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 | 343.19 | ||
Character | \(\chi\) | \(=\) | 380.343 |
Dual form | 380.2.k.c.267.19 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.683080 | + | 1.23831i | 0.483011 | + | 0.875614i | ||||
\(3\) | −0.494605 | + | 0.494605i | −0.285560 | + | 0.285560i | −0.835322 | − | 0.549762i | \(-0.814719\pi\) |
0.549762 | + | 0.835322i | \(0.314719\pi\) | |||||||
\(4\) | −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 | \(-0.222097\pi\) |
−0.642485 | + | 0.766298i | \(0.722097\pi\) | |||||||
\(8\) | −2.82358 | − | 0.165443i | −0.998288 | − | 0.0584930i | ||||
\(9\) | 2.51073i | 0.836911i | ||||||||
\(10\) | −1.34791 | + | 2.86062i | −0.426248 | + | 0.904606i | ||||
\(11\) | − | 2.94834i | − | 0.888958i | −0.895789 | − | 0.444479i | \(-0.853389\pi\) | ||
0.895789 | − | 0.444479i | \(-0.146611\pi\) | |||||||
\(12\) | −0.309090 | − | 1.36438i | −0.0892265 | − | 0.393863i | ||||
\(13\) | 0.287718 | + | 0.287718i | 0.0797987 | + | 0.0797987i | 0.745880 | − | 0.666081i | \(-0.232029\pi\) |
−0.666081 | + | 0.745880i | \(0.732029\pi\) | |||||||
\(14\) | −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 | −0.886036 | − | 0.463617i | \(-0.846551\pi\) |
0.463617 | + | 0.886036i | \(0.346551\pi\) | |||||||
\(18\) | −3.10905 | + | 1.71503i | −0.732811 | + | 0.404237i | ||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −4.46305 | + | 0.284901i | −0.997969 | + | 0.0637057i | ||||
\(21\) | −0.324042 | −0.0707118 | ||||||||
\(22\) | 3.65095 | − | 2.01395i | 0.778384 | − | 0.429376i | ||||
\(23\) | 0.570036 | − | 0.570036i | 0.118861 | − | 0.118861i | −0.645175 | − | 0.764035i | \(-0.723215\pi\) |
0.764035 | + | 0.645175i | \(0.223215\pi\) | |||||||
\(24\) | 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 | ||||
\(28\) | −0.903630 | + | 0.204710i | −0.170770 | + | 0.0386866i | ||||
\(29\) | 1.85155i | 0.343824i | 0.985112 | + | 0.171912i | \(0.0549945\pi\) | ||||
−0.985112 | + | 0.171912i | \(0.945006\pi\) | |||||||
\(30\) | −0.748189 | − | 2.08156i | −0.136600 | − | 0.380039i | ||||
\(31\) | 1.12279i | 0.201659i | 0.994904 | + | 0.100829i | \(0.0321496\pi\) | ||||
−0.994904 | + | 0.100829i | \(0.967850\pi\) | |||||||
\(32\) | 3.29209 | − | 4.60023i | 0.581965 | − | 0.813214i | ||||
\(33\) | 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 | −0.286743 | − | 0.958007i | \(-0.592573\pi\) |
0.958007 | + | 0.286743i | \(0.0925727\pi\) | |||||||
\(38\) | 0.683080 | + | 1.23831i | 0.110810 | + | 0.200880i | ||||
\(39\) | −0.284614 | −0.0455747 | ||||||||
\(40\) | −3.40142 | − | 5.33201i | −0.537811 | − | 0.843065i | ||||
\(41\) | 10.4815 | 1.63694 | 0.818470 | − | 0.574550i | \(-0.194823\pi\) | ||||
0.818470 | + | 0.574550i | \(0.194823\pi\) | |||||||
\(42\) | −0.221347 | − | 0.401264i | −0.0341546 | − | 0.0619163i | ||||
\(43\) | −7.09760 | + | 7.09760i | −1.08237 | + | 1.08237i | −0.0860866 | + | 0.996288i | \(0.527436\pi\) |
−0.996288 | + | 0.0860866i | \(0.972564\pi\) | |||||||
\(44\) | 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 | \(-0.335557\pi\) |
−0.869497 | + | 0.493938i | \(0.835557\pi\) | |||||||
\(48\) | 2.63789 | + | 0.932630i | 0.380747 | + | 0.134613i | ||||
\(49\) | − | 6.78539i | − | 0.969341i | ||||||
\(50\) | −6.94907 | + | 1.30782i | −0.982747 | + | 0.184953i | ||||
\(51\) | − | 1.72288i | − | 0.241252i | ||||||
\(52\) | −0.793679 | + | 0.179802i | −0.110063 | + | 0.0249340i | ||||
\(53\) | 5.67543 | + | 5.67543i | 0.779580 | + | 0.779580i | 0.979759 | − | 0.200180i | \(-0.0641525\pi\) |
−0.200180 | + | 0.979759i | \(0.564153\pi\) | |||||||
\(54\) | 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 | ||||
\(58\) | −2.29278 | + | 1.26476i | −0.301057 | + | 0.166071i | ||||
\(59\) | 14.1245 | 1.83885 | 0.919425 | − | 0.393265i | \(-0.128655\pi\) | ||||
0.919425 | + | 0.393265i | \(0.128655\pi\) | |||||||
\(60\) | 2.06653 | − | 2.34836i | 0.266788 | − | 0.303172i | ||||
\(61\) | 7.69452 | 0.985182 | 0.492591 | − | 0.870261i | \(-0.336050\pi\) | ||||
0.492591 | + | 0.870261i | \(0.336050\pi\) | |||||||
\(62\) | −1.39036 | + | 0.766955i | −0.176575 | + | 0.0974034i | ||||
\(63\) | −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 | 0.984022 | + | 0.178047i | \(0.0569778\pi\) |
0.178047 | + | 0.984022i | \(0.443022\pi\) | |||||||
\(68\) | −1.08841 | − | 4.80446i | −0.131990 | − | 0.582627i | ||||
\(69\) | 0.563885i | 0.0678837i | ||||||||
\(70\) | −1.37862 | + | 0.495527i | −0.164776 | + | 0.0592267i | ||||
\(71\) | − | 9.19745i | − | 1.09154i | −0.837936 | − | 0.545768i | \(-0.816238\pi\) | ||
0.837936 | − | 0.545768i | \(-0.183762\pi\) | |||||||
\(72\) | 0.415384 | − | 7.08926i | 0.0489535 | − | 0.835478i | ||||
\(73\) | −4.82935 | − | 4.82935i | −0.565233 | − | 0.565233i | 0.365556 | − | 0.930789i | \(-0.380879\pi\) |
−0.930789 | + | 0.365556i | \(0.880879\pi\) | |||||||
\(74\) | 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 | ||||
\(78\) | −0.194414 | − | 0.352439i | −0.0220131 | − | 0.0399058i | ||||
\(79\) | 0.164126 | 0.0184656 | 0.00923281 | − | 0.999957i | \(-0.497061\pi\) | ||||
0.00923281 | + | 0.999957i | \(0.497061\pi\) | |||||||
\(80\) | 4.27922 | − | 7.85419i | 0.478431 | − | 0.878125i | ||||
\(81\) | −4.83597 | −0.537331 | ||||||||
\(82\) | 7.15972 | + | 12.9793i | 0.790659 | + | 1.43333i | ||||
\(83\) | 1.98305 | − | 1.98305i | 0.217667 | − | 0.217667i | −0.589847 | − | 0.807515i | \(-0.700812\pi\) |
0.807515 | + | 0.589847i | \(0.200812\pi\) | |||||||
\(84\) | 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 | ||||
\(88\) | −0.487783 | + | 8.32489i | −0.0519979 | + | 0.887436i | ||||
\(89\) | − | 2.27564i | − | 0.241218i | −0.992700 | − | 0.120609i | \(-0.961515\pi\) | ||
0.992700 | − | 0.120609i | \(-0.0384847\pi\) | |||||||
\(90\) | −7.18224 | − | 3.38425i | −0.757075 | − | 0.356732i | ||||
\(91\) | 0.188500i | 0.0197602i | ||||||||
\(92\) | 0.356228 | + | 1.57246i | 0.0371393 | + | 0.163940i | ||||
\(93\) | −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 | −0.885236 | − | 0.465141i | \(-0.846003\pi\) |
0.465141 | + | 0.885236i | \(0.346003\pi\) | |||||||
\(98\) | 8.40238 | − | 4.63496i | 0.848769 | − | 0.468202i | ||||
\(99\) | 7.40249 | 0.743978 | ||||||||
\(100\) | −6.36625 | − | 7.71173i | −0.636625 | − | 0.771173i | ||||
\(101\) | 4.60617 | 0.458331 | 0.229165 | − | 0.973387i | \(-0.426400\pi\) | ||||
0.229165 | + | 0.973387i | \(0.426400\pi\) | |||||||
\(102\) | 2.13346 | − | 1.17687i | 0.211244 | − | 0.116527i | ||||
\(103\) | −10.8229 | + | 10.8229i | −1.06641 | + | 1.06641i | −0.0687770 | + | 0.997632i | \(0.521910\pi\) |
−0.997632 | + | 0.0687770i | \(0.978090\pi\) | |||||||
\(104\) | −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 | \(-0.136441\pi\) |
−0.415637 | + | 0.909530i | \(0.636441\pi\) | |||||||
\(108\) | 7.51874 | − | 1.70331i | 0.723491 | − | 0.163901i | ||||
