Properties

Label 784.2.m.h.589.4
Level $784$
Weight $2$
Character 784.589
Analytic conductor $6.260$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(197,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.197");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.m (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: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.20138089353117696.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 589.4
Root \(1.37925 - 0.312504i\) of defining polynomial
Character \(\chi\) \(=\) 784.589
Dual form 784.2.m.h.197.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.312504 - 1.37925i) q^{2} +(0.599978 + 0.599978i) q^{3} +(-1.80468 - 0.862045i) q^{4} +(-0.974969 + 0.974969i) q^{5} +(1.01502 - 0.640026i) q^{6} +(-1.75295 + 2.21972i) q^{8} -2.28005i q^{9} +O(q^{10})\) \(q+(0.312504 - 1.37925i) q^{2} +(0.599978 + 0.599978i) q^{3} +(-1.80468 - 0.862045i) q^{4} +(-0.974969 + 0.974969i) q^{5} +(1.01502 - 0.640026i) q^{6} +(-1.75295 + 2.21972i) q^{8} -2.28005i q^{9} +(1.04005 + 1.64941i) q^{10} +(-1.72409 + 1.72409i) q^{11} +(-0.565561 - 1.59998i) q^{12} +(-1.90592 - 1.90592i) q^{13} -1.16992 q^{15} +(2.51376 + 3.11144i) q^{16} -6.71697 q^{17} +(-3.14477 - 0.712526i) q^{18} +(-2.94908 - 2.94908i) q^{19} +(2.59998 - 0.919042i) q^{20} +(1.83917 + 2.91674i) q^{22} -5.29883i q^{23} +(-2.38352 + 0.280053i) q^{24} +3.09887i q^{25} +(-3.22436 + 2.03314i) q^{26} +(3.16792 - 3.16792i) q^{27} +(-3.03004 - 3.03004i) q^{29} +(-0.365605 + 1.61362i) q^{30} -1.19996 q^{31} +(5.07702 - 2.49477i) q^{32} -2.06883 q^{33} +(-2.09908 + 9.26441i) q^{34} +(-1.96551 + 4.11477i) q^{36} +(-2.25002 + 2.25002i) q^{37} +(-4.98913 + 3.14593i) q^{38} -2.28702i q^{39} +(-0.455088 - 3.87323i) q^{40} -3.94994i q^{41} +(-7.02292 + 7.02292i) q^{43} +(4.59768 - 1.62519i) q^{44} +(2.22298 + 2.22298i) q^{45} +(-7.30842 - 1.65591i) q^{46} +3.06186 q^{47} +(-0.358595 + 3.37499i) q^{48} +(4.27413 + 0.968410i) q^{50} +(-4.03004 - 4.03004i) q^{51} +(1.79659 + 5.08258i) q^{52} +(-3.01877 + 3.01877i) q^{53} +(-3.37937 - 5.35935i) q^{54} -3.36187i q^{55} -3.53876i q^{57} +(-5.12609 + 3.23229i) q^{58} +(-4.96785 + 4.96785i) q^{59} +(2.11133 + 1.00852i) q^{60} +(9.69194 + 9.69194i) q^{61} +(-0.374991 + 1.65504i) q^{62} +(-1.85433 - 7.78212i) q^{64} +3.71643 q^{65} +(-0.646519 + 2.85345i) q^{66} +(3.55596 + 3.55596i) q^{67} +(12.1220 + 5.79033i) q^{68} +(3.17918 - 3.17918i) q^{69} -11.5771i q^{71} +(5.06108 + 3.99682i) q^{72} -10.3271i q^{73} +(2.40020 + 3.80648i) q^{74} +(-1.85925 + 1.85925i) q^{75} +(2.77991 + 7.86439i) q^{76} +(-3.15439 - 0.714705i) q^{78} +4.06883 q^{79} +(-5.48439 - 0.582721i) q^{80} -3.03880 q^{81} +(-5.44797 - 1.23437i) q^{82} +(-9.17886 - 9.17886i) q^{83} +(6.54884 - 6.54884i) q^{85} +(7.49169 + 11.8811i) q^{86} -3.63591i q^{87} +(-0.804756 - 6.84925i) q^{88} +16.9287i q^{89} +(3.76075 - 2.37136i) q^{90} +(-4.56783 + 9.56270i) q^{92} +(-0.719947 - 0.719947i) q^{93} +(0.956845 - 4.22309i) q^{94} +5.75052 q^{95} +(4.54291 + 1.54929i) q^{96} +2.51522 q^{97} +(3.93102 + 3.93102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{10} - 8 q^{12} - 24 q^{15} + 10 q^{16} + 8 q^{17} + 20 q^{20} + 14 q^{22} + 8 q^{24} + 20 q^{26} - 4 q^{27} - 4 q^{29} - 28 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{34} - 16 q^{36} - 20 q^{37} - 16 q^{38} + 8 q^{40} + 16 q^{43} + 14 q^{44} - 40 q^{45} - 28 q^{46} - 16 q^{47} - 16 q^{48} + 44 q^{50} - 16 q^{51} + 16 q^{52} + 4 q^{53} - 64 q^{54} + 14 q^{58} + 16 q^{59} + 60 q^{60} + 20 q^{61} - 8 q^{62} - 18 q^{64} + 32 q^{65} - 12 q^{66} + 24 q^{67} + 28 q^{68} + 4 q^{69} + 6 q^{72} - 38 q^{74} + 40 q^{75} - 48 q^{76} - 76 q^{78} + 24 q^{79} - 24 q^{80} - 44 q^{81} + 16 q^{82} + 20 q^{83} - 8 q^{85} + 38 q^{86} - 14 q^{88} + 40 q^{90} + 32 q^{92} - 48 q^{93} + 24 q^{94} + 16 q^{96} - 48 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.312504 1.37925i 0.220974 0.975280i
\(3\) 0.599978 + 0.599978i 0.346397 + 0.346397i 0.858766 0.512368i \(-0.171232\pi\)
−0.512368 + 0.858766i \(0.671232\pi\)
\(4\) −1.80468 0.862045i −0.902341 0.431023i
\(5\) −0.974969 + 0.974969i −0.436020 + 0.436020i −0.890670 0.454650i \(-0.849764\pi\)
0.454650 + 0.890670i \(0.349764\pi\)
\(6\) 1.01502 0.640026i 0.414379 0.261290i
\(7\) 0 0
\(8\) −1.75295 + 2.21972i −0.619762 + 0.784790i
\(9\) 2.28005i 0.760018i
\(10\) 1.04005 + 1.64941i 0.328892 + 0.521590i
\(11\) −1.72409 + 1.72409i −0.519833 + 0.519833i −0.917521 0.397688i \(-0.869813\pi\)
0.397688 + 0.917521i \(0.369813\pi\)
\(12\) −0.565561 1.59998i −0.163263 0.461874i
\(13\) −1.90592 1.90592i −0.528608 0.528608i 0.391549 0.920157i \(-0.371939\pi\)
−0.920157 + 0.391549i \(0.871939\pi\)
\(14\) 0 0
\(15\) −1.16992 −0.302072
\(16\) 2.51376 + 3.11144i 0.628439 + 0.777859i
\(17\) −6.71697 −1.62910 −0.814552 0.580090i \(-0.803017\pi\)
−0.814552 + 0.580090i \(0.803017\pi\)
\(18\) −3.14477 0.712526i −0.741230 0.167944i
\(19\) −2.94908 2.94908i −0.676565 0.676565i 0.282656 0.959221i \(-0.408784\pi\)
−0.959221 + 0.282656i \(0.908784\pi\)
\(20\) 2.59998 0.919042i 0.581373 0.205504i
\(21\) 0 0
\(22\) 1.83917 + 2.91674i 0.392113 + 0.621852i
\(23\) 5.29883i 1.10488i −0.833552 0.552441i \(-0.813697\pi\)
0.833552 0.552441i \(-0.186303\pi\)
\(24\) −2.38352 + 0.280053i −0.486533 + 0.0571655i
\(25\) 3.09887i 0.619774i
\(26\) −3.22436 + 2.03314i −0.632349 + 0.398732i
\(27\) 3.16792 3.16792i 0.609666 0.609666i
\(28\) 0 0
\(29\) −3.03004 3.03004i −0.562663 0.562663i 0.367400 0.930063i \(-0.380248\pi\)
−0.930063 + 0.367400i \(0.880248\pi\)
\(30\) −0.365605 + 1.61362i −0.0667501 + 0.294605i
\(31\) −1.19996 −0.215518 −0.107759 0.994177i \(-0.534368\pi\)
−0.107759 + 0.994177i \(0.534368\pi\)
\(32\) 5.07702 2.49477i 0.897499 0.441017i
\(33\) −2.06883 −0.360138
\(34\) −2.09908 + 9.26441i −0.359990 + 1.58883i
\(35\) 0 0
\(36\) −1.96551 + 4.11477i −0.327585 + 0.685795i
\(37\) −2.25002 + 2.25002i −0.369901 + 0.369901i −0.867441 0.497540i \(-0.834237\pi\)
0.497540 + 0.867441i \(0.334237\pi\)
\(38\) −4.98913 + 3.14593i −0.809343 + 0.510337i
\(39\) 2.28702i 0.366217i
\(40\) −0.455088 3.87323i −0.0719557 0.612412i
\(41\) 3.94994i 0.616877i −0.951244 0.308438i \(-0.900194\pi\)
0.951244 0.308438i \(-0.0998064\pi\)
\(42\) 0 0
\(43\) −7.02292 + 7.02292i −1.07098 + 1.07098i −0.0737045 + 0.997280i \(0.523482\pi\)
−0.997280 + 0.0737045i \(0.976518\pi\)
\(44\) 4.59768 1.62519i 0.693126 0.245007i
\(45\) 2.22298 + 2.22298i 0.331383 + 0.331383i
\(46\) −7.30842 1.65591i −1.07757 0.244150i
\(47\) 3.06186 0.446619 0.223309 0.974748i \(-0.428314\pi\)
0.223309 + 0.974748i \(0.428314\pi\)
\(48\) −0.358595 + 3.37499i −0.0517588 + 0.487138i
\(49\) 0 0
\(50\) 4.27413 + 0.968410i 0.604453 + 0.136954i
\(51\) −4.03004 4.03004i −0.564318 0.564318i
\(52\) 1.79659 + 5.08258i 0.249143 + 0.704827i
\(53\) −3.01877 + 3.01877i −0.414660 + 0.414660i −0.883358 0.468698i \(-0.844723\pi\)
0.468698 + 0.883358i \(0.344723\pi\)
\(54\) −3.37937 5.35935i −0.459874 0.729315i
