Properties

Label 273.2.j.b.100.5
Level $273$
Weight $2$
Character 273.100
Analytic conductor $2.180$
Analytic rank $0$
Dimension $16$
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(100,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.j (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + 1005 x^{6} - 544 x^{5} + 811 x^{4} - 312 x^{3} + 195 x^{2} + 13 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.5
Root \(0.379240 + 0.656863i\) of defining polynomial
Character \(\chi\) \(=\) 273.100
Dual form 273.2.j.b.172.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.379240 + 0.656863i) q^{2} -1.00000 q^{3} +(0.712354 - 1.23383i) q^{4} +(-0.357869 + 0.619848i) q^{5} +(-0.379240 - 0.656863i) q^{6} +(-1.32176 - 2.29193i) q^{7} +2.59757 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.379240 + 0.656863i) q^{2} -1.00000 q^{3} +(0.712354 - 1.23383i) q^{4} +(-0.357869 + 0.619848i) q^{5} +(-0.379240 - 0.656863i) q^{6} +(-1.32176 - 2.29193i) q^{7} +2.59757 q^{8} +1.00000 q^{9} -0.542874 q^{10} +4.48772 q^{11} +(-0.712354 + 1.23383i) q^{12} +(3.26504 - 1.52954i) q^{13} +(1.00422 - 1.73741i) q^{14} +(0.357869 - 0.619848i) q^{15} +(-0.439604 - 0.761417i) q^{16} +(1.88727 - 3.26885i) q^{17} +(0.379240 + 0.656863i) q^{18} -5.92010 q^{19} +(0.509859 + 0.883102i) q^{20} +(1.32176 + 2.29193i) q^{21} +(1.70192 + 2.94782i) q^{22} +(0.465673 + 0.806569i) q^{23} -2.59757 q^{24} +(2.24386 + 3.88648i) q^{25} +(2.24293 + 1.56463i) q^{26} -1.00000 q^{27} +(-3.76942 - 0.00184259i) q^{28} +(-1.12150 + 1.94250i) q^{29} +0.542874 q^{30} +(0.191136 + 0.331058i) q^{31} +(2.93100 - 5.07665i) q^{32} -4.48772 q^{33} +2.86291 q^{34} +(1.89367 + 0.000925671i) q^{35} +(0.712354 - 1.23383i) q^{36} +(0.328723 + 0.569365i) q^{37} +(-2.24514 - 3.88870i) q^{38} +(-3.26504 + 1.52954i) q^{39} +(-0.929592 + 1.61010i) q^{40} +(-2.29549 + 3.97591i) q^{41} +(-1.00422 + 1.73741i) q^{42} +(-2.50110 - 4.33202i) q^{43} +(3.19684 - 5.53710i) q^{44} +(-0.357869 + 0.619848i) q^{45} +(-0.353203 + 0.611766i) q^{46} +(-4.18536 + 7.24926i) q^{47} +(0.439604 + 0.761417i) q^{48} +(-3.50593 + 6.05875i) q^{49} +(-1.70192 + 2.94782i) q^{50} +(-1.88727 + 3.26885i) q^{51} +(0.438674 - 5.11809i) q^{52} +(-1.21338 - 2.10164i) q^{53} +(-0.379240 - 0.656863i) q^{54} +(-1.60602 + 2.78170i) q^{55} +(-3.43336 - 5.95347i) q^{56} +5.92010 q^{57} -1.70127 q^{58} +(-2.80700 + 4.86187i) q^{59} +(-0.509859 - 0.883102i) q^{60} +1.99378 q^{61} +(-0.144973 + 0.251101i) q^{62} +(-1.32176 - 2.29193i) q^{63} +2.68780 q^{64} +(-0.220379 + 2.57121i) q^{65} +(-1.70192 - 2.94782i) q^{66} -14.4655 q^{67} +(-2.68881 - 4.65715i) q^{68} +(-0.465673 - 0.806569i) q^{69} +(0.717546 + 1.24423i) q^{70} +(2.14741 + 3.71943i) q^{71} +2.59757 q^{72} +(-1.34127 - 2.32315i) q^{73} +(-0.249330 + 0.431852i) q^{74} +(-2.24386 - 3.88648i) q^{75} +(-4.21721 + 7.30442i) q^{76} +(-5.93167 - 10.2856i) q^{77} +(-2.24293 - 1.56463i) q^{78} +(2.75173 - 4.76614i) q^{79} +0.629283 q^{80} +1.00000 q^{81} -3.48217 q^{82} +11.5302 q^{83} +(3.76942 + 0.00184259i) q^{84} +(1.35079 + 2.33964i) q^{85} +(1.89703 - 3.28575i) q^{86} +(1.12150 - 1.94250i) q^{87} +11.6572 q^{88} +(6.05088 + 10.4804i) q^{89} -0.542874 q^{90} +(-7.82119 - 5.46159i) q^{91} +1.32689 q^{92} +(-0.191136 - 0.331058i) q^{93} -6.34903 q^{94} +(2.11862 - 3.66956i) q^{95} +(-2.93100 + 5.07665i) q^{96} +(-1.79870 - 3.11544i) q^{97} +(-5.30936 - 0.00519069i) q^{98} +4.48772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.379240 + 0.656863i 0.268163 + 0.464472i 0.968388 0.249451i \(-0.0802500\pi\)
−0.700224 + 0.713923i \(0.746917\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.712354 1.23383i 0.356177 0.616917i
\(5\) −0.357869 + 0.619848i −0.160044 + 0.277204i −0.934884 0.354953i \(-0.884497\pi\)
0.774840 + 0.632157i \(0.217830\pi\)
\(6\) −0.379240 0.656863i −0.154824 0.268163i
\(7\) −1.32176 2.29193i −0.499577 0.866270i
\(8\) 2.59757 0.918381
\(9\) 1.00000 0.333333
\(10\) −0.542874 −0.171672
\(11\) 4.48772 1.35310 0.676549 0.736398i \(-0.263475\pi\)
0.676549 + 0.736398i \(0.263475\pi\)
\(12\) −0.712354 + 1.23383i −0.205639 + 0.356177i
\(13\) 3.26504 1.52954i 0.905560 0.424217i
\(14\) 1.00422 1.73741i 0.268390 0.464341i
\(15\) 0.357869 0.619848i 0.0924015 0.160044i
\(16\) −0.439604 0.761417i −0.109901 0.190354i
\(17\) 1.88727 3.26885i 0.457730 0.792812i −0.541110 0.840952i \(-0.681996\pi\)
0.998841 + 0.0481394i \(0.0153292\pi\)
\(18\) 0.379240 + 0.656863i 0.0893877 + 0.154824i
\(19\) −5.92010 −1.35816 −0.679082 0.734062i \(-0.737622\pi\)
−0.679082 + 0.734062i \(0.737622\pi\)
\(20\) 0.509859 + 0.883102i 0.114008 + 0.197468i
\(21\) 1.32176 + 2.29193i 0.288431 + 0.500141i
\(22\) 1.70192 + 2.94782i 0.362851 + 0.628477i
\(23\) 0.465673 + 0.806569i 0.0970995 + 0.168181i 0.910483 0.413547i \(-0.135710\pi\)
−0.813383 + 0.581728i \(0.802377\pi\)
\(24\) −2.59757 −0.530227
\(25\) 2.24386 + 3.88648i 0.448772 + 0.777296i
\(26\) 2.24293 + 1.56463i 0.439875 + 0.306848i
\(27\) −1.00000 −0.192450
\(28\) −3.76942 0.00184259i −0.712354 0.000348216i
\(29\) −1.12150 + 1.94250i −0.208257 + 0.360713i −0.951166 0.308681i \(-0.900113\pi\)
0.742908 + 0.669393i \(0.233446\pi\)
\(30\) 0.542874 0.0991147
\(31\) 0.191136 + 0.331058i 0.0343291 + 0.0594597i 0.882679 0.469975i \(-0.155737\pi\)
−0.848350 + 0.529435i \(0.822404\pi\)
\(32\) 2.93100 5.07665i 0.518133 0.897433i
\(33\) −4.48772 −0.781211
\(34\) 2.86291 0.490986
\(35\) 1.89367 0.000925671i 0.320088 0.000156467i
\(36\) 0.712354 1.23383i 0.118726 0.205639i
\(37\) 0.328723 + 0.569365i 0.0540417 + 0.0936030i 0.891781 0.452468i \(-0.149456\pi\)
−0.837739 + 0.546071i \(0.816123\pi\)
\(38\) −2.24514 3.88870i −0.364210 0.630830i
\(39\) −3.26504 + 1.52954i −0.522826 + 0.244922i
\(40\) −0.929592 + 1.61010i −0.146981 + 0.254579i
\(41\) −2.29549 + 3.97591i −0.358495 + 0.620932i −0.987710 0.156300i \(-0.950043\pi\)
0.629214 + 0.777232i \(0.283377\pi\)
\(42\) −1.00422 + 1.73741i −0.154955 + 0.268088i
\(43\) −2.50110 4.33202i −0.381413 0.660627i 0.609851 0.792516i \(-0.291229\pi\)
−0.991265 + 0.131889i \(0.957896\pi\)
\(44\) 3.19684 5.53710i 0.481942 0.834749i
\(45\) −0.357869 + 0.619848i −0.0533480 + 0.0924015i
\(46\) −0.353203 + 0.611766i −0.0520770 + 0.0902000i
\(47\) −4.18536 + 7.24926i −0.610498 + 1.05741i 0.380659 + 0.924716i \(0.375697\pi\)
−0.991157 + 0.132698i \(0.957636\pi\)
\(48\) 0.439604 + 0.761417i 0.0634514 + 0.109901i
\(49\) −3.50593 + 6.05875i −0.500846 + 0.865536i
\(50\) −1.70192 + 2.94782i −0.240688 + 0.416884i
\(51\) −1.88727 + 3.26885i −0.264271 + 0.457730i
\(52\) 0.438674 5.11809i 0.0608332 0.709752i
\(53\) −1.21338 2.10164i −0.166671 0.288682i 0.770577 0.637347i \(-0.219968\pi\)
−0.937247 + 0.348665i \(0.886635\pi\)
\(54\) −0.379240 0.656863i −0.0516080 0.0893877i
\(55\) −1.60602 + 2.78170i −0.216555 + 0.375085i
\(56\) −3.43336 5.95347i −0.458802 0.795565i
\(57\) 5.92010 0.784137
\(58\) −1.70127 −0.223388
\(59\) −2.80700 + 4.86187i −0.365441 + 0.632962i −0.988847 0.148937i \(-0.952415\pi\)
0.623406 + 0.781898i \(0.285748\pi\)
\(60\) −0.509859 0.883102i −0.0658225 0.114008i
\(61\) 1.99378 0.255277 0.127639 0.991821i \(-0.459260\pi\)
0.127639 + 0.991821i \(0.459260\pi\)
\(62\) −0.144973 + 0.251101i −0.0184116 + 0.0318898i
\(63\) −1.32176 2.29193i −0.166526 0.288757i
\(64\) 2.68780 0.335975
\(65\) −0.220379 + 2.57121i −0.0273347 + 0.318919i