\(109\) | − | 5.24030i | − | 0.501930i | −0.967996 | − | 0.250965i | \(-0.919252\pi\) | ||
0.967996 | − | 0.250965i | \(-0.0807479\pi\) | |||||||
\(110\) | 8.43407 | + | 3.97411i | 0.804157 | + | 0.378917i | ||||
\(111\) | 4.03908i | 0.383372i | ||||||||
\(112\) | 0.617681 | − | 1.74708i | 0.0583654 | − | 0.165083i | ||||
\(113\) | −9.13170 | − | 9.13170i | −0.859038 | − | 0.859038i | 0.132186 | − | 0.991225i | \(-0.457800\pi\) |
−0.991225 | + | 0.132186i | \(0.957800\pi\) | |||||||
\(114\) | −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 | ||||
\(118\) | 9.64815 | + | 17.4904i | 0.888185 | + | 1.61012i | ||||
\(119\) | −1.14107 | −0.104601 | ||||||||
\(120\) | 4.31960 | + | 0.954882i | 0.394323 | + | 0.0871684i | ||||
\(121\) | 2.30729 | 0.209754 | ||||||||
\(122\) | 5.25597 | + | 9.52816i | 0.475853 | + | 0.862639i | ||||
\(123\) | −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 | \(-0.257175\pi\) |
−0.722864 | + | 0.690990i | \(0.757175\pi\) | |||||||
\(128\) | 4.27032 | + | 10.4769i | 0.377446 | + | 0.926031i | ||||
\(129\) | − | 7.02101i | − | 0.618166i | ||||||
\(130\) | −1.21087 | + | 0.435232i | −0.106200 | + | 0.0381724i | ||||
\(131\) | − | 7.07602i | − | 0.618235i | −0.951024 | − | 0.309117i | \(-0.899966\pi\) | ||
0.951024 | − | 0.309117i | \(-0.100034\pi\) | |||||||
\(132\) | −4.02266 | + | 0.911301i | −0.350127 | + | 0.0793186i | ||||
\(133\) | 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 | −0.497651 | − | 0.867377i | \(-0.665804\pi\) |
0.867377 | + | 0.497651i | \(0.165804\pi\) | |||||||
\(138\) | −0.698261 | + | 0.385178i | −0.0594400 | + | 0.0327886i | ||||
\(139\) | −11.4346 | −0.969873 | −0.484937 | − | 0.874549i | \(-0.661157\pi\) | ||||
−0.484937 | + | 0.874549i | \(0.661157\pi\) | |||||||
\(140\) | −1.55532 | − | 1.36867i | −0.131449 | − | 0.115673i | ||||
\(141\) | 2.54692 | 0.214490 | ||||||||
\(142\) | 11.3893 | − | 6.28260i | 0.955765 | − | 0.527224i | ||||
\(143\) | 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 | ||||
\(148\) | 2.55165 | + | 11.2635i | 0.209744 | + | 0.925850i | ||||
\(149\) | − | 13.1136i | − | 1.07431i | −0.843484 | − | 0.537155i | \(-0.819499\pi\) | ||
0.843484 | − | 0.537155i | \(-0.180501\pi\) | |||||||
\(150\) | 2.79019 | − | 4.08390i | 0.227818 | − | 0.333449i | ||||
\(151\) | 2.25997i | 0.183914i | 0.995763 | + | 0.0919569i | \(0.0293122\pi\) | ||||
−0.995763 | + | 0.0919569i | \(0.970688\pi\) | |||||||
\(152\) | −2.82358 | − | 0.165443i | −0.229023 | − | 0.0134192i | ||||
\(153\) | −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 | −0.996633 | − | 0.0819909i | \(-0.973872\pi\) |
0.0819909 | + | 0.996633i | \(0.473872\pi\) | |||||||
\(158\) | 0.112111 | + | 0.203238i | 0.00891909 | + | 0.0161688i | ||||
\(159\) | −5.61418 | −0.445234 | ||||||||
\(160\) | 12.6489 | − | 0.0660585i | 0.999986 | − | 0.00522239i | ||||
\(161\) | 0.373461 | 0.0294329 | ||||||||
\(162\) | −3.30336 | − | 5.98842i | −0.259536 | − | 0.470494i | ||||
\(163\) | 10.4983 | − | 10.4983i | 0.822289 | − | 0.822289i | −0.164147 | − | 0.986436i | \(-0.552487\pi\) |
0.986436 | + | 0.164147i | \(0.0524870\pi\) | |||||||
\(164\) | −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 | −0.961405 | − | 0.275136i | \(-0.911277\pi\) |
−0.275136 | − | 0.961405i | \(-0.588723\pi\) | |||||||
\(168\) | 0.914961 | + | 0.0536106i | 0.0705908 | + | 0.00413615i | ||||
\(169\) | − | 12.8344i | − | 0.987264i | ||||||
\(170\) | −2.63464 | − | 7.32990i | −0.202068 | − | 0.562178i | ||||
\(171\) | 2.51073i | 0.192001i | ||||||||
\(172\) | −4.43545 | − | 19.5789i | −0.338200 | − | 1.49288i | ||||
\(173\) | −12.7302 | − | 12.7302i | −0.967858 | − | 0.967858i | 0.0316413 | − | 0.999499i | \(-0.489927\pi\) |
−0.999499 | + | 0.0316413i | \(0.989927\pi\) | |||||||
\(174\) | 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 | ||||
\(178\) | 2.81794 | − | 1.55445i | 0.211214 | − | 0.116511i | ||||
\(179\) | −3.57919 | −0.267522 | −0.133761 | − | 0.991014i | \(-0.542705\pi\) | ||||
−0.133761 | + | 0.991014i | \(0.542705\pi\) | |||||||
\(180\) | −0.715309 | − | 11.2055i | −0.0533160 | − | 0.835211i | ||||
\(181\) | −7.40488 | −0.550400 | −0.275200 | − | 0.961387i | \(-0.588744\pi\) | ||||
−0.275200 | + | 0.961387i | \(0.588744\pi\) | |||||||
\(182\) | −0.233421 | + | 0.128761i | −0.0173023 | + | 0.00954437i | ||||
\(183\) | −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 | ||||
\(188\) | 7.10239 | − | 1.60899i | 0.517995 | − | 0.117348i | ||||
\(189\) | − | 1.78571i | − | 0.129891i | ||||||
\(190\) | −1.34791 | + | 2.86062i | −0.0977880 | + | 0.207531i | ||||
\(191\) | 4.12918i | 0.298777i | 0.988779 | + | 0.149388i | \(0.0477304\pi\) | ||||
−0.988779 | + | 0.149388i | \(0.952270\pi\) | |||||||
\(192\) | −4.39186 | + | 3.46766i | −0.316955 | + | 0.250257i | ||||
\(193\) | 5.54163 | + | 5.54163i | 0.398895 | + | 0.398895i | 0.877843 | − | 0.478948i | \(-0.158982\pi\) |
−0.478948 | + | 0.877843i | \(0.658982\pi\) | |||||||
\(194\) | −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 | −0.466784 | − | 0.884371i | \(-0.654587\pi\) |
0.884371 | + | 0.466784i | \(0.154587\pi\) | |||||||
\(198\) | 5.05650 | + | 9.16655i | 0.359350 | + | 0.651438i | ||||
\(199\) | −14.7472 | −1.04540 | −0.522701 | − | 0.852516i | \(-0.675076\pi\) | ||||
−0.522701 | + | 0.852516i | \(0.675076\pi\) | |||||||
\(200\) | 5.20082 | − | 13.1511i | 0.367754 | − | 0.929923i | ||||
\(201\) | −9.40930 | −0.663681 | ||||||||
\(202\) | 3.14638 | + | 5.70385i | 0.221379 | + | 0.401321i | ||||
\(203\) | −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 | ||||
\(208\) | 0.542524 | − | 1.53450i | 0.0376172 | − | 0.106398i | ||||
\(209\) | − | 2.94834i | − | 0.203941i | ||||||
\(210\) | 0.436781 | − | 0.926961i | 0.0301408 | − | 0.0639664i | ||||
\(211\) | 3.44024i | 0.236836i | 0.992964 | + | 0.118418i | \(0.0377822\pi\) | ||||
−0.992964 | + | 0.118418i | \(0.962218\pi\) | |||||||
\(212\) | −15.6558 | + | 3.54670i | −1.07525 | + | 0.243588i | ||||
\(213\) | 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 | ||||
\(218\) | 6.48910 | − | 3.57955i | 0.439497 | − | 0.242438i | ||||
\(219\) | 4.77724 | 0.322816 | ||||||||
\(220\) | 0.839984 | + | 13.1586i | 0.0566317 | + | 0.887152i | ||||
\(221\) | −1.00223 | −0.0674170 | ||||||||
\(222\) | −5.00162 | + | 2.75902i | −0.335686 | + | 0.185173i | ||||
\(223\) | −9.96172 | + | 9.96172i | −0.667086 | + | 0.667086i | −0.957040 | − | 0.289955i | \(-0.906360\pi\) |
0.289955 | + | 0.957040i | \(0.406360\pi\) | |||||||
\(224\) | 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 | \(-0.120232\pi\) |
−0.368802 | + | 0.929508i | \(0.620232\pi\) | |||||||
\(228\) | −0.309090 | − | 1.36438i | −0.0204700 | − | 0.0903583i | ||||
\(229\) | − | 8.64013i | − | 0.570956i | −0.958385 | − | 0.285478i | \(-0.907848\pi\) | ||
0.958385 | − | 0.285478i | \(-0.0921524\pi\) | |||||||
\(230\) | 0.862294 | + | 2.39901i | 0.0568580 | + | 0.158186i | ||||
