Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 157.5 | ||
Character | \(\chi\) | \(=\) | 429.157 |
Dual form | 429.2.n.c.235.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.788916 | − | 0.573181i | 0.557848 | − | 0.405300i | −0.272823 | − | 0.962064i | \(-0.587957\pi\) |
0.830671 | + | 0.556764i | \(0.187957\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | −0.324182 | + | 0.997729i | −0.162091 | + | 0.498864i | ||||
\(5\) | −2.91208 | − | 2.11575i | −1.30232 | − | 0.946191i | −0.302344 | − | 0.953199i | \(-0.597769\pi\) |
−0.999975 | + | 0.00700796i | \(0.997769\pi\) | |||||||
\(6\) | −0.788916 | − | 0.573181i | −0.322074 | − | 0.234000i | ||||
\(7\) | −1.06635 | + | 3.28188i | −0.403041 | + | 1.24043i | 0.519479 | + | 0.854483i | \(0.326126\pi\) |
−0.922520 | + | 0.385949i | \(0.873874\pi\) | |||||||
\(8\) | 0.918806 | + | 2.82779i | 0.324847 | + | 0.999776i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −3.51009 | −1.10999 | ||||||||
\(11\) | 0.466640 | + | 3.28363i | 0.140697 | + | 0.990053i | ||||
\(12\) | 1.04907 | 0.302842 | ||||||||
\(13\) | −0.809017 | + | 0.587785i | −0.224381 | + | 0.163022i | ||||
\(14\) | 1.03985 | + | 3.20034i | 0.277912 | + | 0.855326i | ||||
\(15\) | −1.11231 | + | 3.42335i | −0.287198 | + | 0.883905i | ||||
\(16\) | 0.648261 | + | 0.470989i | 0.162065 | + | 0.117747i | ||||
\(17\) | −6.51477 | − | 4.73326i | −1.58006 | − | 1.14798i | −0.916621 | − | 0.399756i | \(-0.869095\pi\) |
−0.663443 | − | 0.748227i | \(-0.730905\pi\) | |||||||
\(18\) | −0.301339 | + | 0.927427i | −0.0710263 | + | 0.218597i | ||||
\(19\) | 1.40012 | + | 4.30911i | 0.321209 | + | 0.988579i | 0.973123 | + | 0.230286i | \(0.0739662\pi\) |
−0.651914 | + | 0.758293i | \(0.726034\pi\) | |||||||
\(20\) | 3.05498 | − | 2.21958i | 0.683115 | − | 0.496312i | ||||
\(21\) | 3.45077 | 0.753020 | ||||||||
\(22\) | 2.25026 | + | 2.32304i | 0.479756 | + | 0.495274i | ||||
\(23\) | 5.38284 | 1.12240 | 0.561200 | − | 0.827680i | \(-0.310340\pi\) | ||||
0.561200 | + | 0.827680i | \(0.310340\pi\) | |||||||
\(24\) | 2.40546 | − | 1.74767i | 0.491013 | − | 0.356742i | ||||
\(25\) | 2.45872 | + | 7.56715i | 0.491743 | + | 1.51343i | ||||
\(26\) | −0.301339 | + | 0.927427i | −0.0590975 | + | 0.181883i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | −2.92873 | − | 2.12785i | −0.553478 | − | 0.402126i | ||||
\(29\) | −0.565134 | + | 1.73930i | −0.104943 | + | 0.322981i | −0.989717 | − | 0.143039i | \(-0.954313\pi\) |
0.884774 | + | 0.466020i | \(0.154313\pi\) | |||||||
\(30\) | 1.08468 | + | 3.33829i | 0.198034 | + | 0.609486i | ||||
\(31\) | −6.04966 | + | 4.39534i | −1.08655 | + | 0.789426i | −0.978814 | − | 0.204753i | \(-0.934361\pi\) |
−0.107738 | + | 0.994179i | \(0.534361\pi\) | |||||||
\(32\) | −5.16525 | −0.913096 | ||||||||
\(33\) | 2.97872 | − | 1.45850i | 0.518529 | − | 0.253892i | ||||
\(34\) | −7.85262 | −1.34671 | ||||||||
\(35\) | 10.0489 | − | 7.30095i | 1.69857 | − | 1.23409i | ||||
\(36\) | −0.324182 | − | 0.997729i | −0.0540303 | − | 0.166288i | ||||
\(37\) | 0.848128 | − | 2.61027i | 0.139431 | − | 0.429126i | −0.856822 | − | 0.515613i | \(-0.827564\pi\) |
0.996253 | + | 0.0864874i | \(0.0275642\pi\) | |||||||
\(38\) | 3.57448 | + | 2.59701i | 0.579857 | + | 0.421291i | ||||
\(39\) | 0.809017 | + | 0.587785i | 0.129546 | + | 0.0941210i | ||||
\(40\) | 3.30726 | − | 10.1787i | 0.522924 | − | 1.60940i | ||||
\(41\) | −2.68180 | − | 8.25373i | −0.418827 | − | 1.28902i | −0.908783 | − | 0.417269i | \(-0.862987\pi\) |
0.489956 | − | 0.871747i | \(-0.337013\pi\) | |||||||
\(42\) | 2.72237 | − | 1.97792i | 0.420071 | − | 0.305199i | ||||
\(43\) | −6.68750 | −1.01983 | −0.509917 | − | 0.860224i | \(-0.670324\pi\) | ||||
−0.509917 | + | 0.860224i | \(0.670324\pi\) | |||||||
\(44\) | −3.42745 | − | 0.598914i | −0.516708 | − | 0.0902897i | ||||
\(45\) | 3.59952 | 0.536585 | ||||||||
\(46\) | 4.24661 | − | 3.08534i | 0.626129 | − | 0.454909i | ||||
\(47\) | 0.462046 | + | 1.42203i | 0.0673963 | + | 0.207425i | 0.979083 | − | 0.203462i | \(-0.0652193\pi\) |
−0.911687 | + | 0.410886i | \(0.865219\pi\) | |||||||
\(48\) | 0.247614 | − | 0.762077i | 0.0357400 | − | 0.109996i | ||||
\(49\) | −3.97050 | − | 2.88474i | −0.567214 | − | 0.412105i | ||||
\(50\) | 6.27707 | + | 4.56056i | 0.887712 | + | 0.644960i | ||||
\(51\) | −2.48842 | + | 7.65857i | −0.348449 | + | 1.07241i | ||||
\(52\) | −0.324182 | − | 0.997729i | −0.0449559 | − | 0.138360i | ||||
\(53\) | −6.30053 | + | 4.57760i | −0.865444 | + | 0.628782i | −0.929361 | − | 0.369173i | \(-0.879641\pi\) |
0.0639162 | + | 0.997955i | \(0.479641\pi\) | |||||||
\(54\) | 0.975154 | 0.132702 | ||||||||
\(55\) | 5.58845 | − | 10.5495i | 0.753546 | − | 1.42249i | ||||
\(56\) | −10.2602 | −1.37108 | ||||||||
\(57\) | 3.66555 | − | 2.66318i | 0.485514 | − | 0.352747i | ||||
\(58\) | 0.551093 | + | 1.69609i | 0.0723621 | + | 0.222708i | ||||
\(59\) | −1.57629 | + | 4.85133i | −0.205216 | + | 0.631589i | 0.794489 | + | 0.607279i | \(0.207739\pi\) |
−0.999704 | + | 0.0243100i | \(0.992261\pi\) | |||||||
\(60\) | −3.05498 | − | 2.21958i | −0.394397 | − | 0.286546i | ||||
\(61\) | −1.09627 | − | 0.796490i | −0.140363 | − | 0.101980i | 0.515388 | − | 0.856957i | \(-0.327648\pi\) |
−0.655751 | + | 0.754977i | \(0.727648\pi\) | |||||||
\(62\) | −2.25335 | + | 6.93511i | −0.286176 | + | 0.880760i | ||||
\(63\) | −1.06635 | − | 3.28188i | −0.134347 | − | 0.413478i | ||||
\(64\) | −5.37147 | + | 3.90260i | −0.671434 | + | 0.487825i | ||||
\(65\) | 3.59952 | 0.446466 | ||||||||
\(66\) | 1.51398 | − | 2.85798i | 0.186358 | − | 0.351793i | ||||
\(67\) | 4.00675 | 0.489502 | 0.244751 | − | 0.969586i | \(-0.421294\pi\) | ||||
0.244751 | + | 0.969586i | \(0.421294\pi\) | |||||||
\(68\) | 6.83448 | − | 4.96554i | 0.828802 | − | 0.602160i | ||||
\(69\) | −1.66339 | − | 5.11939i | −0.200249 | − | 0.616302i | ||||
\(70\) | 3.74297 | − | 11.5197i | 0.447371 | − | 1.37687i | ||||
\(71\) | 7.39649 | + | 5.37386i | 0.877802 | + | 0.637760i | 0.932669 | − | 0.360733i | \(-0.117474\pi\) |
−0.0548672 | + | 0.998494i | \(0.517474\pi\) | |||||||
\(72\) | −2.40546 | − | 1.74767i | −0.283487 | − | 0.205965i | ||||
\(73\) | 2.38841 | − | 7.35076i | 0.279542 | − | 0.860342i | −0.708440 | − | 0.705771i | \(-0.750601\pi\) |
0.987982 | − | 0.154571i | \(-0.0493994\pi\) | |||||||
\(74\) | −0.827056 | − | 2.54542i | −0.0961433 | − | 0.295899i | ||||
\(75\) | 6.43700 | − | 4.67675i | 0.743281 | − | 0.540025i | ||||
\(76\) | −4.75322 | −0.545232 | ||||||||
\(77\) | −11.2741 | − | 1.97004i | −1.28480 | − | 0.224506i | ||||
\(78\) | 0.975154 | 0.110414 | ||||||||
\(79\) | 2.72499 | − | 1.97982i | 0.306585 | − | 0.222747i | −0.423845 | − | 0.905735i | \(-0.639320\pi\) |
0.730430 | + | 0.682988i | \(0.239320\pi\) | |||||||
\(80\) | −0.891291 | − | 2.74311i | −0.0996494 | − | 0.306689i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −6.84660 | − | 4.97435i | −0.756081 | − | 0.549325i | ||||
\(83\) | 4.69889 | + | 3.41395i | 0.515771 | + | 0.374729i | 0.815008 | − | 0.579449i | \(-0.196732\pi\) |
−0.299238 | + | 0.954179i | \(0.596732\pi\) | |||||||
\(84\) | −1.11868 | + | 3.44293i | −0.122058 | + | 0.375655i | ||||
\(85\) | 8.95713 | + | 27.5672i | 0.971537 | + | 2.99008i | ||||
\(86\) | −5.27588 | + | 3.83315i | −0.568912 | + | 0.413339i | ||||
\(87\) | 1.82881 | 0.196069 | ||||||||
\(88\) | −8.85668 | + | 4.33658i | −0.944126 | + | 0.462281i | ||||
\(89\) | 16.5060 | 1.74963 | 0.874817 | − | 0.484454i | \(-0.160982\pi\) | ||||
0.874817 | + | 0.484454i | \(0.160982\pi\) | |||||||
\(90\) | 2.83972 | − | 2.06318i | 0.299333 | − | 0.217478i | ||||
\(91\) | −1.06635 | − | 3.28188i | −0.111783 | − | 0.344034i | ||||
\(92\) | −1.74502 | + | 5.37062i | −0.181931 | + | 0.559926i | ||||
\(93\) | 6.04966 | + | 4.39534i | 0.627321 | + | 0.455775i | ||||
\(94\) | 1.17960 | + | 0.857027i | 0.121666 | + | 0.0883956i | ||||
\(95\) | 5.03975 | − | 15.5108i | 0.517068 | − | 1.59137i | ||||
\(96\) | 1.59615 | + | 4.91244i | 0.162906 | + | 0.501374i | ||||
\(97\) | −0.0735643 | + | 0.0534476i | −0.00746932 | + | 0.00542678i | −0.591514 | − | 0.806295i | \(-0.701469\pi\) |
0.584044 | + | 0.811722i | \(0.301469\pi\) | |||||||
\(98\) | −4.78587 | −0.483446 | ||||||||
\(99\) | −2.30759 | − | 2.38223i | −0.231922 | − | 0.239423i | ||||
\(100\) | −8.34703 | −0.834703 | ||||||||
\(101\) | 0.434294 | − | 0.315533i | 0.0432139 | − | 0.0313967i | −0.565969 | − | 0.824427i | \(-0.691498\pi\) |
0.609183 | + | 0.793030i | \(0.291498\pi\) | |||||||
\(102\) | 2.42659 | + | 7.46829i | 0.240269 | + | 0.739471i | ||||
\(103\) | −0.742505 | + | 2.28520i | −0.0731612 | + | 0.225167i | −0.980950 | − | 0.194261i | \(-0.937769\pi\) |
0.907789 | + | 0.419428i | \(0.137769\pi\) | |||||||
\(104\) | −2.40546 | − | 1.74767i | −0.235875 | − | 0.171373i | ||||
\(105\) | −10.0489 | − | 7.30095i | −0.980672 | − | 0.712500i | ||||
\(106\) | −2.34680 | + | 7.22269i | −0.227941 | + | 0.701530i | ||||
\(107\) | −5.04349 | − | 15.5223i | −0.487573 | − | 1.50059i | −0.828220 | − | 0.560403i | \(-0.810646\pi\) |
0.340647 | − | 0.940191i | \(-0.389354\pi\) | |||||||
\(108\) | −0.848719 | + | 0.616630i | −0.0816680 | + | 0.0593353i | ||||
\(109\) | 5.50310 | 0.527101 | 0.263551 | − | 0.964646i | \(-0.415106\pi\) | ||||
0.263551 | + | 0.964646i | \(0.415106\pi\) | |||||||
\(110\) | −1.63795 | − | 11.5259i | −0.156172 | − | 1.09895i | ||||
\(111\) | −2.74460 | −0.260506 | ||||||||
\(112\) | −2.23700 | + | 1.62528i | −0.211377 | + | 0.153574i | ||||
\(113\) | 4.50820 | + | 13.8748i | 0.424096 | + | 1.30523i | 0.903858 | + | 0.427833i | \(0.140723\pi\) |
−0.479762 | + | 0.877399i | \(0.659277\pi\) | |||||||
\(114\) | 1.36533 | − | 4.20205i | 0.127875 | − | 0.393558i | ||||
\(115\) | −15.6752 | − | 11.3887i | −1.46172 | − | 1.06200i | ||||
\(116\) | −1.55215 | − | 1.12770i | −0.144113 | − | 0.104704i | ||||
\(117\) | 0.309017 | − | 0.951057i | 0.0285686 | − | 0.0879252i | ||||
