Properties

Label 243.2.e.c.136.2
Level $243$
Weight $2$
Character 243.136
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [243,2,Mod(28,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.e (of order \(9\), degree \(6\), not 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: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 136.2
Root \(0.500000 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 243.136
Dual form 243.2.e.c.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.807660 + 0.677707i) q^{2} +(-0.154269 - 0.874902i) q^{4} +(1.64050 + 0.597094i) q^{5} +(0.427044 - 2.42189i) q^{7} +(1.52266 - 2.63732i) q^{8} +O(q^{10})\) \(q+(0.807660 + 0.677707i) q^{2} +(-0.154269 - 0.874902i) q^{4} +(1.64050 + 0.597094i) q^{5} +(0.427044 - 2.42189i) q^{7} +(1.52266 - 2.63732i) q^{8} +(0.920313 + 1.59403i) q^{10} +(1.17857 - 0.428966i) q^{11} +(-3.48476 + 2.92406i) q^{13} +(1.98623 - 1.66665i) q^{14} +(1.34747 - 0.490439i) q^{16} +(3.32358 + 5.75662i) q^{17} +(-0.124578 + 0.215776i) q^{19} +(0.269321 - 1.52739i) q^{20} +(1.24260 + 0.452270i) q^{22} +(0.146212 + 0.829209i) q^{23} +(-1.49549 - 1.25487i) q^{25} -4.79615 q^{26} -2.18479 q^{28} +(-0.392508 - 0.329353i) q^{29} +(-0.142392 - 0.807546i) q^{31} +(-4.30264 - 1.56603i) q^{32} +(-1.21697 + 6.90180i) q^{34} +(2.14666 - 3.71812i) q^{35} +(-1.30403 - 2.25865i) q^{37} +(-0.246849 + 0.0898458i) q^{38} +(4.07265 - 3.41736i) q^{40} +(-6.24542 + 5.24053i) q^{41} +(-4.06619 + 1.47997i) q^{43} +(-0.557121 - 0.964962i) q^{44} +(-0.443871 + 0.768808i) q^{46} +(-0.920741 + 5.22178i) q^{47} +(0.894687 + 0.325640i) q^{49} +(-0.357417 - 2.02701i) q^{50} +(3.09586 + 2.59773i) q^{52} -10.4841 q^{53} +2.18959 q^{55} +(-5.73704 - 4.81395i) q^{56} +(-0.0938079 - 0.532011i) q^{58} +(2.82491 + 1.02818i) q^{59} +(0.500658 - 2.83937i) q^{61} +(0.432275 - 0.748722i) q^{62} +(-3.84771 - 6.66442i) q^{64} +(-7.46270 + 2.71620i) q^{65} +(7.72653 - 6.48333i) q^{67} +(4.52375 - 3.79588i) q^{68} +(4.25357 - 1.54817i) q^{70} +(-0.0447378 - 0.0774882i) q^{71} +(2.66057 - 4.60824i) q^{73} +(0.477488 - 2.70797i) q^{74} +(0.208001 + 0.0757062i) q^{76} +(-0.535604 - 3.03756i) q^{77} +(3.65933 + 3.07054i) q^{79} +2.50337 q^{80} -8.59571 q^{82} +(6.15950 + 5.16844i) q^{83} +(2.01511 + 11.4282i) q^{85} +(-4.28708 - 1.56037i) q^{86} +(0.663244 - 3.76144i) q^{88} +(-3.35189 + 5.80564i) q^{89} +(5.59359 + 9.68839i) q^{91} +(0.702921 - 0.255842i) q^{92} +(-4.28248 + 3.59343i) q^{94} +(-0.333209 + 0.279596i) q^{95} +(-5.15946 + 1.87789i) q^{97} +(0.501915 + 0.869342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 3 q^{13} + 6 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} - 21 q^{20} - 15 q^{22} + 24 q^{23} - 15 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 15 q^{31} - 27 q^{32} - 9 q^{34} + 12 q^{35} - 3 q^{37} - 12 q^{38} - 6 q^{40} - 21 q^{41} + 12 q^{43} + 3 q^{44} - 3 q^{46} + 3 q^{47} + 21 q^{49} + 12 q^{50} + 36 q^{52} - 18 q^{53} - 12 q^{55} + 3 q^{56} + 30 q^{58} + 15 q^{59} + 21 q^{61} - 12 q^{62} + 12 q^{64} - 24 q^{65} + 21 q^{67} - 18 q^{68} + 30 q^{70} + 27 q^{71} + 6 q^{73} - 12 q^{74} + 42 q^{76} - 3 q^{77} + 21 q^{79} + 42 q^{80} - 12 q^{82} - 33 q^{83} - 9 q^{85} - 30 q^{86} - 12 q^{88} + 9 q^{89} + 6 q^{91} + 42 q^{92} - 33 q^{94} + 30 q^{95} - 42 q^{97} - 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.807660 + 0.677707i 0.571102 + 0.479211i 0.882011 0.471228i \(-0.156189\pi\)
−0.310910 + 0.950439i \(0.600634\pi\)
\(3\) 0 0
\(4\) −0.154269 0.874902i −0.0771344 0.437451i
\(5\) 1.64050 + 0.597094i 0.733655 + 0.267029i 0.681711 0.731621i \(-0.261236\pi\)
0.0519440 + 0.998650i \(0.483458\pi\)
\(6\) 0 0
\(7\) 0.427044 2.42189i 0.161407 0.915387i −0.791284 0.611448i \(-0.790587\pi\)
0.952692 0.303938i \(-0.0983017\pi\)
\(8\) 1.52266 2.63732i 0.538340 0.932432i
\(9\) 0 0
\(10\) 0.920313 + 1.59403i 0.291029 + 0.504076i
\(11\) 1.17857 0.428966i 0.355354 0.129338i −0.158174 0.987411i \(-0.550561\pi\)
0.513528 + 0.858073i \(0.328338\pi\)
\(12\) 0 0
\(13\) −3.48476 + 2.92406i −0.966498 + 0.810988i −0.981998 0.188892i \(-0.939511\pi\)
0.0154998 + 0.999880i \(0.495066\pi\)
\(14\) 1.98623 1.66665i 0.530843 0.445431i
\(15\) 0 0
\(16\) 1.34747 0.490439i 0.336868 0.122610i
\(17\) 3.32358 + 5.75662i 0.806088 + 1.39618i 0.915554 + 0.402194i \(0.131752\pi\)
−0.109467 + 0.993990i \(0.534914\pi\)
\(18\) 0 0
\(19\) −0.124578 + 0.215776i −0.0285802 + 0.0495023i −0.879962 0.475045i \(-0.842432\pi\)
0.851382 + 0.524547i \(0.175765\pi\)
\(20\) 0.269321 1.52739i 0.0602219 0.341536i
\(21\) 0 0
\(22\) 1.24260 + 0.452270i 0.264923 + 0.0964242i
\(23\) 0.146212 + 0.829209i 0.0304873 + 0.172902i 0.996250 0.0865268i \(-0.0275768\pi\)
−0.965762 + 0.259429i \(0.916466\pi\)
\(24\) 0 0
\(25\) −1.49549 1.25487i −0.299099 0.250974i
\(26\) −4.79615 −0.940603
\(27\) 0 0
\(28\) −2.18479 −0.412887
\(29\) −0.392508 0.329353i −0.0728869 0.0611594i 0.605616 0.795757i \(-0.292927\pi\)
−0.678503 + 0.734597i \(0.737371\pi\)
\(30\) 0 0
\(31\) −0.142392 0.807546i −0.0255744 0.145040i 0.969347 0.245696i \(-0.0790167\pi\)
−0.994921 + 0.100657i \(0.967906\pi\)
\(32\) −4.30264 1.56603i −0.760607 0.276838i
\(33\) 0 0
\(34\) −1.21697 + 6.90180i −0.208709 + 1.18365i
\(35\) 2.14666 3.71812i 0.362852 0.628478i
\(36\) 0 0
\(37\) −1.30403 2.25865i −0.214381 0.371319i 0.738700 0.674035i \(-0.235440\pi\)
−0.953081 + 0.302715i \(0.902107\pi\)
\(38\) −0.246849 + 0.0898458i −0.0400442 + 0.0145749i
\(39\) 0 0
\(40\) 4.07265 3.41736i 0.643942 0.540332i
\(41\) −6.24542 + 5.24053i −0.975370 + 0.818433i −0.983385 0.181535i \(-0.941893\pi\)
0.00801406 + 0.999968i \(0.497449\pi\)
\(42\) 0 0
\(43\) −4.06619 + 1.47997i −0.620087 + 0.225693i −0.632911 0.774224i \(-0.718140\pi\)
0.0128237 + 0.999918i \(0.495918\pi\)
\(44\) −0.557121 0.964962i −0.0839891 0.145473i
\(45\) 0 0
\(46\) −0.443871 + 0.768808i −0.0654452 + 0.113354i
\(47\) −0.920741 + 5.22178i −0.134304 + 0.761675i 0.841038 + 0.540976i \(0.181945\pi\)
−0.975342 + 0.220699i \(0.929166\pi\)
\(48\) 0 0
\(49\) 0.894687 + 0.325640i 0.127812 + 0.0465199i
\(50\) −0.357417 2.02701i −0.0505464 0.286663i
\(51\) 0 0
\(52\) 3.09586 + 2.59773i 0.429318 + 0.360241i
\(53\) −10.4841 −1.44010 −0.720052 0.693920i \(-0.755882\pi\)
−0.720052 + 0.693920i \(0.755882\pi\)
\(54\) 0 0
\(55\) 2.18959 0.295244
\(56\) −5.73704 4.81395i −0.766644 0.643291i
\(57\) 0 0
\(58\) −0.0938079 0.532011i −0.0123176 0.0698565i
\(59\) 2.82491 + 1.02818i 0.367772 + 0.133858i 0.519293 0.854596i \(-0.326195\pi\)
