Properties

Label 546.2.bb.a.269.1
Level $546$
Weight $2$
Character 546.269
Analytic conductor $4.360$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(269,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.269");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(38\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.1
Character \(\chi\) \(=\) 546.269
Dual form 546.2.bb.a.341.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.68782 - 0.388948i) q^{3} -1.00000 q^{4} +(-0.386492 - 0.669424i) q^{5} +(-0.388948 + 1.68782i) q^{6} +(1.88739 + 1.85412i) q^{7} +1.00000i q^{8} +(2.69744 + 1.31294i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.68782 - 0.388948i) q^{3} -1.00000 q^{4} +(-0.386492 - 0.669424i) q^{5} +(-0.388948 + 1.68782i) q^{6} +(1.88739 + 1.85412i) q^{7} +1.00000i q^{8} +(2.69744 + 1.31294i) q^{9} +(-0.669424 + 0.386492i) q^{10} +(2.34039 - 1.35122i) q^{11} +(1.68782 + 0.388948i) q^{12} +(-3.14302 + 1.76675i) q^{13} +(1.85412 - 1.88739i) q^{14} +(0.391956 + 1.28019i) q^{15} +1.00000 q^{16} +2.64755 q^{17} +(1.31294 - 2.69744i) q^{18} +(4.04565 + 2.33575i) q^{19} +(0.386492 + 0.669424i) q^{20} +(-2.46440 - 3.86351i) q^{21} +(-1.35122 - 2.34039i) q^{22} -5.38541i q^{23} +(0.388948 - 1.68782i) q^{24} +(2.20125 - 3.81267i) q^{25} +(1.76675 + 3.14302i) q^{26} +(-4.04211 - 3.26517i) q^{27} +(-1.88739 - 1.85412i) q^{28} +(4.22905 + 2.44165i) q^{29} +(1.28019 - 0.391956i) q^{30} +(-3.24180 - 1.87166i) q^{31} -1.00000i q^{32} +(-4.47570 + 1.37033i) q^{33} -2.64755i q^{34} +(0.511734 - 1.98007i) q^{35} +(-2.69744 - 1.31294i) q^{36} +4.56832 q^{37} +(2.33575 - 4.04565i) q^{38} +(5.99201 - 1.75948i) q^{39} +(0.669424 - 0.386492i) q^{40} +(4.90014 - 8.48729i) q^{41} +(-3.86351 + 2.46440i) q^{42} +(-5.66191 - 9.80672i) q^{43} +(-2.34039 + 1.35122i) q^{44} +(-0.163624 - 2.31317i) q^{45} -5.38541 q^{46} +(2.63336 + 4.56112i) q^{47} +(-1.68782 - 0.388948i) q^{48} +(0.124461 + 6.99889i) q^{49} +(-3.81267 - 2.20125i) q^{50} +(-4.46858 - 1.02976i) q^{51} +(3.14302 - 1.76675i) q^{52} +(3.16257 + 1.82591i) q^{53} +(-3.26517 + 4.04211i) q^{54} +(-1.80908 - 1.04447i) q^{55} +(-1.85412 + 1.88739i) q^{56} +(-5.91981 - 5.51587i) q^{57} +(2.44165 - 4.22905i) q^{58} -11.2248 q^{59} +(-0.391956 - 1.28019i) q^{60} +(11.2735 + 6.50875i) q^{61} +(-1.87166 + 3.24180i) q^{62} +(2.65676 + 7.47941i) q^{63} -1.00000 q^{64} +(2.39746 + 1.42118i) q^{65} +(1.37033 + 4.47570i) q^{66} +(3.47068 + 6.01140i) q^{67} -2.64755 q^{68} +(-2.09464 + 9.08958i) q^{69} +(-1.98007 - 0.511734i) q^{70} +(9.71163 - 5.60701i) q^{71} +(-1.31294 + 2.69744i) q^{72} +(8.99614 + 5.19392i) q^{73} -4.56832i q^{74} +(-5.19823 + 5.57892i) q^{75} +(-4.04565 - 2.33575i) q^{76} +(6.92255 + 1.78908i) q^{77} +(-1.75948 - 5.99201i) q^{78} +(5.14638 + 8.91380i) q^{79} +(-0.386492 - 0.669424i) q^{80} +(5.55236 + 7.08317i) q^{81} +(-8.48729 - 4.90014i) q^{82} -16.3639 q^{83} +(2.46440 + 3.86351i) q^{84} +(-1.02326 - 1.77234i) q^{85} +(-9.80672 + 5.66191i) q^{86} +(-6.18819 - 5.76593i) q^{87} +(1.35122 + 2.34039i) q^{88} +10.3497 q^{89} +(-2.31317 + 0.163624i) q^{90} +(-9.20787 - 2.49300i) q^{91} +5.38541i q^{92} +(4.74359 + 4.41990i) q^{93} +(4.56112 - 2.63336i) q^{94} -3.61100i q^{95} +(-0.388948 + 1.68782i) q^{96} +(-6.86925 + 3.96597i) q^{97} +(6.99889 - 0.124461i) q^{98} +(8.08713 - 0.572048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.68782 0.388948i −0.974460 0.224559i
\(4\) −1.00000 −0.500000
\(5\) −0.386492 0.669424i −0.172845 0.299376i 0.766569 0.642162i \(-0.221962\pi\)
−0.939413 + 0.342787i \(0.888629\pi\)
\(6\) −0.388948 + 1.68782i −0.158787 + 0.689048i
\(7\) 1.88739 + 1.85412i 0.713365 + 0.700792i
\(8\) 1.00000i 0.353553i
\(9\) 2.69744 + 1.31294i 0.899147 + 0.437648i
\(10\) −0.669424 + 0.386492i −0.211690 + 0.122220i
\(11\) 2.34039 1.35122i 0.705653 0.407409i −0.103796 0.994599i \(-0.533099\pi\)
0.809449 + 0.587190i \(0.199766\pi\)
\(12\) 1.68782 + 0.388948i 0.487230 + 0.112279i
\(13\) −3.14302 + 1.76675i −0.871717 + 0.490009i
\(14\) 1.85412 1.88739i 0.495535 0.504425i
\(15\) 0.391956 + 1.28019i 0.101203 + 0.330543i
\(16\) 1.00000 0.250000
\(17\) 2.64755 0.642126 0.321063 0.947058i \(-0.395960\pi\)
0.321063 + 0.947058i \(0.395960\pi\)
\(18\) 1.31294 2.69744i 0.309464 0.635793i
\(19\) 4.04565 + 2.33575i 0.928135 + 0.535859i 0.886221 0.463262i \(-0.153321\pi\)
0.0419135 + 0.999121i \(0.486655\pi\)
\(20\) 0.386492 + 0.669424i 0.0864223 + 0.149688i
\(21\) −2.46440 3.86351i −0.537777 0.843087i
\(22\) −1.35122 2.34039i −0.288082 0.498972i
\(23\) 5.38541i 1.12294i −0.827499 0.561468i \(-0.810237\pi\)
0.827499 0.561468i \(-0.189763\pi\)
\(24\) 0.388948 1.68782i 0.0793936 0.344524i
\(25\) 2.20125 3.81267i 0.440250 0.762535i
\(26\) 1.76675 + 3.14302i 0.346489 + 0.616397i
\(27\) −4.04211 3.26517i −0.777905 0.628382i
\(28\) −1.88739 1.85412i −0.356683 0.350396i
\(29\) 4.22905 + 2.44165i 0.785316 + 0.453402i 0.838311 0.545193i \(-0.183543\pi\)
−0.0529953 + 0.998595i \(0.516877\pi\)
\(30\) 1.28019 0.391956i 0.233730 0.0715611i
\(31\) −3.24180 1.87166i −0.582245 0.336159i 0.179780 0.983707i \(-0.442461\pi\)
−0.762025 + 0.647547i \(0.775795\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −4.47570 + 1.37033i −0.779119 + 0.238543i
\(34\) 2.64755i 0.454052i
\(35\) 0.511734 1.98007i 0.0864988 0.334692i
\(36\) −2.69744 1.31294i −0.449573 0.218824i
