Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 117.6 | ||
Root | \(0.536506 - 0.536506i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.117 |
Dual form | 370.2.h.e.253.6 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.536506 | + | 0.536506i | 0.309752 | + | 0.309752i | 0.844813 | − | 0.535061i | \(-0.179712\pi\) |
−0.535061 | + | 0.844813i | \(0.679712\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.23241 | − | 0.127776i | −0.998366 | − | 0.0571431i | ||||
\(6\) | −0.536506 | − | 0.536506i | −0.219027 | − | 0.219027i | ||||
\(7\) | 0.767774 | + | 0.767774i | 0.290191 | + | 0.290191i | 0.837156 | − | 0.546964i | \(-0.184217\pi\) |
−0.546964 | + | 0.837156i | \(0.684217\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 2.42432i | − | 0.808108i | ||||||
\(10\) | 2.23241 | + | 0.127776i | 0.705951 | + | 0.0404063i | ||||
\(11\) | 4.39414i | 1.32488i | 0.749114 | + | 0.662442i | \(0.230480\pi\) | ||||
−0.749114 | + | 0.662442i | \(0.769520\pi\) | |||||||
\(12\) | 0.536506 | + | 0.536506i | 0.154876 | + | 0.154876i | ||||
\(13\) | 6.74274 | 1.87010 | 0.935050 | − | 0.354516i | \(-0.115355\pi\) | ||||
0.935050 | + | 0.354516i | \(0.115355\pi\) | |||||||
\(14\) | −0.767774 | − | 0.767774i | −0.205196 | − | 0.205196i | ||||
\(15\) | −1.12915 | − | 1.26626i | −0.291545 | − | 0.326946i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.34365i | 1.78110i | 0.454889 | + | 0.890548i | \(0.349679\pi\) | ||||
−0.454889 | + | 0.890548i | \(0.650321\pi\) | |||||||
\(18\) | 2.42432i | 0.571419i | ||||||||
\(19\) | −2.59760 | + | 2.59760i | −0.595930 | + | 0.595930i | −0.939227 | − | 0.343297i | \(-0.888456\pi\) |
0.343297 | + | 0.939227i | \(0.388456\pi\) | |||||||
\(20\) | −2.23241 | − | 0.127776i | −0.499183 | − | 0.0285715i | ||||
\(21\) | 0.823831i | 0.179775i | ||||||||
\(22\) | − | 4.39414i | − | 0.936834i | ||||||
\(23\) | 1.20395 | 0.251040 | 0.125520 | − | 0.992091i | \(-0.459940\pi\) | ||||
0.125520 | + | 0.992091i | \(0.459940\pi\) | |||||||
\(24\) | −0.536506 | − | 0.536506i | −0.109514 | − | 0.109514i | ||||
\(25\) | 4.96735 | + | 0.570497i | 0.993469 | + | 0.114099i | ||||
\(26\) | −6.74274 | −1.32236 | ||||||||
\(27\) | 2.91018 | − | 2.91018i | 0.560064 | − | 0.560064i | ||||
\(28\) | 0.767774 | + | 0.767774i | 0.145096 | + | 0.145096i | ||||
\(29\) | −1.25185 | − | 1.25185i | −0.232463 | − | 0.232463i | 0.581257 | − | 0.813720i | \(-0.302561\pi\) |
−0.813720 | + | 0.581257i | \(0.802561\pi\) | |||||||
\(30\) | 1.12915 | + | 1.26626i | 0.206154 | + | 0.231185i | ||||
\(31\) | −4.14855 | + | 4.14855i | −0.745101 | + | 0.745101i | −0.973555 | − | 0.228454i | \(-0.926633\pi\) |
0.228454 | + | 0.973555i | \(0.426633\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.35748 | + | 2.35748i | −0.410385 | + | 0.410385i | ||||
\(34\) | − | 7.34365i | − | 1.25943i | ||||||
\(35\) | −1.61589 | − | 1.81209i | −0.273135 | − | 0.306300i | ||||
\(36\) | − | 2.42432i | − | 0.404054i | ||||||
\(37\) | 6.04973 | + | 0.633071i | 0.994569 | + | 0.104076i | ||||
\(38\) | 2.59760 | − | 2.59760i | 0.421386 | − | 0.421386i | ||||
\(39\) | 3.61752 | + | 3.61752i | 0.579266 | + | 0.579266i | ||||
\(40\) | 2.23241 | + | 0.127776i | 0.352976 | + | 0.0202031i | ||||
\(41\) | 4.07091i | 0.635769i | 0.948129 | + | 0.317884i | \(0.102972\pi\) | ||||
−0.948129 | + | 0.317884i | \(0.897028\pi\) | |||||||
\(42\) | − | 0.823831i | − | 0.127120i | ||||||
\(43\) | −8.56098 | −1.30554 | −0.652769 | − | 0.757557i | \(-0.726393\pi\) | ||||
−0.652769 | + | 0.757557i | \(0.726393\pi\) | |||||||
\(44\) | 4.39414i | 0.662442i | ||||||||
\(45\) | −0.309770 | + | 5.41209i | −0.0461778 | + | 0.806787i | ||||
\(46\) | −1.20395 | −0.177512 | ||||||||
\(47\) | 7.68569 | + | 7.68569i | 1.12107 | + | 1.12107i | 0.991580 | + | 0.129493i | \(0.0413351\pi\) |
0.129493 | + | 0.991580i | \(0.458665\pi\) | |||||||
\(48\) | 0.536506 | + | 0.536506i | 0.0774379 | + | 0.0774379i | ||||
\(49\) | − | 5.82104i | − | 0.831578i | ||||||
\(50\) | −4.96735 | − | 0.570497i | −0.702489 | − | 0.0806805i | ||||
\(51\) | −3.93991 | + | 3.93991i | −0.551697 | + | 0.551697i | ||||
\(52\) | 6.74274 | 0.935050 | ||||||||
\(53\) | 2.31983 | − | 2.31983i | 0.318653 | − | 0.318653i | −0.529596 | − | 0.848250i | \(-0.677657\pi\) |
0.848250 | + | 0.529596i | \(0.177657\pi\) | |||||||
\(54\) | −2.91018 | + | 2.91018i | −0.396025 | + | 0.396025i | ||||
\(55\) | 0.561465 | − | 9.80954i | 0.0757079 | − | 1.32272i | ||||
\(56\) | −0.767774 | − | 0.767774i | −0.102598 | − | 0.102598i | ||||
\(57\) | −2.78725 | −0.369181 | ||||||||
\(58\) | 1.25185 | + | 1.25185i | 0.164376 | + | 0.164376i | ||||
\(59\) | 7.61323 | − | 7.61323i | 0.991158 | − | 0.991158i | −0.00880307 | − | 0.999961i | \(-0.502802\pi\) |
0.999961 | + | 0.00880307i | \(0.00280214\pi\) | |||||||
\(60\) | −1.12915 | − | 1.26626i | −0.145773 | − | 0.163473i | ||||
\(61\) | 1.14451 | − | 1.14451i | 0.146539 | − | 0.146539i | −0.630031 | − | 0.776570i | \(-0.716958\pi\) |
0.776570 | + | 0.630031i | \(0.216958\pi\) | |||||||
\(62\) | 4.14855 | − | 4.14855i | 0.526866 | − | 0.526866i | ||||
\(63\) | 1.86133 | − | 1.86133i | 0.234506 | − | 0.234506i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −15.0526 | − | 0.861559i | −1.86704 | − | 0.106863i | ||||
\(66\) | 2.35748 | − | 2.35748i | 0.290186 | − | 0.290186i | ||||
\(67\) | 6.25304 | − | 6.25304i | 0.763930 | − | 0.763930i | −0.213100 | − | 0.977030i | \(-0.568356\pi\) |
0.977030 | + | 0.213100i | \(0.0683560\pi\) | |||||||
\(68\) | 7.34365i | 0.890548i | ||||||||
\(69\) | 0.645925 | + | 0.645925i | 0.0777602 | + | 0.0777602i | ||||
\(70\) | 1.61589 | + | 1.81209i | 0.193136 | + | 0.216587i | ||||
\(71\) | −5.46460 | −0.648529 | −0.324265 | − | 0.945966i | \(-0.605117\pi\) | ||||
−0.324265 | + | 0.945966i | \(0.605117\pi\) | |||||||
\(72\) | 2.42432i | 0.285709i | ||||||||
\(73\) | −1.88159 | − | 1.88159i | −0.220224 | − | 0.220224i | 0.588369 | − | 0.808593i | \(-0.299770\pi\) |
−0.808593 | + | 0.588369i | \(0.799770\pi\) | |||||||
\(74\) | −6.04973 | − | 0.633071i | −0.703267 | − | 0.0735930i | ||||
\(75\) | 2.35893 | + | 2.97108i | 0.272386 | + | 0.343071i | ||||
\(76\) | −2.59760 | + | 2.59760i | −0.297965 | + | 0.297965i | ||||
\(77\) | −3.37371 | + | 3.37371i | −0.384470 | + | 0.384470i | ||||
\(78\) | −3.61752 | − | 3.61752i | −0.409603 | − | 0.409603i | ||||
\(79\) | −5.13322 | + | 5.13322i | −0.577533 | + | 0.577533i | −0.934223 | − | 0.356690i | \(-0.883905\pi\) |
0.356690 | + | 0.934223i | \(0.383905\pi\) | |||||||
\(80\) | −2.23241 | − | 0.127776i | −0.249591 | − | 0.0142858i | ||||
\(81\) | −4.15032 | −0.461146 | ||||||||
\(82\) | − | 4.07091i | − | 0.449557i | ||||||
\(83\) | 0.570350 | − | 0.570350i | 0.0626041 | − | 0.0626041i | −0.675112 | − | 0.737716i | \(-0.735905\pi\) |
0.737716 | + | 0.675112i | \(0.235905\pi\) | |||||||
\(84\) | 0.823831i | 0.0898873i | ||||||||
\(85\) | 0.938340 | − | 16.3941i | 0.101777 | − | 1.77819i | ||||
\(86\) | 8.56098 | 0.923155 | ||||||||
\(87\) | − | 1.34325i | − | 0.144012i | ||||||
\(88\) | − | 4.39414i | − | 0.468417i | ||||||
\(89\) | −7.54653 | − | 7.54653i | −0.799931 | − | 0.799931i | 0.183153 | − | 0.983084i | \(-0.441370\pi\) |
−0.983084 | + | 0.183153i | \(0.941370\pi\) | |||||||
\(90\) | 0.309770 | − | 5.41209i | 0.0326526 | − | 0.570485i | ||||
\(91\) | 5.17690 | + | 5.17690i | 0.542687 | + | 0.542687i | ||||
\(92\) | 1.20395 | 0.125520 | ||||||||
\(93\) | −4.45144 | −0.461593 | ||||||||
\(94\) | −7.68569 | − | 7.68569i | −0.792719 | − | 0.792719i | ||||
\(95\) | 6.13083 | − | 5.46701i | 0.629009 | − | 0.560903i | ||||
\(96\) | −0.536506 | − | 0.536506i | −0.0547569 | − | 0.0547569i | ||||
\(97\) | − | 5.39443i | − | 0.547721i | −0.961769 | − | 0.273861i | \(-0.911699\pi\) | ||
0.961769 | − | 0.273861i | \(-0.0883007\pi\) | |||||||
\(98\) | 5.82104i | 0.588014i | ||||||||
\(99\) | 10.6528 | 1.07065 | ||||||||
\(100\) | 4.96735 | + | 0.570497i | 0.496735 | + | 0.0570497i | ||||
\(101\) | − | 14.5684i | − | 1.44961i | −0.688956 | − | 0.724803i | \(-0.741931\pi\) | ||
0.688956 | − | 0.724803i | \(-0.258069\pi\) | |||||||
\(102\) | 3.93991 | − | 3.93991i | 0.390109 | − | 0.390109i | ||||
\(103\) | 10.1623i | 1.00132i | 0.865643 | + | 0.500662i | \(0.166910\pi\) | ||||
−0.865643 | + | 0.500662i | \(0.833090\pi\) | |||||||
\(104\) | −6.74274 | −0.661180 | ||||||||
\(105\) | 0.105266 | − | 1.83913i | 0.0102729 | − | 0.179481i | ||||
\(106\) | −2.31983 | + | 2.31983i | −0.225322 | + | 0.225322i | ||||
\(107\) | −13.4161 | − | 13.4161i | −1.29698 | − | 1.29698i | −0.930378 | − | 0.366601i | \(-0.880521\pi\) |
−0.366601 | − | 0.930378i | \(-0.619479\pi\) | |||||||
\(108\) | 2.91018 | − | 2.91018i | 0.280032 | − | 0.280032i | ||||
\(109\) | −4.78437 | + | 4.78437i | −0.458259 | + | 0.458259i | −0.898084 | − | 0.439824i | \(-0.855041\pi\) |
0.439824 | + | 0.898084i | \(0.355041\pi\) | |||||||
\(110\) | −0.561465 | + | 9.80954i | −0.0535336 | + | 0.935303i | ||||
\(111\) | 2.90607 | + | 3.58536i | 0.275832 | + | 0.340307i | ||||
\(112\) | 0.767774 | + | 0.767774i | 0.0725479 | + | 0.0725479i | ||||
\(113\) | − | 18.0037i | − | 1.69365i | −0.531872 | − | 0.846825i | \(-0.678511\pi\) | ||
0.531872 | − | 0.846825i | \(-0.321489\pi\) | |||||||
\(114\) | 2.78725 | 0.261050 | ||||||||
\(115\) | −2.68771 | − | 0.153835i | −0.250630 | − | 0.0143452i | ||||
