Properties

Label 273.2.ba.c.38.10
Level $273$
Weight $2$
Character 273.38
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(38,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.38");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 38.10
Character \(\chi\) \(=\) 273.38
Dual form 273.2.ba.c.194.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.697858 - 1.20873i) q^{2} +(1.40218 - 1.01680i) q^{3} +(0.0259885 - 0.0450133i) q^{4} +(-0.529415 + 0.305658i) q^{5} +(-2.20756 - 0.985265i) q^{6} +(2.05092 + 1.67145i) q^{7} -2.86398 q^{8} +(0.932217 - 2.85149i) q^{9} +O(q^{10})\) \(q+(-0.697858 - 1.20873i) q^{2} +(1.40218 - 1.01680i) q^{3} +(0.0259885 - 0.0450133i) q^{4} +(-0.529415 + 0.305658i) q^{5} +(-2.20756 - 0.985265i) q^{6} +(2.05092 + 1.67145i) q^{7} -2.86398 q^{8} +(0.932217 - 2.85149i) q^{9} +(0.738913 + 0.426611i) q^{10} +(2.64913 - 4.58843i) q^{11} +(-0.00932927 - 0.0895420i) q^{12} +(-1.58197 - 3.23996i) q^{13} +(0.589074 - 3.64543i) q^{14} +(-0.431541 + 0.966899i) q^{15} +(1.94667 + 3.37174i) q^{16} +(-3.19826 + 5.53956i) q^{17} +(-4.09722 + 0.863138i) q^{18} +(-0.126699 - 0.219449i) q^{19} +0.0317743i q^{20} +(4.57529 + 0.258290i) q^{21} -7.39488 q^{22} +(3.72378 - 2.14993i) q^{23} +(-4.01581 + 2.91210i) q^{24} +(-2.31315 + 4.00649i) q^{25} +(-2.81223 + 4.17321i) q^{26} +(-1.59227 - 4.94618i) q^{27} +(0.128538 - 0.0488802i) q^{28} +6.32377i q^{29} +(1.46987 - 0.153144i) q^{30} +(0.113692 - 0.196920i) q^{31} +(-0.146975 + 0.254569i) q^{32} +(-0.950979 - 9.12746i) q^{33} +8.92774 q^{34} +(-1.59668 - 0.258011i) q^{35} +(-0.104128 - 0.116068i) q^{36} +(6.03926 - 3.48677i) q^{37} +(-0.176836 + 0.306288i) q^{38} +(-5.51262 - 2.93445i) q^{39} +(1.51623 - 0.875397i) q^{40} +3.84707i q^{41} +(-2.88070 - 5.71052i) q^{42} -1.18356 q^{43} +(-0.137694 - 0.238493i) q^{44} +(0.378049 + 1.79456i) q^{45} +(-5.19734 - 3.00069i) q^{46} +(-1.65276 + 0.954224i) q^{47} +(6.15798 + 2.74839i) q^{48} +(1.41252 + 6.85600i) q^{49} +6.45699 q^{50} +(1.14810 + 11.0195i) q^{51} +(-0.186955 - 0.0129917i) q^{52} +(-2.56191 - 1.47912i) q^{53} +(-4.86739 + 5.37635i) q^{54} +3.23891i q^{55} +(-5.87378 - 4.78699i) q^{56} +(-0.400791 - 0.178879i) q^{57} +(7.64371 - 4.41310i) q^{58} +(2.91541 + 1.68321i) q^{59} +(0.0323083 + 0.0445533i) q^{60} +(11.0288 - 6.36746i) q^{61} -0.317362 q^{62} +(6.67801 - 4.29001i) q^{63} +8.19696 q^{64} +(1.82784 + 1.23174i) q^{65} +(-10.3689 + 7.51914i) q^{66} +(9.31510 + 5.37808i) q^{67} +(0.166236 + 0.287929i) q^{68} +(3.03536 - 6.80094i) q^{69} +(0.802389 + 2.11000i) q^{70} +6.51849 q^{71} +(-2.66985 + 8.16659i) q^{72} +(-6.09089 + 10.5497i) q^{73} +(-8.42909 - 4.86654i) q^{74} +(0.830367 + 7.96983i) q^{75} -0.0131708 q^{76} +(13.1025 - 4.98260i) q^{77} +(0.300079 + 8.71108i) q^{78} +(-4.15569 - 7.19787i) q^{79} +(-2.06119 - 1.19003i) q^{80} +(-7.26194 - 5.31641i) q^{81} +(4.65005 - 2.68471i) q^{82} +14.1762i q^{83} +(0.130531 - 0.199237i) q^{84} -3.91030i q^{85} +(0.825955 + 1.43060i) q^{86} +(6.43004 + 8.86707i) q^{87} +(-7.58706 + 13.1412i) q^{88} +(6.09840 - 3.52092i) q^{89} +(1.90530 - 1.70930i) q^{90} +(2.17094 - 9.28908i) q^{91} -0.223493i q^{92} +(-0.0408127 - 0.391719i) q^{93} +(2.30679 + 1.33183i) q^{94} +(0.134153 + 0.0774530i) q^{95} +(0.0527608 + 0.506396i) q^{96} -14.2272 q^{97} +(7.30129 - 6.49186i) q^{98} +(-10.6143 - 11.8314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 12 q^{3} - 40 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 12 q^{3} - 40 q^{4} - 12 q^{9} - 12 q^{10} - 6 q^{12} - 32 q^{16} - 24 q^{22} + 28 q^{25} - 22 q^{30} + 44 q^{36} + 6 q^{39} - 108 q^{40} + 24 q^{42} + 20 q^{49} + 28 q^{51} + 36 q^{52} + 48 q^{61} + 32 q^{64} + 90 q^{66} - 60 q^{75} - 68 q^{78} + 16 q^{79} + 60 q^{81} + 120 q^{82} + 60 q^{87} + 12 q^{88} - 32 q^{91} + 168 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.697858 1.20873i −0.493460 0.854698i 0.506511 0.862233i \(-0.330935\pi\)
−0.999972 + 0.00753522i \(0.997601\pi\)
\(3\) 1.40218 1.01680i 0.809549 0.587052i
\(4\) 0.0259885 0.0450133i 0.0129942 0.0225067i
\(5\) −0.529415 + 0.305658i −0.236762 + 0.136694i −0.613687 0.789549i \(-0.710314\pi\)
0.376926 + 0.926243i \(0.376981\pi\)
\(6\) −2.20756 0.985265i −0.901233 0.402233i
\(7\) 2.05092 + 1.67145i 0.775174 + 0.631748i
\(8\) −2.86398 −1.01257
\(9\) 0.932217 2.85149i 0.310739 0.950495i
\(10\) 0.738913 + 0.426611i 0.233665 + 0.134906i
\(11\) 2.64913 4.58843i 0.798744 1.38346i −0.121691 0.992568i \(-0.538832\pi\)
0.920435 0.390897i \(-0.127835\pi\)
\(12\) −0.00932927 0.0895420i −0.00269313 0.0258485i
\(13\) −1.58197 3.23996i −0.438761 0.898604i
\(14\) 0.589074 3.64543i 0.157437 0.974282i
\(15\) −0.431541 + 0.966899i −0.111423 + 0.249652i
\(16\) 1.94667 + 3.37174i 0.486668 + 0.842934i
\(17\) −3.19826 + 5.53956i −0.775693 + 1.34354i 0.158711 + 0.987325i \(0.449266\pi\)
−0.934404 + 0.356215i \(0.884067\pi\)
\(18\) −4.09722 + 0.863138i −0.965724 + 0.203444i
\(19\) −0.126699 0.219449i −0.0290667 0.0503450i 0.851126 0.524961i \(-0.175920\pi\)
−0.880193 + 0.474616i \(0.842587\pi\)
\(20\) 0.0317743i 0.00710495i
\(21\) 4.57529 + 0.258290i 0.998410 + 0.0563636i
\(22\) −7.39488 −1.57659
\(23\) 3.72378 2.14993i 0.776462 0.448291i −0.0587126 0.998275i \(-0.518700\pi\)
0.835175 + 0.549984i \(0.185366\pi\)
\(24\) −4.01581 + 2.91210i −0.819724 + 0.594431i
\(25\) −2.31315 + 4.00649i −0.462629 + 0.801297i
\(26\) −2.81223 + 4.17321i −0.551524 + 0.818433i
\(27\) −1.59227 4.94618i −0.306432 0.951892i
\(28\) 0.128538 0.0488802i 0.0242913 0.00923749i
\(29\) 6.32377i 1.17430i 0.809480 + 0.587148i \(0.199749\pi\)
−0.809480 + 0.587148i \(0.800251\pi\)
\(30\) 1.46987 0.153144i 0.268360 0.0279601i
\(31\) 0.113692 0.196920i 0.0204196 0.0353678i −0.855635 0.517580i \(-0.826833\pi\)
0.876055 + 0.482212i \(0.160166\pi\)
\(32\) −0.146975 + 0.254569i −0.0259818 + 0.0450018i
\(33\) −0.950979 9.12746i −0.165544 1.58889i
\(34\) 8.92774 1.53109
\(35\) −1.59668 0.258011i −0.269888 0.0436118i
\(36\) −0.104128 0.116068i −0.0173547 0.0193447i
\(37\) 6.03926 3.48677i 0.992848 0.573221i 0.0867235 0.996232i \(-0.472360\pi\)
0.906124 + 0.423011i \(0.139027\pi\)
\(38\) −0.176836 + 0.306288i −0.0286865 + 0.0496865i
\(39\) −5.51262 2.93445i −0.882726 0.469888i
\(40\) 1.51623 0.875397i 0.239737 0.138412i
\(41\) 3.84707i 0.600811i 0.953812 + 0.300406i \(0.0971221\pi\)
−0.953812 + 0.300406i \(0.902878\pi\)
\(42\) −2.88070 5.71052i −0.444502 0.881152i
\(43\) −1.18356 −0.180491 −0.0902454 0.995920i \(-0.528765\pi\)
−0.0902454 + 0.995920i \(0.528765\pi\)
\(44\) −0.137694 0.238493i −0.0207581 0.0359541i
\(45\) 0.378049 + 1.79456i 0.0563563 + 0.267517i
\(46\) −5.19734 3.00069i −0.766307 0.442427i
\(47\) −1.65276 + 0.954224i −0.241080 + 0.139188i −0.615673 0.788002i \(-0.711116\pi\)
0.374593 + 0.927189i \(0.377783\pi\)
\(48\) 6.15798 + 2.74839i 0.888828 + 0.396697i
\(49\) 1.41252 + 6.85600i 0.201788 + 0.979429i
\(50\) 6.45699 0.913156
\(51\) 1.14810 + 11.0195i 0.160767 + 1.54303i
\(52\) −0.186955 0.0129917i −0.0259259 0.00180163i
\(53\) −2.56191 1.47912i −0.351905 0.203173i 0.313619 0.949549i \(-0.398459\pi\)
−0.665524 + 0.746376i \(0.731792\pi\)
\(54\) −4.86739 + 5.37635i −0.662369 + 0.731628i
\(55\) 3.23891i 0.436735i
\(56\) −5.87378 4.78699i −0.784917 0.639689i
\(57\) −0.400791 0.178879i −0.0530861 0.0236931i
\(58\) 7.64371 4.41310i 1.00367 0.579468i
\(59\) 2.91541 + 1.68321i 0.379554 + 0.219136i 0.677624 0.735408i \(-0.263010\pi\)
−0.298070 + 0.954544i \(0.596343\pi\)
\(60\) 0.0323083 + 0.0445533i 0.00417098 + 0.00575180i
\(61\) 11.0288 6.36746i 1.41209 0.815270i 0.416503 0.909134i \(-0.363255\pi\)
0.995585 + 0.0938647i \(0.0299221\pi\)
\(62\) −0.317362 −0.0403051
\(63\) 6.67801 4.29001i 0.841350 0.540490i