\(231\) | 0.955387i | 0.0628599i | ||||||||
\(232\) | 0.306326 | − | 5.22801i | 0.0201113 | − | 0.343235i | ||||
\(233\) | −4.54741 | − | 4.54741i | −0.297911 | − | 0.297911i | 0.542284 | − | 0.840195i | \(-0.317560\pi\) |
−0.840195 | + | 0.542284i | \(0.817560\pi\) | |||||||
\(234\) | −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 | ||||
\(238\) | −0.779441 | − | 1.41299i | −0.0505236 | − | 0.0915906i | ||||
\(239\) | −23.0971 | −1.49403 | −0.747013 | − | 0.664810i | \(-0.768513\pi\) | ||||
−0.747013 | + | 0.664810i | \(0.768513\pi\) | |||||||
\(240\) | 1.76820 | + | 6.00124i | 0.114137 | + | 0.387378i | ||||
\(241\) | 19.8422 | 1.27815 | 0.639075 | − | 0.769145i | \(-0.279317\pi\) | ||||
0.639075 | + | 0.769145i | \(0.279317\pi\) | |||||||
\(242\) | 1.57607 | + | 2.85713i | 0.101313 | + | 0.183663i | ||||
\(243\) | 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 | ||||
\(248\) | 0.185758 | − | 3.17029i | 0.0117956 | − | 0.201314i | ||||
\(249\) | 1.96165i | 0.124314i | ||||||||
\(250\) | −11.4780 | − | 10.8745i | −0.725933 | − | 0.687766i | ||||
\(251\) | − | 5.82734i | − | 0.367819i | −0.982943 | − | 0.183909i | \(-0.941125\pi\) | ||
0.982943 | − | 0.183909i | \(-0.0588753\pi\) | |||||||
\(252\) | −0.513973 | − | 2.26877i | −0.0323772 | − | 0.142919i | ||||
\(253\) | −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 | −0.487200 | − | 0.873290i | \(-0.661982\pi\) |
0.873290 | + | 0.487200i | \(0.161982\pi\) | |||||||
\(258\) | 8.69416 | − | 4.79592i | 0.541275 | − | 0.298581i | ||||
\(259\) | 2.67509 | 0.166222 | ||||||||
\(260\) | −1.36607 | − | 1.20213i | −0.0847203 | − | 0.0745530i | ||||
\(261\) | −4.64874 | −0.287750 | ||||||||
\(262\) | 8.76227 | − | 4.83349i | 0.541335 | − | 0.298614i | ||||
\(263\) | 8.45067 | − | 8.45067i | 0.521091 | − | 0.521091i | −0.396810 | − | 0.917901i | \(-0.629883\pi\) |
0.917901 | + | 0.396810i | \(0.129883\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | −26.2390 | + | 5.94423i | −1.60280 | + | 0.363101i | ||||
\(269\) | 1.50260i | 0.0916154i | 0.998950 | + | 0.0458077i | \(0.0145861\pi\) | ||||
−0.998950 | + | 0.0458077i | \(0.985414\pi\) | |||||||
\(270\) | 11.4709 | − | 4.12307i | 0.698098 | − | 0.250922i | ||||
\(271\) | 29.6188i | 1.79921i | 0.436702 | + | 0.899606i | \(0.356146\pi\) | ||||
−0.436702 | + | 0.899606i | \(0.643854\pi\) | |||||||
\(272\) | 9.28895 | + | 3.28412i | 0.563226 | + | 0.199129i | ||||
\(273\) | −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 | −0.100825 | + | 0.994904i | \(0.532148\pi\) |
−0.994904 | + | 0.100825i | \(0.967852\pi\) | |||||||
\(278\) | −7.81078 | − | 14.1596i | −0.468459 | − | 0.849235i | ||||
\(279\) | −2.81902 | −0.168771 | ||||||||
\(280\) | 0.632419 | − | 2.86087i | 0.0377943 | − | 0.170970i | ||||
\(281\) | 16.2476 | 0.969249 | 0.484625 | − | 0.874722i | \(-0.338956\pi\) | ||||
0.484625 | + | 0.874722i | \(0.338956\pi\) | |||||||
\(282\) | 1.73975 | + | 3.15387i | 0.103601 | + | 0.187810i | ||||
\(283\) | 6.63046 | − | 6.63046i | 0.394140 | − | 0.394140i | −0.482020 | − | 0.876160i | \(-0.660097\pi\) |
0.876160 | + | 0.482020i | \(0.160097\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | 11.5500 | + | 8.26556i | 0.680587 | + | 0.487053i | ||||
\(289\) | 10.9331i | 0.643125i | ||||||||
\(290\) | −5.29657 | − | 2.49573i | −0.311025 | − | 0.146554i | ||||
\(291\) | − | 4.09281i | − | 0.239925i | ||||||
\(292\) | 13.3219 | − | 3.01797i | 0.779605 | − | 0.176613i | ||||
\(293\) | −14.4511 | − | 14.4511i | −0.844244 | − | 0.844244i | 0.145164 | − | 0.989408i | \(-0.453629\pi\) |
−0.989408 | + | 0.145164i | \(0.953629\pi\) | |||||||
\(294\) | −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 | ||||
\(298\) | 16.2387 | − | 8.95765i | 0.940681 | − | 0.518903i | ||||
\(299\) | 0.328019 | 0.0189699 | ||||||||
\(300\) | 6.96304 | + | 0.665481i | 0.402011 | + | 0.0384216i | ||||
\(301\) | −4.65002 | −0.268023 | ||||||||
\(302\) | −2.79853 | + | 1.54374i | −0.161038 | + | 0.0888323i | ||||
\(303\) | −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 | \(-0.0983310\pi\) |
−0.304026 | + | 0.952664i | \(0.598331\pi\) | |||||||
\(308\) | 0.603556 | + | 2.66421i | 0.0343908 | + | 0.151807i | ||||
\(309\) | − | 10.7061i | − | 0.609048i | ||||||
\(310\) | −3.21187 | − | 1.51342i | −0.182422 | − | 0.0859567i | ||||
\(311\) | − | 31.6342i | − | 1.79381i | −0.442225 | − | 0.896904i | \(-0.645811\pi\) | ||
0.442225 | − | 0.896904i | \(-0.354189\pi\) | |||||||
\(312\) | 0.803631 | + | 0.0470874i | 0.0454966 | + | 0.00266580i | ||||
\(313\) | −4.11199 | − | 4.11199i | −0.232424 | − | 0.232424i | 0.581280 | − | 0.813704i | \(-0.302552\pi\) |
−0.813704 | + | 0.581280i | \(0.802552\pi\) | |||||||
\(314\) | −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 | 0.226149 | − | 0.974093i | \(-0.427386\pi\) |
0.974093 | − | 0.226149i | \(-0.0726137\pi\) | |||||||
\(318\) | −3.83494 | − | 6.95208i | −0.215053 | − | 0.389853i | ||||
\(319\) | 5.45900 | 0.305645 | ||||||||
\(320\) | 8.72204 | + | 15.6181i | 0.487577 | + | 0.873080i | ||||
\(321\) | −5.05374 | −0.282072 | ||||||||
\(322\) | 0.255104 | + | 0.462459i | 0.0142164 | + | 0.0257718i | ||||
\(323\) | −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 | ||||
\(328\) | −29.5955 | − | 1.73410i | −1.63414 | − | 0.0957496i | ||||
\(329\) | − | 1.68683i | − | 0.0929979i | ||||||
\(330\) | −6.13714 | + | 2.20592i | −0.337839 | + | 0.121432i | ||||
\(331\) | − | 28.8144i | − | 1.58378i | −0.610661 | − | 0.791892i | \(-0.709096\pi\) | ||
0.610661 | − | 0.791892i | \(-0.290904\pi\) | |||||||
\(332\) | 1.23925 | + | 5.47028i | 0.0680127 | + | 0.300221i | ||||
\(333\) | 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 | −0.971019 | − | 0.239003i | \(-0.923179\pi\) |
0.239003 | + | 0.971019i | \(0.423179\pi\) | |||||||
\(338\) | 15.8930 | − | 8.76695i | 0.864463 | − | 0.476859i | ||||
\(339\) | 9.03317 | 0.490614 | ||||||||
\(340\) | 7.27699 | − | 8.26940i | 0.394650 | − | 0.448471i | ||||
\(341\) | 3.31036 | 0.179266 | ||||||||
\(342\) | −3.10905 | + | 1.71503i | −0.168118 | + | 0.0927383i | ||||
\(343\) | 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 | 0.998241 | + | 0.0592835i | \(0.0188816\pi\) |
0.0592835 | + | 0.998241i | \(0.481118\pi\) | |||||||
\(348\) | 2.52622 | − | 0.572295i | 0.135419 | − | 0.0306782i | ||||
\(349\) | 7.57450i | 0.405454i | 0.979235 | + | 0.202727i | \(0.0649804\pi\) | ||||
−0.979235 | + | 0.202727i | \(0.935020\pi\) | |||||||
\(350\) | −2.70477 | − | 1.84795i | −0.144576 | − | 0.0987769i | ||||
\(351\) | − | 1.56843i | − | 0.0837166i | ||||||
\(352\) | −13.5630 | − | 9.70620i | −0.722913 | − | 0.517342i | ||||
\(353\) | −12.3157 | − | 12.3157i | −0.655498 | − | 0.655498i | 0.298814 | − | 0.954311i | \(-0.403409\pi\) |
−0.954311 | + | 0.298814i | \(0.903409\pi\) | |||||||
\(354\) | −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 | ||||