\(116\) | −1.25185 | − | 1.25185i | −0.116232 | − | 0.116232i | ||||
\(117\) | − | 16.3466i | − | 1.51124i | ||||||
\(118\) | −7.61323 | + | 7.61323i | −0.700855 | + | 0.700855i | ||||
\(119\) | −5.63827 | + | 5.63827i | −0.516859 | + | 0.516859i | ||||
\(120\) | 1.12915 | + | 1.26626i | 0.103077 | + | 0.115593i | ||||
\(121\) | −8.30847 | −0.755316 | ||||||||
\(122\) | −1.14451 | + | 1.14451i | −0.103619 | + | 0.103619i | ||||
\(123\) | −2.18406 | + | 2.18406i | −0.196930 | + | 0.196930i | ||||
\(124\) | −4.14855 | + | 4.14855i | −0.372551 | + | 0.372551i | ||||
\(125\) | −11.0163 | − | 1.90829i | −0.985326 | − | 0.170683i | ||||
\(126\) | −1.86133 | + | 1.86133i | −0.165821 | + | 0.165821i | ||||
\(127\) | 9.21023 | + | 9.21023i | 0.817275 | + | 0.817275i | 0.985712 | − | 0.168437i | \(-0.0538720\pi\) |
−0.168437 | + | 0.985712i | \(0.553872\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.59302 | − | 4.59302i | −0.404393 | − | 0.404393i | ||||
\(130\) | 15.0526 | + | 0.861559i | 1.32020 | + | 0.0755637i | ||||
\(131\) | −1.53844 | + | 1.53844i | −0.134414 | + | 0.134414i | −0.771113 | − | 0.636698i | \(-0.780300\pi\) |
0.636698 | + | 0.771113i | \(0.280300\pi\) | |||||||
\(132\) | −2.35748 | + | 2.35748i | −0.205192 | + | 0.205192i | ||||
\(133\) | −3.98874 | −0.345868 | ||||||||
\(134\) | −6.25304 | + | 6.25304i | −0.540180 | + | 0.540180i | ||||
\(135\) | −6.86858 | + | 6.12488i | −0.591153 | + | 0.527145i | ||||
\(136\) | − | 7.34365i | − | 0.629713i | ||||||
\(137\) | 11.9150 | + | 11.9150i | 1.01797 | + | 1.01797i | 0.999836 | + | 0.0181339i | \(0.00577252\pi\) |
0.0181339 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(138\) | −0.645925 | − | 0.645925i | −0.0549847 | − | 0.0549847i | ||||
\(139\) | 6.75745 | 0.573159 | 0.286580 | − | 0.958056i | \(-0.407482\pi\) | ||||
0.286580 | + | 0.958056i | \(0.407482\pi\) | |||||||
\(140\) | −1.61589 | − | 1.81209i | −0.136567 | − | 0.153150i | ||||
\(141\) | 8.24684i | 0.694509i | ||||||||
\(142\) | 5.46460 | 0.458579 | ||||||||
\(143\) | 29.6285i | 2.47766i | ||||||||
\(144\) | − | 2.42432i | − | 0.202027i | ||||||
\(145\) | 2.63470 | + | 2.95461i | 0.218800 | + | 0.245367i | ||||
\(146\) | 1.88159 | + | 1.88159i | 0.155722 | + | 0.155722i | ||||
\(147\) | 3.12302 | − | 3.12302i | 0.257583 | − | 0.257583i | ||||
\(148\) | 6.04973 | + | 0.633071i | 0.497285 | + | 0.0520381i | ||||
\(149\) | 5.18543i | 0.424807i | 0.977182 | + | 0.212404i | \(0.0681291\pi\) | ||||
−0.977182 | + | 0.212404i | \(0.931871\pi\) | |||||||
\(150\) | −2.35893 | − | 2.97108i | −0.192606 | − | 0.242588i | ||||
\(151\) | − | 12.5372i | − | 1.02026i | −0.860097 | − | 0.510131i | \(-0.829597\pi\) | ||
0.860097 | − | 0.510131i | \(-0.170403\pi\) | |||||||
\(152\) | 2.59760 | − | 2.59760i | 0.210693 | − | 0.210693i | ||||
\(153\) | 17.8034 | 1.43932 | ||||||||
\(154\) | 3.37371 | − | 3.37371i | 0.271861 | − | 0.271861i | ||||
\(155\) | 9.79136 | − | 8.73119i | 0.786461 | − | 0.701306i | ||||
\(156\) | 3.61752 | + | 3.61752i | 0.289633 | + | 0.289633i | ||||
\(157\) | −0.530292 | − | 0.530292i | −0.0423219 | − | 0.0423219i | 0.685629 | − | 0.727951i | \(-0.259527\pi\) |
−0.727951 | + | 0.685629i | \(0.759527\pi\) | |||||||
\(158\) | 5.13322 | − | 5.13322i | 0.408377 | − | 0.408377i | ||||
\(159\) | 2.48921 | 0.197407 | ||||||||
\(160\) | 2.23241 | + | 0.127776i | 0.176488 | + | 0.0101016i | ||||
\(161\) | 0.924360 | + | 0.924360i | 0.0728498 | + | 0.0728498i | ||||
\(162\) | 4.15032 | 0.326080 | ||||||||
\(163\) | 13.0393i | 1.02132i | 0.859783 | + | 0.510660i | \(0.170599\pi\) | ||||
−0.859783 | + | 0.510660i | \(0.829401\pi\) | |||||||
\(164\) | 4.07091i | 0.317884i | ||||||||
\(165\) | 5.56410 | − | 4.96164i | 0.433165 | − | 0.386264i | ||||
\(166\) | −0.570350 | + | 0.570350i | −0.0442678 | + | 0.0442678i | ||||
\(167\) | 24.6405i | 1.90674i | 0.301805 | + | 0.953370i | \(0.402411\pi\) | ||||
−0.301805 | + | 0.953370i | \(0.597589\pi\) | |||||||
\(168\) | − | 0.823831i | − | 0.0635599i | ||||||
\(169\) | 32.4645 | 2.49727 | ||||||||
\(170\) | −0.938340 | + | 16.3941i | −0.0719674 | + | 1.25737i | ||||
\(171\) | 6.29742 | + | 6.29742i | 0.481576 | + | 0.481576i | ||||
\(172\) | −8.56098 | −0.652769 | ||||||||
\(173\) | −5.32250 | − | 5.32250i | −0.404662 | − | 0.404662i | 0.475210 | − | 0.879872i | \(-0.342372\pi\) |
−0.879872 | + | 0.475210i | \(0.842372\pi\) | |||||||
\(174\) | 1.34325i | 0.101832i | ||||||||
\(175\) | 3.37579 | + | 4.25182i | 0.255186 | + | 0.321407i | ||||
\(176\) | 4.39414i | 0.331221i | ||||||||
\(177\) | 8.16908 | 0.614026 | ||||||||
\(178\) | 7.54653 | + | 7.54653i | 0.565637 | + | 0.565637i | ||||
\(179\) | −7.93007 | − | 7.93007i | −0.592721 | − | 0.592721i | 0.345644 | − | 0.938366i | \(-0.387660\pi\) |
−0.938366 | + | 0.345644i | \(0.887660\pi\) | |||||||
\(180\) | −0.309770 | + | 5.41209i | −0.0230889 | + | 0.403394i | ||||
\(181\) | −4.29385 | −0.319160 | −0.159580 | − | 0.987185i | \(-0.551014\pi\) | ||||
−0.159580 | + | 0.987185i | \(0.551014\pi\) | |||||||
\(182\) | −5.17690 | − | 5.17690i | −0.383738 | − | 0.383738i | ||||
\(183\) | 1.22807 | 0.0907813 | ||||||||
\(184\) | −1.20395 | −0.0887562 | ||||||||
\(185\) | −13.4246 | − | 2.18628i | −0.986997 | − | 0.160739i | ||||
\(186\) | 4.45144 | 0.326395 | ||||||||
\(187\) | −32.2690 | −2.35974 | ||||||||
\(188\) | 7.68569 | + | 7.68569i | 0.560537 | + | 0.560537i | ||||
\(189\) | 4.46872 | 0.325052 | ||||||||
\(190\) | −6.13083 | + | 5.46701i | −0.444777 | + | 0.396618i | ||||
\(191\) | 2.08620 | + | 2.08620i | 0.150952 | + | 0.150952i | 0.778543 | − | 0.627591i | \(-0.215959\pi\) |
−0.627591 | + | 0.778543i | \(0.715959\pi\) | |||||||
\(192\) | 0.536506 | + | 0.536506i | 0.0387190 | + | 0.0387190i | ||||
\(193\) | −13.6280 | −0.980961 | −0.490481 | − | 0.871452i | \(-0.663179\pi\) | ||||
−0.490481 | + | 0.871452i | \(0.663179\pi\) | |||||||
\(194\) | 5.39443i | 0.387298i | ||||||||
\(195\) | −7.61357 | − | 8.53803i | −0.545219 | − | 0.611421i | ||||
\(196\) | − | 5.82104i | − | 0.415789i | ||||||
\(197\) | 5.05224 | + | 5.05224i | 0.359957 | + | 0.359957i | 0.863797 | − | 0.503840i | \(-0.168080\pi\) |
−0.503840 | + | 0.863797i | \(0.668080\pi\) | |||||||
\(198\) | −10.6528 | −0.757063 | ||||||||
\(199\) | 12.1515 | + | 12.1515i | 0.861395 | + | 0.861395i | 0.991500 | − | 0.130105i | \(-0.0415314\pi\) |
−0.130105 | + | 0.991500i | \(0.541531\pi\) | |||||||
\(200\) | −4.96735 | − | 0.570497i | −0.351244 | − | 0.0403402i | ||||
\(201\) | 6.70958 | 0.473257 | ||||||||
\(202\) | 14.5684i | 1.02503i | ||||||||
\(203\) | − | 1.92228i | − | 0.134918i | ||||||
\(204\) | −3.93991 | + | 3.93991i | −0.275849 | + | 0.275849i | ||||
\(205\) | 0.520163 | − | 9.08795i | 0.0363298 | − | 0.634730i | ||||
\(206\) | − | 10.1623i | − | 0.708043i | ||||||
\(207\) | − | 2.91876i | − | 0.202868i | ||||||
\(208\) | 6.74274 | 0.467525 | ||||||||
\(209\) | −11.4142 | − | 11.4142i | −0.789538 | − | 0.789538i | ||||
\(210\) | −0.105266 | + | 1.83913i | −0.00726402 | + | 0.126912i | ||||
\(211\) | 8.27973 | 0.570000 | 0.285000 | − | 0.958527i | \(-0.408006\pi\) | ||||
0.285000 | + | 0.958527i | \(0.408006\pi\) | |||||||
\(212\) | 2.31983 | − | 2.31983i | 0.159327 | − | 0.159327i | ||||
\(213\) | −2.93179 | − | 2.93179i | −0.200883 | − | 0.200883i | ||||
\(214\) | 13.4161 | + | 13.4161i | 0.917103 | + | 0.917103i | ||||
\(215\) | 19.1117 | + | 1.09389i | 1.30340 | + | 0.0746024i | ||||
\(216\) | −2.91018 | + | 2.91018i | −0.198013 | + | 0.198013i | ||||
\(217\) | −6.37030 | −0.432444 | ||||||||
\(218\) | 4.78437 | − | 4.78437i | 0.324038 | − | 0.324038i | ||||
\(219\) | − | 2.01897i | − | 0.136429i | ||||||
\(220\) | 0.561465 | − | 9.80954i | 0.0378539 | − | 0.661359i | ||||
\(221\) | 49.5163i | 3.33083i | ||||||||
\(222\) | −2.90607 | − | 3.58536i | −0.195042 | − | 0.240634i | ||||
\(223\) | 9.35468 | − | 9.35468i | 0.626436 | − | 0.626436i | −0.320733 | − | 0.947169i | \(-0.603929\pi\) |
0.947169 | + | 0.320733i | \(0.103929\pi\) | |||||||
\(224\) | −0.767774 | − | 0.767774i | −0.0512991 | − | 0.0512991i | ||||
\(225\) | 1.38307 | − | 12.0425i | 0.0922046 | − | 0.802830i | ||||
\(226\) | 18.0037i | 1.19759i | ||||||||
\(227\) | − | 20.1807i | − | 1.33944i | −0.742613 | − | 0.669721i | \(-0.766414\pi\) | ||
0.742613 | − | 0.669721i | \(-0.233586\pi\) | |||||||
\(228\) | −2.78725 | −0.184590 | ||||||||
\(229\) | − | 3.02631i | − | 0.199984i | −0.994988 | − | 0.0999920i | \(-0.968118\pi\) | ||
0.994988 | − | 0.0999920i | \(-0.0318817\pi\) | |||||||
\(230\) | 2.68771 | + | 0.153835i | 0.177222 | + | 0.0101436i | ||||
\(231\) | −3.62003 | −0.238180 | ||||||||
\(232\) | 1.25185 | + | 1.25185i | 0.0821882 | + | 0.0821882i | ||||
\(233\) | −4.33931 | − | 4.33931i | −0.284278 | − | 0.284278i | 0.550534 | − | 0.834812i | \(-0.314424\pi\) |
−0.834812 | + | 0.550534i | \(0.814424\pi\) | |||||||
\(234\) | 16.3466i | 1.06861i | ||||||||
\(235\) | −16.1756 | − | 18.1397i | −1.05518 | − | 1.18330i | ||||
\(236\) | 7.61323 | − | 7.61323i | 0.495579 | − | 0.495579i | ||||
\(237\) | −5.50801 | −0.357783 | ||||||||
\(238\) | 5.63827 | − | 5.63827i | 0.365474 | − | 0.365474i | ||||
\(239\) | 2.92398 | − | 2.92398i | 0.189137 | − | 0.189137i | −0.606186 | − | 0.795323i | \(-0.707301\pi\) |
0.795323 | + | 0.606186i | \(0.207301\pi\) | |||||||
\(240\) | −1.12915 | − | 1.26626i | −0.0728863 | − | 0.0817364i | ||||