−0.151522 + 0.988454i \(0.548417\pi\)
\(60\) 0 0
\(61\) 0.500658 2.83937i 0.0641026 0.363544i −0.935836 0.352437i \(-0.885353\pi\)
0.999938 0.0111075i \(-0.00353569\pi\)
\(62\) 0.432275 0.748722i 0.0548990 0.0950878i
\(63\) 0 0
\(64\) −3.84771 6.66442i −0.480963 0.833053i
\(65\) −7.46270 + 2.71620i −0.925634 + 0.336903i
\(66\) 0 0
\(67\) 7.72653 6.48333i 0.943945 0.792064i −0.0343221 0.999411i \(-0.510927\pi\)
0.978268 + 0.207347i \(0.0664828\pi\)
\(68\) 4.52375 3.79588i 0.548586 0.460318i
\(69\) 0 0
\(70\) 4.25357 1.54817i 0.508399 0.185042i
\(71\) −0.0447378 0.0774882i −0.00530940 0.00919615i 0.863358 0.504591i \(-0.168357\pi\)
−0.868668 + 0.495395i \(0.835023\pi\)
\(72\) 0 0
\(73\) 2.66057 4.60824i 0.311396 0.539354i −0.667269 0.744817i \(-0.732537\pi\)
0.978665 + 0.205463i \(0.0658701\pi\)
\(74\) 0.477488 2.70797i 0.0555069 0.314795i
\(75\) 0 0
\(76\) 0.208001 + 0.0757062i 0.0238594 + 0.00868410i
\(77\) −0.535604 3.03756i −0.0610377 0.346162i
\(78\) 0 0
\(79\) 3.65933 + 3.07054i 0.411707 + 0.345463i 0.824998 0.565136i \(-0.191176\pi\)
−0.413291 + 0.910599i \(0.635621\pi\)
\(80\) 2.50337 0.279885
\(81\) 0 0
\(82\) −8.59571 −0.949238
\(83\) 6.15950 + 5.16844i 0.676093 + 0.567310i 0.914862 0.403767i \(-0.132299\pi\)
−0.238769 + 0.971077i \(0.576744\pi\)
\(84\) 0 0
\(85\) 2.01511 + 11.4282i 0.218569 + 1.23957i
\(86\) −4.28708 1.56037i −0.462288 0.168259i
\(87\) 0 0
\(88\) 0.663244 3.76144i 0.0707020 0.400971i
\(89\) −3.35189 + 5.80564i −0.355299 + 0.615396i −0.987169 0.159678i \(-0.948954\pi\)
0.631870 + 0.775074i \(0.282288\pi\)
\(90\) 0 0
\(91\) 5.59359 + 9.68839i 0.586368 + 1.01562i
\(92\) 0.702921 0.255842i 0.0732846 0.0266734i
\(93\) 0 0
\(94\) −4.28248 + 3.59343i −0.441704 + 0.370634i
\(95\) −0.333209 + 0.279596i −0.0341865 + 0.0286859i
\(96\) 0 0
\(97\) −5.15946 + 1.87789i −0.523863 + 0.190671i −0.590396 0.807114i \(-0.701028\pi\)
0.0665329 + 0.997784i \(0.478806\pi\)
\(98\) 0.501915 + 0.869342i 0.0507010 + 0.0878168i
\(99\) 0 0
\(100\) −0.867179 + 1.50200i −0.0867179 + 0.150200i
\(101\) 0.869190 4.92942i 0.0864876 0.490496i −0.910538 0.413425i \(-0.864332\pi\)
0.997026 0.0770703i \(-0.0245566\pi\)
\(102\) 0 0
\(103\) −10.9184 3.97399i −1.07583 0.391569i −0.257473 0.966285i \(-0.582890\pi\)
−0.818352 + 0.574717i \(0.805112\pi\)
\(104\) 2.40558 + 13.6427i 0.235887 + 1.33778i
\(105\) 0 0
\(106\) −8.46760 7.10516i −0.822446 0.690114i
\(107\) 19.4581 1.88109 0.940544 0.339673i \(-0.110316\pi\)
0.940544 + 0.339673i \(0.110316\pi\)
\(108\) 0 0
\(109\) 6.31515 0.604881 0.302441 0.953168i \(-0.402199\pi\)
0.302441 + 0.953168i \(0.402199\pi\)
\(110\) 1.76844 + 1.48390i 0.168614 + 0.141484i
\(111\) 0 0
\(112\) −0.612359 3.47286i −0.0578625 0.328154i
\(113\) 6.49866 + 2.36532i 0.611342 + 0.222510i 0.629090 0.777332i \(-0.283428\pi\)
−0.0177483 + 0.999842i \(0.505650\pi\)
\(114\) 0 0
\(115\) −0.255255 + 1.44762i −0.0238026 + 0.134991i
\(116\) −0.227600 + 0.394215i −0.0211322 + 0.0366020i
\(117\) 0 0
\(118\) 1.58476 + 2.74488i 0.145889 + 0.252687i
\(119\) 15.3612 5.59101i 1.40816 0.512527i
\(120\) 0 0
\(121\) −7.22146 + 6.05953i −0.656497 + 0.550866i
\(122\) 2.32862 1.95395i 0.210824 0.176902i
\(123\) 0 0
\(124\) −0.684557 + 0.249158i −0.0614750 + 0.0223751i
\(125\) −6.06855 10.5110i −0.542788 0.940136i
\(126\) 0 0
\(127\) −6.01162 + 10.4124i −0.533445 + 0.923954i 0.465792 + 0.884894i \(0.345770\pi\)
−0.999237 + 0.0390598i \(0.987564\pi\)
\(128\) −0.181303 + 1.02822i −0.0160251 + 0.0908828i
\(129\) 0 0
\(130\) −7.86811 2.86376i −0.690079 0.251168i
\(131\) −2.44580 13.8708i −0.213690 1.21190i −0.883164 0.469063i \(-0.844592\pi\)
0.669474 0.742835i \(-0.266520\pi\)
\(132\) 0 0
\(133\) 0.469383 + 0.393859i 0.0407007 + 0.0341519i
\(134\) 10.6342 0.918655
\(135\) 0 0
\(136\) 20.2427 1.73580
\(137\) 1.72984 + 1.45150i 0.147790 + 0.124010i 0.713685 0.700467i \(-0.247025\pi\)
−0.565895 + 0.824477i \(0.691469\pi\)
\(138\) 0 0
\(139\) −1.38486 7.85393i −0.117462 0.666162i −0.985502 0.169666i \(-0.945731\pi\)
0.868039 0.496496i \(-0.165380\pi\)
\(140\) −3.58416 1.30453i −0.302917 0.110253i
\(141\) 0 0
\(142\) 0.0163813 0.0929032i 0.00137469 0.00779626i
\(143\) −2.85273 + 4.94107i −0.238557 + 0.413193i
\(144\) 0 0
\(145\) −0.447256 0.774670i −0.0371426 0.0643328i
\(146\) 5.27187 1.91880i 0.436303 0.158801i
\(147\) 0 0
\(148\) −1.77492 + 1.48934i −0.145898 + 0.122423i
\(149\) −0.0819196 + 0.0687387i −0.00671111 + 0.00563129i −0.646137 0.763221i \(-0.723617\pi\)
0.639426 + 0.768853i \(0.279172\pi\)
\(150\) 0 0
\(151\) 19.0376 6.92913i 1.54926 0.563884i 0.581016 0.813892i \(-0.302655\pi\)
0.968244 + 0.250008i \(0.0804333\pi\)
\(152\) 0.379379 + 0.657104i 0.0307717 + 0.0532982i
\(153\) 0 0
\(154\) 1.62599 2.81630i 0.131026 0.226944i
\(155\) 0.248586 1.40980i 0.0199669 0.113238i
\(156\) 0 0
\(157\) 19.4985 + 7.09686i 1.55615 + 0.566391i 0.969850 0.243704i \(-0.0783626\pi\)
0.586298 + 0.810096i \(0.300585\pi\)
\(158\) 0.874566 + 4.95991i 0.0695767 + 0.394589i
\(159\) 0 0
\(160\) −6.12343 5.13816i −0.484099 0.406208i
\(161\) 2.07069 0.163193
\(162\) 0 0
\(163\) −20.1346 −1.57706 −0.788531 0.614995i \(-0.789158\pi\)
−0.788531 + 0.614995i \(0.789158\pi\)
\(164\) 5.54842 + 4.65568i 0.433259 + 0.363548i
\(165\) 0 0
\(166\) 1.47210 + 8.34868i 0.114257 + 0.647983i
\(167\) 18.6647 + 6.79341i 1.44432 + 0.525690i 0.940999 0.338409i \(-0.109889\pi\)
0.503322 + 0.864099i \(0.332111\pi\)
\(168\) 0 0
\(169\) 1.33599 7.57678i 0.102769 0.582830i
\(170\) −6.11748 + 10.5958i −0.469189 + 0.812660i
\(171\) 0 0
\(172\) 1.92212 + 3.32920i 0.146560 + 0.253849i
\(173\) −17.7838 + 6.47277i −1.35208 + 0.492116i −0.913595 0.406625i \(-0.866706\pi\)
−0.438481 + 0.898740i \(0.644483\pi\)
\(174\) 0 0
\(175\) −3.67779 + 3.08603i −0.278015 + 0.233282i
\(176\) 1.37771 1.15604i 0.103849 0.0871397i
\(177\) 0 0
\(178\) −6.64170 + 2.41738i −0.497817 + 0.181190i
\(179\) −5.45683 9.45151i −0.407863 0.706439i 0.586787 0.809741i \(-0.300392\pi\)
−0.994650 + 0.103302i \(0.967059\pi\)
\(180\) 0 0
\(181\) 8.97393 15.5433i 0.667027 1.15532i −0.311704 0.950179i \(-0.600900\pi\)
0.978731 0.205146i \(-0.0657668\pi\)
\(182\) −2.04817 + 11.6157i −0.151820 + 0.861016i
\(183\) 0 0
\(184\) 2.40952 + 0.876993i 0.177632 + 0.0646528i
\(185\) −0.790641 4.48395i −0.0581291 0.329666i
\(186\) 0 0
\(187\) 6.38649 + 5.35890i 0.467026 + 0.391881i
\(188\) 4.71059 0.343555
\(189\) 0 0
\(190\) −0.458604 −0.0332706
\(191\) −20.6572 17.3334i −1.49470 1.25420i −0.888485 0.458905i \(-0.848242\pi\)
−0.606217 0.795299i \(-0.707314\pi\)
