Properties

Label 273.2.bz.a.73.1
Level $273$
Weight $2$
Character 273.73
Analytic conductor $2.180$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(31,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 2, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bz (of order \(12\), degree \(4\), 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: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 73.1
Character \(\chi\) \(=\) 273.73
Dual form 273.2.bz.a.187.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.566824 + 2.11542i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.42164 - 1.39814i) q^{4} +(0.631372 + 0.169176i) q^{5} +(-1.54859 + 1.54859i) q^{6} +(1.92845 + 1.81137i) q^{7} +(1.23310 - 1.23310i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.566824 + 2.11542i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.42164 - 1.39814i) q^{4} +(0.631372 + 0.169176i) q^{5} +(-1.54859 + 1.54859i) q^{6} +(1.92845 + 1.81137i) q^{7} +(1.23310 - 1.23310i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.715753 + 1.23972i) q^{10} +(0.659241 + 2.46032i) q^{11} +(-1.39814 - 2.42164i) q^{12} +(-1.72632 - 3.16541i) q^{13} +(-4.92490 + 3.05275i) q^{14} +(0.462196 + 0.462196i) q^{15} +(-0.886704 - 1.53582i) q^{16} +(-2.99130 + 5.18109i) q^{17} +(-2.11542 + 0.566824i) q^{18} +(1.70449 + 0.456716i) q^{19} +(-1.29243 - 1.29243i) q^{20} +(0.764403 + 2.53292i) q^{21} -5.57827 q^{22} +(4.55977 - 2.63259i) q^{23} +(1.68444 - 0.451346i) q^{24} +(-3.96012 - 2.28637i) q^{25} +(7.67468 - 1.85765i) q^{26} +1.00000i q^{27} +(-2.13748 - 7.08273i) q^{28} -0.0763835 q^{29} +(-1.23972 + 0.715753i) q^{30} +(-2.04058 - 7.61556i) q^{31} +(7.12039 - 1.90790i) q^{32} +(-0.659241 + 2.46032i) q^{33} +(-9.26461 - 9.26461i) q^{34} +(0.911131 + 1.46990i) q^{35} -2.79627i q^{36} +(10.6873 + 2.86365i) q^{37} +(-1.93229 + 3.34682i) q^{38} +(0.0876680 - 3.60449i) q^{39} +(0.987154 - 0.569934i) q^{40} +(-1.05558 + 1.05558i) q^{41} +(-5.79146 + 0.181311i) q^{42} -0.901426i q^{43} +(1.84342 - 6.87972i) q^{44} +(0.169176 + 0.631372i) q^{45} +(2.98443 + 11.1380i) q^{46} +(0.875544 - 3.26758i) q^{47} -1.77341i q^{48} +(0.437863 + 6.98629i) q^{49} +(7.08132 - 7.08132i) q^{50} +(-5.18109 + 2.99130i) q^{51} +(-0.245144 + 10.0791i) q^{52} +(0.696069 - 1.20563i) q^{53} +(-2.11542 - 0.566824i) q^{54} +1.66490i q^{55} +(4.61158 - 0.144373i) q^{56} +(1.24777 + 1.24777i) q^{57} +(0.0432960 - 0.161583i) q^{58} +(-5.09918 + 1.36632i) q^{59} +(-0.473061 - 1.76549i) q^{60} +(2.64864 - 1.52919i) q^{61} +17.2667 q^{62} +(-0.604468 + 2.57578i) q^{63} +12.5972i q^{64} +(-0.554440 - 2.29060i) q^{65} +(-4.83093 - 2.78914i) q^{66} +(-3.51049 + 0.940634i) q^{67} +(14.4877 - 8.36449i) q^{68} +5.26517 q^{69} +(-3.62589 + 1.09425i) q^{70} +(4.48225 + 4.48225i) q^{71} +(1.68444 + 0.451346i) q^{72} +(14.9605 - 4.00866i) q^{73} +(-12.1156 + 20.9849i) q^{74} +(-2.28637 - 3.96012i) q^{75} +(-3.48911 - 3.48911i) q^{76} +(-3.18524 + 5.93874i) q^{77} +(7.57529 + 2.22856i) q^{78} +(5.60217 + 9.70324i) q^{79} +(-0.300017 - 1.11968i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.63466 - 2.83131i) q^{82} +(6.20423 - 6.20423i) q^{83} +(1.69026 - 7.20257i) q^{84} +(-2.76514 + 2.76514i) q^{85} +(1.90689 + 0.510949i) q^{86} +(-0.0661501 - 0.0381918i) q^{87} +(3.84673 + 2.22091i) q^{88} +(2.39127 - 8.92433i) q^{89} -1.43151 q^{90} +(2.40461 - 9.23135i) q^{91} -14.7229 q^{92} +(2.04058 - 7.61556i) q^{93} +(6.41600 + 3.70428i) q^{94} +(0.998900 + 0.576715i) q^{95} +(7.12039 + 1.90790i) q^{96} +(6.89422 - 6.89422i) q^{97} +(-15.0271 - 3.03374i) q^{98} +(-1.80108 + 1.80108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.566824 + 2.11542i −0.400805 + 1.49582i 0.410858 + 0.911699i \(0.365229\pi\)
−0.811663 + 0.584125i \(0.801438\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −2.42164 1.39814i −1.21082 0.699068i
\(5\) 0.631372 + 0.169176i 0.282358 + 0.0756576i 0.397219 0.917724i \(-0.369975\pi\)
−0.114861 + 0.993382i \(0.536642\pi\)
\(6\) −1.54859 + 1.54859i −0.632210 + 0.632210i
\(7\) 1.92845 + 1.81137i 0.728887 + 0.684634i
\(8\) 1.23310 1.23310i 0.435966 0.435966i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −0.715753 + 1.23972i −0.226341 + 0.392034i
\(11\) 0.659241 + 2.46032i 0.198769 + 0.741815i 0.991259 + 0.131930i \(0.0421175\pi\)
−0.792490 + 0.609884i \(0.791216\pi\)
\(12\) −1.39814 2.42164i −0.403607 0.699068i
\(13\) −1.72632 3.16541i −0.478795 0.877927i
\(14\) −4.92490 + 3.05275i −1.31623 + 0.815882i
\(15\) 0.462196 + 0.462196i 0.119339 + 0.119339i
\(16\) −0.886704 1.53582i −0.221676 0.383954i
\(17\) −2.99130 + 5.18109i −0.725497 + 1.25660i 0.233272 + 0.972412i \(0.425057\pi\)
−0.958769 + 0.284186i \(0.908277\pi\)
\(18\) −2.11542 + 0.566824i −0.498608 + 0.133602i
\(19\) 1.70449 + 0.456716i 0.391036 + 0.104778i 0.448980 0.893542i \(-0.351788\pi\)
−0.0579434 + 0.998320i \(0.518454\pi\)
\(20\) −1.29243 1.29243i −0.288995 0.288995i
\(21\) 0.764403 + 2.53292i 0.166806 + 0.552729i
\(22\) −5.57827 −1.18929
\(23\) 4.55977 2.63259i 0.950779 0.548932i 0.0574559 0.998348i \(-0.481701\pi\)
0.893323 + 0.449416i \(0.148368\pi\)
\(24\) 1.68444 0.451346i 0.343836 0.0921305i
\(25\) −3.96012 2.28637i −0.792023 0.457275i
\(26\) 7.67468 1.85765i 1.50513 0.364316i
\(27\) 1.00000i 0.192450i
\(28\) −2.13748 7.08273i −0.403946 1.33851i
\(29\) −0.0763835 −0.0141841 −0.00709203 0.999975i \(-0.502257\pi\)
−0.00709203 + 0.999975i \(0.502257\pi\)
\(30\) −1.23972 + 0.715753i −0.226341 + 0.130678i
\(31\) −2.04058 7.61556i −0.366500 1.36780i −0.865377 0.501122i \(-0.832921\pi\)
0.498877 0.866673i \(-0.333746\pi\)
\(32\) 7.12039 1.90790i 1.25872 0.337273i
\(33\) −0.659241 + 2.46032i −0.114759 + 0.428287i
\(34\) −9.26461 9.26461i −1.58887 1.58887i
\(35\) 0.911131 + 1.46990i 0.154009 + 0.248458i
\(36\) 2.79627i 0.466045i
\(37\) 10.6873 + 2.86365i 1.75698 + 0.470781i 0.986093 0.166193i \(-0.0531476\pi\)
0.770885 + 0.636974i \(0.219814\pi\)
\(38\) −1.93229 + 3.34682i −0.313458 + 0.542926i
\(39\) 0.0876680 3.60449i 0.0140381 0.577180i
\(40\) 0.987154 0.569934i 0.156083 0.0901144i
\(41\) −1.05558 + 1.05558i −0.164853 + 0.164853i −0.784713 0.619860i \(-0.787190\pi\)
0.619860 + 0.784713i \(0.287190\pi\)
\(42\) −5.79146 + 0.181311i −0.893642 + 0.0279768i
\(43\) 0.901426i 0.137466i −0.997635 0.0687331i \(-0.978104\pi\)
0.997635 0.0687331i \(-0.0218957\pi\)
\(44\) 1.84342 6.87972i 0.277905 1.03716i
\(45\) 0.169176 + 0.631372i 0.0252192 + 0.0941193i
\(46\) 2.98443 + 11.1380i 0.440030 + 1.64221i
\(47\) 0.875544 3.26758i 0.127711 0.476625i −0.872211 0.489131i \(-0.837314\pi\)
0.999922 + 0.0125057i \(0.00398078\pi\)
\(48\) 1.77341i 0.255970i
\(49\) 0.437863 + 6.98629i 0.0625518 + 0.998042i
\(50\) 7.08132 7.08132i 1.00145 1.00145i
\(51\) −5.18109 + 2.99130i −0.725497 + 0.418866i
\(52\) −0.245144 + 10.0791i −0.0339953 + 1.39772i
\(53\) 0.696069 1.20563i 0.0956124 0.165606i −0.814252 0.580512i \(-0.802852\pi\)
0.909864 + 0.414907i \(0.136186\pi\)
\(54\) −2.11542 0.566824i −0.287872 0.0771350i
\(55\) 1.66490i 0.224496i
\(56\) 4.61158 0.144373i 0.616248 0.0192926i
\(57\) 1.24777 + 1.24777i 0.165271 + 0.165271i
\(58\) 0.0432960 0.161583i 0.00568504 0.0212169i
\(59\) −5.09918 + 1.36632i −0.663857 + 0.177880i −0.574986 0.818163i \(-0.694992\pi\)
−0.0888707 + 0.996043i \(0.528326\pi\)
\(60\) −0.473061 1.76549i −0.0610719 0.227923i
\(61\) 2.64864 1.52919i 0.339124 0.195793i −0.320761 0.947160i \(-0.603939\pi\)
0.659884 + 0.751367i \(0.270605\pi\)
\(62\) 17.2667 2.19288
\(63\) −0.604468 + 2.57578i −0.0761558 + 0.324517i
\(64\) 12.5972i 1.57465i
\(65\) −0.554440 2.29060i −0.0687698 0.284114i
\(66\) −4.83093 2.78914i −0.594646 0.343319i
\(67\) −3.51049 + 0.940634i −0.428875 + 0.114917i −0.466798 0.884364i \(-0.654593\pi\)