\(118\) | 1.53713 | + | 4.73079i | 0.141504 | + | 0.435505i | ||||
\(119\) | 22.4810 | − | 16.3334i | 2.06083 | − | 1.49728i | ||||
\(120\) | −10.7025 | −0.977003 | ||||||||
\(121\) | −10.5645 | + | 3.06455i | −0.960409 | + | 0.278595i | ||||
\(122\) | −1.32140 | −0.119634 | ||||||||
\(123\) | −7.02104 | + | 5.10109i | −0.633066 | + | 0.459949i | ||||
\(124\) | −2.42416 | − | 7.46081i | −0.217696 | − | 0.670001i | ||||
\(125\) | 3.28863 | − | 10.1214i | 0.294144 | − | 0.905283i | ||||
\(126\) | −2.72237 | − | 1.97792i | −0.242528 | − | 0.176207i | ||||
\(127\) | −1.54386 | − | 1.12168i | −0.136996 | − | 0.0995331i | 0.517177 | − | 0.855879i | \(-0.326983\pi\) |
−0.654172 | + | 0.756345i | \(0.726983\pi\) | |||||||
\(128\) | 1.19156 | − | 3.66723i | 0.105320 | − | 0.324141i | ||||
\(129\) | 2.06655 | + | 6.36019i | 0.181950 | + | 0.559983i | ||||
\(130\) | 2.83972 | − | 2.06318i | 0.249060 | − | 0.180953i | ||||
\(131\) | −9.46219 | −0.826716 | −0.413358 | − | 0.910569i | \(-0.635644\pi\) | ||||
−0.413358 | + | 0.910569i | \(0.635644\pi\) | |||||||
\(132\) | 0.489540 | + | 3.44478i | 0.0426090 | + | 0.299829i | ||||
\(133\) | −15.6350 | −1.35573 | ||||||||
\(134\) | 3.16099 | − | 2.29659i | 0.273068 | − | 0.198396i | ||||
\(135\) | −1.11231 | − | 3.42335i | −0.0957327 | − | 0.294635i | ||||
\(136\) | 7.39887 | − | 22.7714i | 0.634448 | − | 1.95263i | ||||
\(137\) | 9.21812 | + | 6.69736i | 0.787557 | + | 0.572194i | 0.907238 | − | 0.420619i | \(-0.138187\pi\) |
−0.119680 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(138\) | −4.24661 | − | 3.08534i | −0.361496 | − | 0.262642i | ||||
\(139\) | −3.91169 | + | 12.0390i | −0.331786 | + | 1.02113i | 0.636498 | + | 0.771278i | \(0.280382\pi\) |
−0.968284 | + | 0.249853i | \(0.919618\pi\) | |||||||
\(140\) | 4.02670 | + | 12.3929i | 0.340318 | + | 1.04739i | ||||
\(141\) | 1.20965 | − | 0.878864i | 0.101871 | − | 0.0740137i | ||||
\(142\) | 8.91541 | 0.748165 | ||||||||
\(143\) | −2.30759 | − | 2.38223i | −0.192970 | − | 0.199212i | ||||
\(144\) | −0.801295 | −0.0667746 | ||||||||
\(145\) | 5.32564 | − | 3.86931i | 0.442271 | − | 0.321328i | ||||
\(146\) | −2.32907 | − | 7.16813i | −0.192755 | − | 0.593239i | ||||
\(147\) | −1.51660 | + | 4.66760i | −0.125087 | + | 0.384977i | ||||
\(148\) | 2.32939 | + | 1.69240i | 0.191475 | + | 0.139115i | ||||
\(149\) | 1.05367 | + | 0.765538i | 0.0863202 | + | 0.0627153i | 0.630108 | − | 0.776507i | \(-0.283010\pi\) |
−0.543788 | + | 0.839223i | \(0.683010\pi\) | |||||||
\(150\) | 2.39763 | − | 7.37914i | 0.195765 | − | 0.602504i | ||||
\(151\) | 4.72220 | + | 14.5334i | 0.384288 | + | 1.18272i | 0.936996 | + | 0.349341i | \(0.113594\pi\) |
−0.552708 | + | 0.833375i | \(0.686406\pi\) | |||||||
\(152\) | −10.8988 | + | 7.91848i | −0.884013 | + | 0.642273i | ||||
\(153\) | 8.05270 | 0.651022 | ||||||||
\(154\) | −10.0235 | + | 4.90790i | −0.807716 | + | 0.395490i | ||||
\(155\) | 26.9165 | 2.16199 | ||||||||
\(156\) | −0.848719 | + | 0.616630i | −0.0679519 | + | 0.0493699i | ||||
\(157\) | 1.07631 | + | 3.31255i | 0.0858991 | + | 0.264370i | 0.984775 | − | 0.173833i | \(-0.0556152\pi\) |
−0.898876 | + | 0.438203i | \(0.855615\pi\) | |||||||
\(158\) | 1.01499 | − | 3.12382i | 0.0807483 | − | 0.248518i | ||||
\(159\) | 6.30053 | + | 4.57760i | 0.499665 | + | 0.363028i | ||||
\(160\) | 15.0416 | + | 10.9284i | 1.18914 | + | 0.863963i | ||||
\(161\) | −5.73997 | + | 17.6658i | −0.452373 | + | 1.39226i | ||||
\(162\) | −0.301339 | − | 0.927427i | −0.0236754 | − | 0.0728655i | ||||
\(163\) | 4.08300 | − | 2.96647i | 0.319805 | − | 0.232352i | −0.416287 | − | 0.909233i | \(-0.636669\pi\) |
0.736092 | + | 0.676881i | \(0.236669\pi\) | |||||||
\(164\) | 9.10438 | 0.710932 | ||||||||
\(165\) | −11.7601 | − | 2.05496i | −0.915521 | − | 0.159978i | ||||
\(166\) | 5.66384 | 0.439600 | ||||||||
\(167\) | −16.3880 | + | 11.9066i | −1.26814 | + | 0.921360i | −0.999127 | − | 0.0417761i | \(-0.986698\pi\) |
−0.269016 | + | 0.963136i | \(0.586698\pi\) | |||||||
\(168\) | 3.17059 | + | 9.75806i | 0.244616 | + | 0.752851i | ||||
\(169\) | 0.309017 | − | 0.951057i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | 22.8674 | + | 16.6142i | 1.75385 | + | 1.27425i | ||||
\(171\) | −3.66555 | − | 2.66318i | −0.280312 | − | 0.203658i | ||||
\(172\) | 2.16796 | − | 6.67231i | 0.165306 | − | 0.508759i | ||||
\(173\) | −1.22295 | − | 3.76386i | −0.0929793 | − | 0.286161i | 0.893743 | − | 0.448580i | \(-0.148070\pi\) |
−0.986722 | + | 0.162420i | \(0.948070\pi\) | |||||||
\(174\) | 1.44278 | − | 1.04824i | 0.109377 | − | 0.0794670i | ||||
\(175\) | −27.4563 | −2.07550 | ||||||||
\(176\) | −1.24405 | + | 2.34843i | −0.0937739 | + | 0.177020i | ||||
\(177\) | 5.10099 | 0.383414 | ||||||||
\(178\) | 13.0219 | − | 9.46094i | 0.976030 | − | 0.709127i | ||||
\(179\) | −5.55628 | − | 17.1005i | −0.415296 | − | 1.27815i | −0.911986 | − | 0.410222i | \(-0.865451\pi\) |
0.496690 | − | 0.867928i | \(-0.334549\pi\) | |||||||
\(180\) | −1.16690 | + | 3.59135i | −0.0869756 | + | 0.267683i | ||||
\(181\) | 10.8595 | + | 7.88988i | 0.807180 | + | 0.586450i | 0.913012 | − | 0.407934i | \(-0.133751\pi\) |
−0.105832 | + | 0.994384i | \(0.533751\pi\) | |||||||
\(182\) | −2.72237 | − | 1.97792i | −0.201795 | − | 0.146613i | ||||
\(183\) | −0.418739 | + | 1.28875i | −0.0309541 | + | 0.0952669i | ||||
\(184\) | 4.94579 | + | 15.2216i | 0.364608 | + | 1.12215i | ||||
\(185\) | −7.99248 | + | 5.80688i | −0.587619 | + | 0.426930i | ||||
\(186\) | 7.29200 | 0.534676 | ||||||||
\(187\) | 12.5022 | − | 23.6008i | 0.914254 | − | 1.72586i | ||||
\(188\) | −1.56859 | −0.114401 | ||||||||
\(189\) | −2.79173 | + | 2.02831i | −0.203069 | + | 0.147538i | ||||
\(190\) | −4.91453 | − | 15.1254i | −0.356538 | − | 1.09731i | ||||
\(191\) | −0.868334 | + | 2.67246i | −0.0628304 | + | 0.193372i | −0.977544 | − | 0.210730i | \(-0.932416\pi\) |
0.914714 | + | 0.404102i | \(0.132416\pi\) | |||||||
\(192\) | 5.37147 | + | 3.90260i | 0.387653 | + | 0.281646i | ||||
\(193\) | 17.0374 | + | 12.3784i | 1.22638 | + | 0.891017i | 0.996613 | − | 0.0822291i | \(-0.0262039\pi\) |
0.229766 | + | 0.973246i | \(0.426204\pi\) | |||||||
\(194\) | −0.0274009 | + | 0.0843313i | −0.00196727 | + | 0.00605464i | ||||
\(195\) | −1.11231 | − | 3.42335i | −0.0796545 | − | 0.245151i | ||||
\(196\) | 4.16535 | − | 3.02630i | 0.297525 | − | 0.216164i | ||||
\(197\) | −5.16249 | −0.367812 | −0.183906 | − | 0.982944i | \(-0.558874\pi\) | ||||
−0.183906 | + | 0.982944i | \(0.558874\pi\) | |||||||
\(198\) | −3.18595 | − | 0.556713i | −0.226415 | − | 0.0395639i | ||||
\(199\) | 26.3950 | 1.87109 | 0.935547 | − | 0.353202i | \(-0.114907\pi\) | ||||
0.935547 | + | 0.353202i | \(0.114907\pi\) | |||||||
\(200\) | −19.1392 | + | 13.9055i | −1.35335 | + | 0.983266i | ||||
\(201\) | −1.23815 | − | 3.81065i | −0.0873326 | − | 0.268782i | ||||
\(202\) | 0.161764 | − | 0.497858i | 0.0113817 | − | 0.0350292i | ||||
\(203\) | −5.10555 | − | 3.70940i | −0.358340 | − | 0.260349i | ||||
\(204\) | −6.83448 | − | 4.96554i | −0.478509 | − | 0.347657i | ||||
\(205\) | −9.65320 | + | 29.7095i | −0.674209 | + | 2.07500i | ||||
\(206\) | 0.724057 | + | 2.22842i | 0.0504475 | + | 0.155261i | ||||
\(207\) | −4.35481 | + | 3.16396i | −0.302680 | + | 0.219910i | ||||
\(208\) | −0.801295 | −0.0555598 | ||||||||
\(209\) | −13.4962 | + | 6.60827i | −0.933552 | + | 0.457104i | ||||
\(210\) | −12.1125 | −0.835843 | ||||||||
\(211\) | −6.15420 | + | 4.47129i | −0.423673 | + | 0.307816i | −0.779114 | − | 0.626882i | \(-0.784331\pi\) |
0.355441 | + | 0.934699i | \(0.384331\pi\) | |||||||
\(212\) | −2.52469 | − | 7.77020i | −0.173396 | − | 0.533659i | ||||
\(213\) | 2.82521 | − | 8.69509i | 0.193580 | − | 0.595778i | ||||
\(214\) | −12.8760 | − | 9.35494i | −0.880183 | − | 0.639490i | ||||
\(215\) | 19.4745 | + | 14.1491i | 1.32815 | + | 0.964957i | ||||
\(216\) | −0.918806 | + | 2.82779i | −0.0625168 | + | 0.192407i | ||||
\(217\) | −7.97392 | − | 24.5412i | −0.541305 | − | 1.66597i | ||||
\(218\) | 4.34149 | − | 3.15427i | 0.294042 | − | 0.213634i | ||||
\(219\) | −7.72905 | −0.522281 | ||||||||
\(220\) | 8.71385 | + | 8.99570i | 0.587488 | + | 0.606490i | ||||
\(221\) | 8.05270 | 0.541683 | ||||||||
\(222\) | −2.16526 | + | 1.57315i | −0.145323 | + | 0.105583i | ||||
\(223\) | 1.33792 | + | 4.11769i | 0.0895936 | + | 0.275741i | 0.985807 | − | 0.167882i | \(-0.0536929\pi\) |
−0.896213 | + | 0.443623i | \(0.853693\pi\) | |||||||
\(224\) | 5.50794 | − | 16.9517i | 0.368015 | − | 1.13263i | ||||
\(225\) | −6.43700 | − | 4.67675i | −0.429133 | − | 0.311784i | ||||
\(226\) | 11.5094 | + | 8.36205i | 0.765592 | + | 0.556235i | ||||
\(227\) | 3.11528 | − | 9.58785i | 0.206768 | − | 0.636368i | −0.792868 | − | 0.609394i | \(-0.791413\pi\) |
0.999636 | − | 0.0269740i | \(-0.00858714\pi\) | |||||||
\(228\) | 1.46883 | + | 4.52058i | 0.0972754 | + | 0.299383i | ||||
\(229\) | −9.91078 | + | 7.20061i | −0.654923 | + | 0.475829i | −0.864945 | − | 0.501867i | \(-0.832647\pi\) |
0.210022 | + | 0.977697i | \(0.432647\pi\) | |||||||
\(230\) | −18.8943 | −1.24585 | ||||||||
\(231\) | 1.61027 | + | 11.3311i | 0.105948 | + | 0.745529i | ||||
\(232\) | −5.43764 | −0.356999 | ||||||||
\(233\) | 3.67299 | − | 2.66859i | 0.240626 | − | 0.174825i | −0.460936 | − | 0.887433i | \(-0.652486\pi\) |
0.701562 | + | 0.712608i | \(0.252486\pi\) | |||||||
\(234\) | −0.301339 | − | 0.927427i | −0.0196992 | − | 0.0606278i | ||||
\(235\) | 1.66315 | − | 5.11863i | 0.108492 | − | 0.333903i | ||||
\(236\) | −4.32930 | − | 3.14542i | −0.281814 | − | 0.204750i | ||||
\(237\) | −2.72499 | − | 1.97982i | −0.177007 | − | 0.128603i | ||||
\(238\) | 8.37362 | − | 25.7713i | 0.542781 | − | 1.67051i | ||||
\(239\) | 5.99242 | + | 18.4428i | 0.387618 | + | 1.19296i | 0.934563 | + | 0.355796i | \(0.115790\pi\) |
−0.546946 | + | 0.837168i | \(0.684210\pi\) | |||||||
\(240\) | −2.33343 | + | 1.69534i | −0.150622 | + | 0.109434i | ||||