\(55\) 3.36187i 0.453315i
\(56\) 0 0
\(57\) 3.53876i 0.468721i
\(58\) −5.12609 + 3.23229i −0.673088 + 0.424420i
\(59\) −4.96785 + 4.96785i −0.646759 + 0.646759i −0.952208 0.305449i \(-0.901193\pi\)
0.305449 + 0.952208i \(0.401193\pi\)
\(60\) 2.11133 + 1.00852i 0.272572 + 0.130200i
\(61\) 9.69194 + 9.69194i 1.24093 + 1.24093i 0.959617 + 0.281308i \(0.0907684\pi\)
0.281308 + 0.959617i \(0.409232\pi\)
\(62\) −0.374991 + 1.65504i −0.0476240 + 0.210191i
\(63\) 0 0
\(64\) −1.85433 7.78212i −0.231791 0.972766i
\(65\) 3.71643 0.460967
\(66\) −0.646519 + 2.85345i −0.0795810 + 0.351235i
\(67\) 3.55596 + 3.55596i 0.434430 + 0.434430i 0.890132 0.455702i \(-0.150612\pi\)
−0.455702 + 0.890132i \(0.650612\pi\)
\(68\) 12.1220 + 5.79033i 1.47001 + 0.702181i
\(69\) 3.17918 3.17918i 0.382728 0.382728i
\(70\) 0 0
\(71\) 11.5771i 1.37395i −0.726682 0.686974i \(-0.758939\pi\)
0.726682 0.686974i \(-0.241061\pi\)
\(72\) 5.06108 + 3.99682i 0.596454 + 0.471030i
\(73\) 10.3271i 1.20869i −0.796722 0.604346i \(-0.793434\pi\)
0.796722 0.604346i \(-0.206566\pi\)
\(74\) 2.40020 + 3.80648i 0.279018 + 0.442495i
\(75\) −1.85925 + 1.85925i −0.214688 + 0.214688i
\(76\) 2.77991 + 7.86439i 0.318877 + 0.902107i
\(77\) 0 0
\(78\) −3.15439 0.714705i −0.357164 0.0809244i
\(79\) 4.06883 0.457780 0.228890 0.973452i \(-0.426490\pi\)
0.228890 + 0.973452i \(0.426490\pi\)
\(80\) −5.48439 0.582721i −0.613173 0.0651501i
\(81\) −3.03880 −0.337644
\(82\) −5.44797 1.23437i −0.601627 0.136314i
\(83\) −9.17886 9.17886i −1.00751 1.00751i −0.999972 0.00753873i \(-0.997600\pi\)
−0.00753873 0.999972i \(-0.502400\pi\)
\(84\) 0 0
\(85\) 6.54884 6.54884i 0.710322 0.710322i
\(86\) 7.49169 + 11.8811i 0.807850 + 1.28117i
\(87\) 3.63591i 0.389810i
\(88\) −0.804756 6.84925i −0.0857873 0.730132i
\(89\) 16.9287i 1.79444i 0.441582 + 0.897221i \(0.354417\pi\)
−0.441582 + 0.897221i \(0.645583\pi\)
\(90\) 3.76075 2.37136i 0.396418 0.249964i
\(91\) 0 0
\(92\) −4.56783 + 9.56270i −0.476229 + 0.996980i
\(93\) −0.719947 0.719947i −0.0746551 0.0746551i
\(94\) 0.956845 4.22309i 0.0986910 0.435578i
\(95\) 5.75052 0.589991
\(96\) 4.54291 + 1.54929i 0.463659 + 0.158124i
\(97\) 2.51522 0.255382 0.127691 0.991814i \(-0.459243\pi\)
0.127691 + 0.991814i \(0.459243\pi\)
\(98\) 0 0
\(99\) 3.93102 + 3.93102i 0.395082 + 0.395082i
\(100\) 2.67137 5.59247i 0.267137 0.559247i
\(101\) 8.56282 8.56282i 0.852033 0.852033i −0.138351 0.990383i \(-0.544180\pi\)
0.990383 + 0.138351i \(0.0441801\pi\)
\(102\) −6.81785 + 4.29904i −0.675067 + 0.425668i
\(103\) 17.8356i 1.75739i −0.477382 0.878696i \(-0.658414\pi\)
0.477382 0.878696i \(-0.341586\pi\)
\(104\) 7.57161 0.889630i 0.742457 0.0872354i
\(105\) 0 0
\(106\) 3.22027 + 5.10703i 0.312781 + 0.496039i
\(107\) 8.49285 8.49285i 0.821034 0.821034i −0.165222 0.986256i \(-0.552834\pi\)
0.986256 + 0.165222i \(0.0528341\pi\)
\(108\) −8.44797 + 2.98619i −0.812906 + 0.287347i
\(109\) 7.26700 + 7.26700i 0.696052 + 0.696052i 0.963557 0.267504i \(-0.0861990\pi\)
−0.267504 + 0.963557i \(0.586199\pi\)
\(110\) −4.63687 1.05060i −0.442109 0.100171i
\(111\) −2.69992 −0.256265
\(112\) 0 0
\(113\) −13.8351 −1.30150 −0.650749 0.759293i \(-0.725545\pi\)
−0.650749 + 0.759293i \(0.725545\pi\)
\(114\) −4.88085 1.10588i −0.457134 0.103575i
\(115\) 5.16619 + 5.16619i 0.481750 + 0.481750i
\(116\) 2.85622 + 8.08028i 0.265194 + 0.750235i
\(117\) −4.34560 + 4.34560i −0.401751 + 0.401751i
\(118\) 5.29945 + 8.40440i 0.487854 + 0.773688i
\(119\) 0 0
\(120\) 2.05081 2.59690i 0.187213 0.237063i
\(121\) 5.05502i 0.459547i
\(122\) 16.3964 10.3389i 1.48446 0.936038i
\(123\) 2.36988 2.36988i 0.213685 0.213685i
\(124\) 2.16554 + 1.03442i 0.194471 + 0.0928934i
\(125\) −7.89615 7.89615i −0.706253 0.706253i
\(126\) 0 0
\(127\) 14.1434 1.25502 0.627512 0.778607i \(-0.284073\pi\)
0.627512 + 0.778607i \(0.284073\pi\)
\(128\) −11.3130 + 0.125645i −0.999938 + 0.0111055i
\(129\) −8.42719 −0.741973
\(130\) 1.16140 5.12590i 0.101862 0.449572i
\(131\) 3.04995 + 3.04995i 0.266475 + 0.266475i 0.827678 0.561203i \(-0.189661\pi\)
−0.561203 + 0.827678i \(0.689661\pi\)
\(132\) 3.73359 + 1.78343i 0.324967 + 0.155228i
\(133\) 0 0
\(134\) 6.01583 3.79332i 0.519688 0.327693i
\(135\) 6.17724i 0.531652i
\(136\) 11.7745 14.9098i 1.00966 1.27851i
\(137\) 11.5811i 0.989440i 0.869052 + 0.494720i \(0.164729\pi\)
−0.869052 + 0.494720i \(0.835271\pi\)
\(138\) −3.39139 5.37840i −0.288694 0.457840i
\(139\) 2.25088 2.25088i 0.190917 0.190917i −0.605175 0.796092i \(-0.706897\pi\)
0.796092 + 0.605175i \(0.206897\pi\)
\(140\) 0 0
\(141\) 1.83705 + 1.83705i 0.154708 + 0.154708i
\(142\) −15.9677 3.61789i −1.33998 0.303607i
\(143\) 6.57197 0.549576
\(144\) 7.09424 5.73149i 0.591186 0.477625i
\(145\) 5.90838 0.490665
\(146\) −14.2436 3.22725i −1.17881 0.267089i
\(147\) 0 0
\(148\) 6.00018 2.12095i 0.493212 0.174341i
\(149\) −2.29883 + 2.29883i −0.188327 + 0.188327i −0.794973 0.606645i \(-0.792515\pi\)
0.606645 + 0.794973i \(0.292515\pi\)
\(150\) 1.98336 + 3.14541i 0.161940 + 0.256821i
\(151\) 18.1587i 1.47774i −0.673850 0.738868i \(-0.735361\pi\)
0.673850 0.738868i \(-0.264639\pi\)
\(152\) 11.7157 1.37655i 0.950270 0.111653i
\(153\) 15.3150i 1.23815i
\(154\) 0 0
\(155\) 1.16992 1.16992i 0.0939703 0.0939703i
\(156\) −1.97152 + 4.12735i −0.157848 + 0.330453i
\(157\) 10.8110 + 10.8110i 0.862816 + 0.862816i 0.991664 0.128849i \(-0.0411281\pi\)
−0.128849 + 0.991664i \(0.541128\pi\)
\(158\) 1.27153 5.61195i 0.101157 0.446463i
\(159\) −3.62239 −0.287275
\(160\) −2.51761 + 7.38226i −0.199035 + 0.583619i
\(161\) 0 0
\(162\) −0.949637 + 4.19127i −0.0746106 + 0.329298i
\(163\) −6.43105 6.43105i −0.503719 0.503719i 0.408873 0.912591i \(-0.365922\pi\)
−0.912591 + 0.408873i \(0.865922\pi\)
\(164\) −3.40503 + 7.12838i −0.265888 + 0.556633i
\(165\) 2.01705 2.01705i 0.157027 0.157027i
\(166\) −15.5284 + 9.79154i −1.20524 + 0.759971i
\(167\) 0.661950i 0.0512232i 0.999672 + 0.0256116i \(0.00815332\pi\)
−0.999672 + 0.0256116i \(0.991847\pi\)
\(168\) 0 0
\(169\) 5.73492i 0.441148i
\(170\) −6.98597 11.0791i −0.535800 0.849725i
\(171\) −6.72405 + 6.72405i −0.514201 + 0.514201i
\(172\) 18.7282 6.62006i 1.42801 0.504775i
\(173\) −6.35590 6.35590i −0.483230 0.483230i 0.422932 0.906162i \(-0.361001\pi\)
−0.906162 + 0.422932i \(0.861001\pi\)
\(174\) −5.01484 1.13624i −0.380174 0.0861379i
\(175\) 0 0
\(176\) −9.69834 1.03046i −0.731040 0.0776735i
\(177\) −5.96120 −0.448071
\(178\) 23.3490 + 5.29030i 1.75008 + 0.396525i
\(179\) −7.61603 7.61603i −0.569249 0.569249i 0.362669 0.931918i \(-0.381866\pi\)
−0.931918 + 0.362669i \(0.881866\pi\)
\(180\) −2.09546 5.92809i −0.156187 0.441854i
\(181\) −13.9902 + 13.9902i −1.03989 + 1.03989i −0.0407146 + 0.999171i \(0.512963\pi\)
−0.999171 + 0.0407146i \(0.987037\pi\)
\(182\) 0 0
\(183\) 11.6299i 0.859707i
\(184\) 11.7619 + 9.28858i 0.867100 + 0.684763i
\(185\) 4.38740i 0.322568i
\(186\) −1.21798 + 0.768004i −0.0893064 + 0.0563127i
\(187\) 11.5807 11.5807i 0.846862 0.846862i
