Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(91,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.p (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.17 | ||
Character | \(\chi\) | \(=\) | 1380.91 |
Dual form | 1380.2.p.b.91.18 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.698077 | − | 1.22991i | −0.493615 | − | 0.869681i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.02538 | + | 1.71715i | −0.512689 | + | 0.858574i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −1.22991 | + | 0.698077i | −0.502110 | + | 0.284989i | ||||
\(7\) | −0.344556 | −0.130230 | −0.0651149 | − | 0.997878i | \(-0.520741\pi\) | ||||
−0.0651149 | + | 0.997878i | \(0.520741\pi\) | |||||||
\(8\) | 2.82774 | + | 0.0624257i | 0.999756 | + | 0.0220708i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.22991 | − | 0.698077i | 0.388933 | − | 0.220751i | ||||
\(11\) | −1.11761 | −0.336972 | −0.168486 | − | 0.985704i | \(-0.553888\pi\) | ||||
−0.168486 | + | 0.985704i | \(0.553888\pi\) | |||||||
\(12\) | 1.71715 | + | 1.02538i | 0.495698 | + | 0.296001i | ||||
\(13\) | −4.23633 | −1.17495 | −0.587474 | − | 0.809243i | \(-0.699878\pi\) | ||||
−0.587474 | + | 0.809243i | \(0.699878\pi\) | |||||||
\(14\) | 0.240526 | + | 0.423774i | 0.0642834 | + | 0.113258i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −1.89720 | − | 3.52145i | −0.474300 | − | 0.880363i | ||||
\(17\) | − | 3.31506i | − | 0.804019i | −0.915635 | − | 0.402010i | \(-0.868312\pi\) | ||
0.915635 | − | 0.402010i | \(-0.131688\pi\) | |||||||
\(18\) | 0.698077 | + | 1.22991i | 0.164538 | + | 0.289894i | ||||
\(19\) | 1.10641 | 0.253828 | 0.126914 | − | 0.991914i | \(-0.459493\pi\) | ||||
0.126914 | + | 0.991914i | \(0.459493\pi\) | |||||||
\(20\) | −1.71715 | − | 1.02538i | −0.383966 | − | 0.229282i | ||||
\(21\) | 0.344556i | 0.0751882i | ||||||||
\(22\) | 0.780176 | + | 1.37456i | 0.166334 | + | 0.293058i | ||||
\(23\) | 4.54924 | + | 1.51804i | 0.948582 | + | 0.316533i | ||||
\(24\) | 0.0624257 | − | 2.82774i | 0.0127426 | − | 0.577210i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.95729 | + | 5.21033i | 0.579971 | + | 1.02183i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.353300 | − | 0.591654i | 0.0667674 | − | 0.111812i | ||||
\(29\) | 0.696902 | 0.129411 | 0.0647057 | − | 0.997904i | \(-0.479389\pi\) | ||||
0.0647057 | + | 0.997904i | \(0.479389\pi\) | |||||||
\(30\) | −0.698077 | − | 1.22991i | −0.127451 | − | 0.224551i | ||||
\(31\) | 1.78017i | 0.319728i | 0.987139 | + | 0.159864i | \(0.0511056\pi\) | ||||
−0.987139 | + | 0.159864i | \(0.948894\pi\) | |||||||
\(32\) | −3.00669 | + | 4.79164i | −0.531514 | + | 0.847050i | ||||
\(33\) | 1.11761i | 0.194551i | ||||||||
\(34\) | −4.07723 | + | 2.31416i | −0.699240 | + | 0.396876i | ||||
\(35\) | − | 0.344556i | − | 0.0582406i | ||||||
\(36\) | 1.02538 | − | 1.71715i | 0.170896 | − | 0.286191i | ||||
\(37\) | 8.80960i | 1.44829i | 0.689649 | + | 0.724144i | \(0.257765\pi\) | ||||
−0.689649 | + | 0.724144i | \(0.742235\pi\) | |||||||
\(38\) | −0.772359 | − | 1.36079i | −0.125293 | − | 0.220749i | ||||
\(39\) | 4.23633i | 0.678356i | ||||||||
\(40\) | −0.0624257 | + | 2.82774i | −0.00987037 | + | 0.447105i | ||||
\(41\) | −9.74007 | −1.52114 | −0.760572 | − | 0.649254i | \(-0.775081\pi\) | ||||
−0.760572 | + | 0.649254i | \(0.775081\pi\) | |||||||
\(42\) | 0.423774 | − | 0.240526i | 0.0653898 | − | 0.0371140i | ||||
\(43\) | 8.82654 | 1.34603 | 0.673017 | − | 0.739627i | \(-0.264998\pi\) | ||||
0.673017 | + | 0.739627i | \(0.264998\pi\) | |||||||
\(44\) | 1.14597 | − | 1.91910i | 0.172762 | − | 0.289315i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | −1.30866 | − | 6.65488i | −0.192951 | − | 0.981208i | ||||
\(47\) | 8.35120i | 1.21815i | 0.793113 | + | 0.609074i | \(0.208459\pi\) | ||||
−0.793113 | + | 0.609074i | \(0.791541\pi\) | |||||||
\(48\) | −3.52145 | + | 1.89720i | −0.508278 | + | 0.273837i | ||||
\(49\) | −6.88128 | −0.983040 | ||||||||
\(50\) | 0.698077 | + | 1.22991i | 0.0987229 | + | 0.173936i | ||||
\(51\) | −3.31506 | −0.464201 | ||||||||
\(52\) | 4.34384 | − | 7.27442i | 0.602383 | − | 1.00878i | ||||
\(53\) | 12.1249i | 1.66548i | 0.553663 | + | 0.832741i | \(0.313229\pi\) | ||||
−0.553663 | + | 0.832741i | \(0.686771\pi\) | |||||||
\(54\) | 1.22991 | − | 0.698077i | 0.167370 | − | 0.0949962i | ||||
\(55\) | − | 1.11761i | − | 0.150698i | ||||||
\(56\) | −0.974314 | − | 0.0215091i | −0.130198 | − | 0.00287428i | ||||
\(57\) | − | 1.10641i | − | 0.146548i | ||||||
\(58\) | −0.486491 | − | 0.857130i | −0.0638794 | − | 0.112547i | ||||
\(59\) | 14.6024i | 1.90107i | 0.310623 | + | 0.950533i | \(0.399462\pi\) | ||||
−0.310623 | + | 0.950533i | \(0.600538\pi\) | |||||||
\(60\) | −1.02538 | + | 1.71715i | −0.132376 | + | 0.221683i | ||||
\(61\) | − | 7.06741i | − | 0.904889i | −0.891793 | − | 0.452444i | \(-0.850552\pi\) | ||
0.891793 | − | 0.452444i | \(-0.149448\pi\) | |||||||
\(62\) | 2.18946 | − | 1.24270i | 0.278061 | − | 0.157822i | ||||
\(63\) | 0.344556 | 0.0434100 | ||||||||
\(64\) | 7.99221 | + | 0.353047i | 0.999026 | + | 0.0441309i | ||||
\(65\) | − | 4.23633i | − | 0.525453i | ||||||
\(66\) | 1.37456 | − | 0.780176i | 0.169197 | − | 0.0960331i | ||||
\(67\) | −2.20028 | −0.268807 | −0.134403 | − | 0.990927i | \(-0.542912\pi\) | ||||
−0.134403 | + | 0.990927i | \(0.542912\pi\) | |||||||
\(68\) | 5.69244 | + | 3.39919i | 0.690310 | + | 0.412212i | ||||
\(69\) | 1.51804 | − | 4.54924i | 0.182750 | − | 0.547664i | ||||
\(70\) | −0.423774 | + | 0.240526i | −0.0506507 | + | 0.0287484i | ||||
\(71\) | 16.5411i | 1.96306i | 0.191301 | + | 0.981531i | \(0.438729\pi\) | ||||
−0.191301 | + | 0.981531i | \(0.561271\pi\) | |||||||
\(72\) | −2.82774 | − | 0.0624257i | −0.333252 | − | 0.00735694i | ||||
\(73\) | 2.68382 | 0.314118 | 0.157059 | − | 0.987589i | \(-0.449799\pi\) | ||||
0.157059 | + | 0.987589i | \(0.449799\pi\) | |||||||
\(74\) | 10.8350 | − | 6.14977i | 1.25955 | − | 0.714897i | ||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | −1.13449 | + | 1.89987i | −0.130135 | + | 0.217930i | ||||
\(77\) | 0.385078 | 0.0438838 | ||||||||
\(78\) | 5.21033 | − | 2.95729i | 0.589953 | − | 0.334847i | ||||
\(79\) | −15.3762 | −1.72996 | −0.864979 | − | 0.501808i | \(-0.832669\pi\) | ||||
−0.864979 | + | 0.501808i | \(0.832669\pi\) | |||||||
\(80\) | 3.52145 | − | 1.89720i | 0.393710 | − | 0.212113i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.79932 | + | 11.9795i | 0.750859 | + | 1.32291i | ||||
\(83\) | 17.0787 | 1.87463 | 0.937313 | − | 0.348489i | \(-0.113305\pi\) | ||||
0.937313 | + | 0.348489i | \(0.113305\pi\) | |||||||
\(84\) | −0.591654 | − | 0.353300i | −0.0645547 | − | 0.0385482i | ||||
\(85\) | 3.31506 | 0.359568 | ||||||||
\(86\) | −6.16160 | − | 10.8559i | −0.664422 | − | 1.17062i | ||||
\(87\) | − | 0.696902i | − | 0.0747158i | ||||||
\(88\) | −3.16030 | − | 0.0697675i | −0.336890 | − | 0.00743724i | ||||
\(89\) | 11.9834i | 1.27023i | 0.772416 | + | 0.635117i | \(0.219048\pi\) | ||||
−0.772416 | + | 0.635117i | \(0.780952\pi\) | |||||||
\(90\) | −1.22991 | + | 0.698077i | −0.129644 | + | 0.0735837i | ||||
\(91\) | 1.45965 | 0.153013 | ||||||||
\(92\) | −7.27139 | + | 6.25515i | −0.758094 | + | 0.652145i | ||||
\(93\) | 1.78017 | 0.184595 | ||||||||
\(94\) | 10.2713 | − | 5.82978i | 1.05940 | − | 0.601296i | ||||
\(95\) | 1.10641i | 0.113515i | ||||||||
\(96\) | 4.79164 | + | 3.00669i | 0.489044 | + | 0.306870i | ||||
\(97\) | 9.50481i | 0.965068i | 0.875877 | + | 0.482534i | \(0.160283\pi\) | ||||
−0.875877 | + | 0.482534i | \(0.839717\pi\) | |||||||
\(98\) | 4.80366 | + | 8.46339i | 0.485243 | + | 0.854931i | ||||
\(99\) | 1.11761 | 0.112324 | ||||||||
\(100\) | 1.02538 | − | 1.71715i | 0.102538 | − | 0.171715i | ||||
\(101\) | 8.14918 | 0.810874 | 0.405437 | − | 0.914123i | \(-0.367119\pi\) | ||||
0.405437 | + | 0.914123i | \(0.367119\pi\) | |||||||
\(102\) | 2.31416 | + | 4.07723i | 0.229136 | + | 0.403706i | ||||
\(103\) | 3.46429 | 0.341347 | 0.170673 | − | 0.985328i | \(-0.445406\pi\) | ||||
0.170673 | + | 0.985328i | \(0.445406\pi\) | |||||||
\(104\) | −11.9792 | − | 0.264456i | −1.17466 | − | 0.0259321i | ||||
\(105\) | −0.344556 | −0.0336252 | ||||||||
\(106\) | 14.9126 | − | 8.46410i | 1.44844 | − | 0.822106i | ||||
\(107\) | −12.1330 | −1.17294 | −0.586470 | − | 0.809971i | \(-0.699483\pi\) | ||||
−0.586470 | + | 0.809971i | \(0.699483\pi\) | |||||||
\(108\) | −1.71715 | − | 1.02538i | −0.165233 | − | 0.0986671i | ||||
\(109\) | − | 16.4638i | − | 1.57695i | −0.615069 | − | 0.788473i | \(-0.710872\pi\) | ||
0.615069 | − | 0.788473i | \(-0.289128\pi\) | |||||||
\(110\) | −1.37456 | + | 0.780176i | −0.131059 | + | 0.0743869i | ||||
\(111\) | 8.80960 | 0.836170 | ||||||||
\(112\) | 0.653691 | + | 1.21334i | 0.0617680 | + | 0.114650i | ||||
\(113\) | − | 16.1919i | − | 1.52320i | −0.648045 | − | 0.761602i | \(-0.724413\pi\) | ||
0.648045 | − | 0.761602i | \(-0.275587\pi\) | |||||||
\(114\) | −1.36079 | + | 0.772359i | −0.127450 | + | 0.0723380i | ||||
\(115\) | −1.51804 | + | 4.54924i | −0.141558 | + | 0.424219i | ||||
\(116\) | −0.714588 | + | 1.19668i | −0.0663478 | + | 0.111109i | ||||
