Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 7 x^{10} - 9 x^{9} + 55 x^{8} - 32 x^{7} + 287 x^{6} - 302 x^{5} + 1175 x^{4} + \cdots + 361 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 421.3 | ||
Root | \(-0.666872 + 2.05242i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.421 |
Dual form | 770.2.n.h.631.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0.357855 | + | 1.10136i | 0.206608 | + | 0.635873i | 0.999644 | + | 0.0266981i | \(0.00849928\pi\) |
−0.793036 | + | 0.609175i | \(0.791501\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0.809017 | + | 0.587785i | 0.361803 | + | 0.262866i | ||||
\(6\) | −0.936877 | − | 0.680681i | −0.382478 | − | 0.277887i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 1.34211 | − | 0.975098i | 0.447369 | − | 0.325033i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.83465 | + | 1.72185i | 0.854678 | + | 0.519158i | ||||
\(12\) | 1.15804 | 0.334298 | ||||||||
\(13\) | 2.90157 | − | 2.10811i | 0.804751 | − | 0.584686i | −0.107553 | − | 0.994199i | \(-0.534302\pi\) |
0.912304 | + | 0.409514i | \(0.134302\pi\) | |||||||
\(14\) | 0.309017 | + | 0.951057i | 0.0825883 | + | 0.254181i | ||||
\(15\) | −0.357855 | + | 1.10136i | −0.0923978 | + | 0.284371i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −3.47089 | − | 2.52175i | −0.841814 | − | 0.611614i | 0.0810629 | − | 0.996709i | \(-0.474169\pi\) |
−0.922877 | + | 0.385095i | \(0.874169\pi\) | |||||||
\(18\) | −0.512639 | + | 1.57774i | −0.120830 | + | 0.371877i | ||||
\(19\) | −1.51209 | − | 4.65373i | −0.346897 | − | 1.06764i | −0.960561 | − | 0.278071i | \(-0.910305\pi\) |
0.613664 | − | 0.789567i | \(-0.289695\pi\) | |||||||
\(20\) | 0.809017 | − | 0.587785i | 0.180902 | − | 0.131433i | ||||
\(21\) | 1.15804 | 0.252706 | ||||||||
\(22\) | −3.30536 | + | 0.273157i | −0.704704 | + | 0.0582372i | ||||
\(23\) | 2.85699 | 0.595724 | 0.297862 | − | 0.954609i | \(-0.403726\pi\) | ||||
0.297862 | + | 0.954609i | \(0.403726\pi\) | |||||||
\(24\) | −0.936877 | + | 0.680681i | −0.191239 | + | 0.138943i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | −1.10830 | + | 3.41100i | −0.217356 | + | 0.668952i | ||||
\(27\) | 4.36485 | + | 3.17125i | 0.840015 | + | 0.610307i | ||||
\(28\) | −0.809017 | − | 0.587785i | −0.152890 | − | 0.111081i | ||||
\(29\) | −0.233254 | + | 0.717882i | −0.0433142 | + | 0.133307i | −0.970375 | − | 0.241603i | \(-0.922327\pi\) |
0.927061 | + | 0.374911i | \(0.122327\pi\) | |||||||
\(30\) | −0.357855 | − | 1.10136i | −0.0653351 | − | 0.201081i | ||||
\(31\) | 7.56718 | − | 5.49788i | 1.35910 | − | 0.987448i | 0.360604 | − | 0.932719i | \(-0.382571\pi\) |
0.998501 | − | 0.0547284i | \(-0.0174293\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.881993 | + | 3.73815i | −0.153535 | + | 0.650729i | ||||
\(34\) | 4.29025 | 0.735772 | ||||||||
\(35\) | 0.809017 | − | 0.587785i | 0.136749 | − | 0.0993538i | ||||
\(36\) | −0.512639 | − | 1.57774i | −0.0854399 | − | 0.262957i | ||||
\(37\) | −1.31048 | + | 4.03324i | −0.215441 | + | 0.663061i | 0.783681 | + | 0.621164i | \(0.213340\pi\) |
−0.999122 | + | 0.0418964i | \(0.986660\pi\) | |||||||
\(38\) | 3.95870 | + | 2.87616i | 0.642185 | + | 0.466575i | ||||
\(39\) | 3.36014 | + | 2.44129i | 0.538054 | + | 0.390919i | ||||
\(40\) | −0.309017 | + | 0.951057i | −0.0488599 | + | 0.150375i | ||||
\(41\) | 0.626966 | + | 1.92960i | 0.0979157 | + | 0.301354i | 0.988003 | − | 0.154437i | \(-0.0493565\pi\) |
−0.890087 | + | 0.455791i | \(0.849356\pi\) | |||||||
\(42\) | −0.936877 | + | 0.680681i | −0.144563 | + | 0.105031i | ||||
\(43\) | −0.0689189 | −0.0105100 | −0.00525502 | − | 0.999986i | \(-0.501673\pi\) | ||||
−0.00525502 | + | 0.999986i | \(0.501673\pi\) | |||||||
\(44\) | 2.51353 | − | 2.16383i | 0.378929 | − | 0.326209i | ||||
\(45\) | 1.65894 | 0.247300 | ||||||||
\(46\) | −2.31136 | + | 1.67930i | −0.340791 | + | 0.247599i | ||||
\(47\) | 0.691535 | + | 2.12833i | 0.100871 | + | 0.310448i | 0.988739 | − | 0.149649i | \(-0.0478145\pi\) |
−0.887868 | + | 0.460097i | \(0.847814\pi\) | |||||||
\(48\) | 0.357855 | − | 1.10136i | 0.0516519 | − | 0.158968i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | −0.809017 | − | 0.587785i | −0.114412 | − | 0.0831254i | ||||
\(51\) | 1.53529 | − | 4.72513i | 0.214983 | − | 0.661651i | ||||
\(52\) | −1.10830 | − | 3.41100i | −0.153694 | − | 0.473021i | ||||
\(53\) | −10.6002 | + | 7.70149i | −1.45605 | + | 1.05788i | −0.471678 | + | 0.881771i | \(0.656351\pi\) |
−0.984371 | + | 0.176110i | \(0.943649\pi\) | |||||||
\(54\) | −5.39525 | −0.734200 | ||||||||
\(55\) | 1.28120 | + | 3.05917i | 0.172757 | + | 0.412499i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 4.58434 | − | 3.33072i | 0.607211 | − | 0.441164i | ||||
\(58\) | −0.233254 | − | 0.717882i | −0.0306278 | − | 0.0942626i | ||||
\(59\) | 0.378583 | − | 1.16516i | 0.0492873 | − | 0.151691i | −0.923384 | − | 0.383878i | \(-0.874588\pi\) |
0.972671 | + | 0.232187i | \(0.0745883\pi\) | |||||||
\(60\) | 0.936877 | + | 0.680681i | 0.120950 | + | 0.0878755i | ||||
\(61\) | 3.26063 | + | 2.36898i | 0.417481 | + | 0.303317i | 0.776623 | − | 0.629965i | \(-0.216931\pi\) |
−0.359143 | + | 0.933283i | \(0.616931\pi\) | |||||||
\(62\) | −2.89040 | + | 8.89575i | −0.367082 | + | 1.12976i | ||||
\(63\) | −0.512639 | − | 1.57774i | −0.0645865 | − | 0.198777i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 3.58654 | 0.444855 | ||||||||
\(66\) | −1.48368 | − | 3.54265i | −0.182629 | − | 0.436070i | ||||
\(67\) | −14.3059 | −1.74774 | −0.873870 | − | 0.486159i | \(-0.838398\pi\) | ||||
−0.873870 | + | 0.486159i | \(0.838398\pi\) | |||||||
\(68\) | −3.47089 | + | 2.52175i | −0.420907 | + | 0.305807i | ||||
\(69\) | 1.02239 | + | 3.14659i | 0.123081 | + | 0.378805i | ||||
\(70\) | −0.309017 | + | 0.951057i | −0.0369346 | + | 0.113673i | ||||
\(71\) | 4.69029 | + | 3.40769i | 0.556635 | + | 0.404419i | 0.830226 | − | 0.557427i | \(-0.188211\pi\) |
−0.273591 | + | 0.961846i | \(0.588211\pi\) | |||||||
\(72\) | 1.34211 | + | 0.975098i | 0.158169 | + | 0.114916i | ||||
\(73\) | −2.80171 | + | 8.62277i | −0.327915 | + | 1.00922i | 0.642192 | + | 0.766543i | \(0.278025\pi\) |
−0.970108 | + | 0.242675i | \(0.921975\pi\) | |||||||
\(74\) | −1.31048 | − | 4.03324i | −0.152340 | − | 0.468855i | ||||
\(75\) | −0.936877 | + | 0.680681i | −0.108181 | + | 0.0785982i | ||||
\(76\) | −4.89322 | −0.561291 | ||||||||
\(77\) | 2.51353 | − | 2.16383i | 0.286444 | − | 0.246591i | ||||
\(78\) | −4.15337 | −0.470276 | ||||||||
\(79\) | 4.07153 | − | 2.95814i | 0.458083 | − | 0.332817i | −0.334696 | − | 0.942326i | \(-0.608633\pi\) |
0.792779 | + | 0.609509i | \(0.208633\pi\) | |||||||
\(80\) | −0.309017 | − | 0.951057i | −0.0345492 | − | 0.106331i | ||||
\(81\) | −0.392798 | + | 1.20891i | −0.0436443 | + | 0.134323i | ||||
\(82\) | −1.64142 | − | 1.19256i | −0.181264 | − | 0.131696i | ||||
\(83\) | 13.4506 | + | 9.77240i | 1.47639 | + | 1.07266i | 0.978698 | + | 0.205307i | \(0.0658194\pi\) |
0.497693 | + | 0.867353i | \(0.334181\pi\) | |||||||
\(84\) | 0.357855 | − | 1.10136i | 0.0390452 | − | 0.120169i | ||||
\(85\) | −1.32576 | − | 4.08027i | −0.143799 | − | 0.442568i | ||||
\(86\) | 0.0557565 | − | 0.0405095i | 0.00601238 | − | 0.00436825i | ||||
\(87\) | −0.874121 | −0.0937156 | ||||||||
\(88\) | −0.761624 | + | 3.22799i | −0.0811894 | + | 0.344105i | ||||
\(89\) | 9.92243 | 1.05177 | 0.525887 | − | 0.850554i | \(-0.323733\pi\) | ||||
0.525887 | + | 0.850554i | \(0.323733\pi\) | |||||||
\(90\) | −1.34211 | + | 0.975098i | −0.141471 | + | 0.102784i | ||||
\(91\) | −1.10830 | − | 3.41100i | −0.116182 | − | 0.357570i | ||||
\(92\) | 0.882859 | − | 2.71716i | 0.0920444 | − | 0.283284i | ||||
\(93\) | 8.76312 | + | 6.36678i | 0.908693 | + | 0.660204i | ||||
\(94\) | −1.81046 | − | 1.31538i | −0.186735 | − | 0.135671i | ||||
\(95\) | 1.51209 | − | 4.65373i | 0.155137 | − | 0.477462i | ||||
\(96\) | 0.357855 | + | 1.10136i | 0.0365234 | + | 0.112408i | ||||
\(97\) | 5.43443 | − | 3.94835i | 0.551783 | − | 0.400894i | −0.276659 | − | 0.960968i | \(-0.589227\pi\) |
0.828443 | + | 0.560074i | \(0.189227\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 5.48338 | − | 0.453150i | 0.551100 | − | 0.0455432i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.55591 | + | 1.85698i | −0.254322 | + | 0.184776i | −0.707640 | − | 0.706573i | \(-0.750240\pi\) |
0.453318 | + | 0.891349i | \(0.350240\pi\) | |||||||
\(102\) | 1.53529 | + | 4.72513i | 0.152016 | + | 0.467858i | ||||
\(103\) | −4.47448 | + | 13.7710i | −0.440884 | + | 1.35690i | 0.446051 | + | 0.895008i | \(0.352830\pi\) |
−0.886935 | + | 0.461894i | \(0.847170\pi\) | |||||||
\(104\) | 2.90157 | + | 2.10811i | 0.284522 | + | 0.206718i | ||||
\(105\) | 0.936877 | + | 0.680681i | 0.0914298 | + | 0.0664276i | ||||
\(106\) | 4.04891 | − | 12.4613i | 0.393265 | − | 1.21035i | ||||
\(107\) | −2.19761 | − | 6.76354i | −0.212451 | − | 0.653856i | −0.999325 | − | 0.0367425i | \(-0.988302\pi\) |
0.786874 | − | 0.617114i | \(-0.211698\pi\) | |||||||
\(108\) | 4.36485 | − | 3.17125i | 0.420008 | − | 0.305153i | ||||
\(109\) | −15.0710 | −1.44354 | −0.721770 | − | 0.692133i | \(-0.756671\pi\) | ||||
−0.721770 | + | 0.692133i | \(0.756671\pi\) | |||||||
\(110\) | −2.83465 | − | 1.72185i | −0.270273 | − | 0.164172i | ||||
\(111\) | −4.91103 | −0.466134 | ||||||||
\(112\) | −0.809017 | + | 0.587785i | −0.0764449 | + | 0.0555405i | ||||
\(113\) | 0.174057 | + | 0.535693i | 0.0163739 | + | 0.0503937i | 0.958910 | − | 0.283712i | \(-0.0915659\pi\) |
−0.942536 | + | 0.334105i | \(0.891566\pi\) | |||||||
\(114\) | −1.75106 | + | 5.38922i | −0.164002 | + | 0.504746i | ||||
\(115\) | 2.31136 | + | 1.67930i | 0.215535 | + | 0.156595i | ||||
\(116\) | 0.610667 | + | 0.443676i | 0.0566990 | + | 0.0411942i | ||||
\(117\) | 1.83860 | − | 5.65863i | 0.169979 | − | 0.523141i | ||||
\(118\) | 0.378583 | + | 1.16516i | 0.0348514 | + | 0.107262i | ||||
\(119\) | −3.47089 | + | 2.52175i | −0.318176 | + | 0.231168i | ||||
