Properties

Label 414.2.i.a.127.1
Level $414$
Weight $2$
Character 414.127
Analytic conductor $3.306$
Analytic rank $0$
Dimension $10$
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] = [414,2,Mod(55,414)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(414, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("414.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 414.i (of order \(11\), degree \(10\), 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: \(3.30580664368\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 138)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 127.1
Root \(0.142315 + 0.989821i\) of defining polynomial
Character \(\chi\) \(=\) 414.127
Dual form 414.2.i.a.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(-1.78074 + 0.522874i) q^{5} +(-2.54487 - 2.93694i) q^{7} +(-0.142315 - 0.989821i) q^{8} +O(q^{10})\) \(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(-1.78074 + 0.522874i) q^{5} +(-2.54487 - 2.93694i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-1.21537 + 1.40261i) q^{10} +(-1.81329 - 1.16533i) q^{11} +(4.55742 - 5.25954i) q^{13} +(-3.72871 - 1.09485i) q^{14} +(-0.654861 - 0.755750i) q^{16} +(-2.36483 - 5.17825i) q^{17} +(-0.810827 + 1.77546i) q^{19} +(-0.264125 + 1.83703i) q^{20} -2.15546 q^{22} +(4.40644 + 1.89296i) q^{23} +(-1.30862 + 0.840996i) q^{25} +(0.990421 - 6.88853i) q^{26} +(-3.72871 + 1.09485i) q^{28} +(0.0455430 + 0.0997253i) q^{29} +(1.21361 + 8.44082i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-4.78899 - 3.07770i) q^{34} +(6.06741 + 3.89929i) q^{35} +(1.65904 + 0.487137i) q^{37} +(0.277777 + 1.93198i) q^{38} +(0.770978 + 1.68821i) q^{40} +(7.89200 - 2.31730i) q^{41} +(0.147532 - 1.02611i) q^{43} +(-1.81329 + 1.16533i) q^{44} +(4.73034 - 0.789845i) q^{46} -3.27175 q^{47} +(-1.15303 + 8.01948i) q^{49} +(-0.646201 + 1.41498i) q^{50} +(-2.89102 - 6.33046i) q^{52} +(-7.20264 - 8.31229i) q^{53} +(3.83833 + 1.12704i) q^{55} +(-2.54487 + 2.93694i) q^{56} +(0.0922288 + 0.0592718i) q^{58} +(-1.62990 + 1.88101i) q^{59} +(0.899677 + 6.25739i) q^{61} +(5.58440 + 6.44475i) q^{62} +(-0.959493 + 0.281733i) q^{64} +(-5.36552 + 11.7488i) q^{65} +(-3.07739 + 1.97772i) q^{67} -5.69269 q^{68} +7.21234 q^{70} +(0.478315 - 0.307394i) q^{71} +(5.79550 - 12.6904i) q^{73} +(1.65904 - 0.487137i) q^{74} +(1.27819 + 1.47511i) q^{76} +(1.19209 + 8.29114i) q^{77} +(9.59166 - 11.0694i) q^{79} +(1.56130 + 1.00339i) q^{80} +(5.38635 - 6.21618i) q^{82} +(9.91575 + 2.91153i) q^{83} +(6.91872 + 7.98463i) q^{85} +(-0.430643 - 0.942977i) q^{86} +(-0.895412 + 1.96068i) q^{88} +(0.730279 - 5.07920i) q^{89} -27.0449 q^{91} +(3.55240 - 3.22188i) q^{92} +(-2.75237 + 1.76884i) q^{94} +(0.515533 - 3.58561i) q^{95} +(6.38188 - 1.87389i) q^{97} +(3.36567 + 7.36979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32} - 11 q^{34} + 26 q^{35} - 11 q^{37} - 11 q^{38} + 9 q^{40} + 10 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 8 q^{47} + 25 q^{49} - 21 q^{50} + 2 q^{52} - 9 q^{53} - 23 q^{55} + 2 q^{56} - 5 q^{58} + 21 q^{59} - 4 q^{61} - 8 q^{62} - q^{64} - 29 q^{65} - 32 q^{67} - 22 q^{68} - 18 q^{70} - 22 q^{71} + 43 q^{73} - 11 q^{74} - 10 q^{77} - 16 q^{79} - 2 q^{80} + 32 q^{82} + 3 q^{83} + 33 q^{85} - 32 q^{86} - 6 q^{88} + 11 q^{89} - 70 q^{91} + 21 q^{92} + 3 q^{94} + 39 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(1\) \(e\left(\frac{10}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.841254 0.540641i 0.594856 0.382291i
\(3\) 0 0
\(4\) 0.415415 0.909632i 0.207708 0.454816i
\(5\) −1.78074 + 0.522874i −0.796373 + 0.233836i −0.654513 0.756051i \(-0.727126\pi\)
−0.141860 + 0.989887i \(0.545308\pi\)
\(6\) 0 0
\(7\) −2.54487 2.93694i −0.961870 1.11006i −0.993868 0.110569i \(-0.964733\pi\)
0.0319983 0.999488i \(-0.489813\pi\)
\(8\) −0.142315 0.989821i −0.0503159 0.349955i
\(9\) 0 0
\(10\) −1.21537 + 1.40261i −0.384334 + 0.443545i
\(11\) −1.81329 1.16533i −0.546728 0.351361i 0.237937 0.971281i \(-0.423529\pi\)
−0.784665 + 0.619920i \(0.787165\pi\)
\(12\) 0 0
\(13\) 4.55742 5.25954i 1.26400 1.45873i 0.434056 0.900886i \(-0.357082\pi\)
0.829944 0.557847i \(-0.188373\pi\)
\(14\) −3.72871 1.09485i −0.996539 0.292610i
\(15\) 0 0
\(16\) −0.654861 0.755750i −0.163715 0.188937i
\(17\) −2.36483 5.17825i −0.573555 1.25591i −0.944883 0.327408i \(-0.893825\pi\)
0.371328 0.928502i \(-0.378902\pi\)
\(18\) 0 0
\(19\) −0.810827 + 1.77546i −0.186017 + 0.407319i −0.979548 0.201209i \(-0.935513\pi\)
0.793532 + 0.608529i \(0.208240\pi\)
\(20\) −0.264125 + 1.83703i −0.0590602 + 0.410773i
\(21\) 0 0
\(22\) −2.15546 −0.459547
\(23\) 4.40644 + 1.89296i 0.918806 + 0.394709i
\(24\) 0 0
\(25\) −1.30862 + 0.840996i −0.261723 + 0.168199i
\(26\) 0.990421 6.88853i 0.194238 1.35095i
\(27\) 0 0
\(28\) −3.72871 + 1.09485i −0.704659 + 0.206907i
\(29\) 0.0455430 + 0.0997253i 0.00845712 + 0.0185185i 0.913813 0.406134i \(-0.133123\pi\)
−0.905356 + 0.424653i \(0.860396\pi\)
\(30\) 0 0
\(31\) 1.21361 + 8.44082i 0.217970 + 1.51602i 0.745515 + 0.666489i \(0.232204\pi\)
−0.527545 + 0.849527i \(0.676887\pi\)
\(32\) −0.959493 0.281733i −0.169616 0.0498038i
\(33\) 0 0
\(34\) −4.78899 3.07770i −0.821305 0.527821i
\(35\) 6.06741 + 3.89929i 1.02558 + 0.659100i
\(36\) 0 0
\(37\) 1.65904 + 0.487137i 0.272744 + 0.0800848i 0.415244 0.909710i \(-0.363696\pi\)
−0.142501 + 0.989795i \(0.545514\pi\)
\(38\) 0.277777 + 1.93198i 0.0450614 + 0.313409i
\(39\) 0 0
\(40\) 0.770978 + 1.68821i 0.121902 + 0.266929i
\(41\) 7.89200 2.31730i 1.23252 0.361902i 0.400322 0.916375i \(-0.368898\pi\)
0.832202 + 0.554473i \(0.187080\pi\)
\(42\) 0 0
\(43\) 0.147532 1.02611i 0.0224984 0.156480i −0.975475 0.220109i \(-0.929359\pi\)
0.997974 + 0.0636297i \(0.0202677\pi\)
\(44\) −1.81329 + 1.16533i −0.273364 + 0.175680i
\(45\) 0 0
\(46\) 4.73034 0.789845i 0.697451 0.116456i
\(47\) −3.27175 −0.477234 −0.238617 0.971114i \(-0.576694\pi\)
−0.238617 + 0.971114i \(0.576694\pi\)
\(48\) 0 0
\(49\) −1.15303 + 8.01948i −0.164718 + 1.14564i
\(50\) −0.646201 + 1.41498i −0.0913866 + 0.200109i
\(51\) 0 0
\(52\) −2.89102 6.33046i −0.400913 0.877877i
\(53\) −7.20264 8.31229i −0.989359 1.14178i −0.989898 0.141781i \(-0.954717\pi\)
0.000538809 1.00000i \(-0.499828\pi\)
\(54\) 0 0
\(55\) 3.83833 + 1.12704i 0.517560 + 0.151969i
\(56\) −2.54487 + 2.93694i −0.340072 + 0.392465i
\(57\) 0 0
\(58\) 0.0922288 + 0.0592718i 0.0121102 + 0.00778277i