\(117\) | 4.23633 | 0.391649 | ||||||||
\(118\) | 17.9597 | − | 10.1936i | 1.65332 | − | 0.938394i | ||||
\(119\) | 1.14222i | 0.104707i | ||||||||
\(120\) | 2.82774 | + | 0.0624257i | 0.258136 | + | 0.00569866i | ||||
\(121\) | −9.75095 | −0.886450 | ||||||||
\(122\) | −8.69230 | + | 4.93359i | −0.786964 | + | 0.446666i | ||||
\(123\) | 9.74007i | 0.878233i | ||||||||
\(124\) | −3.05682 | − | 1.82535i | −0.274510 | − | 0.163921i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −0.240526 | − | 0.423774i | −0.0214278 | − | 0.0377528i | ||||
\(127\) | − | 0.639825i | − | 0.0567753i | −0.999597 | − | 0.0283877i | \(-0.990963\pi\) | ||
0.999597 | − | 0.0283877i | \(-0.00903729\pi\) | |||||||
\(128\) | −5.14495 | − | 10.0762i | −0.454754 | − | 0.890617i | ||||
\(129\) | − | 8.82654i | − | 0.777133i | ||||||
\(130\) | −5.21033 | + | 2.95729i | −0.456976 | + | 0.259371i | ||||
\(131\) | − | 1.67592i | − | 0.146425i | −0.997316 | − | 0.0732127i | \(-0.976675\pi\) | ||
0.997316 | − | 0.0732127i | \(-0.0233252\pi\) | |||||||
\(132\) | −1.91910 | − | 1.14597i | −0.167036 | − | 0.0997440i | ||||
\(133\) | −0.381220 | −0.0330560 | ||||||||
\(134\) | 1.53596 | + | 2.70615i | 0.132687 | + | 0.233776i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0.206945 | − | 9.37411i | 0.0177454 | − | 0.803823i | ||||
\(137\) | 10.2084i | 0.872160i | 0.899908 | + | 0.436080i | \(0.143634\pi\) | ||||
−0.899908 | + | 0.436080i | \(0.856366\pi\) | |||||||
\(138\) | −6.65488 | + | 1.30866i | −0.566501 | + | 0.111400i | ||||
\(139\) | − | 8.48317i | − | 0.719533i | −0.933042 | − | 0.359767i | \(-0.882856\pi\) | ||
0.933042 | − | 0.359767i | \(-0.117144\pi\) | |||||||
\(140\) | 0.591654 | + | 0.353300i | 0.0500039 | + | 0.0298593i | ||||
\(141\) | 8.35120 | 0.703298 | ||||||||
\(142\) | 20.3441 | − | 11.5469i | 1.70724 | − | 0.968997i | ||||
\(143\) | 4.73456 | 0.395924 | ||||||||
\(144\) | 1.89720 | + | 3.52145i | 0.158100 | + | 0.293454i | ||||
\(145\) | 0.696902i | 0.0578746i | ||||||||
\(146\) | −1.87351 | − | 3.30087i | −0.155053 | − | 0.273182i | ||||
\(147\) | 6.88128i | 0.567559i | ||||||||
\(148\) | −15.1274 | − | 9.03317i | −1.24346 | − | 0.742522i | ||||
\(149\) | − | 8.00893i | − | 0.656117i | −0.944657 | − | 0.328058i | \(-0.893606\pi\) | ||
0.944657 | − | 0.328058i | \(-0.106394\pi\) | |||||||
\(150\) | 1.22991 | − | 0.698077i | 0.100422 | − | 0.0569977i | ||||
\(151\) | − | 15.9200i | − | 1.29555i | −0.761832 | − | 0.647774i | \(-0.775700\pi\) | ||
0.761832 | − | 0.647774i | \(-0.224300\pi\) | |||||||
\(152\) | 3.12864 | + | 0.0690684i | 0.253766 | + | 0.00560219i | ||||
\(153\) | 3.31506i | 0.268006i | ||||||||
\(154\) | −0.268814 | − | 0.473613i | −0.0216617 | − | 0.0381649i | ||||
\(155\) | −1.78017 | −0.142987 | ||||||||
\(156\) | −7.27442 | − | 4.34384i | −0.582419 | − | 0.347786i | ||||
\(157\) | 11.4730i | 0.915644i | 0.889044 | + | 0.457822i | \(0.151370\pi\) | ||||
−0.889044 | + | 0.457822i | \(0.848630\pi\) | |||||||
\(158\) | 10.7338 | + | 18.9114i | 0.853933 | + | 1.50451i | ||||
\(159\) | 12.1249 | 0.961566 | ||||||||
\(160\) | −4.79164 | − | 3.00669i | −0.378812 | − | 0.237700i | ||||
\(161\) | −1.56747 | − | 0.523049i | −0.123534 | − | 0.0412220i | ||||
\(162\) | −0.698077 | − | 1.22991i | −0.0548461 | − | 0.0966312i | ||||
\(163\) | − | 11.6276i | − | 0.910746i | −0.890301 | − | 0.455373i | \(-0.849506\pi\) | ||
0.890301 | − | 0.455373i | \(-0.150494\pi\) | |||||||
\(164\) | 9.98725 | − | 16.7251i | 0.779874 | − | 1.30601i | ||||
\(165\) | −1.11761 | −0.0870057 | ||||||||
\(166\) | −11.9222 | − | 21.0053i | −0.925343 | − | 1.63033i | ||||
\(167\) | 18.3392i | 1.41913i | 0.704641 | + | 0.709564i | \(0.251108\pi\) | ||||
−0.704641 | + | 0.709564i | \(0.748892\pi\) | |||||||
\(168\) | −0.0215091 | + | 0.974314i | −0.00165947 | + | 0.0751699i | ||||
\(169\) | 4.94653 | 0.380502 | ||||||||
\(170\) | −2.31416 | − | 4.07723i | −0.177488 | − | 0.312710i | ||||
\(171\) | −1.10641 | −0.0846093 | ||||||||
\(172\) | −9.05054 | + | 15.1565i | −0.690097 | + | 1.15567i | ||||
\(173\) | 7.02511 | 0.534109 | 0.267055 | − | 0.963681i | \(-0.413950\pi\) | ||||
0.267055 | + | 0.963681i | \(0.413950\pi\) | |||||||
\(174\) | −0.857130 | + | 0.486491i | −0.0649788 | + | 0.0368808i | ||||
\(175\) | 0.344556 | 0.0260460 | ||||||||
\(176\) | 2.12033 | + | 3.93561i | 0.159826 | + | 0.296657i | ||||
\(177\) | 14.6024 | 1.09758 | ||||||||
\(178\) | 14.7385 | − | 8.36531i | 1.10470 | − | 0.627006i | ||||
\(179\) | − | 3.75048i | − | 0.280324i | −0.990129 | − | 0.140162i | \(-0.955238\pi\) | ||
0.990129 | − | 0.140162i | \(-0.0447624\pi\) | |||||||
\(180\) | 1.71715 | + | 1.02538i | 0.127989 | + | 0.0764272i | ||||
\(181\) | − | 9.93221i | − | 0.738255i | −0.929379 | − | 0.369128i | \(-0.879657\pi\) | ||
0.929379 | − | 0.369128i | \(-0.120343\pi\) | |||||||
\(182\) | −1.01895 | − | 1.79525i | −0.0755296 | − | 0.133073i | ||||
\(183\) | −7.06741 | −0.522438 | ||||||||
\(184\) | 12.7693 | + | 4.57661i | 0.941364 | + | 0.337392i | ||||
\(185\) | −8.80960 | −0.647694 | ||||||||
\(186\) | −1.24270 | − | 2.18946i | −0.0911188 | − | 0.160539i | ||||
\(187\) | 3.70493i | 0.270932i | ||||||||
\(188\) | −14.3403 | − | 8.56314i | −1.04587 | − | 0.624531i | ||||
\(189\) | − | 0.344556i | − | 0.0250627i | ||||||
\(190\) | 1.36079 | − | 0.772359i | 0.0987220 | − | 0.0560328i | ||||
\(191\) | −1.74084 | −0.125963 | −0.0629813 | − | 0.998015i | \(-0.520061\pi\) | ||||
−0.0629813 | + | 0.998015i | \(0.520061\pi\) | |||||||
\(192\) | 0.353047 | − | 7.99221i | 0.0254790 | − | 0.576788i | ||||
\(193\) | −8.74766 | −0.629670 | −0.314835 | − | 0.949146i | \(-0.601949\pi\) | ||||
−0.314835 | + | 0.949146i | \(0.601949\pi\) | |||||||
\(194\) | 11.6901 | − | 6.63509i | 0.839301 | − | 0.476372i | ||||
\(195\) | −4.23633 | −0.303370 | ||||||||
\(196\) | 7.05591 | − | 11.8162i | 0.503994 | − | 0.844013i | ||||
\(197\) | −7.94495 | −0.566054 | −0.283027 | − | 0.959112i | \(-0.591339\pi\) | ||||
−0.283027 | + | 0.959112i | \(0.591339\pi\) | |||||||
\(198\) | −0.780176 | − | 1.37456i | −0.0554447 | − | 0.0976859i | ||||
\(199\) | 12.6767 | 0.898625 | 0.449313 | − | 0.893375i | \(-0.351669\pi\) | ||||
0.449313 | + | 0.893375i | \(0.351669\pi\) | |||||||
\(200\) | −2.82774 | − | 0.0624257i | −0.199951 | − | 0.00441416i | ||||
\(201\) | 2.20028i | 0.155196i | ||||||||
\(202\) | −5.68875 | − | 10.0228i | −0.400259 | − | 0.705201i | ||||
\(203\) | −0.240122 | −0.0168532 | ||||||||
\(204\) | 3.39919 | − | 5.69244i | 0.237991 | − | 0.398551i | ||||
\(205\) | − | 9.74007i | − | 0.680276i | ||||||
\(206\) | −2.41834 | − | 4.26078i | −0.168494 | − | 0.296863i | ||||
\(207\) | −4.54924 | − | 1.51804i | −0.316194 | − | 0.105511i | ||||
\(208\) | 8.03717 | + | 14.9181i | 0.557278 | + | 1.03438i | ||||
\(209\) | −1.23653 | −0.0855328 | ||||||||
\(210\) | 0.240526 | + | 0.423774i | 0.0165979 | + | 0.0292432i | ||||
\(211\) | 14.8224i | 1.02041i | 0.860051 | + | 0.510207i | \(0.170431\pi\) | ||||
−0.860051 | + | 0.510207i | \(0.829569\pi\) | |||||||
\(212\) | −20.8202 | − | 12.4326i | −1.42994 | − | 0.853874i | ||||
\(213\) | 16.5411 | 1.13337 | ||||||||
\(214\) | 8.46975 | + | 14.9225i | 0.578980 | + | 1.02008i | ||||
\(215\) | 8.82654i | 0.601965i | ||||||||
\(216\) | −0.0624257 | + | 2.82774i | −0.00424753 | + | 0.192403i | ||||
\(217\) | − | 0.613368i | − | 0.0416381i | ||||||
\(218\) | −20.2491 | + | 11.4930i | −1.37144 | + | 0.778404i | ||||
\(219\) | − | 2.68382i | − | 0.181356i | ||||||
\(220\) | 1.91910 | + | 1.14597i | 0.129386 | + | 0.0772614i | ||||
\(221\) | 14.0437i | 0.944680i | ||||||||
\(222\) | −6.14977 | − | 10.8350i | −0.412746 | − | 0.727201i | ||||
\(223\) | 2.35237i | 0.157526i | 0.996893 | + | 0.0787630i | \(0.0250970\pi\) | ||||
−0.996893 | + | 0.0787630i | \(0.974903\pi\) | |||||||
\(224\) | 1.03597 | − | 1.65099i | 0.0692189 | − | 0.110311i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −19.9146 | + | 11.3032i | −1.32470 | + | 0.751876i | ||||
\(227\) | −8.45514 | −0.561187 | −0.280594 | − | 0.959827i | \(-0.590531\pi\) | ||||
−0.280594 | + | 0.959827i | \(0.590531\pi\) | |||||||
\(228\) | 1.89987 | + | 1.13449i | 0.125822 | + | 0.0751333i | ||||
\(229\) | 22.5195i | 1.48813i | 0.668108 | + | 0.744065i | \(0.267105\pi\) | ||||
−0.668108 | + | 0.744065i | \(0.732895\pi\) | |||||||
\(230\) | 6.65488 | − | 1.30866i | 0.438810 | − | 0.0862904i | ||||
\(231\) | − | 0.385078i | − | 0.0253363i | ||||||
\(232\) | 1.97066 | + | 0.0435046i | 0.129380 | + | 0.00285622i | ||||
\(233\) | −15.1809 | −0.994536 | −0.497268 | − | 0.867597i | \(-0.665663\pi\) | ||||
−0.497268 | + | 0.867597i | \(0.665663\pi\) | |||||||
\(234\) | −2.95729 | − | 5.21033i | −0.193324 | − | 0.340610i | ||||
\(235\) | −8.35120 | −0.544772 | ||||||||
\(236\) | −25.0744 | − | 14.9729i | −1.63221 | − | 0.974656i | ||||
\(237\) | 15.3762i | 0.998792i | ||||||||
\(238\) | 1.40483 | − | 0.797358i | 0.0910619 | − | 0.0516851i | ||||
\(239\) | 5.81077i | 0.375867i | 0.982182 | + | 0.187934i | \(0.0601790\pi\) | ||||
−0.982182 | + | 0.187934i | \(0.939821\pi\) | |||||||
