Properties

Label 441.2.f.g.295.2
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(148,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.2
Root \(-1.82904 - 1.05600i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.g.148.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23025 + 2.13086i) q^{2} +(1.66238 + 0.486291i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.82904 + 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(2.52704 + 1.61680i) q^{9} +O(q^{10})\) \(q+(-1.23025 + 2.13086i) q^{2} +(1.66238 + 0.486291i) q^{3} +(-2.02704 - 3.51094i) q^{4} +(1.82904 + 3.16799i) q^{5} +(-3.08137 + 2.94405i) q^{6} +5.05408 q^{8} +(2.52704 + 1.61680i) q^{9} -9.00071 q^{10} +(-0.203210 + 0.351971i) q^{11} +(-1.66238 - 6.82226i) q^{12} +(0.243398 + 0.421578i) q^{13} +(1.50000 + 6.15585i) q^{15} +(-2.16372 + 3.74766i) q^{16} +4.85584 q^{17} +(-6.55408 + 3.39569i) q^{18} -1.97351 q^{19} +(7.41507 - 12.8433i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.32383 - 4.02499i) q^{23} +(8.40183 + 2.45776i) q^{24} +(-4.19076 + 7.25860i) q^{25} -1.19777 q^{26} +(3.41468 + 3.91663i) q^{27} +(-3.82383 + 6.62307i) q^{29} +(-14.9626 - 4.37697i) q^{30} +(-3.51360 - 6.08573i) q^{31} +(-0.269748 - 0.467216i) q^{32} +(-0.508974 + 0.486291i) q^{33} +(-5.97391 + 10.3471i) q^{34} +(0.554084 - 12.1496i) q^{36} +2.32743 q^{37} +(2.42792 - 4.20528i) q^{38} +(0.199612 + 0.819187i) q^{39} +(9.24411 + 16.0113i) q^{40} +(-3.75700 - 6.50731i) q^{41} +(1.16372 - 2.01561i) q^{43} +1.64766 q^{44} +(-0.499960 + 10.9628i) q^{45} +11.4356 q^{46} +(3.15811 - 5.47002i) q^{47} +(-5.41938 + 5.17786i) q^{48} +(-10.3114 - 17.8598i) q^{50} +(8.07227 + 2.36135i) q^{51} +(0.986757 - 1.70911i) q^{52} -3.56867 q^{53} +(-12.5467 + 2.45776i) q^{54} -1.48672 q^{55} +(-3.28074 - 0.959702i) q^{57} +(-9.40856 - 16.2961i) q^{58} +(-3.05919 - 5.29868i) q^{59} +(18.5723 - 17.7446i) q^{60} +(4.01356 - 6.95169i) q^{61} +17.2905 q^{62} -7.32743 q^{64} +(-0.890369 + 1.54216i) q^{65} +(-0.410052 - 1.68281i) q^{66} +(-1.80039 - 3.11836i) q^{67} +(-9.84299 - 17.0486i) q^{68} +(-1.90578 - 7.82115i) q^{69} +8.46050 q^{71} +(12.7719 + 8.17147i) q^{72} +1.97351 q^{73} +(-2.86333 + 4.95943i) q^{74} +(-10.4964 + 10.0287i) q^{75} +(4.00040 + 6.92889i) q^{76} +(-1.99115 - 0.582462i) q^{78} +(-4.08113 + 7.06872i) q^{79} -15.8301 q^{80} +(3.77188 + 8.17147i) q^{81} +18.4882 q^{82} +(-6.08600 + 10.5413i) q^{83} +(8.88151 + 15.3832i) q^{85} +(2.86333 + 4.95943i) q^{86} +(-9.57742 + 9.15059i) q^{87} +(-1.02704 + 1.77889i) q^{88} +14.8301 q^{89} +(-22.7452 - 14.5524i) q^{90} +(-9.42101 + 16.3177i) q^{92} +(-2.88151 - 11.8255i) q^{93} +(7.77056 + 13.4590i) q^{94} +(-3.60963 - 6.25206i) q^{95} +(-0.221221 - 0.907869i) q^{96} +(4.74375 - 8.21642i) q^{97} +(-1.08259 + 0.560893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43} - 28 q^{44} + 24 q^{46} - 56 q^{50} - 18 q^{51} + 56 q^{53} - 6 q^{57} - 18 q^{58} + 108 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} + 60 q^{72} - 36 q^{74} + 36 q^{78} + 6 q^{79} - 48 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23025 + 2.13086i −0.869920 + 1.50675i −0.00784213 + 0.999969i \(0.502496\pi\)
−0.862078 + 0.506776i \(0.830837\pi\)
\(3\) 1.66238 + 0.486291i 0.959778 + 0.280760i
\(4\) −2.02704 3.51094i −1.01352 1.75547i
\(5\) 1.82904 + 3.16799i 0.817970 + 1.41677i 0.907175 + 0.420753i \(0.138234\pi\)
−0.0892047 + 0.996013i \(0.528433\pi\)
\(6\) −3.08137 + 2.94405i −1.25796 + 1.20190i
\(7\) 0 0
\(8\) 5.05408 1.78689
\(9\) 2.52704 + 1.61680i 0.842347 + 0.538935i
\(10\) −9.00071 −2.84628
\(11\) −0.203210 + 0.351971i −0.0612702 + 0.106123i −0.895033 0.445999i \(-0.852848\pi\)
0.833763 + 0.552122i \(0.186182\pi\)
\(12\) −1.66238 6.82226i −0.479889 1.96942i
\(13\) 0.243398 + 0.421578i 0.0675065 + 0.116925i 0.897803 0.440397i \(-0.145162\pi\)
−0.830297 + 0.557322i \(0.811829\pi\)
\(14\) 0 0
\(15\) 1.50000 + 6.15585i 0.387298 + 1.58943i
\(16\) −2.16372 + 3.74766i −0.540929 + 0.936916i
\(17\) 4.85584 1.17771 0.588857 0.808237i \(-0.299578\pi\)
0.588857 + 0.808237i \(0.299578\pi\)
\(18\) −6.55408 + 3.39569i −1.54481 + 0.800373i
\(19\) −1.97351 −0.452755 −0.226378 0.974040i \(-0.572688\pi\)
−0.226378 + 0.974040i \(0.572688\pi\)
\(20\) 7.41507 12.8433i 1.65806 2.87185i
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) −2.32383 4.02499i −0.484552 0.839269i 0.515290 0.857016i \(-0.327684\pi\)
−0.999843 + 0.0177464i \(0.994351\pi\)
\(24\) 8.40183 + 2.45776i 1.71502 + 0.501687i
\(25\) −4.19076 + 7.25860i −0.838151 + 1.45172i
\(26\) −1.19777 −0.234901
\(27\) 3.41468 + 3.91663i 0.657155 + 0.753756i
\(28\) 0 0
\(29\) −3.82383 + 6.62307i −0.710068 + 1.22987i 0.254764 + 0.967003i \(0.418002\pi\)
−0.964831 + 0.262870i \(0.915331\pi\)
\(30\) −14.9626 4.37697i −2.73179 0.799121i
\(31\) −3.51360 6.08573i −0.631061 1.09303i −0.987335 0.158648i \(-0.949286\pi\)
0.356274 0.934381i \(-0.384047\pi\)
\(32\) −0.269748 0.467216i −0.0476851 0.0825930i
\(33\) −0.508974 + 0.486291i −0.0886010 + 0.0846524i
\(34\) −5.97391 + 10.3471i −1.02452 + 1.77452i
\(35\) 0 0
\(36\) 0.554084 12.1496i 0.0923474 2.02494i
\(37\) 2.32743 0.382627 0.191314 0.981529i \(-0.438725\pi\)
0.191314 + 0.981529i \(0.438725\pi\)
\(38\) 2.42792 4.20528i 0.393861 0.682187i
\(39\) 0.199612 + 0.819187i 0.0319635 + 0.131175i
\(40\) 9.24411 + 16.0113i 1.46162 + 2.53160i
\(41\) −3.75700 6.50731i −0.586744 1.01627i −0.994655 0.103249i \(-0.967076\pi\)
0.407911 0.913022i \(-0.366257\pi\)
\(42\) 0 0
\(43\) 1.16372 2.01561i 0.177465 0.307378i −0.763547 0.645753i \(-0.776544\pi\)
0.941012 + 0.338374i \(0.109877\pi\)
\(44\) 1.64766 0.248395
\(45\) −0.499960 + 10.9628i −0.0745297 + 1.63424i
\(46\) 11.4356 1.68609
\(47\) 3.15811 5.47002i 0.460658 0.797884i −0.538335 0.842731i \(-0.680947\pi\)
0.998994 + 0.0448469i \(0.0142800\pi\)
\(48\) −5.41938 + 5.17786i −0.782220 + 0.747360i
\(49\) 0 0
\(50\) −10.3114 17.8598i −1.45825 2.52576i
\(51\) 8.07227 + 2.36135i 1.13034 + 0.330655i
\(52\) 0.986757 1.70911i 0.136839 0.237011i
\(53\) −3.56867 −0.490195 −0.245097 0.969498i \(-0.578820\pi\)
−0.245097 + 0.969498i \(0.578820\pi\)
\(54\) −12.5467 + 2.45776i −1.70739 + 0.334458i
\(55\) −1.48672 −0.200469
\(56\) 0 0
\(57\) −3.28074 0.959702i −0.434544 0.127116i
\(58\) −9.40856 16.2961i −1.23540 2.13978i
\(59\) −3.05919 5.29868i −0.398273 0.689829i 0.595240 0.803548i \(-0.297057\pi\)
−0.993513 + 0.113719i \(0.963724\pi\)
\(60\) 18.5723 17.7446i 2.39767 2.29082i
\(61\) 4.01356 6.95169i 0.513884 0.890073i −0.485987 0.873966i \(-0.661540\pi\)
0.999870 0.0161063i \(-0.00512703\pi\)
\(62\) 17.2905 2.19589
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) −0.890369 + 1.54216i −0.110437 + 0.191282i
\(66\) −0.410052 1.68281i −0.0504739 0.207140i
\(67\) −1.80039 3.11836i −0.219952 0.380969i 0.734841 0.678240i \(-0.237257\pi\)
−0.954793 + 0.297271i \(0.903924\pi\)
\(68\) −9.84299 17.0486i −1.19364 2.06744i
\(69\) −1.90578 7.82115i −0.229429 0.941555i
