Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(267,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, 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("380.267");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 267.5 | ||
Character | \(\chi\) | \(=\) | 380.267 |
Dual form | 380.2.k.d.343.5 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23831 | + | 0.683080i | −0.875614 | + | 0.483011i | ||||
\(3\) | 0.494605 | + | 0.494605i | 0.285560 | + | 0.285560i | 0.835322 | − | 0.549762i | \(-0.185281\pi\) |
−0.549762 | + | 0.835322i | \(0.685281\pi\) | |||||||
\(4\) | 1.06680 | − | 1.69172i | 0.533401 | − | 0.845862i | ||||
\(5\) | 1.31079 | − | 1.81158i | 0.586204 | − | 0.810164i | ||||
\(6\) | −0.950327 | − | 0.274617i | −0.387969 | − | 0.112112i | ||||
\(7\) | −0.327577 | + | 0.327577i | −0.123813 | + | 0.123813i | −0.766298 | − | 0.642485i | \(-0.777903\pi\) |
0.642485 | + | 0.766298i | \(0.277903\pi\) | |||||||
\(8\) | −0.165443 | + | 2.82358i | −0.0584930 | + | 0.998288i | ||||
\(9\) | − | 2.51073i | − | 0.836911i | ||||||
\(10\) | −0.385706 | + | 3.13867i | −0.121971 | + | 0.992534i | ||||
\(11\) | − | 2.94834i | − | 0.888958i | −0.895789 | − | 0.444479i | \(-0.853389\pi\) | ||
0.895789 | − | 0.444479i | \(-0.146611\pi\) | |||||||
\(12\) | 1.36438 | − | 0.309090i | 0.393863 | − | 0.0892265i | ||||
\(13\) | 0.287718 | − | 0.287718i | 0.0797987 | − | 0.0797987i | −0.666081 | − | 0.745880i | \(-0.732029\pi\) |
0.745880 | + | 0.666081i | \(0.232029\pi\) | |||||||
\(14\) | 0.181879 | − | 0.629402i | 0.0486092 | − | 0.168215i | ||||
\(15\) | 1.54434 | − | 0.247693i | 0.398747 | − | 0.0639539i | ||||
\(16\) | −1.72387 | − | 3.60947i | −0.430966 | − | 0.902368i | ||||
\(17\) | −1.74168 | − | 1.74168i | −0.422419 | − | 0.422419i | 0.463617 | − | 0.886036i | \(-0.346551\pi\) |
−0.886036 | + | 0.463617i | \(0.846551\pi\) | |||||||
\(18\) | 1.71503 | + | 3.10905i | 0.404237 | + | 0.732811i | ||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −1.66634 | − | 4.15010i | −0.372605 | − | 0.927990i | ||||
\(21\) | −0.324042 | −0.0707118 | ||||||||
\(22\) | 2.01395 | + | 3.65095i | 0.429376 | + | 0.778384i | ||||
\(23\) | −0.570036 | − | 0.570036i | −0.118861 | − | 0.118861i | 0.645175 | − | 0.764035i | \(-0.276785\pi\) |
−0.764035 | + | 0.645175i | \(0.776785\pi\) | |||||||
\(24\) | −1.47839 | + | 1.31473i | −0.301774 | + | 0.268368i | ||||
\(25\) | −1.56365 | − | 4.74921i | −0.312730 | − | 0.949842i | ||||
\(26\) | −0.159749 | + | 0.552818i | −0.0313293 | + | 0.108417i | ||||
\(27\) | 2.72563 | − | 2.72563i | 0.524549 | − | 0.524549i | ||||
\(28\) | 0.204710 | + | 0.903630i | 0.0386866 | + | 0.170770i | ||||
\(29\) | − | 1.85155i | − | 0.343824i | −0.985112 | − | 0.171912i | \(-0.945006\pi\) | ||
0.985112 | − | 0.171912i | \(-0.0549945\pi\) | |||||||
\(30\) | −1.74317 | + | 1.36163i | −0.318258 | + | 0.248598i | ||||
\(31\) | 1.12279i | 0.201659i | 0.994904 | + | 0.100829i | \(0.0321496\pi\) | ||||
−0.994904 | + | 0.100829i | \(0.967850\pi\) | |||||||
\(32\) | 4.60023 | + | 3.29209i | 0.813214 | + | 0.581965i | ||||
\(33\) | 1.45826 | − | 1.45826i | 0.253851 | − | 0.253851i | ||||
\(34\) | 3.34643 | + | 0.967023i | 0.573909 | + | 0.165843i | ||||
\(35\) | 0.164047 | + | 1.02282i | 0.0277290 | + | 0.172888i | ||||
\(36\) | −4.24747 | − | 2.67846i | −0.707911 | − | 0.446409i | ||||
\(37\) | 4.08314 | + | 4.08314i | 0.671264 | + | 0.671264i | 0.958007 | − | 0.286743i | \(-0.0925727\pi\) |
−0.286743 | + | 0.958007i | \(0.592573\pi\) | |||||||
\(38\) | 1.23831 | − | 0.683080i | 0.200880 | − | 0.110810i | ||||
\(39\) | 0.284614 | 0.0455747 | ||||||||
\(40\) | 4.89829 | + | 4.00085i | 0.774488 | + | 0.632589i | ||||
\(41\) | 10.4815 | 1.63694 | 0.818470 | − | 0.574550i | \(-0.194823\pi\) | ||||
0.818470 | + | 0.574550i | \(0.194823\pi\) | |||||||
\(42\) | 0.401264 | − | 0.221347i | 0.0619163 | − | 0.0341546i | ||||
\(43\) | 7.09760 | + | 7.09760i | 1.08237 | + | 1.08237i | 0.996288 | + | 0.0860866i | \(0.0274362\pi\) |
0.0860866 | + | 0.996288i | \(0.472564\pi\) | |||||||
\(44\) | −4.98778 | − | 3.14530i | −0.751936 | − | 0.474171i | ||||
\(45\) | −4.54839 | − | 3.29105i | −0.678035 | − | 0.490600i | ||||
\(46\) | 1.09526 | + | 0.316498i | 0.161487 | + | 0.0466651i | ||||
\(47\) | 2.57471 | − | 2.57471i | 0.375559 | − | 0.375559i | −0.493938 | − | 0.869497i | \(-0.664443\pi\) |
0.869497 | + | 0.493938i | \(0.164443\pi\) | |||||||
\(48\) | 0.932630 | − | 2.63789i | 0.134613 | − | 0.380747i | ||||
\(49\) | 6.78539i | 0.969341i | ||||||||
\(50\) | 5.18037 | + | 4.81288i | 0.732615 | + | 0.680643i | ||||
\(51\) | − | 1.72288i | − | 0.241252i | ||||||
\(52\) | −0.179802 | − | 0.793679i | −0.0249340 | − | 0.110063i | ||||
\(53\) | 5.67543 | − | 5.67543i | 0.779580 | − | 0.779580i | −0.200180 | − | 0.979759i | \(-0.564153\pi\) |
0.979759 | + | 0.200180i | \(0.0641525\pi\) | |||||||
\(54\) | −1.51334 | + | 5.23700i | −0.205940 | + | 0.712665i | ||||
\(55\) | −5.34116 | − | 3.86466i | −0.720201 | − | 0.521111i | ||||
\(56\) | −0.870746 | − | 0.979137i | −0.116358 | − | 0.130843i | ||||
\(57\) | −0.494605 | − | 0.494605i | −0.0655120 | − | 0.0655120i | ||||
\(58\) | 1.26476 | + | 2.29278i | 0.166071 | + | 0.301057i | ||||
\(59\) | −14.1245 | −1.83885 | −0.919425 | − | 0.393265i | \(-0.871345\pi\) | ||||
−0.919425 | + | 0.393265i | \(0.871345\pi\) | |||||||
\(60\) | 1.22848 | − | 2.87684i | 0.158596 | − | 0.371398i | ||||
\(61\) | 7.69452 | 0.985182 | 0.492591 | − | 0.870261i | \(-0.336050\pi\) | ||||
0.492591 | + | 0.870261i | \(0.336050\pi\) | |||||||
\(62\) | −0.766955 | − | 1.39036i | −0.0974034 | − | 0.176575i | ||||
\(63\) | 0.822459 | + | 0.822459i | 0.103620 | + | 0.103620i | ||||
\(64\) | −7.94526 | − | 0.934286i | −0.993157 | − | 0.116786i | ||||
\(65\) | −0.144086 | − | 0.898364i | −0.0178717 | − | 0.111428i | ||||
\(66\) | −0.809664 | + | 2.80189i | −0.0996628 | + | 0.344888i | ||||
\(67\) | −9.51194 | + | 9.51194i | −1.16207 | + | 1.16207i | −0.178047 | + | 0.984022i | \(0.556978\pi\) |
−0.984022 | + | 0.178047i | \(0.943022\pi\) | |||||||
\(68\) | −4.80446 | + | 1.08841i | −0.582627 | + | 0.131990i | ||||
\(69\) | − | 0.563885i | − | 0.0678837i | ||||||
\(70\) | −0.901807 | − | 1.15450i | −0.107787 | − | 0.137990i | ||||
\(71\) | − | 9.19745i | − | 1.09154i | −0.837936 | − | 0.545768i | \(-0.816238\pi\) | ||
0.837936 | − | 0.545768i | \(-0.183762\pi\) | |||||||
\(72\) | 7.08926 | + | 0.415384i | 0.835478 | + | 0.0489535i | ||||
\(73\) | −4.82935 | + | 4.82935i | −0.565233 | + | 0.565233i | −0.930789 | − | 0.365556i | \(-0.880879\pi\) |
0.365556 | + | 0.930789i | \(0.380879\pi\) | |||||||
\(74\) | −7.84529 | − | 2.26706i | −0.911996 | − | 0.263541i | ||||
\(75\) | 1.57559 | − | 3.12237i | 0.181934 | − | 0.360540i | ||||
\(76\) | −1.06680 | + | 1.69172i | −0.122371 | + | 0.194054i | ||||
\(77\) | 0.965809 | + | 0.965809i | 0.110064 | + | 0.110064i | ||||
\(78\) | −0.352439 | + | 0.194414i | −0.0399058 | + | 0.0220131i | ||||
\(79\) | −0.164126 | −0.0184656 | −0.00923281 | − | 0.999957i | \(-0.502939\pi\) | ||||
−0.00923281 | + | 0.999957i | \(0.502939\pi\) | |||||||
\(80\) | −8.79848 | − | 1.60834i | −0.983700 | − | 0.179818i | ||||
\(81\) | −4.83597 | −0.537331 | ||||||||
\(82\) | −12.9793 | + | 7.15972i | −1.43333 | + | 0.790659i | ||||
\(83\) | −1.98305 | − | 1.98305i | −0.217667 | − | 0.217667i | 0.589847 | − | 0.807515i | \(-0.299188\pi\) |
−0.807515 | + | 0.589847i | \(0.799188\pi\) | |||||||
\(84\) | −0.345689 | + | 0.548191i | −0.0377178 | + | 0.0598125i | ||||
\(85\) | −5.43817 | + | 0.872213i | −0.589852 | + | 0.0946048i | ||||
\(86\) | −13.6372 | − | 3.94077i | −1.47054 | − | 0.424944i | ||||
\(87\) | 0.915785 | − | 0.915785i | 0.0981825 | − | 0.0981825i | ||||
\(88\) | 8.32489 | + | 0.487783i | 0.887436 | + | 0.0519979i | ||||
\(89\) | 2.27564i | 0.241218i | 0.992700 | + | 0.120609i | \(0.0384847\pi\) | ||||
−0.992700 | + | 0.120609i | \(0.961515\pi\) | |||||||
\(90\) | 7.88035 | + | 0.968404i | 0.830662 | + | 0.102079i | ||||
\(91\) | 0.188500i | 0.0197602i | ||||||||
\(92\) | −1.57246 | + | 0.356228i | −0.163940 | + | 0.0371393i | ||||
\(93\) | −0.555337 | + | 0.555337i | −0.0575857 | + | 0.0575857i | ||||
\(94\) | −1.42954 | + | 4.94700i | −0.147446 | + | 0.510244i | ||||
\(95\) | −1.31079 | + | 1.81158i | −0.134484 | + | 0.185864i | ||||
\(96\) | 0.647013 | + | 3.90358i | 0.0660355 | + | 0.398407i | ||||
\(97\) | −4.13745 | − | 4.13745i | −0.420095 | − | 0.420095i | 0.465141 | − | 0.885236i | \(-0.346003\pi\) |
−0.885236 | + | 0.465141i | \(0.846003\pi\) | |||||||
\(98\) | −4.63496 | − | 8.40238i | −0.468202 | − | 0.848769i | ||||
\(99\) | −7.40249 | −0.743978 | ||||||||
\(100\) | −9.70246 | − | 2.42120i | −0.970246 | − | 0.242120i | ||||
\(101\) | 4.60617 | 0.458331 | 0.229165 | − | 0.973387i | \(-0.426400\pi\) | ||||
0.229165 | + | 0.973387i | \(0.426400\pi\) | |||||||
\(102\) | 1.17687 | + | 2.13346i | 0.116527 | + | 0.211244i | ||||
\(103\) | 10.8229 | + | 10.8229i | 1.06641 | + | 1.06641i | 0.997632 | + | 0.0687770i | \(0.0219097\pi\) |
0.0687770 | + | 0.997632i | \(0.478090\pi\) | |||||||
\(104\) | 0.764796 | + | 0.859998i | 0.0749944 | + | 0.0843298i | ||||
\(105\) | −0.424752 | + | 0.587029i | −0.0414516 | + | 0.0572882i | ||||
\(106\) | −3.15114 | + | 10.9047i | −0.306066 | + | 1.05916i | ||||
\(107\) | −5.10887 | + | 5.10887i | −0.493893 | + | 0.493893i | −0.909530 | − | 0.415637i | \(-0.863559\pi\) |
0.415637 | + | 0.909530i | \(0.363559\pi\) | |||||||
\(108\) | −1.70331 | − | 7.51874i | −0.163901 | − | 0.723491i | ||||
\(109\) | 5.24030i | 0.501930i | 0.967996 | + | 0.250965i | \(0.0807479\pi\) | ||||
−0.967996 | + | 0.250965i | \(0.919252\pi\) | |||||||
\(110\) | 9.25386 | + | 1.13719i | 0.882321 | + | 0.108427i | ||||
\(111\) | 4.03908i | 0.383372i | ||||||||
\(112\) | 1.74708 | + | 0.617681i | 0.165083 | + | 0.0583654i | ||||
\(113\) | −9.13170 | + | 9.13170i | −0.859038 | + | 0.859038i | −0.991225 | − | 0.132186i | \(-0.957800\pi\) |
0.132186 | + | 0.991225i | \(0.457800\pi\) | |||||||