\(66\) −1.70192 2.94782i −0.209492 0.362851i
\(67\) −14.4655 −1.76724 −0.883618 0.468208i \(-0.844900\pi\)
−0.883618 + 0.468208i \(0.844900\pi\)
\(68\) −2.68881 4.65715i −0.326066 0.564763i
\(69\) −0.465673 0.806569i −0.0560604 0.0970995i
\(70\) 0.717546 + 1.24423i 0.0857632 + 0.148714i
\(71\) 2.14741 + 3.71943i 0.254851 + 0.441415i 0.964855 0.262783i \(-0.0846402\pi\)
−0.710004 + 0.704198i \(0.751307\pi\)
\(72\) 2.59757 0.306127
\(73\) −1.34127 2.32315i −0.156984 0.271905i 0.776796 0.629753i \(-0.216844\pi\)
−0.933780 + 0.357848i \(0.883511\pi\)
\(74\) −0.249330 + 0.431852i −0.0289840 + 0.0502018i
\(75\) −2.24386 3.88648i −0.259099 0.448772i
\(76\) −4.21721 + 7.30442i −0.483747 + 0.837874i
\(77\) −5.93167 10.2856i −0.675976 1.17215i
\(78\) −2.24293 1.56463i −0.253962 0.177159i
\(79\) 2.75173 4.76614i 0.309594 0.536233i −0.668679 0.743551i \(-0.733140\pi\)
0.978274 + 0.207318i \(0.0664735\pi\)
\(80\) 0.629283 0.0703560
\(81\) 1.00000 0.111111
\(82\) −3.48217 −0.384541
\(83\) 11.5302 1.26560 0.632800 0.774316i \(-0.281906\pi\)
0.632800 + 0.774316i \(0.281906\pi\)
\(84\) 3.76942 + 0.00184259i 0.411278 + 0.000201043i
\(85\) 1.35079 + 2.33964i 0.146514 + 0.253770i
\(86\) 1.89703 3.28575i 0.204562 0.354312i
\(87\) 1.12150 1.94250i 0.120238 0.208257i
\(88\) 11.6572 1.24266
\(89\) 6.05088 + 10.4804i 0.641392 + 1.11092i 0.985122 + 0.171856i \(0.0549763\pi\)
−0.343730 + 0.939069i \(0.611690\pi\)
\(90\) −0.542874 −0.0572239
\(91\) −7.82119 5.46159i −0.819883 0.572531i
\(92\) 1.32689 0.138338
\(93\) −0.191136 0.331058i −0.0198199 0.0343291i
\(94\) −6.34903 −0.654852
\(95\) 2.11862 3.66956i 0.217366 0.376489i
\(96\) −2.93100 + 5.07665i −0.299144 + 0.518133i
\(97\) −1.79870 3.11544i −0.182630 0.316325i 0.760145 0.649753i \(-0.225128\pi\)
−0.942775 + 0.333429i \(0.891794\pi\)
\(98\) −5.30936 0.00519069i −0.536326 0.000524339i
\(99\) 4.48772 0.451033
\(100\) 6.39369 0.639369
\(101\) 11.9792 1.19197 0.595986 0.802995i \(-0.296761\pi\)
0.595986 + 0.802995i \(0.296761\pi\)
\(102\) −2.86291 −0.283471
\(103\) −1.54966 + 2.68409i −0.152692 + 0.264471i −0.932216 0.361901i \(-0.882128\pi\)
0.779524 + 0.626372i \(0.215461\pi\)
\(104\) 8.48119 3.97308i 0.831649 0.389593i
\(105\) −1.89367 0.000925671i −0.184803 9.03363e-5i
\(106\) 0.920325 1.59405i 0.0893898 0.154828i
\(107\) −5.59313 9.68758i −0.540708 0.936534i −0.998864 0.0476618i \(-0.984823\pi\)
0.458155 0.888872i \(-0.348510\pi\)
\(108\) −0.712354 + 1.23383i −0.0685463 + 0.118726i
\(109\) 10.1906 + 17.6506i 0.976082 + 1.69062i 0.676316 + 0.736611i \(0.263575\pi\)
0.299766 + 0.954013i \(0.403091\pi\)
\(110\) −2.43626 −0.232289
\(111\) −0.328723 0.569365i −0.0312010 0.0540417i
\(112\) −1.16407 + 2.01395i −0.109994 + 0.190300i
\(113\) 8.55107 + 14.8109i 0.804417 + 1.39329i 0.916684 + 0.399613i \(0.130856\pi\)
−0.112266 + 0.993678i \(0.535811\pi\)
\(114\) 2.24514 + 3.88870i 0.210277 + 0.364210i
\(115\) −0.666600 −0.0621608
\(116\) 1.59781 + 2.76749i 0.148353 + 0.256955i
\(117\) 3.26504 1.52954i 0.301853 0.141406i
\(118\) −4.25811 −0.391991
\(119\) −9.98650 0.00488165i −0.915461 0.000447500i
\(120\) 0.929592 1.61010i 0.0848597 0.146981i
\(121\) 9.13961 0.830874
\(122\) 0.756122 + 1.30964i 0.0684560 + 0.118569i
\(123\) 2.29549 3.97591i 0.206977 0.358495i
\(124\) 0.544627 0.0489089
\(125\) −6.79073 −0.607381
\(126\) 1.00422 1.73741i 0.0894634 0.154780i
\(127\) 9.01920 15.6217i 0.800325 1.38620i −0.119077 0.992885i \(-0.537994\pi\)
0.919402 0.393318i \(-0.128673\pi\)
\(128\) −4.84269 8.38778i −0.428037 0.741382i
\(129\) 2.50110 + 4.33202i 0.220209 + 0.381413i
\(130\) −1.77251 + 0.830345i −0.155459 + 0.0728261i
\(131\) −9.83728 + 17.0387i −0.859487 + 1.48868i 0.0129316 + 0.999916i \(0.495884\pi\)
−0.872419 + 0.488759i \(0.837450\pi\)
\(132\) −3.19684 + 5.53710i −0.278250 + 0.481942i
\(133\) 7.82493 + 13.5685i 0.678507 + 1.17654i
\(134\) −5.48588 9.50182i −0.473908 0.820832i
\(135\) 0.357869 0.619848i 0.0308005 0.0533480i
\(136\) 4.90232 8.49107i 0.420371 0.728104i
\(137\) −9.64137 + 16.6993i −0.823718 + 1.42672i 0.0791773 + 0.996861i \(0.474771\pi\)
−0.902895 + 0.429861i \(0.858563\pi\)
\(138\) 0.353203 0.611766i 0.0300667 0.0520770i
\(139\) −1.31388 2.27571i −0.111442 0.193023i 0.804910 0.593397i \(-0.202214\pi\)
−0.916352 + 0.400374i \(0.868880\pi\)
\(140\) 1.35010 2.33581i 0.114105 0.197412i
\(141\) 4.18536 7.24926i 0.352471 0.610498i
\(142\) −1.62877 + 2.82111i −0.136683 + 0.236743i
\(143\) 14.6526 6.86413i 1.22531 0.574007i
\(144\) −0.439604 0.761417i −0.0366337 0.0634514i
\(145\) −0.802702 1.39032i −0.0666607 0.115460i
\(146\) 1.01733 1.76207i 0.0841948 0.145830i
\(147\) 3.50593 6.05875i 0.289164 0.499718i
\(148\) 0.936669 0.0769937
\(149\) −15.5896 −1.27715 −0.638573 0.769561i \(-0.720475\pi\)
−0.638573 + 0.769561i \(0.720475\pi\)
\(150\) 1.70192 2.94782i 0.138961 0.240688i
\(151\) 4.61134 + 7.98707i 0.375265 + 0.649978i 0.990367 0.138470i \(-0.0442183\pi\)
−0.615102 + 0.788448i \(0.710885\pi\)
\(152\) −15.3779 −1.24731
\(153\) 1.88727 3.26885i 0.152577 0.264271i
\(154\) 4.50668 7.79699i 0.363158 0.628299i
\(155\) −0.273607 −0.0219767
\(156\) −0.438674 + 5.11809i −0.0351221 + 0.409775i
\(157\) −9.20539 15.9442i −0.734670 1.27249i −0.954868 0.297031i \(-0.904003\pi\)
0.220197 0.975455i \(-0.429330\pi\)
\(158\) 4.17427 0.332087
\(159\) 1.21338 + 2.10164i 0.0962273 + 0.166671i
\(160\) 2.09783 + 3.63355i 0.165848 + 0.287258i
\(161\) 1.23310 2.13338i 0.0971817 0.168134i
\(162\) 0.379240 + 0.656863i 0.0297959 + 0.0516080i
\(163\) 11.1686 0.874793 0.437396 0.899269i \(-0.355901\pi\)
0.437396 + 0.899269i \(0.355901\pi\)
\(164\) 3.27040 + 5.66451i 0.255376 + 0.442324i
\(165\) 1.60602 2.78170i 0.125028 0.216555i
\(166\) 4.37270 + 7.57374i 0.339387 + 0.587836i
\(167\) 7.09719 12.2927i 0.549197 0.951237i −0.449133 0.893465i \(-0.648267\pi\)
0.998330 0.0577721i \(-0.0183997\pi\)
\(168\) 3.43336 + 5.95347i 0.264889 + 0.459320i
\(169\) 8.32104 9.98801i 0.640080 0.768309i
\(170\) −1.02455 + 1.77457i −0.0785794 + 0.136103i
\(171\) −5.92010 −0.452722
\(172\) −7.12666 −0.543403
\(173\) 19.2725 1.46526 0.732630 0.680627i \(-0.238293\pi\)
0.732630 + 0.680627i \(0.238293\pi\)
\(174\) 1.70127 0.128973
\(175\) 5.94172 10.2798i 0.449152 0.777076i
\(176\) −1.97282 3.41702i −0.148707 0.257568i
\(177\) 2.80700 4.86187i 0.210987 0.365441i
\(178\) −4.58948 + 7.94921i −0.343996 + 0.595818i
\(179\) −11.2324 −0.839553 −0.419776 0.907628i \(-0.637891\pi\)
−0.419776 + 0.907628i \(0.637891\pi\)
\(180\) 0.509859 + 0.883102i 0.0380027 + 0.0658225i
\(181\) 2.43304 0.180846 0.0904232 0.995903i \(-0.471178\pi\)
0.0904232 + 0.995903i \(0.471178\pi\)
\(182\) 0.621412 7.20871i 0.0460621 0.534345i
\(183\) −1.99378 −0.147385
\(184\) 1.20962 + 2.09512i 0.0891743 + 0.154454i
\(185\) −0.470560 −0.0345962
\(186\) 0.144973 0.251101i 0.0106299 0.0184116i
\(187\) 8.46954 14.6697i 0.619354 1.07275i
\(188\) 5.96292 + 10.3281i 0.434890 + 0.753252i
\(189\) 1.32176 + 2.29193i 0.0961436 + 0.166714i
\(190\) 3.21387 0.233158
\(191\) −13.7391 −0.994124 −0.497062 0.867715i \(-0.665588\pi\)
−0.497062 + 0.867715i \(0.665588\pi\)
\(192\) −2.68780 −0.193975
\(193\) −13.8673 −0.998187 −0.499094 0.866548i \(-0.666334\pi\)
−0.499094 + 0.866548i \(0.666334\pi\)
\(194\) 1.36428 2.36300i 0.0979493 0.169653i
\(195\) 0.220379 2.57121i 0.0157817 0.184128i
\(196\) 4.97803 + 8.64170i 0.355574 + 0.617265i