\(188\) −5.52569 2.63946i −0.403002 0.192503i
\(189\) 0 0
\(190\) 1.79706 7.93143i 0.130373 0.575406i
\(191\) −22.4422 −1.62386 −0.811929 0.583756i \(-0.801582\pi\)
−0.811929 + 0.583756i \(0.801582\pi\)
\(192\) 3.55655 5.78166i 0.256672 0.417255i
\(193\) −6.31408 −0.454498 −0.227249 0.973837i \(-0.572973\pi\)
−0.227249 + 0.973837i \(0.572973\pi\)
\(194\) 0.786018 3.46913i 0.0564328 0.249069i
\(195\) 2.22978 + 2.22978i 0.159678 + 0.159678i
\(196\) 0 0
\(197\) 3.81709 3.81709i 0.271957 0.271957i −0.557931 0.829887i \(-0.688405\pi\)
0.829887 + 0.557931i \(0.188405\pi\)
\(198\) 6.65033 4.19341i 0.472618 0.298013i
\(199\) 25.6304i 1.81689i −0.418005 0.908445i \(-0.637270\pi\)
0.418005 0.908445i \(-0.362730\pi\)
\(200\) −6.87863 5.43216i −0.486392 0.384112i
\(201\) 4.26700i 0.300971i
\(202\) −9.13439 14.4862i −0.642693 1.01925i
\(203\) 0 0
\(204\) 3.79886 + 10.7470i 0.265973 + 0.752441i
\(205\) 3.85107 + 3.85107i 0.268970 + 0.268970i
\(206\) −24.5998 5.57369i −1.71395 0.388338i
\(207\) −12.0816 −0.839729
\(208\) 1.13913 10.7212i 0.0789847 0.743380i
\(209\) 10.1690 0.703401
\(210\) 0 0
\(211\) 0.737145 + 0.737145i 0.0507472 + 0.0507472i 0.732025 0.681278i \(-0.238575\pi\)
−0.681278 + 0.732025i \(0.738575\pi\)
\(212\) 8.05024 2.84561i 0.552893 0.195437i
\(213\) 6.94600 6.94600i 0.475932 0.475932i
\(214\) −9.05974 14.3678i −0.619311 0.982165i
\(215\) 13.6943i 0.933941i
\(216\) 1.47869 + 12.5851i 0.100612 + 0.856307i
\(217\) 0 0
\(218\) 12.2940 7.75207i 0.832655 0.525036i
\(219\) 6.19601 6.19601i 0.418688 0.418688i
\(220\) −2.89809 + 6.06711i −0.195389 + 0.409045i
\(221\) 12.8020 + 12.8020i 0.861158 + 0.861158i
\(222\) −0.843737 + 3.72388i −0.0566279 + 0.249930i
\(223\) 5.76178 0.385838 0.192919 0.981215i \(-0.438205\pi\)
0.192919 + 0.981215i \(0.438205\pi\)
\(224\) 0 0
\(225\) 7.06558 0.471039
\(226\) −4.32353 + 19.0821i −0.287597 + 1.26932i
\(227\) 18.2179 + 18.2179i 1.20916 + 1.20916i 0.971299 + 0.237864i \(0.0764472\pi\)
0.237864 + 0.971299i \(0.423553\pi\)
\(228\) −3.05058 + 6.38634i −0.202029 + 0.422946i
\(229\) −0.512762 + 0.512762i −0.0338843 + 0.0338843i −0.723846 0.689962i \(-0.757627\pi\)
0.689962 + 0.723846i \(0.257627\pi\)
\(230\) 8.73995 5.51103i 0.576295 0.363387i
\(231\) 0 0
\(232\) 12.0373 1.41433i 0.790290 0.0928556i
\(233\) 14.4425i 0.946160i 0.881019 + 0.473080i \(0.156858\pi\)
−0.881019 + 0.473080i \(0.843142\pi\)
\(234\) 4.63567 + 7.35171i 0.303043 + 0.480596i
\(235\) −2.98522 + 2.98522i −0.194734 + 0.194734i
\(236\) 13.2479 4.68288i 0.862365 0.304829i
\(237\) 2.44121 + 2.44121i 0.158574 + 0.158574i
\(238\) 0 0
\(239\) −7.34716 −0.475248 −0.237624 0.971357i \(-0.576369\pi\)
−0.237624 + 0.971357i \(0.576369\pi\)
\(240\) −2.94089 3.64013i −0.189834 0.234970i
\(241\) −3.25347 −0.209575 −0.104787 0.994495i \(-0.533416\pi\)
−0.104787 + 0.994495i \(0.533416\pi\)
\(242\) 6.97216 + 1.57972i 0.448187 + 0.101548i
\(243\) −11.3270 11.3270i −0.726625 0.726625i
\(244\) −9.13598 25.8458i −0.584871 1.65461i
\(245\) 0 0
\(246\) −2.52806 4.00926i −0.161184 0.255621i
\(247\) 11.2414i 0.715275i
\(248\) 2.10346 2.66357i 0.133570 0.169137i
\(249\) 11.0142i 0.697998i
\(250\) −13.3584 + 8.42321i −0.844858 + 0.532731i
\(251\) −2.08074 + 2.08074i −0.131335 + 0.131335i −0.769719 0.638383i \(-0.779604\pi\)
0.638383 + 0.769719i \(0.279604\pi\)
\(252\) 0 0
\(253\) 9.13566 + 9.13566i 0.574354 + 0.574354i
\(254\) 4.41987 19.5073i 0.277328 1.22400i
\(255\) 7.85832 0.492107
\(256\) −3.36207 + 15.6428i −0.210129 + 0.977674i
\(257\) −10.9620 −0.683788 −0.341894 0.939738i \(-0.611068\pi\)
−0.341894 + 0.939738i \(0.611068\pi\)
\(258\) −2.63353 + 11.6232i −0.163957 + 0.723631i
\(259\) 0 0
\(260\) −6.70698 3.20373i −0.415949 0.198687i
\(261\) −6.90864 + 6.90864i −0.427634 + 0.427634i
\(262\) 5.15978 3.25353i 0.318772 0.201004i
\(263\) 10.1931i 0.628534i −0.949335 0.314267i \(-0.898241\pi\)
0.949335 0.314267i \(-0.101759\pi\)
\(264\) 3.62656 4.59223i 0.223199 0.282633i
\(265\) 5.88642i 0.361600i
\(266\) 0 0
\(267\) −10.1569 + 10.1569i −0.621590 + 0.621590i
\(268\) −3.35198 9.48278i −0.204755 0.579253i
\(269\) −1.75782 1.75782i −0.107176 0.107176i 0.651485 0.758661i \(-0.274146\pi\)
−0.758661 + 0.651485i \(0.774146\pi\)
\(270\) 8.51999 + 1.93041i 0.518510 + 0.117481i
\(271\) 5.66166 0.343921 0.171961 0.985104i \(-0.444990\pi\)
0.171961 + 0.985104i \(0.444990\pi\)
\(272\) −16.8848 20.8994i −1.02379 1.26721i
\(273\) 0 0
\(274\) 15.9733 + 3.61914i 0.964981 + 0.218640i
\(275\) −5.34273 5.34273i −0.322179 0.322179i
\(276\) −8.47800 + 2.99681i −0.510316 + 0.180387i
\(277\) 21.3329 21.3329i 1.28177 1.28177i 0.342106 0.939662i \(-0.388860\pi\)
0.939662 0.342106i \(-0.111140\pi\)
\(278\) −2.40112 3.80794i −0.144010 0.228385i
\(279\) 2.73596i 0.163798i
\(280\) 0 0
\(281\) 1.60009i 0.0954532i −0.998860 0.0477266i \(-0.984802\pi\)
0.998860 0.0477266i \(-0.0151976\pi\)
\(282\) 3.10784 1.95967i 0.185069 0.116697i
\(283\) −14.3940 + 14.3940i −0.855635 + 0.855635i −0.990820 0.135186i \(-0.956837\pi\)
0.135186 + 0.990820i \(0.456837\pi\)
\(284\) −9.97997 + 20.8930i −0.592203 + 1.23977i
\(285\) 3.45019 + 3.45019i 0.204371 + 0.204371i
\(286\) 2.05377 9.06441i 0.121442 0.535990i
\(287\) 0 0
\(288\) −5.68821 11.5759i −0.335181 0.682115i
\(289\) 28.1177 1.65398
\(290\) 1.84640 8.14916i 0.108424 0.478535i
\(291\) 1.50908 + 1.50908i 0.0884638 + 0.0884638i
\(292\) −8.90240 + 18.6371i −0.520974 + 1.09065i
\(293\) −0.267863 + 0.267863i −0.0156487 + 0.0156487i −0.714888 0.699239i \(-0.753522\pi\)
0.699239 + 0.714888i \(0.253522\pi\)
\(294\) 0 0
\(295\) 9.68700i 0.563999i
\(296\) −1.05024 8.93858i −0.0610442 0.519544i
\(297\) 10.9235i 0.633849i
\(298\) 2.45227 + 3.88906i 0.142056 + 0.225287i
\(299\) −10.0992 + 10.0992i −0.584049 + 0.584049i
\(300\) 4.95812 1.75260i 0.286257 0.101186i
\(301\) 0 0
\(302\) −25.0455 5.67468i −1.44121 0.326541i
\(303\) 10.2750 0.590284
\(304\) 1.76261 16.5891i 0.101092 0.951452i
\(305\) −18.8987 −1.08214
\(306\) 21.1233 + 4.78602i 1.20754 + 0.273598i
\(307\) 12.3805 + 12.3805i 0.706594 + 0.706594i 0.965817 0.259223i \(-0.0834665\pi\)
−0.259223 + 0.965817i \(0.583466\pi\)
\(308\) 0 0
\(309\) 10.7010 10.7010i 0.608756 0.608756i
\(310\) −1.24801 1.97922i −0.0708823 0.112412i
\(311\) 3.69468i 0.209506i −0.994498 0.104753i \(-0.966595\pi\)
0.994498 0.104753i \(-0.0334053\pi\)
\(312\) 5.07656 + 4.00904i 0.287403 + 0.226967i
\(313\) 10.4700i 0.591799i −0.955219 0.295900i \(-0.904381\pi\)
0.955219 0.295900i \(-0.0956194\pi\)
\(314\) 18.2897 11.5327i 1.03215 0.650827i
\(315\) 0 0
\(316\) −7.34295 3.50752i −0.413073 0.197313i
\(317\) −15.7941 15.7941i −0.887085 0.887085i 0.107157 0.994242i \(-0.465825\pi\)
−0.994242 + 0.107157i \(0.965825\pi\)
\(318\) −1.13201 + 4.99620i −0.0634802 + 0.280173i
\(319\) 10.4481 0.584982
\(320\) 9.39525 + 5.77942i 0.525210 + 0.323079i
\(321\) 10.1910 0.568809
\(322\) 0 0
\(323\) 19.8089 + 19.8089i 1.10219 + 1.10219i
\(324\) 5.48406 + 2.61958i 0.304670 + 0.145532i
\(325\) 5.90620 5.90620i 0.327617 0.327617i