\(192\) 0 0
\(193\) −2.97890 16.8942i −0.214426 1.21607i −0.881900 0.471437i \(-0.843735\pi\)
0.667474 0.744633i \(-0.267376\pi\)
\(194\) −5.43974 1.97990i −0.390551 0.142149i
\(195\) 0 0
\(196\) 0.146880 0.833000i 0.0104915 0.0595000i
\(197\) −1.25612 + 2.17567i −0.0894951 + 0.155010i −0.907298 0.420489i \(-0.861859\pi\)
0.817803 + 0.575499i \(0.195192\pi\)
\(198\) 0 0
\(199\) −9.26942 16.0551i −0.657092 1.13812i −0.981365 0.192153i \(-0.938453\pi\)
0.324273 0.945964i \(-0.394880\pi\)
\(200\) −5.58660 + 2.03336i −0.395033 + 0.143780i
\(201\) 0 0
\(202\) 4.04271 3.39224i 0.284444 0.238677i
\(203\) −0.965274 + 0.809961i −0.0677490 + 0.0568481i
\(204\) 0 0
\(205\) −13.3747 + 4.86800i −0.934131 + 0.339996i
\(206\) −6.12519 10.6091i −0.426762 0.739173i
\(207\) 0 0
\(208\) −3.26154 + 5.64915i −0.226147 + 0.391698i
\(209\) −0.0542642 + 0.307747i −0.00375353 + 0.0212873i
\(210\) 0 0
\(211\) 3.46857 + 1.26246i 0.238787 + 0.0869112i 0.458642 0.888621i \(-0.348336\pi\)
−0.219855 + 0.975533i \(0.570558\pi\)
\(212\) 1.61737 + 9.17258i 0.111082 + 0.629975i
\(213\) 0 0
\(214\) 15.7155 + 13.1869i 1.07429 + 0.901438i
\(215\) −7.55427 −0.515197
\(216\) 0 0
\(217\) −2.01659 −0.136895
\(218\) 5.10049 + 4.27982i 0.345449 + 0.289866i
\(219\) 0 0
\(220\) −0.337785 1.91568i −0.0227735 0.129155i
\(221\) −28.4146 10.3421i −1.91137 0.695682i
\(222\) 0 0
\(223\) −3.68847 + 20.9183i −0.246998 + 1.40080i 0.568808 + 0.822470i \(0.307405\pi\)
−0.815806 + 0.578326i \(0.803706\pi\)
\(224\) −5.63017 + 9.75174i −0.376181 + 0.651565i
\(225\) 0 0
\(226\) 3.64571 + 6.31456i 0.242509 + 0.420038i
\(227\) 13.4752 4.90459i 0.894383 0.325529i 0.146383 0.989228i \(-0.453237\pi\)
0.748000 + 0.663699i \(0.231014\pi\)
\(228\) 0 0
\(229\) 12.9353 10.8540i 0.854787 0.717252i −0.106051 0.994361i \(-0.533821\pi\)
0.960839 + 0.277109i \(0.0893763\pi\)
\(230\) −1.18722 + 0.996198i −0.0782832 + 0.0656874i
\(231\) 0 0
\(232\) −1.46626 + 0.533676i −0.0962650 + 0.0350376i
\(233\) −2.79972 4.84926i −0.183416 0.317686i 0.759626 0.650361i \(-0.225382\pi\)
−0.943042 + 0.332675i \(0.892049\pi\)
\(234\) 0 0
\(235\) −4.62837 + 8.01658i −0.301922 + 0.522944i
\(236\) 0.463764 2.63013i 0.0301884 0.171207i
\(237\) 0 0
\(238\) 16.1957 + 5.89474i 1.04981 + 0.382100i
\(239\) −0.915868 5.19415i −0.0592426 0.335981i 0.940753 0.339094i \(-0.110120\pi\)
−0.999995 + 0.00311238i \(0.999009\pi\)
\(240\) 0 0
\(241\) −6.81969 5.72240i −0.439295 0.368612i 0.396150 0.918186i \(-0.370346\pi\)
−0.835446 + 0.549573i \(0.814790\pi\)
\(242\) −9.93907 −0.638907
\(243\) 0 0
\(244\) −2.56141 −0.163977
\(245\) 1.27330 + 1.06843i 0.0813481 + 0.0682592i
\(246\) 0 0
\(247\) −0.196816 1.11620i −0.0125231 0.0710221i
\(248\) −2.34657 0.854081i −0.149007 0.0542342i
\(249\) 0 0
\(250\) 2.22208 12.6020i 0.140537 0.797024i
\(251\) 3.89010 6.73786i 0.245541 0.425290i −0.716742 0.697338i \(-0.754368\pi\)
0.962284 + 0.272048i \(0.0877010\pi\)
\(252\) 0 0
\(253\) 0.528024 + 0.914565i 0.0331966 + 0.0574982i
\(254\) −11.9119 + 4.33559i −0.747421 + 0.272039i
\(255\) 0 0
\(256\) −12.6333 + 10.6006i −0.789583 + 0.662538i
\(257\) −15.6553 + 13.1364i −0.976551 + 0.819424i −0.983566 0.180552i \(-0.942212\pi\)
0.00701430 + 0.999975i \(0.497767\pi\)
\(258\) 0 0
\(259\) −6.02706 + 2.19367i −0.374503 + 0.136308i
\(260\) 3.52767 + 6.11011i 0.218777 + 0.378933i
\(261\) 0 0
\(262\) 7.42498 12.8604i 0.458717 0.794520i
\(263\) 1.95872 11.1084i 0.120780 0.684976i −0.862946 0.505297i \(-0.831383\pi\)
0.983725 0.179679i \(-0.0575059\pi\)
\(264\) 0 0
\(265\) −17.1992 6.26001i −1.05654 0.384549i
\(266\) 0.112181 + 0.636209i 0.00687824 + 0.0390085i
\(267\) 0 0
\(268\) −6.86424 5.75978i −0.419300 0.351835i
\(269\) −0.307761 −0.0187645 −0.00938226 0.999956i \(-0.502987\pi\)
−0.00938226 + 0.999956i \(0.502987\pi\)
\(270\) 0 0
\(271\) −2.22251 −0.135008 −0.0675040 0.997719i \(-0.521504\pi\)
−0.0675040 + 0.997719i \(0.521504\pi\)
\(272\) 7.30171 + 6.12686i 0.442731 + 0.371495i
\(273\) 0 0
\(274\) 0.413424 + 2.34464i 0.0249759 + 0.141645i
\(275\) −2.30085 0.837439i −0.138746 0.0504995i
\(276\) 0 0
\(277\) −4.05116 + 22.9753i −0.243411 + 1.38045i 0.580744 + 0.814087i \(0.302762\pi\)
−0.824154 + 0.566365i \(0.808349\pi\)
\(278\) 4.20417 7.28184i 0.252149 0.436735i
\(279\) 0 0
\(280\) −6.53725 11.3228i −0.390675 0.676670i
\(281\) −6.78971 + 2.47125i −0.405040 + 0.147422i −0.536503 0.843899i \(-0.680255\pi\)
0.131463 + 0.991321i \(0.458033\pi\)
\(282\) 0 0
\(283\) 5.45446 4.57683i 0.324234 0.272065i −0.466112 0.884726i \(-0.654345\pi\)
0.790346 + 0.612661i \(0.209901\pi\)
\(284\) −0.0608929 + 0.0510952i −0.00361333 + 0.00303194i
\(285\) 0 0
\(286\) −5.65263 + 2.05739i −0.334247 + 0.121656i
\(287\) 10.0249 + 17.3636i 0.591751 + 1.02494i
\(288\) 0 0
\(289\) −13.5924 + 23.5428i −0.799555 + 1.38487i
\(290\) 0.163769 0.928778i 0.00961682 0.0545397i
\(291\) 0 0
\(292\) −4.44220 1.61683i −0.259960 0.0946178i
\(293\) 0.0959380 + 0.544092i 0.00560476 + 0.0317862i 0.987482 0.157732i \(-0.0504184\pi\)
−0.981877 + 0.189519i \(0.939307\pi\)
\(294\) 0 0
\(295\) 4.02035 + 3.37347i 0.234074 + 0.196411i
\(296\) −7.94236 −0.461640
\(297\) 0 0
\(298\) −0.112748 −0.00653131
\(299\) −2.93417 2.46206i −0.169687 0.142385i
\(300\) 0 0
\(301\) 1.84788 + 10.4798i 0.106510 + 0.604048i
\(302\) 20.0718 + 7.30555i 1.15500 + 0.420387i
\(303\) 0 0
\(304\) −0.0620405 + 0.351849i −0.00355827 + 0.0201799i
\(305\) 2.51670 4.35906i 0.144106 0.249599i
\(306\) 0 0
\(307\) −3.36438 5.82728i −0.192015 0.332580i 0.753903 0.656986i \(-0.228169\pi\)
−0.945918 + 0.324406i \(0.894836\pi\)
\(308\) −2.57494 + 0.937202i −0.146721 + 0.0534020i
\(309\) 0 0
\(310\) 1.15621 0.970173i 0.0656681 0.0551021i
\(311\) 11.8151 9.91400i 0.669970 0.562172i −0.243087 0.970005i \(-0.578160\pi\)
0.913057 + 0.407833i \(0.133715\pi\)
\(312\) 0 0
\(313\) 22.1400 8.05829i 1.25143 0.455482i 0.370542 0.928816i \(-0.379172\pi\)
0.880883 + 0.473334i \(0.156950\pi\)
\(314\) 10.9385 + 18.9461i 0.617297 + 1.06919i
\(315\) 0 0
\(316\) 2.12191 3.67525i 0.119367 0.206749i
\(317\) 1.25930 7.14187i 0.0707296 0.401127i −0.928804 0.370573i \(-0.879161\pi\)
0.999533 0.0305547i \(-0.00972739\pi\)
\(318\) 0 0
\(319\) −0.603882 0.219795i −0.0338109 0.0123062i
\(320\) −2.33289 13.2305i −0.130412 0.739605i
\(321\) 0 0
\(322\) 1.67241 + 1.40332i 0.0931998 + 0.0782039i
\(323\) −1.65618 −0.0921525
\(324\) 0 0
\(325\) 8.88074 0.492615
\(326\) −16.2619 13.6453i −0.900663 0.755746i
\(327\) 0 0
\(328\) 4.31131 + 24.4507i 0.238052 + 1.35006i