\(241\) | −14.9825 | − | 14.9825i | −0.965105 | − | 0.965105i | 0.0343063 | − | 0.999411i | \(-0.489078\pi\) |
−0.999411 | + | 0.0343063i | \(0.989078\pi\) | |||||||
\(242\) | 8.30847 | 0.534089 | ||||||||
\(243\) | −10.9572 | − | 10.9572i | −0.702905 | − | 0.702905i | ||||
\(244\) | 1.14451 | − | 1.14451i | 0.0732694 | − | 0.0732694i | ||||
\(245\) | −0.743789 | + | 12.9950i | −0.0475189 | + | 0.830219i | ||||
\(246\) | 2.18406 | − | 2.18406i | 0.139251 | − | 0.139251i | ||||
\(247\) | −17.5149 | + | 17.5149i | −1.11445 | + | 1.11445i | ||||
\(248\) | 4.14855 | − | 4.14855i | 0.263433 | − | 0.263433i | ||||
\(249\) | 0.611992 | 0.0387834 | ||||||||
\(250\) | 11.0163 | + | 1.90829i | 0.696731 | + | 0.120691i | ||||
\(251\) | 9.25271 | − | 9.25271i | 0.584026 | − | 0.584026i | −0.351981 | − | 0.936007i | \(-0.614492\pi\) |
0.936007 | + | 0.351981i | \(0.114492\pi\) | |||||||
\(252\) | 1.86133 | − | 1.86133i | 0.117253 | − | 0.117253i | ||||
\(253\) | 5.29031i | 0.332599i | ||||||||
\(254\) | −9.21023 | − | 9.21023i | −0.577901 | − | 0.577901i | ||||
\(255\) | 9.29893 | − | 8.29208i | 0.582322 | − | 0.519270i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 11.5476i | − | 0.720317i | −0.932891 | − | 0.360158i | \(-0.882723\pi\) | ||
0.932891 | − | 0.360158i | \(-0.117277\pi\) | |||||||
\(258\) | 4.59302 | + | 4.59302i | 0.285949 | + | 0.285949i | ||||
\(259\) | 4.15877 | + | 5.13088i | 0.258414 | + | 0.318818i | ||||
\(260\) | −15.0526 | − | 0.861559i | −0.933522 | − | 0.0534316i | ||||
\(261\) | −3.03490 | + | 3.03490i | −0.187855 | + | 0.187855i | ||||
\(262\) | 1.53844 | − | 1.53844i | 0.0950454 | − | 0.0950454i | ||||
\(263\) | −6.36639 | − | 6.36639i | −0.392569 | − | 0.392569i | 0.483033 | − | 0.875602i | \(-0.339535\pi\) |
−0.875602 | + | 0.483033i | \(0.839535\pi\) | |||||||
\(264\) | 2.35748 | − | 2.35748i | 0.145093 | − | 0.145093i | ||||
\(265\) | −5.47524 | + | 4.88241i | −0.336342 | + | 0.299924i | ||||
\(266\) | 3.98874 | 0.244565 | ||||||||
\(267\) | − | 8.09751i | − | 0.495560i | ||||||
\(268\) | 6.25304 | − | 6.25304i | 0.381965 | − | 0.381965i | ||||
\(269\) | − | 3.72238i | − | 0.226958i | −0.993540 | − | 0.113479i | \(-0.963801\pi\) | ||
0.993540 | − | 0.113479i | \(-0.0361994\pi\) | |||||||
\(270\) | 6.86858 | − | 6.12488i | 0.418008 | − | 0.372748i | ||||
\(271\) | 23.2312 | 1.41120 | 0.705598 | − | 0.708612i | \(-0.250678\pi\) | ||||
0.705598 | + | 0.708612i | \(0.250678\pi\) | |||||||
\(272\) | 7.34365i | 0.445274i | ||||||||
\(273\) | 5.55488i | 0.336196i | ||||||||
\(274\) | −11.9150 | − | 11.9150i | −0.719813 | − | 0.719813i | ||||
\(275\) | −2.50684 | + | 21.8272i | −0.151168 | + | 1.31623i | ||||
\(276\) | 0.645925 | + | 0.645925i | 0.0388801 | + | 0.0388801i | ||||
\(277\) | −12.8392 | −0.771434 | −0.385717 | − | 0.922617i | \(-0.626046\pi\) | ||||
−0.385717 | + | 0.922617i | \(0.626046\pi\) | |||||||
\(278\) | −6.75745 | −0.405285 | ||||||||
\(279\) | 10.0574 | + | 10.0574i | 0.602122 | + | 0.602122i | ||||
\(280\) | 1.61589 | + | 1.81209i | 0.0965678 | + | 0.108293i | ||||
\(281\) | 15.2770 | + | 15.2770i | 0.911350 | + | 0.911350i | 0.996378 | − | 0.0850287i | \(-0.0270982\pi\) |
−0.0850287 | + | 0.996378i | \(0.527098\pi\) | |||||||
\(282\) | − | 8.24684i | − | 0.491092i | ||||||
\(283\) | 20.7901i | 1.23584i | 0.786241 | + | 0.617920i | \(0.212025\pi\) | ||||
−0.786241 | + | 0.617920i | \(0.787975\pi\) | |||||||
\(284\) | −5.46460 | −0.324265 | ||||||||
\(285\) | 6.22230 | + | 0.356143i | 0.368577 | + | 0.0210961i | ||||
\(286\) | − | 29.6285i | − | 1.75197i | ||||||
\(287\) | −3.12554 | + | 3.12554i | −0.184495 | + | 0.184495i | ||||
\(288\) | 2.42432i | 0.142855i | ||||||||
\(289\) | −36.9292 | −2.17230 | ||||||||
\(290\) | −2.63470 | − | 2.95461i | −0.154715 | − | 0.173501i | ||||
\(291\) | 2.89414 | − | 2.89414i | 0.169658 | − | 0.169658i | ||||
\(292\) | −1.88159 | − | 1.88159i | −0.110112 | − | 0.110112i | ||||
\(293\) | 0.449201 | − | 0.449201i | 0.0262426 | − | 0.0262426i | −0.693864 | − | 0.720106i | \(-0.744093\pi\) |
0.720106 | + | 0.693864i | \(0.244093\pi\) | |||||||
\(294\) | −3.12302 | + | 3.12302i | −0.182138 | + | 0.182138i | ||||
\(295\) | −17.9687 | + | 16.0231i | −1.04618 | + | 0.932901i | ||||
\(296\) | −6.04973 | − | 0.633071i | −0.351633 | − | 0.0367965i | ||||
\(297\) | 12.7877 | + | 12.7877i | 0.742020 | + | 0.742020i | ||||
\(298\) | − | 5.18543i | − | 0.300384i | ||||||
\(299\) | 8.11790 | 0.469471 | ||||||||
\(300\) | 2.35893 | + | 2.97108i | 0.136193 | + | 0.171536i | ||||
\(301\) | −6.57291 | − | 6.57291i | −0.378856 | − | 0.378856i | ||||
\(302\) | 12.5372i | 0.721434i | ||||||||
\(303\) | 7.81601 | − | 7.81601i | 0.449018 | − | 0.449018i | ||||
\(304\) | −2.59760 | + | 2.59760i | −0.148982 | + | 0.148982i | ||||
\(305\) | −2.70125 | + | 2.40877i | −0.154673 | + | 0.137926i | ||||
\(306\) | −17.8034 | −1.01775 | ||||||||
\(307\) | −0.0144735 | + | 0.0144735i | −0.000826048 | + | 0.000826048i | −0.707520 | − | 0.706694i | \(-0.750186\pi\) |
0.706694 | + | 0.707520i | \(0.250186\pi\) | |||||||
\(308\) | −3.37371 | + | 3.37371i | −0.192235 | + | 0.192235i | ||||
\(309\) | −5.45215 | + | 5.45215i | −0.310162 | + | 0.310162i | ||||
\(310\) | −9.79136 | + | 8.73119i | −0.556112 | + | 0.495899i | ||||
\(311\) | 22.9260 | − | 22.9260i | 1.30001 | − | 1.30001i | 0.371635 | − | 0.928379i | \(-0.378797\pi\) |
0.928379 | − | 0.371635i | \(-0.121203\pi\) | |||||||
\(312\) | −3.61752 | − | 3.61752i | −0.204802 | − | 0.204802i | ||||
\(313\) | 14.6520 | 0.828177 | 0.414089 | − | 0.910237i | \(-0.364100\pi\) | ||||
0.414089 | + | 0.910237i | \(0.364100\pi\) | |||||||
\(314\) | 0.530292 | + | 0.530292i | 0.0299261 | + | 0.0299261i | ||||
\(315\) | −4.39310 | + | 3.91743i | −0.247523 | + | 0.220722i | ||||
\(316\) | −5.13322 | + | 5.13322i | −0.288766 | + | 0.288766i | ||||
\(317\) | 14.2710 | − | 14.2710i | 0.801537 | − | 0.801537i | −0.181799 | − | 0.983336i | \(-0.558192\pi\) |
0.983336 | + | 0.181799i | \(0.0581919\pi\) | |||||||
\(318\) | −2.48921 | −0.139588 | ||||||||
\(319\) | 5.50082 | − | 5.50082i | 0.307987 | − | 0.307987i | ||||
\(320\) | −2.23241 | − | 0.127776i | −0.124796 | − | 0.00714288i | ||||
\(321\) | − | 14.3956i | − | 0.803483i | ||||||
\(322\) | −0.924360 | − | 0.924360i | −0.0515126 | − | 0.0515126i | ||||
\(323\) | −19.0758 | − | 19.0758i | −1.06141 | − | 1.06141i | ||||
\(324\) | −4.15032 | −0.230573 | ||||||||
\(325\) | 33.4935 | + | 3.84671i | 1.85789 | + | 0.213377i | ||||
\(326\) | − | 13.0393i | − | 0.722183i | ||||||
\(327\) | −5.13368 | −0.283893 | ||||||||
\(328\) | − | 4.07091i | − | 0.224778i | ||||||
\(329\) | 11.8018i | 0.650652i | ||||||||
\(330\) | −5.56410 | + | 4.96164i | −0.306294 | + | 0.273130i | ||||
\(331\) | −19.0443 | − | 19.0443i | −1.04677 | − | 1.04677i | −0.998851 | − | 0.0479194i | \(-0.984741\pi\) |
−0.0479194 | − | 0.998851i | \(-0.515259\pi\) | |||||||
\(332\) | 0.570350 | − | 0.570350i | 0.0313020 | − | 0.0313020i | ||||
\(333\) | 1.53477 | − | 14.6665i | 0.0841048 | − | 0.803719i | ||||
\(334\) | − | 24.6405i | − | 1.34827i | ||||||
\(335\) | −14.7584 | + | 13.1604i | −0.806336 | + | 0.719029i | ||||
\(336\) | 0.823831i | 0.0449436i | ||||||||
\(337\) | −11.2643 | + | 11.2643i | −0.613604 | + | 0.613604i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) |
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(338\) | −32.4645 | −1.76584 | ||||||||
\(339\) | 9.65911 | − | 9.65911i | 0.524611 | − | 0.524611i | ||||
\(340\) | 0.938340 | − | 16.3941i | 0.0508886 | − | 0.889093i | ||||
\(341\) | −18.2293 | − | 18.2293i | −0.987172 | − | 0.987172i | ||||
\(342\) | −6.29742 | − | 6.29742i | −0.340525 | − | 0.340525i | ||||
\(343\) | 9.84367 | − | 9.84367i | 0.531508 | − | 0.531508i | ||||
\(344\) | 8.56098 | 0.461577 | ||||||||
\(345\) | −1.35944 | − | 1.52450i | −0.0731897 | − | 0.0820766i | ||||
\(346\) | 5.32250 | + | 5.32250i | 0.286139 | + | 0.286139i | ||||
\(347\) | −2.40110 | −0.128898 | −0.0644489 | − | 0.997921i | \(-0.520529\pi\) | ||||
−0.0644489 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(348\) | − | 1.34325i | − | 0.0720059i | ||||||
\(349\) | − | 13.3892i | − | 0.716708i | −0.933586 | − | 0.358354i | \(-0.883338\pi\) | ||
0.933586 | − | 0.358354i | \(-0.116662\pi\) | |||||||
\(350\) | −3.37579 | − | 4.25182i | −0.180444 | − | 0.227269i | ||||
\(351\) | 19.6226 | − | 19.6226i | 1.04738 | − | 1.04738i | ||||
\(352\) | − | 4.39414i | − | 0.234208i | ||||||
\(353\) | 7.34993i | 0.391198i | 0.980684 | + | 0.195599i | \(0.0626650\pi\) | ||||
−0.980684 | + | 0.195599i | \(0.937335\pi\) | |||||||
\(354\) | −8.16908 | −0.434182 | ||||||||
\(355\) | 12.1993 | + | 0.698244i | 0.647470 | + | 0.0370590i | ||||
\(356\) | −7.54653 | − | 7.54653i | −0.399965 | − | 0.399965i | ||||
\(357\) | −6.04992 | −0.320196 | ||||||||
\(358\) | 7.93007 | + | 7.93007i | 0.419117 | + | 0.419117i | ||||
\(359\) | 24.0685i | 1.27029i | 0.772394 | + | 0.635143i | \(0.219059\pi\) | ||||
−0.772394 | + | 0.635143i | \(0.780941\pi\) | |||||||
\(360\) | 0.309770 | − | 5.41209i | 0.0163263 | − | 0.285242i | ||||
\(361\) | 5.50496i | 0.289735i | ||||||||
\(362\) | 4.29385 | 0.225680 | ||||||||
\(363\) | −4.45754 | − | 4.45754i | −0.233960 | − | 0.233960i | ||||
\(364\) | 5.17690 | + | 5.17690i | 0.271343 | + | 0.271343i | ||||
\(365\) | 3.96007 | + | 4.44092i | 0.207280 | + | 0.232448i | ||||
\(366\) | −1.22807 | −0.0641921 | ||||||||