\(120\) | −1.15804 | −0.105714 | ||||||||
\(121\) | 5.07045 | + | 9.76169i | 0.460950 | + | 0.887426i | ||||
\(122\) | −4.03036 | −0.364891 | ||||||||
\(123\) | −1.90083 | + | 1.38104i | −0.171392 | + | 0.124524i | ||||
\(124\) | −2.89040 | − | 8.89575i | −0.259566 | − | 0.798862i | ||||
\(125\) | −0.309017 | + | 0.951057i | −0.0276393 | + | 0.0850651i | ||||
\(126\) | 1.34211 | + | 0.975098i | 0.119564 | + | 0.0868687i | ||||
\(127\) | −9.95873 | − | 7.23544i | −0.883694 | − | 0.642041i | 0.0505321 | − | 0.998722i | \(-0.483908\pi\) |
−0.934226 | + | 0.356681i | \(0.883908\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | −0.0246630 | − | 0.0759048i | −0.00217145 | − | 0.00668305i | ||||
\(130\) | −2.90157 | + | 2.10811i | −0.254485 | + | 0.184894i | ||||
\(131\) | −14.9957 | −1.31018 | −0.655090 | − | 0.755551i | \(-0.727369\pi\) | ||||
−0.655090 | + | 0.755551i | \(0.727369\pi\) | |||||||
\(132\) | 3.28264 | + | 1.99398i | 0.285717 | + | 0.173554i | ||||
\(133\) | −4.89322 | −0.424296 | ||||||||
\(134\) | 11.5737 | − | 8.40878i | 0.999815 | − | 0.726408i | ||||
\(135\) | 1.66722 | + | 5.13119i | 0.143492 | + | 0.441622i | ||||
\(136\) | 1.32576 | − | 4.08027i | 0.113683 | − | 0.349881i | ||||
\(137\) | 0.342984 | + | 0.249192i | 0.0293031 | + | 0.0212899i | 0.602340 | − | 0.798239i | \(-0.294235\pi\) |
−0.573037 | + | 0.819529i | \(0.694235\pi\) | |||||||
\(138\) | −2.67665 | − | 1.94470i | −0.227851 | − | 0.165544i | ||||
\(139\) | 5.99462 | − | 18.4495i | 0.508457 | − | 1.56487i | −0.286424 | − | 0.958103i | \(-0.592466\pi\) |
0.794880 | − | 0.606766i | \(-0.207534\pi\) | |||||||
\(140\) | −0.309017 | − | 0.951057i | −0.0261167 | − | 0.0803789i | ||||
\(141\) | −2.09659 | + | 1.52326i | −0.176565 | + | 0.128282i | ||||
\(142\) | −5.79751 | −0.486517 | ||||||||
\(143\) | 11.8548 | − | 0.979687i | 0.991348 | − | 0.0819256i | ||||
\(144\) | −1.65894 | −0.138245 | ||||||||
\(145\) | −0.610667 | + | 0.443676i | −0.0507131 | + | 0.0368453i | ||||
\(146\) | −2.80171 | − | 8.62277i | −0.231871 | − | 0.713625i | ||||
\(147\) | 0.357855 | − | 1.10136i | 0.0295154 | − | 0.0908390i | ||||
\(148\) | 3.43088 | + | 2.49268i | 0.282016 | + | 0.204897i | ||||
\(149\) | −16.3583 | − | 11.8850i | −1.34012 | − | 0.973656i | −0.999439 | − | 0.0334774i | \(-0.989342\pi\) |
−0.340683 | − | 0.940178i | \(-0.610658\pi\) | |||||||
\(150\) | 0.357855 | − | 1.10136i | 0.0292187 | − | 0.0899260i | ||||
\(151\) | −4.75400 | − | 14.6313i | −0.386875 | − | 1.19068i | −0.935111 | − | 0.354355i | \(-0.884701\pi\) |
0.548236 | − | 0.836323i | \(-0.315299\pi\) | |||||||
\(152\) | 3.95870 | − | 2.87616i | 0.321093 | − | 0.233287i | ||||
\(153\) | −7.11726 | −0.575396 | ||||||||
\(154\) | −0.761624 | + | 3.22799i | −0.0613734 | + | 0.260119i | ||||
\(155\) | 9.35354 | 0.751295 | ||||||||
\(156\) | 3.36014 | − | 2.44129i | 0.269027 | − | 0.195459i | ||||
\(157\) | −1.49516 | − | 4.60164i | −0.119327 | − | 0.367251i | 0.873498 | − | 0.486828i | \(-0.161846\pi\) |
−0.992825 | + | 0.119577i | \(0.961846\pi\) | |||||||
\(158\) | −1.55519 | + | 4.78638i | −0.123724 | + | 0.380784i | ||||
\(159\) | −12.2755 | − | 8.91866i | −0.973509 | − | 0.707295i | ||||
\(160\) | 0.809017 | + | 0.587785i | 0.0639584 | + | 0.0464685i | ||||
\(161\) | 0.882859 | − | 2.71716i | 0.0695790 | − | 0.214142i | ||||
\(162\) | −0.392798 | − | 1.20891i | −0.0308612 | − | 0.0949809i | ||||
\(163\) | −3.22178 | + | 2.34076i | −0.252349 | + | 0.183343i | −0.706767 | − | 0.707446i | \(-0.749847\pi\) |
0.454418 | + | 0.890789i | \(0.349847\pi\) | |||||||
\(164\) | 2.02891 | 0.158431 | ||||||||
\(165\) | −2.91078 | + | 2.50581i | −0.226604 | + | 0.195077i | ||||
\(166\) | −16.6258 | −1.29041 | ||||||||
\(167\) | 19.3789 | − | 14.0796i | 1.49958 | − | 1.08951i | 0.529037 | − | 0.848599i | \(-0.322553\pi\) |
0.970547 | − | 0.240913i | \(-0.0774469\pi\) | |||||||
\(168\) | 0.357855 | + | 1.10136i | 0.0276091 | + | 0.0849721i | ||||
\(169\) | −0.0422541 | + | 0.130045i | −0.00325032 | + | 0.0100034i | ||||
\(170\) | 3.47089 | + | 2.52175i | 0.266205 | + | 0.193409i | ||||
\(171\) | −6.56722 | − | 4.77137i | −0.502208 | − | 0.364876i | ||||
\(172\) | −0.0212971 | + | 0.0655458i | −0.00162389 | + | 0.00499782i | ||||
\(173\) | 2.88213 | + | 8.87028i | 0.219124 | + | 0.674395i | 0.998835 | + | 0.0482550i | \(0.0153660\pi\) |
−0.779711 | + | 0.626140i | \(0.784634\pi\) | |||||||
\(174\) | 0.707179 | − | 0.513795i | 0.0536111 | − | 0.0389507i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.28120 | − | 3.05917i | −0.0965740 | − | 0.230594i | ||||
\(177\) | 1.41874 | 0.106639 | ||||||||
\(178\) | −8.02741 | + | 5.83226i | −0.601680 | + | 0.437146i | ||||
\(179\) | 6.49431 | + | 19.9874i | 0.485407 | + | 1.49393i | 0.831390 | + | 0.555689i | \(0.187546\pi\) |
−0.345983 | + | 0.938241i | \(0.612454\pi\) | |||||||
\(180\) | 0.512639 | − | 1.57774i | 0.0382099 | − | 0.117598i | ||||
\(181\) | 1.79022 | + | 1.30067i | 0.133066 | + | 0.0966783i | 0.652327 | − | 0.757937i | \(-0.273793\pi\) |
−0.519261 | + | 0.854616i | \(0.673793\pi\) | |||||||
\(182\) | 2.90157 | + | 2.10811i | 0.215079 | + | 0.156264i | ||||
\(183\) | −1.44228 | + | 4.43889i | −0.106617 | + | 0.328132i | ||||
\(184\) | 0.882859 | + | 2.71716i | 0.0650852 | + | 0.200312i | ||||
\(185\) | −3.43088 | + | 2.49268i | −0.252243 | + | 0.183265i | ||||
\(186\) | −10.8318 | −0.794227 | ||||||||
\(187\) | −5.49667 | − | 13.1246i | −0.401956 | − | 0.959767i | ||||
\(188\) | 2.23785 | 0.163212 | ||||||||
\(189\) | 4.36485 | − | 3.17125i | 0.317496 | − | 0.230674i | ||||
\(190\) | 1.51209 | + | 4.65373i | 0.109698 | + | 0.337617i | ||||
\(191\) | 5.92237 | − | 18.2272i | 0.428527 | − | 1.31887i | −0.471049 | − | 0.882107i | \(-0.656124\pi\) |
0.899576 | − | 0.436764i | \(-0.143876\pi\) | |||||||
\(192\) | −0.936877 | − | 0.680681i | −0.0676132 | − | 0.0491239i | ||||
\(193\) | −6.83340 | − | 4.96475i | −0.491879 | − | 0.357371i | 0.314028 | − | 0.949414i | \(-0.398322\pi\) |
−0.805906 | + | 0.592043i | \(0.798322\pi\) | |||||||
\(194\) | −2.07577 | + | 6.38856i | −0.149032 | + | 0.458672i | ||||
\(195\) | 1.28346 | + | 3.95009i | 0.0919105 | + | 0.282872i | ||||
\(196\) | −0.809017 | + | 0.587785i | −0.0577869 | + | 0.0419847i | ||||
\(197\) | −11.1821 | −0.796693 | −0.398347 | − | 0.917235i | \(-0.630416\pi\) | ||||
−0.398347 | + | 0.917235i | \(0.630416\pi\) | |||||||
\(198\) | −4.16979 | + | 3.58965i | −0.296334 | + | 0.255106i | ||||
\(199\) | −4.23045 | −0.299888 | −0.149944 | − | 0.988694i | \(-0.547909\pi\) | ||||
−0.149944 | + | 0.988694i | \(0.547909\pi\) | |||||||
\(200\) | −0.809017 | + | 0.587785i | −0.0572061 | + | 0.0415627i | ||||
\(201\) | −5.11943 | − | 15.7560i | −0.361097 | − | 1.11134i | ||||
\(202\) | 0.976270 | − | 3.00465i | 0.0686901 | − | 0.211406i | ||||
\(203\) | 0.610667 | + | 0.443676i | 0.0428604 | + | 0.0311399i | ||||
\(204\) | −4.01944 | − | 2.92029i | −0.281417 | − | 0.204461i | ||||
\(205\) | −0.626966 | + | 1.92960i | −0.0437892 | + | 0.134769i | ||||
\(206\) | −4.47448 | − | 13.7710i | −0.311752 | − | 0.959474i | ||||
\(207\) | 3.83439 | − | 2.78585i | 0.266509 | − | 0.193630i | ||||
\(208\) | −3.58654 | −0.248682 | ||||||||
\(209\) | 3.72679 | − | 15.7953i | 0.257788 | − | 1.09258i | ||||
\(210\) | −1.15804 | −0.0799126 | ||||||||
\(211\) | 2.25309 | − | 1.63697i | 0.155109 | − | 0.112694i | −0.507524 | − | 0.861638i | \(-0.669439\pi\) |
0.662633 | + | 0.748944i | \(0.269439\pi\) | |||||||
\(212\) | 4.04891 | + | 12.4613i | 0.278080 | + | 0.855844i | ||||
\(213\) | −2.07467 | + | 6.38518i | −0.142154 | + | 0.437505i | ||||
\(214\) | 5.75341 | + | 4.18010i | 0.393295 | + | 0.285746i | ||||
\(215\) | −0.0557565 | − | 0.0405095i | −0.00380256 | − | 0.00276273i | ||||
\(216\) | −1.66722 | + | 5.13119i | −0.113440 | + | 0.349133i | ||||
\(217\) | −2.89040 | − | 8.89575i | −0.196213 | − | 0.603883i | ||||
\(218\) | 12.1927 | − | 8.85852i | 0.825794 | − | 0.599974i | ||||
\(219\) | −10.4994 | −0.709485 | ||||||||
\(220\) | 3.30536 | − | 0.273157i | 0.222847 | − | 0.0184162i | ||||
\(221\) | −15.3872 | −1.03505 | ||||||||
\(222\) | 3.97311 | − | 2.88663i | 0.266657 | − | 0.193738i | ||||
\(223\) | −3.47965 | − | 10.7093i | −0.233015 | − | 0.717146i | −0.997379 | − | 0.0723607i | \(-0.976947\pi\) |
0.764364 | − | 0.644785i | \(-0.223053\pi\) | |||||||
\(224\) | 0.309017 | − | 0.951057i | 0.0206471 | − | 0.0635451i | ||||
\(225\) | 1.34211 | + | 0.975098i | 0.0894738 | + | 0.0650065i | ||||
\(226\) | −0.455688 | − | 0.331076i | −0.0303119 | − | 0.0220229i | ||||
\(227\) | 1.28917 | − | 3.96765i | 0.0855650 | − | 0.263342i | −0.899115 | − | 0.437712i | \(-0.855789\pi\) |
0.984680 | + | 0.174370i | \(0.0557889\pi\) | |||||||
\(228\) | −1.75106 | − | 5.38922i | −0.115967 | − | 0.356910i | ||||
\(229\) | −11.4699 | + | 8.33335i | −0.757951 | + | 0.550683i | −0.898281 | − | 0.439421i | \(-0.855184\pi\) |
0.140330 | + | 0.990105i | \(0.455184\pi\) | |||||||
\(230\) | −2.85699 | −0.188384 | ||||||||
\(231\) | 3.28264 | + | 1.99398i | 0.215982 | + | 0.131194i | ||||
\(232\) | −0.754826 | −0.0495568 | ||||||||
\(233\) | 7.68390 | − | 5.58268i | 0.503389 | − | 0.365733i | −0.306921 | − | 0.951735i | \(-0.599299\pi\) |
0.810310 | + | 0.586002i | \(0.199299\pi\) | |||||||
\(234\) | 1.83860 | + | 5.65863i | 0.120193 | + | 0.369916i | ||||
\(235\) | −0.691535 | + | 2.12833i | −0.0451108 | + | 0.138837i | ||||
\(236\) | −0.991144 | − | 0.720108i | −0.0645180 | − | 0.0468750i | ||||
\(237\) | 4.71501 | + | 3.42566i | 0.306273 | + | 0.222520i | ||||
\(238\) | 1.32576 | − | 4.08027i | 0.0859363 | − | 0.264485i | ||||
\(239\) | 0.627860 | + | 1.93235i | 0.0406129 | + | 0.124994i | 0.969307 | − | 0.245852i | \(-0.0790678\pi\) |
−0.928694 | + | 0.370846i | \(0.879068\pi\) | |||||||
\(240\) | 0.936877 | − | 0.680681i | 0.0604751 | − | 0.0439377i | ||||
\(241\) | −18.6496 | −1.20133 | −0.600663 | − | 0.799502i | \(-0.705097\pi\) | ||||
−0.600663 | + | 0.799502i | \(0.705097\pi\) | |||||||