\(329\) 12.2534 + 4.45986i 0.675549 + 0.245880i
\(330\) 0 0
\(331\) 5.04178 28.5934i 0.277121 1.57163i −0.455020 0.890481i \(-0.650368\pi\)
0.732142 0.681152i \(-0.238521\pi\)
\(332\) 3.57166 6.18629i 0.196020 0.339517i
\(333\) 0 0
\(334\) 10.4708 + 18.1360i 0.572938 + 0.992357i
\(335\) 16.5465 6.02245i 0.904035 0.329042i
\(336\) 0 0
\(337\) −0.887919 + 0.745052i −0.0483680 + 0.0405856i −0.666651 0.745370i \(-0.732273\pi\)
0.618283 + 0.785955i \(0.287828\pi\)
\(338\) 6.21387 5.21405i 0.337990 0.283607i
\(339\) 0 0
\(340\) 9.68773 3.52604i 0.525391 0.191227i
\(341\) −0.514230 0.890672i −0.0278471 0.0482326i
\(342\) 0 0
\(343\) 9.77810 16.9362i 0.527968 0.914467i
\(344\) −2.28825 + 12.9773i −0.123374 + 0.699689i
\(345\) 0 0
\(346\) −18.7499 6.82440i −1.00800 0.366882i
\(347\) 1.02274 + 5.80023i 0.0549034 + 0.311373i 0.999876 0.0157782i \(-0.00502256\pi\)
−0.944972 + 0.327151i \(0.893911\pi\)
\(348\) 0 0
\(349\) −23.4354 19.6646i −1.25447 1.05262i −0.996249 0.0865352i \(-0.972420\pi\)
−0.258217 0.966087i \(-0.583135\pi\)
\(350\) −5.06182 −0.270566
\(351\) 0 0
\(352\) −5.74276 −0.306090
\(353\) 28.3140 + 23.7582i 1.50700 + 1.26452i 0.869348 + 0.494200i \(0.164539\pi\)
0.637653 + 0.770324i \(0.279906\pi\)
\(354\) 0 0
\(355\) −0.0271248 0.153832i −0.00143963 0.00816457i
\(356\) 5.59646 + 2.03694i 0.296612 + 0.107958i
\(357\) 0 0
\(358\) 1.99809 11.3317i 0.105602 0.598901i
\(359\) 13.1880 22.8423i 0.696037 1.20557i −0.273792 0.961789i \(-0.588278\pi\)
0.969830 0.243783i \(-0.0783886\pi\)
\(360\) 0 0
\(361\) 9.46896 + 16.4007i 0.498366 + 0.863196i
\(362\) 17.7817 6.47201i 0.934585 0.340161i
\(363\) 0 0
\(364\) 7.61347 6.38846i 0.399055 0.334846i
\(365\) 7.11623 5.97122i 0.372480 0.312548i
\(366\) 0 0
\(367\) 10.6309 3.86932i 0.554927 0.201977i −0.0493074 0.998784i \(-0.515701\pi\)
0.604234 + 0.796807i \(0.293479\pi\)
\(368\) 0.603693 + 1.04563i 0.0314697 + 0.0545071i
\(369\) 0 0
\(370\) 2.40023 4.15733i 0.124782 0.216129i
\(371\) −4.47717 + 25.3913i −0.232443 + 1.31825i
\(372\) 0 0
\(373\) −5.49164 1.99879i −0.284346 0.103494i 0.195910 0.980622i \(-0.437234\pi\)
−0.480256 + 0.877128i \(0.659456\pi\)
\(374\) 1.52634 + 8.65633i 0.0789254 + 0.447608i
\(375\) 0 0
\(376\) 12.3695 + 10.3793i 0.637909 + 0.535269i
\(377\) 2.33085 0.120045
\(378\) 0 0
\(379\) 24.3265 1.24957 0.624783 0.780798i \(-0.285187\pi\)
0.624783 + 0.780798i \(0.285187\pi\)
\(380\) 0.296023 + 0.248393i 0.0151856 + 0.0127423i
\(381\) 0 0
\(382\) −4.93699 27.9991i −0.252598 1.43256i
\(383\) 3.58591 + 1.30517i 0.183232 + 0.0666909i 0.432007 0.901870i \(-0.357806\pi\)
−0.248775 + 0.968561i \(0.580028\pi\)
\(384\) 0 0
\(385\) 0.935050 5.30293i 0.0476546 0.270262i
\(386\) 9.04337 15.6636i 0.460295 0.797255i
\(387\) 0 0
\(388\) 2.43891 + 4.22432i 0.123817 + 0.214457i
\(389\) −10.1880 + 3.70813i −0.516552 + 0.188010i −0.587124 0.809497i \(-0.699740\pi\)
0.0705716 + 0.997507i \(0.477518\pi\)
\(390\) 0 0
\(391\) −4.28749 + 3.59763i −0.216828 + 0.181940i
\(392\) 2.22111 1.86374i 0.112183 0.0941329i
\(393\) 0 0
\(394\) −2.48899 + 0.905917i −0.125393 + 0.0456394i
\(395\) 4.16974 + 7.22221i 0.209802 + 0.363389i
\(396\) 0 0
\(397\) 5.25461 9.10124i 0.263721 0.456778i −0.703507 0.710689i \(-0.748383\pi\)
0.967228 + 0.253910i \(0.0817168\pi\)
\(398\) 3.39412 19.2490i 0.170132 0.964866i
\(399\) 0 0
\(400\) −2.63057 0.957449i −0.131529 0.0478725i
\(401\) 2.49456 + 14.1473i 0.124572 + 0.706484i 0.981561 + 0.191149i \(0.0612214\pi\)
−0.856989 + 0.515335i \(0.827668\pi\)
\(402\) 0 0
\(403\) 2.85751 + 2.39774i 0.142343 + 0.119440i
\(404\) −4.44685 −0.221239
\(405\) 0 0
\(406\) −1.32853 −0.0659338
\(407\) −2.50578 2.10260i −0.124207 0.104222i
\(408\) 0 0
\(409\) 3.07049 + 17.4136i 0.151826 + 0.861048i 0.961630 + 0.274348i \(0.0884621\pi\)
−0.809804 + 0.586700i \(0.800427\pi\)
\(410\) −14.1013 5.13245i −0.696413 0.253474i
\(411\) 0 0
\(412\) −1.79248 + 10.1656i −0.0883089 + 0.500825i
\(413\) 3.69650 6.40252i 0.181893 0.315047i
\(414\) 0 0
\(415\) 7.01864 + 12.1566i 0.344532 + 0.596746i
\(416\) 19.5728 7.12393i 0.959637 0.349279i
\(417\) 0 0
\(418\) −0.252390 + 0.211780i −0.0123448 + 0.0103585i
\(419\) 6.99687 5.87107i 0.341819 0.286821i −0.455676 0.890146i \(-0.650602\pi\)
0.797495 + 0.603325i \(0.206158\pi\)
\(420\) 0 0
\(421\) −22.7358 + 8.27515i −1.10807 + 0.403306i −0.830287 0.557337i \(-0.811823\pi\)
−0.277787 + 0.960643i \(0.589601\pi\)
\(422\) 1.94585 + 3.37031i 0.0947226 + 0.164064i
\(423\) 0 0
\(424\) −15.9637 + 27.6499i −0.775265 + 1.34280i
\(425\) 2.25340 12.7796i 0.109306 0.619904i
\(426\) 0 0
\(427\) −6.66283 2.42507i −0.322437 0.117357i
\(428\) −3.00178 17.0240i −0.145097 0.822884i
\(429\) 0 0
\(430\) −6.10128 5.11958i −0.294230 0.246888i
\(431\) −29.5332 −1.42256 −0.711282 0.702907i \(-0.751885\pi\)
−0.711282 + 0.702907i \(0.751885\pi\)
\(432\) 0 0
\(433\) 0.669754 0.0321863 0.0160932 0.999870i \(-0.494877\pi\)
0.0160932 + 0.999870i \(0.494877\pi\)
\(434\) −1.62872 1.36666i −0.0781810 0.0656017i
\(435\) 0 0
\(436\) −0.974231 5.52514i −0.0466572 0.264606i
\(437\) −0.197138 0.0717523i −0.00943038 0.00343238i
\(438\) 0 0
\(439\) −1.10247 + 6.25242i −0.0526180 + 0.298412i −0.999748 0.0224379i \(-0.992857\pi\)
0.947130 + 0.320849i \(0.103968\pi\)
\(440\) 3.33399 5.77464i 0.158942 0.275295i
\(441\) 0 0
\(442\) −15.9404 27.6096i −0.758209 1.31326i
\(443\) −14.4280 + 5.25135i −0.685494 + 0.249499i −0.661204 0.750206i \(-0.729954\pi\)
−0.0242891 + 0.999705i \(0.507732\pi\)
\(444\) 0 0
\(445\) −8.96529 + 7.52277i −0.424996 + 0.356614i
\(446\) −17.1555 + 14.3952i −0.812338 + 0.681633i
\(447\) 0 0
\(448\) −17.7836 + 6.47270i −0.840196 + 0.305806i
\(449\) 16.0199 + 27.7473i 0.756027 + 1.30948i 0.944862 + 0.327468i \(0.106195\pi\)
−0.188836 + 0.982009i \(0.560471\pi\)
\(450\) 0 0
\(451\) −5.11268 + 8.85543i −0.240747 + 0.416986i
\(452\) 1.06688 6.05058i 0.0501819 0.284596i
\(453\) 0 0
\(454\) 14.2073 + 5.17103i 0.666781 + 0.242688i
\(455\) 3.39143 + 19.2337i 0.158992 + 0.901691i
\(456\) 0 0
\(457\) 14.6836 + 12.3210i 0.686868 + 0.576351i 0.918004 0.396570i \(-0.129800\pi\)
−0.231136 + 0.972921i \(0.574244\pi\)
\(458\) 17.8031 0.831886
\(459\) 0 0
\(460\) 1.30591 0.0608882
\(461\) −3.99898 3.35554i −0.186251 0.156283i 0.544895 0.838504i \(-0.316570\pi\)
−0.731146 + 0.682221i \(0.761014\pi\)
\(462\) 0 0
\(463\) 0.294749 + 1.67160i 0.0136981 + 0.0776859i 0.990890 0.134670i \(-0.0429975\pi\)
−0.977192 + 0.212356i \(0.931886\pi\)
\(464\) −0.690421 0.251293i −0.0320520 0.0116660i
\(465\) 0 0