\(358\) | −2.44488 | − | 4.43214i | −0.129216 | − | 0.234246i | ||||
\(359\) | −23.4554 | −1.23793 | −0.618966 | − | 0.785418i | \(-0.712448\pi\) | ||||
−0.618966 | + | 0.785418i | \(0.712448\pi\) | |||||||
\(360\) | 13.3873 | − | 8.54005i | 0.705570 | − | 0.450100i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.05813 | − | 9.16950i | −0.265849 | − | 0.481938i | ||||
\(363\) | −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 | −0.967914 | − | 0.251282i | \(-0.919148\pi\) |
−0.251282 | − | 0.967914i | \(-0.580852\pi\) | |||||||
\(368\) | −3.04019 | − | 1.07486i | −0.158481 | − | 0.0560311i | ||||
\(369\) | 26.3163i | 1.36997i | ||||||||
\(370\) | 6.17657 | + | 17.1840i | 0.321105 | + | 0.893355i | ||||
\(371\) | 3.71828i | 0.193043i | ||||||||
\(372\) | 1.53191 | − | 0.347042i | 0.0794259 | − | 0.0179933i | ||||
\(373\) | 6.12552 | + | 6.12552i | 0.317168 | + | 0.317168i | 0.847678 | − | 0.530511i | \(-0.178000\pi\) |
−0.530511 | + | 0.847678i | \(0.678000\pi\) | |||||||
\(374\) | −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 | ||||
\(378\) | 2.21126 | − | 1.21978i | 0.113735 | − | 0.0627389i | ||||
\(379\) | 22.9714 | 1.17996 | 0.589981 | − | 0.807417i | \(-0.299135\pi\) | ||||
0.589981 | + | 0.807417i | \(0.299135\pi\) | |||||||
\(380\) | −4.46305 | + | 0.284901i | −0.228950 | + | 0.0146151i | ||||
\(381\) | 0.355331 | 0.0182041 | ||||||||
\(382\) | −5.11318 | + | 2.82056i | −0.261613 | + | 0.144312i | ||||
\(383\) | 18.5545 | − | 18.5545i | 0.948090 | − | 0.948090i | −0.0506273 | − | 0.998718i | \(-0.516122\pi\) |
0.998718 | + | 0.0506273i | \(0.0161221\pi\) | |||||||
\(384\) | −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 | ||||
\(388\) | −2.58559 | − | 11.4133i | −0.131263 | − | 0.579422i | ||||
\(389\) | 37.2211i | 1.88718i | 0.331112 | + | 0.943592i | \(0.392576\pi\) | ||||
−0.331112 | + | 0.943592i | \(0.607424\pi\) | |||||||
\(390\) | 0.383635 | − | 0.814171i | 0.0194261 | − | 0.0412271i | ||||
\(391\) | 1.98564i | 0.100418i | ||||||||
\(392\) | −1.12260 | + | 19.1591i | −0.0566997 | + | 0.967681i | ||||
\(393\) | 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 | −0.470200 | − | 0.882560i | \(-0.655818\pi\) |
0.882560 | + | 0.470200i | \(0.155818\pi\) | |||||||
\(398\) | −10.0735 | − | 18.2616i | −0.504941 | − | 0.915369i | ||||
\(399\) | −0.324042 | −0.0162224 | ||||||||
\(400\) | 19.8377 | − | 2.54305i | 0.991883 | − | 0.127153i | ||||
\(401\) | 28.5885 | 1.42764 | 0.713821 | − | 0.700328i | \(-0.246963\pi\) | ||||
0.713821 | + | 0.700328i | \(0.246963\pi\) | |||||||
\(402\) | −6.42731 | − | 11.6516i | −0.320565 | − | 0.581129i | ||||
\(403\) | −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 | ||||
\(408\) | −0.285040 | + | 4.86471i | −0.0141116 | + | 0.240839i | ||||
\(409\) | − | 8.40060i | − | 0.415383i | −0.978194 | − | 0.207691i | \(-0.933405\pi\) | ||
0.978194 | − | 0.207691i | \(-0.0665950\pi\) | |||||||
\(410\) | −14.1282 | + | 29.9836i | −0.697742 | + | 1.48079i | ||||
\(411\) | 4.28083i | 0.211158i | ||||||||
\(412\) | −6.76346 | − | 29.8552i | −0.333212 | − | 1.47086i | ||||
\(413\) | 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 | ||||
\(418\) | 3.65095 | − | 2.01395i | 0.178574 | − | 0.0985057i | ||||
\(419\) | 14.2962 | 0.698416 | 0.349208 | − | 0.937045i | \(-0.386451\pi\) | ||||
0.349208 | + | 0.937045i | \(0.386451\pi\) | |||||||
\(420\) | 1.44622 | − | 0.0923198i | 0.0705682 | − | 0.00450475i | ||||
\(421\) | 40.0754 | 1.95316 | 0.976579 | − | 0.215161i | \(-0.0690275\pi\) | ||||
0.976579 | + | 0.215161i | \(0.0690275\pi\) | |||||||
\(422\) | −4.26007 | + | 2.34996i | −0.207377 | + | 0.114394i | ||||
\(423\) | 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 | ||||
\(428\) | −14.0930 | + | 3.19265i | −0.681209 | + | 0.154322i | ||||
\(429\) | 0.839138i | 0.0405140i | ||||||||
\(430\) | −10.7366 | − | 29.8705i | −0.517763 | − | 1.44048i | ||||
\(431\) | 30.3005i | 1.45952i | 0.683702 | + | 0.729761i | \(0.260369\pi\) | ||||
−0.683702 | + | 0.729761i | \(0.739631\pi\) | |||||||
\(432\) | −5.13947 | + | 14.5367i | −0.247273 | + | 0.699399i | ||||
\(433\) | 4.16829 | + | 4.16829i | 0.200315 | + | 0.200315i | 0.800135 | − | 0.599820i | \(-0.204761\pi\) |
−0.599820 | + | 0.800135i | \(0.704761\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 3.26324 | + | 5.91568i | 0.155924 | + | 0.282662i | ||||
\(439\) | −19.3441 | −0.923241 | −0.461621 | − | 0.887077i | \(-0.652732\pi\) | ||||
−0.461621 | + | 0.887077i | \(0.652732\pi\) | |||||||
\(440\) | −15.7206 | + | 10.0285i | −0.749450 | + | 0.478092i | ||||
\(441\) | 17.0363 | 0.811252 | ||||||||
\(442\) | −0.684600 | − | 1.24106i | −0.0325631 | − | 0.0590313i | ||||
\(443\) | 4.15922 | − | 4.15922i | 0.197611 | − | 0.197611i | −0.601364 | − | 0.798975i | \(-0.705376\pi\) |
0.798975 | + | 0.601364i | \(0.205376\pi\) | |||||||
\(444\) | −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 | ||||
\(448\) | 2.29663 | + | 2.90874i | 0.108506 | + | 0.137425i | ||||
\(449\) | − | 22.1626i | − | 1.04592i | −0.852358 | − | 0.522959i | \(-0.824828\pi\) | ||
0.852358 | − | 0.522959i | \(-0.175172\pi\) | |||||||
\(450\) | −3.28358 | − | 17.4473i | −0.154789 | − | 0.822472i | ||||
\(451\) | − | 30.9031i | − | 1.45517i | ||||||
\(452\) | 25.1901 | − | 5.70661i | 1.18484 | − | 0.268416i | ||||
\(453\) | −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 | −0.406392 | − | 0.913699i | \(-0.633213\pi\) |
0.913699 | + | 0.406392i | \(0.133213\pi\) | |||||||
\(458\) | 10.6991 | − | 5.90191i | 0.499937 | − | 0.275778i | ||||
\(459\) | 9.49435 | 0.443158 | ||||||||
\(460\) | −2.38169 | + | 2.70650i | −0.111047 | + | 0.126191i | ||||
\(461\) | −6.29625 | −0.293245 | −0.146623 | − | 0.989192i | \(-0.546840\pi\) | ||||
−0.146623 | + | 0.989192i | \(0.546840\pi\) | |||||||
\(462\) | −1.18306 | + | 0.652606i | −0.0550410 | + | 0.0303620i | ||||
\(463\) | −5.60774 | + | 5.60774i | −0.260614 | + | 0.260614i | −0.825303 | − | 0.564690i | \(-0.808996\pi\) |
0.564690 | + | 0.825303i | \(0.308996\pi\) | |||||||
\(464\) | 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 | −0.994946 | − | 0.100413i | \(-0.967983\pi\) |
−0.100413 | − | 0.994946i | \(-0.532017\pi\) | |||||||
\(468\) | −0.451434 | − | 1.99272i | −0.0208675 | − | 0.0921133i | ||||
\(469\) | 6.23179i | 0.287757i | ||||||||
\(470\) | 10.8357 | − | 3.89476i | 0.499815 | − | 0.179652i | ||||
\(471\) | − | 11.3368i | − | 0.522371i | ||||||
\(472\) | −39.8817 | − | 2.33680i | −1.83570 | − | 0.107560i | ||||
\(473\) | 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 | ||||
\(478\) | −15.7772 | − | 28.6012i | −0.721631 | − | 1.30819i | ||||
\(479\) | −12.8003 | −0.584863 | −0.292431 | − | 0.956286i | \(-0.594464\pi\) | ||||
−0.292431 | + | 0.956286i | \(0.594464\pi\) | |||||||
\(480\) | −6.22355 | + | 6.28890i | −0.284065 | + | 0.287048i | ||||