\(64\) 8.19696 1.02462
\(65\) 1.82784 + 1.23174i 0.226716 + 0.152779i
\(66\) −10.3689 + 7.51914i −1.27633 + 0.925543i
\(67\) 9.31510 + 5.37808i 1.13802 + 0.657036i 0.945940 0.324343i \(-0.105143\pi\)
0.192081 + 0.981379i \(0.438476\pi\)
\(68\) 0.166236 + 0.287929i 0.0201591 + 0.0349165i
\(69\) 3.03536 6.80094i 0.365414 0.818738i
\(70\) 0.802389 + 2.11000i 0.0959039 + 0.252193i
\(71\) 6.51849 0.773602 0.386801 0.922163i \(-0.373580\pi\)
0.386801 + 0.922163i \(0.373580\pi\)
\(72\) −2.66985 + 8.16659i −0.314645 + 0.962442i
\(73\) −6.09089 + 10.5497i −0.712885 + 1.23475i 0.250885 + 0.968017i \(0.419278\pi\)
−0.963770 + 0.266735i \(0.914055\pi\)
\(74\) −8.42909 4.86654i −0.979862 0.565723i
\(75\) 0.830367 + 7.96983i 0.0958825 + 0.920277i
\(76\) −0.0131708 −0.00151080
\(77\) 13.1025 4.98260i 1.49317 0.567820i
\(78\) 0.300079 + 8.71108i 0.0339772 + 0.986335i
\(79\) −4.15569 7.19787i −0.467552 0.809823i 0.531761 0.846895i \(-0.321531\pi\)
−0.999313 + 0.0370712i \(0.988197\pi\)
\(80\) −2.06119 1.19003i −0.230449 0.133050i
\(81\) −7.26194 5.31641i −0.806883 0.590712i
\(82\) 4.65005 2.68471i 0.513512 0.296476i
\(83\) 14.1762i 1.55604i 0.628242 + 0.778018i \(0.283775\pi\)
−0.628242 + 0.778018i \(0.716225\pi\)
\(84\) 0.130531 0.199237i 0.0142421 0.0217385i
\(85\) 3.91030i 0.424131i
\(86\) 0.825955 + 1.43060i 0.0890650 + 0.154265i
\(87\) 6.43004 + 8.86707i 0.689373 + 0.950649i
\(88\) −7.58706 + 13.1412i −0.808783 + 1.40085i
\(89\) 6.09840 3.52092i 0.646430 0.373216i −0.140657 0.990058i \(-0.544922\pi\)
0.787087 + 0.616842i \(0.211588\pi\)
\(90\) 1.90530 1.70930i 0.200837 0.180177i
\(91\) 2.17094 9.28908i 0.227576 0.973760i
\(92\) 0.223493i 0.0233008i
\(93\) −0.0408127 0.391719i −0.00423208 0.0406193i
\(94\) 2.30679 + 1.33183i 0.237927 + 0.137367i
\(95\) 0.134153 + 0.0774530i 0.0137638 + 0.00794651i
\(96\) 0.0527608 + 0.506396i 0.00538488 + 0.0516839i
\(97\) −14.2272 −1.44455 −0.722275 0.691606i \(-0.756904\pi\)
−0.722275 + 0.691606i \(0.756904\pi\)
\(98\) 7.30129 6.49186i 0.737542 0.655777i
\(99\) −10.6143 11.8314i −1.06678 1.18910i
\(100\) 0.120230 + 0.208245i 0.0120230 + 0.0208245i
\(101\) −0.206024 + 0.356844i −0.0205001 + 0.0355073i −0.876093 0.482141i \(-0.839859\pi\)
0.855593 + 0.517649i \(0.173193\pi\)
\(102\) 12.5183 9.07777i 1.23950 0.898833i
\(103\) −11.3885 + 6.57513i −1.12214 + 0.647867i −0.941946 0.335764i \(-0.891005\pi\)
−0.180193 + 0.983631i \(0.557672\pi\)
\(104\) 4.53074 + 9.27918i 0.444275 + 0.909898i
\(105\) −2.50118 + 1.26173i −0.244090 + 0.123132i
\(106\) 4.12886i 0.401030i
\(107\) 5.35323 3.09069i 0.517516 0.298788i −0.218402 0.975859i \(-0.570084\pi\)
0.735918 + 0.677071i \(0.236751\pi\)
\(108\) −0.264025 0.0568703i −0.0254058 0.00547234i
\(109\) −13.2626 7.65714i −1.27032 0.733421i −0.295274 0.955413i \(-0.595411\pi\)
−0.975049 + 0.221991i \(0.928744\pi\)
\(110\) 3.91496 2.26030i 0.373276 0.215511i
\(111\) 4.92276 11.0298i 0.467248 1.04690i
\(112\) −1.64322 + 10.1689i −0.155270 + 0.960872i
\(113\) 6.14805i 0.578360i 0.957275 + 0.289180i \(0.0933826\pi\)
−0.957275 + 0.289180i \(0.906617\pi\)
\(114\) 0.0634800 + 0.609279i 0.00594545 + 0.0570642i
\(115\) −1.31428 + 2.27641i −0.122558 + 0.212276i
\(116\) 0.284654 + 0.164345i 0.0264295 + 0.0152591i
\(117\) −10.7135 + 1.49063i −0.990459 + 0.137809i
\(118\) 4.69858i 0.432539i
\(119\) −15.8185 + 6.01543i −1.45008 + 0.551434i
\(120\) 1.23592 2.76918i 0.112824 0.252790i
\(121\) −8.53581 14.7845i −0.775983 1.34404i
\(122\) −15.3930 8.88716i −1.39362 0.804606i
\(123\) 3.91172 + 5.39428i 0.352708 + 0.486386i
\(124\) −0.00590934 0.0102353i −0.000530674 0.000919155i
\(125\) 5.88470i 0.526344i
\(126\) −9.84574 5.07807i −0.877129 0.452390i
\(127\) 1.45913 0.129477 0.0647384 0.997902i \(-0.479379\pi\)
0.0647384 + 0.997902i \(0.479379\pi\)
\(128\) −5.42636 9.39874i −0.479627 0.830739i
\(129\) −1.65956 + 1.20345i −0.146116 + 0.105958i
\(130\) 0.213265 3.06894i 0.0187046 0.269164i
\(131\) 2.34758 + 4.06612i 0.205109 + 0.355259i 0.950167 0.311740i \(-0.100912\pi\)
−0.745059 + 0.666999i \(0.767578\pi\)
\(132\) −0.435572 0.194402i −0.0379117 0.0169205i
\(133\) 0.106949 0.661842i 0.00927363 0.0573890i
\(134\) 15.0125i 1.29689i
\(135\) 2.35481 + 2.13189i 0.202670 + 0.183484i
\(136\) 9.15976 15.8652i 0.785443 1.36043i
\(137\) 7.95042 13.7705i 0.679250 1.17650i −0.295957 0.955201i \(-0.595638\pi\)
0.975207 0.221295i \(-0.0710282\pi\)
\(138\) −10.3387 + 1.07718i −0.880091 + 0.0916956i
\(139\) 10.0341i 0.851078i 0.904940 + 0.425539i \(0.139915\pi\)
−0.904940 + 0.425539i \(0.860085\pi\)
\(140\) −0.0531091 + 0.0651664i −0.00448854 + 0.00550757i
\(141\) −1.34721 + 3.01853i −0.113456 + 0.254206i
\(142\) −4.54898 7.87907i −0.381742 0.661196i
\(143\) −19.0572 1.32431i −1.59364 0.110745i
\(144\) 11.4292 2.40772i 0.952431 0.200643i
\(145\) −1.93291 3.34790i −0.160519 0.278028i
\(146\) 17.0023 1.40712
\(147\) 8.95182 + 8.17710i 0.738334 + 0.674436i
\(148\) 0.362463i 0.0297943i
\(149\) −5.66226 9.80732i −0.463870 0.803447i 0.535279 0.844675i \(-0.320206\pi\)
−0.999150 + 0.0412280i \(0.986873\pi\)
\(150\) 9.05386 6.56550i 0.739245 0.536071i
\(151\) 2.48203 + 1.43300i 0.201985 + 0.116616i 0.597581 0.801809i \(-0.296129\pi\)
−0.395596 + 0.918425i \(0.629462\pi\)
\(152\) 0.362863 + 0.628497i 0.0294320 + 0.0509778i
\(153\) 12.8145 + 14.2839i 1.03599 + 1.15478i
\(154\) −15.1663 12.3602i −1.22213 0.996010i
\(155\) 0.139003i 0.0111650i
\(156\) −0.275354 + 0.171880i −0.0220460 + 0.0137614i
\(157\) 9.60863 + 5.54754i 0.766852 + 0.442742i 0.831751 0.555150i \(-0.187339\pi\)
−0.0648984 + 0.997892i \(0.520672\pi\)
\(158\) −5.80016 + 10.0462i −0.461436 + 0.799231i
\(159\) −5.09623 + 0.530970i −0.404157 + 0.0421087i
\(160\) 0.179697i 0.0142063i
\(161\) 11.2307 + 1.81479i 0.885100 + 0.143026i
\(162\) −1.35827 + 12.4878i −0.106716 + 0.981134i
\(163\) −14.7955 + 8.54216i −1.15887 + 0.669074i −0.951033 0.309090i \(-0.899976\pi\)
−0.207837 + 0.978164i \(0.566642\pi\)
\(164\) 0.173169 + 0.0999794i 0.0135223 + 0.00780708i
\(165\) 3.29334 + 4.54154i 0.256386 + 0.353558i
\(166\) 17.1351 9.89295i 1.32994 0.767842i
\(167\) 3.12753i 0.242016i 0.992652 + 0.121008i \(0.0386126\pi\)
−0.992652 + 0.121008i \(0.961387\pi\)
\(168\) −13.1035 0.739738i −1.01096 0.0570720i
\(169\) −7.99472 + 10.2511i −0.614978 + 0.788544i
\(170\) −4.72648 + 2.72883i −0.362504 + 0.209292i
\(171\) −0.743866 + 0.156706i −0.0568849 + 0.0119836i
\(172\) −0.0307588 + 0.0532759i −0.00234534 + 0.00406225i
\(173\) −1.33169 2.30656i −0.101247 0.175364i 0.810952 0.585113i \(-0.198950\pi\)
−0.912199 + 0.409749i \(0.865616\pi\)
\(174\) 6.23059 13.9601i 0.472340 1.05831i
\(175\) −11.4407 + 4.35067i −0.864836 + 0.328879i
\(176\) 20.6280 1.55489
\(177\) 5.79943 0.604236i 0.435912 0.0454172i
\(178\) −8.51164 4.91420i −0.637974 0.368335i
\(179\) −22.8750 13.2069i −1.70976 0.987129i −0.934843 0.355062i \(-0.884460\pi\)
−0.774914 0.632066i \(-0.782207\pi\)
\(180\) 0.0906040 + 0.0296205i 0.00675322 + 0.00220778i
\(181\) 7.12997i 0.529967i −0.964253 0.264983i \(-0.914634\pi\)
0.964253 0.264983i \(-0.0853665\pi\)
\(182\) −12.7430 + 3.85839i −0.944571 + 0.286003i
\(183\) 8.98985 20.1424i 0.664549 1.48897i
\(184\) −10.6648 + 6.15734i −0.786222 + 0.453925i
\(185\) −2.13152 + 3.69189i −0.156712 + 0.271433i
\(186\) −0.444999 + 0.322695i −0.0326289 + 0.0236612i
\(187\) 16.9453 + 29.3501i 1.23916 + 2.14629i
\(188\) 0.0991952i 0.00723455i
\(189\) 5.00167 12.8056i 0.363818 0.931470i
\(190\) 0.216205i 0.0156851i
\(191\) 2.02679 1.17017i 0.146654 0.0846705i −0.424878 0.905251i \(-0.639683\pi\)
0.571531 + 0.820580i \(0.306350\pi\)
\(192\) 11.4936 8.33471i 0.829480 0.601506i
\(193\) −10.2861 5.93866i −0.740407 0.427474i 0.0818104 0.996648i \(-0.473930\pi\)