\(37\) 4.56832 0.751028 0.375514 0.926817i \(-0.377466\pi\)
0.375514 + 0.926817i \(0.377466\pi\)
\(38\) 2.33575 4.04565i 0.378909 0.656290i
\(39\) 5.99201 1.75948i 0.959490 0.281743i
\(40\) 0.669424 0.386492i 0.105845 0.0611098i
\(41\) 4.90014 8.48729i 0.765273 1.32549i −0.174829 0.984599i \(-0.555937\pi\)
0.940102 0.340894i \(-0.110730\pi\)
\(42\) −3.86351 + 2.46440i −0.596153 + 0.380266i
\(43\) −5.66191 9.80672i −0.863434 1.49551i −0.868594 0.495525i \(-0.834976\pi\)
0.00516013 0.999987i \(-0.498357\pi\)
\(44\) −2.34039 + 1.35122i −0.352827 + 0.203705i
\(45\) −0.163624 2.31317i −0.0243916 0.344828i
\(46\) −5.38541 −0.794035
\(47\) 2.63336 + 4.56112i 0.384116 + 0.665308i 0.991646 0.128989i \(-0.0411731\pi\)
−0.607530 + 0.794296i \(0.707840\pi\)
\(48\) −1.68782 0.388948i −0.243615 0.0561397i
\(49\) 0.124461 + 6.99889i 0.0177802 + 0.999842i
\(50\) −3.81267 2.20125i −0.539193 0.311303i
\(51\) −4.46858 1.02976i −0.625726 0.144195i
\(52\) 3.14302 1.76675i 0.435859 0.245005i
\(53\) 3.16257 + 1.82591i 0.434413 + 0.250808i 0.701225 0.712940i \(-0.252637\pi\)
−0.266812 + 0.963749i \(0.585970\pi\)
\(54\) −3.26517 + 4.04211i −0.444333 + 0.550062i
\(55\) −1.80908 1.04447i −0.243937 0.140837i
\(56\) −1.85412 + 1.88739i −0.247768 + 0.252213i
\(57\) −5.91981 5.51587i −0.784099 0.730594i
\(58\) 2.44165 4.22905i 0.320604 0.555302i
\(59\) −11.2248 −1.46135 −0.730675 0.682726i \(-0.760794\pi\)
−0.730675 + 0.682726i \(0.760794\pi\)
\(60\) −0.391956 1.28019i −0.0506014 0.165272i
\(61\) 11.2735 + 6.50875i 1.44342 + 0.833359i 0.998076 0.0619997i \(-0.0197478\pi\)
0.445345 + 0.895359i \(0.353081\pi\)
\(62\) −1.87166 + 3.24180i −0.237701 + 0.411710i
\(63\) 2.65676 + 7.47941i 0.334720 + 0.942318i
\(64\) −1.00000 −0.125000
\(65\) 2.39746 + 1.42118i 0.297368 + 0.176275i
\(66\) 1.37033 + 4.47570i 0.168676 + 0.550920i
\(67\) 3.47068 + 6.01140i 0.424011 + 0.734409i 0.996328 0.0856238i \(-0.0272883\pi\)
−0.572316 + 0.820033i \(0.693955\pi\)
\(68\) −2.64755 −0.321063
\(69\) −2.09464 + 9.08958i −0.252165 + 1.09426i
\(70\) −1.98007 0.511734i −0.236663 0.0611639i
\(71\) 9.71163 5.60701i 1.15256 0.665430i 0.203049 0.979169i \(-0.434915\pi\)
0.949509 + 0.313739i \(0.101582\pi\)
\(72\) −1.31294 + 2.69744i −0.154732 + 0.317896i
\(73\) 8.99614 + 5.19392i 1.05292 + 0.607903i 0.923465 0.383683i \(-0.125344\pi\)
0.129453 + 0.991586i \(0.458678\pi\)
\(74\) 4.56832i 0.531057i
\(75\) −5.19823 + 5.57892i −0.600240 + 0.644198i
\(76\) −4.04565 2.33575i −0.464067 0.267929i
\(77\) 6.92255 + 1.78908i 0.788898 + 0.203885i
\(78\) −1.75948 5.99201i −0.199222 0.678462i
\(79\) 5.14638 + 8.91380i 0.579013 + 1.00288i 0.995593 + 0.0937812i \(0.0298954\pi\)
−0.416580 + 0.909099i \(0.636771\pi\)
\(80\) −0.386492 0.669424i −0.0432111 0.0748439i
\(81\) 5.55236 + 7.08317i 0.616929 + 0.787019i
\(82\) −8.48729 4.90014i −0.937265 0.541130i
\(83\) −16.3639 −1.79617 −0.898086 0.439820i \(-0.855042\pi\)
−0.898086 + 0.439820i \(0.855042\pi\)
\(84\) 2.46440 + 3.86351i 0.268889 + 0.421544i
\(85\) −1.02326 1.77234i −0.110988 0.192237i
\(86\) −9.80672 + 5.66191i −1.05749 + 0.610540i
\(87\) −6.18819 5.76593i −0.663443 0.618172i
\(88\) 1.35122 + 2.34039i 0.144041 + 0.249486i
\(89\) 10.3497 1.09706 0.548532 0.836130i \(-0.315187\pi\)
0.548532 + 0.836130i \(0.315187\pi\)
\(90\) −2.31317 + 0.163624i −0.243830 + 0.0172474i
\(91\) −9.20787 2.49300i −0.965248 0.261337i
\(92\) 5.38541i 0.561468i
\(93\) 4.74359 + 4.41990i 0.491887 + 0.458322i
\(94\) 4.56112 2.63336i 0.470444 0.271611i
\(95\) 3.61100i 0.370481i
\(96\) −0.388948 + 1.68782i −0.0396968 + 0.172262i
\(97\) −6.86925 + 3.96597i −0.697467 + 0.402683i −0.806403 0.591366i \(-0.798589\pi\)
0.108936 + 0.994049i \(0.465256\pi\)
\(98\) 6.99889 0.124461i 0.706995 0.0125725i
\(99\) 8.08713 0.572048i 0.812787 0.0574929i
\(100\) −2.20125 + 3.81267i −0.220125 + 0.381267i
\(101\) −5.08348 8.80484i −0.505825 0.876115i −0.999977 0.00673938i \(-0.997855\pi\)
0.494152 0.869375i \(-0.335479\pi\)
\(102\) −1.02976 + 4.46858i −0.101961 + 0.442455i
\(103\) 8.01582 4.62793i 0.789822 0.456004i −0.0500780 0.998745i \(-0.515947\pi\)
0.839900 + 0.542741i \(0.182614\pi\)
\(104\) −1.76675 3.14302i −0.173244 0.308199i
\(105\) −1.63385 + 3.14295i −0.159448 + 0.306720i
\(106\) 1.82591 3.16257i 0.177348 0.307176i
\(107\) 1.21168i 0.117137i −0.998283 0.0585686i \(-0.981346\pi\)
0.998283 0.0585686i \(-0.0186536\pi\)
\(108\) 4.04211 + 3.26517i 0.388953 + 0.314191i
\(109\) −3.83041 + 6.63447i −0.366887 + 0.635467i −0.989077 0.147400i \(-0.952910\pi\)
0.622190 + 0.782866i \(0.286243\pi\)
\(110\) −1.04447 + 1.80908i −0.0995867 + 0.172489i
\(111\) −7.71048 1.77684i −0.731847 0.168650i
\(112\) 1.88739 + 1.85412i 0.178341 + 0.175198i
\(113\) 8.89202 5.13381i 0.836491 0.482948i −0.0195790 0.999808i \(-0.506233\pi\)
0.856070 + 0.516860i \(0.172899\pi\)
\(114\) −5.51587 + 5.91981i −0.516608 + 0.554441i
\(115\) −3.60512 + 2.08142i −0.336180 + 0.194093i
\(116\) −4.22905 2.44165i −0.392658 0.226701i
\(117\) −10.7978 + 0.639100i −0.998253 + 0.0590849i
\(118\) 11.2248i 1.03333i
\(119\) 4.99696 + 4.90889i 0.458070 + 0.449997i
\(120\) −1.28019 + 0.391956i −0.116865 + 0.0357806i
\(121\) −1.84839 + 3.20151i −0.168036 + 0.291046i
\(122\) 6.50875 11.2735i 0.589274 1.02065i
\(123\) −11.5716 + 12.4191i −1.04338 + 1.11979i
\(124\) 3.24180 + 1.87166i 0.291123 + 0.168080i
\(125\) −7.26798 −0.650068
\(126\) 7.47941 2.65676i 0.666319 0.236683i