\(70\) 0 0
\(71\) 8.46050 1.00408 0.502039 0.864845i \(-0.332584\pi\)
0.502039 + 0.864845i \(0.332584\pi\)
\(72\) 12.7719 + 8.17147i 1.50518 + 0.963017i
\(73\) 1.97351 0.230982 0.115491 0.993309i \(-0.463156\pi\)
0.115491 + 0.993309i \(0.463156\pi\)
\(74\) −2.86333 + 4.95943i −0.332855 + 0.576522i
\(75\) −10.4964 + 10.0287i −1.21202 + 1.15801i
\(76\) 4.00040 + 6.92889i 0.458877 + 0.794798i
\(77\) 0 0
\(78\) −1.99115 0.582462i −0.225453 0.0659509i
\(79\) −4.08113 + 7.06872i −0.459163 + 0.795293i −0.998917 0.0465297i \(-0.985184\pi\)
0.539754 + 0.841823i \(0.318517\pi\)
\(80\) −15.8301 −1.76986
\(81\) 3.77188 + 8.17147i 0.419098 + 0.907941i
\(82\) 18.4882 2.04168
\(83\) −6.08600 + 10.5413i −0.668025 + 1.15705i 0.310431 + 0.950596i \(0.399527\pi\)
−0.978456 + 0.206457i \(0.933807\pi\)
\(84\) 0 0
\(85\) 8.88151 + 15.3832i 0.963336 + 1.66855i
\(86\) 2.86333 + 4.95943i 0.308760 + 0.534789i
\(87\) −9.57742 + 9.15059i −1.02681 + 0.981047i
\(88\) −1.02704 + 1.77889i −0.109483 + 0.189630i
\(89\) 14.8301 1.57199 0.785996 0.618231i \(-0.212151\pi\)
0.785996 + 0.618231i \(0.212151\pi\)
\(90\) −22.7452 14.5524i −2.39755 1.53396i
\(91\) 0 0
\(92\) −9.42101 + 16.3177i −0.982208 + 1.70123i
\(93\) −2.88151 11.8255i −0.298799 1.22624i
\(94\) 7.77056 + 13.4590i 0.801472 + 1.38819i
\(95\) −3.60963 6.25206i −0.370340 0.641448i
\(96\) −0.221221 0.907869i −0.0225783 0.0926590i
\(97\) 4.74375 8.21642i 0.481655 0.834251i −0.518123 0.855306i \(-0.673369\pi\)
0.999778 + 0.0210547i \(0.00670241\pi\)
\(98\) 0 0
\(99\) −1.08259 + 0.560893i −0.108804 + 0.0563719i
\(100\) 33.9794 3.39794
\(101\) −4.35588 + 7.54461i −0.433426 + 0.750716i −0.997166 0.0752364i \(-0.976029\pi\)
0.563739 + 0.825953i \(0.309362\pi\)
\(102\) −14.9626 + 14.2958i −1.48152 + 1.41550i
\(103\) −4.01356 6.95169i −0.395468 0.684970i 0.597693 0.801725i \(-0.296084\pi\)
−0.993161 + 0.116755i \(0.962751\pi\)
\(104\) 1.23016 + 2.13069i 0.120627 + 0.208931i
\(105\) 0 0
\(106\) 4.39037 7.60434i 0.426430 0.738599i
\(107\) 12.8420 1.24148 0.620742 0.784015i \(-0.286831\pi\)
0.620742 + 0.784015i \(0.286831\pi\)
\(108\) 6.82935 19.9279i 0.657155 1.91756i
\(109\) 2.60078 0.249109 0.124555 0.992213i \(-0.460250\pi\)
0.124555 + 0.992213i \(0.460250\pi\)
\(110\) 1.82904 3.16799i 0.174392 0.302056i
\(111\) 3.86908 + 1.13181i 0.367237 + 0.107427i
\(112\) 0 0
\(113\) 6.97509 + 12.0812i 0.656162 + 1.13651i 0.981601 + 0.190942i \(0.0611544\pi\)
−0.325440 + 0.945563i \(0.605512\pi\)
\(114\) 6.08113 5.81012i 0.569550 0.544167i
\(115\) 8.50075 14.7237i 0.792699 1.37300i
\(116\) 31.0043 2.87867
\(117\) −0.0665320 + 1.45887i −0.00615088 + 0.134873i
\(118\) 15.0543 1.38586
\(119\) 0 0
\(120\) 7.58113 + 31.1122i 0.692059 + 2.84014i
\(121\) 5.41741 + 9.38323i 0.492492 + 0.853021i
\(122\) 9.87538 + 17.1047i 0.894075 + 1.54858i
\(123\) −3.08113 12.6446i −0.277816 1.14013i
\(124\) −14.2444 + 24.6721i −1.27919 + 2.21562i
\(125\) −12.3698 −1.10639
\(126\) 0 0
\(127\) −15.5438 −1.37929 −0.689643 0.724149i \(-0.742233\pi\)
−0.689643 + 0.724149i \(0.742233\pi\)
\(128\) 9.55408 16.5482i 0.844470 1.46266i
\(129\) 2.91472 2.78482i 0.256626 0.245190i
\(130\) −2.19076 3.79450i −0.192142 0.332800i
\(131\) 4.25696 + 7.37327i 0.371932 + 0.644205i 0.989863 0.142027i \(-0.0453621\pi\)
−0.617931 + 0.786233i \(0.712029\pi\)
\(132\) 2.73905 + 0.801244i 0.238404 + 0.0697393i
\(133\) 0 0
\(134\) 8.85973 0.765364
\(135\) −6.16225 + 17.9813i −0.530362 + 1.54758i
\(136\) 24.5418 2.10444
\(137\) −0.188621 + 0.326702i −0.0161150 + 0.0279120i −0.873970 0.485979i \(-0.838463\pi\)
0.857855 + 0.513891i \(0.171796\pi\)
\(138\) 19.0104 + 5.56103i 1.61827 + 0.473386i
\(139\) 9.50067 + 16.4556i 0.805837 + 1.39575i 0.915725 + 0.401806i \(0.131617\pi\)
−0.109888 + 0.993944i \(0.535049\pi\)
\(140\) 0 0
\(141\) 7.91002 7.55750i 0.666144 0.636457i
\(142\) −10.4086 + 18.0281i −0.873467 + 1.51289i
\(143\) −0.197844 −0.0165446
\(144\) −11.5270 + 5.97220i −0.960587 + 0.497683i
\(145\) −27.9757 −2.32326
\(146\) −2.42792 + 4.20528i −0.200936 + 0.348032i
\(147\) 0 0
\(148\) −4.71780 8.17147i −0.387801 0.671691i
\(149\) 4.85087 + 8.40196i 0.397399 + 0.688315i 0.993404 0.114665i \(-0.0365795\pi\)
−0.596005 + 0.802981i \(0.703246\pi\)
\(150\) −8.45640 34.7042i −0.690462 2.83359i
\(151\) 6.41741 11.1153i 0.522242 0.904549i −0.477424 0.878673i \(-0.658429\pi\)
0.999665 0.0258756i \(-0.00823738\pi\)
\(152\) −9.97430 −0.809023
\(153\) 12.2709 + 7.85095i 0.992045 + 0.634711i
\(154\) 0 0
\(155\) 12.8530 22.2621i 1.03238 1.78813i
\(156\) 2.47150 2.36135i 0.197878 0.189059i
\(157\) −10.4743 18.1420i −0.835937 1.44789i −0.893265 0.449531i \(-0.851591\pi\)
0.0573276 0.998355i \(-0.481742\pi\)
\(158\) −10.0416 17.3926i −0.798869 1.38368i
\(159\) −5.93251 1.73541i −0.470478 0.137627i
\(160\) 0.986757 1.70911i 0.0780100 0.135117i
\(161\) 0 0
\(162\) −22.0526 2.01561i −1.73262 0.158362i
\(163\) −11.1623 −0.874295 −0.437148 0.899390i \(-0.644011\pi\)
−0.437148 + 0.899390i \(0.644011\pi\)
\(164\) −15.2312 + 26.3812i −1.18936 + 2.06002i
\(165\) −2.47150 0.722977i −0.192406 0.0562837i
\(166\) −14.9746 25.9368i −1.16226 2.01309i
\(167\) −1.73012 2.99665i −0.133880 0.231888i 0.791289 0.611443i \(-0.209410\pi\)
−0.925169 + 0.379555i \(0.876077\pi\)
\(168\) 0 0
\(169\) 6.38151 11.0531i 0.490886 0.850239i
\(170\) −43.7060 −3.35210
\(171\) −4.98715 3.19079i −0.381377 0.244006i
\(172\) −9.43560 −0.719458
\(173\) 3.02680 5.24258i 0.230124 0.398586i −0.727721 0.685874i \(-0.759420\pi\)
0.957844 + 0.287288i \(0.0927536\pi\)
\(174\) −7.71599 31.6657i −0.584948 2.40057i
\(175\) 0 0
\(176\) −0.879379 1.52313i −0.0662857 0.114810i
\(177\) −2.50885 10.2961i −0.188577 0.773902i
\(178\) −18.2448 + 31.6010i −1.36751 + 2.36859i
\(179\) 9.13307 0.682638 0.341319 0.939948i \(-0.389126\pi\)
0.341319 + 0.939948i \(0.389126\pi\)
\(180\) 39.5033 20.4668i 2.94440 1.52550i
\(181\) 11.9478 0.888074 0.444037 0.896008i \(-0.353546\pi\)
0.444037 + 0.896008i \(0.353546\pi\)
\(182\) 0 0
\(183\) 10.0526 9.60462i 0.743111 0.709994i
\(184\) −11.7448 20.3427i −0.865841 1.49968i
\(185\) 4.25696 + 7.37327i 0.312978 + 0.542093i
\(186\) 28.7434 + 8.40819i 2.10757 + 0.616519i
\(187\) −0.986757 + 1.70911i −0.0721588 + 0.124983i
\(188\) −25.6065 −1.86755
\(189\) 0 0
\(190\) 17.7630 1.28867
\(191\) −4.57014 + 7.91571i −0.330683 + 0.572760i −0.982646 0.185491i \(-0.940613\pi\)
0.651963 + 0.758251i \(0.273946\pi\)
\(192\) −12.1810 3.56326i −0.879088 0.257156i
\(193\) −8.47150 14.6731i −0.609792 1.05619i −0.991274 0.131814i \(-0.957920\pi\)
0.381483 0.924376i \(-0.375414\pi\)
\(194\) 11.6720 + 20.2165i 0.838003 + 1.45146i
\(195\) −2.23008 + 2.13069i −0.159699 + 0.152582i
\(196\) 0 0
\(197\) −21.3173 −1.51880 −0.759398 0.650627i \(-0.774506\pi\)
−0.759398 + 0.650627i \(0.774506\pi\)
\(198\) 0.136673 2.99689i 0.00971293 0.212979i
\(199\) 9.97430 0.707060 0.353530 0.935423i \(-0.384981\pi\)
0.353530 + 0.935423i \(0.384981\pi\)