\(197\) −9.15733 + 15.8610i −0.652433 + 1.13005i 0.330098 + 0.943947i \(0.392918\pi\)
−0.982531 + 0.186100i \(0.940415\pi\)
\(198\) 1.70192 + 2.94782i 0.120950 + 0.209492i
\(199\) 3.55862 6.16371i 0.252264 0.436933i −0.711885 0.702296i \(-0.752158\pi\)
0.964149 + 0.265363i \(0.0854916\pi\)
\(200\) 5.82859 + 10.0954i 0.412143 + 0.713853i
\(201\) 14.4655 1.02031
\(202\) 4.54298 + 7.86867i 0.319643 + 0.553638i
\(203\) 5.93442 + 0.00290089i 0.416515 + 0.000203603i
\(204\) 2.68881 + 4.65715i 0.188254 + 0.326066i
\(205\) −1.64297 2.84571i −0.114750 0.198753i
\(206\) −2.35077 −0.163786
\(207\) 0.465673 + 0.806569i 0.0323665 + 0.0560604i
\(208\) −2.59994 1.81367i −0.180274 0.125755i
\(209\) −26.5678 −1.83773
\(210\) −0.717546 1.24423i −0.0495154 0.0858601i
\(211\) −5.95003 + 10.3058i −0.409617 + 0.709478i −0.994847 0.101390i \(-0.967671\pi\)
0.585230 + 0.810868i \(0.301004\pi\)
\(212\) −3.45742 −0.237457
\(213\) −2.14741 3.71943i −0.147138 0.254851i
\(214\) 4.24228 7.34784i 0.289996 0.502288i
\(215\) 3.58026 0.244172
\(216\) −2.59757 −0.176742
\(217\) 0.506127 0.875649i 0.0343581 0.0594429i
\(218\) −7.72937 + 13.3877i −0.523499 + 0.906726i
\(219\) 1.34127 + 2.32315i 0.0906349 + 0.156984i
\(220\) 2.28810 + 3.96311i 0.154264 + 0.267193i
\(221\) 1.16220 13.5596i 0.0781780 0.912117i
\(222\) 0.249330 0.431852i 0.0167339 0.0289840i
\(223\) 11.9432 20.6863i 0.799778 1.38526i −0.119982 0.992776i \(-0.538284\pi\)
0.919760 0.392481i \(-0.128383\pi\)
\(224\) −15.5094 0.00758139i −1.03627 0.000506553i
\(225\) 2.24386 + 3.88648i 0.149591 + 0.259099i
\(226\) −6.48582 + 11.2338i −0.431430 + 0.747259i
\(227\) −6.29391 + 10.9014i −0.417741 + 0.723549i −0.995712 0.0925083i \(-0.970512\pi\)
0.577971 + 0.816058i \(0.303845\pi\)
\(228\) 4.21721 7.30442i 0.279291 0.483747i
\(229\) 7.66365 13.2738i 0.506429 0.877160i −0.493544 0.869721i \(-0.664299\pi\)
0.999972 0.00743905i \(-0.00236795\pi\)
\(230\) −0.252801 0.437865i −0.0166692 0.0288720i
\(231\) 5.93167 + 10.2856i 0.390275 + 0.676740i
\(232\) −2.91318 + 5.04578i −0.191260 + 0.331271i
\(233\) 13.3343 23.0957i 0.873559 1.51305i 0.0152699 0.999883i \(-0.495139\pi\)
0.858289 0.513166i \(-0.171527\pi\)
\(234\) 2.24293 + 1.56463i 0.146625 + 0.102283i
\(235\) −2.99563 5.18858i −0.195413 0.338465i
\(236\) 3.99916 + 6.92675i 0.260323 + 0.450893i
\(237\) −2.75173 + 4.76614i −0.178744 + 0.309594i
\(238\) −3.78407 6.56161i −0.245285 0.425326i
\(239\) −14.5891 −0.943693 −0.471846 0.881681i \(-0.656412\pi\)
−0.471846 + 0.881681i \(0.656412\pi\)
\(240\) −0.629283 −0.0406201
\(241\) −6.44615 + 11.1651i −0.415233 + 0.719204i −0.995453 0.0952555i \(-0.969633\pi\)
0.580220 + 0.814460i \(0.302967\pi\)
\(242\) 3.46611 + 6.00347i 0.222810 + 0.385918i
\(243\) −1.00000 −0.0641500
\(244\) 1.42028 2.45999i 0.0909240 0.157485i
\(245\) −2.50084 4.34138i −0.159773 0.277361i
\(246\) 3.48217 0.222015
\(247\) −19.3294 + 9.05501i −1.22990 + 0.576157i
\(248\) 0.496490 + 0.859947i 0.0315272 + 0.0546067i
\(249\) −11.5302 −0.730694
\(250\) −2.57532 4.46058i −0.162877 0.282112i
\(251\) −12.0203 20.8198i −0.758717 1.31414i −0.943505 0.331359i \(-0.892493\pi\)
0.184787 0.982779i \(-0.440840\pi\)
\(252\) −3.76942 0.00184259i −0.237451 0.000116072i
\(253\) 2.08981 + 3.61965i 0.131385 + 0.227566i
\(254\) 13.6818 0.858471
\(255\) −1.35079 2.33964i −0.0845899 0.146514i
\(256\) 6.36088 11.0174i 0.397555 0.688586i
\(257\) −9.35724 16.2072i −0.583689 1.01098i −0.995038 0.0995004i \(-0.968276\pi\)
0.411349 0.911478i \(-0.365058\pi\)
\(258\) −1.89703 + 3.28575i −0.118104 + 0.204562i
\(259\) 0.870456 1.50597i 0.0540875 0.0935766i
\(260\) 3.01545 + 2.10352i 0.187010 + 0.130455i
\(261\) −1.12150 + 1.94250i −0.0694192 + 0.120238i
\(262\) −14.9228 −0.921931
\(263\) −9.37129 −0.577859 −0.288929 0.957350i \(-0.593299\pi\)
−0.288929 + 0.957350i \(0.593299\pi\)
\(264\) −11.6572 −0.717450
\(265\) 1.73693 0.106699
\(266\) −5.94511 + 10.2856i −0.364518 + 0.630652i
\(267\) −6.05088 10.4804i −0.370308 0.641392i
\(268\) −10.3045 + 17.8480i −0.629449 + 1.09024i
\(269\) −6.07464 + 10.5216i −0.370377 + 0.641512i −0.989624 0.143685i \(-0.954105\pi\)
0.619246 + 0.785197i \(0.287438\pi\)
\(270\) 0.542874 0.0330382
\(271\) 7.32926 + 12.6946i 0.445221 + 0.771145i 0.998068 0.0621380i \(-0.0197919\pi\)
−0.552847 + 0.833283i \(0.686459\pi\)
\(272\) −3.31861 −0.201220
\(273\) 7.82119 + 5.46159i 0.473360 + 0.330551i
\(274\) −14.6256 −0.883563
\(275\) 10.0698 + 17.4414i 0.607232 + 1.05176i
\(276\) −1.32689 −0.0798697
\(277\) 2.51608 4.35797i 0.151176 0.261845i −0.780484 0.625176i \(-0.785027\pi\)
0.931660 + 0.363331i \(0.118361\pi\)
\(278\) 0.996555 1.72608i 0.0597694 0.103524i
\(279\) 0.191136 + 0.331058i 0.0114430 + 0.0198199i
\(280\) 4.91894 + 0.00240450i 0.293963 + 0.000143696i
\(281\) 0.854888 0.0509984 0.0254992 0.999675i \(-0.491882\pi\)
0.0254992 + 0.999675i \(0.491882\pi\)
\(282\) 6.34903 0.378079
\(283\) −31.2774 −1.85925 −0.929625 0.368506i \(-0.879869\pi\)
−0.929625 + 0.368506i \(0.879869\pi\)
\(284\) 6.11888 0.363088
\(285\) −2.11862 + 3.66956i −0.125496 + 0.217366i
\(286\) 10.0656 + 7.02160i 0.595194 + 0.415196i
\(287\) 12.1466 + 0.00593756i 0.716991 + 0.000350483i
\(288\) 2.93100 5.07665i 0.172711 0.299144i
\(289\) 1.37642 + 2.38403i 0.0809657 + 0.140237i
\(290\) 0.608833 1.05453i 0.0357519 0.0619241i
\(291\) 1.79870 + 3.11544i 0.105442 + 0.182630i
\(292\) −3.82185 −0.223657
\(293\) 0.339044 + 0.587241i 0.0198071 + 0.0343070i 0.875759 0.482748i \(-0.160361\pi\)
−0.855952 + 0.517055i \(0.827028\pi\)
\(294\) 5.30936 + 0.00519069i 0.309648 + 0.000302727i
\(295\) −2.00908 3.47983i −0.116973 0.202603i
\(296\) 0.853882 + 1.47897i 0.0496309 + 0.0859632i
\(297\) −4.48772 −0.260404
\(298\) −5.91219 10.2402i −0.342484 0.593199i
\(299\) 2.75412 + 1.92122i 0.159275 + 0.111107i
\(300\) −6.39369 −0.369140
\(301\) −6.62288 + 11.4582i −0.381736 + 0.660441i
\(302\) −3.49761 + 6.05803i −0.201265 + 0.348601i
\(303\) −11.9792 −0.688185
\(304\) 2.60250 + 4.50766i 0.149264 + 0.258532i
\(305\) −0.713513 + 1.23584i −0.0408556 + 0.0707640i
\(306\) 2.86291 0.163662
\(307\) −27.2103 −1.55297 −0.776487 0.630134i \(-0.783000\pi\)
−0.776487 + 0.630134i \(0.783000\pi\)
\(308\) −16.9161 0.00826901i −0.963885 0.000471171i
\(309\) 1.54966 2.68409i 0.0881569 0.152692i
\(310\) −0.103763 0.179722i −0.00589333 0.0102076i
\(311\) 7.06426 + 12.2357i 0.400577 + 0.693821i 0.993796 0.111221i \(-0.0354762\pi\)
−0.593218 + 0.805042i \(0.702143\pi\)
\(312\) −8.48119 + 3.97308i −0.480153 + 0.224932i
\(313\) 9.84907 17.0591i 0.556703 0.964237i −0.441066 0.897475i \(-0.645400\pi\)
0.997769 0.0667627i \(-0.0212670\pi\)
\(314\) 6.98211 12.0934i 0.394023 0.682468i
\(315\) 1.89367 0.000925671i 0.106696 5.21557e-5i
\(316\) −3.92042 6.79036i −0.220541 0.381988i
\(317\) −7.83931 + 13.5781i −0.440299 + 0.762621i −0.997711 0.0676152i \(-0.978461\pi\)
0.557412 + 0.830236i \(0.311794\pi\)
\(318\) −0.920325 + 1.59405i −0.0516092 + 0.0893898i
\(319\) −5.03298 + 8.71738i −0.281793 + 0.488079i
\(320\) −0.961881 + 1.66603i −0.0537708 + 0.0931338i
\(321\) 5.59313 + 9.68758i 0.312178 + 0.540708i
\(322\) 1.86898 0.000913602i 0.104154 5.09131e-5i
\(323\) −11.1728 + 19.3519i −0.621673 + 1.07677i
\(324\) 0.712354 1.23383i 0.0395752 0.0685463i
\(325\) 13.2708 + 9.25746i 0.736132 + 0.513511i
\(326\) 4.23558 + 7.33625i 0.234587 + 0.406317i
\(327\) −10.1906 17.6506i −0.563541 0.976082i
\(328\) −5.96270 + 10.3277i −0.329235 + 0.570252i