\(59\) −1.62990 + 1.88101i −0.212195 + 0.244886i −0.851862 0.523766i \(-0.824527\pi\)
0.639667 + 0.768652i \(0.279072\pi\)
\(60\) 0 0
\(61\) 0.899677 + 6.25739i 0.115192 + 0.801177i 0.962734 + 0.270449i \(0.0871722\pi\)
−0.847542 + 0.530728i \(0.821919\pi\)
\(62\) 5.58440 + 6.44475i 0.709220 + 0.818484i
\(63\) 0 0
\(64\) −0.959493 + 0.281733i −0.119937 + 0.0352166i
\(65\) −5.36552 + 11.7488i −0.665510 + 1.45726i
\(66\) 0 0
\(67\) −3.07739 + 1.97772i −0.375963 + 0.241617i −0.714952 0.699174i \(-0.753551\pi\)
0.338989 + 0.940790i \(0.389915\pi\)
\(68\) −5.69269 −0.690340
\(69\) 0 0
\(70\) 7.21234 0.862039
\(71\) 0.478315 0.307394i 0.0567656 0.0364810i −0.511950 0.859015i \(-0.671077\pi\)
0.568716 + 0.822534i \(0.307440\pi\)
\(72\) 0 0
\(73\) 5.79550 12.6904i 0.678312 1.48530i −0.186110 0.982529i \(-0.559588\pi\)
0.864422 0.502767i \(-0.167685\pi\)
\(74\) 1.65904 0.487137i 0.192859 0.0566285i
\(75\) 0 0
\(76\) 1.27819 + 1.47511i 0.146618 + 0.169207i
\(77\) 1.19209 + 8.29114i 0.135851 + 0.944863i
\(78\) 0 0
\(79\) 9.59166 11.0694i 1.07915 1.24540i 0.111319 0.993785i \(-0.464492\pi\)
0.967827 0.251617i \(-0.0809622\pi\)
\(80\) 1.56130 + 1.00339i 0.174559 + 0.112182i
\(81\) 0 0
\(82\) 5.38635 6.21618i 0.594823 0.686462i
\(83\) 9.91575 + 2.91153i 1.08839 + 0.319582i 0.776232 0.630447i \(-0.217128\pi\)
0.312163 + 0.950029i \(0.398947\pi\)
\(84\) 0 0
\(85\) 6.91872 + 7.98463i 0.750441 + 0.866055i
\(86\) −0.430643 0.942977i −0.0464374 0.101684i
\(87\) 0 0
\(88\) −0.895412 + 1.96068i −0.0954513 + 0.209009i
\(89\) 0.730279 5.07920i 0.0774094 0.538394i −0.913807 0.406148i \(-0.866872\pi\)
0.991217 0.132247i \(-0.0422191\pi\)
\(90\) 0 0
\(91\) −27.0449 −2.83508
\(92\) 3.55240 3.22188i 0.370363 0.335904i
\(93\) 0 0
\(94\) −2.75237 + 1.76884i −0.283885 + 0.182442i
\(95\) 0.515533 3.58561i 0.0528925 0.367876i
\(96\) 0 0
\(97\) 6.38188 1.87389i 0.647982 0.190265i 0.0588058 0.998269i \(-0.481271\pi\)
0.589176 + 0.808005i \(0.299453\pi\)
\(98\) 3.36567 + 7.36979i 0.339984 + 0.744461i
\(99\) 0 0
\(100\) 0.221378 + 1.53972i 0.0221378 + 0.153972i
\(101\) 8.33312 + 2.44683i 0.829177 + 0.243468i 0.668663 0.743565i \(-0.266867\pi\)
0.160514 + 0.987034i \(0.448685\pi\)
\(102\) 0 0
\(103\) 7.87385 + 5.06021i 0.775833 + 0.498598i 0.867648 0.497178i \(-0.165631\pi\)
−0.0918152 + 0.995776i \(0.529267\pi\)
\(104\) −5.85459 3.76252i −0.574090 0.368945i
\(105\) 0 0
\(106\) −10.5532 3.09870i −1.02502 0.300973i
\(107\) 0.332225 + 2.31068i 0.0321174 + 0.223382i 0.999558 0.0297151i \(-0.00946000\pi\)
−0.967441 + 0.253097i \(0.918551\pi\)
\(108\) 0 0
\(109\) 3.35656 + 7.34985i 0.321500 + 0.703988i 0.999518 0.0310584i \(-0.00988778\pi\)
−0.678017 + 0.735046i \(0.737161\pi\)
\(110\) 3.83833 1.12704i 0.365970 0.107459i
\(111\) 0 0
\(112\) −0.553053 + 3.84657i −0.0522586 + 0.363466i
\(113\) 7.30000 4.69142i 0.686726 0.441332i −0.150194 0.988656i \(-0.547990\pi\)
0.836921 + 0.547324i \(0.184354\pi\)
\(114\) 0 0
\(115\) −8.83652 1.06686i −0.824010 0.0994853i
\(116\) 0.109633 0.0101791
\(117\) 0 0
\(118\) −0.354212 + 2.46360i −0.0326078 + 0.226792i
\(119\) −9.19001 + 20.1233i −0.842447 + 1.84470i
\(120\) 0 0
\(121\) −2.63954 5.77978i −0.239958 0.525434i
\(122\) 4.13986 + 4.77765i 0.374805 + 0.432548i
\(123\) 0 0
\(124\) 8.18219 + 2.40251i 0.734783 + 0.215752i
\(125\) 7.96743 9.19490i 0.712628 0.822417i
\(126\) 0 0
\(127\) −9.37135 6.02260i −0.831573 0.534419i 0.0542046 0.998530i \(-0.482738\pi\)
−0.885777 + 0.464111i \(0.846374\pi\)
\(128\) −0.654861 + 0.755750i −0.0578821 + 0.0667995i
\(129\) 0 0
\(130\) 1.83814 + 12.7846i 0.161216 + 1.12128i
\(131\) −8.82678 10.1867i −0.771200 0.890012i 0.225241 0.974303i \(-0.427683\pi\)
−0.996441 + 0.0842910i \(0.973137\pi\)
\(132\) 0 0
\(133\) 7.27787 2.13698i 0.631072 0.185299i
\(134\) −1.51963 + 3.32753i −0.131276 + 0.287454i
\(135\) 0 0
\(136\) −4.78899 + 3.07770i −0.410653 + 0.263910i
\(137\) −6.04662 −0.516598 −0.258299 0.966065i \(-0.583162\pi\)
−0.258299 + 0.966065i \(0.583162\pi\)
\(138\) 0 0
\(139\) −1.93190 −0.163862 −0.0819308 0.996638i \(-0.526109\pi\)
−0.0819308 + 0.996638i \(0.526109\pi\)
\(140\) 6.06741 3.89929i 0.512789 0.329550i
\(141\) 0 0
\(142\) 0.236194 0.517193i 0.0198210 0.0434019i
\(143\) −14.3930 + 4.22618i −1.20361 + 0.353411i
\(144\) 0 0
\(145\) −0.133244 0.153772i −0.0110653 0.0127701i
\(146\) −1.98545 13.8091i −0.164317 1.14285i
\(147\) 0 0
\(148\) 1.13230 1.30675i 0.0930748 0.107414i
\(149\) 10.7428 + 6.90400i 0.880087 + 0.565598i 0.900823 0.434187i \(-0.142964\pi\)
−0.0207353 + 0.999785i \(0.506601\pi\)
\(150\) 0 0
\(151\) −3.46657 + 4.00064i −0.282106 + 0.325567i −0.879063 0.476706i \(-0.841831\pi\)
0.596957 + 0.802273i \(0.296376\pi\)
\(152\) 1.87279 + 0.549899i 0.151903 + 0.0446027i
\(153\) 0 0
\(154\) 5.48538 + 6.33046i 0.442024 + 0.510123i
\(155\) −6.57461 14.3964i −0.528085 1.15635i
\(156\) 0 0
\(157\) −2.53347 + 5.54753i −0.202193 + 0.442741i −0.983381 0.181555i \(-0.941887\pi\)
0.781188 + 0.624296i \(0.214614\pi\)
\(158\) 2.08447 14.4978i 0.165831 1.15338i
\(159\) 0 0
\(160\) 1.85592 0.146724
\(161\) −5.65432 17.7588i −0.445623 1.39959i
\(162\) 0 0
\(163\) 1.84938 1.18853i 0.144855 0.0930926i −0.466206 0.884676i \(-0.654379\pi\)
0.611061 + 0.791584i \(0.290743\pi\)
\(164\) 1.17057 8.14146i 0.0914058 0.635741i
\(165\) 0 0
\(166\) 9.91575 2.91153i 0.769611 0.225978i
\(167\) 7.68773 + 16.8338i 0.594894 + 1.30264i 0.932439 + 0.361328i \(0.117676\pi\)
−0.337545 + 0.941310i \(0.609596\pi\)
\(168\) 0 0
\(169\) −5.04261 35.0721i −0.387893 2.69785i
\(170\) 10.1372 + 2.97655i 0.777489 + 0.228291i
\(171\) 0 0
\(172\) −0.872092 0.560459i −0.0664964 0.0427346i
\(173\) 19.2766 + 12.3883i 1.46557 + 0.941866i 0.998332 + 0.0577352i \(0.0183879\pi\)
0.467240 + 0.884131i \(0.345248\pi\)
\(174\) 0 0
\(175\) 5.80021 + 1.70309i 0.438454 + 0.128742i
\(176\) 0.306755 + 2.13353i 0.0231225 + 0.160821i
\(177\) 0 0
\(178\) −2.13167 4.66772i −0.159776 0.349860i
\(179\) −0.953987 + 0.280116i −0.0713043 + 0.0209368i −0.317190 0.948362i \(-0.602739\pi\)
0.245886 + 0.969299i \(0.420921\pi\)
\(180\) 0 0
\(181\) 1.19175 8.28881i 0.0885821 0.616102i −0.896374 0.443298i \(-0.853808\pi\)
0.984956 0.172804i \(-0.0552827\pi\)
\(182\) −22.7517 + 14.6216i −1.68647 + 1.08383i
\(183\) 0 0
\(184\) 1.24659 4.63098i 0.0918997 0.341401i
\(185\) −3.20903 −0.235932
\(186\) 0 0
\(187\) −1.74626 + 12.1455i −0.127699 + 0.888166i