\(466\) 1.02516 5.81395i 0.0474894 0.269326i
\(467\) −9.84136 + 17.0457i −0.455404 + 0.788783i −0.998711 0.0507511i \(-0.983838\pi\)
0.543307 + 0.839534i \(0.317172\pi\)
\(468\) 0 0
\(469\) −12.4023 21.4814i −0.572685 0.991920i
\(470\) −9.17104 + 3.33799i −0.423029 + 0.153970i
\(471\) 0 0
\(472\) 7.01300 5.88461i 0.322800 0.270861i
\(473\) −4.15745 + 3.48851i −0.191160 + 0.160402i
\(474\) 0 0
\(475\) 0.457076 0.166362i 0.0209721 0.00763321i
\(476\) −7.26134 12.5770i −0.332823 0.576467i
\(477\) 0 0
\(478\) 2.78040 4.81579i 0.127173 0.220269i
\(479\) −5.07980 + 28.8090i −0.232102 + 1.31632i 0.616529 + 0.787332i \(0.288538\pi\)
−0.848631 + 0.528985i \(0.822573\pi\)
\(480\) 0 0
\(481\) 11.1487 + 4.05778i 0.508335 + 0.185019i
\(482\) −1.62988 9.24351i −0.0742390 0.421030i
\(483\) 0 0
\(484\) 6.41554 + 5.38328i 0.291616 + 0.244694i
\(485\) −9.58538 −0.435250
\(486\) 0 0
\(487\) −20.5056 −0.929199 −0.464600 0.885521i \(-0.653802\pi\)
−0.464600 + 0.885521i \(0.653802\pi\)
\(488\) −6.72599 5.64378i −0.304471 0.255482i
\(489\) 0 0
\(490\) 0.304314 + 1.72585i 0.0137475 + 0.0779659i
\(491\) −16.4700 5.99458i −0.743280 0.270532i −0.0575048 0.998345i \(-0.518314\pi\)
−0.685775 + 0.727813i \(0.740537\pi\)
\(492\) 0 0
\(493\) 0.591428 3.35415i 0.0266366 0.151063i
\(494\) 0.597496 1.03489i 0.0268826 0.0465620i
\(495\) 0 0
\(496\) −0.587922 1.01831i −0.0263985 0.0457235i
\(497\) −0.206772 + 0.0752590i −0.00927501 + 0.00337583i
\(498\) 0 0
\(499\) −14.6360 + 12.2811i −0.655199 + 0.549777i −0.908643 0.417573i \(-0.862881\pi\)
0.253445 + 0.967350i \(0.418436\pi\)
\(500\) −8.25995 + 6.93092i −0.369396 + 0.309960i
\(501\) 0 0
\(502\) 7.70817 2.80555i 0.344033 0.125218i
\(503\) 5.48381 + 9.49824i 0.244511 + 0.423506i 0.961994 0.273070i \(-0.0880392\pi\)
−0.717483 + 0.696576i \(0.754706\pi\)
\(504\) 0 0
\(505\) 4.36924 7.56774i 0.194429 0.336760i
\(506\) −0.193343 + 1.09650i −0.00859515 + 0.0487455i
\(507\) 0 0
\(508\) 10.0373 + 3.65327i 0.445332 + 0.162088i
\(509\) −3.45549 19.5970i −0.153162 0.868624i −0.960447 0.278462i \(-0.910175\pi\)
0.807285 0.590161i \(-0.200936\pi\)
\(510\) 0 0
\(511\) −10.0245 8.41151i −0.443456 0.372103i
\(512\) −15.2994 −0.676143
\(513\) 0 0
\(514\) −21.5468 −0.950387
\(515\) −15.5389 13.0387i −0.684725 0.574553i
\(516\) 0 0
\(517\) 1.15480 + 6.54922i 0.0507883 + 0.288035i
\(518\) −6.35448 2.31284i −0.279200 0.101620i
\(519\) 0 0
\(520\) −4.19964 + 23.8173i −0.184166 + 1.04446i
\(521\) −17.5583 + 30.4119i −0.769244 + 1.33237i 0.168729 + 0.985662i \(0.446034\pi\)
−0.937973 + 0.346708i \(0.887300\pi\)
\(522\) 0 0
\(523\) 7.12269 + 12.3369i 0.311453 + 0.539453i 0.978677 0.205404i \(-0.0658509\pi\)
−0.667224 + 0.744857i \(0.732518\pi\)
\(524\) −11.7583 + 4.27967i −0.513664 + 0.186958i
\(525\) 0 0
\(526\) 9.11025 7.64441i 0.397226 0.333312i
\(527\) 4.17548 3.50364i 0.181887 0.152621i
\(528\) 0 0
\(529\) 20.9467 7.62398i 0.910727 0.331478i
\(530\) −9.64867 16.7120i −0.419111 0.725922i
\(531\) 0 0
\(532\) 0.272177 0.471425i 0.0118004 0.0204389i
\(533\) 6.44016 36.5240i 0.278954 1.58203i
\(534\) 0 0
\(535\) 31.9211 + 11.6183i 1.38007 + 0.502304i
\(536\) −5.33374 30.2492i −0.230383 1.30657i
\(537\) 0 0
\(538\) −0.248566 0.208572i −0.0107164 0.00899217i
\(539\) 1.19414 0.0514354
\(540\) 0 0
\(541\) −13.2368 −0.569094 −0.284547 0.958662i \(-0.591843\pi\)
−0.284547 + 0.958662i \(0.591843\pi\)
\(542\) −1.79503 1.50621i −0.0771033 0.0646974i
\(543\) 0 0
\(544\) −5.28514 29.9735i −0.226598 1.28510i
\(545\) 10.3600 + 3.77074i 0.443775 + 0.161521i
\(546\) 0 0
\(547\) −2.83132 + 16.0572i −0.121058 + 0.686557i 0.862513 + 0.506035i \(0.168890\pi\)
−0.983571 + 0.180521i \(0.942222\pi\)
\(548\) 1.00306 1.73736i 0.0428488 0.0742163i
\(549\) 0 0
\(550\) −1.29076 2.23567i −0.0550383 0.0953291i
\(551\) 0.119964 0.0436635i 0.00511065 0.00186013i
\(552\) 0 0
\(553\) 8.99920 7.55123i 0.382685 0.321111i
\(554\) −18.8425 + 15.8107i −0.800540 + 0.671733i
\(555\) 0 0
\(556\) −6.65778 + 2.42324i −0.282353 + 0.102768i
\(557\) −15.4486 26.7577i −0.654577 1.13376i −0.982000 0.188883i \(-0.939513\pi\)
0.327422 0.944878i \(-0.393820\pi\)
\(558\) 0 0
\(559\) 9.84215 17.0471i 0.416279 0.721016i
\(560\) 1.06905 6.06287i 0.0451755 0.256203i
\(561\) 0 0
\(562\) −7.15856 2.60550i −0.301965 0.109906i
\(563\) 4.64959 + 26.3692i 0.195957 + 1.11133i 0.911049 + 0.412298i \(0.135274\pi\)
−0.715092 + 0.699030i \(0.753615\pi\)
\(564\) 0 0
\(565\) 9.24875 + 7.76062i 0.389098 + 0.326492i
\(566\) 7.50710 0.315547
\(567\) 0 0
\(568\) −0.272481 −0.0114331
\(569\) 14.6013 + 12.2519i 0.612118 + 0.513628i 0.895315 0.445434i \(-0.146950\pi\)
−0.283197 + 0.959062i \(0.591395\pi\)
\(570\) 0 0
\(571\) −3.26011 18.4890i −0.136431 0.773740i −0.973852 0.227182i \(-0.927049\pi\)
0.837421 0.546558i \(-0.184062\pi\)
\(572\) 4.76304 + 1.73360i 0.199153 + 0.0724856i
\(573\) 0 0
\(574\) −3.67075 + 20.8178i −0.153214 + 0.868920i
\(575\) 0.821889 1.42355i 0.0342751 0.0593663i
\(576\) 0 0
\(577\) 2.42981 + 4.20856i 0.101154 + 0.175204i 0.912161 0.409833i \(-0.134413\pi\)
−0.811006 + 0.585038i \(0.801080\pi\)
\(578\) −26.9332 + 9.80287i −1.12027 + 0.407746i
\(579\) 0 0
\(580\) −0.608763 + 0.510813i −0.0252775 + 0.0212103i
\(581\) 15.1477 12.7105i 0.628434 0.527319i
\(582\) 0 0
\(583\) −12.3563 + 4.49733i −0.511746 + 0.186260i
\(584\) −8.10226 14.0335i −0.335274 0.580712i
\(585\) 0 0
\(586\) −0.291249 + 0.504459i −0.0120314 + 0.0208390i
\(587\) −5.69520 + 32.2991i −0.235066 + 1.33313i 0.607409 + 0.794390i \(0.292209\pi\)
−0.842475 + 0.538736i \(0.818902\pi\)
\(588\) 0 0
\(589\) 0.191988 + 0.0698778i 0.00791071 + 0.00287926i
\(590\) 0.960847 + 5.44923i 0.0395574 + 0.224341i
\(591\) 0 0
\(592\) −2.86487 2.40391i −0.117746 0.0988003i
\(593\) 17.3446 0.712258 0.356129 0.934437i \(-0.384096\pi\)
0.356129 + 0.934437i \(0.384096\pi\)
\(594\) 0 0
\(595\) 28.5384 1.16996
\(596\) 0.0727773 + 0.0610674i 0.00298107 + 0.00250142i
\(597\) 0 0
\(598\) −0.701255 3.97702i −0.0286765 0.162632i
\(599\) −22.9359 8.34800i −0.937137 0.341090i −0.172102 0.985079i \(-0.555056\pi\)
−0.765035 + 0.643989i \(0.777278\pi\)
\(600\) 0 0
\(601\) 1.36666 7.75070i 0.0557471 0.316158i −0.944164 0.329475i \(-0.893128\pi\)
0.999911 + 0.0133177i \(0.00423928\pi\)
\(602\) −5.60981 + 9.71647i −0.228639 + 0.396014i
\(603\) 0 0
\(604\) −8.99922 15.5871i −0.366173 0.634230i
\(605\) −15.4649 + 5.62878i −0.628739 + 0.228842i
\(606\) 0 0
\(607\) −7.84236 + 6.58052i −0.318311 + 0.267095i −0.787917 0.615781i \(-0.788841\pi\)
0.469606 + 0.882876i \(0.344396\pi\)