\(240\) | −1.89720 | − | 3.52145i | −0.122464 | − | 0.227309i | ||||
\(241\) | 4.01399i | 0.258564i | 0.991608 | + | 0.129282i | \(0.0412672\pi\) | ||||
−0.991608 | + | 0.129282i | \(0.958733\pi\) | |||||||
\(242\) | 6.80691 | + | 11.9928i | 0.437565 | + | 0.770929i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 12.1358 | + | 7.24676i | 0.776914 | + | 0.463926i | ||||
\(245\) | − | 6.88128i | − | 0.439629i | ||||||
\(246\) | 11.9795 | − | 6.79932i | 0.763782 | − | 0.433509i | ||||
\(247\) | −4.68712 | −0.298234 | ||||||||
\(248\) | −0.111128 | + | 5.03385i | −0.00705666 | + | 0.319650i | ||||
\(249\) | − | 17.0787i | − | 1.08232i | ||||||
\(250\) | −1.22991 | + | 0.698077i | −0.0777866 | + | 0.0441502i | ||||
\(251\) | 14.1494 | 0.893104 | 0.446552 | − | 0.894758i | \(-0.352652\pi\) | ||||
0.446552 | + | 0.894758i | \(0.352652\pi\) | |||||||
\(252\) | −0.353300 | + | 0.591654i | −0.0222558 | + | 0.0372707i | ||||
\(253\) | −5.08427 | − | 1.69657i | −0.319645 | − | 0.106663i | ||||
\(254\) | −0.786930 | + | 0.446647i | −0.0493764 | + | 0.0280251i | ||||
\(255\) | − | 3.31506i | − | 0.207597i | ||||||
\(256\) | −8.80127 | + | 13.3618i | −0.550079 | + | 0.835112i | ||||
\(257\) | 3.78305 | 0.235980 | 0.117990 | − | 0.993015i | \(-0.462355\pi\) | ||||
0.117990 | + | 0.993015i | \(0.462355\pi\) | |||||||
\(258\) | −10.8559 | + | 6.16160i | −0.675858 | + | 0.383604i | ||||
\(259\) | − | 3.03540i | − | 0.188610i | ||||||
\(260\) | 7.27442 | + | 4.34384i | 0.451140 | + | 0.269394i | ||||
\(261\) | −0.696902 | −0.0431372 | ||||||||
\(262\) | −2.06123 | + | 1.16992i | −0.127343 | + | 0.0722778i | ||||
\(263\) | 11.5227 | 0.710520 | 0.355260 | − | 0.934768i | \(-0.384392\pi\) | ||||
0.355260 | + | 0.934768i | \(0.384392\pi\) | |||||||
\(264\) | −0.0697675 | + | 3.16030i | −0.00429389 | + | 0.194503i | ||||
\(265\) | −12.1249 | −0.744826 | ||||||||
\(266\) | 0.266121 | + | 0.468868i | 0.0163169 | + | 0.0287481i | ||||
\(267\) | 11.9834 | 0.733370 | ||||||||
\(268\) | 2.25612 | − | 3.77820i | 0.137814 | − | 0.230790i | ||||
\(269\) | −25.4362 | −1.55087 | −0.775435 | − | 0.631428i | \(-0.782469\pi\) | ||||
−0.775435 | + | 0.631428i | \(0.782469\pi\) | |||||||
\(270\) | 0.698077 | + | 1.22991i | 0.0424836 | + | 0.0748502i | ||||
\(271\) | 6.86367i | 0.416938i | 0.978029 | + | 0.208469i | \(0.0668480\pi\) | ||||
−0.978029 | + | 0.208469i | \(0.933152\pi\) | |||||||
\(272\) | −11.6738 | + | 6.28932i | −0.707829 | + | 0.381346i | ||||
\(273\) | − | 1.45965i | − | 0.0883423i | ||||||
\(274\) | 12.5554 | − | 7.12622i | 0.758501 | − | 0.430511i | ||||
\(275\) | 1.11761 | 0.0673943 | ||||||||
\(276\) | 6.25515 | + | 7.27139i | 0.376516 | + | 0.437686i | ||||
\(277\) | −16.6149 | −0.998292 | −0.499146 | − | 0.866518i | \(-0.666353\pi\) | ||||
−0.499146 | + | 0.866518i | \(0.666353\pi\) | |||||||
\(278\) | −10.4336 | + | 5.92190i | −0.625764 | + | 0.355172i | ||||
\(279\) | − | 1.78017i | − | 0.106576i | ||||||
\(280\) | 0.0215091 | − | 0.974314i | 0.00128542 | − | 0.0582264i | ||||
\(281\) | − | 6.82628i | − | 0.407221i | −0.979052 | − | 0.203611i | \(-0.934732\pi\) | ||
0.979052 | − | 0.203611i | \(-0.0652677\pi\) | |||||||
\(282\) | −5.82978 | − | 10.2713i | −0.347158 | − | 0.611645i | ||||
\(283\) | 0.162801 | 0.00967753 | 0.00483876 | − | 0.999988i | \(-0.498460\pi\) | ||||
0.00483876 | + | 0.999988i | \(0.498460\pi\) | |||||||
\(284\) | −28.4035 | − | 16.9608i | −1.68544 | − | 1.00644i | ||||
\(285\) | 1.10641 | 0.0655381 | ||||||||
\(286\) | −3.30509 | − | 5.82311i | −0.195434 | − | 0.344327i | ||||
\(287\) | 3.35600 | 0.198098 | ||||||||
\(288\) | 3.00669 | − | 4.79164i | 0.177171 | − | 0.282350i | ||||
\(289\) | 6.01041 | 0.353553 | ||||||||
\(290\) | 0.857130 | − | 0.486491i | 0.0503324 | − | 0.0285677i | ||||
\(291\) | 9.50481 | 0.557182 | ||||||||
\(292\) | −2.75193 | + | 4.60852i | −0.161045 | + | 0.269693i | ||||
\(293\) | 14.9580i | 0.873854i | 0.899497 | + | 0.436927i | \(0.143933\pi\) | ||||
−0.899497 | + | 0.436927i | \(0.856067\pi\) | |||||||
\(294\) | 8.46339 | − | 4.80366i | 0.493595 | − | 0.280155i | ||||
\(295\) | −14.6024 | −0.850183 | ||||||||
\(296\) | −0.549945 | + | 24.9112i | −0.0319649 | + | 1.44794i | ||||
\(297\) | − | 1.11761i | − | 0.0648502i | ||||||
\(298\) | −9.85029 | + | 5.59084i | −0.570612 | + | 0.323869i | ||||
\(299\) | −19.2721 | − | 6.43092i | −1.11453 | − | 0.371910i | ||||
\(300\) | −1.71715 | − | 1.02538i | −0.0991396 | − | 0.0592002i | ||||
\(301\) | −3.04123 | −0.175294 | ||||||||
\(302\) | −19.5802 | + | 11.1134i | −1.12671 | + | 0.639502i | ||||
\(303\) | − | 8.14918i | − | 0.468158i | ||||||
\(304\) | −2.09908 | − | 3.89617i | −0.120391 | − | 0.223461i | ||||
\(305\) | 7.06741 | 0.404678 | ||||||||
\(306\) | 4.07723 | − | 2.31416i | 0.233080 | − | 0.132292i | ||||
\(307\) | − | 8.69634i | − | 0.496326i | −0.968718 | − | 0.248163i | \(-0.920173\pi\) | ||
0.968718 | − | 0.248163i | \(-0.0798269\pi\) | |||||||
\(308\) | −0.394851 | + | 0.661237i | −0.0224987 | + | 0.0376775i | ||||
\(309\) | − | 3.46429i | − | 0.197077i | ||||||
\(310\) | 1.24270 | + | 2.18946i | 0.0705803 | + | 0.124353i | ||||
\(311\) | − | 5.74489i | − | 0.325763i | −0.986646 | − | 0.162881i | \(-0.947921\pi\) | ||
0.986646 | − | 0.162881i | \(-0.0520788\pi\) | |||||||
\(312\) | −0.264456 | + | 11.9792i | −0.0149719 | + | 0.678191i | ||||
\(313\) | − | 0.954025i | − | 0.0539247i | −0.999636 | − | 0.0269623i | \(-0.991417\pi\) | ||
0.999636 | − | 0.0269623i | \(-0.00858342\pi\) | |||||||
\(314\) | 14.1108 | − | 8.00902i | 0.796318 | − | 0.451975i | ||||
\(315\) | 0.344556i | 0.0194135i | ||||||||
\(316\) | 15.7664 | − | 26.4032i | 0.886931 | − | 1.48530i | ||||
\(317\) | 3.33114 | 0.187095 | 0.0935476 | − | 0.995615i | \(-0.470179\pi\) | ||||
0.0935476 | + | 0.995615i | \(0.470179\pi\) | |||||||
\(318\) | −8.46410 | − | 14.9126i | −0.474643 | − | 0.836255i | ||||
\(319\) | −0.778864 | −0.0436080 | ||||||||
\(320\) | −0.353047 | + | 7.99221i | −0.0197359 | + | 0.446778i | ||||
\(321\) | 12.1330i | 0.677197i | ||||||||
\(322\) | 0.450906 | + | 2.29298i | 0.0251280 | + | 0.127783i | ||||
\(323\) | − | 3.66781i | − | 0.204082i | ||||||
\(324\) | −1.02538 | + | 1.71715i | −0.0569654 | + | 0.0953972i | ||||
\(325\) | 4.23633 | 0.234990 | ||||||||
\(326\) | −14.3010 | + | 8.11697i | −0.792058 | + | 0.449558i | ||||
\(327\) | −16.4638 | −0.910451 | ||||||||
\(328\) | −27.5424 | − | 0.608031i | −1.52077 | − | 0.0335729i | ||||
\(329\) | − | 2.87746i | − | 0.158639i | ||||||
\(330\) | 0.780176 | + | 1.37456i | 0.0429473 | + | 0.0756672i | ||||
\(331\) | − | 21.3748i | − | 1.17486i | −0.809274 | − | 0.587431i | \(-0.800139\pi\) | ||
0.809274 | − | 0.587431i | \(-0.199861\pi\) | |||||||
\(332\) | −17.5121 | + | 29.3266i | −0.961100 | + | 1.60951i | ||||
\(333\) | − | 8.80960i | − | 0.482763i | ||||||
\(334\) | 22.5556 | − | 12.8021i | 1.23419 | − | 0.700502i | ||||
\(335\) | − | 2.20028i | − | 0.120214i | ||||||
\(336\) | 1.21334 | − | 0.653691i | 0.0661930 | − | 0.0356618i | ||||
\(337\) | 23.7780i | 1.29527i | 0.761950 | + | 0.647636i | \(0.224242\pi\) | ||||
−0.761950 | + | 0.647636i | \(0.775758\pi\) | |||||||
\(338\) | −3.45306 | − | 6.08381i | −0.187821 | − | 0.330915i | ||||
\(339\) | −16.1919 | −0.879422 | ||||||||
\(340\) | −3.39919 | + | 5.69244i | −0.184347 | + | 0.308716i | ||||
\(341\) | − | 1.98953i | − | 0.107739i | ||||||
\(342\) | 0.772359 | + | 1.36079i | 0.0417644 | + | 0.0735831i | ||||
\(343\) | 4.78288 | 0.258251 | ||||||||
\(344\) | 24.9591 | + | 0.551003i | 1.34571 | + | 0.0297081i | ||||
\(345\) | 4.54924 | + | 1.51804i | 0.244923 | + | 0.0817285i | ||||
\(346\) | −4.90406 | − | 8.64028i | −0.263644 | − | 0.464504i | ||||
\(347\) | − | 27.0291i | − | 1.45100i | −0.688223 | − | 0.725499i | \(-0.741609\pi\) | ||
0.688223 | − | 0.725499i | \(-0.258391\pi\) | |||||||
\(348\) | 1.19668 | + | 0.714588i | 0.0641490 | + | 0.0383059i | ||||
\(349\) | −15.3747 | −0.822986 | −0.411493 | − | 0.911413i | \(-0.634993\pi\) | ||||
−0.411493 | + | 0.911413i | \(0.634993\pi\) | |||||||
\(350\) | −0.240526 | − | 0.423774i | −0.0128567 | − | 0.0226517i | ||||
\(351\) | − | 4.23633i | − | 0.226119i | ||||||
\(352\) | 3.36031 | − | 5.35517i | 0.179105 | − | 0.285432i | ||||
\(353\) | −14.9106 | −0.793611 | −0.396806 | − | 0.917903i | \(-0.629881\pi\) | ||||
−0.396806 | + | 0.917903i | \(0.629881\pi\) | |||||||
\(354\) | −10.1936 | − | 17.9597i | −0.541782 | − | 0.954545i | ||||
\(355\) | −16.5411 | −0.877908 | ||||||||
\(356\) | −20.5772 | − | 12.2875i | −1.09059 | − | 0.651235i | ||||
\(357\) | 1.14222 | 0.0604528 | ||||||||
\(358\) | −4.61277 | + | 2.61812i | −0.243792 | + | 0.138372i | ||||
\(359\) | 34.0479 | 1.79698 | 0.898491 | − | 0.438993i | \(-0.144665\pi\) | ||||
0.898491 | + | 0.438993i | \(0.144665\pi\) | |||||||
\(360\) | 0.0624257 | − | 2.82774i | 0.00329012 | − | 0.149035i | ||||
\(361\) | −17.7759 | −0.935571 | ||||||||
\(362\) | −12.2158 | + | 6.93344i | −0.642046 | + | 0.364414i | ||||
\(363\) | 9.75095i | 0.511792i | ||||||||
\(364\) | −1.49670 | + | 2.50644i | −0.0784482 | + | 0.131373i | ||||
\(365\) | 2.68382i | 0.140478i | ||||||||