\(127\) −3.63055 + 6.28830i −0.322159 + 0.557996i −0.980933 0.194345i \(-0.937742\pi\)
0.658774 + 0.752341i \(0.271075\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 5.74196 + 18.7541i 0.505552 + 1.65121i
\(130\) 1.42118 2.39746i 0.124646 0.210271i
\(131\) −5.48186 9.49487i −0.478953 0.829570i 0.520756 0.853706i \(-0.325650\pi\)
−0.999709 + 0.0241352i \(0.992317\pi\)
\(132\) 4.47570 1.37033i 0.389559 0.119272i
\(133\) 3.30492 + 11.9096i 0.286573 + 1.03269i
\(134\) 6.01140 3.47068i 0.519306 0.299821i
\(135\) −0.623537 + 3.96785i −0.0536655 + 0.341498i
\(136\) 2.64755i 0.227026i
\(137\) 4.98739i 0.426102i −0.977041 0.213051i \(-0.931660\pi\)
0.977041 0.213051i \(-0.0683400\pi\)
\(138\) 9.08958 + 2.09464i 0.773756 + 0.178308i
\(139\) 0.244965 0.141431i 0.0207777 0.0119960i −0.489575 0.871961i \(-0.662848\pi\)
0.510353 + 0.859965i \(0.329515\pi\)
\(140\) −0.511734 + 1.98007i −0.0432494 + 0.167346i
\(141\) −2.67059 8.72257i −0.224905 0.734573i
\(142\) −5.60701 9.71163i −0.470530 0.814982i
\(143\) −4.96861 + 8.38181i −0.415496 + 0.700922i
\(144\) 2.69744 + 1.31294i 0.224787 + 0.109412i
\(145\) 3.77471i 0.313472i
\(146\) 5.19392 8.99614i 0.429852 0.744525i
\(147\) 2.51214 11.8612i 0.207197 0.978299i
\(148\) −4.56832 −0.375514
\(149\) −0.346111 0.199827i −0.0283545 0.0163705i 0.485756 0.874095i \(-0.338544\pi\)
−0.514110 + 0.857724i \(0.671878\pi\)
\(150\) 5.57892 + 5.19823i 0.455517 + 0.424434i
\(151\) 3.60132 6.23766i 0.293071 0.507614i −0.681463 0.731852i \(-0.738656\pi\)
0.974534 + 0.224238i \(0.0719894\pi\)
\(152\) −2.33575 + 4.04565i −0.189455 + 0.328145i
\(153\) 7.14162 + 3.47609i 0.577365 + 0.281025i
\(154\) 1.78908 6.92255i 0.144168 0.557835i
\(155\) 2.89352i 0.232413i
\(156\) −5.99201 + 1.75948i −0.479745 + 0.140871i
\(157\) −10.4752 6.04786i −0.836012 0.482672i 0.0198945 0.999802i \(-0.493667\pi\)
−0.855907 + 0.517130i \(0.827000\pi\)
\(158\) 8.91380 5.14638i 0.709144 0.409424i
\(159\) −4.62765 4.31188i −0.366997 0.341954i
\(160\) −0.669424 + 0.386492i −0.0529226 + 0.0305549i
\(161\) 9.98521 10.1644i 0.786945 0.801063i
\(162\) 7.08317 5.55236i 0.556506 0.436235i
\(163\) 4.72234 8.17934i 0.369883 0.640655i −0.619664 0.784867i \(-0.712731\pi\)
0.989547 + 0.144212i \(0.0460646\pi\)
\(164\) −4.90014 + 8.48729i −0.382637 + 0.662746i
\(165\) 2.64715 + 2.46652i 0.206080 + 0.192018i
\(166\) 16.3639i 1.27009i
\(167\) −9.42868 + 16.3310i −0.729614 + 1.26373i 0.227433 + 0.973794i \(0.426967\pi\)
−0.957047 + 0.289934i \(0.906367\pi\)
\(168\) 3.86351 2.46440i 0.298076 0.190133i
\(169\) 6.75717 11.1059i 0.519782 0.854299i
\(170\) −1.77234 + 1.02326i −0.135932 + 0.0784804i
\(171\) 7.84617 + 11.6123i 0.600012 + 0.888012i
\(172\) 5.66191 + 9.80672i 0.431717 + 0.747756i
\(173\) −6.00907 + 10.4080i −0.456861 + 0.791307i −0.998793 0.0491157i \(-0.984360\pi\)
0.541932 + 0.840422i \(0.317693\pi\)
\(174\) −5.76593 + 6.18819i −0.437114 + 0.469125i
\(175\) 11.2238 3.11461i 0.848437 0.235442i
\(176\) 2.34039 1.35122i 0.176413 0.101852i
\(177\) 18.9455 + 4.36587i 1.42403 + 0.328159i
\(178\) 10.3497i 0.775741i
\(179\) −11.8611 + 6.84801i −0.886541 + 0.511844i −0.872809 0.488061i \(-0.837704\pi\)
−0.0137312 + 0.999906i \(0.504371\pi\)
\(180\) 0.163624 + 2.31317i 0.0121958 + 0.172414i
\(181\) 13.0400i 0.969257i 0.874720 + 0.484628i \(0.161045\pi\)
−0.874720 + 0.484628i \(0.838955\pi\)
\(182\) −2.49300 + 9.20787i −0.184793 + 0.682533i
\(183\) −16.4960 15.3704i −1.21942 1.13621i
\(184\) 5.38541 0.397018
\(185\) −1.76562 3.05815i −0.129811 0.224839i
\(186\) 4.41990 4.74359i 0.324083 0.347817i
\(187\) 6.19630 3.57744i 0.453118 0.261608i
\(188\) −2.63336 4.56112i −0.192058 0.332654i
\(189\) −1.57501 13.6572i −0.114565 0.993416i
\(190\) −3.61100 −0.261970
\(191\) 1.68042 + 0.970190i 0.121591 + 0.0702005i 0.559562 0.828789i \(-0.310969\pi\)
−0.437971 + 0.898989i \(0.644303\pi\)
\(192\) 1.68782 + 0.388948i 0.121808 + 0.0280699i
\(193\) −5.02278 8.69971i −0.361548 0.626219i 0.626668 0.779286i \(-0.284418\pi\)
−0.988216 + 0.153067i \(0.951085\pi\)
\(194\) 3.96597 + 6.86925i 0.284740 + 0.493184i
\(195\) −3.49371 3.33117i −0.250189 0.238550i
\(196\) −0.124461 6.99889i −0.00889008 0.499921i
\(197\) −2.55609 1.47576i −0.182114 0.105143i 0.406172 0.913797i \(-0.366863\pi\)
−0.588285 + 0.808653i \(0.700197\pi\)
\(198\) −0.572048 8.08713i −0.0406536 0.574727i
\(199\) 2.80034i 0.198511i 0.995062 + 0.0992553i \(0.0316461\pi\)
−0.995062 + 0.0992553i \(0.968354\pi\)
\(200\) 3.81267 + 2.20125i 0.269597 + 0.155652i
\(201\) −3.51975 11.4960i −0.248264 0.810868i
\(202\) −8.80484 + 5.08348i −0.619507 + 0.357672i
\(203\) 3.45475 + 12.4495i 0.242476 + 0.873784i
\(204\) 4.46858 + 1.02976i 0.312863 + 0.0720976i
\(205\) −7.57546 −0.529093
\(206\) −4.62793 8.01582i −0.322443 0.558488i
\(207\) 7.07074 14.5268i 0.491450 1.00968i
\(208\) −3.14302 + 1.76675i −0.217929 + 0.122502i
\(209\) 12.6245 0.873255
\(210\) 3.14295 + 1.63385i 0.216884 + 0.112747i
\(211\) −6.57341 + 11.3855i −0.452532 + 0.783809i −0.998543 0.0539696i \(-0.982813\pi\)
0.546010 + 0.837778i \(0.316146\pi\)
\(212\) −3.16257 1.82591i −0.217206 0.125404i
\(213\) −18.5723 + 5.68628i −1.27255 + 0.389618i
\(214\) −1.21168 −0.0828285
\(215\) −4.37657 + 7.58044i −0.298480 + 0.516982i
\(216\) 3.26517 4.04211i 0.222167 0.275031i
\(217\) −2.64826 9.54324i −0.179776 0.647837i
\(218\) 6.63447 + 3.83041i 0.449343 + 0.259428i