\(242\) | −9.83986 | − | 4.91703i | −0.632530 | − | 0.316079i | ||||
\(243\) | 14.7137 | 0.943886 | ||||||||
\(244\) | 3.26063 | − | 2.36898i | 0.208740 | − | 0.151659i | ||||
\(245\) | −0.309017 | − | 0.951057i | −0.0197424 | − | 0.0607608i | ||||
\(246\) | 0.726054 | − | 2.23457i | 0.0462915 | − | 0.142471i | ||||
\(247\) | −14.1980 | − | 10.3155i | −0.903398 | − | 0.656357i | ||||
\(248\) | 7.56718 | + | 5.49788i | 0.480516 | + | 0.349115i | ||||
\(249\) | −5.94963 | + | 18.3111i | −0.377042 | + | 1.16042i | ||||
\(250\) | −0.309017 | − | 0.951057i | −0.0195440 | − | 0.0601501i | ||||
\(251\) | 11.7363 | − | 8.52690i | 0.740787 | − | 0.538213i | −0.152170 | − | 0.988354i | \(-0.548626\pi\) |
0.892958 | + | 0.450141i | \(0.148626\pi\) | |||||||
\(252\) | −1.65894 | −0.104503 | ||||||||
\(253\) | 8.09857 | + | 4.91932i | 0.509152 | + | 0.309275i | ||||
\(254\) | 12.3097 | 0.772377 | ||||||||
\(255\) | 4.01944 | − | 2.92029i | 0.251707 | − | 0.182876i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −4.58714 | + | 14.1178i | −0.286138 | + | 0.880642i | 0.699917 | + | 0.714224i | \(0.253220\pi\) |
−0.986055 | + | 0.166418i | \(0.946780\pi\) | |||||||
\(258\) | 0.0645685 | + | 0.0469118i | 0.00401986 | + | 0.00292060i | ||||
\(259\) | 3.43088 | + | 2.49268i | 0.213184 | + | 0.154888i | ||||
\(260\) | 1.10830 | − | 3.41100i | 0.0687339 | − | 0.211541i | ||||
\(261\) | 0.386954 | + | 1.19092i | 0.0239518 | + | 0.0737161i | ||||
\(262\) | 12.1318 | − | 8.81425i | 0.749504 | − | 0.544546i | ||||
\(263\) | −31.6286 | −1.95030 | −0.975152 | − | 0.221539i | \(-0.928892\pi\) | ||||
−0.975152 | + | 0.221539i | \(0.928892\pi\) | |||||||
\(264\) | −3.82775 | + | 0.316327i | −0.235581 | + | 0.0194686i | ||||
\(265\) | −13.1026 | −0.804884 | ||||||||
\(266\) | 3.95870 | − | 2.87616i | 0.242723 | − | 0.176349i | ||||
\(267\) | 3.55079 | + | 10.9282i | 0.217305 | + | 0.668795i | ||||
\(268\) | −4.42076 | + | 13.6057i | −0.270041 | + | 0.831100i | ||||
\(269\) | −8.98185 | − | 6.52569i | −0.547633 | − | 0.397879i | 0.279279 | − | 0.960210i | \(-0.409905\pi\) |
−0.826912 | + | 0.562331i | \(0.809905\pi\) | |||||||
\(270\) | −4.36485 | − | 3.17125i | −0.265636 | − | 0.192996i | ||||
\(271\) | −4.42291 | + | 13.6123i | −0.268672 | + | 0.826889i | 0.722152 | + | 0.691734i | \(0.243153\pi\) |
−0.990825 | + | 0.135155i | \(0.956847\pi\) | |||||||
\(272\) | 1.32576 | + | 4.08027i | 0.0803861 | + | 0.247403i | ||||
\(273\) | 3.36014 | − | 2.44129i | 0.203365 | − | 0.147753i | ||||
\(274\) | −0.423951 | −0.0256118 | ||||||||
\(275\) | −0.761624 | + | 3.22799i | −0.0459277 | + | 0.194655i | ||||
\(276\) | 3.30852 | 0.199149 | ||||||||
\(277\) | −3.14189 | + | 2.28272i | −0.188778 | + | 0.137155i | −0.678160 | − | 0.734914i | \(-0.737222\pi\) |
0.489382 | + | 0.872069i | \(0.337222\pi\) | |||||||
\(278\) | 5.99462 | + | 18.4495i | 0.359533 | + | 1.10653i | ||||
\(279\) | 4.79500 | − | 14.7575i | 0.287069 | − | 0.883507i | ||||
\(280\) | 0.809017 | + | 0.587785i | 0.0483480 | + | 0.0351269i | ||||
\(281\) | 19.1609 | + | 13.9212i | 1.14305 | + | 0.830471i | 0.987541 | − | 0.157364i | \(-0.0502996\pi\) |
0.155505 | + | 0.987835i | \(0.450300\pi\) | |||||||
\(282\) | 0.800827 | − | 2.46469i | 0.0476886 | − | 0.146770i | ||||
\(283\) | 2.76857 | + | 8.52079i | 0.164574 | + | 0.506508i | 0.999005 | − | 0.0446055i | \(-0.0142031\pi\) |
−0.834430 | + | 0.551114i | \(0.814203\pi\) | |||||||
\(284\) | 4.69029 | − | 3.40769i | 0.278317 | − | 0.202209i | ||||
\(285\) | 5.66656 | 0.335658 | ||||||||
\(286\) | −9.01488 | + | 7.76066i | −0.533061 | + | 0.458897i | ||||
\(287\) | 2.02891 | 0.119763 | ||||||||
\(288\) | 1.34211 | − | 0.975098i | 0.0790844 | − | 0.0574582i | ||||
\(289\) | 0.434562 | + | 1.33744i | 0.0255625 | + | 0.0786731i | ||||
\(290\) | 0.233254 | − | 0.717882i | 0.0136972 | − | 0.0421555i | ||||
\(291\) | 6.29331 | + | 4.57236i | 0.368920 | + | 0.268036i | ||||
\(292\) | 7.33497 | + | 5.32916i | 0.429246 | + | 0.311866i | ||||
\(293\) | 3.93783 | − | 12.1194i | 0.230051 | − | 0.708023i | −0.767689 | − | 0.640823i | \(-0.778593\pi\) |
0.997739 | − | 0.0672005i | \(-0.0214067\pi\) | |||||||
\(294\) | 0.357855 | + | 1.10136i | 0.0208705 | + | 0.0642329i | ||||
\(295\) | 0.991144 | − | 0.720108i | 0.0577066 | − | 0.0419263i | ||||
\(296\) | −4.24080 | −0.246491 | ||||||||
\(297\) | 6.91239 | + | 16.5050i | 0.401097 | + | 0.957717i | ||||
\(298\) | 20.2199 | 1.17131 | ||||||||
\(299\) | 8.28977 | − | 6.02287i | 0.479410 | − | 0.348311i | ||||
\(300\) | 0.357855 | + | 1.10136i | 0.0206608 | + | 0.0635873i | ||||
\(301\) | −0.0212971 | + | 0.0655458i | −0.00122754 | + | 0.00377799i | ||||
\(302\) | 12.4461 | + | 9.04264i | 0.716194 | + | 0.520345i | ||||
\(303\) | −2.95985 | − | 2.15046i | −0.170039 | − | 0.123541i | ||||
\(304\) | −1.51209 | + | 4.65373i | −0.0867242 | + | 0.266910i | ||||
\(305\) | 1.24545 | + | 3.83310i | 0.0713142 | + | 0.219483i | ||||
\(306\) | 5.75798 | − | 4.18342i | 0.329162 | − | 0.239150i | ||||
\(307\) | −5.75775 | −0.328612 | −0.164306 | − | 0.986409i | \(-0.552538\pi\) | ||||
−0.164306 | + | 0.986409i | \(0.552538\pi\) | |||||||
\(308\) | −1.28120 | − | 3.05917i | −0.0730031 | − | 0.174312i | ||||
\(309\) | −16.7682 | −0.953907 | ||||||||
\(310\) | −7.56718 | + | 5.49788i | −0.429787 | + | 0.312258i | ||||
\(311\) | 3.77168 | + | 11.6080i | 0.213872 | + | 0.658232i | 0.999232 | + | 0.0391914i | \(0.0124782\pi\) |
−0.785359 | + | 0.619040i | \(0.787522\pi\) | |||||||
\(312\) | −1.28346 | + | 3.95009i | −0.0726617 | + | 0.223630i | ||||
\(313\) | −16.4362 | − | 11.9416i | −0.929026 | − | 0.674977i | 0.0167279 | − | 0.999860i | \(-0.494675\pi\) |
−0.945754 | + | 0.324883i | \(0.894675\pi\) | |||||||
\(314\) | 3.91439 | + | 2.84397i | 0.220902 | + | 0.160495i | ||||
\(315\) | 0.512639 | − | 1.57774i | 0.0288840 | − | 0.0888957i | ||||
\(316\) | −1.55519 | − | 4.78638i | −0.0874861 | − | 0.269255i | ||||
\(317\) | −21.4627 | + | 15.5936i | −1.20547 | + | 0.875823i | −0.994811 | − | 0.101737i | \(-0.967560\pi\) |
−0.210656 | + | 0.977560i | \(0.567560\pi\) | |||||||
\(318\) | 15.1733 | 0.850878 | ||||||||
\(319\) | −1.89728 | + | 1.63331i | −0.106227 | + | 0.0914480i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 6.66270 | − | 4.84073i | 0.371876 | − | 0.270183i | ||||
\(322\) | 0.882859 | + | 2.71716i | 0.0491998 | + | 0.151421i | ||||
\(323\) | −6.48724 | + | 19.9657i | −0.360960 | + | 1.11092i | ||||
\(324\) | 1.02836 | + | 0.747147i | 0.0571311 | + | 0.0415082i | ||||
\(325\) | 2.90157 | + | 2.10811i | 0.160950 | + | 0.116937i | ||||
\(326\) | 1.23061 | − | 3.78743i | 0.0681573 | − | 0.209766i | ||||
\(327\) | −5.39323 | − | 16.5987i | −0.298247 | − | 0.917909i | ||||
\(328\) | −1.64142 | + | 1.19256i | −0.0906322 | + | 0.0658482i | ||||
\(329\) | 2.23785 | 0.123377 | ||||||||
\(330\) | 0.881993 | − | 3.73815i | 0.0485521 | − | 0.205779i | ||||
\(331\) | 0.393891 | 0.0216502 | 0.0108251 | − | 0.999941i | \(-0.496554\pi\) | ||||
0.0108251 | + | 0.999941i | \(0.496554\pi\) | |||||||
\(332\) | 13.4506 | − | 9.77240i | 0.738195 | − | 0.536330i | ||||
\(333\) | 2.17400 | + | 6.69089i | 0.119135 | + | 0.366658i | ||||
\(334\) | −7.40208 | + | 22.7813i | −0.405024 | + | 1.24654i | ||||
\(335\) | −11.5737 | − | 8.40878i | −0.632339 | − | 0.459421i | ||||
\(336\) | −0.936877 | − | 0.680681i | −0.0511108 | − | 0.0371342i | ||||
\(337\) | −0.384350 | + | 1.18291i | −0.0209369 | + | 0.0644371i | −0.960979 | − | 0.276621i | \(-0.910785\pi\) |
0.940042 | + | 0.341058i | \(0.110785\pi\) | |||||||
\(338\) | −0.0422541 | − | 0.130045i | −0.00229832 | − | 0.00707350i | ||||
\(339\) | −0.527706 | + | 0.383401i | −0.0286610 | + | 0.0208235i | ||||
\(340\) | −4.29025 | −0.232672 | ||||||||
\(341\) | 30.9168 | − | 2.55498i | 1.67424 | − | 0.138360i | ||||
\(342\) | 8.11754 | 0.438946 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | −0.0212971 | − | 0.0655458i | −0.00114826 | − | 0.00353399i | ||||
\(345\) | −1.02239 | + | 3.14659i | −0.0550436 | + | 0.169407i | ||||
\(346\) | −7.54551 | − | 5.48213i | −0.405649 | − | 0.294721i | ||||
\(347\) | 12.7096 | + | 9.23407i | 0.682287 | + | 0.495711i | 0.874116 | − | 0.485718i | \(-0.161442\pi\) |
−0.191828 | + | 0.981428i | \(0.561442\pi\) | |||||||
\(348\) | −0.270118 | + | 0.831339i | −0.0144799 | + | 0.0445644i | ||||
\(349\) | 5.07147 | + | 15.6084i | 0.271469 | + | 0.835497i | 0.990132 | + | 0.140138i | \(0.0447546\pi\) |
−0.718663 | + | 0.695359i | \(0.755245\pi\) | |||||||
\(350\) | −0.809017 | + | 0.587785i | −0.0432438 | + | 0.0314184i | ||||
\(351\) | 19.3503 | 1.03284 | ||||||||
\(352\) | 2.83465 | + | 1.72185i | 0.151087 | + | 0.0917750i | ||||
\(353\) | 22.8233 | 1.21476 | 0.607382 | − | 0.794410i | \(-0.292220\pi\) | ||||
0.607382 | + | 0.794410i | \(0.292220\pi\) | |||||||
\(354\) | −1.14779 | + | 0.833916i | −0.0610042 | + | 0.0443221i | ||||
\(355\) | 1.79153 | + | 5.51376i | 0.0950846 | + | 0.292640i | ||||
\(356\) | 3.06620 | − | 9.43679i | 0.162508 | − | 0.500149i | ||||
\(357\) | −4.01944 | − | 2.92029i | −0.212731 | − | 0.154558i | ||||
\(358\) | −17.0023 | − | 12.3529i | −0.898600 | − | 0.652871i | ||||
\(359\) | −3.35431 | + | 10.3235i | −0.177034 | + | 0.544854i | −0.999721 | − | 0.0236409i | \(-0.992474\pi\) |
0.822687 | + | 0.568495i | \(0.192474\pi\) | |||||||
\(360\) | 0.512639 | + | 1.57774i | 0.0270185 | + | 0.0831543i | ||||
\(361\) | −3.99944 | + | 2.90576i | −0.210497 | + | 0.152935i | ||||
\(362\) | −2.21284 | −0.116304 | ||||||||
\(363\) | −8.93669 | + | 9.07768i | −0.469054 | + | 0.476455i | ||||
\(364\) | −3.58654 | −0.187986 | ||||||||
\(365\) | −7.33497 | + | 5.32916i | −0.383930 | + | 0.278941i | ||||
\(366\) | −1.44228 | − | 4.43889i | −0.0753894 | − | 0.232025i | ||||
\(367\) | 6.60984 | − | 20.3430i | 0.345031 | − | 1.06190i | −0.616537 | − | 0.787326i | \(-0.711465\pi\) |
0.961567 | − | 0.274569i | \(-0.0885352\pi\) | |||||||
\(368\) | −2.31136 | − | 1.67930i | −0.120488 | − | 0.0875394i | ||||