\(200\) −21.1804 + 36.6856i −1.49768 + 2.59406i
\(201\) −1.47650 6.05943i −0.104145 0.427399i
\(202\) −10.7177 18.5635i −0.754092 1.30613i
\(203\) 0 0
\(204\) −8.07227 33.1278i −0.565172 2.31941i
\(205\) 13.7434 23.8042i 0.959879 1.66256i
\(206\) 19.7508 1.37610
\(207\) 0.635211 13.9285i 0.0441502 0.968099i
\(208\) −2.10658 −0.146065
\(209\) 0.401038 0.694619i 0.0277404 0.0480478i
\(210\) 0 0
\(211\) −2.44592 4.23645i −0.168384 0.291649i 0.769468 0.638685i \(-0.220521\pi\)
−0.937852 + 0.347036i \(0.887188\pi\)
\(212\) 7.23385 + 12.5294i 0.496823 + 0.860523i
\(213\) 14.0646 + 4.11427i 0.963691 + 0.281905i
\(214\) −15.7989 + 27.3645i −1.07999 + 1.87060i
\(215\) 8.51392 0.580644
\(216\) 17.2581 + 19.7950i 1.17426 + 1.34688i
\(217\) 0 0
\(218\) −3.19961 + 5.54189i −0.216705 + 0.375344i
\(219\) 3.28074 + 0.959702i 0.221692 + 0.0648507i
\(220\) 3.01364 + 5.21978i 0.203179 + 0.351917i
\(221\) 1.18190 + 2.04712i 0.0795034 + 0.137704i
\(222\) −7.17167 + 6.85206i −0.481331 + 0.459880i
\(223\) 11.7044 20.2727i 0.783786 1.35756i −0.145936 0.989294i \(-0.546619\pi\)
0.929722 0.368263i \(-0.120047\pi\)
\(224\) 0 0
\(225\) −22.3260 + 11.5672i −1.48840 + 0.771144i
\(226\) −34.3245 −2.28323
\(227\) 3.05919 5.29868i 0.203046 0.351686i −0.746463 0.665427i \(-0.768249\pi\)
0.949508 + 0.313742i \(0.101583\pi\)
\(228\) 3.28074 + 13.4638i 0.217272 + 0.891664i
\(229\) −0.730195 1.26473i −0.0482526 0.0835760i 0.840890 0.541206i \(-0.182032\pi\)
−0.889143 + 0.457630i \(0.848699\pi\)
\(230\) 20.9161 + 36.2278i 1.37917 + 2.38879i
\(231\) 0 0
\(232\) −19.3260 + 33.4736i −1.26881 + 2.19765i
\(233\) −13.2484 −0.867934 −0.433967 0.900929i \(-0.642887\pi\)
−0.433967 + 0.900929i \(0.642887\pi\)
\(234\) −3.02680 1.93655i −0.197868 0.126596i
\(235\) 23.1052 1.50722
\(236\) −12.4022 + 21.4813i −0.807316 + 1.39831i
\(237\) −10.2219 + 9.76631i −0.663981 + 0.634390i
\(238\) 0 0
\(239\) −9.69436 16.7911i −0.627076 1.08613i −0.988136 0.153584i \(-0.950918\pi\)
0.361060 0.932543i \(-0.382415\pi\)
\(240\) −26.3157 7.69802i −1.69867 0.496905i
\(241\) 2.52684 4.37662i 0.162768 0.281923i −0.773092 0.634294i \(-0.781291\pi\)
0.935860 + 0.352371i \(0.114624\pi\)
\(242\) −26.6591 −1.71371
\(243\) 2.29661 + 15.4184i 0.147327 + 0.989088i
\(244\) −32.5426 −2.08333
\(245\) 0 0
\(246\) 30.7345 + 8.99066i 1.95956 + 0.573223i
\(247\) −0.480350 0.831990i −0.0305639 0.0529383i
\(248\) −17.7580 30.7578i −1.12764 1.95312i
\(249\) −15.2434 + 14.5640i −0.966010 + 0.922959i
\(250\) 15.2180 26.3584i 0.962472 1.66705i
\(251\) −15.0928 −0.952647 −0.476324 0.879270i \(-0.658031\pi\)
−0.476324 + 0.879270i \(0.658031\pi\)
\(252\) 0 0
\(253\) 1.88891 0.118755
\(254\) 19.1228 33.1216i 1.19987 2.07823i
\(255\) 7.28376 + 29.8918i 0.456127 + 1.87190i
\(256\) 16.1804 + 28.0253i 1.01128 + 1.75158i
\(257\) 3.85592 + 6.67865i 0.240526 + 0.416603i 0.960864 0.277020i \(-0.0893469\pi\)
−0.720338 + 0.693623i \(0.756014\pi\)
\(258\) 2.34822 + 9.63688i 0.146194 + 0.599966i
\(259\) 0 0
\(260\) 7.21926 0.447720
\(261\) −20.3712 + 10.5544i −1.26095 + 0.653300i
\(262\) −20.9485 −1.29420
\(263\) −2.10603 + 3.64776i −0.129864 + 0.224930i −0.923624 0.383301i \(-0.874787\pi\)
0.793760 + 0.608231i \(0.208121\pi\)
\(264\) −2.57240 + 2.45776i −0.158320 + 0.151264i
\(265\) −6.52724 11.3055i −0.400965 0.694492i
\(266\) 0 0
\(267\) 24.6534 + 7.21177i 1.50876 + 0.441353i
\(268\) −7.29893 + 12.6421i −0.445853 + 0.772240i
\(269\) −20.7507 −1.26519 −0.632596 0.774482i \(-0.718011\pi\)
−0.632596 + 0.774482i \(0.718011\pi\)
\(270\) −30.7345 35.2524i −1.87044 2.14540i
\(271\) 28.4889 1.73057 0.865287 0.501276i \(-0.167136\pi\)
0.865287 + 0.501276i \(0.167136\pi\)
\(272\) −10.5067 + 18.1981i −0.637060 + 1.10342i
\(273\) 0 0
\(274\) −0.464103 0.803851i −0.0280375 0.0485624i
\(275\) −1.70321 2.95005i −0.102707 0.177895i
\(276\) −23.5965 + 22.5449i −1.42034 + 1.35704i
\(277\) −8.58113 + 14.8629i −0.515590 + 0.893028i 0.484246 + 0.874932i \(0.339094\pi\)
−0.999836 + 0.0180962i \(0.994239\pi\)
\(278\) −46.7529 −2.80405
\(279\) 0.960429 21.0597i 0.0574994 1.26081i
\(280\) 0 0
\(281\) −4.72140 + 8.17770i −0.281655 + 0.487841i −0.971793 0.235837i \(-0.924217\pi\)
0.690138 + 0.723678i \(0.257550\pi\)
\(282\) 6.37266 + 26.1528i 0.379486 + 1.55738i
\(283\) 8.43422 + 14.6085i 0.501362 + 0.868385i 0.999999 + 0.00157378i \(0.000500949\pi\)
−0.498636 + 0.866811i \(0.666166\pi\)
\(284\) −17.1498 29.7043i −1.01765 1.76263i
\(285\) −2.96027 12.1487i −0.175351 0.719625i
\(286\) 0.243398 0.421578i 0.0143924 0.0249284i
\(287\) 0 0
\(288\) 0.0737345 1.61680i 0.00434485 0.0952711i
\(289\) 6.57918 0.387011
\(290\) 34.4172 59.6124i 2.02105 3.50056i
\(291\) 11.8815 11.3520i 0.696507 0.665466i
\(292\) −4.00040 6.92889i −0.234105 0.405483i
\(293\) −1.86143 3.22409i −0.108746 0.188353i 0.806517 0.591211i \(-0.201350\pi\)
−0.915262 + 0.402858i \(0.868017\pi\)
\(294\) 0 0
\(295\) 11.1908 19.3830i 0.651551 1.12852i
\(296\) 11.7630 0.683712
\(297\) −2.07244 + 0.405967i −0.120255 + 0.0235566i
\(298\) −23.8712 −1.38282
\(299\) 1.13123 1.95935i 0.0654209 0.113312i
\(300\) 56.4868 + 16.5239i 3.26126 + 0.954006i
\(301\) 0 0
\(302\) 15.7901 + 27.3492i 0.908617 + 1.57377i
\(303\) −10.9100 + 10.4238i −0.626764 + 0.598832i
\(304\) 4.27012 7.39607i 0.244908 0.424194i
\(305\) 29.3638 1.68137
\(306\) −31.8256 + 16.4889i −1.81935 + 0.942610i
\(307\) −30.5691 −1.74467 −0.872335 0.488908i \(-0.837395\pi\)
−0.872335 + 0.488908i \(0.837395\pi\)
\(308\) 0 0
\(309\) −3.29153 13.5081i −0.187249 0.768451i
\(310\) 31.6249 + 54.7759i 1.79617 + 3.11106i
\(311\) −5.21739 9.03678i −0.295851 0.512429i 0.679332 0.733831i \(-0.262270\pi\)
−0.975182 + 0.221403i \(0.928936\pi\)
\(312\) 1.00885 + 4.14024i 0.0571151 + 0.234395i
\(313\) −0.309930 + 0.536815i −0.0175183 + 0.0303426i −0.874652 0.484752i \(-0.838910\pi\)
0.857133 + 0.515095i \(0.172243\pi\)
\(314\) 51.5440 2.90879
\(315\) 0 0
\(316\) 33.0905 1.86148
\(317\) −5.12422 + 8.87541i −0.287805 + 0.498493i −0.973285 0.229598i \(-0.926259\pi\)
0.685481 + 0.728091i \(0.259592\pi\)
\(318\) 10.9964 10.5063i 0.616648 0.589166i
\(319\) −1.55408 2.69175i −0.0870120 0.150709i
\(320\) −13.4021 23.2132i −0.749203 1.29766i
\(321\) 21.3484 + 6.24496i 1.19155 + 0.348560i
\(322\) 0 0
\(323\) −9.58307 −0.533216
\(324\) 21.0438 29.8068i 1.16910 1.65593i
\(325\) −4.08009 −0.226323
\(326\) 13.7324 23.7852i 0.760567 1.31734i
\(327\) 4.32349 + 1.26473i 0.239090 + 0.0699400i
\(328\) −18.9882 32.8885i −1.04845 1.81596i
\(329\) 0 0
\(330\) 4.58113 4.37697i 0.252183 0.240944i
\(331\) 10.1819 17.6356i 0.559648 0.969339i −0.437878 0.899035i \(-0.644270\pi\)
0.997526 0.0703042i \(-0.0223970\pi\)
\(332\) 49.3463 2.70823
\(333\) 5.88151 + 3.76300i 0.322305 + 0.206211i
\(334\) 8.51392 0.465861
\(335\) 6.58596 11.4072i 0.359829 0.623242i
\(336\) 0 0
\(337\) 2.85594 + 4.94662i 0.155573 + 0.269460i 0.933267 0.359182i \(-0.116944\pi\)
−0.777695 + 0.628642i \(0.783611\pi\)
\(338\) 15.7017 + 27.1962i 0.854062 + 1.47928i