−0.822217 + 0.569174i \(0.807263\pi\)
\(194\) 9.92855 + 17.1967i 0.712828 + 1.23465i
\(195\) 3.81540 0.131433i 0.273227 0.00941209i
\(196\) 0.345321 + 0.114595i 0.0246658 + 0.00818535i
\(197\) −17.6724 −1.25910 −0.629552 0.776958i \(-0.716762\pi\)
−0.629552 + 0.776958i \(0.716762\pi\)
\(198\) −6.89363 + 21.0864i −0.489909 + 1.49854i
\(199\) −1.38591 0.800155i −0.0982445 0.0567215i 0.450073 0.892992i \(-0.351398\pi\)
−0.548317 + 0.836270i \(0.684731\pi\)
\(200\) 6.62480 11.4745i 0.468444 0.811369i
\(201\) 18.5299 1.93061i 1.30700 0.136175i
\(202\) 0.575102 0.0404640
\(203\) −10.5699 + 12.9695i −0.741859 + 0.910283i
\(204\) 0.525860 + 0.234699i 0.0368176 + 0.0164322i
\(205\) −1.17589 2.03670i −0.0821275 0.142249i
\(206\) 15.8951 + 9.17702i 1.10746 + 0.639393i
\(207\) −2.65911 12.6225i −0.184821 0.877325i
\(208\) 7.84471 11.6411i 0.543933 0.807168i
\(209\) −1.34257 −0.0928674
\(210\) 3.27055 + 2.14273i 0.225689 + 0.147862i
\(211\) 1.05553 0.0726655 0.0363328 0.999340i \(-0.488432\pi\)
0.0363328 + 0.999340i \(0.488432\pi\)
\(212\) −0.133160 + 0.0768800i −0.00914547 + 0.00528014i
\(213\) 9.14010 6.62803i 0.626269 0.454145i
\(214\) −7.47159 4.31372i −0.510747 0.294880i
\(215\) 0.626593 0.361764i 0.0427333 0.0246721i
\(216\) 4.56022 + 14.1657i 0.310284 + 0.963857i
\(217\) 0.562313 0.213836i 0.0381723 0.0145161i
\(218\) 21.3744i 1.44766i
\(219\) 2.18649 + 20.9859i 0.147749 + 1.41809i
\(220\) 0.145794 + 0.0841744i 0.00982945 + 0.00567503i
\(221\) 23.0075 + 1.59883i 1.54765 + 0.107549i
\(222\) −16.7674 + 1.74698i −1.12536 + 0.117249i
\(223\) 3.29430 0.220603 0.110301 0.993898i \(-0.464818\pi\)
0.110301 + 0.993898i \(0.464818\pi\)
\(224\) −0.726933 + 0.276438i −0.0485702 + 0.0184703i
\(225\) 9.26809 + 10.3308i 0.617873 + 0.688721i
\(226\) 7.43131 4.29047i 0.494323 0.285398i
\(227\) 7.64728 + 4.41516i 0.507567 + 0.293044i 0.731833 0.681484i \(-0.238665\pi\)
−0.224266 + 0.974528i \(0.571998\pi\)
\(228\) −0.0184679 + 0.0133922i −0.00122307 + 0.000886918i
\(229\) 9.15938 + 15.8645i 0.605269 + 1.04836i 0.992009 + 0.126168i \(0.0402678\pi\)
−0.386740 + 0.922189i \(0.626399\pi\)
\(230\) 3.66873 0.241909
\(231\) 13.3057 20.3092i 0.875451 1.33625i
\(232\) 18.1111i 1.18905i
\(233\) 1.15726 0.668143i 0.0758145 0.0437715i −0.461614 0.887081i \(-0.652729\pi\)
0.537428 + 0.843310i \(0.319396\pi\)
\(234\) 9.27823 + 11.9094i 0.606537 + 0.778540i
\(235\) 0.583332 1.01036i 0.0380524 0.0659086i
\(236\) 0.151534 0.0874883i 0.00986404 0.00569500i
\(237\) −13.1459 5.86718i −0.853915 0.381114i
\(238\) 18.3100 + 14.9223i 1.18686 + 0.967266i
\(239\) −7.76160 −0.502056 −0.251028 0.967980i \(-0.580769\pi\)
−0.251028 + 0.967980i \(0.580769\pi\)
\(240\) −4.10019 + 0.427194i −0.264666 + 0.0275753i
\(241\) −0.515453 + 0.892790i −0.0332032 + 0.0575097i −0.882150 0.470969i \(-0.843904\pi\)
0.848946 + 0.528479i \(0.177238\pi\)
\(242\) −11.9136 + 20.6349i −0.765833 + 1.32646i
\(243\) −15.5883 0.0705805i −0.999990 0.00452774i
\(244\) 0.661922i 0.0423752i
\(245\) −2.84340 3.19792i −0.181658 0.204308i
\(246\) 3.79038 8.49264i 0.241666 0.541471i
\(247\) −0.510572 + 0.757662i −0.0324869 + 0.0482089i
\(248\) −0.325610 + 0.563973i −0.0206763 + 0.0358123i
\(249\) 14.4144 + 19.8775i 0.913475 + 1.25969i
\(250\) −7.11299 + 4.10669i −0.449865 + 0.259730i
\(251\) −23.4625 −1.48094 −0.740470 0.672090i \(-0.765397\pi\)
−0.740470 + 0.672090i \(0.765397\pi\)
\(252\) −0.0195563 0.412090i −0.00123193 0.0259592i
\(253\) 22.7818i 1.43228i
\(254\) −1.01826 1.76369i −0.0638916 0.110664i
\(255\) −3.97601 5.48294i −0.248987 0.343355i
\(256\) 0.623298 1.07958i 0.0389561 0.0674740i
\(257\) −7.45122 12.9059i −0.464795 0.805048i 0.534398 0.845233i \(-0.320539\pi\)
−0.999192 + 0.0401853i \(0.987205\pi\)
\(258\) 2.61277 + 1.16612i 0.162664 + 0.0725994i
\(259\) 18.2140 + 2.94324i 1.13176 + 0.182884i
\(260\) 0.102948 0.0502661i 0.00638454 0.00311737i
\(261\) 18.0321 + 5.89513i 1.11616 + 0.364899i
\(262\) 3.27655 5.67516i 0.202426 0.350612i
\(263\) 16.1197 + 9.30674i 0.993986 + 0.573878i 0.906463 0.422284i \(-0.138772\pi\)
0.0875227 + 0.996163i \(0.472105\pi\)
\(264\) 2.72358 + 26.1408i 0.167625 + 1.60886i
\(265\) 1.80842 0.111090
\(266\) −0.874620 + 0.332600i −0.0536264 + 0.0203930i
\(267\) 4.97098 11.1378i 0.304219 0.681625i
\(268\) 0.484170 0.279536i 0.0295754 0.0170754i
\(269\) 8.01136 13.8761i 0.488461 0.846040i −0.511451 0.859313i \(-0.670892\pi\)
0.999912 + 0.0132729i \(0.00422501\pi\)
\(270\) 0.933549 4.33407i 0.0568140 0.263763i
\(271\) −5.30174 9.18288i −0.322058 0.557820i 0.658855 0.752270i \(-0.271041\pi\)
−0.980912 + 0.194450i \(0.937708\pi\)
\(272\) −24.9039 −1.51002
\(273\) −6.40114 15.2324i −0.387415 0.921906i
\(274\) −22.1931 −1.34073
\(275\) 12.2557 + 21.2274i 0.739045 + 1.28006i
\(276\) −0.227249 0.313378i −0.0136788 0.0188631i
\(277\) −8.66166 + 15.0024i −0.520429 + 0.901409i 0.479289 + 0.877657i \(0.340895\pi\)
−0.999718 + 0.0237519i \(0.992439\pi\)
\(278\) 12.1284 7.00235i 0.727414 0.419973i
\(279\) −0.455528 0.507762i −0.0272718 0.0303989i
\(280\) 4.57285 + 0.738938i 0.273280 + 0.0441600i
\(281\) 5.94001 0.354351 0.177176 0.984179i \(-0.443304\pi\)
0.177176 + 0.984179i \(0.443304\pi\)
\(282\) 4.58874 0.478095i 0.273255 0.0284701i
\(283\) −19.2541 11.1164i −1.14454 0.660799i −0.196987 0.980406i \(-0.563116\pi\)
−0.947550 + 0.319607i \(0.896449\pi\)
\(284\) 0.169406 0.293419i 0.0100524 0.0174112i
\(285\) 0.266861 0.0278039i 0.0158075 0.00164696i
\(286\) 11.6985 + 23.9591i 0.691747 + 1.41673i
\(287\) −6.43018 + 7.89002i −0.379562 + 0.465733i
\(288\) 0.588886 + 0.656411i 0.0347005 + 0.0386794i
\(289\) −11.9578 20.7115i −0.703400 1.21832i
\(290\) −2.69779 + 4.67272i −0.158420 + 0.274391i
\(291\) −19.9491 + 14.4663i −1.16943 + 0.848027i
\(292\) 0.316586 + 0.548342i 0.0185268 + 0.0320893i
\(293\) 6.79656i 0.397059i −0.980095 0.198530i \(-0.936383\pi\)
0.980095 0.198530i \(-0.0636166\pi\)
\(294\) 3.63676 16.5267i 0.212100 0.963859i
\(295\) −2.05795 −0.119819
\(296\) −17.2963 + 9.98602i −1.00533 + 0.580426i
\(297\) −26.9133 5.79707i −1.56167 0.336380i
\(298\) −7.90291 + 13.6882i −0.457803 + 0.792938i
\(299\) −12.8566 8.66379i −0.743517 0.501040i
\(300\) 0.380329 + 0.169746i 0.0219583 + 0.00980030i
\(301\) −2.42738 1.97826i −0.139912 0.114025i
\(302\) 4.00013i 0.230182i
\(303\) 0.0739579 + 0.709845i 0.00424877 + 0.0407796i
\(304\) 0.493282 0.854390i 0.0282917 0.0490026i
\(305\) −3.89253 + 6.74205i −0.222885 + 0.386049i
\(306\) 8.32259 25.4573i 0.475771 1.45530i
\(307\) −25.1764 −1.43690 −0.718448 0.695581i \(-0.755147\pi\)
−0.718448 + 0.695581i \(0.755147\pi\)
\(308\) 0.116230 0.719277i 0.00662280 0.0409846i
\(309\) −9.28305 + 20.7994i −0.528094 + 1.18323i
\(310\) 0.168016 0.0970043i 0.00954269 0.00550947i
\(311\) 4.54000 7.86350i 0.257440 0.445898i −0.708116 0.706096i \(-0.750455\pi\)
0.965555 + 0.260198i \(0.0837879\pi\)
\(312\) 15.7880 + 8.40420i 0.893821 + 0.475794i
\(313\) 1.97646 1.14111i 0.111716 0.0644995i −0.443101 0.896472i \(-0.646122\pi\)
0.554817 + 0.831972i \(0.312788\pi\)
\(314\) 15.4856i 0.873903i
\(315\) −2.22416 + 4.31238i −0.125317 + 0.242975i
\(316\) −0.432000 −0.0243019
\(317\) 0.0939520 + 0.162730i 0.00527687 + 0.00913981i 0.868652 0.495423i \(-0.164987\pi\)
−0.863375 + 0.504563i \(0.831654\pi\)
\(318\) 4.19824 + 5.78940i 0.235426 + 0.324654i
\(319\) 29.0162 + 16.7525i 1.62460 + 0.937961i
\(320\) −4.33959 + 2.50547i −0.242591 + 0.140060i
\(321\) 4.36356 9.77689i 0.243550 0.545693i
\(322\) −5.64382 14.8413i −0.314518 0.827071i
\(323\) 1.62087 0.0901874
\(324\) −0.428036 + 0.188719i −0.0237798 + 0.0104844i
\(325\) 16.6402 + 1.15635i 0.923033 + 0.0641428i
\(326\) 20.6503 + 11.9224i 1.14371 + 0.660322i
\(327\) −26.3823 + 2.74874i −1.45895 + 0.152006i