\(369\) | 2.72301 | + | 1.97838i | 0.141754 | + | 0.102990i | ||||
\(370\) | 1.31048 | − | 4.03324i | 0.0681286 | − | 0.209678i | ||||
\(371\) | 4.04891 | + | 12.4613i | 0.210209 | + | 0.646957i | ||||
\(372\) | 8.76312 | − | 6.36678i | 0.454346 | − | 0.330102i | ||||
\(373\) | 2.90463 | 0.150396 | 0.0751981 | − | 0.997169i | \(-0.476041\pi\) | ||||
0.0751981 | + | 0.997169i | \(0.476041\pi\) | |||||||
\(374\) | 12.1614 | + | 7.38718i | 0.628849 | + | 0.381982i | ||||
\(375\) | −1.15804 | −0.0598011 | ||||||||
\(376\) | −1.81046 | + | 1.31538i | −0.0933675 | + | 0.0678354i | ||||
\(377\) | 0.836575 | + | 2.57471i | 0.0430858 | + | 0.132604i | ||||
\(378\) | −1.66722 | + | 5.13119i | −0.0857527 | + | 0.263920i | ||||
\(379\) | −0.0507588 | − | 0.0368784i | −0.00260731 | − | 0.00189432i | 0.586481 | − | 0.809963i | \(-0.300513\pi\) |
−0.589088 | + | 0.808069i | \(0.700513\pi\) | |||||||
\(380\) | −3.95870 | − | 2.87616i | −0.203077 | − | 0.147544i | ||||
\(381\) | 4.40507 | − | 13.5574i | 0.225679 | − | 0.694568i | ||||
\(382\) | 5.92237 | + | 18.2272i | 0.303015 | + | 0.932583i | ||||
\(383\) | 6.82320 | − | 4.95735i | 0.348649 | − | 0.253309i | −0.399653 | − | 0.916667i | \(-0.630869\pi\) |
0.748302 | + | 0.663358i | \(0.230869\pi\) | |||||||
\(384\) | 1.15804 | 0.0590961 | ||||||||
\(385\) | 3.30536 | − | 0.273157i | 0.168457 | − | 0.0139214i | ||||
\(386\) | 8.44654 | 0.429918 | ||||||||
\(387\) | −0.0924966 | + | 0.0672027i | −0.00470186 | + | 0.00341610i | ||||
\(388\) | −2.07577 | − | 6.38856i | −0.105381 | − | 0.324330i | ||||
\(389\) | −11.3311 | + | 34.8734i | −0.574508 | + | 1.76815i | 0.0633405 | + | 0.997992i | \(0.479825\pi\) |
−0.637848 | + | 0.770162i | \(0.720175\pi\) | |||||||
\(390\) | −3.36014 | − | 2.44129i | −0.170148 | − | 0.123619i | ||||
\(391\) | −9.91630 | − | 7.20461i | −0.501489 | − | 0.364353i | ||||
\(392\) | 0.309017 | − | 0.951057i | 0.0156077 | − | 0.0480356i | ||||
\(393\) | −5.36629 | − | 16.5157i | −0.270693 | − | 0.833108i | ||||
\(394\) | 9.04653 | − | 6.57269i | 0.455758 | − | 0.331127i | ||||
\(395\) | 5.03269 | 0.253222 | ||||||||
\(396\) | 1.26349 | − | 5.35503i | 0.0634925 | − | 0.269100i | ||||
\(397\) | −2.91177 | −0.146137 | −0.0730687 | − | 0.997327i | \(-0.523279\pi\) | ||||
−0.0730687 | + | 0.997327i | \(0.523279\pi\) | |||||||
\(398\) | 3.42250 | − | 2.48659i | 0.171555 | − | 0.124642i | ||||
\(399\) | −1.75106 | − | 5.38922i | −0.0876628 | − | 0.269798i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | −12.4204 | − | 9.02397i | −0.620247 | − | 0.450636i | 0.232761 | − | 0.972534i | \(-0.425224\pi\) |
−0.853008 | + | 0.521898i | \(0.825224\pi\) | |||||||
\(402\) | 13.4028 | + | 9.73773i | 0.668473 | + | 0.485674i | ||||
\(403\) | 10.3665 | − | 31.9050i | 0.516395 | − | 1.58930i | ||||
\(404\) | 0.976270 | + | 3.00465i | 0.0485712 | + | 0.149487i | ||||
\(405\) | −1.02836 | + | 0.747147i | −0.0510996 | + | 0.0371260i | ||||
\(406\) | −0.754826 | −0.0374614 | ||||||||
\(407\) | −10.6594 | + | 9.17636i | −0.528366 | + | 0.454855i | ||||
\(408\) | 4.96830 | 0.245967 | ||||||||
\(409\) | 12.1303 | − | 8.81315i | 0.599803 | − | 0.435782i | −0.246006 | − | 0.969268i | \(-0.579118\pi\) |
0.845809 | + | 0.533486i | \(0.179118\pi\) | |||||||
\(410\) | −0.626966 | − | 1.92960i | −0.0309637 | − | 0.0952964i | ||||
\(411\) | −0.151713 | + | 0.466925i | −0.00748345 | + | 0.0230317i | ||||
\(412\) | 11.7144 | + | 8.51098i | 0.577125 | + | 0.419306i | ||||
\(413\) | −0.991144 | − | 0.720108i | −0.0487710 | − | 0.0354342i | ||||
\(414\) | −1.46461 | + | 4.50760i | −0.0719815 | + | 0.221536i | ||||
\(415\) | 5.13766 | + | 15.8121i | 0.252198 | + | 0.776184i | ||||
\(416\) | 2.90157 | − | 2.10811i | 0.142261 | − | 0.103359i | ||||
\(417\) | 22.4649 | 1.10011 | ||||||||
\(418\) | 6.26919 | + | 14.9692i | 0.306636 | + | 0.732167i | ||||
\(419\) | 26.8166 | 1.31008 | 0.655038 | − | 0.755596i | \(-0.272653\pi\) | ||||
0.655038 | + | 0.755596i | \(0.272653\pi\) | |||||||
\(420\) | 0.936877 | − | 0.680681i | 0.0457149 | − | 0.0332138i | ||||
\(421\) | 12.0721 | + | 37.1541i | 0.588358 | + | 1.81078i | 0.585343 | + | 0.810786i | \(0.300960\pi\) |
0.00301552 | + | 0.999995i | \(0.499040\pi\) | |||||||
\(422\) | −0.860605 | + | 2.64867i | −0.0418936 | + | 0.128935i | ||||
\(423\) | 3.00344 | + | 2.18213i | 0.146032 | + | 0.106099i | ||||
\(424\) | −10.6002 | − | 7.70149i | −0.514791 | − | 0.374017i | ||||
\(425\) | 1.32576 | − | 4.08027i | 0.0643089 | − | 0.197922i | ||||
\(426\) | −2.07467 | − | 6.38518i | −0.100518 | − | 0.309363i | ||||
\(427\) | 3.26063 | − | 2.36898i | 0.157793 | − | 0.114643i | ||||
\(428\) | −7.11161 | −0.343753 | ||||||||
\(429\) | 5.32129 | + | 12.7059i | 0.256914 | + | 0.613445i | ||||
\(430\) | 0.0689189 | 0.00332356 | ||||||||
\(431\) | −29.8622 | + | 21.6962i | −1.43841 | + | 1.04507i | −0.450041 | + | 0.893008i | \(0.648590\pi\) |
−0.988371 | + | 0.152059i | \(0.951410\pi\) | |||||||
\(432\) | −1.66722 | − | 5.13119i | −0.0802143 | − | 0.246874i | ||||
\(433\) | −3.85368 | + | 11.8604i | −0.185196 | + | 0.569975i | −0.999952 | − | 0.00982950i | \(-0.996871\pi\) |
0.814756 | + | 0.579805i | \(0.196871\pi\) | |||||||
\(434\) | 7.56718 | + | 5.49788i | 0.363236 | + | 0.263906i | ||||
\(435\) | −0.707179 | − | 0.513795i | −0.0339066 | − | 0.0246346i | ||||
\(436\) | −4.65720 | + | 14.3334i | −0.223039 | + | 0.686444i | ||||
\(437\) | −4.32002 | − | 13.2957i | −0.206655 | − | 0.636018i | ||||
\(438\) | 8.49421 | − | 6.17140i | 0.405869 | − | 0.294881i | ||||
\(439\) | −5.79416 | −0.276540 | −0.138270 | − | 0.990395i | \(-0.544154\pi\) | ||||
−0.138270 | + | 0.990395i | \(0.544154\pi\) | |||||||
\(440\) | −2.51353 | + | 2.16383i | −0.119828 | + | 0.103156i | ||||
\(441\) | −1.65894 | −0.0789970 | ||||||||
\(442\) | 12.4485 | − | 9.04435i | 0.592114 | − | 0.430196i | ||||
\(443\) | 3.66425 | + | 11.2774i | 0.174094 | + | 0.535806i | 0.999591 | − | 0.0286006i | \(-0.00910510\pi\) |
−0.825497 | + | 0.564406i | \(0.809105\pi\) | |||||||
\(444\) | −1.51759 | + | 4.67067i | −0.0720217 | + | 0.221660i | ||||
\(445\) | 8.02741 | + | 5.83226i | 0.380536 | + | 0.276475i | ||||
\(446\) | 9.10985 | + | 6.61870i | 0.431364 | + | 0.313404i | ||||
\(447\) | 7.23581 | − | 22.2695i | 0.342242 | − | 1.05331i | ||||
\(448\) | 0.309017 | + | 0.951057i | 0.0145997 | + | 0.0449332i | ||||
\(449\) | 5.07184 | − | 3.68491i | 0.239355 | − | 0.173902i | −0.461641 | − | 0.887067i | \(-0.652739\pi\) |
0.700996 | + | 0.713165i | \(0.252739\pi\) | |||||||
\(450\) | −1.65894 | −0.0782030 | ||||||||
\(451\) | −1.54526 | + | 6.54929i | −0.0727636 | + | 0.308394i | ||||
\(452\) | 0.563261 | 0.0264936 | ||||||||
\(453\) | 14.4131 | − | 10.4718i | 0.677189 | − | 0.492007i | ||||
\(454\) | 1.28917 | + | 3.96765i | 0.0605036 | + | 0.186211i | ||||
\(455\) | 1.10830 | − | 3.41100i | 0.0519580 | − | 0.159910i | ||||
\(456\) | 4.58434 | + | 3.33072i | 0.214681 | + | 0.155975i | ||||
\(457\) | 24.3010 | + | 17.6557i | 1.13675 | + | 0.825900i | 0.986664 | − | 0.162772i | \(-0.0520436\pi\) |
0.150090 | + | 0.988672i | \(0.452044\pi\) | |||||||
\(458\) | 4.38110 | − | 13.4836i | 0.204716 | − | 0.630050i | ||||
\(459\) | −7.15281 | − | 22.0141i | −0.333865 | − | 1.02753i | ||||
\(460\) | 2.31136 | − | 1.67930i | 0.107767 | − | 0.0782977i | ||||
\(461\) | −37.8904 | −1.76473 | −0.882365 | − | 0.470566i | \(-0.844050\pi\) | ||||
−0.882365 | + | 0.470566i | \(0.844050\pi\) | |||||||
\(462\) | −3.82775 | + | 0.316327i | −0.178083 | + | 0.0147169i | ||||
\(463\) | 2.23043 | 0.103657 | 0.0518285 | − | 0.998656i | \(-0.483495\pi\) | ||||
0.0518285 | + | 0.998656i | \(0.483495\pi\) | |||||||
\(464\) | 0.610667 | − | 0.443676i | 0.0283495 | − | 0.0205971i | ||||
\(465\) | 3.34721 | + | 10.3017i | 0.155223 | + | 0.477728i | ||||
\(466\) | −2.93499 | + | 9.03296i | −0.135961 | + | 0.418444i | ||||
\(467\) | −32.4981 | − | 23.6113i | −1.50383 | − | 1.09260i | −0.968823 | − | 0.247753i | \(-0.920308\pi\) |
−0.535010 | − | 0.844846i | \(-0.679692\pi\) | |||||||
\(468\) | −4.81352 | − | 3.49723i | −0.222505 | − | 0.161659i | ||||
\(469\) | −4.42076 | + | 13.6057i | −0.204132 | + | 0.628253i | ||||
\(470\) | −0.691535 | − | 2.12833i | −0.0318981 | − | 0.0981723i | ||||
\(471\) | 4.53303 | − | 3.29344i | 0.208871 | − | 0.151754i | ||||
\(472\) | 1.22512 | 0.0563908 | ||||||||
\(473\) | −0.195361 | − | 0.118668i | −0.00898270 | − | 0.00545636i | ||||
\(474\) | −5.82808 | −0.267692 | ||||||||
\(475\) | 3.95870 | − | 2.87616i | 0.181637 | − | 0.131967i | ||||
\(476\) | 1.32576 | + | 4.08027i | 0.0607662 | + | 0.187019i | ||||
\(477\) | −6.71689 | + | 20.6725i | −0.307545 | + | 0.946527i | ||||
\(478\) | −1.64376 | − | 1.19426i | −0.0751837 | − | 0.0546242i | ||||
\(479\) | 12.5114 | + | 9.09003i | 0.571658 | + | 0.415334i | 0.835707 | − | 0.549175i | \(-0.185058\pi\) |
−0.264049 | + | 0.964509i | \(0.585058\pi\) | |||||||
\(480\) | −0.357855 | + | 1.10136i | −0.0163338 | + | 0.0502702i | ||||
\(481\) | 4.70008 | + | 14.4654i | 0.214305 | + | 0.659564i | ||||
\(482\) | 15.0879 | − | 10.9620i | 0.687233 | − | 0.499304i | ||||
\(483\) | 3.30852 | 0.150543 | ||||||||
\(484\) | 10.8508 | − | 1.80576i | 0.493217 | − | 0.0820800i | ||||
\(485\) | 6.71733 | 0.305018 | ||||||||
\(486\) | −11.9037 | + | 8.64851i | −0.539961 | + | 0.392305i | ||||
\(487\) | −5.53709 | − | 17.0414i | −0.250910 | − | 0.772220i | −0.994608 | − | 0.103705i | \(-0.966930\pi\) |
0.743699 | − | 0.668515i | \(-0.233070\pi\) | |||||||
\(488\) | −1.24545 | + | 3.83310i | −0.0563788 | + | 0.173516i | ||||
\(489\) | −3.73096 | − | 2.71070i | −0.168720 | − | 0.122582i | ||||
\(490\) | 0.809017 | + | 0.587785i | 0.0365477 | + | 0.0265534i | ||||
\(491\) | 8.23260 | − | 25.3373i | 0.371532 | − | 1.14346i | −0.574256 | − | 0.818675i | \(-0.694709\pi\) |
0.945789 | − | 0.324783i | \(-0.105291\pi\) | |||||||
\(492\) | 0.726054 | + | 2.23457i | 0.0327331 | + | 0.100742i | ||||
\(493\) | 2.61992 | − | 1.90348i | 0.117995 | − | 0.0857285i | ||||