\(114\) | 0.950327 | + | 0.274617i | 0.0890062 | + | 0.0257202i | ||||
\(115\) | −1.77986 | + | 0.285468i | −0.165973 | + | 0.0266200i | ||||
\(116\) | −3.13231 | − | 1.97524i | −0.290828 | − | 0.183396i | ||||
\(117\) | −0.722384 | − | 0.722384i | −0.0667844 | − | 0.0667844i | ||||
\(118\) | 17.4904 | − | 9.64815i | 1.61012 | − | 0.888185i | ||||
\(119\) | 1.14107 | 0.104601 | ||||||||
\(120\) | 0.443880 | + | 4.40155i | 0.0405205 | + | 0.401805i | ||||
\(121\) | 2.30729 | 0.209754 | ||||||||
\(122\) | −9.52816 | + | 5.25597i | −0.862639 | + | 0.475853i | ||||
\(123\) | 5.18421 | + | 5.18421i | 0.467445 | + | 0.467445i | ||||
\(124\) | 1.89945 | + | 1.19779i | 0.170576 | + | 0.107565i | ||||
\(125\) | −10.6532 | − | 3.39255i | −0.952851 | − | 0.303439i | ||||
\(126\) | −1.58026 | − | 0.456650i | −0.140781 | − | 0.0406816i | ||||
\(127\) | 0.359207 | − | 0.359207i | 0.0318744 | − | 0.0318744i | −0.690990 | − | 0.722864i | \(-0.742825\pi\) |
0.722864 | + | 0.690990i | \(0.242825\pi\) | |||||||
\(128\) | 10.4769 | − | 4.27032i | 0.926031 | − | 0.377446i | ||||
\(129\) | 7.02101i | 0.618166i | ||||||||
\(130\) | 0.792078 | + | 1.01403i | 0.0694698 | + | 0.0889360i | ||||
\(131\) | − | 7.07602i | − | 0.618235i | −0.951024 | − | 0.309117i | \(-0.899966\pi\) | ||
0.951024 | − | 0.309117i | \(-0.100034\pi\) | |||||||
\(132\) | −0.911301 | − | 4.02266i | −0.0793186 | − | 0.350127i | ||||
\(133\) | 0.327577 | − | 0.327577i | 0.0284045 | − | 0.0284045i | ||||
\(134\) | 5.28127 | − | 18.2761i | 0.456232 | − | 1.57882i | ||||
\(135\) | −1.36497 | − | 8.51044i | −0.117478 | − | 0.732462i | ||||
\(136\) | 5.20592 | − | 4.62962i | 0.446404 | − | 0.396987i | ||||
\(137\) | 4.32753 | + | 4.32753i | 0.369726 | + | 0.369726i | 0.867377 | − | 0.497651i | \(-0.165804\pi\) |
−0.497651 | + | 0.867377i | \(0.665804\pi\) | |||||||
\(138\) | 0.385178 | + | 0.698261i | 0.0327886 | + | 0.0594400i | ||||
\(139\) | 11.4346 | 0.969873 | 0.484937 | − | 0.874549i | \(-0.338843\pi\) | ||||
0.484937 | + | 0.874549i | \(0.338843\pi\) | |||||||
\(140\) | 1.90533 | + | 0.813622i | 0.161030 | + | 0.0687636i | ||||
\(141\) | 2.54692 | 0.214490 | ||||||||
\(142\) | 6.28260 | + | 11.3893i | 0.527224 | + | 0.955765i | ||||
\(143\) | −0.848292 | − | 0.848292i | −0.0709377 | − | 0.0709377i | ||||
\(144\) | −9.06242 | + | 4.32817i | −0.755201 | + | 0.360680i | ||||
\(145\) | −3.35423 | − | 2.42700i | −0.278554 | − | 0.201551i | ||||
\(146\) | 2.68138 | − | 9.27905i | 0.221912 | − | 0.767939i | ||||
\(147\) | −3.35608 | + | 3.35608i | −0.276805 | + | 0.276805i | ||||
\(148\) | 11.2635 | − | 2.55165i | 0.925850 | − | 0.209744i | ||||
\(149\) | 13.1136i | 1.07431i | 0.843484 | + | 0.537155i | \(0.180501\pi\) | ||||
−0.843484 | + | 0.537155i | \(0.819499\pi\) | |||||||
\(150\) | 0.181764 | + | 4.94271i | 0.0148409 | + | 0.403570i | ||||
\(151\) | 2.25997i | 0.183914i | 0.995763 | + | 0.0919569i | \(0.0293122\pi\) | ||||
−0.995763 | + | 0.0919569i | \(0.970688\pi\) | |||||||
\(152\) | 0.165443 | − | 2.82358i | 0.0134192 | − | 0.229023i | ||||
\(153\) | −4.37289 | + | 4.37289i | −0.353527 | + | 0.353527i | ||||
\(154\) | −1.85569 | − | 0.536242i | −0.149536 | − | 0.0432116i | ||||
\(155\) | 2.03402 | + | 1.47174i | 0.163377 | + | 0.118213i | ||||
\(156\) | 0.303627 | − | 0.481488i | 0.0243096 | − | 0.0385499i | ||||
\(157\) | −11.4604 | − | 11.4604i | −0.914642 | − | 0.914642i | 0.0819909 | − | 0.996633i | \(-0.473872\pi\) |
−0.996633 | + | 0.0819909i | \(0.973872\pi\) | |||||||
\(158\) | 0.203238 | − | 0.112111i | 0.0161688 | − | 0.00891909i | ||||
\(159\) | 5.61418 | 0.445234 | ||||||||
\(160\) | 11.9938 | − | 4.01845i | 0.948196 | − | 0.317686i | ||||
\(161\) | 0.373461 | 0.0294329 | ||||||||
\(162\) | 5.98842 | − | 3.30336i | 0.470494 | − | 0.259536i | ||||
\(163\) | −10.4983 | − | 10.4983i | −0.822289 | − | 0.822289i | 0.164147 | − | 0.986436i | \(-0.447513\pi\) |
−0.986436 | + | 0.164147i | \(0.947513\pi\) | |||||||
\(164\) | 11.1817 | − | 17.7319i | 0.873145 | − | 1.38463i | ||||
\(165\) | −0.730282 | − | 4.55324i | −0.0568524 | − | 0.354469i | ||||
\(166\) | 3.81020 | + | 1.10104i | 0.295729 | + | 0.0854570i | ||||
\(167\) | 15.9796 | − | 15.9796i | 1.23654 | − | 1.23654i | 0.275136 | − | 0.961405i | \(-0.411277\pi\) |
0.961405 | − | 0.275136i | \(-0.0887228\pi\) | |||||||
\(168\) | 0.0536106 | − | 0.914961i | 0.00413615 | − | 0.0705908i | ||||
\(169\) | 12.8344i | 0.987264i | ||||||||
\(170\) | 6.13832 | − | 4.79477i | 0.470788 | − | 0.367742i | ||||
\(171\) | 2.51073i | 0.192001i | ||||||||
\(172\) | 19.5789 | − | 4.43545i | 1.49288 | − | 0.338200i | ||||
\(173\) | −12.7302 | + | 12.7302i | −0.967858 | + | 0.967858i | −0.999499 | − | 0.0316413i | \(-0.989927\pi\) |
0.0316413 | + | 0.999499i | \(0.489927\pi\) | |||||||
\(174\) | −0.508467 | + | 1.75958i | −0.0385468 | + | 0.133393i | ||||
\(175\) | 2.06795 | + | 1.04352i | 0.156322 | + | 0.0788825i | ||||
\(176\) | −10.6419 | + | 5.08254i | −0.802167 | + | 0.383111i | ||||
\(177\) | −6.98603 | − | 6.98603i | −0.525102 | − | 0.525102i | ||||
\(178\) | −1.55445 | − | 2.81794i | −0.116511 | − | 0.211214i | ||||
\(179\) | 3.57919 | 0.267522 | 0.133761 | − | 0.991014i | \(-0.457295\pi\) | ||||
0.133761 | + | 0.991014i | \(0.457295\pi\) | |||||||
\(180\) | −10.4198 | + | 4.18373i | −0.776645 | + | 0.311837i | ||||
\(181\) | −7.40488 | −0.550400 | −0.275200 | − | 0.961387i | \(-0.588744\pi\) | ||||
−0.275200 | + | 0.961387i | \(0.588744\pi\) | |||||||
\(182\) | −0.128761 | − | 0.233421i | −0.00954437 | − | 0.0173023i | ||||
\(183\) | 3.80574 | + | 3.80574i | 0.281329 | + | 0.281329i | ||||
\(184\) | 1.70385 | − | 1.51523i | 0.125610 | − | 0.111705i | ||||
\(185\) | 12.7491 | − | 2.04479i | 0.937331 | − | 0.150336i | ||||
\(186\) | 0.308337 | − | 1.06702i | 0.0226084 | − | 0.0782374i | ||||
\(187\) | −5.13506 | + | 5.13506i | −0.375513 | + | 0.375513i | ||||
\(188\) | −1.60899 | − | 7.10239i | −0.117348 | − | 0.517995i | ||||
\(189\) | 1.78571i | 0.129891i | ||||||||
\(190\) | 0.385706 | − | 3.13867i | 0.0279820 | − | 0.227703i | ||||
\(191\) | 4.12918i | 0.298777i | 0.988779 | + | 0.149388i | \(0.0477304\pi\) | ||||
−0.988779 | + | 0.149388i | \(0.952270\pi\) | |||||||
\(192\) | −3.46766 | − | 4.39186i | −0.250257 | − | 0.316955i | ||||
\(193\) | 5.54163 | − | 5.54163i | 0.398895 | − | 0.398895i | −0.478948 | − | 0.877843i | \(-0.658982\pi\) |
0.877843 | + | 0.478948i | \(0.158982\pi\) | |||||||
\(194\) | 7.94965 | + | 2.29722i | 0.570751 | + | 0.164931i | ||||
\(195\) | 0.373069 | − | 0.515601i | 0.0267161 | − | 0.0369229i | ||||
\(196\) | 11.4790 | + | 7.23867i | 0.819929 | + | 0.517048i | ||||
\(197\) | 5.86112 | + | 5.86112i | 0.417588 | + | 0.417588i | 0.884371 | − | 0.466784i | \(-0.154587\pi\) |
−0.466784 | + | 0.884371i | \(0.654587\pi\) | |||||||
\(198\) | 9.16655 | − | 5.05650i | 0.651438 | − | 0.359350i | ||||
\(199\) | 14.7472 | 1.04540 | 0.522701 | − | 0.852516i | \(-0.324924\pi\) | ||||
0.522701 | + | 0.852516i | \(0.324924\pi\) | |||||||
\(200\) | 13.6685 | − | 3.62937i | 0.966508 | − | 0.256635i | ||||
\(201\) | −9.40930 | −0.663681 | ||||||||
\(202\) | −5.70385 | + | 3.14638i | −0.401321 | + | 0.221379i | ||||
\(203\) | 0.606525 | + | 0.606525i | 0.0425697 | + | 0.0425697i | ||||
\(204\) | −2.91464 | − | 1.83798i | −0.204066 | − | 0.128684i | ||||
\(205\) | 13.7391 | − | 18.9881i | 0.959580 | − | 1.32619i | ||||
\(206\) | −20.7949 | − | 6.00913i | −1.44885 | − | 0.418676i | ||||
\(207\) | −1.43121 | + | 1.43121i | −0.0994757 | + | 0.0994757i | ||||
\(208\) | −1.53450 | − | 0.542524i | −0.106398 | − | 0.0376172i | ||||
\(209\) | 2.94834i | 0.203941i | ||||||||
\(210\) | 0.124985 | − | 1.01706i | 0.00862478 | − | 0.0701839i | ||||
\(211\) | 3.44024i | 0.236836i | 0.992964 | + | 0.118418i | \(0.0377822\pi\) | ||||
−0.992964 | + | 0.118418i | \(0.962218\pi\) | |||||||
\(212\) | −3.54670 | − | 15.6558i | −0.243588 | − | 1.07525i | ||||
\(213\) | 4.54910 | − | 4.54910i | 0.311699 | − | 0.311699i | ||||
\(214\) | 2.83657 | − | 9.81611i | 0.193904 | − | 0.671015i | ||||
\(215\) | 22.1614 | − | 3.55440i | 1.51139 | − | 0.242408i | ||||
\(216\) | 7.24512 | + | 8.14700i | 0.492968 | + | 0.554333i | ||||
\(217\) | −0.367800 | − | 0.367800i | −0.0249679 | − | 0.0249679i | ||||
\(218\) | −3.57955 | − | 6.48910i | −0.242438 | − | 0.439497i | ||||
\(219\) | −4.77724 | −0.322816 | ||||||||
\(220\) | −12.2359 | + | 4.91294i | −0.824944 | + | 0.331230i | ||||
\(221\) | −1.00223 | −0.0674170 | ||||||||
\(222\) | −2.75902 | − | 5.00162i | −0.185173 | − | 0.335686i | ||||
\(223\) | 9.96172 | + | 9.96172i | 0.667086 | + | 0.667086i | 0.957040 | − | 0.289955i | \(-0.0936402\pi\) |
−0.289955 | + | 0.957040i | \(0.593640\pi\) | |||||||
\(224\) | −2.58534 | + | 0.428517i | −0.172741 | + | 0.0286315i | ||||
\(225\) | −11.9240 | + | 3.92591i | −0.794933 | + | 0.261727i | ||||
\(226\) | 5.07015 | − | 17.5455i | 0.337262 | − | 1.16711i | ||||
\(227\) | −8.44789 | + | 8.44789i | −0.560706 | + | 0.560706i | −0.929508 | − | 0.368802i | \(-0.879768\pi\) |
0.368802 | + | 0.929508i | \(0.379768\pi\) | |||||||
\(228\) | −1.36438 | + | 0.309090i | −0.0903583 | + | 0.0204700i | ||||
\(229\) | 8.64013i | 0.570956i | 0.958385 | + | 0.285478i | \(0.0921524\pi\) | ||||
−0.958385 | + | 0.285478i | \(0.907848\pi\) | |||||||
\(230\) | 2.00902 | − | 1.56929i | 0.132471 | − | 0.103476i | ||||
\(231\) | 0.955387i | 0.0628599i | ||||||||
\(232\) | 5.22801 | + | 0.306326i | 0.343235 | + | 0.0201113i | ||||
\(233\) | −4.54741 | + | 4.54741i | −0.297911 | + | 0.297911i | −0.840195 | − | 0.542284i | \(-0.817560\pi\) |
0.542284 | + | 0.840195i | \(0.317560\pi\) | |||||||
\(234\) | 1.38798 | + | 0.401086i | 0.0907350 | + | 0.0262198i | ||||
\(235\) | −1.28938 | − | 8.03919i | −0.0841101 | − | 0.524419i | ||||
\(236\) | −15.0680 | + | 23.8947i | −0.980845 | + | 1.55541i | ||||
\(237\) | −0.0811775 | − | 0.0811775i | −0.00527304 | − | 0.00527304i | ||||
\(238\) | −1.41299 | + | 0.779441i | −0.0915906 | + | 0.0505236i | ||||