\(219\) −13.1637 12.2654i −0.889517 0.828819i
\(220\) 1.80908 + 1.04447i 0.121968 + 0.0704184i
\(221\) −8.32132 + 4.67757i −0.559752 + 0.314648i
\(222\) −1.77684 + 7.71048i −0.119254 + 0.517494i
\(223\) −2.33020 1.34534i −0.156042 0.0900908i 0.419946 0.907549i \(-0.362049\pi\)
−0.575988 + 0.817458i \(0.695382\pi\)
\(224\) 1.85412 1.88739i 0.123884 0.126106i
\(225\) 10.9436 7.39434i 0.729570 0.492956i
\(226\) −5.13381 8.89202i −0.341496 0.591488i
\(227\) −5.28026 −0.350463 −0.175232 0.984527i \(-0.556067\pi\)
−0.175232 + 0.984527i \(0.556067\pi\)
\(228\) 5.91981 + 5.51587i 0.392049 + 0.365297i
\(229\) 22.9130 13.2288i 1.51414 0.874187i 0.514273 0.857626i \(-0.328062\pi\)
0.999863 0.0165604i \(-0.00527159\pi\)
\(230\) 2.08142 + 3.60512i 0.137245 + 0.237715i
\(231\) −10.9881 5.71215i −0.722965 0.375832i
\(232\) −2.44165 + 4.22905i −0.160302 + 0.277651i
\(233\) −3.01825 + 1.74259i −0.197732 + 0.114161i −0.595597 0.803283i \(-0.703085\pi\)
0.397865 + 0.917444i \(0.369751\pi\)
\(234\) 0.639100 + 10.7978i 0.0417793 + 0.705871i
\(235\) 2.03555 3.52567i 0.132785 0.229990i
\(236\) 11.2248 0.730675
\(237\) −5.21914 17.0465i −0.339020 1.10729i
\(238\) 4.90889 4.99696i 0.318196 0.323905i
\(239\) 11.0001i 0.711539i −0.934574 0.355769i \(-0.884219\pi\)
0.934574 0.355769i \(-0.115781\pi\)
\(240\) 0.391956 + 1.28019i 0.0253007 + 0.0826359i
\(241\) 2.31184i 0.148919i 0.997224 + 0.0744594i \(0.0237231\pi\)
−0.997224 + 0.0744594i \(0.976277\pi\)
\(242\) 3.20151 + 1.84839i 0.205801 + 0.118819i
\(243\) −6.61638 14.1147i −0.424441 0.905456i
\(244\) −11.2735 6.50875i −0.721710 0.416680i
\(245\) 4.63712 2.78834i 0.296255 0.178140i
\(246\) 12.4191 + 11.5716i 0.791812 + 0.737781i
\(247\) −16.8423 0.193671i −1.07165 0.0123230i
\(248\) 1.87166 3.24180i 0.118850 0.205855i
\(249\) 27.6192 + 6.36470i 1.75030 + 0.403346i
\(250\) 7.26798i 0.459668i
\(251\) −4.19795 7.27107i −0.264973 0.458946i 0.702584 0.711601i \(-0.252030\pi\)
−0.967556 + 0.252655i \(0.918696\pi\)
\(252\) −2.65676 7.47941i −0.167360 0.471159i
\(253\) −7.27689 12.6039i −0.457494 0.792403i
\(254\) 6.28830 + 3.63055i 0.394563 + 0.227801i
\(255\) 1.03773 + 3.38937i 0.0649849 + 0.212251i
\(256\) 1.00000 0.0625000
\(257\) −24.6420 −1.53713 −0.768564 0.639773i \(-0.779028\pi\)
−0.768564 + 0.639773i \(0.779028\pi\)
\(258\) 18.7541 5.74196i 1.16758 0.357479i
\(259\) 8.62219 + 8.47023i 0.535757 + 0.526314i
\(260\) −2.39746 1.42118i −0.148684 0.0881377i
\(261\) 8.20188 + 12.1387i 0.507683 + 0.751367i
\(262\) −9.49487 + 5.48186i −0.586595 + 0.338671i
\(263\) −19.7538 + 11.4049i −1.21807 + 0.703254i −0.964505 0.264065i \(-0.914937\pi\)
−0.253566 + 0.967318i \(0.581603\pi\)
\(264\) −1.37033 4.47570i −0.0843378 0.275460i
\(265\) 2.82280i 0.173403i
\(266\) 11.9096 3.30492i 0.730224 0.202638i
\(267\) −17.4683 4.02548i −1.06905 0.246356i
\(268\) −3.47068 6.01140i −0.212006 0.367205i
\(269\) −1.82889 −0.111510 −0.0557548 0.998444i \(-0.517757\pi\)
−0.0557548 + 0.998444i \(0.517757\pi\)
\(270\) 3.96785 + 0.623537i 0.241476 + 0.0379472i
\(271\) 7.29891i 0.443377i −0.975118 0.221689i \(-0.928843\pi\)
0.975118 0.221689i \(-0.0711568\pi\)
\(272\) 2.64755 0.160532
\(273\) 14.5715 + 7.78910i 0.881910 + 0.471418i
\(274\) −4.98739 −0.301299
\(275\) 11.8975i 0.717447i
\(276\) 2.09464 9.08958i 0.126083 0.547128i
\(277\) −16.9183 −1.01652 −0.508260 0.861203i \(-0.669711\pi\)
−0.508260 + 0.861203i \(0.669711\pi\)
\(278\) −0.141431 0.244965i −0.00848244 0.0146920i
\(279\) −6.28719 9.30498i −0.376404 0.557075i
\(280\) 1.98007 + 0.511734i 0.118332 + 0.0305819i
\(281\) 31.6214i 1.88637i 0.332263 + 0.943187i \(0.392188\pi\)
−0.332263 + 0.943187i \(0.607812\pi\)
\(282\) −8.72257 + 2.67059i −0.519421 + 0.159032i
\(283\) 0.590743 0.341066i 0.0351161 0.0202743i −0.482339 0.875985i \(-0.660213\pi\)
0.517455 + 0.855710i \(0.326879\pi\)
\(284\) −9.71163 + 5.60701i −0.576279 + 0.332715i
\(285\) −1.40449 + 6.09471i −0.0831949 + 0.361019i
\(286\) 8.38181 + 4.96861i 0.495627 + 0.293800i
\(287\) 24.9849 6.93335i 1.47481 0.409263i
\(288\) 1.31294 2.69744i 0.0773659 0.158948i
\(289\) −9.99046 −0.587674
\(290\) −3.77471 −0.221658
\(291\) 13.1366 4.02204i 0.770080 0.235776i
\(292\) −8.99614 5.19392i −0.526459 0.303951i
\(293\) −3.90007 6.75511i −0.227844 0.394638i 0.729325 0.684168i \(-0.239834\pi\)
−0.957169 + 0.289530i \(0.906501\pi\)
\(294\) −11.8612 2.51214i −0.691762 0.146511i
\(295\) 4.33831 + 7.51418i 0.252586 + 0.437492i
\(296\) 4.56832i 0.265528i
\(297\) −13.8721 2.17996i −0.804940 0.126494i
\(298\) −0.199827 + 0.346111i −0.0115757 + 0.0200497i
\(299\) 9.51469 + 16.9265i 0.550249 + 0.978883i
\(300\) 5.19823 5.57892i 0.300120 0.322099i
\(301\) 7.49664 29.0070i 0.432099 1.67193i
\(302\) −6.23766 3.60132i −0.358937 0.207233i
\(303\) 5.15535 + 16.8382i 0.296167 + 0.967327i
\(304\) 4.04565 + 2.33575i 0.232034 + 0.133965i
\(305\) 10.0623i 0.576167i
\(306\) 3.47609 7.14162i 0.198715 0.408259i
\(307\) 1.62307i 0.0926335i −0.998927 0.0463167i \(-0.985252\pi\)
0.998927 0.0463167i \(-0.0147484\pi\)
\(308\) −6.92255 1.78908i −0.394449 0.101942i
\(309\) −15.3292 + 4.69336i −0.872050 + 0.266996i
\(310\) 2.89352 0.164341
\(311\) 15.1988 26.3252i 0.861847 1.49276i −0.00829636 0.999966i \(-0.502641\pi\)
0.870144 0.492798i \(-0.164026\pi\)
\(312\) 1.75948 + 5.99201i 0.0996110 + 0.339231i
\(313\) 4.29992 2.48256i 0.243046 0.140323i −0.373530 0.927618i \(-0.621853\pi\)