\(339\) 5.72030 + 23.4755i 0.310684 + 1.27502i
\(340\) 36.0064 62.3649i 1.95272 3.38221i
\(341\) 2.85600 0.154661
\(342\) 12.9346 6.70145i 0.699422 0.362373i
\(343\) 0 0
\(344\) 5.88151 10.1871i 0.317110 0.549251i
\(345\) 21.2915 20.3427i 1.14630 1.09521i
\(346\) 7.44746 + 12.8994i 0.400378 + 0.693475i
\(347\) −4.44066 7.69145i −0.238387 0.412899i 0.721865 0.692034i \(-0.243285\pi\)
−0.960252 + 0.279136i \(0.909952\pi\)
\(348\) 51.5410 + 15.0771i 2.76289 + 0.808217i
\(349\) −10.4874 + 18.1648i −0.561379 + 0.972337i 0.435997 + 0.899948i \(0.356396\pi\)
−0.997376 + 0.0723893i \(0.976938\pi\)
\(350\) 0 0
\(351\) −0.820039 + 2.39285i −0.0437704 + 0.127721i
\(352\) 0.219262 0.0116867
\(353\) 7.38268 12.7872i 0.392941 0.680593i −0.599895 0.800078i \(-0.704791\pi\)
0.992836 + 0.119485i \(0.0381245\pi\)
\(354\) 25.0261 + 7.32078i 1.33012 + 0.389095i
\(355\) 15.4746 + 26.8028i 0.821306 + 1.42254i
\(356\) −30.0613 52.0677i −1.59325 2.75959i
\(357\) 0 0
\(358\) −11.2360 + 19.4613i −0.593840 + 1.02856i
\(359\) 7.21206 0.380638 0.190319 0.981722i \(-0.439048\pi\)
0.190319 + 0.981722i \(0.439048\pi\)
\(360\) −2.52684 + 55.4071i −0.133176 + 2.92021i
\(361\) −15.1052 −0.795013
\(362\) −14.6988 + 25.4591i −0.772554 + 1.33810i
\(363\) 4.44284 + 18.2330i 0.233188 + 0.956983i
\(364\) 0 0
\(365\) 3.60963 + 6.25206i 0.188937 + 0.327248i
\(366\) 8.09884 + 33.2368i 0.423333 + 1.73732i
\(367\) 5.48711 9.50396i 0.286425 0.496103i −0.686529 0.727103i \(-0.740866\pi\)
0.972954 + 0.231000i \(0.0741998\pi\)
\(368\) 20.1124 1.04843
\(369\) 1.02696 22.5186i 0.0534614 1.17227i
\(370\) −20.9485 −1.08906
\(371\) 0 0
\(372\) −35.6775 + 34.0875i −1.84979 + 1.76736i
\(373\) 0.271884 + 0.470916i 0.0140776 + 0.0243831i 0.872978 0.487759i \(-0.162185\pi\)
−0.858901 + 0.512142i \(0.828852\pi\)
\(374\) −2.42792 4.20528i −0.125545 0.217450i
\(375\) −20.5634 6.01534i −1.06189 0.310631i
\(376\) 15.9614 27.6459i 0.823145 1.42573i
\(377\) −3.72286 −0.191737
\(378\) 0 0
\(379\) −22.6912 −1.16557 −0.582785 0.812626i \(-0.698037\pi\)
−0.582785 + 0.812626i \(0.698037\pi\)
\(380\) −14.6337 + 25.3464i −0.750695 + 1.30024i
\(381\) −25.8397 7.55879i −1.32381 0.387249i
\(382\) −11.2448 19.4766i −0.575336 0.996511i
\(383\) −17.8569 30.9291i −0.912447 1.58041i −0.810596 0.585606i \(-0.800857\pi\)
−0.101851 0.994800i \(-0.532477\pi\)
\(384\) 23.9298 22.8633i 1.22116 1.16674i
\(385\) 0 0
\(386\) 41.6883 2.12188
\(387\) 6.19961 3.21204i 0.315144 0.163277i
\(388\) −38.4632 −1.95267
\(389\) −19.3296 + 33.4798i −0.980048 + 1.69749i −0.317892 + 0.948127i \(0.602975\pi\)
−0.662156 + 0.749366i \(0.730359\pi\)
\(390\) −1.79665 7.37327i −0.0909768 0.373360i
\(391\) −11.2842 19.5447i −0.570664 0.988420i
\(392\) 0 0
\(393\) 3.49115 + 14.3273i 0.176105 + 0.722718i
\(394\) 26.2257 45.4242i 1.32123 2.28844i
\(395\) −29.8581 −1.50233
\(396\) 4.16372 + 2.66395i 0.209235 + 0.133869i
\(397\) −11.9478 −0.599644 −0.299822 0.953995i \(-0.596927\pi\)
−0.299822 + 0.953995i \(0.596927\pi\)
\(398\) −12.2709 + 21.2538i −0.615085 + 1.06536i
\(399\) 0 0
\(400\) −18.1352 31.4111i −0.906761 1.57056i
\(401\) −16.1783 28.0216i −0.807906 1.39933i −0.914312 0.405011i \(-0.867268\pi\)
0.106406 0.994323i \(-0.466066\pi\)
\(402\) 14.7283 + 4.30841i 0.734579 + 0.214884i
\(403\) 1.71041 2.96251i 0.0852015 0.147573i
\(404\) 35.3182 1.75715
\(405\) −18.9882 + 26.8952i −0.943530 + 1.33643i
\(406\) 0 0
\(407\) −0.472958 + 0.819187i −0.0234437 + 0.0406056i
\(408\) 40.7979 + 11.9345i 2.01980 + 0.590844i
\(409\) −9.48751 16.4328i −0.469127 0.812552i 0.530250 0.847841i \(-0.322098\pi\)
−0.999377 + 0.0352893i \(0.988765\pi\)
\(410\) 33.8157 + 58.5704i 1.67004 + 2.89259i
\(411\) −0.472433 + 0.451379i −0.0233034 + 0.0222649i
\(412\) −16.2713 + 28.1827i −0.801630 + 1.38846i
\(413\) 0 0
\(414\) 28.8982 + 18.4891i 1.42027 + 0.908691i
\(415\) −44.5261 −2.18570
\(416\) 0.131312 0.227439i 0.00643811 0.0111511i
\(417\) 7.79153 + 31.9757i 0.381553 + 1.56586i
\(418\) 0.986757 + 1.70911i 0.0482639 + 0.0835955i
\(419\) 8.64523 + 14.9740i 0.422347 + 0.731526i 0.996169 0.0874539i \(-0.0278730\pi\)
−0.573822 + 0.818980i \(0.694540\pi\)
\(420\) 0 0
\(421\) −9.30039 + 16.1087i −0.453273 + 0.785092i −0.998587 0.0531397i \(-0.983077\pi\)
0.545314 + 0.838232i \(0.316410\pi\)
\(422\) 12.0364 0.585922
\(423\) 16.8246 8.71690i 0.818042 0.423830i
\(424\) −18.0364 −0.875924
\(425\) −20.3496 + 35.2466i −0.987103 + 1.70971i
\(426\) −26.0699 + 24.9081i −1.26309 + 1.20680i
\(427\) 0 0
\(428\) −26.0313 45.0876i −1.25827 2.17939i
\(429\) −0.328893 0.0962098i −0.0158791 0.00464505i
\(430\) −10.4743 + 18.1420i −0.505114 + 0.874883i
\(431\) −15.8784 −0.764835 −0.382418 0.923990i \(-0.624908\pi\)
−0.382418 + 0.923990i \(0.624908\pi\)
\(432\) −22.0666 + 4.32260i −1.06168 + 0.207971i
\(433\) 40.4367 1.94326 0.971631 0.236501i \(-0.0760007\pi\)
0.971631 + 0.236501i \(0.0760007\pi\)
\(434\) 0 0
\(435\) −46.5064 13.6043i −2.22981 0.652278i
\(436\) −5.27188 9.13117i −0.252477 0.437304i
\(437\) 4.58611 + 7.94338i 0.219384 + 0.379984i
\(438\) −6.08113 + 5.81012i −0.290567 + 0.277618i
\(439\) −6.23047 + 10.7915i −0.297364 + 0.515050i −0.975532 0.219857i \(-0.929441\pi\)
0.678168 + 0.734907i \(0.262774\pi\)
\(440\) −7.51399 −0.358216
\(441\) 0 0
\(442\) −5.81616 −0.276646
\(443\) 4.11537 7.12802i 0.195527 0.338663i −0.751546 0.659680i \(-0.770692\pi\)
0.947073 + 0.321018i \(0.104025\pi\)
\(444\) −3.86908 15.8783i −0.183619 0.753553i
\(445\) 27.1249 + 46.9817i 1.28584 + 2.22715i
\(446\) 28.7988 + 49.8810i 1.36366 + 2.36193i
\(447\) 3.97822 + 16.3262i 0.188163 + 0.772204i
\(448\) 0 0
\(449\) 5.64474 0.266392 0.133196 0.991090i \(-0.457476\pi\)
0.133196 + 0.991090i \(0.457476\pi\)
\(450\) 2.81858 61.8040i 0.132869 2.91347i
\(451\) 3.05384 0.143800
\(452\) 28.2776 48.9783i 1.33007 2.30374i
\(453\) 16.0735 15.3571i 0.755197 0.721541i
\(454\) 7.52716 + 13.0374i 0.353267 + 0.611876i
\(455\) 0 0
\(456\) −16.5811 4.85041i −0.776482 0.227141i
\(457\) −2.53443 + 4.38977i −0.118556 + 0.205345i −0.919196 0.393801i \(-0.871160\pi\)
0.800640 + 0.599146i \(0.204493\pi\)
\(458\) 3.59330 0.167904
\(459\) 16.5811 + 19.0185i 0.773941 + 0.887709i
\(460\) −68.9255 −3.21367
\(461\) 3.88831 6.73475i 0.181097 0.313669i −0.761158 0.648567i \(-0.775369\pi\)
0.942254 + 0.334898i \(0.108702\pi\)
\(462\) 0 0
\(463\) 4.58998 + 7.95008i 0.213314 + 0.369472i 0.952750 0.303756i \(-0.0982408\pi\)
−0.739435 + 0.673228i \(0.764907\pi\)
\(464\) −16.5474 28.6609i −0.768192 1.33055i
\(465\) 32.1925 30.7578i 1.49289 1.42636i
\(466\) 16.2989 28.2306i 0.755033 1.30776i
\(467\) −13.7654 −0.636989 −0.318494 0.947925i \(-0.603177\pi\)
−0.318494 + 0.947925i \(0.603177\pi\)
\(468\) 5.25688 2.72361i 0.242999 0.125899i
\(469\) 0 0
\(470\) −28.4253 + 49.2340i −1.31116 + 2.27100i
\(471\) −8.58998 35.2524i −0.395805 1.62435i
\(472\) −15.4614 26.7800i −0.711669 1.23265i
\(473\) 0.472958 + 0.819187i 0.0217466 + 0.0376663i
