Properties

Label 385.2.i.b.221.3
Level $385$
Weight $2$
Character 385.221
Analytic conductor $3.074$
Analytic rank $0$
Dimension $12$
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] = [385,2,Mod(221,385)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(385, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("385.221");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.i (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: \(3.07424047782\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 13 x^{10} - 12 x^{9} + 49 x^{8} - 38 x^{7} + 136 x^{6} - 34 x^{5} + 113 x^{4} - 72 x^{3} + 58 x^{2} - 16 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 221.3
Root \(0.271923 + 0.470985i\) of defining polynomial
Character \(\chi\) \(=\) 385.221
Dual form 385.2.i.b.331.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.228077 + 0.395041i) q^{2} +(0.0572064 - 0.0990845i) q^{3} +(0.895962 - 1.55185i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.0521899 q^{6} +(-1.96234 - 1.77460i) q^{7} +1.72970 q^{8} +(1.49345 + 2.58674i) q^{9} +O(q^{10})\) \(q+(0.228077 + 0.395041i) q^{2} +(0.0572064 - 0.0990845i) q^{3} +(0.895962 - 1.55185i) q^{4} +(0.500000 + 0.866025i) q^{5} +0.0521899 q^{6} +(-1.96234 - 1.77460i) q^{7} +1.72970 q^{8} +(1.49345 + 2.58674i) q^{9} +(-0.228077 + 0.395041i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.102510 - 0.177552i) q^{12} +4.50529 q^{13} +(0.253475 - 1.17995i) q^{14} +0.114413 q^{15} +(-1.39742 - 2.42040i) q^{16} +(2.20225 - 3.81441i) q^{17} +(-0.681245 + 1.17995i) q^{18} +(1.37904 + 2.38857i) q^{19} +1.79192 q^{20} +(-0.288094 + 0.0929191i) q^{21} +0.456154 q^{22} +(-4.31975 - 7.48202i) q^{23} +(0.0989500 - 0.171386i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.02755 + 1.77977i) q^{26} +0.684980 q^{27} +(-4.51210 + 1.45529i) q^{28} +4.71355 q^{29} +(0.0260949 + 0.0451978i) q^{30} +(-5.12634 + 8.87908i) q^{31} +(2.36714 - 4.10000i) q^{32} +(-0.0572064 - 0.0990845i) q^{33} +2.00913 q^{34} +(0.555678 - 2.58674i) q^{35} +5.35231 q^{36} +(1.13479 + 1.96552i) q^{37} +(-0.629055 + 1.08956i) q^{38} +(0.257731 - 0.446404i) q^{39} +(0.864850 + 1.49796i) q^{40} -1.26433 q^{41} +(-0.102414 - 0.0926162i) q^{42} -10.4536 q^{43} +(-0.895962 - 1.55185i) q^{44} +(-1.49345 + 2.58674i) q^{45} +(1.97047 - 3.41295i) q^{46} +(5.76655 + 9.98796i) q^{47} -0.319765 q^{48} +(0.701583 + 6.96475i) q^{49} -0.456154 q^{50} +(-0.251966 - 0.436418i) q^{51} +(4.03656 - 6.99154i) q^{52} +(2.86987 - 4.97076i) q^{53} +(0.156228 + 0.270595i) q^{54} +1.00000 q^{55} +(-3.39427 - 3.06953i) q^{56} +0.315560 q^{57} +(1.07505 + 1.86205i) q^{58} +(-4.43080 + 7.67438i) q^{59} +(0.102510 - 0.177552i) q^{60} +(-2.35391 - 4.07710i) q^{61} -4.67680 q^{62} +(1.65976 - 7.72636i) q^{63} -3.43012 q^{64} +(2.25264 + 3.90169i) q^{65} +(0.0260949 - 0.0451978i) q^{66} +(-0.542943 + 0.940405i) q^{67} +(-3.94627 - 6.83514i) q^{68} -0.988469 q^{69} +(1.14861 - 0.370460i) q^{70} -12.8021 q^{71} +(2.58323 + 4.47429i) q^{72} +(-5.32506 + 9.22327i) q^{73} +(-0.517641 + 0.896580i) q^{74} +(0.0572064 + 0.0990845i) q^{75} +4.94228 q^{76} +(-2.51802 + 0.812139i) q^{77} +0.235130 q^{78} +(4.62203 + 8.00559i) q^{79} +(1.39742 - 2.42040i) q^{80} +(-4.44118 + 7.69235i) q^{81} +(-0.288364 - 0.499461i) q^{82} -2.60431 q^{83} +(-0.113925 + 0.530331i) q^{84} +4.40450 q^{85} +(-2.38423 - 4.12961i) q^{86} +(0.269646 - 0.467040i) q^{87} +(0.864850 - 1.49796i) q^{88} +(-2.00155 - 3.46679i) q^{89} -1.36249 q^{90} +(-8.84092 - 7.99509i) q^{91} -15.4813 q^{92} +(0.586519 + 1.01588i) q^{93} +(-2.63043 + 4.55605i) q^{94} +(-1.37904 + 2.38857i) q^{95} +(-0.270831 - 0.469093i) q^{96} -5.03725 q^{97} +(-2.59135 + 1.86565i) q^{98} +2.98691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(276\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.228077 + 0.395041i 0.161275 + 0.279336i 0.935326 0.353787i \(-0.115106\pi\)
−0.774051 + 0.633123i \(0.781773\pi\)
\(3\) 0.0572064 0.0990845i 0.0330282 0.0572064i −0.849039 0.528330i \(-0.822818\pi\)
0.882067 + 0.471124i \(0.156152\pi\)
\(4\) 0.895962 1.55185i 0.447981 0.775926i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0.0521899 0.0213064
\(7\) −1.96234 1.77460i −0.741696 0.670736i
\(8\) 1.72970 0.611542
\(9\) 1.49345 + 2.58674i 0.497818 + 0.862247i
\(10\) −0.228077 + 0.395041i −0.0721243 + 0.124923i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) −0.102510 0.177552i −0.0295920 0.0512548i
\(13\) 4.50529 1.24954 0.624771 0.780808i \(-0.285192\pi\)
0.624771 + 0.780808i \(0.285192\pi\)
\(14\) 0.253475 1.17995i 0.0677439 0.315355i
\(15\) 0.114413 0.0295413
\(16\) −1.39742 2.42040i −0.349355 0.605100i
\(17\) 2.20225 3.81441i 0.534125 0.925131i −0.465081 0.885268i \(-0.653975\pi\)
0.999205 0.0398625i \(-0.0126920\pi\)
\(18\) −0.681245 + 1.17995i −0.160571 + 0.278117i
\(19\) 1.37904 + 2.38857i 0.316374 + 0.547976i 0.979729 0.200329i \(-0.0642012\pi\)
−0.663355 + 0.748305i \(0.730868\pi\)
\(20\) 1.79192 0.400686
\(21\) −0.288094 + 0.0929191i −0.0628673 + 0.0202766i
\(22\) 0.456154 0.0972523
\(23\) −4.31975 7.48202i −0.900729 1.56011i −0.826550 0.562864i \(-0.809700\pi\)
−0.0741796 0.997245i \(-0.523634\pi\)
\(24\) 0.0989500 0.171386i 0.0201981 0.0349841i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.02755 + 1.77977i 0.201520 + 0.349042i
\(27\) 0.684980 0.131824
\(28\) −4.51210 + 1.45529i −0.852707 + 0.275024i
\(29\) 4.71355 0.875285 0.437642 0.899149i \(-0.355814\pi\)
0.437642 + 0.899149i \(0.355814\pi\)
\(30\) 0.0260949 + 0.0451978i 0.00476426 + 0.00825195i
\(31\) −5.12634 + 8.87908i −0.920718 + 1.59473i −0.122411 + 0.992480i \(0.539062\pi\)
−0.798307 + 0.602250i \(0.794271\pi\)
\(32\) 2.36714 4.10000i 0.418455 0.724785i
\(33\) −0.0572064 0.0990845i −0.00995836 0.0172484i
\(34\) 2.00913 0.344563
\(35\) 0.555678 2.58674i 0.0939267 0.437239i
\(36\) 5.35231 0.892052
\(37\) 1.13479 + 1.96552i 0.186559 + 0.323130i 0.944101 0.329657i \(-0.106933\pi\)
−0.757542 + 0.652787i \(0.773600\pi\)
\(38\) −0.629055 + 1.08956i −0.102046 + 0.176749i
\(39\) 0.257731 0.446404i 0.0412701 0.0714818i
\(40\) 0.864850 + 1.49796i 0.136745 + 0.236849i
\(41\) −1.26433 −0.197455 −0.0987274 0.995115i \(-0.531477\pi\)
−0.0987274 + 0.995115i \(0.531477\pi\)
\(42\) −0.102414 0.0926162i −0.0158029 0.0142910i
\(43\) −10.4536 −1.59416 −0.797082 0.603871i \(-0.793624\pi\)
−0.797082 + 0.603871i \(0.793624\pi\)
\(44\) −0.895962 1.55185i −0.135071 0.233950i
\(45\) −1.49345 + 2.58674i −0.222631 + 0.385608i
\(46\) 1.97047 3.41295i 0.290530 0.503212i
\(47\) 5.76655 + 9.98796i 0.841138 + 1.45689i 0.888934 + 0.458036i \(0.151447\pi\)
−0.0477959 + 0.998857i \(0.515220\pi\)
\(48\) −0.319765 −0.0461542
\(49\) 0.701583 + 6.96475i 0.100226 + 0.994965i
\(50\) −0.456154 −0.0645099
\(51\) −0.251966 0.436418i −0.0352823 0.0611107i
\(52\) 4.03656 6.99154i 0.559771 0.969551i
\(53\) 2.86987 4.97076i 0.394207 0.682786i −0.598793 0.800904i \(-0.704353\pi\)
0.993000 + 0.118118i \(0.0376861\pi\)
\(54\) 0.156228 + 0.270595i 0.0212599 + 0.0368233i
\(55\) 1.00000 0.134840
\(56\) −3.39427 3.06953i −0.453578 0.410183i
\(57\) 0.315560 0.0417970
\(58\) 1.07505 + 1.86205i 0.141161 + 0.244499i
\(59\) −4.43080 + 7.67438i −0.576842 + 0.999119i 0.418997 + 0.907988i \(0.362382\pi\)
−0.995839 + 0.0911315i \(0.970952\pi\)
\(60\) 0.102510 0.177552i 0.0132339 0.0229218i