\(239\) | 23.0971 | 1.49403 | 0.747013 | − | 0.664810i | \(-0.231487\pi\) | ||||
0.747013 | + | 0.664810i | \(0.231487\pi\) | |||||||
\(240\) | −3.55627 | − | 5.14726i | −0.229557 | − | 0.332254i | ||||
\(241\) | 19.8422 | 1.27815 | 0.639075 | − | 0.769145i | \(-0.279317\pi\) | ||||
0.639075 | + | 0.769145i | \(0.279317\pi\) | |||||||
\(242\) | −2.85713 | + | 1.57607i | −0.183663 | + | 0.101313i | ||||
\(243\) | −10.5688 | − | 10.5688i | −0.677989 | − | 0.677989i | ||||
\(244\) | 8.20853 | − | 13.0170i | 0.525497 | − | 0.833328i | ||||
\(245\) | 12.2923 | + | 8.89423i | 0.785325 | + | 0.568231i | ||||
\(246\) | −9.96087 | − | 2.87841i | −0.635082 | − | 0.183520i | ||||
\(247\) | −0.287718 | + | 0.287718i | −0.0183071 | + | 0.0183071i | ||||
\(248\) | −3.17029 | − | 0.185758i | −0.201314 | − | 0.0117956i | ||||
\(249\) | − | 1.96165i | − | 0.124314i | ||||||
\(250\) | 15.5093 | − | 3.07598i | 0.980894 | − | 0.194542i | ||||
\(251\) | − | 5.82734i | − | 0.367819i | −0.982943 | − | 0.183909i | \(-0.941125\pi\) | ||
0.982943 | − | 0.183909i | \(-0.0588753\pi\) | |||||||
\(252\) | 2.26877 | − | 0.513973i | 0.142919 | − | 0.0323772i | ||||
\(253\) | −1.68066 | + | 1.68066i | −0.105662 | + | 0.105662i | ||||
\(254\) | −0.199441 | + | 0.690175i | −0.0125140 | + | 0.0433054i | ||||
\(255\) | −3.12114 | − | 2.25834i | −0.195454 | − | 0.141423i | ||||
\(256\) | −10.0566 | + | 12.4445i | −0.628536 | + | 0.777781i | ||||
\(257\) | 6.18949 | + | 6.18949i | 0.386090 | + | 0.386090i | 0.873290 | − | 0.487200i | \(-0.161982\pi\) |
−0.487200 | + | 0.873290i | \(0.661982\pi\) | |||||||
\(258\) | −4.79592 | − | 8.69416i | −0.298581 | − | 0.541275i | ||||
\(259\) | −2.67509 | −0.166222 | ||||||||
\(260\) | −1.67350 | − | 0.714623i | −0.103786 | − | 0.0443190i | ||||
\(261\) | −4.64874 | −0.287750 | ||||||||
\(262\) | 4.83349 | + | 8.76227i | 0.298614 | + | 0.541335i | ||||
\(263\) | −8.45067 | − | 8.45067i | −0.521091 | − | 0.521091i | 0.396810 | − | 0.917901i | \(-0.370117\pi\) |
−0.917901 | + | 0.396810i | \(0.870117\pi\) | |||||||
\(264\) | 3.87627 | + | 4.35879i | 0.238568 | + | 0.268265i | ||||
\(265\) | −2.84219 | − | 17.7208i | −0.174594 | − | 1.08858i | ||||
\(266\) | −0.181879 | + | 0.629402i | −0.0111517 | + | 0.0385911i | ||||
\(267\) | −1.12554 | + | 1.12554i | −0.0688821 | + | 0.0688821i | ||||
\(268\) | 5.94423 | + | 26.2390i | 0.363101 | + | 1.60280i | ||||
\(269\) | − | 1.50260i | − | 0.0916154i | −0.998950 | − | 0.0458077i | \(-0.985414\pi\) | ||
0.998950 | − | 0.0458077i | \(-0.0145861\pi\) | |||||||
\(270\) | 7.50357 | + | 9.60615i | 0.456652 | + | 0.584612i | ||||
\(271\) | 29.6188i | 1.79921i | 0.436702 | + | 0.899606i | \(0.356146\pi\) | ||||
−0.436702 | + | 0.899606i | \(0.643854\pi\) | |||||||
\(272\) | −3.28412 | + | 9.28895i | −0.199129 | + | 0.563226i | ||||
\(273\) | −0.0932330 | + | 0.0932330i | −0.00564272 | + | 0.00564272i | ||||
\(274\) | −8.31485 | − | 2.40275i | −0.502319 | − | 0.145156i | ||||
\(275\) | −14.0023 | + | 4.61017i | −0.844370 | + | 0.278004i | ||||
\(276\) | −0.953937 | − | 0.601553i | −0.0574203 | − | 0.0362093i | ||||
\(277\) | −18.2366 | − | 18.2366i | −1.09573 | − | 1.09573i | −0.994904 | − | 0.100825i | \(-0.967852\pi\) |
−0.100825 | − | 0.994904i | \(-0.532148\pi\) | |||||||
\(278\) | −14.1596 | + | 7.81078i | −0.849235 | + | 0.468459i | ||||
\(279\) | 2.81902 | 0.168771 | ||||||||
\(280\) | −2.91515 | + | 0.293982i | −0.174214 | + | 0.0175688i | ||||
\(281\) | 16.2476 | 0.969249 | 0.484625 | − | 0.874722i | \(-0.338956\pi\) | ||||
0.484625 | + | 0.874722i | \(0.338956\pi\) | |||||||
\(282\) | −3.15387 | + | 1.73975i | −0.187810 | + | 0.103601i | ||||
\(283\) | −6.63046 | − | 6.63046i | −0.394140 | − | 0.394140i | 0.482020 | − | 0.876160i | \(-0.339903\pi\) |
−0.876160 | + | 0.482020i | \(0.839903\pi\) | |||||||
\(284\) | −15.5596 | − | 9.81186i | −0.923290 | − | 0.582227i | ||||
\(285\) | −1.54434 | + | 0.247693i | −0.0914788 | + | 0.0146720i | ||||
\(286\) | 1.62990 | + | 0.470993i | 0.0963778 | + | 0.0278504i | ||||
\(287\) | −3.43351 | + | 3.43351i | −0.202674 | + | 0.202674i | ||||
\(288\) | 8.26556 | − | 11.5500i | 0.487053 | − | 0.680587i | ||||
\(289\) | − | 10.9331i | − | 0.643125i | ||||||
\(290\) | 5.81140 | + | 0.714153i | 0.341257 | + | 0.0419365i | ||||
\(291\) | − | 4.09281i | − | 0.239925i | ||||||
\(292\) | 3.01797 | + | 13.3219i | 0.176613 | + | 0.779605i | ||||
\(293\) | −14.4511 | + | 14.4511i | −0.844244 | + | 0.844244i | −0.989408 | − | 0.145164i | \(-0.953629\pi\) |
0.145164 | + | 0.989408i | \(0.453629\pi\) | |||||||
\(294\) | 1.86338 | − | 6.44833i | 0.108675 | − | 0.376074i | ||||
\(295\) | −18.5142 | + | 25.5876i | −1.07794 | + | 1.48977i | ||||
\(296\) | −12.2046 | + | 10.8536i | −0.709379 | + | 0.630850i | ||||
\(297\) | −8.03610 | − | 8.03610i | −0.466302 | − | 0.466302i | ||||
\(298\) | −8.95765 | − | 16.2387i | −0.518903 | − | 0.940681i | ||||
\(299\) | −0.328019 | −0.0189699 | ||||||||
\(300\) | −3.60134 | − | 5.99642i | −0.207924 | − | 0.346204i | ||||
\(301\) | −4.65002 | −0.268023 | ||||||||
\(302\) | −1.54374 | − | 2.79853i | −0.0888323 | − | 0.161038i | ||||
\(303\) | 2.27823 | + | 2.27823i | 0.130881 | + | 0.130881i | ||||
\(304\) | 1.72387 | + | 3.60947i | 0.0988705 | + | 0.207017i | ||||
\(305\) | 10.0859 | − | 13.9392i | 0.577517 | − | 0.798158i | ||||
\(306\) | 2.42794 | − | 8.40200i | 0.138796 | − | 0.480310i | ||||
\(307\) | −11.3650 | + | 11.3650i | −0.648638 | + | 0.648638i | −0.952664 | − | 0.304026i | \(-0.901669\pi\) |
0.304026 | + | 0.952664i | \(0.401669\pi\) | |||||||
\(308\) | 2.66421 | − | 0.603556i | 0.151807 | − | 0.0343908i | ||||
\(309\) | 10.7061i | 0.609048i | ||||||||
\(310\) | −3.52406 | − | 0.433066i | −0.200153 | − | 0.0245965i | ||||
\(311\) | − | 31.6342i | − | 1.79381i | −0.442225 | − | 0.896904i | \(-0.645811\pi\) | ||
0.442225 | − | 0.896904i | \(-0.354189\pi\) | |||||||
\(312\) | −0.0470874 | + | 0.803631i | −0.00266580 | + | 0.0454966i | ||||
\(313\) | −4.11199 | + | 4.11199i | −0.232424 | + | 0.232424i | −0.813704 | − | 0.581280i | \(-0.802552\pi\) |
0.581280 | + | 0.813704i | \(0.302552\pi\) | |||||||
\(314\) | 22.0199 | + | 6.36312i | 1.24266 | + | 0.359092i | ||||
\(315\) | 2.56802 | − | 0.411878i | 0.144692 | − | 0.0232067i | ||||
\(316\) | −0.175090 | + | 0.277656i | −0.00984958 | + | 0.0156194i | ||||
\(317\) | 21.3697 | + | 21.3697i | 1.20024 | + | 1.20024i | 0.974093 | + | 0.226149i | \(0.0726137\pi\) |
0.226149 | + | 0.974093i | \(0.427386\pi\) | |||||||
\(318\) | −6.95208 | + | 3.83494i | −0.389853 | + | 0.215053i | ||||
\(319\) | −5.45900 | −0.305645 | ||||||||
\(320\) | −12.1071 | + | 13.1688i | −0.676808 | + | 0.736159i | ||||
\(321\) | −5.05374 | −0.282072 | ||||||||
\(322\) | −0.462459 | + | 0.255104i | −0.0257718 | + | 0.0142164i | ||||
\(323\) | 1.74168 | + | 1.74168i | 0.0969095 | + | 0.0969095i | ||||
\(324\) | −5.15903 | + | 8.18114i | −0.286613 | + | 0.454508i | ||||
\(325\) | −1.81633 | − | 0.916545i | −0.100752 | − | 0.0508407i | ||||
\(326\) | 20.1713 | + | 5.82891i | 1.11718 | + | 0.322834i | ||||
\(327\) | −2.59188 | + | 2.59188i | −0.143331 | + | 0.143331i | ||||
\(328\) | −1.73410 | + | 29.5955i | −0.0957496 | + | 1.63414i | ||||
\(329\) | 1.68683i | 0.0929979i | ||||||||
\(330\) | 4.01454 | + | 5.13946i | 0.220993 | + | 0.282918i | ||||
\(331\) | − | 28.8144i | − | 1.58378i | −0.610661 | − | 0.791892i | \(-0.709096\pi\) | ||
0.610661 | − | 0.791892i | \(-0.290904\pi\) | |||||||
\(332\) | −5.47028 | + | 1.23925i | −0.300221 | + | 0.0680127i | ||||
\(333\) | 10.2517 | − | 10.2517i | 0.561788 | − | 0.561788i | ||||
\(334\) | −8.87230 | + | 30.7030i | −0.485471 | + | 1.68000i | ||||
\(335\) | 4.76348 | + | 29.6998i | 0.260256 | + | 1.62268i | ||||
\(336\) | 0.558606 | + | 1.16962i | 0.0304744 | + | 0.0638081i | ||||
\(337\) | −13.4380 | − | 13.4380i | −0.732016 | − | 0.732016i | 0.239003 | − | 0.971019i | \(-0.423179\pi\) |
−0.971019 | + | 0.239003i | \(0.923179\pi\) | |||||||
\(338\) | −8.76695 | − | 15.8930i | −0.476859 | − | 0.864463i | ||||
\(339\) | −9.03317 | −0.490614 | ||||||||
\(340\) | −4.32590 | + | 10.1304i | −0.234605 | + | 0.549396i | ||||
\(341\) | 3.31036 | 0.179266 | ||||||||
\(342\) | −1.71503 | − | 3.10905i | −0.0927383 | − | 0.168118i | ||||
\(343\) | −4.51578 | − | 4.51578i | −0.243829 | − | 0.243829i | ||||
\(344\) | −21.2149 | + | 18.8664i | −1.14383 | + | 1.01721i | ||||
\(345\) | −1.02152 | − | 0.739135i | −0.0549969 | − | 0.0397937i | ||||
\(346\) | 7.06812 | − | 24.4596i | 0.379985 | − | 1.31496i | ||||
\(347\) | −19.6995 | + | 19.6995i | −1.05752 | + | 1.05752i | −0.0592835 | + | 0.998241i | \(0.518882\pi\) |
−0.998241 | + | 0.0592835i | \(0.981118\pi\) | |||||||
\(348\) | −0.572295 | − | 2.52622i | −0.0306782 | − | 0.135419i | ||||
\(349\) | − | 7.57450i | − | 0.405454i | −0.979235 | − | 0.202727i | \(-0.935020\pi\) | ||
0.979235 | − | 0.202727i | \(-0.0649804\pi\) | |||||||
\(350\) | −3.27356 | + | 0.120382i | −0.174979 | + | 0.00643470i | ||||
\(351\) | − | 1.56843i | − | 0.0837166i | ||||||
\(352\) | 9.70620 | − | 13.5630i | 0.517342 | − | 0.722913i | ||||
\(353\) | −12.3157 | + | 12.3157i | −0.655498 | + | 0.655498i | −0.954311 | − | 0.298814i | \(-0.903409\pi\) |
0.298814 | + | 0.954311i | \(0.403409\pi\) | |||||||
\(354\) | 13.4229 | + | 3.87882i | 0.713417 | + | 0.206157i | ||||
\(355\) | −16.6619 | − | 12.0559i | −0.884323 | − | 0.639863i | ||||
\(356\) | 3.84976 | + | 2.42766i | 0.204037 | + | 0.128666i | ||||
\(357\) | 0.564377 | + | 0.564377i | 0.0298700 | + | 0.0298700i | ||||
\(358\) | −4.43214 | + | 2.44488i | −0.234246 | + | 0.129216i | ||||
\(359\) | 23.4554 | 1.23793 | 0.618966 | − | 0.785418i | \(-0.287552\pi\) | ||||
0.618966 | + | 0.785418i | \(0.287552\pi\) | |||||||
\(360\) | 10.0451 | − | 12.2983i | 0.529421 | − | 0.648177i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 9.16950 | − | 5.05813i | 0.481938 | − | 0.265849i | ||||
\(363\) | 1.14120 | + | 1.14120i | 0.0598973 | + | 0.0598973i | ||||
\(364\) | 0.318890 | + | 0.201092i | 0.0167144 | + | 0.0105401i | ||||