\(241\) | −20.0668 | −1.29261 | −0.646307 | − | 0.763078i | \(-0.723687\pi\) | ||||
−0.646307 | + | 0.763078i | \(0.723687\pi\) | |||||||
\(242\) | −6.57796 | + | 8.47304i | −0.422847 | + | 0.544668i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.15007 | − | 0.835577i | 0.0736259 | − | 0.0534923i | ||||
\(245\) | 5.45902 | + | 16.8011i | 0.348764 | + | 1.07339i | ||||
\(246\) | −2.61517 | + | 8.04866i | −0.166737 | + | 0.513164i | ||||
\(247\) | −3.66555 | − | 2.66318i | −0.233233 | − | 0.169454i | ||||
\(248\) | −17.9876 | − | 13.0687i | −1.14221 | − | 0.829866i | ||||
\(249\) | 1.79482 | − | 5.52388i | 0.113742 | − | 0.350062i | ||||
\(250\) | −3.20693 | − | 9.86990i | −0.202824 | − | 0.624227i | ||||
\(251\) | −19.0356 | + | 13.8301i | −1.20151 | + | 0.872951i | −0.994433 | − | 0.105373i | \(-0.966396\pi\) |
−0.207081 | + | 0.978324i | \(0.566396\pi\) | |||||||
\(252\) | 3.62011 | 0.228046 | ||||||||
\(253\) | 2.51185 | + | 17.6753i | 0.157919 | + | 1.11124i | ||||
\(254\) | −1.86090 | −0.116764 | ||||||||
\(255\) | 23.4501 | − | 17.0375i | 1.46850 | − | 1.06693i | ||||
\(256\) | −5.26539 | − | 16.2052i | −0.329087 | − | 1.01283i | ||||
\(257\) | −3.08890 | + | 9.50666i | −0.192680 | + | 0.593009i | 0.807315 | + | 0.590120i | \(0.200920\pi\) |
−0.999996 | + | 0.00288904i | \(0.999080\pi\) | |||||||
\(258\) | 5.27588 | + | 3.83315i | 0.328462 | + | 0.238641i | ||||
\(259\) | 7.66218 | + | 5.56690i | 0.476105 | + | 0.345910i | ||||
\(260\) | −1.16690 | + | 3.59135i | −0.0723681 | + | 0.222726i | ||||
\(261\) | −0.565134 | − | 1.73930i | −0.0349809 | − | 0.107660i | ||||
\(262\) | −7.46488 | + | 5.42355i | −0.461182 | + | 0.335068i | ||||
\(263\) | −4.34580 | −0.267973 | −0.133987 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133987 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(264\) | 6.86120 | + | 7.08313i | 0.422278 | + | 0.435937i | ||||
\(265\) | 28.0327 | 1.72203 | ||||||||
\(266\) | −12.3347 | + | 8.96168i | −0.756289 | + | 0.549476i | ||||
\(267\) | −5.10064 | − | 15.6981i | −0.312154 | − | 0.960711i | ||||
\(268\) | −1.29892 | + | 3.99765i | −0.0793439 | + | 0.244195i | ||||
\(269\) | −13.8368 | − | 10.0530i | −0.843645 | − | 0.612944i | 0.0797415 | − | 0.996816i | \(-0.474591\pi\) |
−0.923386 | + | 0.383872i | \(0.874591\pi\) | |||||||
\(270\) | −2.83972 | − | 2.06318i | −0.172820 | − | 0.125561i | ||||
\(271\) | −3.11505 | + | 9.58714i | −0.189226 | + | 0.582377i | −0.999996 | − | 0.00298814i | \(-0.999049\pi\) |
0.810770 | + | 0.585365i | \(0.199049\pi\) | |||||||
\(272\) | −1.99396 | − | 6.13677i | −0.120902 | − | 0.372097i | ||||
\(273\) | −2.79173 | + | 2.02831i | −0.168963 | + | 0.122759i | ||||
\(274\) | 11.1111 | 0.671248 | ||||||||
\(275\) | −23.7004 | + | 11.6047i | −1.42919 | + | 0.699787i | ||||
\(276\) | 5.64700 | 0.339909 | ||||||||
\(277\) | −2.30454 | + | 1.67435i | −0.138467 | + | 0.100602i | −0.654862 | − | 0.755748i | \(-0.727273\pi\) |
0.516396 | + | 0.856350i | \(0.327273\pi\) | |||||||
\(278\) | 3.81451 | + | 11.7398i | 0.228779 | + | 0.704109i | ||||
\(279\) | 2.31077 | − | 7.11181i | 0.138342 | − | 0.425773i | ||||
\(280\) | 29.8786 | + | 21.7081i | 1.78559 | + | 1.29730i | ||||
\(281\) | −26.8784 | − | 19.5283i | −1.60343 | − | 1.16496i | −0.880502 | − | 0.474042i | \(-0.842794\pi\) |
−0.722931 | − | 0.690920i | \(-0.757206\pi\) | |||||||
\(282\) | 0.450566 | − | 1.38670i | 0.0268308 | − | 0.0825768i | ||||
\(283\) | −7.41358 | − | 22.8166i | −0.440691 | − | 1.35631i | −0.887141 | − | 0.461499i | \(-0.847312\pi\) |
0.446449 | − | 0.894809i | \(-0.352688\pi\) | |||||||
\(284\) | −7.75947 | + | 5.63758i | −0.460440 | + | 0.334529i | ||||
\(285\) | −16.3090 | −0.966060 | ||||||||
\(286\) | −3.18595 | − | 0.556713i | −0.188389 | − | 0.0329191i | ||||
\(287\) | 29.9475 | 1.76774 | ||||||||
\(288\) | 4.17877 | − | 3.03606i | 0.246237 | − | 0.178901i | ||||
\(289\) | 14.7852 | + | 45.5042i | 0.869719 | + | 2.67672i | ||||
\(290\) | 1.98367 | − | 6.10512i | 0.116485 | − | 0.358505i | ||||
\(291\) | 0.0735643 | + | 0.0534476i | 0.00431241 | + | 0.00313315i | ||||
\(292\) | 6.55979 | + | 4.76597i | 0.383883 | + | 0.278907i | ||||
\(293\) | −1.27879 | + | 3.93570i | −0.0747076 | + | 0.229926i | −0.981436 | − | 0.191788i | \(-0.938571\pi\) |
0.906729 | + | 0.421714i | \(0.138571\pi\) | |||||||
\(294\) | 1.47891 | + | 4.55163i | 0.0862521 | + | 0.265457i | ||||
\(295\) | 14.8545 | − | 10.7924i | 0.864860 | − | 0.628357i | ||||
\(296\) | 8.16057 | 0.474323 | ||||||||
\(297\) | −1.55255 | + | 2.93080i | −0.0900882 | + | 0.170062i | ||||
\(298\) | 1.27005 | 0.0735721 | ||||||||
\(299\) | −4.35481 | + | 3.16396i | −0.251845 | + | 0.182976i | ||||
\(300\) | 2.57938 | + | 7.93850i | 0.148920 | + | 0.458330i | ||||
\(301\) | 7.13119 | − | 21.9475i | 0.411035 | − | 1.26504i | ||||
\(302\) | 12.0557 | + | 8.75900i | 0.693729 | + | 0.504024i | ||||
\(303\) | −0.434294 | − | 0.315533i | −0.0249495 | − | 0.0181269i | ||||
\(304\) | −1.12191 | + | 3.45287i | −0.0643457 | + | 0.198036i | ||||
\(305\) | 1.50726 | + | 4.63888i | 0.0863056 | + | 0.265621i | ||||
\(306\) | 6.35291 | − | 4.61566i | 0.363171 | − | 0.263860i | ||||
\(307\) | 7.71681 | 0.440422 | 0.220211 | − | 0.975452i | \(-0.429325\pi\) | ||||
0.220211 | + | 0.975452i | \(0.429325\pi\) | |||||||
\(308\) | 5.62041 | − | 10.6098i | 0.320253 | − | 0.604551i | ||||
\(309\) | 2.40280 | 0.136690 | ||||||||
\(310\) | 21.2349 | − | 15.4280i | 1.20606 | − | 0.876254i | ||||
\(311\) | 9.69726 | + | 29.8451i | 0.549881 | + | 1.69236i | 0.709093 | + | 0.705115i | \(0.249105\pi\) |
−0.159211 | + | 0.987245i | \(0.550895\pi\) | |||||||
\(312\) | −0.918806 | + | 2.82779i | −0.0520171 | + | 0.160092i | ||||
\(313\) | 4.12939 | + | 3.00017i | 0.233407 | + | 0.169580i | 0.698341 | − | 0.715765i | \(-0.253922\pi\) |
−0.464934 | + | 0.885345i | \(0.653922\pi\) | |||||||
\(314\) | 2.74781 | + | 1.99640i | 0.155068 | + | 0.112663i | ||||
\(315\) | −3.83834 | + | 11.8132i | −0.216266 | + | 0.665598i | ||||
\(316\) | 1.09193 | + | 3.36062i | 0.0614259 | + | 0.189049i | ||||
\(317\) | 5.06307 | − | 3.67854i | 0.284370 | − | 0.206607i | −0.436451 | − | 0.899728i | \(-0.643765\pi\) |
0.720821 | + | 0.693121i | \(0.243765\pi\) | |||||||
\(318\) | 7.59439 | 0.425872 | ||||||||
\(319\) | −5.97495 | − | 1.04407i | −0.334533 | − | 0.0584564i | ||||
\(320\) | 23.8991 | 1.33600 | ||||||||
\(321\) | −13.2040 | + | 9.59329i | −0.736977 | + | 0.535445i | ||||
\(322\) | 5.59736 | + | 17.2269i | 0.311929 | + | 0.960018i | ||||
\(323\) | 11.2747 | − | 34.7000i | 0.627342 | − | 1.93076i | ||||
\(324\) | 0.848719 | + | 0.616630i | 0.0471510 | + | 0.0342572i | ||||
\(325\) | −6.43700 | − | 4.67675i | −0.357061 | − | 0.259420i | ||||
\(326\) | 1.52082 | − | 4.68060i | 0.0842303 | − | 0.259234i | ||||
\(327\) | −1.70055 | − | 5.23376i | −0.0940407 | − | 0.289428i | ||||
\(328\) | 20.8758 | − | 15.1672i | 1.15267 | − | 0.837466i | ||||
\(329\) | −5.15963 | −0.284460 | ||||||||
\(330\) | −10.4556 | + | 5.11946i | −0.575561 | + | 0.281817i | ||||
\(331\) | −24.1969 | −1.32998 | −0.664991 | − | 0.746851i | \(-0.731565\pi\) | ||||
−0.664991 | + | 0.746851i | \(0.731565\pi\) | |||||||
\(332\) | −4.92949 | + | 3.58148i | −0.270541 | + | 0.196559i | ||||
\(333\) | 0.848128 | + | 2.61027i | 0.0464771 | + | 0.143042i | ||||
\(334\) | −6.10414 | + | 18.7866i | −0.334004 | + | 1.02796i | ||||
\(335\) | −11.6680 | − | 8.47727i | −0.637489 | − | 0.463163i | ||||
\(336\) | 2.23700 | + | 1.62528i | 0.122038 | + | 0.0886660i | ||||
\(337\) | 5.22924 | − | 16.0939i | 0.284855 | − | 0.876693i | −0.701587 | − | 0.712584i | \(-0.747525\pi\) |
0.986442 | − | 0.164110i | \(-0.0524751\pi\) | |||||||
\(338\) | −0.301339 | − | 0.927427i | −0.0163907 | − | 0.0504454i | ||||
\(339\) | 11.8026 | − | 8.57510i | 0.641030 | − | 0.465736i | ||||
\(340\) | −30.4083 | −1.64912 | ||||||||
\(341\) | −17.2557 | − | 17.8138i | −0.934448 | − | 0.964673i | ||||
\(342\) | −4.41830 | −0.238914 | ||||||||
\(343\) | −5.84084 | + | 4.24362i | −0.315376 | + | 0.229134i | ||||
\(344\) | −6.14451 | − | 18.9109i | −0.331290 | − | 1.01961i | ||||
\(345\) | −5.98741 | + | 18.4274i | −0.322351 | + | 0.992095i | ||||
\(346\) | −3.12218 | − | 2.26840i | −0.167849 | − | 0.121950i | ||||
\(347\) | −7.33189 | − | 5.32693i | −0.393596 | − | 0.285964i | 0.373331 | − | 0.927698i | \(-0.378215\pi\) |
−0.766928 | + | 0.641734i | \(0.778215\pi\) | |||||||
\(348\) | −0.592868 | + | 1.82466i | −0.0317811 | + | 0.0978120i | ||||
\(349\) | 9.12335 | + | 28.0788i | 0.488362 | + | 1.50302i | 0.827052 | + | 0.562125i | \(0.190016\pi\) |
−0.338690 | + | 0.940898i | \(0.609984\pi\) | |||||||
\(350\) | −21.6607 | + | 15.7374i | −1.15781 | + | 0.841201i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −2.41031 | − | 16.9608i | −0.128470 | − | 0.904013i | ||||
\(353\) | 9.51258 | 0.506304 | 0.253152 | − | 0.967427i | \(-0.418533\pi\) | ||||
0.253152 | + | 0.967427i | \(0.418533\pi\) | |||||||
\(354\) | 4.02425 | − | 2.92379i | 0.213887 | − | 0.155398i | ||||
\(355\) | −10.1694 | − | 31.2982i | −0.539736 | − | 1.66114i | ||||
\(356\) | −5.35095 | + | 16.4685i | −0.283600 | + | 0.872830i | ||||
\(357\) | −22.4810 | − | 16.3334i | −1.18982 | − | 0.864454i | ||||
\(358\) | −14.1851 | − | 10.3061i | −0.749707 | − | 0.544694i | ||||
\(359\) | 6.36899 | − | 19.6017i | 0.336143 | − | 1.03454i | −0.630014 | − | 0.776584i | \(-0.716951\pi\) |
0.966156 | − | 0.257957i | \(-0.0830492\pi\) | |||||||
\(360\) | 3.30726 | + | 10.1787i | 0.174308 | + | 0.536465i | ||||
\(361\) | −1.23682 | + | 0.898599i | −0.0650956 | + | 0.0472947i | ||||
\(362\) | 13.0896 | 0.687972 | ||||||||
\(363\) | 6.17917 | + | 9.10043i | 0.324322 | + | 0.477649i | ||||
\(364\) | 3.62011 | 0.189745 | ||||||||
\(365\) | −22.5076 | + | 16.3527i | −1.17810 | + | 0.855940i | ||||
\(366\) | 0.408335 | + | 1.25673i | 0.0213440 | + | 0.0656902i | ||||
\(367\) | 4.84907 | − | 14.9239i | 0.253120 | − | 0.779022i | −0.741075 | − | 0.671422i | \(-0.765684\pi\) |