\(328\) 11.0179i 0.608363i
\(329\) −4.98462 0.805477i −0.274811 0.0444074i
\(330\) 3.19119 7.15010i 0.175669 0.393600i
\(331\) 18.3872 10.6159i 1.01065 0.583502i 0.0992714 0.995060i \(-0.468349\pi\)
0.911383 + 0.411559i \(0.135015\pi\)
\(332\) 0.638116 + 0.368417i 0.0350212 + 0.0202195i
\(333\) −4.31257 20.4713i −0.236327 1.12182i
\(334\) 3.78033 2.18257i 0.206850 0.119425i
\(335\) −6.57540 −0.359253
\(336\) 8.03571 + 15.9295i 0.438384 + 0.869024i
\(337\) 21.2121 1.15549 0.577747 0.816216i \(-0.303932\pi\)
0.577747 + 0.816216i \(0.303932\pi\)
\(338\) 17.9699 + 2.50963i 0.977434 + 0.136506i
\(339\) 6.25137 + 8.62067i 0.339528 + 0.468211i
\(340\) −0.176016 0.101623i −0.00954578 0.00551126i
\(341\) −0.602368 1.04333i −0.0326201 0.0564996i
\(342\) 0.708528 + 0.789771i 0.0383128 + 0.0427059i
\(343\) −8.56250 + 16.4220i −0.462332 + 0.886707i
\(344\) 3.38968 0.182759
\(345\) 0.471798 + 4.52830i 0.0254008 + 0.243796i
\(346\) −1.85866 + 3.21930i −0.0999223 + 0.173071i
\(347\) 6.28808 + 3.63043i 0.337562 + 0.194892i 0.659193 0.751973i \(-0.270898\pi\)
−0.321631 + 0.946865i \(0.604231\pi\)
\(348\) 0.566243 0.0589962i 0.0303538 0.00316253i
\(349\) 8.93350 0.478199 0.239100 0.970995i \(-0.423148\pi\)
0.239100 + 0.970995i \(0.423148\pi\)
\(350\) 13.2428 + 10.7925i 0.707855 + 0.576885i
\(351\) −13.5065 + 12.9836i −0.720924 + 0.693014i
\(352\) 0.778715 + 1.34877i 0.0415056 + 0.0718899i
\(353\) 12.3163 + 7.11081i 0.655530 + 0.378470i 0.790572 0.612369i \(-0.209783\pi\)
−0.135042 + 0.990840i \(0.543117\pi\)
\(354\) −4.77754 6.58825i −0.253923 0.350162i
\(355\) −3.45099 + 1.99243i −0.183159 + 0.105747i
\(356\) 0.366013i 0.0193986i
\(357\) −16.0638 + 24.5190i −0.850187 + 1.29768i
\(358\) 36.8661i 1.94843i
\(359\) −10.6132 18.3827i −0.560145 0.970199i −0.997483 0.0709023i \(-0.977412\pi\)
0.437338 0.899297i \(-0.355921\pi\)
\(360\) −1.08272 5.13957i −0.0570646 0.270879i
\(361\) 9.46789 16.3989i 0.498310 0.863099i
\(362\) −8.61818 + 4.97571i −0.452961 + 0.261517i
\(363\) −27.0017 12.0512i −1.41722 0.632525i
\(364\) −0.361713 0.339130i −0.0189589 0.0177752i
\(365\) 7.44691i 0.389789i
\(366\) −30.6203 + 3.19029i −1.60055 + 0.166759i
\(367\) −8.54454 4.93320i −0.446022 0.257511i 0.260127 0.965574i \(-0.416236\pi\)
−0.706149 + 0.708064i \(0.749569\pi\)
\(368\) 14.4980 + 8.37041i 0.755759 + 0.436338i
\(369\) 10.9699 + 3.58630i 0.571068 + 0.186695i
\(370\) 5.94998 0.309325
\(371\) −2.78199 7.31565i −0.144434 0.379809i
\(372\) −0.0186932 0.00834305i −0.000969199 0.000432567i
\(373\) 3.41256 + 5.91072i 0.176695 + 0.306046i 0.940747 0.339110i \(-0.110126\pi\)
−0.764051 + 0.645156i \(0.776793\pi\)
\(374\) 23.6508 40.9643i 1.22295 2.11822i
\(375\) −5.98359 8.25141i −0.308991 0.426101i
\(376\) 4.73348 2.73287i 0.244110 0.140937i
\(377\) 20.4888 10.0040i 1.05523 0.515234i
\(378\) −18.9689 + 2.89084i −0.975655 + 0.148689i
\(379\) 9.65252i 0.495817i −0.968783 0.247908i \(-0.920257\pi\)
0.968783 0.247908i \(-0.0797432\pi\)
\(380\) 0.00697283 0.00402577i 0.000357699 0.000206518i
\(381\) 2.04596 1.48365i 0.104818 0.0760096i
\(382\) −2.82883 1.63322i −0.144735 0.0835630i
\(383\) −0.534935 + 0.308845i −0.0273339 + 0.0157812i −0.513605 0.858027i \(-0.671690\pi\)
0.486271 + 0.873808i \(0.338357\pi\)
\(384\) −17.1654 7.66117i −0.875969 0.390957i
\(385\) −5.41368 + 6.64274i −0.275907 + 0.338545i
\(386\) 16.5774i 0.843766i
\(387\) −1.10333 + 3.37490i −0.0560855 + 0.171556i
\(388\) −0.369742 + 0.640412i −0.0187708 + 0.0325120i
\(389\) −6.04565 3.49046i −0.306527 0.176973i 0.338845 0.940842i \(-0.389964\pi\)
−0.645371 + 0.763869i \(0.723297\pi\)
\(390\) −2.82147 4.52005i −0.142871 0.228882i
\(391\) 27.5041i 1.39094i
\(392\) −4.04542 19.6354i −0.204325 0.991739i
\(393\) 7.42618 + 3.31441i 0.374601 + 0.167190i
\(394\) 12.3328 + 21.3611i 0.621318 + 1.07615i
\(395\) 4.40017 + 2.54044i 0.221397 + 0.127823i
\(396\) −0.808419 + 0.170305i −0.0406246 + 0.00855815i
\(397\) −11.7435 20.3403i −0.589388 1.02085i −0.994313 0.106500i \(-0.966036\pi\)
0.404925 0.914350i \(-0.367298\pi\)
\(398\) 2.23358i 0.111959i
\(399\) −0.523003 1.03677i −0.0261829 0.0519033i
\(400\) −18.0118 −0.900588
\(401\) 3.07594 + 5.32768i 0.153605 + 0.266052i 0.932550 0.361040i \(-0.117578\pi\)
−0.778945 + 0.627092i \(0.784245\pi\)
\(402\) −15.2648 21.0503i −0.761340 1.04989i
\(403\) −0.817869 0.0568349i −0.0407410 0.00283115i
\(404\) 0.0107085 + 0.0185476i 0.000532767 + 0.000922780i
\(405\) 5.46958 + 0.594915i 0.271786 + 0.0295616i
\(406\) 23.0529 + 3.72517i 1.14409 + 0.184877i
\(407\) 36.9476i 1.83143i
\(408\) −3.28814 31.5595i −0.162787 1.56243i
\(409\) 2.13589 3.69946i 0.105613 0.182927i −0.808376 0.588667i \(-0.799653\pi\)
0.913988 + 0.405740i \(0.132986\pi\)
\(410\) −1.64120 + 2.84265i −0.0810533 + 0.140388i
\(411\) −2.85402 27.3928i −0.140778 1.35119i
\(412\) 0.683510i 0.0336741i
\(413\) 3.16586 + 8.32510i 0.155782 + 0.409651i
\(414\) −13.4015 + 12.0229i −0.658646 + 0.590891i
\(415\) −4.33306 7.50507i −0.212701 0.368409i
\(416\) 1.05730 + 0.0734736i 0.0518386 + 0.00360234i
\(417\) 10.2027 + 14.0696i 0.499627 + 0.688989i
\(418\) 0.936922 + 1.62280i 0.0458264 + 0.0793736i
\(419\) −22.0324 −1.07635 −0.538177 0.842832i \(-0.680887\pi\)
−0.538177 + 0.842832i \(0.680887\pi\)
\(420\) −0.00820699 + 0.145377i −0.000400460 + 0.00709366i
\(421\) 1.74256i 0.0849272i 0.999098 + 0.0424636i \(0.0135206\pi\)
−0.999098 + 0.0424636i \(0.986479\pi\)
\(422\) −0.736609 1.27584i −0.0358575 0.0621071i
\(423\) 1.18022 + 5.60238i 0.0573843 + 0.272397i
\(424\) 7.33725 + 4.23616i 0.356328 + 0.205726i
\(425\) −14.7961 25.6276i −0.717717 1.24312i
\(426\) −14.3900 6.42244i −0.697196 0.311168i
\(427\) 33.2620 + 5.37488i 1.60966 + 0.260109i
\(428\) 0.321289i 0.0155301i
\(429\) −28.0682 + 17.5205i −1.35515 + 0.845900i
\(430\) −0.874546 0.504919i −0.0421743 0.0243494i
\(431\) 1.03348 1.79003i 0.0497808 0.0862228i −0.840061 0.542491i \(-0.817481\pi\)
0.889842 + 0.456269i \(0.150814\pi\)
\(432\) 13.5776 14.9973i 0.653252 0.721558i
\(433\) 10.3446i 0.497130i −0.968615 0.248565i \(-0.920041\pi\)
0.968615 0.248565i \(-0.0799590\pi\)
\(434\) −0.650884 0.530455i −0.0312434 0.0254626i
\(435\) −6.11445 2.72896i −0.293165 0.130844i
\(436\) −0.689347 + 0.397995i −0.0330137 + 0.0190605i
\(437\) −0.943598 0.544787i −0.0451384 0.0260607i
\(438\) 23.8403 17.2880i 1.13913 0.826053i
\(439\) 7.84541 4.52955i 0.374441 0.216184i −0.300956 0.953638i \(-0.597306\pi\)
0.675397 + 0.737454i \(0.263972\pi\)
\(440\) 9.27617i 0.442224i
\(441\) 20.8666 + 2.36351i 0.993646 + 0.112548i
\(442\) −14.1234 28.9255i −0.671784 1.37585i
\(443\) 25.6171 14.7901i 1.21711 0.702697i 0.252809 0.967516i \(-0.418646\pi\)
0.964298 + 0.264819i \(0.0853123\pi\)
\(444\) −0.368554 0.508238i −0.0174908 0.0241199i
\(445\) −2.15239 + 3.72805i −0.102033 + 0.176727i
\(446\) −2.29895 3.98190i −0.108859 0.188549i
\(447\) −17.9116 7.99422i −0.847191 0.378114i
\(448\) 16.8113 + 13.7008i 0.794258 + 0.647302i
\(449\) −10.8480 −0.511947 −0.255974 0.966684i \(-0.582396\pi\)
−0.255974 + 0.966684i \(0.582396\pi\)
\(450\) 6.01932 18.4120i 0.283753 0.867951i
\(451\) 17.6520 + 10.1914i 0.831201 + 0.479894i
\(452\) 0.276744 + 0.159778i 0.0130170 + 0.00751534i
\(453\) 4.93734 0.514415i 0.231976 0.0241693i
\(454\) 12.3246i 0.578423i
\(455\) 1.68995 + 5.58134i 0.0792263 + 0.261657i
\(456\) 1.14786 + 0.512305i 0.0537533 + 0.0239909i
\(457\) 4.25565 2.45700i 0.199071 0.114934i −0.397151 0.917753i \(-0.630001\pi\)
0.596222 + 0.802820i \(0.296668\pi\)
\(458\) 12.7839 22.1424i 0.597352 1.03464i
\(459\) 32.4921 + 6.99873i 1.51660 + 0.326673i
\(460\) 0.0683124 + 0.118321i 0.00318508 + 0.00551673i
\(461\) 27.4391i 1.27797i −0.769221 0.638983i \(-0.779355\pi\)