\(481\) | 2.34959 | 0.107132 | ||||||||
\(482\) | 13.5538 | + | 24.5707i | 0.617360 | + | 1.11917i | ||||
\(483\) | −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 | \(-0.361956\pi\) |
−0.907426 | + | 0.420211i | \(0.861956\pi\) | |||||||
\(488\) | −21.7261 | − | 1.27301i | −0.983495 | − | 0.0576263i | ||||
\(489\) | 10.3850i | 0.469626i | ||||||||
\(490\) | 19.4104 | + | 9.14612i | 0.876872 | + | 0.413180i | ||||
\(491\) | 39.2711i | 1.77228i | 0.463417 | + | 0.886140i | \(0.346623\pi\) | ||||
−0.463417 | + | 0.886140i | \(0.653377\pi\) | |||||||
\(492\) | −3.23973 | − | 14.3008i | −0.146058 | − | 0.644729i | ||||
\(493\) | −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 | ||||
\(498\) | −2.42912 | + | 1.33996i | −0.108851 | + | 0.0600452i | ||||
\(499\) | 35.8517 | 1.60494 | 0.802471 | − | 0.596692i | \(-0.203518\pi\) | ||||
0.802471 | + | 0.596692i | \(0.203518\pi\) | |||||||
\(500\) | 5.62560 | − | 21.6415i | 0.251584 | − | 0.967835i | ||||
\(501\) | 15.8072 | 0.706214 | ||||||||
\(502\) | 7.21603 | − | 3.98054i | 0.322067 | − | 0.177660i | ||||
\(503\) | 8.36832 | − | 8.36832i | 0.373125 | − | 0.373125i | −0.495489 | − | 0.868614i | \(-0.665011\pi\) |
0.868614 | + | 0.495489i | \(0.165011\pi\) | |||||||
\(504\) | 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 | ||||
\(508\) | 0.990881 | − | 0.224476i | 0.0439632 | − | 0.00995953i | ||||
\(509\) | 8.31464i | 0.368540i | 0.982876 | + | 0.184270i | \(0.0589921\pi\) | ||||
−0.982876 | + | 0.184270i | \(0.941008\pi\) | |||||||
\(510\) | 4.92851 | + | 2.32230i | 0.218238 | + | 0.102833i | ||||
\(511\) | − | 3.16397i | − | 0.139966i | ||||||
\(512\) | −22.2795 | − | 3.95253i | −0.984626 | − | 0.174679i | ||||
\(513\) | −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 | ||||
\(518\) | 1.82730 | + | 3.31257i | 0.0802869 | + | 0.145546i | ||||
\(519\) | 12.5928 | 0.552763 | ||||||||
\(520\) | 0.555468 | − | 2.51277i | 0.0243589 | − | 0.110192i | ||||
\(521\) | −35.8196 | −1.56928 | −0.784642 | − | 0.619949i | \(-0.787153\pi\) | ||||
−0.784642 | + | 0.619949i | \(0.787153\pi\) | |||||||
\(522\) | −3.17547 | − | 5.75657i | −0.138986 | − | 0.251958i | ||||
\(523\) | −14.4962 | + | 14.4962i | −0.633874 | + | 0.633874i | −0.949038 | − | 0.315163i | \(-0.897941\pi\) |
0.315163 | + | 0.949038i | \(0.397941\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 2.74971 | − | 7.77741i | 0.119666 | − | 0.338468i | ||||
\(529\) | 22.3501i | 0.971744i | ||||||||
\(530\) | −23.8852 | + | 8.58523i | −1.03751 | + | 0.372918i | ||||
\(531\) | 35.4628i | 1.53895i | ||||||||
\(532\) | −0.903630 | + | 0.204710i | −0.0391773 | + | 0.00887532i | ||||
\(533\) | 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 | ||||
\(538\) | −1.86068 | + | 1.02640i | −0.0802198 | + | 0.0442512i | ||||
\(539\) | −20.0056 | −0.861703 | ||||||||
\(540\) | 12.9412 | + | 11.3881i | 0.556900 | + | 0.490066i | ||||
\(541\) | −43.9873 | −1.89116 | −0.945580 | − | 0.325390i | \(-0.894504\pi\) | ||||
−0.945580 | + | 0.325390i | \(0.894504\pi\) | |||||||
\(542\) | −36.6771 | + | 20.2320i | −1.57542 | + | 0.869039i | ||||
\(543\) | 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 | −0.996348 | − | 0.0853805i | \(-0.972789\pi\) |
−0.0853805 | − | 0.996348i | \(-0.527211\pi\) | |||||||
\(548\) | 2.70437 | + | 11.9376i | 0.115525 | + | 0.509949i | ||||
\(549\) | 19.3189i | 0.824509i | ||||||||
\(550\) | 3.85589 | + | 20.4882i | 0.164416 | + | 0.873621i | ||||
\(551\) | 1.85155i | 0.0788787i | ||||||||
\(552\) | 0.0932909 | − | 1.59218i | 0.00397073 | − | 0.0677675i | ||||
\(553\) | 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 | −0.903905 | − | 0.427733i | \(-0.859312\pi\) |
0.427733 | + | 0.903905i | \(0.359312\pi\) | |||||||
\(558\) | −1.92562 | − | 3.49081i | −0.0815180 | − | 0.147778i | ||||
\(559\) | −4.08422 | −0.172744 | ||||||||
\(560\) | 3.97463 | − | 1.17108i | 0.167959 | − | 0.0494871i | ||||
\(561\) | −5.07965 | −0.214463 | ||||||||
\(562\) | 11.0984 | + | 20.1195i | 0.468158 | + | 0.848689i | ||||
\(563\) | 0.343770 | − | 0.343770i | 0.0144882 | − | 0.0144882i | −0.699826 | − | 0.714314i | \(-0.746739\pi\) |
0.714314 | + | 0.699826i | \(0.246739\pi\) | |||||||
\(564\) | −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 | ||||
\(568\) | −1.52166 | + | 25.9698i | −0.0638473 | + | 1.08967i | ||||
\(569\) | 14.2062i | 0.595555i | 0.954635 | + | 0.297777i | \(0.0962453\pi\) | ||||
−0.954635 | + | 0.297777i | \(0.903755\pi\) | |||||||
\(570\) | −0.748189 | − | 2.08156i | −0.0313382 | − | 0.0871869i | ||||
\(571\) | 19.1090i | 0.799688i | 0.916583 | + | 0.399844i | \(0.130936\pi\) | ||||
−0.916583 | + | 0.399844i | \(0.869064\pi\) | |||||||
\(572\) | 0.530117 | + | 2.34004i | 0.0221653 | + | 0.0978418i | ||||
\(573\) | −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 | −0.0601462 | + | 0.998190i | \(0.519157\pi\) |
−0.998190 | + | 0.0601462i | \(0.980843\pi\) | |||||||
\(578\) | −13.5385 | + | 7.46820i | −0.563129 | + | 0.310636i | ||||
\(579\) | −5.48183 | −0.227817 | ||||||||
\(580\) | −0.527507 | − | 8.26356i | −0.0219036 | − | 0.343126i | ||||
\(581\) | 1.29920 | 0.0538999 | ||||||||
\(582\) | 5.06815 | − | 2.79572i | 0.210082 | − | 0.115886i | ||||
\(583\) | 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 | 0.970595 | + | 0.240717i | \(0.0773825\pi\) |
0.240717 | + | 0.970595i | \(0.422617\pi\) | |||||||
\(588\) | −9.25785 | + | 2.09729i | −0.381787 | + | 0.0864909i | ||||
\(589\) | 1.12279i | 0.0462637i | ||||||||
\(590\) | −19.0386 | + | 40.4047i | −0.783806 | + | 1.66344i | ||||
\(591\) | 5.79788i | 0.238493i | ||||||||
\(592\) | −21.7768 | − | 7.69919i | −0.895019 | − | 0.316435i | ||||
\(593\) | 4.78725 | + | 4.78725i | 0.196589 | + | 0.196589i | 0.798536 | − | 0.601947i | \(-0.205608\pi\) |
−0.601947 | + | 0.798536i | \(0.705608\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | 0.224064 | + | 0.406188i | 0.00916265 | + | 0.0166103i | ||||
\(599\) | 8.94617 | 0.365531 | 0.182765 | − | 0.983157i | \(-0.441495\pi\) | ||||
0.182765 | + | 0.983157i | \(0.441495\pi\) | |||||||
\(600\) | 3.93225 | + | 9.07695i | 0.160533 | + | 0.370565i | ||||
\(601\) | −31.5967 | −1.28886 | −0.644429 | − | 0.764664i | \(-0.722905\pi\) | ||||
−0.644429 | + | 0.764664i | \(0.722905\pi\) | |||||||
\(602\) | −3.17634 | − | 5.75815i | −0.129458 | − | 0.234685i | ||||
\(603\) | −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 | \(-0.302844\pi\) |
−0.814237 | + | 0.580533i | \(0.802844\pi\) | |||||||
\(608\) | 3.29209 | − | 4.60023i | 0.133512 | − | 0.186564i | ||||
\(609\) | − | 0.599980i | − | 0.0243124i | ||||||
\(610\) | −10.3716 | + | 22.0111i | −0.419932 | + | 0.891202i | ||||
\(611\) | − | 1.48158i | − | 0.0599383i | ||||||
\(612\) | 12.0627 | − | 2.73271i | 0.487607 | − | 0.110463i | ||||
\(613\) | −24.9646 | − | 24.9646i | −1.00831 | − | 1.00831i | −0.999965 | − | 0.00834470i | \(-0.997344\pi\) |