0.994194 | − | 0.107599i | \(-0.0343164\pi\) | |||||||
\(368\) | 3.48949 | + | 2.53526i | 0.181902 | + | 0.132160i | ||||
\(369\) | 7.02104 | + | 5.10109i | 0.365501 | + | 0.265552i | ||||
\(370\) | −2.97701 | + | 9.16228i | −0.154767 | + | 0.476324i | ||||
\(371\) | −8.30458 | − | 25.5589i | −0.431152 | − | 1.32695i | ||||
\(372\) | −6.34655 | + | 4.61104i | −0.329053 | + | 0.239071i | ||||
\(373\) | 16.4971 | 0.854188 | 0.427094 | − | 0.904207i | \(-0.359537\pi\) | ||||
0.427094 | + | 0.904207i | \(0.359537\pi\) | |||||||
\(374\) | −3.66435 | − | 25.7851i | −0.189479 | − | 1.33332i | ||||
\(375\) | −10.6422 | −0.549563 | ||||||||
\(376\) | −3.59668 | + | 2.61314i | −0.185485 | + | 0.134762i | ||||
\(377\) | −0.565134 | − | 1.73930i | −0.0291059 | − | 0.0895787i | ||||
\(378\) | −1.03985 | + | 3.20034i | −0.0534842 | + | 0.164608i | ||||
\(379\) | 25.0141 | + | 18.1738i | 1.28489 | + | 0.933527i | 0.999689 | − | 0.0249403i | \(-0.00793956\pi\) |
0.285201 | + | 0.958468i | \(0.407940\pi\) | |||||||
\(380\) | 13.8417 | + | 10.0566i | 0.710066 | + | 0.515893i | ||||
\(381\) | −0.589703 | + | 1.81492i | −0.0302114 | + | 0.0929811i | ||||
\(382\) | 0.846759 | + | 2.60606i | 0.0433240 | + | 0.133338i | ||||
\(383\) | 28.9288 | − | 21.0180i | 1.47819 | − | 1.07397i | 0.500057 | − | 0.865992i | \(-0.333312\pi\) |
0.978134 | − | 0.207976i | \(-0.0666877\pi\) | |||||||
\(384\) | −3.85596 | −0.196774 | ||||||||
\(385\) | 28.6629 | + | 29.5900i | 1.46080 | + | 1.50805i | ||||
\(386\) | 20.5362 | 1.04526 | ||||||||
\(387\) | 5.41030 | − | 3.93081i | 0.275021 | − | 0.199814i | ||||
\(388\) | −0.0294780 | − | 0.0907239i | −0.00149652 | − | 0.00460581i | ||||
\(389\) | −8.84943 | + | 27.2358i | −0.448684 | + | 1.38091i | 0.429708 | + | 0.902968i | \(0.358616\pi\) |
−0.878393 | + | 0.477940i | \(0.841384\pi\) | |||||||
\(390\) | −2.83972 | − | 2.06318i | −0.143795 | − | 0.104473i | ||||
\(391\) | −35.0680 | − | 25.4784i | −1.77346 | − | 1.28850i | ||||
\(392\) | 4.50932 | − | 13.8783i | 0.227755 | − | 0.700958i | ||||
\(393\) | 2.92398 | + | 8.99908i | 0.147495 | + | 0.453944i | ||||
\(394\) | −4.07277 | + | 2.95904i | −0.205183 | + | 0.149074i | ||||
\(395\) | −12.1242 | −0.610033 | ||||||||
\(396\) | 3.12490 | − | 1.53007i | 0.157032 | − | 0.0768891i | ||||
\(397\) | −16.7426 | −0.840286 | −0.420143 | − | 0.907458i | \(-0.638020\pi\) | ||||
−0.420143 | + | 0.907458i | \(0.638020\pi\) | |||||||
\(398\) | 20.8235 | − | 15.1291i | 1.04379 | − | 0.758355i | ||||
\(399\) | 4.83148 | + | 14.8698i | 0.241876 | + | 0.744419i | ||||
\(400\) | −1.97016 | + | 6.06352i | −0.0985078 | + | 0.303176i | ||||
\(401\) | −28.9160 | − | 21.0087i | −1.44400 | − | 1.04913i | −0.987188 | − | 0.159561i | \(-0.948992\pi\) |
−0.456809 | − | 0.889565i | \(-0.651008\pi\) | |||||||
\(402\) | −3.16099 | − | 2.29659i | −0.157656 | − | 0.114544i | ||||
\(403\) | 2.31077 | − | 7.11181i | 0.115107 | − | 0.354264i | ||||
\(404\) | 0.174026 | + | 0.535598i | 0.00865813 | + | 0.0266470i | ||||
\(405\) | −2.91208 | + | 2.11575i | −0.144702 | + | 0.105132i | ||||
\(406\) | −6.15401 | −0.305419 | ||||||||
\(407\) | 8.96694 | + | 1.56689i | 0.444475 | + | 0.0776676i | ||||
\(408\) | −23.9432 | −1.18537 | ||||||||
\(409\) | 12.4228 | − | 9.02568i | 0.614267 | − | 0.446291i | −0.236647 | − | 0.971596i | \(-0.576049\pi\) |
0.850914 | + | 0.525304i | \(0.176049\pi\) | |||||||
\(410\) | 9.41336 | + | 28.9713i | 0.464893 | + | 1.43079i | ||||
\(411\) | 3.52101 | − | 10.8366i | 0.173679 | − | 0.534528i | ||||
\(412\) | −2.03930 | − | 1.48164i | −0.100469 | − | 0.0729951i | ||||
\(413\) | −14.2406 | − | 10.3464i | −0.700733 | − | 0.509112i | ||||
\(414\) | −1.62206 | + | 4.99219i | −0.0797200 | + | 0.245353i | ||||
\(415\) | −6.46049 | − | 19.8833i | −0.317133 | − | 0.976035i | ||||
\(416\) | 4.17877 | − | 3.03606i | 0.204881 | − | 0.148855i | ||||
\(417\) | 12.6585 | 0.619890 | ||||||||
\(418\) | −6.85964 | + | 12.9491i | −0.335516 | + | 0.633363i | ||||
\(419\) | −25.7895 | −1.25990 | −0.629949 | − | 0.776636i | \(-0.716924\pi\) | ||||
−0.629949 | + | 0.776636i | \(0.716924\pi\) | |||||||
\(420\) | 10.5420 | − | 7.65924i | 0.514399 | − | 0.373733i | ||||
\(421\) | 2.84403 | + | 8.75302i | 0.138609 | + | 0.426596i | 0.996134 | − | 0.0878470i | \(-0.0279987\pi\) |
−0.857524 | + | 0.514443i | \(0.827999\pi\) | |||||||
\(422\) | −2.29229 | + | 7.05495i | −0.111587 | + | 0.343429i | ||||
\(423\) | −1.20965 | − | 0.878864i | −0.0588153 | − | 0.0427318i | ||||
\(424\) | −18.7335 | − | 13.6107i | −0.909778 | − | 0.660993i | ||||
\(425\) | 19.7993 | − | 60.9360i | 0.960407 | − | 2.95583i | ||||
\(426\) | −2.75501 | − | 8.47906i | −0.133481 | − | 0.410812i | ||||
\(427\) | 3.78299 | − | 2.74850i | 0.183072 | − | 0.133009i | ||||
\(428\) | 17.1220 | 0.827624 | ||||||||
\(429\) | −1.55255 | + | 2.93080i | −0.0749579 | + | 0.141500i | ||||
\(430\) | 23.4737 | 1.13200 | ||||||||
\(431\) | 2.23576 | − | 1.62438i | 0.107693 | − | 0.0782435i | −0.532635 | − | 0.846345i | \(-0.678798\pi\) |
0.640328 | + | 0.768101i | \(0.278798\pi\) | |||||||
\(432\) | 0.247614 | + | 0.762077i | 0.0119133 | + | 0.0366654i | ||||
\(433\) | 9.44391 | − | 29.0654i | 0.453846 | − | 1.39679i | −0.418640 | − | 0.908152i | \(-0.637493\pi\) |
0.872485 | − | 0.488641i | \(-0.162507\pi\) | |||||||
\(434\) | −20.3573 | − | 14.7905i | −0.977182 | − | 0.709964i | ||||
\(435\) | −5.32564 | − | 3.86931i | −0.255345 | − | 0.185519i | ||||
\(436\) | −1.78400 | + | 5.49060i | −0.0854383 | + | 0.262952i | ||||
\(437\) | 7.53660 | + | 23.1953i | 0.360525 | + | 1.10958i | ||||
\(438\) | −6.09758 | + | 4.43015i | −0.291353 | + | 0.211681i | ||||
\(439\) | 32.6429 | 1.55796 | 0.778980 | − | 0.627049i | \(-0.215738\pi\) | ||||
0.778980 | + | 0.627049i | \(0.215738\pi\) | |||||||
\(440\) | 34.9664 | + | 6.11005i | 1.66696 | + | 0.291285i | ||||
\(441\) | 4.90781 | 0.233705 | ||||||||
\(442\) | 6.35291 | − | 4.61566i | 0.302177 | − | 0.219544i | ||||
\(443\) | −8.08711 | − | 24.8896i | −0.384230 | − | 1.18254i | −0.937037 | − | 0.349230i | \(-0.886443\pi\) |
0.552807 | − | 0.833309i | \(-0.313557\pi\) | |||||||
\(444\) | 0.889749 | − | 2.73837i | 0.0422256 | − | 0.129957i | ||||
\(445\) | −48.0668 | − | 34.9225i | −2.27858 | − | 1.65549i | ||||
\(446\) | 3.41569 | + | 2.48164i | 0.161738 | + | 0.117509i | ||||
\(447\) | 0.402467 | − | 1.23867i | 0.0190360 | − | 0.0585869i | ||||
\(448\) | −7.08001 | − | 21.7900i | −0.334499 | − | 1.02948i | ||||
\(449\) | 6.76729 | − | 4.91672i | 0.319368 | − | 0.232034i | −0.416538 | − | 0.909118i | \(-0.636757\pi\) |
0.735906 | + | 0.677084i | \(0.236757\pi\) | |||||||
\(450\) | −7.75888 | −0.365757 | ||||||||
\(451\) | 25.8508 | − | 12.6576i | 1.21727 | − | 0.596022i | ||||
\(452\) | −15.3048 | −0.719876 | ||||||||
\(453\) | 12.3629 | − | 8.98217i | 0.580859 | − | 0.422019i | ||||
\(454\) | −3.03788 | − | 9.34963i | −0.142575 | − | 0.438800i | ||||
\(455\) | −3.83834 | + | 11.8132i | −0.179944 | + | 0.553811i | ||||
\(456\) | 10.8988 | + | 7.91848i | 0.510385 | + | 0.370817i | ||||
\(457\) | −19.2928 | − | 14.0170i | −0.902478 | − | 0.655689i | 0.0366232 | − | 0.999329i | \(-0.488340\pi\) |
−0.939101 | + | 0.343640i | \(0.888340\pi\) | |||||||
\(458\) | −3.69153 | + | 11.3614i | −0.172494 | + | 0.530881i | ||||
\(459\) | −2.48842 | − | 7.65857i | −0.116150 | − | 0.357472i | ||||
\(460\) | 16.4445 | − | 11.9476i | 0.766728 | − | 0.557061i | ||||
\(461\) | −23.8611 | −1.11132 | −0.555662 | − | 0.831408i | \(-0.687535\pi\) | ||||
−0.555662 | + | 0.831408i | \(0.687535\pi\) | |||||||
\(462\) | 7.76512 | + | 8.01628i | 0.361266 | + | 0.372951i | ||||
\(463\) | −15.1085 | −0.702152 | −0.351076 | − | 0.936347i | \(-0.614184\pi\) | ||||
−0.351076 | + | 0.936347i | \(0.614184\pi\) | |||||||
\(464\) | −1.18555 | + | 0.861351i | −0.0550377 | + | 0.0399872i | ||||
\(465\) | −8.31766 | − | 25.5991i | −0.385722 | − | 1.18713i | ||||
\(466\) | 1.36810 | − | 4.21058i | 0.0633761 | − | 0.195051i | ||||
\(467\) | −15.5595 | − | 11.3046i | −0.720007 | − | 0.523116i | 0.166380 | − | 0.986062i | \(-0.446792\pi\) |
−0.886386 | + | 0.462946i | \(0.846792\pi\) | |||||||
\(468\) | 0.848719 | + | 0.616630i | 0.0392320 | + | 0.0285037i | ||||
\(469\) | −4.27258 | + | 13.1497i | −0.197290 | + | 0.607195i | ||||
\(470\) | −1.62182 | − | 4.99146i | −0.0748091 | − | 0.230239i | ||||
\(471\) | 2.81782 | − | 2.04727i | 0.129838 | − | 0.0943331i | ||||
\(472\) | −15.1668 | −0.698111 | ||||||||
\(473\) | −3.12065 | − | 21.9593i | −0.143488 | − | 1.00969i | ||||
\(474\) | −3.28458 | −0.150866 | ||||||||
\(475\) | −29.1652 | + | 21.1898i | −1.33819 | + | 0.972253i | ||||
\(476\) | 9.00836 | + | 27.7249i | 0.412898 | + | 1.27077i | ||||
\(477\) | 2.40659 | − | 7.40672i | 0.110190 | − | 0.339130i | ||||
\(478\) | 15.2986 | + | 11.1151i | 0.699741 | + | 0.508391i | ||||
\(479\) | 17.3873 | + | 12.6326i | 0.794447 | + | 0.577200i | 0.909280 | − | 0.416185i | \(-0.136633\pi\) |
−0.114833 | + | 0.993385i | \(0.536633\pi\) | |||||||
\(480\) | 5.74538 | − | 17.6825i | 0.262239 | − | 0.807090i | ||||
\(481\) | 0.848128 | + | 2.61027i | 0.0386713 | + | 0.119018i | ||||
\(482\) | −15.8310 | + | 11.5019i | −0.721082 | + | 0.523897i | ||||
\(483\) | 18.5749 | 0.845189 | ||||||||
\(484\) | 0.367229 | − | 11.5340i | 0.0166922 | − | 0.524271i | ||||
\(485\) | 0.327306 | 0.0148622 | ||||||||
\(486\) | −0.788916 | + | 0.573181i | −0.0357860 | + | 0.0260000i | ||||
\(487\) | 9.68532 | + | 29.8084i | 0.438884 | + | 1.35075i | 0.889054 | + | 0.457803i | \(0.151363\pi\) |
−0.450170 | + | 0.892943i | \(0.648637\pi\) | |||||||
\(488\) | 1.24505 | − | 3.83185i | 0.0563605 | − | 0.173460i | ||||
\(489\) | −4.08300 | − | 2.96647i | −0.184640 | − | 0.134149i | ||||
\(490\) | 13.9368 | + | 10.1257i | 0.629601 | + | 0.457432i | ||||
\(491\) | −5.01272 | + | 15.4276i | −0.226221 | + | 0.696236i | 0.771945 | + | 0.635690i | \(0.219284\pi\) |