\(61\) −2.35391 4.07710i −0.301388 0.522019i 0.675063 0.737760i \(-0.264117\pi\)
−0.976451 + 0.215741i \(0.930783\pi\)
\(62\) −4.67680 −0.593954
\(63\) 1.65976 7.72636i 0.209110 0.973430i
\(64\) −3.43012 −0.428765
\(65\) 2.25264 + 3.90169i 0.279406 + 0.483945i
\(66\) 0.0260949 0.0451978i 0.00321207 0.00556346i
\(67\) −0.542943 + 0.940405i −0.0663311 + 0.114889i −0.897284 0.441454i \(-0.854463\pi\)
0.830953 + 0.556343i \(0.187796\pi\)
\(68\) −3.94627 6.83514i −0.478555 0.828882i
\(69\) −0.988469 −0.118998
\(70\) 1.14861 0.370460i 0.137285 0.0442785i
\(71\) −12.8021 −1.51933 −0.759667 0.650312i \(-0.774638\pi\)
−0.759667 + 0.650312i \(0.774638\pi\)
\(72\) 2.58323 + 4.47429i 0.304437 + 0.527300i
\(73\) −5.32506 + 9.22327i −0.623251 + 1.07950i 0.365625 + 0.930762i \(0.380855\pi\)
−0.988876 + 0.148740i \(0.952478\pi\)
\(74\) −0.517641 + 0.896580i −0.0601745 + 0.104225i
\(75\) 0.0572064 + 0.0990845i 0.00660563 + 0.0114413i
\(76\) 4.94228 0.566918
\(77\) −2.51802 + 0.812139i −0.286955 + 0.0925518i
\(78\) 0.235130 0.0266233
\(79\) 4.62203 + 8.00559i 0.520019 + 0.900700i 0.999729 + 0.0232725i \(0.00740853\pi\)
−0.479710 + 0.877427i \(0.659258\pi\)
\(80\) 1.39742 2.42040i 0.156236 0.270609i
\(81\) −4.44118 + 7.69235i −0.493464 + 0.854705i
\(82\) −0.288364 0.499461i −0.0318445 0.0551563i
\(83\) −2.60431 −0.285860 −0.142930 0.989733i \(-0.545652\pi\)
−0.142930 + 0.989733i \(0.545652\pi\)
\(84\) −0.113925 + 0.530331i −0.0124302 + 0.0578639i
\(85\) 4.40450 0.477736
\(86\) −2.38423 4.12961i −0.257099 0.445308i
\(87\) 0.269646 0.467040i 0.0289090 0.0500719i
\(88\) 0.864850 1.49796i 0.0921934 0.159684i
\(89\) −2.00155 3.46679i −0.212164 0.367479i 0.740227 0.672357i \(-0.234718\pi\)
−0.952392 + 0.304878i \(0.901384\pi\)
\(90\) −1.36249 −0.143619
\(91\) −8.84092 7.99509i −0.926780 0.838113i
\(92\) −15.4813 −1.61404
\(93\) 0.586519 + 1.01588i 0.0608192 + 0.105342i
\(94\) −2.63043 + 4.55605i −0.271309 + 0.469920i
\(95\) −1.37904 + 2.38857i −0.141487 + 0.245062i
\(96\) −0.270831 0.469093i −0.0276416 0.0478766i
\(97\) −5.03725 −0.511455 −0.255728 0.966749i \(-0.582315\pi\)
−0.255728 + 0.966749i \(0.582315\pi\)
\(98\) −2.59135 + 1.86565i −0.261766 + 0.188459i
\(99\) 2.98691 0.300196
\(100\) 0.895962 + 1.55185i 0.0895962 + 0.155185i
\(101\) 6.72616 11.6501i 0.669278 1.15922i −0.308828 0.951118i \(-0.599937\pi\)
0.978106 0.208106i \(-0.0667300\pi\)
\(102\) 0.114935 0.199074i 0.0113803 0.0197112i
\(103\) 0.291429 + 0.504770i 0.0287154 + 0.0497365i 0.880026 0.474926i \(-0.157525\pi\)
−0.851311 + 0.524662i \(0.824192\pi\)
\(104\) 7.79280 0.764147
\(105\) −0.224517 0.203037i −0.0219107 0.0198144i
\(106\) 2.61820 0.254302
\(107\) −7.07851 12.2603i −0.684305 1.18525i −0.973655 0.228028i \(-0.926772\pi\)
0.289350 0.957223i \(-0.406561\pi\)
\(108\) 0.613716 1.06299i 0.0590548 0.102286i
\(109\) 2.69792 4.67293i 0.258414 0.447586i −0.707403 0.706810i \(-0.750134\pi\)
0.965817 + 0.259224i \(0.0834669\pi\)
\(110\) 0.228077 + 0.395041i 0.0217463 + 0.0376657i
\(111\) 0.259670 0.0246468
\(112\) −1.55303 + 7.22952i −0.146747 + 0.683125i
\(113\) −14.2416 −1.33974 −0.669869 0.742479i \(-0.733650\pi\)
−0.669869 + 0.742479i \(0.733650\pi\)
\(114\) 0.0719720 + 0.124659i 0.00674080 + 0.0116754i
\(115\) 4.31975 7.48202i 0.402818 0.697702i
\(116\) 4.22316 7.31473i 0.392111 0.679156i
\(117\) 6.72844 + 11.6540i 0.622045 + 1.07741i
\(118\) −4.04226 −0.372120
\(119\) −11.0906 + 3.57707i −1.01668 + 0.327909i
\(120\) 0.197900 0.0180657
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 1.07375 1.85978i 0.0972125 0.168377i
\(123\) −0.0723277 + 0.125275i −0.00652157 + 0.0112957i
\(124\) 9.18601 + 15.9106i 0.824928 + 1.42882i
\(125\) −1.00000 −0.0894427
\(126\) 3.43078 1.10653i 0.305638 0.0985776i
\(127\) −1.61303 −0.143133 −0.0715666 0.997436i \(-0.522800\pi\)
−0.0715666 + 0.997436i \(0.522800\pi\)
\(128\) −5.51661 9.55504i −0.487604 0.844555i
\(129\) −0.598015 + 1.03579i −0.0526523 + 0.0911965i
\(130\) −1.02755 + 1.77977i −0.0901223 + 0.156096i
\(131\) 7.15742 + 12.3970i 0.625347 + 1.08313i 0.988474 + 0.151393i \(0.0483759\pi\)
−0.363127 + 0.931740i \(0.618291\pi\)
\(132\) −0.205019 −0.0178446
\(133\) 1.53261 7.13445i 0.132894 0.618635i
\(134\) −0.495331 −0.0427901
\(135\) 0.342490 + 0.593210i 0.0294768 + 0.0510554i
\(136\) 3.80924 6.59779i 0.326639 0.565756i
\(137\) 4.05676 7.02651i 0.346592 0.600315i −0.639050 0.769165i \(-0.720672\pi\)
0.985642 + 0.168850i \(0.0540055\pi\)
\(138\) −0.225447 0.390486i −0.0191913 0.0332403i
\(139\) 16.3917 1.39033 0.695163 0.718852i \(-0.255332\pi\)
0.695163 + 0.718852i \(0.255332\pi\)
\(140\) −3.51637 3.17995i −0.297187 0.268755i
\(141\) 1.31954 0.111125
\(142\) −2.91987 5.05737i −0.245030 0.424405i
\(143\) 2.25264 3.90169i 0.188375 0.326276i
\(144\) 4.17396 7.22952i 0.347830 0.602460i
\(145\) 2.35678 + 4.08206i 0.195720 + 0.338996i
\(146\) −4.85809 −0.402059
\(147\) 0.730234 + 0.328913i 0.0602287 + 0.0271283i
\(148\) 4.06693 0.334299
\(149\) 7.45484 + 12.9122i 0.610725 + 1.05781i 0.991119 + 0.132981i \(0.0424551\pi\)
−0.380394 + 0.924825i \(0.624212\pi\)
\(150\) −0.0260949 + 0.0451978i −0.00213064 + 0.00369038i
\(151\) 11.4730 19.8719i 0.933663 1.61715i 0.156661 0.987652i \(-0.449927\pi\)
0.777001 0.629499i \(-0.216740\pi\)
\(152\) 2.38533 + 4.13151i 0.193476 + 0.335110i
\(153\) 13.1559 1.06359
\(154\) −0.895131 0.809491i −0.0721317 0.0652307i
\(155\) −10.2527 −0.823515
\(156\) −0.461835 0.799922i −0.0369764 0.0640450i
\(157\) −8.91886 + 15.4479i −0.711803 + 1.23288i 0.252377 + 0.967629i \(0.418788\pi\)
−0.964180 + 0.265249i \(0.914546\pi\)
\(158\) −2.10836 + 3.65178i −0.167732 + 0.290520i
\(159\) −0.328350 0.568718i −0.0260398 0.0451023i
\(160\) 4.73428 0.374277
\(161\) −4.80077 + 22.3481i −0.378354 + 1.76128i
\(162\) −4.05172 −0.318333
\(163\) 10.8525 + 18.7970i 0.850030 + 1.47229i 0.881181 + 0.472780i \(0.156749\pi\)
−0.0311508 + 0.999515i \(0.509917\pi\)
\(164\) −1.13279 + 1.96205i −0.0884560 + 0.153210i
\(165\) 0.0572064 0.0990845i 0.00445352 0.00771372i
\(166\) −0.593984 1.02881i −0.0461021 0.0798511i
\(167\) 2.53749 0.196357 0.0981784 0.995169i \(-0.468698\pi\)
0.0981784 + 0.995169i \(0.468698\pi\)
\(168\) −0.498317 + 0.160722i −0.0384460 + 0.0124000i
\(169\) 7.29761 0.561354
\(170\) 1.00457 + 1.73996i 0.0770467 + 0.133449i
\(171\) −4.11907 + 7.13445i −0.314993 + 0.545585i
\(172\) −9.36606 + 16.2225i −0.714155 + 1.23695i
\(173\) −4.96057 8.59196i −0.377145 0.653234i 0.613501 0.789694i \(-0.289761\pi\)
−0.990646 + 0.136460i \(0.956428\pi\)
\(174\) 0.246000 0.0186492
\(175\) 2.51802 0.812139i 0.190345 0.0613919i
\(176\) −2.79484 −0.210669
\(177\) 0.506941 + 0.878048i 0.0381040 + 0.0659981i
\(178\) 0.913016 1.58139i 0.0684334 0.118530i
\(179\) 2.93234 5.07896i 0.219173 0.379619i −0.735382 0.677653i \(-0.762997\pi\)
0.954555 + 0.298033i \(0.0963307\pi\)
\(180\) 2.67616 + 4.63524i 0.199469 + 0.345490i
\(181\) −17.1905 −1.27776 −0.638880 0.769307i \(-0.720602\pi\)
−0.638880 + 0.769307i \(0.720602\pi\)
\(182\) 1.14198 5.31602i 0.0846489 0.394050i
\(183\) −0.538636 −0.0398171
\(184\) −7.47187 12.9417i −0.550833 0.954071i
\(185\) −1.13479 + 1.96552i −0.0834317 + 0.144508i
\(186\) −0.267543 + 0.463398i −0.0196172 + 0.0339780i
\(187\) −2.20225 3.81441i −0.161045 0.278937i
\(188\) 20.6664 1.50725
\(189\) −1.34417 1.21557i −0.0977736 0.0884194i
\(190\) −1.25811 −0.0912729
\(191\) 6.47512 + 11.2152i 0.468523 + 0.811506i 0.999353 0.0359724i \(-0.0114528\pi\)