\(366\) | 4.93359 | + | 8.69230i | 0.257883 | + | 0.454354i | ||||
\(367\) | −7.09991 | −0.370612 | −0.185306 | − | 0.982681i | \(-0.559328\pi\) | ||||
−0.185306 | + | 0.982681i | \(0.559328\pi\) | |||||||
\(368\) | −3.28511 | − | 18.8999i | −0.171248 | − | 0.985228i | ||||
\(369\) | 9.74007 | 0.507048 | ||||||||
\(370\) | 6.14977 | + | 10.8350i | 0.319711 | + | 0.563287i | ||||
\(371\) | − | 4.17770i | − | 0.216895i | ||||||
\(372\) | −1.82535 | + | 3.05682i | −0.0946398 | + | 0.158489i | ||||
\(373\) | − | 0.274698i | − | 0.0142233i | −0.999975 | − | 0.00711167i | \(-0.997736\pi\) | ||
0.999975 | − | 0.00711167i | \(-0.00226373\pi\) | |||||||
\(374\) | 4.55675 | − | 2.58633i | 0.235624 | − | 0.133736i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −0.521330 | + | 23.6150i | −0.0268855 | + | 1.21785i | ||||
\(377\) | −2.95231 | −0.152052 | ||||||||
\(378\) | −0.423774 | + | 0.240526i | −0.0217966 | + | 0.0123713i | ||||
\(379\) | 12.9574 | 0.665576 | 0.332788 | − | 0.943002i | \(-0.392011\pi\) | ||||
0.332788 | + | 0.943002i | \(0.392011\pi\) | |||||||
\(380\) | −1.89987 | − | 1.13449i | −0.0974613 | − | 0.0581980i | ||||
\(381\) | −0.639825 | −0.0327792 | ||||||||
\(382\) | 1.21524 | + | 2.14108i | 0.0621770 | + | 0.109547i | ||||
\(383\) | 31.2410 | 1.59634 | 0.798170 | − | 0.602432i | \(-0.205802\pi\) | ||||
0.798170 | + | 0.602432i | \(0.205802\pi\) | |||||||
\(384\) | −10.0762 | + | 5.14495i | −0.514198 | + | 0.262552i | ||||
\(385\) | 0.385078i | 0.0196254i | ||||||||
\(386\) | 6.10654 | + | 10.7589i | 0.310814 | + | 0.547612i | ||||
\(387\) | −8.82654 | −0.448678 | ||||||||
\(388\) | −16.3212 | − | 9.74603i | −0.828582 | − | 0.494780i | ||||
\(389\) | − | 33.0691i | − | 1.67667i | −0.545157 | − | 0.838334i | \(-0.683530\pi\) | ||
0.545157 | − | 0.838334i | \(-0.316470\pi\) | |||||||
\(390\) | 2.95729 | + | 5.21033i | 0.149748 | + | 0.263835i | ||||
\(391\) | 5.03238 | − | 15.0810i | 0.254499 | − | 0.762678i | ||||
\(392\) | −19.4585 | − | 0.429569i | −0.982801 | − | 0.0216965i | ||||
\(393\) | −1.67592 | −0.0845388 | ||||||||
\(394\) | 5.54619 | + | 9.77161i | 0.279413 | + | 0.492287i | ||||
\(395\) | − | 15.3762i | − | 0.773661i | ||||||
\(396\) | −1.14597 | + | 1.91910i | −0.0575872 | + | 0.0964384i | ||||
\(397\) | 32.4640 | 1.62932 | 0.814661 | − | 0.579938i | \(-0.196923\pi\) | ||||
0.814661 | + | 0.579938i | \(0.196923\pi\) | |||||||
\(398\) | −8.84929 | − | 15.5912i | −0.443575 | − | 0.781517i | ||||
\(399\) | 0.381220i | 0.0190849i | ||||||||
\(400\) | 1.89720 | + | 3.52145i | 0.0948600 | + | 0.176073i | ||||
\(401\) | 28.3869i | 1.41757i | 0.705423 | + | 0.708786i | \(0.250757\pi\) | ||||
−0.705423 | + | 0.708786i | \(0.749243\pi\) | |||||||
\(402\) | 2.70615 | − | 1.53596i | 0.134971 | − | 0.0766068i | ||||
\(403\) | − | 7.54140i | − | 0.375664i | ||||||
\(404\) | −8.35599 | + | 13.9934i | −0.415726 | + | 0.696196i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0.167623 | + | 0.295329i | 0.00831901 | + | 0.0146569i | ||||
\(407\) | − | 9.84568i | − | 0.488032i | ||||||
\(408\) | −9.37411 | − | 0.206945i | −0.464088 | − | 0.0102453i | ||||
\(409\) | −35.5814 | −1.75939 | −0.879694 | − | 0.475541i | \(-0.842252\pi\) | ||||
−0.879694 | + | 0.475541i | \(0.842252\pi\) | |||||||
\(410\) | −11.9795 | + | 6.79932i | −0.591623 | + | 0.335794i | ||||
\(411\) | 10.2084 | 0.503542 | ||||||||
\(412\) | −3.55221 | + | 5.94870i | −0.175005 | + | 0.293072i | ||||
\(413\) | − | 5.03133i | − | 0.247576i | ||||||
\(414\) | 1.30866 | + | 6.65488i | 0.0643171 | + | 0.327069i | ||||
\(415\) | 17.0787i | 0.838358i | ||||||||
\(416\) | 12.7374 | − | 20.2990i | 0.624501 | − | 0.995239i | ||||
\(417\) | −8.48317 | −0.415423 | ||||||||
\(418\) | 0.863195 | + | 1.52083i | 0.0422202 | + | 0.0743862i | ||||
\(419\) | −38.1656 | −1.86451 | −0.932255 | − | 0.361802i | \(-0.882162\pi\) | ||||
−0.932255 | + | 0.361802i | \(0.882162\pi\) | |||||||
\(420\) | 0.353300 | − | 0.591654i | 0.0172393 | − | 0.0288697i | ||||
\(421\) | 16.9679i | 0.826965i | 0.910512 | + | 0.413483i | \(0.135688\pi\) | ||||
−0.910512 | + | 0.413483i | \(0.864312\pi\) | |||||||
\(422\) | 18.2303 | − | 10.3472i | 0.887435 | − | 0.503692i | ||||
\(423\) | − | 8.35120i | − | 0.406049i | ||||||
\(424\) | −0.756904 | + | 34.2860i | −0.0367585 | + | 1.66508i | ||||
\(425\) | 3.31506i | 0.160804i | ||||||||
\(426\) | −11.5469 | − | 20.3441i | −0.559451 | − | 0.985674i | ||||
\(427\) | 2.43512i | 0.117844i | ||||||||
\(428\) | 12.4409 | − | 20.8341i | 0.601353 | − | 1.00706i | ||||
\(429\) | − | 4.73456i | − | 0.228587i | ||||||
\(430\) | 10.8559 | − | 6.16160i | 0.523517 | − | 0.297139i | ||||
\(431\) | −23.2458 | −1.11971 | −0.559856 | − | 0.828590i | \(-0.689144\pi\) | ||||
−0.559856 | + | 0.828590i | \(0.689144\pi\) | |||||||
\(432\) | 3.52145 | − | 1.89720i | 0.169426 | − | 0.0912791i | ||||
\(433\) | − | 21.1065i | − | 1.01432i | −0.861853 | − | 0.507158i | \(-0.830696\pi\) | ||
0.861853 | − | 0.507158i | \(-0.169304\pi\) | |||||||
\(434\) | −0.754390 | + | 0.428178i | −0.0362119 | + | 0.0205532i | ||||
\(435\) | 0.696902 | 0.0334139 | ||||||||
\(436\) | 28.2708 | + | 16.8816i | 1.35393 | + | 0.808483i | ||||
\(437\) | 5.03332 | + | 1.67957i | 0.240776 | + | 0.0803449i | ||||
\(438\) | −3.30087 | + | 1.87351i | −0.157722 | + | 0.0895200i | ||||
\(439\) | 15.7660i | 0.752471i | 0.926524 | + | 0.376235i | \(0.122782\pi\) | ||||
−0.926524 | + | 0.376235i | \(0.877218\pi\) | |||||||
\(440\) | 0.0697675 | − | 3.16030i | 0.00332603 | − | 0.150662i | ||||
\(441\) | 6.88128 | 0.327680 | ||||||||
\(442\) | 17.2725 | − | 9.80357i | 0.821570 | − | 0.466308i | ||||
\(443\) | − | 17.9865i | − | 0.854563i | −0.904119 | − | 0.427281i | \(-0.859471\pi\) | ||
0.904119 | − | 0.427281i | \(-0.140529\pi\) | |||||||
\(444\) | −9.03317 | + | 15.1274i | −0.428695 | + | 0.717914i | ||||
\(445\) | −11.9834 | −0.568066 | ||||||||
\(446\) | 2.89321 | − | 1.64213i | 0.136997 | − | 0.0777572i | ||||
\(447\) | −8.00893 | −0.378809 | ||||||||
\(448\) | −2.75376 | − | 0.121644i | −0.130103 | − | 0.00574716i | ||||
\(449\) | 6.47433 | 0.305542 | 0.152771 | − | 0.988262i | \(-0.451180\pi\) | ||||
0.152771 | + | 0.988262i | \(0.451180\pi\) | |||||||
\(450\) | −0.698077 | − | 1.22991i | −0.0329076 | − | 0.0579787i | ||||
\(451\) | 10.8856 | 0.512582 | ||||||||
\(452\) | 27.8039 | + | 16.6028i | 1.30778 | + | 0.780930i | ||||
\(453\) | −15.9200 | −0.747985 | ||||||||
\(454\) | 5.90234 | + | 10.3991i | 0.277010 | + | 0.488054i | ||||
\(455\) | 1.45965i | 0.0684296i | ||||||||
\(456\) | 0.0690684 | − | 3.12864i | 0.00323442 | − | 0.146512i | ||||
\(457\) | 27.2895i | 1.27655i | 0.769809 | + | 0.638274i | \(0.220351\pi\) | ||||
−0.769809 | + | 0.638274i | \(0.779649\pi\) | |||||||
\(458\) | 27.6970 | − | 15.7203i | 1.29420 | − | 0.734562i | ||||
\(459\) | 3.31506 | 0.154734 | ||||||||
\(460\) | −6.25515 | − | 7.27139i | −0.291648 | − | 0.339030i | ||||
\(461\) | 21.5131 | 1.00197 | 0.500983 | − | 0.865457i | \(-0.332972\pi\) | ||||
0.500983 | + | 0.865457i | \(0.332972\pi\) | |||||||
\(462\) | −0.473613 | + | 0.268814i | −0.0220345 | + | 0.0125064i | ||||
\(463\) | − | 24.6597i | − | 1.14603i | −0.819544 | − | 0.573016i | \(-0.805773\pi\) | ||
0.819544 | − | 0.573016i | \(-0.194227\pi\) | |||||||
\(464\) | −1.32216 | − | 2.45411i | −0.0613799 | − | 0.113929i | ||||
\(465\) | 1.78017i | 0.0825534i | ||||||||
\(466\) | 10.5975 | + | 18.6713i | 0.490918 | + | 0.864929i | ||||
\(467\) | −10.2882 | −0.476082 | −0.238041 | − | 0.971255i | \(-0.576505\pi\) | ||||
−0.238041 | + | 0.971255i | \(0.576505\pi\) | |||||||
\(468\) | −4.34384 | + | 7.27442i | −0.200794 | + | 0.336260i | ||||
\(469\) | 0.758118 | 0.0350066 | ||||||||
\(470\) | 5.82978 | + | 10.2713i | 0.268908 | + | 0.473778i | ||||
\(471\) | 11.4730 | 0.528647 | ||||||||
\(472\) | −0.911563 | + | 41.2917i | −0.0419581 | + | 1.90060i | ||||
\(473\) | −9.86461 | −0.453575 | ||||||||
\(474\) | 18.9114 | − | 10.7338i | 0.868630 | − | 0.493018i | ||||
\(475\) | −1.10641 | −0.0507656 | ||||||||
\(476\) | −1.96136 | − | 1.17121i | −0.0898990 | − | 0.0536823i | ||||
\(477\) | − | 12.1249i | − | 0.555160i | ||||||
\(478\) | 7.14674 | − | 4.05636i | 0.326884 | − | 0.185534i | ||||
\(479\) | −33.9683 | −1.55205 | −0.776026 | − | 0.630700i | \(-0.782768\pi\) | ||||
−0.776026 | + | 0.630700i | \(0.782768\pi\) | |||||||
\(480\) | −3.00669 | + | 4.79164i | −0.137236 | + | 0.218707i | ||||
\(481\) | − | 37.3204i | − | 1.70166i | ||||||
\(482\) | 4.93686 | − | 2.80207i | 0.224868 | − | 0.127631i | ||||
\(483\) | −0.523049 | + | 1.56747i | −0.0237996 | + | 0.0713222i | ||||
\(484\) | 9.99841 | − | 16.7438i | 0.454473 | − | 0.761083i | ||||
\(485\) | −9.50481 | −0.431591 | ||||||||
\(486\) | −1.22991 | + | 0.698077i | −0.0557900 | + | 0.0316654i | ||||
\(487\) | − | 10.1278i | − | 0.458936i | −0.973316 | − | 0.229468i | \(-0.926301\pi\) | ||
0.973316 | − | 0.229468i | \(-0.0736987\pi\) | |||||||
\(488\) | 0.441188 | − | 19.9848i | 0.0199716 | − | 0.904668i | ||||
\(489\) | −11.6276 | −0.525819 | ||||||||
\(490\) | −8.46339 | + | 4.80366i | −0.382337 | + | 0.217007i | ||||