−0.998165 | + | 0.0605463i | \(0.980716\pi\) | |||||||
\(492\) | −2.81341 | − | 8.65878i | −0.126838 | − | 0.390368i | ||||
\(493\) | 11.9143 | − | 8.65624i | 0.536593 | − | 0.389858i | ||||
\(494\) | −4.41830 | −0.198789 | ||||||||
\(495\) | 1.67968 | + | 11.8195i | 0.0754960 | + | 0.531248i | ||||
\(496\) | −5.99192 | −0.269045 | ||||||||
\(497\) | −25.5236 | + | 18.5440i | −1.14489 | + | 0.831810i | ||||
\(498\) | −1.75022 | − | 5.38664i | −0.0784294 | − | 0.241381i | ||||
\(499\) | 5.00853 | − | 15.4147i | 0.224212 | − | 0.690055i | −0.774158 | − | 0.632992i | \(-0.781826\pi\) |
0.998371 | − | 0.0570628i | \(-0.0181735\pi\) | |||||||
\(500\) | 9.03227 | + | 6.56233i | 0.403936 | + | 0.293476i | ||||
\(501\) | 16.3880 | + | 11.9066i | 0.732163 | + | 0.531947i | ||||
\(502\) | −7.09029 | + | 21.8217i | −0.316455 | + | 0.973948i | ||||
\(503\) | 3.01691 | + | 9.28510i | 0.134517 | + | 0.414002i | 0.995515 | − | 0.0946076i | \(-0.0301596\pi\) |
−0.860997 | + | 0.508610i | \(0.830160\pi\) | |||||||
\(504\) | 8.30070 | − | 6.03081i | 0.369743 | − | 0.268634i | ||||
\(505\) | −1.93228 | −0.0859855 | ||||||||
\(506\) | 12.1128 | + | 12.5046i | 0.538479 | + | 0.555896i | ||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 1.61963 | − | 1.17673i | 0.0718593 | − | 0.0522088i | ||||
\(509\) | 6.85866 | + | 21.1088i | 0.304005 | + | 0.935631i | 0.980047 | + | 0.198768i | \(0.0636939\pi\) |
−0.676042 | + | 0.736863i | \(0.736306\pi\) | |||||||
\(510\) | 8.73458 | − | 26.8823i | 0.386774 | − | 1.19037i | ||||
\(511\) | 21.5774 | + | 15.6769i | 0.954529 | + | 0.693506i | ||||
\(512\) | −7.20340 | − | 5.23358i | −0.318348 | − | 0.231294i | ||||
\(513\) | −1.40012 | + | 4.30911i | −0.0618166 | + | 0.190252i | ||||
\(514\) | 3.01215 | + | 9.27046i | 0.132860 | + | 0.408902i | ||||
\(515\) | 6.99713 | − | 5.08371i | 0.308330 | − | 0.224015i | ||||
\(516\) | −7.01568 | −0.308848 | ||||||||
\(517\) | −4.45382 | + | 2.18077i | −0.195879 | + | 0.0959100i | ||||
\(518\) | 9.23567 | 0.405792 | ||||||||
\(519\) | −3.20173 | + | 2.32619i | −0.140540 | + | 0.102109i | ||||
\(520\) | 3.30726 | + | 10.1787i | 0.145033 | + | 0.446366i | ||||
\(521\) | 8.20347 | − | 25.2477i | 0.359400 | − | 1.10612i | −0.594013 | − | 0.804455i | \(-0.702457\pi\) |
0.953414 | − | 0.301666i | \(-0.0975426\pi\) | |||||||
\(522\) | −1.44278 | − | 1.04824i | −0.0631488 | − | 0.0458803i | ||||
\(523\) | 0.214500 | + | 0.155843i | 0.00937943 | + | 0.00681456i | 0.592465 | − | 0.805596i | \(-0.298155\pi\) |
−0.583086 | + | 0.812411i | \(0.698155\pi\) | |||||||
\(524\) | 3.06747 | − | 9.44070i | 0.134003 | − | 0.412419i | ||||
\(525\) | 8.48446 | + | 26.1125i | 0.370292 | + | 1.13964i | ||||
\(526\) | −3.42847 | + | 2.49093i | −0.149488 | + | 0.108610i | ||||
\(527\) | 60.2164 | 2.62307 | ||||||||
\(528\) | 2.61793 | + | 0.457457i | 0.113931 | + | 0.0199083i | ||||
\(529\) | 5.97499 | 0.259782 | ||||||||
\(530\) | 22.1154 | − | 16.0678i | 0.960633 | − | 0.697941i | ||||
\(531\) | −1.57629 | − | 4.85133i | −0.0684052 | − | 0.210530i | ||||
\(532\) | 5.06858 | − | 15.5995i | 0.219751 | − | 0.676323i | ||||
\(533\) | 7.02104 | + | 5.10109i | 0.304115 | + | 0.220953i | ||||
\(534\) | −13.0219 | − | 9.46094i | −0.563511 | − | 0.409415i | ||||
\(535\) | −18.1542 | + | 55.8728i | −0.784873 | + | 2.41559i | ||||
\(536\) | 3.68143 | + | 11.3303i | 0.159013 | + | 0.489393i | ||||
\(537\) | −14.5465 | + | 10.5687i | −0.627730 | + | 0.456072i | ||||
\(538\) | −16.6783 | −0.719052 | ||||||||
\(539\) | 7.61962 | − | 14.3838i | 0.328200 | − | 0.619554i | ||||
\(540\) | 3.77617 | 0.162500 | ||||||||
\(541\) | −19.0666 | + | 13.8527i | −0.819739 | + | 0.595575i | −0.916638 | − | 0.399719i | \(-0.869108\pi\) |
0.0968986 | + | 0.995294i | \(0.469108\pi\) | |||||||
\(542\) | 3.03765 | + | 9.34894i | 0.130478 | + | 0.401571i | ||||
\(543\) | 4.14796 | − | 12.7661i | 0.178006 | − | 0.547846i | ||||
\(544\) | 33.6504 | + | 24.4485i | 1.44275 | + | 1.04822i | ||||
\(545\) | −16.0254 | − | 11.6432i | −0.686455 | − | 0.498738i | ||||
\(546\) | −1.03985 | + | 3.20034i | −0.0445016 | + | 0.136962i | ||||
\(547\) | 6.26515 | + | 19.2821i | 0.267878 | + | 0.824445i | 0.991016 | + | 0.133741i | \(0.0426990\pi\) |
−0.723138 | + | 0.690704i | \(0.757301\pi\) | |||||||
\(548\) | −9.67049 | + | 7.02602i | −0.413103 | + | 0.300137i | ||||
\(549\) | 1.35507 | 0.0578329 | ||||||||
\(550\) | −12.0461 | + | 22.7397i | −0.513646 | + | 0.969625i | ||||
\(551\) | −8.28612 | −0.353000 | ||||||||
\(552\) | 12.9482 | − | 9.40744i | 0.551113 | − | 0.400407i | ||||
\(553\) | 3.59174 | + | 11.0542i | 0.152736 | + | 0.470074i | ||||
\(554\) | −0.858387 | + | 2.64184i | −0.0364694 | + | 0.112241i | ||||
\(555\) | 7.99248 | + | 5.80688i | 0.339262 | + | 0.246488i | ||||
\(556\) | −10.7435 | − | 7.80562i | −0.455627 | − | 0.331032i | ||||
\(557\) | −3.39898 | + | 10.4610i | −0.144019 | + | 0.443246i | −0.996884 | − | 0.0788868i | \(-0.974863\pi\) |
0.852864 | + | 0.522133i | \(0.174863\pi\) | |||||||
\(558\) | −2.25335 | − | 6.93511i | −0.0953920 | − | 0.293587i | ||||
\(559\) | 5.41030 | − | 3.93081i | 0.228831 | − | 0.166256i | ||||
\(560\) | 9.95298 | 0.420590 | ||||||||
\(561\) | −26.3091 | − | 4.59727i | −1.11077 | − | 0.194097i | ||||
\(562\) | −32.3981 | −1.36663 | ||||||||
\(563\) | −22.0934 | + | 16.0518i | −0.931126 | + | 0.676502i | −0.946268 | − | 0.323383i | \(-0.895180\pi\) |
0.0151425 | + | 0.999885i | \(0.495180\pi\) | |||||||
\(564\) | 0.484720 | + | 1.49182i | 0.0204104 | + | 0.0628168i | ||||
\(565\) | 16.2274 | − | 49.9427i | 0.682690 | − | 2.10110i | ||||
\(566\) | −18.9268 | − | 13.7511i | −0.795551 | − | 0.578002i | ||||
\(567\) | 2.79173 | + | 2.02831i | 0.117242 | + | 0.0851811i | ||||
\(568\) | −8.40024 | + | 25.8533i | −0.352466 | + | 1.08478i | ||||
\(569\) | 0.414645 | + | 1.27615i | 0.0173828 | + | 0.0534988i | 0.959372 | − | 0.282145i | \(-0.0910460\pi\) |
−0.941989 | + | 0.335644i | \(0.891046\pi\) | |||||||
\(570\) | −12.8664 | + | 9.34800i | −0.538915 | + | 0.391545i | ||||
\(571\) | 35.9461 | 1.50430 | 0.752150 | − | 0.658992i | \(-0.229017\pi\) | ||||
0.752150 | + | 0.658992i | \(0.229017\pi\) | |||||||
\(572\) | 3.12490 | − | 1.53007i | 0.130659 | − | 0.0639756i | ||||
\(573\) | 2.80999 | 0.117389 | ||||||||
\(574\) | 23.6260 | − | 17.1653i | 0.986132 | − | 0.716467i | ||||
\(575\) | 13.2349 | + | 40.7328i | 0.551933 | + | 1.69867i | ||||
\(576\) | 2.05172 | − | 6.31454i | 0.0854883 | − | 0.263106i | ||||
\(577\) | 19.3160 | + | 14.0339i | 0.804135 | + | 0.584239i | 0.912124 | − | 0.409914i | \(-0.134441\pi\) |
−0.107989 | + | 0.994152i | \(0.534441\pi\) | |||||||
\(578\) | 37.7465 | + | 27.4244i | 1.57005 | + | 1.14071i | ||||
\(579\) | 6.50771 | − | 20.0287i | 0.270451 | − | 0.832363i | ||||
\(580\) | 2.13404 | + | 6.56791i | 0.0886113 | + | 0.272717i | ||||
\(581\) | −16.2148 | + | 11.7807i | −0.672703 | + | 0.488747i | ||||
\(582\) | 0.0886712 | 0.00367554 | ||||||||
\(583\) | −17.9712 | − | 18.5525i | −0.744293 | − | 0.768368i | ||||
\(584\) | 22.9809 | 0.950957 | ||||||||
\(585\) | −2.91208 | + | 2.11575i | −0.120400 | + | 0.0874754i | ||||
\(586\) | 1.24702 | + | 3.83792i | 0.0515137 | + | 0.158543i | ||||
\(587\) | −7.98885 | + | 24.5871i | −0.329735 | + | 1.01482i | 0.639523 | + | 0.768772i | \(0.279132\pi\) |
−0.969258 | + | 0.246048i | \(0.920868\pi\) | |||||||
\(588\) | −4.16535 | − | 3.02630i | −0.171776 | − | 0.124803i | ||||
\(589\) | −27.4102 | − | 19.9147i | −1.12942 | − | 0.820571i | ||||
\(590\) | 5.53292 | − | 17.0286i | 0.227787 | − | 0.701056i | ||||
\(591\) | 1.59530 | + | 4.90982i | 0.0656218 | + | 0.201963i | ||||
\(592\) | 1.77922 | − | 1.29268i | 0.0731254 | − | 0.0531287i | ||||
\(593\) | −15.3155 | −0.628934 | −0.314467 | − | 0.949268i | \(-0.601826\pi\) | ||||
−0.314467 | + | 0.949268i | \(0.601826\pi\) | |||||||
\(594\) | 0.455046 | + | 3.20205i | 0.0186708 | + | 0.131382i | ||||
\(595\) | −100.024 | −4.10057 | ||||||||
\(596\) | −1.10538 | + | 0.803106i | −0.0452782 | + | 0.0328965i | ||||
\(597\) | −8.15651 | − | 25.1032i | −0.333824 | − | 1.02740i | ||||
\(598\) | −1.62206 | + | 4.99219i | −0.0663310 | + | 0.204146i | ||||
\(599\) | −33.6533 | − | 24.4505i | −1.37504 | − | 0.999022i | −0.997325 | − | 0.0730989i | \(-0.976711\pi\) |
−0.377711 | − | 0.925923i | \(-0.623289\pi\) | |||||||
\(600\) | 19.1392 | + | 13.9055i | 0.781357 | + | 0.567689i | ||||
\(601\) | −8.19403 | + | 25.2186i | −0.334242 | + | 1.02869i | 0.632853 | + | 0.774272i | \(0.281884\pi\) |
−0.967094 | + | 0.254418i | \(0.918116\pi\) | |||||||
\(602\) | −6.95401 | − | 21.4022i | −0.283424 | − | 0.872290i | ||||
\(603\) | −3.24153 | + | 2.35511i | −0.132005 | + | 0.0959074i | ||||
\(604\) | −16.0313 | −0.652304 | ||||||||
\(605\) | 37.2484 | + | 13.4276i | 1.51436 | + | 0.545910i | ||||
\(606\) | −0.523479 | −0.0212649 | ||||||||
\(607\) | −4.75411 | + | 3.45407i | −0.192964 | + | 0.140196i | −0.680072 | − | 0.733145i | \(-0.738052\pi\) |
0.487109 | + | 0.873341i | \(0.338052\pi\) | |||||||
\(608\) | −7.23195 | − | 22.2576i | −0.293294 | − | 0.902667i | ||||
\(609\) | −1.95015 | + | 6.00194i | −0.0790240 | + | 0.243211i | ||||
\(610\) | 3.84802 | + | 2.79575i | 0.155802 | + | 0.113197i | ||||
\(611\) | −1.20965 | − | 0.878864i | −0.0489373 | − | 0.0355550i | ||||
\(612\) | −2.61054 | + | 8.03441i | −0.105525 | + | 0.324772i | ||||
\(613\) | −8.48776 | − | 26.1227i | −0.342818 | − | 1.05508i | −0.962742 | − | 0.270422i | \(-0.912837\pi\) |
0.619924 | − | 0.784662i | \(-0.287163\pi\) | |||||||
\(614\) | 6.08792 | − | 4.42313i | 0.245688 | − | 0.178503i | ||||
\(615\) | 31.2384 | 1.25965 | ||||||||
\(616\) | −4.78783 | − | 33.6908i | −0.192907 | − | 1.35744i | ||||
\(617\) | 17.2096 | 0.692832 | 0.346416 | − | 0.938081i | \(-0.387399\pi\) | ||||
0.346416 | + | 0.938081i | \(0.387399\pi\) | |||||||
\(618\) | 1.89561 | − | 1.37724i | 0.0762525 | − | 0.0554007i | ||||
\(619\) | −2.36986 | − | 7.29368i | −0.0952528 | − | 0.293158i | 0.892067 | − | 0.451904i | \(-0.149255\pi\) |
