Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [465,2,Mod(32,465)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(465, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("465.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 465 = 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 465.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71304369399\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(30\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 32.3 | ||
Character | \(\chi\) | \(=\) | 465.32 |
Dual form | 465.2.k.a.218.3 |
$q$-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 \(\left(\mathbb{Z}/465\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(406\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.74033 | + | 1.74033i | −1.23060 | + | 1.23060i | −0.266864 | + | 0.963734i | \(0.585987\pi\) |
−0.963734 | + | 0.266864i | \(0.914013\pi\) | |||||||
\(3\) | 1.27567 | + | 1.17160i | 0.736510 | + | 0.676426i | ||||
\(4\) | − | 4.05749i | − | 2.02874i | ||||||
\(5\) | 0.384493 | + | 2.20276i | 0.171950 | + | 0.985106i | ||||
\(6\) | −4.25907 | + | 0.181113i | −1.73876 | + | 0.0739392i | ||||
\(7\) | 1.30230 | + | 1.30230i | 0.492222 | + | 0.492222i | 0.909006 | − | 0.416784i | \(-0.136843\pi\) |
−0.416784 | + | 0.909006i | \(0.636843\pi\) | |||||||
\(8\) | 3.58070 | + | 3.58070i | 1.26597 | + | 1.26597i | ||||
\(9\) | 0.254684 | + | 2.98917i | 0.0848948 | + | 0.996390i | ||||
\(10\) | −4.50267 | − | 3.16439i | −1.42387 | − | 1.00067i | ||||
\(11\) | 2.55932i | 0.771663i | 0.922569 | + | 0.385832i | \(0.126085\pi\) | ||||
−0.922569 | + | 0.385832i | \(0.873915\pi\) | |||||||
\(12\) | 4.75377 | − | 5.17603i | 1.37230 | − | 1.49419i | ||||
\(13\) | 2.37097 | − | 2.37097i | 0.657588 | − | 0.657588i | −0.297221 | − | 0.954809i | \(-0.596060\pi\) |
0.954809 | + | 0.297221i | \(0.0960597\pi\) | |||||||
\(14\) | −4.53284 | −1.21145 | ||||||||
\(15\) | −2.09028 | + | 3.26048i | −0.539708 | + | 0.841852i | ||||
\(16\) | −4.34822 | −1.08705 | ||||||||
\(17\) | 3.38670 | − | 3.38670i | 0.821396 | − | 0.821396i | −0.164913 | − | 0.986308i | \(-0.552734\pi\) |
0.986308 | + | 0.164913i | \(0.0527342\pi\) | |||||||
\(18\) | −5.64537 | − | 4.75890i | −1.33063 | − | 1.12168i | ||||
\(19\) | 4.69306i | 1.07666i | 0.842733 | + | 0.538331i | \(0.180945\pi\) | ||||
−0.842733 | + | 0.538331i | \(0.819055\pi\) | |||||||
\(20\) | 8.93768 | − | 1.56007i | 1.99853 | − | 0.348843i | ||||
\(21\) | 0.135528 | + | 3.18708i | 0.0295746 | + | 0.695478i | ||||
\(22\) | −4.45405 | − | 4.45405i | −0.949607 | − | 0.949607i | ||||
\(23\) | −0.268531 | − | 0.268531i | −0.0559927 | − | 0.0559927i | 0.678556 | − | 0.734549i | \(-0.262606\pi\) |
−0.734549 | + | 0.678556i | \(0.762606\pi\) | |||||||
\(24\) | 0.372638 | + | 8.76297i | 0.0760644 | + | 1.78873i | ||||
\(25\) | −4.70433 | + | 1.69389i | −0.940866 | + | 0.338779i | ||||
\(26\) | 8.25253i | 1.61845i | ||||||||
\(27\) | −3.17723 | + | 4.11159i | −0.611458 | + | 0.791277i | ||||
\(28\) | 5.28405 | − | 5.28405i | 0.998591 | − | 0.998591i | ||||
\(29\) | −5.68539 | −1.05575 | −0.527875 | − | 0.849322i | \(-0.677011\pi\) | ||||
−0.527875 | + | 0.849322i | \(0.677011\pi\) | |||||||
\(30\) | −2.03653 | − | 9.31208i | −0.371818 | − | 1.70015i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 0.405926 | − | 0.405926i | 0.0717582 | − | 0.0717582i | ||||
\(33\) | −2.99851 | + | 3.26485i | −0.521973 | + | 0.568338i | ||||
\(34\) | 11.7879i | 2.02162i | ||||||||
\(35\) | −2.36793 | + | 3.36937i | −0.400253 | + | 0.569528i | ||||
\(36\) | 12.1285 | − | 1.03338i | 2.02142 | − | 0.172230i | ||||
\(37\) | −2.80395 | − | 2.80395i | −0.460967 | − | 0.460967i | 0.438005 | − | 0.898972i | \(-0.355685\pi\) |
−0.898972 | + | 0.438005i | \(0.855685\pi\) | |||||||
\(38\) | −8.16747 | − | 8.16747i | −1.32494 | − | 1.32494i | ||||
\(39\) | 5.80242 | − | 0.246743i | 0.929131 | − | 0.0395105i | ||||
\(40\) | −6.51068 | + | 9.26419i | −1.02943 | + | 1.46480i | ||||
\(41\) | − | 3.76694i | − | 0.588297i | −0.955760 | − | 0.294148i | \(-0.904964\pi\) | ||
0.955760 | − | 0.294148i | \(-0.0950360\pi\) | |||||||
\(42\) | −5.78243 | − | 5.31070i | −0.892248 | − | 0.819459i | ||||
\(43\) | 7.57956 | − | 7.57956i | 1.15587 | − | 1.15587i | 0.170518 | − | 0.985355i | \(-0.445456\pi\) |
0.985355 | − | 0.170518i | \(-0.0545441\pi\) | |||||||
\(44\) | 10.3844 | 1.56551 | ||||||||
\(45\) | −6.48651 | + | 1.71032i | −0.966952 | + | 0.254960i | ||||
\(46\) | 0.934666 | 0.137809 | ||||||||
\(47\) | 2.85488 | − | 2.85488i | 0.416427 | − | 0.416427i | −0.467544 | − | 0.883970i | \(-0.654861\pi\) |
0.883970 | + | 0.467544i | \(0.154861\pi\) | |||||||
\(48\) | −5.54691 | − | 5.09439i | −0.800627 | − | 0.735312i | ||||
\(49\) | − | 3.60805i | − | 0.515436i | ||||||
\(50\) | 5.23915 | − | 11.1350i | 0.740928 | − | 1.57473i | ||||
\(51\) | 8.28820 | − | 0.352449i | 1.16058 | − | 0.0493527i | ||||
\(52\) | −9.62017 | − | 9.62017i | −1.33408 | − | 1.33408i | ||||
\(53\) | 3.33548 | + | 3.33548i | 0.458164 | + | 0.458164i | 0.898052 | − | 0.439888i | \(-0.144982\pi\) |
−0.439888 | + | 0.898052i | \(0.644982\pi\) | |||||||
\(54\) | −1.62610 | − | 12.6849i | −0.221284 | − | 1.72620i | ||||
\(55\) | −5.63757 | + | 0.984039i | −0.760170 | + | 0.132688i | ||||
\(56\) | 9.32626i | 1.24627i | ||||||||
\(57\) | −5.49842 | + | 5.98682i | −0.728283 | + | 0.792973i | ||||
\(58\) | 9.89445 | − | 9.89445i | 1.29920 | − | 1.29920i | ||||
\(59\) | −12.5260 | −1.63075 | −0.815375 | − | 0.578933i | \(-0.803469\pi\) | ||||
−0.815375 | + | 0.578933i | \(0.803469\pi\) | |||||||
\(60\) | 13.2293 | + | 8.48128i | 1.70790 | + | 1.09493i | ||||
\(61\) | −7.79487 | −0.998031 | −0.499016 | − | 0.866593i | \(-0.666305\pi\) | ||||
−0.499016 | + | 0.866593i | \(0.666305\pi\) | |||||||
\(62\) | −1.74033 | + | 1.74033i | −0.221022 | + | 0.221022i | ||||
\(63\) | −3.56111 | + | 4.22446i | −0.448658 | + | 0.532232i | ||||
\(64\) | − | 7.28355i | − | 0.910443i | ||||||
\(65\) | 6.13430 | + | 4.31106i | 0.760866 | + | 0.534721i | ||||
\(66\) | −0.463526 | − | 10.9003i | −0.0570562 | − | 1.34173i | ||||
\(67\) | −4.02116 | − | 4.02116i | −0.491263 | − | 0.491263i | 0.417441 | − | 0.908704i | \(-0.362927\pi\) |
−0.908704 | + | 0.417441i | \(0.862927\pi\) | |||||||
\(68\) | −13.7415 | − | 13.7415i | −1.66640 | − | 1.66640i | ||||
\(69\) | −0.0279457 | − | 0.657171i | −0.00336426 | − | 0.0791141i | ||||
\(70\) | −1.74285 | − | 9.98478i | −0.208310 | − | 1.19341i | ||||
\(71\) | − | 1.18160i | − | 0.140230i | −0.997539 | − | 0.0701152i | \(-0.977663\pi\) | ||
0.997539 | − | 0.0701152i | \(-0.0223367\pi\) | |||||||
\(72\) | −9.79137 | + | 11.6153i | −1.15392 | + | 1.36887i | ||||
\(73\) | 3.86864 | − | 3.86864i | 0.452790 | − | 0.452790i | −0.443490 | − | 0.896279i | \(-0.646260\pi\) |
0.896279 | + | 0.443490i | \(0.146260\pi\) | |||||||
\(74\) | 9.75960 | 1.13453 | ||||||||
\(75\) | −7.98576 | − | 3.35076i | −0.922116 | − | 0.386913i | ||||
\(76\) | 19.0420 | 2.18427 | ||||||||
\(77\) | −3.33299 | + | 3.33299i | −0.379829 | + | 0.379829i | ||||
\(78\) | −9.66870 | + | 10.5275i | −1.09476 | + | 1.19201i | ||||
\(79\) | 4.46527i | 0.502383i | 0.967937 | + | 0.251191i | \(0.0808223\pi\) | ||||
−0.967937 | + | 0.251191i | \(0.919178\pi\) | |||||||
\(80\) | −1.67186 | − | 9.57809i | −0.186919 | − | 1.07086i | ||||
\(81\) | −8.87027 | + | 1.52259i | −0.985586 | + | 0.169177i | ||||
\(82\) | 6.55571 | + | 6.55571i | 0.723957 | + | 0.723957i | ||||
\(83\) | 4.02931 | + | 4.02931i | 0.442274 | + | 0.442274i | 0.892776 | − | 0.450502i | \(-0.148755\pi\) |
−0.450502 | + | 0.892776i | \(0.648755\pi\) | |||||||
\(84\) | 12.9315 | − | 0.549903i | 1.41095 | − | 0.0599993i | ||||
\(85\) | 8.76226 | + | 6.15794i | 0.950401 | + | 0.667922i | ||||
\(86\) | 26.3819i | 2.84483i | ||||||||
\(87\) | −7.25270 | − | 6.66103i | −0.777571 | − | 0.714137i | ||||
\(88\) | −9.16415 | + | 9.16415i | −0.976901 | + | 0.976901i | ||||
\(89\) | 16.4656 | 1.74535 | 0.872675 | − | 0.488301i | \(-0.162383\pi\) | ||||
0.872675 | + | 0.488301i | \(0.162383\pi\) | |||||||
\(90\) | 8.31213 | − | 14.2652i | 0.876175 | − | 1.50368i | ||||
\(91\) | 6.17540 | 0.647358 | ||||||||
\(92\) | −1.08956 | + | 1.08956i | −0.113595 | + | 0.113595i | ||||
\(93\) | 1.27567 | + | 1.17160i | 0.132281 | + | 0.121490i | ||||
\(94\) | 9.93684i | 1.02491i | ||||||||
\(95\) | −10.3377 | + | 1.80445i | −1.06063 | + | 0.185133i | ||||
\(96\) | 0.993414 | − | 0.0422441i | 0.101390 | − | 0.00431152i | ||||
\(97\) | 13.6813 | + | 13.6813i | 1.38912 | + | 1.38912i | 0.827165 | + | 0.561959i | \(0.189952\pi\) |
0.561959 | + | 0.827165i | \(0.310048\pi\) | |||||||
\(98\) | 6.27919 | + | 6.27919i | 0.634294 | + | 0.634294i | ||||
\(99\) | −7.65023 | + | 0.651818i | −0.768877 | + | 0.0655102i | ||||
\(100\) | 6.87295 | + | 19.0878i | 0.687295 | + | 1.90878i | ||||
\(101\) | − | 18.5916i | − | 1.84993i | −0.380047 | − | 0.924967i | \(-0.624092\pi\) | ||
0.380047 | − | 0.924967i | \(-0.375908\pi\) | |||||||
\(102\) | −13.8108 | + | 15.0376i | −1.36747 | + | 1.48894i | ||||
\(103\) | 2.22600 | − | 2.22600i | 0.219334 | − | 0.219334i | −0.588884 | − | 0.808218i | \(-0.700432\pi\) |
0.808218 | + | 0.588884i | \(0.200432\pi\) | |||||||
\(104\) | 16.9795 | 1.66497 | ||||||||
\(105\) | −6.96827 | + | 1.52395i | −0.680034 | + | 0.148722i | ||||
\(106\) | −11.6097 | −1.12763 | ||||||||
\(107\) | −1.86365 | + | 1.86365i | −0.180166 | + | 0.180166i | −0.791428 | − | 0.611262i | \(-0.790662\pi\) |
0.611262 | + | 0.791428i | \(0.290662\pi\) | |||||||
\(108\) | 16.6827 | + | 12.8916i | 1.60530 | + | 1.24049i | ||||
\(109\) | 18.6614i | 1.78744i | 0.448629 | + | 0.893718i | \(0.351912\pi\) | ||||
−0.448629 | + | 0.893718i | \(0.648088\pi\) | |||||||
\(110\) | 8.09867 | − | 11.5238i | 0.772178 | − | 1.09875i | ||||