−0.530829 + 0.847479i \(0.678119\pi\)
\(192\) −0.196225 + 0.339871i −0.0141613 + 0.0245281i
\(193\) 1.41535 2.45146i 0.101879 0.176460i −0.810580 0.585628i \(-0.800848\pi\)
0.912459 + 0.409168i \(0.134181\pi\)
\(194\) −1.14888 1.98992i −0.0824848 0.142868i
\(195\) 0.515463 0.0369131
\(196\) 11.4369 + 5.15140i 0.816918 + 0.367957i
\(197\) 1.57926 0.112517 0.0562586 0.998416i \(-0.482083\pi\)
0.0562586 + 0.998416i \(0.482083\pi\)
\(198\) 0.681245 + 1.17995i 0.0484140 + 0.0838555i
\(199\) 10.2009 17.6684i 0.723120 1.25248i −0.236624 0.971601i \(-0.576041\pi\)
0.959743 0.280878i \(-0.0906258\pi\)
\(200\) −0.864850 + 1.49796i −0.0611542 + 0.105922i
\(201\) 0.0621197 + 0.107594i 0.00438159 + 0.00758913i
\(202\) 6.13633 0.431751
\(203\) −9.24961 8.36468i −0.649195 0.587085i
\(204\) −0.903008 −0.0632232
\(205\) −0.632164 1.09494i −0.0441523 0.0764739i
\(206\) −0.132937 + 0.230253i −0.00926213 + 0.0160425i
\(207\) 12.9027 22.3481i 0.896799 1.55330i
\(208\) −6.29577 10.9046i −0.436533 0.756098i
\(209\) 2.75808 0.190781
\(210\) 0.0290008 0.135002i 0.00200124 0.00931600i
\(211\) −16.3729 −1.12716 −0.563580 0.826061i \(-0.690576\pi\)
−0.563580 + 0.826061i \(0.690576\pi\)
\(212\) −5.14258 8.90721i −0.353194 0.611750i
\(213\) −0.732365 + 1.26849i −0.0501808 + 0.0869157i
\(214\) 3.22889 5.59260i 0.220722 0.382302i
\(215\) −5.22682 9.05311i −0.356466 0.617417i
\(216\) 1.18481 0.0806161
\(217\) 25.8165 8.32660i 1.75254 0.565246i
\(218\) 2.46133 0.166702
\(219\) 0.609256 + 1.05526i 0.0411697 + 0.0713080i
\(220\) 0.895962 1.55185i 0.0604057 0.104626i
\(221\) 9.92178 17.1850i 0.667411 1.15599i
\(222\) 0.0592248 + 0.102580i 0.00397491 + 0.00688474i
\(223\) 12.9854 0.869569 0.434785 0.900534i \(-0.356825\pi\)
0.434785 + 0.900534i \(0.356825\pi\)
\(224\) −11.9210 + 3.84489i −0.796506 + 0.256898i
\(225\) −2.98691 −0.199127
\(226\) −3.24818 5.62602i −0.216066 0.374237i
\(227\) 7.48569 12.9656i 0.496843 0.860557i −0.503150 0.864199i \(-0.667826\pi\)
0.999993 + 0.00364156i \(0.00115915\pi\)
\(228\) 0.282730 0.489703i 0.0187243 0.0324314i
\(229\) 5.60355 + 9.70564i 0.370293 + 0.641367i 0.989611 0.143774i \(-0.0459239\pi\)
−0.619317 + 0.785141i \(0.712591\pi\)
\(230\) 3.94094 0.259858
\(231\) −0.0635767 + 0.295956i −0.00418304 + 0.0194725i
\(232\) 8.15304 0.535273
\(233\) 3.93590 + 6.81718i 0.257849 + 0.446608i 0.965666 0.259788i \(-0.0836528\pi\)
−0.707816 + 0.706397i \(0.750319\pi\)
\(234\) −3.06920 + 5.31602i −0.200640 + 0.347519i
\(235\) −5.76655 + 9.98796i −0.376168 + 0.651542i
\(236\) 7.93966 + 13.7519i 0.516828 + 0.895172i
\(237\) 1.05764 0.0687011
\(238\) −3.94261 3.56541i −0.255561 0.231111i
\(239\) 14.8640 0.961472 0.480736 0.876865i \(-0.340370\pi\)
0.480736 + 0.876865i \(0.340370\pi\)
\(240\) −0.159883 0.276925i −0.0103204 0.0178754i
\(241\) −4.49062 + 7.77799i −0.289266 + 0.501024i −0.973635 0.228112i \(-0.926745\pi\)
0.684368 + 0.729136i \(0.260078\pi\)
\(242\) 0.228077 0.395041i 0.0146613 0.0253942i
\(243\) 1.53560 + 2.65973i 0.0985086 + 0.170622i
\(244\) −8.43607 −0.540064
\(245\) −5.68086 + 4.08996i −0.362937 + 0.261298i
\(246\) −0.0659851 −0.00420706
\(247\) 6.21298 + 10.7612i 0.395322 + 0.684718i
\(248\) −8.86703 + 15.3582i −0.563057 + 0.975244i
\(249\) −0.148983 + 0.258047i −0.00944145 + 0.0163531i
\(250\) −0.228077 0.395041i −0.0144249 0.0249846i
\(251\) 0.937051 0.0591461 0.0295731 0.999563i \(-0.490585\pi\)
0.0295731 + 0.999563i \(0.490585\pi\)
\(252\) −10.5031 9.49822i −0.661632 0.598332i
\(253\) −8.63949 −0.543160
\(254\) −0.367895 0.637212i −0.0230838 0.0399823i
\(255\) 0.251966 0.436418i 0.0157787 0.0273296i
\(256\) −0.913694 + 1.58257i −0.0571059 + 0.0989103i
\(257\) −0.184203 0.319049i −0.0114903 0.0199017i 0.860223 0.509918i \(-0.170324\pi\)
−0.871713 + 0.490016i \(0.836991\pi\)
\(258\) −0.545574 −0.0339660
\(259\) 1.26116 5.87083i 0.0783647 0.364796i
\(260\) 8.07313 0.500674
\(261\) 7.03948 + 12.1927i 0.435733 + 0.754711i
\(262\) −3.26489 + 5.65495i −0.201705 + 0.349364i
\(263\) 2.89322 5.01120i 0.178403 0.309004i −0.762930 0.646481i \(-0.776240\pi\)
0.941334 + 0.337477i \(0.109573\pi\)
\(264\) −0.0989500 0.171386i −0.00608995 0.0105481i
\(265\) 5.73973 0.352589
\(266\) 3.16795 1.02176i 0.194239 0.0626481i
\(267\) −0.458007 −0.0280296
\(268\) 0.972913 + 1.68513i 0.0594301 + 0.102936i
\(269\) 5.08076 8.80014i 0.309779 0.536554i −0.668535 0.743681i \(-0.733078\pi\)
0.978314 + 0.207127i \(0.0664114\pi\)
\(270\) −0.156228 + 0.270595i −0.00950774 + 0.0164679i
\(271\) −10.7032 18.5385i −0.650174 1.12613i −0.983080 0.183175i \(-0.941363\pi\)
0.332906 0.942960i \(-0.391971\pi\)
\(272\) −12.3099 −0.746396
\(273\) −1.29795 + 0.418627i −0.0785553 + 0.0253365i
\(274\) 3.70101 0.223586
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) −0.885631 + 1.53396i −0.0533087 + 0.0923334i
\(277\) 0.555299 0.961805i 0.0333647 0.0577893i −0.848861 0.528616i \(-0.822711\pi\)
0.882226 + 0.470827i \(0.156044\pi\)
\(278\) 3.73857 + 6.47539i 0.224225 + 0.388368i
\(279\) −30.6238 −1.83340
\(280\) 0.961156 4.47429i 0.0574401 0.267390i
\(281\) 1.63227 0.0973730 0.0486865 0.998814i \(-0.484496\pi\)
0.0486865 + 0.998814i \(0.484496\pi\)
\(282\) 0.300956 + 0.521270i 0.0179216 + 0.0310412i
\(283\) −5.64650 + 9.78002i −0.335649 + 0.581362i −0.983609 0.180313i \(-0.942289\pi\)
0.647960 + 0.761674i \(0.275622\pi\)
\(284\) −11.4702 + 19.8670i −0.680633 + 1.17889i
\(285\) 0.157780 + 0.273283i 0.00934609 + 0.0161879i
\(286\) 2.05510 0.121521
\(287\) 2.48105 + 2.24368i 0.146452 + 0.132440i
\(288\) 14.1409 0.833258
\(289\) −1.19983 2.07816i −0.0705781 0.122245i
\(290\) −1.07505 + 1.86205i −0.0631293 + 0.109343i
\(291\) −0.288163 + 0.499113i −0.0168924 + 0.0292585i
\(292\) 9.54210 + 16.5274i 0.558409 + 0.967193i
\(293\) −1.08939 −0.0636429 −0.0318214 0.999494i \(-0.510131\pi\)
−0.0318214 + 0.999494i \(0.510131\pi\)
\(294\) 0.0366155 + 0.363490i 0.00213546 + 0.0211991i
\(295\) −8.86161 −0.515943
\(296\) 1.96285 + 3.39976i 0.114089 + 0.197607i
\(297\) 0.342490 0.593210i 0.0198733 0.0344215i
\(298\) −3.40056 + 5.88994i −0.196989 + 0.341195i
\(299\) −19.4617 33.7086i −1.12550 1.94942i
\(300\) 0.205019 0.0118368
\(301\) 20.5136 + 18.5510i 1.18239 + 1.06926i
\(302\) 10.4669 0.602305
\(303\) −0.769560 1.33292i −0.0442101 0.0765741i
\(304\) 3.85420 6.67567i 0.221053 0.382876i
\(305\) 2.35391 4.07710i 0.134785 0.233454i
\(306\) 3.00055 + 5.19710i 0.171530 + 0.297098i
\(307\) −18.5398 −1.05812 −0.529060 0.848585i \(-0.677455\pi\)
−0.529060 + 0.848585i \(0.677455\pi\)
\(308\) −0.995732 + 4.63524i −0.0567371 + 0.264117i
\(309\) 0.0666865 0.00379366
\(310\) −2.33840 4.05023i −0.132812 0.230037i
\(311\) −4.27772 + 7.40923i −0.242567 + 0.420139i −0.961445 0.274998i \(-0.911323\pi\)
0.718878 + 0.695137i \(0.244656\pi\)
\(312\) 0.445798 0.772145i 0.0252384 0.0437141i
\(313\) −5.21356 9.03015i −0.294688 0.510414i 0.680224 0.733004i \(-0.261882\pi\)
−0.974912 + 0.222590i \(0.928549\pi\)
\(314\) −8.13675 −0.459183
\(315\) 7.52110 2.42578i 0.423766 0.136677i
\(316\) 16.5647 0.931835
\(317\) 0.661522 + 1.14579i 0.0371548 + 0.0643540i 0.884005 0.467478i \(-0.154837\pi\)
−0.846850 + 0.531832i \(0.821504\pi\)
\(318\) 0.149778 0.259423i 0.00839913 0.0145477i
\(319\) 2.35678 4.08206i 0.131954 0.228551i
\(320\) −1.71506 2.97057i −0.0958747 0.166060i
\(321\) −1.61974 −0.0904053