\(494\) | 17.5497 | 0.789599 | ||||||||
\(495\) | 4.70250 | + | 2.85644i | 0.211362 | + | 0.128388i | ||||
\(496\) | −9.35354 | −0.419987 | ||||||||
\(497\) | 4.69029 | − | 3.40769i | 0.210388 | − | 0.152856i | ||||
\(498\) | −5.94963 | − | 18.3111i | −0.266609 | − | 0.820539i | ||||
\(499\) | 9.09434 | − | 27.9895i | 0.407119 | − | 1.25298i | −0.511994 | − | 0.858989i | \(-0.671093\pi\) |
0.919113 | − | 0.393994i | \(-0.128907\pi\) | |||||||
\(500\) | 0.809017 | + | 0.587785i | 0.0361803 | + | 0.0262866i | ||||
\(501\) | 22.4416 | + | 16.3048i | 1.00262 | + | 0.728444i | ||||
\(502\) | −4.48286 | + | 13.7968i | −0.200080 | + | 0.615782i | ||||
\(503\) | −7.78005 | − | 23.9445i | −0.346895 | − | 1.06763i | −0.960561 | − | 0.278068i | \(-0.910306\pi\) |
0.613666 | − | 0.789566i | \(-0.289694\pi\) | |||||||
\(504\) | 1.34211 | − | 0.975098i | 0.0597822 | − | 0.0434343i | ||||
\(505\) | −3.15928 | −0.140586 | ||||||||
\(506\) | −9.44338 | + | 0.780407i | −0.419809 | + | 0.0346933i | ||||
\(507\) | −0.158348 | −0.00703246 | ||||||||
\(508\) | −9.95873 | + | 7.23544i | −0.441847 | + | 0.321021i | ||||
\(509\) | 8.91049 | + | 27.4237i | 0.394951 | + | 1.21553i | 0.929000 | + | 0.370080i | \(0.120670\pi\) |
−0.534049 | + | 0.845453i | \(0.679330\pi\) | |||||||
\(510\) | −1.53529 | + | 4.72513i | −0.0679837 | + | 0.209232i | ||||
\(511\) | 7.33497 | + | 5.32916i | 0.324480 | + | 0.235748i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | 8.15809 | − | 25.1080i | 0.360188 | − | 1.10855i | ||||
\(514\) | −4.58714 | − | 14.1178i | −0.202330 | − | 0.622708i | ||||
\(515\) | −11.7144 | + | 8.51098i | −0.516196 | + | 0.375038i | ||||
\(516\) | −0.0798110 | −0.00351348 | ||||||||
\(517\) | −1.70440 | + | 7.22377i | −0.0749596 | + | 0.317701i | ||||
\(518\) | −4.24080 | −0.186330 | ||||||||
\(519\) | −8.73802 | + | 6.34854i | −0.383557 | + | 0.278670i | ||||
\(520\) | 1.10830 | + | 3.41100i | 0.0486022 | + | 0.149582i | ||||
\(521\) | 2.73874 | − | 8.42896i | 0.119986 | − | 0.369280i | −0.872968 | − | 0.487777i | \(-0.837808\pi\) |
0.992954 | + | 0.118498i | \(0.0378078\pi\) | |||||||
\(522\) | −1.01306 | − | 0.736030i | −0.0443403 | − | 0.0322151i | ||||
\(523\) | 18.7966 | + | 13.6565i | 0.821918 | + | 0.597159i | 0.917261 | − | 0.398286i | \(-0.130395\pi\) |
−0.0953431 | + | 0.995444i | \(0.530395\pi\) | |||||||
\(524\) | −4.63393 | + | 14.2618i | −0.202434 | + | 0.623028i | ||||
\(525\) | 0.357855 | + | 1.10136i | 0.0156181 | + | 0.0480675i | ||||
\(526\) | 25.5881 | − | 18.5908i | 1.11569 | − | 0.810599i | ||||
\(527\) | −40.1291 | −1.74805 | ||||||||
\(528\) | 2.91078 | − | 2.50581i | 0.126675 | − | 0.109051i | ||||
\(529\) | −14.8376 | −0.645113 | ||||||||
\(530\) | 10.6002 | − | 7.70149i | 0.460443 | − | 0.334531i | ||||
\(531\) | −0.628045 | − | 1.93292i | −0.0272548 | − | 0.0838818i | ||||
\(532\) | −1.51209 | + | 4.65373i | −0.0655573 | + | 0.201765i | ||||
\(533\) | 5.88702 | + | 4.27717i | 0.254995 | + | 0.185265i | ||||
\(534\) | −9.29609 | − | 6.75400i | −0.402281 | − | 0.292274i | ||||
\(535\) | 2.19761 | − | 6.76354i | 0.0950109 | − | 0.292413i | ||||
\(536\) | −4.42076 | − | 13.6057i | −0.190948 | − | 0.587677i | ||||
\(537\) | −19.6894 | + | 14.3052i | −0.849661 | + | 0.617315i | ||||
\(538\) | 11.1022 | 0.478649 | ||||||||
\(539\) | −1.28120 | − | 3.05917i | −0.0551851 | − | 0.131768i | ||||
\(540\) | 5.39525 | 0.232175 | ||||||||
\(541\) | 17.1941 | − | 12.4922i | 0.739231 | − | 0.537083i | −0.153239 | − | 0.988189i | \(-0.548970\pi\) |
0.892470 | + | 0.451106i | \(0.148970\pi\) | |||||||
\(542\) | −4.42291 | − | 13.6123i | −0.189980 | − | 0.584699i | ||||
\(543\) | −0.791875 | + | 2.43714i | −0.0339826 | + | 0.104588i | ||||
\(544\) | −3.47089 | − | 2.52175i | −0.148813 | − | 0.108119i | ||||
\(545\) | −12.1927 | − | 8.85852i | −0.522278 | − | 0.379457i | ||||
\(546\) | −1.28346 | + | 3.95009i | −0.0549271 | + | 0.169048i | ||||
\(547\) | 12.3157 | + | 37.9038i | 0.526581 | + | 1.62065i | 0.761169 | + | 0.648554i | \(0.224626\pi\) |
−0.234588 | + | 0.972095i | \(0.575374\pi\) | |||||||
\(548\) | 0.342984 | − | 0.249192i | 0.0146515 | − | 0.0106450i | ||||
\(549\) | 6.68611 | 0.285356 | ||||||||
\(550\) | −1.28120 | − | 3.05917i | −0.0546305 | − | 0.130444i | ||||
\(551\) | 3.69353 | 0.157350 | ||||||||
\(552\) | −2.67665 | + | 1.94470i | −0.113926 | + | 0.0827719i | ||||
\(553\) | −1.55519 | − | 4.78638i | −0.0661333 | − | 0.203537i | ||||
\(554\) | 1.20010 | − | 3.69351i | 0.0509872 | − | 0.156922i | ||||
\(555\) | −3.97311 | − | 2.88663i | −0.168649 | − | 0.122531i | ||||
\(556\) | −15.6941 | − | 11.4024i | −0.665579 | − | 0.483571i | ||||
\(557\) | 6.09550 | − | 18.7600i | 0.258275 | − | 0.794888i | −0.734892 | − | 0.678184i | \(-0.762767\pi\) |
0.993167 | − | 0.116704i | \(-0.0372328\pi\) | |||||||
\(558\) | 4.79500 | + | 14.7575i | 0.202988 | + | 0.624734i | ||||
\(559\) | −0.199973 | + | 0.145289i | −0.00845796 | + | 0.00614507i | ||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 12.4880 | − | 10.7505i | 0.527243 | − | 0.453888i | ||||
\(562\) | −23.6842 | −0.999058 | ||||||||
\(563\) | −16.6358 | + | 12.0866i | −0.701116 | + | 0.509391i | −0.880296 | − | 0.474426i | \(-0.842656\pi\) |
0.179179 | + | 0.983816i | \(0.442656\pi\) | |||||||
\(564\) | 0.800827 | + | 2.46469i | 0.0337209 | + | 0.103782i | ||||
\(565\) | −0.174057 | + | 0.535693i | −0.00732264 | + | 0.0225368i | ||||
\(566\) | −7.24821 | − | 5.26614i | −0.304665 | − | 0.221352i | ||||
\(567\) | 1.02836 | + | 0.747147i | 0.0431870 | + | 0.0313772i | ||||
\(568\) | −1.79153 | + | 5.51376i | −0.0751709 | + | 0.231352i | ||||
\(569\) | 6.77142 | + | 20.8403i | 0.283873 | + | 0.873671i | 0.986734 | + | 0.162344i | \(0.0519054\pi\) |
−0.702861 | + | 0.711327i | \(0.748095\pi\) | |||||||
\(570\) | −4.58434 | + | 3.33072i | −0.192017 | + | 0.139508i | ||||
\(571\) | −17.3899 | −0.727745 | −0.363872 | − | 0.931449i | \(-0.618546\pi\) | ||||
−0.363872 | + | 0.931449i | \(0.618546\pi\) | |||||||
\(572\) | 2.73159 | − | 11.5773i | 0.114214 | − | 0.484072i | ||||
\(573\) | 22.1941 | 0.927172 | ||||||||
\(574\) | −1.64142 | + | 1.19256i | −0.0685115 | + | 0.0497765i | ||||
\(575\) | 0.882859 | + | 2.71716i | 0.0368178 | + | 0.113313i | ||||
\(576\) | −0.512639 | + | 1.57774i | −0.0213600 | + | 0.0657393i | ||||
\(577\) | −20.7119 | − | 15.0481i | −0.862249 | − | 0.626461i | 0.0662468 | − | 0.997803i | \(-0.478898\pi\) |
−0.928496 | + | 0.371343i | \(0.878898\pi\) | |||||||
\(578\) | −1.13770 | − | 0.826585i | −0.0473220 | − | 0.0343814i | ||||
\(579\) | 3.02264 | − | 9.30272i | 0.125617 | − | 0.386608i | ||||
\(580\) | 0.233254 | + | 0.717882i | 0.00968535 | + | 0.0298084i | ||||
\(581\) | 13.4506 | − | 9.77240i | 0.558023 | − | 0.405428i | ||||
\(582\) | −7.77896 | −0.322448 | ||||||||
\(583\) | −43.3086 | + | 3.57905i | −1.79366 | + | 0.148229i | ||||
\(584\) | −9.06652 | −0.375175 | ||||||||
\(585\) | 4.81352 | − | 3.49723i | 0.199015 | − | 0.144593i | ||||
\(586\) | 3.93783 | + | 12.1194i | 0.162670 | + | 0.500648i | ||||
\(587\) | −11.8257 | + | 36.3958i | −0.488100 | + | 1.50222i | 0.339341 | + | 0.940664i | \(0.389796\pi\) |
−0.827441 | + | 0.561553i | \(0.810204\pi\) | |||||||
\(588\) | −0.936877 | − | 0.680681i | −0.0386361 | − | 0.0280708i | ||||
\(589\) | −37.0278 | − | 26.9023i | −1.52571 | − | 1.10849i | ||||
\(590\) | −0.378583 | + | 1.16516i | −0.0155860 | + | 0.0479688i | ||||
\(591\) | −4.00158 | − | 12.3156i | −0.164603 | − | 0.506596i | ||||
\(592\) | 3.43088 | − | 2.49268i | 0.141008 | − | 0.102448i | ||||
\(593\) | −11.8855 | −0.488078 | −0.244039 | − | 0.969765i | \(-0.578473\pi\) | ||||
−0.244039 | + | 0.969765i | \(0.578473\pi\) | |||||||
\(594\) | −15.2936 | − | 9.28982i | −0.627505 | − | 0.381166i | ||||
\(595\) | −4.29025 | −0.175883 | ||||||||
\(596\) | −16.3583 | + | 11.8850i | −0.670061 | + | 0.486828i | ||||
\(597\) | −1.51389 | − | 4.65926i | −0.0619593 | − | 0.190691i | ||||
\(598\) | −3.16641 | + | 9.74520i | −0.129484 | + | 0.398511i | ||||
\(599\) | 3.76491 | + | 2.73537i | 0.153830 | + | 0.111764i | 0.662038 | − | 0.749470i | \(-0.269692\pi\) |
−0.508208 | + | 0.861234i | \(0.669692\pi\) | |||||||
\(600\) | −0.936877 | − | 0.680681i | −0.0382478 | − | 0.0277887i | ||||
\(601\) | −4.08848 | + | 12.5831i | −0.166773 | + | 0.513274i | −0.999163 | − | 0.0409168i | \(-0.986972\pi\) |
0.832390 | + | 0.554191i | \(0.186972\pi\) | |||||||
\(602\) | −0.0212971 | − | 0.0655458i | −0.000868005 | − | 0.00267145i | ||||
\(603\) | −19.2000 | + | 13.9496i | −0.781885 | + | 0.568073i | ||||
\(604\) | −15.3843 | −0.625977 | ||||||||
\(605\) | −1.63569 | + | 10.8777i | −0.0665003 | + | 0.442242i | ||||
\(606\) | 3.65858 | 0.148620 | ||||||||
\(607\) | −24.5243 | + | 17.8180i | −0.995412 | + | 0.723209i | −0.961100 | − | 0.276202i | \(-0.910924\pi\) |
−0.0343124 | + | 0.999411i | \(0.510924\pi\) | |||||||
\(608\) | −1.51209 | − | 4.65373i | −0.0613232 | − | 0.188734i | ||||
\(609\) | −0.270118 | + | 0.831339i | −0.0109457 | + | 0.0336875i | ||||
\(610\) | −3.26063 | − | 2.36898i | −0.132019 | − | 0.0959174i | ||||
\(611\) | 6.49329 | + | 4.71765i | 0.262691 | + | 0.190856i | ||||
\(612\) | −2.19935 | + | 6.76891i | −0.0889036 | + | 0.273617i | ||||
\(613\) | −3.90353 | − | 12.0138i | −0.157662 | − | 0.485235i | 0.840759 | − | 0.541410i | \(-0.182109\pi\) |
−0.998421 | + | 0.0561755i | \(0.982109\pi\) | |||||||
\(614\) | 4.65812 | − | 3.38432i | 0.187986 | − | 0.136580i | ||||
\(615\) | −2.34956 | −0.0947434 | ||||||||
\(616\) | 2.83465 | + | 1.72185i | 0.114211 | + | 0.0693754i | ||||
\(617\) | −48.4310 | −1.94976 | −0.974880 | − | 0.222731i | \(-0.928503\pi\) | ||||
−0.974880 | + | 0.222731i | \(0.928503\pi\) | |||||||
\(618\) | 13.5657 | − | 9.85608i | 0.545693 | − | 0.396470i | ||||
\(619\) | −0.855584 | − | 2.63322i | −0.0343888 | − | 0.105838i | 0.932389 | − | 0.361457i | \(-0.117721\pi\) |
−0.966778 | + | 0.255619i | \(0.917721\pi\) | |||||||