\(474\) −8.23518 33.7964i −0.378254 1.55232i
\(475\) 8.27052 14.3250i 0.379477 0.657274i
\(476\) 0 0
\(477\) −9.01819 5.76985i −0.412914 0.264183i
\(478\) 47.7060 2.18202
\(479\) −4.35588 + 7.54461i −0.199025 + 0.344722i −0.948213 0.317636i \(-0.897111\pi\)
0.749187 + 0.662358i \(0.230444\pi\)
\(480\) 2.47150 2.36135i 0.112808 0.107780i
\(481\) 0.566492 + 0.981194i 0.0258298 + 0.0447386i
\(482\) 6.21731 + 10.7687i 0.283191 + 0.490501i
\(483\) 0 0
\(484\) 21.9626 38.0404i 0.998302 1.72911i
\(485\) 34.7060 1.57592
\(486\) −35.6798 14.0747i −1.61847 0.638442i
\(487\) −18.0364 −0.817306 −0.408653 0.912690i \(-0.634001\pi\)
−0.408653 + 0.912690i \(0.634001\pi\)
\(488\) 20.2849 35.1344i 0.918253 1.59046i
\(489\) −18.5560 5.42810i −0.839129 0.245467i
\(490\) 0 0
\(491\) −1.02344 1.77266i −0.0461874 0.0799989i 0.842007 0.539466i \(-0.181374\pi\)
−0.888195 + 0.459467i \(0.848040\pi\)
\(492\) −38.1490 + 36.4489i −1.71989 + 1.64324i
\(493\) −18.5679 + 32.1606i −0.836257 + 1.44844i
\(494\) 2.36381 0.106353
\(495\) −3.75700 2.40373i −0.168864 0.108040i
\(496\) 30.4097 1.36544
\(497\) 0 0
\(498\) −12.2807 50.3990i −0.550313 2.25843i
\(499\) 19.5438 + 33.8508i 0.874899 + 1.51537i 0.856870 + 0.515532i \(0.172406\pi\)
0.0180291 + 0.999837i \(0.494261\pi\)
\(500\) 25.0742 + 43.4297i 1.12135 + 1.94224i
\(501\) −1.41887 5.82292i −0.0633906 0.260149i
\(502\) 18.5679 32.1606i 0.828727 1.43540i
\(503\) 5.11846 0.228221 0.114111 0.993468i \(-0.463598\pi\)
0.114111 + 0.993468i \(0.463598\pi\)
\(504\) 0 0
\(505\) −31.8683 −1.41812
\(506\) −2.32383 + 4.02499i −0.103307 + 0.178933i
\(507\) 15.9836 15.2712i 0.709855 0.678219i
\(508\) 31.5079 + 54.5732i 1.39794 + 2.42130i
\(509\) 14.7636 + 25.5713i 0.654386 + 1.13343i 0.982047 + 0.188634i \(0.0604060\pi\)
−0.327662 + 0.944795i \(0.606261\pi\)
\(510\) −72.6562 21.2538i −3.21727 0.941136i
\(511\) 0 0
\(512\) −41.4078 −1.82998
\(513\) −6.73891 7.72952i −0.297530 0.341267i
\(514\) −18.9750 −0.836952
\(515\) 14.6819 25.4298i 0.646962 1.12057i
\(516\) −15.6856 4.58845i −0.690520 0.201995i
\(517\) 1.28352 + 2.22313i 0.0564493 + 0.0977730i
\(518\) 0 0
\(519\) 7.58113 7.24327i 0.332775 0.317944i
\(520\) −4.50000 + 7.79423i −0.197338 + 0.341800i
\(521\) 1.06470 0.0466454 0.0233227 0.999728i \(-0.492575\pi\)
0.0233227 + 0.999728i \(0.492575\pi\)
\(522\) 2.57179 56.3927i 0.112564 2.46824i
\(523\) 13.3819 0.585149 0.292574 0.956243i \(-0.405488\pi\)
0.292574 + 0.956243i \(0.405488\pi\)
\(524\) 17.2581 29.8918i 0.753922 1.30583i
\(525\) 0 0
\(526\) −5.18190 8.97532i −0.225942 0.391343i
\(527\) −17.0615 29.5513i −0.743210 1.28728i
\(528\) −0.721181 2.95966i −0.0313854 0.128803i
\(529\) 0.699612 1.21176i 0.0304179 0.0526853i
\(530\) 32.1206 1.39523
\(531\) 0.836219 18.3361i 0.0362888 0.795719i
\(532\) 0 0
\(533\) 1.82889 3.16774i 0.0792181 0.137210i
\(534\) −45.6972 + 43.6606i −1.97751 + 1.88938i
\(535\) 23.4885 + 40.6833i 1.01550 + 1.75889i
\(536\) −9.09931 15.7605i −0.393031 0.680749i
\(537\) 15.1827 + 4.44133i 0.655181 + 0.191658i
\(538\) 25.5286 44.2168i 1.10062 1.90632i
\(539\) 0 0
\(540\) 75.6224 14.8136i 3.25427 0.637475i
\(541\) −34.0875 −1.46554 −0.732769 0.680478i \(-0.761772\pi\)
−0.732769 + 0.680478i \(0.761772\pi\)
\(542\) −35.0485 + 60.7058i −1.50546 + 2.60754i
\(543\) 19.8619 + 5.81012i 0.852354 + 0.249336i
\(544\) −1.30985 2.26873i −0.0561594 0.0972709i
\(545\) 4.75692 + 8.23922i 0.203764 + 0.352930i
\(546\) 0 0
\(547\) 2.97150 5.14678i 0.127052 0.220060i −0.795481 0.605978i \(-0.792782\pi\)
0.922533 + 0.385918i \(0.126115\pi\)
\(548\) 1.52937 0.0653316
\(549\) 21.3820 11.0781i 0.912560 0.472800i
\(550\) 8.38151 0.357389
\(551\) 7.54638 13.0707i 0.321487 0.556831i
\(552\) −9.63198 39.5287i −0.409964 1.68245i
\(553\) 0 0
\(554\) −21.1139 36.5704i −0.897044 1.55373i
\(555\) 3.49115 + 14.3273i 0.148191 + 0.608161i
\(556\) 38.5165 66.7126i 1.63346 2.82924i
\(557\) −30.0803 −1.27454 −0.637272 0.770639i \(-0.719937\pi\)
−0.637272 + 0.770639i \(0.719937\pi\)
\(558\) 43.6937 + 27.9553i 1.84970 + 1.18344i
\(559\) 1.13298 0.0479202
\(560\) 0 0
\(561\) −2.47150 + 2.36135i −0.104347 + 0.0996963i
\(562\) −11.6170 20.1213i −0.490035 0.848765i
\(563\) −9.81060 16.9925i −0.413468 0.716147i 0.581799 0.813333i \(-0.302349\pi\)
−0.995266 + 0.0971860i \(0.969016\pi\)
\(564\) −42.5679 12.4522i −1.79243 0.524333i
\(565\) −25.5154 + 44.1940i −1.07344 + 1.85926i
\(566\) −41.5049 −1.74458
\(567\) 0 0
\(568\) 42.7601 1.79417
\(569\) 0.687159 1.19019i 0.0288072 0.0498955i −0.851262 0.524740i \(-0.824162\pi\)
0.880070 + 0.474845i \(0.157496\pi\)
\(570\) 29.5290 + 8.63800i 1.23683 + 0.361806i
\(571\) −8.69076 15.0528i −0.363697 0.629941i 0.624869 0.780729i \(-0.285152\pi\)
−0.988566 + 0.150788i \(0.951819\pi\)
\(572\) 0.401038 + 0.694619i 0.0167683 + 0.0290435i
\(573\) −11.4467 + 10.9365i −0.478191 + 0.456880i
\(574\) 0 0
\(575\) 38.9545 1.62451
\(576\) −18.5167 11.8470i −0.771530 0.493626i
\(577\) 27.0548 1.12631 0.563153 0.826353i \(-0.309588\pi\)
0.563153 + 0.826353i \(0.309588\pi\)
\(578\) −8.09406 + 14.0193i −0.336668 + 0.583127i
\(579\) −6.94750 28.5119i −0.288728 1.18491i
\(580\) 56.7080 + 98.2211i 2.35467 + 4.07841i
\(581\) 0 0
\(582\) 9.57227 + 39.2837i 0.396783 + 1.62836i
\(583\) 0.725191 1.25607i 0.0300344 0.0520210i
\(584\) 9.97430 0.412740
\(585\) −4.74338 + 2.45756i −0.196115 + 0.101608i
\(586\) 9.16010 0.378400
\(587\) 3.75700 6.50731i 0.155068 0.268585i −0.778016 0.628245i \(-0.783774\pi\)
0.933084 + 0.359659i \(0.117107\pi\)
\(588\) 0 0
\(589\) 6.93414 + 12.0103i 0.285716 + 0.494875i
\(590\) 27.5349 + 47.6919i 1.13359 + 1.96344i
\(591\) −35.4376 10.3664i −1.45771 0.426417i
\(592\) −5.03590 + 8.72243i −0.206974 + 0.358490i
\(593\) −35.5808 −1.46113 −0.730565 0.682843i \(-0.760743\pi\)
−0.730565 + 0.682843i \(0.760743\pi\)
\(594\) 1.68456 4.91551i 0.0691184 0.201686i
\(595\) 0 0
\(596\) 19.6659 34.0623i 0.805545 1.39524i
\(597\) 16.5811 + 4.85041i 0.678620 + 0.198514i
\(598\) 2.78340 + 4.82100i 0.113822 + 0.197145i
\(599\) 5.74105 + 9.94379i 0.234573 + 0.406292i 0.959148 0.282903i \(-0.0912975\pi\)
−0.724576 + 0.689195i \(0.757964\pi\)
\(600\) −53.0499 + 50.6857i −2.16575 + 2.06924i
\(601\) −0.190030 + 0.329142i −0.00775150 + 0.0134260i −0.869875 0.493272i \(-0.835801\pi\)
0.862124 + 0.506698i \(0.169134\pi\)
\(602\) 0 0
\(603\) 0.492129 10.7911i 0.0200411 0.439448i
\(604\) −52.0335 −2.11721
\(605\) −19.8173 + 34.3246i −0.805688 + 1.39549i
\(606\) −8.78959 36.0716i −0.357053 1.46531i
\(607\) −9.27044 16.0569i −0.376275 0.651728i 0.614242 0.789118i \(-0.289462\pi\)
−0.990517 + 0.137390i \(0.956129\pi\)
\(608\) 0.532351 + 0.922058i 0.0215897 + 0.0373944i
\(609\) 0 0
\(610\) −36.1249 + 62.5702i −1.46265 + 2.53339i
\(611\) 3.07472 0.124390
\(612\) 2.69054 58.9966i 0.108759 2.38480i
\(613\) 7.32451 0.295834 0.147917 0.989000i \(-0.452743\pi\)
0.147917 + 0.989000i \(0.452743\pi\)
\(614\) 37.6077 65.1385i 1.51772 2.62877i
\(615\) 34.4226 32.8885i 1.38805 1.32619i