0.769221 0.638983i \(-0.220645\pi\)
\(462\) −33.8337 1.91002i −1.57409 0.0888624i
\(463\) 38.3413i 1.78187i 0.454129 + 0.890936i \(0.349951\pi\)
−0.454129 + 0.890936i \(0.650049\pi\)
\(464\) −21.3221 + 12.3103i −0.989853 + 0.571492i
\(465\) 0.141339 + 0.194907i 0.00655443 + 0.00903860i
\(466\) −1.61520 0.932538i −0.0748229 0.0431990i
\(467\) 6.50434 + 11.2658i 0.300985 + 0.521321i 0.976359 0.216154i \(-0.0693513\pi\)
−0.675374 + 0.737475i \(0.736018\pi\)
\(468\) −0.211328 + 0.520987i −0.00976864 + 0.0240826i
\(469\) 10.1153 + 26.5997i 0.467082 + 1.22826i
\(470\) −1.62833 −0.0751093
\(471\) 19.1138 1.99144i 0.880717 0.0917608i
\(472\) −8.34968 4.82069i −0.384325 0.221890i
\(473\) −3.13540 + 5.43068i −0.144166 + 0.249703i
\(474\) 2.08213 + 19.9842i 0.0956353 + 0.917904i
\(475\) 1.17229 0.0537885
\(476\) −0.140323 + 0.868373i −0.00643168 + 0.0398018i
\(477\) −6.60594 + 5.92639i −0.302465 + 0.271351i
\(478\) 5.41650 + 9.38164i 0.247745 + 0.429106i
\(479\) 10.1280 + 5.84739i 0.462759 + 0.267174i 0.713204 0.700957i \(-0.247243\pi\)
−0.250444 + 0.968131i \(0.580577\pi\)
\(480\) −0.182716 0.251967i −0.00833982 0.0115007i
\(481\) −20.8509 14.0510i −0.950721 0.640670i
\(482\) 1.43885 0.0655379
\(483\) 17.5927 8.87473i 0.800495 0.403814i
\(484\) −0.887331 −0.0403332
\(485\) 7.53208 4.34865i 0.342014 0.197462i
\(486\) 10.7931 + 18.8912i 0.489585 + 0.856923i
\(487\) −30.6998 17.7246i −1.39114 0.803177i −0.397701 0.917515i \(-0.630192\pi\)
−0.993442 + 0.114338i \(0.963525\pi\)
\(488\) −31.5861 + 18.2363i −1.42984 + 0.825516i
\(489\) −12.0602 + 27.0217i −0.545380 + 1.22196i
\(490\) −1.88112 + 5.66859i −0.0849804 + 0.256081i
\(491\) 10.2320i 0.461763i 0.972982 + 0.230882i \(0.0741610\pi\)
−0.972982 + 0.230882i \(0.925839\pi\)
\(492\) 0.344474 0.0358903i 0.0155301 0.00161806i
\(493\) −35.0309 20.2251i −1.57771 0.910893i
\(494\) 1.27211 + 0.0884009i 0.0572350 + 0.00397734i
\(495\) 9.23571 + 3.01937i 0.415115 + 0.135711i
\(496\) 0.885281 0.0397503
\(497\) 13.3689 + 10.8953i 0.599676 + 0.488722i
\(498\) 13.9673 31.2947i 0.625889 1.40235i
\(499\) 32.2543 18.6220i 1.44390 0.833637i 0.445794 0.895135i \(-0.352921\pi\)
0.998107 + 0.0614985i \(0.0195879\pi\)
\(500\) −0.264890 0.152934i −0.0118462 0.00683943i
\(501\) 3.18009 + 4.38536i 0.142076 + 0.195924i
\(502\) 16.3735 + 28.3597i 0.730785 + 1.26576i
\(503\) 5.85048 0.260860 0.130430 0.991458i \(-0.458364\pi\)
0.130430 + 0.991458i \(0.458364\pi\)
\(504\) −19.1257 + 12.2865i −0.851925 + 0.547283i
\(505\) 0.251891i 0.0112090i
\(506\) −27.5369 + 15.8984i −1.22417 + 0.706772i
\(507\) −0.786697 + 22.5029i −0.0349384 + 0.999389i
\(508\) 0.0379205 0.0656803i 0.00168245 0.00291409i
\(509\) 21.2894 12.2915i 0.943638 0.544810i 0.0525391 0.998619i \(-0.483269\pi\)
0.891099 + 0.453809i \(0.149935\pi\)
\(510\) −3.85268 + 8.63222i −0.170600 + 0.382241i
\(511\) −30.1252 + 11.4560i −1.33266 + 0.506784i
\(512\) −23.4453 −1.03615
\(513\) −0.883695 + 0.976097i −0.0390161 + 0.0430957i
\(514\) −10.3998 + 18.0130i −0.458715 + 0.794518i
\(515\) 4.01948 6.96195i 0.177120 0.306780i
\(516\) 0.0110417 + 0.105978i 0.000486085 + 0.00466543i
\(517\) 10.1115i 0.444702i
\(518\) −9.15319 24.0696i −0.402168 1.05756i
\(519\) −4.21259 1.88014i −0.184912 0.0825289i
\(520\) −5.23489 3.52768i −0.229565 0.154699i
\(521\) −18.0672 + 31.2933i −0.791538 + 1.37098i 0.133477 + 0.991052i \(0.457386\pi\)
−0.925015 + 0.379931i \(0.875948\pi\)
\(522\) −5.45829 25.9099i −0.238903 1.13404i
\(523\) 12.8468 7.41710i 0.561751 0.324327i −0.192097 0.981376i \(-0.561529\pi\)
0.753848 + 0.657049i \(0.228195\pi\)
\(524\) 0.244040 0.0106609
\(525\) −11.6182 + 17.7334i −0.507058 + 0.773948i
\(526\) 25.9791i 1.13274i
\(527\) 0.727232 + 1.25960i 0.0316787 + 0.0548691i
\(528\) 28.9241 20.9746i 1.25876 0.912803i
\(529\) −2.25563 + 3.90686i −0.0980707 + 0.169863i
\(530\) −1.26202 2.18588i −0.0548185 0.0949485i
\(531\) 7.51746 6.74414i 0.326230 0.292671i
\(532\) −0.0270123 0.0220144i −0.00117113 0.000954444i
\(533\) 12.4644 6.08596i 0.539892 0.263612i
\(534\) −16.9316 + 1.76409i −0.732703 + 0.0763395i
\(535\) −1.88939 + 3.27251i −0.0816853 + 0.141483i
\(536\) −26.6782 15.4027i −1.15232 0.665295i
\(537\) −45.5037 + 4.74097i −1.96363 + 0.204588i
\(538\) −22.3632 −0.964145
\(539\) 35.2003 + 11.6812i 1.51618 + 0.503146i
\(540\) 0.157161 0.0505932i 0.00676315 0.00217719i
\(541\) 32.9004 18.9950i 1.41450 0.816661i 0.418690 0.908129i \(-0.362490\pi\)
0.995808 + 0.0914689i \(0.0291562\pi\)
\(542\) −7.39972 + 12.8167i −0.317845 + 0.550524i
\(543\) −7.24979 9.99750i −0.311118 0.429034i
\(544\) −0.940132 1.62836i −0.0403078 0.0698152i
\(545\) 9.36186 0.401018
\(546\) −13.9447 + 18.3673i −0.596777 + 0.786046i
\(547\) 16.9980 0.726783 0.363391 0.931637i \(-0.381619\pi\)
0.363391 + 0.931637i \(0.381619\pi\)
\(548\) −0.413238 0.715750i −0.0176527 0.0305753i
\(549\) −7.87552 37.3842i −0.336119 1.59552i
\(550\) 17.1054 29.6275i 0.729378 1.26332i
\(551\) 1.38774 0.801215i 0.0591199 0.0341329i
\(552\) −8.69320 + 19.4777i −0.370007 + 0.829028i
\(553\) 3.50789 21.7083i 0.149171 0.923129i
\(554\) 24.1784 1.02724
\(555\) 0.765166 + 7.34403i 0.0324795 + 0.311737i
\(556\) 0.451666 + 0.260770i 0.0191549 + 0.0110591i
\(557\) −19.6161 + 33.9761i −0.831162 + 1.43961i 0.0659552 + 0.997823i \(0.478991\pi\)
−0.897117 + 0.441792i \(0.854343\pi\)
\(558\) −0.295850 + 0.904954i −0.0125243 + 0.0383098i
\(559\) 1.87236 + 3.83468i 0.0791923 + 0.162190i
\(560\) −2.23826 5.88584i −0.0945838 0.248722i
\(561\) 53.6036 + 23.9240i 2.26314 + 1.01007i
\(562\) −4.14528 7.17984i −0.174858 0.302863i
\(563\) −21.6399 + 37.4814i −0.912013 + 1.57965i −0.100798 + 0.994907i \(0.532139\pi\)
−0.811216 + 0.584747i \(0.801194\pi\)
\(564\) 0.100862 + 0.139090i 0.00424706 + 0.00585673i
\(565\) −1.87920 3.25487i −0.0790585 0.136933i
\(566\) 31.0305i 1.30431i
\(567\) −6.00754 23.0415i −0.252293 0.967651i
\(568\) −18.6688 −0.783326
\(569\) −13.6713 + 7.89310i −0.573129 + 0.330896i −0.758398 0.651792i \(-0.774018\pi\)
0.185269 + 0.982688i \(0.440684\pi\)
\(570\) −0.219838 0.303158i −0.00920800 0.0126979i
\(571\) −6.44955 + 11.1709i −0.269905 + 0.467489i −0.968837 0.247699i \(-0.920326\pi\)
0.698932 + 0.715188i \(0.253659\pi\)
\(572\) −0.554879 + 0.823412i −0.0232007 + 0.0344286i
\(573\) 1.65209 3.70164i 0.0690172 0.154638i
\(574\) 14.0242 + 2.26621i 0.585360 + 0.0945897i
\(575\) 19.8924i 0.829570i
\(576\) 7.64134 23.3735i 0.318389 0.973897i
\(577\) 3.83077 6.63508i 0.159477 0.276222i −0.775203 0.631712i \(-0.782353\pi\)
0.934680 + 0.355490i \(0.115686\pi\)
\(578\) −16.6897 + 28.9074i −0.694199 + 1.20239i
\(579\) −20.4614 + 2.13184i −0.850345 + 0.0885964i
\(580\) −0.200933 −0.00834331
\(581\) −23.6947 + 29.0741i −0.983023 + 1.20620i
\(582\) 31.4073 + 14.0175i 1.30188 + 0.581046i
\(583\) −13.5737 + 7.83676i −0.562164 + 0.324566i
\(584\) 17.4442 30.2142i 0.721845 1.25027i
\(585\) 5.21624 4.06381i 0.215665 0.168018i
\(586\) −8.21518 + 4.74303i −0.339366 + 0.195933i
\(587\) 8.55584i 0.353137i 0.984288 + 0.176569i \(0.0564998\pi\)
−0.984288 + 0.176569i \(0.943500\pi\)
\(588\) 0.600722 0.190441i 0.0247734 0.00785366i
\(589\) −0.0576184 −0.00237412
\(590\) 1.43616 + 2.48750i 0.0591257 + 0.102409i
\(591\) −24.7799 + 17.9694i −1.01931 + 0.739160i
\(592\) 23.5129 + 13.5752i 0.966375 + 0.557937i
\(593\) 34.6087 19.9814i 1.42121 0.820536i 0.424807 0.905284i \(-0.360342\pi\)
0.996402 + 0.0847480i \(0.0270085\pi\)
\(594\) 11.7746 + 36.5764i 0.483119 + 1.50075i
\(595\) 6.53586 8.01970i 0.267944 0.328775i
\(596\) −0.588614 −0.0241106
\(597\) −2.75690 + 0.287238i −0.112832 + 0.0117559i
\(598\) −1.50006 + 21.5862i −0.0613419 + 0.882726i
\(599\) 18.1081 + 10.4547i 0.739877 + 0.427168i 0.822024 0.569452i \(-0.192845\pi\)
