − | 0.311728i | ||||
\(850\) | −5.15552 | − | 15.8671i | −0.176833 | − | 0.544235i | ||||
\(851\) | 6.80986 | − | 20.9586i | 0.233439 | − | 0.718451i | ||||
\(852\) | −6.49557 | − | 4.71931i | −0.222535 | − | 0.161681i | ||||
\(853\) | −7.51467 | − | 5.45973i | −0.257297 | − | 0.186938i | 0.451657 | − | 0.892191i | \(-0.350833\pi\) |
−0.708955 | + | 0.705254i | \(0.750833\pi\) | |||||||
\(854\) | −2.31353 | + | 7.12030i | −0.0791672 | + | 0.243652i | ||||
\(855\) | 0.524757 | + | 1.61503i | 0.0179463 | + | 0.0552330i | ||||
\(856\) | 11.5190 | − | 8.36904i | 0.393711 | − | 0.286048i | ||||
\(857\) | −29.7644 | −1.01673 | −0.508365 | − | 0.861141i | \(-0.669750\pi\) | ||||
−0.508365 | + | 0.861141i | \(0.669750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2611 | 1.13485 | 0.567427 | − | 0.823424i | \(-0.307939\pi\) | ||||
0.567427 | + | 0.823424i | \(0.307939\pi\) | |||||||
\(860\) | 1.18279 | − | 0.859350i | 0.0403329 | − | 0.0293036i | ||||
\(861\) | −0.255556 | − | 0.786521i | −0.00870933 | − | 0.0268046i | ||||
\(862\) | −6.70129 | + | 20.6244i | −0.228247 | + | 0.702471i | ||||
\(863\) | 15.0216 | + | 10.9138i | 0.511340 | + | 0.371510i | 0.813332 | − | 0.581800i | \(-0.197652\pi\) |
−0.301992 | + | 0.953311i | \(0.597652\pi\) | |||||||
\(864\) | −16.4443 | − | 11.9475i | −0.559445 | − | 0.406461i | ||||
\(865\) | 0.712517 | − | 2.19290i | 0.0242263 | − | 0.0745609i | ||||
\(866\) | 7.09884 | + | 21.8480i | 0.241229 | + | 0.742425i | ||||
\(867\) | −0.894438 | + | 0.649847i | −0.0303767 | + | 0.0220700i | ||||
\(868\) | −9.61454 | −0.326339 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.403520 | −0.0136806 | ||||||||
\(871\) | −6.71697 | + | 4.88016i | −0.227596 | + | 0.165358i | ||||
\(872\) | 4.40448 | + | 13.5556i | 0.149154 | + | 0.459050i | ||||
\(873\) | 7.32477 | − | 22.5433i | 0.247906 | − | 0.762976i | ||||
\(874\) | −7.14704 | − | 5.19263i | −0.241752 | − | 0.175643i | ||||
\(875\) | 1.79128 | + | 1.30144i | 0.0605562 | + | 0.0439967i | ||||
\(876\) | −1.48961 | + | 4.58455i | −0.0503293 | + | 0.154898i | ||||
\(877\) | −6.95044 | − | 21.3913i | −0.234700 | − | 0.722332i | −0.997161 | − | 0.0752979i | \(-0.976009\pi\) |
0.762461 | − | 0.647034i | \(-0.223991\pi\) | |||||||
\(878\) | −21.1756 | + | 15.3849i | −0.714641 | + | 0.519217i | ||||
\(879\) | −0.281259 | −0.00948664 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.06565 | 0.238048 | 0.119024 | − | 0.992891i | \(-0.462023\pi\) | ||||
0.119024 | + | 0.992891i | \(0.462023\pi\) | |||||||
\(882\) | −1.64674 | + | 1.19643i | −0.0554486 | + | 0.0402857i | ||||
\(883\) | −6.16125 | − | 18.9624i | −0.207342 | − | 0.638134i | −0.999609 | − | 0.0279593i | \(-0.991099\pi\) |
0.792267 | − | 0.610175i | \(-0.208901\pi\) | |||||||