\(111\) | −0.291803 | − | 6.86205i | −0.0276967 | − | 0.651317i | ||||
\(112\) | −5.66267 | − | 5.66267i | −0.535072 | − | 0.535072i | ||||
\(113\) | −6.99502 | − | 6.99502i | −0.658036 | − | 0.658036i | 0.296879 | − | 0.954915i | \(-0.404054\pi\) |
−0.954915 | + | 0.296879i | \(0.904054\pi\) | |||||||
\(114\) | −0.849977 | − | 19.9881i | −0.0796076 | − | 1.87206i | ||||
\(115\) | 0.488263 | − | 0.694759i | 0.0455307 | − | 0.0647866i | ||||
\(116\) | 23.0684i | 2.14185i | ||||||||
\(117\) | 7.69108 | + | 6.48338i | 0.711040 | + | 0.599388i | ||||
\(118\) | 21.7994 | − | 21.7994i | 2.00680 | − | 2.00680i | ||||
\(119\) | 8.82097 | 0.808617 | ||||||||
\(120\) | −19.1595 | + | 4.19013i | −1.74901 | + | 0.382505i | ||||
\(121\) | 4.44990 | 0.404536 | ||||||||
\(122\) | 13.5656 | − | 13.5656i | 1.22818 | − | 1.22818i | ||||
\(123\) | 4.41336 | − | 4.80538i | 0.397940 | − | 0.433287i | ||||
\(124\) | − | 4.05749i | − | 0.364373i | ||||||
\(125\) | −5.54003 | − | 9.71124i | −0.495515 | − | 0.868599i | ||||
\(126\) | −1.15445 | − | 13.5494i | −0.102846 | − | 1.20708i | ||||
\(127\) | 12.1010 | + | 12.1010i | 1.07379 | + | 1.07379i | 0.997051 | + | 0.0767411i | \(0.0244515\pi\) |
0.0767411 | + | 0.997051i | \(0.475548\pi\) | |||||||
\(128\) | 13.4876 | + | 13.4876i | 1.19215 | + | 1.19215i | ||||
\(129\) | 18.5493 | − | 0.788794i | 1.63317 | − | 0.0694494i | ||||
\(130\) | −18.1784 | + | 3.17304i | −1.59435 | + | 0.278294i | ||||
\(131\) | − | 4.42153i | − | 0.386311i | −0.981168 | − | 0.193155i | \(-0.938128\pi\) | ||
0.981168 | − | 0.193155i | \(-0.0618721\pi\) | |||||||
\(132\) | 13.2471 | + | 12.1664i | 1.15301 | + | 1.05895i | ||||
\(133\) | −6.11176 | + | 6.11176i | −0.529957 | + | 0.529957i | ||||
\(134\) | 13.9963 | 1.20909 | ||||||||
\(135\) | −10.2785 | − | 5.41781i | −0.884631 | − | 0.466291i | ||||
\(136\) | 24.2535 | 2.07972 | ||||||||
\(137\) | −14.4439 | + | 14.4439i | −1.23403 | + | 1.23403i | −0.271625 | + | 0.962403i | \(0.587561\pi\) |
−0.962403 | + | 0.271625i | \(0.912439\pi\) | |||||||
\(138\) | 1.19233 | + | 1.09506i | 0.101498 | + | 0.0932176i | ||||
\(139\) | 20.0382i | 1.69961i | 0.527094 | + | 0.849807i | \(0.323282\pi\) | ||||
−0.527094 | + | 0.849807i | \(0.676718\pi\) | |||||||
\(140\) | 13.6712 | + | 9.60783i | 1.15543 | + | 0.812009i | ||||
\(141\) | 6.98668 | − | 0.297103i | 0.588384 | − | 0.0250206i | ||||
\(142\) | 2.05638 | + | 2.05638i | 0.172567 | + | 0.172567i | ||||
\(143\) | 6.06806 | + | 6.06806i | 0.507437 | + | 0.507437i | ||||
\(144\) | −1.10742 | − | 12.9976i | −0.0922853 | − | 1.08313i | ||||
\(145\) | −2.18599 | − | 12.5236i | −0.181537 | − | 1.04003i | ||||
\(146\) | 13.4654i | 1.11440i | ||||||||
\(147\) | 4.22721 | − | 4.60269i | 0.348654 | − | 0.379624i | ||||
\(148\) | −11.3770 | + | 11.3770i | −0.935184 | + | 0.935184i | ||||
\(149\) | 9.91574 | 0.812329 | 0.406165 | − | 0.913800i | \(-0.366866\pi\) | ||||
0.406165 | + | 0.913800i | \(0.366866\pi\) | |||||||
\(150\) | 19.7293 | − | 8.06642i | 1.61089 | − | 0.658620i | ||||
\(151\) | 10.0111 | 0.814695 | 0.407347 | − | 0.913273i | \(-0.366454\pi\) | ||||
0.407347 | + | 0.913273i | \(0.366454\pi\) | |||||||
\(152\) | −16.8045 | + | 16.8045i | −1.36302 | + | 1.36302i | ||||
\(153\) | 10.9860 | + | 9.26088i | 0.888163 | + | 0.748698i | ||||
\(154\) | − | 11.6010i | − | 0.934834i | ||||||
\(155\) | 0.384493 | + | 2.20276i | 0.0308832 | + | 0.176930i | ||||
\(156\) | −1.00116 | − | 23.5432i | −0.0801567 | − | 1.88497i | ||||
\(157\) | −15.3890 | − | 15.3890i | −1.22818 | − | 1.22818i | −0.964652 | − | 0.263527i | \(-0.915114\pi\) |
−0.263527 | − | 0.964652i | \(-0.584886\pi\) | |||||||
\(158\) | −7.77104 | − | 7.77104i | −0.618231 | − | 0.618231i | ||||
\(159\) | 0.347119 | + | 8.16286i | 0.0275283 | + | 0.647357i | ||||
\(160\) | 1.05023 | + | 0.738083i | 0.0830283 | + | 0.0583506i | ||||
\(161\) | − | 0.699415i | − | 0.0551216i | ||||||
\(162\) | 12.7874 | − | 18.0870i | 1.00467 | − | 1.42105i | ||||
\(163\) | 15.0954 | − | 15.0954i | 1.18237 | − | 1.18237i | 0.203235 | − | 0.979130i | \(-0.434854\pi\) |
0.979130 | − | 0.203235i | \(-0.0651457\pi\) | |||||||
\(164\) | −15.2843 | −1.19350 | ||||||||
\(165\) | −8.34460 | − | 5.34969i | −0.649626 | − | 0.416473i | ||||
\(166\) | −14.0246 | −1.08852 | ||||||||
\(167\) | 4.70977 | − | 4.70977i | 0.364453 | − | 0.364453i | −0.500996 | − | 0.865449i | \(-0.667033\pi\) |
0.865449 | + | 0.500996i | \(0.167033\pi\) | |||||||
\(168\) | −10.9267 | + | 11.8973i | −0.843013 | + | 0.917894i | ||||
\(169\) | 1.75702i | 0.135155i | ||||||||
\(170\) | −25.9660 | + | 4.53238i | −1.99151 | + | 0.347618i | ||||
\(171\) | −14.0284 | + | 1.19525i | −1.07278 | + | 0.0914031i | ||||
\(172\) | −30.7540 | − | 30.7540i | −2.34497 | − | 2.34497i | ||||
\(173\) | 2.26329 | + | 2.26329i | 0.172074 | + | 0.172074i | 0.787890 | − | 0.615816i | \(-0.211173\pi\) |
−0.615816 | + | 0.787890i | \(0.711173\pi\) | |||||||
\(174\) | 24.2145 | − | 1.02970i | 1.83569 | − | 0.0780614i | ||||
\(175\) | −8.33238 | − | 3.92048i | −0.629869 | − | 0.296360i | ||||
\(176\) | − | 11.1285i | − | 0.838840i | ||||||
\(177\) | −15.9791 | − | 14.6756i | −1.20106 | − | 1.10308i | ||||
\(178\) | −28.6556 | + | 28.6556i | −2.14782 | + | 2.14782i | ||||
\(179\) | 1.55392 | 0.116145 | 0.0580725 | − | 0.998312i | \(-0.481505\pi\) | ||||
0.0580725 | + | 0.998312i | \(0.481505\pi\) | |||||||
\(180\) | 6.93961 | + | 26.3189i | 0.517248 | + | 1.96170i | ||||
\(181\) | −12.4886 | −0.928271 | −0.464135 | − | 0.885764i | \(-0.653635\pi\) | ||||
−0.464135 | + | 0.885764i | \(0.653635\pi\) | |||||||
\(182\) | −10.7472 | + | 10.7472i | −0.796638 | + | 0.796638i | ||||
\(183\) | −9.94371 | − | 9.13251i | −0.735060 | − | 0.675095i | ||||
\(184\) | − | 1.92306i | − | 0.141770i | ||||||
\(185\) | 5.09835 | − | 7.25455i | 0.374838 | − | 0.533365i | ||||
\(186\) | −4.25907 | + | 0.181113i | −0.312290 | + | 0.0132799i | ||||
\(187\) | 8.66764 | + | 8.66764i | 0.633841 | + | 0.633841i | ||||
\(188\) | −11.5836 | − | 11.5836i | −0.844822 | − | 0.844822i | ||||
\(189\) | −9.49221 | + | 1.21682i | −0.690456 | + | 0.0885103i | ||||
\(190\) | 14.8507 | − | 21.1313i | 1.07738 | − | 1.53303i | ||||
\(191\) | − | 6.16936i | − | 0.446399i | −0.974773 | − | 0.223200i | \(-0.928350\pi\) | ||
0.974773 | − | 0.223200i | \(-0.0716502\pi\) | |||||||
\(192\) | 8.53344 | − | 9.29143i | 0.615848 | − | 0.670551i | ||||
\(193\) | −13.8267 | + | 13.8267i | −0.995270 | + | 0.995270i | −0.999989 | − | 0.00471859i | \(-0.998498\pi\) |
0.00471859 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(194\) | −47.6199 | −3.41891 | ||||||||
\(195\) | 2.77450 | + | 12.6865i | 0.198686 | + | 0.908498i | ||||
\(196\) | −14.6396 | −1.04569 | ||||||||
\(197\) | 10.2230 | − | 10.2230i | 0.728359 | − | 0.728359i | −0.241934 | − | 0.970293i | \(-0.577782\pi\) |
0.970293 | + | 0.241934i | \(0.0777817\pi\) | |||||||
\(198\) | 12.1795 | − | 14.4483i | 0.865562 | − | 1.02680i | ||||
\(199\) | − | 3.18566i | − | 0.225825i | −0.993605 | − | 0.112913i | \(-0.963982\pi\) | ||
0.993605 | − | 0.112913i | \(-0.0360180\pi\) | |||||||
\(200\) | −22.9101 | − | 10.7795i | −1.61999 | − | 0.762224i | ||||
\(201\) | −0.418476 | − | 9.84089i | −0.0295170 | − | 0.694123i | ||||
\(202\) | 32.3555 | + | 32.3555i | 2.27653 | + | 2.27653i | ||||
\(203\) | −7.40406 | − | 7.40406i | −0.519663 | − | 0.519663i | ||||
\(204\) | −1.43006 | − | 33.6292i | −0.100124 | − | 2.35452i | ||||
\(205\) | 8.29767 | − | 1.44836i | 0.579535 | − | 0.101158i | ||||
\(206\) | 7.74794i | 0.539825i | ||||||||
\(207\) | 0.734295 | − | 0.871077i | 0.0510370 | − | 0.0605440i | ||||
\(208\) | −10.3095 | + | 10.3095i | −0.714834 | + | 0.714834i | ||||
\(209\) | −12.0110 | −0.830821 | ||||||||
\(210\) | 9.47492 | − | 14.7792i | 0.653831 | − | 1.01986i | ||||
\(211\) | 9.18742 | 0.632488 | 0.316244 | − | 0.948678i | \(-0.397578\pi\) | ||||
0.316244 | + | 0.948678i | \(0.397578\pi\) | |||||||
\(212\) | 13.5337 | − | 13.5337i | 0.929497 | − | 0.929497i | ||||
\(213\) | 1.38437 | − | 1.50734i | 0.0948555 | − | 0.103281i | ||||
\(214\) | − | 6.48673i | − | 0.443424i | ||||||
\(215\) | 19.6103 | + | 13.7817i | 1.33741 | + | 0.939904i | ||||
\(216\) | −26.0991 | + | 3.34567i | −1.77582 | + | 0.227644i | ||||
\(217\) | 1.30230 | + | 1.30230i | 0.0884056 | + | 0.0884056i | ||||
\(218\) | −32.4769 | − | 32.4769i | −2.19962 | − | 2.19962i | ||||
\(219\) | 9.46763 | − | 0.402603i | 0.639763 | − | 0.0272054i | ||||
\(220\) | 3.99272 | + | 22.8744i | 0.269189 | + | 1.54219i | ||||
\(221\) | − | 16.0595i | − | 1.08028i | ||||||
\(222\) | 12.4501 | + | 11.4344i | 0.835593 | + | 0.767426i | ||||
\(223\) | 18.3841 | − | 18.3841i | 1.23109 | − | 1.23109i | 0.267545 | − | 0.963545i | \(-0.413788\pi\) |
0.963545 | − | 0.267545i | \(-0.0862125\pi\) | |||||||
\(224\) | 1.05727 | 0.0706419 | ||||||||
\(225\) | −6.26145 | − | 13.6306i | −0.417430 | − | 0.908709i | ||||
\(226\) | 24.3473 | 1.61956 | ||||||||
\(227\) | 4.46148 | − | 4.46148i | 0.296119 | − | 0.296119i | −0.543373 | − | 0.839492i | \(-0.682853\pi\) |
0.839492 | + | 0.543373i | \(0.182853\pi\) | |||||||
\(228\) | 24.2914 | + | 22.3097i | 1.60874 | + | 1.47750i | ||||
\(229\) | − | 7.03878i | − | 0.465136i | −0.972580 | − | 0.232568i | \(-0.925287\pi\) | ||
0.972580 | − | 0.232568i | \(-0.0747128\pi\) | |||||||
\(230\) | 0.359372 | + | 2.05885i | 0.0236963 | + | 0.135756i | ||||
\(231\) | −8.15675 | + | 0.346859i | −0.536675 | + | 0.0228216i | ||||
\(232\) | −20.3577 | − | 20.3577i | −1.33655 | − | 1.33655i | ||||
\(233\) | 6.31425 | + | 6.31425i | 0.413660 | + | 0.413660i | 0.883012 | − | 0.469351i | \(-0.155512\pi\) |
−0.469351 | + | 0.883012i | \(0.655512\pi\) | |||||||
\(234\) | −24.6682 | + | 2.10179i | −1.61261 | + | 0.137398i | ||||