0.0379229 + 0.999281i \(0.487926\pi\)
\(68\) 14.4877 8.36449i 1.75689 1.01434i
\(69\) 5.26517 0.633852
\(70\) −3.62589 + 1.09425i −0.433377 + 0.130788i
\(71\) 4.48225 + 4.48225i 0.531946 + 0.531946i 0.921151 0.389205i \(-0.127250\pi\)
−0.389205 + 0.921151i \(0.627250\pi\)
\(72\) 1.68444 + 0.451346i 0.198514 + 0.0531916i
\(73\) 14.9605 4.00866i 1.75100 0.469178i 0.766158 0.642652i \(-0.222166\pi\)
0.984839 + 0.173474i \(0.0554992\pi\)
\(74\) −12.1156 + 20.9849i −1.40841 + 2.43944i
\(75\) −2.28637 3.96012i −0.264008 0.457275i
\(76\) −3.48911 3.48911i −0.400228 0.400228i
\(77\) −3.18524 + 5.93874i −0.362992 + 0.676783i
\(78\) 7.57529 + 2.22856i 0.857733 + 0.252335i
\(79\) 5.60217 + 9.70324i 0.630293 + 1.09170i 0.987492 + 0.157671i \(0.0503987\pi\)
−0.357198 + 0.934029i \(0.616268\pi\)
\(80\) −0.300017 1.11968i −0.0335430 0.125184i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.63466 2.83131i −0.180518 0.312666i
\(83\) 6.20423 6.20423i 0.681002 0.681002i −0.279224 0.960226i \(-0.590077\pi\)
0.960226 + 0.279224i \(0.0900771\pi\)
\(84\) 1.69026 7.20257i 0.184422 0.785865i
\(85\) −2.76514 + 2.76514i −0.299921 + 0.299921i
\(86\) 1.90689 + 0.510949i 0.205625 + 0.0550971i
\(87\) −0.0661501 0.0381918i −0.00709203 0.00409459i
\(88\) 3.84673 + 2.22091i 0.410063 + 0.236750i
\(89\) 2.39127 8.92433i 0.253474 0.945977i −0.715459 0.698654i \(-0.753783\pi\)
0.968933 0.247323i \(-0.0795508\pi\)
\(90\) −1.43151 −0.150894
\(91\) 2.40461 9.23135i 0.252071 0.967709i
\(92\) −14.7229 −1.53496
\(93\) 2.04058 7.61556i 0.211599 0.789697i
\(94\) 6.41600 + 3.70428i 0.661760 + 0.382067i
\(95\) 0.998900 + 0.576715i 0.102485 + 0.0591697i
\(96\) 7.12039 + 1.90790i 0.726721 + 0.194724i
\(97\) 6.89422 6.89422i 0.700002 0.700002i −0.264409 0.964411i \(-0.585177\pi\)
0.964411 + 0.264409i \(0.0851769\pi\)
\(98\) −15.0271 3.03374i −1.51797 0.306454i
\(99\) −1.80108 + 1.80108i −0.181015 + 0.181015i
\(100\) 6.39332 + 11.0736i 0.639332 + 1.10736i
\(101\) −3.07469 + 5.32552i −0.305943 + 0.529909i −0.977471 0.211070i \(-0.932305\pi\)
0.671528 + 0.740979i \(0.265638\pi\)
\(102\) −3.39108 12.6557i −0.335767 1.25310i
\(103\) −8.10374 14.0361i −0.798485 1.38302i −0.920603 0.390501i \(-0.872302\pi\)
0.122118 0.992516i \(-0.461031\pi\)
\(104\) −6.03199 1.77454i −0.591485 0.174008i
\(105\) 0.0541144 + 1.72853i 0.00528103 + 0.168688i
\(106\) 2.15585 + 2.15585i 0.209395 + 0.209395i
\(107\) −8.76076 15.1741i −0.846935 1.46693i −0.883931 0.467618i \(-0.845112\pi\)
0.0369960 0.999315i \(-0.488221\pi\)
\(108\) 1.39814 2.42164i 0.134536 0.233023i
\(109\) −14.4056 + 3.85998i −1.37981 + 0.369719i −0.871052 0.491190i \(-0.836562\pi\)
−0.508758 + 0.860909i \(0.669895\pi\)
\(110\) −3.52196 0.943707i −0.335806 0.0899790i
\(111\) 7.82363 + 7.82363i 0.742586 + 0.742586i
\(112\) 1.07197 4.56790i 0.101291 0.431626i
\(113\) −0.944250 −0.0888276 −0.0444138 0.999013i \(-0.514142\pi\)
−0.0444138 + 0.999013i \(0.514142\pi\)
\(114\) −3.34682 + 1.93229i −0.313458 + 0.180975i
\(115\) 3.32428 0.890739i 0.309991 0.0830618i
\(116\) 0.184974 + 0.106795i 0.0171744 + 0.00991562i
\(117\) 1.87817 3.07774i 0.173636 0.284537i
\(118\) 11.5613i 1.06431i
\(119\) −15.1535 + 4.57312i −1.38912 + 0.419217i
\(120\) 1.13987 0.104055
\(121\) 3.90770 2.25611i 0.355246 0.205101i
\(122\) 1.73357 + 6.46976i 0.156950 + 0.585744i
\(123\) −1.44194 + 0.386368i −0.130016 + 0.0348376i
\(124\) −5.70602 + 21.2952i −0.512416 + 1.91236i
\(125\) −4.42449 4.42449i −0.395738 0.395738i
\(126\) −5.10621 2.73871i −0.454897 0.243984i
\(127\) 15.9116i 1.41192i 0.708250 + 0.705962i \(0.249485\pi\)
−0.708250 + 0.705962i \(0.750515\pi\)
\(128\) −12.4075 3.32459i −1.09668 0.293855i
\(129\) 0.450713 0.780657i 0.0396830 0.0687331i
\(130\) 5.15984 + 0.125497i 0.452548 + 0.0110068i
\(131\) −12.6166 + 7.28421i −1.10232 + 0.636424i −0.936829 0.349787i \(-0.886254\pi\)
−0.165490 + 0.986212i \(0.552920\pi\)
\(132\) 5.03631 5.03631i 0.438354 0.438354i
\(133\) 2.45974 + 3.96822i 0.213287 + 0.344088i
\(134\) 7.95933i 0.687581i
\(135\) −0.169176 + 0.631372i −0.0145603 + 0.0543398i
\(136\) 2.70022 + 10.0774i 0.231542 + 0.864127i
\(137\) 0.352195 + 1.31441i 0.0300900 + 0.112297i 0.979338 0.202233i \(-0.0648197\pi\)
−0.949247 + 0.314530i \(0.898153\pi\)
\(138\) −2.98443 + 11.1380i −0.254051 + 0.948132i
\(139\) 10.4193i 0.883752i −0.897076 0.441876i \(-0.854313\pi\)
0.897076 0.441876i \(-0.145687\pi\)
\(140\) −0.151319 4.83345i −0.0127888 0.408501i
\(141\) 2.39203 2.39203i 0.201445 0.201445i
\(142\) −12.0225 + 6.94118i −1.00890 + 0.582491i
\(143\) 6.64986 6.33407i 0.556089 0.529681i
\(144\) 0.886704 1.53582i 0.0738920 0.127985i
\(145\) −0.0482264 0.0129222i −0.00400498 0.00107313i
\(146\) 33.9199i 2.80723i
\(147\) −3.11395 + 6.26924i −0.256834 + 0.517078i
\(148\) −21.8770 21.8770i −1.79828 1.79828i
\(149\) 1.17141 4.37174i 0.0959653 0.358147i −0.901199 0.433406i \(-0.857312\pi\)
0.997164 + 0.0752588i \(0.0239783\pi\)
\(150\) 9.67326 2.59194i 0.789819 0.211631i
\(151\) −1.12463 4.19719i −0.0915214 0.341563i 0.904948 0.425523i \(-0.139910\pi\)
−0.996469 + 0.0839602i \(0.973243\pi\)
\(152\) 2.66498 1.53863i 0.216158 0.124799i
\(153\) −5.98260 −0.483665
\(154\) −10.7574 10.1043i −0.866859 0.814230i
\(155\) 5.15347i 0.413936i
\(156\) −5.25186 + 8.60620i −0.420485 + 0.689048i
\(157\) −4.21329 2.43255i −0.336257 0.194138i 0.322358 0.946618i \(-0.395524\pi\)
−0.658616 + 0.752479i \(0.728858\pi\)
\(158\) −23.7018 + 6.35089i −1.88562 + 0.505249i
\(159\) 1.20563 0.696069i 0.0956124 0.0552019i
\(160\) 4.81838 0.380926
\(161\) 13.5619 + 3.18263i 1.06883 + 0.250826i
\(162\) −1.54859 1.54859i −0.121669 0.121669i
\(163\) −0.288424 0.0772829i −0.0225911 0.00605326i 0.247506 0.968886i \(-0.420389\pi\)
−0.270097 + 0.962833i \(0.587056\pi\)
\(164\) 4.03206 1.08039i 0.314851 0.0843642i
\(165\) −0.832452 + 1.44185i −0.0648063 + 0.112248i
\(166\) 9.60781 + 16.6412i 0.745711 + 1.29161i
\(167\) −7.94164 7.94164i −0.614543 0.614543i 0.329584 0.944126i \(-0.393092\pi\)
−0.944126 + 0.329584i \(0.893092\pi\)
\(168\) 4.06593 + 2.18076i 0.313693 + 0.168249i
\(169\) −7.03964 + 10.9290i −0.541511 + 0.840694i
\(170\) −4.28207 7.41676i −0.328420 0.568839i
\(171\) 0.456716 + 1.70449i 0.0349259 + 0.130345i
\(172\) −1.26032 + 2.18293i −0.0960981 + 0.166447i
\(173\) −4.93150 8.54161i −0.374935 0.649407i 0.615382 0.788229i \(-0.289002\pi\)
−0.990317 + 0.138822i \(0.955668\pi\)
\(174\) 0.118287 0.118287i 0.00896730 0.00896730i
\(175\) −3.49542 11.5824i −0.264229 0.875548i
\(176\) 3.19405 3.19405i 0.240761 0.240761i
\(177\) −5.09918 1.36632i −0.383278 0.102699i
\(178\) 17.5232 + 10.1170i 1.31342 + 0.758305i
\(179\) −20.7836 11.9994i −1.55344 0.896880i −0.997858 0.0654199i \(-0.979161\pi\)
−0.555584 0.831460i \(-0.687505\pi\)
\(180\) 0.473061 1.76549i 0.0352599 0.131592i
\(181\) 6.83963 0.508386 0.254193 0.967154i \(-0.418190\pi\)
0.254193 + 0.967154i \(0.418190\pi\)
\(182\) 18.1652 + 10.3193i 1.34649 + 0.764917i
\(183\) 3.05839 0.226082
\(184\) 2.37641 8.86889i 0.175192 0.653824i
\(185\) 6.26319 + 3.61605i 0.460479 + 0.265858i
\(186\) 14.9534 + 8.63336i 1.09644 + 0.633029i
\(187\) −14.7191 3.94398i −1.07637 0.288412i
\(188\) −6.68877 + 6.68877i −0.487829 + 0.487829i
\(189\) −1.81137 + 1.92845i −0.131758 + 0.140274i
\(190\) −1.78619 + 1.78619i −0.129584 + 0.129584i
\(191\) 1.45631 + 2.52239i 0.105375 + 0.182514i 0.913891 0.405959i \(-0.133063\pi\)
−0.808517 + 0.588473i \(0.799729\pi\)
\(192\) −6.29860 + 10.9095i −0.454562 + 0.787325i
\(193\) 1.70763 + 6.37298i 0.122918 + 0.458737i 0.999757 0.0220476i \(-0.00701854\pi\)
−0.876839 + 0.480785i \(0.840352\pi\)
\(194\) 10.6763 + 18.4919i 0.766515 + 1.32764i
\(195\) 0.665142 2.26094i 0.0476318 0.161909i