\(326\) −10.8798 + 6.86032i −0.602576 + 0.379958i
\(327\) 8.72008i 0.482221i
\(328\) 8.76777 + 6.92405i 0.484119 + 0.382317i
\(329\) 0 0
\(330\) −2.15169 3.41236i −0.118446 0.187844i
\(331\) 6.76260 6.76260i 0.371706 0.371706i −0.496392 0.868098i \(-0.665342\pi\)
0.868098 + 0.496392i \(0.165342\pi\)
\(332\) 8.65233 + 24.4775i 0.474858 + 1.34338i
\(333\) 5.13016 + 5.13016i 0.281131 + 0.281131i
\(334\) 0.912997 + 0.206862i 0.0499570 + 0.0113190i
\(335\) −6.93391 −0.378840
\(336\) 0 0
\(337\) −27.1949 −1.48140 −0.740700 0.671836i \(-0.765506\pi\)
−0.740700 + 0.671836i \(0.765506\pi\)
\(338\) −7.90991 1.79219i −0.430242 0.0974821i
\(339\) −8.30076 8.30076i −0.450835 0.450835i
\(340\) −17.4640 + 6.17318i −0.947117 + 0.334788i
\(341\) 2.06883 2.06883i 0.112034 0.112034i
\(342\) 7.17288 + 11.3755i 0.387865 + 0.615115i
\(343\) 0 0
\(344\) −3.27810 27.8997i −0.176743 1.50425i
\(345\) 6.19920i 0.333754i
\(346\) −10.7526 + 6.78015i −0.578065 + 0.364503i
\(347\) −4.18157 + 4.18157i −0.224479 + 0.224479i −0.810381 0.585903i \(-0.800740\pi\)
0.585903 + 0.810381i \(0.300740\pi\)
\(348\) −3.13432 + 6.56166i −0.168017 + 0.351742i
\(349\) 24.5827 + 24.5827i 1.31588 + 1.31588i 0.917004 + 0.398877i \(0.130600\pi\)
0.398877 + 0.917004i \(0.369400\pi\)
\(350\) 0 0
\(351\) −12.0756 −0.644548
\(352\) −4.45203 + 13.0545i −0.237294 + 0.695805i
\(353\) −33.3458 −1.77482 −0.887409 0.460982i \(-0.847497\pi\)
−0.887409 + 0.460982i \(0.847497\pi\)
\(354\) −1.86290 + 8.22201i −0.0990121 + 0.436995i
\(355\) 11.2873 + 11.2873i 0.599068 + 0.599068i
\(356\) 14.5933 30.5510i 0.773445 1.61920i
\(357\) 0 0
\(358\) −12.8845 + 8.12440i −0.680966 + 0.429388i
\(359\) 7.89898i 0.416892i 0.978034 + 0.208446i \(0.0668406\pi\)
−0.978034 + 0.208446i \(0.933159\pi\)
\(360\) −8.83118 + 1.03762i −0.465444 + 0.0546876i
\(361\) 1.60588i 0.0845202i
\(362\) 14.9241 + 23.6681i 0.784392 + 1.24397i
\(363\) −3.03290 + 3.03290i −0.159186 + 0.159186i
\(364\) 0 0
\(365\) 10.0686 + 10.0686i 0.527013 + 0.527013i
\(366\) 16.0406 + 3.63439i 0.838455 + 0.189973i
\(367\) −29.5941 −1.54480 −0.772401 0.635136i \(-0.780944\pi\)
−0.772401 + 0.635136i \(0.780944\pi\)
\(368\) 16.4870 13.3199i 0.859442 0.694350i
\(369\) −9.00607 −0.468837
\(370\) −6.05133 1.37108i −0.314594 0.0712791i
\(371\) 0 0
\(372\) 0.678649 + 1.91990i 0.0351863 + 0.0995424i
\(373\) −4.31630 + 4.31630i −0.223490 + 0.223490i −0.809966 0.586477i \(-0.800515\pi\)
0.586477 + 0.809966i \(0.300515\pi\)
\(374\) −12.3537 19.5917i −0.638793 1.01306i
\(375\) 9.47503i 0.489289i
\(376\) −5.36729 + 6.79648i −0.276797 + 0.350502i
\(377\) 11.5500i 0.594857i
\(378\) 0 0
\(379\) −15.1468 + 15.1468i −0.778037 + 0.778037i −0.979497 0.201460i \(-0.935432\pi\)
0.201460 + 0.979497i \(0.435432\pi\)
\(380\) −10.3779 4.95721i −0.532373 0.254300i
\(381\) 8.48573 + 8.48573i 0.434737 + 0.434737i
\(382\) −7.01327 + 30.9534i −0.358830 + 1.58372i
\(383\) −6.62147 −0.338341 −0.169171 0.985587i \(-0.554109\pi\)
−0.169171 + 0.985587i \(0.554109\pi\)
\(384\) −6.86294 6.71217i −0.350223 0.342529i
\(385\) 0 0
\(386\) −1.97318 + 8.70872i −0.100432 + 0.443262i
\(387\) 16.0126 + 16.0126i 0.813967 + 0.813967i
\(388\) −4.53918 2.16824i −0.230442 0.110076i
\(389\) −25.6610 + 25.6610i −1.30106 + 1.30106i −0.373386 + 0.927676i \(0.621803\pi\)
−0.927676 + 0.373386i \(0.878197\pi\)
\(390\) 3.77225 2.37861i 0.191015 0.120446i
\(391\) 35.5921i 1.79997i
\(392\) 0 0
\(393\) 3.65981i 0.184613i
\(394\) −4.07188 6.45760i −0.205138 0.325329i
\(395\) −3.96699 + 3.96699i −0.199601 + 0.199601i
\(396\) −3.70552 10.4830i −0.186209 0.526788i
\(397\) 9.47099 + 9.47099i 0.475336 + 0.475336i 0.903636 0.428301i \(-0.140888\pi\)
−0.428301 + 0.903636i \(0.640888\pi\)
\(398\) −35.3508 8.00960i −1.77198 0.401485i
\(399\) 0 0
\(400\) −9.64193 + 7.78980i −0.482097 + 0.389490i
\(401\) 17.5138 0.874598 0.437299 0.899316i \(-0.355935\pi\)
0.437299 + 0.899316i \(0.355935\pi\)
\(402\) 5.88527 + 1.33346i 0.293531 + 0.0665067i
\(403\) 2.28702 + 2.28702i 0.113925 + 0.113925i
\(404\) −22.8347 + 8.07163i −1.13607 + 0.401579i
\(405\) 2.96274 2.96274i 0.147220 0.147220i
\(406\) 0 0
\(407\) 7.75847i 0.384573i
\(408\) 16.0100 1.88111i 0.792614 0.0931286i
\(409\) 10.3755i 0.513037i 0.966539 + 0.256519i \(0.0825755\pi\)
−0.966539 + 0.256519i \(0.917425\pi\)
\(410\) 6.51508 4.10813i 0.321757 0.202886i
\(411\) −6.94840 + 6.94840i −0.342739 + 0.342739i
\(412\) −15.3751 + 32.1875i −0.757476 + 1.58577i
\(413\) 0 0
\(414\) −3.77555 + 16.6636i −0.185558 + 0.818971i
\(415\) 17.8982 0.878589
\(416\) −14.4312 4.92157i −0.707550 0.241300i
\(417\) 2.70096 0.132266
\(418\) 3.17784 14.0256i 0.155433 0.686013i
\(419\) −12.6045 12.6045i −0.615771 0.615771i 0.328673 0.944444i \(-0.393399\pi\)
−0.944444 + 0.328673i \(0.893399\pi\)
\(420\) 0 0
\(421\) −17.6588 + 17.6588i −0.860635 + 0.860635i −0.991412 0.130777i \(-0.958253\pi\)
0.130777 + 0.991412i \(0.458253\pi\)
\(422\) 1.24707 0.786350i 0.0607065 0.0382789i
\(423\) 6.98121i 0.339438i
\(424\) −1.40908 11.9926i −0.0684308 0.582412i
\(425\) 20.8150i 1.00968i
\(426\) −7.40964 11.7509i −0.358998 0.569335i
\(427\) 0 0
\(428\) −22.6481 + 8.00567i −1.09474 + 0.386969i
\(429\) 3.94304 + 3.94304i 0.190372 + 0.190372i
\(430\) −18.8879 4.27951i −0.910853 0.206377i
\(431\) 9.58438 0.461663 0.230832 0.972994i \(-0.425855\pi\)
0.230832 + 0.972994i \(0.425855\pi\)
\(432\) 17.8201 + 1.89340i 0.857372 + 0.0910964i
\(433\) 0.958633 0.0460690 0.0230345 0.999735i \(-0.492667\pi\)
0.0230345 + 0.999735i \(0.492667\pi\)
\(434\) 0 0
\(435\) 3.54490 + 3.54490i 0.169965 + 0.169965i
\(436\) −6.85014 19.3791i −0.328062 0.928091i
\(437\) −15.6266 + 15.6266i −0.747524 + 0.747524i
\(438\) −6.60960 10.4822i −0.315819 0.500857i
\(439\) 9.97389i 0.476028i 0.971262 + 0.238014i \(0.0764964\pi\)
−0.971262 + 0.238014i \(0.923504\pi\)
\(440\) 7.46242 + 5.89319i 0.355757 + 0.280947i
\(441\) 0 0
\(442\) 21.6579 13.6566i 1.03016 0.649576i
\(443\) −15.4846 + 15.4846i −0.735697 + 0.735697i −0.971742 0.236045i \(-0.924149\pi\)
0.236045 + 0.971742i \(0.424149\pi\)
\(444\) 4.87250 + 2.32746i 0.231239 + 0.110456i
\(445\) −16.5050 16.5050i −0.782412 0.782412i
\(446\) 1.80058 7.94696i 0.0852600 0.376300i
\(447\) −2.75849 −0.130472
\(448\) 0 0
\(449\) −8.77877 −0.414296 −0.207148 0.978310i \(-0.566418\pi\)
−0.207148 + 0.978310i \(0.566418\pi\)
\(450\) 2.20803 9.74523i 0.104087 0.459395i
\(451\) 6.81005 + 6.81005i 0.320673 + 0.320673i
\(452\) 24.9680 + 11.9265i 1.17439 + 0.560975i
\(453\) 10.8948 10.8948i 0.511884 0.511884i
\(454\) 30.8202 19.4339i 1.44646 0.912078i
\(455\) 0 0
\(456\) 7.85507 + 6.20328i 0.367847 + 0.290495i
\(457\) 1.87158i 0.0875486i 0.999041 + 0.0437743i \(0.0139383\pi\)
−0.999041 + 0.0437743i \(0.986062\pi\)
\(458\) 0.546989 + 0.867469i 0.0255591 + 0.0405342i
\(459\) −21.2788 + 21.2788i −0.993209 + 0.993209i
\(460\) −4.86984 13.7768i −0.227058 0.642348i
\(461\) −13.2713 13.2713i −0.618107 0.618107i 0.326939 0.945046i \(-0.393983\pi\)