\(188\) −1.35913 + 2.97609i −0.0991250 + 0.217054i
\(189\) 0 0
\(190\) −1.50483 3.29512i −0.109172 0.239053i
\(191\) −15.6550 18.0669i −1.13276 1.30727i −0.945743 0.324917i \(-0.894664\pi\)
−0.187016 0.982357i \(-0.559882\pi\)
\(192\) 0 0
\(193\) −14.9056 4.37669i −1.07293 0.315041i −0.302883 0.953028i \(-0.597949\pi\)
−0.770047 + 0.637987i \(0.779767\pi\)
\(194\) 4.35568 5.02672i 0.312719 0.360897i
\(195\) 0 0
\(196\) 6.81579 + 4.38024i 0.486842 + 0.312875i
\(197\) −11.3013 + 13.0424i −0.805186 + 0.929235i −0.998654 0.0518720i \(-0.983481\pi\)
0.193467 + 0.981107i \(0.438027\pi\)
\(198\) 0 0
\(199\) 3.15100 + 21.9157i 0.223369 + 1.55356i 0.725164 + 0.688576i \(0.241764\pi\)
−0.501796 + 0.864986i \(0.667327\pi\)
\(200\) 1.01867 + 1.17561i 0.0720309 + 0.0831281i
\(201\) 0 0
\(202\) 8.33312 2.44683i 0.586316 0.172158i
\(203\) 0.176986 0.387545i 0.0124220 0.0272003i
\(204\) 0 0
\(205\) −12.8420 + 8.25304i −0.896923 + 0.576417i
\(206\) 9.35966 0.652118
\(207\) 0 0
\(208\) −6.95937 −0.482545
\(209\) 3.53927 2.27455i 0.244817 0.157334i
\(210\) 0 0
\(211\) −9.02879 + 19.7703i −0.621568 + 1.36104i 0.292806 + 0.956172i \(0.405411\pi\)
−0.914374 + 0.404872i \(0.867316\pi\)
\(212\) −10.5532 + 3.09870i −0.724798 + 0.212820i
\(213\) 0 0
\(214\) 1.52873 + 1.76425i 0.104502 + 0.120602i
\(215\) 0.273807 + 1.90437i 0.0186735 + 0.129877i
\(216\) 0 0
\(217\) 21.7017 25.0451i 1.47321 1.70017i
\(218\) 6.79735 + 4.36839i 0.460374 + 0.295865i
\(219\) 0 0
\(220\) 2.61969 3.02328i 0.176619 0.203830i
\(221\) −38.0127 11.1615i −2.55701 0.750806i
\(222\) 0 0
\(223\) −11.9479 13.7886i −0.800089 0.923352i 0.198297 0.980142i \(-0.436459\pi\)
−0.998386 + 0.0567898i \(0.981914\pi\)
\(224\) 1.61435 + 3.53494i 0.107864 + 0.236188i
\(225\) 0 0
\(226\) 3.60477 7.89336i 0.239786 0.525058i
\(227\) 0.612472 4.25983i 0.0406512 0.282735i −0.959349 0.282223i \(-0.908928\pi\)
1.00000 0.000511662i \(-0.000162867\pi\)
\(228\) 0 0
\(229\) −9.84706 −0.650712 −0.325356 0.945592i \(-0.605484\pi\)
−0.325356 + 0.945592i \(0.605484\pi\)
\(230\) −8.01054 + 3.87988i −0.528199 + 0.255832i
\(231\) 0 0
\(232\) 0.0922288 0.0592718i 0.00605511 0.00389139i
\(233\) −0.315630 + 2.19525i −0.0206776 + 0.143816i −0.997545 0.0700309i \(-0.977690\pi\)
0.976867 + 0.213847i \(0.0685993\pi\)
\(234\) 0 0
\(235\) 5.82615 1.71071i 0.380056 0.111594i
\(236\) 1.03394 + 2.26401i 0.0673037 + 0.147375i
\(237\) 0 0
\(238\) 3.14836 + 21.8973i 0.204078 + 1.41939i
\(239\) −11.5400 3.38846i −0.746462 0.219181i −0.113687 0.993517i \(-0.536266\pi\)
−0.632775 + 0.774336i \(0.718084\pi\)
\(240\) 0 0
\(241\) −14.5401 9.34433i −0.936608 0.601921i −0.0191767 0.999816i \(-0.506105\pi\)
−0.917431 + 0.397895i \(0.869741\pi\)
\(242\) −5.34530 3.43522i −0.343609 0.220824i
\(243\) 0 0
\(244\) 6.06566 + 1.78104i 0.388314 + 0.114019i
\(245\) −2.13993 14.8835i −0.136715 0.950874i
\(246\) 0 0
\(247\) 5.64284 + 12.3561i 0.359046 + 0.786200i
\(248\) 8.18219 2.40251i 0.519570 0.152559i
\(249\) 0 0
\(250\) 1.73149 12.0428i 0.109509 0.761651i
\(251\) −2.24670 + 1.44387i −0.141810 + 0.0911360i −0.609622 0.792692i \(-0.708679\pi\)
0.467812 + 0.883828i \(0.345042\pi\)
\(252\) 0 0
\(253\) −5.78424 8.56745i −0.363652 0.538631i
\(254\) −11.1397 −0.698970
\(255\) 0 0
\(256\) −0.142315 + 0.989821i −0.00889468 + 0.0618638i
\(257\) 12.1446 26.5930i 0.757561 1.65883i 0.00527932 0.999986i \(-0.498320\pi\)
0.752282 0.658841i \(-0.228953\pi\)
\(258\) 0 0
\(259\) −2.79134 6.11218i −0.173445 0.379792i
\(260\) 8.45821 + 9.76129i 0.524556 + 0.605370i
\(261\) 0 0
\(262\) −12.9329 3.79744i −0.798996 0.234606i
\(263\) 7.66080 8.84103i 0.472385 0.545161i −0.468688 0.883364i \(-0.655273\pi\)
0.941074 + 0.338202i \(0.109819\pi\)
\(264\) 0 0
\(265\) 17.1723 + 11.0360i 1.05489 + 0.677936i
\(266\) 4.96720 5.73246i 0.304559 0.351479i
\(267\) 0 0
\(268\) 0.520602 + 3.62087i 0.0318008 + 0.221180i
\(269\) 15.5355 + 17.9289i 0.947215 + 1.09314i 0.995543 + 0.0943124i \(0.0300653\pi\)
−0.0483281 + 0.998832i \(0.515389\pi\)
\(270\) 0 0
\(271\) 15.9753 4.69076i 0.970428 0.284943i 0.242160 0.970236i \(-0.422144\pi\)
0.728268 + 0.685293i \(0.240326\pi\)
\(272\) −2.36483 + 5.17825i −0.143389 + 0.313977i
\(273\) 0 0
\(274\) −5.08674 + 3.26905i −0.307301 + 0.197491i
\(275\) 3.35294 0.202190
\(276\) 0 0
\(277\) 8.80188 0.528854 0.264427 0.964406i \(-0.414817\pi\)
0.264427 + 0.964406i \(0.414817\pi\)
\(278\) −1.62522 + 1.04446i −0.0974741 + 0.0626428i
\(279\) 0 0
\(280\) 2.99611 6.56058i 0.179052 0.392069i
\(281\) 0.904628 0.265623i 0.0539656 0.0158457i −0.254638 0.967036i \(-0.581956\pi\)
0.308604 + 0.951191i \(0.400138\pi\)
\(282\) 0 0
\(283\) 7.65735 + 8.83706i 0.455182 + 0.525309i 0.936231 0.351386i \(-0.114289\pi\)
−0.481048 + 0.876694i \(0.659744\pi\)
\(284\) −0.0809166 0.562787i −0.00480151 0.0333953i
\(285\) 0 0
\(286\) −9.82335 + 11.3367i −0.580867 + 0.670356i
\(287\) −26.8899 17.2811i −1.58726 1.02007i
\(288\) 0 0
\(289\) −10.0892 + 11.6436i −0.593484 + 0.684917i
\(290\) −0.195227 0.0573240i −0.0114642 0.00336618i
\(291\) 0 0
\(292\) −9.13604 10.5435i −0.534646 0.617014i
\(293\) 12.2058 + 26.7270i 0.713072 + 1.56141i 0.823366 + 0.567511i \(0.192093\pi\)
−0.110294 + 0.993899i \(0.535179\pi\)
\(294\) 0 0
\(295\) 1.91891 4.20183i 0.111723 0.244640i
\(296\) 0.246073 1.71148i 0.0143027 0.0994775i
\(297\) 0 0
\(298\) 12.7700 0.739748
\(299\) 30.0381 14.5488i 1.73715 0.841381i
\(300\) 0 0
\(301\) −3.38906 + 2.17801i −0.195342 + 0.125539i
\(302\) −0.753358 + 5.23972i −0.0433509 + 0.301512i
\(303\) 0 0
\(304\) 1.87279 0.549899i 0.107412 0.0315389i
\(305\) −4.87392 10.6724i −0.279080 0.611100i
\(306\) 0 0
\(307\) −0.325579 2.26445i −0.0185818 0.129239i 0.978419 0.206631i \(-0.0662499\pi\)
−0.997001 + 0.0773917i \(0.975341\pi\)
\(308\) 8.03710 + 2.35990i 0.457956 + 0.134468i
\(309\) 0 0
\(310\) −13.3142 8.55650i −0.756195 0.485977i
\(311\) 9.37165 + 6.02279i 0.531417 + 0.341521i 0.778674 0.627429i \(-0.215893\pi\)
−0.247256 + 0.968950i \(0.579529\pi\)
\(312\) 0 0
\(313\) −16.8630 4.95142i −0.953152 0.279871i −0.232053 0.972703i \(-0.574544\pi\)
−0.721099 + 0.692832i \(0.756363\pi\)
\(314\) 0.867929 + 6.03658i 0.0489801 + 0.340664i
\(315\) 0 0
\(316\) −6.08453 13.3233i −0.342282 0.749492i
\(317\) 7.29900 2.14318i 0.409953 0.120373i −0.0702524 0.997529i \(-0.522380\pi\)
0.480205 + 0.877156i \(0.340562\pi\)
\(318\) 0 0
\(319\) 0.0336303 0.233904i 0.00188293 0.0130961i