0.616576 + 0.787296i \(0.288519\pi\)
\(314\) −6.04786 + 10.4752i −0.341301 + 0.591150i
\(315\) 3.98009 4.66923i 0.224252 0.263081i
\(316\) −5.14638 8.91380i −0.289507 0.501440i
\(317\) 11.5891 6.69094i 0.650906 0.375801i −0.137897 0.990447i \(-0.544034\pi\)
0.788803 + 0.614646i \(0.210701\pi\)
\(318\) −4.31188 + 4.62765i −0.241798 + 0.259506i
\(319\) 13.1968 0.738881
\(320\) 0.386492 + 0.669424i 0.0216056 + 0.0374219i
\(321\) −0.471278 + 2.04508i −0.0263042 + 0.114145i
\(322\) −10.1644 9.98521i −0.566437 0.556454i
\(323\) 10.7111 + 6.18403i 0.595979 + 0.344089i
\(324\) −5.55236 7.08317i −0.308464 0.393509i
\(325\) −0.182518 + 15.8724i −0.0101243 + 0.880441i
\(326\) −8.17934 4.72234i −0.453012 0.261546i
\(327\) 9.04548 9.70792i 0.500216 0.536849i
\(328\) 8.48729 + 4.90014i 0.468632 + 0.270565i
\(329\) −3.48670 + 13.4912i −0.192228 + 0.743793i
\(330\) 2.46652 2.64715i 0.135777 0.145721i
\(331\) 14.7575 25.5607i 0.811145 1.40494i −0.100918 0.994895i \(-0.532178\pi\)
0.912063 0.410049i \(-0.134489\pi\)
\(332\) 16.3639 0.898086
\(333\) 12.3228 + 5.99795i 0.675284 + 0.328686i
\(334\) 16.3310 + 9.42868i 0.893590 + 0.515915i
\(335\) 2.68278 4.64672i 0.146576 0.253877i
\(336\) −2.46440 3.86351i −0.134444 0.210772i
\(337\) −30.1118 −1.64030 −0.820148 0.572152i \(-0.806109\pi\)
−0.820148 + 0.572152i \(0.806109\pi\)
\(338\) −11.1059 6.75717i −0.604080 0.367542i
\(339\) −17.0049 + 5.20639i −0.923578 + 0.282772i
\(340\) 1.02326 + 1.77234i 0.0554940 + 0.0961184i
\(341\) −10.1161 −0.547818
\(342\) 11.6123 7.84617i 0.627919 0.424272i
\(343\) −12.7419 + 13.4404i −0.687998 + 0.725713i
\(344\) 9.80672 5.66191i 0.528743 0.305270i
\(345\) 6.89435 2.11085i 0.371179 0.113644i
\(346\) 10.4080 + 6.00907i 0.559538 + 0.323050i
\(347\) 13.4578i 0.722453i 0.932478 + 0.361227i \(0.117642\pi\)
−0.932478 + 0.361227i \(0.882358\pi\)
\(348\) 6.18819 + 5.76593i 0.331722 + 0.309086i
\(349\) 8.96543 + 5.17619i 0.479908 + 0.277075i 0.720378 0.693581i \(-0.243968\pi\)
−0.240470 + 0.970657i \(0.577302\pi\)
\(350\) −3.11461 11.2238i −0.166483 0.599936i
\(351\) 18.4732 + 3.12108i 0.986026 + 0.166591i
\(352\) −1.35122 2.34039i −0.0720204 0.124743i
\(353\) 14.9512 + 25.8963i 0.795775 + 1.37832i 0.922346 + 0.386364i \(0.126269\pi\)
−0.126572 + 0.991957i \(0.540397\pi\)
\(354\) 4.36587 18.9455i 0.232044 1.00694i
\(355\) −7.50694 4.33413i −0.398427 0.230032i
\(356\) −10.3497 −0.548532
\(357\) −6.52464 10.2288i −0.345321 0.541368i
\(358\) 6.84801 + 11.8611i 0.361929 + 0.626879i
\(359\) −5.15529 + 2.97641i −0.272086 + 0.157089i −0.629835 0.776729i \(-0.716878\pi\)
0.357749 + 0.933818i \(0.383544\pi\)
\(360\) 2.31317 0.163624i 0.121915 0.00862372i
\(361\) 1.41150 + 2.44478i 0.0742893 + 0.128673i
\(362\) 13.0400 0.685368
\(363\) 4.36497 4.68463i 0.229101 0.245879i
\(364\) 9.20787 + 2.49300i 0.482624 + 0.130669i
\(365\) 8.02964i 0.420291i
\(366\) −15.3704 + 16.4960i −0.803421 + 0.862259i
\(367\) −14.7758 + 8.53079i −0.771288 + 0.445303i −0.833334 0.552770i \(-0.813571\pi\)
0.0620458 + 0.998073i \(0.480238\pi\)
\(368\) 5.38541i 0.280734i
\(369\) 24.3612 16.4604i 1.26819 0.856892i
\(370\) −3.05815 + 1.76562i −0.158985 + 0.0917903i
\(371\) 2.58353 + 9.31000i 0.134130 + 0.483351i
\(372\) −4.74359 4.41990i −0.245944 0.229161i
\(373\) −11.8330 + 20.4954i −0.612690 + 1.06121i 0.378096 + 0.925767i \(0.376579\pi\)
−0.990785 + 0.135443i \(0.956754\pi\)
\(374\) −3.57744 6.19630i −0.184985 0.320403i
\(375\) 12.2670 + 2.82686i 0.633466 + 0.145979i
\(376\) −4.56112 + 2.63336i −0.235222 + 0.135805i
\(377\) −17.6058 0.202451i −0.906744 0.0104268i
\(378\) −13.6572 + 1.57501i −0.702451 + 0.0810099i
\(379\) 13.2966 23.0303i 0.682998 1.18299i −0.291063 0.956704i \(-0.594009\pi\)
0.974061 0.226284i \(-0.0726576\pi\)
\(380\) 3.61100i 0.185241i
\(381\) 8.57352 9.20139i 0.439235 0.471402i
\(382\) 0.970190 1.68042i 0.0496392 0.0859777i
\(383\) 7.81768 13.5406i 0.399465 0.691893i −0.594195 0.804321i \(-0.702529\pi\)
0.993660 + 0.112428i \(0.0358627\pi\)
\(384\) 0.388948 1.68782i 0.0198484 0.0861310i
\(385\) −1.47786 5.32559i −0.0753185 0.271417i
\(386\) −8.69971 + 5.02278i −0.442804 + 0.255653i
\(387\) −2.39700 33.8868i −0.121846 1.72256i
\(388\) 6.86925 3.96597i 0.348734 0.201341i
\(389\) 4.64668 + 2.68276i 0.235596 + 0.136021i 0.613151 0.789966i \(-0.289902\pi\)
−0.377555 + 0.925987i \(0.623235\pi\)
\(390\) −3.33117 + 3.49371i −0.168680 + 0.176911i
\(391\) 14.2582i 0.721066i
\(392\) −6.99889 + 0.124461i −0.353498 + 0.00628624i
\(393\) 5.55937 + 18.1577i 0.280433 + 0.915937i
\(394\) −1.47576 + 2.55609i −0.0743476 + 0.128774i
\(395\) 3.97807 6.89023i 0.200159 0.346685i
\(396\) −8.08713 + 0.572048i −0.406394 + 0.0287465i
\(397\) 5.03723 + 2.90825i 0.252812 + 0.145961i 0.621051 0.783770i \(-0.286706\pi\)
−0.368239 + 0.929731i \(0.620039\pi\)
\(398\) 2.80034 0.140368
\(399\) −0.945895 21.3866i −0.0473540 1.07067i
\(400\) 2.20125 3.81267i 0.110062 0.190634i
\(401\) 8.68621i 0.433769i 0.976197 + 0.216884i \(0.0695895\pi\)
−0.976197 + 0.216884i \(0.930411\pi\)
\(402\) −11.4960 + 3.51975i −0.573370 + 0.175549i
\(403\) 13.4958 + 0.155190i 0.672274 + 0.00773057i
\(404\) 5.08348 + 8.80484i 0.252913 + 0.438057i
\(405\) 2.59570 6.45447i 0.128981 0.320725i
\(406\) 12.4495 3.45475i 0.617859 0.171457i
\(407\) 10.6916 6.17282i 0.529965 0.305975i
\(408\) 1.02976 4.46858i 0.0509807 0.221228i