\(196\) 8.70744 17.5305i 0.621960 1.25218i
\(197\) 16.8890 + 16.8890i 1.20329 + 1.20329i 0.973160 + 0.230132i \(0.0739156\pi\)
0.230132 + 0.973160i \(0.426084\pi\)
\(198\) −2.78914 4.83093i −0.198215 0.343319i
\(199\) −0.402906 + 0.697854i −0.0285612 + 0.0494695i −0.879953 0.475061i \(-0.842426\pi\)
0.851391 + 0.524531i \(0.175759\pi\)
\(200\) −7.70254 + 2.06389i −0.544652 + 0.145939i
\(201\) −3.51049 0.940634i −0.247611 0.0663472i
\(202\) −9.52288 9.52288i −0.670028 0.670028i
\(203\) −0.147302 0.138359i −0.0103386 0.00971089i
\(204\) 16.7290 1.17126
\(205\) −0.845038 + 0.487883i −0.0590200 + 0.0340752i
\(206\) 34.2855 9.18678i 2.38879 0.640073i
\(207\) 4.55977 + 2.63259i 0.316926 + 0.182977i
\(208\) −3.33076 + 5.45809i −0.230946 + 0.378451i
\(209\) 4.49467i 0.310903i
\(210\) −3.68724 0.865299i −0.254444 0.0597113i
\(211\) 17.5503 1.20821 0.604106 0.796904i \(-0.293531\pi\)
0.604106 + 0.796904i \(0.293531\pi\)
\(212\) −3.37126 + 1.94640i −0.231539 + 0.133679i
\(213\) 1.64062 + 6.12287i 0.112413 + 0.419532i
\(214\) 37.0653 9.93161i 2.53373 0.678911i
\(215\) 0.152499 0.569135i 0.0104004 0.0388147i
\(216\) 1.23310 + 1.23310i 0.0839018 + 0.0839018i
\(217\) 9.85944 18.3825i 0.669303 1.24789i
\(218\) 32.6619i 2.21214i
\(219\) 14.9605 + 4.00866i 1.01094 + 0.270880i
\(220\) 2.32776 4.03180i 0.156938 0.271824i
\(221\) 21.5642 + 0.524483i 1.45057 + 0.0352805i
\(222\) −20.9849 + 12.1156i −1.40841 + 0.813147i
\(223\) −2.56243 + 2.56243i −0.171593 + 0.171593i −0.787679 0.616086i \(-0.788717\pi\)
0.616086 + 0.787679i \(0.288717\pi\)
\(224\) 17.1873 + 9.21837i 1.14837 + 0.615928i
\(225\) 4.57275i 0.304850i
\(226\) 0.535223 1.99748i 0.0356025 0.132870i
\(227\) −3.36001 12.5397i −0.223011 0.832290i −0.983191 0.182577i \(-0.941556\pi\)
0.760180 0.649712i \(-0.225111\pi\)
\(228\) −1.27710 4.76621i −0.0845781 0.315650i
\(229\) −3.00815 + 11.2266i −0.198784 + 0.741872i 0.792471 + 0.609910i \(0.208794\pi\)
−0.991255 + 0.131962i \(0.957872\pi\)
\(230\) 7.53713i 0.496984i
\(231\) −5.72787 + 3.55048i −0.376866 + 0.233605i
\(232\) −0.0941884 + 0.0941884i −0.00618377 + 0.00618377i
\(233\) −22.4370 + 12.9540i −1.46990 + 0.848645i −0.999430 0.0337727i \(-0.989248\pi\)
−0.470467 + 0.882418i \(0.655914\pi\)
\(234\) 5.44611 + 5.71764i 0.356024 + 0.373774i
\(235\) 1.10559 1.91493i 0.0721206 0.124917i
\(236\) 14.2587 + 3.82060i 0.928162 + 0.248700i
\(237\) 11.2043i 0.727800i
\(238\) −1.08471 34.6480i −0.0703113 2.24590i
\(239\) −10.8915 10.8915i −0.704511 0.704511i 0.260864 0.965375i \(-0.415992\pi\)
−0.965375 + 0.260864i \(0.915992\pi\)
\(240\) 0.300017 1.11968i 0.0193660 0.0722751i
\(241\) −11.2755 + 3.02126i −0.726318 + 0.194616i −0.602989 0.797749i \(-0.706024\pi\)
−0.123329 + 0.992366i \(0.539357\pi\)
\(242\) 2.55764 + 9.54523i 0.164411 + 0.613591i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −8.55208 −0.547491
\(245\) −0.905456 + 4.48502i −0.0578474 + 0.286538i
\(246\) 3.26931i 0.208444i
\(247\) −1.49680 6.18384i −0.0952389 0.393468i
\(248\) −11.9070 6.87450i −0.756094 0.436531i
\(249\) 8.47513 2.27090i 0.537090 0.143913i
\(250\) 11.8675 6.85173i 0.750569 0.433341i
\(251\) −3.55707 −0.224520 −0.112260 0.993679i \(-0.535809\pi\)
−0.112260 + 0.993679i \(0.535809\pi\)
\(252\) 5.06509 5.39248i 0.319071 0.339694i
\(253\) 9.48300 + 9.48300i 0.596191 + 0.596191i
\(254\) −33.6596 9.01906i −2.11199 0.565906i
\(255\) −3.77725 + 1.01211i −0.236540 + 0.0633808i
\(256\) 1.46858 2.54365i 0.0917861 0.158978i
\(257\) 7.55184 + 13.0802i 0.471071 + 0.815918i 0.999452 0.0330886i \(-0.0105343\pi\)
−0.528382 + 0.849007i \(0.677201\pi\)
\(258\) 1.39594 + 1.39594i 0.0869074 + 0.0869074i
\(259\) 15.4228 + 24.8811i 0.958325 + 1.54603i
\(260\) −1.85992 + 6.32220i −0.115347 + 0.392086i
\(261\) −0.0381918 0.0661501i −0.00236401 0.00409459i
\(262\) −8.25772 30.8182i −0.510164 1.90396i
\(263\) −11.0113 + 19.0721i −0.678984 + 1.17604i 0.296303 + 0.955094i \(0.404246\pi\)
−0.975287 + 0.220941i \(0.929087\pi\)
\(264\) 2.22091 + 3.84673i 0.136688 + 0.236750i
\(265\) 0.643441 0.643441i 0.0395263 0.0395263i
\(266\) −9.78866 + 2.95409i −0.600181 + 0.181127i
\(267\) 6.53306 6.53306i 0.399817 0.399817i
\(268\) 9.81630 + 2.63027i 0.599626 + 0.160669i
\(269\) −26.0922 15.0643i −1.59087 0.918488i −0.993158 0.116775i \(-0.962744\pi\)
−0.597709 0.801713i \(-0.703922\pi\)
\(270\) −1.23972 0.715753i −0.0754470 0.0435593i
\(271\) −6.94335 + 25.9129i −0.421779 + 1.57410i 0.349080 + 0.937093i \(0.386494\pi\)
−0.770858 + 0.637007i \(0.780172\pi\)
\(272\) 10.6096 0.643302
\(273\) 6.69813 6.79228i 0.405389 0.411088i
\(274\) −2.98015 −0.180038
\(275\) 3.01454 11.2504i 0.181784 0.678426i
\(276\) −12.7504 7.36143i −0.767482 0.443106i
\(277\) 2.12102 + 1.22457i 0.127440 + 0.0735775i 0.562365 0.826889i \(-0.309892\pi\)
−0.434925 + 0.900467i \(0.643225\pi\)
\(278\) 22.0411 + 5.90590i 1.32194 + 0.354212i
\(279\) 5.57498 5.57498i 0.333765 0.333765i
\(280\) 2.93604 + 0.689013i 0.175462 + 0.0411764i
\(281\) −20.1404 + 20.1404i −1.20147 + 1.20147i −0.227754 + 0.973719i \(0.573138\pi\)
−0.973719 + 0.227754i \(0.926862\pi\)
\(282\) 3.70428 + 6.41600i 0.220587 + 0.382067i
\(283\) −3.04663 + 5.27692i −0.181103 + 0.313680i −0.942257 0.334892i \(-0.891300\pi\)
0.761153 + 0.648572i \(0.224634\pi\)
\(284\) −4.58761 17.1212i −0.272225 1.01596i
\(285\) 0.576715 + 0.998900i 0.0341617 + 0.0591697i
\(286\) 9.62988 + 17.6575i 0.569427 + 1.04411i
\(287\) −3.94767 + 0.123588i −0.233024 + 0.00729516i
\(288\) 5.21248 + 5.21248i 0.307149 + 0.307149i
\(289\) −9.39577 16.2739i −0.552692 0.957291i
\(290\) 0.0546717 0.0946942i 0.00321043 0.00556064i
\(291\) 9.41767 2.52346i 0.552074 0.147928i
\(292\) −41.8337 11.2093i −2.44813 0.655975i
\(293\) 6.26592 + 6.26592i 0.366059 + 0.366059i 0.866038 0.499979i \(-0.166659\pi\)
−0.499979 + 0.866038i \(0.666659\pi\)
\(294\) −11.4970 10.1408i −0.670518 0.591426i
\(295\) −3.45063 −0.200903
\(296\) 16.7096 9.64732i 0.971228 0.560739i
\(297\) −2.46032 + 0.659241i −0.142762 + 0.0382530i
\(298\) 8.58407 + 4.95602i 0.497262 + 0.287094i
\(299\) −16.2048 9.88887i −0.937150 0.571888i
\(300\) 12.7866i 0.738237i
\(301\) 1.63282 1.73836i 0.0941140 0.100197i
\(302\) 9.51627 0.547600
\(303\) −5.32552 + 3.07469i −0.305943 + 0.176636i
\(304\) −0.809944 3.02275i −0.0464535 0.173367i
\(305\) 1.93098 0.517404i 0.110568 0.0296265i
\(306\) 3.39108 12.6557i 0.193855 0.723478i
\(307\) −20.3624 20.3624i −1.16214 1.16214i −0.984006 0.178135i \(-0.942994\pi\)
−0.178135 0.984006i \(-0.557006\pi\)
\(308\) 16.0167 9.92811i 0.912635 0.565707i
\(309\) 16.2075i 0.922011i
\(310\) 10.9017 + 2.92111i 0.619176 + 0.165908i
\(311\) −1.47429 + 2.55354i −0.0835991 + 0.144798i −0.904793 0.425851i \(-0.859975\pi\)
0.821194 + 0.570649i \(0.193308\pi\)
\(312\) −4.33658 4.55279i −0.245511 0.257751i
\(313\) 10.7571 6.21061i 0.608027 0.351044i −0.164166 0.986433i \(-0.552493\pi\)
0.772193 + 0.635388i \(0.219160\pi\)
\(314\) 7.53404 7.53404i 0.425170 0.425170i
\(315\) −0.817402 + 1.52401i −0.0460554 + 0.0858683i
\(316\) 31.3304i 1.76247i
\(317\) 3.95195 14.7489i 0.221964 0.828379i −0.761635 0.648007i \(-0.775603\pi\)
0.983598 0.180373i \(-0.0577304\pi\)
\(318\) 0.789097 + 2.94495i 0.0442504 + 0.165145i
\(319\) −0.0503551 0.187928i −0.00281935 0.0105219i
\(320\) −2.13114 + 7.95352i −0.119134 + 0.444615i
\(321\) 17.5215i 0.977956i
\(322\) −14.4198 + 26.8851i −0.803583 + 1.49825i
\(323\) −7.46492 + 7.46492i −0.415359 + 0.415359i
\(324\) 2.42164 1.39814i 0.134536 0.0776742i
\(325\) −0.400884 + 16.4824i −0.0222370 + 0.914279i
\(326\) 0.326971 0.566330i 0.0181092 0.0313661i
\(327\) −14.4056 3.85998i −0.796634 0.213457i
\(328\) 2.60326i 0.143741i
\(329\) 7.60724 4.71543i 0.419401 0.259970i