−0.987319 | + | 0.158746i | \(0.949255\pi\) | |||||||
\(620\) | −8.72584 | + | 26.8554i | −0.350438 | + | 1.07854i | ||||
\(621\) | 4.35481 | + | 3.16396i | 0.174753 | + | 0.126965i | ||||
\(622\) | 24.7570 | + | 17.9870i | 0.992664 | + | 0.721213i | ||||
\(623\) | −17.6011 | + | 54.1707i | −0.705174 | + | 2.17030i | ||||
\(624\) | 0.247614 | + | 0.762077i | 0.00991248 | + | 0.0305075i | ||||
\(625\) | 1.19398 | − | 0.867476i | 0.0477592 | − | 0.0346991i | ||||
\(626\) | 4.97738 | 0.198936 | ||||||||
\(627\) | 10.4554 | + | 10.7936i | 0.417548 | + | 0.431054i | ||||
\(628\) | −3.65395 | −0.145808 | ||||||||
\(629\) | −17.8804 | + | 12.9909i | −0.712940 | + | 0.517981i | ||||
\(630\) | 3.74297 | + | 11.5197i | 0.149124 | + | 0.458955i | ||||
\(631\) | −0.975564 | + | 3.00248i | −0.0388366 | + | 0.119527i | −0.968595 | − | 0.248643i | \(-0.920015\pi\) |
0.929759 | + | 0.368170i | \(0.120015\pi\) | |||||||
\(632\) | 8.10225 | + | 5.88663i | 0.322290 | + | 0.234157i | ||||
\(633\) | 6.15420 | + | 4.47129i | 0.244608 | + | 0.177718i | ||||
\(634\) | 1.88587 | − | 5.80411i | 0.0748975 | − | 0.230511i | ||||
\(635\) | 2.12265 | + | 6.53284i | 0.0842348 | + | 0.259248i | ||||
\(636\) | −6.60972 | + | 4.80225i | −0.262093 | + | 0.190421i | ||||
\(637\) | 4.90781 | 0.194454 | ||||||||
\(638\) | −5.31218 | + | 2.60105i | −0.210311 | + | 0.102977i | ||||
\(639\) | −9.14256 | −0.361674 | ||||||||
\(640\) | −11.2288 | + | 8.15823i | −0.443859 | + | 0.322482i | ||||
\(641\) | −2.74336 | − | 8.44319i | −0.108356 | − | 0.333486i | 0.882147 | − | 0.470973i | \(-0.156097\pi\) |
−0.990503 | + | 0.137488i | \(0.956097\pi\) | |||||||
\(642\) | −4.91818 | + | 15.1366i | −0.194105 | + | 0.597394i | ||||
\(643\) | 20.0644 | + | 14.5776i | 0.791262 | + | 0.574885i | 0.908338 | − | 0.418238i | \(-0.137352\pi\) |
−0.117076 | + | 0.993123i | \(0.537352\pi\) | |||||||
\(644\) | −15.7649 | − | 11.4539i | −0.621224 | − | 0.451346i | ||||
\(645\) | 7.43860 | − | 22.8936i | 0.292894 | − | 0.901437i | ||||
\(646\) | −10.9946 | − | 33.8379i | −0.432576 | − | 1.33133i | ||||
\(647\) | 2.66450 | − | 1.93587i | 0.104752 | − | 0.0761071i | −0.534176 | − | 0.845373i | \(-0.679378\pi\) |
0.638928 | + | 0.769266i | \(0.279378\pi\) | |||||||
\(648\) | 2.97332 | 0.116803 | ||||||||
\(649\) | −16.6655 | − | 2.91214i | −0.654179 | − | 0.114312i | ||||
\(650\) | −7.75888 | −0.304328 | ||||||||
\(651\) | −20.8760 | + | 15.1673i | −0.818195 | + | 0.594453i | ||||
\(652\) | 1.63610 | + | 5.03540i | 0.0640747 | + | 0.197202i | ||||
\(653\) | 8.29862 | − | 25.5405i | 0.324750 | − | 0.999478i | −0.646803 | − | 0.762657i | \(-0.723894\pi\) |
0.971553 | − | 0.236821i | \(-0.0761056\pi\) | |||||||
\(654\) | −4.34149 | − | 3.15427i | −0.169766 | − | 0.123342i | ||||
\(655\) | 27.5546 | + | 20.0196i | 1.07665 | + | 0.782231i | ||||
\(656\) | 2.14891 | − | 6.61367i | 0.0839009 | − | 0.258221i | ||||
\(657\) | 2.38841 | + | 7.35076i | 0.0931807 | + | 0.286781i | ||||
\(658\) | −4.07052 | + | 2.95740i | −0.158685 | + | 0.115292i | ||||
\(659\) | 13.0411 | 0.508011 | 0.254005 | − | 0.967203i | \(-0.418252\pi\) | ||||
0.254005 | + | 0.967203i | \(0.418252\pi\) | |||||||
\(660\) | 5.86270 | − | 11.0672i | 0.228205 | − | 0.430790i | ||||
\(661\) | −8.88151 | −0.345451 | −0.172725 | − | 0.984970i | \(-0.555257\pi\) | ||||
−0.172725 | + | 0.984970i | \(0.555257\pi\) | |||||||
\(662\) | −19.0893 | + | 13.8692i | −0.741928 | + | 0.539042i | ||||
\(663\) | −2.48842 | − | 7.65857i | −0.0966423 | − | 0.297434i | ||||
\(664\) | −5.33656 | + | 16.4243i | −0.207099 | + | 0.637385i | ||||
\(665\) | 45.5303 | + | 33.0797i | 1.76559 | + | 1.28277i | ||||
\(666\) | 2.16526 | + | 1.57315i | 0.0839021 | + | 0.0609584i | ||||
\(667\) | −3.04203 | + | 9.36240i | −0.117788 | + | 0.362514i | ||||
\(668\) | −6.56685 | − | 20.2107i | −0.254079 | − | 0.781975i | ||||
\(669\) | 3.50272 | − | 2.54487i | 0.135423 | − | 0.0983904i | ||||
\(670\) | −14.0641 | −0.543342 | ||||||||
\(671\) | 2.10381 | − | 3.97143i | 0.0812169 | − | 0.153316i | ||||
\(672\) | −17.8241 | −0.687579 | ||||||||
\(673\) | 4.43775 | − | 3.22422i | 0.171063 | − | 0.124284i | −0.498960 | − | 0.866625i | \(-0.666284\pi\) |
0.670023 | + | 0.742341i | \(0.266284\pi\) | |||||||
\(674\) | −5.09932 | − | 15.6941i | −0.196418 | − | 0.604513i | ||||
\(675\) | −2.45872 | + | 7.56715i | −0.0946360 | + | 0.291260i | ||||
\(676\) | 0.848719 | + | 0.616630i | 0.0326430 | + | 0.0237166i | ||||
\(677\) | 8.79714 | + | 6.39149i | 0.338101 | + | 0.245645i | 0.743860 | − | 0.668335i | \(-0.232993\pi\) |
−0.405759 | + | 0.913980i | \(0.632993\pi\) | |||||||
\(678\) | 4.39619 | − | 13.5301i | 0.168835 | − | 0.519619i | ||||
\(679\) | −0.0969633 | − | 0.298422i | −0.00372111 | − | 0.0114524i | ||||
\(680\) | −69.7245 | + | 50.6578i | −2.67381 | + | 1.94264i | ||||
\(681\) | −10.0813 | −0.386315 | ||||||||
\(682\) | −23.8239 | − | 4.16299i | −0.912263 | − | 0.159409i | ||||
\(683\) | 14.6191 | 0.559386 | 0.279693 | − | 0.960090i | \(-0.409767\pi\) | ||||
0.279693 | + | 0.960090i | \(0.409767\pi\) | |||||||
\(684\) | 3.84544 | − | 2.79387i | 0.147034 | − | 0.106826i | ||||
\(685\) | −12.6740 | − | 39.0064i | −0.484247 | − | 1.49036i | ||||
\(686\) | −2.17557 | + | 6.69572i | −0.0830637 | + | 0.255644i | ||||
\(687\) | 9.91078 | + | 7.20061i | 0.378120 | + | 0.274720i | ||||
\(688\) | −4.33524 | − | 3.14974i | −0.165280 | − | 0.120083i | ||||
\(689\) | 2.40659 | − | 7.40672i | 0.0916837 | − | 0.282173i | ||||
\(690\) | 5.83865 | + | 17.9695i | 0.222274 | + | 0.684088i | ||||
\(691\) | −7.07864 | + | 5.14293i | −0.269284 | + | 0.195646i | −0.714230 | − | 0.699911i | \(-0.753223\pi\) |
0.444946 | + | 0.895557i | \(0.353223\pi\) | |||||||
\(692\) | 4.15177 | 0.157827 | ||||||||
\(693\) | 10.2789 | − | 5.03294i | 0.390462 | − | 0.191186i | ||||
\(694\) | −8.83754 | −0.335468 | ||||||||
\(695\) | 36.8625 | − | 26.7822i | 1.39828 | − | 1.01591i | ||||
\(696\) | 1.68032 | + | 5.17151i | 0.0636925 | + | 0.196025i | ||||
\(697\) | −21.5957 | + | 66.4648i | −0.817997 | + | 2.51753i | ||||
\(698\) | 23.2918 | + | 16.9225i | 0.881608 | + | 0.640525i | ||||
\(699\) | −3.67299 | − | 2.66859i | −0.138925 | − | 0.100935i | ||||
\(700\) | 8.90083 | − | 27.3939i | 0.336420 | − | 1.03539i | ||||
\(701\) | −11.3874 | − | 35.0469i | −0.430097 | − | 1.32370i | −0.898028 | − | 0.439938i | \(-0.855000\pi\) |
0.467931 | − | 0.883765i | \(-0.345000\pi\) | |||||||
\(702\) | −0.788916 | + | 0.573181i | −0.0297757 | + | 0.0216333i | ||||
\(703\) | 12.4354 | 0.469011 | ||||||||
\(704\) | −15.3213 | − | 15.8168i | −0.577442 | − | 0.596119i | ||||
\(705\) | −5.38205 | −0.202700 | ||||||||
\(706\) | 7.50463 | − | 5.45243i | 0.282441 | − | 0.205205i | ||||
\(707\) | 0.572432 | + | 1.76177i | 0.0215285 | + | 0.0662580i | ||||
\(708\) | −1.65365 | + | 5.08940i | −0.0621478 | + | 0.191271i | ||||
\(709\) | −30.2905 | − | 22.0073i | −1.13758 | − | 0.826502i | −0.150802 | − | 0.988564i | \(-0.548186\pi\) |
−0.986781 | + | 0.162062i | \(0.948186\pi\) | |||||||
\(710\) | −25.9623 | − | 18.8628i | −0.974350 | − | 0.707906i | ||||
\(711\) | −1.04085 | + | 3.20341i | −0.0390350 | + | 0.120137i | ||||
\(712\) | 15.1658 | + | 46.6756i | 0.568363 | + | 1.74924i | ||||
\(713\) | −32.5644 | + | 23.6594i | −1.21955 | + | 0.886052i | ||||
\(714\) | −27.0976 | −1.01410 | ||||||||
\(715\) | 1.67968 | + | 11.8195i | 0.0628165 | + | 0.442025i | ||||
\(716\) | 18.8629 | 0.704939 | ||||||||
\(717\) | 15.6884 | − | 11.3983i | 0.585893 | − | 0.425676i | ||||
\(718\) | −6.21075 | − | 19.1147i | −0.231783 | − | 0.713355i | ||||
\(719\) | −7.35174 | + | 22.6263i | −0.274174 | + | 0.843820i | 0.715263 | + | 0.698855i | \(0.246307\pi\) |
−0.989437 | + | 0.144965i | \(0.953693\pi\) | |||||||
\(720\) | 2.33343 | + | 1.69534i | 0.0869618 | + | 0.0631815i | ||||
\(721\) | −6.70796 | − | 4.87362i | −0.249818 | − | 0.181503i | ||||
\(722\) | −0.460684 | + | 1.41784i | −0.0171449 | + | 0.0527665i | ||||
\(723\) | 6.20097 | + | 19.0846i | 0.230616 | + | 0.709764i | ||||
\(724\) | −11.3924 | + | 8.27707i | −0.423396 | + | 0.307615i | ||||
\(725\) | −14.5511 | −0.540414 | ||||||||
\(726\) | 10.0910 | + | 3.63770i | 0.374514 | + | 0.135008i | ||||
\(727\) | −38.9674 | −1.44522 | −0.722611 | − | 0.691255i | \(-0.757058\pi\) | ||||
−0.722611 | + | 0.691255i | \(0.757058\pi\) | |||||||
\(728\) | 8.30070 | − | 6.03081i | 0.307645 | − | 0.223517i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −8.38353 | + | 25.8019i | −0.310288 | + | 0.954969i | ||||
\(731\) | 43.5675 | + | 31.6537i | 1.61140 | + | 1.17075i | ||||
\(732\) | −1.15007 | − | 0.835577i | −0.0425079 | − | 0.0308838i | ||||
\(733\) | 0.553803 | − | 1.70443i | 0.0204552 | − | 0.0629545i | −0.940308 | − | 0.340325i | \(-0.889463\pi\) |
0.960763 | + | 0.277370i | \(0.0894629\pi\) | |||||||
\(734\) | −4.72859 | − | 14.5531i | −0.174536 | − | 0.537165i | ||||
\(735\) | 14.2919 | − | 10.3837i | 0.527165 | − | 0.383008i | ||||
\(736\) | −27.8037 | −1.02486 | ||||||||
\(737\) | 1.86971 | + | 13.1567i | 0.0688716 | + | 0.484633i | ||||
\(738\) | 8.46286 | 0.311522 | ||||||||
\(739\) | −30.5011 | + | 22.1603i | −1.12200 | + | 0.815181i | −0.984511 | − | 0.175322i | \(-0.943903\pi\) |
−0.137489 | + | 0.990503i | \(0.543903\pi\) | |||||||
\(740\) | −3.20267 | − | 9.85681i | −0.117733 | − | 0.362344i | ||||
\(741\) | −1.40012 | + | 4.30911i | −0.0514345 | + | 0.158299i | ||||
\(742\) | −21.2015 | − | 15.4038i | −0.778331 | − | 0.565491i | ||||
\(743\) | 36.7180 | + | 26.6772i | 1.34705 | + | 0.978691i | 0.999153 | + | 0.0411601i | \(0.0131054\pi\) |
0.347901 | + | 0.937531i | \(0.386895\pi\) | |||||||
\(744\) | −6.87064 | + | 21.1457i | −0.251890 | + | 0.775237i | ||||
\(745\) | −1.44869 | − | 4.45861i | −0.0530759 | − | 0.163351i | ||||
\(746\) | 13.0148 | − | 9.45584i | 0.476507 | − | 0.346203i | ||||
\(747\) | −5.80815 | −0.212509 | ||||||||