\(616\) 0 0
\(617\) 12.7427 + 22.0710i 0.513002 + 0.888546i 0.999886 + 0.0150791i \(0.00480000\pi\)
−0.486884 + 0.873466i \(0.661867\pi\)
\(618\) 32.8334 + 9.60462i 1.32075 + 0.386354i
\(619\) 16.4482 28.4891i 0.661108 1.14507i −0.319217 0.947682i \(-0.603420\pi\)
0.980325 0.197391i \(-0.0632468\pi\)
\(620\) −104.214 −4.18535
\(621\) 7.82927 22.8456i 0.314178 0.916764i
\(622\) 25.6748 1.02947
\(623\) 0 0
\(624\) −3.50194 1.02441i −0.140190 0.0410092i
\(625\) −1.67111 2.89444i −0.0668443 0.115778i
\(626\) −0.762585 1.32084i −0.0304790 0.0527912i
\(627\) 1.00447 0.959702i 0.0401145 0.0383268i
\(628\) −42.4636 + 73.5490i −1.69448 + 2.93493i
\(629\) 11.3016 0.450626
\(630\) 0 0
\(631\) 29.8683 1.18904 0.594519 0.804082i \(-0.297343\pi\)
0.594519 + 0.804082i \(0.297343\pi\)
\(632\) −20.6264 + 35.7259i −0.820472 + 1.42110i
\(633\) −2.00590 8.23203i −0.0797275 0.327194i
\(634\) −12.6082 21.8380i −0.500734 0.867297i
\(635\) −28.4301 49.2424i −1.12822 1.95413i
\(636\) 5.93251 + 24.3464i 0.235239 + 0.965399i
\(637\) 0 0
\(638\) 7.64766 0.302774
\(639\) 21.3801 + 13.6790i 0.845782 + 0.541132i
\(640\) 69.8991 2.76301
\(641\) −5.73025 + 9.92509i −0.226331 + 0.392017i −0.956718 0.291016i \(-0.906007\pi\)
0.730387 + 0.683034i \(0.239340\pi\)
\(642\) −39.5710 + 37.8075i −1.56174 + 1.49214i
\(643\) −8.69078 15.0529i −0.342731 0.593627i 0.642208 0.766531i \(-0.278019\pi\)
−0.984939 + 0.172903i \(0.944685\pi\)
\(644\) 0 0
\(645\) 14.1534 + 4.14024i 0.557290 + 0.163022i
\(646\) 11.7896 20.4202i 0.463855 0.803421i
\(647\) −25.3439 −0.996372 −0.498186 0.867070i \(-0.666000\pi\)
−0.498186 + 0.867070i \(0.666000\pi\)
\(648\) 19.0634 + 41.2993i 0.748882 + 1.62239i
\(649\) 2.48664 0.0976091
\(650\) 5.01954 8.69410i 0.196883 0.341011i
\(651\) 0 0
\(652\) 22.6264 + 39.1900i 0.886116 + 1.53480i
\(653\) −7.04163 12.1965i −0.275560 0.477284i 0.694716 0.719284i \(-0.255530\pi\)
−0.970276 + 0.242000i \(0.922197\pi\)
\(654\) −8.01396 + 7.65681i −0.313370 + 0.299405i
\(655\) −15.5723 + 26.9720i −0.608459 + 1.05388i
\(656\) 32.5163 1.26955
\(657\) 4.98715 + 3.19079i 0.194567 + 0.124484i
\(658\) 0 0
\(659\) −19.0854 + 33.0569i −0.743462 + 1.28771i 0.207449 + 0.978246i \(0.433484\pi\)
−0.950910 + 0.309467i \(0.899849\pi\)
\(660\) 2.47150 + 10.1428i 0.0962028 + 0.394807i
\(661\) −0.176866 0.306341i −0.00687930 0.0119153i 0.862565 0.505946i \(-0.168856\pi\)
−0.869445 + 0.494031i \(0.835523\pi\)
\(662\) 25.0526 + 43.3924i 0.973698 + 1.68649i
\(663\) 0.969283 + 3.97784i 0.0376438 + 0.154487i
\(664\) −30.7591 + 53.2764i −1.19369 + 2.06752i
\(665\) 0 0
\(666\) −15.2542 + 7.90324i −0.591087 + 0.306244i
\(667\) 35.5438 1.37626
\(668\) −7.01403 + 12.1487i −0.271381 + 0.470046i
\(669\) 29.3157 28.0092i 1.13341 1.08290i
\(670\) 16.2048 + 28.0675i 0.626045 + 1.08434i
\(671\) 1.63119 + 2.82531i 0.0629715 + 0.109070i
\(672\) 0 0
\(673\) 10.5555 18.2827i 0.406886 0.704748i −0.587653 0.809113i \(-0.699948\pi\)
0.994539 + 0.104365i \(0.0332811\pi\)
\(674\) −14.0541 −0.541343
\(675\) −42.7393 + 8.37215i −1.64504 + 0.322244i
\(676\) −51.7424 −1.99009
\(677\) 10.5732 18.3133i 0.406361 0.703837i −0.588118 0.808775i \(-0.700131\pi\)
0.994479 + 0.104938i \(0.0334643\pi\)
\(678\) −57.0605 16.6917i −2.19140 0.641041i
\(679\) 0 0
\(680\) 44.8879 + 77.7482i 1.72137 + 2.98151i
\(681\) 7.66225 7.32078i 0.293618 0.280533i
\(682\) −3.51360 + 6.08573i −0.134543 + 0.233035i
\(683\) 34.7716 1.33050 0.665249 0.746622i \(-0.268326\pi\)
0.665249 + 0.746622i \(0.268326\pi\)
\(684\) −1.09349 + 23.9775i −0.0418107 + 0.916801i
\(685\) −1.37998 −0.0527264
\(686\) 0 0
\(687\) −0.598835 2.45756i −0.0228470 0.0937618i
\(688\) 5.03590 + 8.72243i 0.191992 + 0.332539i
\(689\) −0.868609 1.50447i −0.0330914 0.0573159i
\(690\) 17.1534 + 70.3959i 0.653019 + 2.67993i
\(691\) 17.3246 30.0071i 0.659059 1.14152i −0.321801 0.946807i \(-0.604288\pi\)
0.980860 0.194716i \(-0.0623785\pi\)
\(692\) −24.5418 −0.932940
\(693\) 0 0
\(694\) 21.8525 0.829511
\(695\) −34.7542 + 60.1960i −1.31830 + 2.28336i
\(696\) −48.4051 + 46.2479i −1.83479 + 1.75302i
\(697\) −18.2434 31.5985i −0.691017 1.19688i
\(698\) −25.8044 44.6945i −0.976710 1.69171i
\(699\) −22.0240 6.44260i −0.833024 0.243681i
\(700\) 0 0
\(701\) −48.6050 −1.83579 −0.917894 0.396826i \(-0.870111\pi\)
−0.917894 + 0.396826i \(0.870111\pi\)
\(702\) −4.08998 4.69120i −0.154366 0.177058i
\(703\) −4.59322 −0.173236
\(704\) 1.48901 2.57904i 0.0561192 0.0972012i
\(705\) 38.4098 + 11.2359i 1.44660 + 0.423167i
\(706\) 18.1651 + 31.4629i 0.683654 + 1.18412i
\(707\) 0 0
\(708\) −31.0634 + 29.6791i −1.16743 + 1.11541i
\(709\) −2.05408 + 3.55778i −0.0771428 + 0.133615i −0.902016 0.431702i \(-0.857913\pi\)
0.824873 + 0.565318i \(0.191246\pi\)
\(710\) −76.1506 −2.85788
\(711\) −21.7419 + 11.2646i −0.815386 + 0.422454i
\(712\) 74.9528 2.80898
\(713\) −16.3300 + 28.2844i −0.611564 + 1.05926i
\(714\) 0 0
\(715\) −0.361864 0.626767i −0.0135330 0.0234398i
\(716\) −18.5131 32.0657i −0.691868 1.19835i
\(717\) −7.95037 32.6276i −0.296912 1.21850i
\(718\) −8.87266 + 15.3679i −0.331125 + 0.573525i
\(719\) −48.2816 −1.80060 −0.900299 0.435271i \(-0.856653\pi\)
−0.900299 + 0.435271i \(0.856653\pi\)
\(720\) −40.0032 25.5941i −1.49083 0.953837i
\(721\) 0 0
\(722\) 18.5833 32.1872i 0.691597 1.19788i
\(723\) 6.32889 6.04684i 0.235374 0.224884i
\(724\) −24.2187 41.9481i −0.900082 1.55899i
\(725\) −32.0495 55.5114i −1.19029 2.06164i
\(726\) −44.3177 12.9641i −1.64478 0.481143i
\(727\) −20.5151 + 35.5332i −0.760863 + 1.31785i 0.181543 + 0.983383i \(0.441891\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(728\) 0 0
\(729\) −3.67996 + 26.7480i −0.136295 + 0.990668i
\(730\) −17.7630 −0.657439
\(731\) 5.65082 9.78750i 0.209003 0.362004i
\(732\) −54.0983 15.8252i −1.99953 0.584916i
\(733\) 15.2714 + 26.4508i 0.564062 + 0.976983i 0.997136 + 0.0756253i \(0.0240953\pi\)
−0.433075 + 0.901358i \(0.642571\pi\)
\(734\) 13.5011 + 23.3845i 0.498334 + 0.863139i
\(735\) 0 0
\(736\) −1.25370 + 2.17147i −0.0462118 + 0.0800413i
\(737\) 1.46343 0.0539061
\(738\) 46.7205 + 29.8918i 1.71981 + 1.10033i
\(739\) 23.8200 0.876234 0.438117 0.898918i \(-0.355646\pi\)
0.438117 + 0.898918i \(0.355646\pi\)
\(740\) 17.2581 29.8918i 0.634419 1.09885i
\(741\) −0.393936 1.61668i −0.0144716 0.0593901i
\(742\) 0 0
\(743\) −5.26089 9.11213i −0.193003 0.334292i 0.753241 0.657745i \(-0.228490\pi\)
−0.946244 + 0.323453i \(0.895156\pi\)
\(744\) −14.5634 59.7669i −0.533921 2.19116i
\(745\) −17.7449 + 30.7350i −0.650121 + 1.12604i
\(746\) −1.33794 −0.0489855
\(747\) −32.4227 + 16.7983i −1.18629 + 0.614619i
\(748\) 8.00079 0.292538
\(749\) 0 0
\(750\) 38.1160 36.4174i 1.39180 1.32977i
\(751\) 5.13521 + 8.89445i 0.187386 + 0.324563i 0.944378 0.328862i \(-0.106665\pi\)
−0.756992 + 0.653425i \(0.773332\pi\)
\(752\) 13.6665 + 23.6711i 0.498367 + 0.863197i
\(753\) −25.0900 7.33948i −0.914330 0.267465i
\(754\) 4.58005 7.93288i 0.166796 0.288899i