−0.00834470 | − | 0.999965i | \(-0.502656\pi\) | |||||||
\(614\) | −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 | 0.116689 | − | 0.993168i | \(-0.462772\pi\) |
0.993168 | − | 0.116689i | \(-0.0372281\pi\) | |||||||
\(618\) | 13.2574 | − | 7.31312i | 0.533291 | − | 0.294177i | ||||
\(619\) | −36.0285 | −1.44811 | −0.724054 | − | 0.689743i | \(-0.757723\pi\) | ||||
−0.724054 | + | 0.689743i | \(0.757723\pi\) | |||||||
\(620\) | −0.319883 | − | 5.01107i | −0.0128468 | − | 0.201249i | ||||
\(621\) | −3.10742 | −0.124696 | ||||||||
\(622\) | 39.1728 | − | 21.6087i | 1.57068 | − | 0.866429i | ||||
\(623\) | 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 | ||||
\(628\) | −7.16188 | − | 31.6139i | −0.285790 | − | 1.26153i | ||||
\(629\) | 14.2230i | 0.567109i | ||||||||
\(630\) | −1.24413 | − | 3.46134i | −0.0495675 | − | 0.137903i | ||||
\(631\) | − | 20.6862i | − | 0.823504i | −0.911296 | − | 0.411752i | \(-0.864917\pi\) | ||
0.911296 | − | 0.411752i | \(-0.135083\pi\) | |||||||
\(632\) | −0.463424 | − | 0.0271535i | −0.0184340 | − | 0.00108011i | ||||
\(633\) | −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 | ||||
\(638\) | 3.72893 | + | 6.75991i | 0.147630 | + | 0.267627i | ||||
\(639\) | 23.0923 | 0.913519 | ||||||||
\(640\) | −13.3822 | + | 21.4690i | −0.528976 | + | 0.848637i | ||||
\(641\) | −5.19156 | −0.205054 | −0.102527 | − | 0.994730i | \(-0.532693\pi\) | ||||
−0.102527 | + | 0.994730i | \(0.532693\pi\) | |||||||
\(642\) | −3.45211 | − | 6.25808i | −0.136244 | − | 0.246987i | ||||
\(643\) | −6.88159 | + | 6.88159i | −0.271384 | + | 0.271384i | −0.829657 | − | 0.558273i | \(-0.811464\pi\) |
0.558273 | + | 0.829657i | \(0.311464\pi\) | |||||||
\(644\) | −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 | \(-0.440328\pi\) |
−0.982480 | + | 0.186368i | \(0.940328\pi\) | |||||||
\(648\) | 13.6548 | + | 0.800080i | 0.536410 | + | 0.0314301i | ||||
\(649\) | − | 41.6438i | − | 1.63466i | ||||||
\(650\) | −2.37566 | − | 1.62309i | −0.0931810 | − | 0.0636630i | ||||
\(651\) | − | 0.363831i | − | 0.0142597i | ||||||
\(652\) | 6.56062 | + | 28.9598i | 0.256934 | + | 1.13415i | ||||
\(653\) | 10.5859 | + | 10.5859i | 0.414257 | + | 0.414257i | 0.883219 | − | 0.468961i | \(-0.155372\pi\) |
−0.468961 | + | 0.883219i | \(0.655372\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | 2.08881 | − | 1.15224i | 0.0814303 | − | 0.0449190i | ||||
\(659\) | 29.9506 | 1.16671 | 0.583354 | − | 0.812218i | \(-0.301740\pi\) | ||||
0.583354 | + | 0.812218i | \(0.301740\pi\) | |||||||
\(660\) | −6.92376 | − | 6.09284i | −0.269507 | − | 0.237164i | ||||
\(661\) | −42.9876 | −1.67202 | −0.836012 | − | 0.548711i | \(-0.815119\pi\) | ||||
−0.836012 | + | 0.548711i | \(0.815119\pi\) | |||||||
\(662\) | 35.6811 | − | 19.6826i | 1.38678 | − | 0.764985i | ||||
\(663\) | 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 | ||||
\(668\) | 44.0803 | − | 9.98603i | 1.70552 | − | 0.386371i | ||||
\(669\) | − | 9.85422i | − | 0.380986i | ||||||
\(670\) | −40.0313 | + | 14.3887i | −1.54654 | + | 0.555885i | ||||
\(671\) | − | 22.6860i | − | 0.875785i | ||||||
\(672\) | −1.06678 | + | 1.49067i | −0.0411518 | + | 0.0575039i | ||||
\(673\) | 8.30925 | + | 8.30925i | 0.320298 | + | 0.320298i | 0.848881 | − | 0.528583i | \(-0.177277\pi\) |
−0.528583 | + | 0.848881i | \(0.677277\pi\) | |||||||
\(674\) | −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 | −0.674507 | − | 0.738268i | \(-0.735644\pi\) |
0.738268 | + | 0.674507i | \(0.235644\pi\) | |||||||
\(678\) | 6.17038 | + | 11.1858i | 0.236972 | + | 0.429589i | ||||
\(679\) | −2.71067 | −0.104026 | ||||||||
\(680\) | 15.2108 | + | 3.36247i | 0.583308 | + | 0.128945i | ||||
\(681\) | −8.35673 | −0.320230 | ||||||||
\(682\) | 2.26125 | + | 4.09924i | 0.0865875 | + | 0.156968i | ||||
\(683\) | −3.72871 | + | 3.72871i | −0.142675 | + | 0.142675i | −0.774837 | − | 0.632161i | \(-0.782168\pi\) |
0.632161 | + | 0.774837i | \(0.282168\pi\) | |||||||
\(684\) | −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 | ||||
\(688\) | 37.8539 | + | 13.3833i | 1.44317 | + | 0.510233i | ||||
\(689\) | 3.26585i | 0.124419i | ||||||||
\(690\) | −1.61306 | − | 0.760068i | −0.0614080 | − | 0.0289353i | ||||
\(691\) | 0.815388i | 0.0310188i | 0.999880 | + | 0.0155094i | \(0.00493700\pi\) | ||||
−0.999880 | + | 0.0155094i | \(0.995063\pi\) | |||||||
\(692\) | 35.1166 | − | 7.95538i | 1.33493 | − | 0.302418i | ||||
\(693\) | 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 | ||||
\(698\) | −9.37955 | + | 5.17399i | −0.355021 | + | 0.195839i | ||||
\(699\) | 4.49834 | 0.170143 | ||||||||
\(700\) | 0.440749 | − | 4.61163i | 0.0166587 | − | 0.174303i | ||||
\(701\) | 9.25242 | 0.349459 | 0.174730 | − | 0.984616i | \(-0.444095\pi\) | ||||
0.174730 | + | 0.984616i | \(0.444095\pi\) | |||||||
\(702\) | 1.94220 | − | 1.07136i | 0.0733035 | − | 0.0404360i | ||||
\(703\) | 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 | ||||
\(708\) | −4.36573 | − | 19.2712i | −0.164074 | − | 0.724255i | ||||
\(709\) | − | 25.0837i | − | 0.942038i | −0.882123 | − | 0.471019i | \(-0.843886\pi\) | ||
0.882123 | − | 0.471019i | \(-0.156114\pi\) | |||||||
\(710\) | 26.3104 | + | 12.3974i | 0.987411 | + | 0.465265i | ||||
\(711\) | 0.412076i | 0.0154541i | ||||||||
\(712\) | −0.376490 | + | 6.42547i | −0.0141096 | + | 0.240805i | ||||
\(713\) | 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 | ||||
\(718\) | −16.0220 | − | 29.0450i | −0.597934 | − | 1.08395i | ||||
\(719\) | −37.6238 | −1.40313 | −0.701565 | − | 0.712606i | \(-0.747515\pi\) | ||||
−0.701565 | + | 0.712606i | \(0.747515\pi\) | |||||||
\(720\) | 19.7198 | + | 10.7440i | 0.734912 | + | 0.400404i | ||||
\(721\) | −7.09065 | −0.264070 | ||||||||
\(722\) | 0.683080 | + | 1.23831i | 0.0254216 | + | 0.0460850i | ||||
\(723\) | −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 | 0.999264 | + | 0.0383634i | \(0.0122145\pi\) |
0.0383634 | + | 0.999264i | \(0.487786\pi\) | |||||||
\(728\) | 0.0311861 | − | 0.532246i | 0.00115583 | − | 0.0197263i | ||||
\(729\) | − | 4.05317i | − | 0.150117i | ||||||
\(730\) | 20.3245 | − | 7.30537i | 0.752243 | − | 0.270384i | ||||
\(731\) | − | 24.7235i | − | 0.914430i | ||||||
\(732\) | −2.37829 | − | 10.4982i | −0.0879043 | − | 0.388026i | ||||
\(733\) | 13.9853 | + | 13.9853i | 0.516559 | + | 0.516559i | 0.916528 | − | 0.399970i | \(-0.130979\pi\) |
−0.399970 | + | 0.916528i | \(0.630979\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | −32.5876 | + | 17.9762i | −1.19957 | + | 0.661711i | ||||
\(739\) | −40.9090 | −1.50486 | −0.752431 | − | 0.658671i | \(-0.771119\pi\) | ||||
−0.752431 | + | 0.658671i | \(0.771119\pi\) | |||||||
\(740\) | −17.0600 | + | 19.3866i | −0.627137 | + | 0.712664i | ||||
\(741\) | −0.284614 | −0.0104555 | ||||||||
\(742\) | −4.60437 | + | 2.53988i | −0.169032 | + | 0.0932421i | ||||