−0.0821478 + 0.996620i \(0.526178\pi\)
\(600\) −2.37815 22.8254i −0.0970877 0.931844i
\(601\) 35.0469i 1.42959i 0.699332 + 0.714797i \(0.253481\pi\)
−0.699332 + 0.714797i \(0.746519\pi\)
\(602\) −0.697203 + 4.31458i −0.0284159 + 0.175849i
\(603\) 24.0192 21.5483i 0.978137 0.877516i
\(604\) 0.129008 0.0744831i 0.00524928 0.00303067i
\(605\) 9.03797 + 5.21808i 0.367446 + 0.212145i
\(606\) 0.806396 0.584766i 0.0327576 0.0237545i
\(607\) 11.1151 6.41731i 0.451148 0.260470i −0.257167 0.966367i \(-0.582789\pi\)
0.708315 + 0.705897i \(0.249456\pi\)
\(608\) 0.0744864 0.00302082
\(609\) −1.63337 + 28.9331i −0.0661875 + 1.17243i
\(610\) 10.8657 0.439940
\(611\) 5.70628 + 3.84534i 0.230851 + 0.155566i
\(612\) 0.975994 0.205607i 0.0394522 0.00831117i
\(613\) 7.75091 + 4.47499i 0.313056 + 0.180743i 0.648293 0.761391i \(-0.275483\pi\)
−0.335237 + 0.942134i \(0.608816\pi\)
\(614\) 17.5696 + 30.4314i 0.709051 + 1.22811i
\(615\) −3.71973 1.66017i −0.149994 0.0669444i
\(616\) −37.5252 + 14.2701i −1.51193 + 0.574957i
\(617\) −32.7471 −1.31835 −0.659173 0.751991i \(-0.729094\pi\)
−0.659173 + 0.751991i \(0.729094\pi\)
\(618\) 31.6190 3.29434i 1.27190 0.132518i
\(619\) 2.42018 4.19187i 0.0972751 0.168485i −0.813281 0.581871i \(-0.802321\pi\)
0.910556 + 0.413386i \(0.135654\pi\)
\(620\) 0.00625698 + 0.00361247i 0.000251286 + 0.000145080i
\(621\) −16.5632 14.9952i −0.664658 0.601738i
\(622\) −12.6731 −0.508145
\(623\) 18.3923 + 2.97207i 0.736874 + 0.119073i
\(624\) −0.837068 24.2995i −0.0335096 0.972759i
\(625\) −9.76703 16.9170i −0.390681 0.676680i
\(626\) −2.75858 1.59267i −0.110255 0.0636559i
\(627\) −1.88252 + 1.36513i −0.0751807 + 0.0545180i
\(628\) 0.499427 0.288344i 0.0199293 0.0115062i
\(629\) 44.6064i 1.77857i
\(630\) 6.76463 0.321025i 0.269509 0.0127899i
\(631\) 28.4404i 1.13219i 0.824339 + 0.566097i \(0.191547\pi\)
−0.824339 + 0.566097i \(0.808453\pi\)
\(632\) 11.9018 + 20.6145i 0.473428 + 0.820002i
\(633\) 1.48004 1.07327i 0.0588263 0.0426585i
\(634\) 0.131130 0.227124i 0.00520785 0.00902026i
\(635\) −0.772484 + 0.445994i −0.0306551 + 0.0176987i
\(636\) −0.108542 + 0.243197i −0.00430399 + 0.00964340i
\(637\) 19.9786 15.4225i 0.791582 0.611063i
\(638\) 46.7635i 1.85139i
\(639\) 6.07665 18.5874i 0.240388 0.735305i
\(640\) 5.74560 + 3.31722i 0.227115 + 0.131125i
\(641\) 22.1719 + 12.8009i 0.875736 + 0.505606i 0.869250 0.494373i \(-0.164602\pi\)
0.00648579 + 0.999979i \(0.497935\pi\)
\(642\) −14.8627 + 1.54853i −0.586585 + 0.0611156i
\(643\) 15.5299 0.612438 0.306219 0.951961i \(-0.400936\pi\)
0.306219 + 0.951961i \(0.400936\pi\)
\(644\) 0.373557 0.458366i 0.0147202 0.0180621i
\(645\) 0.510753 1.14438i 0.0201109 0.0450599i
\(646\) −1.13113 1.95918i −0.0445039 0.0770830i
\(647\) 4.96931 8.60711i 0.195364 0.338380i −0.751656 0.659556i \(-0.770745\pi\)
0.947020 + 0.321175i \(0.104078\pi\)
\(648\) 20.7980 + 15.2261i 0.817024 + 0.598136i
\(649\) 15.4466 8.91812i 0.606334 0.350067i
\(650\) −10.2148 20.9204i −0.400657 0.820566i
\(651\) 0.571034 0.871599i 0.0223806 0.0341607i
\(652\) 0.887990i 0.0347764i
\(653\) −33.6494 + 19.4275i −1.31680 + 0.760256i −0.983213 0.182462i \(-0.941593\pi\)
−0.333590 + 0.942718i \(0.608260\pi\)
\(654\) 21.7336 + 29.9707i 0.849850 + 1.17195i
\(655\) −2.48569 1.43511i −0.0971238 0.0560744i
\(656\) −12.9713 + 7.48898i −0.506444 + 0.292396i
\(657\) 24.4044 + 27.2027i 0.952105 + 1.06128i
\(658\) 2.50495 + 6.58714i 0.0976533 + 0.256794i
\(659\) 17.6554i 0.687756i −0.939014 0.343878i \(-0.888259\pi\)
0.939014 0.343878i \(-0.111741\pi\)
\(660\) 0.290019 0.0302167i 0.0112890 0.00117618i
\(661\) 19.0185 32.9410i 0.739733 1.28126i −0.212882 0.977078i \(-0.568285\pi\)
0.952615 0.304178i \(-0.0983816\pi\)
\(662\) −25.6634 14.8168i −0.997436 0.575870i
\(663\) 33.8864 21.1523i 1.31604 0.821488i
\(664\) 40.6002i 1.57559i
\(665\) 0.145677 + 0.383079i 0.00564911 + 0.0148552i
\(666\) −21.7346 + 19.4988i −0.842199 + 0.755562i
\(667\) 13.5957 + 23.5484i 0.526426 + 0.911796i
\(668\) 0.140781 + 0.0812798i 0.00544697 + 0.00314481i
\(669\) 4.61920 3.34966i 0.178589 0.129505i
\(670\) 4.58870 + 7.94786i 0.177277 + 0.307052i
\(671\) 67.4730i 2.60477i
\(672\) −0.738208 + 1.12676i −0.0284770 + 0.0434659i
\(673\) 29.5036 1.13728 0.568639 0.822587i \(-0.307470\pi\)
0.568639 + 0.822587i \(0.307470\pi\)
\(674\) −14.8030 25.6396i −0.570191 0.987599i
\(675\) 23.5000 + 5.06183i 0.904514 + 0.194830i
\(676\) 0.253664 + 0.626278i 0.00975633 + 0.0240876i
\(677\) −16.7042 28.9325i −0.641994 1.11197i −0.984987 0.172628i \(-0.944774\pi\)
0.342993 0.939338i \(-0.388559\pi\)
\(678\) 6.05746 13.5722i 0.232635 0.521237i
\(679\) −29.1787 23.7800i −1.11978 0.912592i
\(680\) 11.1990i 0.429462i
\(681\) 15.2122 1.58494i 0.582933 0.0607351i
\(682\) −0.840735 + 1.45620i −0.0321934 + 0.0557606i
\(683\) −4.11356 + 7.12490i −0.157401 + 0.272627i −0.933931 0.357454i \(-0.883645\pi\)
0.776530 + 0.630081i \(0.216978\pi\)
\(684\) −0.0122781 + 0.0375564i −0.000469464 + 0.00143601i
\(685\) 9.72043i 0.371399i
\(686\) 25.8252 1.11054i 0.986009 0.0424006i
\(687\) 28.9742 + 12.9316i 1.10544 + 0.493371i
\(688\) −2.30400 3.99064i −0.0878391 0.152142i
\(689\) −0.739417 + 10.6404i −0.0281696 + 0.405367i
\(690\) 5.14423 3.73039i 0.195837 0.142013i
\(691\) −17.2978 29.9606i −0.658039 1.13976i −0.981123 0.193386i \(-0.938053\pi\)
0.323084 0.946370i \(-0.395280\pi\)
\(692\) −0.138434 −0.00526249
\(693\) −1.99347 42.0064i −0.0757257 1.59569i
\(694\) 10.1341i 0.384685i
\(695\) −3.06699 5.31218i −0.116337 0.201502i
\(696\) −18.4155 25.3951i −0.698037 0.962598i
\(697\) −21.3111 12.3039i −0.807214 0.466045i
\(698\) −6.23432 10.7982i −0.235972 0.408716i
\(699\) 0.943313 2.11356i 0.0356794 0.0799423i
\(700\) −0.101488 + 0.628052i −0.00383590 + 0.0237381i
\(701\) 4.51184i 0.170410i 0.996363 + 0.0852050i \(0.0271545\pi\)
−0.996363 + 0.0852050i \(0.972845\pi\)
\(702\) 25.1192 + 7.26494i 0.948065 + 0.274198i
\(703\) −1.53033 0.883539i −0.0577176 0.0333233i
\(704\) 21.7148 37.6112i 0.818409 1.41753i
\(705\) −0.209403 2.00984i −0.00788657 0.0756950i
\(706\) 19.8494i 0.747040i
\(707\) −1.01898 + 0.387499i −0.0383228 + 0.0145734i
\(708\) 0.123520 0.276755i 0.00464215 0.0104011i
\(709\) −41.6758 + 24.0615i −1.56517 + 0.903649i −0.568446 + 0.822720i \(0.692455\pi\)
−0.996720 + 0.0809288i \(0.974211\pi\)
\(710\) 4.81660 + 2.78086i 0.180764 + 0.104364i
\(711\) −24.3986 + 5.13992i −0.915020 + 0.192762i
\(712\) −17.4657 + 10.0838i −0.654554 + 0.377907i
\(713\) 0.977714i 0.0366157i
\(714\) 40.8470 + 2.30595i 1.52866 + 0.0862980i
\(715\) 10.4940 5.12388i 0.392452 0.191622i
\(716\) −1.18897 + 0.686453i −0.0444339 + 0.0256540i
\(717\) −10.8832 + 7.89203i −0.406439 + 0.294733i
\(718\) −14.8131 + 25.6570i −0.552818 + 0.957509i
\(719\) 1.88336 + 3.26208i 0.0702376 + 0.121655i 0.899005 0.437938i \(-0.144291\pi\)
−0.828768 + 0.559593i \(0.810958\pi\)
\(720\) −5.31484 + 4.76810i −0.198072 + 0.177697i
\(721\) −34.3468 5.55019i −1.27914 0.206700i
\(722\) −26.4290 −0.983585
\(723\) 0.185036 + 1.77597i 0.00688156 + 0.0660489i
\(724\) −0.320944 0.185297i −0.0119278 0.00688651i
\(725\) −25.3361 14.6278i −0.940960 0.543263i
\(726\) 4.27670 + 41.0476i 0.158723 + 1.52342i
\(727\) 16.5111i 0.612364i 0.951973 + 0.306182i \(0.0990517\pi\)
−0.951973 + 0.306182i \(0.900948\pi\)
\(728\) −6.21751 + 26.6037i −0.230436 + 0.985999i
\(729\) −21.9294 + 15.7513i −0.812199 + 0.583381i
\(730\) −9.00127 + 5.19689i −0.333152 + 0.192345i
\(731\) 3.78533 6.55639i 0.140006 0.242497i
\(732\) −0.673045 0.928133i −0.0248765 0.0343048i
\(733\) 10.6248 + 18.4026i 0.392435 + 0.679717i 0.992770 0.120031i \(-0.0382996\pi\)
−0.600335 + 0.799748i \(0.704966\pi\)
\(734\) 13.7707i 0.508285i
\(735\) −7.23862 1.59288i −0.267001 0.0587543i