\(322\) −9.92336 + 3.20059i −0.553007 + 0.178362i
\(323\) 12.1480 0.675932
\(324\) 7.95825 + 13.7841i 0.442125 + 0.765783i
\(325\) −2.25264 + 3.90169i −0.124954 + 0.216427i
\(326\) −4.95039 + 8.57432i −0.274177 + 0.474888i
\(327\) −0.308677 0.534644i −0.0170699 0.0295659i
\(328\) −2.18691 −0.120752
\(329\) 6.40869 29.8331i 0.353322 1.64475i
\(330\) 0.0521899 0.00287296
\(331\) −11.4434 19.8206i −0.628987 1.08944i −0.987755 0.156010i \(-0.950137\pi\)
0.358769 0.933426i \(-0.383197\pi\)
\(332\) −2.33337 + 4.04151i −0.128060 + 0.221807i
\(333\) −3.38953 + 5.87083i −0.185745 + 0.321720i
\(334\) 0.578742 + 1.00241i 0.0316674 + 0.0548495i
\(335\) −1.08589 −0.0593283
\(336\) 0.627490 + 0.567456i 0.0342324 + 0.0309573i
\(337\) −18.4079 −1.00274 −0.501372 0.865232i \(-0.667171\pi\)
−0.501372 + 0.865232i \(0.667171\pi\)
\(338\) 1.66442 + 2.88285i 0.0905323 + 0.156807i
\(339\) −0.814712 + 1.41112i −0.0442491 + 0.0766417i
\(340\) 3.94627 6.83514i 0.214016 0.370687i
\(341\) 5.12634 + 8.87908i 0.277607 + 0.480829i
\(342\) −3.75786 −0.203202
\(343\) 10.9829 14.9123i 0.593021 0.805187i
\(344\) −18.0817 −0.974898
\(345\) −0.494235 0.856039i −0.0266087 0.0460876i
\(346\) 2.26278 3.91925i 0.121648 0.210700i
\(347\) −4.99277 + 8.64773i −0.268026 + 0.464234i −0.968352 0.249589i \(-0.919705\pi\)
0.700326 + 0.713823i \(0.253038\pi\)
\(348\) −0.483184 0.836900i −0.0259014 0.0448625i
\(349\) −24.0504 −1.28739 −0.643694 0.765283i \(-0.722599\pi\)
−0.643694 + 0.765283i \(0.722599\pi\)
\(350\) 0.895131 + 0.809491i 0.0478467 + 0.0432691i
\(351\) 3.08603 0.164720
\(352\) −2.36714 4.10000i −0.126169 0.218531i
\(353\) 11.8135 20.4616i 0.628770 1.08906i −0.359028 0.933327i \(-0.616892\pi\)
0.987799 0.155736i \(-0.0497748\pi\)
\(354\) −0.231243 + 0.400525i −0.0122904 + 0.0212877i
\(355\) −6.40107 11.0870i −0.339733 0.588435i
\(356\) −7.17326 −0.380182
\(357\) −0.280024 + 1.30354i −0.0148204 + 0.0689907i
\(358\) 2.67520 0.141388
\(359\) −1.83335 3.17545i −0.0967603 0.167594i 0.813582 0.581451i \(-0.197515\pi\)
−0.910342 + 0.413857i \(0.864181\pi\)
\(360\) −2.58323 + 4.47429i −0.136148 + 0.235816i
\(361\) 5.69649 9.86660i 0.299815 0.519295i
\(362\) −3.92076 6.79095i −0.206070 0.356924i
\(363\) −0.114413 −0.00600512
\(364\) −20.3283 + 6.55650i −1.06549 + 0.343654i
\(365\) −10.6501 −0.557453
\(366\) −0.122851 0.212783i −0.00642150 0.0111224i
\(367\) −9.64824 + 16.7112i −0.503634 + 0.872320i 0.496357 + 0.868118i \(0.334671\pi\)
−0.999991 + 0.00420139i \(0.998663\pi\)
\(368\) −12.0730 + 20.9110i −0.629348 + 1.09006i
\(369\) −1.88822 3.27049i −0.0982967 0.170255i
\(370\) −1.03528 −0.0538217
\(371\) −14.4528 + 4.66146i −0.750350 + 0.242011i
\(372\) 2.10200 0.108983
\(373\) 9.95630 + 17.2448i 0.515518 + 0.892903i 0.999838 + 0.0180120i \(0.00573370\pi\)
−0.484320 + 0.874891i \(0.660933\pi\)
\(374\) 1.00457 1.73996i 0.0519449 0.0899711i
\(375\) −0.0572064 + 0.0990845i −0.00295413 + 0.00511670i
\(376\) 9.97440 + 17.2762i 0.514391 + 0.890951i
\(377\) 21.2359 1.09370
\(378\) 0.173625 0.808243i 0.00893030 0.0415715i
\(379\) 15.7649 0.809789 0.404894 0.914363i \(-0.367308\pi\)
0.404894 + 0.914363i \(0.367308\pi\)
\(380\) 2.47114 + 4.28014i 0.126767 + 0.219566i
\(381\) −0.0922757 + 0.159826i −0.00472743 + 0.00818814i
\(382\) −2.95365 + 5.11588i −0.151122 + 0.261751i
\(383\) 2.35543 + 4.07972i 0.120357 + 0.208464i 0.919908 0.392133i \(-0.128263\pi\)
−0.799552 + 0.600597i \(0.794930\pi\)
\(384\) −1.26234 −0.0644186
\(385\) −1.96234 1.77460i −0.100010 0.0904420i
\(386\) 1.29124 0.0657222
\(387\) −15.6120 27.0408i −0.793604 1.37456i
\(388\) −4.51319 + 7.81707i −0.229122 + 0.396851i
\(389\) −3.54729 + 6.14409i −0.179855 + 0.311517i −0.941831 0.336088i \(-0.890896\pi\)
0.761976 + 0.647605i \(0.224229\pi\)
\(390\) 0.117565 + 0.203629i 0.00595314 + 0.0103111i
\(391\) −38.0527 −1.92441
\(392\) 1.21353 + 12.0469i 0.0612924 + 0.608462i
\(393\) 1.63780 0.0826162
\(394\) 0.360192 + 0.623870i 0.0181462 + 0.0314301i
\(395\) −4.62203 + 8.00559i −0.232560 + 0.402805i
\(396\) 2.67616 4.63524i 0.134482 0.232930i
\(397\) 0.362935 + 0.628622i 0.0182152 + 0.0315497i 0.874989 0.484142i \(-0.160868\pi\)
−0.856774 + 0.515692i \(0.827535\pi\)
\(398\) 9.30632 0.466484
\(399\) −0.619238 0.559994i −0.0310007 0.0280348i
\(400\) 2.79484 0.139742
\(401\) −15.8456 27.4454i −0.791292 1.37056i −0.925167 0.379560i \(-0.876075\pi\)
0.133875 0.990998i \(-0.457258\pi\)
\(402\) −0.0283361 + 0.0490796i −0.00141328 + 0.00244787i
\(403\) −23.0956 + 40.0028i −1.15048 + 1.99268i
\(404\) −12.0528 20.8760i −0.599648 1.03862i
\(405\) −8.88236 −0.441368
\(406\) 1.19477 5.56176i 0.0592952 0.276026i
\(407\) 2.26959 0.112499
\(408\) −0.435826 0.754872i −0.0215766 0.0373718i
\(409\) −9.41335 + 16.3044i −0.465460 + 0.806201i −0.999222 0.0394338i \(-0.987445\pi\)
0.533762 + 0.845635i \(0.320778\pi\)
\(410\) 0.288364 0.499461i 0.0142413 0.0246666i
\(411\) −0.464145 0.803923i −0.0228946 0.0396546i
\(412\) 1.04444 0.0514558
\(413\) 22.3137 7.19686i 1.09799 0.354134i
\(414\) 11.7712 0.578524
\(415\) −1.30216 2.25540i −0.0639203 0.110713i
\(416\) 10.6646 18.4717i 0.522877 0.905649i
\(417\) 0.937711 1.62416i 0.0459199 0.0795356i
\(418\) 0.629055 + 1.08956i 0.0307681 + 0.0532919i
\(419\) −9.64442 −0.471161 −0.235580 0.971855i \(-0.575699\pi\)
−0.235580 + 0.971855i \(0.575699\pi\)
\(420\) −0.516243 + 0.166504i −0.0251901 + 0.00812456i
\(421\) 33.7268 1.64374 0.821872 0.569672i \(-0.192930\pi\)
0.821872 + 0.569672i \(0.192930\pi\)
\(422\) −3.73429 6.46798i −0.181782 0.314856i
\(423\) −17.2242 + 29.8331i −0.837467 + 1.45054i
\(424\) 4.96401 8.59792i 0.241074 0.417552i
\(425\) 2.20225 + 3.81441i 0.106825 + 0.185026i
\(426\) −0.668142 −0.0323716
\(427\) −2.61604 + 12.1779i −0.126599 + 0.589331i
\(428\) −25.3683 −1.22622
\(429\) −0.257731 0.446404i −0.0124434 0.0215526i
\(430\) 2.38423 4.12961i 0.114978 0.199148i
\(431\) −2.02474 + 3.50696i −0.0975285 + 0.168924i −0.910661 0.413154i \(-0.864427\pi\)
0.813133 + 0.582079i \(0.197760\pi\)
\(432\) −0.957203 1.65793i −0.0460535 0.0797670i
\(433\) 28.2700 1.35857 0.679284 0.733876i \(-0.262290\pi\)
0.679284 + 0.733876i \(0.262290\pi\)
\(434\) 9.17749 + 8.29945i 0.440533 + 0.398386i
\(435\) 0.539291 0.0258570
\(436\) −4.83446 8.37354i −0.231529 0.401020i
\(437\) 11.9142 20.6360i 0.569934 0.987155i
\(438\) −0.277914 + 0.481362i −0.0132793 + 0.0230003i
\(439\) 7.88172 + 13.6515i 0.376174 + 0.651552i 0.990502 0.137499i \(-0.0439062\pi\)
−0.614328 + 0.789051i \(0.710573\pi\)
\(440\) 1.72970 0.0824602
\(441\) −16.9682 + 12.2164i −0.808010 + 0.581731i
\(442\) 9.05171 0.430546
\(443\) 0.745210 + 1.29074i 0.0354060 + 0.0613250i 0.883185 0.469024i \(-0.155394\pi\)
−0.847779 + 0.530349i \(0.822061\pi\)
\(444\) 0.232655 0.402969i 0.0110413 0.0191241i
\(445\) 2.00155 3.46679i 0.0948827 0.164342i
\(446\) 2.96168 + 5.12978i 0.140240 + 0.242902i
\(447\) 1.70586 0.0806844
\(448\) 6.73107 + 6.08709i 0.318013 + 0.287588i
\(449\) −39.0741 −1.84402 −0.922011 0.387163i \(-0.873455\pi\)
−0.922011 + 0.387163i \(0.873455\pi\)
\(450\) −0.681245 1.17995i −0.0321142 0.0556234i
\(451\) −0.632164 + 1.09494i −0.0297674 + 0.0515587i
\(452\) −12.7599 + 22.1009i −0.600177 + 1.03954i
\(453\) −1.31266 2.27360i −0.0616743 0.106823i
\(454\) 6.82926 0.320513
\(455\) 2.50349 11.6540i 0.117365 0.546348i
\(456\) 0.545825 0.0255606
\(457\) 5.33822 + 9.24607i 0.249711 + 0.432513i 0.963446 0.267904i \(-0.0863309\pi\)