\(330\) −2.57826 2.57826i −0.141928 0.141928i
\(331\) −4.04016 + 15.0781i −0.222067 + 0.828766i 0.761491 + 0.648175i \(0.224468\pi\)
−0.983558 + 0.180591i \(0.942199\pi\)
\(332\) −23.6988 + 6.35006i −1.30064 + 0.348505i
\(333\) 2.86365 + 10.6873i 0.156927 + 0.585659i
\(334\) 21.3014 12.2984i 1.16556 0.672936i
\(335\) −2.37556 −0.129791
\(336\) 3.21230 3.41994i 0.175246 0.186573i
\(337\) 1.81266i 0.0987418i 0.998781 + 0.0493709i \(0.0157216\pi\)
−0.998781 + 0.0493709i \(0.984278\pi\)
\(338\) −19.1292 21.0866i −1.04049 1.14696i
\(339\) −0.817745 0.472125i −0.0444138 0.0256423i
\(340\) 10.5622 2.83013i 0.572816 0.153486i
\(341\) 17.3915 10.0410i 0.941802 0.543749i
\(342\) −3.86458 −0.208972
\(343\) −11.8104 + 14.2659i −0.637700 + 0.770284i
\(344\) −1.11155 1.11155i −0.0599306 0.0599306i
\(345\) 3.32428 + 0.890739i 0.178973 + 0.0479558i
\(346\) 20.8644 5.59059i 1.12167 0.300552i
\(347\) 18.4617 31.9767i 0.991078 1.71660i 0.380110 0.924941i \(-0.375886\pi\)
0.610968 0.791656i \(-0.290781\pi\)
\(348\) 0.106795 + 0.184974i 0.00572479 + 0.00991562i
\(349\) 19.8750 + 19.8750i 1.06388 + 1.06388i 0.997815 + 0.0660671i \(0.0210451\pi\)
0.0660671 + 0.997815i \(0.478955\pi\)
\(350\) 26.4829 0.829088i 1.41557 0.0443166i
\(351\) 3.16541 1.72632i 0.168957 0.0921441i
\(352\) 9.38810 + 16.2607i 0.500387 + 0.866696i
\(353\) 6.70223 + 25.0131i 0.356724 + 1.33131i 0.878301 + 0.478107i \(0.158677\pi\)
−0.521578 + 0.853204i \(0.674656\pi\)
\(354\) 5.78067 10.0124i 0.307239 0.532154i
\(355\) 2.07168 + 3.58826i 0.109953 + 0.190445i
\(356\) −18.2682 + 18.2682i −0.968214 + 0.968214i
\(357\) −15.4098 3.61629i −0.815575 0.191394i
\(358\) 37.1645 37.1645i 1.96420 1.96420i
\(359\) 30.6453 + 8.21137i 1.61739 + 0.433380i 0.950235 0.311535i \(-0.100843\pi\)
0.667160 + 0.744914i \(0.267510\pi\)
\(360\) 0.987154 + 0.569934i 0.0520276 + 0.0300381i
\(361\) −13.7578 7.94307i −0.724095 0.418056i
\(362\) −3.87686 + 14.4687i −0.203763 + 0.760456i
\(363\) 4.51222 0.236830
\(364\) −18.7298 + 18.9931i −0.981707 + 0.995507i
\(365\) 10.1238 0.529905
\(366\) −1.73357 + 6.46976i −0.0906150 + 0.338180i
\(367\) −22.8752 13.2070i −1.19408 0.689400i −0.234848 0.972032i \(-0.575459\pi\)
−0.959229 + 0.282632i \(0.908793\pi\)
\(368\) −8.08634 4.66865i −0.421530 0.243370i
\(369\) −1.44194 0.386368i −0.0750646 0.0201135i
\(370\) −11.1996 + 11.1996i −0.582238 + 0.582238i
\(371\) 3.52617 1.06415i 0.183070 0.0552482i
\(372\) −15.5891 + 15.5891i −0.808260 + 0.808260i
\(373\) 1.37665 + 2.38442i 0.0712801 + 0.123461i 0.899463 0.436998i \(-0.143958\pi\)
−0.828182 + 0.560459i \(0.810625\pi\)
\(374\) 16.6863 28.9015i 0.862828 1.49446i
\(375\) −1.61948 6.04396i −0.0836293 0.312109i
\(376\) −2.94961 5.10888i −0.152115 0.263470i
\(377\) 0.131862 + 0.241785i 0.00679126 + 0.0124526i
\(378\) −3.05275 4.92490i −0.157017 0.253309i
\(379\) 5.33831 + 5.33831i 0.274211 + 0.274211i 0.830793 0.556582i \(-0.187887\pi\)
−0.556582 + 0.830793i \(0.687887\pi\)
\(380\) −1.61265 2.79319i −0.0827273 0.143288i
\(381\) −7.95578 + 13.7798i −0.407587 + 0.705962i
\(382\) −6.16138 + 1.65094i −0.315244 + 0.0844693i
\(383\) −25.5546 6.84734i −1.30578 0.349883i −0.462147 0.886803i \(-0.652921\pi\)
−0.843633 + 0.536921i \(0.819587\pi\)
\(384\) −9.08295 9.08295i −0.463512 0.463512i
\(385\) −3.01576 + 3.21069i −0.153697 + 0.163632i
\(386\) −14.4494 −0.735456
\(387\) 0.780657 0.450713i 0.0396830 0.0229110i
\(388\) −26.3344 + 7.05627i −1.33693 + 0.358228i
\(389\) −5.09402 2.94103i −0.258277 0.149116i 0.365271 0.930901i \(-0.380976\pi\)
−0.623548 + 0.781785i \(0.714310\pi\)
\(390\) 4.40581 + 2.68861i 0.223097 + 0.136143i
\(391\) 31.4994i 1.59300i
\(392\) 9.15472 + 8.07486i 0.462383 + 0.407842i
\(393\) −14.5684 −0.734879
\(394\) −45.3003 + 26.1542i −2.28220 + 1.31763i
\(395\) 1.89550 + 7.07410i 0.0953730 + 0.355937i
\(396\) 6.87972 1.84342i 0.345719 0.0926352i
\(397\) 2.19733 8.20055i 0.110281 0.411574i −0.888610 0.458664i \(-0.848328\pi\)
0.998891 + 0.0470903i \(0.0149948\pi\)
\(398\) −1.24787 1.24787i −0.0625502 0.0625502i
\(399\) 0.146090 + 4.66645i 0.00731366 + 0.233614i
\(400\) 8.10935i 0.405468i
\(401\) 37.8352 + 10.1379i 1.88940 + 0.506263i 0.998660 + 0.0517442i \(0.0164780\pi\)
0.890737 + 0.454518i \(0.150189\pi\)
\(402\) 3.97966 6.89298i 0.198488 0.343791i
\(403\) −20.5837 + 19.6062i −1.02535 + 0.976653i
\(404\) 14.8916 8.59767i 0.740885 0.427750i
\(405\) −0.462196 + 0.462196i −0.0229667 + 0.0229667i
\(406\) 0.376181 0.233180i 0.0186695 0.0115725i
\(407\) 28.1820i 1.39693i
\(408\) −2.70022 + 10.0774i −0.133681 + 0.498904i
\(409\) 0.495968 + 1.85098i 0.0245240 + 0.0915249i 0.977103 0.212766i \(-0.0682472\pi\)
−0.952579 + 0.304291i \(0.901581\pi\)
\(410\) −0.553088 2.06415i −0.0273150 0.101941i
\(411\) −0.352195 + 1.31441i −0.0173725 + 0.0648350i
\(412\) 45.3205i 2.23278i
\(413\) −12.3084 6.60163i −0.605659 0.324845i
\(414\) −8.15360 + 8.15360i −0.400728 + 0.400728i
\(415\) 4.96678 2.86757i 0.243809 0.140763i
\(416\) −18.3314 19.2453i −0.898769 0.943578i
\(417\) 5.20964 9.02337i 0.255117 0.441876i
\(418\) −9.50809 2.54769i −0.465056 0.124611i
\(419\) 6.41207i 0.313250i −0.987658 0.156625i \(-0.949939\pi\)
0.987658 0.156625i \(-0.0500614\pi\)
\(420\) 2.28568 4.26155i 0.111530 0.207942i
\(421\) −5.78368 5.78368i −0.281879 0.281879i 0.551979 0.833858i \(-0.313873\pi\)
−0.833858 + 0.551979i \(0.813873\pi\)
\(422\) −9.94792 + 37.1261i −0.484257 + 1.80727i
\(423\) 3.26758 0.875544i 0.158875 0.0425704i
\(424\) −0.628335 2.34498i −0.0305147 0.113882i
\(425\) 23.6918 13.6785i 1.14922 0.663503i
\(426\) −13.8824 −0.672603
\(427\) 7.87772 + 1.84870i 0.381229 + 0.0894647i
\(428\) 48.9949i 2.36826i
\(429\) 8.92598 2.16053i 0.430951 0.104311i
\(430\) 1.11752 + 0.645198i 0.0538914 + 0.0311142i
\(431\) 9.40305 2.51954i 0.452929 0.121362i −0.0251405 0.999684i \(-0.508003\pi\)
0.478070 + 0.878322i \(0.341337\pi\)
\(432\) 1.53582 0.886704i 0.0738920 0.0426616i
\(433\) −13.1342 −0.631190 −0.315595 0.948894i \(-0.602204\pi\)
−0.315595 + 0.948894i \(0.602204\pi\)
\(434\) 33.2981 + 31.2765i 1.59836 + 1.50132i
\(435\) −0.0353042 0.0353042i −0.00169271 0.00169271i
\(436\) 40.2821 + 10.7936i 1.92916 + 0.516918i
\(437\) 8.97442 2.40469i 0.429305 0.115032i
\(438\) −16.9600 + 29.3755i −0.810378 + 1.40362i
\(439\) −3.44914 5.97409i −0.164619 0.285128i 0.771901 0.635743i \(-0.219306\pi\)
−0.936520 + 0.350615i \(0.885973\pi\)
\(440\) 2.05299 + 2.05299i 0.0978726 + 0.0978726i
\(441\) −5.83138 + 3.87235i −0.277685 + 0.184397i
\(442\) −13.3326 + 45.3200i −0.634167 + 2.15565i
\(443\) −11.6463 20.1720i −0.553332 0.958400i −0.998031 0.0627195i \(-0.980023\pi\)
0.444699 0.895680i \(-0.353311\pi\)
\(444\) −8.00754 29.8845i −0.380021 1.41826i
\(445\) 3.01956 5.23003i 0.143141 0.247927i
\(446\) −3.96816 6.87306i −0.187898 0.325449i
\(447\) 3.20034 3.20034i 0.151371 0.151371i
\(448\) −22.8182 + 24.2931i −1.07806 + 1.14774i
\(449\) −10.6650 + 10.6650i −0.503312 + 0.503312i −0.912465 0.409154i \(-0.865824\pi\)
0.409154 + 0.912465i \(0.365824\pi\)
\(450\) 9.67326 + 2.59194i 0.456002 + 0.122185i
\(451\) −3.29293 1.90118i −0.155058 0.0895229i
\(452\) 2.28664 + 1.32019i 0.107554 + 0.0620965i
\(453\) 1.12463 4.19719i 0.0528399 0.197201i
\(454\) 28.4312 1.33434
\(455\) 3.07992 5.42161i 0.144389 0.254169i
\(456\) 3.07725 0.144105
\(457\) −3.21576 + 12.0014i −0.150427 + 0.561401i 0.849027 + 0.528350i \(0.177189\pi\)
−0.999454 + 0.0330510i \(0.989478\pi\)
\(458\) −22.0437 12.7270i −1.03004 0.594692i
\(459\) −5.18109 2.99130i −0.241832 0.139622i
\(460\) −9.29559 2.49075i −0.433409 0.116132i
\(461\) −16.0625 + 16.0625i −0.748103 + 0.748103i −0.974123 0.226019i \(-0.927429\pi\)
0.226019 + 0.974123i \(0.427429\pi\)
\(462\) −4.26405 14.1293i −0.198382 0.657356i