−0.945046 + 0.326939i \(0.893983\pi\)
\(462\) 0 0
\(463\) −1.89824 −0.0882189 −0.0441095 0.999027i \(-0.514045\pi\)
−0.0441095 + 0.999027i \(0.514045\pi\)
\(464\) 1.81099 17.0445i 0.0840733 0.791272i
\(465\) 1.40385 0.0651021
\(466\) 19.9199 + 4.51335i 0.922771 + 0.209077i
\(467\) −1.08393 1.08393i −0.0501585 0.0501585i 0.681583 0.731741i \(-0.261292\pi\)
−0.731741 + 0.681583i \(0.761292\pi\)
\(468\) 11.5885 4.09633i 0.535681 0.189353i
\(469\) 0 0
\(470\) 3.18448 + 5.05027i 0.146889 + 0.232952i
\(471\) 12.9728i 0.597754i
\(472\) −2.31885 19.7356i −0.106734 0.908406i
\(473\) 24.2163i 1.11347i
\(474\) 4.12994 2.60416i 0.189694 0.119613i
\(475\) 9.13880 9.13880i 0.419317 0.419317i
\(476\) 0 0
\(477\) 6.88296 + 6.88296i 0.315149 + 0.315149i
\(478\) −2.29602 + 10.1336i −0.105018 + 0.463500i
\(479\) 28.2972 1.29293 0.646466 0.762942i \(-0.276246\pi\)
0.646466 + 0.762942i \(0.276246\pi\)
\(480\) −5.93971 + 2.91868i −0.271109 + 0.133219i
\(481\) 8.57672 0.391065
\(482\) −1.01672 + 4.48737i −0.0463105 + 0.204394i
\(483\) 0 0
\(484\) 4.35766 9.12271i 0.198075 0.414668i
\(485\) −2.45227 + 2.45227i −0.111352 + 0.111352i
\(486\) −19.1625 + 12.0830i −0.869228 + 0.548097i
\(487\) 6.19712i 0.280818i 0.990094 + 0.140409i \(0.0448418\pi\)
−0.990094 + 0.140409i \(0.955158\pi\)
\(488\) −38.5029 + 4.52392i −1.74294 + 0.204788i
\(489\) 7.71698i 0.348974i
\(490\) 0 0
\(491\) 21.5658 21.5658i 0.973249 0.973249i −0.0264026 0.999651i \(-0.508405\pi\)
0.999651 + 0.0264026i \(0.00840519\pi\)
\(492\) −6.31982 + 2.23393i −0.284919 + 0.100713i
\(493\) 20.3527 + 20.3527i 0.916638 + 0.916638i
\(494\) 15.5048 + 3.51299i 0.697593 + 0.158057i
\(495\) −7.66525 −0.344527
\(496\) −3.01640 3.73359i −0.135440 0.167643i
\(497\) 0 0
\(498\) −15.1914 3.44199i −0.680743 0.154239i
\(499\) 2.45487 + 2.45487i 0.109895 + 0.109895i 0.759916 0.650021i \(-0.225240\pi\)
−0.650021 + 0.759916i \(0.725240\pi\)
\(500\) 7.44320 + 21.0569i 0.332870 + 0.941692i
\(501\) −0.397156 + 0.397156i −0.0177436 + 0.0177436i
\(502\) 2.21963 + 3.52012i 0.0990671 + 0.157110i
\(503\) 13.1803i 0.587680i 0.955855 + 0.293840i \(0.0949332\pi\)
−0.955855 + 0.293840i \(0.905067\pi\)
\(504\) 0 0
\(505\) 16.6970i 0.743006i
\(506\) 15.4553 9.74546i 0.687073 0.433238i
\(507\) 3.44082 3.44082i 0.152812 0.152812i
\(508\) −25.5243 12.1923i −1.13246 0.540944i
\(509\) 1.53507 + 1.53507i 0.0680410 + 0.0680410i 0.740308 0.672267i \(-0.234679\pi\)
−0.672267 + 0.740308i \(0.734679\pi\)
\(510\) 2.45576 10.8386i 0.108743 0.479942i
\(511\) 0 0
\(512\) 20.5247 + 9.52558i 0.907072 + 0.420975i
\(513\) −18.6849 −0.824957
\(514\) −3.42566 + 15.1193i −0.151099 + 0.666885i
\(515\) 17.3891 + 17.3891i 0.766257 + 0.766257i
\(516\) 15.2084 + 7.26462i 0.669513 + 0.319807i
\(517\) −5.27893 + 5.27893i −0.232167 + 0.232167i
\(518\) 0 0
\(519\) 7.62680i 0.334779i
\(520\) −6.51472 + 8.24945i −0.285689 + 0.361762i
\(521\) 10.0170i 0.438854i −0.975629 0.219427i \(-0.929581\pi\)
0.975629 0.219427i \(-0.0704189\pi\)
\(522\) 7.36979 + 11.6877i 0.322567 + 0.511559i
\(523\) 16.3284 16.3284i 0.713992 0.713992i −0.253376 0.967368i \(-0.581541\pi\)
0.967368 + 0.253376i \(0.0815409\pi\)
\(524\) −2.87500 8.13339i −0.125595 0.355309i
\(525\) 0 0
\(526\) −14.0589 3.18539i −0.612997 0.138890i
\(527\) 8.06007 0.351102
\(528\) −5.20054 6.43704i −0.226324 0.280136i
\(529\) −5.07755 −0.220763
\(530\) −8.11887 1.83953i −0.352661 0.0799042i
\(531\) 11.3270 + 11.3270i 0.491548 + 0.491548i
\(532\) 0 0
\(533\) −7.52828 + 7.52828i −0.326086 + 0.326086i
\(534\) 10.8348 + 17.1830i 0.468869 + 0.743579i
\(535\) 16.5605i 0.715974i
\(536\) −14.1267 + 1.65982i −0.610179 + 0.0716934i
\(537\) 9.13891i 0.394373i
\(538\) −2.97380 + 1.87515i −0.128210 + 0.0808436i
\(539\) 0 0
\(540\) 5.32506 11.1480i 0.229154 0.479732i
\(541\) −6.69916 6.69916i −0.288020 0.288020i 0.548277 0.836297i \(-0.315284\pi\)
−0.836297 + 0.548277i \(0.815284\pi\)
\(542\) 1.76929 7.80887i 0.0759977 0.335420i
\(543\) −16.7877 −0.720427
\(544\) −34.1022 + 16.7573i −1.46212 + 0.718463i
\(545\) −14.1702 −0.606985
\(546\) 0 0
\(547\) −21.2058 21.2058i −0.906695 0.906695i 0.0893091 0.996004i \(-0.471534\pi\)
−0.996004 + 0.0893091i \(0.971534\pi\)
\(548\) 9.98343 20.9002i 0.426471 0.892812i
\(549\) 22.0981 22.0981i 0.943125 0.943125i
\(550\) −9.03861 + 5.69936i −0.385408 + 0.243021i
\(551\) 17.8716i 0.761357i
\(552\) 1.48395 + 12.6298i 0.0631611 + 0.537561i
\(553\) 0 0
\(554\) −22.7568 36.0900i −0.966844 1.53332i
\(555\) 2.63234 2.63234i 0.111737 0.111737i
\(556\) −6.00248 + 2.12176i −0.254562 + 0.0899827i
\(557\) −16.9582 16.9582i −0.718543 0.718543i 0.249764 0.968307i \(-0.419647\pi\)
−0.968307 + 0.249764i \(0.919647\pi\)
\(558\) 3.77359 + 0.855000i 0.159749 + 0.0361950i
\(559\) 26.7703 1.13226
\(560\) 0 0
\(561\) 13.8963 0.586702
\(562\) −2.20693 0.500034i −0.0930936 0.0210927i
\(563\) −7.49559 7.49559i −0.315901 0.315901i 0.531289 0.847191i \(-0.321708\pi\)
−0.847191 + 0.531289i \(0.821708\pi\)
\(564\) −1.73167 4.89891i −0.0729165 0.206281i
\(565\) 13.4888 13.4888i 0.567478 0.567478i
\(566\) 15.3548 + 24.3512i 0.645410 + 1.02356i
\(567\) 0 0
\(568\) 25.6979 + 20.2941i 1.07826 + 0.851520i
\(569\) 44.0529i 1.84679i −0.383848 0.923396i \(-0.625401\pi\)
0.383848 0.923396i \(-0.374599\pi\)
\(570\) 5.83688 3.68048i 0.244480 0.154159i
\(571\) 9.43664 9.43664i 0.394911 0.394911i −0.481523 0.876434i \(-0.659916\pi\)
0.876434 + 0.481523i \(0.159916\pi\)
\(572\) −11.8603 5.66533i −0.495905 0.236880i
\(573\) −13.4648 13.4648i −0.562500 0.562500i
\(574\) 0 0
\(575\) 16.4204 0.684777
\(576\) −17.7437 + 4.22797i −0.739319 + 0.176165i
\(577\) −16.4631 −0.685369 −0.342685 0.939450i \(-0.611336\pi\)
−0.342685 + 0.939450i \(0.611336\pi\)
\(578\) 8.78690 38.7815i 0.365487 1.61310i
\(579\) −3.78831 3.78831i −0.157437 0.157437i
\(580\) −10.6628 5.09330i −0.442747 0.211488i
\(581\) 0 0
\(582\) 2.55300 1.60981i 0.105825 0.0667287i
\(583\) 10.4093i 0.431108i
\(584\) 22.9232 + 18.1028i 0.948570 + 0.749101i
\(585\) 8.47366i 0.350343i
\(586\) 0.285743 + 0.453160i 0.0118039 + 0.0187199i
\(587\) 21.5452 21.5452i 0.889267 0.889267i −0.105186 0.994453i \(-0.533544\pi\)
0.994453 + 0.105186i \(0.0335438\pi\)
\(588\) 0 0
\(589\) 3.53876 + 3.53876i 0.145812 + 0.145812i
\(590\) −13.3608 3.02723i −0.550057 0.124629i
\(591\) 4.58034 0.188410
\(592\) −12.6568 1.34479i −0.520190 0.0552706i
\(593\) −26.2918 −1.07967 −0.539837 0.841770i \(-0.681514\pi\)
−0.539837 + 0.841770i \(0.681514\pi\)
\(594\) 15.0663 + 3.41366i 0.618180 + 0.140064i
\(595\) 0 0
\(596\) 6.13034 2.16696i 0.251109 0.0887620i
\(597\) 15.3777 15.3777i 0.629366 0.629366i
\(598\) 10.7733 + 17.0853i 0.440552 + 0.698671i
\(599\) 27.8214i 1.13675i 0.822769 + 0.568376i \(0.192428\pi\)
−0.822769 + 0.568376i \(0.807572\pi\)
\(600\) −0.867846 7.38620i −0.0354297 0.301541i
\(601\) 18.3631i 0.749047i −0.927217 0.374523i \(-0.877806\pi\)
0.927217 0.374523i \(-0.122194\pi\)
\(602\) 0 0
\(603\) 8.10778 8.10778i 0.330174 0.330174i