−0.713734 + 0.700417i \(0.752998\pi\)
\(458\) −2.55608 + 4.42726i −0.119438 + 0.206872i
\(459\) 1.50850 2.61279i 0.0704106 0.121955i
\(460\) −7.74065 13.4072i −0.360910 0.625114i
\(461\) −15.6778 −0.730190 −0.365095 0.930970i \(-0.618963\pi\)
−0.365095 + 0.930970i \(0.618963\pi\)
\(462\) −0.131415 + 0.0423854i −0.00611399 + 0.00197195i
\(463\) 11.0374 0.512953 0.256476 0.966551i \(-0.417438\pi\)
0.256476 + 0.966551i \(0.417438\pi\)
\(464\) −6.58681 11.4087i −0.305785 0.529635i
\(465\) −0.586519 + 1.01588i −0.0271992 + 0.0471104i
\(466\) −1.79538 + 3.10968i −0.0831692 + 0.144053i
\(467\) −5.86901 10.1654i −0.271585 0.470399i 0.697683 0.716407i \(-0.254215\pi\)
−0.969268 + 0.246007i \(0.920881\pi\)
\(468\) 24.1137 1.11466
\(469\) 2.73429 0.881890i 0.126258 0.0407219i
\(470\) −5.26087 −0.242666
\(471\) 1.02043 + 1.76744i 0.0470191 + 0.0814394i
\(472\) −7.66397 + 13.2744i −0.352763 + 0.611003i
\(473\) −5.22682 + 9.05311i −0.240329 + 0.416263i
\(474\) 0.241223 + 0.417811i 0.0110798 + 0.0191907i
\(475\) −2.75808 −0.126550
\(476\) −4.38571 + 20.4159i −0.201019 + 0.935763i
\(477\) 17.1441 0.784973
\(478\) 3.39013 + 5.87188i 0.155061 + 0.268574i
\(479\) 18.2677 31.6406i 0.834674 1.44570i −0.0596215 0.998221i \(-0.518989\pi\)
0.894296 0.447477i \(-0.147677\pi\)
\(480\) 0.270831 0.469093i 0.0123617 0.0214111i
\(481\) 5.11257 + 8.85523i 0.233113 + 0.403764i
\(482\) −4.09683 −0.186605
\(483\) 1.93972 + 1.75414i 0.0882601 + 0.0798161i
\(484\) −1.79192 −0.0814511
\(485\) −2.51863 4.36239i −0.114365 0.198086i
\(486\) −0.700469 + 1.21325i −0.0317739 + 0.0550340i
\(487\) 12.7359 22.0592i 0.577119 0.999599i −0.418689 0.908130i \(-0.637510\pi\)
0.995808 0.0914697i \(-0.0291565\pi\)
\(488\) −4.07157 7.05216i −0.184311 0.319236i
\(489\) 2.48332 0.112300
\(490\) −2.91138 1.31135i −0.131523 0.0592406i
\(491\) 16.7966 0.758018 0.379009 0.925393i \(-0.376265\pi\)
0.379009 + 0.925393i \(0.376265\pi\)
\(492\) 0.129606 + 0.224484i 0.00584308 + 0.0101205i
\(493\) 10.3804 17.9794i 0.467511 0.809753i
\(494\) −2.83407 + 4.90876i −0.127511 + 0.220856i
\(495\) 1.49345 + 2.58674i 0.0671258 + 0.116265i
\(496\) 28.6546 1.28663
\(497\) 25.1222 + 22.7187i 1.12688 + 1.01907i
\(498\) −0.135919 −0.00609067
\(499\) −7.10185 12.3008i −0.317922 0.550658i 0.662132 0.749387i \(-0.269652\pi\)
−0.980054 + 0.198730i \(0.936318\pi\)
\(500\) −0.895962 + 1.55185i −0.0400686 + 0.0694009i
\(501\) 0.145161 0.251426i 0.00648530 0.0112329i
\(502\) 0.213720 + 0.370173i 0.00953878 + 0.0165217i
\(503\) 26.3324 1.17410 0.587051 0.809550i \(-0.300289\pi\)
0.587051 + 0.809550i \(0.300289\pi\)
\(504\) 2.87089 13.3643i 0.127879 0.595293i
\(505\) 13.4523 0.598621
\(506\) −1.97047 3.41295i −0.0875980 0.151724i
\(507\) 0.417470 0.723080i 0.0185405 0.0321131i
\(508\) −1.44521 + 2.50318i −0.0641209 + 0.111061i
\(509\) 3.56023 + 6.16650i 0.157804 + 0.273325i 0.934077 0.357073i \(-0.116225\pi\)
−0.776272 + 0.630398i \(0.782892\pi\)
\(510\) 0.229871 0.0101788
\(511\) 26.8172 8.64937i 1.18632 0.382626i
\(512\) −22.9000 −1.01205
\(513\) 0.944616 + 1.63612i 0.0417058 + 0.0722366i
\(514\) 0.0840248 0.145535i 0.00370617 0.00641928i
\(515\) −0.291429 + 0.504770i −0.0128419 + 0.0222428i
\(516\) 1.07160 + 1.85606i 0.0471745 + 0.0817086i
\(517\) 11.5331 0.507225
\(518\) 2.60686 0.840792i 0.114539 0.0369423i
\(519\) −1.13511 −0.0498256
\(520\) 3.89640 + 6.74876i 0.170868 + 0.295953i
\(521\) 1.07498 1.86192i 0.0470957 0.0815721i −0.841517 0.540231i \(-0.818337\pi\)
0.888612 + 0.458659i \(0.151670\pi\)
\(522\) −3.21109 + 5.56176i −0.140545 + 0.243432i
\(523\) −8.45938 14.6521i −0.369903 0.640691i 0.619647 0.784881i \(-0.287276\pi\)
−0.989550 + 0.144190i \(0.953942\pi\)
\(524\) 25.6511 1.12057
\(525\) 0.0635767 0.295956i 0.00277472 0.0129166i
\(526\) 2.63950 0.115088
\(527\) 22.5790 + 39.1079i 0.983556 + 1.70357i
\(528\) −0.159883 + 0.276925i −0.00695800 + 0.0120516i
\(529\) −25.8204 + 44.7223i −1.12263 + 1.94445i
\(530\) 1.30910 + 2.26743i 0.0568637 + 0.0984908i
\(531\) −26.4688 −1.14865
\(532\) −9.69844 8.77057i −0.420481 0.380252i
\(533\) −5.69616 −0.246728
\(534\) −0.104461 0.180931i −0.00452046 0.00782967i
\(535\) 7.07851 12.2603i 0.306031 0.530060i
\(536\) −0.939129 + 1.62662i −0.0405642 + 0.0702593i
\(537\) −0.335497 0.581099i −0.0144778 0.0250763i
\(538\) 4.63522 0.199838
\(539\) 6.38244 + 2.87479i 0.274911 + 0.123826i
\(540\) 1.22743 0.0528202
\(541\) −0.217764 0.377178i −0.00936239 0.0162161i 0.861306 0.508086i \(-0.169647\pi\)
−0.870669 + 0.491870i \(0.836314\pi\)
\(542\) 4.88231 8.45641i 0.209713 0.363234i
\(543\) −0.983407 + 1.70331i −0.0422020 + 0.0730961i
\(544\) −10.4261 18.0585i −0.447014 0.774251i
\(545\) 5.39584 0.231132
\(546\) −0.461407 0.417263i −0.0197464 0.0178572i
\(547\) 2.04321 0.0873612 0.0436806 0.999046i \(-0.486092\pi\)
0.0436806 + 0.999046i \(0.486092\pi\)
\(548\) −7.26940 12.5910i −0.310533 0.537859i
\(549\) 7.03093 12.1779i 0.300073 0.519741i
\(550\) −0.228077 + 0.395041i −0.00972523 + 0.0168446i
\(551\) 6.50019 + 11.2587i 0.276917 + 0.479635i
\(552\) −1.70976 −0.0727720
\(553\) 5.13672 23.9120i 0.218436 1.01684i
\(554\) 0.506603 0.0215235
\(555\) 0.129835 + 0.224881i 0.00551119 + 0.00954566i
\(556\) 14.6863 25.4375i 0.622840 1.07879i
\(557\) 13.6958 23.7219i 0.580311 1.00513i −0.415131 0.909762i \(-0.636264\pi\)
0.995442 0.0953669i \(-0.0304024\pi\)
\(558\) −6.98459 12.0977i −0.295681 0.512135i
\(559\) −47.0966 −1.99198
\(560\) −7.03746 + 2.26980i −0.297387 + 0.0959164i
\(561\) −0.503932 −0.0212760
\(562\) 0.372283 + 0.644813i 0.0157038 + 0.0271998i
\(563\) 1.57601 2.72973i 0.0664209 0.115044i −0.830902 0.556418i \(-0.812175\pi\)
0.897323 + 0.441374i \(0.145509\pi\)
\(564\) 1.18225 2.04772i 0.0497818 0.0862247i
\(565\) −7.12081 12.3336i −0.299575 0.518878i
\(566\) −5.15134 −0.216527
\(567\) 22.3660 7.21371i 0.939282 0.302947i
\(568\) −22.1439 −0.929136
\(569\) 21.0547 + 36.4678i 0.882659 + 1.52881i 0.848373 + 0.529398i \(0.177582\pi\)
0.0342855 + 0.999412i \(0.489084\pi\)
\(570\) −0.0719720 + 0.124659i −0.00301458 + 0.00522140i
\(571\) 12.8882 22.3230i 0.539353 0.934186i −0.459586 0.888133i \(-0.652002\pi\)
0.998939 0.0460533i \(-0.0146644\pi\)
\(572\) −4.03656 6.99154i −0.168777 0.292331i
\(573\) 1.48167 0.0618979
\(574\) −0.320475 + 1.49185i −0.0133764 + 0.0622684i
\(575\) 8.63949 0.360292
\(576\) −5.12272 8.87282i −0.213447 0.369701i
\(577\) −8.31003 + 14.3934i −0.345951 + 0.599205i −0.985526 0.169524i \(-0.945777\pi\)
0.639575 + 0.768729i \(0.279110\pi\)
\(578\) 0.547306 0.947962i 0.0227649 0.0394300i
\(579\) −0.161934 0.280479i −0.00672976 0.0116563i
\(580\) 8.44633 0.350715
\(581\) 5.11056 + 4.62162i 0.212022 + 0.191737i
\(582\) −0.262894 −0.0108973
\(583\) −2.86987 4.97076i −0.118858 0.205868i
\(584\) −9.21076 + 15.9535i −0.381144 + 0.660161i
\(585\) −6.72844 + 11.6540i −0.278187 + 0.481834i
\(586\) −0.248465 0.430354i −0.0102640 0.0177777i
\(587\) 12.5734 0.518958 0.259479 0.965749i \(-0.416449\pi\)
0.259479 + 0.965749i \(0.416449\pi\)
\(588\) 1.16469 0.838521i 0.0480308 0.0345800i
\(589\) −28.2778 −1.16516
\(590\) −2.02113 3.50070i −0.0832085 0.144121i
\(591\) 0.0903436 0.156480i 0.00371624 0.00643671i
\(592\) 3.17157 5.49331i 0.130351 0.225774i
\(593\) −6.12297 10.6053i −0.251440 0.435507i 0.712482 0.701690i \(-0.247571\pi\)
−0.963923 + 0.266183i \(0.914237\pi\)
\(594\) 0.312456 0.0128202