\(320\) 1.56130 1.00339i 0.0872794 0.0560910i
\(321\) 0 0
\(322\) −14.3578 11.8827i −0.800130 0.662195i
\(323\) 11.1113 0.618247
\(324\) 0 0
\(325\) −1.54065 + 10.7155i −0.0854601 + 0.594388i
\(326\) 0.913235 1.99971i 0.0505794 0.110753i
\(327\) 0 0
\(328\) −3.41686 7.48189i −0.188665 0.413118i
\(329\) 8.32617 + 9.60892i 0.459037 + 0.529757i
\(330\) 0 0
\(331\) −18.0608 5.30313i −0.992711 0.291486i −0.255249 0.966875i \(-0.582158\pi\)
−0.737462 + 0.675389i \(0.763976\pi\)
\(332\) 6.76757 7.81019i 0.371419 0.428640i
\(333\) 0 0
\(334\) 15.5684 + 10.0052i 0.851863 + 0.547459i
\(335\) 4.44595 5.13090i 0.242908 0.280331i
\(336\) 0 0
\(337\) 1.88842 + 13.1343i 0.102869 + 0.715469i 0.974350 + 0.225039i \(0.0722510\pi\)
−0.871481 + 0.490430i \(0.836840\pi\)
\(338\) −23.2035 26.7783i −1.26211 1.45655i
\(339\) 0 0
\(340\) 10.1372 2.97655i 0.549768 0.161426i
\(341\) 7.63574 16.7199i 0.413498 0.905435i
\(342\) 0 0
\(343\) 3.60251 2.31519i 0.194517 0.125009i
\(344\) −1.03666 −0.0558928
\(345\) 0 0
\(346\) 22.9141 1.23187
\(347\) 0.676473 0.434743i 0.0363150 0.0233382i −0.522357 0.852727i \(-0.674947\pi\)
0.558672 + 0.829388i \(0.311311\pi\)
\(348\) 0 0
\(349\) 4.66638 10.2179i 0.249786 0.546954i −0.742656 0.669673i \(-0.766434\pi\)
0.992441 + 0.122719i \(0.0391614\pi\)
\(350\) 5.80021 1.70309i 0.310034 0.0910342i
\(351\) 0 0
\(352\) 1.41153 + 1.62899i 0.0752348 + 0.0868255i
\(353\) 0.254081 + 1.76717i 0.0135233 + 0.0940569i 0.995465 0.0951256i \(-0.0303253\pi\)
−0.981942 + 0.189183i \(0.939416\pi\)
\(354\) 0 0
\(355\) −0.691028 + 0.797489i −0.0366760 + 0.0423263i
\(356\) −4.31684 2.77426i −0.228792 0.147036i
\(357\) 0 0
\(358\) −0.651103 + 0.751413i −0.0344118 + 0.0397134i
\(359\) −23.2504 6.82692i −1.22711 0.360311i −0.396950 0.917840i \(-0.629931\pi\)
−0.830157 + 0.557529i \(0.811750\pi\)
\(360\) 0 0
\(361\) 9.94752 + 11.4801i 0.523554 + 0.604213i
\(362\) −3.47870 7.61730i −0.182837 0.400356i
\(363\) 0 0
\(364\) −11.2349 + 24.6009i −0.588868 + 1.28944i
\(365\) −3.68484 + 25.6286i −0.192873 + 1.34146i
\(366\) 0 0
\(367\) −1.63035 −0.0851034 −0.0425517 0.999094i \(-0.513549\pi\)
−0.0425517 + 0.999094i \(0.513549\pi\)
\(368\) −1.45500 4.56979i −0.0758473 0.238217i
\(369\) 0 0
\(370\) −2.69961 + 1.73493i −0.140346 + 0.0901948i
\(371\) −6.08289 + 42.3074i −0.315808 + 2.19649i
\(372\) 0 0
\(373\) 2.17490 0.638609i 0.112612 0.0330659i −0.224941 0.974372i \(-0.572219\pi\)
0.337553 + 0.941306i \(0.390401\pi\)
\(374\) 5.09730 + 11.1615i 0.263575 + 0.577149i
\(375\) 0 0
\(376\) 0.465618 + 3.23845i 0.0240124 + 0.167010i
\(377\) 0.732067 + 0.214954i 0.0377034 + 0.0110707i
\(378\) 0 0
\(379\) 5.98176 + 3.84425i 0.307262 + 0.197466i 0.685180 0.728374i \(-0.259723\pi\)
−0.377918 + 0.925839i \(0.623360\pi\)
\(380\) −3.04742 1.95846i −0.156330 0.100467i
\(381\) 0 0
\(382\) −22.9375 6.73507i −1.17359 0.344596i
\(383\) 5.33120 + 37.0793i 0.272412 + 1.89466i 0.423100 + 0.906083i \(0.360942\pi\)
−0.150689 + 0.988581i \(0.548149\pi\)
\(384\) 0 0
\(385\) −6.45802 14.1411i −0.329131 0.720697i
\(386\) −14.9056 + 4.37669i −0.758677 + 0.222768i
\(387\) 0 0
\(388\) 0.946579 6.58360i 0.0480553 0.334232i
\(389\) −0.904743 + 0.581443i −0.0458723 + 0.0294803i −0.563376 0.826201i \(-0.690498\pi\)
0.517504 + 0.855681i \(0.326861\pi\)
\(390\) 0 0
\(391\) −0.618266 27.2942i −0.0312671 1.38032i
\(392\) 8.10195 0.409210
\(393\) 0 0
\(394\) −2.45601 + 17.0820i −0.123732 + 0.860576i
\(395\) −11.2924 + 24.7269i −0.568183 + 1.24415i
\(396\) 0 0
\(397\) 4.96350 + 10.8686i 0.249111 + 0.545477i 0.992337 0.123564i \(-0.0394323\pi\)
−0.743226 + 0.669041i \(0.766705\pi\)
\(398\) 14.4993 + 16.7331i 0.726785 + 0.838754i
\(399\) 0 0
\(400\) 1.49254 + 0.438250i 0.0746272 + 0.0219125i
\(401\) −19.5043 + 22.5092i −0.974001 + 1.12406i 0.0182538 + 0.999833i \(0.494189\pi\)
−0.992254 + 0.124223i \(0.960356\pi\)
\(402\) 0 0
\(403\) 49.9257 + 32.0853i 2.48698 + 1.59828i
\(404\) 5.68742 6.56363i 0.282959 0.326553i
\(405\) 0 0
\(406\) −0.0606326 0.421709i −0.00300915 0.0209291i
\(407\) −2.44064 2.81665i −0.120978 0.139616i
\(408\) 0 0
\(409\) 27.2851 8.01164i 1.34916 0.396150i 0.474233 0.880400i \(-0.342726\pi\)
0.874930 + 0.484250i \(0.160907\pi\)
\(410\) −6.34143 + 13.8858i −0.313181 + 0.685771i
\(411\) 0 0
\(412\) 7.87385 5.06021i 0.387917 0.249299i
\(413\) 9.67229 0.475942
\(414\) 0 0
\(415\) −19.1798 −0.941498
\(416\) −5.85459 + 3.76252i −0.287045 + 0.184473i
\(417\) 0 0
\(418\) 1.74771 3.82695i 0.0854833 0.187182i
\(419\) 31.4611 9.23780i 1.53697 0.451296i 0.599797 0.800152i \(-0.295248\pi\)
0.937176 + 0.348856i \(0.113430\pi\)
\(420\) 0 0
\(421\) 23.2803 + 26.8669i 1.13461 + 1.30941i 0.944821 + 0.327587i \(0.106236\pi\)
0.189791 + 0.981825i \(0.439219\pi\)
\(422\) 3.09313 + 21.5132i 0.150571 + 1.04724i
\(423\) 0 0
\(424\) −7.20264 + 8.31229i −0.349791 + 0.403681i
\(425\) 7.44954 + 4.78753i 0.361356 + 0.232229i
\(426\) 0 0
\(427\) 16.0880 18.5665i 0.778553 0.898498i
\(428\) 2.23988 + 0.657687i 0.108269 + 0.0317905i
\(429\) 0 0
\(430\) 1.25992 + 1.45403i 0.0607589 + 0.0701195i
\(431\) 11.5054 + 25.1933i 0.554196 + 1.21352i 0.954794 + 0.297267i \(0.0960751\pi\)
−0.400598 + 0.916254i \(0.631198\pi\)
\(432\) 0 0
\(433\) −9.87651 + 21.6265i −0.474635 + 1.03931i 0.509269 + 0.860607i \(0.329916\pi\)
−0.983904 + 0.178698i \(0.942811\pi\)
\(434\) 4.71623 32.8021i 0.226386 1.57455i
\(435\) 0 0
\(436\) 8.08002 0.386963
\(437\) −6.93374 + 6.28862i −0.331686 + 0.300825i
\(438\) 0 0
\(439\) 28.3616 18.2269i 1.35363 0.869922i 0.355719 0.934593i \(-0.384236\pi\)
0.997907 + 0.0646707i \(0.0205997\pi\)
\(440\) 0.569313 3.95966i 0.0271409 0.188769i
\(441\) 0 0
\(442\) −38.0127 + 11.1615i −1.80808 + 0.530900i
\(443\) −4.97713 10.8984i −0.236471 0.517798i 0.753775 0.657133i \(-0.228231\pi\)
−0.990245 + 0.139335i \(0.955504\pi\)
\(444\) 0 0
\(445\) 1.35534 + 9.42660i 0.0642493 + 0.446864i
\(446\) −17.5059 5.14019i −0.828927 0.243395i
\(447\) 0 0
\(448\) 3.26921 + 2.10100i 0.154456 + 0.0992628i
\(449\) 0.606817 + 0.389978i 0.0286375 + 0.0184042i 0.554881 0.831930i \(-0.312764\pi\)
−0.526244 + 0.850334i \(0.676400\pi\)
\(450\) 0 0
\(451\) −17.0109 4.99486i −0.801014 0.235199i
\(452\) −1.23494 8.58920i −0.0580867 0.404002i
\(453\) 0 0
\(454\) −1.78780 3.91473i −0.0839054 0.183727i
\(455\) 48.1601 14.1411i 2.25778 0.662944i
\(456\) 0 0