\(608\) 0.873926 0.733311i 0.0354424 0.0297397i
\(609\) 0 0
\(610\) 4.98680 1.81505i 0.201910 0.0734891i
\(611\) −12.0602 20.8889i −0.487905 0.845076i
\(612\) 0 0
\(613\) −1.11753 + 1.93563i −0.0451368 + 0.0781792i −0.887711 0.460401i \(-0.847706\pi\)
0.842574 + 0.538580i \(0.181039\pi\)
\(614\) 1.23191 6.98652i 0.0497159 0.281953i
\(615\) 0 0
\(616\) −8.82655 3.21260i −0.355632 0.129439i
\(617\) 5.89982 + 33.4595i 0.237518 + 1.34703i 0.837246 + 0.546826i \(0.184164\pi\)
−0.599729 + 0.800203i \(0.704725\pi\)
\(618\) 0 0
\(619\) −22.1050 18.5483i −0.888473 0.745518i 0.0794301 0.996840i \(-0.474690\pi\)
−0.967903 + 0.251323i \(0.919134\pi\)
\(620\) −1.27179 −0.0510763
\(621\) 0 0
\(622\) 16.2613 0.652020
\(623\) 12.6292 + 10.5971i 0.505977 + 0.424565i
\(624\) 0 0
\(625\) −1.98439 11.2541i −0.0793758 0.450162i
\(626\) 23.3427 + 8.49606i 0.932963 + 0.339571i
\(627\) 0 0
\(628\) 3.20105 18.1541i 0.127736 0.724427i
\(629\) 8.66811 15.0136i 0.345620 0.598632i
\(630\) 0 0
\(631\) 1.57039 + 2.71999i 0.0625162 + 0.108281i 0.895590 0.444881i \(-0.146754\pi\)
−0.833073 + 0.553163i \(0.813421\pi\)
\(632\) 13.6699 4.97544i 0.543759 0.197912i
\(633\) 0 0
\(634\) 5.85718 4.91476i 0.232618 0.195190i
\(635\) −16.0793 + 13.4921i −0.638087 + 0.535419i
\(636\) 0 0
\(637\) −4.06996 + 1.48134i −0.161258 + 0.0586930i
\(638\) −0.338774 0.586774i −0.0134122 0.0232306i
\(639\) 0 0
\(640\) −0.911374 + 1.57855i −0.0360252 + 0.0623975i
\(641\) −5.52593 + 31.3391i −0.218261 + 1.23782i 0.656896 + 0.753981i \(0.271869\pi\)
−0.875157 + 0.483838i \(0.839242\pi\)
\(642\) 0 0
\(643\) 12.0723 + 4.39396i 0.476085 + 0.173281i 0.568907 0.822402i \(-0.307367\pi\)
−0.0928219 + 0.995683i \(0.529589\pi\)
\(644\) −0.319443 1.81165i −0.0125878 0.0713890i
\(645\) 0 0
\(646\) −1.33763 1.12241i −0.0526285 0.0441605i
\(647\) 28.2444 1.11040 0.555200 0.831717i \(-0.312642\pi\)
0.555200 + 0.831717i \(0.312642\pi\)
\(648\) 0 0
\(649\) 3.77042 0.148002
\(650\) 7.17262 + 6.01854i 0.281333 + 0.236067i
\(651\) 0 0
\(652\) 3.10614 + 17.6158i 0.121646 + 0.689888i
\(653\) −24.4231 8.88927i −0.955749 0.347864i −0.183383 0.983042i \(-0.558705\pi\)
−0.772366 + 0.635178i \(0.780927\pi\)
\(654\) 0 0
\(655\) 4.26984 24.2155i 0.166837 0.946178i
\(656\) −5.84536 + 10.1245i −0.228223 + 0.395294i
\(657\) 0 0
\(658\) 6.87407 + 11.9062i 0.267979 + 0.464153i
\(659\) 44.7461 16.2863i 1.74306 0.634422i 0.743644 0.668576i \(-0.233096\pi\)
0.999417 + 0.0341533i \(0.0108735\pi\)
\(660\) 0 0
\(661\) −0.671444 + 0.563408i −0.0261161 + 0.0219140i −0.655752 0.754976i \(-0.727648\pi\)
0.629636 + 0.776890i \(0.283204\pi\)
\(662\) 23.4500 19.6769i 0.911409 0.764763i
\(663\) 0 0
\(664\) 23.0096 8.37481i 0.892946 0.325006i
\(665\) 0.534854 + 0.926394i 0.0207407 + 0.0359240i
\(666\) 0 0
\(667\) 0.215714 0.373627i 0.00835246 0.0144669i
\(668\) 3.06418 17.3778i 0.118557 0.672369i
\(669\) 0 0
\(670\) 17.4454 + 6.34962i 0.673976 + 0.245307i
\(671\) −0.627931 3.56118i −0.0242410 0.137478i
\(672\) 0 0
\(673\) 28.6037 + 24.0013i 1.10259 + 0.925183i 0.997597 0.0692894i \(-0.0220732\pi\)
0.104994 + 0.994473i \(0.466518\pi\)
\(674\) −1.22206 −0.0470721
\(675\) 0 0
\(676\) −6.83505 −0.262886
\(677\) −10.5095 8.81851i −0.403913 0.338923i 0.418091 0.908405i \(-0.362699\pi\)
−0.822004 + 0.569482i \(0.807144\pi\)
\(678\) 0 0
\(679\) 2.34472 + 13.2975i 0.0899820 + 0.510313i
\(680\) 33.2082 + 12.0868i 1.27348 + 0.463508i
\(681\) 0 0
\(682\) 0.188292 1.06786i 0.00721007 0.0408903i
\(683\) −24.9943 + 43.2914i −0.956381 + 1.65650i −0.225206 + 0.974311i \(0.572306\pi\)
−0.731175 + 0.682190i \(0.761028\pi\)
\(684\) 0 0
\(685\) 1.97112 + 3.41407i 0.0753125 + 0.130445i
\(686\) 19.3751 7.05197i 0.739746 0.269245i
\(687\) 0 0
\(688\) −4.75323 + 3.98843i −0.181215 + 0.152058i
\(689\) 36.5346 30.6562i 1.39186 1.16791i
\(690\) 0 0
\(691\) −22.3788 + 8.14523i −0.851331 + 0.309859i −0.730583 0.682824i \(-0.760752\pi\)
−0.120748 + 0.992683i \(0.538529\pi\)
\(692\) 8.40653 + 14.5605i 0.319568 + 0.553508i
\(693\) 0 0
\(694\) −3.10483 + 5.37773i −0.117858 + 0.204136i
\(695\) 2.41767 13.7113i 0.0917075 0.520099i
\(696\) 0 0
\(697\) −50.9249 18.5351i −1.92892 0.702069i
\(698\) −5.60096 31.7646i −0.211999 1.20231i
\(699\) 0 0
\(700\) 3.26734 + 2.74163i 0.123494 + 0.103624i
\(701\) 34.4493 1.30113 0.650565 0.759450i \(-0.274532\pi\)
0.650565 + 0.759450i \(0.274532\pi\)
\(702\) 0 0
\(703\) 0.649815 0.0245082
\(704\) −7.39362 6.20398i −0.278658 0.233821i
\(705\) 0 0
\(706\) 6.76693 + 38.3772i 0.254677 + 1.44434i
\(707\) −11.5673 4.21016i −0.435033 0.158339i
\(708\) 0 0
\(709\) 2.69559 15.2874i 0.101235 0.574132i −0.891423 0.453173i \(-0.850292\pi\)
0.992658 0.120959i \(-0.0385969\pi\)
\(710\) 0.0823456 0.142627i 0.00309038 0.00535269i
\(711\) 0 0
\(712\) 10.2075 + 17.6800i 0.382543 + 0.662585i
\(713\) 0.648805 0.236146i 0.0242979 0.00884373i
\(714\) 0 0
\(715\) −7.63019 + 6.40249i −0.285353 + 0.239439i
\(716\) −7.42733 + 6.23227i −0.277572 + 0.232911i
\(717\) 0 0
\(718\) 26.1318 9.51121i 0.975232 0.354955i
\(719\) −6.02686 10.4388i −0.224764 0.389303i 0.731485 0.681858i \(-0.238828\pi\)
−0.956249 + 0.292555i \(0.905494\pi\)
\(720\) 0 0
\(721\) −14.2872 + 24.7461i −0.532083 + 0.921594i
\(722\) −3.46718 + 19.6634i −0.129035 + 0.731795i
\(723\) 0 0
\(724\) −14.9833 5.45347i −0.556849 0.202676i
\(725\) 0.173698 + 0.985092i 0.00645099 + 0.0365854i
\(726\) 0 0
\(727\) −24.2302 20.3315i −0.898647 0.754055i 0.0712781 0.997456i \(-0.477292\pi\)
−0.969926 + 0.243402i \(0.921737\pi\)
\(728\) 34.0685 1.26266
\(729\) 0 0
\(730\) 9.79423 0.362501
\(731\) −22.0339 18.4887i −0.814955 0.683828i
\(732\) 0 0
\(733\) −3.30466 18.7417i −0.122060 0.692239i −0.983010 0.183550i \(-0.941241\pi\)
0.860950 0.508690i \(-0.169870\pi\)
\(734\) 11.2084 + 4.07952i 0.413709 + 0.150578i
\(735\) 0 0
\(736\) 0.669471 3.79676i 0.0246770 0.139950i
\(737\) 6.32516 10.9555i 0.232990 0.403551i
\(738\) 0 0
\(739\) −8.30036 14.3767i −0.305334 0.528854i 0.672002 0.740550i \(-0.265435\pi\)
−0.977336 + 0.211696i \(0.932101\pi\)
\(740\) −3.80105 + 1.38347i −0.139729 + 0.0508573i
\(741\) 0 0
\(742\) −20.8239 + 17.4733i −0.764470 + 0.641466i
\(743\) −25.5120 + 21.4071i −0.935944 + 0.785350i −0.976875 0.213812i \(-0.931412\pi\)
0.0409308 + 0.999162i \(0.486968\pi\)
\(744\) 0 0
\(745\) −0.175433 + 0.0638523i −0.00642736 + 0.00233937i
\(746\) −3.08078 5.33606i −0.112795 0.195367i
\(747\) 0 0
\(748\) 3.70328 6.41426i 0.135405 0.234529i
\(749\) 8.30947 47.1253i 0.303621 1.72192i
\(750\) 0 0