\(604\) −15.6536 + 32.7707i −0.636938 + 1.33342i
\(605\) −4.92849 4.92849i −0.200372 0.200372i
\(606\) 3.21099 14.1718i 0.130437 0.575692i
\(607\) −9.91188 −0.402311 −0.201155 0.979559i \(-0.564470\pi\)
−0.201155 + 0.979559i \(0.564470\pi\)
\(608\) −22.3298 7.61526i −0.905593 0.308839i
\(609\) 0 0
\(610\) −5.90592 + 26.0661i −0.239124 + 1.05539i
\(611\) −5.83567 5.83567i −0.236086 0.236086i
\(612\) 13.2023 27.6388i 0.533670 1.11723i
\(613\) 30.5010 30.5010i 1.23193 1.23193i 0.268702 0.963223i \(-0.413405\pi\)
0.963223 0.268702i \(-0.0865948\pi\)
\(614\) 20.9449 13.2069i 0.845266 0.532988i
\(615\) 4.62112i 0.186341i
\(616\) 0 0
\(617\) 7.78309i 0.313336i −0.987651 0.156668i \(-0.949925\pi\)
0.987651 0.156668i \(-0.0500752\pi\)
\(618\) −11.4152 18.1034i −0.459188 0.728227i
\(619\) −27.6514 + 27.6514i −1.11140 + 1.11140i −0.118441 + 0.992961i \(0.537790\pi\)
−0.992961 + 0.118441i \(0.962210\pi\)
\(620\) −3.11986 + 1.10281i −0.125297 + 0.0442899i
\(621\) −16.7862 16.7862i −0.673608 0.673608i
\(622\) −5.09591 1.15460i −0.204327 0.0462954i
\(623\) 0 0
\(624\) 7.11593 5.74902i 0.284865 0.230145i
\(625\) −0.0973335 −0.00389334
\(626\) −14.4408 3.27192i −0.577170 0.130772i
\(627\) 6.10115 + 6.10115i 0.243656 + 0.243656i
\(628\) −10.1909 28.8301i −0.406661 1.15045i
\(629\) 15.1133 15.1133i 0.602607 0.602607i
\(630\) 0 0
\(631\) 6.10120i 0.242885i −0.992598 0.121442i \(-0.961248\pi\)
0.992598 0.121442i \(-0.0387520\pi\)
\(632\) −7.13246 + 9.03168i −0.283714 + 0.359261i
\(633\) 0.884542i 0.0351574i
\(634\) −26.7198 + 16.8483i −1.06118 + 0.669133i
\(635\) −13.7894 + 13.7894i −0.547215 + 0.547215i
\(636\) 6.53727 + 3.12267i 0.259220 + 0.123822i
\(637\) 0 0
\(638\) 3.26508 14.4106i 0.129266 0.570521i
\(639\) −26.3964 −1.04422
\(640\) 10.9073 11.1523i 0.431151 0.440835i
\(641\) 8.80169 0.347646 0.173823 0.984777i \(-0.444388\pi\)
0.173823 + 0.984777i \(0.444388\pi\)
\(642\) 3.18474 14.0560i 0.125692 0.554747i
\(643\) −20.3898 20.3898i −0.804095 0.804095i 0.179638 0.983733i \(-0.442507\pi\)
−0.983733 + 0.179638i \(0.942507\pi\)
\(644\) 0 0
\(645\) 8.21625 8.21625i 0.323515 0.323515i
\(646\) 33.5118 21.1311i 1.31850 0.831392i
\(647\) 50.8466i 1.99898i −0.0318632 0.999492i \(-0.510144\pi\)
0.0318632 0.999492i \(-0.489856\pi\)
\(648\) 5.32686 6.74529i 0.209259 0.264980i
\(649\) 17.1300i 0.672413i
\(650\) −6.30044 9.99187i −0.247124 0.391913i
\(651\) 0 0
\(652\) 6.06215 + 17.1499i 0.237412 + 0.671641i
\(653\) −1.69069 1.69069i −0.0661618 0.0661618i 0.673252 0.739413i \(-0.264897\pi\)
−0.739413 + 0.673252i \(0.764897\pi\)
\(654\) 12.0272 + 2.72506i 0.470301 + 0.106558i
\(655\) −5.94722 −0.232377
\(656\) 12.2900 9.92918i 0.479843 0.387669i
\(657\) −23.5463 −0.918627
\(658\) 0 0
\(659\) −3.01195 3.01195i −0.117329 0.117329i 0.646005 0.763334i \(-0.276439\pi\)
−0.763334 + 0.646005i \(0.776439\pi\)
\(660\) −5.37892 + 1.90134i −0.209374 + 0.0740097i
\(661\) −1.93721 + 1.93721i −0.0753488 + 0.0753488i −0.743777 0.668428i \(-0.766967\pi\)
0.668428 + 0.743777i \(0.266967\pi\)
\(662\) −7.21400 11.4407i −0.280380 0.444655i
\(663\) 15.3619i 0.596606i
\(664\) 36.4646 4.28443i 1.41510 0.166268i
\(665\) 0 0
\(666\) 8.67899 5.47259i 0.336304 0.212059i
\(667\) −16.0556 + 16.0556i −0.621676 + 0.621676i
\(668\) 0.570631 1.19461i 0.0220784 0.0462208i
\(669\) 3.45694 + 3.45694i 0.133653 + 0.133653i
\(670\) −2.16688 + 9.56362i −0.0837137 + 0.369475i
\(671\) −33.4196 −1.29015
\(672\) 0 0
\(673\) 17.6937 0.682041 0.341021 0.940056i \(-0.389227\pi\)
0.341021 + 0.940056i \(0.389227\pi\)
\(674\) −8.49852 + 37.5087i −0.327351 + 1.44478i
\(675\) 9.81696 + 9.81696i 0.377855 + 0.377855i
\(676\) −4.94376 + 10.3497i −0.190145 + 0.398066i
\(677\) −11.2232 + 11.2232i −0.431342 + 0.431342i −0.889085 0.457742i \(-0.848658\pi\)
0.457742 + 0.889085i \(0.348658\pi\)
\(678\) −14.0429 + 8.85483i −0.539314 + 0.340068i
\(679\) 0 0
\(680\) 3.05681 + 26.0164i 0.117223 + 0.997684i
\(681\) 21.8606i 0.837702i
\(682\) −2.20693 3.49997i −0.0845076 0.134021i
\(683\) 6.78769 6.78769i 0.259724 0.259724i −0.565218 0.824942i \(-0.691208\pi\)
0.824942 + 0.565218i \(0.191208\pi\)
\(684\) 17.9312 6.33834i 0.685617 0.242352i
\(685\) −11.2912 11.2912i −0.431415 0.431415i
\(686\) 0 0
\(687\) −0.615292 −0.0234749
\(688\) −39.5052 4.19746i −1.50612 0.160027i
\(689\) 11.5071 0.438385
\(690\) 8.55028 + 1.93728i 0.325503 + 0.0737509i
\(691\) 34.3472 + 34.3472i 1.30663 + 1.30663i 0.923833 + 0.382795i \(0.125038\pi\)
0.382795 + 0.923833i \(0.374962\pi\)
\(692\) 5.99130 + 16.9494i 0.227755 + 0.644321i
\(693\) 0 0
\(694\) 4.46069 + 7.07421i 0.169326 + 0.268533i
\(695\) 4.38908i 0.166487i
\(696\) 8.07071 + 6.37357i 0.305919 + 0.241590i
\(697\) 26.5316i 1.00496i
\(698\) 41.5880 26.2236i 1.57413 0.992577i
\(699\) −8.66519 + 8.66519i −0.327747 + 0.327747i
\(700\) 0 0
\(701\) 4.68514 + 4.68514i 0.176955 + 0.176955i 0.790027 0.613072i \(-0.210066\pi\)
−0.613072 + 0.790027i \(0.710066\pi\)
\(702\) −3.77368 + 16.6553i −0.142428 + 0.628615i
\(703\) 13.2709 0.500523
\(704\) 16.6141 + 10.2201i 0.626168 + 0.385183i
\(705\) −3.58214 −0.134911
\(706\) −10.4207 + 45.9923i −0.392189 + 1.73094i
\(707\) 0 0
\(708\) 10.7581 + 5.13883i 0.404313 + 0.193129i
\(709\) 17.0134 17.0134i 0.638951 0.638951i −0.311346 0.950297i \(-0.600780\pi\)
0.950297 + 0.311346i \(0.100780\pi\)
\(710\) 19.0954 12.0407i 0.716637 0.451880i
\(711\) 9.27715i 0.347920i
\(712\) −37.5771 29.6752i −1.40826 1.11213i
\(713\) 6.35836i 0.238122i
\(714\) 0 0
\(715\) −6.40747 + 6.40747i −0.239626 + 0.239626i
\(716\) 7.17915 + 20.3099i 0.268298 + 0.759016i
\(717\) −4.40814 4.40814i −0.164625 0.164625i
\(718\) 10.8947 + 2.46847i 0.406587 + 0.0921223i
\(719\) 24.5042 0.913853 0.456927 0.889504i \(-0.348950\pi\)
0.456927 + 0.889504i \(0.348950\pi\)
\(720\) −1.32863 + 12.5047i −0.0495152 + 0.466023i
\(721\) 0 0
\(722\) −2.21492 0.501845i −0.0824308 0.0186768i
\(723\) −1.95201 1.95201i −0.0725961 0.0725961i
\(724\) 37.3081 13.1877i 1.38655 0.490117i
\(725\) 9.38968 9.38968i 0.348724 0.348724i
\(726\) 3.23535 + 5.13094i 0.120075 + 0.190427i
\(727\) 41.6544i 1.54488i −0.635090 0.772438i \(-0.719037\pi\)
0.635090 0.772438i \(-0.280963\pi\)
\(728\) 0 0
\(729\) 4.47546i 0.165758i
\(730\) 17.0336 10.7407i 0.630442 0.397529i
\(731\) 47.1727 47.1727i 1.74475 1.74475i
\(732\) 10.0255 20.9883i 0.370553 0.775749i
\(733\) −18.5348 18.5348i −0.684598 0.684598i 0.276434 0.961033i \(-0.410847\pi\)
−0.961033 + 0.276434i \(0.910847\pi\)
\(734\) −9.24829 + 40.8178i −0.341361 + 1.50661i
\(735\) 0 0
\(736\) −13.2193 26.9022i −0.487272 0.991630i
\(737\) −12.2616 −0.451662
\(738\) −2.81444 + 12.4217i −0.103601 + 0.457247i
\(739\) 4.93924 + 4.93924i 0.181693 + 0.181693i 0.792093 0.610400i \(-0.208991\pi\)
−0.610400 + 0.792093i \(0.708991\pi\)
\(740\) −3.78213 + 7.91786i −0.139034 + 0.291066i
\(741\) −6.74461 + 6.74461i −0.247769 + 0.247769i
\(742\) 0 0
\(743\) 17.8484i 0.654796i −0.944887 0.327398i \(-0.893828\pi\)
0.944887 0.327398i \(-0.106172\pi\)