\(457\) −0.596629 + 4.14965i −0.0279091 + 0.194112i −0.999006 0.0445729i \(-0.985807\pi\)
0.971097 + 0.238685i \(0.0767164\pi\)
\(458\) −8.28387 + 5.32372i −0.387080 + 0.248761i
\(459\) 0 0
\(460\) −4.64127 + 7.59479i −0.216400 + 0.354109i
\(461\) −18.6186 −0.867156 −0.433578 0.901116i \(-0.642749\pi\)
−0.433578 + 0.901116i \(0.642749\pi\)
\(462\) 0 0
\(463\) 1.57410 10.9481i 0.0731545 0.508801i −0.919993 0.391935i \(-0.871806\pi\)
0.993148 0.116866i \(-0.0372849\pi\)
\(464\) 0.0455430 0.0997253i 0.00211428 0.00462963i
\(465\) 0 0
\(466\) 0.921318 + 2.01741i 0.0426793 + 0.0934545i
\(467\) −15.5954 17.9980i −0.721669 0.832850i 0.269838 0.962906i \(-0.413030\pi\)
−0.991507 + 0.130056i \(0.958484\pi\)
\(468\) 0 0
\(469\) 13.6400 + 4.00506i 0.629836 + 0.184937i
\(470\) 3.97639 4.58899i 0.183417 0.211675i
\(471\) 0 0
\(472\) 2.09382 + 1.34562i 0.0963759 + 0.0619371i
\(473\) −1.46327 + 1.68871i −0.0672813 + 0.0776468i
\(474\) 0 0
\(475\) −0.432097 3.00530i −0.0198260 0.137893i
\(476\) 14.4871 + 16.7191i 0.664017 + 0.766316i
\(477\) 0 0
\(478\) −11.5400 + 3.38846i −0.527829 + 0.154984i
\(479\) −9.71459 + 21.2720i −0.443871 + 0.971942i 0.547001 + 0.837132i \(0.315770\pi\)
−0.990872 + 0.134810i \(0.956958\pi\)
\(480\) 0 0
\(481\) 10.1230 6.50568i 0.461570 0.296633i
\(482\) −17.2838 −0.787256
\(483\) 0 0
\(484\) −6.35397 −0.288817
\(485\) −10.3847 + 6.67383i −0.471544 + 0.303043i
\(486\) 0 0
\(487\) −5.87931 + 12.8739i −0.266417 + 0.583372i −0.994806 0.101792i \(-0.967542\pi\)
0.728389 + 0.685164i \(0.240270\pi\)
\(488\) 6.06566 1.78104i 0.274580 0.0806239i
\(489\) 0 0
\(490\) −9.84687 11.3639i −0.444836 0.513368i
\(491\) −0.835757 5.81282i −0.0377172 0.262329i 0.962234 0.272224i \(-0.0877592\pi\)
−0.999951 + 0.00989541i \(0.996850\pi\)
\(492\) 0 0
\(493\) 0.408701 0.471666i 0.0184070 0.0212428i
\(494\) 11.4273 + 7.34387i 0.514138 + 0.330416i
\(495\) 0 0
\(496\) 5.58440 6.44475i 0.250747 0.289378i
\(497\) −2.12005 0.622502i −0.0950971 0.0279230i
\(498\) 0 0
\(499\) −0.558955 0.645068i −0.0250223 0.0288772i 0.743101 0.669180i \(-0.233354\pi\)
−0.768123 + 0.640303i \(0.778809\pi\)
\(500\) −5.05419 11.0671i −0.226030 0.494937i
\(501\) 0 0
\(502\) −1.10943 + 2.42931i −0.0495163 + 0.108426i
\(503\) 4.10013 28.5170i 0.182816 1.27151i −0.667250 0.744834i \(-0.732529\pi\)
0.850065 0.526677i \(-0.176562\pi\)
\(504\) 0 0
\(505\) −16.1185 −0.717266
\(506\) −9.49793 4.08020i −0.422234 0.181387i
\(507\) 0 0
\(508\) −9.37135 + 6.02260i −0.415786 + 0.267210i
\(509\) −2.40455 + 16.7240i −0.106580 + 0.741277i 0.864519 + 0.502600i \(0.167623\pi\)
−0.971099 + 0.238678i \(0.923286\pi\)
\(510\) 0 0
\(511\) −52.0196 + 15.2743i −2.30121 + 0.675697i
\(512\) 0.415415 + 0.909632i 0.0183589 + 0.0402004i
\(513\) 0 0
\(514\) −4.16056 28.9374i −0.183515 1.27637i
\(515\) −16.6672 4.89392i −0.734443 0.215652i
\(516\) 0 0
\(517\) 5.93264 + 3.81267i 0.260917 + 0.167681i
\(518\) −5.65272 3.63278i −0.248366 0.159615i
\(519\) 0 0
\(520\) 12.3928 + 3.63887i 0.543462 + 0.159575i
\(521\) 0.639077 + 4.44488i 0.0279985 + 0.194734i 0.999020 0.0442577i \(-0.0140923\pi\)
−0.971022 + 0.238992i \(0.923183\pi\)
\(522\) 0 0
\(523\) 4.80446 + 10.5203i 0.210084 + 0.460020i 0.985114 0.171905i \(-0.0549922\pi\)
−0.775029 + 0.631925i \(0.782265\pi\)
\(524\) −12.9329 + 3.79744i −0.564976 + 0.165892i
\(525\) 0 0
\(526\) 1.66485 11.5793i 0.0725909 0.504881i
\(527\) 40.8387 26.2454i 1.77896 1.14327i
\(528\) 0 0
\(529\) 15.8334 + 16.6824i 0.688410 + 0.725322i
\(530\) 20.4128 0.886676
\(531\) 0 0
\(532\) 1.07948 7.50792i 0.0468012 0.325510i
\(533\) 23.7792 52.0692i 1.02999 2.25537i
\(534\) 0 0
\(535\) −1.79980 3.94101i −0.0778122 0.170385i
\(536\) 2.39555 + 2.76461i 0.103472 + 0.119413i
\(537\) 0 0
\(538\) 22.7624 + 6.68363i 0.981355 + 0.288152i
\(539\) 11.4361 13.1980i 0.492589 0.568478i
\(540\) 0 0
\(541\) −24.8837 15.9918i −1.06983 0.687539i −0.117645 0.993056i \(-0.537534\pi\)
−0.952187 + 0.305517i \(0.901171\pi\)
\(542\) 10.9032 12.5830i 0.468334 0.540486i
\(543\) 0 0
\(544\) 0.810154 + 5.63474i 0.0347350 + 0.241588i
\(545\) −9.82022 11.3331i −0.420652 0.485458i
\(546\) 0 0
\(547\) 19.1886 5.63427i 0.820444 0.240904i 0.155537 0.987830i \(-0.450289\pi\)
0.664907 + 0.746926i \(0.268471\pi\)
\(548\) −2.51186 + 5.50020i −0.107301 + 0.234957i
\(549\) 0 0
\(550\) 2.82067 1.81274i 0.120274 0.0772954i
\(551\) −0.213986 −0.00911612
\(552\) 0 0
\(553\) −56.9196 −2.42047
\(554\) 7.40462 4.75866i 0.314592 0.202176i
\(555\) 0 0
\(556\) −0.802540 + 1.75732i −0.0340353 + 0.0745269i
\(557\) −14.2834 + 4.19399i −0.605208 + 0.177705i −0.569959 0.821673i \(-0.693041\pi\)
−0.0352494 + 0.999379i \(0.511223\pi\)
\(558\) 0 0
\(559\) −4.72448 5.45234i −0.199824 0.230609i
\(560\) −1.02642 7.13893i −0.0433743 0.301675i
\(561\) 0 0
\(562\) 0.617415 0.712535i 0.0260441 0.0300565i
\(563\) 3.69059 + 2.37180i 0.155540 + 0.0999595i 0.616096 0.787671i \(-0.288713\pi\)
−0.460556 + 0.887631i \(0.652350\pi\)
\(564\) 0 0
\(565\) −10.5464 + 12.1712i −0.443691 + 0.512046i
\(566\) 11.2194 + 3.29433i 0.471589 + 0.138471i
\(567\) 0 0
\(568\) −0.372337 0.429700i −0.0156229 0.0180298i
\(569\) −1.65647 3.62716i −0.0694427 0.152058i 0.871728 0.489991i \(-0.163000\pi\)
−0.941170 + 0.337932i \(0.890273\pi\)
\(570\) 0 0
\(571\) 12.2072 26.7300i 0.510855 1.11862i −0.461932 0.886915i \(-0.652844\pi\)
0.972787 0.231701i \(-0.0744292\pi\)
\(572\) −2.13482 + 14.8480i −0.0892612 + 0.620825i
\(573\) 0 0
\(574\) −31.9641 −1.33415
\(575\) −7.35831 + 1.22865i −0.306863 + 0.0512381i
\(576\) 0 0
\(577\) 10.1425 6.51818i 0.422237 0.271355i −0.312221 0.950010i \(-0.601073\pi\)
0.734458 + 0.678654i \(0.237436\pi\)
\(578\) −2.19260 + 15.2499i −0.0912000 + 0.634310i
\(579\) 0 0
\(580\) −0.195227 + 0.0573240i −0.00810638 + 0.00238025i
\(581\) −16.6833 36.5314i −0.692141 1.51558i
\(582\) 0 0
\(583\) 3.37391 + 23.4661i 0.139733 + 0.971866i
\(584\) −13.3860 3.93048i −0.553916 0.162645i
\(585\) 0 0
\(586\) 24.7179 + 15.8852i 1.02109 + 0.656213i
\(587\) −10.9528 7.03894i −0.452071 0.290528i 0.294724 0.955582i \(-0.404772\pi\)
−0.746795 + 0.665054i \(0.768408\pi\)
\(588\) 0 0
\(589\) −15.9704 4.68933i −0.658049 0.193221i
\(590\) −0.657389 4.57224i −0.0270643 0.188236i
\(591\) 0 0
\(592\) −0.718284 1.57282i −0.0295213 0.0646426i
\(593\) 2.83339 0.831957i 0.116353 0.0341644i −0.223038 0.974810i \(-0.571597\pi\)
0.339391 + 0.940645i \(0.389779\pi\)
\(594\) 0 0
\(595\) 5.84310 40.6397i 0.239544 1.66606i