\(463\) −4.57548 + 4.57548i −0.212641 + 0.212641i −0.805388 0.592748i \(-0.798043\pi\)
0.592748 + 0.805388i \(0.298043\pi\)
\(464\) 0.0677296 + 0.117311i 0.00314427 + 0.00544603i
\(465\) 2.57673 4.46303i 0.119493 0.206968i
\(466\) −14.6853 54.8062i −0.680282 2.53885i
\(467\) −15.0139 26.0049i −0.694762 1.20336i −0.970261 0.242062i \(-0.922176\pi\)
0.275499 0.961301i \(-0.411157\pi\)
\(468\) −8.85135 + 4.82726i −0.409154 + 0.223140i
\(469\) −8.47366 4.54484i −0.391277 0.209861i
\(470\) 3.42421 + 3.42421i 0.157947 + 0.157947i
\(471\) −2.43255 4.21329i −0.112086 0.194138i
\(472\) −4.60299 + 7.97260i −0.211870 + 0.366969i
\(473\) 2.21780 0.594257i 0.101974 0.0273239i
\(474\) −23.7018 6.35089i −1.08866 0.291706i
\(475\) −5.70574 5.70574i −0.261798 0.261798i
\(476\) 43.0901 + 10.1121i 1.97503 + 0.463489i
\(477\) 1.39214 0.0637416
\(478\) 29.2135 16.8665i 1.33620 0.771453i
\(479\) 36.4814 9.77517i 1.66688 0.446639i 0.702613 0.711572i \(-0.252017\pi\)
0.964267 + 0.264933i \(0.0853498\pi\)
\(480\) 4.17284 + 2.40919i 0.190463 + 0.109964i
\(481\) −9.38505 38.7732i −0.427921 1.76791i
\(482\) 25.5649i 1.16445i
\(483\) 10.1536 + 9.53719i 0.462007 + 0.433957i
\(484\) −12.6174 −0.573518
\(485\) 5.51915 3.18648i 0.250612 0.144691i
\(486\) −0.566824 2.11542i −0.0257117 0.0959572i
\(487\) 19.7195 5.28383i 0.893577 0.239433i 0.217321 0.976100i \(-0.430268\pi\)
0.676256 + 0.736667i \(0.263601\pi\)
\(488\) 1.38039 5.15168i 0.0624873 0.233206i
\(489\) −0.211141 0.211141i −0.00954812 0.00954812i
\(490\) −8.97445 4.45763i −0.405424 0.201375i
\(491\) 34.5398i 1.55876i −0.626552 0.779380i \(-0.715534\pi\)
0.626552 0.779380i \(-0.284466\pi\)
\(492\) 4.03206 + 1.08039i 0.181780 + 0.0487077i
\(493\) 0.228486 0.395750i 0.0102905 0.0178237i
\(494\) 13.9298 + 0.338800i 0.626732 + 0.0152433i
\(495\) −1.44185 + 0.832452i −0.0648063 + 0.0374159i
\(496\) −9.88671 + 9.88671i −0.443927 + 0.443927i
\(497\) 0.524787 + 16.7628i 0.0235399 + 0.751916i
\(498\) 19.2156i 0.861073i
\(499\) −0.432031 + 1.61236i −0.0193404 + 0.0721793i −0.974922 0.222549i \(-0.928562\pi\)
0.955581 + 0.294728i \(0.0952290\pi\)
\(500\) 4.52849 + 16.9006i 0.202520 + 0.755816i
\(501\) −2.90684 10.8485i −0.129868 0.484675i
\(502\) 2.01623 7.52469i 0.0899889 0.335843i
\(503\) 28.9670i 1.29157i −0.763518 0.645787i \(-0.776530\pi\)
0.763518 0.645787i \(-0.223470\pi\)
\(504\) 2.43082 + 3.92156i 0.108277 + 0.174680i
\(505\) −2.84222 + 2.84222i −0.126477 + 0.126477i
\(506\) −25.4357 + 14.6853i −1.13075 + 0.652841i
\(507\) −11.5610 + 5.94499i −0.513443 + 0.264026i
\(508\) 22.2465 38.5321i 0.987030 1.70959i
\(509\) 22.8308 + 6.11751i 1.01196 + 0.271154i 0.726448 0.687221i \(-0.241170\pi\)
0.285512 + 0.958375i \(0.407836\pi\)
\(510\) 8.56413i 0.379226i
\(511\) 36.1118 + 19.3686i 1.59749 + 0.856815i
\(512\) −13.6174 13.6174i −0.601812 0.601812i
\(513\) −0.456716 + 1.70449i −0.0201645 + 0.0752549i
\(514\) −31.9505 + 8.56112i −1.40928 + 0.377615i
\(515\) −2.74191 10.2329i −0.120823 0.450917i
\(516\) −2.18293 + 1.26032i −0.0960981 + 0.0554823i
\(517\) 8.61648 0.378952
\(518\) −61.3758 + 18.5224i −2.69670 + 0.813829i
\(519\) 9.86301i 0.432938i
\(520\) −3.50822 2.14086i −0.153846 0.0938829i
\(521\) −8.01013 4.62465i −0.350930 0.202610i 0.314165 0.949369i \(-0.398276\pi\)
−0.665095 + 0.746759i \(0.731609\pi\)
\(522\) 0.161583 0.0432960i 0.00707229 0.00189501i
\(523\) 23.8793 13.7867i 1.04417 0.602852i 0.123158 0.992387i \(-0.460698\pi\)
0.921011 + 0.389536i \(0.127364\pi\)
\(524\) 40.7372 1.77961
\(525\) 2.76408 11.7784i 0.120634 0.514050i
\(526\) −34.1039 34.1039i −1.48700 1.48700i
\(527\) 45.5609 + 12.2080i 1.98466 + 0.531789i
\(528\) 4.36315 1.16910i 0.189882 0.0508787i
\(529\) 2.36103 4.08942i 0.102653 0.177801i
\(530\) 0.996427 + 1.72586i 0.0432820 + 0.0749667i
\(531\) −3.73286 3.73286i −0.161992 0.161992i
\(532\) −0.408508 13.0486i −0.0177111 0.565731i
\(533\) 5.16359 + 1.51907i 0.223660 + 0.0657982i
\(534\) 10.1170 + 17.5232i 0.437807 + 0.758305i
\(535\) −2.96421 11.0626i −0.128154 0.478278i
\(536\) −3.16889 + 5.48868i −0.136875 + 0.237075i
\(537\) −11.9994 20.7836i −0.517814 0.896880i
\(538\) 46.6570 46.6570i 2.01152 2.01152i
\(539\) −16.8999 + 5.68293i −0.727929 + 0.244781i
\(540\) 1.29243 1.29243i 0.0556172 0.0556172i
\(541\) −8.25664 2.21236i −0.354981 0.0951167i 0.0769218 0.997037i \(-0.475491\pi\)
−0.431902 + 0.901920i \(0.642157\pi\)
\(542\) −50.8810 29.3762i −2.18553 1.26181i
\(543\) 5.92329 + 3.41981i 0.254193 + 0.146758i
\(544\) −11.4142 + 42.5984i −0.489381 + 1.82639i
\(545\) −9.74833 −0.417573
\(546\) 10.5718 + 18.0193i 0.452433 + 0.771157i
\(547\) 40.4129 1.72793 0.863965 0.503552i \(-0.167974\pi\)
0.863965 + 0.503552i \(0.167974\pi\)
\(548\) 0.984832 3.67544i 0.0420699 0.157007i
\(549\) 2.64864 + 1.52919i 0.113041 + 0.0652644i
\(550\) 22.0906 + 12.7540i 0.941947 + 0.543833i
\(551\) −0.130195 0.0348856i −0.00554648 0.00148617i
\(552\) 6.49248 6.49248i 0.276338 0.276338i
\(553\) −6.77266 + 28.8599i −0.288003 + 1.22725i
\(554\) −3.79273 + 3.79273i −0.161138 + 0.161138i
\(555\) 3.61605 + 6.26319i 0.153493 + 0.265858i
\(556\) −14.5676 + 25.2318i −0.617803 + 1.07007i
\(557\) 4.63910 + 17.3133i 0.196565 + 0.733590i 0.991856 + 0.127362i \(0.0406512\pi\)
−0.795291 + 0.606227i \(0.792682\pi\)
\(558\) 8.63336 + 14.9534i 0.365479 + 0.633029i
\(559\) −2.85338 + 1.55615i −0.120685 + 0.0658181i
\(560\) 1.44959 2.70269i 0.0612563 0.114210i
\(561\) −10.7751 10.7751i −0.454927 0.454927i
\(562\) −31.1892 54.0213i −1.31564 2.27875i
\(563\) −3.28323 + 5.68672i −0.138372 + 0.239667i −0.926880 0.375357i \(-0.877520\pi\)
0.788509 + 0.615024i \(0.210854\pi\)
\(564\) −9.13703 + 2.44826i −0.384738 + 0.103090i
\(565\) −0.596173 0.159744i −0.0250812 0.00672048i
\(566\) −9.43598 9.43598i −0.396624 0.396624i
\(567\) −2.53292 + 0.764403i −0.106373 + 0.0321019i
\(568\) 11.0541 0.463821
\(569\) 24.6318 14.2212i 1.03262 0.596182i 0.114884 0.993379i \(-0.463350\pi\)
0.917733 + 0.397197i \(0.130017\pi\)
\(570\) −2.43998 + 0.653792i −0.102200 + 0.0273843i
\(571\) −19.7578 11.4072i −0.826839 0.477376i 0.0259302 0.999664i \(-0.491745\pi\)
−0.852769 + 0.522288i \(0.825079\pi\)
\(572\) −24.9595 + 6.04144i −1.04361 + 0.252605i
\(573\) 2.91261i 0.121676i
\(574\) 1.97619 8.42101i 0.0824847 0.351486i
\(575\) −24.0763 −1.00405
\(576\) −10.9095 + 6.29860i −0.454562 + 0.262442i
\(577\) −10.9943 41.0315i −0.457701 1.70816i −0.680025 0.733189i \(-0.738031\pi\)
0.222324 0.974973i \(-0.428636\pi\)
\(578\) 39.7519 10.6515i 1.65346 0.443044i
\(579\) −1.70763 + 6.37298i −0.0709669 + 0.264852i
\(580\) 0.0987200 + 0.0987200i 0.00409913 + 0.00409913i
\(581\) 23.2027 0.726397i 0.962611 0.0301360i
\(582\) 21.3527i 0.885096i
\(583\) 3.42511 + 0.917754i 0.141853 + 0.0380095i
\(584\) 13.5047 23.3909i 0.558830 0.967922i
\(585\) 1.70650 1.62546i 0.0705551 0.0672045i
\(586\) −16.8067 + 9.70336i −0.694279 + 0.400842i
\(587\) 9.03045 9.03045i 0.372727 0.372727i −0.495743 0.868469i \(-0.665104\pi\)
0.868469 + 0.495743i \(0.165104\pi\)
\(588\) 16.3061 10.8281i 0.672453 0.446545i
\(589\) 13.9126i 0.573258i
\(590\) 1.95590 7.29951i 0.0805230 0.300516i
\(591\) 6.18180 + 23.0708i 0.254285 + 0.949006i
\(592\) −5.07842 18.9529i −0.208722 0.778960i
\(593\) −5.75416 + 21.4748i −0.236295 + 0.881865i 0.741266 + 0.671212i \(0.234226\pi\)
−0.977561 + 0.210654i \(0.932441\pi\)
\(594\) 5.57827i 0.228879i
\(595\) −10.3411 + 0.323745i −0.423945 + 0.0132723i
\(596\) −8.94902 + 8.94902i −0.366566 + 0.366566i
\(597\) −0.697854 + 0.402906i −0.0285612 + 0.0164898i
\(598\) 30.1044 28.6747i 1.23106 1.17260i
\(599\) −13.9125 + 24.0971i −0.568448 + 0.984581i 0.428272 + 0.903650i \(0.359123\pi\)
−0.996720 + 0.0809310i \(0.974211\pi\)