\(329\) 22.1469 + 0.0108259i 1.22100 + 0.000596853i
\(330\) 2.43626 0.134112
\(331\) 14.4236 0.792793 0.396396 0.918079i \(-0.370261\pi\)
0.396396 + 0.918079i \(0.370261\pi\)
\(332\) 8.21355 14.2263i 0.450777 0.780769i
\(333\) 0.328723 + 0.569365i 0.0180139 + 0.0312010i
\(334\) 10.7662 0.589098
\(335\) 5.17674 8.96638i 0.282836 0.489886i
\(336\) 1.16407 2.01395i 0.0635051 0.109870i
\(337\) 14.4299 0.786049 0.393025 0.919528i \(-0.371429\pi\)
0.393025 + 0.919528i \(0.371429\pi\)
\(338\) 9.71643 + 1.67793i 0.528504 + 0.0912672i
\(339\) −8.55107 14.8109i −0.464431 0.804417i
\(340\) 3.84897 0.208740
\(341\) 0.857766 + 1.48569i 0.0464506 + 0.0804548i
\(342\) −2.24514 3.88870i −0.121403 0.210277i
\(343\) 18.5202 + 0.0271595i 0.999999 + 0.00146647i
\(344\) −6.49678 11.2527i −0.350283 0.606707i
\(345\) 0.666600 0.0358885
\(346\) 7.30890 + 12.6594i 0.392929 + 0.680573i
\(347\) 2.33434 4.04319i 0.125314 0.217050i −0.796542 0.604584i \(-0.793340\pi\)
0.921856 + 0.387534i \(0.126673\pi\)
\(348\) −1.59781 2.76749i −0.0856517 0.148353i
\(349\) 2.06807 3.58201i 0.110701 0.191740i −0.805352 0.592797i \(-0.798024\pi\)
0.916053 + 0.401057i \(0.131357\pi\)
\(350\) 9.00573 + 0.00440222i 0.481376 + 0.000235309i
\(351\) −3.26504 + 1.52954i −0.174275 + 0.0816406i
\(352\) 13.1535 22.7826i 0.701085 1.21431i
\(353\) 35.7899 1.90491 0.952453 0.304684i \(-0.0985509\pi\)
0.952453 + 0.304684i \(0.0985509\pi\)
\(354\) 4.25811 0.226316
\(355\) −3.07397 −0.163150
\(356\) 17.2415 0.913797
\(357\) 9.98650 + 0.00488165i 0.528541 + 0.000258364i
\(358\) −4.25979 7.37818i −0.225137 0.389949i
\(359\) 12.6381 21.8899i 0.667014 1.15530i −0.311721 0.950174i \(-0.600905\pi\)
0.978735 0.205129i \(-0.0657614\pi\)
\(360\) −0.929592 + 1.61010i −0.0489938 + 0.0848597i
\(361\) 16.0476 0.844611
\(362\) 0.922706 + 1.59817i 0.0484964 + 0.0839982i
\(363\) −9.13961 −0.479705
\(364\) −12.3102 + 5.75945i −0.645227 + 0.301877i
\(365\) 1.92000 0.100498
\(366\) −0.756122 1.30964i −0.0395231 0.0684560i
\(367\) 35.3997 1.84785 0.923925 0.382573i \(-0.124962\pi\)
0.923925 + 0.382573i \(0.124962\pi\)
\(368\) 0.409423 0.709142i 0.0213427 0.0369666i
\(369\) −2.29549 + 3.97591i −0.119498 + 0.206977i
\(370\) −0.178455 0.309093i −0.00927744 0.0160690i
\(371\) −3.21302 + 5.55884i −0.166812 + 0.288600i
\(372\) −0.544627 −0.0282376
\(373\) −32.7804 −1.69730 −0.848652 0.528951i \(-0.822586\pi\)
−0.848652 + 0.528951i \(0.822586\pi\)
\(374\) 12.8480 0.664352
\(375\) 6.79073 0.350672
\(376\) −10.8718 + 18.8305i −0.560669 + 0.971108i
\(377\) −0.690631 + 8.05771i −0.0355693 + 0.414993i
\(378\) −1.00422 + 1.73741i −0.0516517 + 0.0893625i
\(379\) −6.04308 + 10.4669i −0.310412 + 0.537650i −0.978452 0.206476i \(-0.933800\pi\)
0.668039 + 0.744126i \(0.267134\pi\)
\(380\) −3.01842 5.22806i −0.154842 0.268194i
\(381\) −9.01920 + 15.6217i −0.462068 + 0.800325i
\(382\) −5.21040 9.02468i −0.266587 0.461743i
\(383\) −0.512172 −0.0261708 −0.0130854 0.999914i \(-0.504165\pi\)
−0.0130854 + 0.999914i \(0.504165\pi\)
\(384\) 4.84269 + 8.38778i 0.247127 + 0.428037i
\(385\) 8.49824 + 0.00415415i 0.433110 + 0.000211715i
\(386\) −5.25902 9.10889i −0.267677 0.463630i
\(387\) −2.50110 4.33202i −0.127138 0.220209i
\(388\) −5.12524 −0.260195
\(389\) −17.7577 30.7573i −0.900353 1.55946i −0.827037 0.562148i \(-0.809975\pi\)
−0.0733162 0.997309i \(-0.523358\pi\)
\(390\) 1.77251 0.830345i 0.0897544 0.0420462i
\(391\) 3.51540 0.177781
\(392\) −9.10690 + 15.7381i −0.459968 + 0.794892i
\(393\) 9.83728 17.0387i 0.496225 0.859487i
\(394\) −13.8913 −0.699834
\(395\) 1.96952 + 3.41131i 0.0990974 + 0.171642i
\(396\) 3.19684 5.53710i 0.160647 0.278250i
\(397\) −8.29730 −0.416430 −0.208215 0.978083i \(-0.566765\pi\)
−0.208215 + 0.978083i \(0.566765\pi\)
\(398\) 5.39828 0.270591
\(399\) −7.82493 13.5685i −0.391736 0.679274i
\(400\) 1.97282 3.41702i 0.0986410 0.170851i
\(401\) −6.96021 12.0554i −0.347576 0.602019i 0.638242 0.769836i \(-0.279662\pi\)
−0.985818 + 0.167816i \(0.946329\pi\)
\(402\) 5.48588 + 9.50182i 0.273611 + 0.473908i
\(403\) 1.13043 + 0.788568i 0.0563109 + 0.0392814i
\(404\) 8.53341 14.7803i 0.424553 0.735347i
\(405\) −0.357869 + 0.619848i −0.0177827 + 0.0308005i
\(406\) 2.24867 + 3.89920i 0.111599 + 0.193514i
\(407\) 1.47522 + 2.55515i 0.0731238 + 0.126654i
\(408\) −4.90232 + 8.49107i −0.242701 + 0.420371i
\(409\) 2.45871 4.25862i 0.121576 0.210575i −0.798814 0.601579i \(-0.794539\pi\)
0.920389 + 0.391004i \(0.127872\pi\)
\(410\) 1.24616 2.15841i 0.0615435 0.106597i
\(411\) 9.64137 16.6993i 0.475574 0.823718i
\(412\) 2.20781 + 3.82404i 0.108771 + 0.188397i
\(413\) 14.8533 + 0.00726064i 0.730881 + 0.000357273i
\(414\) −0.353203 + 0.611766i −0.0173590 + 0.0300667i
\(415\) −4.12629 + 7.14694i −0.202552 + 0.350830i
\(416\) 1.80494 21.0586i 0.0884945 1.03248i
\(417\) 1.31388 + 2.27571i 0.0643412 + 0.111442i
\(418\) −10.0756 17.4514i −0.492812 0.853575i
\(419\) 4.85147 8.40299i 0.237010 0.410513i −0.722845 0.691010i \(-0.757166\pi\)
0.959855 + 0.280497i \(0.0904993\pi\)
\(420\) −1.35010 + 2.33581i −0.0658783 + 0.113976i
\(421\) −15.2944 −0.745405 −0.372702 0.927951i \(-0.621569\pi\)
−0.372702 + 0.927951i \(0.621569\pi\)
\(422\) −9.02596 −0.439377
\(423\) −4.18536 + 7.24926i −0.203499 + 0.352471i
\(424\) −3.15184 5.45915i −0.153067 0.265120i
\(425\) 16.9391 0.821666
\(426\) 1.62877 2.82111i 0.0789142 0.136683i
\(427\) −2.63529 4.56961i −0.127531 0.221139i
\(428\) −15.9371 −0.770351
\(429\) −14.6526 + 6.86413i −0.707434 + 0.331403i
\(430\) 1.35778 + 2.35174i 0.0654779 + 0.113411i
\(431\) 32.6580 1.57308 0.786541 0.617538i \(-0.211870\pi\)
0.786541 + 0.617538i \(0.211870\pi\)
\(432\) 0.439604 + 0.761417i 0.0211505 + 0.0366337i
\(433\) 9.28189 + 16.0767i 0.446059 + 0.772597i 0.998125 0.0612034i \(-0.0194938\pi\)
−0.552066 + 0.833800i \(0.686160\pi\)
\(434\) 0.767125 0.000374990i 0.0368232 1.80001e-5i
\(435\) 0.802702 + 1.39032i 0.0384866 + 0.0666607i
\(436\) 29.0372 1.39063
\(437\) −2.75683 4.77497i −0.131877 0.228418i
\(438\) −1.01733 + 1.76207i −0.0486099 + 0.0841948i
\(439\) −4.72738 8.18806i −0.225625 0.390795i 0.730881 0.682504i \(-0.239109\pi\)
−0.956507 + 0.291710i \(0.905776\pi\)
\(440\) −4.17175 + 7.22568i −0.198880 + 0.344471i
\(441\) −3.50593 + 6.05875i −0.166949 + 0.288512i
\(442\) 9.34755 4.37893i 0.444617 0.208285i
\(443\) −3.71593 + 6.43618i −0.176549 + 0.305792i −0.940696 0.339250i \(-0.889827\pi\)
0.764147 + 0.645042i \(0.223160\pi\)
\(444\) −0.936669 −0.0444523
\(445\) −8.66170 −0.410604
\(446\) 18.1174 0.857885
\(447\) 15.5896 0.737361
\(448\) −3.55261 6.16026i −0.167845 0.291045i
\(449\) −9.42362 16.3222i −0.444728 0.770291i 0.553305 0.832979i \(-0.313366\pi\)
−0.998033 + 0.0626872i \(0.980033\pi\)
\(450\) −1.70192 + 2.94782i −0.0802294 + 0.138961i
\(451\) −10.3015 + 17.8427i −0.485079 + 0.840182i
\(452\) 24.3656 1.14606
\(453\) −4.61134 7.98707i −0.216659 0.375265i
\(454\) −9.54761 −0.448092
\(455\) 6.18432 2.89341i 0.289925 0.135645i
\(456\) 15.3779 0.720136
\(457\) 3.40003 + 5.88903i 0.159047 + 0.275477i 0.934525 0.355897i \(-0.115825\pi\)
−0.775478 + 0.631374i \(0.782491\pi\)
\(458\) 11.6255 0.543222
\(459\) −1.88727 + 3.26885i −0.0880903 + 0.152577i
\(460\) −0.474855 + 0.822473i −0.0221402 + 0.0383480i
\(461\) −4.80595 8.32415i −0.223836 0.387694i 0.732134 0.681161i \(-0.238525\pi\)
−0.955969 + 0.293466i \(0.905191\pi\)