\(751\) −26.1062 9.50187i −0.952627 0.346728i −0.181487 0.983393i \(-0.558091\pi\)
−0.771140 + 0.636665i \(0.780313\pi\)
\(752\) 1.32030 + 7.48777i 0.0481462 + 0.273051i
\(753\) 0 0
\(754\) 1.88253 + 1.57963i 0.0685577 + 0.0575267i
\(755\) 35.3686 1.28720
\(756\) 0 0
\(757\) −3.12036 −0.113411 −0.0567057 0.998391i \(-0.518060\pi\)
−0.0567057 + 0.998391i \(0.518060\pi\)
\(758\) 19.6475 + 16.4862i 0.713629 + 0.598806i
\(759\) 0 0
\(760\) 0.230020 + 1.30451i 0.00834369 + 0.0473194i
\(761\) 41.3081 + 15.0349i 1.49742 + 0.545016i 0.955391 0.295345i \(-0.0954345\pi\)
0.542028 + 0.840360i \(0.317657\pi\)
\(762\) 0 0
\(763\) 2.69684 15.2946i 0.0976323 0.553700i
\(764\) −11.9783 + 20.7470i −0.433360 + 0.750602i
\(765\) 0 0
\(766\) 2.01168 + 3.48433i 0.0726849 + 0.125894i
\(767\) −12.8506 + 4.67723i −0.464008 + 0.168885i
\(768\) 0 0
\(769\) 2.84421 2.38658i 0.102565 0.0860622i −0.590063 0.807357i \(-0.700897\pi\)
0.692628 + 0.721295i \(0.256453\pi\)
\(770\) 4.34904 3.64927i 0.156728 0.131511i
\(771\) 0 0
\(772\) −14.3212 + 5.21250i −0.515432 + 0.187602i
\(773\) 4.48452 + 7.76741i 0.161297 + 0.279374i 0.935334 0.353766i \(-0.115099\pi\)
−0.774037 + 0.633140i \(0.781766\pi\)
\(774\) 0 0
\(775\) −0.800417 + 1.38636i −0.0287518 + 0.0497996i
\(776\) −2.90349 + 16.4665i −0.104229 + 0.591113i
\(777\) 0 0
\(778\) −10.7415 3.90957i −0.385100 0.140165i
\(779\) −0.352736 2.00046i −0.0126381 0.0716741i
\(780\) 0 0
\(781\) −0.0859667 0.0721346i −0.00307613 0.00258118i
\(782\) −5.90098 −0.211018
\(783\) 0 0
\(784\) 1.36527 0.0487597
\(785\) 27.7498 + 23.2849i 0.990433 + 0.831072i
\(786\) 0 0
\(787\) 7.61472 + 43.1852i 0.271435 + 1.53939i 0.750061 + 0.661368i \(0.230024\pi\)
−0.478626 + 0.878019i \(0.658865\pi\)
\(788\) 2.09728 + 0.763347i 0.0747125 + 0.0271931i
\(789\) 0 0
\(790\) −1.52681 + 8.65895i −0.0543213 + 0.308072i
\(791\) 8.50374 14.7289i 0.302358 0.523699i
\(792\) 0 0
\(793\) 6.55782 + 11.3585i 0.232875 + 0.403351i
\(794\) 10.4119 3.78962i 0.369505 0.134489i
\(795\) 0 0
\(796\) −12.6167 + 10.5866i −0.447186 + 0.375234i
\(797\) 9.20480 7.72375i 0.326051 0.273589i −0.465038 0.885291i \(-0.653959\pi\)
0.791088 + 0.611702i \(0.209515\pi\)
\(798\) 0 0
\(799\) −33.1200 + 12.0547i −1.17170 + 0.426464i
\(800\) 4.46940 + 7.74124i 0.158017 + 0.273694i
\(801\) 0 0
\(802\) −7.57299 + 13.1168i −0.267412 + 0.463171i
\(803\) 1.15890 6.57245i 0.0408967 0.231937i
\(804\) 0 0
\(805\) 3.39697 + 1.23640i 0.119727 + 0.0435772i
\(806\) 0.682935 + 3.87312i 0.0240554 + 0.136425i
\(807\) 0 0
\(808\) −11.6770 9.79814i −0.410794 0.344697i
\(809\) −8.02937 −0.282298 −0.141149 0.989988i \(-0.545080\pi\)
−0.141149 + 0.989988i \(0.545080\pi\)
\(810\) 0 0
\(811\) −12.8345 −0.450681 −0.225341 0.974280i \(-0.572349\pi\)
−0.225341 + 0.974280i \(0.572349\pi\)
\(812\) 0.857549 + 0.719569i 0.0300941 + 0.0252519i
\(813\) 0 0
\(814\) −0.598872 3.39637i −0.0209904 0.119043i
\(815\) −33.0308 12.0222i −1.15702 0.421121i
\(816\) 0 0
\(817\) 0.187216 1.06176i 0.00654986 0.0371461i
\(818\) −9.32142 + 16.1452i −0.325916 + 0.564503i
\(819\) 0 0
\(820\) 6.32233 + 10.9506i 0.220785 + 0.382411i
\(821\) 27.8763 10.1462i 0.972891 0.354103i 0.193819 0.981037i \(-0.437913\pi\)
0.779072 + 0.626934i \(0.215690\pi\)
\(822\) 0 0
\(823\) 37.9504 31.8442i 1.32287 1.11002i 0.337179 0.941440i \(-0.390527\pi\)
0.985688 0.168577i \(-0.0539173\pi\)
\(824\) −27.1057 + 22.7444i −0.944271 + 0.792338i
\(825\) 0 0
\(826\) 7.32454 2.66592i 0.254854 0.0927591i
\(827\) −20.4215 35.3711i −0.710126 1.22997i −0.964809 0.262950i \(-0.915305\pi\)
0.254683 0.967025i \(-0.418029\pi\)
\(828\) 0 0
\(829\) 4.72638 8.18633i 0.164154 0.284323i −0.772201 0.635379i \(-0.780844\pi\)
0.936355 + 0.351056i \(0.114177\pi\)
\(830\) −2.56997 + 14.5750i −0.0892049 + 0.505906i
\(831\) 0 0
\(832\) 32.8955 + 11.9730i 1.14045 + 0.415088i
\(833\) 1.09899 + 6.23266i 0.0380776 + 0.215949i
\(834\) 0 0
\(835\) 26.5633 + 22.2892i 0.919259 + 0.771350i
\(836\) 0.277620 0.00960170
\(837\) 0 0
\(838\) 9.62995 0.332661
\(839\) −9.41230 7.89786i −0.324949 0.272664i 0.465689 0.884948i \(-0.345806\pi\)
−0.790638 + 0.612284i \(0.790251\pi\)
\(840\) 0 0
\(841\) −4.99021 28.3009i −0.172076 0.975892i
\(842\) −23.9709 8.72469i −0.826092 0.300673i
\(843\) 0 0
\(844\) 0.569434 3.22942i 0.0196007 0.111161i
\(845\) 6.71575 11.6320i 0.231029 0.400154i
\(846\) 0 0
\(847\) 11.5916 + 20.0772i 0.398292 + 0.689862i
\(848\) −14.1270 + 5.14182i −0.485125 + 0.176571i
\(849\) 0 0
\(850\) 10.4808 8.79446i 0.359489 0.301647i
\(851\) 1.68223 1.41156i 0.0576660 0.0483875i
\(852\) 0 0
\(853\) 29.0044 10.5567i 0.993092 0.361456i 0.206175 0.978515i \(-0.433898\pi\)
0.786917 + 0.617059i \(0.211676\pi\)
\(854\) −3.73781 6.47408i −0.127905 0.221538i
\(855\) 0 0
\(856\) 29.6280 51.3172i 1.01266 1.75399i
\(857\) 1.93549 10.9767i 0.0661150 0.374957i −0.933740 0.357951i \(-0.883475\pi\)
0.999855 0.0170059i \(-0.00541339\pi\)
\(858\) 0 0
\(859\) −3.89848 1.41893i −0.133014 0.0484133i 0.274655 0.961543i \(-0.411436\pi\)
−0.407670 + 0.913129i \(0.633659\pi\)
\(860\) 1.16539 + 6.60925i 0.0397394 + 0.225374i
\(861\) 0 0
\(862\) −23.8528 20.0149i −0.812429 0.681709i
\(863\) −47.2534 −1.60852 −0.804262 0.594275i \(-0.797439\pi\)
−0.804262 + 0.594275i \(0.797439\pi\)
\(864\) 0 0
\(865\) −33.0392 −1.12337
\(866\) 0.540933 + 0.453897i 0.0183817 + 0.0154240i
\(867\) 0 0
\(868\) 0.311097 + 1.76432i 0.0105593 + 0.0598849i
\(869\) 5.62996 + 2.04914i 0.190983 + 0.0695122i
\(870\) 0 0
\(871\) −7.96745 + 45.1857i −0.269967 + 1.53106i
\(872\) 9.61579 16.6550i 0.325632 0.564011i
\(873\) 0 0
\(874\) −0.110593 0.191553i −0.00374087 0.00647938i
\(875\) −28.0481 + 10.2087i −0.948198 + 0.345116i
\(876\) 0 0
\(877\) 26.9268 22.5943i 0.909253 0.762954i −0.0627236 0.998031i \(-0.519979\pi\)
0.971977 + 0.235077i \(0.0755342\pi\)
\(878\) −5.12773 + 4.30267i −0.173052 + 0.145208i
\(879\) 0 0
\(880\) 2.95041 1.07386i 0.0994582 0.0361998i
\(881\) 9.67981 + 16.7659i 0.326121 + 0.564858i 0.981739 0.190235i \(-0.0609250\pi\)
−0.655618 + 0.755093i \(0.727592\pi\)
\(882\) 0 0
\(883\) 6.89302 11.9391i 0.231969 0.401781i −0.726419 0.687252i \(-0.758817\pi\)
0.958387 + 0.285471i \(0.0921500\pi\)
\(884\) −4.66481 + 26.4554i −0.156895 + 0.889793i
\(885\) 0 0
\(886\) −15.2118 5.53663i −0.511049 0.186007i
\(887\) −5.17775 29.3645i −0.173852 0.985962i −0.939461 0.342656i \(-0.888673\pi\)
0.765609 0.643306i \(-0.222438\pi\)
\(888\) 0 0
\(889\) 22.6505 + 19.0060i 0.759673 + 0.637442i
\(890\) −12.3391 −0.413609
\(891\) 0 0
\(892\) 18.8705 0.631832