\(755\) 46.9507 1.70871
\(756\) 0 0
\(757\) 8.03930 0.292193 0.146097 0.989270i \(-0.453329\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(758\) 27.9159 48.3518i 1.01395 1.75622i
\(759\) 3.14009 + 0.918558i 0.113978 + 0.0333416i
\(760\) −18.2434 31.5985i −0.661757 1.14620i
\(761\) 13.8302 + 23.9547i 0.501345 + 0.868355i 0.999999 + 0.00155404i \(0.000494668\pi\)
−0.498654 + 0.866801i \(0.666172\pi\)
\(762\) 47.8961 45.7616i 1.73509 1.65777i
\(763\) 0 0
\(764\) 37.0554 1.34062
\(765\) −2.42773 + 53.2338i −0.0877747 + 1.92467i
\(766\) 87.8742 3.17502
\(767\) 1.48920 2.57938i 0.0537720 0.0931359i
\(768\) 13.2696 + 54.4573i 0.478827 + 1.96506i
\(769\) −16.9613 29.3778i −0.611640 1.05939i −0.990964 0.134128i \(-0.957177\pi\)
0.379324 0.925264i \(-0.376157\pi\)
\(770\) 0 0
\(771\) 3.16225 + 12.9776i 0.113886 + 0.467376i
\(772\) −34.3442 + 59.4858i −1.23607 + 2.14094i
\(773\) 28.5956 1.02851 0.514256 0.857637i \(-0.328068\pi\)
0.514256 + 0.857637i \(0.328068\pi\)
\(774\) −0.782679 + 17.1621i −0.0281328 + 0.616880i
\(775\) 58.8986 2.11570
\(776\) 23.9753 41.5265i 0.860664 1.49071i
\(777\) 0 0
\(778\) −47.5605 82.3772i −1.70513 2.95337i
\(779\) 7.41449 + 12.8423i 0.265652 + 0.460122i
\(780\) 12.0012 + 3.51066i 0.429711 + 0.125702i
\(781\) −1.71926 + 2.97785i −0.0615200 + 0.106556i
\(782\) 55.5294 1.98573
\(783\) −38.9973 + 7.63912i −1.39365 + 0.273000i
\(784\) 0 0
\(785\) 38.3157 66.3647i 1.36754 2.36866i
\(786\) −34.8245 10.1871i −1.24215 0.363361i
\(787\) 23.0017 + 39.8402i 0.819923 + 1.42015i 0.905738 + 0.423838i \(0.139317\pi\)
−0.0858145 + 0.996311i \(0.527349\pi\)
\(788\) 43.2111 + 74.8438i 1.53933 + 2.66620i
\(789\) −5.27491 + 5.03983i −0.187792 + 0.179423i
\(790\) 36.7330 63.6235i 1.30690 2.26362i
\(791\) 0 0
\(792\) −5.47150 + 2.83480i −0.194421 + 0.100730i
\(793\) 3.90757 0.138762
\(794\) 14.6988 25.4591i 0.521642 0.903511i
\(795\) −5.35301 21.9682i −0.189852 0.779133i
\(796\) −20.2183 35.0192i −0.716620 1.24122i
\(797\) −18.4558 31.9664i −0.653739 1.13231i −0.982208 0.187795i \(-0.939866\pi\)
0.328469 0.944515i \(-0.393467\pi\)
\(798\) 0 0
\(799\) 15.3353 26.5615i 0.542524 0.939679i
\(800\) 4.52179 0.159869
\(801\) 37.4764 + 23.9775i 1.32416 + 0.847202i
\(802\) 79.6136 2.81125
\(803\) −0.401038 + 0.694619i −0.0141523 + 0.0245126i
\(804\) −18.2814 + 17.4666i −0.644734 + 0.616001i
\(805\) 0 0
\(806\) 4.20847 + 7.28928i 0.148237 + 0.256754i
\(807\) −34.4956 10.0909i −1.21430 0.355216i
\(808\) −22.0150 + 38.1311i −0.774484 + 1.34145i
\(809\) 47.6887 1.67665 0.838323 0.545174i \(-0.183537\pi\)
0.838323 + 0.545174i \(0.183537\pi\)
\(810\) −33.9496 73.5490i −1.19287 2.58425i
\(811\) 6.02728 0.211646 0.105823 0.994385i \(-0.466252\pi\)
0.105823 + 0.994385i \(0.466252\pi\)
\(812\) 0 0
\(813\) 47.3594 + 13.8539i 1.66097 + 0.485877i
\(814\) −1.16372 2.01561i −0.0407882 0.0706472i
\(815\) −20.4162 35.3619i −0.715148 1.23867i
\(816\) −26.3157 + 25.1429i −0.921232 + 0.880177i
\(817\) −2.29661 + 3.97784i −0.0803481 + 0.139167i
\(818\) 46.6881 1.63241
\(819\) 0 0
\(820\) −111.434 −3.89143
\(821\) 19.6321 34.0038i 0.685165 1.18674i −0.288220 0.957564i \(-0.593064\pi\)
0.973385 0.229176i \(-0.0736031\pi\)
\(822\) −0.380613 1.56200i −0.0132754 0.0544809i
\(823\) −11.3815 19.7134i −0.396735 0.687165i 0.596586 0.802549i \(-0.296523\pi\)
−0.993321 + 0.115384i \(0.963190\pi\)
\(824\) −20.2849 35.1344i −0.706657 1.22397i
\(825\) −1.39681 5.73237i −0.0486306 0.199575i
\(826\) 0 0
\(827\) −28.9286 −1.00595 −0.502973 0.864302i \(-0.667760\pi\)
−0.502973 + 0.864302i \(0.667760\pi\)
\(828\) −50.1898 + 26.0035i −1.74422 + 0.903684i
\(829\) −33.9767 −1.18006 −0.590029 0.807382i \(-0.700884\pi\)
−0.590029 + 0.807382i \(0.700884\pi\)
\(830\) 54.7783 94.8788i 1.90138 3.29329i
\(831\) −21.4928 + 20.5350i −0.745579 + 0.712351i
\(832\) −1.78348 3.08908i −0.0618312 0.107095i
\(833\) 0 0
\(834\) −77.7213 22.7355i −2.69127 0.787267i
\(835\) 6.32889 10.9620i 0.219020 0.379354i
\(836\) −3.25169 −0.112462
\(837\) 11.8377 34.5423i 0.409172 1.19396i
\(838\) −42.5432 −1.46963
\(839\) −19.0206 + 32.9446i −0.656663 + 1.13737i 0.324811 + 0.945779i \(0.394699\pi\)
−0.981474 + 0.191595i \(0.938634\pi\)
\(840\) 0 0
\(841\) −14.7434 25.5363i −0.508392 0.880561i
\(842\) −22.8837 39.6356i −0.788623 1.36593i
\(843\) −11.8255 + 11.2985i −0.407293 + 0.389141i
\(844\) −9.91595 + 17.1749i −0.341321 + 0.591185i
\(845\) 46.6881 1.60612
\(846\) −2.12405 + 46.5749i −0.0730264 + 1.60128i
\(847\) 0 0
\(848\) 7.72159 13.3742i 0.265161 0.459272i
\(849\) 6.91693 + 28.3864i 0.237388 + 0.974219i
\(850\) −50.0704 86.7245i −1.71740 2.97463i
\(851\) −5.40856 9.36790i −0.185403 0.321127i
\(852\) −14.0646 57.7198i −0.481846 1.97745i
\(853\) −4.90746 + 8.49996i −0.168028 + 0.291033i −0.937726 0.347374i \(-0.887073\pi\)
0.769698 + 0.638408i \(0.220407\pi\)
\(854\) 0 0
\(855\) 0.986679 21.6353i 0.0337437 0.739912i
\(856\) 64.9046 2.21840
\(857\) −13.3680 + 23.1541i −0.456642 + 0.790928i −0.998781 0.0493613i \(-0.984281\pi\)
0.542139 + 0.840289i \(0.317615\pi\)
\(858\) 0.609631 0.582462i 0.0208125 0.0198849i
\(859\) 9.24411 + 16.0113i 0.315405 + 0.546297i 0.979523 0.201330i \(-0.0645263\pi\)
−0.664119 + 0.747627i \(0.731193\pi\)
\(860\) −17.2581 29.8918i −0.588495 1.01930i
\(861\) 0 0
\(862\) 19.5344 33.8346i 0.665345 1.15241i
\(863\) −9.14786 −0.311397 −0.155698 0.987805i \(-0.549763\pi\)
−0.155698 + 0.987805i \(0.549763\pi\)
\(864\) 0.908813 2.65189i 0.0309184 0.0902193i
\(865\) 22.1445 0.752937
\(866\) −49.7473 + 86.1649i −1.69048 + 2.92800i
\(867\) 10.9371 + 3.19940i 0.371444 + 0.108657i
\(868\) 0 0
\(869\) −1.65865 2.87287i −0.0562660 0.0974555i
\(870\) 86.2036 82.3619i 2.92257 2.79233i
\(871\) 0.876423 1.51801i 0.0296964 0.0514358i
\(872\) 13.1445 0.445130
\(873\) 25.2720 13.0935i 0.855328 0.443149i
\(874\) −22.5683 −0.763385
\(875\) 0 0
\(876\) −3.28074 13.4638i −0.110846 0.454901i
\(877\) −11.3442 19.6487i −0.383065 0.663488i 0.608434 0.793605i \(-0.291798\pi\)
−0.991499 + 0.130117i \(0.958465\pi\)
\(878\) −15.3301 26.5525i −0.517366 0.896104i
\(879\) −1.52656 6.26487i −0.0514897 0.211309i
\(880\) 3.21683 5.57172i 0.108439 0.187823i
\(881\) 15.3696 0.517815 0.258907 0.965902i \(-0.416638\pi\)
0.258907 + 0.965902i \(0.416638\pi\)
\(882\) 0 0
\(883\) 29.6372 0.997370 0.498685 0.866783i \(-0.333817\pi\)
0.498685 + 0.866783i \(0.333817\pi\)
\(884\) 4.79153 8.29918i 0.161157 0.279132i
\(885\) 28.0291 26.7800i 0.942188 0.900199i
\(886\) 10.1259 + 17.5385i 0.340185 + 0.589219i
\(887\) 9.38252 + 16.2510i 0.315034 + 0.545655i 0.979445 0.201712i \(-0.0646506\pi\)
−0.664410 + 0.747368i \(0.731317\pi\)
\(888\) 19.5547 + 5.72026i 0.656212 + 0.191959i
\(889\) 0 0
\(890\) −133.482 −4.47432
\(891\) −3.64260 0.332935i −0.122032 0.0111537i
\(892\) −94.9014 −3.17753
\(893\) −6.23258 + 10.7952i −0.208565 + 0.361246i
\(894\) −39.6831 11.6083i −1.32720 0.388241i
\(895\) 16.7047 + 28.9335i 0.558378 + 0.967139i
\(896\) 0 0