\(596\) 10.7428 6.90400i 0.440044 0.282799i
\(597\) 0 0
\(598\) 17.4039 28.4791i 0.711699 1.16460i
\(599\) −24.7280 −1.01036 −0.505179 0.863015i \(-0.668574\pi\)
−0.505179 + 0.863015i \(0.668574\pi\)
\(600\) 0 0
\(601\) 2.95561 20.5567i 0.120562 0.838525i −0.836360 0.548180i \(-0.815321\pi\)
0.956922 0.290345i \(-0.0937700\pi\)
\(602\) −1.67353 + 3.66452i −0.0682081 + 0.149355i
\(603\) 0 0
\(604\) 2.19904 + 4.81523i 0.0894777 + 0.195929i
\(605\) 7.72243 + 8.91216i 0.313961 + 0.362331i
\(606\) 0 0
\(607\) −29.3134 8.60719i −1.18979 0.349355i −0.373851 0.927489i \(-0.621963\pi\)
−0.815942 + 0.578134i \(0.803781\pi\)
\(608\) 1.27819 1.47511i 0.0518374 0.0598236i
\(609\) 0 0
\(610\) −9.87013 6.34315i −0.399630 0.256827i
\(611\) −14.9107 + 17.2079i −0.603223 + 0.696157i
\(612\) 0 0
\(613\) 3.16868 + 22.0386i 0.127982 + 0.890133i 0.948108 + 0.317949i \(0.102994\pi\)
−0.820126 + 0.572183i \(0.806097\pi\)
\(614\) −1.49815 1.72896i −0.0604604 0.0697751i
\(615\) 0 0
\(616\) 8.03710 2.35990i 0.323824 0.0950833i
\(617\) 6.02311 13.1888i 0.242481 0.530960i −0.748789 0.662809i \(-0.769364\pi\)
0.991270 + 0.131849i \(0.0420915\pi\)
\(618\) 0 0
\(619\) −13.4184 + 8.62351i −0.539333 + 0.346608i −0.781778 0.623557i \(-0.785687\pi\)
0.242445 + 0.970165i \(0.422051\pi\)
\(620\) −15.8266 −0.635611
\(621\) 0 0
\(622\) 11.1401 0.446677
\(623\) −16.7758 + 10.7811i −0.672106 + 0.431937i
\(624\) 0 0
\(625\) −6.14917 + 13.4648i −0.245967 + 0.538592i
\(626\) −16.8630 + 4.95142i −0.673980 + 0.197898i
\(627\) 0 0
\(628\) 3.99377 + 4.60905i 0.159369 + 0.183921i
\(629\) −1.40082 9.74289i −0.0558542 0.388475i
\(630\) 0 0
\(631\) 19.1810 22.1361i 0.763584 0.881222i −0.232227 0.972662i \(-0.574601\pi\)
0.995811 + 0.0914391i \(0.0291467\pi\)
\(632\) −12.3217 7.91870i −0.490132 0.314989i
\(633\) 0 0
\(634\) 4.98162 5.74909i 0.197845 0.228326i
\(635\) 19.8370 + 5.82468i 0.787208 + 0.231145i
\(636\) 0 0
\(637\) 36.9239 + 42.6125i 1.46298 + 1.68837i
\(638\) −0.0981663 0.214954i −0.00388644 0.00851012i
\(639\) 0 0
\(640\) 0.770978 1.68821i 0.0304756 0.0667322i
\(641\) −1.97160 + 13.7128i −0.0778735 + 0.541622i 0.913118 + 0.407696i \(0.133668\pi\)
−0.990991 + 0.133926i \(0.957241\pi\)
\(642\) 0 0
\(643\) 21.6577 0.854097 0.427048 0.904229i \(-0.359553\pi\)
0.427048 + 0.904229i \(0.359553\pi\)
\(644\) −18.5028 2.23390i −0.729113 0.0880281i
\(645\) 0 0
\(646\) 9.34739 6.00720i 0.367768 0.236350i
\(647\) 1.88070 13.0806i 0.0739381 0.514251i −0.918872 0.394555i \(-0.870899\pi\)
0.992811 0.119696i \(-0.0381921\pi\)
\(648\) 0 0
\(649\) 5.14749 1.51144i 0.202057 0.0593292i
\(650\) 4.49715 + 9.84738i 0.176393 + 0.386246i
\(651\) 0 0
\(652\) −0.312860 2.17599i −0.0122526 0.0852184i
\(653\) 1.32064 + 0.387774i 0.0516806 + 0.0151748i 0.307471 0.951558i \(-0.400517\pi\)
−0.255790 + 0.966732i \(0.582336\pi\)
\(654\) 0 0
\(655\) 21.0446 + 13.5245i 0.822280 + 0.528447i
\(656\) −6.91946 4.44687i −0.270160 0.173621i
\(657\) 0 0
\(658\) 12.1994 + 3.58207i 0.475582 + 0.139643i
\(659\) 0.897828 + 6.24453i 0.0349744 + 0.243253i 0.999808 0.0196101i \(-0.00624249\pi\)
−0.964833 + 0.262863i \(0.915333\pi\)
\(660\) 0 0
\(661\) 1.03841 + 2.27381i 0.0403897 + 0.0884410i 0.928751 0.370703i \(-0.120883\pi\)
−0.888362 + 0.459144i \(0.848156\pi\)
\(662\) −18.0608 + 5.30313i −0.701953 + 0.206112i
\(663\) 0 0
\(664\) 1.47073 10.2292i 0.0570755 0.396969i
\(665\) −11.8427 + 7.61082i −0.459239 + 0.295135i
\(666\) 0 0
\(667\) 0.0119069 + 0.525644i 0.000461036 + 0.0203530i
\(668\) 18.5061 0.716024
\(669\) 0 0
\(670\) 0.966197 6.72004i 0.0373274 0.259618i
\(671\) 5.66056 12.3949i 0.218524 0.478500i
\(672\) 0 0
\(673\) −1.76124 3.85657i −0.0678907 0.148660i 0.872645 0.488356i \(-0.162403\pi\)
−0.940535 + 0.339696i \(0.889676\pi\)
\(674\) 8.68956 + 10.0283i 0.334709 + 0.386275i
\(675\) 0 0
\(676\) −33.9975 9.98256i −1.30760 0.383945i
\(677\) 24.8481 28.6762i 0.954990 1.10212i −0.0397010 0.999212i \(-0.512641\pi\)
0.994691 0.102906i \(-0.0328140\pi\)
\(678\) 0 0
\(679\) −21.7445 13.9744i −0.834479 0.536287i
\(680\) 6.91872 7.98463i 0.265321 0.306197i
\(681\) 0 0
\(682\) −2.61589 18.1939i −0.100167 0.696680i
\(683\) 30.9769 + 35.7493i 1.18530 + 1.36791i 0.914153 + 0.405370i \(0.132857\pi\)
0.271147 + 0.962538i \(0.412597\pi\)
\(684\) 0 0
\(685\) 10.7675 3.16162i 0.411405 0.120799i
\(686\) 1.77894 3.89533i 0.0679201 0.148724i
\(687\) 0 0
\(688\) −0.872092 + 0.560459i −0.0332482 + 0.0213673i
\(689\) −76.5443 −2.91610
\(690\) 0 0
\(691\) −31.2607 −1.18921 −0.594607 0.804017i \(-0.702692\pi\)
−0.594607 + 0.804017i \(0.702692\pi\)
\(692\) 19.2766 12.3883i 0.732786 0.470933i
\(693\) 0 0
\(694\) 0.334046 0.731458i 0.0126802 0.0277658i
\(695\) 3.44022 1.01014i 0.130495 0.0383168i
\(696\) 0 0
\(697\) −30.6628 35.3867i −1.16144 1.34037i
\(698\) −1.59863 11.1187i −0.0605091 0.420850i
\(699\) 0 0
\(700\) 3.95868 4.56856i 0.149624 0.172675i
\(701\) −29.2493 18.7974i −1.10473 0.709967i −0.144591 0.989491i \(-0.546187\pi\)
−0.960138 + 0.279525i \(0.909823\pi\)
\(702\) 0 0
\(703\) −2.21009 + 2.55058i −0.0833550 + 0.0961968i
\(704\) 2.06815 + 0.607265i 0.0779465 + 0.0228871i
\(705\) 0 0
\(706\) 1.16915 + 1.34927i 0.0440015 + 0.0507805i
\(707\) −14.0205 30.7007i −0.527297 1.15462i
\(708\) 0 0
\(709\) −4.46658 + 9.78045i −0.167746 + 0.367312i −0.974772 0.223204i \(-0.928348\pi\)
0.807026 + 0.590516i \(0.201076\pi\)
\(710\) −0.150175 + 1.04449i −0.00563596 + 0.0391990i
\(711\) 0 0
\(712\) −5.13143 −0.192309
\(713\) −10.6304 + 39.4913i −0.398113 + 1.47896i
\(714\) 0 0
\(715\) 23.4206 15.0515i 0.875879 0.562893i
\(716\) −0.141498 + 0.984141i −0.00528803 + 0.0367791i
\(717\) 0 0
\(718\) −23.2504 + 6.82692i −0.867696 + 0.254779i
\(719\) −13.8708 30.3727i −0.517292 1.13271i −0.970455 0.241284i \(-0.922431\pi\)
0.453162 0.891428i \(-0.350296\pi\)
\(720\) 0 0
\(721\) −5.17639 36.0026i −0.192779 1.34081i
\(722\) 14.5750 + 4.27960i 0.542424 + 0.159270i
\(723\) 0 0
\(724\) −7.04469 4.52735i −0.261814 0.168258i
\(725\) −0.143467 0.0922005i −0.00532822 0.00342424i
\(726\) 0 0
\(727\) 9.75305 + 2.86375i 0.361721 + 0.106211i 0.457543 0.889188i \(-0.348730\pi\)
−0.0958219 + 0.995398i \(0.530548\pi\)
\(728\) 3.84890 + 26.7697i 0.142650 + 0.992150i
\(729\) 0 0
\(730\) 10.7560 + 23.5524i 0.398097 + 0.871712i
\(731\) −5.66232 + 1.66261i −0.209428 + 0.0614937i
\(732\) 0 0