\(620\) | 2.89040 | − | 8.89575i | 0.116081 | − | 0.357262i | ||||
\(621\) | 12.4703 | + | 9.06023i | 0.500417 | + | 0.363574i | ||||
\(622\) | −9.87439 | − | 7.17416i | −0.395927 | − | 0.287658i | ||||
\(623\) | 3.06620 | − | 9.43679i | 0.122845 | − | 0.378077i | ||||
\(624\) | −1.28346 | − | 3.95009i | −0.0513796 | − | 0.158130i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 20.3162 | 0.811999 | ||||||||
\(627\) | 18.7300 | − | 1.54786i | 0.748004 | − | 0.0618155i | ||||
\(628\) | −4.83845 | −0.193075 | ||||||||
\(629\) | 14.7193 | − | 10.6942i | 0.586898 | − | 0.426407i | ||||
\(630\) | 0.512639 | + | 1.57774i | 0.0204240 | + | 0.0628587i | ||||
\(631\) | 6.51639 | − | 20.0554i | 0.259413 | − | 0.798392i | −0.733515 | − | 0.679674i | \(-0.762121\pi\) |
0.992928 | − | 0.118718i | \(-0.0378786\pi\) | |||||||
\(632\) | 4.07153 | + | 2.95814i | 0.161957 | + | 0.117669i | ||||
\(633\) | 2.60918 | + | 1.89568i | 0.103706 | + | 0.0753465i | ||||
\(634\) | 8.19804 | − | 25.2310i | 0.325586 | − | 1.00205i | ||||
\(635\) | −3.80390 | − | 11.7072i | −0.150953 | − | 0.464585i | ||||
\(636\) | −12.2755 | + | 8.91866i | −0.486754 | + | 0.353648i | ||||
\(637\) | −3.58654 | −0.142104 | ||||||||
\(638\) | 0.574894 | − | 2.43657i | 0.0227603 | − | 0.0964648i | ||||
\(639\) | 9.61771 | 0.380471 | ||||||||
\(640\) | 0.809017 | − | 0.587785i | 0.0319792 | − | 0.0232343i | ||||
\(641\) | 3.35890 | + | 10.3376i | 0.132668 | + | 0.408311i | 0.995220 | − | 0.0976576i | \(-0.0311350\pi\) |
−0.862552 | + | 0.505969i | \(0.831135\pi\) | |||||||
\(642\) | −2.54492 | + | 7.83247i | −0.100440 | + | 0.309123i | ||||
\(643\) | −3.00291 | − | 2.18174i | −0.118423 | − | 0.0860396i | 0.526997 | − | 0.849867i | \(-0.323318\pi\) |
−0.645420 | + | 0.763827i | \(0.723318\pi\) | |||||||
\(644\) | −2.31136 | − | 1.67930i | −0.0910802 | − | 0.0661736i | ||||
\(645\) | 0.0246630 | − | 0.0759048i | 0.000971103 | − | 0.00298875i | ||||
\(646\) | −6.48724 | − | 19.9657i | −0.255237 | − | 0.785539i | ||||
\(647\) | 20.3304 | − | 14.7709i | 0.799269 | − | 0.580703i | −0.111430 | − | 0.993772i | \(-0.535543\pi\) |
0.910700 | + | 0.413069i | \(0.135543\pi\) | |||||||
\(648\) | −1.27112 | −0.0499344 | ||||||||
\(649\) | 3.07938 | − | 2.65095i | 0.120876 | − | 0.104059i | ||||
\(650\) | −3.58654 | −0.140676 | ||||||||
\(651\) | 8.76312 | − | 6.36678i | 0.343454 | − | 0.249534i | ||||
\(652\) | 1.23061 | + | 3.78743i | 0.0481945 | + | 0.148327i | ||||
\(653\) | 8.45069 | − | 26.0085i | 0.330701 | − | 1.01779i | −0.638100 | − | 0.769953i | \(-0.720279\pi\) |
0.968801 | − | 0.247839i | \(-0.0797205\pi\) | |||||||
\(654\) | 14.1197 | + | 10.2585i | 0.552123 | + | 0.401141i | ||||
\(655\) | −12.1318 | − | 8.81425i | −0.474028 | − | 0.344401i | ||||
\(656\) | 0.626966 | − | 1.92960i | 0.0244789 | − | 0.0753384i | ||||
\(657\) | 4.64785 | + | 14.3046i | 0.181330 | + | 0.558077i | ||||
\(658\) | −1.81046 | + | 1.31538i | −0.0705792 | + | 0.0512788i | ||||
\(659\) | −6.74968 | −0.262930 | −0.131465 | − | 0.991321i | \(-0.541968\pi\) | ||||
−0.131465 | + | 0.991321i | \(0.541968\pi\) | |||||||
\(660\) | 1.48368 | + | 3.54265i | 0.0577523 | + | 0.137898i | ||||
\(661\) | −34.5615 | −1.34429 | −0.672144 | − | 0.740421i | \(-0.734626\pi\) | ||||
−0.672144 | + | 0.740421i | \(0.734626\pi\) | |||||||
\(662\) | −0.318664 | + | 0.231523i | −0.0123852 | + | 0.00899841i | ||||
\(663\) | −5.50637 | − | 16.9469i | −0.213850 | − | 0.658162i | ||||
\(664\) | −5.13766 | + | 15.8121i | −0.199380 | + | 0.613628i | ||||
\(665\) | −3.95870 | − | 2.87616i | −0.153512 | − | 0.111533i | ||||
\(666\) | −5.69161 | − | 4.13520i | −0.220545 | − | 0.160236i | ||||
\(667\) | −0.666405 | + | 2.05098i | −0.0258033 | + | 0.0794144i | ||||
\(668\) | −7.40208 | − | 22.7813i | −0.286395 | − | 0.881433i | ||||
\(669\) | 10.5496 | − | 7.66474i | 0.407871 | − | 0.296336i | ||||
\(670\) | 14.3059 | 0.552684 | ||||||||
\(671\) | 5.16369 | + | 12.3296i | 0.199342 | + | 0.475977i | ||||
\(672\) | 1.15804 | 0.0446725 | ||||||||
\(673\) | −2.41678 | + | 1.75590i | −0.0931602 | + | 0.0676848i | −0.633390 | − | 0.773833i | \(-0.718337\pi\) |
0.540230 | + | 0.841517i | \(0.318337\pi\) | |||||||
\(674\) | −0.384350 | − | 1.18291i | −0.0148046 | − | 0.0455639i | ||||
\(675\) | −1.66722 | + | 5.13119i | −0.0641715 | + | 0.197499i | ||||
\(676\) | 0.110623 | + | 0.0803721i | 0.00425472 | + | 0.00309123i | ||||
\(677\) | −4.36533 | − | 3.17160i | −0.167773 | − | 0.121894i | 0.500730 | − | 0.865603i | \(-0.333065\pi\) |
−0.668504 | + | 0.743709i | \(0.733065\pi\) | |||||||
\(678\) | 0.201566 | − | 0.620355i | 0.00774108 | − | 0.0238246i | ||||
\(679\) | −2.07577 | − | 6.38856i | −0.0796607 | − | 0.245170i | ||||
\(680\) | 3.47089 | − | 2.52175i | 0.133102 | − | 0.0967046i | ||||
\(681\) | 4.83116 | 0.185130 | ||||||||
\(682\) | −23.5104 | + | 20.2395i | −0.900261 | + | 0.775009i | ||||
\(683\) | 2.39397 | 0.0916028 | 0.0458014 | − | 0.998951i | \(-0.485416\pi\) | ||||
0.0458014 | + | 0.998951i | \(0.485416\pi\) | |||||||
\(684\) | −6.56722 | + | 4.77137i | −0.251104 | + | 0.182438i | ||||
\(685\) | 0.131008 | + | 0.403202i | 0.00500556 | + | 0.0154055i | ||||
\(686\) | 0.309017 | − | 0.951057i | 0.0117983 | − | 0.0363115i | ||||
\(687\) | −13.2826 | − | 9.65038i | −0.506763 | − | 0.368185i | ||||
\(688\) | 0.0557565 | + | 0.0405095i | 0.00212570 | + | 0.00154441i | ||||
\(689\) | −14.5216 | + | 44.6928i | −0.553228 | + | 1.70266i | ||||
\(690\) | −1.02239 | − | 3.14659i | −0.0389217 | − | 0.119789i | ||||
\(691\) | 22.8731 | − | 16.6183i | 0.870132 | − | 0.632188i | −0.0604902 | − | 0.998169i | \(-0.519266\pi\) |
0.930622 | + | 0.365981i | \(0.119266\pi\) | |||||||
\(692\) | 9.32676 | 0.354550 | ||||||||
\(693\) | 1.26349 | − | 5.35503i | 0.0479959 | − | 0.203421i | ||||
\(694\) | −15.7099 | −0.596341 | ||||||||
\(695\) | 15.6941 | − | 11.4024i | 0.595312 | − | 0.432519i | ||||
\(696\) | −0.270118 | − | 0.831339i | −0.0102388 | − | 0.0315118i | ||||
\(697\) | 2.68984 | − | 8.27849i | 0.101885 | − | 0.313570i | ||||
\(698\) | −13.2773 | − | 9.64650i | −0.502552 | − | 0.365126i | ||||
\(699\) | 8.89828 | + | 6.46498i | 0.336564 | + | 0.244528i | ||||
\(700\) | 0.309017 | − | 0.951057i | 0.0116797 | − | 0.0359466i | ||||
\(701\) | 13.1855 | + | 40.5808i | 0.498009 | + | 1.53271i | 0.812215 | + | 0.583359i | \(0.198262\pi\) |
−0.314206 | + | 0.949355i | \(0.601738\pi\) | |||||||
\(702\) | −15.6547 | + | 11.3738i | −0.590849 | + | 0.429277i | ||||
\(703\) | 20.7512 | 0.782645 | ||||||||
\(704\) | −3.30536 | + | 0.273157i | −0.124575 | + | 0.0102950i | ||||
\(705\) | −2.59153 | −0.0976027 | ||||||||
\(706\) | −18.4645 | + | 13.4152i | −0.694919 | + | 0.504888i | ||||
\(707\) | 0.976270 | + | 3.00465i | 0.0367164 | + | 0.113001i | ||||
\(708\) | 0.438416 | − | 1.34930i | 0.0164767 | − | 0.0507100i | ||||
\(709\) | −39.7414 | − | 28.8738i | −1.49252 | − | 1.08438i | −0.973245 | − | 0.229770i | \(-0.926203\pi\) |
−0.519274 | − | 0.854608i | \(-0.673797\pi\) | |||||||
\(710\) | −4.69029 | − | 3.40769i | −0.176023 | − | 0.127888i | ||||
\(711\) | 2.57996 | − | 7.94029i | 0.0967559 | − | 0.297784i | ||||
\(712\) | 3.06620 | + | 9.43679i | 0.114911 | + | 0.353659i | ||||
\(713\) | 21.6194 | − | 15.7074i | 0.809651 | − | 0.588246i | ||||
\(714\) | 4.96830 | 0.185934 | ||||||||
\(715\) | 10.1666 | + | 6.17549i | 0.380208 | + | 0.230950i | ||||
\(716\) | 21.0160 | 0.785405 | ||||||||
\(717\) | −1.90354 | + | 1.38300i | −0.0710891 | + | 0.0516492i | ||||
\(718\) | −3.35431 | − | 10.3235i | −0.125182 | − | 0.385270i | ||||
\(719\) | 9.59918 | − | 29.5433i | 0.357989 | − | 1.10178i | −0.596267 | − | 0.802786i | \(-0.703350\pi\) |
0.954256 | − | 0.298991i | \(-0.0966500\pi\) | |||||||
\(720\) | −1.34211 | − | 0.975098i | −0.0500174 | − | 0.0363398i | ||||
\(721\) | 11.7144 | + | 8.51098i | 0.436265 | + | 0.316965i | ||||
\(722\) | 1.52765 | − | 4.70163i | 0.0568533 | − | 0.174976i | ||||
\(723\) | −6.67386 | − | 20.5400i | −0.248203 | − | 0.763891i | ||||
\(724\) | 1.79022 | − | 1.30067i | 0.0665331 | − | 0.0483391i | ||||
\(725\) | −0.754826 | −0.0280335 | ||||||||
\(726\) | 1.89420 | − | 12.5969i | 0.0703004 | − | 0.467513i | ||||
\(727\) | 41.2246 | 1.52894 | 0.764468 | − | 0.644662i | \(-0.223002\pi\) | ||||
0.764468 | + | 0.644662i | \(0.223002\pi\) | |||||||
\(728\) | 2.90157 | − | 2.10811i | 0.107539 | − | 0.0781319i | ||||
\(729\) | 6.44378 | + | 19.8319i | 0.238658 | + | 0.734515i | ||||
\(730\) | 2.80171 | − | 8.62277i | 0.103696 | − | 0.319143i | ||||
\(731\) | 0.239210 | + | 0.173796i | 0.00884749 | + | 0.00642808i | ||||
\(732\) | 3.77595 | + | 2.74339i | 0.139563 | + | 0.101398i | ||||
\(733\) | 13.9107 | − | 42.8128i | 0.513804 | − | 1.58133i | −0.271643 | − | 0.962398i | \(-0.587567\pi\) |
0.785447 | − | 0.618929i | \(-0.212433\pi\) | |||||||
\(734\) | 6.60984 | + | 20.3430i | 0.243974 | + | 0.750873i | ||||
\(735\) | 0.936877 | − | 0.680681i | 0.0345572 | − | 0.0251073i | ||||
\(736\) | 2.85699 | 0.105310 | ||||||||
\(737\) | −40.5521 | − | 24.6326i | −1.49376 | − | 0.907353i | ||||
\(738\) | −3.36583 | −0.123898 | ||||||||
\(739\) | 31.9117 | − | 23.1852i | 1.17389 | − | 0.852881i | 0.182420 | − | 0.983221i | \(-0.441607\pi\) |
0.991469 | + | 0.130340i | \(0.0416068\pi\) | |||||||
\(740\) | 1.31048 | + | 4.03324i | 0.0481742 | + | 0.148265i | ||||
\(741\) | 6.28025 | − | 19.3286i | 0.230711 | − | 0.710055i | ||||
\(742\) | −10.6002 | − | 7.70149i | −0.389145 | − | 0.282731i | ||||
\(743\) | −30.7337 | − | 22.3293i | −1.12751 | − | 0.819184i | −0.142180 | − | 0.989841i | \(-0.545411\pi\) |
−0.985331 | + | 0.170657i | \(0.945411\pi\) | |||||||
\(744\) | −3.34721 | + | 10.3017i | −0.122715 | + | 0.377677i | ||||
\(745\) | −6.24831 | − | 19.2303i | −0.228920 | − | 0.704544i | ||||
\(746\) | −2.34990 | + | 1.70730i | −0.0860358 | + | 0.0625087i | ||||
\(747\) | 27.5811 | 1.00914 | ||||||||
\(748\) | −14.1808 | + | 1.17191i | −0.518502 | + | 0.0428493i | ||||
\(749\) | −7.11161 | −0.259852 | ||||||||