\(884\) | 12.2054 | − | 37.5643i | 0.410511 | − | 1.26342i | ||||
\(885\) | −1.06063 | − | 0.770590i | −0.0356525 | − | 0.0259031i | ||||
\(886\) | 6.49549 | + | 4.71925i | 0.218220 | + | 0.158546i | ||||
\(887\) | 2.14915 | − | 6.61442i | 0.0721615 | − | 0.222090i | −0.908471 | − | 0.417949i | \(-0.862749\pi\) |
0.980632 | + | 0.195858i | \(0.0627492\pi\) | |||||||
\(888\) | −2.85043 | − | 8.77273i | −0.0956543 | − | 0.294394i | ||||
\(889\) | 1.61583 | − | 1.17397i | 0.0541934 | − | 0.0393738i | ||||
\(890\) | 1.37045 | 0.0459376 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.998136 | −0.0334201 | ||||||||
\(893\) | −14.2571 | + | 10.3584i | −0.477097 | + | 0.346631i | ||||
\(894\) | 1.07353 | + | 3.30400i | 0.0359043 | + | 0.110502i | ||||
\(895\) | 1.60966 | − | 4.95402i | 0.0538049 | − | 0.165595i | ||||
\(896\) | 7.53831 | + | 5.47690i | 0.251837 | + | 0.182970i | ||||
\(897\) | 12.7259 | + | 9.24594i | 0.424907 | + | 0.308713i | ||||
\(898\) | 0.662590 | − | 2.03924i | 0.0221109 | − | 0.0680504i | ||||
\(899\) | 8.03481 | + | 24.7286i | 0.267976 | + | 0.824745i | ||||
\(900\) | 14.6324 | − | 10.6311i | 0.487748 | − | 0.354369i | ||||
\(901\) | 7.44650 | 0.248079 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90983 | 0.0968331 | ||||||||
\(904\) | 35.2322 | − | 25.5977i | 1.17181 | − | 0.851367i | ||||
\(905\) | 0.943135 | + | 2.90267i | 0.0313509 | + | 0.0964880i | ||||
\(906\) | −1.20863 | + | 3.71978i | −0.0401541 | + | 0.123582i | ||||
\(907\) | 18.9635 | + | 13.7778i | 0.629672 | + | 0.457483i | 0.856286 | − | 0.516501i | \(-0.172766\pi\) |
−0.226615 | + | 0.973984i | \(0.572766\pi\) | |||||||
\(908\) | −6.00810 | − | 4.36514i | −0.199386 | − | 0.144862i | ||||
\(909\) | 15.5413 | − | 47.8314i | 0.515474 | − | 1.58647i | ||||
\(910\) | −0.349074 | − | 1.07434i | −0.0115717 | − | 0.0356140i | ||||
\(911\) | −37.8698 | + | 27.5140i | −1.25468 | + | 0.911580i | −0.998484 | − | 0.0550445i | \(-0.982470\pi\) |
−0.256198 | + | 0.966624i | \(0.582470\pi\) | |||||||
\(912\) | 1.33048 | 0.0440564 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 31.3563 | 1.03718 | ||||||||
\(915\) | −1.07135 | + | 0.778381i | −0.0354177 | + | 0.0257325i | ||||
\(916\) | 2.84977 | + | 8.77068i | 0.0941589 | + | 0.289791i | ||||
\(917\) | −0.423382 | + | 1.30304i | −0.0139813 | + | 0.0430301i | ||||
\(918\) | 9.46665 | + | 6.87792i | 0.312446 | + | 0.227005i | ||||
\(919\) | −8.59768 | − | 6.24658i | −0.283611 | − | 0.206056i | 0.436880 | − | 0.899520i | \(-0.356084\pi\) |
−0.720491 | + | 0.693464i | \(0.756084\pi\) | |||||||
\(920\) | 0.707584 | − | 2.17772i | 0.0233283 | − | 0.0717973i | ||||
\(921\) | −1.53470 | − | 4.72331i | −0.0505700 | − | 0.155638i | ||||