\(748\) | 19.4942 | + | 20.1248i | 0.712780 | + | 0.735836i | ||||
\(749\) | 56.3203 | 2.05790 | ||||||||
\(750\) | −8.39584 | + | 6.09994i | −0.306573 | + | 0.222738i | ||||
\(751\) | −1.84965 | − | 5.69264i | −0.0674947 | − | 0.207727i | 0.911621 | − | 0.411032i | \(-0.134832\pi\) |
−0.979115 | + | 0.203305i | \(0.934832\pi\) | |||||||
\(752\) | −0.370235 | + | 1.13947i | −0.0135011 | + | 0.0415521i | ||||
\(753\) | 19.0356 | + | 13.8301i | 0.693694 | + | 0.503998i | ||||
\(754\) | −1.44278 | − | 1.04824i | −0.0525430 | − | 0.0381747i | ||||
\(755\) | 16.9977 | − | 52.3135i | 0.618609 | − | 1.90388i | ||||
\(756\) | −1.11868 | − | 3.44293i | −0.0406859 | − | 0.125218i | ||||
\(757\) | 33.5229 | − | 24.3558i | 1.21841 | − | 0.885228i | 0.222445 | − | 0.974945i | \(-0.428596\pi\) |
0.995967 | + | 0.0897169i | \(0.0285962\pi\) | |||||||
\(758\) | 30.1510 | 1.09513 | ||||||||
\(759\) | 16.0340 | − | 7.85087i | 0.581997 | − | 0.284969i | ||||
\(760\) | 48.4918 | 1.75898 | ||||||||
\(761\) | 12.3817 | − | 8.99582i | 0.448836 | − | 0.326098i | −0.340300 | − | 0.940317i | \(-0.610529\pi\) |
0.789136 | + | 0.614219i | \(0.210529\pi\) | |||||||
\(762\) | 0.575051 | + | 1.76983i | 0.0208319 | + | 0.0641140i | ||||
\(763\) | −5.86821 | + | 18.0605i | −0.212443 | + | 0.653834i | ||||
\(764\) | −2.38489 | − | 1.73272i | −0.0862823 | − | 0.0626877i | ||||
\(765\) | −23.4501 | − | 17.0375i | −0.847839 | − | 0.615991i | ||||
\(766\) | 10.7753 | − | 33.1629i | 0.389326 | − | 1.19822i | ||||
\(767\) | −1.57629 | − | 4.85133i | −0.0569166 | − | 0.175171i | ||||
\(768\) | −13.7850 | + | 10.0154i | −0.497422 | + | 0.361398i | ||||
\(769\) | 24.0709 | 0.868018 | 0.434009 | − | 0.900909i | \(-0.357099\pi\) | ||||
0.434009 | + | 0.900909i | \(0.357099\pi\) | |||||||
\(770\) | 39.5730 | + | 6.91501i | 1.42611 | + | 0.249200i | ||||
\(771\) | 9.99589 | 0.359993 | ||||||||
\(772\) | −17.8735 | + | 12.9859i | −0.643282 | + | 0.467371i | ||||
\(773\) | 10.5409 | + | 32.4415i | 0.379129 | + | 1.16684i | 0.940650 | + | 0.339378i | \(0.110216\pi\) |
−0.561521 | + | 0.827463i | \(0.689784\pi\) | |||||||
\(774\) | 2.01521 | − | 6.20216i | 0.0724351 | − | 0.222932i | ||||
\(775\) | −48.1346 | − | 34.9718i | −1.72904 | − | 1.25622i | ||||
\(776\) | −0.218730 | − | 0.158917i | −0.00785195 | − | 0.00570477i | ||||
\(777\) | 2.92669 | − | 9.00744i | 0.104995 | − | 0.323140i | ||||
\(778\) | 8.62956 | + | 26.5591i | 0.309385 | + | 0.952188i | ||||
\(779\) | 31.8114 | − | 23.1124i | 1.13976 | − | 0.828086i | ||||
\(780\) | 3.77617 | 0.135208 | ||||||||
\(781\) | −14.1943 | + | 26.7950i | −0.507912 | + | 0.958801i | ||||
\(782\) | −42.2694 | −1.51155 | ||||||||
\(783\) | −1.47954 | + | 1.07495i | −0.0528745 | + | 0.0384156i | ||||
\(784\) | −1.21524 | − | 3.74013i | −0.0434014 | − | 0.133576i | ||||
\(785\) | 3.87421 | − | 11.9236i | 0.138277 | − | 0.425571i | ||||
\(786\) | 7.46488 | + | 5.42355i | 0.266263 | + | 0.193452i | ||||
\(787\) | −7.14984 | − | 5.19466i | −0.254864 | − | 0.185170i | 0.453016 | − | 0.891503i | \(-0.350348\pi\) |
−0.707880 | + | 0.706333i | \(0.750348\pi\) | |||||||
\(788\) | 1.67359 | − | 5.15077i | 0.0596190 | − | 0.183488i | ||||
\(789\) | 1.34293 | + | 4.13310i | 0.0478094 | + | 0.147142i | ||||
\(790\) | −9.56495 | + | 6.94934i | −0.340305 | + | 0.247246i | ||||
\(791\) | −50.3427 | −1.78998 | ||||||||
\(792\) | 4.61623 | − | 8.71420i | 0.164031 | − | 0.309645i | ||||
\(793\) | 1.35507 | 0.0481199 | ||||||||
\(794\) | −13.2085 | + | 9.59653i | −0.468752 | + | 0.340568i | ||||
\(795\) | −8.66257 | − | 26.6607i | −0.307230 | − | 0.945556i | ||||
\(796\) | −8.55679 | + | 26.3351i | −0.303287 | + | 0.933422i | ||||
\(797\) | 25.1042 | + | 18.2393i | 0.889236 | + | 0.646068i | 0.935679 | − | 0.352853i | \(-0.114788\pi\) |
−0.0464424 | + | 0.998921i | \(0.514788\pi\) | |||||||
\(798\) | 12.3347 | + | 8.96168i | 0.436644 | + | 0.317240i | ||||
\(799\) | 3.72072 | − | 11.4512i | 0.131629 | − | 0.405114i | ||||
\(800\) | −12.6999 | − | 39.0862i | −0.449009 | − | 1.38191i | ||||
\(801\) | −13.3536 | + | 9.70199i | −0.471828 | + | 0.342803i | ||||
\(802\) | −34.8541 | −1.23074 | ||||||||
\(803\) | 25.2517 | + | 4.41250i | 0.891115 | + | 0.155714i | ||||
\(804\) | 4.20338 | 0.148242 | ||||||||
\(805\) | 54.0916 | − | 39.2999i | 1.90648 | − | 1.38514i | ||||
\(806\) | −2.25335 | − | 6.93511i | −0.0793710 | − | 0.244279i | ||||
\(807\) | −5.28519 | + | 16.2661i | −0.186047 | + | 0.572595i | ||||
\(808\) | 1.29129 | + | 0.938180i | 0.0454275 | + | 0.0330050i | ||||
\(809\) | −9.39939 | − | 6.82906i | −0.330465 | − | 0.240097i | 0.410163 | − | 0.912012i | \(-0.365472\pi\) |
−0.740628 | + | 0.671915i | \(0.765472\pi\) | |||||||
\(810\) | −1.08468 | + | 3.33829i | −0.0381117 | + | 0.117296i | ||||
\(811\) | −4.45764 | − | 13.7192i | −0.156529 | − | 0.481746i | 0.841784 | − | 0.539815i | \(-0.181506\pi\) |
−0.998313 | + | 0.0580686i | \(0.981506\pi\) | |||||||
\(812\) | 5.35611 | − | 3.89144i | 0.187962 | − | 0.136563i | ||||
\(813\) | 10.0805 | 0.353539 | ||||||||
\(814\) | 7.97227 | − | 3.90354i | 0.279428 | − | 0.136819i | ||||
\(815\) | −18.1663 | −0.636338 | ||||||||
\(816\) | −5.22025 | + | 3.79273i | −0.182745 | + | 0.132772i | ||||
\(817\) | −9.36327 | − | 28.8172i | −0.327579 | − | 1.00819i | ||||
\(818\) | 4.62719 | − | 14.2410i | 0.161786 | − | 0.497925i | ||||
\(819\) | 2.79173 | + | 2.02831i | 0.0975510 | + | 0.0708749i | ||||
\(820\) | −26.5126 | − | 19.2626i | −0.925861 | − | 0.672678i | ||||
\(821\) | 8.15624 | − | 25.1023i | 0.284655 | − | 0.876077i | −0.701847 | − | 0.712327i | \(-0.747641\pi\) |
0.986502 | − | 0.163750i | \(-0.0523589\pi\) | |||||||
\(822\) | −3.43353 | − | 10.5673i | −0.119758 | − | 0.368577i | ||||
\(823\) | 10.9551 | − | 7.95936i | 0.381871 | − | 0.277446i | −0.380245 | − | 0.924886i | \(-0.624160\pi\) |
0.762116 | + | 0.647440i | \(0.224160\pi\) | |||||||
\(824\) | −7.14428 | −0.248883 | ||||||||
\(825\) | 18.3605 | + | 18.9544i | 0.639231 | + | 0.659907i | ||||
\(826\) | −17.1650 | −0.597246 | ||||||||
\(827\) | −5.81710 | + | 4.22637i | −0.202280 | + | 0.146965i | −0.684314 | − | 0.729187i | \(-0.739898\pi\) |
0.482034 | + | 0.876153i | \(0.339898\pi\) | |||||||
\(828\) | −1.74502 | − | 5.37062i | −0.0606436 | − | 0.186642i | ||||
\(829\) | −15.0065 | + | 46.1853i | −0.521198 | + | 1.60408i | 0.250516 | + | 0.968112i | \(0.419400\pi\) |
−0.771714 | + | 0.635970i | \(0.780600\pi\) | |||||||
\(830\) | −16.4935 | − | 11.9833i | −0.572499 | − | 0.415945i | ||||
\(831\) | 2.30454 | + | 1.67435i | 0.0799437 | + | 0.0580825i | ||||
\(832\) | 2.05172 | − | 6.31454i | 0.0711306 | − | 0.218917i | ||||
\(833\) | 12.2127 | + | 37.5868i | 0.423145 | + | 1.30231i | ||||
\(834\) | 9.98651 | − | 7.25562i | 0.345804 | − | 0.251242i | ||||
\(835\) | 72.9145 | 2.52331 | ||||||||
\(836\) | −2.21804 | − | 15.6078i | −0.0767126 | − | 0.539808i | ||||
\(837\) | −7.47780 | −0.258470 | ||||||||
\(838\) | −20.3457 | + | 14.7820i | −0.702832 | + | 0.510637i | ||||
\(839\) | −9.93676 | − | 30.5822i | −0.343055 | − | 1.05582i | −0.962617 | − | 0.270867i | \(-0.912690\pi\) |
0.619562 | − | 0.784948i | \(-0.287310\pi\) | |||||||
\(840\) | 11.4126 | − | 35.1244i | 0.393772 | − | 1.21191i | ||||
\(841\) | 20.7557 | + | 15.0799i | 0.715713 | + | 0.519996i | ||||
\(842\) | 7.26077 | + | 5.27526i | 0.250223 | + | 0.181797i | ||||
\(843\) | −10.2666 | + | 31.5975i | −0.353602 | + | 1.08828i | ||||
\(844\) | −2.46605 | − | 7.58974i | −0.0848851 | − | 0.261249i | ||||
\(845\) | −2.91208 | + | 2.11575i | −0.100178 | + | 0.0727839i | ||||
\(846\) | −1.45806 | −0.0501292 | ||||||||
\(847\) | 1.20794 | − | 37.9392i | 0.0415054 | − | 1.30361i | ||||
\(848\) | −6.24039 | −0.214296 | ||||||||
\(849\) | −19.4090 | + | 14.1015i | −0.666115 | + | 0.483961i | ||||
\(850\) | −19.3074 | − | 59.4220i | −0.662237 | − | 2.03816i | ||||
\(851\) | 4.56534 | − | 14.0507i | 0.156498 | − | 0.481651i | ||||
\(852\) | 7.75947 | + | 5.63758i | 0.265835 | + | 0.193140i | ||||
\(853\) | 39.3020 | + | 28.5546i | 1.34568 | + | 0.977691i | 0.999215 | + | 0.0396267i | \(0.0126169\pi\) |
0.346461 | + | 0.938064i | \(0.387383\pi\) | |||||||
\(854\) | 1.40907 | − | 4.33668i | 0.0482174 | − | 0.148398i | ||||
\(855\) | 5.03975 | + | 15.5108i | 0.172356 | + | 0.530457i | ||||
\(856\) | 39.2598 | − | 28.5239i | 1.34187 | − | 0.974927i | ||||
\(857\) | 8.19897 | 0.280071 | 0.140036 | − | 0.990146i | \(-0.455278\pi\) | ||||
0.140036 | + | 0.990146i | \(0.455278\pi\) | |||||||
\(858\) | 0.455046 | + | 3.20205i | 0.0155350 | + | 0.109316i | ||||
\(859\) | 19.8006 | 0.675589 | 0.337795 | − | 0.941220i | \(-0.390319\pi\) | ||||
0.337795 | + | 0.941220i | \(0.390319\pi\) | |||||||
\(860\) | −20.4302 | + | 14.8434i | −0.696664 | + | 0.506156i | ||||
\(861\) | −9.25427 | − | 28.4817i | −0.315385 | − | 0.970654i | ||||
\(862\) | 0.832767 | − | 2.56299i | 0.0283642 | − | 0.0872959i | ||||
\(863\) | −12.9159 | − | 9.38392i | −0.439661 | − | 0.319432i | 0.345839 | − | 0.938294i | \(-0.387594\pi\) |
−0.785500 | + | 0.618861i | \(0.787594\pi\) | |||||||
\(864\) | −4.17877 | − | 3.03606i | −0.142165 | − | 0.103289i | ||||
\(865\) | −4.40204 | + | 13.5481i | −0.149674 | + | 0.460649i | ||||
\(866\) | −9.20927 | − | 28.3432i | −0.312944 | − | 0.963142i | ||||
\(867\) | 38.7082 | − | 28.1232i | 1.31460 | − | 0.955112i | ||||
\(868\) | 27.0705 | 0.918831 | ||||||||
\(869\) | 7.77258 | + | 8.02399i | 0.263667 | + | 0.272195i | ||||
\(870\) | −6.41930 | −0.217635 | ||||||||
\(871\) | −3.24153 | + | 2.35511i | −0.109835 | + | 0.0797998i | ||||
\(872\) | 5.05628 | + | 15.5616i | 0.171227 | + | 0.526983i | ||||
\(873\) | 0.0280991 | − | 0.0864800i | 0.000951009 | − | 0.00292690i | ||||
\(874\) | 19.2408 | + | 13.9793i | 0.650831 | + | 0.472857i | ||||
\(875\) | 29.7103 | + | 21.5858i | 1.00439 | + | 0.729733i | ||||
\(876\) | 2.50562 | − | 7.71150i | 0.0846570 | − | 0.260547i | ||||