\(743\) | −4.46740 | + | 4.46740i | −0.163893 | + | 0.163893i | −0.784289 | − | 0.620396i | \(-0.786972\pi\) |
0.620396 | + | 0.784289i | \(0.286972\pi\) | |||||||
\(744\) | 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 | ||||
\(748\) | −14.1652 | + | 3.20901i | −0.517931 | + | 0.117333i | ||||
\(749\) | 3.34710i | 0.122300i | ||||||||
\(750\) | 11.0557 | − | 0.298479i | 0.403696 | − | 0.0108989i | ||||
\(751\) | 37.1200i | 1.35453i | 0.735740 | + | 0.677264i | \(0.236834\pi\) | ||||
−0.735740 | + | 0.677264i | \(0.763166\pi\) | |||||||
\(752\) | −4.85488 | + | 13.7318i | −0.177039 | + | 0.500746i | ||||
\(753\) | 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 | −0.301829 | − | 0.953362i | \(-0.597597\pi\) |
0.953362 | + | 0.301829i | \(0.0975972\pi\) | |||||||
\(758\) | 15.6913 | + | 28.4456i | 0.569934 | + | 1.03319i | ||||
\(759\) | 1.66252 | 0.0603458 | ||||||||
\(760\) | −3.40142 | − | 5.33201i | −0.123382 | − | 0.193412i | ||||
\(761\) | −31.7582 | −1.15123 | −0.575617 | − | 0.817719i | \(-0.695238\pi\) | ||||
−0.575617 | + | 0.817719i | \(0.695238\pi\) | |||||||
\(762\) | 0.242719 | + | 0.440008i | 0.00879279 | + | 0.0159398i | ||||
\(763\) | 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 | ||||
\(768\) | −1.18107 | − | 11.1291i | −0.0426184 | − | 0.401588i | ||||
\(769\) | − | 32.9935i | − | 1.18977i | −0.803809 | − | 0.594887i | \(-0.797197\pi\) | ||
0.803809 | − | 0.594887i | \(-0.202803\pi\) | |||||||
\(770\) | 1.46098 | + | 4.06464i | 0.0526501 | + | 0.146479i | ||||
\(771\) | 6.12270i | 0.220504i | ||||||||
\(772\) | −15.2867 | + | 3.46309i | −0.550182 | + | 0.124639i | ||||
\(773\) | −13.8810 | − | 13.8810i | −0.499265 | − | 0.499265i | 0.411944 | − | 0.911209i | \(-0.364850\pi\) |
−0.911209 | + | 0.411944i | \(0.864850\pi\) | |||||||
\(774\) | 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 | ||||
\(778\) | −46.0911 | + | 25.4250i | −1.65244 | + | 0.911530i | ||||
\(779\) | 10.4815 | 0.375540 | ||||||||
\(780\) | 1.27025 | − | 0.0810866i | 0.0454821 | − | 0.00290337i | ||||
\(781\) | −27.1172 | −0.970330 | ||||||||
\(782\) | −2.45882 | + | 1.35635i | −0.0879274 | + | 0.0485029i | ||||
\(783\) | 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 | −0.999891 | − | 0.0147356i | \(-0.995309\pi\) |
−0.0147356 | − | 0.999891i | \(-0.504691\pi\) | |||||||
\(788\) | 3.66275 | + | 16.1681i | 0.130480 | + | 0.575963i | ||||
\(789\) | 8.35948i | 0.297605i | ||||||||
\(790\) | −0.221228 | + | 0.469501i | −0.00787093 | + | 0.0167041i | ||||
\(791\) | − | 5.98267i | − | 0.212719i | ||||||
\(792\) | −20.9016 | − | 1.22469i | −0.742705 | − | 0.0435176i | ||||
\(793\) | 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 | −0.232779 | − | 0.972530i | \(-0.574782\pi\) |
0.972530 | + | 0.232779i | \(0.0747820\pi\) | |||||||
\(798\) | −0.221347 | − | 0.401264i | −0.00783560 | − | 0.0142046i | ||||
\(799\) | 8.96861 | 0.317287 | ||||||||
\(800\) | 16.6998 | + | 22.8280i | 0.590427 | + | 0.807091i | ||||
\(801\) | 5.71353 | 0.201878 | ||||||||
\(802\) | 19.5283 | + | 35.4013i | 0.689567 | + | 1.25006i | ||||
\(803\) | −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 | ||||
\(808\) | −13.0059 | − | 0.762060i | −0.457546 | − | 0.0268092i | ||||
\(809\) | 23.6436i | 0.831266i | 0.909532 | + | 0.415633i | \(0.136440\pi\) | ||||
−0.909532 | + | 0.415633i | \(0.863560\pi\) | |||||||
\(810\) | 6.51848 | − | 13.8339i | 0.229036 | − | 0.486073i | ||||
\(811\) | − | 2.24873i | − | 0.0789635i | −0.999220 | − | 0.0394817i | \(-0.987429\pi\) | ||
0.999220 | − | 0.0394817i | \(-0.0125707\pi\) | |||||||
\(812\) | −0.379031 | − | 1.67312i | −0.0133014 | − | 0.0587149i | ||||
\(813\) | −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 | ||||
\(818\) | 10.4025 | − | 5.73828i | 0.363715 | − | 0.200634i | ||||
\(819\) | −0.473273 | −0.0165375 | ||||||||
\(820\) | −46.7796 | + | 2.98619i | −1.63361 | + | 0.104282i | ||||
\(821\) | −26.4934 | −0.924625 | −0.462312 | − | 0.886717i | \(-0.652980\pi\) | ||||
−0.462312 | + | 0.886717i | \(0.652980\pi\) | |||||||
\(822\) | −5.30098 | + | 2.92415i | −0.184893 | + | 0.101991i | ||||
\(823\) | 34.3245 | − | 34.3245i | 1.19648 | − | 1.19648i | 0.221262 | − | 0.975214i | \(-0.428982\pi\) |
0.975214 | − | 0.221262i | \(-0.0710177\pi\) | |||||||
\(824\) | 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 | \(-0.0154295\pi\) |
−0.0484541 | + | 0.998825i | \(0.515429\pi\) | |||||||
\(828\) | −3.94802 | + | 0.894393i | −0.137203 | + | 0.0310823i | ||||
\(829\) | − | 27.1022i | − | 0.941297i | −0.882321 | − | 0.470648i | \(-0.844020\pi\) | ||
0.882321 | − | 0.470648i | \(-0.155980\pi\) | |||||||
\(830\) | 2.99976 | + | 8.34571i | 0.104123 | + | 0.289684i | ||||
\(831\) | − | 18.0398i | − | 0.625793i | ||||||
\(832\) | 2.01719 | + | 2.55481i | 0.0699333 | + | 0.0885720i | ||||
\(833\) | 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 | ||||
\(838\) | 9.76546 | + | 17.7031i | 0.337342 | + | 0.611543i | ||||
\(839\) | 32.8801 | 1.13515 | 0.567573 | − | 0.823323i | \(-0.307882\pi\) | ||||
0.567573 | + | 0.823323i | \(0.307882\pi\) | |||||||
\(840\) | 1.10220 | + | 1.72780i | 0.0380296 | + | 0.0596147i | ||||
\(841\) | 25.5718 | 0.881785 | ||||||||
\(842\) | 27.3747 | + | 49.6256i | 0.943396 | + | 1.71021i | ||||
\(843\) | −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 | ||||
\(848\) | 10.7016 | − | 30.2690i | 0.367495 | − | 1.03944i | ||||
\(849\) | 6.55891i | 0.225101i | ||||||||
\(850\) | 9.82525 | − | 14.3808i | 0.337003 | − | 0.493259i | ||||
\(851\) | − | 4.65507i | − | 0.159574i | ||||||
\(852\) | −12.5488 | + | 2.84284i | −0.429916 | + | 0.0973940i | ||||
\(853\) | 20.4055 | + | 20.4055i | 0.698672 | + | 0.698672i | 0.964124 | − | 0.265452i | \(-0.0855212\pi\) |
−0.265452 | + | 0.964124i | \(0.585521\pi\) | |||||||
\(854\) | −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 | −0.661754 | − | 0.749721i | \(-0.730188\pi\) |
0.749721 | + | 0.661754i | \(0.230188\pi\) | |||||||
\(858\) | −1.03911 | + | 0.573199i | −0.0354746 | + | 0.0195687i | ||||
\(859\) | 48.7635 | 1.66379 | 0.831895 | − | 0.554933i | \(-0.187256\pi\) | ||||
0.831895 | + | 0.554933i | \(0.187256\pi\) | |||||||
\(860\) | 29.6549 | − | 33.6991i | 1.01122 | − | 1.14913i | ||||
\(861\) | −3.39646 | −0.115751 | ||||||||
\(862\) | −37.5213 | + | 20.6977i | −1.27798 | + | 0.704965i | ||||
\(863\) | 0.809522 | − | 0.809522i | 0.0275565 | − | 0.0275565i | −0.693194 | − | 0.720751i | \(-0.743797\pi\) |
0.720751 | + | 0.693194i | \(0.243797\pi\) | |||||||
\(864\) | −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 | ||||
\(868\) | −0.229847 | − | 1.01459i | −0.00780150 | − | 0.0344373i | ||||
\(869\) | − | 0.483899i | − | 0.0164152i | ||||||
\(870\) | 3.85411 | − | 1.38531i | 0.130667 | − | 0.0469664i | ||||
\(871\) | 5.47352i | 0.185463i | ||||||||