\(922\) | −21.5275 | + | 15.6407i | −0.708971 | + | 0.515098i | ||||
\(923\) | −60.7848 | −2.00075 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.9876 | 0.920228 | ||||||||
\(926\) | 0.444921 | − | 0.323254i | 0.0146210 | − | 0.0106228i | ||||
\(927\) | −13.1371 | − | 40.4317i | −0.431478 | − | 1.32795i | ||||
\(928\) | 6.82721 | − | 21.0120i | 0.224114 | − | 0.689752i | ||||
\(929\) | 29.6674 | + | 21.5546i | 0.973357 | + | 0.707185i | 0.956214 | − | 0.292668i | \(-0.0945431\pi\) |
0.0171426 | + | 0.999853i | \(0.494543\pi\) | |||||||
\(930\) | 0.595957 | + | 0.432988i | 0.0195422 | + | 0.0141982i | ||||
\(931\) | 0.900787 | − | 2.77234i | 0.0295221 | − | 0.0908596i | ||||
\(932\) | 4.12141 | + | 12.6844i | 0.135001 | + | 0.415491i | ||||
\(933\) | −0.0684824 | + | 0.0497554i | −0.00224201 | + | 0.00162892i | ||||
\(934\) | 22.2302 | 0.727393 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −45.1290 | −1.47509 | ||||||||
\(937\) | 32.5365 | − | 23.6392i | 1.06292 | − | 0.772258i | 0.0882954 | − | 0.996094i | \(-0.471858\pi\) |
0.974627 | + | 0.223836i | \(0.0718581\pi\) | |||||||
\(938\) | 0.305497 | + | 0.940223i | 0.00997483 | + | 0.0306994i | ||||
\(939\) | −2.92012 | + | 8.98720i | −0.0952944 | + | 0.293286i | ||||
\(940\) | −1.51876 | − | 1.10344i | −0.0495364 | − | 0.0359903i | ||||
\(941\) | −20.1523 | − | 14.6415i | −0.656948 | − | 0.477300i | 0.208683 | − | 0.977983i | \(-0.433082\pi\) |
−0.865631 | + | 0.500683i | \(0.833082\pi\) | |||||||
\(942\) | −2.99221 | + | 9.20907i | −0.0974914 | + | 0.300048i | ||||
\(943\) | −1.61180 | − | 4.96061i | −0.0524875 | − | 0.161540i | ||||
\(944\) | 5.69566 | − | 4.13814i | 0.185378 | − | 0.134685i | ||||
\(945\) | −0.772605 | −0.0251328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.2061 | −1.04656 | −0.523279 | − | 0.852161i | \(-0.675292\pi\) | ||||
−0.523279 | + | 0.852161i | \(0.675292\pi\) | |||||||
\(948\) | −3.16053 | + | 2.29626i | −0.102649 | + | 0.0745791i | ||||
\(949\) | 11.2774 | + | 34.7082i | 0.366079 | + | 1.12668i | ||||
\(950\) | 3.46706 | − | 10.6705i | 0.112486 | − | 0.346197i | ||||
\(951\) | 16.4963 | + | 11.9852i | 0.534928 | + | 0.388648i | ||||
\(952\) | −9.25776 | − | 6.72615i | −0.300046 | − | 0.217996i | ||||
\(953\) | 13.9247 | − | 42.8557i | 0.451064 | − | 1.38823i | −0.424631 | − | 0.905367i | \(-0.639596\pi\) |
0.875695 | − | 0.482865i | \(-0.160404\pi\) | |||||||
\(954\) | −1.08057 | − | 3.32564i | −0.0349846 | − | 0.107671i | ||||
\(955\) | −2.16472 | + | 1.57276i | −0.0700486 | + | 0.0508933i | ||||
\(956\) | −37.4650 | −1.21170 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.96296 | 0.128038 | ||||||||
\(959\) | 2.02193 | − | 1.46902i | 0.0652915 | − | 0.0474370i | ||||