\(877\) | 7.64594 | + | 23.5318i | 0.258185 | + | 0.794612i | 0.993185 | + | 0.116545i | \(0.0371820\pi\) |
−0.735000 | + | 0.678067i | \(0.762818\pi\) | |||||||
\(878\) | 25.7525 | − | 18.7103i | 0.869104 | − | 0.631441i | ||||
\(879\) | 4.13824 | 0.139580 | ||||||||
\(880\) | 8.59146 | − | 4.20672i | 0.289618 | − | 0.141808i | ||||
\(881\) | 56.9520 | 1.91876 | 0.959381 | − | 0.282113i | \(-0.0910354\pi\) | ||||
0.959381 | + | 0.282113i | \(0.0910354\pi\) | |||||||
\(882\) | 3.87185 | − | 2.81306i | 0.130372 | − | 0.0947208i | ||||
\(883\) | −8.59376 | − | 26.4489i | −0.289203 | − | 0.890076i | −0.985107 | − | 0.171941i | \(-0.944996\pi\) |
0.695904 | − | 0.718135i | \(-0.255004\pi\) | |||||||
\(884\) | −2.61054 | + | 8.03441i | −0.0878019 | + | 0.270226i | ||||
\(885\) | −14.8545 | − | 10.7924i | −0.499327 | − | 0.362782i | ||||
\(886\) | −20.6463 | − | 15.0004i | −0.693626 | − | 0.503949i | ||||
\(887\) | −4.57256 | + | 14.0729i | −0.153532 | + | 0.472522i | −0.998009 | − | 0.0630693i | \(-0.979911\pi\) |
0.844478 | + | 0.535591i | \(0.179911\pi\) | |||||||
\(888\) | −2.52175 | − | 7.76116i | −0.0846245 | − | 0.260447i | ||||
\(889\) | 5.32751 | − | 3.87066i | 0.178679 | − | 0.129818i | ||||
\(890\) | −57.9376 | −1.94207 | ||||||||
\(891\) | 3.26712 | + | 0.570898i | 0.109453 | + | 0.0191258i | ||||
\(892\) | −4.54207 | −0.152080 | ||||||||
\(893\) | −5.48078 | + | 3.98202i | −0.183407 | + | 0.133253i | ||||
\(894\) | −0.392468 | − | 1.20789i | −0.0131261 | − | 0.0403979i | ||||
\(895\) | −20.0000 | + | 61.5536i | −0.668525 | + | 2.05751i | ||||
\(896\) | 10.7648 | + | 7.82108i | 0.359627 | + | 0.261284i | ||||
\(897\) | 4.35481 | + | 3.16396i | 0.145403 | + | 0.105641i | ||||
\(898\) | 2.52065 | − | 7.75776i | 0.0841152 | − | 0.258880i | ||||
\(899\) | −4.22596 | − | 13.0062i | −0.140944 | − | 0.433780i | ||||
\(900\) | 6.75289 | − | 4.90626i | 0.225096 | − | 0.163542i | ||||
\(901\) | 62.7135 | 2.08929 | ||||||||
\(902\) | 13.1390 | − | 24.8030i | 0.437482 | − | 0.825848i | ||||
\(903\) | −23.0770 | −0.767955 | ||||||||
\(904\) | −35.0929 | + | 25.4965i | −1.16717 | + | 0.848001i | ||||
\(905\) | −14.9307 | − | 45.9519i | −0.496312 | − | 1.52749i | ||||
\(906\) | 4.60488 | − | 14.1724i | 0.152987 | − | 0.470845i | ||||
\(907\) | −7.48813 | − | 5.44045i | −0.248639 | − | 0.180647i | 0.456484 | − | 0.889732i | \(-0.349108\pi\) |
−0.705124 | + | 0.709084i | \(0.749108\pi\) | |||||||
\(908\) | 8.55616 | + | 6.21641i | 0.283946 | + | 0.206299i | ||||
\(909\) | −0.165885 | + | 0.510543i | −0.00550207 | + | 0.0169336i | ||||
\(910\) | 3.74297 | + | 11.5197i | 0.124078 | + | 0.381874i | ||||
\(911\) | 4.14946 | − | 3.01476i | 0.137478 | − | 0.0998834i | −0.516921 | − | 0.856033i | \(-0.672922\pi\) |
0.654399 | + | 0.756150i | \(0.272922\pi\) | |||||||
\(912\) | 3.63056 | 0.120220 | ||||||||
\(913\) | −9.01746 | + | 17.0225i | −0.298434 | + | 0.563363i | ||||
\(914\) | −23.2547 | −0.769197 | ||||||||
\(915\) | 3.94606 | − | 2.86698i | 0.130453 | − | 0.0947795i | ||||
\(916\) | −3.97136 | − | 12.2226i | −0.131217 | − | 0.403845i | ||||
\(917\) | 10.0900 | − | 31.0538i | 0.333200 | − | 1.02549i | ||||
\(918\) | −6.35291 | − | 4.61566i | −0.209677 | − | 0.152339i | ||||
\(919\) | −17.6132 | − | 12.7968i | −0.581007 | − | 0.422126i | 0.258080 | − | 0.966124i | \(-0.416910\pi\) |
−0.839087 | + | 0.543997i | \(0.816910\pi\) | |||||||
\(920\) | 17.8025 | − | 54.7904i | 0.586930 | − | 1.80639i | ||||
\(921\) | −2.38463 | − | 7.33913i | −0.0785761 | − | 0.241832i | ||||
\(922\) | −18.8244 | + | 13.6768i | −0.619950 | + | 0.450420i | ||||
\(923\) | −9.14256 | −0.300931 | ||||||||
\(924\) | −11.8273 | − | 2.06671i | −0.389091 | − | 0.0679899i | ||||
\(925\) | 21.8376 | 0.718016 | ||||||||
\(926\) | −11.9193 | + | 8.65991i | −0.391694 | + | 0.284582i | ||||
\(927\) | −0.742505 | − | 2.28520i | −0.0243871 | − | 0.0750557i | ||||
\(928\) | 2.91906 | − | 8.98394i | 0.0958228 | − | 0.294912i | ||||
\(929\) | −33.3216 | − | 24.2096i | −1.09325 | − | 0.794291i | −0.113303 | − | 0.993561i | \(-0.536143\pi\) |
−0.979945 | + | 0.199270i | \(0.936143\pi\) | |||||||
\(930\) | −21.2349 | − | 15.4280i | −0.696319 | − | 0.505905i | ||||
\(931\) | 6.87150 | − | 21.1483i | 0.225204 | − | 0.693108i | ||||
\(932\) | 1.47181 | + | 4.52976i | 0.0482107 | + | 0.148377i | ||||
\(933\) | 25.3878 | − | 18.4453i | 0.831158 | − | 0.603871i | ||||
\(934\) | −18.7547 | −0.613673 | ||||||||
\(935\) | −86.3409 | + | 42.2759i | −2.82365 | + | 1.38257i | ||||
\(936\) | 2.97332 | 0.0971859 | ||||||||
\(937\) | 47.6127 | − | 34.5927i | 1.55544 | − | 1.13009i | 0.615813 | − | 0.787892i | \(-0.288828\pi\) |
0.939627 | − | 0.342201i | \(-0.111172\pi\) | |||||||
\(938\) | 4.16643 | + | 12.8229i | 0.136039 | + | 0.418684i | ||||
\(939\) | 1.57728 | − | 4.85438i | 0.0514727 | − | 0.158417i | ||||
\(940\) | 4.56785 | + | 3.31874i | 0.148987 | + | 0.108245i | ||||
\(941\) | 29.5661 | + | 21.4810i | 0.963827 | + | 0.700261i | 0.954036 | − | 0.299691i | \(-0.0968835\pi\) |
0.00979074 | + | 0.999952i | \(0.496883\pi\) | |||||||
\(942\) | 1.04957 | − | 3.23025i | 0.0341969 | − | 0.105247i | ||||
\(943\) | −14.4357 | − | 44.4285i | −0.470091 | − | 1.44679i | ||||
\(944\) | −3.30677 | + | 2.40251i | −0.107626 | + | 0.0781950i | ||||
\(945\) | 12.4211 | 0.404059 | ||||||||
\(946\) | −15.0486 | − | 15.5353i | −0.489272 | − | 0.505098i | ||||
\(947\) | −24.8578 | −0.807770 | −0.403885 | − | 0.914810i | \(-0.632340\pi\) | ||||
−0.403885 | + | 0.914810i | \(0.632340\pi\) | |||||||
\(948\) | 2.85871 | − | 2.07698i | 0.0928466 | − | 0.0674570i | ||||
\(949\) | 2.38841 | + | 7.35076i | 0.0775310 | + | 0.238616i | ||||
\(950\) | −10.8633 | + | 33.4339i | −0.352453 | + | 1.08474i | ||||
\(951\) | −5.06307 | − | 3.67854i | −0.164181 | − | 0.119285i | ||||
\(952\) | 66.8431 | + | 48.5643i | 2.16640 | + | 1.57398i | ||||
\(953\) | −0.884064 | + | 2.72087i | −0.0286376 | + | 0.0881376i | −0.964354 | − | 0.264616i | \(-0.914755\pi\) |
0.935716 | + | 0.352754i | \(0.114755\pi\) | |||||||
\(954\) | −2.34680 | − | 7.22269i | −0.0759803 | − | 0.233843i | ||||
\(955\) | 8.18290 | − | 5.94522i | 0.264792 | − | 0.192383i | ||||
\(956\) | −20.3435 | −0.657957 | ||||||||
\(957\) | 0.853397 | + | 6.00515i | 0.0275864 | + | 0.194119i | ||||
\(958\) | 20.9579 | 0.677120 | ||||||||
\(959\) | −31.8096 | + | 23.1110i | −1.02719 | + | 0.746294i | ||||
\(960\) | −7.38521 | − | 22.7293i | −0.238357 | − | 0.733587i | ||||
\(961\) | 7.69991 | − | 23.6979i | 0.248384 | − | 0.764448i | ||||
\(962\) | 2.16526 | + | 1.57315i | 0.0698108 | + | 0.0507205i | ||||
\(963\) | 13.2040 | + | 9.59329i | 0.425494 | + | 0.309139i | ||||
\(964\) | 6.50527 | − | 20.0212i | 0.209521 | − | 0.644839i | ||||
\(965\) | −23.4247 | − | 72.0937i | −0.754066 | − | 2.32078i | ||||
\(966\) | 14.6541 | − | 10.6468i | 0.471487 | − | 0.342556i | ||||
\(967\) | −21.8776 | −0.703536 | −0.351768 | − | 0.936087i | \(-0.614419\pi\) | ||||
−0.351768 | + | 0.936087i | \(0.614419\pi\) | |||||||
\(968\) | −18.3726 | − | 27.0585i | −0.590519 | − | 0.869693i | ||||
\(969\) | −36.4857 | −1.17209 | ||||||||
\(970\) | 0.258217 | − | 0.187606i | 0.00829086 | − | 0.00602366i | ||||
\(971\) | 13.5570 | + | 41.7240i | 0.435063 | + | 1.33899i | 0.893022 | + | 0.450014i | \(0.148581\pi\) |
−0.457958 | + | 0.888974i | \(0.651419\pi\) | |||||||
\(972\) | 0.324182 | − | 0.997729i | 0.0103981 | − | 0.0320022i | ||||
\(973\) | −35.3392 | − | 25.6754i | −1.13292 | − | 0.823115i | ||||
\(974\) | 24.7265 | + | 17.9649i | 0.792288 | + | 0.575631i | ||||
\(975\) | −2.45872 | + | 7.56715i | −0.0787419 | + | 0.242343i | ||||
\(976\) | −0.335534 | − | 1.03267i | −0.0107402 | − | 0.0330548i | ||||
\(977\) | −46.7323 | + | 33.9530i | −1.49510 | + | 1.08625i | −0.522815 | + | 0.852446i | \(0.675118\pi\) |
−0.972283 | + | 0.233807i | \(0.924882\pi\) | |||||||
\(978\) | −4.92147 | −0.157371 | ||||||||
\(979\) | 7.70236 | + | 54.1997i | 0.246168 | + | 1.73223i | ||||
\(980\) | −18.5327 | −0.592005 | ||||||||
\(981\) | −4.45210 | + | 3.23464i | −0.142145 | + | 0.103274i | ||||
\(982\) | 4.88817 | + | 15.0443i | 0.155988 | + | 0.480081i | ||||
\(983\) | −14.8878 | + | 45.8201i | −0.474849 | + | 1.46143i | 0.371313 | + | 0.928508i | \(0.378908\pi\) |
−0.846162 | + | 0.532926i | \(0.821092\pi\) | |||||||
\(984\) | −20.8758 | − | 15.1672i | −0.665496 | − | 0.483511i | ||||
\(985\) | 15.0336 | + | 10.9225i | 0.479009 | + | 0.348020i | ||||
\(986\) | 4.43779 | − | 13.6581i | 0.141328 | − | 0.434963i | ||||
\(987\) | 1.59441 | + | 4.90710i | 0.0507507 | + | 0.156195i | ||||
\(988\) | 3.84544 | − | 2.79387i | 0.122340 | − | 0.0888849i | ||||
\(989\) | −35.9977 | −1.14466 | ||||||||
\(990\) | 8.09985 | + | 8.36185i | 0.257430 | + | 0.265757i | ||||
\(991\) | −4.09824 | −0.130185 | −0.0650925 | − | 0.997879i | \(-0.520734\pi\) | ||||
−0.0650925 | + | 0.997879i | \(0.520734\pi\) | |||||||
\(992\) | 31.2480 | − | 22.7030i | 0.992126 | − | 0.720821i | ||||
\(993\) | 7.47726 | + | 23.0126i | 0.237284 | + | 0.730284i | ||||
\(994\) | −9.50691 | + | 29.2593i | −0.301541 | + | 0.928048i | ||||
\(995\) | −76.8643 | − | 55.8452i | −2.43676 | − | 1.77041i | ||||
\(996\) | 4.92949 | + | 3.58148i | 0.156197 | + | 0.113484i | ||||
\(997\) | 8.55282 | − | 26.3229i | 0.270871 | − | 0.833654i | −0.719412 | − | 0.694584i | \(-0.755589\pi\) |
0.990283 | − | 0.139070i | \(-0.0444114\pi\) | |||||||
\(998\) | −4.88409 | − | 15.0317i | −0.154603 | − | 0.475819i | ||||
\(999\) | 2.22043 | − | 1.61324i | 0.0702512 | − | 0.0510405i |
(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 | 429.2.n.c.157.5 | ✓ | 28 | |
11.2 | odd | 10 | 4719.2.a.bo.1.10 | 14 | |||
11.4 | even | 5 | inner | 429.2.n.c.235.5 | yes | 28 | |
11.9 | even | 5 | 4719.2.a.bp.1.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.c.157.5 | ✓ | 28 | 1.1 | even | 1 | trivial | |
429.2.n.c.235.5 | yes | 28 | 11.4 | even | 5 | inner | |
4719.2.a.bo.1.10 | 14 | 11.2 | odd | 10 | |||
4719.2.a.bp.1.5 | 14 | 11.9 | even | 5 |