\(600\) −7.70254 2.06389i −0.314455 0.0842580i
\(601\) 17.9740i 0.733174i 0.930384 + 0.366587i \(0.119474\pi\)
−0.930384 + 0.366587i \(0.880526\pi\)
\(602\) 2.75183 + 4.43943i 0.112156 + 0.180938i
\(603\) −2.56986 2.56986i −0.104653 0.104653i
\(604\) −3.14478 + 11.7365i −0.127959 + 0.477551i
\(605\) 2.84889 0.763358i 0.115824 0.0310349i
\(606\) −3.48562 13.0085i −0.141593 0.528434i
\(607\) 11.4792 6.62754i 0.465928 0.269004i −0.248606 0.968605i \(-0.579972\pi\)
0.714534 + 0.699601i \(0.246639\pi\)
\(608\) 13.0080 0.527543
\(609\) −0.0583878 0.193473i −0.00236599 0.00783994i
\(610\) 4.37810i 0.177264i
\(611\) −11.8547 + 2.86943i −0.479589 + 0.116085i
\(612\) 14.4877 + 8.36449i 0.585631 + 0.338114i
\(613\) −7.78962 + 2.08722i −0.314620 + 0.0843021i −0.412673 0.910879i \(-0.635405\pi\)
0.0980538 + 0.995181i \(0.468738\pi\)
\(614\) 54.6167 31.5330i 2.20415 1.27257i
\(615\) −0.975766 −0.0393467
\(616\) 3.39534 + 11.2508i 0.136802 + 0.453307i
\(617\) −12.9666 12.9666i −0.522016 0.522016i 0.396163 0.918180i \(-0.370341\pi\)
−0.918180 + 0.396163i \(0.870341\pi\)
\(618\) 34.2855 + 9.18678i 1.37917 + 0.369547i
\(619\) −29.9041 + 8.01277i −1.20195 + 0.322061i −0.803597 0.595173i \(-0.797083\pi\)
−0.398349 + 0.917234i \(0.630417\pi\)
\(620\) −7.20525 + 12.4799i −0.289370 + 0.501203i
\(621\) 2.63259 + 4.55977i 0.105642 + 0.182977i
\(622\) −4.56613 4.56613i −0.183085 0.183085i
\(623\) 20.7767 12.8787i 0.832402 0.515973i
\(624\) −5.61357 + 3.06147i −0.224722 + 0.122557i
\(625\) 9.38689 + 16.2586i 0.375476 + 0.650343i
\(626\) 7.04064 + 26.2760i 0.281401 + 1.05020i
\(627\) −2.24733 + 3.89250i −0.0897499 + 0.155451i
\(628\) 6.80206 + 11.7815i 0.271432 + 0.470133i
\(629\) −46.8057 + 46.8057i −1.86626 + 1.86626i
\(630\) −2.76059 2.59299i −0.109985 0.103307i
\(631\) 25.6189 25.6189i 1.01987 1.01987i 0.0200749 0.999798i \(-0.493610\pi\)
0.999798 0.0200749i \(-0.00639046\pi\)
\(632\) 18.8731 + 5.05703i 0.750731 + 0.201158i
\(633\) 15.1990 + 8.77514i 0.604106 + 0.348780i
\(634\) 28.9599 + 16.7200i 1.15015 + 0.664037i
\(635\) −2.69185 + 10.0461i −0.106823 + 0.398668i
\(636\) −3.89280 −0.154359
\(637\) 21.3586 13.4466i 0.846258 0.532773i
\(638\) 0.426088 0.0168690
\(639\) −1.64062 + 6.12287i −0.0649019 + 0.242217i
\(640\) −7.27133 4.19810i −0.287425 0.165945i
\(641\) 33.3576 + 19.2590i 1.31755 + 0.760687i 0.983334 0.181811i \(-0.0581958\pi\)
0.334214 + 0.942497i \(0.391529\pi\)
\(642\) 37.0653 + 9.93161i 1.46285 + 0.391970i
\(643\) 19.0170 19.0170i 0.749958 0.749958i −0.224513 0.974471i \(-0.572079\pi\)
0.974471 + 0.224513i \(0.0720790\pi\)
\(644\) −28.3923 26.6686i −1.11881 1.05089i
\(645\) 0.416635 0.416635i 0.0164050 0.0164050i
\(646\) −11.5601 20.0227i −0.454826 0.787782i
\(647\) −24.4519 + 42.3520i −0.961305 + 1.66503i −0.242074 + 0.970258i \(0.577828\pi\)
−0.719231 + 0.694771i \(0.755506\pi\)
\(648\) 0.451346 + 1.68444i 0.0177305 + 0.0661712i
\(649\) −6.72318 11.6449i −0.263908 0.457102i
\(650\) −34.6399 10.1907i −1.35869 0.399710i
\(651\) 17.7298 10.9900i 0.694885 0.430732i
\(652\) 0.590407 + 0.590407i 0.0231221 + 0.0231221i
\(653\) 19.4880 + 33.7542i 0.762625 + 1.32090i 0.941493 + 0.337032i \(0.109423\pi\)
−0.178868 + 0.983873i \(0.557244\pi\)
\(654\) 16.3309 28.2860i 0.638590 1.10607i
\(655\) −9.19808 + 2.46462i −0.359399 + 0.0963006i
\(656\) 2.55715 + 0.685188i 0.0998401 + 0.0267521i
\(657\) 10.9519 + 10.9519i 0.427273 + 0.427273i
\(658\) 5.66313 + 18.7653i 0.220772 + 0.731547i
\(659\) −5.25399 −0.204666 −0.102333 0.994750i \(-0.532631\pi\)
−0.102333 + 0.994750i \(0.532631\pi\)
\(660\) 4.03180 2.32776i 0.156938 0.0906080i
\(661\) −5.18442 + 1.38916i −0.201650 + 0.0540321i −0.358230 0.933633i \(-0.616620\pi\)
0.156580 + 0.987665i \(0.449953\pi\)
\(662\) −29.6063 17.0932i −1.15068 0.664347i
\(663\) 18.4129 + 11.2363i 0.715098 + 0.436382i
\(664\) 15.3009i 0.593788i
\(665\) 0.881686 + 2.92155i 0.0341903 + 0.113293i
\(666\) −24.2312 −0.938941
\(667\) −0.348292 + 0.201086i −0.0134859 + 0.00778609i
\(668\) 8.12832 + 30.3353i 0.314494 + 1.17371i
\(669\) −3.50035 + 0.937916i −0.135331 + 0.0362619i
\(670\) 1.34652 5.02530i 0.0520208 0.194144i
\(671\) 5.50840 + 5.50840i 0.212649 + 0.212649i
\(672\) 10.2754 + 16.5770i 0.396383 + 0.639470i
\(673\) 40.2628i 1.55202i −0.630722 0.776008i \(-0.717241\pi\)
0.630722 0.776008i \(-0.282759\pi\)
\(674\) −3.83453 1.02746i −0.147700 0.0395762i
\(675\) 2.28637 3.96012i 0.0880026 0.152425i
\(676\) 32.3277 16.6238i 1.24337 0.639377i
\(677\) 23.1527 13.3672i 0.889832 0.513745i 0.0159443 0.999873i \(-0.494925\pi\)
0.873887 + 0.486128i \(0.161591\pi\)
\(678\) 1.46226 1.46226i 0.0561577 0.0561577i
\(679\) 25.7832 0.807182i 0.989467 0.0309768i
\(680\) 6.81937i 0.261511i
\(681\) 3.36001 12.5397i 0.128756 0.480523i
\(682\) 11.3829 + 42.4817i 0.435875 + 1.62671i
\(683\) 8.54301 + 31.8830i 0.326889 + 1.21997i 0.912399 + 0.409302i \(0.134228\pi\)
−0.585510 + 0.810665i \(0.699106\pi\)
\(684\) 1.27710 4.76621i 0.0488312 0.182241i
\(685\) 0.889463i 0.0339846i
\(686\) −23.4838 33.0701i −0.896617 1.26262i
\(687\) −8.21841 + 8.21841i −0.313552 + 0.313552i
\(688\) −1.38442 + 0.799298i −0.0527807 + 0.0304730i
\(689\) −5.01794 0.122046i −0.191168 0.00464958i
\(690\) −3.76856 + 6.52735i −0.143467 + 0.248492i
\(691\) 19.8084 + 5.30765i 0.753548 + 0.201913i 0.615091 0.788456i \(-0.289119\pi\)
0.138457 + 0.990369i \(0.455786\pi\)
\(692\) 27.5796i 1.04842i
\(693\) −6.73572 + 0.210872i −0.255869 + 0.00801037i
\(694\) 57.1794 + 57.1794i 2.17050 + 2.17050i
\(695\) 1.76269 6.57844i 0.0668626 0.249535i
\(696\) −0.128664 + 0.0344754i −0.00487699 + 0.00130679i
\(697\) −2.31148 8.62657i −0.0875537 0.326755i
\(698\) −53.3094 + 30.7782i −2.01779 + 1.16497i
\(699\) −25.9080 −0.979931
\(700\) −7.72912 + 32.9355i −0.292133 + 1.24485i
\(701\) 44.2019i 1.66948i −0.550641 0.834742i \(-0.685617\pi\)
0.550641 0.834742i \(-0.314383\pi\)
\(702\) 1.85765 + 7.67468i 0.0701126 + 0.289662i
\(703\) 16.9085 + 9.76210i 0.637715 + 0.368185i
\(704\) −30.9932 + 8.30459i −1.16810 + 0.312991i
\(705\) 1.91493 1.10559i 0.0721206 0.0416389i
\(706\) −56.7120 −2.13438
\(707\) −15.5759 + 4.70061i −0.585792 + 0.176785i
\(708\) 10.4381 + 10.4381i 0.392287 + 0.392287i
\(709\) −39.5912 10.6084i −1.48688 0.398408i −0.578196 0.815898i \(-0.696243\pi\)
−0.908681 + 0.417490i \(0.862910\pi\)
\(710\) −8.76493 + 2.34856i −0.328942 + 0.0881397i
\(711\) −5.60217 + 9.70324i −0.210098 + 0.363900i
\(712\) −8.05592 13.9533i −0.301908 0.522920i
\(713\) −29.3532 29.3532i −1.09929 1.09929i
\(714\) 16.3846 30.5484i 0.613179 1.14325i
\(715\) 5.27010 2.87416i 0.197091 0.107487i
\(716\) 33.5537 + 58.1167i 1.25396 + 2.17192i
\(717\) −3.98656 14.8780i −0.148881 0.555630i
\(718\) −34.7409 + 60.1731i −1.29652 + 2.24564i
\(719\) 1.43809 + 2.49085i 0.0536317 + 0.0928929i 0.891595 0.452834i \(-0.149587\pi\)
−0.837963 + 0.545727i \(0.816254\pi\)
\(720\) 0.819663 0.819663i 0.0305470 0.0305470i
\(721\) 9.79689 41.7468i 0.364855 1.55473i
\(722\) 24.6011 24.6011i 0.915559 0.915559i
\(723\) −11.2755 3.02126i −0.419340 0.112362i
\(724\) −16.5631 9.56273i −0.615564 0.355396i
\(725\) 0.302488 + 0.174641i 0.0112341 + 0.00648602i
\(726\) −2.55764 + 9.54523i −0.0949228 + 0.354257i
\(727\) 26.3024 0.975502 0.487751 0.872983i \(-0.337817\pi\)
0.487751 + 0.872983i \(0.337817\pi\)
\(728\) −8.41805 14.3483i −0.311994 0.531783i
\(729\) −1.00000 −0.0370370
\(730\) −5.73842 + 21.4161i −0.212389 + 0.792645i
\(731\) 4.67036 + 2.69644i 0.172740 + 0.0997313i
\(732\) −7.40632 4.27604i −0.273745 0.158047i
\(733\) 39.5431 + 10.5955i 1.46056 + 0.391355i 0.899682 0.436546i \(-0.143798\pi\)
0.560875 + 0.827901i \(0.310465\pi\)
\(734\) 40.9045 40.9045i 1.50981 1.50981i
\(735\) −3.02666 + 3.43142i −0.111640 + 0.126570i