\(750\) | 0.936877 | − | 0.680681i | 0.0342099 | − | 0.0248549i | ||||
\(751\) | 13.8373 | + | 42.5867i | 0.504929 | + | 1.55401i | 0.800890 | + | 0.598812i | \(0.204360\pi\) |
−0.295960 | + | 0.955200i | \(0.595640\pi\) | |||||||
\(752\) | 0.691535 | − | 2.12833i | 0.0252177 | − | 0.0776121i | ||||
\(753\) | 13.5911 | + | 9.87452i | 0.495288 | + | 0.359848i | ||||
\(754\) | −2.19018 | − | 1.59126i | −0.0797617 | − | 0.0579503i | ||||
\(755\) | 4.75400 | − | 14.6313i | 0.173016 | − | 0.532487i | ||||
\(756\) | −1.66722 | − | 5.13119i | −0.0606363 | − | 0.186619i | ||||
\(757\) | 36.9761 | − | 26.8647i | 1.34392 | − | 0.976414i | 0.344629 | − | 0.938739i | \(-0.388005\pi\) |
0.999290 | − | 0.0376754i | \(-0.0119953\pi\) | |||||||
\(758\) | 0.0627414 | 0.00227887 | ||||||||
\(759\) | −2.51985 | + | 10.6799i | −0.0914647 | + | 0.387655i | ||||
\(760\) | 4.89322 | 0.177496 | ||||||||
\(761\) | 17.5122 | − | 12.7233i | 0.634815 | − | 0.461220i | −0.223250 | − | 0.974761i | \(-0.571667\pi\) |
0.858065 | + | 0.513541i | \(0.171667\pi\) | |||||||
\(762\) | 4.40507 | + | 13.5574i | 0.159579 | + | 0.491134i | ||||
\(763\) | −4.65720 | + | 14.3334i | −0.168602 | + | 0.518903i | ||||
\(764\) | −15.5050 | − | 11.2650i | −0.560950 | − | 0.407554i | ||||
\(765\) | −5.75798 | − | 4.18342i | −0.208180 | − | 0.151252i | ||||
\(766\) | −2.60623 | + | 8.02116i | −0.0941670 | + | 0.289816i | ||||
\(767\) | −1.35780 | − | 4.17889i | −0.0490274 | − | 0.150891i | ||||
\(768\) | −0.936877 | + | 0.680681i | −0.0338066 | + | 0.0245619i | ||||
\(769\) | −38.7211 | −1.39632 | −0.698159 | − | 0.715942i | \(-0.745997\pi\) | ||||
−0.698159 | + | 0.715942i | \(0.745997\pi\) | |||||||
\(770\) | −2.51353 | + | 2.16383i | −0.0905814 | + | 0.0779790i | ||||
\(771\) | −17.1903 | −0.619095 | ||||||||
\(772\) | −6.83340 | + | 4.96475i | −0.245939 | + | 0.178685i | ||||
\(773\) | −9.78512 | − | 30.1155i | −0.351946 | − | 1.08318i | −0.957759 | − | 0.287572i | \(-0.907152\pi\) |
0.605813 | − | 0.795607i | \(-0.292848\pi\) | |||||||
\(774\) | 0.0353305 | − | 0.108736i | 0.00126993 | − | 0.00390844i | ||||
\(775\) | 7.56718 | + | 5.49788i | 0.271821 | + | 0.197490i | ||||
\(776\) | 5.43443 | + | 3.94835i | 0.195085 | + | 0.141737i | ||||
\(777\) | −1.51759 | + | 4.67067i | −0.0544433 | + | 0.167559i | ||||
\(778\) | −11.3311 | − | 34.8734i | −0.406239 | − | 1.25027i | ||||
\(779\) | 8.03182 | − | 5.83546i | 0.287770 | − | 0.209077i | ||||
\(780\) | 4.15337 | 0.148714 | ||||||||
\(781\) | 7.42777 | + | 17.7356i | 0.265786 | + | 0.634629i | ||||
\(782\) | 12.2572 | 0.438317 | ||||||||
\(783\) | −3.29470 | + | 2.39374i | −0.117743 | + | 0.0855453i | ||||
\(784\) | 0.309017 | + | 0.951057i | 0.0110363 | + | 0.0339663i | ||||
\(785\) | 1.49516 | − | 4.60164i | 0.0533647 | − | 0.164240i | ||||
\(786\) | 14.0491 | + | 10.2073i | 0.501115 | + | 0.364082i | ||||
\(787\) | 34.3142 | + | 24.9307i | 1.22317 | + | 0.888685i | 0.996359 | − | 0.0852536i | \(-0.0271700\pi\) |
0.226811 | + | 0.973939i | \(0.427170\pi\) | |||||||
\(788\) | −3.45547 | + | 10.6348i | −0.123096 | + | 0.378850i | ||||
\(789\) | −11.3185 | − | 34.8346i | −0.402948 | − | 1.24015i | ||||
\(790\) | −4.07153 | + | 2.95814i | −0.144859 | + | 0.105246i | ||||
\(791\) | 0.563261 | 0.0200272 | ||||||||
\(792\) | 2.12543 | + | 5.07497i | 0.0755238 | + | 0.180331i | ||||
\(793\) | 14.4550 | 0.513313 | ||||||||
\(794\) | 2.35567 | − | 1.71149i | 0.0835995 | − | 0.0607386i | ||||
\(795\) | −4.68882 | − | 14.4307i | −0.166295 | − | 0.511804i | ||||
\(796\) | −1.30728 | + | 4.02339i | −0.0463353 | + | 0.142605i | ||||
\(797\) | −11.1036 | − | 8.06726i | −0.393311 | − | 0.285757i | 0.373500 | − | 0.927630i | \(-0.378158\pi\) |
−0.766811 | + | 0.641873i | \(0.778158\pi\) | |||||||
\(798\) | 4.58434 | + | 3.33072i | 0.162284 | + | 0.117906i | ||||
\(799\) | 2.96686 | − | 9.13106i | 0.104960 | − | 0.323034i | ||||
\(800\) | 0.309017 | + | 0.951057i | 0.0109254 | + | 0.0336249i | ||||
\(801\) | 13.3170 | − | 9.67534i | 0.470532 | − | 0.341861i | ||||
\(802\) | 15.3525 | 0.542116 | ||||||||
\(803\) | −22.7890 | + | 19.6184i | −0.804206 | + | 0.692318i | ||||
\(804\) | −16.5668 | −0.584267 | ||||||||
\(805\) | 2.31136 | − | 1.67930i | 0.0814646 | − | 0.0591875i | ||||
\(806\) | 10.3665 | + | 31.9050i | 0.365146 | + | 1.12380i | ||||
\(807\) | 3.97297 | − | 12.2275i | 0.139855 | − | 0.430430i | ||||
\(808\) | −2.55591 | − | 1.85698i | −0.0899165 | − | 0.0653282i | ||||
\(809\) | 25.9649 | + | 18.8646i | 0.912876 | + | 0.663243i | 0.941741 | − | 0.336340i | \(-0.109189\pi\) |
−0.0288645 | + | 0.999583i | \(0.509189\pi\) | |||||||
\(810\) | 0.392798 | − | 1.20891i | 0.0138015 | − | 0.0424767i | ||||
\(811\) | 13.8739 | + | 42.6994i | 0.487178 | + | 1.49938i | 0.828801 | + | 0.559543i | \(0.189023\pi\) |
−0.341623 | + | 0.939837i | \(0.610977\pi\) | |||||||
\(812\) | 0.610667 | − | 0.443676i | 0.0214302 | − | 0.0155700i | ||||
\(813\) | −16.5749 | −0.581306 | ||||||||
\(814\) | 3.22989 | − | 13.6893i | 0.113208 | − | 0.479808i | ||||
\(815\) | −3.98234 | −0.139495 | ||||||||
\(816\) | −4.01944 | + | 2.92029i | −0.140708 | + | 0.102231i | ||||
\(817\) | 0.104211 | + | 0.320730i | 0.00364589 | + | 0.0112209i | ||||
\(818\) | −4.63335 | + | 14.2600i | −0.162001 | + | 0.498589i | ||||
\(819\) | −4.81352 | − | 3.49723i | −0.168198 | − | 0.122203i | ||||
\(820\) | 1.64142 | + | 1.19256i | 0.0573209 | + | 0.0416460i | ||||
\(821\) | −12.7555 | + | 39.2573i | −0.445169 | + | 1.37009i | 0.437130 | + | 0.899398i | \(0.355995\pi\) |
−0.882299 | + | 0.470690i | \(0.844005\pi\) | |||||||
\(822\) | −0.151713 | − | 0.466925i | −0.00529160 | − | 0.0162859i | ||||
\(823\) | −11.9364 | + | 8.67228i | −0.416076 | + | 0.302297i | −0.776057 | − | 0.630663i | \(-0.782783\pi\) |
0.359981 | + | 0.932960i | \(0.382783\pi\) | |||||||
\(824\) | −14.4797 | −0.504426 | ||||||||
\(825\) | −3.82775 | + | 0.316327i | −0.133265 | + | 0.0110131i | ||||
\(826\) | 1.22512 | 0.0426274 | ||||||||
\(827\) | −41.7264 | + | 30.3160i | −1.45097 | + | 1.05419i | −0.465366 | + | 0.885118i | \(0.654077\pi\) |
−0.985604 | + | 0.169073i | \(0.945923\pi\) | |||||||
\(828\) | −1.46461 | − | 4.50760i | −0.0508986 | − | 0.156650i | ||||
\(829\) | 3.30075 | − | 10.1587i | 0.114640 | − | 0.352825i | −0.877232 | − | 0.480067i | \(-0.840612\pi\) |
0.991872 | + | 0.127242i | \(0.0406125\pi\) | |||||||
\(830\) | −13.4506 | − | 9.77240i | −0.466876 | − | 0.339205i | ||||
\(831\) | −3.63844 | − | 2.64348i | −0.126216 | − | 0.0917015i | ||||
\(832\) | −1.10830 | + | 3.41100i | −0.0384234 | + | 0.118255i | ||||
\(833\) | 1.32576 | + | 4.08027i | 0.0459349 | + | 0.141373i | ||||
\(834\) | −18.1745 | + | 13.2045i | −0.629330 | + | 0.457235i | ||||
\(835\) | 23.9536 | 0.828950 | ||||||||
\(836\) | −13.8705 | − | 8.42540i | −0.479723 | − | 0.291398i | ||||
\(837\) | 50.4647 | 1.74432 | ||||||||
\(838\) | −21.6951 | + | 15.7624i | −0.749444 | + | 0.544503i | ||||
\(839\) | −8.47516 | − | 26.0839i | −0.292595 | − | 0.900515i | −0.984019 | − | 0.178065i | \(-0.943016\pi\) |
0.691424 | − | 0.722449i | \(-0.256984\pi\) | |||||||
\(840\) | −0.357855 | + | 1.10136i | −0.0123472 | + | 0.0380007i | ||||
\(841\) | 23.0005 | + | 16.7109i | 0.793122 | + | 0.576237i | ||||
\(842\) | −31.6052 | − | 22.9625i | −1.08919 | − | 0.791340i | ||||
\(843\) | −8.47551 | + | 26.0850i | −0.291912 | + | 0.898413i | ||||
\(844\) | −0.860605 | − | 2.64867i | −0.0296232 | − | 0.0911710i | ||||
\(845\) | −0.110623 | + | 0.0803721i | −0.00380554 | + | 0.00276488i | ||||
\(846\) | −3.71246 | −0.127637 | ||||||||
\(847\) | 10.8508 | − | 1.80576i | 0.372837 | − | 0.0620467i | ||||
\(848\) | 13.1026 | 0.449944 | ||||||||
\(849\) | −8.39374 | + | 6.09841i | −0.288073 | + | 0.209297i | ||||
\(850\) | 1.32576 | + | 4.08027i | 0.0454732 | + | 0.139952i | ||||
\(851\) | −3.74403 | + | 11.5229i | −0.128344 | + | 0.395001i | ||||
\(852\) | 5.43156 | + | 3.94626i | 0.186082 | + | 0.135196i | ||||
\(853\) | −40.6324 | − | 29.5212i | −1.39123 | − | 1.01079i | −0.995729 | − | 0.0923196i | \(-0.970572\pi\) |
−0.395498 | − | 0.918467i | \(-0.629428\pi\) | |||||||
\(854\) | −1.24545 | + | 3.83310i | −0.0426184 | + | 0.131166i | ||||
\(855\) | −2.50846 | − | 7.72024i | −0.0857874 | − | 0.264026i | ||||
\(856\) | 5.75341 | − | 4.18010i | 0.196648 | − | 0.142873i | ||||
\(857\) | −2.69776 | −0.0921539 | −0.0460769 | − | 0.998938i | \(-0.514672\pi\) | ||||
−0.0460769 | + | 0.998938i | \(0.514672\pi\) | |||||||
\(858\) | −11.7733 | − | 7.15148i | −0.401935 | − | 0.244148i | ||||
\(859\) | 19.0873 | 0.651252 | 0.325626 | − | 0.945499i | \(-0.394425\pi\) | ||||
0.325626 | + | 0.945499i | \(0.394425\pi\) | |||||||
\(860\) | −0.0557565 | + | 0.0405095i | −0.00190128 | + | 0.00138136i | ||||
\(861\) | 0.726054 | + | 2.23457i | 0.0247439 | + | 0.0761538i | ||||
\(862\) | 11.4063 | − | 35.1051i | 0.388502 | − | 1.19569i | ||||
\(863\) | 17.2195 | + | 12.5107i | 0.586159 | + | 0.425869i | 0.840939 | − | 0.541130i | \(-0.182003\pi\) |
−0.254781 | + | 0.966999i | \(0.582003\pi\) | |||||||
\(864\) | 4.36485 | + | 3.17125i | 0.148495 | + | 0.107888i | ||||
\(865\) | −2.88213 | + | 8.87028i | −0.0979953 | + | 0.301598i | ||||
\(866\) | −3.85368 | − | 11.8604i | −0.130953 | − | 0.403033i | ||||
\(867\) | −1.31750 | + | 0.957222i | −0.0447447 | + | 0.0325090i | ||||
\(868\) | −9.35354 | −0.317480 | ||||||||
\(869\) | 16.6348 | − | 1.37471i | 0.564299 | − | 0.0466340i | ||||
\(870\) | 0.874121 | 0.0296355 | ||||||||
\(871\) | −41.5095 | + | 30.1584i | −1.40650 | + | 1.02188i | ||||
\(872\) | −4.65720 | − | 14.3334i | −0.157713 | − | 0.485389i | ||||
\(873\) | 3.44357 | − | 10.5982i | 0.116547 | − | 0.358695i | ||||
\(874\) | 11.3100 | + | 8.21717i | 0.382565 | + | 0.277950i | ||||
\(875\) | 0.809017 | + | 0.587785i | 0.0273498 | + | 0.0198708i | ||||
\(876\) | −3.24450 | + | 9.98554i | −0.109621 | + | 0.337380i | ||||
\(877\) | 4.57247 | + | 14.0726i | 0.154401 | + | 0.475199i | 0.998100 | − | 0.0616188i | \(-0.0196263\pi\) |