\(462\) −4.50668 + 7.79699i −0.209670 + 0.362749i
\(463\) −23.4929 −1.09181 −0.545905 0.837847i \(-0.683814\pi\)
−0.545905 + 0.837847i \(0.683814\pi\)
\(464\) 1.97207 0.0915508
\(465\) 0.273607 0.0126882
\(466\) 20.2276 0.937026
\(467\) 7.24654 12.5514i 0.335330 0.580808i −0.648218 0.761455i \(-0.724486\pi\)
0.983548 + 0.180646i \(0.0578189\pi\)
\(468\) 0.438674 5.11809i 0.0202777 0.236584i
\(469\) 19.1198 + 33.1539i 0.882870 + 1.53090i
\(470\) 2.27212 3.93543i 0.104805 0.181528i
\(471\) 9.20539 + 15.9442i 0.424162 + 0.734670i
\(472\) −7.29139 + 12.6291i −0.335614 + 0.581300i
\(473\) −11.2242 19.4409i −0.516090 0.893894i
\(474\) −4.17427 −0.191731
\(475\) −13.2839 23.0083i −0.609506 1.05570i
\(476\) −7.11994 + 12.3182i −0.326342 + 0.564604i
\(477\) −1.21338 2.10164i −0.0555569 0.0962273i
\(478\) −5.53279 9.58307i −0.253064 0.438319i
\(479\) 14.5134 0.663134 0.331567 0.943432i \(-0.392423\pi\)
0.331567 + 0.943432i \(0.392423\pi\)
\(480\) −2.09783 3.63355i −0.0957525 0.165848i
\(481\) 1.94416 + 1.35621i 0.0886461 + 0.0618378i
\(482\) −9.77855 −0.445401
\(483\) −1.23310 + 2.13338i −0.0561079 + 0.0970720i
\(484\) 6.51064 11.2768i 0.295938 0.512580i
\(485\) 2.57480 0.116915
\(486\) −0.379240 0.656863i −0.0172027 0.0297959i
\(487\) −11.6964 + 20.2587i −0.530013 + 0.918009i 0.469374 + 0.882999i \(0.344480\pi\)
−0.999387 + 0.0350099i \(0.988854\pi\)
\(488\) 5.17899 0.234442
\(489\) −11.1686 −0.505062
\(490\) 1.90327 3.28914i 0.0859812 0.148588i
\(491\) 0.786824 1.36282i 0.0355089 0.0615032i −0.847725 0.530436i \(-0.822028\pi\)
0.883234 + 0.468933i \(0.155361\pi\)
\(492\) −3.27040 5.66451i −0.147441 0.255376i
\(493\) 4.23315 + 7.33203i 0.190652 + 0.330218i
\(494\) −13.2784 9.26275i −0.597423 0.416751i
\(495\) −1.60602 + 2.78170i −0.0721851 + 0.125028i
\(496\) 0.168049 0.291069i 0.00754560 0.0130694i
\(497\) 5.68633 9.83791i 0.255067 0.441291i
\(498\) −4.37270 7.57374i −0.195945 0.339387i
\(499\) −7.86689 + 13.6259i −0.352170 + 0.609977i −0.986629 0.162980i \(-0.947890\pi\)
0.634459 + 0.772956i \(0.281223\pi\)
\(500\) −4.83740 + 8.37862i −0.216335 + 0.374703i
\(501\) −7.09719 + 12.2927i −0.317079 + 0.549197i
\(502\) 9.11719 15.7914i 0.406920 0.704807i
\(503\) 17.7055 + 30.6668i 0.789447 + 1.36736i 0.926306 + 0.376773i \(0.122966\pi\)
−0.136858 + 0.990591i \(0.543701\pi\)
\(504\) −3.43336 5.95347i −0.152934 0.265188i
\(505\) −4.28698 + 7.42526i −0.190768 + 0.330420i
\(506\) −1.58508 + 2.74543i −0.0704653 + 0.122049i
\(507\) −8.32104 + 9.98801i −0.369550 + 0.443583i
\(508\) −12.8497 22.2564i −0.570115 0.987467i
\(509\) 5.20477 + 9.01493i 0.230697 + 0.399580i 0.958014 0.286723i \(-0.0925659\pi\)
−0.727316 + 0.686303i \(0.759233\pi\)
\(510\) 1.02455 1.77457i 0.0453678 0.0785794i
\(511\) −3.55168 + 6.14475i −0.157117 + 0.271828i
\(512\) −9.72154 −0.429635
\(513\) 5.92010 0.261379
\(514\) 7.09728 12.2929i 0.313048 0.542214i
\(515\) −1.10915 1.92110i −0.0488750 0.0846540i
\(516\) 7.12666 0.313734
\(517\) −18.7827 + 32.5326i −0.826063 + 1.43078i
\(518\) 1.31933 0.000644921i 0.0579680 2.83362e-5i
\(519\) −19.2725 −0.845968
\(520\) −0.572451 + 6.67889i −0.0251037 + 0.292889i
\(521\) −0.513222 0.888926i −0.0224847 0.0389446i 0.854564 0.519346i \(-0.173824\pi\)
−0.877049 + 0.480401i \(0.840491\pi\)
\(522\) −1.70127 −0.0744627
\(523\) 9.02138 + 15.6255i 0.394477 + 0.683255i 0.993034 0.117826i \(-0.0375924\pi\)
−0.598557 + 0.801080i \(0.704259\pi\)
\(524\) 14.0153 + 24.2751i 0.612259 + 1.06046i
\(525\) −5.94172 + 10.2798i −0.259318 + 0.448645i
\(526\) −3.55397 6.15566i −0.154960 0.268399i
\(527\) 1.44290 0.0628539
\(528\) 1.97282 + 3.41702i 0.0858559 + 0.148707i
\(529\) 11.0663 19.1674i 0.481143 0.833365i
\(530\) 0.658712 + 1.14092i 0.0286126 + 0.0495585i
\(531\) −2.80700 + 4.86187i −0.121814 + 0.210987i
\(532\) 22.3154 + 0.0109083i 0.967494 + 0.000472935i
\(533\) −1.41359 + 16.4926i −0.0612292 + 0.714372i
\(534\) 4.58948 7.94921i 0.198606 0.343996i
\(535\) 8.00644 0.346148
\(536\) −37.5751 −1.62300
\(537\) 11.2324 0.484716
\(538\) −9.21499 −0.397286
\(539\) −15.7336 + 27.1900i −0.677694 + 1.17116i
\(540\) −0.509859 0.883102i −0.0219408 0.0380027i
\(541\) 16.7318 28.9803i 0.719355 1.24596i −0.241900 0.970301i \(-0.577771\pi\)
0.961256 0.275659i \(-0.0888960\pi\)
\(542\) −5.55910 + 9.62864i −0.238784 + 0.413585i
\(543\) −2.43304 −0.104412
\(544\) −11.0632 19.1620i −0.474331 0.821565i
\(545\) −14.5876 −0.624865
\(546\) −0.621412 + 7.20871i −0.0265940 + 0.308504i
\(547\) 30.7718 1.31571 0.657853 0.753146i \(-0.271465\pi\)
0.657853 + 0.753146i \(0.271465\pi\)
\(548\) 13.7361 + 23.7917i 0.586779 + 1.01633i
\(549\) 1.99378 0.0850925
\(550\) −7.63775 + 13.2290i −0.325675 + 0.564085i
\(551\) 6.63940 11.4998i 0.282848 0.489907i
\(552\) −1.20962 2.09512i −0.0514848 0.0891743i
\(553\) −14.5608 0.00711768i −0.619188 0.000302675i
\(554\) 3.81679 0.162160
\(555\) 0.470560 0.0199741
\(556\) −3.74380 −0.158773
\(557\) 15.6343 0.662446 0.331223 0.943553i \(-0.392539\pi\)
0.331223 + 0.943553i \(0.392539\pi\)
\(558\) −0.144973 + 0.251101i −0.00613720 + 0.0106299i
\(559\) −14.7922 10.3187i −0.625642 0.436436i
\(560\) −0.831759 1.44228i −0.0351482 0.0609473i
\(561\) −8.46954 + 14.6697i −0.357584 + 0.619354i
\(562\) 0.324208 + 0.561545i 0.0136759 + 0.0236873i
\(563\) −16.7621 + 29.0328i −0.706438 + 1.22359i 0.259733 + 0.965681i \(0.416366\pi\)
−0.966170 + 0.257905i \(0.916968\pi\)
\(564\) −5.96292 10.3281i −0.251084 0.434890i
\(565\) −12.2407 −0.514969
\(566\) −11.8617 20.5450i −0.498583 0.863570i
\(567\) −1.32176 2.29193i −0.0555085 0.0962522i
\(568\) 5.57806 + 9.66149i 0.234050 + 0.405387i
\(569\) −10.6031 18.3651i −0.444504 0.769903i 0.553514 0.832840i \(-0.313287\pi\)
−0.998018 + 0.0629368i \(0.979953\pi\)
\(570\) −3.21387 −0.134614
\(571\) −0.869647 1.50627i −0.0363936 0.0630356i 0.847255 0.531187i \(-0.178254\pi\)
−0.883648 + 0.468151i \(0.844920\pi\)
\(572\) 1.96865 22.9686i 0.0823133 0.960364i
\(573\) 13.7391 0.573958
\(574\) 4.60258 + 7.98090i 0.192108 + 0.333116i
\(575\) −2.08981 + 3.61965i −0.0871510 + 0.150950i
\(576\) 2.68780 0.111992
\(577\) −2.83193 4.90504i −0.117895 0.204199i 0.801039 0.598613i \(-0.204281\pi\)
−0.918933 + 0.394413i \(0.870948\pi\)
\(578\) −1.04399 + 1.80824i −0.0434241 + 0.0752127i
\(579\) 13.8673 0.576304
\(580\) −2.28723 −0.0949721
\(581\) −15.2401 26.4264i −0.632264 1.09635i
\(582\) −1.36428 + 2.36300i −0.0565511 + 0.0979493i
\(583\) −5.44531 9.43155i −0.225522 0.390615i
\(584\) −3.48406 6.03456i −0.144171 0.249712i
\(585\) −0.220379 + 2.57121i −0.00911157 + 0.106306i
\(586\) −0.257158 + 0.445411i −0.0106231 + 0.0183997i
\(587\) 8.06910 13.9761i 0.333047 0.576855i −0.650060 0.759882i \(-0.725256\pi\)
0.983108 + 0.183028i \(0.0585898\pi\)
\(588\) −4.97803 8.64170i −0.205291 0.356378i
\(589\) −1.13155 1.95990i −0.0466246 0.0807561i
\(590\) 1.52385 2.63938i 0.0627358 0.108662i
\(591\) 9.15733 15.8610i 0.376682 0.652433i
\(592\) 0.289016 0.500590i 0.0118785 0.0205741i
\(593\) −21.1595 + 36.6493i −0.868917 + 1.50501i −0.00581233 + 0.999983i \(0.501850\pi\)
−0.863105 + 0.505025i \(0.831483\pi\)
\(594\) −1.70192 2.94782i −0.0698307 0.120950i
\(595\) 3.57689 6.18836i 0.146638 0.253698i
\(596\) −11.1053 + 19.2349i −0.454890 + 0.787893i
\(597\) −3.55862 + 6.16371i −0.145644 + 0.252264i
\(598\) −0.217506 + 2.53768i −0.00889448 + 0.103774i
\(599\) 22.9026 + 39.6685i 0.935776 + 1.62081i 0.773244 + 0.634108i \(0.218633\pi\)