\(960\) | −0.130654 | − | 0.402113i | −0.00421685 | − | 0.0129781i | ||||
\(961\) | 5.08838 | − | 15.6604i | 0.164141 | − | 0.505175i | ||||
\(962\) | −23.2194 | − | 16.8699i | −0.748623 | − | 0.543906i | ||||
\(963\) | −11.4233 | − | 8.29952i | −0.368111 | − | 0.267448i | ||||
\(964\) | −8.13589 | + | 25.0397i | −0.262039 | + | 0.806474i | ||||
\(965\) | −1.09220 | − | 3.36144i | −0.0351591 | − | 0.108208i | ||||
\(966\) | 1.51530 | − | 1.10093i | 0.0487540 | − | 0.0354218i | ||||
\(967\) | 1.81387 | 0.0583300 | 0.0291650 | − | 0.999575i | \(-0.490715\pi\) | ||||
0.0291650 | + | 0.999575i | \(0.490715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.80912 | −0.250865 | ||||||||
\(970\) | 1.26720 | − | 0.920677i | 0.0406874 | − | 0.0295612i | ||||
\(971\) | 7.12405 | + | 21.9256i | 0.228622 | + | 0.703625i | 0.997904 | + | 0.0647158i | \(0.0206141\pi\) |
−0.769282 | + | 0.638909i | \(0.779386\pi\) | |||||||
\(972\) | −6.01331 | + | 18.5071i | −0.192877 | + | 0.593615i | ||||
\(973\) | −3.85302 | − | 2.79938i | −0.123522 | − | 0.0897441i | ||||
\(974\) | 18.3594 | + | 13.3389i | 0.588272 | + | 0.427405i | ||||
\(975\) | −6.17342 | + | 18.9998i | −0.197708 | + | 0.608481i | ||||
\(976\) | −2.19754 | − | 6.76335i | −0.0703417 | − | 0.216489i | ||||
\(977\) | 5.73956 | − | 4.17004i | 0.183625 | − | 0.133411i | −0.492175 | − | 0.870496i | \(-0.663798\pi\) |
0.675800 | + | 0.737085i | \(0.263798\pi\) | |||||||
\(978\) | −3.57236 | −0.114232 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.310525 | 0.00991935 | ||||||||
\(981\) | 11.4353 | − | 8.30823i | 0.365101 | − | 0.265261i | ||||
\(982\) | −7.24226 | − | 22.2894i | −0.231110 | − | 0.711283i | ||||
\(983\) | 11.8509 | − | 36.4732i | 0.377984 | − | 1.16332i | −0.563459 | − | 0.826144i | \(-0.690530\pi\) |
0.941443 | − | 0.337172i | \(-0.109470\pi\) | |||||||
\(984\) | −1.76628 | − | 1.28328i | −0.0563069 | − | 0.0409094i | ||||
\(985\) | 2.21487 | + | 1.60920i | 0.0705716 | + | 0.0512733i | ||||
\(986\) | −3.93029 | + | 12.0962i | −0.125166 | + | 0.385221i | ||||
\(987\) | −1.15459 | − | 3.55348i | −0.0367512 | − | 0.113108i | ||||
\(988\) | 21.4890 | − | 15.6126i | 0.683655 | − | 0.496705i | ||||
\(989\) | 18.3524 | 0.583572 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.2722 | 0.643967 | 0.321984 | − | 0.946745i | \(-0.395650\pi\) | ||||
0.321984 | + | 0.946745i | \(0.395650\pi\) | |||||||
\(992\) | −32.6295 | + | 23.7067i | −1.03599 | + | 0.752690i | ||||
\(993\) | 5.64039 | + | 17.3593i | 0.178992 | + | 0.550882i | ||||
\(994\) | −2.23659 | + | 6.88351i | −0.0709402 | + | 0.218332i | ||||
\(995\) | 2.74736 | + | 1.99607i | 0.0870971 | + | 0.0632798i | ||||
\(996\) | 7.87335 | + | 5.72032i | 0.249477 | + | 0.181255i | ||||