\(235\) | 7.38630 | + | 5.19094i | 0.481829 | + | 0.338619i | ||||
\(236\) | 50.8242i | 3.30837i | ||||||||
\(237\) | −5.23154 | + | 5.69623i | −0.339825 | + | 0.370010i | ||||
\(238\) | −15.3514 | + | 15.3514i | −0.995083 | + | 0.995083i | ||||
\(239\) | −6.05585 | −0.391720 | −0.195860 | − | 0.980632i | \(-0.562750\pi\) | ||||
−0.195860 | + | 0.980632i | \(0.562750\pi\) | |||||||
\(240\) | 9.08900 | − | 14.1773i | 0.586692 | − | 0.915139i | ||||
\(241\) | −19.4218 | −1.25107 | −0.625533 | − | 0.780198i | \(-0.715118\pi\) | ||||
−0.625533 | + | 0.780198i | \(0.715118\pi\) | |||||||
\(242\) | −7.74428 | + | 7.74428i | −0.497821 | + | 0.497821i | ||||
\(243\) | −13.0994 | − | 8.45012i | −0.840330 | − | 0.542076i | ||||
\(244\) | 31.6276i | 2.02475i | ||||||||
\(245\) | 7.94768 | − | 1.38727i | 0.507759 | − | 0.0886294i | ||||
\(246\) | 0.682243 | + | 16.0436i | 0.0434982 | + | 1.02291i | ||||
\(247\) | 11.1271 | + | 11.1271i | 0.708001 | + | 0.708001i | ||||
\(248\) | 3.58070 | + | 3.58070i | 0.227375 | + | 0.227375i | ||||
\(249\) | 0.419324 | + | 9.86084i | 0.0265736 | + | 0.624905i | ||||
\(250\) | 26.5422 | + | 7.25928i | 1.67868 | + | 0.459117i | ||||
\(251\) | 0.334433i | 0.0211092i | 0.999944 | + | 0.0105546i | \(0.00335970\pi\) | ||||
−0.999944 | + | 0.0105546i | \(0.996640\pi\) | |||||||
\(252\) | 17.1407 | + | 14.4491i | 1.07976 | + | 0.910211i | ||||
\(253\) | 0.687257 | − | 0.687257i | 0.0432075 | − | 0.0432075i | ||||
\(254\) | −42.1195 | −2.64281 | ||||||||
\(255\) | 3.96311 | + | 18.1214i | 0.248180 | + | 1.13481i | ||||
\(256\) | −32.3787 | −2.02367 | ||||||||
\(257\) | 21.6611 | − | 21.6611i | 1.35118 | − | 1.35118i | 0.466838 | − | 0.884343i | \(-0.345393\pi\) |
0.884343 | − | 0.466838i | \(-0.154607\pi\) | |||||||
\(258\) | −30.9091 | + | 33.6546i | −1.92432 | + | 2.09525i | ||||
\(259\) | − | 7.30315i | − | 0.453796i | ||||||
\(260\) | 17.4921 | − | 24.8898i | 1.08481 | − | 1.54360i | ||||
\(261\) | −1.44798 | − | 16.9946i | −0.0896278 | − | 1.05194i | ||||
\(262\) | 7.69491 | + | 7.69491i | 0.475393 | + | 0.475393i | ||||
\(263\) | 9.30589 | + | 9.30589i | 0.573826 | + | 0.573826i | 0.933195 | − | 0.359370i | \(-0.117008\pi\) |
−0.359370 | + | 0.933195i | \(0.617008\pi\) | |||||||
\(264\) | −22.4272 | + | 0.953699i | −1.38030 | + | 0.0586961i | ||||
\(265\) | −6.06481 | + | 8.62975i | −0.372558 | + | 0.530121i | ||||
\(266\) | − | 21.2729i | − | 1.30433i | ||||||
\(267\) | 21.0047 | + | 19.2912i | 1.28547 | + | 1.18060i | ||||
\(268\) | −16.3158 | + | 16.3158i | −0.996646 | + | 0.996646i | ||||
\(269\) | 2.97259 | 0.181242 | 0.0906210 | − | 0.995885i | \(-0.471115\pi\) | ||||
0.0906210 | + | 0.995885i | \(0.471115\pi\) | |||||||
\(270\) | 27.3167 | − | 8.45918i | 1.66244 | − | 0.514809i | ||||
\(271\) | 4.29904 | 0.261148 | 0.130574 | − | 0.991439i | \(-0.458318\pi\) | ||||
0.130574 | + | 0.991439i | \(0.458318\pi\) | |||||||
\(272\) | −14.7261 | + | 14.7261i | −0.892902 | + | 0.892902i | ||||
\(273\) | 7.87780 | + | 7.23513i | 0.476786 | + | 0.437890i | ||||
\(274\) | − | 50.2744i | − | 3.03719i | ||||||
\(275\) | −4.33521 | − | 12.0399i | −0.261423 | − | 0.726032i | ||||
\(276\) | −2.66646 | + | 0.113389i | −0.160502 | + | 0.00682522i | ||||
\(277\) | −7.69471 | − | 7.69471i | −0.462330 | − | 0.462330i | 0.437088 | − | 0.899419i | \(-0.356010\pi\) |
−0.899419 | + | 0.437088i | \(0.856010\pi\) | |||||||
\(278\) | −34.8730 | − | 34.8730i | −2.09154 | − | 2.09154i | ||||
\(279\) | 0.254684 | + | 2.98917i | 0.0152476 | + | 0.178957i | ||||
\(280\) | −20.5435 | + | 3.58588i | −1.22771 | + | 0.214297i | ||||
\(281\) | 14.7446i | 0.879591i | 0.898098 | + | 0.439796i | \(0.144949\pi\) | ||||
−0.898098 | + | 0.439796i | \(0.855051\pi\) | |||||||
\(282\) | −11.6421 | + | 12.6762i | −0.693274 | + | 0.754855i | ||||
\(283\) | −10.3694 | + | 10.3694i | −0.616398 | + | 0.616398i | −0.944606 | − | 0.328208i | \(-0.893555\pi\) |
0.328208 | + | 0.944606i | \(0.393555\pi\) | |||||||
\(284\) | −4.79433 | −0.284491 | ||||||||
\(285\) | −15.3016 | − | 9.80982i | −0.906391 | − | 0.581084i | ||||
\(286\) | −21.1208 | −1.24890 | ||||||||
\(287\) | 4.90567 | − | 4.90567i | 0.289572 | − | 0.289572i | ||||
\(288\) | 1.31676 | + | 1.11000i | 0.0775911 | + | 0.0654073i | ||||
\(289\) | − | 5.93949i | − | 0.349382i | ||||||
\(290\) | 25.5995 | + | 17.9908i | 1.50325 | + | 1.05645i | ||||
\(291\) | 1.42379 | + | 33.4819i | 0.0834641 | + | 1.96274i | ||||
\(292\) | −15.6969 | − | 15.6969i | −0.918594 | − | 0.918594i | ||||
\(293\) | −4.21552 | − | 4.21552i | −0.246273 | − | 0.246273i | 0.573166 | − | 0.819439i | \(-0.305715\pi\) |
−0.819439 | + | 0.573166i | \(0.805715\pi\) | |||||||
\(294\) | 0.653466 | + | 15.3669i | 0.0381109 | + | 0.896218i | ||||
\(295\) | −4.81617 | − | 27.5919i | −0.280408 | − | 1.60646i | ||||
\(296\) | − | 20.0802i | − | 1.16714i | ||||||
\(297\) | −10.5229 | − | 8.13154i | −0.610599 | − | 0.471840i | ||||
\(298\) | −17.2566 | + | 17.2566i | −0.999651 | + | 0.999651i | ||||
\(299\) | −1.27336 | −0.0736402 | ||||||||
\(300\) | −13.5957 | + | 32.4021i | −0.784946 | + | 1.87074i | ||||
\(301\) | 19.7417 | 1.13789 | ||||||||
\(302\) | −17.4227 | + | 17.4227i | −1.00256 | + | 1.00256i | ||||
\(303\) | 21.7820 | − | 23.7168i | 1.25134 | − | 1.36250i | ||||
\(304\) | − | 20.4065i | − | 1.17039i | ||||||
\(305\) | −2.99707 | − | 17.1703i | −0.171612 | − | 0.983166i | ||||
\(306\) | −35.2362 | + | 3.00221i | −2.01432 | + | 0.171625i | ||||
\(307\) | 7.61622 | + | 7.61622i | 0.434681 | + | 0.434681i | 0.890217 | − | 0.455536i | \(-0.150553\pi\) |
−0.455536 | + | 0.890217i | \(0.650553\pi\) | |||||||
\(308\) | 13.5236 | + | 13.5236i | 0.770576 | + | 0.770576i | ||||
\(309\) | 5.44764 | − | 0.231656i | 0.309905 | − | 0.0131785i | ||||
\(310\) | −4.50267 | − | 3.16439i | −0.255735 | − | 0.179725i | ||||
\(311\) | 7.65741i | 0.434212i | 0.976148 | + | 0.217106i | \(0.0696618\pi\) | ||||
−0.976148 | + | 0.217106i | \(0.930338\pi\) | |||||||
\(312\) | 21.6602 | + | 19.8932i | 1.22627 | + | 1.12623i | ||||
\(313\) | −2.60386 | + | 2.60386i | −0.147179 | + | 0.147179i | −0.776856 | − | 0.629678i | \(-0.783187\pi\) |
0.629678 | + | 0.776856i | \(0.283187\pi\) | |||||||
\(314\) | 53.5640 | 3.02279 | ||||||||
\(315\) | −10.6747 | − | 6.22001i | −0.601451 | − | 0.350458i | ||||
\(316\) | 18.1178 | 1.01921 | ||||||||
\(317\) | −8.97912 | + | 8.97912i | −0.504318 | + | 0.504318i | −0.912777 | − | 0.408459i | \(-0.866066\pi\) |
0.408459 | + | 0.912777i | \(0.366066\pi\) | |||||||
\(318\) | −14.8101 | − | 13.6019i | −0.830512 | − | 0.762759i | ||||
\(319\) | − | 14.5507i | − | 0.814684i | ||||||
\(320\) | 16.0439 | − | 2.80047i | 0.896883 | − | 0.156551i | ||||
\(321\) | −4.56087 | + | 0.193947i | −0.254563 | + | 0.0108251i | ||||
\(322\) | 1.21721 | + | 1.21721i | 0.0678325 | + | 0.0678325i | ||||
\(323\) | 15.8940 | + | 15.8940i | 0.884366 | + | 0.884366i | ||||
\(324\) | 6.17789 | + | 35.9910i | 0.343216 | + | 1.99950i | ||||
\(325\) | −7.13765 | + | 15.1700i | −0.395926 | + | 0.841479i | ||||
\(326\) | 52.5420i | 2.91003i | ||||||||
\(327\) | −21.8638 | + | 23.8058i | −1.20907 | + | 1.31647i | ||||
\(328\) | 13.4883 | − | 13.4883i | 0.744766 | − | 0.744766i | ||||
\(329\) | 7.43579 | 0.409948 | ||||||||
\(330\) | 23.8326 | − | 5.21213i | 1.31194 | − | 0.286918i | ||||
\(331\) | −1.32694 | −0.0729354 | −0.0364677 | − | 0.999335i | \(-0.511611\pi\) | ||||
−0.0364677 | + | 0.999335i | \(0.511611\pi\) | |||||||
\(332\) | 16.3489 | − | 16.3489i | 0.897260 | − | 0.897260i | ||||
\(333\) | 7.66737 | − | 9.09562i | 0.420169 | − | 0.498437i | ||||
\(334\) | 16.3931i | 0.896990i | ||||||||
\(335\) | 7.31155 | − | 10.4038i | 0.399473 | − | 0.568418i | ||||
\(336\) | −0.589305 | − | 13.8581i | −0.0321492 | − | 0.756022i | ||||
\(337\) | −12.2571 | − | 12.2571i | −0.667686 | − | 0.667686i | 0.289494 | − | 0.957180i | \(-0.406513\pi\) |
−0.957180 | + | 0.289494i | \(0.906513\pi\) | |||||||
\(338\) | −3.05779 | − | 3.05779i | −0.166322 | − | 0.166322i | ||||
\(339\) | −0.727961 | − | 17.1188i | −0.0395374 | − | 0.929764i | ||||
\(340\) | 24.9857 | − | 35.5528i | 1.35504 | − | 1.92812i | ||||
\(341\) | 2.55932i | 0.138595i | ||||||||
\(342\) | 22.3338 | − | 26.4941i | 1.20768 | − | 1.43264i | ||||
\(343\) | 13.8148 | − | 13.8148i | 0.745930 | − | 0.745930i | ||||
\(344\) | 54.2803 | 2.92660 | ||||||||
\(345\) | 1.43685 | − | 0.314235i | 0.0773572 | − | 0.0169178i | ||||
\(346\) | −7.87772 | −0.423509 | ||||||||
\(347\) | 16.8052 | − | 16.8052i | 0.902153 | − | 0.902153i | −0.0934693 | − | 0.995622i | \(-0.529796\pi\) |
0.995622 | + | 0.0934693i | \(0.0297957\pi\) | |||||||
\(348\) | −27.0270 | + | 29.4277i | −1.44880 | + | 1.57749i | ||||
\(349\) | − | 18.5688i | − | 0.993965i | −0.867761 | − | 0.496983i | \(-0.834441\pi\) | ||
0.867761 | − | 0.496983i | \(-0.165559\pi\) | |||||||
\(350\) | 21.3240 | − | 7.67815i | 1.13982 | − | 0.410415i | ||||
\(351\) | 2.21534 | + | 17.2816i | 0.118246 | + | 0.922422i | ||||
\(352\) | 1.03889 | + | 1.03889i | 0.0553732 | + | 0.0553732i | ||||
\(353\) | −19.3920 | − | 19.3920i | −1.03213 | − | 1.03213i | −0.999466 | − | 0.0326657i | \(-0.989600\pi\) |
−0.0326657 | − | 0.999466i | \(-0.510400\pi\) | |||||||
\(354\) | 53.3492 | − | 2.26863i | 2.83548 | − | 0.120576i | ||||
\(355\) | 2.60279 | − | 0.454317i | 0.138142 | − | 0.0241127i | ||||
\(356\) | − | 66.8089i | − | 3.54087i | ||||||
\(357\) | 11.2527 | + | 10.3347i | 0.595555 | + | 0.546970i | ||||
\(358\) | −2.70432 | + | 2.70432i | −0.142928 | + | 0.142928i | ||||
\(359\) | −2.35818 | −0.124460 | −0.0622300 | − | 0.998062i | \(-0.519821\pi\) | ||||
−0.0622300 | + | 0.998062i | \(0.519821\pi\) | |||||||
\(360\) | −29.3504 | − | 17.1021i | −1.54690 | − | 0.901359i | ||||
\(361\) | −3.02486 | −0.159203 | ||||||||