\(744\) 2.86011 0.336051i 0.104857 0.0123202i
\(745\) 4.48257i 0.164229i
\(746\) 4.60441 + 7.30214i 0.168580 + 0.267350i
\(747\) −20.9283 + 20.9283i −0.765726 + 0.765726i
\(748\) −30.8825 + 10.9164i −1.12918 + 0.399142i
\(749\) 0 0
\(750\) −13.0685 2.96099i −0.477193 0.108120i
\(751\) 18.3471 0.669495 0.334747 0.942308i \(-0.391349\pi\)
0.334747 + 0.942308i \(0.391349\pi\)
\(752\) 7.69677 + 9.52679i 0.280672 + 0.347406i
\(753\) −2.49680 −0.0909885
\(754\) 15.9304 + 3.60943i 0.580152 + 0.131448i
\(755\) 17.7042 + 17.7042i 0.644322 + 0.644322i
\(756\) 0 0
\(757\) 4.90437 4.90437i 0.178252 0.178252i −0.612341 0.790594i \(-0.709772\pi\)
0.790594 + 0.612341i \(0.209772\pi\)
\(758\) 16.1578 + 25.6247i 0.586878 + 0.930730i
\(759\) 10.9624i 0.397909i
\(760\) −10.0804 + 12.7646i −0.365654 + 0.463019i
\(761\) 3.48443i 0.126311i 0.998004 + 0.0631553i \(0.0201163\pi\)
−0.998004 + 0.0631553i \(0.979884\pi\)
\(762\) 14.3558 9.05215i 0.520056 0.327925i
\(763\) 0 0
\(764\) 40.5010 + 19.3462i 1.46527 + 0.699920i
\(765\) −14.9317 14.9317i −0.539857 0.539857i
\(766\) −2.06924 + 9.13269i −0.0747646 + 0.329978i
\(767\) 18.9367 0.683764
\(768\) −11.4025 + 7.36816i −0.411452 + 0.265875i
\(769\) 13.5559 0.488837 0.244418 0.969670i \(-0.421403\pi\)
0.244418 + 0.969670i \(0.421403\pi\)
\(770\) 0 0
\(771\) −6.57694 6.57694i −0.236863 0.236863i
\(772\) 11.3949 + 5.44303i 0.410112 + 0.195899i
\(773\) −20.3801 + 20.3801i −0.733022 + 0.733022i −0.971217 0.238195i \(-0.923444\pi\)
0.238195 + 0.971217i \(0.423444\pi\)
\(774\) 27.0895 17.0815i 0.973711 0.613980i
\(775\) 3.71851i 0.133573i
\(776\) −4.40906 + 5.58310i −0.158276 + 0.200422i
\(777\) 0 0
\(778\) 27.3738 + 43.4121i 0.981399 + 1.55640i
\(779\) −11.6487 + 11.6487i −0.417357 + 0.417357i
\(780\) −2.10187 5.94621i −0.0752590 0.212909i
\(781\) 19.9599 + 19.9599i 0.714223 + 0.714223i
\(782\) 49.0905 + 11.1227i 1.75547 + 0.397746i
\(783\) −19.1978 −0.686073
\(784\) 0 0
\(785\) −21.0809 −0.752409
\(786\) 5.04780 + 1.14371i 0.180049 + 0.0407946i
\(787\) −27.7178 27.7178i −0.988034 0.988034i 0.0118952 0.999929i \(-0.496214\pi\)
−0.999929 + 0.0118952i \(0.996214\pi\)
\(788\) −10.1791 + 3.59813i −0.362617 + 0.128178i
\(789\) 6.11565 6.11565i 0.217723 0.217723i
\(790\) 4.23178 + 6.71118i 0.150560 + 0.238773i
\(791\) 0 0
\(792\) −15.6166 + 1.83489i −0.554913 + 0.0651999i
\(793\) 36.9442i 1.31193i
\(794\) 16.0226 10.1032i 0.568622 0.358548i
\(795\) 3.53172 3.53172i 0.125257 0.125257i
\(796\) −22.0946 + 46.2547i −0.783121 + 1.63945i
\(797\) 2.87837 + 2.87837i 0.101957 + 0.101957i 0.756245 0.654288i \(-0.227032\pi\)
−0.654288 + 0.756245i \(0.727032\pi\)
\(798\) 0 0
\(799\) −20.5664 −0.727588
\(800\) 7.73096 + 15.7330i 0.273331 + 0.556246i
\(801\) 38.5984 1.36381
\(802\) 5.47314 24.1560i 0.193263 0.852978i
\(803\) 17.8048 + 17.8048i 0.628318 + 0.628318i
\(804\) 3.67835 7.70058i 0.129725 0.271578i
\(805\) 0 0
\(806\) 3.86909 2.43968i 0.136283 0.0859341i
\(807\) 2.10931i 0.0742511i
\(808\) 3.99688 + 34.0173i 0.140610 + 1.19672i
\(809\) 21.5478i 0.757581i −0.925482 0.378791i \(-0.876340\pi\)
0.925482 0.378791i \(-0.123660\pi\)
\(810\) −3.16050 5.01223i −0.111049 0.176112i
\(811\) −20.4977 + 20.4977i −0.719772 + 0.719772i −0.968558 0.248787i \(-0.919968\pi\)
0.248787 + 0.968558i \(0.419968\pi\)
\(812\) 0 0
\(813\) 3.39687 + 3.39687i 0.119134 + 0.119134i
\(814\) −10.7009 2.42455i −0.375066 0.0849806i
\(815\) 12.5402 0.439263
\(816\) 2.40867 22.6697i 0.0843205 0.793599i
\(817\) 41.4222 1.44918
\(818\) 14.3105 + 3.24240i 0.500355 + 0.113368i
\(819\) 0 0
\(820\) −3.63016 10.2698i −0.126771 0.358635i
\(821\) −9.10771 + 9.10771i −0.317861 + 0.317861i −0.847945 0.530084i \(-0.822160\pi\)
0.530084 + 0.847945i \(0.322160\pi\)
\(822\) 7.41221 + 11.7550i 0.258530 + 0.410003i
\(823\) 41.4587i 1.44516i 0.691287 + 0.722580i \(0.257044\pi\)
−0.691287 + 0.722580i \(0.742956\pi\)
\(824\) 39.5900 + 31.2649i 1.37918 + 1.08916i
\(825\) 6.41104i 0.223204i
\(826\) 0 0
\(827\) 14.8134 14.8134i 0.515111 0.515111i −0.400977 0.916088i \(-0.631329\pi\)
0.916088 + 0.400977i \(0.131329\pi\)
\(828\) 21.8034 + 10.4149i 0.757722 + 0.361942i
\(829\) −17.2948 17.2948i −0.600675 0.600675i 0.339817 0.940492i \(-0.389635\pi\)
−0.940492 + 0.339817i \(0.889635\pi\)
\(830\) 5.59327 24.6862i 0.194145 0.856870i
\(831\) 25.5985 0.888002
\(832\) −11.2979 + 18.3663i −0.391685 + 0.636738i
\(833\) 0 0
\(834\) 0.844060 3.72530i 0.0292274 0.128997i
\(835\) −0.645381 0.645381i −0.0223343 0.0223343i
\(836\) −18.3517 8.76610i −0.634708 0.303182i
\(837\) −3.80136 + 3.80136i −0.131394 + 0.131394i
\(838\) −21.3238 + 13.4459i −0.736618 + 0.464479i
\(839\) 26.6645i 0.920562i −0.887773 0.460281i \(-0.847749\pi\)
0.887773 0.460281i \(-0.152251\pi\)
\(840\) 0 0
\(841\) 10.6378i 0.366820i
\(842\) 18.8375 + 29.8743i 0.649182 + 1.02954i
\(843\) 0.960018 0.960018i 0.0330648 0.0330648i
\(844\) −0.694860 1.96577i −0.0239181 0.0676645i
\(845\) 5.59137 + 5.59137i 0.192349 + 0.192349i
\(846\) −9.62886 2.18166i −0.331047 0.0750069i
\(847\) 0 0
\(848\) −16.9812 1.80426i −0.583136 0.0619586i
\(849\) −17.2722 −0.592779
\(850\) −28.7092 6.50478i −0.984717 0.223112i
\(851\) 11.9224 + 11.9224i 0.408696 + 0.408696i
\(852\) −18.5231 + 6.54755i −0.634590 + 0.224315i
\(853\) 12.4072 12.4072i 0.424815 0.424815i −0.462043 0.886858i \(-0.652883\pi\)
0.886858 + 0.462043i \(0.152883\pi\)
\(854\) 0 0
\(855\) 13.1115i 0.448404i
\(856\) 3.96422 + 33.7393i 0.135494 + 1.15319i
\(857\) 2.47165i 0.0844298i −0.999109 0.0422149i \(-0.986559\pi\)
0.999109 0.0422149i \(-0.0134414\pi\)
\(858\) 6.67066 4.20623i 0.227733 0.143598i
\(859\) −18.9839 + 18.9839i −0.647723 + 0.647723i −0.952442 0.304719i \(-0.901437\pi\)
0.304719 + 0.952442i \(0.401437\pi\)
\(860\) −11.8051 + 24.7138i −0.402550 + 0.842733i
\(861\) 0 0
\(862\) 2.99516 13.2193i 0.102016 0.450251i
\(863\) −35.3848 −1.20451 −0.602255 0.798303i \(-0.705731\pi\)
−0.602255 + 0.798303i \(0.705731\pi\)
\(864\) 8.18035 23.9868i 0.278301 0.816047i
\(865\) 12.3936 0.421395
\(866\) 0.299577 1.32220i 0.0101800 0.0449301i
\(867\) 16.8700 + 16.8700i 0.572935 + 0.572935i
\(868\) 0 0
\(869\) −7.01504 + 7.01504i −0.237969 + 0.237969i
\(870\) 5.99712 3.78152i 0.203321 0.128206i
\(871\) 13.5548i 0.459286i
\(872\) −28.8694 + 3.39203i −0.977641 + 0.114869i
\(873\) 5.73484i 0.194095i
\(874\) 16.6697 + 26.4365i 0.563862 + 0.894228i
\(875\) 0 0
\(876\) −16.5231 + 5.84059i −0.558263 + 0.197335i
\(877\) 4.32355 + 4.32355i 0.145996 + 0.145996i 0.776327 0.630331i \(-0.217081\pi\)
−0.630331 + 0.776327i \(0.717081\pi\)
\(878\) 13.7565 + 3.11688i 0.464260 + 0.105190i
\(879\) −0.321424 −0.0108414
\(880\) 10.4603 8.45092i 0.352615 0.284881i
\(881\) 26.3944 0.889249 0.444625 0.895717i \(-0.353337\pi\)
0.444625 + 0.895717i \(0.353337\pi\)
\(882\) 0 0
\(883\) −29.3078 29.3078i −0.986286 0.986286i 0.0136216 0.999907i \(-0.495664\pi\)
−0.999907 + 0.0136216i \(0.995664\pi\)
\(884\) −12.0677 34.1395i −0.405879 1.14824i
\(885\) 5.81199 5.81199i 0.195368 0.195368i