\(733\) 6.31365 43.9124i 0.233200 1.62194i −0.450915 0.892567i \(-0.648902\pi\)
0.684115 0.729374i \(-0.260189\pi\)
\(734\) −1.37153 + 0.881432i −0.0506243 + 0.0325342i
\(735\) 0 0
\(736\) −3.69464 3.05772i −0.136186 0.112709i
\(737\) 7.88491 0.290444
\(738\) 0 0
\(739\) −1.82504 + 12.6935i −0.0671353 + 0.466937i 0.928326 + 0.371768i \(0.121248\pi\)
−0.995461 + 0.0951689i \(0.969661\pi\)
\(740\) −1.33308 + 2.91904i −0.0490050 + 0.107306i
\(741\) 0 0
\(742\) 17.7559 + 38.8799i 0.651838 + 1.42733i
\(743\) 18.0493 + 20.8300i 0.662165 + 0.764180i 0.983129 0.182912i \(-0.0585523\pi\)
−0.320964 + 0.947091i \(0.604007\pi\)
\(744\) 0 0
\(745\) −22.7402 6.67711i −0.833135 0.244631i
\(746\) 1.48439 1.71307i 0.0543472 0.0627200i
\(747\) 0 0
\(748\) 10.3225 + 6.63387i 0.377428 + 0.242558i
\(749\) 5.94084 6.85610i 0.217074 0.250516i
\(750\) 0 0
\(751\) −2.52158 17.5380i −0.0920137 0.639969i −0.982680 0.185311i \(-0.940671\pi\)
0.890666 0.454658i \(-0.150238\pi\)
\(752\) 2.14254 + 2.47262i 0.0781304 + 0.0901673i
\(753\) 0 0
\(754\) 0.732067 0.214954i 0.0266603 0.00782817i
\(755\) 4.08125 8.93669i 0.148532 0.325239i
\(756\) 0 0
\(757\) −6.95768 + 4.47143i −0.252881 + 0.162517i −0.660940 0.750439i \(-0.729842\pi\)
0.408059 + 0.912956i \(0.366206\pi\)
\(758\) 7.11053 0.258266
\(759\) 0 0
\(760\) −3.62248 −0.131401
\(761\) 13.5041 8.67855i 0.489523 0.314597i −0.272491 0.962158i \(-0.587847\pi\)
0.762013 + 0.647561i \(0.224211\pi\)
\(762\) 0 0
\(763\) 13.0440 28.5624i 0.472225 1.03403i
\(764\) −22.9375 + 6.73507i −0.829851 + 0.243666i
\(765\) 0 0
\(766\) 24.5315 + 28.3108i 0.886358 + 1.02291i
\(767\) 2.46509 + 17.1451i 0.0890092 + 0.619073i
\(768\) 0 0
\(769\) −17.0848 + 19.7170i −0.616095 + 0.711012i −0.974961 0.222377i \(-0.928618\pi\)
0.358865 + 0.933389i \(0.383164\pi\)
\(770\) −13.0781 8.40477i −0.471301 0.302887i
\(771\) 0 0
\(772\) −10.1732 + 11.7405i −0.366141 + 0.422550i
\(773\) 27.4217 + 8.05173i 0.986289 + 0.289601i 0.734818 0.678264i \(-0.237268\pi\)
0.251471 + 0.967865i \(0.419086\pi\)
\(774\) 0 0
\(775\) −8.68684 10.0252i −0.312041 0.360114i
\(776\) −2.76305 6.05024i −0.0991877 0.217191i
\(777\) 0 0
\(778\) −0.446767 + 0.978282i −0.0160174 + 0.0350731i
\(779\) −2.28477 + 15.8909i −0.0818603 + 0.569351i
\(780\) 0 0
\(781\) −1.22554 −0.0438533
\(782\) −15.2765 22.6270i −0.546285 0.809142i
\(783\) 0 0
\(784\) 6.81579 4.38024i 0.243421 0.156437i
\(785\) 1.61081 11.2034i 0.0574922 0.399867i
\(786\) 0 0
\(787\) −49.8749 + 14.6446i −1.77785 + 0.522023i −0.994972 0.100156i \(-0.968066\pi\)
−0.782875 + 0.622179i \(0.786248\pi\)
\(788\) 7.16907 + 15.6981i 0.255388 + 0.559221i
\(789\) 0 0
\(790\) 3.86861 + 26.9068i 0.137639 + 0.957300i
\(791\) −32.3560 9.50057i −1.15045 0.337801i
\(792\) 0 0
\(793\) 37.0112 + 23.7856i 1.31431 + 0.844653i
\(794\) 10.0516 + 6.45974i 0.356716 + 0.229248i
\(795\) 0 0
\(796\) 21.2442 + 6.23786i 0.752980 + 0.221095i
\(797\) 6.09049 + 42.3603i 0.215736 + 1.50048i 0.753536 + 0.657406i \(0.228346\pi\)
−0.537800 + 0.843072i \(0.680744\pi\)
\(798\) 0 0
\(799\) 7.73712 + 16.9419i 0.273720 + 0.599362i
\(800\) 1.49254 0.438250i 0.0527694 0.0154945i
\(801\) 0 0
\(802\) −4.23870 + 29.4808i −0.149674 + 1.04100i
\(803\) −25.2974 + 16.2577i −0.892728 + 0.573721i
\(804\) 0 0
\(805\) 19.3545 + 28.6673i 0.682156 + 1.01039i
\(806\) 59.3468 2.09040
\(807\) 0 0
\(808\) 1.23599 8.59652i 0.0434821 0.302425i
\(809\) 3.41357 7.47467i 0.120015 0.262795i −0.840084 0.542456i \(-0.817495\pi\)
0.960099 + 0.279660i \(0.0902219\pi\)
\(810\) 0 0
\(811\) 10.7657 + 23.5736i 0.378035 + 0.827782i 0.999033 + 0.0439694i \(0.0140004\pi\)
−0.620998 + 0.783813i \(0.713272\pi\)
\(812\) −0.279000 0.321984i −0.00979100 0.0112994i
\(813\) 0 0
\(814\) −3.57599 1.05001i −0.125338 0.0368027i
\(815\) −2.67183 + 3.08346i −0.0935901 + 0.108009i
\(816\) 0 0
\(817\) 1.70219 + 1.09393i 0.0595522 + 0.0382718i
\(818\) 18.6223 21.4913i 0.651113 0.751425i
\(819\) 0 0
\(820\) 2.17248 + 15.1099i 0.0758662 + 0.527661i
\(821\) −12.1733 14.0488i −0.424852 0.490305i 0.502457 0.864602i \(-0.332429\pi\)
−0.927309 + 0.374297i \(0.877884\pi\)
\(822\) 0 0
\(823\) 10.2202 3.00091i 0.356253 0.104605i −0.0987088 0.995116i \(-0.531471\pi\)
0.454961 + 0.890511i \(0.349653\pi\)
\(824\) 3.88814 8.51385i 0.135450 0.296594i
\(825\) 0 0
\(826\) 8.13685 5.22923i 0.283117 0.181948i
\(827\) 26.5475 0.923148 0.461574 0.887102i \(-0.347285\pi\)
0.461574 + 0.887102i \(0.347285\pi\)
\(828\) 0 0
\(829\) 5.30529 0.184260 0.0921301 0.995747i \(-0.470632\pi\)
0.0921301 + 0.995747i \(0.470632\pi\)
\(830\) −16.1350 + 10.3694i −0.560056 + 0.359926i
\(831\) 0 0
\(832\) −2.89102 + 6.33046i −0.100228 + 0.219469i
\(833\) 44.2536 12.9940i 1.53330 0.450216i
\(834\) 0 0
\(835\) −22.4918 25.9569i −0.778361 0.898277i
\(836\) −0.598739 4.16432i −0.0207078 0.144026i
\(837\) 0 0
\(838\) 21.4724 24.7805i 0.741752 0.856027i
\(839\) 46.4479 + 29.8502i 1.60356 + 1.03054i 0.965447 + 0.260601i \(0.0839207\pi\)
0.638112 + 0.769944i \(0.279716\pi\)
\(840\) 0 0
\(841\) 18.9831 21.9077i 0.654589 0.755436i
\(842\) 34.1100 + 10.0156i 1.17551 + 0.345160i
\(843\) 0 0
\(844\) 14.2330 + 16.4258i 0.489920 + 0.565398i
\(845\) 27.3179 + 59.8178i 0.939763 + 2.05779i
\(846\) 0 0
\(847\) −10.2576 + 22.4609i −0.352454 + 0.771766i
\(848\) −1.56528 + 10.8868i −0.0537521 + 0.373854i
\(849\) 0 0
\(850\) 8.85528 0.303734
\(851\) 6.38831 + 5.28702i 0.218989 + 0.181237i
\(852\) 0 0
\(853\) −35.3409 + 22.7122i −1.21005 + 0.777651i −0.980667 0.195686i \(-0.937307\pi\)
−0.229382 + 0.973337i \(0.573670\pi\)
\(854\) 3.49626 24.3170i 0.119639 0.832110i
\(855\) 0 0
\(856\) 2.23988 0.657687i 0.0765574 0.0224793i
\(857\) −16.7460 36.6686i −0.572032 1.25258i −0.945708 0.325016i \(-0.894630\pi\)
0.373676 0.927559i \(-0.378097\pi\)
\(858\) 0 0
\(859\) 0.822115 + 5.71794i 0.0280502 + 0.195093i 0.999028 0.0440753i \(-0.0140342\pi\)
−0.970978 + 0.239169i \(0.923125\pi\)
\(860\) 1.84602 + 0.542041i 0.0629488 + 0.0184834i
\(861\) 0 0
\(862\) 23.2995 + 14.9737i 0.793585 + 0.510006i
\(863\) −12.7377 8.18600i −0.433595 0.278655i 0.305582 0.952166i \(-0.401149\pi\)
−0.739177 + 0.673511i \(0.764785\pi\)
\(864\) 0 0
\(865\) −40.8042 11.9812i −1.38738 0.407373i
\(866\) 3.38354 + 23.5331i 0.114977 + 0.799686i
\(867\) 0 0
\(868\) −13.7666 30.1446i −0.467269 1.02318i
\(869\) −30.2920 + 8.89453i −1.02759 + 0.301726i
\(870\) 0 0
\(871\) −3.62306 + 25.1989i −0.122763 + 0.853833i