\(367\) | −0.833192 | − | 0.833192i | −0.0434923 | − | 0.0434923i | 0.685026 | − | 0.728518i | \(-0.259791\pi\) |
−0.728518 | + | 0.685026i | \(0.759791\pi\) | |||||||
\(368\) | 1.20395 | 0.0627601 | ||||||||
\(369\) | 9.86920 | 0.513770 | ||||||||
\(370\) | 13.4246 | + | 2.18628i | 0.697912 | + | 0.113660i | ||||
\(371\) | 3.56222 | 0.184941 | ||||||||
\(372\) | −4.45144 | −0.230796 | ||||||||
\(373\) | 2.09090 | + | 2.09090i | 0.108262 | + | 0.108262i | 0.759163 | − | 0.650901i | \(-0.225609\pi\) |
−0.650901 | + | 0.759163i | \(0.725609\pi\) | |||||||
\(374\) | 32.2690 | 1.66859 | ||||||||
\(375\) | −4.88649 | − | 6.93410i | −0.252337 | − | 0.358076i | ||||
\(376\) | −7.68569 | − | 7.68569i | −0.396359 | − | 0.396359i | ||||
\(377\) | −8.44092 | − | 8.44092i | −0.434729 | − | 0.434729i | ||||
\(378\) | −4.46872 | −0.229846 | ||||||||
\(379\) | 4.36102i | 0.224010i | 0.993708 | + | 0.112005i | \(0.0357273\pi\) | ||||
−0.993708 | + | 0.112005i | \(0.964273\pi\) | |||||||
\(380\) | 6.13083 | − | 5.46701i | 0.314505 | − | 0.280451i | ||||
\(381\) | 9.88267i | 0.506305i | ||||||||
\(382\) | −2.08620 | − | 2.08620i | −0.106739 | − | 0.106739i | ||||
\(383\) | −16.6051 | −0.848480 | −0.424240 | − | 0.905550i | \(-0.639459\pi\) | ||||
−0.424240 | + | 0.905550i | \(0.639459\pi\) | |||||||
\(384\) | −0.536506 | − | 0.536506i | −0.0273784 | − | 0.0273784i | ||||
\(385\) | 7.96259 | − | 7.10044i | 0.405811 | − | 0.361872i | ||||
\(386\) | 13.6280 | 0.693644 | ||||||||
\(387\) | 20.7546i | 1.05502i | ||||||||
\(388\) | − | 5.39443i | − | 0.273861i | ||||||
\(389\) | 12.9306 | − | 12.9306i | 0.655609 | − | 0.655609i | −0.298729 | − | 0.954338i | \(-0.596563\pi\) |
0.954338 | + | 0.298729i | \(0.0965627\pi\) | |||||||
\(390\) | 7.61357 | + | 8.53803i | 0.385528 | + | 0.432340i | ||||
\(391\) | 8.84137i | 0.447127i | ||||||||
\(392\) | 5.82104i | 0.294007i | ||||||||
\(393\) | −1.65077 | −0.0832702 | ||||||||
\(394\) | −5.05224 | − | 5.05224i | −0.254528 | − | 0.254528i | ||||
\(395\) | 12.1154 | − | 10.8036i | 0.609591 | − | 0.543587i | ||||
\(396\) | 10.6528 | 0.535324 | ||||||||
\(397\) | −1.98404 | + | 1.98404i | −0.0995762 | + | 0.0995762i | −0.755140 | − | 0.655564i | \(-0.772431\pi\) |
0.655564 | + | 0.755140i | \(0.272431\pi\) | |||||||
\(398\) | −12.1515 | − | 12.1515i | −0.609098 | − | 0.609098i | ||||
\(399\) | −2.13998 | − | 2.13998i | −0.107133 | − | 0.107133i | ||||
\(400\) | 4.96735 | + | 0.570497i | 0.248367 | + | 0.0285248i | ||||
\(401\) | −14.2034 | + | 14.2034i | −0.709283 | + | 0.709283i | −0.966384 | − | 0.257101i | \(-0.917233\pi\) |
0.257101 | + | 0.966384i | \(0.417233\pi\) | |||||||
\(402\) | −6.70958 | −0.334644 | ||||||||
\(403\) | −27.9726 | + | 27.9726i | −1.39341 | + | 1.39341i | ||||
\(404\) | − | 14.5684i | − | 0.724803i | ||||||
\(405\) | 9.26522 | + | 0.530310i | 0.460393 | + | 0.0263513i | ||||
\(406\) | 1.92228i | 0.0954012i | ||||||||
\(407\) | −2.78180 | + | 26.5834i | −0.137889 | + | 1.31769i | ||||
\(408\) | 3.93991 | − | 3.93991i | 0.195054 | − | 0.195054i | ||||
\(409\) | 13.7291 | + | 13.7291i | 0.678859 | + | 0.678859i | 0.959742 | − | 0.280883i | \(-0.0906273\pi\) |
−0.280883 | + | 0.959742i | \(0.590627\pi\) | |||||||
\(410\) | −0.520163 | + | 9.08795i | −0.0256890 | + | 0.448822i | ||||
\(411\) | 12.7850i | 0.630635i | ||||||||
\(412\) | 10.1623i | 0.500662i | ||||||||
\(413\) | 11.6905 | 0.575251 | ||||||||
\(414\) | 2.91876i | 0.143449i | ||||||||
\(415\) | −1.34614 | + | 1.20038i | −0.0660792 | + | 0.0589244i | ||||
\(416\) | −6.74274 | −0.330590 | ||||||||
\(417\) | 3.62541 | + | 3.62541i | 0.177537 | + | 0.177537i | ||||
\(418\) | 11.4142 | + | 11.4142i | 0.558287 | + | 0.558287i | ||||
\(419\) | 10.6476i | 0.520169i | 0.965586 | + | 0.260084i | \(0.0837504\pi\) | ||||
−0.965586 | + | 0.260084i | \(0.916250\pi\) | |||||||
\(420\) | 0.105266 | − | 1.83913i | 0.00513644 | − | 0.0897404i | ||||
\(421\) | 21.3367 | − | 21.3367i | 1.03989 | − | 1.03989i | 0.0407156 | − | 0.999171i | \(-0.487036\pi\) |
0.999171 | − | 0.0407156i | \(-0.0129638\pi\) | |||||||
\(422\) | −8.27973 | −0.403051 | ||||||||
\(423\) | 18.6326 | − | 18.6326i | 0.905948 | − | 0.905948i | ||||
\(424\) | −2.31983 | + | 2.31983i | −0.112661 | + | 0.112661i | ||||
\(425\) | −4.18953 | + | 36.4784i | −0.203222 | + | 1.76946i | ||||
\(426\) | 2.93179 | + | 2.93179i | 0.142046 | + | 0.142046i | ||||
\(427\) | 1.75744 | 0.0850487 | ||||||||
\(428\) | −13.4161 | − | 13.4161i | −0.648490 | − | 0.648490i | ||||
\(429\) | −15.8959 | + | 15.8959i | −0.767460 | + | 0.767460i | ||||
\(430\) | −19.1117 | − | 1.09389i | −0.921646 | − | 0.0527519i | ||||
\(431\) | −5.16220 | + | 5.16220i | −0.248655 | + | 0.248655i | −0.820418 | − | 0.571764i | \(-0.806259\pi\) |
0.571764 | + | 0.820418i | \(0.306259\pi\) | |||||||
\(432\) | 2.91018 | − | 2.91018i | 0.140016 | − | 0.140016i | ||||
\(433\) | 2.75289 | − | 2.75289i | 0.132296 | − | 0.132296i | −0.637858 | − | 0.770154i | \(-0.720179\pi\) |
0.770154 | + | 0.637858i | \(0.220179\pi\) | |||||||
\(434\) | 6.37030 | 0.305784 | ||||||||
\(435\) | −0.171635 | + | 2.99870i | −0.00822927 | + | 0.143776i | ||||
\(436\) | −4.78437 | + | 4.78437i | −0.229130 | + | 0.229130i | ||||
\(437\) | −3.12737 | + | 3.12737i | −0.149602 | + | 0.149602i | ||||
\(438\) | 2.01897i | 0.0964701i | ||||||||
\(439\) | −28.9545 | − | 28.9545i | −1.38192 | − | 1.38192i | −0.841200 | − | 0.540725i | \(-0.818150\pi\) |
−0.540725 | − | 0.841200i | \(-0.681850\pi\) | |||||||
\(440\) | −0.561465 | + | 9.80954i | −0.0267668 | + | 0.467652i | ||||
\(441\) | −14.1121 | −0.672005 | ||||||||
\(442\) | − | 49.5163i | − | 2.35525i | ||||||
\(443\) | −19.2383 | − | 19.2383i | −0.914040 | − | 0.914040i | 0.0825469 | − | 0.996587i | \(-0.473695\pi\) |
−0.996587 | + | 0.0825469i | \(0.973695\pi\) | |||||||
\(444\) | 2.90607 | + | 3.58536i | 0.137916 | + | 0.170154i | ||||
\(445\) | 15.8827 | + | 17.8113i | 0.752913 | + | 0.844334i | ||||
\(446\) | −9.35468 | + | 9.35468i | −0.442957 | + | 0.442957i | ||||
\(447\) | −2.78201 | + | 2.78201i | −0.131585 | + | 0.131585i | ||||
\(448\) | 0.767774 | + | 0.767774i | 0.0362739 | + | 0.0362739i | ||||
\(449\) | 21.0464 | − | 21.0464i | 0.993243 | − | 0.993243i | −0.00673470 | − | 0.999977i | \(-0.502144\pi\) |
0.999977 | + | 0.00673470i | \(0.00214374\pi\) | |||||||
\(450\) | −1.38307 | + | 12.0425i | −0.0651985 | + | 0.567687i | ||||
\(451\) | −17.8881 | −0.842320 | ||||||||
\(452\) | − | 18.0037i | − | 0.846825i | ||||||
\(453\) | 6.72627 | − | 6.72627i | 0.316028 | − | 0.316028i | ||||
\(454\) | 20.1807i | 0.947129i | ||||||||
\(455\) | −10.8955 | − | 12.2185i | −0.510789 | − | 0.572811i | ||||
\(456\) | 2.78725 | 0.130525 | ||||||||
\(457\) | 21.7070i | 1.01541i | 0.861531 | + | 0.507705i | \(0.169506\pi\) | ||||
−0.861531 | + | 0.507705i | \(0.830494\pi\) | |||||||
\(458\) | 3.02631i | 0.141410i | ||||||||
\(459\) | 21.3713 | + | 21.3713i | 0.997528 | + | 0.997528i | ||||
\(460\) | −2.68771 | − | 0.153835i | −0.125315 | − | 0.00717261i | ||||
\(461\) | 1.31376 | + | 1.31376i | 0.0611879 | + | 0.0611879i | 0.737039 | − | 0.675851i | \(-0.236224\pi\) |
−0.675851 | + | 0.737039i | \(0.736224\pi\) | |||||||
\(462\) | 3.62003 | 0.168419 | ||||||||
\(463\) | −8.05167 | −0.374193 | −0.187096 | − | 0.982342i | \(-0.559908\pi\) | ||||
−0.187096 | + | 0.982342i | \(0.559908\pi\) | |||||||
\(464\) | −1.25185 | − | 1.25185i | −0.0581158 | − | 0.0581158i | ||||
\(465\) | 9.93746 | + | 0.568786i | 0.460838 | + | 0.0263768i | ||||
\(466\) | 4.33931 | + | 4.33931i | 0.201015 | + | 0.201015i | ||||
\(467\) | − | 5.04806i | − | 0.233596i | −0.993156 | − | 0.116798i | \(-0.962737\pi\) | ||
0.993156 | − | 0.116798i | \(-0.0372631\pi\) | |||||||
\(468\) | − | 16.3466i | − | 0.755621i | ||||||
\(469\) | 9.60185 | 0.443372 | ||||||||
\(470\) | 16.1756 | + | 18.1397i | 0.746125 | + | 0.836722i | ||||
\(471\) | − | 0.569009i | − | 0.0262186i | ||||||
\(472\) | −7.61323 | + | 7.61323i | −0.350427 | + | 0.350427i | ||||
\(473\) | − | 37.6182i | − | 1.72969i | ||||||
\(474\) | 5.50801 | 0.252991 | ||||||||
\(475\) | −14.3851 | + | 11.4213i | −0.660033 | + | 0.524043i | ||||
\(476\) | −5.63827 | + | 5.63827i | −0.258429 | + | 0.258429i | ||||
\(477\) | −5.62402 | − | 5.62402i | −0.257506 | − | 0.257506i | ||||
\(478\) | −2.92398 | + | 2.92398i | −0.133740 | + | 0.133740i | ||||
\(479\) | 4.20701 | − | 4.20701i | 0.192223 | − | 0.192223i | −0.604433 | − | 0.796656i | \(-0.706600\pi\) |
0.796656 | + | 0.604433i | \(0.206600\pi\) | |||||||
\(480\) | 1.12915 | + | 1.26626i | 0.0515384 | + | 0.0577964i | ||||
\(481\) | 40.7917 | + | 4.26863i | 1.85994 | + | 0.194633i | ||||
\(482\) | 14.9825 | + | 14.9825i | 0.682432 | + | 0.682432i | ||||
\(483\) | 0.991849i | 0.0451307i | ||||||||
\(484\) | −8.30847 | −0.377658 | ||||||||
\(485\) | −0.689278 | + | 12.0426i | −0.0312985 | + | 0.546826i | ||||
\(486\) | 10.9572 | + | 10.9572i | 0.497029 | + | 0.497029i | ||||
\(487\) | − | 23.0440i | − | 1.04422i | −0.852877 | − | 0.522111i | \(-0.825145\pi\) | ||
0.852877 | − | 0.522111i | \(-0.174855\pi\) | |||||||
\(488\) | −1.14451 | + | 1.14451i | −0.0518093 | + | 0.0518093i | ||||
\(489\) | −6.99568 | + | 6.99568i | −0.316356 | + | 0.316356i | ||||
\(490\) | 0.743789 | − | 12.9950i | 0.0336009 | − | 0.587053i | ||||
\(491\) | 17.5204 | 0.790684 | 0.395342 | − | 0.918534i | \(-0.370626\pi\) | ||||