\(595\) −8.64315 7.81624i −0.354335 0.320434i
\(596\) 26.7170 1.09437
\(597\) −1.16711 2.02149i −0.0477666 0.0827342i
\(598\) 8.87753 15.3763i 0.363029 0.628785i
\(599\) 15.4057 26.6834i 0.629460 1.09026i −0.358201 0.933645i \(-0.616610\pi\)
0.987660 0.156611i \(-0.0500570\pi\)
\(600\) 0.0989500 + 0.171386i 0.00403962 + 0.00699682i
\(601\) −35.2612 −1.43833 −0.719166 0.694838i \(-0.755476\pi\)
−0.719166 + 0.694838i \(0.755476\pi\)
\(602\) −2.64973 + 12.3348i −0.107995 + 0.502728i
\(603\) −3.24344 −0.132083
\(604\) −20.5588 35.6089i −0.836526 1.44891i
\(605\) 0.500000 0.866025i 0.0203279 0.0352089i
\(606\) 0.351038 0.608015i 0.0142599 0.0246989i
\(607\) −1.43290 2.48185i −0.0581595 0.100735i 0.835480 0.549521i \(-0.185190\pi\)
−0.893639 + 0.448786i \(0.851857\pi\)
\(608\) 13.0575 0.529553
\(609\) −1.35795 + 0.437979i −0.0550268 + 0.0177478i
\(610\) 2.14749 0.0869495
\(611\) 25.9800 + 44.9986i 1.05104 + 1.82045i
\(612\) 11.7871 20.4159i 0.476467 0.825265i
\(613\) −2.28952 + 3.96556i −0.0924728 + 0.160168i −0.908551 0.417774i \(-0.862810\pi\)
0.816078 + 0.577941i \(0.196144\pi\)
\(614\) −4.22849 7.32396i −0.170648 0.295571i
\(615\) −0.144655 −0.00583307
\(616\) −4.35542 + 1.40476i −0.175485 + 0.0565993i
\(617\) 24.5005 0.986353 0.493176 0.869929i \(-0.335836\pi\)
0.493176 + 0.869929i \(0.335836\pi\)
\(618\) 0.0152097 + 0.0263439i 0.000611822 + 0.00105971i
\(619\) 17.2517 29.8809i 0.693405 1.20101i −0.277310 0.960780i \(-0.589443\pi\)
0.970715 0.240232i \(-0.0772237\pi\)
\(620\) −9.18601 + 15.9106i −0.368919 + 0.638986i
\(621\) −2.95894 5.12503i −0.118738 0.205660i
\(622\) −3.90260 −0.156480
\(623\) −2.22444 + 10.3550i −0.0891202 + 0.414864i
\(624\) −1.44064 −0.0576716
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 2.37819 4.11914i 0.0950514 0.164634i
\(627\) 0.157780 0.273283i 0.00630113 0.0109139i
\(628\) 15.9819 + 27.6815i 0.637748 + 1.10461i
\(629\) 9.99641 0.398583
\(630\) 2.67367 + 2.41788i 0.106522 + 0.0963305i
\(631\) 41.4967 1.65196 0.825979 0.563702i \(-0.190623\pi\)
0.825979 + 0.563702i \(0.190623\pi\)
\(632\) 7.99473 + 13.8473i 0.318013 + 0.550815i
\(633\) −0.936638 + 1.62230i −0.0372280 + 0.0644808i
\(634\) −0.301756 + 0.522656i −0.0119843 + 0.0207573i
\(635\) −0.806515 1.39692i −0.0320056 0.0554352i
\(636\) −1.17676 −0.0466614
\(637\) 3.16083 + 31.3782i 0.125237 + 1.24325i
\(638\) 2.15011 0.0851235
\(639\) −19.1194 33.1158i −0.756352 1.31004i
\(640\) 5.51661 9.55504i 0.218063 0.377696i
\(641\) −2.77652 + 4.80907i −0.109666 + 0.189947i −0.915635 0.402011i \(-0.868311\pi\)
0.805969 + 0.591958i \(0.201645\pi\)
\(642\) −0.369426 0.639865i −0.0145801 0.0252535i
\(643\) −47.5230 −1.87412 −0.937061 0.349164i \(-0.886465\pi\)
−0.937061 + 0.349164i \(0.886465\pi\)
\(644\) 30.3796 + 27.4731i 1.19713 + 1.08259i
\(645\) −1.19603 −0.0470937
\(646\) 2.77068 + 4.79895i 0.109011 + 0.188812i
\(647\) 11.9333 20.6691i 0.469147 0.812587i −0.530231 0.847853i \(-0.677895\pi\)
0.999378 + 0.0352665i \(0.0112280\pi\)
\(648\) −7.68191 + 13.3055i −0.301774 + 0.522688i
\(649\) 4.43080 + 7.67438i 0.173924 + 0.301246i
\(650\) −2.05510 −0.0806078
\(651\) 0.651832 3.03435i 0.0255473 0.118925i
\(652\) 38.8935 1.52319
\(653\) 8.46747 + 14.6661i 0.331358 + 0.573928i 0.982778 0.184788i \(-0.0591600\pi\)
−0.651421 + 0.758717i \(0.725827\pi\)
\(654\) 0.140804 0.243880i 0.00550587 0.00953645i
\(655\) −7.15742 + 12.3970i −0.279664 + 0.484392i
\(656\) 1.76680 + 3.06018i 0.0689818 + 0.119480i
\(657\) −31.8109 −1.24106
\(658\) 13.2470 4.27255i 0.516421 0.166562i
\(659\) 12.5122 0.487407 0.243703 0.969850i \(-0.421638\pi\)
0.243703 + 0.969850i \(0.421638\pi\)
\(660\) −0.102510 0.177552i −0.00399018 0.00691119i
\(661\) −5.00645 + 8.67142i −0.194728 + 0.337279i −0.946811 0.321789i \(-0.895716\pi\)
0.752083 + 0.659068i \(0.229049\pi\)
\(662\) 5.21995 9.04123i 0.202879 0.351397i
\(663\) −1.13518 1.96619i −0.0440867 0.0763604i
\(664\) −4.50468 −0.174816
\(665\) 6.94491 2.23995i 0.269312 0.0868614i
\(666\) −3.09229 −0.119824
\(667\) −20.3614 35.2669i −0.788395 1.36554i
\(668\) 2.27349 3.93780i 0.0879641 0.152358i
\(669\) 0.742851 1.28666i 0.0287203 0.0497450i
\(670\) −0.247666 0.428969i −0.00956816 0.0165725i
\(671\) −4.70783 −0.181744
\(672\) −0.300990 + 1.40114i −0.0116109 + 0.0540501i
\(673\) 14.6357 0.564163 0.282082 0.959390i \(-0.408975\pi\)
0.282082 + 0.959390i \(0.408975\pi\)
\(674\) −4.19843 7.27189i −0.161717 0.280103i
\(675\) −0.342490 + 0.593210i −0.0131824 + 0.0228327i
\(676\) 6.53838 11.3248i 0.251476 0.435569i
\(677\) −18.8759 32.6939i −0.725458 1.25653i −0.958785 0.284132i \(-0.908295\pi\)
0.233327 0.972398i \(-0.425039\pi\)
\(678\) −0.743268 −0.0285450
\(679\) 9.88482 + 8.93911i 0.379345 + 0.343052i
\(680\) 7.61847 0.292155
\(681\) −0.856460 1.48343i −0.0328196 0.0568452i
\(682\) −2.33840 + 4.05023i −0.0895420 + 0.155091i
\(683\) −14.7844 + 25.6073i −0.565709 + 0.979837i 0.431274 + 0.902221i \(0.358064\pi\)
−0.996983 + 0.0776158i \(0.975269\pi\)
\(684\) 7.38107 + 12.7844i 0.282222 + 0.488823i
\(685\) 8.11351 0.310001
\(686\) 8.39590 + 0.937554i 0.320557 + 0.0357960i
\(687\) 1.28224 0.0489204
\(688\) 14.6081 + 25.3020i 0.556929 + 0.964629i
\(689\) 12.9296 22.3947i 0.492577 0.853169i
\(690\) 0.225447 0.390486i 0.00858262 0.0148655i
\(691\) −1.34742 2.33380i −0.0512583 0.0887819i 0.839258 0.543734i \(-0.182990\pi\)
−0.890516 + 0.454952i \(0.849657\pi\)
\(692\) −17.7779 −0.675815
\(693\) −5.86134 5.30057i −0.222654 0.201352i
\(694\) −4.55494 −0.172903
\(695\) 8.19585 + 14.1956i 0.310886 + 0.538471i
\(696\) 0.466406 0.807839i 0.0176791 0.0306211i
\(697\) −2.78437 + 4.82267i −0.105466 + 0.182672i
\(698\) −5.48534 9.50089i −0.207623 0.359614i
\(699\) 0.900635 0.0340652
\(700\) 0.995732 4.63524i 0.0376351 0.175196i
\(701\) −36.6363 −1.38373 −0.691867 0.722025i \(-0.743211\pi\)
−0.691867 + 0.722025i \(0.743211\pi\)
\(702\) 0.703852 + 1.21911i 0.0265652 + 0.0460123i
\(703\) −3.12986 + 5.42107i −0.118045 + 0.204460i
\(704\) −1.71506 + 2.97057i −0.0646387 + 0.111957i
\(705\) 0.659768 + 1.14275i 0.0248483 + 0.0430385i
\(706\) 10.7776 0.405619
\(707\) −33.8733 + 10.9252i −1.27393 + 0.410883i
\(708\) 1.81680 0.0682795
\(709\) 8.77583 + 15.2002i 0.329583 + 0.570855i 0.982429 0.186636i \(-0.0597584\pi\)
−0.652846 + 0.757491i \(0.726425\pi\)
\(710\) 2.91987 5.05737i 0.109581 0.189800i
\(711\) −13.8056 + 23.9120i −0.517750 + 0.896769i
\(712\) −3.46209 5.99651i −0.129747 0.224729i
\(713\) 88.5779 3.31727
\(714\) −0.578819 + 0.186687i −0.0216618 + 0.00698658i
\(715\) 4.50529 0.168488
\(716\) −5.25453 9.10111i −0.196371 0.340124i
\(717\) 0.850316 1.47279i 0.0317556 0.0550024i
\(718\) 0.836288 1.44849i 0.0312100 0.0540573i
\(719\) 8.10580 + 14.0397i 0.302295 + 0.523591i 0.976655 0.214812i \(-0.0689138\pi\)
−0.674360 + 0.738403i \(0.735580\pi\)
\(720\) 8.34793 0.311109
\(721\) 0.323882 1.50770i 0.0120620 0.0561498i
\(722\) 5.19695 0.193410
\(723\) 0.513785 + 0.889902i 0.0191079 + 0.0330958i
\(724\) −15.4020 + 26.6771i −0.572412 + 0.991447i
\(725\) −2.35678 + 4.08206i −0.0875285 + 0.151604i
\(726\) −0.0260949 0.0451978i −0.000968474 0.00167745i
\(727\) 14.4655 0.536497 0.268248 0.963350i \(-0.413555\pi\)
0.268248 + 0.963350i \(0.413555\pi\)
\(728\) −15.2921 13.8291i −0.566765 0.512541i
\(729\) −26.2957 −0.973914
\(730\) −2.42905 4.20723i −0.0899031 0.155717i
\(731\) −23.0215 + 39.8745i −0.851482 + 1.47481i