\(409\) 10.0665i 0.497758i 0.968535 + 0.248879i \(0.0800621\pi\)
−0.968535 + 0.248879i \(0.919938\pi\)
\(410\) 7.57546i 0.374126i
\(411\) −1.93983 + 8.41779i −0.0956849 + 0.415219i
\(412\) −8.01582 + 4.62793i −0.394911 + 0.228002i
\(413\) −21.1856 20.8122i −1.04248 1.02410i
\(414\) −14.5268 7.07074i −0.713954 0.347508i
\(415\) 6.32452 + 10.9544i 0.310458 + 0.537730i
\(416\) 1.76675 + 3.14302i 0.0866222 + 0.154099i
\(417\) −0.468465 + 0.143430i −0.0229408 + 0.00702381i
\(418\) 12.6245i 0.617484i
\(419\) −6.88362 + 11.9228i −0.336287 + 0.582466i −0.983731 0.179647i \(-0.942505\pi\)
0.647444 + 0.762113i \(0.275838\pi\)
\(420\) 1.63385 3.14295i 0.0797239 0.153360i
\(421\) 5.26092 0.256402 0.128201 0.991748i \(-0.459080\pi\)
0.128201 + 0.991748i \(0.459080\pi\)
\(422\) 11.3855 + 6.57341i 0.554237 + 0.319989i
\(423\) 1.11485 + 15.7608i 0.0542058 + 0.766316i
\(424\) −1.82591 + 3.16257i −0.0886741 + 0.153588i
\(425\) 5.82792 10.0943i 0.282696 0.489643i
\(426\) 5.68628 + 18.5723i 0.275501 + 0.899829i
\(427\) 9.20941 + 33.1869i 0.445674 + 1.60603i
\(428\) 1.21168i 0.0585686i
\(429\) 11.6462 12.2144i 0.562283 0.589717i
\(430\) 7.58044 + 4.37657i 0.365561 + 0.211057i
\(431\) −19.1377 + 11.0492i −0.921832 + 0.532220i −0.884219 0.467073i \(-0.845309\pi\)
−0.0376127 + 0.999292i \(0.511975\pi\)
\(432\) −4.04211 3.26517i −0.194476 0.157095i
\(433\) −0.698470 + 0.403262i −0.0335663 + 0.0193795i −0.516689 0.856173i \(-0.672836\pi\)
0.483123 + 0.875553i \(0.339502\pi\)
\(434\) −9.54324 + 2.64826i −0.458090 + 0.127121i
\(435\) −1.46816 + 6.37101i −0.0703930 + 0.305466i
\(436\) 3.83041 6.63447i 0.183443 0.317733i
\(437\) 12.5790 21.7875i 0.601735 1.04224i
\(438\) −12.2654 + 13.1637i −0.586064 + 0.628984i
\(439\) 22.1127i 1.05538i 0.849437 + 0.527691i \(0.176942\pi\)
−0.849437 + 0.527691i \(0.823058\pi\)
\(440\) 1.04447 1.80908i 0.0497934 0.0862446i
\(441\) −8.85342 + 19.0425i −0.421592 + 0.906786i
\(442\) 4.67757 + 8.32132i 0.222489 + 0.395805i
\(443\) −22.9597 + 13.2558i −1.09085 + 0.629800i −0.933802 0.357791i \(-0.883530\pi\)
−0.157044 + 0.987592i \(0.550197\pi\)
\(444\) 7.71048 + 1.77684i 0.365923 + 0.0843250i
\(445\) −4.00007 6.92833i −0.189622 0.328434i
\(446\) −1.34534 + 2.33020i −0.0637038 + 0.110338i
\(447\) 0.506450 + 0.471891i 0.0239542 + 0.0223197i
\(448\) −1.88739 1.85412i −0.0891707 0.0875990i
\(449\) −32.5645 + 18.8011i −1.53681 + 0.887279i −0.537789 + 0.843079i \(0.680740\pi\)
−0.999023 + 0.0441993i \(0.985926\pi\)
\(450\) −7.39434 10.9436i −0.348573 0.515884i
\(451\) 26.4847i 1.24712i
\(452\) −8.89202 + 5.13381i −0.418245 + 0.241474i
\(453\) −8.50448 + 9.12730i −0.399575 + 0.428838i
\(454\) 5.28026i 0.247815i
\(455\) 1.88990 + 7.12750i 0.0885998 + 0.334142i
\(456\) 5.51587 5.91981i 0.258304 0.277221i
\(457\) 19.1061 0.893745 0.446873 0.894598i \(-0.352538\pi\)
0.446873 + 0.894598i \(0.352538\pi\)
\(458\) −13.2288 22.9130i −0.618143 1.07066i
\(459\) −10.7017 8.64471i −0.499513 0.403500i
\(460\) 3.60512 2.08142i 0.168090 0.0970467i
\(461\) 2.14345 + 3.71257i 0.0998306 + 0.172912i 0.911614 0.411046i \(-0.134837\pi\)
−0.811784 + 0.583958i \(0.801503\pi\)
\(462\) −5.71215 + 10.9881i −0.265753 + 0.511214i
\(463\) 30.5605 1.42027 0.710134 0.704066i \(-0.248634\pi\)
0.710134 + 0.704066i \(0.248634\pi\)
\(464\) 4.22905 + 2.44165i 0.196329 + 0.113351i
\(465\) 1.12543 4.88373i 0.0521905 0.226478i
\(466\) 1.74259 + 3.01825i 0.0807239 + 0.139818i
\(467\) −9.65321 16.7199i −0.446697 0.773703i 0.551471 0.834194i \(-0.314067\pi\)
−0.998169 + 0.0604912i \(0.980733\pi\)
\(468\) 10.7978 0.639100i 0.499126 0.0295424i
\(469\) −4.59535 + 17.7809i −0.212193 + 0.821046i
\(470\) −3.52567 2.03555i −0.162627 0.0938929i
\(471\) 15.3279 + 14.2820i 0.706273 + 0.658079i
\(472\) 11.2248i 0.516665i
\(473\) −26.5021 15.3010i −1.21857 0.703541i
\(474\) −17.0465 + 5.21914i −0.782972 + 0.239723i
\(475\) 17.8109 10.2831i 0.817222 0.471823i
\(476\) −4.99696 4.90889i −0.229035 0.224999i
\(477\) 6.13353 + 9.07756i 0.280835 + 0.415633i
\(478\) −11.0001 −0.503134
\(479\) 18.8035 + 32.5686i 0.859152 + 1.48810i 0.872739 + 0.488188i \(0.162342\pi\)
−0.0135862 + 0.999908i \(0.504325\pi\)
\(480\) 1.28019 0.391956i 0.0584324 0.0178903i
\(481\) −14.3583 + 8.07110i −0.654684 + 0.368010i
\(482\) 2.31184 0.105302
\(483\) −20.8066 + 13.2718i −0.946733 + 0.603889i
\(484\) 1.84839 3.20151i 0.0840179 0.145523i
\(485\) 5.30983 + 3.06563i 0.241107 + 0.139203i
\(486\) −14.1147 + 6.61638i −0.640254 + 0.300125i
\(487\) −35.0418 −1.58790 −0.793948 0.607986i \(-0.791978\pi\)
−0.793948 + 0.607986i \(0.791978\pi\)
\(488\) −6.50875 + 11.2735i −0.294637 + 0.510326i
\(489\) −11.1518 + 11.9685i −0.504301 + 0.541233i
\(490\) −2.78834 4.63712i −0.125964 0.209484i
\(491\) 21.2054 + 12.2429i 0.956985 + 0.552516i 0.895244 0.445576i \(-0.147001\pi\)
0.0617415 + 0.998092i \(0.480335\pi\)
\(492\) 11.5716 12.4191i 0.521690 0.559895i
\(493\) 11.1966 + 6.46439i 0.504272 + 0.291141i
\(494\) −0.193671 + 16.8423i −0.00871368 + 0.757769i
\(495\) −3.50856 5.19263i −0.157698 0.233391i
\(496\) −3.24180 1.87166i −0.145561 0.0840399i
\(497\) 28.7257 + 7.42394i 1.28852 + 0.333009i
\(498\) 6.36470 27.6192i 0.285209 1.23765i
\(499\) 9.94836 + 17.2311i 0.445350 + 0.771368i 0.998077 0.0619941i \(-0.0197460\pi\)
−0.552727 + 0.833363i \(0.686413\pi\)
\(500\) 7.26798 0.325034
\(501\) 22.2658 23.8964i 0.994761 1.06761i