0.395342 | + | 0.918534i | \(0.370626\pi\) | |||||||
\(492\) | −2.18406 | + | 2.18406i | −0.0984652 | + | 0.0984652i | ||||
\(493\) | 9.19317 | − | 9.19317i | 0.414039 | − | 0.414039i | ||||
\(494\) | 17.5149 | − | 17.5149i | 0.788034 | − | 0.788034i | ||||
\(495\) | −23.7815 | − | 1.36117i | −1.06890 | − | 0.0611801i | ||||
\(496\) | −4.14855 | + | 4.14855i | −0.186275 | + | 0.186275i | ||||
\(497\) | −4.19558 | − | 4.19558i | −0.188198 | − | 0.188198i | ||||
\(498\) | −0.611992 | −0.0274240 | ||||||||
\(499\) | −3.14878 | − | 3.14878i | −0.140959 | − | 0.140959i | 0.633106 | − | 0.774065i | \(-0.281780\pi\) |
−0.774065 | + | 0.633106i | \(0.781780\pi\) | |||||||
\(500\) | −11.0163 | − | 1.90829i | −0.492663 | − | 0.0853414i | ||||
\(501\) | −13.2198 | + | 13.2198i | −0.590616 | + | 0.590616i | ||||
\(502\) | −9.25271 | + | 9.25271i | −0.412969 | + | 0.412969i | ||||
\(503\) | 38.5464 | 1.71870 | 0.859349 | − | 0.511390i | \(-0.170869\pi\) | ||||
0.859349 | + | 0.511390i | \(0.170869\pi\) | |||||||
\(504\) | −1.86133 | + | 1.86133i | −0.0829104 | + | 0.0829104i | ||||
\(505\) | −1.86148 | + | 32.5226i | −0.0828350 | + | 1.44724i | ||||
\(506\) | − | 5.29031i | − | 0.235183i | ||||||
\(507\) | 17.4174 | + | 17.4174i | 0.773534 | + | 0.773534i | ||||
\(508\) | 9.21023 | + | 9.21023i | 0.408638 | + | 0.408638i | ||||
\(509\) | 18.2209 | 0.807627 | 0.403814 | − | 0.914841i | \(-0.367684\pi\) | ||||
0.403814 | + | 0.914841i | \(0.367684\pi\) | |||||||
\(510\) | −9.29893 | + | 8.29208i | −0.411764 | + | 0.367180i | ||||
\(511\) | − | 2.88928i | − | 0.127814i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 15.1190i | 0.667518i | ||||||||
\(514\) | 11.5476i | 0.509341i | ||||||||
\(515\) | 1.29850 | − | 22.6865i | 0.0572188 | − | 0.999688i | ||||
\(516\) | −4.59302 | − | 4.59302i | −0.202196 | − | 0.202196i | ||||
\(517\) | −33.7720 | + | 33.7720i | −1.48529 | + | 1.48529i | ||||
\(518\) | −4.15877 | − | 5.13088i | −0.182726 | − | 0.225438i | ||||
\(519\) | − | 5.71110i | − | 0.250689i | ||||||
\(520\) | 15.0526 | + | 0.861559i | 0.660100 | + | 0.0377819i | ||||
\(521\) | − | 8.10778i | − | 0.355208i | −0.984102 | − | 0.177604i | \(-0.943165\pi\) | ||
0.984102 | − | 0.177604i | \(-0.0568347\pi\) | |||||||
\(522\) | 3.03490 | − | 3.03490i | 0.132834 | − | 0.132834i | ||||
\(523\) | 9.18819 | 0.401772 | 0.200886 | − | 0.979615i | \(-0.435618\pi\) | ||||
0.200886 | + | 0.979615i | \(0.435618\pi\) | |||||||
\(524\) | −1.53844 | + | 1.53844i | −0.0672072 | + | 0.0672072i | ||||
\(525\) | −0.469993 | + | 4.09225i | −0.0205122 | + | 0.178601i | ||||
\(526\) | 6.36639 | + | 6.36639i | 0.277588 | + | 0.277588i | ||||
\(527\) | −30.4655 | − | 30.4655i | −1.32710 | − | 1.32710i | ||||
\(528\) | −2.35748 | + | 2.35748i | −0.102596 | + | 0.102596i | ||||
\(529\) | −21.5505 | −0.936979 | ||||||||
\(530\) | 5.47524 | − | 4.88241i | 0.237829 | − | 0.212078i | ||||
\(531\) | −18.4569 | − | 18.4569i | −0.800963 | − | 0.800963i | ||||
\(532\) | −3.98874 | −0.172934 | ||||||||
\(533\) | 27.4491i | 1.18895i | ||||||||
\(534\) | 8.09751i | 0.350414i | ||||||||
\(535\) | 28.2360 | + | 31.6644i | 1.22075 | + | 1.36897i | ||||
\(536\) | −6.25304 | + | 6.25304i | −0.270090 | + | 0.270090i | ||||
\(537\) | − | 8.50905i | − | 0.367193i | ||||||
\(538\) | 3.72238i | 0.160483i | ||||||||
\(539\) | 25.5785 | 1.10174 | ||||||||
\(540\) | −6.86858 | + | 6.12488i | −0.295577 | + | 0.263573i | ||||
\(541\) | −14.3951 | − | 14.3951i | −0.618893 | − | 0.618893i | 0.326355 | − | 0.945247i | \(-0.394180\pi\) |
−0.945247 | + | 0.326355i | \(0.894180\pi\) | |||||||
\(542\) | −23.2312 | −0.997867 | ||||||||
\(543\) | −2.30368 | − | 2.30368i | −0.0988602 | − | 0.0988602i | ||||
\(544\) | − | 7.34365i | − | 0.314856i | ||||||
\(545\) | 11.2920 | − | 10.0694i | 0.483697 | − | 0.431324i | ||||
\(546\) | − | 5.55488i | − | 0.237727i | ||||||
\(547\) | 3.07074 | 0.131295 | 0.0656477 | − | 0.997843i | \(-0.479089\pi\) | ||||
0.0656477 | + | 0.997843i | \(0.479089\pi\) | |||||||
\(548\) | 11.9150 | + | 11.9150i | 0.508985 | + | 0.508985i | ||||
\(549\) | −2.77465 | − | 2.77465i | −0.118419 | − | 0.118419i | ||||
\(550\) | 2.50684 | − | 21.8272i | 0.106892 | − | 0.930716i | ||||
\(551\) | 6.50362 | 0.277064 | ||||||||
\(552\) | −0.645925 | − | 0.645925i | −0.0274924 | − | 0.0274924i | ||||
\(553\) | −7.88232 | −0.335190 | ||||||||
\(554\) | 12.8392 | 0.545486 | ||||||||
\(555\) | −6.02942 | − | 8.37533i | −0.255935 | − | 0.355513i | ||||
\(556\) | 6.75745 | 0.286580 | ||||||||
\(557\) | 33.2382 | 1.40835 | 0.704173 | − | 0.710028i | \(-0.251318\pi\) | ||||
0.704173 | + | 0.710028i | \(0.251318\pi\) | |||||||
\(558\) | −10.0574 | − | 10.0574i | −0.425765 | − | 0.425765i | ||||
\(559\) | −57.7245 | −2.44149 | ||||||||
\(560\) | −1.61589 | − | 1.81209i | −0.0682837 | − | 0.0765749i | ||||
\(561\) | −17.3125 | − | 17.3125i | −0.730935 | − | 0.730935i | ||||
\(562\) | −15.2770 | − | 15.2770i | −0.644422 | − | 0.644422i | ||||
\(563\) | 34.1847 | 1.44071 | 0.720356 | − | 0.693605i | \(-0.243979\pi\) | ||||
0.720356 | + | 0.693605i | \(0.243979\pi\) | |||||||
\(564\) | 8.24684i | 0.347254i | ||||||||
\(565\) | −2.30044 | + | 40.1918i | −0.0967803 | + | 1.69088i | ||||
\(566\) | − | 20.7901i | − | 0.873871i | ||||||
\(567\) | −3.18651 | − | 3.18651i | −0.133821 | − | 0.133821i | ||||
\(568\) | 5.46460 | 0.229290 | ||||||||
\(569\) | −29.8527 | − | 29.8527i | −1.25149 | − | 1.25149i | −0.955052 | − | 0.296438i | \(-0.904201\pi\) |
−0.296438 | − | 0.955052i | \(-0.595799\pi\) | |||||||
\(570\) | −6.22230 | − | 0.356143i | −0.260624 | − | 0.0149172i | ||||
\(571\) | −18.1250 | −0.758508 | −0.379254 | − | 0.925293i | \(-0.623819\pi\) | ||||
−0.379254 | + | 0.925293i | \(0.623819\pi\) | |||||||
\(572\) | 29.6285i | 1.23883i | ||||||||
\(573\) | 2.23851i | 0.0935152i | ||||||||
\(574\) | 3.12554 | − | 3.12554i | 0.130457 | − | 0.130457i | ||||
\(575\) | 5.98042 | + | 0.686848i | 0.249401 | + | 0.0286436i | ||||
\(576\) | − | 2.42432i | − | 0.101013i | ||||||
\(577\) | − | 14.6571i | − | 0.610182i | −0.952323 | − | 0.305091i | \(-0.901313\pi\) | ||
0.952323 | − | 0.305091i | \(-0.0986868\pi\) | |||||||
\(578\) | 36.9292 | 1.53605 | ||||||||
\(579\) | −7.31147 | − | 7.31147i | −0.303854 | − | 0.303854i | ||||
\(580\) | 2.63470 | + | 2.95461i | 0.109400 | + | 0.122684i | ||||
\(581\) | 0.875801 | 0.0363343 | ||||||||
\(582\) | −2.89414 | + | 2.89414i | −0.119966 | + | 0.119966i | ||||
\(583\) | 10.1937 | + | 10.1937i | 0.422179 | + | 0.422179i | ||||
\(584\) | 1.88159 | + | 1.88159i | 0.0778609 | + | 0.0778609i | ||||
\(585\) | −2.08870 | + | 36.4923i | −0.0863570 | + | 1.50877i | ||||
\(586\) | −0.449201 | + | 0.449201i | −0.0185563 | + | 0.0185563i | ||||
\(587\) | 2.78069 | 0.114772 | 0.0573858 | − | 0.998352i | \(-0.481724\pi\) | ||||
0.0573858 | + | 0.998352i | \(0.481724\pi\) | |||||||
\(588\) | 3.12302 | − | 3.12302i | 0.128791 | − | 0.128791i | ||||
\(589\) | − | 21.5525i | − | 0.888056i | ||||||
\(590\) | 17.9687 | − | 16.0231i | 0.739758 | − | 0.659660i | ||||
\(591\) | 5.42111i | 0.222995i | ||||||||
\(592\) | 6.04973 | + | 0.633071i | 0.248642 | + | 0.0260190i | ||||
\(593\) | 4.64974 | − | 4.64974i | 0.190942 | − | 0.190942i | −0.605161 | − | 0.796103i | \(-0.706891\pi\) |
0.796103 | + | 0.605161i | \(0.206891\pi\) | |||||||
\(594\) | −12.7877 | − | 12.7877i | −0.524687 | − | 0.524687i | ||||
\(595\) | 13.3074 | − | 11.8665i | 0.545549 | − | 0.486479i | ||||
\(596\) | 5.18543i | 0.212404i | ||||||||
\(597\) | 13.0387i | 0.533637i | ||||||||
\(598\) | −8.11790 | −0.331966 | ||||||||
\(599\) | 8.57057i | 0.350184i | 0.984552 | + | 0.175092i | \(0.0560223\pi\) | ||||
−0.984552 | + | 0.175092i | \(0.943978\pi\) | |||||||
\(600\) | −2.35893 | − | 2.97108i | −0.0963031 | − | 0.121294i | ||||
\(601\) | −4.61240 | −0.188144 | −0.0940719 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940719 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(602\) | 6.57291 | + | 6.57291i | 0.267892 | + | 0.267892i | ||||
\(603\) | −15.1594 | − | 15.1594i | −0.617338 | − | 0.617338i | ||||
\(604\) | − | 12.5372i | − | 0.510131i | ||||||
\(605\) | 18.5480 | + | 1.06162i | 0.754081 | + | 0.0431611i | ||||
\(606\) | −7.81601 | + | 7.81601i | −0.317504 | + | 0.317504i | ||||
\(607\) | 36.4725 | 1.48037 | 0.740186 | − | 0.672403i | \(-0.234738\pi\) | ||||
0.740186 | + | 0.672403i | \(0.234738\pi\) | |||||||
\(608\) | 2.59760 | − | 2.59760i | 0.105347 | − | 0.105347i | ||||
\(609\) | 1.03131 | − | 1.03131i | 0.0417910 | − | 0.0417910i | ||||
\(610\) | 2.70125 | − | 2.40877i | 0.109370 | − | 0.0975282i | ||||
\(611\) | 51.8226 | + | 51.8226i | 2.09652 | + | 2.09652i | ||||
\(612\) | 17.8034 | 0.719659 | ||||||||
\(613\) | −3.07671 | − | 3.07671i | −0.124267 | − | 0.124267i | 0.642238 | − | 0.766505i | \(-0.278006\pi\) |
−0.766505 | + | 0.642238i | \(0.778006\pi\) | |||||||
\(614\) | 0.0144735 | − | 0.0144735i | 0.000584104 | − | 0.000584104i | ||||
\(615\) | 5.15481 | − | 4.59667i | 0.207862 | − | 0.185355i | ||||
\(616\) | 3.37371 | − | 3.37371i | 0.135931 | − | 0.135931i | ||||
\(617\) | 6.95912 | − | 6.95912i | 0.280164 | − | 0.280164i | −0.553011 | − | 0.833174i | \(-0.686521\pi\) |
0.833174 | + | 0.553011i | \(0.186521\pi\) | |||||||
\(618\) | 5.45215 | − | 5.45215i | 0.219318 | − | 0.219318i | ||||
\(619\) | −28.9801 | −1.16481 | −0.582405 | − | 0.812899i | \(-0.697888\pi\) | ||||