\(732\) −0.482598 + 0.835883i −0.0178373 + 0.0308951i
\(733\) −18.3024 31.7007i −0.676014 1.17089i −0.976171 0.217001i \(-0.930372\pi\)
0.300157 0.953890i \(-0.402961\pi\)
\(734\) −8.80217 −0.324894
\(735\) 0.0802701 + 0.796858i 0.00296081 + 0.0293925i
\(736\) −40.9017 −1.50766
\(737\) 0.542943 + 0.940405i 0.0199996 + 0.0346403i
\(738\) 0.861317 1.49185i 0.0317055 0.0549156i
\(739\) −18.8352 + 32.6235i −0.692863 + 1.20007i 0.278032 + 0.960572i \(0.410318\pi\)
−0.970896 + 0.239503i \(0.923016\pi\)
\(740\) 2.03346 + 3.52206i 0.0747516 + 0.129474i
\(741\) 1.42169 0.0522271
\(742\) −5.13781 4.64626i −0.188615 0.170570i
\(743\) −21.1779 −0.776943 −0.388471 0.921461i \(-0.626997\pi\)
−0.388471 + 0.921461i \(0.626997\pi\)
\(744\) 1.01450 + 1.75717i 0.0371935 + 0.0644210i
\(745\) −7.45484 + 12.9122i −0.273124 + 0.473065i
\(746\) −4.54161 + 7.86629i −0.166280 + 0.288005i
\(747\) −3.88942 6.73668i −0.142307 0.246482i
\(748\) −7.89253 −0.288580
\(749\) −7.86674 + 36.6205i −0.287444 + 1.33808i
\(750\) −0.0521899 −0.00190571
\(751\) −11.9923 20.7712i −0.437605 0.757954i 0.559900 0.828560i \(-0.310840\pi\)
−0.997504 + 0.0706070i \(0.977506\pi\)
\(752\) 16.1166 27.9147i 0.587711 1.01795i
\(753\) 0.0536054 0.0928472i 0.00195349 0.00338354i
\(754\) 4.84342 + 8.38905i 0.176387 + 0.305511i
\(755\) 22.9461 0.835093
\(756\) −3.09070 + 0.996844i −0.112408 + 0.0362549i
\(757\) 9.27258 0.337018 0.168509 0.985700i \(-0.446105\pi\)
0.168509 + 0.985700i \(0.446105\pi\)
\(758\) 3.59561 + 6.22778i 0.130598 + 0.226203i
\(759\) −0.494235 + 0.856039i −0.0179396 + 0.0310723i
\(760\) −2.38533 + 4.13151i −0.0865250 + 0.149866i
\(761\) −1.77411 3.07284i −0.0643113 0.111390i 0.832077 0.554660i \(-0.187152\pi\)
−0.896388 + 0.443270i \(0.853818\pi\)
\(762\) −0.0841838 −0.00304966
\(763\) −13.5868 + 4.38217i −0.491876 + 0.158645i
\(764\) 23.2058 0.839558
\(765\) 6.57793 + 11.3933i 0.237825 + 0.411926i
\(766\) −1.07444 + 1.86098i −0.0388210 + 0.0672399i
\(767\) −19.9620 + 34.5753i −0.720788 + 1.24844i
\(768\) 0.104538 + 0.181066i 0.00377221 + 0.00653365i
\(769\) 27.6695 0.997787 0.498893 0.866663i \(-0.333740\pi\)
0.498893 + 0.866663i \(0.333740\pi\)
\(770\) 0.253475 1.17995i 0.00913459 0.0425225i
\(771\) −0.0421503 −0.00151801
\(772\) −2.53620 4.39283i −0.0912799 0.158101i
\(773\) −7.04182 + 12.1968i −0.253277 + 0.438688i −0.964426 0.264353i \(-0.914842\pi\)
0.711149 + 0.703041i \(0.248175\pi\)
\(774\) 7.12149 12.3348i 0.255977 0.443365i
\(775\) −5.12634 8.87908i −0.184144 0.318946i
\(776\) −8.71294 −0.312776
\(777\) −0.509562 0.460811i −0.0182804 0.0165315i
\(778\) −3.23622 −0.116024
\(779\) −1.74356 3.01994i −0.0624696 0.108200i
\(780\) 0.461835 0.799922i 0.0165363 0.0286418i
\(781\) −6.40107 + 11.0870i −0.229048 + 0.396723i
\(782\) −8.67894 15.0324i −0.310358 0.537556i
\(783\) 3.22869 0.115384
\(784\) 15.8771 11.4308i 0.567039 0.408242i
\(785\) −17.8377 −0.636656
\(786\) 0.373545 + 0.646999i 0.0133239 + 0.0230777i
\(787\) −21.4169 + 37.0952i −0.763431 + 1.32230i 0.177641 + 0.984095i \(0.443153\pi\)
−0.941072 + 0.338206i \(0.890180\pi\)
\(788\) 1.41495 2.45077i 0.0504056 0.0873050i
\(789\) −0.331021 0.573345i −0.0117847 0.0204116i
\(790\) −4.21671 −0.150024
\(791\) 27.9469 + 25.2732i 0.993679 + 0.898611i
\(792\) 5.16646 0.183582
\(793\) −10.6051 18.3685i −0.376597 0.652285i
\(794\) −0.165554 + 0.286749i −0.00587530 + 0.0101763i
\(795\) 0.328350 0.568718i 0.0116454 0.0201704i
\(796\) −18.2792 31.6604i −0.647887 1.12217i
\(797\) −47.6777 −1.68883 −0.844415 0.535689i \(-0.820052\pi\)
−0.844415 + 0.535689i \(0.820052\pi\)
\(798\) 0.0799865 0.372346i 0.00283149 0.0131809i
\(799\) 50.7976 1.79709
\(800\) 2.36714 + 4.10000i 0.0836910 + 0.144957i
\(801\) 5.97846 10.3550i 0.211238 0.365876i
\(802\) 7.22804 12.5193i 0.255231 0.442073i
\(803\) 5.32506 + 9.22327i 0.187917 + 0.325482i
\(804\) 0.222628 0.00785147
\(805\) −21.7544 + 7.01647i −0.766743 + 0.247298i
\(806\) −21.0703 −0.742170
\(807\) −0.581305 1.00685i −0.0204629 0.0354428i
\(808\) 11.6343 20.1511i 0.409292 0.708914i
\(809\) 26.4555 45.8223i 0.930127 1.61103i 0.147027 0.989132i \(-0.453030\pi\)
0.783100 0.621895i \(-0.213637\pi\)
\(810\) −2.02586 3.50889i −0.0711815 0.123290i
\(811\) −9.70911 −0.340933 −0.170466 0.985363i \(-0.554527\pi\)
−0.170466 + 0.985363i \(0.554527\pi\)
\(812\) −21.2680 + 6.85959i −0.746362 + 0.240724i
\(813\) −2.44917 −0.0858962
\(814\) 0.517641 + 0.896580i 0.0181433 + 0.0314251i
\(815\) −10.8525 + 18.7970i −0.380145 + 0.658430i
\(816\) −0.704204 + 1.21972i −0.0246521 + 0.0426986i
\(817\) −14.4160 24.9693i −0.504352 0.873564i
\(818\) −8.58788 −0.300268
\(819\) 7.47769 34.8095i 0.261292 1.21634i
\(820\) −2.26558 −0.0791175
\(821\) −9.41313 16.3040i −0.328521 0.569014i 0.653698 0.756756i \(-0.273217\pi\)
−0.982219 + 0.187741i \(0.939883\pi\)
\(822\) 0.211722 0.366713i 0.00738464 0.0127906i
\(823\) −9.43420 + 16.3405i −0.328855 + 0.569594i −0.982285 0.187393i \(-0.939996\pi\)
0.653430 + 0.756987i \(0.273330\pi\)
\(824\) 0.504085 + 0.873102i 0.0175606 + 0.0304159i
\(825\) 0.114413 0.00398335
\(826\) 7.93230 + 7.17339i 0.276000 + 0.249594i
\(827\) 4.27820 0.148768 0.0743838 0.997230i \(-0.476301\pi\)
0.0743838 + 0.997230i \(0.476301\pi\)
\(828\) −23.1206 40.0461i −0.803498 1.39170i
\(829\) −8.60101 + 14.8974i −0.298725 + 0.517407i −0.975845 0.218466i \(-0.929895\pi\)
0.677119 + 0.735873i \(0.263228\pi\)
\(830\) 0.593984 1.02881i 0.0206175 0.0357105i
\(831\) −0.0635333 0.110043i −0.00220395 0.00381735i
\(832\) −15.4537 −0.535759
\(833\) 28.1115 + 12.6620i 0.974006 + 0.438713i
\(834\) 0.855481 0.0296229
\(835\) 1.26874 + 2.19753i 0.0439067 + 0.0760486i
\(836\) 2.47114 4.28014i 0.0854661 0.148032i
\(837\) −3.51144 + 6.08199i −0.121373 + 0.210224i
\(838\) −2.19967 3.80994i −0.0759863 0.131612i
\(839\) 1.07278 0.0370363 0.0185182 0.999829i \(-0.494105\pi\)
0.0185182 + 0.999829i \(0.494105\pi\)
\(840\) −0.388348 0.351194i −0.0133993 0.0121173i
\(841\) −6.78242 −0.233876
\(842\) 7.69231 + 13.3235i 0.265094 + 0.459157i
\(843\) 0.0933763 0.161732i 0.00321605 0.00557036i
\(844\) −14.6695 + 25.4084i −0.504946 + 0.874592i
\(845\) 3.64880 + 6.31991i 0.125523 + 0.217412i
\(846\) −15.7137 −0.540249
\(847\) −0.555678 + 2.58674i −0.0190933 + 0.0888814i
\(848\) −16.0416 −0.550872
\(849\) 0.646032 + 1.11896i 0.0221718 + 0.0384026i
\(850\) −1.00457 + 1.73996i −0.0344563 + 0.0596801i
\(851\) 9.80404 16.9811i 0.336078 0.582105i
\(852\) 1.31234 + 2.27304i 0.0449601 + 0.0778731i
\(853\) −57.2538 −1.96033 −0.980167 0.198173i \(-0.936499\pi\)
−0.980167 + 0.198173i \(0.936499\pi\)
\(854\) −5.40744 + 1.74406i −0.185039 + 0.0596806i
\(855\) −8.23815 −0.281739
\(856\) −12.2437 21.2067i −0.418481 0.724830i
\(857\) −7.35987 + 12.7477i −0.251408 + 0.435452i −0.963914 0.266214i \(-0.914227\pi\)
0.712505 + 0.701667i \(0.247560\pi\)
\(858\) 0.117565 0.203629i 0.00401361 0.00695178i
\(859\) 8.84371 + 15.3177i 0.301743 + 0.522635i 0.976531 0.215377i \(-0.0690981\pi\)
−0.674788 + 0.738012i \(0.735765\pi\)
\(860\) −18.7321 −0.638760
\(861\) 0.364245 0.117480i 0.0124135 0.00400372i
\(862\) −1.84719 −0.0629155
\(863\) 9.83005 + 17.0261i 0.334619 + 0.579577i 0.983412 0.181388i \(-0.0580591\pi\)
−0.648793 + 0.760965i \(0.724726\pi\)
\(864\) 1.62144 2.80842i 0.0551626 0.0955444i
\(865\) 4.96057 8.59196i 0.168664 0.292135i
\(866\) 6.44773 + 11.1678i 0.219103 + 0.379497i