\(362\) | 21.7343 | − | 21.7343i | 1.14233 | − | 1.14233i | ||||
\(363\) | 5.67661 | + | 5.21352i | 0.297945 | + | 0.273639i | ||||
\(364\) | − | 25.0566i | − | 1.31332i | ||||||
\(365\) | 10.0092 | + | 7.03423i | 0.523903 | + | 0.368188i | ||||
\(366\) | 33.1989 | − | 1.41176i | 1.73533 | − | 0.0737936i | ||||
\(367\) | −9.30245 | − | 9.30245i | −0.485584 | − | 0.485584i | 0.421326 | − | 0.906909i | \(-0.361565\pi\) |
−0.906909 | + | 0.421326i | \(0.861565\pi\) | |||||||
\(368\) | 1.16763 | + | 1.16763i | 0.0608671 | + | 0.0608671i | ||||
\(369\) | 11.2600 | − | 0.959381i | 0.586173 | − | 0.0499434i | ||||
\(370\) | 3.75250 | + | 21.4981i | 0.195083 | + | 1.11763i | ||||
\(371\) | 8.68757i | 0.451036i | ||||||||
\(372\) | 4.75377 | − | 5.17603i | 0.246471 | − | 0.268364i | ||||
\(373\) | −5.91864 | + | 5.91864i | −0.306455 | + | 0.306455i | −0.843533 | − | 0.537077i | \(-0.819528\pi\) |
0.537077 | + | 0.843533i | \(0.319528\pi\) | |||||||
\(374\) | −30.1691 | −1.56001 | ||||||||
\(375\) | 4.31047 | − | 18.8791i | 0.222592 | − | 0.974912i | ||||
\(376\) | 20.4449 | 1.05437 | ||||||||
\(377\) | −13.4799 | + | 13.4799i | −0.694249 | + | 0.694249i | ||||
\(378\) | 14.4019 | − | 18.6372i | 0.740754 | − | 0.958595i | ||||
\(379\) | − | 18.1658i | − | 0.933116i | −0.884491 | − | 0.466558i | \(-0.845494\pi\) | ||
0.884491 | − | 0.466558i | \(-0.154506\pi\) | |||||||
\(380\) | 7.32153 | + | 41.9451i | 0.375586 | + | 2.15174i | ||||
\(381\) | 1.25934 | + | 29.6146i | 0.0645177 | + | 1.51720i | ||||
\(382\) | 10.7367 | + | 10.7367i | 0.549338 | + | 0.549338i | ||||
\(383\) | 19.5567 | + | 19.5567i | 0.999299 | + | 0.999299i | 1.00000 | 0.000700330i | \(-0.000222922\pi\) | |
−0.000700330 | 1.00000i | \(0.500223\pi\) | ||||||||
\(384\) | 1.40364 | + | 33.0079i | 0.0716290 | + | 1.68443i | ||||
\(385\) | −8.62329 | − | 6.06027i | −0.439484 | − | 0.308860i | ||||
\(386\) | − | 48.1261i | − | 2.44956i | ||||||
\(387\) | 24.5870 | + | 20.7262i | 1.24983 | + | 1.05357i | ||||
\(388\) | 55.5116 | − | 55.5116i | 2.81818 | − | 2.81818i | ||||
\(389\) | −31.6425 | −1.60434 | −0.802170 | − | 0.597095i | \(-0.796321\pi\) | ||||
−0.802170 | + | 0.597095i | \(0.796321\pi\) | |||||||
\(390\) | −26.9072 | − | 17.2501i | −1.36250 | − | 0.873493i | ||||
\(391\) | −1.81887 | −0.0919843 | ||||||||
\(392\) | 12.9194 | − | 12.9194i | 0.652526 | − | 0.652526i | ||||
\(393\) | 5.18028 | − | 5.64042i | 0.261311 | − | 0.284522i | ||||
\(394\) | 35.5828i | 1.79263i | ||||||||
\(395\) | −9.83594 | + | 1.71687i | −0.494900 | + | 0.0863849i | ||||
\(396\) | 2.64474 | + | 31.0407i | 0.132903 | + | 1.55985i | ||||
\(397\) | −18.4634 | − | 18.4634i | −0.926651 | − | 0.926651i | 0.0708365 | − | 0.997488i | \(-0.477433\pi\) |
−0.997488 | + | 0.0708365i | \(0.977433\pi\) | |||||||
\(398\) | 5.54409 | + | 5.54409i | 0.277900 | + | 0.277900i | ||||
\(399\) | −14.9572 | + | 0.636041i | −0.748795 | + | 0.0318419i | ||||
\(400\) | 20.4555 | − | 7.36542i | 1.02277 | − | 0.368271i | ||||
\(401\) | − | 1.22570i | − | 0.0612083i | −0.999532 | − | 0.0306041i | \(-0.990257\pi\) | ||
0.999532 | − | 0.0306041i | \(-0.00974312\pi\) | |||||||
\(402\) | 17.8547 | + | 16.3981i | 0.890510 | + | 0.817863i | ||||
\(403\) | 2.37097 | − | 2.37097i | 0.118106 | − | 0.118106i | ||||
\(404\) | −75.4352 | −3.75304 | ||||||||
\(405\) | −6.76446 | − | 18.9537i | −0.336129 | − | 0.941816i | ||||
\(406\) | 25.7710 | 1.27899 | ||||||||
\(407\) | 7.17621 | − | 7.17621i | 0.355711 | − | 0.355711i | ||||
\(408\) | 30.9396 | + | 28.4155i | 1.53174 | + | 1.40678i | ||||
\(409\) | 33.9950i | 1.68094i | 0.541854 | + | 0.840472i | \(0.317722\pi\) | ||||
−0.541854 | + | 0.840472i | \(0.682278\pi\) | |||||||
\(410\) | −11.9201 | + | 16.9613i | −0.588689 | + | 0.837659i | ||||
\(411\) | −35.3483 | + | 1.50316i | −1.74360 | + | 0.0741453i | ||||
\(412\) | −9.03196 | − | 9.03196i | −0.444973 | − | 0.444973i | ||||
\(413\) | −16.3126 | − | 16.3126i | −0.802690 | − | 0.802690i | ||||
\(414\) | 0.238045 | + | 2.79387i | 0.0116993 | + | 0.137311i | ||||
\(415\) | −7.32637 | + | 10.4248i | −0.359637 | + | 0.511736i | ||||
\(416\) | − | 1.92487i | − | 0.0943748i | ||||||
\(417\) | −23.4768 | + | 25.5621i | −1.14966 | + | 1.25178i | ||||
\(418\) | 20.9032 | − | 20.9032i | 1.02241 | − | 1.02241i | ||||
\(419\) | −25.8945 | −1.26503 | −0.632514 | − | 0.774549i | \(-0.717977\pi\) | ||||
−0.632514 | + | 0.774549i | \(0.717977\pi\) | |||||||
\(420\) | 6.18339 | + | 28.2737i | 0.301718 | + | 1.37961i | ||||
\(421\) | −11.4846 | −0.559724 | −0.279862 | − | 0.960040i | \(-0.590289\pi\) | ||||
−0.279862 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(422\) | −15.9891 | + | 15.9891i | −0.778338 | + | 0.778338i | ||||
\(423\) | 9.26080 | + | 7.80662i | 0.450276 | + | 0.379571i | ||||
\(424\) | 23.8867i | 1.16004i | ||||||||
\(425\) | −10.1955 | + | 21.6689i | −0.494552 | + | 1.05109i | ||||
\(426\) | 0.214004 | + | 5.03252i | 0.0103685 | + | 0.243827i | ||||
\(427\) | −10.1512 | − | 10.1512i | −0.491252 | − | 0.491252i | ||||
\(428\) | 7.56174 | + | 7.56174i | 0.365510 | + | 0.365510i | ||||
\(429\) | 0.631494 | + | 14.8502i | 0.0304888 | + | 0.716976i | ||||
\(430\) | −58.1130 | + | 10.1436i | −2.80246 | + | 0.489169i | ||||
\(431\) | − | 25.7652i | − | 1.24107i | −0.784180 | − | 0.620533i | \(-0.786916\pi\) | ||
0.784180 | − | 0.620533i | \(-0.213084\pi\) | |||||||
\(432\) | 13.8153 | − | 17.8781i | 0.664689 | − | 0.860161i | ||||
\(433\) | 2.29857 | − | 2.29857i | 0.110462 | − | 0.110462i | −0.649715 | − | 0.760178i | \(-0.725112\pi\) |
0.760178 | + | 0.649715i | \(0.225112\pi\) | |||||||
\(434\) | −4.53284 | −0.217584 | ||||||||
\(435\) | 11.8841 | − | 18.5371i | 0.569797 | − | 0.888786i | ||||
\(436\) | 75.7183 | 3.62625 | ||||||||
\(437\) | 1.26024 | − | 1.26024i | 0.0602852 | − | 0.0602852i | ||||
\(438\) | −15.7761 | + | 17.1774i | −0.753812 | + | 0.820770i | ||||
\(439\) | − | 4.69778i | − | 0.224213i | −0.993696 | − | 0.112106i | \(-0.964240\pi\) | ||
0.993696 | − | 0.112106i | \(-0.0357597\pi\) | |||||||
\(440\) | −23.7100 | − | 16.6629i | −1.13033 | − | 0.794373i | ||||
\(441\) | 10.7851 | − | 0.918915i | 0.513575 | − | 0.0437578i | ||||
\(442\) | 27.9488 | + | 27.9488i | 1.32939 | + | 1.32939i | ||||
\(443\) | −12.8335 | − | 12.8335i | −0.609737 | − | 0.609737i | 0.333140 | − | 0.942877i | \(-0.391892\pi\) |
−0.942877 | + | 0.333140i | \(0.891892\pi\) | |||||||
\(444\) | −27.8427 | + | 1.18399i | −1.32136 | + | 0.0561895i | ||||
\(445\) | 6.33090 | + | 36.2698i | 0.300114 | + | 1.71935i | ||||
\(446\) | 63.9887i | 3.02995i | ||||||||
\(447\) | 12.6492 | + | 11.6173i | 0.598289 | + | 0.549481i | ||||
\(448\) | 9.48533 | − | 9.48533i | 0.448140 | − | 0.448140i | ||||
\(449\) | 38.3820 | 1.81136 | 0.905679 | − | 0.423963i | \(-0.139361\pi\) | ||||
0.905679 | + | 0.423963i | \(0.139361\pi\) | |||||||
\(450\) | 34.6188 | + | 12.8248i | 1.63194 | + | 0.604567i | ||||
\(451\) | 9.64079 | 0.453967 | ||||||||
\(452\) | −28.3822 | + | 28.3822i | −1.33499 | + | 1.33499i | ||||
\(453\) | 12.7709 | + | 11.7291i | 0.600031 | + | 0.551081i | ||||
\(454\) | 15.5289i | 0.728806i | ||||||||
\(455\) | 2.37440 | + | 13.6030i | 0.111314 | + | 0.637716i | ||||
\(456\) | −41.1252 | + | 1.74881i | −1.92586 | + | 0.0818957i | ||||
\(457\) | 7.32388 | + | 7.32388i | 0.342597 | + | 0.342597i | 0.857343 | − | 0.514746i | \(-0.172114\pi\) |
−0.514746 | + | 0.857343i | \(0.672114\pi\) | |||||||
\(458\) | 12.2498 | + | 12.2498i | 0.572395 | + | 0.572395i | ||||
\(459\) | 3.16441 | + | 24.6851i | 0.147702 | + | 1.15220i | ||||
\(460\) | −2.81898 | − | 1.98112i | −0.131435 | − | 0.0923701i | ||||
\(461\) | − | 29.3813i | − | 1.36842i | −0.729284 | − | 0.684212i | \(-0.760147\pi\) | ||
0.729284 | − | 0.684212i | \(-0.239853\pi\) | |||||||
\(462\) | 13.5918 | − | 14.7991i | 0.632346 | − | 0.688515i | ||||
\(463\) | −7.50791 | + | 7.50791i | −0.348922 | + | 0.348922i | −0.859708 | − | 0.510786i | \(-0.829354\pi\) |
0.510786 | + | 0.859708i | \(0.329354\pi\) | |||||||
\(464\) | 24.7213 | 1.14766 | ||||||||
\(465\) | −2.09028 | + | 3.26048i | −0.0969344 | + | 0.151201i | ||||
\(466\) | −21.9777 | −1.01810 | ||||||||
\(467\) | −22.5049 | + | 22.5049i | −1.04140 | + | 1.04140i | −0.0422999 | + | 0.999105i | \(0.513468\pi\) |
−0.999105 | + | 0.0422999i | \(0.986532\pi\) | |||||||
\(468\) | 26.3062 | − | 31.2064i | 1.21601 | − | 1.44252i | ||||
\(469\) | − | 10.4735i | − | 0.483620i | ||||||
\(470\) | −21.8885 | + | 3.82064i | −1.00964 | + | 0.176233i | ||||
\(471\) | −1.60151 | − | 37.6613i | −0.0737939 | − | 1.73534i | ||||
\(472\) | −44.8519 | − | 44.8519i | −2.06448 | − | 2.06448i | ||||
\(473\) | 19.3985 | + | 19.3985i | 0.891944 | + | 0.891944i | ||||
\(474\) | −0.808721 | − | 19.0179i | −0.0371458 | − | 0.873521i | ||||
\(475\) | −7.94955 | − | 22.0777i | −0.364750 | − | 1.01300i | ||||
\(476\) | − | 35.7910i | − | 1.64048i | ||||||
\(477\) | −9.12083 | + | 10.8198i | −0.417614 | + | 0.495406i | ||||
\(478\) | 10.5392 | − | 10.5392i | 0.482050 | − | 0.482050i | ||||
\(479\) | −14.3792 | −0.657004 | −0.328502 | − | 0.944503i | \(-0.606544\pi\) | ||||
−0.328502 | + | 0.944503i | \(0.606544\pi\) | |||||||
\(480\) | 0.475014 | + | 2.17201i | 0.0216813 | + | 0.0991383i | ||||
\(481\) | −13.2962 | −0.606253 | ||||||||
\(482\) | 33.8002 | − | 33.8002i | 1.53956 | − | 1.53956i | ||||
\(483\) | 0.819437 | − | 0.892224i | 0.0372857 | − | 0.0405976i | ||||
\(484\) | − | 18.0554i | − | 0.820699i | ||||||
\(485\) | −24.8763 | + | 35.3970i | −1.12957 | + | 1.60729i | ||||
\(486\) | 37.5033 | − | 8.09134i | 1.70119 | − | 0.367031i | ||||
\(487\) | −9.90705 | − | 9.90705i | −0.448931 | − | 0.448931i | 0.446068 | − | 0.894999i | \(-0.352824\pi\) |
−0.894999 | + | 0.446068i | \(0.852824\pi\) | |||||||