−0.582405 | + | 0.812899i | \(0.697888\pi\) | |||||||
\(620\) | 9.79136 | − | 8.73119i | 0.393231 | − | 0.350653i | ||||
\(621\) | 3.50370 | − | 3.50370i | 0.140599 | − | 0.140599i | ||||
\(622\) | −22.9260 | + | 22.9260i | −0.919249 | + | 0.919249i | ||||
\(623\) | − | 11.5881i | − | 0.464266i | ||||||
\(624\) | 3.61752 | + | 3.61752i | 0.144817 | + | 0.144817i | ||||
\(625\) | 24.3491 | + | 5.66771i | 0.973963 | + | 0.226708i | ||||
\(626\) | −14.6520 | −0.585610 | ||||||||
\(627\) | − | 12.2476i | − | 0.489121i | ||||||
\(628\) | −0.530292 | − | 0.530292i | −0.0211610 | − | 0.0211610i | ||||
\(629\) | −4.64905 | + | 44.4271i | −0.185370 | + | 1.77142i | ||||
\(630\) | 4.39310 | − | 3.91743i | 0.175025 | − | 0.156074i | ||||
\(631\) | −8.58133 | + | 8.58133i | −0.341617 | + | 0.341617i | −0.856975 | − | 0.515358i | \(-0.827659\pi\) |
0.515358 | + | 0.856975i | \(0.327659\pi\) | |||||||
\(632\) | 5.13322 | − | 5.13322i | 0.204189 | − | 0.204189i | ||||
\(633\) | 4.44212 | + | 4.44212i | 0.176559 | + | 0.176559i | ||||
\(634\) | −14.2710 | + | 14.2710i | −0.566772 | + | 0.566772i | ||||
\(635\) | −19.3842 | − | 21.7379i | −0.769238 | − | 0.862642i | ||||
\(636\) | 2.48921 | 0.0987034 | ||||||||
\(637\) | − | 39.2498i | − | 1.55513i | ||||||
\(638\) | −5.50082 | + | 5.50082i | −0.217779 | + | 0.217779i | ||||
\(639\) | 13.2480i | 0.524082i | ||||||||
\(640\) | 2.23241 | + | 0.127776i | 0.0882439 | + | 0.00505078i | ||||
\(641\) | −39.7584 | −1.57036 | −0.785181 | − | 0.619267i | \(-0.787430\pi\) | ||||
−0.785181 | + | 0.619267i | \(0.787430\pi\) | |||||||
\(642\) | 14.3956i | 0.568148i | ||||||||
\(643\) | − | 0.0494458i | − | 0.00194995i | −1.00000 | 0.000974976i | \(-0.999690\pi\) | |||
1.00000 | 0.000974976i | \(-0.000310345\pi\) | ||||||||
\(644\) | 0.924360 | + | 0.924360i | 0.0364249 | + | 0.0364249i | ||||
\(645\) | 9.66664 | + | 10.8404i | 0.380623 | + | 0.426840i | ||||
\(646\) | 19.0758 | + | 19.0758i | 0.750529 | + | 0.750529i | ||||
\(647\) | −20.0867 | −0.789689 | −0.394844 | − | 0.918748i | \(-0.629202\pi\) | ||||
−0.394844 | + | 0.918748i | \(0.629202\pi\) | |||||||
\(648\) | 4.15032 | 0.163040 | ||||||||
\(649\) | 33.4536 | + | 33.4536i | 1.31317 | + | 1.31317i | ||||
\(650\) | −33.4935 | − | 3.84671i | −1.31372 | − | 0.150880i | ||||
\(651\) | −3.41770 | − | 3.41770i | −0.133950 | − | 0.133950i | ||||
\(652\) | 13.0393i | 0.510660i | ||||||||
\(653\) | − | 2.91044i | − | 0.113894i | −0.998377 | − | 0.0569471i | \(-0.981863\pi\) | ||
0.998377 | − | 0.0569471i | \(-0.0181366\pi\) | |||||||
\(654\) | 5.13368 | 0.200743 | ||||||||
\(655\) | 3.63102 | − | 3.23787i | 0.141876 | − | 0.126514i | ||||
\(656\) | 4.07091i | 0.158942i | ||||||||
\(657\) | −4.56159 | + | 4.56159i | −0.177965 | + | 0.177965i | ||||
\(658\) | − | 11.8018i | − | 0.460080i | ||||||
\(659\) | −18.9341 | −0.737568 | −0.368784 | − | 0.929515i | \(-0.620226\pi\) | ||||
−0.368784 | + | 0.929515i | \(0.620226\pi\) | |||||||
\(660\) | 5.56410 | − | 4.96164i | 0.216582 | − | 0.193132i | ||||
\(661\) | −14.8550 | + | 14.8550i | −0.577792 | + | 0.577792i | −0.934294 | − | 0.356502i | \(-0.883969\pi\) |
0.356502 | + | 0.934294i | \(0.383969\pi\) | |||||||
\(662\) | 19.0443 | + | 19.0443i | 0.740179 | + | 0.740179i | ||||
\(663\) | −26.5658 | + | 26.5658i | −1.03173 | + | 1.03173i | ||||
\(664\) | −0.570350 | + | 0.570350i | −0.0221339 | + | 0.0221339i | ||||
\(665\) | 8.90452 | + | 0.509664i | 0.345302 | + | 0.0197639i | ||||
\(666\) | −1.53477 | + | 14.6665i | −0.0594711 | + | 0.568315i | ||||
\(667\) | −1.50717 | − | 1.50717i | −0.0583577 | − | 0.0583577i | ||||
\(668\) | 24.6405i | 0.953370i | ||||||||
\(669\) | 10.0377 | 0.388079 | ||||||||
\(670\) | 14.7584 | − | 13.1604i | 0.570165 | − | 0.508430i | ||||
\(671\) | 5.02912 | + | 5.02912i | 0.194147 | + | 0.194147i | ||||
\(672\) | − | 0.823831i | − | 0.0317800i | ||||||
\(673\) | −4.39502 | + | 4.39502i | −0.169416 | + | 0.169416i | −0.786722 | − | 0.617307i | \(-0.788224\pi\) |
0.617307 | + | 0.786722i | \(0.288224\pi\) | |||||||
\(674\) | 11.2643 | − | 11.2643i | 0.433884 | − | 0.433884i | ||||
\(675\) | 16.1161 | − | 12.7956i | 0.620310 | − | 0.492504i | ||||
\(676\) | 32.4645 | 1.24864 | ||||||||
\(677\) | 15.6334 | − | 15.6334i | 0.600841 | − | 0.600841i | −0.339695 | − | 0.940536i | \(-0.610324\pi\) |
0.940536 | + | 0.339695i | \(0.110324\pi\) | |||||||
\(678\) | −9.65911 | + | 9.65911i | −0.370956 | + | 0.370956i | ||||
\(679\) | 4.14171 | − | 4.14171i | 0.158944 | − | 0.158944i | ||||
\(680\) | −0.938340 | + | 16.3941i | −0.0359837 | + | 0.628684i | ||||
\(681\) | 10.8271 | − | 10.8271i | 0.414895 | − | 0.414895i | ||||
\(682\) | 18.2293 | + | 18.2293i | 0.698036 | + | 0.698036i | ||||
\(683\) | −2.66101 | −0.101821 | −0.0509104 | − | 0.998703i | \(-0.516212\pi\) | ||||
−0.0509104 | + | 0.998703i | \(0.516212\pi\) | |||||||
\(684\) | 6.29742 | + | 6.29742i | 0.240788 | + | 0.240788i | ||||
\(685\) | −25.0768 | − | 28.1217i | −0.958136 | − | 1.07448i | ||||
\(686\) | −9.84367 | + | 9.84367i | −0.375833 | + | 0.375833i | ||||
\(687\) | 1.62363 | − | 1.62363i | 0.0619454 | − | 0.0619454i | ||||
\(688\) | −8.56098 | −0.326384 | ||||||||
\(689\) | 15.6420 | − | 15.6420i | 0.595914 | − | 0.595914i | ||||
\(690\) | 1.35944 | + | 1.52450i | 0.0517529 | + | 0.0580369i | ||||
\(691\) | − | 6.84103i | − | 0.260245i | −0.991498 | − | 0.130123i | \(-0.958463\pi\) | ||
0.991498 | − | 0.130123i | \(-0.0415371\pi\) | |||||||
\(692\) | −5.32250 | − | 5.32250i | −0.202331 | − | 0.202331i | ||||
\(693\) | 8.17896 | + | 8.17896i | 0.310693 | + | 0.310693i | ||||
\(694\) | 2.40110 | 0.0911445 | ||||||||
\(695\) | −15.0854 | − | 0.863438i | −0.572223 | − | 0.0327521i | ||||
\(696\) | 1.34325i | 0.0509158i | ||||||||
\(697\) | −29.8953 | −1.13237 | ||||||||
\(698\) | 13.3892i | 0.506789i | ||||||||
\(699\) | − | 4.65613i | − | 0.176111i | ||||||
\(700\) | 3.37579 | + | 4.25182i | 0.127593 | + | 0.160704i | ||||
\(701\) | −15.1890 | − | 15.1890i | −0.573682 | − | 0.573682i | 0.359473 | − | 0.933155i | \(-0.382956\pi\) |
−0.933155 | + | 0.359473i | \(0.882956\pi\) | |||||||
\(702\) | −19.6226 | + | 19.6226i | −0.740607 | + | 0.740607i | ||||
\(703\) | −17.3592 | + | 14.0703i | −0.654716 | + | 0.530672i | ||||
\(704\) | 4.39414i | 0.165610i | ||||||||
\(705\) | 1.05375 | − | 18.4104i | 0.0396864 | − | 0.693374i | ||||
\(706\) | − | 7.34993i | − | 0.276618i | ||||||
\(707\) | 11.1852 | − | 11.1852i | 0.420663 | − | 0.420663i | ||||
\(708\) | 8.16908 | 0.307013 | ||||||||
\(709\) | 13.9085 | − | 13.9085i | 0.522343 | − | 0.522343i | −0.395935 | − | 0.918278i | \(-0.629580\pi\) |
0.918278 | + | 0.395935i | \(0.129580\pi\) | |||||||
\(710\) | −12.1993 | − | 0.698244i | −0.457830 | − | 0.0262046i | ||||
\(711\) | 12.4446 | + | 12.4446i | 0.466709 | + | 0.466709i | ||||
\(712\) | 7.54653 | + | 7.54653i | 0.282818 | + | 0.282818i | ||||
\(713\) | −4.99463 | + | 4.99463i | −0.187051 | + | 0.187051i | ||||
\(714\) | 6.04992 | 0.226413 | ||||||||
\(715\) | 3.78581 | − | 66.1432i | 0.141581 | − | 2.47362i | ||||
\(716\) | −7.93007 | − | 7.93007i | −0.296361 | − | 0.296361i | ||||
\(717\) | 3.13746 | 0.117171 | ||||||||
\(718\) | − | 24.0685i | − | 0.898228i | ||||||
\(719\) | 23.7742i | 0.886629i | 0.896366 | + | 0.443314i | \(0.146197\pi\) | ||||
−0.896366 | + | 0.443314i | \(0.853803\pi\) | |||||||
\(720\) | −0.309770 | + | 5.41209i | −0.0115444 | + | 0.201697i | ||||
\(721\) | −7.80238 | + | 7.80238i | −0.290576 | + | 0.290576i | ||||
\(722\) | − | 5.50496i | − | 0.204874i | ||||||
\(723\) | − | 16.0763i | − | 0.597886i | ||||||
\(724\) | −4.29385 | −0.159580 | ||||||||
\(725\) | −5.50421 | − | 6.93257i | −0.204421 | − | 0.257469i | ||||
\(726\) | 4.45754 | + | 4.45754i | 0.165435 | + | 0.165435i | ||||
\(727\) | −0.783597 | −0.0290620 | −0.0145310 | − | 0.999894i | \(-0.504626\pi\) | ||||
−0.0145310 | + | 0.999894i | \(0.504626\pi\) | |||||||
\(728\) | −5.17690 | − | 5.17690i | −0.191869 | − | 0.191869i | ||||
\(729\) | 0.693741i | 0.0256941i | ||||||||
\(730\) | −3.96007 | − | 4.44092i | −0.146569 | − | 0.164366i | ||||
\(731\) | − | 62.8689i | − | 2.32529i | ||||||
\(732\) | 1.22807 | 0.0453907 | ||||||||
\(733\) | 8.72850 | + | 8.72850i | 0.322395 | + | 0.322395i | 0.849685 | − | 0.527291i | \(-0.176792\pi\) |
−0.527291 | + | 0.849685i | \(0.676792\pi\) | |||||||
\(734\) | 0.833192 | + | 0.833192i | 0.0307537 | + | 0.0307537i | ||||
\(735\) | −7.37093 | + | 6.57283i | −0.271881 | + | 0.242443i | ||||
\(736\) | −1.20395 | −0.0443781 | ||||||||
\(737\) | 27.4767 | + | 27.4767i | 1.01212 | + | 1.01212i | ||||
\(738\) | −9.86920 | −0.363290 | ||||||||
\(739\) | −11.2844 | −0.415102 | −0.207551 | − | 0.978224i | \(-0.566549\pi\) | ||||
−0.207551 | + | 0.978224i | \(0.566549\pi\) | |||||||
\(740\) | −13.4246 | − | 2.18628i | −0.493498 | − | 0.0803694i | ||||
\(741\) | −18.7937 | −0.690404 | ||||||||
\(742\) | −3.56222 | −0.130773 | ||||||||
\(743\) | 11.8850 | + | 11.8850i | 0.436018 | + | 0.436018i | 0.890669 | − | 0.454652i | \(-0.150236\pi\) |
−0.454652 | + | 0.890669i | \(0.650236\pi\) | |||||||
\(744\) | 4.45144 | 0.163198 | ||||||||
\(745\) | 0.662573 | − | 11.5760i | 0.0242748 | − | 0.424113i | ||||
\(746\) | −2.09090 | − | 2.09090i | −0.0765531 | − | 0.0765531i | ||||
\(747\) | −1.38271 | − | 1.38271i | −0.0505909 | − | 0.0505909i | ||||