\(736\) 1.26395i 0.0465896i
\(737\) 49.3539 28.4945i 1.81797 1.04961i
\(738\) −3.32055 15.7623i −0.122231 0.580218i
\(739\) 15.3472 + 8.86071i 0.564556 + 0.325946i 0.754972 0.655757i \(-0.227650\pi\)
−0.190416 + 0.981703i \(0.560984\pi\)
\(740\) 0.110790 + 0.191893i 0.00407271 + 0.00705413i
\(741\) 0.0544805 + 1.58153i 0.00200139 + 0.0580990i
\(742\) −6.90117 + 8.46794i −0.253350 + 0.310868i
\(743\) −4.99199 −0.183138 −0.0915692 0.995799i \(-0.529188\pi\)
−0.0915692 + 0.995799i \(0.529188\pi\)
\(744\) 0.116887 + 1.12187i 0.00428527 + 0.0411299i
\(745\) 5.99537 + 3.46143i 0.219653 + 0.126817i
\(746\) 4.76296 8.24969i 0.174384 0.302043i
\(747\) 40.4231 + 13.2153i 1.47901 + 0.483521i
\(748\) 1.76152 0.0644077
\(749\) 16.1450 + 2.60890i 0.589924 + 0.0953273i
\(750\) −5.79799 + 12.9908i −0.211713 + 0.474358i
\(751\) 15.6605 + 27.1247i 0.571459 + 0.989796i 0.996416 + 0.0845825i \(0.0269557\pi\)
−0.424958 + 0.905213i \(0.639711\pi\)
\(752\) −6.43478 3.71512i −0.234652 0.135477i
\(753\) −32.8986 + 23.8568i −1.19889 + 0.869389i
\(754\) −26.3904 17.7839i −0.961082 0.647652i
\(755\) −1.75203 −0.0637630
\(756\) −0.446437 0.557940i −0.0162367 0.0202921i
\(757\) 6.10098 0.221744 0.110872 0.993835i \(-0.464636\pi\)
0.110872 + 0.993835i \(0.464636\pi\)
\(758\) −11.6672 + 6.73609i −0.423774 + 0.244666i
\(759\) −23.1646 31.9441i −0.840822 1.15950i
\(760\) −0.384210 0.221824i −0.0139368 0.00804639i
\(761\) −46.9258 + 27.0926i −1.70106 + 0.982106i −0.756366 + 0.654149i \(0.773027\pi\)
−0.944693 + 0.327957i \(0.893640\pi\)
\(762\) −3.22111 1.43763i −0.116689 0.0520798i
\(763\) −14.4019 37.8719i −0.521383 1.37105i
\(764\) 0.121644i 0.00440091i
\(765\) −11.1502 3.64525i −0.403135 0.131794i
\(766\) 0.746618 + 0.431060i 0.0269764 + 0.0155748i
\(767\) 0.841446 12.1086i 0.0303829 0.437217i
\(768\) −0.223750 2.14754i −0.00807388 0.0774928i
\(769\) −17.5752 −0.633777 −0.316888 0.948463i \(-0.602638\pi\)
−0.316888 + 0.948463i \(0.602638\pi\)
\(770\) 11.8072 + 1.90796i 0.425503 + 0.0687581i
\(771\) −23.5707 10.5200i −0.848879 0.378867i
\(772\) −0.534638 + 0.308673i −0.0192420 + 0.0111094i
\(773\) −24.2049 13.9747i −0.870589 0.502635i −0.00304507 0.999995i \(-0.500969\pi\)
−0.867544 + 0.497361i \(0.834303\pi\)
\(774\) 4.84929 1.02157i 0.174304 0.0367197i
\(775\) 0.525971 + 0.911008i 0.0188934 + 0.0327244i
\(776\) 40.7463 1.46271
\(777\) 28.5320 14.3931i 1.02358 0.516349i
\(778\) 9.74338i 0.349317i
\(779\) 0.844235 0.487419i 0.0302479 0.0174636i
\(780\) 0.0932402 0.175160i 0.00333853 0.00627172i
\(781\) 17.2683 29.9097i 0.617910 1.07025i
\(782\) 33.2450 19.1940i 1.18884 0.686376i
\(783\) 31.2785 10.0691i 1.11780 0.359842i
\(784\) −20.3669 + 18.1090i −0.727390 + 0.646751i
\(785\) −6.78260 −0.242081
\(786\) −1.17621 11.2892i −0.0419540 0.402673i
\(787\) −16.8958 + 29.2644i −0.602271 + 1.04316i 0.390205 + 0.920728i \(0.372404\pi\)
−0.992476 + 0.122436i \(0.960929\pi\)
\(788\) −0.459278 + 0.795493i −0.0163611 + 0.0283382i
\(789\) 32.0659 3.34091i 1.14158 0.118940i
\(790\) 7.09146i 0.252303i
\(791\) −10.2762 + 12.6091i −0.365378 + 0.448329i
\(792\) 30.3991 + 33.8848i 1.08018 + 1.20404i
\(793\) −38.0775 25.6596i −1.35217 0.911200i
\(794\) −16.3905 + 28.3893i −0.581679 + 1.00750i
\(795\) 2.53572 1.83881i 0.0899329 0.0652157i
\(796\) −0.0720353 + 0.0415896i −0.00255322 + 0.00147410i
\(797\) 26.1108 0.924891 0.462445 0.886648i \(-0.346972\pi\)
0.462445 + 0.886648i \(0.346972\pi\)
\(798\) −0.888186 + 1.35568i −0.0314414 + 0.0479907i
\(799\) 12.2074i 0.431868i
\(800\) −0.679951 1.17771i −0.0240399 0.0416383i
\(801\) −4.35481 20.6718i −0.153869 0.730401i
\(802\) 4.29314 7.43593i 0.151596 0.262572i
\(803\) 32.2712 + 55.8953i 1.13882 + 1.97250i
\(804\) 0.394660 0.884266i 0.0139186 0.0311857i
\(805\) −6.50038 + 2.47196i −0.229108 + 0.0871252i
\(806\) 0.502059 + 1.02824i 0.0176843 + 0.0362183i
\(807\) −2.87590 27.6028i −0.101236 0.971663i
\(808\) 0.590048 1.02199i 0.0207578 0.0359536i
\(809\) −12.7232 7.34575i −0.447325 0.258263i 0.259375 0.965777i \(-0.416483\pi\)
−0.706700 + 0.707514i \(0.749817\pi\)
\(810\) −3.09790 7.02639i −0.108849 0.246882i
\(811\) 2.00604 0.0704415 0.0352208 0.999380i \(-0.488787\pi\)
0.0352208 + 0.999380i \(0.488787\pi\)
\(812\) 0.309107 + 0.812843i 0.0108475 + 0.0285252i
\(813\) −16.7712 7.48522i −0.588191 0.262518i
\(814\) −44.6596 + 25.7842i −1.56532 + 0.903736i
\(815\) 5.22196 9.04469i 0.182917 0.316822i
\(816\) −34.9197 + 25.3224i −1.22244 + 0.886461i
\(817\) 0.149955 + 0.259730i 0.00524628 + 0.00908682i
\(818\) −5.96218 −0.208463
\(819\) −24.4639 14.8498i −0.854838 0.518895i
\(820\) −0.122238 −0.00426873
\(821\) 20.6223 + 35.7188i 0.719721 + 1.24659i 0.961110 + 0.276166i \(0.0890638\pi\)
−0.241389 + 0.970429i \(0.577603\pi\)
\(822\) −31.1187 + 22.5660i −1.08539 + 0.787080i
\(823\) 20.4970 35.5019i 0.714481 1.23752i −0.248679 0.968586i \(-0.579996\pi\)
0.963159 0.268931i \(-0.0866704\pi\)
\(824\) 32.6163 18.8310i 1.13624 0.656010i
\(825\) 38.7688 + 17.3031i 1.34976 + 0.602416i
\(826\) 7.85343 9.63639i 0.273256 0.335293i
\(827\) 9.94898 0.345960 0.172980 0.984925i \(-0.444660\pi\)
0.172980 + 0.984925i \(0.444660\pi\)
\(828\) −0.637288 0.208344i −0.0221473 0.00724046i
\(829\) −20.0570 11.5799i −0.696607 0.402187i 0.109475 0.993990i \(-0.465083\pi\)
−0.806083 + 0.591803i \(0.798416\pi\)
\(830\) −6.04771 + 10.4749i −0.209919 + 0.363591i
\(831\) 3.10934 + 29.8433i 0.107862 + 1.03525i
\(832\) −12.9674 26.5578i −0.449563 0.920728i
\(833\) −42.4968 14.1026i −1.47243 0.488626i
\(834\) 9.88621 22.1508i 0.342331 0.767019i
\(835\) −0.955955 1.65576i −0.0330822 0.0573000i
\(836\) −0.0348913 + 0.0604335i −0.00120674 + 0.00209014i
\(837\) −1.15503 0.248790i −0.0399236 0.00859944i
\(838\) 15.3755 + 26.6312i 0.531138 + 0.919958i
\(839\) 14.8268i 0.511879i −0.966693 0.255940i \(-0.917615\pi\)
0.966693 0.255940i \(-0.0823848\pi\)
\(840\) 7.16331 3.61357i 0.247158 0.124680i
\(841\) −10.9901 −0.378969
\(842\) 2.10628 1.21606i 0.0725871 0.0419082i
\(843\) 8.32896 6.03983i 0.286865 0.208023i
\(844\) 0.0274315 0.0475128i 0.000944233 0.00163546i
\(845\) 1.09920 7.87072i 0.0378137 0.270761i
\(846\) 5.94811 5.33623i 0.204500 0.183463i
\(847\) 7.20523 44.5889i 0.247575 1.53209i
\(848\) 11.5174i 0.395510i
\(849\) −38.3009 + 3.99052i −1.31448 + 0.136954i
\(850\) −20.6512 + 35.7689i −0.708329 + 1.22686i
\(851\) 14.9926 25.9679i 0.513939 0.890169i
\(852\) −0.0608127 0.583678i −0.00208341 0.0199965i
\(853\) −6.01677 −0.206010 −0.103005 0.994681i \(-0.532846\pi\)
−0.103005 + 0.994681i \(0.532846\pi\)
\(854\) −16.7154 43.9555i −0.571988 1.50413i
\(855\) 0.345915 0.310331i 0.0118301 0.0106131i
\(856\) −15.3315 + 8.85166i −0.524021 + 0.302543i
\(857\) 1.00768 1.74536i 0.0344219 0.0596204i −0.848301 0.529514i \(-0.822374\pi\)
0.882723 + 0.469893i \(0.155708\pi\)
\(858\) 40.7651 + 21.6999i 1.39170 + 0.740823i
\(859\) −20.5220 + 11.8484i −0.700201 + 0.404261i −0.807422 0.589974i \(-0.799138\pi\)
0.107221 + 0.994235i \(0.465805\pi\)
\(860\) 0.0376067i 0.00128238i
\(861\) −0.993661 + 17.6015i −0.0338639 + 0.599856i
\(862\) −2.88488 −0.0982593
\(863\) −23.6286 40.9260i −0.804328 1.39314i −0.916744 0.399476i \(-0.869192\pi\)
0.112416 0.993661i \(-0.464141\pi\)
\(864\) 1.49317 + 0.321625i 0.0507986 + 0.0109419i
\(865\) 1.41003 + 0.814084i 0.0479426 + 0.0276797i
\(866\) −12.5038 + 7.21907i −0.424896 + 0.245314i
\(867\) −37.8265 16.8825i −1.28466 0.573360i
\(868\) 0.00498818 0.0308688i 0.000169310 0.00104776i
\(869\) −44.0359 −1.49382
\(870\) 0.968447 + 9.29512i 0.0328334 + 0.315134i
\(871\) 2.68852 38.6885i 0.0910971 1.31091i
\(872\) 37.9837 + 21.9299i 1.28629 + 0.742639i
\(873\) −13.2628 + 40.5686i −0.448878 + 1.37304i
\(874\) 1.52073i 0.0514396i