\(736\) 27.4446 27.4446i 1.01162 1.01162i
\(737\) −4.62852 8.01684i −0.170494 0.295304i
\(738\) 1.63466 2.83131i 0.0601725 0.104222i
\(739\) −7.35841 27.4620i −0.270684 1.01020i −0.958679 0.284490i \(-0.908176\pi\)
0.687995 0.725715i \(-0.258491\pi\)
\(740\) −10.1115 17.5136i −0.371705 0.643812i
\(741\) 1.79565 6.10376i 0.0659650 0.224227i
\(742\) 0.252409 + 8.06251i 0.00926624 + 0.295984i
\(743\) 15.6997 + 15.6997i 0.575966 + 0.575966i 0.933789 0.357823i \(-0.116481\pi\)
−0.357823 + 0.933789i \(0.616481\pi\)
\(744\) −6.87450 11.9070i −0.252031 0.436531i
\(745\) 1.47918 2.56202i 0.0541931 0.0938653i
\(746\) −5.82436 + 1.56063i −0.213245 + 0.0571388i
\(747\) 8.47513 + 2.27090i 0.310089 + 0.0830880i
\(748\) 30.1302 + 30.1302i 1.10167 + 1.10167i
\(749\) 10.5912 45.1315i 0.386994 1.64907i
\(750\) 13.7035 0.500379
\(751\) −13.2341 + 7.64073i −0.482920 + 0.278814i −0.721633 0.692276i \(-0.756608\pi\)
0.238713 + 0.971090i \(0.423275\pi\)
\(752\) −5.79475 + 1.55270i −0.211313 + 0.0566211i
\(753\) −3.08052 1.77854i −0.112260 0.0648135i
\(754\) −0.586219 + 0.141894i −0.0213488 + 0.00516748i
\(755\) 2.84025i 0.103367i
\(756\) 7.08273 2.13748i 0.257597 0.0777394i
\(757\) −28.2653 −1.02732 −0.513660 0.857994i \(-0.671711\pi\)
−0.513660 + 0.857994i \(0.671711\pi\)
\(758\) −14.3186 + 8.26687i −0.520076 + 0.300266i
\(759\) 3.47102 + 12.9540i 0.125990 + 0.470201i
\(760\) 1.94289 0.520596i 0.0704760 0.0188840i
\(761\) −6.30631 + 23.5355i −0.228603 + 0.853160i 0.752325 + 0.658792i \(0.228932\pi\)
−0.980929 + 0.194368i \(0.937734\pi\)
\(762\) −24.6405 24.6405i −0.892632 0.892632i
\(763\) −34.7725 18.6502i −1.25885 0.675182i
\(764\) 8.14445i 0.294656i
\(765\) −3.77725 1.01211i −0.136567 0.0365929i
\(766\) 28.9699 50.1774i 1.04673 1.81298i
\(767\) 13.1278 + 13.7823i 0.474017 + 0.497650i
\(768\) 2.54365 1.46858i 0.0917861 0.0529927i
\(769\) −36.5890 + 36.5890i −1.31943 + 1.31943i −0.405206 + 0.914225i \(0.632800\pi\)
−0.914225 + 0.405206i \(0.867200\pi\)
\(770\) −5.08254 8.19948i −0.183162 0.295489i
\(771\) 15.1037i 0.543946i
\(772\) 4.77501 17.8206i 0.171856 0.641377i
\(773\) 9.53735 + 35.5939i 0.343035 + 1.28022i 0.894891 + 0.446284i \(0.147253\pi\)
−0.551857 + 0.833939i \(0.686080\pi\)
\(774\) 0.510949 + 1.90689i 0.0183657 + 0.0685417i
\(775\) −9.33108 + 34.8240i −0.335182 + 1.25092i
\(776\) 17.0025i 0.610354i
\(777\) 0.915999 + 29.2590i 0.0328613 + 1.04966i
\(778\) 9.10892 9.10892i 0.326571 0.326571i
\(779\) −2.28131 + 1.31712i −0.0817365 + 0.0471906i
\(780\) −4.77184 + 4.54523i −0.170859 + 0.162745i
\(781\) −8.07290 + 13.9827i −0.288871 + 0.500339i
\(782\) −66.6344 17.8546i −2.38284 0.638480i
\(783\) 0.0763835i 0.00272972i
\(784\) 10.3414 6.86725i 0.369336 0.245259i
\(785\) −2.24863 2.24863i −0.0802569 0.0802569i
\(786\) 8.25772 30.8182i 0.294543 1.09925i
\(787\) 5.47568 1.46720i 0.195187 0.0523002i −0.159901 0.987133i \(-0.551118\pi\)
0.355088 + 0.934833i \(0.384451\pi\)
\(788\) −17.2860 64.5122i −0.615788 2.29815i
\(789\) −19.0721 + 11.0113i −0.678984 + 0.392012i
\(790\) −16.0391 −0.570645
\(791\) −1.82094 1.71039i −0.0647452 0.0608144i
\(792\) 4.44182i 0.157833i
\(793\) −9.41293 5.74416i −0.334263 0.203981i
\(794\) 16.1021 + 9.29653i 0.571441 + 0.329922i
\(795\) 0.878957 0.235516i 0.0311734 0.00835288i
\(796\) 1.95139 1.12663i 0.0691651 0.0399325i
\(797\) −4.66456 −0.165227 −0.0826136 0.996582i \(-0.526327\pi\)
−0.0826136 + 0.996582i \(0.526327\pi\)
\(798\) −9.95428 2.33601i −0.352378 0.0826939i
\(799\) 14.3106 + 14.3106i 0.506272 + 0.506272i
\(800\) −32.5597 8.72436i −1.15116 0.308453i
\(801\) 8.92433 2.39127i 0.315326 0.0844913i
\(802\) −42.8917 + 74.2907i −1.51456 + 2.62329i
\(803\) 19.7252 + 34.1650i 0.696086 + 1.20566i
\(804\) 7.18603 + 7.18603i 0.253432 + 0.253432i
\(805\) 8.02418 + 4.30376i 0.282815 + 0.151688i
\(806\) −29.8079 54.6563i −1.04994 1.92518i
\(807\) −15.0643 26.0922i −0.530289 0.918488i
\(808\) 2.77550 + 10.3583i 0.0976416 + 0.364404i
\(809\) −20.4024 + 35.3380i −0.717310 + 1.24242i 0.244751 + 0.969586i \(0.421294\pi\)
−0.962062 + 0.272832i \(0.912040\pi\)
\(810\) −0.715753 1.23972i −0.0251490 0.0435593i
\(811\) −15.4548 + 15.4548i −0.542690 + 0.542690i −0.924317 0.381626i \(-0.875364\pi\)
0.381626 + 0.924317i \(0.375364\pi\)
\(812\) 0.163268 + 0.541004i 0.00572959 + 0.0189855i
\(813\) −18.9696 + 18.9696i −0.665293 + 0.665293i
\(814\) −59.6166 15.9742i −2.08956 0.559896i
\(815\) −0.169028 0.0975885i −0.00592080 0.00341837i
\(816\) 9.18818 + 5.30480i 0.321651 + 0.185705i
\(817\) 0.411695 1.53647i 0.0144034 0.0537542i
\(818\) −4.19671 −0.146735
\(819\) 9.19689 2.53322i 0.321365 0.0885180i
\(820\) 2.72851 0.0952836
\(821\) 2.31025 8.62197i 0.0806283 0.300909i −0.913822 0.406114i \(-0.866883\pi\)
0.994450 + 0.105206i \(0.0335501\pi\)
\(822\) −2.58089 1.49008i −0.0900188 0.0519724i
\(823\) 15.7750 + 9.10768i 0.549881 + 0.317474i 0.749074 0.662487i \(-0.230499\pi\)
−0.199193 + 0.979960i \(0.563832\pi\)
\(824\) −27.3006 7.31517i −0.951061 0.254836i
\(825\) 8.23589 8.23589i 0.286737 0.286737i
\(826\) 20.9419 22.2955i 0.728662 0.775760i
\(827\) 22.9060 22.9060i 0.796520 0.796520i −0.186025 0.982545i \(-0.559561\pi\)
0.982545 + 0.186025i \(0.0595605\pi\)
\(828\) −7.36143 12.7504i −0.255827 0.443106i
\(829\) 14.1448 24.4995i 0.491268 0.850901i −0.508681 0.860955i \(-0.669867\pi\)
0.999949 + 0.0100536i \(0.00320020\pi\)
\(830\) 3.25081 + 12.1322i 0.112837 + 0.421115i
\(831\) 1.22457 + 2.12102i 0.0424800 + 0.0735775i
\(832\) 39.8753 21.7468i 1.38243 0.753935i
\(833\) −37.5064 18.6295i −1.29952 0.645474i
\(834\) 16.1352 + 16.1352i 0.558717 + 0.558717i
\(835\) −3.67060 6.35766i −0.127026 0.220016i
\(836\) 6.28416 10.8845i 0.217342 0.376448i
\(837\) 7.61556 2.04058i 0.263232 0.0705329i
\(838\) 13.5642 + 3.63452i 0.468567 + 0.125552i
\(839\) 15.9512 + 15.9512i 0.550698 + 0.550698i 0.926642 0.375945i \(-0.122682\pi\)
−0.375945 + 0.926642i \(0.622682\pi\)
\(840\) 2.19818 + 2.06472i 0.0758445 + 0.0712398i
\(841\) −28.9942 −0.999799
\(842\) 15.5132 8.95655i 0.534620 0.308663i
\(843\) −27.5122 + 7.37188i −0.947572 + 0.253901i
\(844\) −42.5005 24.5377i −1.46293 0.844622i
\(845\) −6.29355 + 5.70934i −0.216505 + 0.196407i
\(846\) 7.40856i 0.254712i
\(847\) 11.6225 + 2.72749i 0.399353 + 0.0937178i
\(848\) −2.46883 −0.0847800
\(849\) −5.27692 + 3.04663i −0.181103 + 0.104560i
\(850\) 15.5066 + 57.8713i 0.531871 + 1.98497i
\(851\) 56.2704 15.0776i 1.92892 0.516854i
\(852\) 4.58761 17.1212i 0.157169 0.586563i
\(853\) 22.1904 + 22.1904i 0.759784 + 0.759784i 0.976283 0.216499i \(-0.0694639\pi\)
−0.216499 + 0.976283i \(0.569464\pi\)
\(854\) −8.37604 + 15.6168i −0.286622 + 0.534395i
\(855\) 1.15343i 0.0394465i
\(856\) −29.5140 7.90826i −1.00877 0.270299i
\(857\) 0.305420 0.529004i 0.0104330 0.0180704i −0.860762 0.509008i \(-0.830012\pi\)
0.871195 + 0.490938i \(0.163346\pi\)
\(858\) −0.489036 + 20.1068i −0.0166954 + 0.686435i
\(859\) −22.0653 + 12.7394i −0.752858 + 0.434663i −0.826726 0.562605i \(-0.809799\pi\)
0.0738678 + 0.997268i \(0.476466\pi\)
\(860\) −1.16503 + 1.16503i −0.0397271 + 0.0397271i
\(861\) −3.48058 1.86680i −0.118618 0.0636205i
\(862\) 21.3195i 0.726145i
\(863\) −1.88235 + 7.02503i −0.0640760 + 0.239135i −0.990535 0.137261i \(-0.956170\pi\)
0.926459 + 0.376396i \(0.122837\pi\)
\(864\) 1.90790 + 7.12039i 0.0649081 + 0.242240i
\(865\) −1.66858 6.22722i −0.0567334 0.211732i
\(866\) 7.44479 27.7843i 0.252984 0.944150i
\(867\) 18.7915i 0.638194i
\(868\) −49.5773 + 30.7310i −1.68276 + 1.04308i
\(869\) −20.1799 + 20.1799i −0.684556 + 0.684556i
\(870\) 0.0946942 0.0546717i 0.00321043 0.00185355i
\(871\) 9.03773 + 9.48832i 0.306232 + 0.321499i
\(872\) −13.0039 + 22.5233i −0.440366 + 0.762736i