\(748\) | −32.2690 | −1.17987 | ||||||||
\(749\) | − | 20.6010i | − | 0.752745i | ||||||
\(750\) | 4.88649 | + | 6.93410i | 0.178429 | + | 0.253198i | ||||
\(751\) | 18.7371i | 0.683727i | 0.939750 | + | 0.341864i | \(0.111058\pi\) | ||||
−0.939750 | + | 0.341864i | \(0.888942\pi\) | |||||||
\(752\) | 7.68569 | + | 7.68569i | 0.280268 | + | 0.280268i | ||||
\(753\) | 9.92826 | 0.361806 | ||||||||
\(754\) | 8.44092 | + | 8.44092i | 0.307400 | + | 0.307400i | ||||
\(755\) | −1.60195 | + | 27.9882i | −0.0583009 | + | 1.01859i | ||||
\(756\) | 4.46872 | 0.162526 | ||||||||
\(757\) | − | 5.00038i | − | 0.181742i | −0.995863 | − | 0.0908710i | \(-0.971035\pi\) | ||
0.995863 | − | 0.0908710i | \(-0.0289651\pi\) | |||||||
\(758\) | − | 4.36102i | − | 0.158399i | ||||||
\(759\) | −2.83828 | + | 2.83828i | −0.103023 | + | 0.103023i | ||||
\(760\) | −6.13083 | + | 5.46701i | −0.222388 | + | 0.198309i | ||||
\(761\) | − | 9.44966i | − | 0.342550i | −0.985223 | − | 0.171275i | \(-0.945211\pi\) | ||
0.985223 | − | 0.171275i | \(-0.0547887\pi\) | |||||||
\(762\) | − | 9.88267i | − | 0.358012i | ||||||
\(763\) | −7.34663 | −0.265966 | ||||||||
\(764\) | 2.08620 | + | 2.08620i | 0.0754759 | + | 0.0754759i | ||||
\(765\) | −39.7445 | − | 2.27484i | −1.43697 | − | 0.0822470i | ||||
\(766\) | 16.6051 | 0.599966 | ||||||||
\(767\) | 51.3340 | − | 51.3340i | 1.85356 | − | 1.85356i | ||||
\(768\) | 0.536506 | + | 0.536506i | 0.0193595 | + | 0.0193595i | ||||
\(769\) | 11.4556 | + | 11.4556i | 0.413100 | + | 0.413100i | 0.882817 | − | 0.469717i | \(-0.155644\pi\) |
−0.469717 | + | 0.882817i | \(0.655644\pi\) | |||||||
\(770\) | −7.96259 | + | 7.10044i | −0.286952 | + | 0.255882i | ||||
\(771\) | 6.19533 | − | 6.19533i | 0.223119 | − | 0.223119i | ||||
\(772\) | −13.6280 | −0.490481 | ||||||||
\(773\) | 7.63579 | − | 7.63579i | 0.274640 | − | 0.274640i | −0.556325 | − | 0.830965i | \(-0.687789\pi\) |
0.830965 | + | 0.556325i | \(0.187789\pi\) | |||||||
\(774\) | − | 20.7546i | − | 0.746009i | ||||||
\(775\) | −22.9740 | + | 18.2405i | −0.825251 | + | 0.655220i | ||||
\(776\) | 5.39443i | 0.193649i | ||||||||
\(777\) | −0.521543 | + | 4.98395i | −0.0187102 | + | 0.178798i | ||||
\(778\) | −12.9306 | + | 12.9306i | −0.463585 | + | 0.463585i | ||||
\(779\) | −10.5746 | − | 10.5746i | −0.378874 | − | 0.378874i | ||||
\(780\) | −7.61357 | − | 8.53803i | −0.272609 | − | 0.305710i | ||||
\(781\) | − | 24.0122i | − | 0.859226i | ||||||
\(782\) | − | 8.84137i | − | 0.316167i | ||||||
\(783\) | −7.28623 | −0.260389 | ||||||||
\(784\) | − | 5.82104i | − | 0.207894i | ||||||
\(785\) | 1.11607 | + | 1.25159i | 0.0398344 | + | 0.0446712i | ||||
\(786\) | 1.65077 | 0.0588809 | ||||||||
\(787\) | −28.6364 | − | 28.6364i | −1.02078 | − | 1.02078i | −0.999779 | − | 0.0209994i | \(-0.993315\pi\) |
−0.0209994 | − | 0.999779i | \(-0.506685\pi\) | |||||||
\(788\) | 5.05224 | + | 5.05224i | 0.179979 | + | 0.179979i | ||||
\(789\) | − | 6.83121i | − | 0.243198i | ||||||
\(790\) | −12.1154 | + | 10.8036i | −0.431046 | + | 0.384374i | ||||
\(791\) | 13.8228 | − | 13.8228i | 0.491483 | − | 0.491483i | ||||
\(792\) | −10.6528 | −0.378531 | ||||||||
\(793\) | 7.71710 | − | 7.71710i | 0.274042 | − | 0.274042i | ||||
\(794\) | 1.98404 | − | 1.98404i | 0.0704110 | − | 0.0704110i | ||||
\(795\) | −5.55694 | − | 0.318060i | −0.197084 | − | 0.0112804i | ||||
\(796\) | 12.1515 | + | 12.1515i | 0.430698 | + | 0.430698i | ||||
\(797\) | 14.9042 | 0.527935 | 0.263967 | − | 0.964532i | \(-0.414969\pi\) | ||||
0.263967 | + | 0.964532i | \(0.414969\pi\) | |||||||
\(798\) | 2.13998 | + | 2.13998i | 0.0757545 | + | 0.0757545i | ||||
\(799\) | −56.4410 | + | 56.4410i | −1.99674 | + | 1.99674i | ||||
\(800\) | −4.96735 | − | 0.570497i | −0.175622 | − | 0.0201701i | ||||
\(801\) | −18.2952 | + | 18.2952i | −0.646431 | + | 0.646431i | ||||
\(802\) | 14.2034 | − | 14.2034i | 0.501539 | − | 0.501539i | ||||
\(803\) | 8.26798 | − | 8.26798i | 0.291771 | − | 0.291771i | ||||
\(804\) | 6.70958 | 0.236629 | ||||||||
\(805\) | −1.94544 | − | 2.18167i | −0.0685679 | − | 0.0768936i | ||||
\(806\) | 27.9726 | − | 27.9726i | 0.985292 | − | 0.985292i | ||||
\(807\) | 1.99708 | − | 1.99708i | 0.0703005 | − | 0.0703005i | ||||
\(808\) | 14.5684i | 0.512513i | ||||||||
\(809\) | 34.6791 | + | 34.6791i | 1.21925 | + | 1.21925i | 0.967894 | + | 0.251360i | \(0.0808778\pi\) |
0.251360 | + | 0.967894i | \(0.419122\pi\) | |||||||
\(810\) | −9.26522 | − | 0.530310i | −0.325547 | − | 0.0186332i | ||||
\(811\) | −32.0485 | −1.12538 | −0.562688 | − | 0.826670i | \(-0.690233\pi\) | ||||
−0.562688 | + | 0.826670i | \(0.690233\pi\) | |||||||
\(812\) | − | 1.92228i | − | 0.0674589i | ||||||
\(813\) | 12.4637 | + | 12.4637i | 0.437120 | + | 0.437120i | ||||
\(814\) | 2.78180 | − | 26.5834i | 0.0975021 | − | 0.931746i | ||||
\(815\) | 1.66611 | − | 29.1092i | 0.0583614 | − | 1.01965i | ||||
\(816\) | −3.93991 | + | 3.93991i | −0.137924 | + | 0.137924i | ||||
\(817\) | 22.2380 | − | 22.2380i | 0.778009 | − | 0.778009i | ||||
\(818\) | −13.7291 | − | 13.7291i | −0.480026 | − | 0.480026i | ||||
\(819\) | 12.5505 | − | 12.5505i | 0.438550 | − | 0.438550i | ||||
\(820\) | 0.520163 | − | 9.08795i | 0.0181649 | − | 0.317365i | ||||
\(821\) | −12.7001 | −0.443236 | −0.221618 | − | 0.975134i | \(-0.571134\pi\) | ||||
−0.221618 | + | 0.975134i | \(0.571134\pi\) | |||||||
\(822\) | − | 12.7850i | − | 0.445927i | ||||||
\(823\) | −10.7759 | + | 10.7759i | −0.375625 | + | 0.375625i | −0.869521 | − | 0.493896i | \(-0.835572\pi\) |
0.493896 | + | 0.869521i | \(0.335572\pi\) | |||||||
\(824\) | − | 10.1623i | − | 0.354022i | ||||||
\(825\) | −13.0554 | + | 10.3655i | −0.454529 | + | 0.360880i | ||||
\(826\) | −11.6905 | −0.406764 | ||||||||
\(827\) | 0.404559i | 0.0140679i | 0.999975 | + | 0.00703394i | \(0.00223899\pi\) | ||||
−0.999975 | + | 0.00703394i | \(0.997761\pi\) | |||||||
\(828\) | − | 2.91876i | − | 0.101434i | ||||||
\(829\) | −14.5459 | − | 14.5459i | −0.505200 | − | 0.505200i | 0.407849 | − | 0.913049i | \(-0.366279\pi\) |
−0.913049 | + | 0.407849i | \(0.866279\pi\) | |||||||
\(830\) | 1.34614 | − | 1.20038i | 0.0467250 | − | 0.0416658i | ||||
\(831\) | −6.88831 | − | 6.88831i | −0.238953 | − | 0.238953i | ||||
\(832\) | 6.74274 | 0.233762 | ||||||||
\(833\) | 42.7477 | 1.48112 | ||||||||
\(834\) | −3.62541 | − | 3.62541i | −0.125538 | − | 0.125538i | ||||
\(835\) | 3.14846 | − | 55.0078i | 0.108957 | − | 1.90362i | ||||
\(836\) | −11.4142 | − | 11.4142i | −0.394769 | − | 0.394769i | ||||
\(837\) | 24.1460i | 0.834609i | ||||||||
\(838\) | − | 10.6476i | − | 0.367815i | ||||||
\(839\) | −23.8438 | −0.823180 | −0.411590 | − | 0.911369i | \(-0.635026\pi\) | ||||
−0.411590 | + | 0.911369i | \(0.635026\pi\) | |||||||
\(840\) | −0.105266 | + | 1.83913i | −0.00363201 | + | 0.0634561i | ||||
\(841\) | − | 25.8657i | − | 0.891922i | ||||||
\(842\) | −21.3367 | + | 21.3367i | −0.735311 | + | 0.735311i | ||||
\(843\) | 16.3924i | 0.564584i | ||||||||
\(844\) | 8.27973 | 0.285000 | ||||||||
\(845\) | −72.4743 | − | 4.14818i | −2.49319 | − | 0.142702i | ||||
\(846\) | −18.6326 | + | 18.6326i | −0.640602 | + | 0.640602i | ||||
\(847\) | −6.37903 | − | 6.37903i | −0.219186 | − | 0.219186i | ||||
\(848\) | 2.31983 | − | 2.31983i | 0.0796633 | − | 0.0796633i | ||||
\(849\) | −11.1540 | + | 11.1540i | −0.382804 | + | 0.382804i | ||||
\(850\) | 4.18953 | − | 36.4784i | 0.143700 | − | 1.25120i | ||||
\(851\) | 7.28356 | + | 0.762184i | 0.249677 | + | 0.0261273i | ||||
\(852\) | −2.93179 | − | 2.93179i | −0.100441 | − | 0.100441i | ||||
\(853\) | 7.11096i | 0.243475i | 0.992562 | + | 0.121737i | \(0.0388466\pi\) | ||||
−0.992562 | + | 0.121737i | \(0.961153\pi\) | |||||||
\(854\) | −1.75744 | −0.0601385 | ||||||||
\(855\) | −13.2538 | − | 14.8631i | −0.453270 | − | 0.508307i | ||||
\(856\) | 13.4161 | + | 13.4161i | 0.458551 | + | 0.458551i | ||||
\(857\) | − | 30.9080i | − | 1.05580i | −0.849308 | − | 0.527898i | \(-0.822980\pi\) | ||
0.849308 | − | 0.527898i | \(-0.177020\pi\) | |||||||
\(858\) | 15.8959 | − | 15.8959i | 0.542676 | − | 0.542676i | ||||
\(859\) | 10.1957 | − | 10.1957i | 0.347872 | − | 0.347872i | −0.511444 | − | 0.859317i | \(-0.670889\pi\) |
0.859317 | + | 0.511444i | \(0.170889\pi\) | |||||||
\(860\) | 19.1117 | + | 1.09389i | 0.651702 | + | 0.0373012i | ||||
\(861\) | −3.35374 | −0.114295 | ||||||||
\(862\) | 5.16220 | − | 5.16220i | 0.175825 | − | 0.175825i | ||||
\(863\) | −15.0510 | + | 15.0510i | −0.512343 | + | 0.512343i | −0.915244 | − | 0.402901i | \(-0.868002\pi\) |
0.402901 | + | 0.915244i | \(0.368002\pi\) | |||||||
\(864\) | −2.91018 | + | 2.91018i | −0.0990063 | + | 0.0990063i | ||||
\(865\) | 11.2019 | + | 12.5621i | 0.380877 | + | 0.427124i | ||||
\(866\) | −2.75289 | + | 2.75289i | −0.0935472 | + | 0.0935472i | ||||
\(867\) | −19.8127 | − | 19.8127i | −0.672874 | − | 0.672874i | ||||
\(868\) | −6.37030 | −0.216222 | ||||||||
\(869\) | −22.5561 | − | 22.5561i | −0.765163 | − | 0.765163i | ||||
\(870\) | 0.171635 | − | 2.99870i | 0.00581897 | − | 0.101665i | ||||
\(871\) | 42.1626 | − | 42.1626i | 1.42863 | − | 1.42863i | ||||
\(872\) | 4.78437 | − | 4.78437i | 0.162019 | − | 0.162019i | ||||
\(873\) | −13.0778 | −0.442618 | ||||||||
\(874\) | 3.12737 | − | 3.12737i | 0.105785 | − | 0.105785i | ||||
\(875\) | −6.99288 | − | 9.92316i | −0.236403 | − | 0.335464i | ||||