\(872\) 6.79735 4.36839i 0.230187 0.147932i
\(873\) 0 0
\(874\) −2.43315 + 9.03898i −0.0823026 + 0.305748i
\(875\) −47.2809 −1.59839
\(876\) 0 0
\(877\) −4.64024 + 32.2736i −0.156690 + 1.08980i 0.747990 + 0.663710i \(0.231019\pi\)
−0.904680 + 0.426091i \(0.859890\pi\)
\(878\) 14.0051 30.6669i 0.472649 1.03496i
\(879\) 0 0
\(880\) −1.66182 3.63887i −0.0560198 0.122666i
\(881\) 2.92223 + 3.37243i 0.0984524 + 0.113620i 0.802838 0.596198i \(-0.203323\pi\)
−0.704385 + 0.709818i \(0.748777\pi\)
\(882\) 0 0
\(883\) 25.8754 + 7.59771i 0.870778 + 0.255683i 0.686446 0.727181i \(-0.259170\pi\)
0.184332 + 0.982864i \(0.440988\pi\)
\(884\) −25.9439 + 29.9409i −0.872589 + 1.00702i
\(885\) 0 0
\(886\) −10.0791 6.47747i −0.338615 0.217615i
\(887\) 22.4135 25.8665i 0.752570 0.868513i −0.242244 0.970215i \(-0.577884\pi\)
0.994815 + 0.101703i \(0.0324290\pi\)
\(888\) 0 0
\(889\) 6.16087 + 42.8498i 0.206629 + 1.43714i
\(890\) 6.23659 + 7.19741i 0.209051 + 0.241258i
\(891\) 0 0
\(892\) −17.5059 + 5.14019i −0.586140 + 0.172106i
\(893\) 2.65282 5.80887i 0.0887734 0.194387i
\(894\) 0 0
\(895\) 1.55234 0.997629i 0.0518890 0.0333471i
\(896\) 3.88612 0.129826
\(897\) 0 0
\(898\) 0.721325 0.0240709
\(899\) −0.786492 + 0.505448i −0.0262310 + 0.0168576i
\(900\) 0 0
\(901\) −26.0101 + 56.9542i −0.866523 + 1.89742i
\(902\) −17.0109 + 4.99486i −0.566402 + 0.166311i
\(903\) 0 0
\(904\) −5.68257 6.55804i −0.189000 0.218117i
\(905\) 2.21180 + 15.3834i 0.0735226 + 0.511361i
\(906\) 0 0
\(907\) 23.2630 26.8469i 0.772434 0.891436i −0.224105 0.974565i \(-0.571946\pi\)
0.996539 + 0.0831290i \(0.0264914\pi\)
\(908\) −3.62045 2.32672i −0.120149 0.0772150i
\(909\) 0 0
\(910\) 32.8696 37.9336i 1.08962 1.25749i
\(911\) 16.1581 + 4.74446i 0.535343 + 0.157191i 0.538219 0.842805i \(-0.319097\pi\)
−0.00287613 + 0.999996i \(0.500916\pi\)
\(912\) 0 0
\(913\) −14.5873 16.8346i −0.482768 0.557144i
\(914\) 1.74155 + 3.81347i 0.0576054 + 0.126138i
\(915\) 0 0
\(916\) −4.09062 + 8.95720i −0.135158 + 0.295954i
\(917\) −7.45453 + 51.8474i −0.246170 + 1.71215i
\(918\) 0 0
\(919\) 3.06801 0.101204 0.0506021 0.998719i \(-0.483886\pi\)
0.0506021 + 0.998719i \(0.483886\pi\)
\(920\) 0.201566 + 8.89841i 0.00664545 + 0.293372i
\(921\) 0 0
\(922\) −15.6630 + 10.0660i −0.515833 + 0.331506i
\(923\) 0.563128 3.91664i 0.0185356 0.128918i
\(924\) 0 0
\(925\) −2.58072 + 0.757768i −0.0848536 + 0.0249153i
\(926\) −4.59477 10.0611i −0.150993 0.330630i
\(927\) 0 0
\(928\) −0.0156023 0.108517i −0.000512172 0.00356223i
\(929\) 17.2466 + 5.06406i 0.565842 + 0.166146i 0.552128 0.833760i \(-0.313816\pi\)
0.0137147 + 0.999906i \(0.495634\pi\)
\(930\) 0 0
\(931\) −13.3034 8.54958i −0.436001 0.280201i
\(932\) 1.86575 + 1.19905i 0.0611148 + 0.0392761i
\(933\) 0 0
\(934\) −22.8502 6.70941i −0.747680 0.219539i
\(935\) −3.24092 22.5411i −0.105989 0.737172i
\(936\) 0 0
\(937\) −19.8049 43.3666i −0.646997 1.41673i −0.894158 0.447752i \(-0.852225\pi\)
0.247161 0.968974i \(-0.420502\pi\)
\(938\) 13.6400 4.00506i 0.445361 0.130770i
\(939\) 0 0
\(940\) 0.864151 6.01031i 0.0281855 0.196035i
\(941\) −43.2692 + 27.8074i −1.41054 + 0.906497i −0.999986 0.00534126i \(-0.998300\pi\)
−0.410551 + 0.911838i \(0.634663\pi\)
\(942\) 0 0
\(943\) 39.1622 + 4.72817i 1.27530 + 0.153971i
\(944\) 2.48893 0.0810078
\(945\) 0 0
\(946\) −0.318000 + 2.21174i −0.0103391 + 0.0719097i
\(947\) −17.1709 + 37.5990i −0.557979 + 1.22180i 0.394976 + 0.918691i \(0.370753\pi\)
−0.952955 + 0.303112i \(0.901975\pi\)
\(948\) 0 0
\(949\) −40.3330 88.3170i −1.30927 2.86689i
\(950\) −1.98829 2.29461i −0.0645087 0.0744471i
\(951\) 0 0
\(952\) 21.2264 + 6.23262i 0.687950 + 0.202000i
\(953\) −0.619591 + 0.715046i −0.0200705 + 0.0231626i −0.765696 0.643203i \(-0.777605\pi\)
0.745626 + 0.666365i \(0.232151\pi\)
\(954\) 0 0
\(955\) 37.3243 + 23.9869i 1.20779 + 0.776197i
\(956\) −7.87615 + 9.08956i −0.254733 + 0.293977i
\(957\) 0 0
\(958\) 3.32807 + 23.1472i 0.107525 + 0.747853i
\(959\) 15.3879 + 17.7585i 0.496900 + 0.573453i
\(960\) 0 0
\(961\) −40.0304 + 11.7540i −1.29130 + 0.379160i
\(962\) 4.99880 10.9458i 0.161168 0.352908i
\(963\) 0 0
\(964\) −14.5401 + 9.34433i −0.468304 + 0.300961i
\(965\) 28.8316 0.928121
\(966\) 0 0
\(967\) 51.3969 1.65281 0.826407 0.563074i \(-0.190381\pi\)
0.826407 + 0.563074i \(0.190381\pi\)
\(968\) −5.34530 + 3.43522i −0.171804 + 0.110412i
\(969\) 0 0
\(970\) −5.12801 + 11.2288i −0.164650 + 0.360534i
\(971\) 8.42596 2.47408i 0.270402 0.0793971i −0.143721 0.989618i \(-0.545907\pi\)
0.414122 + 0.910221i \(0.364089\pi\)
\(972\) 0 0
\(973\) 4.91643 + 5.67386i 0.157614 + 0.181896i
\(974\) 2.01416 + 14.0088i 0.0645379 + 0.448871i
\(975\) 0 0
\(976\) 4.13986 4.77765i 0.132514 0.152929i
\(977\) −13.6562 8.77632i −0.436901 0.280779i 0.303644 0.952785i \(-0.401797\pi\)
−0.740546 + 0.672006i \(0.765433\pi\)
\(978\) 0 0
\(979\) −7.24317 + 8.35906i −0.231493 + 0.267157i
\(980\) −14.4275 4.23630i −0.460870 0.135323i
\(981\) 0 0
\(982\) −3.84573 4.43821i −0.122722 0.141629i
\(983\) 2.53187 + 5.54403i 0.0807542 + 0.176827i 0.945702 0.325035i \(-0.105376\pi\)
−0.864948 + 0.501862i \(0.832649\pi\)
\(984\) 0 0
\(985\) 13.3052 29.1344i 0.423940 0.928299i
\(986\) 0.0888192 0.617751i 0.00282858 0.0196732i
\(987\) 0 0
\(988\) 13.5836 0.432153
\(989\) 2.59246 4.24220i 0.0824356 0.134894i
\(990\) 0 0
\(991\) 21.0256 13.5123i 0.667899 0.429233i −0.162269 0.986747i \(-0.551881\pi\)
0.830168 + 0.557514i \(0.188245\pi\)
\(992\) 1.21361 8.44082i 0.0385321 0.267996i
\(993\) 0 0
\(994\) −2.12005 + 0.622502i −0.0672438 + 0.0197446i
\(995\) −17.0703 37.3787i −0.541164 1.18498i
\(996\) 0 0
\(997\) 4.86655 + 33.8476i 0.154125 + 1.07196i 0.909210 + 0.416337i \(0.136686\pi\)
−0.755085 + 0.655627i \(0.772405\pi\)
\(998\) −0.818973 0.240472i −0.0259241 0.00761201i
\(999\) 0 0
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 414.2.i.a.127.1 10
3.2 odd 2 138.2.e.d.127.1 yes 10
23.2 even 11 inner 414.2.i.a.163.1 10
23.5 odd 22 9522.2.a.by.1.2 5
23.18 even 11 9522.2.a.bx.1.4 5
69.2 odd 22 138.2.e.d.25.1 10
69.5 even 22 3174.2.a.w.1.4 5
69.41 odd 22 3174.2.a.x.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.2.e.d.25.1 10 69.2 odd 22
138.2.e.d.127.1 yes 10 3.2 odd 2
414.2.i.a.127.1 10 1.1 even 1 trivial
414.2.i.a.163.1 10 23.2 even 11 inner
3174.2.a.w.1.4 5 69.5 even 22
3174.2.a.x.1.2 5 69.41 odd 22
9522.2.a.bx.1.4 5 23.18 even 11
9522.2.a.by.1.2 5 23.5 odd 22