\(502\) −7.27107 + 4.19795i −0.324524 + 0.187364i
\(503\) −5.22211 9.04495i −0.232842 0.403295i 0.725801 0.687905i \(-0.241469\pi\)
−0.958643 + 0.284610i \(0.908136\pi\)
\(504\) −7.47941 + 2.65676i −0.333160 + 0.118341i
\(505\) −3.92945 + 6.80601i −0.174858 + 0.302863i
\(506\) −12.6039 + 7.27689i −0.560314 + 0.323497i
\(507\) −15.7245 + 16.1165i −0.698348 + 0.715759i
\(508\) 3.63055 6.28830i 0.161080 0.278998i
\(509\) 1.49932 0.0664561 0.0332280 0.999448i \(-0.489421\pi\)
0.0332280 + 0.999448i \(0.489421\pi\)
\(510\) 3.38937 1.03773i 0.150084 0.0459513i
\(511\) 7.34903 + 26.4829i 0.325102 + 1.17153i
\(512\) 1.00000i 0.0441942i
\(513\) −8.72633 22.6511i −0.385277 1.00007i
\(514\) 24.6420i 1.08691i
\(515\) −6.19610 3.57732i −0.273033 0.157636i
\(516\) −5.74196 18.7541i −0.252776 0.825604i
\(517\) 12.3262 + 7.11652i 0.542105 + 0.312984i
\(518\) 8.47023 8.62219i 0.372161 0.378837i
\(519\) 14.1904 15.2296i 0.622888 0.668505i
\(520\) −1.42118 + 2.39746i −0.0623228 + 0.105136i
\(521\) 9.88915 17.1285i 0.433252 0.750414i −0.563900 0.825843i \(-0.690699\pi\)
0.997151 + 0.0754296i \(0.0240328\pi\)
\(522\) 12.1387 8.20188i 0.531296 0.358986i
\(523\) 13.1827i 0.576438i −0.957565 0.288219i \(-0.906937\pi\)
0.957565 0.288219i \(-0.0930630\pi\)
\(524\) 5.48186 + 9.49487i 0.239476 + 0.414785i
\(525\) −20.1551 + 0.891424i −0.879639 + 0.0389050i
\(526\) 11.4049 + 19.7538i 0.497275 + 0.861306i
\(527\) −8.58285 4.95531i −0.373875 0.215857i
\(528\) −4.47570 + 1.37033i −0.194780 + 0.0596358i
\(529\) −6.00265 −0.260985
\(530\) −2.82280 −0.122615
\(531\) −30.2783 14.7376i −1.31397 0.639556i
\(532\) −3.30492 11.9096i −0.143287 0.516346i
\(533\) −0.406300 + 35.3331i −0.0175988 + 1.53045i
\(534\) −4.02548 + 17.4683i −0.174200 + 0.755929i
\(535\) −0.811125 + 0.468303i −0.0350680 + 0.0202465i
\(536\) −6.01140 + 3.47068i −0.259653 + 0.149911i
\(537\) 22.6829 6.94483i 0.978838 0.299692i
\(538\) 1.82889i 0.0788492i
\(539\) 9.74835 + 16.2119i 0.419891 + 0.698298i
\(540\) 0.623537 3.96785i 0.0268328 0.170749i
\(541\) 10.6958 + 18.5257i 0.459848 + 0.796480i 0.998953 0.0457586i \(-0.0145705\pi\)
−0.539104 + 0.842239i \(0.681237\pi\)
\(542\) −7.29891 −0.313515
\(543\) 5.07188 22.0091i 0.217655 0.944502i
\(544\) 2.64755i 0.113513i
\(545\) 5.92170 0.253658
\(546\) 7.78910 14.5715i 0.333343 0.623604i
\(547\) −25.6199 −1.09543 −0.547713 0.836666i \(-0.684501\pi\)
−0.547713 + 0.836666i \(0.684501\pi\)
\(548\) 4.98739i 0.213051i
\(549\) 21.8639 + 32.3584i 0.933129 + 1.38102i
\(550\) −11.8975 −0.507311
\(551\) 11.4062 + 19.7561i 0.485919 + 0.841636i
\(552\) −9.08958 2.09464i −0.386878 0.0891539i
\(553\) −6.81405 + 26.3658i −0.289763 + 1.12119i
\(554\) 16.9183i 0.718789i
\(555\) 1.79058 + 5.84832i 0.0760060 + 0.248247i
\(556\) −0.244965 + 0.141431i −0.0103888 + 0.00599799i
\(557\) −13.7049 + 7.91256i −0.580697 + 0.335266i −0.761410 0.648270i \(-0.775493\pi\)
0.180713 + 0.983536i \(0.442159\pi\)
\(558\) −9.30498 + 6.28719i −0.393911 + 0.266158i
\(559\) 35.1216 + 20.8195i 1.48548 + 0.880573i
\(560\) 0.511734 1.98007i 0.0216247 0.0836731i
\(561\) −11.8496 + 3.62801i −0.500292 + 0.153175i
\(562\) 31.6214 1.33387
\(563\) −9.74601 −0.410745 −0.205373 0.978684i \(-0.565841\pi\)
−0.205373 + 0.978684i \(0.565841\pi\)
\(564\) 2.67059 + 8.72257i 0.112452 + 0.367286i
\(565\) −6.87339 3.96836i −0.289166 0.166950i
\(566\) −0.341066 0.590743i −0.0143361 0.0248308i
\(567\) −2.65361 + 23.6634i −0.111441 + 0.993771i
\(568\) 5.60701 + 9.71163i 0.235265 + 0.407491i
\(569\) 18.5832i 0.779048i 0.921016 + 0.389524i \(0.127360\pi\)
−0.921016 + 0.389524i \(0.872640\pi\)
\(570\) 6.09471 + 1.40449i 0.255279 + 0.0588277i
\(571\) −16.5767 + 28.7116i −0.693712 + 1.20154i 0.276901 + 0.960899i \(0.410693\pi\)
−0.970613 + 0.240646i \(0.922641\pi\)
\(572\) 4.96861 8.38181i 0.207748 0.350461i
\(573\) −2.45888 2.29110i −0.102721 0.0957119i
\(574\) −6.93335 24.9849i −0.289392 1.04285i
\(575\) −20.5328 11.8546i −0.856277 0.494372i
\(576\) −2.69744 1.31294i −0.112393 0.0547060i
\(577\) −31.6525 18.2746i −1.31771 0.760780i −0.334350 0.942449i \(-0.608517\pi\)
−0.983360 + 0.181668i \(0.941850\pi\)
\(578\) 9.99046i 0.415548i
\(579\) 5.09379 + 16.6371i 0.211691 + 0.691414i
\(580\) 3.77471i 0.156736i
\(581\) −30.8850 30.3407i −1.28133 1.25874i
\(582\) −4.02204 13.1366i −0.166719 0.544529i
\(583\) 9.86886 0.408726
\(584\) −5.19392 + 8.99614i −0.214926 + 0.372263i
\(585\) 4.60108 + 6.98127i 0.190231 + 0.288640i
\(586\) −6.75511 + 3.90007i −0.279051 + 0.161110i
\(587\) 17.2008 29.7927i 0.709953 1.22967i −0.254921 0.966962i \(-0.582049\pi\)
0.964874 0.262713i \(-0.0846172\pi\)
\(588\) −2.51214 + 11.8612i −0.103599 + 0.489150i
\(589\) −8.74346 15.1441i −0.360268 0.624002i
\(590\) 7.51418 4.33831i 0.309354 0.178605i
\(591\) 3.74021 + 3.48499i 0.153852 + 0.143353i
\(592\) 4.56832 0.187757
\(593\) −1.21051 2.09667i −0.0497099 0.0861000i 0.840100 0.542432i \(-0.182496\pi\)
−0.889810 + 0.456332i \(0.849163\pi\)
\(594\) −2.17996 + 13.8721i −0.0894448 + 0.569178i
\(595\) 1.35484 5.24233i 0.0555431 0.214915i
\(596\) 0.346111 + 0.199827i 0.0141773 + 0.00818525i
\(597\) 1.08918 4.72645i 0.0445773 0.193441i
\(598\) 16.9265 9.51469i 0.692174 0.389085i
\(599\) −29.8409 17.2287i −1.21927 0.703944i −0.254506 0.967071i \(-0.581913\pi\)
−0.964761 + 0.263127i \(0.915246\pi\)
\(600\) −5.57892 5.19823i −0.227758 0.212217i