\(491\) | 17.7630i | 0.801631i | 0.916159 | + | 0.400816i | \(0.131273\pi\) | ||||
−0.916159 | + | 0.400816i | \(0.868727\pi\) | |||||||
\(492\) | −16.7251 | − | 9.98725i | −0.754028 | − | 0.450260i | ||||
\(493\) | − | 2.31027i | − | 0.104049i | ||||||
\(494\) | 3.27197 | + | 5.76476i | 0.147213 | + | 0.259369i | ||||
\(495\) | 1.11761i | 0.0502328i | ||||||||
\(496\) | 6.26879 | − | 3.37734i | 0.281477 | − | 0.151647i | ||||
\(497\) | − | 5.69932i | − | 0.255649i | ||||||
\(498\) | −21.0053 | + | 11.9222i | −0.941269 | + | 0.534247i | ||||
\(499\) | − | 14.1094i | − | 0.631623i | −0.948822 | − | 0.315811i | \(-0.897723\pi\) | ||
0.948822 | − | 0.315811i | \(-0.102277\pi\) | |||||||
\(500\) | 1.71715 | + | 1.02538i | 0.0767932 | + | 0.0458563i | ||||
\(501\) | 18.3392 | 0.819334 | ||||||||
\(502\) | −9.87739 | − | 17.4026i | −0.440850 | − | 0.776716i | ||||
\(503\) | −8.15173 | −0.363467 | −0.181734 | − | 0.983348i | \(-0.558171\pi\) | ||||
−0.181734 | + | 0.983348i | \(0.558171\pi\) | |||||||
\(504\) | 0.974314 | + | 0.0215091i | 0.0433994 | + | 0.000958093i | ||||
\(505\) | 8.14918i | 0.362634i | ||||||||
\(506\) | 1.46257 | + | 7.43755i | 0.0650191 | + | 0.330639i | ||||
\(507\) | − | 4.94653i | − | 0.219683i | ||||||
\(508\) | 1.09868 | + | 0.656063i | 0.0487458 | + | 0.0291081i | ||||
\(509\) | 39.1703 | 1.73619 | 0.868096 | − | 0.496397i | \(-0.165344\pi\) | ||||
0.868096 | + | 0.496397i | \(0.165344\pi\) | |||||||
\(510\) | −4.07723 | + | 2.31416i | −0.180543 | + | 0.102473i | ||||
\(511\) | −0.924727 | −0.0409075 | ||||||||
\(512\) | 22.5778 | + | 1.49724i | 0.997808 | + | 0.0661694i | ||||
\(513\) | 1.10641i | 0.0488492i | ||||||||
\(514\) | −2.64086 | − | 4.65282i | −0.116483 | − | 0.205227i | ||||
\(515\) | 3.46429i | 0.152655i | ||||||||
\(516\) | 15.1565 | + | 9.05054i | 0.667227 | + | 0.398428i | ||||
\(517\) | − | 9.33337i | − | 0.410481i | ||||||
\(518\) | −3.73328 | + | 2.11894i | −0.164031 | + | 0.0931009i | ||||
\(519\) | − | 7.02511i | − | 0.308368i | ||||||
\(520\) | 0.264456 | − | 11.9792i | 0.0115972 | − | 0.525325i | ||||
\(521\) | − | 26.2040i | − | 1.14802i | −0.818850 | − | 0.574008i | \(-0.805388\pi\) | ||
0.818850 | − | 0.574008i | \(-0.194612\pi\) | |||||||
\(522\) | 0.486491 | + | 0.857130i | 0.0212931 | + | 0.0375156i | ||||
\(523\) | 13.1813 | 0.576376 | 0.288188 | − | 0.957574i | \(-0.406947\pi\) | ||||
0.288188 | + | 0.957574i | \(0.406947\pi\) | |||||||
\(524\) | 2.87780 | + | 1.71845i | 0.125717 | + | 0.0750707i | ||||
\(525\) | − | 0.344556i | − | 0.0150376i | ||||||
\(526\) | −8.04372 | − | 14.1719i | −0.350723 | − | 0.617925i | ||||
\(527\) | 5.90136 | 0.257067 | ||||||||
\(528\) | 3.93561 | − | 2.12033i | 0.171275 | − | 0.0922754i | ||||
\(529\) | 18.3911 | + | 13.8118i | 0.799614 | + | 0.600515i | ||||
\(530\) | 8.46410 | + | 14.9126i | 0.367657 | + | 0.647761i | ||||
\(531\) | − | 14.6024i | − | 0.633689i | ||||||
\(532\) | 0.390895 | − | 0.654612i | 0.0169474 | − | 0.0283810i | ||||
\(533\) | 41.2622 | 1.78726 | ||||||||
\(534\) | −8.36531 | − | 14.7385i | −0.362002 | − | 0.637798i | ||||
\(535\) | − | 12.1330i | − | 0.524555i | ||||||
\(536\) | −6.22181 | − | 0.137354i | −0.268741 | − | 0.00593278i | ||||
\(537\) | −3.75048 | −0.161845 | ||||||||
\(538\) | 17.7564 | + | 31.2843i | 0.765532 | + | 1.34876i | ||||
\(539\) | 7.69058 | 0.331257 | ||||||||
\(540\) | 1.02538 | − | 1.71715i | 0.0441252 | − | 0.0738943i | ||||
\(541\) | 0.429117 | 0.0184492 | 0.00922459 | − | 0.999957i | \(-0.497064\pi\) | ||||
0.00922459 | + | 0.999957i | \(0.497064\pi\) | |||||||
\(542\) | 8.44172 | − | 4.79136i | 0.362603 | − | 0.205807i | ||||
\(543\) | −9.93221 | −0.426232 | ||||||||
\(544\) | 15.8845 | + | 9.96736i | 0.681044 | + | 0.427347i | ||||
\(545\) | 16.4638 | 0.705232 | ||||||||
\(546\) | −1.79525 | + | 1.01895i | −0.0768296 | + | 0.0436070i | ||||
\(547\) | − | 5.27276i | − | 0.225447i | −0.993626 | − | 0.112724i | \(-0.964043\pi\) | ||
0.993626 | − | 0.112724i | \(-0.0359574\pi\) | |||||||
\(548\) | −17.5293 | − | 10.4674i | −0.748814 | − | 0.447147i | ||||
\(549\) | 7.06741i | 0.301630i | ||||||||
\(550\) | −0.780176 | − | 1.37456i | −0.0332668 | − | 0.0586115i | ||||
\(551\) | 0.771060 | 0.0328482 | ||||||||
\(552\) | 4.57661 | − | 12.7693i | 0.194793 | − | 0.543497i | ||||
\(553\) | 5.29796 | 0.225292 | ||||||||
\(554\) | 11.5985 | + | 20.4349i | 0.492772 | + | 0.868195i | ||||
\(555\) | 8.80960i | 0.373946i | ||||||||
\(556\) | 14.5669 | + | 8.69846i | 0.617773 | + | 0.368897i | ||||
\(557\) | − | 18.8981i | − | 0.800739i | −0.916354 | − | 0.400369i | \(-0.868882\pi\) | ||
0.916354 | − | 0.400369i | \(-0.131118\pi\) | |||||||
\(558\) | −2.18946 | + | 1.24270i | −0.0926871 | + | 0.0526075i | ||||
\(559\) | −37.3922 | −1.58152 | ||||||||
\(560\) | −1.21334 | + | 0.653691i | −0.0512729 | + | 0.0276235i | ||||
\(561\) | 3.70493 | 0.156422 | ||||||||
\(562\) | −8.39573 | + | 4.76526i | −0.354153 | + | 0.201010i | ||||
\(563\) | 27.0492 | 1.13999 | 0.569994 | − | 0.821649i | \(-0.306946\pi\) | ||||
0.569994 | + | 0.821649i | \(0.306946\pi\) | |||||||
\(564\) | −8.56314 | + | 14.3403i | −0.360573 | + | 0.603834i | ||||
\(565\) | 16.1919 | 0.681198 | ||||||||
\(566\) | −0.113648 | − | 0.200232i | −0.00477697 | − | 0.00841636i | ||||
\(567\) | −0.344556 | −0.0144700 | ||||||||
\(568\) | −1.03259 | + | 46.7738i | −0.0433264 | + | 1.96258i | ||||
\(569\) | 13.1945i | 0.553143i | 0.960993 | + | 0.276571i | \(0.0891982\pi\) | ||||
−0.960993 | + | 0.276571i | \(0.910802\pi\) | |||||||
\(570\) | −0.772359 | − | 1.36079i | −0.0323506 | − | 0.0569972i | ||||
\(571\) | −1.70748 | −0.0714558 | −0.0357279 | − | 0.999362i | \(-0.511375\pi\) | ||||
−0.0357279 | + | 0.999362i | \(0.511375\pi\) | |||||||
\(572\) | −4.85472 | + | 8.12995i | −0.202986 | + | 0.339930i | ||||
\(573\) | 1.74084i | 0.0727246i | ||||||||
\(574\) | −2.34274 | − | 4.12759i | −0.0977842 | − | 0.172282i | ||||
\(575\) | −4.54924 | − | 1.51804i | −0.189716 | − | 0.0633066i | ||||
\(576\) | −7.99221 | − | 0.353047i | −0.333009 | − | 0.0147103i | ||||
\(577\) | −37.2727 | −1.55168 | −0.775842 | − | 0.630927i | \(-0.782675\pi\) | ||||
−0.775842 | + | 0.630927i | \(0.782675\pi\) | |||||||
\(578\) | −4.19572 | − | 7.39228i | −0.174519 | − | 0.307479i | ||||
\(579\) | 8.74766i | 0.363540i | ||||||||
\(580\) | −1.19668 | − | 0.714588i | −0.0496896 | − | 0.0296717i | ||||
\(581\) | −5.88455 | −0.244132 | ||||||||
\(582\) | −6.63509 | − | 11.6901i | −0.275033 | − | 0.484570i | ||||
\(583\) | − | 13.5509i | − | 0.561220i | ||||||
\(584\) | 7.58915 | + | 0.167539i | 0.314041 | + | 0.00693283i | ||||
\(585\) | 4.23633i | 0.175151i | ||||||||
\(586\) | 18.3970 | − | 10.4418i | 0.759974 | − | 0.431347i | ||||
\(587\) | 14.5005i | 0.598498i | 0.954175 | + | 0.299249i | \(0.0967362\pi\) | ||||
−0.954175 | + | 0.299249i | \(0.903264\pi\) | |||||||
\(588\) | −11.8162 | − | 7.05591i | −0.487291 | − | 0.290981i | ||||
\(589\) | 1.96960i | 0.0811559i | ||||||||
\(590\) | 10.1936 | + | 17.9597i | 0.419663 | + | 0.739387i | ||||
\(591\) | 7.94495i | 0.326812i | ||||||||
\(592\) | 31.0226 | − | 16.7136i | 1.27502 | − | 0.686923i | ||||
\(593\) | 32.2207 | 1.32315 | 0.661574 | − | 0.749880i | \(-0.269889\pi\) | ||||
0.661574 | + | 0.749880i | \(0.269889\pi\) | |||||||
\(594\) | −1.37456 | + | 0.780176i | −0.0563990 | + | 0.0320110i | ||||
\(595\) | −1.14222 | −0.0468265 | ||||||||
\(596\) | 13.7525 | + | 8.21218i | 0.563325 | + | 0.336384i | ||||
\(597\) | − | 12.6767i | − | 0.518821i | ||||||
\(598\) | 5.54392 | + | 28.1923i | 0.226708 | + | 1.15287i | ||||
\(599\) | − | 0.676848i | − | 0.0276553i | −0.999904 | − | 0.0138276i | \(-0.995598\pi\) | ||
0.999904 | − | 0.0138276i | \(-0.00440161\pi\) | |||||||
\(600\) | −0.0624257 | + | 2.82774i | −0.00254852 | + | 0.115442i | ||||
\(601\) | −11.7698 | −0.480100 | −0.240050 | − | 0.970760i | \(-0.577164\pi\) | ||||
−0.240050 | + | 0.970760i | \(0.577164\pi\) | |||||||
\(602\) | 2.12301 | + | 3.74046i | 0.0865276 | + | 0.152450i | ||||
\(603\) | 2.20028 | 0.0896022 | ||||||||
\(604\) | 27.3369 | + | 16.3240i | 1.11232 | + | 0.664213i | ||||
\(605\) | − | 9.75095i | − | 0.396433i | ||||||
\(606\) | −10.0228 | + | 5.68875i | −0.407148 | + | 0.231090i | ||||
\(607\) | 3.30282i | 0.134057i | 0.997751 | + | 0.0670286i | \(0.0213519\pi\) | ||||
−0.997751 | + | 0.0670286i | \(0.978648\pi\) | |||||||
\(608\) | −3.32664 | + | 5.30152i | −0.134913 | + | 0.215005i | ||||
\(609\) | 0.240122i | 0.00973022i | ||||||||
\(610\) | −4.93359 | − | 8.69230i | −0.199755 | − | 0.351941i | ||||
\(611\) | − | 35.3785i | − | 1.43126i | ||||||
\(612\) | −5.69244 | − | 3.39919i | −0.230103 | − | 0.137404i | ||||
\(613\) | 21.2125i | 0.856763i | 0.903598 | + | 0.428382i | \(0.140916\pi\) | ||||
−0.903598 | + | 0.428382i | \(0.859084\pi\) | |||||||
\(614\) | −10.6958 | + | 6.07071i | −0.431646 | + | 0.244994i | ||||
\(615\) | −9.74007 | −0.392758 | ||||||||
\(616\) | 1.08890 | + | 0.0240388i | 0.0438731 | + | 0.000968550i | ||||
\(617\) | − | 28.3728i | − | 1.14225i | −0.820864 | − | 0.571124i | \(-0.806508\pi\) | ||
0.820864 | − | 0.571124i | \(-0.193492\pi\) | |||||||