\(488\) | −27.9111 | − | 27.9111i | −1.26348 | − | 1.26348i | ||||
\(489\) | 36.9427 | − | 1.57096i | 1.67061 | − | 0.0710412i | ||||
\(490\) | −11.4173 | + | 16.2459i | −0.515780 | + | 0.733914i | ||||
\(491\) | 16.4515i | 0.742445i | 0.928544 | + | 0.371223i | \(0.121061\pi\) | ||||
−0.928544 | + | 0.371223i | \(0.878939\pi\) | |||||||
\(492\) | −19.4978 | − | 17.9072i | −0.879027 | − | 0.807317i | ||||
\(493\) | −19.2547 | + | 19.2547i | −0.867189 | + | 0.867189i | ||||
\(494\) | −38.7296 | −1.74253 | ||||||||
\(495\) | −4.37726 | − | 16.6010i | −0.196743 | − | 0.746161i | ||||
\(496\) | −4.34822 | −0.195241 | ||||||||
\(497\) | 1.53880 | − | 1.53880i | 0.0690244 | − | 0.0690244i | ||||
\(498\) | −17.8909 | − | 16.4313i | −0.801708 | − | 0.736305i | ||||
\(499\) | 14.2093i | 0.636096i | 0.948075 | + | 0.318048i | \(0.103027\pi\) | ||||
−0.948075 | + | 0.318048i | \(0.896973\pi\) | |||||||
\(500\) | −39.4032 | + | 22.4786i | −1.76216 | + | 1.00527i | ||||
\(501\) | 11.5261 | − | 0.490139i | 0.514949 | − | 0.0218978i | ||||
\(502\) | −0.582023 | − | 0.582023i | −0.0259770 | − | 0.0259770i | ||||
\(503\) | 3.98638 | + | 3.98638i | 0.177744 | + | 0.177744i | 0.790372 | − | 0.612628i | \(-0.209887\pi\) |
−0.612628 | + | 0.790372i | \(0.709887\pi\) | |||||||
\(504\) | −27.8778 | + | 2.37525i | −1.24178 | + | 0.105802i | ||||
\(505\) | 40.9529 | − | 7.14834i | 1.82238 | − | 0.318097i | ||||
\(506\) | 2.39211i | 0.106342i | ||||||||
\(507\) | −2.05853 | + | 2.24138i | −0.0914226 | + | 0.0995433i | ||||
\(508\) | 49.0997 | − | 49.0997i | 2.17845 | − | 2.17845i | ||||
\(509\) | −3.81193 | −0.168961 | −0.0844803 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844803 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(510\) | −38.4344 | − | 24.6401i | −1.70190 | − | 1.09108i | ||||
\(511\) | 10.0762 | 0.445746 | ||||||||
\(512\) | 29.3743 | − | 29.3743i | 1.29817 | − | 1.29817i | ||||
\(513\) | −19.2960 | − | 14.9110i | −0.851938 | − | 0.658335i | ||||
\(514\) | 75.3948i | 3.32552i | ||||||||
\(515\) | 5.75923 | + | 4.04747i | 0.253782 | + | 0.178353i | ||||
\(516\) | −3.20052 | − | 75.2635i | −0.140895 | − | 3.31329i | ||||
\(517\) | 7.30653 | + | 7.30653i | 0.321341 | + | 0.321341i | ||||
\(518\) | 12.7099 | + | 12.7099i | 0.558440 | + | 0.558440i | ||||
\(519\) | 0.235537 | + | 5.53889i | 0.0103389 | + | 0.243130i | ||||
\(520\) | 6.52848 | + | 37.4017i | 0.286293 | + | 1.64017i | ||||
\(521\) | 8.28196i | 0.362839i | 0.983406 | + | 0.181420i | \(0.0580692\pi\) | ||||
−0.983406 | + | 0.181420i | \(0.941931\pi\) | |||||||
\(522\) | 32.0961 | + | 27.0562i | 1.40481 | + | 1.18422i | ||||
\(523\) | −4.50113 | + | 4.50113i | −0.196820 | + | 0.196820i | −0.798635 | − | 0.601815i | \(-0.794444\pi\) |
0.601815 | + | 0.798635i | \(0.294444\pi\) | |||||||
\(524\) | −17.9403 | −0.783725 | ||||||||
\(525\) | −6.03614 | − | 14.7635i | −0.263439 | − | 0.644332i | ||||
\(526\) | −32.3906 | −1.41230 | ||||||||
\(527\) | 3.38670 | − | 3.38670i | 0.147527 | − | 0.147527i | ||||
\(528\) | 13.0382 | − | 14.1963i | 0.567413 | − | 0.617814i | ||||
\(529\) | − | 22.8558i | − | 0.993730i | ||||||
\(530\) | −4.46384 | − | 25.5734i | −0.193897 | − | 1.11084i | ||||
\(531\) | −3.19018 | − | 37.4424i | −0.138442 | − | 1.62486i | ||||
\(532\) | 24.7984 | + | 24.7984i | 1.07515 | + | 1.07515i | ||||
\(533\) | −8.93129 | − | 8.93129i | −0.386857 | − | 0.386857i | ||||
\(534\) | −70.1281 | + | 2.98214i | −3.03474 | + | 0.129050i | ||||
\(535\) | −4.82174 | − | 3.38862i | −0.208462 | − | 0.146503i | ||||
\(536\) | − | 28.7971i | − | 1.24385i | ||||||
\(537\) | 1.98229 | + | 1.82057i | 0.0855420 | + | 0.0785636i | ||||
\(538\) | −5.17328 | + | 5.17328i | −0.223036 | + | 0.223036i | ||||
\(539\) | 9.23415 | 0.397743 | ||||||||
\(540\) | −21.9827 | + | 41.7048i | −0.945984 | + | 1.79469i | ||||
\(541\) | −29.5788 | −1.27169 | −0.635847 | − | 0.771815i | \(-0.719349\pi\) | ||||
−0.635847 | + | 0.771815i | \(0.719349\pi\) | |||||||
\(542\) | −7.48175 | + | 7.48175i | −0.321369 | + | 0.321369i | ||||
\(543\) | −15.9314 | − | 14.6317i | −0.683681 | − | 0.627907i | ||||
\(544\) | − | 2.74950i | − | 0.117884i | ||||||
\(545\) | −41.1066 | + | 7.17517i | −1.76081 | + | 0.307350i | ||||
\(546\) | −26.3015 | + | 1.11845i | −1.12560 | + | 0.0478652i | ||||
\(547\) | −0.136930 | − | 0.136930i | −0.00585468 | − | 0.00585468i | 0.704173 | − | 0.710028i | \(-0.251318\pi\) |
−0.710028 | + | 0.704173i | \(0.751318\pi\) | |||||||
\(548\) | 58.6060 | + | 58.6060i | 2.50353 | + | 2.50353i | ||||
\(549\) | −1.98523 | − | 23.3002i | −0.0847277 | − | 0.994428i | ||||
\(550\) | 28.4980 | + | 13.4086i | 1.21516 | + | 0.571747i | ||||
\(551\) | − | 26.6819i | − | 1.13669i | ||||||
\(552\) | 2.25307 | − | 2.45320i | 0.0958969 | − | 0.104415i | ||||
\(553\) | −5.81511 | + | 5.81511i | −0.247284 | + | 0.247284i | ||||
\(554\) | 26.7826 | 1.13789 | ||||||||
\(555\) | 15.0033 | − | 3.28118i | 0.636854 | − | 0.139278i | ||||
\(556\) | 81.3045 | 3.44808 | ||||||||
\(557\) | −1.30891 | + | 1.30891i | −0.0554602 | + | 0.0554602i | −0.734293 | − | 0.678833i | \(-0.762486\pi\) |
0.678833 | + | 0.734293i | \(0.262486\pi\) | |||||||
\(558\) | −5.64537 | − | 4.75890i | −0.238988 | − | 0.201460i | ||||
\(559\) | − | 35.9418i | − | 1.52018i | ||||||
\(560\) | 10.2963 | − | 14.6508i | 0.435096 | − | 0.619108i | ||||
\(561\) | 0.902028 | + | 21.2121i | 0.0380837 | + | 0.895577i | ||||
\(562\) | −25.6605 | − | 25.6605i | −1.08242 | − | 1.08242i | ||||
\(563\) | 29.9878 | + | 29.9878i | 1.26383 | + | 1.26383i | 0.949219 | + | 0.314615i | \(0.101875\pi\) |
0.314615 | + | 0.949219i | \(0.398125\pi\) | |||||||
\(564\) | −1.20549 | − | 28.3483i | −0.0507603 | − | 1.19368i | ||||
\(565\) | 12.7188 | − | 18.0979i | 0.535086 | − | 0.761385i | ||||
\(566\) | − | 36.0924i | − | 1.51708i | ||||||
\(567\) | −13.5346 | − | 9.56885i | −0.568399 | − | 0.401854i | ||||
\(568\) | 4.23096 | − | 4.23096i | 0.177527 | − | 0.177527i | ||||
\(569\) | −16.0104 | −0.671189 | −0.335595 | − | 0.942007i | \(-0.608937\pi\) | ||||
−0.335595 | + | 0.942007i | \(0.608937\pi\) | |||||||
\(570\) | 43.7022 | − | 9.55757i | 1.83048 | − | 0.400322i | ||||
\(571\) | 15.7012 | 0.657077 | 0.328538 | − | 0.944491i | \(-0.393444\pi\) | ||||
0.328538 | + | 0.944491i | \(0.393444\pi\) | |||||||
\(572\) | 24.6211 | − | 24.6211i | 1.02946 | − | 1.02946i | ||||
\(573\) | 7.22805 | − | 7.87009i | 0.301956 | − | 0.328778i | ||||
\(574\) | 17.0749i | 0.712695i | ||||||||
\(575\) | 1.71812 | + | 0.808397i | 0.0716507 | + | 0.0337125i | ||||
\(576\) | 21.7718 | − | 1.85501i | 0.907157 | − | 0.0772919i | ||||
\(577\) | −19.5189 | − | 19.5189i | −0.812581 | − | 0.812581i | 0.172439 | − | 0.985020i | \(-0.444835\pi\) |
−0.985020 | + | 0.172439i | \(0.944835\pi\) | |||||||
\(578\) | 10.3367 | + | 10.3367i | 0.429949 | + | 0.429949i | ||||
\(579\) | −33.8379 | + | 1.43893i | −1.40625 | + | 0.0597998i | ||||
\(580\) | −50.8142 | + | 8.86963i | −2.10994 | + | 0.368291i | ||||
\(581\) | 10.4947i | 0.435394i | ||||||||
\(582\) | −60.7474 | − | 55.7917i | −2.51806 | − | 2.31264i | ||||
\(583\) | −8.53656 | + | 8.53656i | −0.353548 | + | 0.353548i | ||||
\(584\) | 27.7049 | 1.14644 | ||||||||
\(585\) | −11.3242 | + | 19.4344i | −0.468197 | + | 0.803515i | ||||
\(586\) | 14.6728 | 0.606126 | ||||||||
\(587\) | 18.4221 | − | 18.4221i | 0.760360 | − | 0.760360i | −0.216027 | − | 0.976387i | \(-0.569310\pi\) |
0.976387 | + | 0.216027i | \(0.0693100\pi\) | |||||||
\(588\) | −18.6754 | − | 17.1518i | −0.770159 | − | 0.707330i | ||||
\(589\) | 4.69306i | 0.193374i | ||||||||
\(590\) | 56.4006 | + | 39.6372i | 2.32198 | + | 1.63184i | ||||
\(591\) | 25.0185 | − | 1.06389i | 1.02912 | − | 0.0437627i | ||||
\(592\) | 12.1922 | + | 12.1922i | 0.501096 | + | 0.501096i | ||||
\(593\) | −4.26981 | − | 4.26981i | −0.175340 | − | 0.175340i | 0.613981 | − | 0.789321i | \(-0.289567\pi\) |
−0.789321 | + | 0.613981i | \(0.789567\pi\) | |||||||
\(594\) | 32.4648 | − | 4.16170i | 1.33205 | − | 0.170757i | ||||
\(595\) | 3.39160 | + | 19.4305i | 0.139042 | + | 0.796573i | ||||
\(596\) | − | 40.2330i | − | 1.64801i | ||||||
\(597\) | 3.73233 | − | 4.06386i | 0.152754 | − | 0.166323i | ||||
\(598\) | 2.21606 | − | 2.21606i | 0.0906215 | − | 0.0906215i | ||||
\(599\) | −1.20371 | −0.0491822 | −0.0245911 | − | 0.999698i | \(-0.507828\pi\) | ||||
−0.0245911 | + | 0.999698i | \(0.507828\pi\) | |||||||
\(600\) | −16.5965 | − | 40.5927i | −0.677551 | − | 1.65719i | ||||
\(601\) | 4.03047 | 0.164406 | 0.0822031 | − | 0.996616i | \(-0.473804\pi\) | ||||
0.0822031 | + | 0.996616i | \(0.473804\pi\) | |||||||
\(602\) | −34.3570 | + | 34.3570i | −1.40029 | + | 1.40029i | ||||
\(603\) | 10.9958 | − | 13.0441i | 0.447784 | − | 0.531195i | ||||
\(604\) | − | 40.6201i | − | 1.65281i | ||||||
\(605\) | 1.71095 | + | 9.80207i | 0.0695601 | + | 0.398511i | ||||
\(606\) | 3.36719 | + | 79.1829i | 0.136783 | + | 3.21659i | ||||
\(607\) | 10.5261 | + | 10.5261i | 0.427241 | + | 0.427241i | 0.887687 | − | 0.460446i | \(-0.152311\pi\) |
−0.460446 | + | 0.887687i | \(0.652311\pi\) | |||||||
\(608\) | 1.90504 | + | 1.90504i | 0.0772594 | + | 0.0772594i | ||||
\(609\) | −0.770529 | − | 18.1198i | −0.0312234 | − | 0.734251i | ||||
\(610\) | 35.0978 | + | 24.6660i | 1.42107 | + | 0.998697i | ||||
\(611\) | − | 13.5376i | − | 0.547674i | ||||||
\(612\) | 37.5759 | − | 44.5754i | 1.51892 | − | 1.80185i | ||||
\(613\) | −5.63618 | + | 5.63618i | −0.227643 | + | 0.227643i | −0.811707 | − | 0.584064i | \(-0.801462\pi\) |
0.584064 | + | 0.811707i | \(0.301462\pi\) | |||||||
\(614\) | −26.5095 | −1.06983 | ||||||||
\(615\) | 12.2820 | + | 7.87396i | 0.495259 | + | 0.317509i | ||||
\(616\) | −23.8689 | −0.961704 | ||||||||