−0.843698 | + | 0.536818i | \(0.819626\pi\) | |||||||
\(878\) | 4.68758 | − | 3.40572i | 0.158198 | − | 0.114938i | ||||
\(879\) | 14.7571 | 0.497743 | ||||||||
\(880\) | 0.761624 | − | 3.22799i | 0.0256743 | − | 0.108816i | ||||
\(881\) | −38.9767 | −1.31316 | −0.656579 | − | 0.754257i | \(-0.727997\pi\) | ||||
−0.656579 | + | 0.754257i | \(0.727997\pi\) | |||||||
\(882\) | 1.34211 | − | 0.975098i | 0.0451911 | − | 0.0328333i | ||||
\(883\) | −12.6374 | − | 38.8938i | −0.425281 | − | 1.30888i | −0.902725 | − | 0.430219i | \(-0.858437\pi\) |
0.477444 | − | 0.878662i | \(-0.341563\pi\) | |||||||
\(884\) | −4.75489 | + | 14.6341i | −0.159924 | + | 0.492197i | ||||
\(885\) | 1.14779 | + | 0.833916i | 0.0385824 | + | 0.0280318i | ||||
\(886\) | −9.59314 | − | 6.96982i | −0.322288 | − | 0.234156i | ||||
\(887\) | −9.57598 | + | 29.4718i | −0.321530 | + | 0.989568i | 0.651453 | + | 0.758689i | \(0.274160\pi\) |
−0.972983 | + | 0.230878i | \(0.925840\pi\) | |||||||
\(888\) | −1.51759 | − | 4.67067i | −0.0509270 | − | 0.156737i | ||||
\(889\) | −9.95873 | + | 7.23544i | −0.334005 | + | 0.242669i | ||||
\(890\) | −9.92243 | −0.332600 | ||||||||
\(891\) | −3.19501 | + | 2.75049i | −0.107037 | + | 0.0921449i | ||||
\(892\) | −11.2604 | −0.377026 | ||||||||
\(893\) | 8.85899 | − | 6.43643i | 0.296455 | − | 0.215387i | ||||
\(894\) | 7.23581 | + | 22.2695i | 0.242002 | + | 0.744804i | ||||
\(895\) | −6.49431 | + | 19.9874i | −0.217081 | + | 0.668106i | ||||
\(896\) | −0.809017 | − | 0.587785i | −0.0270274 | − | 0.0196365i | ||||
\(897\) | 9.59991 | + | 6.97474i | 0.320532 | + | 0.232880i | ||||
\(898\) | −1.93727 | + | 5.96230i | −0.0646475 | + | 0.198965i | ||||
\(899\) | 2.18175 | + | 6.71474i | 0.0727655 | + | 0.223949i | ||||
\(900\) | 1.34211 | − | 0.975098i | 0.0447369 | − | 0.0325033i | ||||
\(901\) | 56.2133 | 1.87274 | ||||||||
\(902\) | −2.59943 | − | 6.20677i | −0.0865516 | − | 0.206663i | ||||
\(903\) | −0.0798110 | −0.00265594 | ||||||||
\(904\) | −0.455688 | + | 0.331076i | −0.0151559 | + | 0.0110114i | ||||
\(905\) | 0.683804 | + | 2.10453i | 0.0227304 | + | 0.0699571i | ||||
\(906\) | −5.50533 | + | 16.9437i | −0.182902 | + | 0.562916i | ||||
\(907\) | 6.40938 | + | 4.65669i | 0.212820 | + | 0.154623i | 0.689089 | − | 0.724677i | \(-0.258011\pi\) |
−0.476269 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(908\) | −3.37508 | − | 2.45214i | −0.112006 | − | 0.0813771i | ||||
\(909\) | −1.61957 | + | 4.98452i | −0.0537177 | + | 0.165326i | ||||
\(910\) | 1.10830 | + | 3.41100i | 0.0367398 | + | 0.113074i | ||||
\(911\) | −24.6947 | + | 17.9418i | −0.818173 | + | 0.594437i | −0.916189 | − | 0.400747i | \(-0.868750\pi\) |
0.0980157 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(912\) | −5.66656 | −0.187638 | ||||||||
\(913\) | 21.3010 | + | 50.8612i | 0.704959 | + | 1.68326i | ||||
\(914\) | −30.0377 | −0.993559 | ||||||||
\(915\) | −3.77595 | + | 2.74339i | −0.124829 | + | 0.0906935i | ||||
\(916\) | 4.38110 | + | 13.4836i | 0.144756 | + | 0.445512i | ||||
\(917\) | −4.63393 | + | 14.2618i | −0.153026 | + | 0.470965i | ||||
\(918\) | 18.7263 | + | 13.6055i | 0.618060 | + | 0.449047i | ||||
\(919\) | 4.15926 | + | 3.02188i | 0.137201 | + | 0.0996827i | 0.654269 | − | 0.756262i | \(-0.272976\pi\) |
−0.517068 | + | 0.855945i | \(0.672976\pi\) | |||||||
\(920\) | −0.882859 | + | 2.71716i | −0.0291070 | + | 0.0895821i | ||||
\(921\) | −2.06044 | − | 6.34138i | −0.0678938 | − | 0.208956i | ||||
\(922\) | 30.6539 | − | 22.2714i | 1.00953 | − | 0.733469i | ||||
\(923\) | 20.7930 | 0.684410 | ||||||||
\(924\) | 2.91078 | − | 2.50581i | 0.0957576 | − | 0.0824350i | ||||
\(925\) | −4.24080 | −0.139437 | ||||||||
\(926\) | −1.80446 | + | 1.31102i | −0.0592982 | + | 0.0430826i | ||||
\(927\) | 7.42288 | + | 22.8453i | 0.243800 | + | 0.750338i | ||||
\(928\) | −0.233254 | + | 0.717882i | −0.00765694 | + | 0.0235656i | ||||
\(929\) | −7.57718 | − | 5.50514i | −0.248599 | − | 0.180618i | 0.456507 | − | 0.889720i | \(-0.349101\pi\) |
−0.705106 | + | 0.709102i | \(0.749101\pi\) | |||||||
\(930\) | −8.76312 | − | 6.36678i | −0.287354 | − | 0.208775i | ||||
\(931\) | −1.51209 | + | 4.65373i | −0.0495567 | + | 0.152520i | ||||
\(932\) | −2.93499 | − | 9.03296i | −0.0961387 | − | 0.295884i | ||||
\(933\) | −11.4350 | + | 8.30799i | −0.374364 | + | 0.271991i | ||||
\(934\) | 40.1699 | 1.31440 | ||||||||
\(935\) | 3.26756 | − | 13.8489i | 0.106861 | − | 0.452907i | ||||
\(936\) | 5.94984 | 0.194477 | ||||||||
\(937\) | 26.2481 | − | 19.0704i | 0.857489 | − | 0.623002i | −0.0697115 | − | 0.997567i | \(-0.522208\pi\) |
0.927201 | + | 0.374565i | \(0.122208\pi\) | |||||||
\(938\) | −4.42076 | − | 13.6057i | −0.144343 | − | 0.444242i | ||||
\(939\) | 7.27025 | − | 22.3755i | 0.237256 | − | 0.730198i | ||||
\(940\) | 1.81046 | + | 1.31538i | 0.0590508 | + | 0.0429029i | ||||
\(941\) | 9.67998 | + | 7.03292i | 0.315558 | + | 0.229267i | 0.734278 | − | 0.678849i | \(-0.237521\pi\) |
−0.418719 | + | 0.908116i | \(0.637521\pi\) | |||||||
\(942\) | −1.73146 | + | 5.32890i | −0.0564141 | + | 0.173625i | ||||
\(943\) | 1.79124 | + | 5.51286i | 0.0583307 | + | 0.179524i | ||||
\(944\) | −0.991144 | + | 0.720108i | −0.0322590 | + | 0.0234375i | ||||
\(945\) | 5.39525 | 0.175507 | ||||||||
\(946\) | 0.227802 | − | 0.0188257i | 0.00740647 | − | 0.000612075i | ||||
\(947\) | 5.99311 | 0.194750 | 0.0973749 | − | 0.995248i | \(-0.468955\pi\) | ||||
0.0973749 | + | 0.995248i | \(0.468955\pi\) | |||||||
\(948\) | 4.71501 | − | 3.42566i | 0.153136 | − | 0.111260i | ||||
\(949\) | 10.0484 | + | 30.9259i | 0.326186 | + | 1.00390i | ||||
\(950\) | −1.51209 | + | 4.65373i | −0.0490586 | + | 0.150987i | ||||
\(951\) | −24.8548 | − | 18.0580i | −0.805971 | − | 0.585572i | ||||
\(952\) | −3.47089 | − | 2.52175i | −0.112492 | − | 0.0817303i | ||||
\(953\) | 11.6471 | − | 35.8460i | 0.377286 | − | 1.16117i | −0.564638 | − | 0.825339i | \(-0.690984\pi\) |
0.941924 | − | 0.335827i | \(-0.109016\pi\) | |||||||
\(954\) | −6.71689 | − | 20.6725i | −0.217467 | − | 0.669295i | ||||
\(955\) | 15.5050 | − | 11.2650i | 0.501728 | − | 0.364527i | ||||
\(956\) | 2.03180 | 0.0657130 | ||||||||
\(957\) | −2.47783 | − | 1.50511i | −0.0800967 | − | 0.0486532i | ||||
\(958\) | −15.4649 | −0.499648 | ||||||||
\(959\) | 0.342984 | − | 0.249192i | 0.0110755 | − | 0.00804684i | ||||
\(960\) | −0.357855 | − | 1.10136i | −0.0115497 | − | 0.0355464i | ||||
\(961\) | 17.4560 | − | 53.7240i | 0.563097 | − | 1.73303i | ||||
\(962\) | −12.3050 | − | 8.94009i | −0.396728 | − | 0.288240i | ||||
\(963\) | −9.54454 | − | 6.93452i | −0.307569 | − | 0.223462i | ||||
\(964\) | −5.76305 | + | 17.7368i | −0.185615 | + | 0.571265i | ||||
\(965\) | −2.61013 | − | 8.03314i | −0.0840229 | − | 0.258596i | ||||
\(966\) | −2.67665 | + | 1.94470i | −0.0861198 | + | 0.0625697i | ||||
\(967\) | −49.5830 | −1.59448 | −0.797241 | − | 0.603662i | \(-0.793708\pi\) | ||||
−0.797241 | + | 0.603662i | \(0.793708\pi\) | |||||||
\(968\) | −7.71706 | + | 7.83881i | −0.248036 | + | 0.251949i | ||||
\(969\) | −24.3110 | −0.780981 | ||||||||
\(970\) | −5.43443 | + | 3.94835i | −0.174489 | + | 0.126774i | ||||
\(971\) | −11.8166 | − | 36.3678i | −0.379213 | − | 1.16710i | −0.940592 | − | 0.339538i | \(-0.889729\pi\) |
0.561380 | − | 0.827558i | \(-0.310271\pi\) | |||||||
\(972\) | 4.54679 | − | 13.9936i | 0.145838 | − | 0.448845i | ||||
\(973\) | −15.6941 | − | 11.4024i | −0.503130 | − | 0.365545i | ||||
\(974\) | 14.4963 | + | 10.5322i | 0.464491 | + | 0.337473i | ||||
\(975\) | −1.28346 | + | 3.95009i | −0.0411036 | + | 0.126504i | ||||
\(976\) | −1.24545 | − | 3.83310i | −0.0398658 | − | 0.122694i | ||||
\(977\) | 5.68077 | − | 4.12732i | 0.181744 | − | 0.132045i | −0.493194 | − | 0.869920i | \(-0.664171\pi\) |
0.674938 | + | 0.737875i | \(0.264171\pi\) | |||||||
\(978\) | 4.61172 | 0.147467 | ||||||||
\(979\) | 28.1266 | + | 17.0849i | 0.898929 | + | 0.546037i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −20.2269 | + | 14.6957i | −0.645796 | + | 0.469198i | ||||
\(982\) | 8.23260 | + | 25.3373i | 0.262713 | + | 0.808547i | ||||
\(983\) | −9.59675 | + | 29.5358i | −0.306089 | + | 0.942045i | 0.673180 | + | 0.739479i | \(0.264928\pi\) |
−0.979269 | + | 0.202566i | \(0.935072\pi\) | |||||||
\(984\) | −1.90083 | − | 1.38104i | −0.0605964 | − | 0.0440259i | ||||
\(985\) | −9.04653 | − | 6.57269i | −0.288246 | − | 0.209423i | ||||
\(986\) | −1.00072 | + | 3.07990i | −0.0318694 | + | 0.0980839i | ||||
\(987\) | 0.800827 | + | 2.46469i | 0.0254906 | + | 0.0784520i | ||||
\(988\) | −14.1980 | + | 10.3155i | −0.451699 | + | 0.328179i | ||||
\(989\) | −0.196901 | −0.00626108 | ||||||||
\(990\) | −5.48338 | + | 0.453150i | −0.174273 | + | 0.0144020i | ||||
\(991\) | 20.2609 | 0.643608 | 0.321804 | − | 0.946806i | \(-0.395711\pi\) | ||||
0.321804 | + | 0.946806i | \(0.395711\pi\) | |||||||
\(992\) | 7.56718 | − | 5.49788i | 0.240258 | − | 0.174558i | ||||
\(993\) | 0.140956 | + | 0.433817i | 0.00447310 | + | 0.0137668i | ||||
\(994\) | −1.79153 | + | 5.51376i | −0.0568239 | + | 0.174886i | ||||
\(995\) | −3.42250 | − | 2.48659i | −0.108501 | − | 0.0788303i | ||||
\(996\) | 15.5763 | + | 11.3169i | 0.493555 | + | 0.358589i | ||||
\(997\) | 4.96877 | − | 15.2923i | 0.157363 | − | 0.484312i | −0.841030 | − | 0.540988i | \(-0.818050\pi\) |
0.998393 | + | 0.0566762i | \(0.0180503\pi\) | |||||||
\(998\) | 9.09434 | + | 27.9895i | 0.287876 | + | 0.885992i | ||||
\(999\) | −18.5104 | + | 13.4486i | −0.585645 | + | 0.425496i |
(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 | 770.2.n.h.421.3 | ✓ | 12 | |
11.2 | odd | 10 | 8470.2.a.cu.1.5 | 6 | |||
11.4 | even | 5 | inner | 770.2.n.h.631.3 | yes | 12 | |
11.9 | even | 5 | 8470.2.a.da.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.h.421.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
770.2.n.h.631.3 | yes | 12 | 11.4 | even | 5 | inner | |
8470.2.a.cu.1.5 | 6 | 11.2 | odd | 10 | |||
8470.2.a.da.1.5 | 6 | 11.9 | even | 5 |