\(365\) | 2.41849 | + | 15.0790i | 0.126589 | + | 0.789273i | ||||
\(366\) | −7.31230 | − | 2.11305i | −0.382220 | − | 0.110451i | ||||
\(367\) | 23.3564 | − | 23.3564i | 1.21920 | − | 1.21920i | 0.251282 | − | 0.967914i | \(-0.419148\pi\) |
0.967914 | − | 0.251282i | \(-0.0808523\pi\) | |||||||
\(368\) | −1.07486 | + | 3.04019i | −0.0560311 | + | 0.158481i | ||||
\(369\) | − | 26.3163i | − | 1.36997i | ||||||
\(370\) | −14.3905 | + | 11.2407i | −0.748127 | + | 0.584377i | ||||
\(371\) | 3.71828i | 0.193043i | ||||||||
\(372\) | 0.347042 | + | 1.53191i | 0.0179933 | + | 0.0794259i | ||||
\(373\) | 6.12552 | − | 6.12552i | 0.317168 | − | 0.317168i | −0.530511 | − | 0.847678i | \(-0.678000\pi\) |
0.847678 | + | 0.530511i | \(0.178000\pi\) | |||||||
\(374\) | 2.85111 | − | 9.86643i | 0.147428 | − | 0.510181i | ||||
\(375\) | −3.59115 | − | 6.94709i | −0.185446 | − | 0.358746i | ||||
\(376\) | 6.84393 | + | 7.69586i | 0.352949 | + | 0.396884i | ||||
\(377\) | −0.532725 | − | 0.532725i | −0.0274367 | − | 0.0274367i | ||||
\(378\) | −1.21978 | − | 2.21126i | −0.0627389 | − | 0.113735i | ||||
\(379\) | −22.9714 | −1.17996 | −0.589981 | − | 0.807417i | \(-0.700865\pi\) | ||||
−0.589981 | + | 0.807417i | \(0.700865\pi\) | |||||||
\(380\) | 1.66634 | + | 4.15010i | 0.0854815 | + | 0.212896i | ||||
\(381\) | 0.355331 | 0.0182041 | ||||||||
\(382\) | −2.82056 | − | 5.11318i | −0.144312 | − | 0.261613i | ||||
\(383\) | −18.5545 | − | 18.5545i | −0.948090 | − | 0.948090i | 0.0506273 | − | 0.998718i | \(-0.483878\pi\) |
−0.998718 | + | 0.0506273i | \(0.983878\pi\) | |||||||
\(384\) | 7.29402 | + | 3.06978i | 0.372221 | + | 0.156654i | ||||
\(385\) | 3.01561 | − | 0.483666i | 0.153690 | − | 0.0246499i | ||||
\(386\) | −3.07685 | + | 10.6476i | −0.156608 | + | 0.541949i | ||||
\(387\) | 17.8202 | − | 17.8202i | 0.905851 | − | 0.905851i | ||||
\(388\) | −11.4133 | + | 2.58559i | −0.579422 | + | 0.131263i | ||||
\(389\) | − | 37.2211i | − | 1.88718i | −0.331112 | − | 0.943592i | \(-0.607424\pi\) | ||
0.331112 | − | 0.943592i | \(-0.392576\pi\) | |||||||
\(390\) | −0.109777 | + | 0.893308i | −0.00555878 | + | 0.0452344i | ||||
\(391\) | 1.98564i | 0.100418i | ||||||||
\(392\) | −19.1591 | − | 1.12260i | −0.967681 | − | 0.0566997i | ||||
\(393\) | 3.49983 | − | 3.49983i | 0.176543 | − | 0.176543i | ||||
\(394\) | −11.2615 | − | 3.25424i | −0.567345 | − | 0.163946i | ||||
\(395\) | −0.215135 | + | 0.297327i | −0.0108246 | + | 0.0149602i | ||||
\(396\) | −7.89700 | + | 12.5230i | −0.396839 | + | 0.629303i | ||||
\(397\) | 8.21621 | + | 8.21621i | 0.412360 | + | 0.412360i | 0.882560 | − | 0.470200i | \(-0.155818\pi\) |
−0.470200 | + | 0.882560i | \(0.655818\pi\) | |||||||
\(398\) | −18.2616 | + | 10.0735i | −0.915369 | + | 0.504941i | ||||
\(399\) | 0.324042 | 0.0162224 | ||||||||
\(400\) | −14.4466 | + | 13.8310i | −0.722331 | + | 0.691548i | ||||
\(401\) | 28.5885 | 1.42764 | 0.713821 | − | 0.700328i | \(-0.246963\pi\) | ||||
0.713821 | + | 0.700328i | \(0.246963\pi\) | |||||||
\(402\) | 11.6516 | − | 6.42731i | 0.581129 | − | 0.320565i | ||||
\(403\) | 0.323047 | + | 0.323047i | 0.0160921 | + | 0.0160921i | ||||
\(404\) | 4.91387 | − | 7.79237i | 0.244474 | − | 0.387685i | ||||
\(405\) | −6.33896 | + | 8.76076i | −0.314985 | + | 0.435326i | ||||
\(406\) | −1.16537 | − | 0.336758i | −0.0578363 | − | 0.0167130i | ||||
\(407\) | 12.0385 | − | 12.0385i | 0.596725 | − | 0.596725i | ||||
\(408\) | 4.86471 | + | 0.285040i | 0.240839 | + | 0.0141116i | ||||
\(409\) | 8.40060i | 0.415383i | 0.978194 | + | 0.207691i | \(0.0665950\pi\) | ||||
−0.978194 | + | 0.207691i | \(0.933405\pi\) | |||||||
\(410\) | −4.04278 | + | 32.8980i | −0.199659 | + | 1.62472i | ||||
\(411\) | 4.28083i | 0.211158i | ||||||||
\(412\) | 29.8552 | − | 6.76346i | 1.47086 | − | 0.333212i | ||||
\(413\) | 4.62686 | − | 4.62686i | 0.227673 | − | 0.227673i | ||||
\(414\) | 0.794642 | − | 2.74990i | 0.0390545 | − | 0.135150i | ||||
\(415\) | −6.19181 | + | 0.993087i | −0.303944 | + | 0.0487487i | ||||
\(416\) | 2.27077 | − | 0.376376i | 0.111334 | − | 0.0184534i | ||||
\(417\) | 5.65562 | + | 5.65562i | 0.276957 | + | 0.276957i | ||||
\(418\) | −2.01395 | − | 3.65095i | −0.0985057 | − | 0.178574i | ||||
\(419\) | −14.2962 | −0.698416 | −0.349208 | − | 0.937045i | \(-0.613549\pi\) | ||||
−0.349208 | + | 0.937045i | \(0.613549\pi\) | |||||||
\(420\) | 0.539965 | + | 1.34481i | 0.0263476 | + | 0.0656199i | ||||
\(421\) | 40.0754 | 1.95316 | 0.976579 | − | 0.215161i | \(-0.0690275\pi\) | ||||
0.976579 | + | 0.215161i | \(0.0690275\pi\) | |||||||
\(422\) | −2.34996 | − | 4.26007i | −0.114394 | − | 0.207377i | ||||
\(423\) | −6.46440 | − | 6.46440i | −0.314310 | − | 0.314310i | ||||
\(424\) | 15.0861 | + | 16.9640i | 0.732645 | + | 0.823845i | ||||
\(425\) | −5.54822 | + | 10.9950i | −0.269128 | + | 0.533334i | ||||
\(426\) | −2.52578 | + | 8.74058i | −0.122374 | + | 0.423483i | ||||
\(427\) | −2.52055 | + | 2.52055i | −0.121978 | + | 0.121978i | ||||
\(428\) | 3.19265 | + | 14.0930i | 0.154322 | + | 0.681209i | ||||
\(429\) | − | 0.839138i | − | 0.0405140i | ||||||
\(430\) | −25.0146 | + | 19.5394i | −1.20631 | + | 0.942275i | ||||
\(431\) | 30.3005i | 1.45952i | 0.683702 | + | 0.729761i | \(0.260369\pi\) | ||||
−0.683702 | + | 0.729761i | \(0.739631\pi\) | |||||||
\(432\) | −14.5367 | − | 5.13947i | −0.699399 | − | 0.247273i | ||||
\(433\) | 4.16829 | − | 4.16829i | 0.200315 | − | 0.200315i | −0.599820 | − | 0.800135i | \(-0.704761\pi\) |
0.800135 | + | 0.599820i | \(0.204761\pi\) | |||||||
\(434\) | 0.706686 | + | 0.204212i | 0.0339220 | + | 0.00980249i | ||||
\(435\) | −0.458615 | − | 2.85942i | −0.0219889 | − | 0.137099i | ||||
\(436\) | 8.86515 | + | 5.59037i | 0.424564 | + | 0.267730i | ||||
\(437\) | 0.570036 | + | 0.570036i | 0.0272685 | + | 0.0272685i | ||||
\(438\) | 5.91568 | − | 3.26324i | 0.282662 | − | 0.155924i | ||||
\(439\) | 19.3441 | 0.923241 | 0.461621 | − | 0.887077i | \(-0.347268\pi\) | ||||
0.461621 | + | 0.887077i | \(0.347268\pi\) | |||||||
\(440\) | 11.7959 | − | 14.4418i | 0.562345 | − | 0.688487i | ||||
\(441\) | 17.0363 | 0.811252 | ||||||||
\(442\) | 1.24106 | − | 0.684600i | 0.0590313 | − | 0.0325631i | ||||
\(443\) | −4.15922 | − | 4.15922i | −0.197611 | − | 0.197611i | 0.601364 | − | 0.798975i | \(-0.294624\pi\) |
−0.798975 | + | 0.601364i | \(0.794624\pi\) | |||||||
\(444\) | 6.83301 | + | 4.30890i | 0.324280 | + | 0.204491i | ||||
\(445\) | 4.12251 | + | 2.98289i | 0.195426 | + | 0.141403i | ||||
\(446\) | −19.1403 | − | 5.53100i | −0.906320 | − | 0.261900i | ||||
\(447\) | −6.48606 | + | 6.48606i | −0.306780 | + | 0.306780i | ||||
\(448\) | 2.90874 | − | 2.29663i | 0.137425 | − | 0.108506i | ||||
\(449\) | 22.1626i | 1.04592i | 0.852358 | + | 0.522959i | \(0.175172\pi\) | ||||
−0.852358 | + | 0.522959i | \(0.824828\pi\) | |||||||
\(450\) | 12.0838 | − | 13.0065i | 0.569638 | − | 0.613133i | ||||
\(451\) | − | 30.9031i | − | 1.45517i | ||||||
\(452\) | 5.70661 | + | 25.1901i | 0.268416 | + | 1.18484i | ||||
\(453\) | −1.11779 | + | 1.11779i | −0.0525184 | + | 0.0525184i | ||||
\(454\) | 4.69048 | − | 16.2317i | 0.220135 | − | 0.761789i | ||||
\(455\) | 0.341483 | + | 0.247084i | 0.0160090 | + | 0.0115835i | ||||
\(456\) | 1.47839 | − | 1.31473i | 0.0692318 | − | 0.0615678i | ||||
\(457\) | 10.8450 | + | 10.8450i | 0.507307 | + | 0.507307i | 0.913699 | − | 0.406392i | \(-0.133213\pi\) |
−0.406392 | + | 0.913699i | \(0.633213\pi\) | |||||||
\(458\) | −5.90191 | − | 10.6991i | −0.275778 | − | 0.499937i | ||||
\(459\) | −9.49435 | −0.443158 | ||||||||
\(460\) | −1.41583 | + | 3.31558i | −0.0660134 | + | 0.154590i | ||||
\(461\) | −6.29625 | −0.293245 | −0.146623 | − | 0.989192i | \(-0.546840\pi\) | ||||
−0.146623 | + | 0.989192i | \(0.546840\pi\) | |||||||
\(462\) | −0.652606 | − | 1.18306i | −0.0303620 | − | 0.0550410i | ||||
\(463\) | 5.60774 | + | 5.60774i | 0.260614 | + | 0.260614i | 0.825303 | − | 0.564690i | \(-0.191004\pi\) |
−0.564690 | + | 0.825303i | \(0.691004\pi\) | |||||||
\(464\) | −6.68312 | + | 3.19182i | −0.310256 | + | 0.148177i | ||||
\(465\) | 0.278107 | + | 1.73397i | 0.0128969 | + | 0.0804109i | ||||
\(466\) | 2.52484 | − | 8.73733i | 0.116961 | − | 0.404749i | ||||
\(467\) | 23.6709 | − | 23.6709i | 1.09536 | − | 1.09536i | 0.100413 | − | 0.994946i | \(-0.467983\pi\) |
0.994946 | − | 0.100413i | \(-0.0320165\pi\) | |||||||
\(468\) | −1.99272 | + | 0.451434i | −0.0921133 | + | 0.0208675i | ||||
\(469\) | − | 6.23179i | − | 0.287757i | ||||||
\(470\) | 7.08806 | + | 9.07422i | 0.326948 | + | 0.418563i | ||||
\(471\) | − | 11.3368i | − | 0.522371i | ||||||
\(472\) | 2.33680 | − | 39.8817i | 0.107560 | − | 1.83570i | ||||
\(473\) | 20.9261 | − | 20.9261i | 0.962185 | − | 0.962185i | ||||
\(474\) | 0.155973 | + | 0.0450718i | 0.00716409 | + | 0.00207022i | ||||
\(475\) | 1.56365 | + | 4.74921i | 0.0717452 | + | 0.217909i | ||||
\(476\) | 1.21729 | − | 1.93037i | 0.0557945 | − | 0.0884785i | ||||
\(477\) | −14.2495 | − | 14.2495i | −0.652439 | − | 0.652439i | ||||
\(478\) | −28.6012 | + | 15.7772i | −1.30819 | + | 0.721631i | ||||
\(479\) | 12.8003 | 0.584863 | 0.292431 | − | 0.956286i | \(-0.405536\pi\) | ||||
0.292431 | + | 0.956286i | \(0.405536\pi\) | |||||||
\(480\) | 7.91975 | + | 3.94466i | 0.361485 | + | 0.180048i | ||||
\(481\) | 2.34959 | 0.107132 | ||||||||
\(482\) | −24.5707 | + | 13.5538i | −1.11917 | + | 0.617360i | ||||
\(483\) | 0.184716 | + | 0.184716i | 0.00840485 | + | 0.00840485i | ||||
\(484\) | 2.46142 | − | 3.90330i | 0.111883 | − | 0.177423i | ||||
\(485\) | −12.9187 | + | 2.07199i | −0.586607 | + | 0.0940843i | ||||
\(486\) | 20.3067 | + | 5.86806i | 0.921133 | + | 0.266181i | ||||
\(487\) | 10.7519 | − | 10.7519i | 0.487215 | − | 0.487215i | −0.420211 | − | 0.907426i | \(-0.638044\pi\) |
0.907426 | + | 0.420211i | \(0.138044\pi\) | |||||||
\(488\) | −1.27301 | + | 21.7261i | −0.0576263 | + | 0.983495i | ||||
\(489\) | − | 10.3850i | − | 0.469626i | ||||||
\(490\) | −21.2971 | − | 2.61716i | −0.962104 | − | 0.118231i | ||||