\(617\) | −11.1982 | + | 11.1982i | −0.450824 | + | 0.450824i | −0.895628 | − | 0.444804i | \(-0.853273\pi\) |
0.444804 | + | 0.895628i | \(0.353273\pi\) | |||||||
\(618\) | −9.07752 | + | 9.88384i | −0.365152 | + | 0.397586i | ||||
\(619\) | 13.0830i | 0.525851i | 0.964816 | + | 0.262926i | \(0.0846874\pi\) | ||||
−0.964816 | + | 0.262926i | \(0.915313\pi\) | |||||||
\(620\) | 8.93768 | − | 1.56007i | 0.358946 | − | 0.0626541i | ||||
\(621\) | 1.95728 | − | 0.250906i | 0.0785429 | − | 0.0100685i | ||||
\(622\) | −13.3264 | − | 13.3264i | −0.534341 | − | 0.534341i | ||||
\(623\) | 21.4431 | + | 21.4431i | 0.859099 | + | 0.859099i | ||||
\(624\) | −25.2302 | + | 1.07289i | −1.01002 | + | 0.0429501i | ||||
\(625\) | 19.2615 | − | 15.9373i | 0.770458 | − | 0.637491i | ||||
\(626\) | − | 9.06314i | − | 0.362236i | ||||||
\(627\) | −15.3222 | − | 14.0722i | −0.611908 | − | 0.561989i | ||||
\(628\) | −62.4408 | + | 62.4408i | −2.49166 | + | 2.49166i | ||||
\(629\) | −18.9923 | −0.757273 | ||||||||
\(630\) | 29.4023 | − | 7.75263i | 1.17142 | − | 0.308872i | ||||
\(631\) | 26.1928 | 1.04272 | 0.521360 | − | 0.853337i | \(-0.325425\pi\) | ||||
0.521360 | + | 0.853337i | \(0.325425\pi\) | |||||||
\(632\) | −15.9888 | + | 15.9888i | −0.636001 | + | 0.636001i | ||||
\(633\) | 11.7201 | + | 10.7640i | 0.465834 | + | 0.427831i | ||||
\(634\) | − | 31.2532i | − | 1.24122i | ||||||
\(635\) | −22.0029 | + | 31.3084i | −0.873160 | + | 1.24244i | ||||
\(636\) | 33.1207 | − | 1.40843i | 1.31332 | − | 0.0558478i | ||||
\(637\) | −8.55457 | − | 8.55457i | −0.338945 | − | 0.338945i | ||||
\(638\) | 25.3230 | + | 25.3230i | 1.00255 | + | 1.00255i | ||||
\(639\) | 3.53201 | − | 0.300936i | 0.139724 | − | 0.0119048i | ||||
\(640\) | −24.5241 | + | 34.8959i | −0.969401 | + | 1.37938i | ||||
\(641\) | − | 4.55409i | − | 0.179876i | −0.995947 | − | 0.0899379i | \(-0.971333\pi\) | ||
0.995947 | − | 0.0899379i | \(-0.0286669\pi\) | |||||||
\(642\) | 7.59988 | − | 8.27495i | 0.299943 | − | 0.326586i | ||||
\(643\) | −27.2969 | + | 27.2969i | −1.07648 | + | 1.07648i | −0.0796607 | + | 0.996822i | \(0.525384\pi\) |
−0.996822 | + | 0.0796607i | \(0.974616\pi\) | |||||||
\(644\) | −2.83786 | −0.111828 | ||||||||
\(645\) | 8.86960 | + | 40.5564i | 0.349240 | + | 1.59691i | ||||
\(646\) | −55.3216 | −2.17660 | ||||||||
\(647\) | 23.8541 | − | 23.8541i | 0.937803 | − | 0.937803i | −0.0603727 | − | 0.998176i | \(-0.519229\pi\) |
0.998176 | + | 0.0603727i | \(0.0192289\pi\) | |||||||
\(648\) | −37.2137 | − | 26.3098i | −1.46189 | − | 1.03355i | ||||
\(649\) | − | 32.0581i | − | 1.25839i | ||||||
\(650\) | −13.9789 | − | 38.8226i | −0.548297 | − | 1.52275i | ||||
\(651\) | 0.135528 | + | 3.18708i | 0.00531176 | + | 0.124912i | ||||
\(652\) | −61.2495 | − | 61.2495i | −2.39872 | − | 2.39872i | ||||
\(653\) | 5.07325 | + | 5.07325i | 0.198532 | + | 0.198532i | 0.799370 | − | 0.600839i | \(-0.205167\pi\) |
−0.600839 | + | 0.799370i | \(0.705167\pi\) | |||||||
\(654\) | −3.37982 | − | 79.4801i | −0.132162 | − | 3.10792i | ||||
\(655\) | 9.73957 | − | 1.70004i | 0.380557 | − | 0.0664262i | ||||
\(656\) | 16.3795i | 0.639511i | ||||||||
\(657\) | 12.5493 | + | 10.5787i | 0.489595 | + | 0.412716i | ||||
\(658\) | −12.9407 | + | 12.9407i | −0.504481 | + | 0.504481i | ||||
\(659\) | 32.9568 | 1.28381 | 0.641907 | − | 0.766782i | \(-0.278143\pi\) | ||||
0.641907 | + | 0.766782i | \(0.278143\pi\) | |||||||
\(660\) | −21.7063 | + | 33.8581i | −0.844916 | + | 1.31792i | ||||
\(661\) | −3.56963 | −0.138842 | −0.0694212 | − | 0.997587i | \(-0.522115\pi\) | ||||
−0.0694212 | + | 0.997587i | \(0.522115\pi\) | |||||||
\(662\) | 2.30932 | − | 2.30932i | 0.0897541 | − | 0.0897541i | ||||
\(663\) | 18.8154 | − | 20.4867i | 0.730730 | − | 0.795638i | ||||
\(664\) | 28.8555i | 1.11981i | ||||||||
\(665\) | −15.8127 | − | 11.1128i | −0.613190 | − | 0.430937i | ||||
\(666\) | 2.48562 | + | 29.1731i | 0.0963158 | + | 1.13043i | ||||
\(667\) | 1.52671 | + | 1.52671i | 0.0591143 | + | 0.0591143i | ||||
\(668\) | −19.1098 | − | 19.1098i | −0.739381 | − | 0.739381i | ||||
\(669\) | 44.9910 | − | 1.91321i | 1.73945 | − | 0.0739688i | ||||
\(670\) | 5.38147 | + | 30.8305i | 0.207904 | + | 1.19109i | ||||
\(671\) | − | 19.9495i | − | 0.770144i | ||||||
\(672\) | 1.34873 | + | 1.23870i | 0.0520285 | + | 0.0477840i | ||||
\(673\) | −16.9220 | + | 16.9220i | −0.652295 | + | 0.652295i | −0.953545 | − | 0.301250i | \(-0.902596\pi\) |
0.301250 | + | 0.953545i | \(0.402596\pi\) | |||||||
\(674\) | 42.6627 | 1.64331 | ||||||||
\(675\) | 7.98215 | − | 24.7242i | 0.307233 | − | 0.951634i | ||||
\(676\) | 7.12908 | 0.274195 | ||||||||
\(677\) | −15.8295 | + | 15.8295i | −0.608377 | + | 0.608377i | −0.942522 | − | 0.334145i | \(-0.891552\pi\) |
0.334145 | + | 0.942522i | \(0.391552\pi\) | |||||||
\(678\) | 31.0592 | + | 28.5254i | 1.19282 | + | 1.09551i | ||||
\(679\) | 35.6342i | 1.36751i | ||||||||
\(680\) | 9.32530 | + | 53.4248i | 0.357609 | + | 2.04875i | ||||
\(681\) | 10.9185 | − | 0.464299i | 0.418397 | − | 0.0177920i | ||||
\(682\) | −4.45405 | − | 4.45405i | −0.170554 | − | 0.170554i | ||||
\(683\) | −0.807396 | − | 0.807396i | −0.0308941 | − | 0.0308941i | 0.691491 | − | 0.722385i | \(-0.256954\pi\) |
−0.722385 | + | 0.691491i | \(0.756954\pi\) | |||||||
\(684\) | 4.84971 | + | 56.9199i | 0.185433 | + | 2.17639i | ||||
\(685\) | −37.3701 | − | 26.2630i | −1.42784 | − | 1.00346i | ||||
\(686\) | 48.0846i | 1.83588i | ||||||||
\(687\) | 8.24667 | − | 8.97919i | 0.314630 | − | 0.342577i | ||||
\(688\) | −32.9576 | + | 32.9576i | −1.25650 | + | 1.25650i | ||||
\(689\) | 15.8167 | 0.602566 | ||||||||
\(690\) | −1.95371 | + | 3.04746i | −0.0743766 | + | 0.116015i | ||||
\(691\) | −26.8549 | −1.02161 | −0.510804 | − | 0.859697i | \(-0.670652\pi\) | ||||
−0.510804 | + | 0.859697i | \(0.670652\pi\) | |||||||
\(692\) | 9.18325 | − | 9.18325i | 0.349095 | − | 0.349095i | ||||
\(693\) | −10.8117 | − | 9.11401i | −0.410704 | − | 0.346212i | ||||
\(694\) | 58.4933i | 2.22037i | ||||||||
\(695\) | −44.1393 | + | 7.70452i | −1.67430 | + | 0.292249i | ||||
\(696\) | −2.11859 | − | 49.8209i | −0.0803051 | − | 1.88846i | ||||
\(697\) | −12.7575 | − | 12.7575i | −0.483225 | − | 0.483225i | ||||
\(698\) | 32.3158 | + | 32.3158i | 1.22317 | + | 1.22317i | ||||
\(699\) | 0.657114 | + | 15.4527i | 0.0248544 | + | 0.584476i | ||||
\(700\) | −15.9073 | + | 33.8085i | −0.601239 | + | 1.27784i | ||||
\(701\) | − | 3.77870i | − | 0.142719i | −0.997451 | − | 0.0713597i | \(-0.977266\pi\) | ||
0.997451 | − | 0.0713597i | \(-0.0227338\pi\) | |||||||
\(702\) | −33.9310 | − | 26.2202i | −1.28064 | − | 0.989617i | ||||
\(703\) | 13.1591 | − | 13.1591i | 0.496306 | − | 0.496306i | ||||
\(704\) | 18.6409 | 0.702556 | ||||||||
\(705\) | 3.34077 | + | 15.2758i | 0.125821 | + | 0.575318i | ||||
\(706\) | 67.4969 | 2.54028 | ||||||||
\(707\) | 24.2118 | − | 24.2118i | 0.910578 | − | 0.910578i | ||||
\(708\) | −59.5458 | + | 64.8350i | −2.23787 | + | 2.43665i | ||||
\(709\) | − | 18.2349i | − | 0.684825i | −0.939550 | − | 0.342413i | \(-0.888756\pi\) | ||
0.939550 | − | 0.342413i | \(-0.111244\pi\) | |||||||
\(710\) | −3.73905 | + | 5.32037i | −0.140324 | + | 0.199670i | ||||
\(711\) | −13.3475 | + | 1.13724i | −0.500569 | + | 0.0426497i | ||||
\(712\) | 58.9584 | + | 58.9584i | 2.20956 | + | 2.20956i | ||||
\(713\) | −0.268531 | − | 0.268531i | −0.0100566 | − | 0.0100566i | ||||
\(714\) | −37.5691 | + | 1.59760i | −1.40599 | + | 0.0597885i | ||||
\(715\) | −11.0334 | + | 15.6996i | −0.412625 | + | 0.587133i | ||||
\(716\) | − | 6.30499i | − | 0.235628i | ||||||
\(717\) | −7.72528 | − | 7.09506i | −0.288506 | − | 0.264970i | ||||
\(718\) | 4.10401 | − | 4.10401i | 0.153160 | − | 0.153160i | ||||
\(719\) | 4.30553 | 0.160569 | 0.0802845 | − | 0.996772i | \(-0.474417\pi\) | ||||
0.0802845 | + | 0.996772i | \(0.474417\pi\) | |||||||
\(720\) | 28.2048 | − | 7.43686i | 1.05113 | − | 0.277155i | ||||
\(721\) | 5.79782 | 0.215922 | ||||||||
\(722\) | 5.26425 | − | 5.26425i | 0.195915 | − | 0.195915i | ||||
\(723\) | −24.7758 | − | 22.7546i | −0.921422 | − | 0.846253i | ||||
\(724\) | 50.6723i | 1.88322i | ||||||||
\(725\) | 26.7460 | − | 9.63044i | 0.993320 | − | 0.357666i | ||||
\(726\) | −18.9524 | + | 0.805935i | −0.703390 | + | 0.0299111i | ||||
\(727\) | 4.10330 | + | 4.10330i | 0.152183 | + | 0.152183i | 0.779092 | − | 0.626909i | \(-0.215680\pi\) |
−0.626909 | + | 0.779092i | \(0.715680\pi\) | |||||||
\(728\) | 22.1123 | + | 22.1123i | 0.819535 | + | 0.819535i | ||||
\(729\) | −6.81040 | − | 26.1270i | −0.252237 | − | 0.967665i | ||||
\(730\) | −29.6611 | + | 5.17735i | −1.09781 | + | 0.191622i | ||||
\(731\) | − | 51.3394i | − | 1.89886i | ||||||
\(732\) | −37.0550 | + | 40.3465i | −1.36959 | + | 1.49125i | ||||
\(733\) | 5.34821 | − | 5.34821i | 0.197541 | − | 0.197541i | −0.601404 | − | 0.798945i | \(-0.705392\pi\) |
0.798945 | + | 0.601404i | \(0.205392\pi\) | |||||||
\(734\) | 32.3786 | 1.19512 | ||||||||
\(735\) | 11.7640 | + | 7.54184i | 0.433921 | + | 0.278185i | ||||
\(736\) | −0.218008 | −0.00803587 | ||||||||
\(737\) | 10.2914 | − | 10.2914i | 0.379089 | − | 0.379089i | ||||
\(738\) | −17.9265 | + | 21.2658i | −0.659883 | + | 0.782804i | ||||
\(739\) | 31.4904i | 1.15839i | 0.815188 | + | 0.579197i | \(0.196634\pi\) | ||||
−0.815188 | + | 0.579197i | \(0.803366\pi\) | |||||||
\(740\) | −29.4352 | − | 20.6865i | −1.08206 | − | 0.760450i | ||||
\(741\) | 1.15798 | + | 27.2311i | 0.0425395 | + | 1.00036i | ||||
\(742\) | −15.1192 | − | 15.1192i | −0.555044 | − | 0.555044i | ||||
\(743\) | 15.5001 | + | 15.5001i | 0.568645 | + | 0.568645i | 0.931749 | − | 0.363104i | \(-0.118283\pi\) |
−0.363104 | + | 0.931749i | \(0.618283\pi\) | |||||||
\(744\) | 0.372638 | + | 8.76297i | 0.0136616 | + | 0.321266i | ||||