\(876\) | − | 2.01897i | − | 0.0682147i | ||||||
\(877\) | 33.9571 | + | 33.9571i | 1.14665 | + | 1.14665i | 0.987207 | + | 0.159441i | \(0.0509693\pi\) |
0.159441 | + | 0.987207i | \(0.449031\pi\) | |||||||
\(878\) | 28.9545 | + | 28.9545i | 0.977168 | + | 0.977168i | ||||
\(879\) | 0.481998 | 0.0162574 | ||||||||
\(880\) | 0.561465 | − | 9.80954i | 0.0189270 | − | 0.330680i | ||||
\(881\) | 28.9969i | 0.976931i | 0.872583 | + | 0.488465i | \(0.162443\pi\) | ||||
−0.872583 | + | 0.488465i | \(0.837557\pi\) | |||||||
\(882\) | 14.1121 | 0.475179 | ||||||||
\(883\) | − | 19.0735i | − | 0.641875i | −0.947100 | − | 0.320938i | \(-0.896002\pi\) | ||
0.947100 | − | 0.320938i | \(-0.103998\pi\) | |||||||
\(884\) | 49.5163i | 1.66541i | ||||||||
\(885\) | −18.2368 | − | 1.04381i | −0.613022 | − | 0.0350873i | ||||
\(886\) | 19.2383 | + | 19.2383i | 0.646324 | + | 0.646324i | ||||
\(887\) | 8.61923 | − | 8.61923i | 0.289405 | − | 0.289405i | −0.547440 | − | 0.836845i | \(-0.684397\pi\) |
0.836845 | + | 0.547440i | \(0.184397\pi\) | |||||||
\(888\) | −2.90607 | − | 3.58536i | −0.0975212 | − | 0.120317i | ||||
\(889\) | 14.1428i | 0.474333i | ||||||||
\(890\) | −15.8827 | − | 17.8113i | −0.532390 | − | 0.597035i | ||||
\(891\) | − | 18.2371i | − | 0.610965i | ||||||
\(892\) | 9.35468 | − | 9.35468i | 0.313218 | − | 0.313218i | ||||
\(893\) | −39.9287 | −1.33616 | ||||||||
\(894\) | 2.78201 | − | 2.78201i | 0.0930444 | − | 0.0930444i | ||||
\(895\) | 16.6899 | + | 18.7165i | 0.557883 | + | 0.625623i | ||||
\(896\) | −0.767774 | − | 0.767774i | −0.0256495 | − | 0.0256495i | ||||
\(897\) | 4.35530 | + | 4.35530i | 0.145419 | + | 0.145419i | ||||
\(898\) | −21.0464 | + | 21.0464i | −0.702329 | + | 0.702329i | ||||
\(899\) | 10.3867 | 0.346417 | ||||||||
\(900\) | 1.38307 | − | 12.0425i | 0.0461023 | − | 0.401415i | ||||
\(901\) | 17.0360 | + | 17.0360i | 0.567552 | + | 0.567552i | ||||
\(902\) | 17.8881 | 0.595610 | ||||||||
\(903\) | − | 7.05280i | − | 0.234703i | ||||||
\(904\) | 18.0037i | 0.598796i | ||||||||
\(905\) | 9.58566 | + | 0.548650i | 0.318638 | + | 0.0182378i | ||||
\(906\) | −6.72627 | + | 6.72627i | −0.223465 | + | 0.223465i | ||||
\(907\) | 41.4022i | 1.37474i | 0.726308 | + | 0.687369i | \(0.241235\pi\) | ||||
−0.726308 | + | 0.687369i | \(0.758765\pi\) | |||||||
\(908\) | − | 20.1807i | − | 0.669721i | ||||||
\(909\) | −35.3184 | −1.17144 | ||||||||
\(910\) | 10.8955 | + | 12.2185i | 0.361183 | + | 0.405039i | ||||
\(911\) | 17.6170 | + | 17.6170i | 0.583678 | + | 0.583678i | 0.935912 | − | 0.352234i | \(-0.114578\pi\) |
−0.352234 | + | 0.935912i | \(0.614578\pi\) | |||||||
\(912\) | −2.78725 | −0.0922951 | ||||||||
\(913\) | 2.50620 | + | 2.50620i | 0.0829431 | + | 0.0829431i | ||||
\(914\) | − | 21.7070i | − | 0.718004i | ||||||
\(915\) | −2.74155 | − | 0.156917i | −0.0906330 | − | 0.00518752i | ||||
\(916\) | − | 3.02631i | − | 0.0999920i | ||||||
\(917\) | −2.36236 | −0.0780118 | ||||||||
\(918\) | −21.3713 | − | 21.3713i | −0.705359 | − | 0.705359i | ||||
\(919\) | −23.1287 | − | 23.1287i | −0.762946 | − | 0.762946i | 0.213908 | − | 0.976854i | \(-0.431381\pi\) |
−0.976854 | + | 0.213908i | \(0.931381\pi\) | |||||||
\(920\) | 2.68771 | + | 0.153835i | 0.0886112 | + | 0.00507180i | ||||
\(921\) | −0.0155303 | −0.000511739 | ||||||||
\(922\) | −1.31376 | − | 1.31376i | −0.0432664 | − | 0.0432664i | ||||
\(923\) | −36.8464 | −1.21281 | ||||||||
\(924\) | −3.62003 | −0.119090 | ||||||||
\(925\) | 29.6899 | + | 6.59603i | 0.976199 | + | 0.216876i | ||||
\(926\) | 8.05167 | 0.264594 | ||||||||
\(927\) | 24.6368 | 0.809178 | ||||||||
\(928\) | 1.25185 | + | 1.25185i | 0.0410941 | + | 0.0410941i | ||||
\(929\) | −28.3619 | −0.930524 | −0.465262 | − | 0.885173i | \(-0.654040\pi\) | ||||
−0.465262 | + | 0.885173i | \(0.654040\pi\) | |||||||
\(930\) | −9.93746 | − | 0.568786i | −0.325862 | − | 0.0186512i | ||||
\(931\) | 15.1207 | + | 15.1207i | 0.495562 | + | 0.495562i | ||||
\(932\) | −4.33931 | − | 4.33931i | −0.142139 | − | 0.142139i | ||||
\(933\) | 24.5999 | 0.805363 | ||||||||
\(934\) | 5.04806i | 0.165178i | ||||||||
\(935\) | 72.0378 | + | 4.12320i | 2.35589 | + | 0.134843i | ||||
\(936\) | 16.3466i | 0.534305i | ||||||||
\(937\) | 42.3748 | + | 42.3748i | 1.38433 | + | 1.38433i | 0.836769 | + | 0.547557i | \(0.184442\pi\) |
0.547557 | + | 0.836769i | \(0.315558\pi\) | |||||||
\(938\) | −9.60185 | −0.313512 | ||||||||
\(939\) | 7.86085 | + | 7.86085i | 0.256529 | + | 0.256529i | ||||
\(940\) | −16.1756 | − | 18.1397i | −0.527590 | − | 0.591652i | ||||
\(941\) | 0.472629 | 0.0154073 | 0.00770363 | − | 0.999970i | \(-0.497548\pi\) | ||||
0.00770363 | + | 0.999970i | \(0.497548\pi\) | |||||||
\(942\) | 0.569009i | 0.0185393i | ||||||||
\(943\) | 4.90116i | 0.159604i | ||||||||
\(944\) | 7.61323 | − | 7.61323i | 0.247790 | − | 0.247790i | ||||
\(945\) | −9.97604 | − | 0.570995i | −0.324521 | − | 0.0185745i | ||||
\(946\) | 37.6182i | 1.22307i | ||||||||
\(947\) | 13.9664i | 0.453848i | 0.973912 | + | 0.226924i | \(0.0728669\pi\) | ||||
−0.973912 | + | 0.226924i | \(0.927133\pi\) | |||||||
\(948\) | −5.50801 | −0.178892 | ||||||||
\(949\) | −12.6871 | − | 12.6871i | −0.411840 | − | 0.411840i | ||||
\(950\) | 14.3851 | − | 11.4213i | 0.466714 | − | 0.370554i | ||||
\(951\) | 15.3129 | 0.496555 | ||||||||
\(952\) | 5.63827 | − | 5.63827i | 0.182737 | − | 0.182737i | ||||
\(953\) | −1.44227 | − | 1.44227i | −0.0467195 | − | 0.0467195i | 0.683361 | − | 0.730081i | \(-0.260518\pi\) |
−0.730081 | + | 0.683361i | \(0.760518\pi\) | |||||||
\(954\) | 5.62402 | + | 5.62402i | 0.182084 | + | 0.182084i | ||||
\(955\) | −4.39069 | − | 4.92382i | −0.142079 | − | 0.159331i | ||||
\(956\) | 2.92398 | − | 2.92398i | 0.0945683 | − | 0.0945683i | ||||
\(957\) | 5.90244 | 0.190799 | ||||||||
\(958\) | −4.20701 | + | 4.20701i | −0.135922 | + | 0.135922i | ||||
\(959\) | 18.2961i | 0.590812i | ||||||||
\(960\) | −1.12915 | − | 1.26626i | −0.0364432 | − | 0.0408682i | ||||
\(961\) | − | 3.42091i | − | 0.110352i | ||||||
\(962\) | −40.7917 | − | 4.26863i | −1.31518 | − | 0.137626i | ||||
\(963\) | −32.5249 | + | 32.5249i | −1.04810 | + | 1.04810i | ||||
\(964\) | −14.9825 | − | 14.9825i | −0.482553 | − | 0.482553i | ||||
\(965\) | 30.4232 | + | 1.74132i | 0.979358 | + | 0.0560551i | ||||
\(966\) | − | 0.991849i | − | 0.0319122i | ||||||
\(967\) | − | 24.1460i | − | 0.776483i | −0.921558 | − | 0.388242i | \(-0.873083\pi\) | ||
0.921558 | − | 0.388242i | \(-0.126917\pi\) | |||||||
\(968\) | 8.30847 | 0.267044 | ||||||||
\(969\) | − | 20.4686i | − | 0.657546i | ||||||
\(970\) | 0.689278 | − | 12.0426i | 0.0221314 | − | 0.386665i | ||||
\(971\) | −2.14562 | −0.0688562 | −0.0344281 | − | 0.999407i | \(-0.510961\pi\) | ||||
−0.0344281 | + | 0.999407i | \(0.510961\pi\) | |||||||
\(972\) | −10.9572 | − | 10.9572i | −0.351453 | − | 0.351453i | ||||
\(973\) | 5.18820 | + | 5.18820i | 0.166326 | + | 0.166326i | ||||
\(974\) | 23.0440i | 0.738377i | ||||||||
\(975\) | 15.9057 | + | 20.0332i | 0.509389 | + | 0.641577i | ||||
\(976\) | 1.14451 | − | 1.14451i | 0.0366347 | − | 0.0366347i | ||||
\(977\) | 31.0494 | 0.993360 | 0.496680 | − | 0.867934i | \(-0.334552\pi\) | ||||
0.496680 | + | 0.867934i | \(0.334552\pi\) | |||||||
\(978\) | 6.99568 | − | 6.99568i | 0.223697 | − | 0.223697i | ||||
\(979\) | 33.1605 | − | 33.1605i | 1.05982 | − | 1.05982i | ||||
\(980\) | −0.743789 | + | 12.9950i | −0.0237595 | + | 0.415110i | ||||
\(981\) | 11.5989 | + | 11.5989i | 0.370323 | + | 0.370323i | ||||
\(982\) | −17.5204 | −0.559098 | ||||||||
\(983\) | −0.777158 | − | 0.777158i | −0.0247875 | − | 0.0247875i | 0.694604 | − | 0.719392i | \(-0.255579\pi\) |
−0.719392 | + | 0.694604i | \(0.755579\pi\) | |||||||
\(984\) | 2.18406 | − | 2.18406i | 0.0696254 | − | 0.0696254i | ||||
\(985\) | −10.6331 | − | 11.9242i | −0.338800 | − | 0.379938i | ||||
\(986\) | −9.19317 | + | 9.19317i | −0.292770 | + | 0.292770i | ||||
\(987\) | −6.33171 | + | 6.33171i | −0.201541 | + | 0.201541i | ||||
\(988\) | −17.5149 | + | 17.5149i | −0.557224 | + | 0.557224i | ||||
\(989\) | −10.3070 | −0.327743 | ||||||||
\(990\) | 23.7815 | + | 1.36117i | 0.755826 | + | 0.0432609i | ||||
\(991\) | 15.5460 | − | 15.5460i | 0.493834 | − | 0.493834i | −0.415678 | − | 0.909512i | \(-0.636456\pi\) |
0.909512 | + | 0.415678i | \(0.136456\pi\) | |||||||
\(992\) | 4.14855 | − | 4.14855i | 0.131717 | − | 0.131717i | ||||
\(993\) | − | 20.4348i | − | 0.648478i | ||||||
\(994\) | 4.19558 | + | 4.19558i | 0.133076 | + | 0.133076i | ||||
\(995\) | −25.5745 | − | 28.6798i | −0.810765 | − | 0.909211i | ||||
\(996\) | 0.611992 | 0.0193917 | ||||||||
\(997\) | − | 42.9037i | − | 1.35877i | −0.733781 | − | 0.679386i | \(-0.762246\pi\) | ||
0.733781 | − | 0.679386i | \(-0.237754\pi\) | |||||||
\(998\) | 3.14878 | + | 3.14878i | 0.0996728 | + | 0.0996728i | ||||
\(999\) | 19.4481 | − | 15.7634i | 0.615312 | − | 0.498733i |
(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 | 370.2.h.e.117.6 | yes | 20 | |
5.3 | odd | 4 | 370.2.g.e.43.5 | ✓ | 20 | ||
37.31 | odd | 4 | 370.2.g.e.327.5 | yes | 20 | ||
185.68 | even | 4 | inner | 370.2.h.e.253.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.5 | ✓ | 20 | 5.3 | odd | 4 | ||
370.2.g.e.327.5 | yes | 20 | 37.31 | odd | 4 | ||
370.2.h.e.117.6 | yes | 20 | 1.1 | even | 1 | trivial | |
370.2.h.e.253.6 | yes | 20 | 185.68 | even | 4 | inner |