\(997\) | 4.76217 | − | 14.6565i | 0.150820 | − | 0.464175i | −0.846894 | − | 0.531762i | \(-0.821530\pi\) |
0.997713 | + | 0.0675872i | \(0.0215301\pi\) | |||||||
\(998\) | −1.42977 | − | 4.40039i | −0.0452587 | − | 0.139292i | ||||
\(999\) | −15.8808 | + | 11.5381i | −0.502447 | + | 0.365049i |
(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 | 847.2.f.p.729.2 | 8 | ||
11.2 | odd | 10 | 847.2.a.k.1.3 | 4 | |||
11.3 | even | 5 | 77.2.f.a.71.1 | yes | 8 | ||
11.4 | even | 5 | inner | 847.2.f.p.323.2 | 8 | ||
11.5 | even | 5 | 77.2.f.a.64.1 | ✓ | 8 | ||
11.6 | odd | 10 | 847.2.f.q.372.2 | 8 | |||
11.7 | odd | 10 | 847.2.f.s.323.1 | 8 | |||
11.8 | odd | 10 | 847.2.f.q.148.2 | 8 | |||
11.9 | even | 5 | 847.2.a.l.1.2 | 4 | |||
11.10 | odd | 2 | 847.2.f.s.729.1 | 8 | |||
33.2 | even | 10 | 7623.2.a.co.1.2 | 4 | |||
33.5 | odd | 10 | 693.2.m.g.64.2 | 8 | |||
33.14 | odd | 10 | 693.2.m.g.379.2 | 8 | |||
33.20 | odd | 10 | 7623.2.a.ch.1.3 | 4 | |||
77.3 | odd | 30 | 539.2.q.b.324.2 | 16 | |||
77.5 | odd | 30 | 539.2.q.b.361.2 | 16 | |||
77.13 | even | 10 | 5929.2.a.bb.1.3 | 4 | |||
77.16 | even | 15 | 539.2.q.c.361.2 | 16 | |||
77.20 | odd | 10 | 5929.2.a.bi.1.2 | 4 | |||
77.25 | even | 15 | 539.2.q.c.324.2 | 16 | |||
77.27 | odd | 10 | 539.2.f.d.295.1 | 8 | |||
77.38 | odd | 30 | 539.2.q.b.471.1 | 16 | |||
77.47 | odd | 30 | 539.2.q.b.214.1 | 16 | |||
77.58 | even | 15 | 539.2.q.c.214.1 | 16 | |||
77.60 | even | 15 | 539.2.q.c.471.1 | 16 | |||
77.69 | odd | 10 | 539.2.f.d.148.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.64.1 | ✓ | 8 | 11.5 | even | 5 | ||
77.2.f.a.71.1 | yes | 8 | 11.3 | even | 5 | ||
539.2.f.d.148.1 | 8 | 77.69 | odd | 10 | |||
539.2.f.d.295.1 | 8 | 77.27 | odd | 10 | |||
539.2.q.b.214.1 | 16 | 77.47 | odd | 30 | |||
539.2.q.b.324.2 | 16 | 77.3 | odd | 30 | |||
539.2.q.b.361.2 | 16 | 77.5 | odd | 30 | |||
539.2.q.b.471.1 | 16 | 77.38 | odd | 30 | |||
539.2.q.c.214.1 | 16 | 77.58 | even | 15 | |||
539.2.q.c.324.2 | 16 | 77.25 | even | 15 | |||
539.2.q.c.361.2 | 16 | 77.16 | even | 15 | |||
539.2.q.c.471.1 | 16 | 77.60 | even | 15 | |||
693.2.m.g.64.2 | 8 | 33.5 | odd | 10 | |||
693.2.m.g.379.2 | 8 | 33.14 | odd | 10 | |||
847.2.a.k.1.3 | 4 | 11.2 | odd | 10 | |||
847.2.a.l.1.2 | 4 | 11.9 | even | 5 | |||
847.2.f.p.323.2 | 8 | 11.4 | even | 5 | inner | ||
847.2.f.p.729.2 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.q.148.2 | 8 | 11.8 | odd | 10 | |||
847.2.f.q.372.2 | 8 | 11.6 | odd | 10 | |||
847.2.f.s.323.1 | 8 | 11.7 | odd | 10 | |||
847.2.f.s.729.1 | 8 | 11.10 | odd | 2 | |||
5929.2.a.bb.1.3 | 4 | 77.13 | even | 10 | |||
5929.2.a.bi.1.2 | 4 | 77.20 | odd | 10 | |||
7623.2.a.ch.1.3 | 4 | 33.20 | odd | 10 | |||
7623.2.a.co.1.2 | 4 | 33.2 | even | 10 |