\(875\) 9.83598 12.0690i 0.332517 0.408008i
\(876\) 1.00147 + 0.446969i 0.0338364 + 0.0151017i
\(877\) 17.6588 10.1953i 0.596297 0.344272i −0.171287 0.985221i \(-0.554792\pi\)
0.767583 + 0.640949i \(0.221459\pi\)
\(878\) −10.9500 6.32197i −0.369544 0.213356i
\(879\) −6.91077 9.53000i −0.233095 0.321439i
\(880\) −10.9208 + 6.30510i −0.368139 + 0.212545i
\(881\) 25.5787 0.861768 0.430884 0.902407i \(-0.358202\pi\)
0.430884 + 0.902407i \(0.358202\pi\)
\(882\) −11.7051 26.8713i −0.394130 0.904805i
\(883\) −15.6631 −0.527106 −0.263553 0.964645i \(-0.584894\pi\)
−0.263553 + 0.964645i \(0.584894\pi\)
\(884\) 0.669899 0.994095i 0.0225311 0.0334350i
\(885\) −2.88562 + 2.09253i −0.0969990 + 0.0703398i
\(886\) −35.7542 20.6427i −1.20119 0.693506i
\(887\) −15.7043 27.2006i −0.527298 0.913307i −0.999494 0.0318132i \(-0.989872\pi\)
0.472196 0.881494i \(-0.343461\pi\)
\(888\) −14.0987 + 31.5891i −0.473121 + 1.06006i
\(889\) 2.99255 + 2.43886i 0.100367 + 0.0817967i
\(890\) 6.00825 0.201397
\(891\) −43.6318 + 19.2371i −1.46172 + 0.644466i
\(892\) 0.0856138 0.148287i 0.00286656 0.00496503i
\(893\) 0.418807 + 0.241798i 0.0140148 + 0.00809147i
\(894\) 2.83696 + 27.2291i 0.0948823 + 0.910677i
\(895\) 16.1471 0.539740
\(896\) 4.58049 28.3459i 0.153023 0.946971i
\(897\) −26.8367 + 0.924468i −0.896050 + 0.0308671i
\(898\) 7.57034 + 13.1122i 0.252626 + 0.437560i
\(899\) 1.24527 + 0.718960i 0.0415322 + 0.0239786i
\(900\) 0.705888 0.148705i 0.0235296 0.00495685i
\(901\) 16.3873 9.46122i 0.545941 0.315199i
\(902\) 28.4486i 0.947235i
\(903\) −5.41512 0.305702i −0.180204 0.0101731i
\(904\) 17.6079i 0.585629i
\(905\) 2.17933 + 3.77471i 0.0724434 + 0.125476i
\(906\) −4.06735 5.60890i −0.135129 0.186343i
\(907\) −26.1019 + 45.2098i −0.866699 + 1.50117i −0.00134835 + 0.999999i \(0.500429\pi\)
−0.865350 + 0.501167i \(0.832904\pi\)
\(908\) 0.397482 0.229486i 0.0131909 0.00761577i
\(909\) 0.825476 + 0.920130i 0.0273793 + 0.0305188i
\(910\) 5.56696 5.93767i 0.184543 0.196832i
\(911\) 39.0422i 1.29353i −0.762691 0.646763i \(-0.776122\pi\)
0.762691 0.646763i \(-0.223878\pi\)
\(912\) −0.177077 1.69958i −0.00586361 0.0562787i
\(913\) 65.0464 + 37.5545i 2.15272 + 1.24287i
\(914\) −5.93967 3.42927i −0.196467 0.113430i
\(915\) 1.39733 + 13.4115i 0.0461943 + 0.443371i
\(916\) 0.952153 0.0314600
\(917\) −1.98163 + 12.2631i −0.0654393 + 0.404965i
\(918\) −14.2154 44.1582i −0.469177 1.45744i
\(919\) −8.28476 14.3496i −0.273289 0.473350i 0.696413 0.717641i \(-0.254778\pi\)
−0.969702 + 0.244291i \(0.921445\pi\)
\(920\) 3.76408 6.51958i 0.124098 0.214944i
\(921\) −35.3019 + 25.5995i −1.16324 + 0.843533i
\(922\) −33.1663 + 19.1486i −1.09227 + 0.630625i
\(923\) −10.3121 21.1197i −0.339426 0.695162i
\(924\) −0.568389 1.12674i −0.0186986 0.0370670i
\(925\) 32.2616i 1.06076i
\(926\) 46.3441 26.7568i 1.52296 0.879283i
\(927\) 8.13238 + 38.6035i 0.267102 + 1.26791i
\(928\) −1.60984 0.929439i −0.0528454 0.0305103i
\(929\) −37.3804 + 21.5816i −1.22641 + 0.708069i −0.966277 0.257504i \(-0.917100\pi\)
−0.260134 + 0.965573i \(0.583767\pi\)
\(930\) 0.136955 0.306857i 0.00449092 0.0100622i
\(931\) 1.32558 1.17862i 0.0434441 0.0386278i
\(932\) 0.0694561i 0.00227511i
\(933\) −1.62976 15.6423i −0.0533558 0.512107i
\(934\) 9.07821 15.7239i 0.297048 0.514502i
\(935\) −17.9421 10.3589i −0.586771 0.338772i
\(936\) 30.6831 4.26912i 1.00291 0.139541i
\(937\) 22.8032i 0.744949i −0.928042 0.372475i \(-0.878509\pi\)
0.928042 0.372475i \(-0.121491\pi\)
\(938\) 25.0927 30.7894i 0.819305 1.00531i
\(939\) 1.61107 3.60972i 0.0525753 0.117799i
\(940\) −0.0303198 0.0525154i −0.000988923 0.00171286i
\(941\) 43.3047 + 25.0020i 1.41169 + 0.815042i 0.995548 0.0942559i \(-0.0300472\pi\)
0.416146 + 0.909298i \(0.363381\pi\)
\(942\) −15.7458 21.7136i −0.513027 0.707467i
\(943\) 8.27092 + 14.3257i 0.269338 + 0.466507i
\(944\) 13.1067i 0.426586i
\(945\) 1.26617 + 8.30827i 0.0411885 + 0.270268i
\(946\) 8.75226 0.284561
\(947\) 20.8849 + 36.1736i 0.678667 + 1.17548i 0.975383 + 0.220519i \(0.0707751\pi\)
−0.296716 + 0.954966i \(0.595892\pi\)
\(948\) −0.605742 + 0.439260i −0.0196736 + 0.0142665i
\(949\) 43.8164 + 3.04486i 1.42234 + 0.0988403i
\(950\) −0.818093 1.41698i −0.0265425 0.0459729i
\(951\) 0.297202 + 0.132645i 0.00963743 + 0.00430132i
\(952\) 45.3037 17.2281i 1.46830 0.558365i
\(953\) 28.8958i 0.936026i 0.883722 + 0.468013i \(0.155030\pi\)
−0.883722 + 0.468013i \(0.844970\pi\)
\(954\) 11.7734 + 3.84899i 0.381177 + 0.124616i
\(955\) −0.715343 + 1.23901i −0.0231479 + 0.0400934i
\(956\) −0.201712 + 0.349376i −0.00652383 + 0.0112996i
\(957\) 57.7200 6.01377i 1.86582 0.194398i
\(958\) 16.3226i 0.527359i
\(959\) 39.3224 14.9535i 1.26979 0.482873i
\(960\) −3.53732 + 7.92563i −0.114167 + 0.255799i
\(961\) 15.4741 + 26.8020i 0.499166 + 0.864581i
\(962\) −2.43280 + 35.0087i −0.0784367 + 1.12872i
\(963\) −3.82268 18.1458i −0.123184 0.584742i
\(964\) 0.0267916 + 0.0464045i 0.000862901 + 0.00149459i
\(965\) 7.26079 0.233733
\(966\) −23.0043 15.0714i −0.740152 0.484916i
\(967\) 27.2038i 0.874814i −0.899264 0.437407i \(-0.855897\pi\)
0.899264 0.437407i \(-0.144103\pi\)
\(968\) 24.4464 + 42.3424i 0.785736 + 1.36094i
\(969\) 2.27275 1.64810i 0.0730111 0.0529447i
\(970\) −10.5126 6.06948i −0.337541 0.194879i
\(971\) 23.3323 + 40.4127i 0.748768 + 1.29690i 0.948414 + 0.317036i \(0.102688\pi\)
−0.199646 + 0.979868i \(0.563979\pi\)
\(972\) −0.408293 + 0.699847i −0.0130960 + 0.0224476i
\(973\) −16.7714 + 20.5790i −0.537667 + 0.659733i
\(974\) 49.4769i 1.58534i
\(975\) 24.5083 15.2984i 0.784895 0.489942i
\(976\) 42.9388 + 24.7907i 1.37444 + 0.793531i
\(977\) 22.0469 38.1863i 0.705341 1.22169i −0.261227 0.965277i \(-0.584127\pi\)
0.966568 0.256410i \(-0.0825396\pi\)
\(978\) 41.0781 4.27988i 1.31353 0.136856i
\(979\) 37.3095i 1.19242i
\(980\) −0.217845 + 0.0448818i −0.00695879 + 0.00143370i
\(981\) −34.1978 + 30.6799i −1.09185 + 0.979533i
\(982\) 12.3677 7.14047i 0.394668 0.227862i
\(983\) −36.5295 21.0903i −1.16511 0.672677i −0.212587 0.977142i \(-0.568189\pi\)
−0.952523 + 0.304465i \(0.901522\pi\)
\(984\) −11.2031 15.4491i −0.357141 0.492499i
\(985\) 9.35602 5.40170i 0.298108 0.172112i
\(986\) 56.4570i 1.79796i
\(987\) −7.80834 + 3.93896i −0.248542 + 0.125378i
\(988\) 0.0208359 + 0.0426730i 0.000662879 + 0.00135761i
\(989\) −4.40731 + 2.54456i −0.140144 + 0.0809124i
\(990\) −2.79563 13.2705i −0.0888509 0.421765i
\(991\) −2.95639 + 5.12063i −0.0939130 + 0.162662i −0.909154 0.416459i \(-0.863271\pi\)
0.815241 + 0.579121i \(0.196604\pi\)
\(992\) 0.0334197 + 0.0578847i 0.00106108 + 0.00183784i
\(993\) 14.9880 33.5816i 0.475628 1.06568i
\(994\) 3.83987 23.7627i 0.121793 0.753707i
\(995\) 0.978295 0.0310140
\(996\) 1.26936 0.132253i 0.0402213 0.00419060i
\(997\) 7.72518 + 4.46013i 0.244659 + 0.141254i 0.617316 0.786715i \(-0.288220\pi\)
−0.372657 + 0.927969i \(0.621553\pi\)
\(998\) −45.0179 25.9911i −1.42502 0.822733i
\(999\) −26.8623 24.3194i −0.849885 0.769431i
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 273.2.ba.c.38.10 yes 64
3.2 odd 2 inner 273.2.ba.c.38.23 yes 64
7.5 odd 6 inner 273.2.ba.c.194.9 yes 64
13.12 even 2 inner 273.2.ba.c.38.24 yes 64
21.5 even 6 inner 273.2.ba.c.194.24 yes 64
39.38 odd 2 inner 273.2.ba.c.38.9 64
91.12 odd 6 inner 273.2.ba.c.194.23 yes 64
273.194 even 6 inner 273.2.ba.c.194.10 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.ba.c.38.9 64 39.38 odd 2 inner
273.2.ba.c.38.10 yes 64 1.1 even 1 trivial
273.2.ba.c.38.23 yes 64 3.2 odd 2 inner
273.2.ba.c.38.24 yes 64 13.12 even 2 inner
273.2.ba.c.194.9 yes 64 7.5 odd 6 inner
273.2.ba.c.194.10 yes 64 273.194 even 6 inner
273.2.ba.c.194.23 yes 64 91.12 odd 6 inner
273.2.ba.c.194.24 yes 64 21.5 even 6 inner