\(745\) | 3.81253 | + | 21.8420i | 0.139680 | + | 0.800230i | ||||
\(746\) | − | 20.6007i | − | 0.754247i | ||||||
\(747\) | −11.0181 | + | 13.0705i | −0.403131 | + | 0.478224i | ||||
\(748\) | 35.1688 | − | 35.1688i | 1.28590 | − | 1.28590i | ||||
\(749\) | −4.85405 | −0.177363 | ||||||||
\(750\) | 25.3542 | + | 40.3574i | 0.925804 | + | 1.47365i | ||||
\(751\) | −31.1823 | −1.13786 | −0.568930 | − | 0.822386i | \(-0.692642\pi\) | ||||
−0.568930 | + | 0.822386i | \(0.692642\pi\) | |||||||
\(752\) | −12.4136 | + | 12.4136i | −0.452678 | + | 0.452678i | ||||
\(753\) | −0.391823 | + | 0.426627i | −0.0142788 | + | 0.0155472i | ||||
\(754\) | − | 46.9188i | − | 1.70868i | ||||||
\(755\) | 3.84921 | + | 22.0522i | 0.140087 | + | 0.802561i | ||||
\(756\) | 4.93721 | + | 38.5145i | 0.179565 | + | 1.40076i | ||||
\(757\) | −25.1331 | − | 25.1331i | −0.913480 | − | 0.913480i | 0.0830643 | − | 0.996544i | \(-0.473529\pi\) |
−0.996544 | + | 0.0830643i | \(0.973529\pi\) | |||||||
\(758\) | 31.6145 | + | 31.6145i | 1.14829 | + | 1.14829i | ||||
\(759\) | 1.68191 | − | 0.0715218i | 0.0610494 | − | 0.00259608i | ||||
\(760\) | −43.4774 | − | 30.5551i | −1.57709 | − | 1.10835i | ||||
\(761\) | 8.72350i | 0.316226i | 0.987421 | + | 0.158113i | \(0.0505411\pi\) | ||||
−0.987421 | + | 0.158113i | \(0.949459\pi\) | |||||||
\(762\) | −53.7307 | − | 49.3474i | −1.94646 | − | 1.78767i | ||||
\(763\) | −24.3026 | + | 24.3026i | −0.879815 | + | 0.879815i | ||||
\(764\) | −25.0321 | −0.905629 | ||||||||
\(765\) | −16.1755 | + | 27.7602i | −0.584827 | + | 1.00367i | ||||
\(766\) | −68.0701 | −2.45947 | ||||||||
\(767\) | −29.6988 | + | 29.6988i | −1.07236 | + | 1.07236i | ||||
\(768\) | −41.3046 | − | 37.9350i | −1.49045 | − | 1.36886i | ||||
\(769\) | 21.7304i | 0.783619i | 0.920046 | + | 0.391809i | \(0.128151\pi\) | ||||
−0.920046 | + | 0.391809i | \(0.871849\pi\) | |||||||
\(770\) | 25.5542 | − | 4.46050i | 0.920910 | − | 0.160745i | ||||
\(771\) | 53.0107 | − | 2.25423i | 1.90913 | − | 0.0811843i | ||||
\(772\) | 56.1018 | + | 56.1018i | 2.01915 | + | 2.01915i | ||||
\(773\) | −16.4735 | − | 16.4735i | −0.592511 | − | 0.592511i | 0.345798 | − | 0.938309i | \(-0.387608\pi\) |
−0.938309 | + | 0.345798i | \(0.887608\pi\) | |||||||
\(774\) | −78.8599 | + | 6.71905i | −2.83456 | + | 0.241511i | ||||
\(775\) | −4.70433 | + | 1.69389i | −0.168985 | + | 0.0608464i | ||||
\(776\) | 97.9772i | 3.51718i | ||||||||
\(777\) | 8.55641 | − | 9.31644i | 0.306960 | − | 0.334225i | ||||
\(778\) | 55.0684 | − | 55.0684i | 1.97430 | − | 1.97430i | ||||
\(779\) | 17.6785 | 0.633398 | ||||||||
\(780\) | 51.4752 | − | 11.2575i | 1.84311 | − | 0.403084i | ||||
\(781\) | 3.02409 | 0.108211 | ||||||||
\(782\) | 3.16543 | − | 3.16543i | 0.113196 | − | 0.113196i | ||||
\(783\) | 18.0638 | − | 23.3760i | 0.645548 | − | 0.835391i | ||||
\(784\) | 15.6886i | 0.560307i | ||||||||
\(785\) | 27.9814 | − | 39.8154i | 0.998700 | − | 1.42107i | ||||
\(786\) | 0.800797 | + | 18.8316i | 0.0285635 | + | 0.671700i | ||||
\(787\) | −11.1899 | − | 11.1899i | −0.398878 | − | 0.398878i | 0.478959 | − | 0.877837i | \(-0.341014\pi\) |
−0.877837 | + | 0.478959i | \(0.841014\pi\) | |||||||
\(788\) | −41.4797 | − | 41.4797i | −1.47765 | − | 1.47765i | ||||
\(789\) | 0.968450 | + | 22.7741i | 0.0344777 | + | 0.810779i | ||||
\(790\) | 14.1299 | − | 20.1057i | 0.502718 | − | 0.715328i | ||||
\(791\) | − | 18.2192i | − | 0.647799i | ||||||
\(792\) | −29.7272 | − | 25.0592i | −1.05631 | − | 0.890441i | ||||
\(793\) | −18.4814 | + | 18.4814i | −0.656294 | + | 0.656294i | ||||
\(794\) | 64.2648 | 2.28067 | ||||||||
\(795\) | −17.8474 | + | 3.90318i | −0.632981 | + | 0.138431i | ||||
\(796\) | −12.9258 | −0.458142 | ||||||||
\(797\) | −26.6744 | + | 26.6744i | −0.944855 | + | 0.944855i | −0.998557 | − | 0.0537016i | \(-0.982898\pi\) |
0.0537016 | + | 0.998557i | \(0.482898\pi\) | |||||||
\(798\) | 24.9235 | − | 27.1373i | 0.882281 | − | 0.960650i | ||||
\(799\) | − | 19.3372i | − | 0.684102i | ||||||
\(800\) | −1.22201 | + | 2.59720i | −0.0432047 | + | 0.0918250i | ||||
\(801\) | 4.19353 | + | 49.2185i | 0.148171 | + | 1.73905i | ||||
\(802\) | 2.13311 | + | 2.13311i | 0.0753228 | + | 0.0753228i | ||||
\(803\) | 9.90107 | + | 9.90107i | 0.349401 | + | 0.349401i | ||||
\(804\) | −39.9293 | + | 1.69796i | −1.40820 | + | 0.0598824i | ||||
\(805\) | 1.54064 | − | 0.268920i | 0.0543006 | − | 0.00947818i | ||||
\(806\) | 8.25253i | 0.290683i | ||||||||
\(807\) | 3.79205 | + | 3.48270i | 0.133487 | + | 0.122597i | ||||
\(808\) | 66.5710 | − | 66.5710i | 2.34196 | − | 2.34196i | ||||
\(809\) | 8.76972 | 0.308327 | 0.154163 | − | 0.988045i | \(-0.450732\pi\) | ||||
0.154163 | + | 0.988045i | \(0.450732\pi\) | |||||||
\(810\) | 44.7580 | + | 21.2132i | 1.57264 | + | 0.745358i | ||||
\(811\) | −6.06391 | −0.212933 | −0.106466 | − | 0.994316i | \(-0.533954\pi\) | ||||
−0.106466 | + | 0.994316i | \(0.533954\pi\) | |||||||
\(812\) | −30.0419 | + | 30.0419i | −1.05426 | + | 1.05426i | ||||
\(813\) | 5.48417 | + | 5.03678i | 0.192338 | + | 0.176648i | ||||
\(814\) | 24.9779i | 0.875475i | ||||||||
\(815\) | 39.0557 | + | 27.4476i | 1.36806 | + | 0.961447i | ||||
\(816\) | −36.0389 | + | 1.53252i | −1.26161 | + | 0.0536491i | ||||
\(817\) | 35.5714 | + | 35.5714i | 1.24449 | + | 1.24449i | ||||
\(818\) | −59.1625 | − | 59.1625i | −2.06857 | − | 2.06857i | ||||
\(819\) | 1.57278 | + | 18.4593i | 0.0549574 | + | 0.645021i | ||||
\(820\) | −5.87670 | − | 33.6677i | −0.205223 | − | 1.17573i | ||||
\(821\) | − | 41.6548i | − | 1.45376i | −0.686763 | − | 0.726881i | \(-0.740969\pi\) | ||
0.686763 | − | 0.726881i | \(-0.259031\pi\) | |||||||
\(822\) | 58.9017 | − | 64.1337i | 2.05443 | − | 2.23692i | ||||
\(823\) | 33.0974 | − | 33.0974i | 1.15370 | − | 1.15370i | 0.167898 | − | 0.985804i | \(-0.446302\pi\) |
0.985804 | − | 0.167898i | \(-0.0536980\pi\) | |||||||
\(824\) | 15.9413 | 0.555341 | ||||||||
\(825\) | 8.57566 | − | 20.4381i | 0.298566 | − | 0.711563i | ||||
\(826\) | 56.7785 | 1.97558 | ||||||||
\(827\) | −27.5595 | + | 27.5595i | −0.958338 | + | 0.958338i | −0.999166 | − | 0.0408287i | \(-0.987000\pi\) |
0.0408287 | + | 0.999166i | \(0.487000\pi\) | |||||||
\(828\) | −3.53438 | − | 2.97939i | −0.122828 | − | 0.103541i | ||||
\(829\) | − | 42.0783i | − | 1.46144i | −0.682677 | − | 0.730720i | \(-0.739185\pi\) | ||
0.682677 | − | 0.730720i | \(-0.260815\pi\) | |||||||
\(830\) | −5.39237 | − | 30.8929i | −0.187172 | − | 1.07231i | ||||
\(831\) | −0.800777 | − | 18.8311i | −0.0277786 | − | 0.653243i | ||||
\(832\) | −17.2691 | − | 17.2691i | −0.598697 | − | 0.598697i | ||||
\(833\) | −12.2194 | − | 12.2194i | −0.423377 | − | 0.423377i | ||||
\(834\) | −3.62918 | − | 85.3438i | −0.125668 | − | 2.95522i | ||||
\(835\) | 12.1854 | + | 8.56364i | 0.421693 | + | 0.296357i | ||||
\(836\) | 48.7346i | 1.68552i | ||||||||
\(837\) | −3.17723 | + | 4.11159i | −0.109821 | + | 0.142117i | ||||
\(838\) | 45.0649 | − | 45.0649i | 1.55674 | − | 1.55674i | ||||
\(839\) | 15.8726 | 0.547983 | 0.273991 | − | 0.961732i | \(-0.411656\pi\) | ||||
0.273991 | + | 0.961732i | \(0.411656\pi\) | |||||||
\(840\) | −30.4081 | − | 19.4945i | −1.04918 | − | 0.672624i | ||||
\(841\) | 3.32367 | 0.114609 | ||||||||
\(842\) | 19.9869 | − | 19.9869i | 0.688795 | − | 0.688795i | ||||
\(843\) | −17.2749 | + | 18.8093i | −0.594979 | + | 0.647828i | ||||
\(844\) | − | 37.2778i | − | 1.28316i | ||||||
\(845\) | −3.87030 | + | 0.675561i | −0.133142 | + | 0.0232400i | ||||
\(846\) | −29.7029 | + | 2.53076i | −1.02121 | + | 0.0870093i | ||||
\(847\) | 5.79508 | + | 5.79508i | 0.199121 | + | 0.199121i | ||||
\(848\) | −14.5034 | − | 14.5034i | −0.498049 | − | 0.498049i | ||||
\(849\) | −25.3768 | + | 1.07913i | −0.870931 | + | 0.0370356i | ||||
\(850\) | −19.9675 | − | 55.4544i | −0.684880 | − | 1.90207i | ||||
\(851\) | 1.50590i | 0.0516216i | ||||||||
\(852\) | −6.11600 | − | 5.61706i | −0.209531 | − | 0.192437i | ||||
\(853\) | 19.7306 | − | 19.7306i | 0.675562 | − | 0.675562i | −0.283431 | − | 0.958993i | \(-0.591473\pi\) |
0.958993 | + | 0.283431i | \(0.0914727\pi\) | |||||||
\(854\) | 35.3329 | 1.20907 | ||||||||
\(855\) | −8.02666 | − | 30.4416i | −0.274506 | − | 1.04108i | ||||
\(856\) | −13.3463 | −0.456169 | ||||||||
\(857\) | 14.1707 | − | 14.1707i | 0.484061 | − | 0.484061i | −0.422365 | − | 0.906426i | \(-0.638800\pi\) |
0.906426 | + | 0.422365i | \(0.138800\pi\) | |||||||
\(858\) | −26.9433 | − | 24.7453i | −0.919828 | − | 0.844790i | ||||
\(859\) | 22.6000i | 0.771102i | 0.922687 | + | 0.385551i | \(0.125989\pi\) | ||||
−0.922687 | + | 0.385551i | \(0.874011\pi\) | |||||||
\(860\) | 55.9190 | − | 79.5684i | 1.90682 | − | 2.71326i | ||||
\(861\) | 12.0055 | − | 0.510525i | 0.409148 | − | 0.0173987i | ||||
\(862\) | 44.8399 | + | 44.8399i | 1.52725 | + | 1.52725i | ||||
\(863\) | −26.4341 | − | 26.4341i | −0.899828 | − | 0.899828i | 0.0955929 | − | 0.995421i | \(-0.469525\pi\) |
−0.995421 | + | 0.0955929i | \(0.969525\pi\) | |||||||
\(864\) | 0.379282 | + | 2.95872i | 0.0129034 | + | 0.100658i | ||||
\(865\) | −4.11526 | + | 5.85570i | −0.139923 | + | 0.199100i | ||||
\(866\) | 8.00054i | 0.271869i | ||||||||
\(867\) | 6.95874 | − | 7.57685i | 0.236331 | − | 0.257323i | ||||
\(868\) | 5.28405 | − | 5.28405i | 0.179352 | − | 0.179352i | ||||
\(869\) | −11.4281 | −0.387670 | ||||||||
\(870\) | 11.5785 | + | 52.9428i | 0.392547 | + | 1.79493i | ||||
\(871\) | −19.0681 | −0.646097 | ||||||||
\(872\) | −66.8208 | + | 66.8208i | −2.26284 | + | 2.26284i | ||||
\(873\) | −37.4113 | + | 44.3801i | −1.26618 | + | 1.50204i | ||||
\(874\) | 4.38645i | 0.148374i | ||||||||
\(875\) | 5.43215 | − | 19.8617i | 0.183640 | − | 0.671447i | ||||
\(876\) | −1.63356 | − | 38.4148i | −0.0551927 | − | 1.29791i | ||||