\(618\) | −4.26078 | + | 2.41834i | −0.171394 | + | 0.0972799i | ||||
\(619\) | −4.37548 | −0.175866 | −0.0879328 | − | 0.996126i | \(-0.528026\pi\) | ||||
−0.0879328 | + | 0.996126i | \(0.528026\pi\) | |||||||
\(620\) | 1.82535 | − | 3.05682i | 0.0733077 | − | 0.122765i | ||||
\(621\) | −1.51804 | + | 4.54924i | −0.0609168 | + | 0.182555i | ||||
\(622\) | −7.06572 | + | 4.01037i | −0.283310 | + | 0.160801i | ||||
\(623\) | − | 4.12894i | − | 0.165422i | ||||||
\(624\) | 14.9181 | − | 8.03717i | 0.597200 | − | 0.321744i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.17337 | + | 0.665982i | −0.0468972 | + | 0.0266180i | ||||
\(627\) | 1.23653i | 0.0493824i | ||||||||
\(628\) | −19.7008 | − | 11.7641i | −0.786148 | − | 0.469440i | ||||
\(629\) | 29.2043 | 1.16445 | ||||||||
\(630\) | 0.423774 | − | 0.240526i | 0.0168836 | − | 0.00958280i | ||||
\(631\) | −38.6015 | −1.53670 | −0.768351 | − | 0.640028i | \(-0.778923\pi\) | ||||
−0.768351 | + | 0.640028i | \(0.778923\pi\) | |||||||
\(632\) | −43.4799 | − | 0.959870i | −1.72954 | − | 0.0381816i | ||||
\(633\) | 14.8224 | 0.589137 | ||||||||
\(634\) | −2.32539 | − | 4.09701i | −0.0923530 | − | 0.162713i | ||||
\(635\) | 0.639825 | 0.0253907 | ||||||||
\(636\) | −12.4326 | + | 20.8202i | −0.492984 | + | 0.825576i | ||||
\(637\) | 29.1514 | 1.15502 | ||||||||
\(638\) | 0.543707 | + | 0.957936i | 0.0215255 | + | 0.0379250i | ||||
\(639\) | − | 16.5411i | − | 0.654354i | ||||||
\(640\) | 10.0762 | − | 5.14495i | 0.398296 | − | 0.203372i | ||||
\(641\) | 42.8647i | 1.69306i | 0.532345 | + | 0.846528i | \(0.321311\pi\) | ||||
−0.532345 | + | 0.846528i | \(0.678689\pi\) | |||||||
\(642\) | 14.9225 | − | 8.46975i | 0.588945 | − | 0.334275i | ||||
\(643\) | 26.5465 | 1.04689 | 0.523446 | − | 0.852059i | \(-0.324646\pi\) | ||||
0.523446 | + | 0.852059i | \(0.324646\pi\) | |||||||
\(644\) | 2.50540 | − | 2.15525i | 0.0987265 | − | 0.0849287i | ||||
\(645\) | 8.82654 | 0.347545 | ||||||||
\(646\) | −4.51109 | + | 2.56041i | −0.177487 | + | 0.100738i | ||||
\(647\) | 35.0008i | 1.37602i | 0.725701 | + | 0.688011i | \(0.241516\pi\) | ||||
−0.725701 | + | 0.688011i | \(0.758484\pi\) | |||||||
\(648\) | 2.82774 | + | 0.0624257i | 0.111084 | + | 0.00245231i | ||||
\(649\) | − | 16.3197i | − | 0.640605i | ||||||
\(650\) | −2.95729 | − | 5.21033i | −0.115994 | − | 0.204366i | ||||
\(651\) | −0.613368 | −0.0240398 | ||||||||
\(652\) | 19.9664 | + | 11.9227i | 0.781943 | + | 0.466929i | ||||
\(653\) | 27.3819 | 1.07154 | 0.535768 | − | 0.844365i | \(-0.320022\pi\) | ||||
0.535768 | + | 0.844365i | \(0.320022\pi\) | |||||||
\(654\) | 11.4930 | + | 20.2491i | 0.449412 | + | 0.791801i | ||||
\(655\) | 1.67592 | 0.0654835 | ||||||||
\(656\) | 18.4789 | + | 34.2992i | 0.721478 | + | 1.33916i | ||||
\(657\) | −2.68382 | −0.104706 | ||||||||
\(658\) | −3.53902 | + | 2.00868i | −0.137965 | + | 0.0783067i | ||||
\(659\) | −25.7125 | −1.00162 | −0.500808 | − | 0.865558i | \(-0.666964\pi\) | ||||
−0.500808 | + | 0.865558i | \(0.666964\pi\) | |||||||
\(660\) | 1.14597 | − | 1.91910i | 0.0446069 | − | 0.0747009i | ||||
\(661\) | − | 1.18452i | − | 0.0460726i | −0.999735 | − | 0.0230363i | \(-0.992667\pi\) | ||
0.999735 | − | 0.0230363i | \(-0.00733333\pi\) | |||||||
\(662\) | −26.2891 | + | 14.9212i | −1.02176 | + | 0.579930i | ||||
\(663\) | 14.0437 | 0.545411 | ||||||||
\(664\) | 48.2940 | + | 1.06615i | 1.87417 | + | 0.0413745i | ||||
\(665\) | − | 0.381220i | − | 0.0147831i | ||||||
\(666\) | −10.8350 | + | 6.14977i | −0.419850 | + | 0.238299i | ||||
\(667\) | 3.17037 | + | 1.05792i | 0.122757 | + | 0.0409630i | ||||
\(668\) | −31.4911 | − | 18.8046i | −1.21843 | − | 0.727571i | ||||
\(669\) | 2.35237 | 0.0909477 | ||||||||
\(670\) | −2.70615 | + | 1.53596i | −0.104548 | + | 0.0593394i | ||||
\(671\) | 7.89859i | 0.304922i | ||||||||
\(672\) | −1.65099 | − | 1.03597i | −0.0636882 | − | 0.0399636i | ||||
\(673\) | −30.4877 | −1.17522 | −0.587608 | − | 0.809146i | \(-0.699930\pi\) | ||||
−0.587608 | + | 0.809146i | \(0.699930\pi\) | |||||||
\(674\) | 29.2449 | − | 16.5989i | 1.12647 | − | 0.639365i | ||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | −5.07206 | + | 8.49393i | −0.195079 | + | 0.326689i | ||||
\(677\) | − | 28.5320i | − | 1.09657i | −0.836290 | − | 0.548287i | \(-0.815280\pi\) | ||
0.836290 | − | 0.548287i | \(-0.184720\pi\) | |||||||
\(678\) | 11.3032 | + | 19.9146i | 0.434096 | + | 0.764817i | ||||
\(679\) | − | 3.27494i | − | 0.125681i | ||||||
\(680\) | 9.37411 | + | 0.206945i | 0.359481 | + | 0.00793596i | ||||
\(681\) | 8.45514i | 0.324002i | ||||||||
\(682\) | −2.44695 | + | 1.38885i | −0.0936987 | + | 0.0531817i | ||||
\(683\) | 8.20988i | 0.314142i | 0.987587 | + | 0.157071i | \(0.0502052\pi\) | ||||
−0.987587 | + | 0.157071i | \(0.949795\pi\) | |||||||
\(684\) | 1.13449 | − | 1.89987i | 0.0433783 | − | 0.0726434i | ||||
\(685\) | −10.2084 | −0.390042 | ||||||||
\(686\) | −3.33881 | − | 5.88253i | −0.127477 | − | 0.224596i | ||||
\(687\) | 22.5195 | 0.859172 | ||||||||
\(688\) | −16.7457 | − | 31.0822i | −0.638424 | − | 1.18500i | ||||
\(689\) | − | 51.3651i | − | 1.95685i | ||||||
\(690\) | −1.30866 | − | 6.65488i | −0.0498198 | − | 0.253347i | ||||
\(691\) | − | 5.68367i | − | 0.216217i | −0.994139 | − | 0.108109i | \(-0.965521\pi\) | ||
0.994139 | − | 0.108109i | \(-0.0344794\pi\) | |||||||
\(692\) | −7.20339 | + | 12.0632i | −0.273832 | + | 0.458572i | ||||
\(693\) | −0.385078 | −0.0146279 | ||||||||
\(694\) | −33.2435 | + | 18.8684i | −1.26191 | + | 0.716234i | ||||
\(695\) | 8.48317 | 0.321785 | ||||||||
\(696\) | 0.0435046 | − | 1.97066i | 0.00164904 | − | 0.0746976i | ||||
\(697\) | 32.2889i | 1.22303i | ||||||||
\(698\) | 10.7327 | + | 18.9095i | 0.406238 | + | 0.715735i | ||||
\(699\) | 15.1809i | 0.574196i | ||||||||
\(700\) | −0.353300 | + | 0.591654i | −0.0133535 | + | 0.0223624i | ||||
\(701\) | 27.0506i | 1.02169i | 0.859674 | + | 0.510843i | \(0.170667\pi\) | ||||
−0.859674 | + | 0.510843i | \(0.829333\pi\) | |||||||
\(702\) | −5.21033 | + | 2.95729i | −0.196651 | + | 0.111616i | ||||
\(703\) | 9.74702i | 0.367616i | ||||||||
\(704\) | −8.93216 | − | 0.394568i | −0.336643 | − | 0.0148709i | ||||
\(705\) | 8.35120i | 0.314524i | ||||||||
\(706\) | 10.4087 | + | 18.3388i | 0.391738 | + | 0.690188i | ||||
\(707\) | −2.80785 | −0.105600 | ||||||||
\(708\) | −14.9729 | + | 25.0744i | −0.562718 | + | 0.942355i | ||||
\(709\) | − | 32.4076i | − | 1.21709i | −0.793518 | − | 0.608547i | \(-0.791753\pi\) | ||
0.793518 | − | 0.608547i | \(-0.208247\pi\) | |||||||
\(710\) | 11.5469 | + | 20.3441i | 0.433349 | + | 0.763500i | ||||
\(711\) | 15.3762 | 0.576653 | ||||||||
\(712\) | −0.748070 | + | 33.8858i | −0.0280351 | + | 1.26992i | ||||
\(713\) | −2.70237 | + | 8.09842i | −0.101204 | + | 0.303288i | ||||
\(714\) | −0.797358 | − | 1.40483i | −0.0298404 | − | 0.0525746i | ||||
\(715\) | 4.73456i | 0.177063i | ||||||||
\(716\) | 6.44013 | + | 3.84566i | 0.240679 | + | 0.143719i | ||||
\(717\) | 5.81077 | 0.217007 | ||||||||
\(718\) | −23.7681 | − | 41.8760i | −0.887016 | − | 1.56280i | ||||
\(719\) | 12.2149i | 0.455538i | 0.973715 | + | 0.227769i | \(0.0731431\pi\) | ||||
−0.973715 | + | 0.227769i | \(0.926857\pi\) | |||||||
\(720\) | −3.52145 | + | 1.89720i | −0.131237 | + | 0.0707045i | ||||
\(721\) | −1.19364 | −0.0444535 | ||||||||
\(722\) | 12.4089 | + | 21.8628i | 0.461812 | + | 0.813648i | ||||
\(723\) | 4.01399 | 0.149282 | ||||||||
\(724\) | 17.0551 | + | 10.1843i | 0.633847 | + | 0.378495i | ||||
\(725\) | −0.696902 | −0.0258823 | ||||||||
\(726\) | 11.9928 | − | 6.80691i | 0.445096 | − | 0.252628i | ||||
\(727\) | 22.7019 | 0.841966 | 0.420983 | − | 0.907068i | \(-0.361685\pi\) | ||||
0.420983 | + | 0.907068i | \(0.361685\pi\) | |||||||
\(728\) | 4.12752 | + | 0.0911199i | 0.152976 | + | 0.00337713i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.30087 | − | 1.87351i | 0.122171 | − | 0.0693419i | ||||
\(731\) | − | 29.2605i | − | 1.08224i | ||||||
\(732\) | 7.24676 | − | 12.1358i | 0.267848 | − | 0.448552i | ||||
\(733\) | 22.3687i | 0.826205i | 0.910685 | + | 0.413103i | \(0.135555\pi\) | ||||
−0.910685 | + | 0.413103i | \(0.864445\pi\) | |||||||
\(734\) | 4.95628 | + | 8.73228i | 0.182940 | + | 0.322314i | ||||
\(735\) | −6.88128 | −0.253820 | ||||||||
\(736\) | −20.9521 | + | 17.2340i | −0.772303 | + | 0.635254i | ||||
\(737\) | 2.45905 | 0.0905802 | ||||||||
\(738\) | −6.79932 | − | 11.9795i | −0.250286 | − | 0.440970i | ||||
\(739\) | − | 3.85801i | − | 0.141919i | −0.997479 | − | 0.0709596i | \(-0.977394\pi\) | ||
0.997479 | − | 0.0709596i | \(-0.0226061\pi\) | |||||||
\(740\) | 9.03317 | − | 15.1274i | 0.332066 | − | 0.556094i | ||||
\(741\) | 4.68712i | 0.172186i | ||||||||
\(742\) | −5.13821 | + | 2.91635i | −0.188630 | + | 0.107063i | ||||
\(743\) | −8.11201 | −0.297601 | −0.148800 | − | 0.988867i | \(-0.547541\pi\) | ||||
−0.148800 | + | 0.988867i | \(0.547541\pi\) | |||||||
\(744\) | 5.03385 | + | 0.111128i | 0.184550 | + | 0.00407416i | ||||
\(745\) | 8.00893 | 0.293424 | ||||||||
\(746\) | −0.337855 | + | 0.191760i | −0.0123698 | + | 0.00702085i | ||||
\(747\) | −17.0787 | −0.624875 | ||||||||