0.162532 + 0.986703i \(0.448034\pi\)
\(600\) −5.82859 10.0954i −0.237951 0.412143i
\(601\) 6.27579 10.8700i 0.255995 0.443396i −0.709170 0.705037i \(-0.750930\pi\)
0.965165 + 0.261641i \(0.0842637\pi\)
\(602\) −10.0381 0.00490689i −0.409124 0.000199990i
\(603\) −14.4655 −0.589079
\(604\) 13.1396 0.534643
\(605\) −3.27079 + 5.66517i −0.132976 + 0.230322i
\(606\) −4.54298 7.86867i −0.184546 0.319643i
\(607\) 34.4923 1.40000 0.700000 0.714143i \(-0.253183\pi\)
0.700000 + 0.714143i \(0.253183\pi\)
\(608\) −17.3518 + 30.0543i −0.703710 + 1.21886i
\(609\) −5.93442 0.00290089i −0.240475 0.000117550i
\(610\) −1.08237 −0.0438239
\(611\) −2.57739 + 30.0708i −0.104270 + 1.21654i
\(612\) −2.68881 4.65715i −0.108689 0.188254i
\(613\) −34.1674 −1.38001 −0.690003 0.723806i \(-0.742391\pi\)
−0.690003 + 0.723806i \(0.742391\pi\)
\(614\) −10.3192 17.8734i −0.416450 0.721313i
\(615\) 1.64297 + 2.84571i 0.0662510 + 0.114750i
\(616\) −15.4079 26.7175i −0.620803 1.07648i
\(617\) −18.4048 31.8781i −0.740950 1.28336i −0.952063 0.305902i \(-0.901042\pi\)
0.211113 0.977462i \(-0.432291\pi\)
\(618\) 2.35077 0.0945618
\(619\) −17.9351 31.0644i −0.720871 1.24858i −0.960651 0.277758i \(-0.910409\pi\)
0.239780 0.970827i \(-0.422925\pi\)
\(620\) −0.194905 + 0.337586i −0.00782758 + 0.0135578i
\(621\) −0.465673 0.806569i −0.0186868 0.0323665i
\(622\) −5.35810 + 9.28050i −0.214840 + 0.372114i
\(623\) 16.0227 27.7208i 0.641935 1.11061i
\(624\) 2.59994 + 1.81367i 0.104081 + 0.0726049i
\(625\) −8.78910 + 15.2232i −0.351564 + 0.608927i
\(626\) 14.9407 0.597149
\(627\) 26.5678 1.06101
\(628\) −26.2300 −1.04669
\(629\) 2.48156 0.0989462
\(630\) 0.717546 + 1.24423i 0.0285877 + 0.0495713i
\(631\) −9.93368 17.2056i −0.395453 0.684945i 0.597706 0.801716i \(-0.296079\pi\)
−0.993159 + 0.116770i \(0.962746\pi\)
\(632\) 7.14783 12.3804i 0.284325 0.492466i
\(633\) 5.95003 10.3058i 0.236493 0.409617i
\(634\) −11.8919 −0.472288
\(635\) 6.45539 + 11.1811i 0.256174 + 0.443707i
\(636\) 3.45742 0.137096
\(637\) −2.17992 + 25.1445i −0.0863715 + 0.996263i
\(638\) −7.63483 −0.302266
\(639\) 2.14741 + 3.71943i 0.0849504 + 0.147138i
\(640\) 6.93220 0.274019
\(641\) 1.27505 2.20844i 0.0503613 0.0872282i −0.839746 0.542980i \(-0.817296\pi\)
0.890107 + 0.455751i \(0.150629\pi\)
\(642\) −4.24228 + 7.34784i −0.167429 + 0.289996i
\(643\) 7.23729 + 12.5354i 0.285411 + 0.494346i 0.972709 0.232029i \(-0.0745366\pi\)
−0.687298 + 0.726376i \(0.741203\pi\)
\(644\) −1.75383 3.04116i −0.0691106 0.119838i
\(645\) −3.58026 −0.140973
\(646\) −16.9488 −0.666840
\(647\) −31.6619 −1.24476 −0.622379 0.782716i \(-0.713834\pi\)
−0.622379 + 0.782716i \(0.713834\pi\)
\(648\) 2.59757 0.102042
\(649\) −12.5970 + 21.8187i −0.494477 + 0.856459i
\(650\) −1.04806 + 12.2279i −0.0411083 + 0.479618i
\(651\) −0.506127 + 0.875649i −0.0198367 + 0.0343194i
\(652\) 7.95600 13.7802i 0.311581 0.539674i
\(653\) −3.52992 6.11399i −0.138136 0.239259i 0.788655 0.614836i \(-0.210778\pi\)
−0.926791 + 0.375577i \(0.877445\pi\)
\(654\) 7.72937 13.3877i 0.302242 0.523499i
\(655\) −7.04092 12.1952i −0.275112 0.476507i
\(656\) 4.03643 0.157596
\(657\) −1.34127 2.32315i −0.0523281 0.0906349i
\(658\) 8.39186 + 14.5516i 0.327149 + 0.567279i
\(659\) 6.73098 + 11.6584i 0.262202 + 0.454147i 0.966827 0.255433i \(-0.0822181\pi\)
−0.704625 + 0.709580i \(0.748885\pi\)
\(660\) −2.28810 3.96311i −0.0890644 0.154264i
\(661\) 4.13958 0.161011 0.0805054 0.996754i \(-0.474347\pi\)
0.0805054 + 0.996754i \(0.474347\pi\)
\(662\) 5.47001 + 9.47433i 0.212598 + 0.368230i
\(663\) −1.16220 + 13.5596i −0.0451361 + 0.526611i
\(664\) 29.9504 1.16230
\(665\) −11.2107 0.00548007i −0.434732 0.000212508i
\(666\) −0.249330 + 0.431852i −0.00966134 + 0.0167339i
\(667\) −2.08901 −0.0808868
\(668\) −10.1114 17.5135i −0.391223 0.677617i
\(669\) −11.9432 + 20.6863i −0.461752 + 0.799778i
\(670\) 7.85291 0.303384
\(671\) 8.94753 0.345415
\(672\) 15.5094 + 0.00758139i 0.598289 + 0.000292458i
\(673\) −3.09545 + 5.36148i −0.119321 + 0.206670i −0.919499 0.393093i \(-0.871405\pi\)
0.800178 + 0.599763i \(0.204738\pi\)
\(674\) 5.47241 + 9.47850i 0.210790 + 0.365098i
\(675\) −2.24386 3.88648i −0.0863662 0.149591i
\(676\) −6.39602 17.3818i −0.246001 0.668530i
\(677\) 8.44416 14.6257i 0.324535 0.562112i −0.656883 0.753993i \(-0.728125\pi\)
0.981418 + 0.191881i \(0.0614587\pi\)
\(678\) 6.48582 11.2338i 0.249086 0.431430i
\(679\) −4.76294 + 8.24034i −0.182785 + 0.316235i
\(680\) 3.50878 + 6.07739i 0.134556 + 0.233057i
\(681\) 6.29391 10.9014i 0.241183 0.417741i
\(682\) −0.650598 + 1.12687i −0.0249127 + 0.0431501i
\(683\) −6.68862 + 11.5850i −0.255933 + 0.443289i −0.965149 0.261703i \(-0.915716\pi\)
0.709215 + 0.704992i \(0.249049\pi\)
\(684\) −4.21721 + 7.30442i −0.161249 + 0.279291i
\(685\) −6.90070 11.9524i −0.263662 0.456676i
\(686\) 7.00578 + 12.1756i 0.267482 + 0.464865i
\(687\) −7.66365 + 13.2738i −0.292387 + 0.506429i
\(688\) −2.19898 + 3.80875i −0.0838354 + 0.145207i
\(689\) −7.17627 5.00603i −0.273394 0.190714i
\(690\) 0.252801 + 0.437865i 0.00962398 + 0.0166692i
\(691\) −4.90190 8.49034i −0.186477 0.322988i 0.757596 0.652723i \(-0.226374\pi\)
−0.944073 + 0.329736i \(0.893040\pi\)
\(692\) 13.7288 23.7790i 0.521892 0.903943i
\(693\) −5.93167 10.2856i −0.225325 0.390716i
\(694\) 3.54110 0.134418
\(695\) 1.88079 0.0713426
\(696\) 2.91318 5.04578i 0.110424 0.191260i
\(697\) 8.66443 + 15.0072i 0.328189 + 0.568439i
\(698\) 3.13718 0.118744
\(699\) −13.3343 + 23.0957i −0.504350 + 0.873559i
\(700\) −8.45089 14.6539i −0.319414 0.553866i
\(701\) 35.6715 1.34729 0.673647 0.739054i \(-0.264727\pi\)
0.673647 + 0.739054i \(0.264727\pi\)
\(702\) −2.24293 1.56463i −0.0846540 0.0590530i
\(703\) −1.94607 3.37070i −0.0733976 0.127128i
\(704\) 12.0621 0.454607
\(705\) 2.99563 + 5.18858i 0.112822 + 0.195413i
\(706\) 13.5730 + 23.5091i 0.510826 + 0.884777i
\(707\) −15.8335 27.4555i −0.595481 1.03257i
\(708\) −3.99916 6.92675i −0.150298 0.260323i
\(709\) 31.7496 1.19238 0.596191 0.802842i \(-0.296680\pi\)
0.596191 + 0.802842i \(0.296680\pi\)
\(710\) −1.16577 2.01918i −0.0437507 0.0757785i
\(711\) 2.75173 4.76614i 0.103198 0.178744i
\(712\) 15.7176 + 27.2237i 0.589043 + 1.02025i
\(713\) −0.178014 + 0.308329i −0.00666667 + 0.0115470i
\(714\) 3.78407 + 6.56161i 0.141615 + 0.245562i
\(715\) −0.989000 + 11.5388i −0.0369865 + 0.431528i
\(716\) −8.00148 + 13.8590i −0.299029 + 0.517934i
\(717\) 14.5891 0.544841
\(718\) 19.1715 0.715475
\(719\) −6.98125 −0.260357 −0.130178 0.991491i \(-0.541555\pi\)
−0.130178 + 0.991491i \(0.541555\pi\)
\(720\) 0.629283 0.0234520
\(721\) 8.20002 + 0.00400837i 0.305385 + 0.000149280i
\(722\) 6.08590 + 10.5411i 0.226494 + 0.392299i
\(723\) 6.44615 11.1651i 0.239735 0.415233i
\(724\) 1.73319 3.00197i 0.0644133 0.111567i
\(725\) −10.0660 −0.373840
\(726\) −3.46611 6.00347i −0.128639 0.222810i
\(727\) −2.58607 −0.0959121 −0.0479561 0.998849i \(-0.515271\pi\)
−0.0479561 + 0.998849i \(0.515271\pi\)
\(728\) −20.3161 14.1869i −0.752965 0.525801i
\(729\) 1.00000 0.0370370
\(730\) 0.728142 + 1.26118i 0.0269498 + 0.0466783i
\(731\) −18.8810 −0.698338
\(732\) −1.42028 + 2.45999i −0.0524950 + 0.0909240i
\(733\) 6.30712 10.9243i 0.232959 0.403497i −0.725719 0.687992i \(-0.758493\pi\)
0.958678 + 0.284495i \(0.0918259\pi\)
\(734\) 13.4250 + 23.2528i 0.495526 + 0.858276i
\(735\) 2.50084 + 4.34138i 0.0922450 + 0.160134i