\(893\) −1.01203 0.849193i −0.0338662 0.0284172i
\(894\) 0 0
\(895\) −3.30851 18.7635i −0.110591 0.627194i
\(896\) 2.41281 + 0.878191i 0.0806063 + 0.0293383i
\(897\) 0 0
\(898\) −5.86590 + 33.2672i −0.195748 + 1.11014i
\(899\) −0.210078 + 0.363866i −0.00700649 + 0.0121356i
\(900\) 0 0
\(901\) −34.8448 60.3530i −1.16085 2.01065i
\(902\) −10.1307 + 3.68727i −0.337315 + 0.122773i
\(903\) 0 0
\(904\) 16.1333 13.5374i 0.536586 0.450249i
\(905\) 24.0026 20.1406i 0.797873 0.669495i
\(906\) 0 0
\(907\) 5.85576 2.13132i 0.194437 0.0707694i −0.242966 0.970035i \(-0.578120\pi\)
0.437403 + 0.899265i \(0.355898\pi\)
\(908\) −6.36984 11.0329i −0.211391 0.366139i
\(909\) 0 0
\(910\) −10.2957 + 17.8327i −0.341300 + 0.591148i
\(911\) −5.49414 + 31.1588i −0.182029 + 1.03234i 0.747685 + 0.664054i \(0.231165\pi\)
−0.929714 + 0.368283i \(0.879946\pi\)
\(912\) 0 0
\(913\) 9.47652 + 3.44917i 0.313627 + 0.114151i
\(914\) 3.50931 + 19.9023i 0.116078 + 0.658310i
\(915\) 0 0
\(916\) −11.4917 9.64268i −0.379696 0.318603i
\(917\) −34.6380 −1.14385
\(918\) 0 0
\(919\) 36.0031 1.18763 0.593816 0.804601i \(-0.297621\pi\)
0.593816 + 0.804601i \(0.297621\pi\)
\(920\) 3.42917 + 2.87742i 0.113057 + 0.0948657i
\(921\) 0 0
\(922\) −0.955739 5.42027i −0.0314756 0.178507i
\(923\) 0.382481 + 0.139212i 0.0125895 + 0.00458220i
\(924\) 0 0
\(925\) −0.884135 + 5.01418i −0.0290702 + 0.164865i
\(926\) −0.894800 + 1.54984i −0.0294049 + 0.0509309i
\(927\) 0 0
\(928\) 1.17304 + 2.03177i 0.0385070 + 0.0666961i
\(929\) −23.9130 + 8.70363i −0.784561 + 0.285557i −0.703073 0.711117i \(-0.748189\pi\)
−0.0814880 + 0.996674i \(0.525967\pi\)
\(930\) 0 0
\(931\) −0.181723 + 0.152484i −0.00595575 + 0.00499746i
\(932\) −3.81072 + 3.19758i −0.124824 + 0.104740i
\(933\) 0 0
\(934\) −19.5005 + 7.09760i −0.638075 + 0.232240i
\(935\) 7.27728 + 12.6046i 0.237993 + 0.412215i
\(936\) 0 0
\(937\) −14.1524 + 24.5127i −0.462338 + 0.800794i −0.999077 0.0429549i \(-0.986323\pi\)
0.536739 + 0.843749i \(0.319656\pi\)
\(938\) 4.54127 25.7548i 0.148278 0.840924i
\(939\) 0 0
\(940\) 7.72774 + 2.81267i 0.252051 + 0.0917391i
\(941\) 1.44031 + 8.16843i 0.0469529 + 0.266283i 0.999243 0.0389123i \(-0.0123893\pi\)
−0.952290 + 0.305195i \(0.901278\pi\)
\(942\) 0 0
\(943\) −5.25865 4.41253i −0.171245 0.143692i
\(944\) 4.31074 0.140303
\(945\) 0 0
\(946\) −5.72199 −0.186038
\(947\) −34.0511 28.5723i −1.10651 0.928475i −0.108668 0.994078i \(-0.534658\pi\)
−0.997846 + 0.0656031i \(0.979103\pi\)
\(948\) 0 0
\(949\) 4.20333 + 23.8383i 0.136446 + 0.773823i
\(950\) 0.481906 + 0.175399i 0.0156351 + 0.00569071i
\(951\) 0 0
\(952\) 8.64452 49.0255i 0.280170 1.58893i
\(953\) 4.83574 8.37576i 0.156645 0.271317i −0.777012 0.629486i \(-0.783265\pi\)
0.933657 + 0.358169i \(0.116599\pi\)
\(954\) 0 0
\(955\) −23.5385 40.7699i −0.761688 1.31928i
\(956\) −4.40308 + 1.60259i −0.142406 + 0.0518315i
\(957\) 0 0
\(958\) −23.6268 + 19.8252i −0.763348 + 0.640525i
\(959\) 4.25409 3.56961i 0.137372 0.115269i
\(960\) 0 0
\(961\) 28.4986 10.3726i 0.919310 0.334602i
\(962\) 6.25433 + 10.8328i 0.201648 + 0.349264i
\(963\) 0 0
\(964\) −3.95448 + 6.84936i −0.127365 + 0.220603i
\(965\) 5.20053 29.4937i 0.167411 0.949434i
\(966\) 0 0
\(967\) 31.1180 + 11.3260i 1.00069 + 0.364220i 0.789850 0.613301i \(-0.210159\pi\)
0.210838 + 0.977521i \(0.432381\pi\)
\(968\) 4.98509 + 28.2719i 0.160227 + 0.908692i
\(969\) 0 0
\(970\) −7.74172 6.49608i −0.248572 0.208576i
\(971\) −27.4309 −0.880298 −0.440149 0.897925i \(-0.645074\pi\)
−0.440149 + 0.897925i \(0.645074\pi\)
\(972\) 0 0
\(973\) −19.6127 −0.628755
\(974\) −16.5616 13.8968i −0.530667 0.445283i
\(975\) 0 0
\(976\) −0.717917 4.07151i −0.0229800 0.130326i
\(977\) −34.1837 12.4419i −1.09363 0.398050i −0.268669 0.963233i \(-0.586584\pi\)
−0.824966 + 0.565182i \(0.808806\pi\)
\(978\) 0 0
\(979\) −1.46003 + 8.28022i −0.0466626 + 0.264637i
\(980\) 0.738337 1.27884i 0.0235853 0.0408510i
\(981\) 0 0
\(982\) −9.23957 16.0034i −0.294847 0.510689i
\(983\) −39.5960 + 14.4118i −1.26292 + 0.459664i −0.884747 0.466072i \(-0.845669\pi\)
−0.378170 + 0.925736i \(0.623447\pi\)
\(984\) 0 0
\(985\) −3.35975 + 2.81917i −0.107051 + 0.0898262i
\(986\) 2.75081 2.30820i 0.0876035 0.0735081i
\(987\) 0 0
\(988\) −0.946203 + 0.344390i −0.0301027 + 0.0109565i
\(989\) −1.82173 3.15533i −0.0579276 0.100334i
\(990\) 0 0
\(991\) −12.7705 + 22.1191i −0.405667 + 0.702635i −0.994399 0.105693i \(-0.966294\pi\)
0.588732 + 0.808328i \(0.299627\pi\)
\(992\) −0.651981 + 3.69757i −0.0207004 + 0.117398i
\(993\) 0 0
\(994\) −0.218005 0.0793475i −0.00691471 0.00251675i
\(995\) −5.62010 31.8732i −0.178169 1.01045i
\(996\) 0 0
\(997\) 18.0272 + 15.1266i 0.570928 + 0.479066i 0.881954 0.471336i \(-0.156228\pi\)
−0.311026 + 0.950402i \(0.600673\pi\)
\(998\) −20.1439 −0.637644
\(999\) 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 243.2.e.c.136.2 12
3.2 odd 2 243.2.e.b.136.1 12
9.2 odd 6 81.2.e.a.73.1 12
9.4 even 3 243.2.e.d.55.1 12
9.5 odd 6 243.2.e.a.55.2 12
9.7 even 3 27.2.e.a.25.2 yes 12
27.2 odd 18 729.2.c.b.244.5 12
27.4 even 9 27.2.e.a.13.2 12
27.5 odd 18 243.2.e.b.109.1 12
27.7 even 9 729.2.a.a.1.5 6
27.11 odd 18 729.2.c.b.487.5 12
27.13 even 9 243.2.e.d.190.1 12
27.14 odd 18 243.2.e.a.190.2 12
27.16 even 9 729.2.c.e.487.2 12
27.20 odd 18 729.2.a.d.1.2 6
27.22 even 9 inner 243.2.e.c.109.2 12
27.23 odd 18 81.2.e.a.10.1 12
27.25 even 9 729.2.c.e.244.2 12
36.7 odd 6 432.2.u.c.241.2 12
45.7 odd 12 675.2.u.b.349.3 24
45.34 even 6 675.2.l.c.376.1 12
45.43 odd 12 675.2.u.b.349.2 24
108.31 odd 18 432.2.u.c.337.2 12
135.4 even 18 675.2.l.c.526.1 12
135.58 odd 36 675.2.u.b.499.3 24
135.112 odd 36 675.2.u.b.499.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.13.2 12 27.4 even 9
27.2.e.a.25.2 yes 12 9.7 even 3
81.2.e.a.10.1 12 27.23 odd 18
81.2.e.a.73.1 12 9.2 odd 6
243.2.e.a.55.2 12 9.5 odd 6
243.2.e.a.190.2 12 27.14 odd 18
243.2.e.b.109.1 12 27.5 odd 18
243.2.e.b.136.1 12 3.2 odd 2
243.2.e.c.109.2 12 27.22 even 9 inner
243.2.e.c.136.2 12 1.1 even 1 trivial
243.2.e.d.55.1 12 9.4 even 3
243.2.e.d.190.1 12 27.13 even 9
432.2.u.c.241.2 12 36.7 odd 6
432.2.u.c.337.2 12 108.31 odd 18
675.2.l.c.376.1 12 45.34 even 6
675.2.l.c.526.1 12 135.4 even 18
675.2.u.b.349.2 24 45.43 odd 12
675.2.u.b.349.3 24 45.7 odd 12
675.2.u.b.499.2 24 135.112 odd 36
675.2.u.b.499.3 24 135.58 odd 36
729.2.a.a.1.5 6 27.7 even 9
729.2.a.d.1.2 6 27.20 odd 18
729.2.c.b.244.5 12 27.2 odd 18
729.2.c.b.487.5 12 27.11 odd 18
729.2.c.e.244.2 12 27.25 even 9
729.2.c.e.487.2 12 27.16 even 9