\(877\) | 9.80802 | + | 9.80802i | 0.331193 | + | 0.331193i | 0.853040 | − | 0.521846i | \(-0.174757\pi\) |
−0.521846 | + | 0.853040i | \(0.674757\pi\) | |||||||
\(878\) | 8.17567 | + | 8.17567i | 0.275916 | + | 0.275916i | ||||
\(879\) | −0.438702 | − | 10.3165i | −0.0147971 | − | 0.347968i | ||||
\(880\) | 24.5134 | − | 4.27882i | 0.826346 | − | 0.144239i | ||||
\(881\) | 17.6496i | 0.594629i | 0.954780 | + | 0.297315i | \(0.0960910\pi\) | ||||
−0.954780 | + | 0.297315i | \(0.903909\pi\) | |||||||
\(882\) | −17.1704 | + | 20.3688i | −0.578156 | + | 0.685853i | ||||
\(883\) | −13.6543 | + | 13.6543i | −0.459503 | + | 0.459503i | −0.898492 | − | 0.438990i | \(-0.855336\pi\) |
0.438990 | + | 0.898492i | \(0.355336\pi\) | |||||||
\(884\) | −65.1613 | −2.19161 | ||||||||
\(885\) | 26.1829 | − | 40.8409i | 0.880129 | − | 1.37285i | ||||
\(886\) | 44.6690 | 1.50068 | ||||||||
\(887\) | 33.6240 | − | 33.6240i | 1.12898 | − | 1.12898i | 0.138639 | − | 0.990343i | \(-0.455727\pi\) |
0.990343 | − | 0.138639i | \(-0.0442729\pi\) | |||||||
\(888\) | 23.5261 | − | 25.6158i | 0.789484 | − | 0.859611i | ||||
\(889\) | 31.5182i | 1.05709i | ||||||||
\(890\) | −74.1392 | − | 52.1035i | −2.48515 | − | 1.74651i | ||||
\(891\) | −3.89679 | − | 22.7018i | −0.130547 | − | 0.760540i | ||||
\(892\) | −74.5932 | − | 74.5932i | −2.49757 | − | 2.49757i | ||||
\(893\) | 13.3981 | + | 13.3981i | 0.448351 | + | 0.448351i | ||||
\(894\) | −42.2318 | + | 1.79587i | −1.41244 | + | 0.0600630i | ||||
\(895\) | 0.597469 | + | 3.42291i | 0.0199712 | + | 0.114415i | ||||
\(896\) | 35.1297i | 1.17360i | ||||||||
\(897\) | −1.62439 | − | 1.49187i | −0.0542368 | − | 0.0498122i | ||||
\(898\) | −66.7973 | + | 66.7973i | −2.22905 | + | 2.22905i | ||||
\(899\) | −5.68539 | −0.189618 | ||||||||
\(900\) | −55.3061 | + | 25.4058i | −1.84354 | + | 0.846859i | ||||
\(901\) | 22.5926 | 0.752668 | ||||||||
\(902\) | −16.7781 | + | 16.7781i | −0.558651 | + | 0.558651i | ||||
\(903\) | 25.1839 | + | 23.1294i | 0.838068 | + | 0.769699i | ||||
\(904\) | − | 50.0942i | − | 1.66611i | ||||||
\(905\) | −4.80178 | − | 27.5094i | −0.159617 | − | 0.914445i | ||||
\(906\) | −42.6381 | + | 1.81315i | −1.41656 | + | 0.0602379i | ||||
\(907\) | −4.29022 | − | 4.29022i | −0.142454 | − | 0.142454i | 0.632283 | − | 0.774737i | \(-0.282118\pi\) |
−0.774737 | + | 0.632283i | \(0.782118\pi\) | |||||||
\(908\) | −18.1024 | − | 18.1024i | −0.600749 | − | 0.600749i | ||||
\(909\) | 55.5735 | − | 4.73500i | 1.84326 | − | 0.157050i | ||||
\(910\) | −27.8058 | − | 19.5414i | −0.921755 | − | 0.647790i | ||||
\(911\) | − | 1.45363i | − | 0.0481610i | −0.999710 | − | 0.0240805i | \(-0.992334\pi\) | ||
0.999710 | − | 0.0240805i | \(-0.00766580\pi\) | |||||||
\(912\) | 23.9083 | − | 26.0320i | 0.791683 | − | 0.862005i | ||||
\(913\) | −10.3123 | + | 10.3123i | −0.341286 | + | 0.341286i | ||||
\(914\) | −25.4919 | −0.843197 | ||||||||
\(915\) | 16.2935 | − | 25.4150i | 0.538646 | − | 0.840195i | ||||
\(916\) | −28.5598 | −0.943641 | ||||||||
\(917\) | 5.75814 | − | 5.75814i | 0.190150 | − | 0.190150i | ||||
\(918\) | −48.4672 | − | 37.4530i | −1.59966 | − | 1.23613i | ||||
\(919\) | 12.9482i | 0.427122i | 0.976930 | + | 0.213561i | \(0.0685063\pi\) | ||||
−0.976930 | + | 0.213561i | \(0.931494\pi\) | |||||||
\(920\) | 4.23605 | − | 0.739403i | 0.139658 | − | 0.0243774i | ||||
\(921\) | 0.792609 | + | 18.6390i | 0.0261173 | + | 0.614176i | ||||
\(922\) | 51.1331 | + | 51.1331i | 1.68398 | + | 1.68398i | ||||
\(923\) | −2.80154 | − | 2.80154i | −0.0922139 | − | 0.0922139i | ||||
\(924\) | 1.40738 | + | 33.0959i | 0.0462993 | + | 1.08877i | ||||
\(925\) | 17.9403 | + | 8.44113i | 0.589874 | + | 0.277543i | ||||
\(926\) | − | 26.1324i | − | 0.858766i | ||||||
\(927\) | 7.22082 | + | 6.08696i | 0.237163 | + | 0.199922i | ||||
\(928\) | −2.30785 | + | 2.30785i | −0.0757588 | + | 0.0757588i | ||||
\(929\) | 34.5433 | 1.13333 | 0.566664 | − | 0.823949i | \(-0.308234\pi\) | ||||
0.566664 | + | 0.823949i | \(0.308234\pi\) | |||||||
\(930\) | −2.03653 | − | 9.31208i | −0.0667805 | − | 0.305355i | ||||
\(931\) | 16.9328 | 0.554951 | ||||||||
\(932\) | 25.6200 | − | 25.6200i | 0.839210 | − | 0.839210i | ||||
\(933\) | −8.97146 | + | 9.76836i | −0.293713 | + | 0.319802i | ||||
\(934\) | − | 78.3320i | − | 2.56310i | ||||||
\(935\) | −15.7601 | + | 22.4254i | −0.515411 | + | 0.733389i | ||||
\(936\) | 4.32440 | + | 50.7545i | 0.141348 | + | 1.65896i | ||||
\(937\) | 32.2161 | + | 32.2161i | 1.05245 | + | 1.05245i | 0.998546 | + | 0.0539082i | \(0.0171678\pi\) |
0.0539082 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(938\) | 18.2273 | + | 18.2273i | 0.595142 | + | 0.595142i | ||||
\(939\) | −6.37237 | + | 0.270980i | −0.207954 | + | 0.00884309i | ||||
\(940\) | 21.0622 | − | 29.9698i | 0.686972 | − | 0.977507i | ||||
\(941\) | − | 19.8742i | − | 0.647879i | −0.946078 | − | 0.323939i | \(-0.894993\pi\) | ||
0.946078 | − | 0.323939i | \(-0.105007\pi\) | |||||||
\(942\) | 68.3301 | + | 62.7558i | 2.22632 | + | 2.04469i | ||||
\(943\) | −1.01154 | + | 1.01154i | −0.0329403 | + | 0.0329403i | ||||
\(944\) | 54.4659 | 1.77271 | ||||||||
\(945\) | −6.33004 | − | 20.4412i | −0.205916 | − | 0.664953i | ||||
\(946\) | −67.5195 | −2.19525 | ||||||||
\(947\) | 16.6962 | − | 16.6962i | 0.542555 | − | 0.542555i | −0.381722 | − | 0.924277i | \(-0.624669\pi\) |
0.924277 | + | 0.381722i | \(0.124669\pi\) | |||||||
\(948\) | 23.1124 | + | 21.2269i | 0.750655 | + | 0.689417i | ||||
\(949\) | − | 18.3448i | − | 0.595498i | ||||||
\(950\) | 52.2573 | + | 24.5877i | 1.69545 | + | 0.797729i | ||||
\(951\) | −21.9744 | + | 0.934443i | −0.712569 | + | 0.0303014i | ||||
\(952\) | 31.5853 | + | 31.5853i | 1.02368 | + | 1.02368i | ||||
\(953\) | 1.45649 | + | 1.45649i | 0.0471804 | + | 0.0471804i | 0.730303 | − | 0.683123i | \(-0.239379\pi\) |
−0.683123 | + | 0.730303i | \(0.739379\pi\) | |||||||
\(954\) | −2.95680 | − | 34.7033i | −0.0957301 | − | 1.12356i | ||||
\(955\) | 13.5896 | − | 2.37207i | 0.439750 | − | 0.0767585i | ||||
\(956\) | 24.5715i | 0.794699i | ||||||||
\(957\) | 17.0477 | − | 18.5620i | 0.551074 | − | 0.600023i | ||||
\(958\) | 25.0246 | − | 25.0246i | 0.808508 | − | 0.808508i | ||||
\(959\) | −37.6205 | −1.21483 | ||||||||
\(960\) | 23.7479 | + | 15.2247i | 0.766459 | + | 0.491374i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 23.1397 | − | 23.1397i | 0.746054 | − | 0.746054i | ||||
\(963\) | −6.04541 | − | 5.09612i | −0.194811 | − | 0.164220i | ||||
\(964\) | 78.8035i | 2.53809i | ||||||||
\(965\) | −35.7733 | − | 25.1407i | −1.15158 | − | 0.809309i | ||||
\(966\) | 0.126673 | + | 2.97885i | 0.00407565 | + | 0.0958430i | ||||
\(967\) | 3.93466 | + | 3.93466i | 0.126530 | + | 0.126530i | 0.767536 | − | 0.641006i | \(-0.221483\pi\) |
−0.641006 | + | 0.767536i | \(0.721483\pi\) | |||||||
\(968\) | 15.9337 | + | 15.9337i | 0.512130 | + | 0.512130i | ||||
\(969\) | 1.65407 | + | 38.8971i | 0.0531362 | + | 1.24955i | ||||
\(970\) | −18.3095 | − | 104.895i | −0.587882 | − | 3.36798i | ||||
\(971\) | 50.7595i | 1.62895i | 0.580199 | + | 0.814475i | \(0.302975\pi\) | ||||
−0.580199 | + | 0.814475i | \(0.697025\pi\) | |||||||
\(972\) | −34.2863 | + | 53.1508i | −1.09973 | + | 1.70481i | ||||
\(973\) | −26.0956 | + | 26.0956i | −0.836587 | + | 0.836587i | ||||
\(974\) | 34.4830 | 1.10491 | ||||||||
\(975\) | −26.8785 | + | 10.9894i | −0.860802 | + | 0.351944i | ||||
\(976\) | 33.8938 | 1.08491 | ||||||||
\(977\) | −18.6011 | + | 18.6011i | −0.595101 | + | 0.595101i | −0.939005 | − | 0.343904i | \(-0.888251\pi\) |
0.343904 | + | 0.939005i | \(0.388251\pi\) | |||||||
\(978\) | −61.5585 | + | 67.0264i | −1.96842 | + | 2.14327i | ||||
\(979\) | 42.1407i | 1.34682i | ||||||||
\(980\) | −5.62883 | − | 32.2476i | −0.179806 | − | 1.03011i | ||||
\(981\) | −55.7820 | + | 4.75276i | −1.78098 | + | 0.151744i | ||||
\(982\) | −28.6310 | − | 28.6310i | −0.913652 | − | 0.913652i | ||||
\(983\) | −7.45897 | − | 7.45897i | −0.237904 | − | 0.237904i | 0.578078 | − | 0.815982i | \(-0.303803\pi\) |
−0.815982 | + | 0.578078i | \(0.803803\pi\) | |||||||
\(984\) | 33.0096 | − | 1.40370i | 1.05231 | − | 0.0447485i | ||||
\(985\) | 26.4495 | + | 18.5882i | 0.842752 | + | 0.592269i | ||||
\(986\) | − | 67.0191i | − | 2.13432i | ||||||
\(987\) | 9.48563 | + | 8.71180i | 0.301931 | + | 0.277300i | ||||
\(988\) | 45.1481 | − | 45.1481i | 1.43635 | − | 1.43635i | ||||
\(989\) | −4.07070 | −0.129441 | ||||||||
\(990\) | 36.5091 | + | 21.2734i | 1.16034 | + | 0.676112i | ||||
\(991\) | −9.46326 | −0.300610 | −0.150305 | − | 0.988640i | \(-0.548026\pi\) | ||||
−0.150305 | + | 0.988640i | \(0.548026\pi\) | |||||||
\(992\) | 0.405926 | − | 0.405926i | 0.0128882 | − | 0.0128882i | ||||
\(993\) | −1.69275 | − | 1.55465i | −0.0537176 | − | 0.0493354i | ||||
\(994\) | 5.35602i | 0.169883i | ||||||||
\(995\) | 7.01725 | − | 1.22486i | 0.222462 | − | 0.0388308i | ||||
\(996\) | 40.0102 | − | 1.70140i | 1.26777 | − | 0.0539109i | ||||
\(997\) | 31.8233 | + | 31.8233i | 1.00785 | + | 1.00785i | 0.999969 | + | 0.00788547i | \(0.00251005\pi\) |
0.00788547 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(998\) | −24.7288 | − | 24.7288i | −0.782778 | − | 0.782778i | ||||
\(999\) | 20.4375 | − | 2.61991i | 0.646615 | − | 0.0828902i |
(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 | 465.2.k.a.32.3 | ✓ | 60 | |
3.2 | odd | 2 | inner | 465.2.k.a.32.28 | yes | 60 | |
5.3 | odd | 4 | inner | 465.2.k.a.218.28 | yes | 60 | |
15.8 | even | 4 | inner | 465.2.k.a.218.3 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
465.2.k.a.32.3 | ✓ | 60 | 1.1 | even | 1 | trivial | |
465.2.k.a.32.28 | yes | 60 | 3.2 | odd | 2 | inner | |
465.2.k.a.218.3 | yes | 60 | 15.8 | even | 4 | inner | |
465.2.k.a.218.28 | yes | 60 | 5.3 | odd | 4 | inner |