\(736\) 5.45955 0.201242
\(737\) −64.9169 −2.39124
\(738\) −3.48217 −0.128180
\(739\) 2.94077 0.108178 0.0540889 0.998536i \(-0.482775\pi\)
0.0540889 + 0.998536i \(0.482775\pi\)
\(740\) −0.335205 + 0.580592i −0.0123224 + 0.0213430i
\(741\) 19.3294 9.05501i 0.710083 0.332644i
\(742\) −4.86990 0.00238053i −0.178780 8.73920e-5i
\(743\) 20.5461 35.5869i 0.753763 1.30556i −0.192224 0.981351i \(-0.561570\pi\)
0.945987 0.324205i \(-0.105097\pi\)
\(744\) −0.496490 0.859947i −0.0182022 0.0315272i
\(745\) 5.57903 9.66316i 0.204400 0.354031i
\(746\) −12.4316 21.5322i −0.455155 0.788351i
\(747\) 11.5302 0.421866
\(748\) −12.0666 20.9000i −0.441199 0.764180i
\(749\) −14.8106 + 25.6237i −0.541166 + 0.936270i
\(750\) 2.57532 + 4.46058i 0.0940372 + 0.162877i
\(751\) 15.2160 + 26.3549i 0.555241 + 0.961705i 0.997885 + 0.0650079i \(0.0207073\pi\)
−0.442644 + 0.896698i \(0.645959\pi\)
\(752\) 7.35961 0.268377
\(753\) 12.0203 + 20.8198i 0.438046 + 0.758717i
\(754\) −5.55473 + 2.60216i −0.202291 + 0.0947650i
\(755\) −6.60102 −0.240236
\(756\) 3.76942 + 0.00184259i 0.137093 + 6.70143e-5i
\(757\) 15.7459 27.2726i 0.572293 0.991241i −0.424037 0.905645i \(-0.639387\pi\)
0.996330 0.0855959i \(-0.0272794\pi\)
\(758\) −9.16711 −0.332965
\(759\) −2.08981 3.61965i −0.0758552 0.131385i
\(760\) 5.50328 9.53196i 0.199625 0.345760i
\(761\) −44.1732 −1.60128 −0.800638 0.599148i \(-0.795506\pi\)
−0.800638 + 0.599148i \(0.795506\pi\)
\(762\) −13.6818 −0.495638
\(763\) 26.9846 46.6860i 0.976909 1.69015i
\(764\) −9.78707 + 16.9517i −0.354084 + 0.613291i
\(765\) 1.35079 + 2.33964i 0.0488380 + 0.0845899i
\(766\) −0.194236 0.336427i −0.00701804 0.0121556i
\(767\) −1.72858 + 20.1676i −0.0624154 + 0.728211i
\(768\) −6.36088 + 11.0174i −0.229529 + 0.397555i
\(769\) 25.4717 44.1182i 0.918532 1.59094i 0.116887 0.993145i \(-0.462709\pi\)
0.801646 0.597799i \(-0.203958\pi\)
\(770\) 3.22014 + 5.58376i 0.116046 + 0.201225i
\(771\) 9.35724 + 16.2072i 0.336993 + 0.583689i
\(772\) −9.87840 + 17.1099i −0.355531 + 0.615798i
\(773\) 2.87103 4.97278i 0.103264 0.178858i −0.809764 0.586756i \(-0.800405\pi\)
0.913028 + 0.407898i \(0.133738\pi\)
\(774\) 1.89703 3.28575i 0.0681874 0.118104i
\(775\) −0.857766 + 1.48569i −0.0308119 + 0.0533677i
\(776\) −4.67225 8.09257i −0.167724 0.290506i
\(777\) −0.870456 + 1.50597i −0.0312274 + 0.0540265i
\(778\) 13.4689 23.3288i 0.482883 0.836378i
\(779\) 13.5895 23.5378i 0.486896 0.843328i
\(780\) −3.01545 2.10352i −0.107970 0.0753181i
\(781\) 9.63699 + 16.6918i 0.344839 + 0.597278i
\(782\) 1.33318 + 2.30914i 0.0476745 + 0.0825746i
\(783\) 1.12150 1.94250i 0.0400792 0.0694192i
\(784\) 6.15445 + 0.00601690i 0.219802 + 0.000214889i
\(785\) 13.1773 0.470318
\(786\) 14.9228 0.532277
\(787\) −15.0412 + 26.0521i −0.536160 + 0.928656i 0.462946 + 0.886386i \(0.346792\pi\)
−0.999106 + 0.0422699i \(0.986541\pi\)
\(788\) 13.0465 + 22.5972i 0.464763 + 0.804993i
\(789\) 9.37129 0.333627
\(790\) −1.49384 + 2.58741i −0.0531486 + 0.0920560i
\(791\) 22.6432 39.1749i 0.805098 1.39290i
\(792\) 11.6572 0.414220
\(793\) 6.50978 3.04956i 0.231169 0.108293i
\(794\) −3.14667 5.45019i −0.111671 0.193420i
\(795\) −1.73693 −0.0616024
\(796\) −5.06999 8.78148i −0.179701 0.311251i
\(797\) −4.03274 6.98491i −0.142847 0.247418i 0.785721 0.618581i \(-0.212292\pi\)
−0.928568 + 0.371163i \(0.878959\pi\)
\(798\) 5.94511 10.2856i 0.210455 0.364107i
\(799\) 15.7978 + 27.3626i 0.558887 + 0.968020i
\(800\) 26.3070 0.930094
\(801\) 6.05088 + 10.4804i 0.213797 + 0.370308i
\(802\) 5.27918 9.14380i 0.186414 0.322879i
\(803\) −6.01926 10.4257i −0.212415 0.367914i
\(804\) 10.3045 17.8480i 0.363412 0.629449i
\(805\) 0.881082 + 1.52780i 0.0310541 + 0.0538480i
\(806\) −0.0892758 + 1.04160i −0.00314461 + 0.0366887i
\(807\) 6.07464 10.5216i 0.213837 0.370377i
\(808\) 31.1168 1.09468
\(809\) −18.5185 −0.651077 −0.325538 0.945529i \(-0.605546\pi\)
−0.325538 + 0.945529i \(0.605546\pi\)
\(810\) −0.542874 −0.0190746
\(811\) 20.3264 0.713755 0.356878 0.934151i \(-0.383841\pi\)
0.356878 + 0.934151i \(0.383841\pi\)
\(812\) 4.23099 7.32002i 0.148479 0.256882i
\(813\) −7.32926 12.6946i −0.257048 0.445221i
\(814\) −1.11892 + 1.93803i −0.0392182 + 0.0679279i
\(815\) −3.99690 + 6.92284i −0.140005 + 0.242496i
\(816\) 3.31861 0.116175
\(817\) 14.8067 + 25.6460i 0.518022 + 0.897241i
\(818\) 3.72977 0.130408
\(819\) −7.82119 5.46159i −0.273294 0.190844i
\(820\) −4.68151 −0.163485
\(821\) 1.20362 + 2.08473i 0.0420067 + 0.0727577i 0.886264 0.463180i \(-0.153292\pi\)
−0.844258 + 0.535938i \(0.819958\pi\)
\(822\) 14.6256 0.510126
\(823\) 15.3210 26.5368i 0.534057 0.925013i −0.465152 0.885231i \(-0.654000\pi\)
0.999208 0.0397824i \(-0.0126665\pi\)
\(824\) −4.02535 + 6.97211i −0.140230 + 0.242885i
\(825\) −10.0698 17.4414i −0.350586 0.607232i
\(826\) 5.62818 + 9.75931i 0.195829 + 0.339570i
\(827\) 3.92281 0.136409 0.0682047 0.997671i \(-0.478273\pi\)
0.0682047 + 0.997671i \(0.478273\pi\)
\(828\) 1.32689 0.0461128
\(829\) 10.6484 0.369834 0.184917 0.982754i \(-0.440798\pi\)
0.184917 + 0.982754i \(0.440798\pi\)
\(830\) −6.25942 −0.217268
\(831\) −2.51608 + 4.35797i −0.0872817 + 0.151176i
\(832\) 8.77579 4.11109i 0.304246 0.142526i
\(833\) 13.1885 + 22.8948i 0.456955 + 0.793259i
\(834\) −0.996555 + 1.72608i −0.0345079 + 0.0597694i
\(835\) 5.07973 + 8.79836i 0.175791 + 0.304480i
\(836\) −18.9256 + 32.7802i −0.654557 + 1.13373i
\(837\) −0.191136 0.331058i −0.00660664 0.0114430i
\(838\) 7.35948 0.254229
\(839\) −13.8289 23.9523i −0.477426 0.826925i 0.522240 0.852799i \(-0.325097\pi\)
−0.999665 + 0.0258735i \(0.991763\pi\)
\(840\) −4.91894 0.00240450i −0.169719 8.29631e-5i
\(841\) 11.9845 + 20.7577i 0.413258 + 0.715783i
\(842\) −5.80026 10.0463i −0.199890 0.346220i
\(843\) −0.854888 −0.0294439
\(844\) 8.47706 + 14.6827i 0.291792 + 0.505399i
\(845\) 3.21320 + 8.73218i 0.110538 + 0.300396i
\(846\) −6.34903 −0.218284
\(847\) −12.0803 20.9474i −0.415085 0.719761i
\(848\) −1.06681 + 1.84778i −0.0366345 + 0.0634529i
\(849\) 31.2774 1.07344
\(850\) 6.42398 + 11.1267i 0.220341 + 0.381641i
\(851\) −0.306155 + 0.530275i −0.0104948 + 0.0181776i
\(852\) −6.11888 −0.209629
\(853\) −8.76490 −0.300105 −0.150052 0.988678i \(-0.547944\pi\)
−0.150052 + 0.988678i \(0.547944\pi\)
\(854\) 2.00220 3.46401i 0.0685140 0.118536i
\(855\) 2.11862 3.66956i 0.0724554 0.125496i
\(856\) −14.5286 25.1642i −0.496576 0.860095i
\(857\) −12.9737 22.4711i −0.443173 0.767598i 0.554750 0.832017i \(-0.312814\pi\)
−0.997923 + 0.0644193i \(0.979480\pi\)
\(858\) −10.0656 7.02160i −0.343636 0.239713i
\(859\) −27.8958 + 48.3170i −0.951793 + 1.64855i −0.210251 + 0.977648i \(0.567428\pi\)
−0.741542 + 0.670906i \(0.765905\pi\)
\(860\) 2.55041 4.41744i 0.0869684 0.150634i
\(861\) −12.1466 0.00593756i −0.413955 0.000202351i
\(862\) 12.3852 + 21.4518i 0.421843 + 0.730653i
\(863\) −5.86854 + 10.1646i −0.199767 + 0.346007i −0.948453 0.316918i \(-0.897352\pi\)
0.748686 + 0.662925i \(0.230685\pi\)
\(864\) −2.93100 + 5.07665i −0.0997148 + 0.172711i
\(865\) −6.89703 + 11.9460i −0.234506 + 0.406176i
\(866\) −7.04013 + 12.1939i −0.239233 + 0.414364i
\(867\) −1.37642 2.38403i −0.0467456 0.0809657i
\(868\) −0.719863 1.24825i −0.0244338 0.0423683i
\(869\) 12.3490 21.3891i 0.418911 0.725576i
\(870\) −0.608833 + 1.05453i −0.0206414 + 0.0357519i
\(871\) −47.2303 + 22.1254i −1.60034 + 0.749692i
\(872\) 26.4708 + 45.8488i 0.896415 + 1.55264i