\(491\) | 39.2711i | 1.77228i | 0.463417 | + | 0.886140i | \(0.346623\pi\) | ||||
−0.463417 | + | 0.886140i | \(0.653377\pi\) | |||||||
\(492\) | 14.3008 | − | 3.23973i | 0.644729 | − | 0.146058i | ||||
\(493\) | −3.22480 | + | 3.22480i | −0.145238 | + | 0.145238i | ||||
\(494\) | 0.159749 | − | 0.552818i | 0.00718743 | − | 0.0248725i | ||||
\(495\) | −9.70313 | + | 13.4102i | −0.436123 | + | 0.602744i | ||||
\(496\) | 4.05268 | − | 1.93554i | 0.181971 | − | 0.0869082i | ||||
\(497\) | 3.01287 | + | 3.01287i | 0.135146 | + | 0.135146i | ||||
\(498\) | 1.33996 | + | 2.42912i | 0.0600452 | + | 0.108851i | ||||
\(499\) | −35.8517 | −1.60494 | −0.802471 | − | 0.596692i | \(-0.796482\pi\) | ||||
−0.802471 | + | 0.596692i | \(0.796482\pi\) | |||||||
\(500\) | −17.1041 | + | 14.4031i | −0.764919 | + | 0.644126i | ||||
\(501\) | 15.8072 | 0.706214 | ||||||||
\(502\) | 3.98054 | + | 7.21603i | 0.177660 | + | 0.322067i | ||||
\(503\) | −8.36832 | − | 8.36832i | −0.373125 | − | 0.373125i | 0.495489 | − | 0.868614i | \(-0.334989\pi\) |
−0.868614 | + | 0.495489i | \(0.834989\pi\) | |||||||
\(504\) | −2.45835 | + | 2.18621i | −0.109504 | + | 0.0973816i | ||||
\(505\) | 6.03773 | − | 8.34445i | 0.268675 | − | 0.371323i | ||||
\(506\) | 0.933144 | − | 3.22919i | 0.0414833 | − | 0.143555i | ||||
\(507\) | −6.34797 | + | 6.34797i | −0.281923 | + | 0.281923i | ||||
\(508\) | −0.224476 | − | 0.990881i | −0.00995953 | − | 0.0439632i | ||||
\(509\) | − | 8.31464i | − | 0.368540i | −0.982876 | − | 0.184270i | \(-0.941008\pi\) | ||
0.982876 | − | 0.184270i | \(-0.0589921\pi\) | |||||||
\(510\) | 5.40756 | + | 0.664526i | 0.239451 | + | 0.0294257i | ||||
\(511\) | − | 3.16397i | − | 0.139966i | ||||||
\(512\) | 3.95253 | − | 22.2795i | 0.174679 | − | 0.984626i | ||||
\(513\) | −2.72563 | + | 2.72563i | −0.120340 | + | 0.120340i | ||||
\(514\) | −11.8924 | − | 3.43656i | −0.524551 | − | 0.151580i | ||||
\(515\) | 33.7930 | − | 5.41997i | 1.48910 | − | 0.238833i | ||||
\(516\) | 11.8776 | + | 7.49003i | 0.522883 | + | 0.329730i | ||||
\(517\) | −7.59111 | − | 7.59111i | −0.333856 | − | 0.333856i | ||||
\(518\) | 3.31257 | − | 1.82730i | 0.145546 | − | 0.0802869i | ||||
\(519\) | −12.5928 | −0.552763 | ||||||||
\(520\) | 2.56044 | − | 0.258211i | 0.112283 | − | 0.0113233i | ||||
\(521\) | −35.8196 | −1.56928 | −0.784642 | − | 0.619949i | \(-0.787153\pi\) | ||||
−0.784642 | + | 0.619949i | \(0.787153\pi\) | |||||||
\(522\) | 5.75657 | − | 3.17547i | 0.251958 | − | 0.138986i | ||||
\(523\) | 14.4962 | + | 14.4962i | 0.633874 | + | 0.633874i | 0.949038 | − | 0.315163i | \(-0.102059\pi\) |
−0.315163 | + | 0.949038i | \(0.602059\pi\) | |||||||
\(524\) | −11.9707 | − | 7.54871i | −0.522941 | − | 0.329767i | ||||
\(525\) | 0.506689 | + | 1.53895i | 0.0221137 | + | 0.0671651i | ||||
\(526\) | 16.2370 | + | 4.69203i | 0.707967 | + | 0.204582i | ||||
\(527\) | 1.95554 | − | 1.95554i | 0.0851845 | − | 0.0851845i | ||||
\(528\) | −7.77741 | − | 2.74971i | −0.338468 | − | 0.119666i | ||||
\(529\) | − | 22.3501i | − | 0.971744i | ||||||
\(530\) | 15.6242 | + | 20.0023i | 0.678673 | + | 0.868845i | ||||
\(531\) | 35.4628i | 1.53895i | ||||||||
\(532\) | −0.204710 | − | 0.903630i | −0.00887532 | − | 0.0391773i | ||||
\(533\) | 3.01573 | − | 3.01573i | 0.130626 | − | 0.130626i | ||||
\(534\) | 0.624930 | − | 2.16260i | 0.0270434 | − | 0.0935850i | ||||
\(535\) | 2.55847 | + | 15.9518i | 0.110612 | + | 0.689656i | ||||
\(536\) | −25.2841 | − | 28.4315i | −1.09211 | − | 1.22805i | ||||
\(537\) | 1.77029 | + | 1.77029i | 0.0763935 | + | 0.0763935i | ||||
\(538\) | 1.02640 | + | 1.86068i | 0.0442512 | + | 0.0802198i | ||||
\(539\) | 20.0056 | 0.861703 | ||||||||
\(540\) | −15.8535 | − | 6.76981i | −0.682225 | − | 0.291326i | ||||
\(541\) | −43.9873 | −1.89116 | −0.945580 | − | 0.325390i | \(-0.894504\pi\) | ||||
−0.945580 | + | 0.325390i | \(0.894504\pi\) | |||||||
\(542\) | −20.2320 | − | 36.6771i | −0.869039 | − | 1.57542i | ||||
\(543\) | −3.66249 | − | 3.66249i | −0.157172 | − | 0.157172i | ||||
\(544\) | −2.27836 | − | 13.7459i | −0.0976839 | − | 0.589350i | ||||
\(545\) | 9.49323 | + | 6.86895i | 0.406645 | + | 0.294233i | ||||
\(546\) | 0.0517653 | − | 0.179137i | 0.00221535 | − | 0.00766634i | ||||
\(547\) | 25.2995 | − | 25.2995i | 1.08173 | − | 1.08173i | 0.0853805 | − | 0.996348i | \(-0.472789\pi\) |
0.996348 | − | 0.0853805i | \(-0.0272106\pi\) | |||||||
\(548\) | 11.9376 | − | 2.70437i | 0.509949 | − | 0.115525i | ||||
\(549\) | − | 19.3189i | − | 0.824509i | ||||||
\(550\) | 14.1900 | − | 15.2735i | 0.605063 | − | 0.651264i | ||||
\(551\) | 1.85155i | 0.0788787i | ||||||||
\(552\) | 1.59218 | + | 0.0932909i | 0.0677675 | + | 0.00397073i | ||||
\(553\) | 0.0537639 | − | 0.0537639i | 0.00228627 | − | 0.00228627i | ||||
\(554\) | 35.0395 | + | 10.1254i | 1.48869 | + | 0.430187i | ||||
\(555\) | 7.31712 | + | 5.29439i | 0.310594 | + | 0.224734i | ||||
\(556\) | 12.1985 | − | 19.3443i | 0.517331 | − | 0.820379i | ||||
\(557\) | −11.2381 | − | 11.2381i | −0.476172 | − | 0.476172i | 0.427733 | − | 0.903905i | \(-0.359312\pi\) |
−0.903905 | + | 0.427733i | \(0.859312\pi\) | |||||||
\(558\) | −3.49081 | + | 1.92562i | −0.147778 | + | 0.0815180i | ||||
\(559\) | 4.08422 | 0.172744 | ||||||||
\(560\) | 3.40904 | − | 2.35532i | 0.144058 | − | 0.0995306i | ||||
\(561\) | −5.07965 | −0.214463 | ||||||||
\(562\) | −20.1195 | + | 11.0984i | −0.848689 | + | 0.468158i | ||||
\(563\) | −0.343770 | − | 0.343770i | −0.0144882 | − | 0.0144882i | 0.699826 | − | 0.714314i | \(-0.253261\pi\) |
−0.714314 | + | 0.699826i | \(0.753261\pi\) | |||||||
\(564\) | 2.71706 | − | 4.30869i | 0.114409 | − | 0.181429i | ||||
\(565\) | 4.57306 | + | 28.5126i | 0.192390 | + | 1.19953i | ||||
\(566\) | 12.7397 | + | 3.68140i | 0.535489 | + | 0.154741i | ||||
\(567\) | 1.58415 | − | 1.58415i | 0.0665282 | − | 0.0665282i | ||||
\(568\) | 25.9698 | + | 1.52166i | 1.08967 | + | 0.0638473i | ||||
\(569\) | − | 14.2062i | − | 0.595555i | −0.954635 | − | 0.297777i | \(-0.903755\pi\) | ||
0.954635 | − | 0.297777i | \(-0.0962453\pi\) | |||||||
\(570\) | 1.74317 | − | 1.36163i | 0.0730134 | − | 0.0570323i | ||||
\(571\) | 19.1090i | 0.799688i | 0.916583 | + | 0.399844i | \(0.130936\pi\) | ||||
−0.916583 | + | 0.399844i | \(0.869064\pi\) | |||||||
\(572\) | −2.34004 | + | 0.530117i | −0.0978418 | + | 0.0221653i | ||||
\(573\) | −2.04231 | + | 2.04231i | −0.0853187 | + | 0.0853187i | ||||
\(574\) | 1.90637 | − | 6.59710i | 0.0795704 | − | 0.275357i | ||||
\(575\) | −1.81588 | + | 3.59855i | −0.0757276 | + | 0.150070i | ||||
\(576\) | −2.34574 | + | 19.9484i | −0.0977393 | + | 0.831184i | ||||
\(577\) | −25.4221 | − | 25.4221i | −1.05834 | − | 1.05834i | −0.998190 | − | 0.0601462i | \(-0.980843\pi\) |
−0.0601462 | − | 0.998190i | \(-0.519157\pi\) | |||||||
\(578\) | 7.46820 | + | 13.5385i | 0.310636 | + | 0.563129i | ||||
\(579\) | 5.48183 | 0.227817 | ||||||||
\(580\) | −7.68411 | + | 3.08531i | −0.319065 | + | 0.128111i | ||||
\(581\) | 1.29920 | 0.0538999 | ||||||||
\(582\) | 2.79572 | + | 5.06815i | 0.115886 | + | 0.210082i | ||||
\(583\) | −16.7331 | − | 16.7331i | −0.693014 | − | 0.693014i | ||||
\(584\) | −12.8371 | − | 14.4351i | −0.531203 | − | 0.597327i | ||||
\(585\) | −2.25555 | + | 0.361762i | −0.0932556 | + | 0.0149570i | ||||
\(586\) | 8.02363 | − | 27.7662i | 0.331453 | − | 1.14701i | ||||
\(587\) | −29.3478 | + | 29.3478i | −1.21131 | + | 1.21131i | −0.240717 | + | 0.970595i | \(0.577383\pi\) |
−0.970595 | + | 0.240717i | \(0.922617\pi\) | |||||||
\(588\) | 2.09729 | + | 9.25785i | 0.0864909 | + | 0.381787i | ||||
\(589\) | − | 1.12279i | − | 0.0462637i | ||||||
\(590\) | 5.44789 | − | 44.3320i | 0.224286 | − | 1.82512i | ||||
\(591\) | 5.79788i | 0.238493i | ||||||||
\(592\) | 7.69919 | − | 21.7768i | 0.316435 | − | 0.895019i | ||||
\(593\) | 4.78725 | − | 4.78725i | 0.196589 | − | 0.196589i | −0.601947 | − | 0.798536i | \(-0.705608\pi\) |
0.798536 | + | 0.601947i | \(0.205608\pi\) | |||||||
\(594\) | 15.4404 | + | 4.46184i | 0.633529 | + | 0.183072i | ||||
\(595\) | 1.49570 | − | 2.06714i | 0.0613178 | − | 0.0847443i | ||||
\(596\) | 22.1846 | + | 13.9896i | 0.908718 | + | 0.573038i | ||||
\(597\) | 7.29404 | + | 7.29404i | 0.298525 | + | 0.298525i | ||||
\(598\) | 0.406188 | − | 0.224064i | 0.0166103 | − | 0.00916265i | ||||
\(599\) | −8.94617 | −0.365531 | −0.182765 | − | 0.983157i | \(-0.558505\pi\) | ||||
−0.182765 | + | 0.983157i | \(0.558505\pi\) | |||||||
\(600\) | 8.55560 | + | 4.96540i | 0.349281 | + | 0.202711i | ||||
\(601\) | −31.5967 | −1.28886 | −0.644429 | − | 0.764664i | \(-0.722905\pi\) | ||||
−0.644429 | + | 0.764664i | \(0.722905\pi\) | |||||||
\(602\) | 5.75815 | − | 3.17634i | 0.234685 | − | 0.129458i | ||||
\(603\) | 23.8819 | + | 23.8819i | 0.972548 | + | 0.972548i | ||||
\(604\) | 3.82325 | + | 2.41094i | 0.155566 | + | 0.0980998i | ||||
\(605\) | 3.02438 | − | 4.17985i | 0.122959 | − | 0.169935i | ||||
\(606\) | −4.37736 | − | 1.26493i | −0.177818 | − | 0.0513844i | ||||
\(607\) | 5.75786 | − | 5.75786i | 0.233704 | − | 0.233704i | −0.580533 | − | 0.814237i | \(-0.697156\pi\) |
0.814237 | + | 0.580533i | \(0.197156\pi\) | |||||||
\(608\) | −4.60023 | − | 3.29209i | −0.186564 | − | 0.133512i | ||||
\(609\) | 0.599980i | 0.0243124i | ||||||||
\(610\) | −2.96782 | + | 24.1505i | −0.120163 | + | 0.977826i | ||||
\(611\) | − | 1.48158i | − | 0.0599383i | ||||||
\(612\) | 2.73271 | + | 12.0627i | 0.110463 | + | 0.487607i | ||||
\(613\) | −24.9646 | + | 24.9646i | −1.00831 | + | 1.00831i | −0.00834470 | + | 0.999965i | \(0.502656\pi\) |
−0.999965 | + | 0.00834470i | \(0.997344\pi\) | |||||||
\(614\) | 6.31016 | − | 21.8366i | 0.254657 | − | 0.881255i | ||||
\(615\) | 16.1870 | − | 2.59620i | 0.652724 | − | 0.104689i | ||||
\(616\) | −2.88683 | + | 2.56726i | −0.116314 | + | 0.103438i | ||||
\(617\) | 27.5683 | + | 27.5683i | 1.10986 | + | 1.10986i | 0.993168 | + | 0.116689i | \(0.0372281\pi\) |
0.116689 | + | 0.993168i | \(0.462772\pi\) | |||||||