\(748\) | −6.36192 | − | 3.79896i | −0.232615 | − | 0.138904i | ||||
\(749\) | 4.18049 | 0.152752 | ||||||||
\(750\) | 0.698077 | + | 1.22991i | 0.0254902 | + | 0.0449101i | ||||
\(751\) | 46.8539 | 1.70972 | 0.854861 | − | 0.518858i | \(-0.173643\pi\) | ||||
0.854861 | + | 0.518858i | \(0.173643\pi\) | |||||||
\(752\) | 29.4084 | − | 15.8439i | 1.07241 | − | 0.577768i | ||||
\(753\) | − | 14.1494i | − | 0.515634i | ||||||
\(754\) | 2.06094 | + | 3.63109i | 0.0750550 | + | 0.132236i | ||||
\(755\) | 15.9200 | 0.579387 | ||||||||
\(756\) | 0.591654 | + | 0.353300i | 0.0215182 | + | 0.0128494i | ||||
\(757\) | − | 18.3340i | − | 0.666359i | −0.942863 | − | 0.333179i | \(-0.891879\pi\) | ||
0.942863 | − | 0.333179i | \(-0.108121\pi\) | |||||||
\(758\) | −9.04524 | − | 15.9365i | −0.328538 | − | 0.578838i | ||||
\(759\) | −1.69657 | + | 5.08427i | −0.0615817 | + | 0.184547i | ||||
\(760\) | −0.0690684 | + | 3.12864i | −0.00250537 | + | 0.113488i | ||||
\(761\) | 44.7295 | 1.62144 | 0.810722 | − | 0.585431i | \(-0.199075\pi\) | ||||
0.810722 | + | 0.585431i | \(0.199075\pi\) | |||||||
\(762\) | 0.446647 | + | 0.786930i | 0.0161803 | + | 0.0285075i | ||||
\(763\) | 5.67270i | 0.205366i | ||||||||
\(764\) | 1.78502 | − | 2.98928i | 0.0645797 | − | 0.108148i | ||||
\(765\) | −3.31506 | −0.119856 | ||||||||
\(766\) | −21.8086 | − | 38.4237i | −0.787977 | − | 1.38831i | ||||
\(767\) | − | 61.8605i | − | 2.23365i | ||||||
\(768\) | 13.3618 | + | 8.80127i | 0.482152 | + | 0.317588i | ||||
\(769\) | − | 35.2621i | − | 1.27158i | −0.771861 | − | 0.635791i | \(-0.780674\pi\) | ||
0.771861 | − | 0.635791i | \(-0.219326\pi\) | |||||||
\(770\) | 0.473613 | − | 0.268814i | 0.0170678 | − | 0.00968739i | ||||
\(771\) | − | 3.78305i | − | 0.136243i | ||||||
\(772\) | 8.96966 | − | 15.0210i | 0.322825 | − | 0.540619i | ||||
\(773\) | 26.9995i | 0.971106i | 0.874207 | + | 0.485553i | \(0.161382\pi\) | ||||
−0.874207 | + | 0.485553i | \(0.838618\pi\) | |||||||
\(774\) | 6.16160 | + | 10.8559i | 0.221474 | + | 0.390207i | ||||
\(775\) | − | 1.78017i | − | 0.0639456i | ||||||
\(776\) | −0.593345 | + | 26.8771i | −0.0212998 | + | 0.964832i | ||||
\(777\) | −3.03540 | −0.108894 | ||||||||
\(778\) | −40.6721 | + | 23.0847i | −1.45817 | + | 0.827628i | ||||
\(779\) | −10.7765 | −0.386109 | ||||||||
\(780\) | 4.34384 | − | 7.27442i | 0.155535 | − | 0.260466i | ||||
\(781\) | − | 18.4864i | − | 0.661496i | ||||||
\(782\) | −22.0613 | + | 4.33828i | −0.788910 | + | 0.155136i | ||||
\(783\) | 0.696902i | 0.0249053i | ||||||||
\(784\) | 13.0552 | + | 24.2321i | 0.466256 | + | 0.865433i | ||||
\(785\) | −11.4730 | −0.409488 | ||||||||
\(786\) | 1.16992 | + | 2.06123i | 0.0417296 | + | 0.0735218i | ||||
\(787\) | −29.4507 | −1.04980 | −0.524902 | − | 0.851163i | \(-0.675898\pi\) | ||||
−0.524902 | + | 0.851163i | \(0.675898\pi\) | |||||||
\(788\) | 8.14658 | − | 13.6427i | 0.290210 | − | 0.486000i | ||||
\(789\) | − | 11.5227i | − | 0.410219i | ||||||
\(790\) | −18.9114 | + | 10.7338i | −0.672838 | + | 0.381890i | ||||
\(791\) | 5.57901i | 0.198367i | ||||||||
\(792\) | 3.16030 | + | 0.0697675i | 0.112297 | + | 0.00247908i | ||||
\(793\) | 29.9399i | 1.06320i | ||||||||
\(794\) | −22.6624 | − | 39.9279i | −0.804257 | − | 1.41699i | ||||
\(795\) | 12.1249i | 0.430025i | ||||||||
\(796\) | −12.9984 | + | 21.7677i | −0.460715 | + | 0.771537i | ||||
\(797\) | − | 36.0729i | − | 1.27777i | −0.769303 | − | 0.638884i | \(-0.779396\pi\) | ||
0.769303 | − | 0.638884i | \(-0.220604\pi\) | |||||||
\(798\) | 0.468868 | − | 0.266121i | 0.0165977 | − | 0.00942057i | ||||
\(799\) | 27.6847 | 0.979414 | ||||||||
\(800\) | 3.00669 | − | 4.79164i | 0.106303 | − | 0.169410i | ||||
\(801\) | − | 11.9834i | − | 0.423411i | ||||||
\(802\) | 34.9134 | − | 19.8162i | 1.23284 | − | 0.699735i | ||||
\(803\) | −2.99946 | −0.105849 | ||||||||
\(804\) | −3.77820 | − | 2.25612i | −0.133247 | − | 0.0795671i | ||||
\(805\) | 0.523049 | − | 1.56747i | 0.0184351 | − | 0.0552459i | ||||
\(806\) | −9.27527 | + | 5.26447i | −0.326707 | + | 0.185433i | ||||
\(807\) | 25.4362i | 0.895395i | ||||||||
\(808\) | 23.0438 | + | 0.508718i | 0.810676 | + | 0.0178966i | ||||
\(809\) | −55.4940 | −1.95106 | −0.975532 | − | 0.219858i | \(-0.929440\pi\) | ||||
−0.975532 | + | 0.219858i | \(0.929440\pi\) | |||||||
\(810\) | 1.22991 | − | 0.698077i | 0.0432148 | − | 0.0245279i | ||||
\(811\) | 34.6894i | 1.21811i | 0.793127 | + | 0.609056i | \(0.208451\pi\) | ||||
−0.793127 | + | 0.609056i | \(0.791549\pi\) | |||||||
\(812\) | 0.246216 | − | 0.412325i | 0.00864047 | − | 0.0144698i | ||||
\(813\) | 6.86367 | 0.240719 | ||||||||
\(814\) | −12.1093 | + | 6.87304i | −0.424432 | + | 0.240900i | ||||
\(815\) | 11.6276 | 0.407298 | ||||||||
\(816\) | 6.28932 | + | 11.6738i | 0.220170 | + | 0.408665i | ||||
\(817\) | 9.76577 | 0.341661 | ||||||||
\(818\) | 24.8385 | + | 43.7621i | 0.868459 | + | 1.53011i | ||||
\(819\) | −1.45965 | −0.0510044 | ||||||||
\(820\) | 16.7251 | + | 9.98725i | 0.584068 | + | 0.348770i | ||||
\(821\) | 39.8207 | 1.38975 | 0.694875 | − | 0.719130i | \(-0.255460\pi\) | ||||
0.694875 | + | 0.719130i | \(0.255460\pi\) | |||||||
\(822\) | −7.12622 | − | 12.5554i | −0.248556 | − | 0.437921i | ||||
\(823\) | 43.6703i | 1.52225i | 0.648605 | + | 0.761126i | \(0.275353\pi\) | ||||
−0.648605 | + | 0.761126i | \(0.724647\pi\) | |||||||
\(824\) | 9.79611 | + | 0.216261i | 0.341264 | + | 0.00753380i | ||||
\(825\) | − | 1.11761i | − | 0.0389101i | ||||||
\(826\) | −6.18810 | + | 3.51225i | −0.215312 | + | 0.122207i | ||||
\(827\) | 25.7183 | 0.894311 | 0.447156 | − | 0.894456i | \(-0.352437\pi\) | ||||
0.447156 | + | 0.894456i | \(0.352437\pi\) | |||||||
\(828\) | 7.27139 | − | 6.25515i | 0.252698 | − | 0.217382i | ||||
\(829\) | 16.0133 | 0.556165 | 0.278083 | − | 0.960557i | \(-0.410301\pi\) | ||||
0.278083 | + | 0.960557i | \(0.410301\pi\) | |||||||
\(830\) | 21.0053 | − | 11.9222i | 0.729104 | − | 0.413826i | ||||
\(831\) | 16.6149i | 0.576364i | ||||||||
\(832\) | −33.8577 | − | 1.49563i | −1.17380 | − | 0.0518515i | ||||
\(833\) | 22.8118i | 0.790383i | ||||||||
\(834\) | 5.92190 | + | 10.4336i | 0.205059 | + | 0.361285i | ||||
\(835\) | −18.3392 | −0.634653 | ||||||||
\(836\) | 1.26791 | − | 2.12331i | 0.0438517 | − | 0.0734363i | ||||
\(837\) | −1.78017 | −0.0615317 | ||||||||
\(838\) | 26.6425 | + | 46.9404i | 0.920350 | + | 1.62153i | ||||
\(839\) | 5.08265 | 0.175473 | 0.0877363 | − | 0.996144i | \(-0.472037\pi\) | ||||
0.0877363 | + | 0.996144i | \(0.472037\pi\) | |||||||
\(840\) | −0.974314 | − | 0.0215091i | −0.0336170 | − | 0.000742136i | ||||
\(841\) | −28.5143 | −0.983253 | ||||||||
\(842\) | 20.8691 | − | 11.8449i | 0.719196 | − | 0.408202i | ||||
\(843\) | −6.82628 | −0.235109 | ||||||||
\(844\) | −25.4522 | − | 15.1985i | −0.876102 | − | 0.523155i | ||||
\(845\) | 4.94653i | 0.170166i | ||||||||
\(846\) | −10.2713 | + | 5.82978i | −0.353133 | + | 0.200432i | ||||
\(847\) | 3.35975 | 0.115442 | ||||||||
\(848\) | 42.6972 | − | 23.0033i | 1.46623 | − | 0.789938i | ||||
\(849\) | − | 0.162801i | − | 0.00558732i | ||||||
\(850\) | 4.07723 | − | 2.31416i | 0.139848 | − | 0.0793751i | ||||
\(851\) | −13.3733 | + | 40.0769i | −0.458431 | + | 1.37382i | ||||
\(852\) | −16.9608 | + | 28.4035i | −0.581069 | + | 0.973087i | ||||
\(853\) | 37.7514 | 1.29258 | 0.646292 | − | 0.763090i | \(-0.276319\pi\) | ||||
0.646292 | + | 0.763090i | \(0.276319\pi\) | |||||||
\(854\) | 2.99498 | − | 1.69990i | 0.102486 | − | 0.0581693i | ||||
\(855\) | − | 1.10641i | − | 0.0378384i | ||||||
\(856\) | −34.3089 | − | 0.757410i | −1.17265 | − | 0.0258877i | ||||
\(857\) | 23.3670 | 0.798201 | 0.399101 | − | 0.916907i | \(-0.369322\pi\) | ||||
0.399101 | + | 0.916907i | \(0.369322\pi\) | |||||||
\(858\) | −5.82311 | + | 3.30509i | −0.198798 | + | 0.112834i | ||||
\(859\) | 44.0917i | 1.50439i | 0.658940 | + | 0.752196i | \(0.271005\pi\) | ||||
−0.658940 | + | 0.752196i | \(0.728995\pi\) | |||||||
\(860\) | −15.1565 | − | 9.05054i | −0.516832 | − | 0.308621i | ||||
\(861\) | − | 3.35600i | − | 0.114372i | ||||||
\(862\) | 16.2274 | + | 28.5904i | 0.552706 | + | 0.973792i | ||||
\(863\) | 7.36620i | 0.250748i | 0.992110 | + | 0.125374i | \(0.0400131\pi\) | ||||
−0.992110 | + | 0.125374i | \(0.959987\pi\) | |||||||
\(864\) | −4.79164 | − | 3.00669i | −0.163015 | − | 0.102290i | ||||
\(865\) | 7.02511i | 0.238861i | ||||||||
\(866\) | −25.9592 | + | 14.7340i | −0.882130 | + | 0.500681i | ||||
\(867\) | − | 6.01041i | − | 0.204124i | ||||||
\(868\) | 1.05324 | + | 0.628934i | 0.0357494 | + | 0.0213474i | ||||
\(869\) | 17.1846 | 0.582947 | ||||||||
\(870\) | −0.486491 | − | 0.857130i | −0.0164936 | − | 0.0290594i | ||||
\(871\) | 9.32111 | 0.315834 | ||||||||
\(872\) | 1.02776 | − | 46.5553i | 0.0348045 | − | 1.57656i | ||||
\(873\) | − | 9.50481i | − | 0.321689i | ||||||
\(874\) | −1.44791 | − | 7.36302i | −0.0489764 | − | 0.249058i | ||||
\(875\) | 0.344556i | 0.0116481i | ||||||||
\(876\) | 4.60852 | + | 2.75193i | 0.155708 | + | 0.0929792i | ||||
\(877\) | −22.1457 | −0.747807 | −0.373904 | − | 0.927468i | \(-0.621981\pi\) | ||||