\(897\) 2.83336 2.70709i 0.0946031 0.0903871i
\(898\) −6.94445 + 12.0281i −0.231739 + 0.401384i
\(899\) 53.7416 1.79238
\(900\) 85.8673 + 54.9380i 2.86224 + 1.83127i
\(901\) −17.3289 −0.577310
\(902\) −3.75700 + 6.50731i −0.125094 + 0.216670i
\(903\) 0 0
\(904\) 35.2527 + 61.0595i 1.17249 + 2.03081i
\(905\) 21.8530 + 37.8505i 0.726419 + 1.25819i
\(906\) 12.9495 + 53.1435i 0.430218 + 1.76557i
\(907\) 15.5541 26.9405i 0.516465 0.894543i −0.483352 0.875426i \(-0.660581\pi\)
0.999817 0.0191175i \(-0.00608567\pi\)
\(908\) −24.8045 −0.823165
\(909\) −23.2056 + 12.0229i −0.769683 + 0.398775i
\(910\) 0 0
\(911\) −8.73764 + 15.1340i −0.289491 + 0.501413i −0.973688 0.227884i \(-0.926819\pi\)
0.684197 + 0.729297i \(0.260153\pi\)
\(912\) 10.6952 10.2186i 0.354154 0.338371i
\(913\) −2.47347 4.28418i −0.0818600 0.141786i
\(914\) −6.23599 10.8010i −0.206268 0.357267i
\(915\) 48.8139 + 14.2794i 1.61374 + 0.472061i
\(916\) −2.96027 + 5.12734i −0.0978101 + 0.169412i
\(917\) 0 0
\(918\) −60.9248 + 11.9345i −2.01082 + 0.393896i
\(919\) 42.1986 1.39200 0.696002 0.718040i \(-0.254960\pi\)
0.696002 + 0.718040i \(0.254960\pi\)
\(920\) 42.9635 74.4150i 1.41647 2.45339i
\(921\) −50.8176 14.8655i −1.67450 0.489834i
\(922\) 9.56720 + 16.5709i 0.315079 + 0.545733i
\(923\) 2.05927 + 3.56676i 0.0677818 + 0.117401i
\(924\) 0 0
\(925\) −9.75370 + 16.8939i −0.320700 + 0.555468i
\(926\) −22.5873 −0.742266
\(927\) 1.09709 24.0564i 0.0360332 0.790114i
\(928\) 4.12588 0.135439
\(929\) −24.2056 + 41.9253i −0.794159 + 1.37552i 0.129213 + 0.991617i \(0.458755\pi\)
−0.923372 + 0.383907i \(0.874578\pi\)
\(930\) 25.9357 + 106.438i 0.850465 + 3.49022i
\(931\) 0 0
\(932\) 26.8551 + 46.5145i 0.879670 + 1.52363i
\(933\) −4.27880 17.5598i −0.140082 0.574881i
\(934\) 16.9350 29.3322i 0.554129 0.959780i
\(935\) −7.21926 −0.236095
\(936\) −0.336258 + 7.37327i −0.0109909 + 0.241003i
\(937\) −22.6750 −0.740762 −0.370381 0.928880i \(-0.620773\pi\)
−0.370381 + 0.928880i \(0.620773\pi\)
\(938\) 0 0
\(939\) −0.776271 + 0.741676i −0.0253327 + 0.0242037i
\(940\) −46.8353 81.1211i −1.52760 2.64588i
\(941\) 24.9753 + 43.2584i 0.814170 + 1.41018i 0.909922 + 0.414779i \(0.136141\pi\)
−0.0957523 + 0.995405i \(0.530526\pi\)
\(942\) 85.6859 + 25.0654i 2.79180 + 0.816674i
\(943\) −17.4613 + 30.2438i −0.568617 + 0.984873i
\(944\) 26.4769 0.861749
\(945\) 0 0
\(946\) −2.32743 −0.0756713
\(947\) −8.85613 + 15.3393i −0.287786 + 0.498459i −0.973281 0.229618i \(-0.926252\pi\)
0.685495 + 0.728077i \(0.259586\pi\)
\(948\) 55.0091 + 16.0916i 1.78661 + 0.522631i
\(949\) 0.480350 + 0.831990i 0.0155928 + 0.0270075i
\(950\) 20.3496 + 35.2466i 0.660230 + 1.14355i
\(951\) −12.8345 + 12.2625i −0.416186 + 0.397638i
\(952\) 0 0
\(953\) 38.0229 1.23168 0.615842 0.787870i \(-0.288816\pi\)
0.615842 + 0.787870i \(0.288816\pi\)
\(954\) 23.3894 12.1181i 0.757259 0.392339i
\(955\) −33.4358 −1.08196
\(956\) −39.3017 + 68.0726i −1.27111 + 2.20163i
\(957\) −1.27451 5.23046i −0.0411990 0.169077i
\(958\) −10.7177 18.5635i −0.346272 0.599761i
\(959\) 0 0
\(960\) −10.9911 45.1066i −0.354738 1.45581i
\(961\) −9.19076 + 15.9189i −0.296476 + 0.513512i
\(962\) −2.78771 −0.0898795
\(963\) 32.4523 + 20.7630i 1.04576 + 0.669080i
\(964\) −20.4881 −0.659876
\(965\) 30.9894 53.6752i 0.997583 1.72786i
\(966\) 0 0
\(967\) 15.5064 + 26.8579i 0.498652 + 0.863691i 0.999999 0.00155529i \(-0.000495066\pi\)
−0.501346 + 0.865247i \(0.667162\pi\)
\(968\) 27.3801 + 47.4236i 0.880028 + 1.52425i
\(969\) −15.9307 4.66016i −0.511769 0.149706i
\(970\) −42.6972 + 73.9537i −1.37092 + 2.37451i
\(971\) −14.5675 −0.467494 −0.233747 0.972297i \(-0.575099\pi\)
−0.233747 + 0.972297i \(0.575099\pi\)
\(972\) 49.4776 39.3169i 1.58699 1.26109i
\(973\) 0 0
\(974\) 22.1893 38.4330i 0.710991 1.23147i
\(975\) −6.78268 1.98411i −0.217220 0.0635424i
\(976\) 17.3684 + 30.0830i 0.555949 + 0.962932i
\(977\) 23.9399 + 41.4651i 0.765904 + 1.32659i 0.939767 + 0.341815i \(0.111042\pi\)
−0.173863 + 0.984770i \(0.555625\pi\)
\(978\) 34.3950 32.8622i 1.09983 1.05082i
\(979\) −3.01364 + 5.21978i −0.0963163 + 0.166825i
\(980\) 0 0
\(981\) 6.57227 + 4.20495i 0.209836 + 0.134254i
\(982\) 5.03638 0.160717
\(983\) 22.2128 38.4737i 0.708479 1.22712i −0.256942 0.966427i \(-0.582715\pi\)
0.965421 0.260695i \(-0.0839517\pi\)
\(984\) −15.5723 63.9071i −0.496426 2.03728i
\(985\) −38.9902 67.5329i −1.24233 2.15178i
\(986\) −45.6864 79.1313i −1.45495 2.52005i
\(987\) 0 0
\(988\) −1.94738 + 3.37296i −0.0619544 + 0.107308i
\(989\) −10.8171 −0.343964
\(990\) 9.74407 5.04844i 0.309687 0.160450i
\(991\) −41.6156 −1.32196 −0.660981 0.750403i \(-0.729860\pi\)
−0.660981 + 0.750403i \(0.729860\pi\)
\(992\) −1.89557 + 3.28322i −0.0601844 + 0.104242i
\(993\) 25.5023 24.3657i 0.809290 0.773223i
\(994\) 0 0
\(995\) 18.2434 + 31.5985i 0.578354 + 1.00174i
\(996\) 82.0325 + 23.9967i 2.59930 + 0.760363i
\(997\) −6.51407 + 11.2827i −0.206303 + 0.357327i −0.950547 0.310581i \(-0.899477\pi\)
0.744244 + 0.667908i \(0.232810\pi\)
\(998\) −96.1751 −3.04437
\(999\) 7.94742 + 9.11568i 0.251445 + 0.288407i
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 441.2.f.g.295.2 yes 12
3.2 odd 2 1323.2.f.g.883.5 12
7.2 even 3 441.2.h.g.214.5 12
7.3 odd 6 441.2.g.g.79.2 12
7.4 even 3 441.2.g.g.79.1 12
7.5 odd 6 441.2.h.g.214.6 12
7.6 odd 2 inner 441.2.f.g.295.1 yes 12
9.2 odd 6 3969.2.a.bd.1.2 6
9.4 even 3 inner 441.2.f.g.148.2 yes 12
9.5 odd 6 1323.2.f.g.442.5 12
9.7 even 3 3969.2.a.be.1.5 6
21.2 odd 6 1323.2.h.g.802.1 12
21.5 even 6 1323.2.h.g.802.2 12
21.11 odd 6 1323.2.g.g.667.6 12
21.17 even 6 1323.2.g.g.667.5 12
21.20 even 2 1323.2.f.g.883.6 12
63.4 even 3 441.2.h.g.373.5 12
63.5 even 6 1323.2.g.g.361.5 12
63.13 odd 6 inner 441.2.f.g.148.1 12
63.20 even 6 3969.2.a.bd.1.1 6
63.23 odd 6 1323.2.g.g.361.6 12
63.31 odd 6 441.2.h.g.373.6 12
63.32 odd 6 1323.2.h.g.226.1 12
63.34 odd 6 3969.2.a.be.1.6 6
63.40 odd 6 441.2.g.g.67.2 12
63.41 even 6 1323.2.f.g.442.6 12
63.58 even 3 441.2.g.g.67.1 12
63.59 even 6 1323.2.h.g.226.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.f.g.148.1 12 63.13 odd 6 inner
441.2.f.g.148.2 yes 12 9.4 even 3 inner
441.2.f.g.295.1 yes 12 7.6 odd 2 inner
441.2.f.g.295.2 yes 12 1.1 even 1 trivial
441.2.g.g.67.1 12 63.58 even 3
441.2.g.g.67.2 12 63.40 odd 6
441.2.g.g.79.1 12 7.4 even 3
441.2.g.g.79.2 12 7.3 odd 6
441.2.h.g.214.5 12 7.2 even 3
441.2.h.g.214.6 12 7.5 odd 6
441.2.h.g.373.5 12 63.4 even 3
441.2.h.g.373.6 12 63.31 odd 6
1323.2.f.g.442.5 12 9.5 odd 6
1323.2.f.g.442.6 12 63.41 even 6
1323.2.f.g.883.5 12 3.2 odd 2
1323.2.f.g.883.6 12 21.20 even 2
1323.2.g.g.361.5 12 63.5 even 6
1323.2.g.g.361.6 12 63.23 odd 6
1323.2.g.g.667.5 12 21.17 even 6
1323.2.g.g.667.6 12 21.11 odd 6
1323.2.h.g.226.1 12 63.32 odd 6
1323.2.h.g.226.2 12 63.59 even 6
1323.2.h.g.802.1 12 21.2 odd 6
1323.2.h.g.802.2 12 21.5 even 6
3969.2.a.bd.1.1 6 63.20 even 6
3969.2.a.bd.1.2 6 9.2 odd 6
3969.2.a.be.1.5 6 9.7 even 3
3969.2.a.be.1.6 6 63.34 odd 6