\(618\) | −7.31312 | − | 13.2574i | −0.294177 | − | 0.533291i | ||||
\(619\) | 36.0285 | 1.44811 | 0.724054 | − | 0.689743i | \(-0.242277\pi\) | ||||
0.724054 | + | 0.689743i | \(0.242277\pi\) | |||||||
\(620\) | 4.65968 | − | 1.87095i | 0.187137 | − | 0.0751391i | ||||
\(621\) | −3.10742 | −0.124696 | ||||||||
\(622\) | 21.6087 | + | 39.1728i | 0.866429 | + | 1.57068i | ||||
\(623\) | −0.745448 | − | 0.745448i | −0.0298658 | − | 0.0298658i | ||||
\(624\) | −0.490636 | − | 1.02731i | −0.0196412 | − | 0.0411251i | ||||
\(625\) | −20.1100 | + | 14.8522i | −0.804400 | + | 0.594088i | ||||
\(626\) | 2.28308 | − | 7.90072i | 0.0912503 | − | 0.315776i | ||||
\(627\) | −1.45826 | + | 1.45826i | −0.0582374 | + | 0.0582374i | ||||
\(628\) | −31.6139 | + | 7.16188i | −1.26153 | + | 0.285790i | ||||
\(629\) | − | 14.2230i | − | 0.567109i | ||||||
\(630\) | −2.89865 | + | 2.26420i | −0.115485 | + | 0.0902078i | ||||
\(631\) | − | 20.6862i | − | 0.823504i | −0.911296 | − | 0.411752i | \(-0.864917\pi\) | ||
0.911296 | − | 0.411752i | \(-0.135083\pi\) | |||||||
\(632\) | 0.0271535 | − | 0.463424i | 0.00108011 | − | 0.0184340i | ||||
\(633\) | −1.70156 | + | 1.70156i | −0.0676308 | + | 0.0676308i | ||||
\(634\) | −41.0594 | − | 11.8650i | −1.63068 | − | 0.471219i | ||||
\(635\) | −0.179887 | − | 1.12158i | −0.00713859 | − | 0.0445084i | ||||
\(636\) | 5.98922 | − | 9.49766i | 0.237488 | − | 0.376607i | ||||
\(637\) | 1.95228 | + | 1.95228i | 0.0773522 | + | 0.0773522i | ||||
\(638\) | 6.75991 | − | 3.72893i | 0.267627 | − | 0.147630i | ||||
\(639\) | −23.0923 | −0.913519 | ||||||||
\(640\) | 5.99694 | − | 24.5772i | 0.237050 | − | 0.971497i | ||||
\(641\) | −5.19156 | −0.205054 | −0.102527 | − | 0.994730i | \(-0.532693\pi\) | ||||
−0.102527 | + | 0.994730i | \(0.532693\pi\) | |||||||
\(642\) | 6.25808 | − | 3.45211i | 0.246987 | − | 0.136244i | ||||
\(643\) | 6.88159 | + | 6.88159i | 0.271384 | + | 0.271384i | 0.829657 | − | 0.558273i | \(-0.188536\pi\) |
−0.558273 | + | 0.829657i | \(0.688536\pi\) | |||||||
\(644\) | 0.398409 | − | 0.631794i | 0.0156995 | − | 0.0248962i | ||||
\(645\) | 12.7191 | + | 9.20309i | 0.500815 | + | 0.362371i | ||||
\(646\) | −3.34643 | − | 0.967023i | −0.131664 | − | 0.0380470i | ||||
\(647\) | 20.2501 | − | 20.2501i | 0.796113 | − | 0.796113i | −0.186368 | − | 0.982480i | \(-0.559672\pi\) |
0.982480 | + | 0.186368i | \(0.0596715\pi\) | |||||||
\(648\) | 0.800080 | − | 13.6548i | 0.0314301 | − | 0.536410i | ||||
\(649\) | 41.6438i | 1.63466i | ||||||||
\(650\) | 2.87524 | − | 0.105734i | 0.112776 | − | 0.00414725i | ||||
\(651\) | − | 0.363831i | − | 0.0142597i | ||||||
\(652\) | −28.9598 | + | 6.56062i | −1.13415 | + | 0.256934i | ||||
\(653\) | 10.5859 | − | 10.5859i | 0.414257 | − | 0.414257i | −0.468961 | − | 0.883219i | \(-0.655372\pi\) |
0.883219 | + | 0.468961i | \(0.155372\pi\) | |||||||
\(654\) | 1.43908 | − | 4.98000i | 0.0562723 | − | 0.194733i | ||||
\(655\) | −12.8188 | − | 9.27519i | −0.500871 | − | 0.362411i | ||||
\(656\) | −18.0687 | − | 37.8328i | −0.705466 | − | 1.47712i | ||||
\(657\) | 12.1252 | + | 12.1252i | 0.473049 | + | 0.473049i | ||||
\(658\) | −1.15224 | − | 2.08881i | −0.0449190 | − | 0.0814303i | ||||
\(659\) | −29.9506 | −1.16671 | −0.583354 | − | 0.812218i | \(-0.698260\pi\) | ||||
−0.583354 | + | 0.812218i | \(0.698260\pi\) | |||||||
\(660\) | −8.48189 | − | 3.62197i | −0.330157 | − | 0.140985i | ||||
\(661\) | −42.9876 | −1.67202 | −0.836012 | − | 0.548711i | \(-0.815119\pi\) | ||||
−0.836012 | + | 0.548711i | \(0.815119\pi\) | |||||||
\(662\) | 19.6826 | + | 35.6811i | 0.764985 | + | 1.38678i | ||||
\(663\) | −0.495705 | − | 0.495705i | −0.0192516 | − | 0.0192516i | ||||
\(664\) | 5.92738 | − | 5.27121i | 0.230027 | − | 0.204563i | ||||
\(665\) | −0.164047 | − | 1.02282i | −0.00636147 | − | 0.0396632i | ||||
\(666\) | −5.69199 | + | 19.6974i | −0.220560 | + | 0.763259i | ||||
\(667\) | −1.05545 | + | 1.05545i | −0.0408671 | + | 0.0408671i | ||||
\(668\) | −9.98603 | − | 44.0803i | −0.386371 | − | 1.70552i | ||||
\(669\) | 9.85422i | 0.380986i | ||||||||
\(670\) | −26.1860 | − | 33.5236i | −1.01165 | − | 1.29513i | ||||
\(671\) | − | 22.6860i | − | 0.875785i | ||||||
\(672\) | −1.49067 | − | 1.06678i | −0.0575039 | − | 0.0411518i | ||||
\(673\) | 8.30925 | − | 8.30925i | 0.320298 | − | 0.320298i | −0.528583 | − | 0.848881i | \(-0.677277\pi\) |
0.848881 | + | 0.528583i | \(0.177277\pi\) | |||||||
\(674\) | 25.8196 | + | 7.46113i | 0.994535 | + | 0.287392i | ||||
\(675\) | −17.2065 | − | 8.68267i | −0.662280 | − | 0.334196i | ||||
\(676\) | 21.7123 | + | 13.6918i | 0.835090 | + | 0.526608i | ||||
\(677\) | 1.65901 | + | 1.65901i | 0.0637610 | + | 0.0637610i | 0.738268 | − | 0.674507i | \(-0.235644\pi\) |
−0.674507 | + | 0.738268i | \(0.735644\pi\) | |||||||
\(678\) | 11.1858 | − | 6.17038i | 0.429589 | − | 0.236972i | ||||
\(679\) | 2.71067 | 0.104026 | ||||||||
\(680\) | −1.56306 | − | 15.4994i | −0.0599405 | − | 0.594376i | ||||
\(681\) | −8.35673 | −0.320230 | ||||||||
\(682\) | −4.09924 | + | 2.26125i | −0.156968 | + | 0.0865875i | ||||
\(683\) | 3.72871 | + | 3.72871i | 0.142675 | + | 0.142675i | 0.774837 | − | 0.632161i | \(-0.217832\pi\) |
−0.632161 | + | 0.774837i | \(0.717832\pi\) | |||||||
\(684\) | 4.24747 | + | 2.67846i | 0.162406 | + | 0.102413i | ||||
\(685\) | 13.5122 | − | 2.16718i | 0.516273 | − | 0.0828036i | ||||
\(686\) | 8.67655 | + | 2.50727i | 0.331272 | + | 0.0957282i | ||||
\(687\) | −4.27345 | + | 4.27345i | −0.163042 | + | 0.163042i | ||||
\(688\) | 13.3833 | − | 37.8539i | 0.510233 | − | 1.44317i | ||||
\(689\) | − | 3.26585i | − | 0.124419i | ||||||
\(690\) | 1.76985 | + | 0.217493i | 0.0673769 | + | 0.00827984i | ||||
\(691\) | 0.815388i | 0.0310188i | 0.999880 | + | 0.0155094i | \(0.00493700\pi\) | ||||
−0.999880 | + | 0.0155094i | \(0.995063\pi\) | |||||||
\(692\) | 7.95538 | + | 35.1166i | 0.302418 | + | 1.33493i | ||||
\(693\) | 2.42489 | − | 2.42489i | 0.0921139 | − | 0.0921139i | ||||
\(694\) | 10.9377 | − | 37.8504i | 0.415188 | − | 1.43678i | ||||
\(695\) | 14.9884 | − | 20.7148i | 0.568543 | − | 0.785756i | ||||
\(696\) | 2.43429 | + | 2.73731i | 0.0922714 | + | 0.103757i | ||||
\(697\) | −18.2554 | − | 18.2554i | −0.691474 | − | 0.691474i | ||||
\(698\) | 5.17399 | + | 9.37955i | 0.195839 | + | 0.355021i | ||||
\(699\) | −4.49834 | −0.170143 | ||||||||
\(700\) | 3.97144 | − | 2.38517i | 0.150106 | − | 0.0901511i | ||||
\(701\) | 9.25242 | 0.349459 | 0.174730 | − | 0.984616i | \(-0.444095\pi\) | ||||
0.174730 | + | 0.984616i | \(0.444095\pi\) | |||||||
\(702\) | 1.07136 | + | 1.94220i | 0.0404360 | + | 0.0733035i | ||||
\(703\) | −4.08314 | − | 4.08314i | −0.153999 | − | 0.153999i | ||||
\(704\) | −2.75459 | + | 23.4253i | −0.103818 | + | 0.882875i | ||||
\(705\) | 3.33848 | − | 4.61396i | 0.125735 | − | 0.173772i | ||||
\(706\) | 6.83798 | − | 23.6632i | 0.257351 | − | 0.890576i | ||||
\(707\) | −1.50888 | + | 1.50888i | −0.0567471 | + | 0.0567471i | ||||
\(708\) | −19.2712 | + | 4.36573i | −0.724255 | + | 0.164074i | ||||
\(709\) | 25.0837i | 0.942038i | 0.882123 | + | 0.471019i | \(0.156114\pi\) | ||||
−0.882123 | + | 0.471019i | \(0.843886\pi\) | |||||||
\(710\) | 28.8677 | + | 3.54751i | 1.08339 | + | 0.133136i | ||||
\(711\) | 0.412076i | 0.0154541i | ||||||||
\(712\) | −6.42547 | − | 0.376490i | −0.240805 | − | 0.0141096i | ||||
\(713\) | 0.640030 | − | 0.640030i | 0.0239693 | − | 0.0239693i | ||||
\(714\) | −1.08439 | − | 0.313357i | −0.0405822 | − | 0.0117271i | ||||
\(715\) | −2.64868 | + | 0.424815i | −0.0990551 | + | 0.0158872i | ||||
\(716\) | 3.81829 | − | 6.05501i | 0.142696 | − | 0.226286i | ||||
\(717\) | 11.4239 | + | 11.4239i | 0.426634 | + | 0.426634i | ||||
\(718\) | −29.0450 | + | 16.0220i | −1.08395 | + | 0.597934i | ||||
\(719\) | 37.6238 | 1.40313 | 0.701565 | − | 0.712606i | \(-0.252485\pi\) | ||||
0.701565 | + | 0.712606i | \(0.252485\pi\) | |||||||
\(720\) | −4.03812 | + | 22.0906i | −0.150492 | + | 0.823269i | ||||
\(721\) | −7.09065 | −0.264070 | ||||||||
\(722\) | −1.23831 | + | 0.683080i | −0.0460850 | + | 0.0254216i | ||||
\(723\) | 9.81405 | + | 9.81405i | 0.364988 | + | 0.364988i | ||||
\(724\) | −7.89954 | + | 12.5270i | −0.293584 | + | 0.465563i | ||||
\(725\) | −8.79340 | + | 2.89517i | −0.326579 | + | 0.107524i | ||||
\(726\) | −2.19268 | − | 0.633622i | −0.0813780 | − | 0.0235159i | ||||
\(727\) | −27.9775 | + | 27.9775i | −1.03763 | + | 1.03763i | −0.0383634 | + | 0.999264i | \(0.512214\pi\) |
−0.999264 | + | 0.0383634i | \(0.987786\pi\) | |||||||
\(728\) | −0.532246 | − | 0.0311861i | −0.0197263 | − | 0.00115583i | ||||
\(729\) | 4.05317i | 0.150117i | ||||||||
\(730\) | −13.2950 | − | 17.0204i | −0.492071 | − | 0.629954i | ||||
\(731\) | − | 24.7235i | − | 0.914430i | ||||||
\(732\) | 10.4982 | − | 2.37829i | 0.388026 | − | 0.0879043i | ||||
\(733\) | 13.9853 | − | 13.9853i | 0.516559 | − | 0.516559i | −0.399970 | − | 0.916528i | \(-0.630979\pi\) |
0.916528 | + | 0.399970i | \(0.130979\pi\) | |||||||
\(734\) | −12.9681 | + | 44.8767i | −0.478661 | + | 1.65643i | ||||
\(735\) | 1.68069 | + | 10.4789i | 0.0619932 | + | 0.386522i | ||||
\(736\) | −0.745687 | − | 4.49890i | −0.0274864 | − | 0.165832i | ||||
\(737\) | 28.0444 | + | 28.0444i | 1.03303 | + | 1.03303i | ||||
\(738\) | 17.9762 | + | 32.5876i | 0.661711 | + | 1.19957i | ||||
\(739\) | 40.9090 | 1.50486 | 0.752431 | − | 0.658671i | \(-0.228881\pi\) | ||||
0.752431 | + | 0.658671i | \(0.228881\pi\) | |||||||
\(740\) | 10.1415 | − | 23.7493i | 0.372810 | − | 0.873043i | ||||
\(741\) | −0.284614 | −0.0104555 | ||||||||
\(742\) | −2.53988 | − | 4.60437i | −0.0932421 | − | 0.169032i | ||||
\(743\) | 4.46740 | + | 4.46740i | 0.163893 | + | 0.163893i | 0.784289 | − | 0.620396i | \(-0.213028\pi\) |
−0.620396 | + | 0.784289i | \(0.713028\pi\) | |||||||
\(744\) | −1.47616 | − | 1.65992i | −0.0541188 | − | 0.0608555i | ||||
\(745\) | 23.7564 | + | 17.1892i | 0.870366 | + | 0.629764i | ||||
\(746\) | −3.40105 | + | 11.7695i | −0.124521 | + | 0.430912i | ||||