\(873\) −1.79870 3.11544i −0.0608767 0.105442i
\(874\) 2.09100 3.62172i 0.0707292 0.122506i
\(875\) 8.97568 + 15.5639i 0.303433 + 0.526156i
\(876\) 3.82185 0.129128
\(877\) −10.9556 −0.369943 −0.184972 0.982744i \(-0.559219\pi\)
−0.184972 + 0.982744i \(0.559219\pi\)
\(878\) 3.58562 6.21048i 0.121009 0.209594i
\(879\) −0.339044 0.587241i −0.0114357 0.0198071i
\(880\) 2.82405 0.0951986
\(881\) −0.925967 + 1.60382i −0.0311966 + 0.0540341i −0.881202 0.472740i \(-0.843265\pi\)
0.850006 + 0.526774i \(0.176598\pi\)
\(882\) −5.30936 0.00519069i −0.178775 0.000174780i
\(883\) −50.8664 −1.71179 −0.855896 0.517149i \(-0.826993\pi\)
−0.855896 + 0.517149i \(0.826993\pi\)
\(884\) −15.9024 11.0932i −0.534855 0.373104i
\(885\) 2.00908 + 3.47983i 0.0675345 + 0.116973i
\(886\) −5.63692 −0.189376
\(887\) 10.5435 + 18.2619i 0.354016 + 0.613174i 0.986949 0.161033i \(-0.0514824\pi\)
−0.632933 + 0.774207i \(0.718149\pi\)
\(888\) −0.853882 1.47897i −0.0286544 0.0496309i
\(889\) −47.7251 0.0233292i −1.60065 0.000782437i
\(890\) −3.28487 5.68955i −0.110109 0.190714i
\(891\) 4.48772 0.150344
\(892\) −17.0156 29.4719i −0.569725 0.986793i
\(893\) 24.7778 42.9164i 0.829157 1.43614i
\(894\) 5.91219 + 10.2402i 0.197733 + 0.342484i
\(895\) 4.01975 6.96241i 0.134365 0.232728i
\(896\) −12.8234 + 22.1857i −0.428399 + 0.741173i
\(897\) −2.75412 1.92122i −0.0919573 0.0641476i
\(898\) 7.14763 12.3801i 0.238519 0.413128i
\(899\) −0.857438 −0.0285972
\(900\) 6.39369 0.213123
\(901\) −9.15991 −0.305161
\(902\) −15.6270 −0.520322
\(903\) 6.62288 11.4582i 0.220396 0.381306i
\(904\) 22.2120 + 38.4724i 0.738761 + 1.27957i
\(905\) −0.870711 + 1.50812i −0.0289434 + 0.0501314i
\(906\) 3.49761 6.05803i 0.116200 0.201265i
\(907\) −10.2256 −0.339537 −0.169768 0.985484i \(-0.554302\pi\)
−0.169768 + 0.985484i \(0.554302\pi\)
\(908\) 8.96698 + 15.5313i 0.297580 + 0.515423i
\(909\) 11.9792 0.397324
\(910\) 4.24592 + 2.96496i 0.140751 + 0.0982873i
\(911\) 35.4885 1.17578 0.587892 0.808939i \(-0.299958\pi\)
0.587892 + 0.808939i \(0.299958\pi\)
\(912\) −2.60250 4.50766i −0.0861774 0.149264i
\(913\) 51.7441 1.71248
\(914\) −2.57886 + 4.46671i −0.0853010 + 0.147746i
\(915\) 0.713513 1.23584i 0.0235880 0.0408556i
\(916\) −10.9185 18.9113i −0.360756 0.624848i
\(917\) 52.0540 + 0.0254453i 1.71897 + 0.000840277i
\(918\) −2.86291 −0.0944903
\(919\) 2.99682 0.0988560 0.0494280 0.998778i \(-0.484260\pi\)
0.0494280 + 0.998778i \(0.484260\pi\)
\(920\) −1.73154 −0.0570872
\(921\) 27.2103 0.896610
\(922\) 3.64522 6.31371i 0.120049 0.207931i
\(923\) 12.7004 + 8.85956i 0.418039 + 0.291616i
\(924\) 16.9161 + 0.00826901i 0.556499 + 0.000272031i
\(925\) −1.47522 + 2.55515i −0.0485048 + 0.0840128i
\(926\) −8.90946 15.4316i −0.292783 0.507115i
\(927\) −1.54966 + 2.68409i −0.0508974 + 0.0881569i
\(928\) 6.57425 + 11.3869i 0.215810 + 0.373794i
\(929\) −59.8495 −1.96360 −0.981800 0.189918i \(-0.939178\pi\)
−0.981800 + 0.189918i \(0.939178\pi\)
\(930\) 0.103763 + 0.179722i 0.00340252 + 0.00589333i
\(931\) 20.7554 35.8684i 0.680232 1.17554i
\(932\) −18.9975 32.9046i −0.622283 1.07783i
\(933\) −7.06426 12.2357i −0.231274 0.400577i
\(934\) 10.9927 0.359693
\(935\) 6.06198 + 10.4997i 0.198248 + 0.343375i
\(936\) 8.48119 3.97308i 0.277216 0.129864i
\(937\) −60.1408 −1.96471 −0.982357 0.187015i \(-0.940119\pi\)
−0.982357 + 0.187015i \(0.940119\pi\)
\(938\) −14.5266 + 25.1324i −0.474309 + 0.820601i
\(939\) −9.84907 + 17.0591i −0.321412 + 0.556703i
\(940\) −8.53578 −0.278407
\(941\) −0.964242 1.67012i −0.0314334 0.0544443i 0.849881 0.526975i \(-0.176674\pi\)
−0.881314 + 0.472531i \(0.843341\pi\)
\(942\) −6.98211 + 12.0934i −0.227489 + 0.394023i
\(943\) −4.27579 −0.139239
\(944\) 4.93588 0.160649
\(945\) −1.89367 0.000925671i −0.0616010 3.01121e-5i
\(946\) 8.51334 14.7455i 0.276793 0.479419i
\(947\) 0.341387 + 0.591300i 0.0110936 + 0.0192147i 0.871519 0.490362i \(-0.163135\pi\)
−0.860425 + 0.509577i \(0.829802\pi\)
\(948\) 3.92042 + 6.79036i 0.127329 + 0.220541i
\(949\) −7.93267 5.53368i −0.257505 0.179631i
\(950\) 10.0756 17.4514i 0.326894 0.566197i
\(951\) 7.83931 13.5781i 0.254207 0.440299i
\(952\) −25.9407 0.0126804i −0.840741 0.000410975i
\(953\) 16.6889 + 28.9060i 0.540606 + 0.936358i 0.998869 + 0.0475411i \(0.0151385\pi\)
−0.458263 + 0.888817i \(0.651528\pi\)
\(954\) 0.920325 1.59405i 0.0297966 0.0516092i
\(955\) 4.91679 8.51613i 0.159104 0.275575i
\(956\) −10.3926 + 18.0006i −0.336122 + 0.582180i
\(957\) 5.03298 8.71738i 0.162693 0.281793i
\(958\) 5.50406 + 9.53332i 0.177828 + 0.308008i
\(959\) 51.0173 + 0.0249385i 1.64744 + 0.000805308i
\(960\) 0.961881 1.66603i 0.0310446 0.0537708i
\(961\) 15.4269 26.7202i 0.497643 0.861943i
\(962\) −0.153540 + 1.79138i −0.00495032 + 0.0577563i
\(963\) −5.59313 9.68758i −0.180236 0.312178i
\(964\) 9.18387 + 15.9069i 0.295793 + 0.512328i
\(965\) 4.96267 8.59559i 0.159754 0.276702i
\(966\) −1.86898 0.000913602i −0.0601333 2.93947e-5i
\(967\) −4.60355 −0.148040 −0.0740201 0.997257i \(-0.523583\pi\)
−0.0740201 + 0.997257i \(0.523583\pi\)
\(968\) 23.7408 0.763059
\(969\) 11.1728 19.3519i 0.358923 0.621673i
\(970\) 0.976465 + 1.69129i 0.0313524 + 0.0543040i
\(971\) −2.13297 −0.0684503 −0.0342251 0.999414i \(-0.510896\pi\)
−0.0342251 + 0.999414i \(0.510896\pi\)
\(972\) −0.712354 + 1.23383i −0.0228488 + 0.0395752i
\(973\) −3.47915 + 6.01927i −0.111537 + 0.192969i
\(974\) −17.7429 −0.568520
\(975\) −13.2708 9.25746i −0.425006 0.296476i
\(976\) −0.876474 1.51810i −0.0280553 0.0485931i
\(977\) −36.3686 −1.16354 −0.581768 0.813355i \(-0.697639\pi\)
−0.581768 + 0.813355i \(0.697639\pi\)
\(978\) −4.23558 7.33625i −0.135439 0.234587i
\(979\) 27.1547 + 47.0333i 0.867867 + 1.50319i
\(980\) −7.13803 0.00697849i −0.228016 0.000222920i
\(981\) 10.1906 + 17.6506i 0.325361 + 0.563541i
\(982\) 1.19358 0.0380887
\(983\) −10.0001 17.3207i −0.318954 0.552444i 0.661316 0.750107i \(-0.269998\pi\)
−0.980270 + 0.197663i \(0.936665\pi\)
\(984\) 5.96270 10.3277i 0.190084 0.329235i
\(985\) −6.55426 11.3523i −0.208836 0.361715i
\(986\) −3.21076 + 5.56120i −0.102251 + 0.177105i
\(987\) −22.1469 0.0108259i −0.704942 0.000344593i
\(988\) −2.59700 + 30.2996i −0.0826215 + 0.963960i
\(989\) 2.32938 4.03461i 0.0740701 0.128293i
\(990\) −2.43626 −0.0774295
\(991\) 20.8006 0.660754 0.330377 0.943849i \(-0.392824\pi\)
0.330377 + 0.943849i \(0.392824\pi\)
\(992\) 2.24088 0.0711482
\(993\) −14.4236 −0.457719
\(994\) 8.61865 + 0.00421301i 0.273367 + 0.000133629i
\(995\) 2.54704 + 4.41160i 0.0807466 + 0.139857i
\(996\) −8.21355 + 14.2263i −0.260256 + 0.450777i
\(997\) 11.0553 19.1483i 0.350124 0.606433i −0.636147 0.771568i \(-0.719473\pi\)
0.986271 + 0.165135i \(0.0528060\pi\)
\(998\) −11.9338 −0.377756
\(999\) −0.328723 0.569365i −0.0104003 0.0180139i
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.j.b.100.5 16
3.2 odd 2 819.2.n.e.100.4 16
7.4 even 3 273.2.l.b.256.4 yes 16
13.3 even 3 273.2.l.b.16.4 yes 16
21.11 odd 6 819.2.s.e.802.5 16
39.29 odd 6 819.2.s.e.289.5 16
91.81 even 3 inner 273.2.j.b.172.5 yes 16
273.263 odd 6 819.2.n.e.172.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.j.b.100.5 16 1.1 even 1 trivial
273.2.j.b.172.5 yes 16 91.81 even 3 inner
273.2.l.b.16.4 yes 16 13.3 even 3
273.2.l.b.256.4 yes 16 7.4 even 3
819.2.n.e.100.4 16 3.2 odd 2
819.2.n.e.172.4 16 273.263 odd 6
819.2.s.e.289.5 16 39.29 odd 6
819.2.s.e.802.5 16 21.11 odd 6