\(886\) 16.5182 + 26.1962i 0.554940 + 0.880080i
\(887\) 18.2241i 0.611904i 0.952047 + 0.305952i \(0.0989747\pi\)
−0.952047 + 0.305952i \(0.901025\pi\)
\(888\) 4.73283 5.99308i 0.158823 0.201114i
\(889\) 0 0
\(890\) −27.9225 + 17.6067i −0.935963 + 0.590178i
\(891\) 5.23916 5.23916i 0.175519 0.175519i
\(892\) −10.3982 4.96692i −0.348157 0.166305i
\(893\) −9.02967 9.02967i −0.302166 0.302166i
\(894\) −0.862040 + 3.80466i −0.0288309 + 0.127247i
\(895\) 14.8508 0.496407
\(896\) 0 0
\(897\) −12.1185 −0.404626
\(898\) −2.74340 + 12.1081i −0.0915485 + 0.404054i
\(899\) 3.63591 + 3.63591i 0.121264 + 0.121264i
\(900\) −12.7511 6.09085i −0.425038 0.203028i
\(901\) 20.2770 20.2770i 0.675525 0.675525i
\(902\) 11.5210 7.26462i 0.383606 0.241885i
\(903\) 0 0
\(904\) 24.2523 30.7101i 0.806618 1.02140i
\(905\) 27.2801i 0.906821i
\(906\) −11.6221 18.4314i −0.386117 0.612343i
\(907\) −13.0697 + 13.0697i −0.433974 + 0.433974i −0.889978 0.456004i \(-0.849280\pi\)
0.456004 + 0.889978i \(0.349280\pi\)
\(908\) −17.1728 48.5821i −0.569900 1.61225i
\(909\) −19.5237 19.5237i −0.647560 0.647560i
\(910\) 0 0
\(911\) 21.3908 0.708708 0.354354 0.935111i \(-0.384701\pi\)
0.354354 + 0.935111i \(0.384701\pi\)
\(912\) 11.0106 8.89559i 0.364599 0.294562i
\(913\) 31.6504 1.04747
\(914\) 2.58138 + 0.584876i 0.0853844 + 0.0193460i
\(915\) −11.3388 11.3388i −0.374849 0.374849i
\(916\) 1.36740 0.483348i 0.0451801 0.0159703i
\(917\) 0 0
\(918\) 22.6991 + 35.9986i 0.749184 + 1.18813i
\(919\) 10.5692i 0.348645i −0.984689 0.174322i \(-0.944227\pi\)
0.984689 0.174322i \(-0.0557735\pi\)
\(920\) −20.5236 + 2.41143i −0.676643 + 0.0795025i
\(921\) 14.8561i 0.489525i
\(922\) −22.4519 + 14.1572i −0.739412 + 0.466241i
\(923\) −22.0650 + 22.0650i −0.726279 + 0.726279i
\(924\) 0 0
\(925\) −6.97251 6.97251i −0.229255 0.229255i
\(926\) −0.593210 + 2.61816i −0.0194941 + 0.0860381i
\(927\) −40.6661 −1.33565
\(928\) −22.9428 7.82431i −0.753134 0.256846i
\(929\) 17.5372 0.575378 0.287689 0.957724i \(-0.407113\pi\)
0.287689 + 0.957724i \(0.407113\pi\)
\(930\) 0.438710 1.93627i 0.0143859 0.0634928i
\(931\) 0 0
\(932\) 12.4501 26.0641i 0.407817 0.853759i
\(933\) 2.21673 2.21673i 0.0725725 0.0725725i
\(934\) −1.83375 + 1.15629i −0.0600023 + 0.0378348i
\(935\) 22.5816i 0.738497i
\(936\) −2.02840 17.2637i −0.0663005 0.564280i
\(937\) 43.7391i 1.42890i −0.699689 0.714448i \(-0.746678\pi\)
0.699689 0.714448i \(-0.253322\pi\)
\(938\) 0 0
\(939\) 6.28177 6.28177i 0.204998 0.204998i
\(940\) 7.96078 2.81398i 0.259652 0.0917819i
\(941\) −7.61563 7.61563i −0.248262 0.248262i 0.571995 0.820257i \(-0.306170\pi\)
−0.820257 + 0.571995i \(0.806170\pi\)
\(942\) 17.8928 + 4.05405i 0.582978 + 0.132088i
\(943\) −20.9300 −0.681576
\(944\) −27.9451 2.96919i −0.909536 0.0966389i
\(945\) 0 0
\(946\) −33.4004 7.56769i −1.08594 0.246047i
\(947\) 9.69441 + 9.69441i 0.315026 + 0.315026i 0.846853 0.531827i \(-0.178494\pi\)
−0.531827 + 0.846853i \(0.678494\pi\)
\(948\) −2.30117 6.51004i −0.0747387 0.211436i
\(949\) −19.6826 + 19.6826i −0.638924 + 0.638924i
\(950\) −9.74882 15.4606i −0.316293 0.501610i
\(951\) 18.9522i 0.614568i
\(952\) 0 0
\(953\) 3.19629i 0.103538i 0.998659 + 0.0517690i \(0.0164860\pi\)
−0.998659 + 0.0517690i \(0.983514\pi\)
\(954\) 11.6443 7.34239i 0.376998 0.237719i
\(955\) 21.8804 21.8804i 0.708034 0.708034i
\(956\) 13.2593 + 6.33359i 0.428836 + 0.204843i
\(957\) 6.26864 + 6.26864i 0.202636 + 0.202636i
\(958\) 8.84300 39.0290i 0.285704 1.26097i
\(959\) 0 0
\(960\) 2.16942 + 9.10447i 0.0700177 + 0.293845i
\(961\) −29.5601 −0.953552
\(962\) 2.68026 11.8295i 0.0864151 0.381397i
\(963\) −19.3641 19.3641i −0.624001 0.624001i
\(964\) 5.87149 + 2.80464i 0.189108 + 0.0903314i
\(965\) 6.15604 6.15604i 0.198170 0.198170i
\(966\) 0 0
\(967\) 25.7940i 0.829479i 0.909940 + 0.414739i \(0.136127\pi\)
−0.909940 + 0.414739i \(0.863873\pi\)
\(968\) −11.2207 8.86120i −0.360648 0.284810i
\(969\) 23.7698i 0.763595i
\(970\) 2.61595 + 4.14864i 0.0839932 + 0.133205i
\(971\) 11.9004 11.9004i 0.381901 0.381901i −0.489885 0.871787i \(-0.662961\pi\)
0.871787 + 0.489885i \(0.162961\pi\)
\(972\) 10.6772 + 30.2059i 0.342472 + 0.968855i
\(973\) 0 0
\(974\) 8.54740 + 1.93663i 0.273876 + 0.0620535i
\(975\) 7.08719 0.226972
\(976\) −5.79269 + 54.5190i −0.185419 + 1.74511i
\(977\) 2.74136 0.0877038 0.0438519 0.999038i \(-0.486037\pi\)
0.0438519 + 0.999038i \(0.486037\pi\)
\(978\) −10.6437 2.41159i −0.340347 0.0771141i
\(979\) −29.1867 29.1867i −0.932810 0.932810i
\(980\) 0 0
\(981\) 16.5691 16.5691i 0.529012 0.529012i
\(982\) −23.0053 36.4840i −0.734127 1.16425i
\(983\) 44.6295i 1.42346i 0.702454 + 0.711729i \(0.252088\pi\)
−0.702454 + 0.711729i \(0.747912\pi\)
\(984\) 1.10619 + 9.41474i 0.0352641 + 0.300131i
\(985\) 7.44310i 0.237157i
\(986\) 34.4318 21.7112i 1.09653 0.691425i
\(987\) 0 0
\(988\) 9.69062 20.2872i 0.308300 0.645422i
\(989\) 37.2132 + 37.2132i 1.18331 + 1.18331i
\(990\) −2.39542 + 10.5723i −0.0761315 + 0.336010i
\(991\) 1.08451 0.0344508 0.0172254 0.999852i \(-0.494517\pi\)
0.0172254 + 0.999852i \(0.494517\pi\)
\(992\) −6.09220 + 2.99361i −0.193428 + 0.0950473i
\(993\) 8.11482 0.257516
\(994\) 0 0
\(995\) 24.9888 + 24.9888i 0.792200 + 0.792200i
\(996\) −9.49476 + 19.8772i −0.300853 + 0.629832i
\(997\) −29.3910 + 29.3910i −0.930823 + 0.930823i −0.997757 0.0669342i \(-0.978678\pi\)
0.0669342 + 0.997757i \(0.478678\pi\)
\(998\) 4.15305 2.61874i 0.131463 0.0828946i
\(999\) 14.2557i 0.451031i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 784.2.m.h.589.4 12
7.2 even 3 784.2.x.m.557.1 24
7.3 odd 6 784.2.x.l.765.5 24
7.4 even 3 784.2.x.m.765.5 24
7.5 odd 6 784.2.x.l.557.1 24
7.6 odd 2 112.2.m.d.29.4 12
16.5 even 4 inner 784.2.m.h.197.4 12
28.27 even 2 448.2.m.d.337.5 12
56.13 odd 2 896.2.m.g.673.5 12
56.27 even 2 896.2.m.h.673.2 12
112.5 odd 12 784.2.x.l.165.5 24
112.13 odd 4 896.2.m.g.225.5 12
112.27 even 4 448.2.m.d.113.5 12
112.37 even 12 784.2.x.m.165.5 24
112.53 even 12 784.2.x.m.373.1 24
112.69 odd 4 112.2.m.d.85.4 yes 12
112.83 even 4 896.2.m.h.225.2 12
112.101 odd 12 784.2.x.l.373.1 24
224.27 even 8 7168.2.a.bi.1.5 12
224.69 odd 8 7168.2.a.bj.1.8 12
224.139 even 8 7168.2.a.bi.1.8 12
224.181 odd 8 7168.2.a.bj.1.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.m.d.29.4 12 7.6 odd 2
112.2.m.d.85.4 yes 12 112.69 odd 4
448.2.m.d.113.5 12 112.27 even 4
448.2.m.d.337.5 12 28.27 even 2
784.2.m.h.197.4 12 16.5 even 4 inner
784.2.m.h.589.4 12 1.1 even 1 trivial
784.2.x.l.165.5 24 112.5 odd 12
784.2.x.l.373.1 24 112.101 odd 12
784.2.x.l.557.1 24 7.5 odd 6
784.2.x.l.765.5 24 7.3 odd 6
784.2.x.m.165.5 24 112.37 even 12
784.2.x.m.373.1 24 112.53 even 12
784.2.x.m.557.1 24 7.2 even 3
784.2.x.m.765.5 24 7.4 even 3
896.2.m.g.225.5 12 112.13 odd 4
896.2.m.g.673.5 12 56.13 odd 2
896.2.m.h.225.2 12 112.83 even 4
896.2.m.h.673.2 12 56.27 even 2
7168.2.a.bi.1.5 12 224.27 even 8
7168.2.a.bi.1.8 12 224.139 even 8
7168.2.a.bj.1.5 12 224.181 odd 8
7168.2.a.bj.1.8 12 224.69 odd 8