\(747\) | −4.97890 | + | 4.97890i | −0.182168 | + | 0.182168i | ||||
\(748\) | 3.20901 | + | 14.1652i | 0.117333 | + | 0.517931i | ||||
\(749\) | − | 3.34710i | − | 0.122300i | ||||||
\(750\) | 9.19237 | + | 6.14958i | 0.335658 | + | 0.224551i | ||||
\(751\) | 37.1200i | 1.35453i | 0.735740 | + | 0.677264i | \(0.236834\pi\) | ||||
−0.735740 | + | 0.677264i | \(0.763166\pi\) | |||||||
\(752\) | −13.7318 | − | 4.85488i | −0.500746 | − | 0.177039i | ||||
\(753\) | 2.88223 | − | 2.88223i | 0.105034 | − | 0.105034i | ||||
\(754\) | 1.02357 | + | 0.295782i | 0.0372762 | + | 0.0107718i | ||||
\(755\) | 4.09412 | + | 2.96235i | 0.149000 | + | 0.107811i | ||||
\(756\) | 3.02093 | + | 1.90500i | 0.109870 | + | 0.0692842i | ||||
\(757\) | 17.9260 | + | 17.9260i | 0.651533 | + | 0.651533i | 0.953362 | − | 0.301829i | \(-0.0975972\pi\) |
−0.301829 | + | 0.953362i | \(0.597597\pi\) | |||||||
\(758\) | 28.4456 | − | 15.6913i | 1.03319 | − | 0.569934i | ||||
\(759\) | −1.66252 | −0.0603458 | ||||||||
\(760\) | −4.89829 | − | 4.00085i | −0.177680 | − | 0.145126i | ||||
\(761\) | −31.7582 | −1.15123 | −0.575617 | − | 0.817719i | \(-0.695238\pi\) | ||||
−0.575617 | + | 0.817719i | \(0.695238\pi\) | |||||||
\(762\) | −0.440008 | + | 0.242719i | −0.0159398 | + | 0.00879279i | ||||
\(763\) | −1.71660 | − | 1.71660i | −0.0621452 | − | 0.0621452i | ||||
\(764\) | 6.98543 | + | 4.40501i | 0.252724 | + | 0.159368i | ||||
\(765\) | 2.18989 | + | 13.6538i | 0.0791757 | + | 0.493653i | ||||
\(766\) | 35.6503 | + | 10.3019i | 1.28810 | + | 0.372224i | ||||
\(767\) | −4.06387 | + | 4.06387i | −0.146738 | + | 0.146738i | ||||
\(768\) | −11.1291 | + | 1.18107i | −0.401588 | + | 0.0426184i | ||||
\(769\) | 32.9935i | 1.18977i | 0.803809 | + | 0.594887i | \(0.202803\pi\) | ||||
−0.803809 | + | 0.594887i | \(0.797197\pi\) | |||||||
\(770\) | −3.40387 | + | 2.65883i | −0.122667 | + | 0.0958177i | ||||
\(771\) | 6.12270i | 0.220504i | ||||||||
\(772\) | −3.46309 | − | 15.2867i | −0.124639 | − | 0.550182i | ||||
\(773\) | −13.8810 | + | 13.8810i | −0.499265 | + | 0.499265i | −0.911209 | − | 0.411944i | \(-0.864850\pi\) |
0.411944 | + | 0.911209i | \(0.364850\pi\) | |||||||
\(774\) | −9.89422 | + | 34.2394i | −0.355640 | + | 1.23071i | ||||
\(775\) | 5.33236 | − | 1.75565i | 0.191544 | − | 0.0630648i | ||||
\(776\) | 12.3670 | − | 10.9979i | 0.443948 | − | 0.394803i | ||||
\(777\) | −1.32311 | − | 1.32311i | −0.0474663 | − | 0.0474663i | ||||
\(778\) | 25.4250 | + | 46.0911i | 0.911530 | + | 1.65244i | ||||
\(779\) | −10.4815 | −0.375540 | ||||||||
\(780\) | −0.474263 | − | 1.18117i | −0.0169814 | − | 0.0422928i | ||||
\(781\) | −27.1172 | −0.970330 | ||||||||
\(782\) | −1.35635 | − | 2.45882i | −0.0485029 | − | 0.0879274i | ||||
\(783\) | −5.04665 | − | 5.04665i | −0.180352 | − | 0.180352i | ||||
\(784\) | 24.4917 | − | 11.6971i | 0.874702 | − | 0.417753i | ||||
\(785\) | −35.7837 | + | 5.73926i | −1.27718 | + | 0.204843i | ||||
\(786\) | −1.94320 | + | 6.72453i | −0.0693115 | + | 0.239856i | ||||
\(787\) | 28.4639 | − | 28.4639i | 1.01463 | − | 1.01463i | 0.0147356 | − | 0.999891i | \(-0.495309\pi\) |
0.999891 | − | 0.0147356i | \(-0.00469066\pi\) | |||||||
\(788\) | 16.1681 | − | 3.66275i | 0.575963 | − | 0.130480i | ||||
\(789\) | − | 8.35948i | − | 0.297605i | ||||||
\(790\) | 0.0633043 | − | 0.515137i | 0.00225227 | − | 0.0183277i | ||||
\(791\) | − | 5.98267i | − | 0.212719i | ||||||
\(792\) | 1.22469 | − | 20.9016i | 0.0435176 | − | 0.742705i | ||||
\(793\) | 2.21385 | − | 2.21385i | 0.0786163 | − | 0.0786163i | ||||
\(794\) | −15.7865 | − | 4.56185i | −0.560243 | − | 0.161894i | ||||
\(795\) | 7.35903 | − | 10.1705i | 0.260998 | − | 0.360712i | ||||
\(796\) | 15.7324 | − | 24.9482i | 0.557619 | − | 0.884266i | ||||
\(797\) | 20.8840 | + | 20.8840i | 0.739750 | + | 0.739750i | 0.972530 | − | 0.232779i | \(-0.0747820\pi\) |
−0.232779 | + | 0.972530i | \(0.574782\pi\) | |||||||
\(798\) | −0.401264 | + | 0.221347i | −0.0142046 | + | 0.00783560i | ||||
\(799\) | −8.96861 | −0.317287 | ||||||||
\(800\) | 8.44168 | − | 26.9951i | 0.298458 | − | 0.954423i | ||||
\(801\) | 5.71353 | 0.201878 | ||||||||
\(802\) | −35.4013 | + | 19.5283i | −1.25006 | + | 0.689567i | ||||
\(803\) | 14.2386 | + | 14.2386i | 0.502468 | + | 0.502468i | ||||
\(804\) | −10.0379 | + | 15.9180i | −0.354008 | + | 0.561383i | ||||
\(805\) | 0.489530 | − | 0.676555i | 0.0172537 | − | 0.0238454i | ||||
\(806\) | −0.620698 | − | 0.179364i | −0.0218632 | − | 0.00631783i | ||||
\(807\) | 0.743195 | − | 0.743195i | 0.0261617 | − | 0.0261617i | ||||
\(808\) | −0.762060 | + | 13.0059i | −0.0268092 | + | 0.457546i | ||||
\(809\) | − | 23.6436i | − | 0.831266i | −0.909532 | − | 0.415633i | \(-0.863560\pi\) | ||
0.909532 | − | 0.415633i | \(-0.136440\pi\) | |||||||
\(810\) | 1.86526 | − | 15.1785i | 0.0655387 | − | 0.533319i | ||||
\(811\) | − | 2.24873i | − | 0.0789635i | −0.999220 | − | 0.0394817i | \(-0.987429\pi\) | ||
0.999220 | − | 0.0394817i | \(-0.0125707\pi\) | |||||||
\(812\) | 1.67312 | − | 0.379031i | 0.0587149 | − | 0.0133014i | ||||
\(813\) | −14.6496 | + | 14.6496i | −0.513783 | + | 0.513783i | ||||
\(814\) | −6.68407 | + | 23.1306i | −0.234277 | + | 0.810726i | ||||
\(815\) | −32.7796 | + | 5.25743i | −1.14822 | + | 0.184160i | ||||
\(816\) | −6.21870 | + | 2.97002i | −0.217698 | + | 0.103971i | ||||
\(817\) | −7.09760 | − | 7.09760i | −0.248314 | − | 0.248314i | ||||
\(818\) | −5.73828 | − | 10.4025i | −0.200634 | − | 0.363715i | ||||
\(819\) | 0.473273 | 0.0165375 | ||||||||
\(820\) | −17.4658 | − | 43.4994i | −0.609932 | − | 1.51906i | ||||
\(821\) | −26.4934 | −0.924625 | −0.462312 | − | 0.886717i | \(-0.652980\pi\) | ||||
−0.462312 | + | 0.886717i | \(0.652980\pi\) | |||||||
\(822\) | −2.92415 | − | 5.30098i | −0.101991 | − | 0.184893i | ||||
\(823\) | −34.3245 | − | 34.3245i | −1.19648 | − | 1.19648i | −0.975214 | − | 0.221262i | \(-0.928982\pi\) |
−0.221262 | − | 0.975214i | \(-0.571018\pi\) | |||||||
\(824\) | −32.3499 | + | 28.7687i | −1.12696 | + | 1.00221i | ||||
\(825\) | −9.20581 | − | 4.64538i | −0.320505 | − | 0.161732i | ||||
\(826\) | −2.56895 | + | 8.88998i | −0.0893851 | + | 0.309322i | ||||
\(827\) | −27.3304 | + | 27.3304i | −0.950371 | + | 0.950371i | −0.998825 | − | 0.0484541i | \(-0.984571\pi\) |
0.0484541 | + | 0.998825i | \(0.484571\pi\) | |||||||
\(828\) | 0.894393 | + | 3.94802i | 0.0310823 | + | 0.137203i | ||||
\(829\) | 27.1022i | 0.941297i | 0.882321 | + | 0.470648i | \(0.155980\pi\) | ||||
−0.882321 | + | 0.470648i | \(0.844020\pi\) | |||||||
\(830\) | 6.98899 | − | 5.45925i | 0.242591 | − | 0.189493i | ||||
\(831\) | − | 18.0398i | − | 0.625793i | ||||||
\(832\) | −2.55481 | + | 2.01719i | −0.0885720 | + | 0.0699333i | ||||
\(833\) | 11.8180 | − | 11.8180i | 0.409468 | − | 0.409468i | ||||
\(834\) | −10.8666 | − | 3.14015i | −0.376281 | − | 0.108734i | ||||
\(835\) | −8.00242 | − | 49.8944i | −0.276935 | − | 1.72667i | ||||
\(836\) | 4.98778 | + | 3.14530i | 0.172506 | + | 0.108782i | ||||
\(837\) | 3.06031 | + | 3.06031i | 0.105780 | + | 0.105780i | ||||
\(838\) | 17.7031 | − | 9.76546i | 0.611543 | − | 0.337342i | ||||
\(839\) | −32.8801 | −1.13515 | −0.567573 | − | 0.823323i | \(-0.692118\pi\) | ||||
−0.567573 | + | 0.823323i | \(0.692118\pi\) | |||||||
\(840\) | −1.58725 | − | 1.29644i | −0.0547654 | − | 0.0447315i | ||||
\(841\) | 25.5718 | 0.881785 | ||||||||
\(842\) | −49.6256 | + | 27.3747i | −1.71021 | + | 0.943396i | ||||
\(843\) | 8.03613 | + | 8.03613i | 0.276779 | + | 0.276779i | ||||
\(844\) | 5.81994 | + | 3.67005i | 0.200330 | + | 0.126328i | ||||
\(845\) | 23.2506 | + | 16.8233i | 0.799846 | + | 0.578738i | ||||
\(846\) | 12.4206 | + | 3.58920i | 0.427029 | + | 0.123399i | ||||
\(847\) | −0.755816 | + | 0.755816i | −0.0259701 | + | 0.0259701i | ||||
\(848\) | −30.2690 | − | 10.7016i | −1.03944 | − | 0.367495i | ||||
\(849\) | − | 6.55891i | − | 0.225101i | ||||||
\(850\) | −0.640054 | − | 17.4050i | −0.0219537 | − | 0.596987i | ||||
\(851\) | − | 4.65507i | − | 0.159574i | ||||||
\(852\) | −2.84284 | − | 12.5488i | −0.0973940 | − | 0.429916i | ||||
\(853\) | 20.4055 | − | 20.4055i | 0.698672 | − | 0.698672i | −0.265452 | − | 0.964124i | \(-0.585521\pi\) |
0.964124 | + | 0.265452i | \(0.0855212\pi\) | |||||||
\(854\) | 1.39947 | − | 4.84295i | 0.0478889 | − | 0.165722i | ||||
\(855\) | 4.54839 | + | 3.29105i | 0.155552 | + | 0.112551i | ||||
\(856\) | −13.5801 | − | 15.2706i | −0.464158 | − | 0.521937i | ||||
\(857\) | 2.57518 | + | 2.57518i | 0.0879665 | + | 0.0879665i | 0.749721 | − | 0.661754i | \(-0.230188\pi\) |
−0.661754 | + | 0.749721i | \(0.730188\pi\) | |||||||
\(858\) | 0.573199 | + | 1.03911i | 0.0195687 | + | 0.0354746i | ||||
\(859\) | −48.7635 | −1.66379 | −0.831895 | − | 0.554933i | \(-0.812744\pi\) | ||||
−0.831895 | + | 0.554933i | \(0.812744\pi\) | |||||||
\(860\) | 17.6287 | − | 41.2828i | 0.601134 | − | 1.40773i | ||||
\(861\) | −3.39646 | −0.115751 | ||||||||
\(862\) | −20.6977 | − | 37.5213i | −0.704965 | − | 1.27798i | ||||
\(863\) | −0.809522 | − | 0.809522i | −0.0275565 | − | 0.0275565i | 0.693194 | − | 0.720751i | \(-0.256203\pi\) |
−0.720751 | + | 0.693194i | \(0.756203\pi\) | |||||||
\(864\) | 21.5116 | − | 3.56552i | 0.731839 | − | 0.121301i | ||||
\(865\) | 6.37514 | + | 39.7484i | 0.216761 | + | 1.35149i | ||||
\(866\) | −2.31434 | + | 8.00890i | −0.0786445 | + | 0.272154i | ||||
\(867\) | 5.40757 | − | 5.40757i | 0.183651 | − | 0.183651i | ||||
\(868\) | −1.01459 | + | 0.229847i | −0.0344373 | + | 0.00780150i | ||||
\(869\) | 0.483899i | 0.0164152i | ||||||||
\(870\) | 2.52112 | + | 3.22757i | 0.0854740 | + | 0.109425i | ||||
\(871\) | 5.47352i | 0.185463i | ||||||||
\(872\) | −14.7964 | − | 0.866973i | −0.501071 | − | 0.0293594i | ||||
\(873\) | −10.3880 | + | 10.3880i | −0.351582 | + | 0.351582i | ||||
\(874\) | −1.09526 | − | 0.316498i | −0.0370477 | − | 0.0107057i | ||||
\(875\) | 4.60107 | − | 2.37842i | 0.155544 | − | 0.0804054i | ||||
\(876\) | −5.09637 | + | 8.08177i | −0.172190 | + | 0.273058i | ||||