\(872\) | −0.866973 | + | 14.7964i | −0.0293594 | + | 0.501071i | ||||
\(873\) | −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 | −0.948238 | − | 0.317562i | \(-0.897136\pi\) |
0.317562 | + | 0.948238i | \(0.397136\pi\) | |||||||
\(878\) | −13.2135 | − | 23.9538i | −0.445935 | − | 0.808403i | ||||
\(879\) | 14.2952 | 0.482165 | ||||||||
\(880\) | −23.1568 | − | 12.6166i | −0.780616 | − | 0.425305i | ||||
\(881\) | −33.9283 | −1.14307 | −0.571536 | − | 0.820577i | \(-0.693652\pi\) | ||||
−0.571536 | + | 0.820577i | \(0.693652\pi\) | |||||||
\(882\) | 11.6372 | + | 21.0961i | 0.391843 | + | 0.710344i | ||||
\(883\) | −16.3593 | + | 16.3593i | −0.550535 | + | 0.550535i | −0.926595 | − | 0.376060i | \(-0.877279\pi\) |
0.376060 | + | 0.926595i | \(0.377279\pi\) | |||||||
\(884\) | 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 | 0.990211 | + | 0.139579i | \(0.0445748\pi\) |
0.139579 | + | 0.990211i | \(0.455425\pi\) | |||||||
\(888\) | 0.668239 | − | 11.4047i | 0.0224246 | − | 0.382716i | ||||
\(889\) | − | 0.235336i | − | 0.00789291i | ||||||
\(890\) | 6.50974 | + | 3.06737i | 0.218207 | + | 0.102819i | ||||
\(891\) | 14.2581i | 0.477664i | ||||||||
\(892\) | −6.22530 | − | 27.4797i | −0.208438 | − | 0.920087i | ||||
\(893\) | −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 | ||||
\(898\) | 27.4441 | − | 15.1388i | 0.915820 | − | 0.505189i | ||||
\(899\) | −2.07890 | −0.0693352 | ||||||||
\(900\) | 19.3621 | − | 15.9840i | 0.645403 | − | 0.532799i | ||||
\(901\) | −19.7695 | −0.658618 | ||||||||
\(902\) | 38.2675 | − | 21.1093i | 1.27417 | − | 0.702863i | ||||
\(903\) | 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 | \(-0.324853\pi\) |
−0.852399 | + | 0.522892i | \(0.824853\pi\) | |||||||
\(908\) | −23.3037 | + | 5.27927i | −0.773361 | + | 0.175199i | ||||
\(909\) | 11.5649i | 0.383582i | ||||||||
\(910\) | −0.539226 | − | 0.254082i | −0.0178752 | − | 0.00842273i | ||||
\(911\) | 32.8155i | 1.08722i | 0.839337 | + | 0.543612i | \(0.182944\pi\) | ||||
−0.839337 | + | 0.543612i | \(0.817056\pi\) | |||||||
\(912\) | 2.63789 | + | 0.932630i | 0.0873494 | + | 0.0308825i | ||||
\(913\) | −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 | ||||
\(918\) | 6.48540 | + | 11.7569i | 0.214050 | + | 0.388036i | ||||
\(919\) | −13.4713 | −0.444377 | −0.222188 | − | 0.975004i | \(-0.571320\pi\) | ||||
−0.222188 | + | 0.975004i | \(0.571320\pi\) | |||||||
\(920\) | −4.97837 | − | 1.10051i | −0.164132 | − | 0.0362827i | ||||
\(921\) | −11.2424 | −0.370450 | ||||||||
\(922\) | −4.30084 | − | 7.79668i | −0.141641 | − | 0.256770i | ||||
\(923\) | 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 | ||||
\(928\) | 8.51756 | + | 6.09547i | 0.279603 | + | 0.200094i | ||||
\(929\) | 30.3568i | 0.995973i | 0.867185 | + | 0.497987i | \(0.165927\pi\) | ||||
−0.867185 | + | 0.497987i | \(0.834073\pi\) | |||||||
\(930\) | 2.33715 | − | 0.840059i | 0.0766382 | − | 0.0275466i | ||||
\(931\) | − | 6.78539i | − | 0.222382i | ||||||
\(932\) | 12.5442 | − | 2.84178i | 0.410897 | − | 0.0930855i | ||||
\(933\) | 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 | −0.995092 | − | 0.0989565i | \(-0.968450\pi\) |
0.0989565 | + | 0.995092i | \(0.468450\pi\) | |||||||
\(938\) | −7.71686 | + | 4.25681i | −0.251964 | + | 0.138990i | ||||
\(939\) | 4.06762 | 0.132742 | ||||||||
\(940\) | 12.2246 | + | 10.7575i | 0.398722 | + | 0.350871i | ||||
\(941\) | 12.9566 | 0.422372 | 0.211186 | − | 0.977446i | \(-0.432267\pi\) | ||||
0.211186 | + | 0.977446i | \(0.432267\pi\) | |||||||
\(942\) | 14.0384 | − | 7.74392i | 0.457395 | − | 0.252311i | ||||
\(943\) | 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 | \(-0.0784946\pi\) |
−0.244106 | + | 0.969748i | \(0.578495\pi\) | |||||||
\(948\) | −0.0507296 | − | 0.223930i | −0.00164762 | − | 0.00727292i | ||||
\(949\) | − | 2.77899i | − | 0.0902097i | ||||||
\(950\) | −6.94907 | + | 1.30782i | −0.225458 | + | 0.0424312i | ||||
\(951\) | 21.1391i | 0.685483i | ||||||||
\(952\) | 3.22190 | + | 0.188782i | 0.104422 | + | 0.00611846i | ||||
\(953\) | 1.79070 | + | 1.79070i | 0.0580064 | + | 0.0580064i | 0.735515 | − | 0.677509i | \(-0.236940\pi\) |
−0.677509 | + | 0.735515i | \(0.736940\pi\) | |||||||
\(954\) | −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 | ||||
\(958\) | −8.74367 | − | 15.8507i | −0.282495 | − | 0.512114i | ||||
\(959\) | 2.83520 | 0.0915533 | ||||||||
\(960\) | −12.0388 | − | 3.41084i | −0.388549 | − | 0.110084i | ||||
\(961\) | 29.7393 | 0.959334 | ||||||||
\(962\) | 1.60496 | + | 2.90951i | 0.0517459 | + | 0.0938063i | ||||
\(963\) | −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 | \(-0.164852\pi\) |
−0.495055 | + | 0.868862i | \(0.664852\pi\) | |||||||
\(968\) | −6.51483 | − | 0.381726i | −0.209395 | − | 0.0122691i | ||||
\(969\) | − | 1.72288i | − | 0.0553470i | ||||||
\(970\) | −6.25873 | − | 17.4126i | −0.200956 | − | 0.559085i | ||||
\(971\) | 16.0160i | 0.513977i | 0.966415 | + | 0.256988i | \(0.0827302\pi\) | ||||
−0.966415 | + | 0.256988i | \(0.917270\pi\) | |||||||
\(972\) | 6.60468 | + | 29.1543i | 0.211845 | + | 0.935125i | ||||
\(973\) | −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 | −0.522459 | − | 0.852664i | \(-0.674985\pi\) |
0.852664 | + | 0.522459i | \(0.174985\pi\) | |||||||
\(978\) | −12.8598 | + | 7.09379i | −0.411211 | + | 0.226834i | ||||
\(979\) | −6.70937 | −0.214432 | ||||||||
\(980\) | 1.93316 | + | 30.2835i | 0.0617525 | + | 0.967372i | ||||
\(981\) | 13.1570 | 0.420071 | ||||||||
\(982\) | −48.6296 | + | 26.8253i | −1.55183 | + | 0.856031i | ||||
\(983\) | 20.0695 | − | 20.0695i | 0.640119 | − | 0.640119i | −0.310466 | − | 0.950585i | \(-0.600485\pi\) |
0.950585 | + | 0.310466i | \(0.100485\pi\) | |||||||
\(984\) | 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 | ||||
\(988\) | −0.793679 | + | 0.179802i | −0.0252503 | + | 0.00572025i | ||||
\(989\) | 8.09177i | 0.257303i | ||||||||
\(990\) | −9.97793 | + | 21.1757i | −0.317119 | + | 0.673008i | ||||
\(991\) | 59.6794i | 1.89578i | 0.318599 | + | 0.947890i | \(0.396788\pi\) | ||||
−0.318599 | + | 0.947890i | \(0.603212\pi\) | |||||||
\(992\) | 5.16509 | + | 3.69632i | 0.163992 | + | 0.117358i | ||||
\(993\) | 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 | −0.832296 | − | 0.554332i | \(-0.812974\pi\) |
0.554332 | + | 0.832296i | \(0.312974\pi\) | |||||||
\(998\) | 24.4896 | + | 44.3953i | 0.775204 | + | 1.40531i | ||||
\(999\) | −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.c.343.19 | yes | 52 | |
4.3 | odd | 2 | 380.2.k.d.343.5 | yes | 52 | ||
5.2 | odd | 4 | 380.2.k.d.267.5 | yes | 52 | ||
20.7 | even | 4 | inner | 380.2.k.c.267.19 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.k.c.267.19 | ✓ | 52 | 20.7 | even | 4 | inner | |
380.2.k.c.343.19 | yes | 52 | 1.1 | even | 1 | trivial | |
380.2.k.d.267.5 | yes | 52 | 5.2 | odd | 4 | ||
380.2.k.d.343.5 | yes | 52 | 4.3 | odd | 2 |