−0.373904 | + | 0.927468i | \(0.621981\pi\) | |||||||
\(878\) | 19.3908 | − | 11.0059i | 0.654409 | − | 0.371431i | ||||
\(879\) | 14.9580 | 0.504520 | ||||||||
\(880\) | −3.93561 | + | 2.12033i | −0.132669 | + | 0.0714762i | ||||
\(881\) | 27.8954i | 0.939821i | 0.882714 | + | 0.469910i | \(0.155714\pi\) | ||||
−0.882714 | + | 0.469910i | \(0.844286\pi\) | |||||||
\(882\) | −4.80366 | − | 8.46339i | −0.161748 | − | 0.284977i | ||||
\(883\) | − | 17.3820i | − | 0.584952i | −0.956273 | − | 0.292476i | \(-0.905521\pi\) | ||
0.956273 | − | 0.292476i | \(-0.0944791\pi\) | |||||||
\(884\) | −24.1151 | − | 14.4001i | −0.811078 | − | 0.484327i | ||||
\(885\) | 14.6024i | 0.490853i | ||||||||
\(886\) | −22.1218 | + | 12.5559i | −0.743197 | + | 0.421825i | ||||
\(887\) | 19.8802i | 0.667513i | 0.942659 | + | 0.333756i | \(0.108316\pi\) | ||||
−0.942659 | + | 0.333756i | \(0.891684\pi\) | |||||||
\(888\) | 24.9112 | + | 0.549945i | 0.835966 | + | 0.0184549i | ||||
\(889\) | 0.220456i | 0.00739384i | ||||||||
\(890\) | 8.36531 | + | 14.7385i | 0.280406 | + | 0.494036i | ||||
\(891\) | −1.11761 | −0.0374413 | ||||||||
\(892\) | −4.03936 | − | 2.41206i | −0.135248 | − | 0.0807619i | ||||
\(893\) | 9.23985i | 0.309200i | ||||||||
\(894\) | 5.59084 | + | 9.85029i | 0.186986 | + | 0.329443i | ||||
\(895\) | 3.75048 | 0.125365 | ||||||||
\(896\) | 1.77272 | + | 3.47181i | 0.0592226 | + | 0.115985i | ||||
\(897\) | −6.43092 | + | 19.2721i | −0.214722 | + | 0.643476i | ||||
\(898\) | −4.51958 | − | 7.96287i | −0.150820 | − | 0.265724i | ||||
\(899\) | 1.24060i | 0.0413765i | ||||||||
\(900\) | −1.02538 | + | 1.71715i | −0.0341793 | + | 0.0572383i | ||||
\(901\) | 40.1947 | 1.33908 | ||||||||
\(902\) | −7.59897 | − | 13.3883i | −0.253018 | − | 0.445783i | ||||
\(903\) | 3.04123i | 0.101206i | ||||||||
\(904\) | 1.01079 | − | 45.7864i | 0.0336184 | − | 1.52283i | ||||
\(905\) | 9.93221 | 0.330158 | ||||||||
\(906\) | 11.1134 | + | 19.5802i | 0.369217 | + | 0.650508i | ||||
\(907\) | −7.49646 | −0.248916 | −0.124458 | − | 0.992225i | \(-0.539719\pi\) | ||||
−0.124458 | + | 0.992225i | \(0.539719\pi\) | |||||||
\(908\) | 8.66972 | − | 14.5187i | 0.287715 | − | 0.481821i | ||||
\(909\) | −8.14918 | −0.270291 | ||||||||
\(910\) | 1.79525 | − | 1.01895i | 0.0595119 | − | 0.0337779i | ||||
\(911\) | 41.7614 | 1.38362 | 0.691808 | − | 0.722081i | \(-0.256814\pi\) | ||||
0.691808 | + | 0.722081i | \(0.256814\pi\) | |||||||
\(912\) | −3.89617 | + | 2.09908i | −0.129015 | + | 0.0695075i | ||||
\(913\) | −19.0872 | −0.631696 | ||||||||
\(914\) | 33.5637 | − | 19.0501i | 1.11019 | − | 0.630123i | ||||
\(915\) | − | 7.06741i | − | 0.233641i | ||||||
\(916\) | −38.6693 | − | 23.0910i | −1.27767 | − | 0.762948i | ||||
\(917\) | 0.577447i | 0.0190690i | ||||||||
\(918\) | −2.31416 | − | 4.07723i | −0.0763788 | − | 0.134569i | ||||
\(919\) | −31.3223 | −1.03323 | −0.516613 | − | 0.856219i | \(-0.672807\pi\) | ||||
−0.516613 | + | 0.856219i | \(0.672807\pi\) | |||||||
\(920\) | −4.57661 | + | 12.7693i | −0.150886 | + | 0.420991i | ||||
\(921\) | −8.69634 | −0.286554 | ||||||||
\(922\) | −15.0178 | − | 26.4593i | −0.494585 | − | 0.871390i | ||||
\(923\) | − | 70.0735i | − | 2.30650i | ||||||
\(924\) | 0.661237 | + | 0.394851i | 0.0217531 | + | 0.0129896i | ||||
\(925\) | − | 8.80960i | − | 0.289658i | ||||||
\(926\) | −30.3293 | + | 17.2143i | −0.996682 | + | 0.565698i | ||||
\(927\) | −3.46429 | −0.113782 | ||||||||
\(928\) | −2.09537 | + | 3.33930i | −0.0687840 | + | 0.109618i | ||||
\(929\) | −39.0276 | −1.28045 | −0.640226 | − | 0.768186i | \(-0.721159\pi\) | ||||
−0.640226 | + | 0.768186i | \(0.721159\pi\) | |||||||
\(930\) | 2.18946 | − | 1.24270i | 0.0717951 | − | 0.0407496i | ||||
\(931\) | −7.61352 | −0.249523 | ||||||||
\(932\) | 15.5662 | − | 26.0679i | 0.509888 | − | 0.853883i | ||||
\(933\) | −5.74489 | −0.188079 | ||||||||
\(934\) | 7.18197 | + | 12.6536i | 0.235001 | + | 0.414040i | ||||
\(935\) | −3.70493 | −0.121164 | ||||||||
\(936\) | 11.9792 | + | 0.264456i | 0.391554 | + | 0.00864402i | ||||
\(937\) | 6.62490i | 0.216426i | 0.994128 | + | 0.108213i | \(0.0345128\pi\) | ||||
−0.994128 | + | 0.108213i | \(0.965487\pi\) | |||||||
\(938\) | −0.529225 | − | 0.932420i | −0.0172798 | − | 0.0304446i | ||||
\(939\) | −0.954025 | −0.0311334 | ||||||||
\(940\) | 8.56314 | − | 14.3403i | 0.279299 | − | 0.467728i | ||||
\(941\) | − | 33.1946i | − | 1.08211i | −0.840987 | − | 0.541056i | \(-0.818025\pi\) | ||
0.840987 | − | 0.541056i | \(-0.181975\pi\) | |||||||
\(942\) | −8.00902 | − | 14.1108i | −0.260948 | − | 0.459754i | ||||
\(943\) | −44.3099 | − | 14.7858i | −1.44293 | − | 0.481492i | ||||
\(944\) | 51.4216 | − | 27.7036i | 1.67363 | − | 0.901675i | ||||
\(945\) | 0.344556 | 0.0112084 | ||||||||
\(946\) | 6.88626 | + | 12.1326i | 0.223891 | + | 0.394466i | ||||
\(947\) | − | 4.95185i | − | 0.160914i | −0.996758 | − | 0.0804568i | \(-0.974362\pi\) | ||
0.996758 | − | 0.0804568i | \(-0.0256379\pi\) | |||||||
\(948\) | −26.4032 | − | 15.7664i | −0.857537 | − | 0.512070i | ||||
\(949\) | −11.3696 | −0.369072 | ||||||||
\(950\) | 0.772359 | + | 1.36079i | 0.0250586 | + | 0.0441498i | ||||
\(951\) | − | 3.33114i | − | 0.108019i | ||||||
\(952\) | −0.0713040 | + | 3.22990i | −0.00231098 | + | 0.104682i | ||||
\(953\) | 0.385951i | 0.0125022i | 0.999980 | + | 0.00625109i | \(0.00198980\pi\) | ||||
−0.999980 | + | 0.00625109i | \(0.998010\pi\) | |||||||
\(954\) | −14.9126 | + | 8.46410i | −0.482812 | + | 0.274035i | ||||
\(955\) | − | 1.74084i | − | 0.0563322i | ||||||
\(956\) | −9.97795 | − | 5.95823i | −0.322710 | − | 0.192703i | ||||
\(957\) | 0.778864i | 0.0251771i | ||||||||
\(958\) | 23.7125 | + | 41.7781i | 0.766116 | + | 1.34979i | ||||
\(959\) | − | 3.51735i | − | 0.113581i | ||||||
\(960\) | 7.99221 | + | 0.353047i | 0.257947 | + | 0.0113945i | ||||
\(961\) | 27.8310 | 0.897774 | ||||||||
\(962\) | −45.9009 | + | 26.0525i | −1.47990 | + | 0.839966i | ||||
\(963\) | 12.1330 | 0.390980 | ||||||||
\(964\) | −6.89261 | − | 4.11586i | −0.221996 | − | 0.132563i | ||||
\(965\) | − | 8.74766i | − | 0.281597i | ||||||
\(966\) | 2.29298 | − | 0.450906i | 0.0737753 | − | 0.0145077i | ||||
\(967\) | 14.9587i | 0.481038i | 0.970644 | + | 0.240519i | \(0.0773176\pi\) | ||||
−0.970644 | + | 0.240519i | \(0.922682\pi\) | |||||||
\(968\) | −27.5731 | − | 0.608710i | −0.886234 | − | 0.0195647i | ||||
\(969\) | −3.66781 | −0.117827 | ||||||||
\(970\) | 6.63509 | + | 11.6901i | 0.213040 | + | 0.375347i | ||||
\(971\) | −11.6718 | −0.374566 | −0.187283 | − | 0.982306i | \(-0.559968\pi\) | ||||
−0.187283 | + | 0.982306i | \(0.559968\pi\) | |||||||
\(972\) | 1.71715 | + | 1.02538i | 0.0550776 | + | 0.0328890i | ||||
\(973\) | 2.92293i | 0.0937047i | ||||||||
\(974\) | −12.4564 | + | 7.07001i | −0.399128 | + | 0.226538i | ||||
\(975\) | − | 4.23633i | − | 0.135671i | ||||||
\(976\) | −24.8875 | + | 13.4083i | −0.796631 | + | 0.429189i | ||||
\(977\) | − | 32.1540i | − | 1.02870i | −0.857581 | − | 0.514349i | \(-0.828034\pi\) | ||
0.857581 | − | 0.514349i | \(-0.171966\pi\) | |||||||
\(978\) | 8.11697 | + | 14.3010i | 0.259552 | + | 0.457295i | ||||
\(979\) | − | 13.3927i | − | 0.428033i | ||||||
\(980\) | 11.8162 | + | 7.05591i | 0.377454 | + | 0.225393i | ||||
\(981\) | 16.4638i | 0.525649i | ||||||||
\(982\) | 21.8469 | − | 12.3999i | 0.697163 | − | 0.395697i | ||||
\(983\) | −6.87025 | −0.219127 | −0.109563 | − | 0.993980i | \(-0.534945\pi\) | ||||
−0.109563 | + | 0.993980i | \(0.534945\pi\) | |||||||
\(984\) | −0.608031 | + | 27.5424i | −0.0193833 | + | 0.878019i | ||||
\(985\) | − | 7.94495i | − | 0.253147i | ||||||
\(986\) | −2.84143 | + | 1.61275i | −0.0904897 | + | 0.0513603i | ||||
\(987\) | −2.87746 | −0.0915904 | ||||||||
\(988\) | 4.80607 | − | 8.04849i | 0.152902 | − | 0.256056i | ||||
\(989\) | 40.1540 | + | 13.3990i | 1.27682 | + | 0.426064i | ||||
\(990\) | 1.37456 | − | 0.780176i | 0.0436865 | − | 0.0247956i | ||||
\(991\) | − | 38.9553i | − | 1.23746i | −0.785605 | − | 0.618728i | \(-0.787648\pi\) | ||
0.785605 | − | 0.618728i | \(-0.212352\pi\) | |||||||
\(992\) | −8.52993 | − | 5.35243i | −0.270826 | − | 0.169940i | ||||
\(993\) | −21.3748 | −0.678307 | ||||||||
\(994\) | −7.00967 | + | 3.97856i | −0.222333 | + | 0.126192i | ||||
\(995\) | 12.6767i | 0.401877i | ||||||||
\(996\) | 29.3266 | + | 17.5121i | 0.929249 | + | 0.554891i | ||||
\(997\) | 56.0474 | 1.77504 | 0.887520 | − | 0.460770i | \(-0.152427\pi\) | ||||
0.887520 | + | 0.460770i | \(0.152427\pi\) | |||||||
\(998\) | −17.3533 | + | 9.84943i | −0.549310 | + | 0.311778i | ||||
\(999\) | −8.80960 | −0.278723 |
(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 | 1380.2.p.b.91.17 | yes | 48 | |
4.3 | odd | 2 | 1380.2.p.a.91.18 | yes | 48 | ||
23.22 | odd | 2 | 1380.2.p.a.91.17 | ✓ | 48 | ||
92.91 | even | 2 | inner | 1380.2.p.b.91.18 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.p.a.91.17 | ✓ | 48 | 23.22 | odd | 2 | ||
1380.2.p.a.91.18 | yes | 48 | 4.3 | odd | 2 | ||
1380.2.p.b.91.17 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.p.b.91.18 | yes | 48 | 92.91 | even | 2 | inner |