\(873\) 9.41767 + 2.52346i 0.318740 + 0.0854061i
\(874\) 20.3477i 0.688270i
\(875\) −0.518024 16.5468i −0.0175124 0.559384i
\(876\) −30.6244 30.6244i −1.03470 1.03470i
\(877\) 5.27177 19.6745i 0.178015 0.664361i −0.818003 0.575214i \(-0.804919\pi\)
0.996018 0.0891479i \(-0.0284144\pi\)
\(878\) 14.5927 3.91011i 0.492481 0.131960i
\(879\) 2.29349 + 8.55941i 0.0773574 + 0.288702i
\(880\) 2.55699 1.47628i 0.0861961 0.0497653i
\(881\) −9.30783 −0.313589 −0.156794 0.987631i \(-0.550116\pi\)
−0.156794 + 0.987631i \(0.550116\pi\)
\(882\) −4.88626 14.5307i −0.164529 0.489275i
\(883\) 20.6192i 0.693891i 0.937885 + 0.346945i \(0.112781\pi\)
−0.937885 + 0.346945i \(0.887219\pi\)
\(884\) −51.4875 31.4198i −1.73171 1.05676i
\(885\) −2.98833 1.72531i −0.100452 0.0579958i
\(886\) 49.2735 13.2028i 1.65538 0.443557i
\(887\) −16.2365 + 9.37414i −0.545168 + 0.314753i −0.747171 0.664632i \(-0.768588\pi\)
0.202003 + 0.979385i \(0.435255\pi\)
\(888\) 19.2946 0.647485
\(889\) −28.8218 + 30.6847i −0.966651 + 1.02913i
\(890\) 9.35212 + 9.35212i 0.313484 + 0.313484i
\(891\) −2.46032 0.659241i −0.0824238 0.0220854i
\(892\) 9.78793 2.62267i 0.327724 0.0878134i
\(893\) 2.98471 5.16967i 0.0998795 0.172996i
\(894\) 4.95602 + 8.58407i 0.165754 + 0.287094i
\(895\) −11.0922 11.0922i −0.370771 0.370771i
\(896\) −17.9053 28.8860i −0.598174 0.965013i
\(897\) −9.08937 16.6664i −0.303485 0.556476i
\(898\) −16.5157 28.6060i −0.551136 0.954596i
\(899\) 0.155867 + 0.581703i 0.00519845 + 0.0194009i
\(900\) −6.39332 + 11.0736i −0.213111 + 0.369119i
\(901\) 4.16430 + 7.21279i 0.138733 + 0.240293i
\(902\) 5.88829 5.88829i 0.196059 0.196059i
\(903\) 2.28324 0.689053i 0.0759815 0.0229302i
\(904\) −1.16435 + 1.16435i −0.0387258 + 0.0387258i
\(905\) 4.31835 + 1.15710i 0.143547 + 0.0384632i
\(906\) 8.24134 + 4.75814i 0.273800 + 0.158079i
\(907\) −8.16685 4.71513i −0.271176 0.156563i 0.358246 0.933627i \(-0.383375\pi\)
−0.629422 + 0.777064i \(0.716708\pi\)
\(908\) −9.39549 + 35.0644i −0.311800 + 1.16365i
\(909\) −6.14938 −0.203962
\(910\) 9.72319 + 9.58841i 0.322321 + 0.317853i
\(911\) 7.10474 0.235391 0.117695 0.993050i \(-0.462449\pi\)
0.117695 + 0.993050i \(0.462449\pi\)
\(912\) 0.809944 3.02275i 0.0268199 0.100093i
\(913\) 19.3545 + 11.1743i 0.640539 + 0.369815i
\(914\) −23.5651 13.6053i −0.779465 0.450025i
\(915\) 1.93098 + 0.517404i 0.0638362 + 0.0171049i
\(916\) 22.9809 22.9809i 0.759310 0.759310i
\(917\) −37.5250 8.80613i −1.23918 0.290804i
\(918\) 9.26461 9.26461i 0.305778 0.305778i
\(919\) 16.9808 + 29.4116i 0.560145 + 0.970199i 0.997483 + 0.0709024i \(0.0225879\pi\)
−0.437338 + 0.899297i \(0.644079\pi\)
\(920\) 3.00080 5.19754i 0.0989335 0.171358i
\(921\) −7.45314 27.8155i −0.245589 0.916552i
\(922\) −24.8742 43.0834i −0.819188 1.41887i
\(923\) 6.45037 21.9260i 0.212316 0.721702i
\(924\) 18.8349 0.589656i 0.619623 0.0193983i
\(925\) −35.7755 35.7755i −1.17629 1.17629i
\(926\) −7.08555 12.2725i −0.232846 0.403301i
\(927\) 8.10374 14.0361i 0.266162 0.461005i
\(928\) −0.543880 + 0.145732i −0.0178537 + 0.00478389i
\(929\) −13.9188 3.72954i −0.456662 0.122362i 0.0231532 0.999732i \(-0.492629\pi\)
−0.479815 + 0.877370i \(0.659296\pi\)
\(930\) 7.98061 + 7.98061i 0.261695 + 0.261695i
\(931\) −2.44442 + 12.1080i −0.0801126 + 0.396824i
\(932\) 72.4458 2.37304
\(933\) −2.55354 + 1.47429i −0.0835991 + 0.0482660i
\(934\) 63.5214 17.0205i 2.07848 0.556928i
\(935\) −8.62601 4.98023i −0.282101 0.162871i
\(936\) −1.47920 6.11113i −0.0483491 0.199748i
\(937\) 5.67717i 0.185465i 0.995691 + 0.0927325i \(0.0295601\pi\)
−0.995691 + 0.0927325i \(0.970440\pi\)
\(938\) 14.4173 15.3492i 0.470742 0.501169i
\(939\) 12.4212 0.405351
\(940\) −5.35468 + 3.09152i −0.174650 + 0.100834i
\(941\) −2.64228 9.86113i −0.0861360 0.321464i 0.909391 0.415942i \(-0.136548\pi\)
−0.995527 + 0.0944787i \(0.969882\pi\)
\(942\) 10.2917 2.75765i 0.335321 0.0898491i
\(943\) −2.03429 + 7.59208i −0.0662457 + 0.247232i
\(944\) 6.61988 + 6.61988i 0.215459 + 0.215459i
\(945\) −1.46990 + 0.911131i −0.0478157 + 0.0296391i
\(946\) 5.02840i 0.163487i
\(947\) −34.3096 9.19324i −1.11491 0.298740i −0.346090 0.938201i \(-0.612491\pi\)
−0.768823 + 0.639461i \(0.779157\pi\)
\(948\) 15.6652 27.1329i 0.508782 0.881235i
\(949\) −38.5157 40.4360i −1.25027 1.31261i
\(950\) 15.3042 8.83587i 0.496533 0.286673i
\(951\) 10.7969 10.7969i 0.350114 0.350114i
\(952\) −13.0466 + 24.3248i −0.422843 + 0.788372i
\(953\) 24.3020i 0.787219i 0.919278 + 0.393609i \(0.128774\pi\)
−0.919278 + 0.393609i \(0.871226\pi\)
\(954\) −0.789097 + 2.94495i −0.0255480 + 0.0953463i
\(955\) 0.492742 + 1.83894i 0.0159448 + 0.0595067i
\(956\) 11.1475 + 41.6030i 0.360536 + 1.34554i
\(957\) 0.0503551 0.187928i 0.00162775 0.00607485i
\(958\) 82.7142i 2.67238i
\(959\) −1.70169 + 3.17273i −0.0549505 + 0.102453i
\(960\) −5.82238 + 5.82238i −0.187916 + 0.187916i
\(961\) −26.9860 + 15.5804i −0.870516 + 0.502593i
\(962\) 87.3411 + 2.12430i 2.81599 + 0.0684903i
\(963\) 8.76076 15.1741i 0.282312 0.488978i
\(964\) 31.5293 + 8.44826i 1.01549 + 0.272100i
\(965\) 4.31261i 0.138828i
\(966\) −25.9304 + 16.0733i −0.834298 + 0.517149i
\(967\) 34.1587 + 34.1587i 1.09847 + 1.09847i 0.994590 + 0.103880i \(0.0331259\pi\)
0.103880 + 0.994590i \(0.466874\pi\)
\(968\) 2.03657 7.60059i 0.0654579 0.244292i
\(969\) −10.1973 + 2.73235i −0.327583 + 0.0877757i
\(970\) 3.61235 + 13.4815i 0.115985 + 0.432864i
\(971\) −23.1545 + 13.3683i −0.743064 + 0.429008i −0.823182 0.567777i \(-0.807803\pi\)
0.0801184 + 0.996785i \(0.474470\pi\)
\(972\) 2.79627 0.0896904
\(973\) 18.8732 20.0931i 0.605047 0.644155i
\(974\) 44.7100i 1.43260i
\(975\) −8.58838 + 14.0737i −0.275048 + 0.450720i
\(976\) −4.69712 2.71189i −0.150351 0.0868053i
\(977\) −23.7744 + 6.37034i −0.760612 + 0.203805i −0.618220 0.786005i \(-0.712146\pi\)
−0.142392 + 0.989810i \(0.545479\pi\)
\(978\) 0.566330 0.326971i 0.0181092 0.0104554i
\(979\) 23.5331 0.752122
\(980\) 8.46336 9.59517i 0.270352 0.306506i
\(981\) −10.5457 10.5457i −0.336697 0.336697i
\(982\) 73.0661 + 19.5780i 2.33163 + 0.624759i
\(983\) 1.19986 0.321501i 0.0382695 0.0102543i −0.239634 0.970863i \(-0.577027\pi\)
0.277903 + 0.960609i \(0.410361\pi\)
\(984\) −1.30163 + 2.25449i −0.0414944 + 0.0718705i
\(985\) 7.80603 + 13.5204i 0.248721 + 0.430797i
\(986\) 0.707663 + 0.707663i 0.0225366 + 0.0225366i
\(987\) 8.94578 0.280062i 0.284747 0.00891446i
\(988\) −5.02114 + 17.0678i −0.159744 + 0.542998i
\(989\) −2.37308 4.11030i −0.0754596 0.130700i
\(990\) −0.943707 3.52196i −0.0299930 0.111935i
\(991\) −13.4870 + 23.3602i −0.428429 + 0.742061i −0.996734 0.0807570i \(-0.974266\pi\)
0.568305 + 0.822818i \(0.307600\pi\)
\(992\) −29.0595 50.3325i −0.922639 1.59806i
\(993\) −11.0379 + 11.0379i −0.350278 + 0.350278i
\(994\) −35.7578 8.39144i −1.13417 0.266160i
\(995\) −0.372443 + 0.372443i −0.0118072 + 0.0118072i
\(996\) −23.6988 6.35006i −0.750924 0.201209i
\(997\) 29.5536 + 17.0628i 0.935973 + 0.540384i 0.888696 0.458498i \(-0.151612\pi\)
0.0472772 + 0.998882i \(0.484946\pi\)
\(998\) −3.16593 1.82785i −0.100216 0.0578596i
\(999\) −2.86365 + 10.6873i −0.0906018 + 0.338131i
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.bz.a.73.1 36
3.2 odd 2 819.2.fn.f.73.9 36
7.5 odd 6 273.2.bz.b.229.9 yes 36
13.5 odd 4 273.2.bz.b.31.9 yes 36
21.5 even 6 819.2.fn.g.775.1 36
39.5 even 4 819.2.fn.g.577.1 36
91.5 even 12 inner 273.2.bz.a.187.1 yes 36
273.5 odd 12 819.2.fn.f.460.9 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bz.a.73.1 36 1.1 even 1 trivial
273.2.bz.a.187.1 yes 36 91.5 even 12 inner
273.2.bz.b.31.9 yes 36 13.5 odd 4
273.2.bz.b.229.9 yes 36 7.5 odd 6
819.2.fn.f.73.9 36 3.2 odd 2
819.2.fn.f.460.9 36 273.5 odd 12
819.2.fn.g.577.1 36 39.5 even 4
819.2.fn.g.775.1 36 21.5 even 6