\(867\) −0.274552 −0.00932426
\(868\) 10.2089 47.5236i 0.346513 1.61306i
\(869\) 9.24406 0.313583
\(870\) 0.123000 + 0.213042i 0.00417009 + 0.00722280i
\(871\) −2.44611 + 4.23680i −0.0828834 + 0.143558i
\(872\) 4.66659 8.08277i 0.158031 0.273717i
\(873\) −7.52291 13.0301i −0.254612 0.441001i
\(874\) 10.8694 0.367664
\(875\) 1.96234 + 1.77460i 0.0663393 + 0.0599925i
\(876\) 2.18348 0.0737729
\(877\) 18.3218 + 31.7344i 0.618685 + 1.07159i 0.989726 + 0.142977i \(0.0456674\pi\)
−0.371041 + 0.928616i \(0.620999\pi\)
\(878\) −3.59527 + 6.22720i −0.121335 + 0.210158i
\(879\) −0.0623201 + 0.107942i −0.00210201 + 0.00364078i
\(880\) −1.39742 2.42040i −0.0471070 0.0815917i
\(881\) 20.9238 0.704940 0.352470 0.935823i \(-0.385342\pi\)
0.352470 + 0.935823i \(0.385342\pi\)
\(882\) −8.69602 3.91687i −0.292810 0.131888i
\(883\) 16.4768 0.554488 0.277244 0.960800i \(-0.410579\pi\)
0.277244 + 0.960800i \(0.410579\pi\)
\(884\) −17.7791 30.7942i −0.597975 1.03572i
\(885\) −0.506941 + 0.878048i −0.0170406 + 0.0295153i
\(886\) −0.339931 + 0.588777i −0.0114202 + 0.0197804i
\(887\) 22.1403 + 38.3481i 0.743398 + 1.28760i 0.950939 + 0.309377i \(0.100121\pi\)
−0.207541 + 0.978226i \(0.566546\pi\)
\(888\) 0.449152 0.0150725
\(889\) 3.16532 + 2.86248i 0.106161 + 0.0960046i
\(890\) 1.82603 0.0612087
\(891\) 4.44118 + 7.69235i 0.148785 + 0.257703i
\(892\) 11.6345 20.1515i 0.389550 0.674721i
\(893\) −15.9046 + 27.5476i −0.532228 + 0.921846i
\(894\) 0.389067 + 0.673885i 0.0130124 + 0.0225381i
\(895\) 5.86468 0.196035
\(896\) −6.13091 + 28.5401i −0.204819 + 0.953456i
\(897\) −4.45334 −0.148693
\(898\) −8.91191 15.4359i −0.297394 0.515102i
\(899\) −24.1633 + 41.8520i −0.805890 + 1.39584i
\(900\) −2.67616 + 4.63524i −0.0892052 + 0.154508i
\(901\) −12.6403 21.8937i −0.421111 0.729385i
\(902\) −0.576728 −0.0192029
\(903\) 3.01163 0.971343i 0.100221 0.0323243i
\(904\) −24.6337 −0.819306
\(905\) −8.59525 14.8874i −0.285716 0.494874i
\(906\) 0.598777 1.03711i 0.0198930 0.0344557i
\(907\) −1.04587 + 1.81150i −0.0347276 + 0.0601499i −0.882867 0.469623i \(-0.844390\pi\)
0.848139 + 0.529773i \(0.177723\pi\)
\(908\) −13.4138 23.2334i −0.445152 0.771027i
\(909\) 40.1809 1.33272
\(910\) 5.17480 1.66903i 0.171543 0.0553278i
\(911\) 13.4632 0.446054 0.223027 0.974812i \(-0.428406\pi\)
0.223027 + 0.974812i \(0.428406\pi\)
\(912\) −0.440970 0.763782i −0.0146020 0.0252914i
\(913\) −1.30216 + 2.25540i −0.0430951 + 0.0746429i
\(914\) −2.43505 + 4.21763i −0.0805443 + 0.139507i
\(915\) −0.269318 0.466473i −0.00890338 0.0154211i
\(916\) 20.0823 0.663537
\(917\) 7.95444 37.0288i 0.262679 1.22280i
\(918\) 1.37621 0.0454218
\(919\) −9.45339 16.3737i −0.311838 0.540120i 0.666922 0.745128i \(-0.267611\pi\)
−0.978760 + 0.205008i \(0.934278\pi\)
\(920\) 7.47187 12.9417i 0.246340 0.426674i
\(921\) −1.06059 + 1.83700i −0.0349477 + 0.0605313i
\(922\) −3.57575 6.19339i −0.117761 0.203968i
\(923\) −57.6773 −1.89847
\(924\) 0.402318 + 0.363827i 0.0132353 + 0.0119690i
\(925\) −2.26959 −0.0746236
\(926\) 2.51738 + 4.36023i 0.0827263 + 0.143286i
\(927\) −0.870473 + 1.50770i −0.0285901 + 0.0495195i
\(928\) 11.1576 19.3256i 0.366267 0.634394i
\(929\) 25.8686 + 44.8057i 0.848721 + 1.47003i 0.882350 + 0.470594i \(0.155960\pi\)
−0.0336285 + 0.999434i \(0.510706\pi\)
\(930\) −0.535086 −0.0175462
\(931\) −15.6683 + 11.2805i −0.513508 + 0.369702i
\(932\) 14.1057 0.462046
\(933\) 0.489426 + 0.847711i 0.0160231 + 0.0277528i
\(934\) 2.67717 4.63700i 0.0875997 0.151727i
\(935\) 2.20225 3.81441i 0.0720213 0.124745i
\(936\) 11.6382 + 20.1579i 0.380406 + 0.658883i
\(937\) −43.2317 −1.41232 −0.706159 0.708053i \(-0.749574\pi\)
−0.706159 + 0.708053i \(0.749574\pi\)
\(938\) 0.972010 + 0.879015i 0.0317373 + 0.0287009i
\(939\) −1.19300 −0.0389320
\(940\) 10.3332 + 17.8977i 0.337032 + 0.583757i
\(941\) 7.73776 13.4022i 0.252244 0.436899i −0.711899 0.702281i \(-0.752165\pi\)
0.964143 + 0.265382i \(0.0854982\pi\)
\(942\) −0.465474 + 0.806225i −0.0151660 + 0.0262682i
\(943\) 5.46158 + 9.45973i 0.177853 + 0.308051i
\(944\) 24.7668 0.806089
\(945\) 0.380628 1.77186i 0.0123818 0.0576387i
\(946\) −4.76847 −0.155036
\(947\) −9.83635 17.0371i −0.319639 0.553630i 0.660774 0.750585i \(-0.270228\pi\)
−0.980413 + 0.196955i \(0.936895\pi\)
\(948\) 0.947605 1.64130i 0.0307768 0.0533069i
\(949\) −23.9909 + 41.5535i −0.778778 + 1.34888i
\(950\) −0.629055 1.08956i −0.0204092 0.0353499i
\(951\) 0.151373 0.00490862
\(952\) −19.1835 + 6.18726i −0.621740 + 0.200530i
\(953\) −60.1478 −1.94838 −0.974188 0.225736i \(-0.927521\pi\)
−0.974188 + 0.225736i \(0.927521\pi\)
\(954\) 3.91017 + 6.77261i 0.126596 + 0.219271i
\(955\) −6.47512 + 11.2152i −0.209530 + 0.362917i
\(956\) 13.3176 23.0667i 0.430721 0.746031i
\(957\) −0.269646 0.467040i −0.00871641 0.0150973i
\(958\) 16.6658 0.538447
\(959\) −20.4300 + 6.58930i −0.659719 + 0.212779i
\(960\) −0.392450 −0.0126663
\(961\) −37.0587 64.1876i −1.19544 2.07057i
\(962\) −2.33212 + 4.03935i −0.0751906 + 0.130234i
\(963\) 21.1429 36.6205i 0.681319 1.18008i
\(964\) 8.04685 + 13.9376i 0.259172 + 0.448898i
\(965\) 2.83070 0.0911235
\(966\) −0.250552 + 1.16635i −0.00806137 + 0.0375266i
\(967\) 31.9509 1.02747 0.513735 0.857949i \(-0.328261\pi\)
0.513735 + 0.857949i \(0.328261\pi\)
\(968\) −0.864850 1.49796i −0.0277973 0.0481464i
\(969\) 0.694943 1.20368i 0.0223248 0.0386677i
\(970\) 1.14888 1.98992i 0.0368883 0.0638925i
\(971\) 6.73204 + 11.6602i 0.216041 + 0.374195i 0.953594 0.301095i \(-0.0973520\pi\)
−0.737553 + 0.675289i \(0.764019\pi\)
\(972\) 5.50335 0.176520
\(973\) −32.1662 29.0887i −1.03120 0.932542i
\(974\) 11.6191 0.372299
\(975\) 0.257731 + 0.446404i 0.00825401 + 0.0142964i
\(976\) −6.57881 + 11.3948i −0.210583 + 0.364740i
\(977\) 17.9353 31.0649i 0.573801 0.993853i −0.422370 0.906424i \(-0.638802\pi\)
0.996171 0.0874290i \(-0.0278651\pi\)
\(978\) 0.566388 + 0.981013i 0.0181111 + 0.0313693i
\(979\) −4.00310 −0.127940
\(980\) 1.25718 + 12.4803i 0.0401592 + 0.398669i
\(981\) 16.1169 0.514572
\(982\) 3.83091 + 6.63533i 0.122249 + 0.211742i
\(983\) 19.1739 33.2102i 0.611552 1.05924i −0.379427 0.925222i \(-0.623879\pi\)
0.990979 0.134018i \(-0.0427879\pi\)
\(984\) −0.125105 + 0.216689i −0.00398821 + 0.00690778i
\(985\) 0.789628 + 1.36767i 0.0251596 + 0.0435777i
\(986\) 9.47015 0.301591
\(987\) −2.58938 2.34165i −0.0824209 0.0745355i
\(988\) 22.2664 0.708388
\(989\) 45.1571 + 78.2143i 1.43591 + 2.48707i
\(990\) −0.681245 + 1.17995i −0.0216514 + 0.0375013i
\(991\) 2.48430 4.30293i 0.0789164 0.136687i −0.823866 0.566784i \(-0.808187\pi\)
0.902783 + 0.430097i \(0.141521\pi\)
\(992\) 24.2695 + 42.0360i 0.770558 + 1.33465i
\(993\) −2.61855 −0.0830971
\(994\) −3.24502 + 15.1059i −0.102926 + 0.479130i
\(995\) 20.4017 0.646778
\(996\) 0.266967 + 0.462400i 0.00845917 + 0.0146517i
\(997\) −9.65030 + 16.7148i −0.305628 + 0.529364i −0.977401 0.211394i \(-0.932200\pi\)
0.671773 + 0.740757i \(0.265533\pi\)
\(998\) 3.23954 5.61104i 0.102546 0.177614i
\(999\) 0.777311 + 1.34634i 0.0245930 + 0.0425964i
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 385.2.i.b.221.3 12
7.2 even 3 inner 385.2.i.b.331.3 yes 12
7.3 odd 6 2695.2.a.q.1.4 6
7.4 even 3 2695.2.a.r.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
385.2.i.b.221.3 12 1.1 even 1 trivial
385.2.i.b.331.3 yes 12 7.2 even 3 inner
2695.2.a.q.1.4 6 7.3 odd 6
2695.2.a.r.1.4 6 7.4 even 3