\(877\) | −18.6769 | − | 18.6769i | −0.630676 | − | 0.630676i | 0.317562 | − | 0.948238i | \(-0.397136\pi\) |
−0.948238 | + | 0.317562i | \(0.897136\pi\) | |||||||
\(878\) | −23.9538 | + | 13.2135i | −0.808403 | + | 0.445935i | ||||
\(879\) | −14.2952 | −0.482165 | ||||||||
\(880\) | −4.74195 | + | 25.9409i | −0.159851 | + | 0.874468i | ||||
\(881\) | −33.9283 | −1.14307 | −0.571536 | − | 0.820577i | \(-0.693652\pi\) | ||||
−0.571536 | + | 0.820577i | \(0.693652\pi\) | |||||||
\(882\) | −21.0961 | + | 11.6372i | −0.710344 | + | 0.391843i | ||||
\(883\) | 16.3593 | + | 16.3593i | 0.550535 | + | 0.550535i | 0.926595 | − | 0.376060i | \(-0.122721\pi\) |
−0.376060 | + | 0.926595i | \(0.622721\pi\) | |||||||
\(884\) | −1.06918 | + | 1.69549i | −0.0359603 | + | 0.0570255i | ||||
\(885\) | −21.8130 | + | 3.49853i | −0.733236 | + | 0.117602i | ||||
\(886\) | 7.99147 | + | 2.30931i | 0.268479 | + | 0.0775827i | ||||
\(887\) | −33.6480 | + | 33.6480i | −1.12979 | + | 1.12979i | −0.139579 | + | 0.990211i | \(0.544575\pi\) |
−0.990211 | + | 0.139579i | \(0.955425\pi\) | |||||||
\(888\) | −11.4047 | − | 0.668239i | −0.382716 | − | 0.0224246i | ||||
\(889\) | 0.235336i | 0.00789291i | ||||||||
\(890\) | −7.14248 | − | 0.877728i | −0.239417 | − | 0.0294215i | ||||
\(891\) | 14.2581i | 0.477664i | ||||||||
\(892\) | 27.4797 | − | 6.22530i | 0.920087 | − | 0.208438i | ||||
\(893\) | −2.57471 | + | 2.57471i | −0.0861592 | + | 0.0861592i | ||||
\(894\) | 3.60122 | − | 12.4622i | 0.120443 | − | 0.416799i | ||||
\(895\) | 4.69158 | − | 6.48400i | 0.156822 | − | 0.216736i | ||||
\(896\) | −2.03312 | + | 4.83084i | −0.0679217 | + | 0.161387i | ||||
\(897\) | −0.162240 | − | 0.162240i | −0.00541703 | − | 0.00541703i | ||||
\(898\) | −15.1388 | − | 27.4441i | −0.505189 | − | 0.915820i | ||||
\(899\) | 2.07890 | 0.0693352 | ||||||||
\(900\) | −6.07899 | + | 24.3603i | −0.202633 | + | 0.812010i | ||||
\(901\) | −19.7695 | −0.658618 | ||||||||
\(902\) | 21.1093 | + | 38.2675i | 0.702863 | + | 1.27417i | ||||
\(903\) | −2.29992 | − | 2.29992i | −0.0765367 | − | 0.0765367i | ||||
\(904\) | −24.2734 | − | 27.2949i | −0.807320 | − | 0.907815i | ||||
\(905\) | −9.70625 | + | 13.4145i | −0.322647 | + | 0.445914i | ||||
\(906\) | 0.620626 | − | 2.14771i | 0.0206189 | − | 0.0713529i | ||||
\(907\) | 9.92358 | − | 9.92358i | 0.329507 | − | 0.329507i | −0.522892 | − | 0.852399i | \(-0.675147\pi\) |
0.852399 | + | 0.522892i | \(0.175147\pi\) | |||||||
\(908\) | 5.27927 | + | 23.3037i | 0.175199 | + | 0.773361i | ||||
\(909\) | − | 11.5649i | − | 0.383582i | ||||||
\(910\) | −0.591639 | − | 0.0727055i | −0.0196126 | − | 0.00241016i | ||||
\(911\) | 32.8155i | 1.08722i | 0.839337 | + | 0.543612i | \(0.182944\pi\) | ||||
−0.839337 | + | 0.543612i | \(0.817056\pi\) | |||||||
\(912\) | −0.932630 | + | 2.63789i | −0.0308825 | + | 0.0873494i | ||||
\(913\) | −5.84669 | + | 5.84669i | −0.193497 | + | 0.193497i | ||||
\(914\) | −20.8374 | − | 6.02141i | −0.689240 | − | 0.199171i | ||||
\(915\) | 11.8829 | − | 1.90587i | 0.392838 | − | 0.0630063i | ||||
\(916\) | 14.6167 | + | 9.21731i | 0.482950 | + | 0.304549i | ||||
\(917\) | 2.31794 | + | 2.31794i | 0.0765452 | + | 0.0765452i | ||||
\(918\) | 11.7569 | − | 6.48540i | 0.388036 | − | 0.214050i | ||||
\(919\) | 13.4713 | 0.444377 | 0.222188 | − | 0.975004i | \(-0.428680\pi\) | ||||
0.222188 | + | 0.975004i | \(0.428680\pi\) | |||||||
\(920\) | −0.511575 | − | 5.07282i | −0.0168661 | − | 0.167246i | ||||
\(921\) | −11.2424 | −0.370450 | ||||||||
\(922\) | 7.79668 | − | 4.30084i | 0.256770 | − | 0.141641i | ||||
\(923\) | −2.64628 | − | 2.64628i | −0.0871032 | − | 0.0871032i | ||||
\(924\) | 1.61625 | + | 1.01921i | 0.0531708 | + | 0.0335295i | ||||
\(925\) | 13.0071 | − | 25.7763i | 0.427670 | − | 0.847519i | ||||
\(926\) | −10.7746 | − | 3.11356i | −0.354077 | − | 0.102318i | ||||
\(927\) | 27.1733 | − | 27.1733i | 0.892489 | − | 0.892489i | ||||
\(928\) | 6.09547 | − | 8.51756i | 0.200094 | − | 0.279603i | ||||
\(929\) | − | 30.3568i | − | 0.995973i | −0.867185 | − | 0.497987i | \(-0.834073\pi\) | ||
0.867185 | − | 0.497987i | \(-0.165927\pi\) | |||||||
\(930\) | −1.52882 | − | 1.95721i | −0.0501320 | − | 0.0641796i | ||||
\(931\) | − | 6.78539i | − | 0.222382i | ||||||
\(932\) | 2.84178 | + | 12.5442i | 0.0930855 | + | 0.410897i | ||||
\(933\) | 15.6464 | − | 15.6464i | 0.512240 | − | 0.512240i | ||||
\(934\) | −13.1427 | + | 45.4810i | −0.430042 | + | 1.48818i | ||||
\(935\) | 2.57158 | + | 16.0336i | 0.0840996 | + | 0.524353i | ||||
\(936\) | 2.15923 | − | 1.92020i | 0.0705765 | − | 0.0627637i | ||||
\(937\) | −27.4311 | − | 27.4311i | −0.896135 | − | 0.896135i | 0.0989565 | − | 0.995092i | \(-0.468450\pi\) |
−0.995092 | + | 0.0989565i | \(0.968450\pi\) | |||||||
\(938\) | 4.25681 | + | 7.71686i | 0.138990 | + | 0.251964i | ||||
\(939\) | −4.06762 | −0.132742 | ||||||||
\(940\) | −14.9756 | − | 6.39494i | −0.488451 | − | 0.208580i | ||||
\(941\) | 12.9566 | 0.422372 | 0.211186 | − | 0.977446i | \(-0.432267\pi\) | ||||
0.211186 | + | 0.977446i | \(0.432267\pi\) | |||||||
\(942\) | 7.74392 | + | 14.0384i | 0.252311 | + | 0.457395i | ||||
\(943\) | −5.97484 | − | 5.97484i | −0.194568 | − | 0.194568i | ||||
\(944\) | 24.3487 | + | 50.9819i | 0.792483 | + | 1.65932i | ||||
\(945\) | 3.23496 | + | 2.34070i | 0.105233 | + | 0.0761428i | ||||
\(946\) | −11.6187 | + | 40.2072i | −0.377757 | + | 1.30725i | ||||
\(947\) | −22.3305 | + | 22.3305i | −0.725642 | + | 0.725642i | −0.969748 | − | 0.244106i | \(-0.921505\pi\) |
0.244106 | + | 0.969748i | \(0.421505\pi\) | |||||||
\(948\) | −0.223930 | + | 0.0507296i | −0.00727292 | + | 0.00164762i | ||||
\(949\) | 2.77899i | 0.0902097i | ||||||||
\(950\) | −5.18037 | − | 4.81288i | −0.168073 | − | 0.156150i | ||||
\(951\) | 21.1391i | 0.685483i | ||||||||
\(952\) | −0.188782 | + | 3.22190i | −0.00611846 | + | 0.104422i | ||||
\(953\) | 1.79070 | − | 1.79070i | 0.0580064 | − | 0.0580064i | −0.677509 | − | 0.735515i | \(-0.736940\pi\) |
0.735515 | + | 0.677509i | \(0.236940\pi\) | |||||||
\(954\) | 27.3787 | + | 7.91167i | 0.886420 | + | 0.256150i | ||||
\(955\) | 7.48033 | + | 5.41249i | 0.242058 | + | 0.175144i | ||||
\(956\) | 24.6400 | − | 39.0739i | 0.796915 | − | 1.26374i | ||||
\(957\) | −2.70005 | − | 2.70005i | −0.0872801 | − | 0.0872801i | ||||
\(958\) | −15.8507 | + | 8.74367i | −0.512114 | + | 0.282495i | ||||
\(959\) | −2.83520 | −0.0915533 | ||||||||
\(960\) | −12.5016 | + | 0.525125i | −0.403487 | + | 0.0169483i | ||||
\(961\) | 29.7393 | 0.959334 | ||||||||
\(962\) | −2.90951 | + | 1.60496i | −0.0938063 | + | 0.0517459i | ||||
\(963\) | 12.8270 | + | 12.8270i | 0.413344 | + | 0.413344i | ||||
\(964\) | 21.1677 | − | 33.5676i | 0.681766 | − | 1.08114i | ||||
\(965\) | −2.77519 | − | 17.3030i | −0.0893364 | − | 0.557004i | ||||
\(966\) | −0.354910 | − | 0.102559i | −0.0114190 | − | 0.00329978i | ||||
\(967\) | −11.6241 | + | 11.6241i | −0.373807 | + | 0.373807i | −0.868862 | − | 0.495055i | \(-0.835148\pi\) |
0.495055 | + | 0.868862i | \(0.335148\pi\) | |||||||
\(968\) | −0.381726 | + | 6.51483i | −0.0122691 | + | 0.209395i | ||||
\(969\) | 1.72288i | 0.0553470i | ||||||||
\(970\) | 14.5819 | − | 11.3903i | 0.468198 | − | 0.365719i | ||||
\(971\) | 16.0160i | 0.513977i | 0.966415 | + | 0.256988i | \(0.0827302\pi\) | ||||
−0.966415 | + | 0.256988i | \(0.917270\pi\) | |||||||
\(972\) | −29.1543 | + | 6.60468i | −0.935125 | + | 0.211845i | ||||
\(973\) | −3.74573 | + | 3.74573i | −0.120082 | + | 0.120082i | ||||
\(974\) | −5.96973 | + | 20.6586i | −0.191282 | + | 0.661943i | ||||
\(975\) | −0.445036 | − | 1.35169i | −0.0142526 | − | 0.0432887i | ||||
\(976\) | −13.2643 | − | 27.7731i | −0.424580 | − | 0.888996i | ||||
\(977\) | 10.3212 | + | 10.3212i | 0.330205 | + | 0.330205i | 0.852664 | − | 0.522459i | \(-0.174985\pi\) |
−0.522459 | + | 0.852664i | \(0.674985\pi\) | |||||||
\(978\) | 7.09379 | + | 12.8598i | 0.226834 | + | 0.411211i | ||||
\(979\) | 6.70937 | 0.214432 | ||||||||
\(980\) | 28.1600 | − | 11.3068i | 0.899539 | − | 0.361181i | ||||
\(981\) | 13.1570 | 0.420071 | ||||||||
\(982\) | −26.8253 | − | 48.6296i | −0.856031 | − | 1.55183i | ||||
\(983\) | −20.0695 | − | 20.0695i | −0.640119 | − | 0.640119i | 0.310466 | − | 0.950585i | \(-0.399515\pi\) |
−0.950585 | + | 0.310466i | \(0.899515\pi\) | |||||||
\(984\) | −15.4958 | + | 13.7804i | −0.493987 | + | 0.439302i | ||||
\(985\) | 18.3006 | − | 2.93519i | 0.583106 | − | 0.0935228i | ||||
\(986\) | 1.79049 | − | 6.19609i | 0.0570209 | − | 0.197324i | ||||
\(987\) | −0.834314 | + | 0.834314i | −0.0265565 | + | 0.0265565i | ||||
\(988\) | 0.179802 | + | 0.793679i | 0.00572025 | + | 0.0252503i | ||||
\(989\) | − | 8.09177i | − | 0.257303i | ||||||
\(990\) | 2.85518 | − | 23.2340i | 0.0907437 | − | 0.738424i | ||||
\(991\) | 59.6794i | 1.89578i | 0.318599 | + | 0.947890i | \(0.396788\pi\) | ||||
−0.318599 | + | 0.947890i | \(0.603212\pi\) | |||||||
\(992\) | −3.69632 | + | 5.16509i | −0.117358 | + | 0.163992i | ||||
\(993\) | 14.2518 | − | 14.2518i | 0.452266 | − | 0.452266i | ||||
\(994\) | −5.78890 | − | 1.67282i | −0.183613 | − | 0.0530588i | ||||
\(995\) | 19.3305 | − | 26.7158i | 0.612819 | − | 0.846947i | ||||
\(996\) | −3.31857 | − | 2.09269i | −0.105153 | − | 0.0663094i | ||||
\(997\) | −8.77680 | − | 8.77680i | −0.277964 | − | 0.277964i | 0.554332 | − | 0.832296i | \(-0.312974\pi\) |
−0.832296 | + | 0.554332i | \(0.812974\pi\) | |||||||
\(998\) | 44.3953 | − | 24.4896i | 1.40531 | − | 0.775204i | ||||
\(999\) | 22.2583 | 0.704221 |
(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 | 380.2.k.d.267.5 | yes | 52 | |
4.3 | odd | 2 | 380.2.k.c.267.19 | ✓ | 52 | ||
5.3 | odd | 4 | 380.2.k.c.343.19 | yes | 52 | ||
20.3 | even | 4 | inner | 380.2.k.d.343.5 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.k.c.267.19 | ✓ | 52 | 4.3 | odd | 2 | ||
380.2.k.c.343.19 | yes | 52 | 5.3 | odd | 4 | ||
380.2.k.d.267.5 | yes | 52 | 1.1 | even | 1 | trivial | |
380.2.k.d.343.5 | yes | 52 | 20.3 | even | 4 | inner |