\(601\) −14.8253 8.55938i −0.604736 0.349145i 0.166166 0.986098i \(-0.446861\pi\)
−0.770903 + 0.636953i \(0.780194\pi\)
\(602\) −29.0070 7.49664i −1.18224 0.305540i
\(603\) 1.46933 + 20.7722i 0.0598358 + 0.845909i
\(604\) −3.60132 + 6.23766i −0.146536 + 0.253807i
\(605\) 2.85756 0.116176
\(606\) 16.8382 5.15535i 0.684003 0.209422i
\(607\) 12.7249 + 7.34672i 0.516488 + 0.298194i 0.735496 0.677529i \(-0.236949\pi\)
−0.219009 + 0.975723i \(0.570282\pi\)
\(608\) 2.33575 4.04565i 0.0947273 0.164073i
\(609\) −0.988777 22.3562i −0.0400673 0.905919i
\(610\) −10.0623 −0.407411
\(611\) −16.3351 9.68319i −0.660847 0.391740i
\(612\) −7.14162 3.47609i −0.288683 0.140512i
\(613\) −14.8270 25.6811i −0.598857 1.03725i −0.992990 0.118198i \(-0.962288\pi\)
0.394133 0.919053i \(-0.371045\pi\)
\(614\) −1.62307 −0.0655018
\(615\) 12.7860 + 2.94646i 0.515581 + 0.118813i
\(616\) −1.78908 + 6.92255i −0.0720842 + 0.278917i
\(617\) 15.2938 8.82986i 0.615704 0.355477i −0.159491 0.987199i \(-0.550985\pi\)
0.775195 + 0.631723i \(0.217652\pi\)
\(618\) 4.69336 + 15.3292i 0.188795 + 0.616632i
\(619\) −21.5803 12.4594i −0.867387 0.500786i −0.000907672 1.00000i \(-0.500289\pi\)
−0.866479 + 0.499214i \(0.833622\pi\)
\(620\) 2.89352i 0.116207i
\(621\) −17.5843 + 21.7684i −0.705632 + 0.873537i
\(622\) −26.3252 15.1988i −1.05554 0.609418i
\(623\) 19.5339 + 19.1896i 0.782607 + 0.768814i
\(624\) 5.99201 1.75948i 0.239873 0.0704356i
\(625\) −8.19722 14.1980i −0.327889 0.567920i
\(626\) −2.48256 4.29992i −0.0992231 0.171859i
\(627\) −21.3078 4.91027i −0.850952 0.196097i
\(628\) 10.4752 + 6.04786i 0.418006 + 0.241336i
\(629\) 12.0949 0.482254
\(630\) −4.66923 3.98009i −0.186027 0.158570i
\(631\) 4.25946 + 7.37761i 0.169567 + 0.293698i 0.938268 0.345910i \(-0.112430\pi\)
−0.768701 + 0.639608i \(0.779097\pi\)
\(632\) −8.91380 + 5.14638i −0.354572 + 0.204712i
\(633\) 15.5231 16.6599i 0.616986 0.662171i
\(634\) −6.69094 11.5891i −0.265731 0.460260i
\(635\) 5.61272 0.222734
\(636\) 4.62765 + 4.31188i 0.183498 + 0.170977i
\(637\) −12.7565 21.7778i −0.505431 0.862867i
\(638\) 13.1968i 0.522467i
\(639\) 33.5582 2.37376i 1.32754 0.0939044i
\(640\) 0.669424 0.386492i 0.0264613 0.0152774i
\(641\) 20.4369i 0.807211i −0.914933 0.403605i \(-0.867757\pi\)
0.914933 0.403605i \(-0.132243\pi\)
\(642\) 2.04508 + 0.471278i 0.0807131 + 0.0185999i
\(643\) 28.2804 16.3277i 1.11527 0.643902i 0.175082 0.984554i \(-0.443981\pi\)
0.940190 + 0.340652i \(0.110648\pi\)
\(644\) −9.98521 + 10.1644i −0.393472 + 0.400532i
\(645\) 10.3352 11.0921i 0.406950 0.436752i
\(646\) 6.18403 10.7111i 0.243308 0.421421i
\(647\) −1.63150 2.82584i −0.0641410 0.111095i 0.832172 0.554518i \(-0.187097\pi\)
−0.896313 + 0.443423i \(0.853764\pi\)
\(648\) −7.08317 + 5.55236i −0.278253 + 0.218117i
\(649\) −26.2705 + 15.1673i −1.03121 + 0.595367i
\(650\) 15.8724 + 0.182518i 0.622566 + 0.00715896i
\(651\) 0.757952 + 17.1373i 0.0297065 + 0.671662i
\(652\) −4.72234 + 8.17934i −0.184941 + 0.320328i
\(653\) 27.2298i 1.06558i 0.846246 + 0.532792i \(0.178857\pi\)
−0.846246 + 0.532792i \(0.821143\pi\)
\(654\) −9.70792 9.04548i −0.379610 0.353706i
\(655\) −4.23739 + 7.33938i −0.165569 + 0.286773i
\(656\) 4.90014 8.48729i 0.191318 0.331373i
\(657\) 17.4472 + 25.8217i 0.680680 + 1.00740i
\(658\) 13.4912 + 3.48670i 0.525941 + 0.135926i
\(659\) −40.7276 + 23.5141i −1.58652 + 0.915980i −0.592650 + 0.805460i \(0.701918\pi\)
−0.993874 + 0.110520i \(0.964748\pi\)
\(660\) −2.64715 2.46652i −0.103040 0.0960091i
\(661\) −3.51184 + 2.02756i −0.136595 + 0.0788630i −0.566740 0.823897i \(-0.691796\pi\)
0.430145 + 0.902760i \(0.358462\pi\)
\(662\) −25.5607 14.7575i −0.993445 0.573566i
\(663\) 15.8642 4.65832i 0.616114 0.180914i
\(664\) 16.3639i 0.635043i
\(665\) 6.69524 6.81536i 0.259630 0.264288i
\(666\) 5.99795 12.3228i 0.232416 0.477498i
\(667\) 13.1493 22.7752i 0.509141 0.881859i
\(668\) 9.42868 16.3310i 0.364807 0.631864i
\(669\) 3.40968 + 3.17701i 0.131826 + 0.122830i
\(670\) −4.64672 2.68278i −0.179518 0.103645i
\(671\) 35.1791 1.35807
\(672\) −3.86351 + 2.46440i −0.149038 + 0.0950665i
\(673\) 20.5401 35.5765i 0.791763 1.37137i −0.133111 0.991101i \(-0.542497\pi\)
0.924874 0.380273i \(-0.124170\pi\)
\(674\) 30.1118i 1.15986i
\(675\) −21.3467 + 8.22381i −0.821635 + 0.316535i
\(676\) −6.75717 + 11.1059i −0.259891 + 0.427149i
\(677\) 0.255669 + 0.442832i 0.00982616 + 0.0170194i 0.870897 0.491466i \(-0.163539\pi\)
−0.861071 + 0.508486i \(0.830206\pi\)
\(678\) 5.20639 + 17.0049i 0.199950 + 0.653068i
\(679\) −20.3183 5.25112i −0.779746 0.201520i
\(680\) 1.77234 1.02326i 0.0679660 0.0392402i
\(681\) 8.91210 + 2.05374i 0.341512 + 0.0786996i
\(682\) 10.1161i 0.387366i
\(683\) 17.4362i 0.667179i −0.942718 0.333589i \(-0.891740\pi\)
0.942718 0.333589i \(-0.108260\pi\)
\(684\) −7.84617 11.6123i −0.300006 0.444006i
\(685\) −3.33868 + 1.92759i −0.127564 + 0.0736493i
\(686\) 13.4404 + 12.7419i 0.513156 + 0.486488i
\(687\) −43.8183 + 13.4159i −1.67177 + 0.511848i
\(688\) −5.66191 9.80672i −0.215858 0.373878i
\(689\) −13.1660 0.151397i −0.501583 0.00576777i
\(690\) −2.11085 6.89435i −0.0803586 0.262463i
\(691\) 9.05150i 0.344335i 0.985068 + 0.172168i \(0.0550771\pi\)
−0.985068 + 0.172168i \(0.944923\pi\)
\(692\) 6.00907 10.4080i 0.228431 0.395653i
\(693\) 16.3242 + 13.9149i 0.620105 + 0.528582i
\(694\) 13.4578 0.510852
\(695\) −0.189354 0.109324i −0.00718261 0.00414688i
\(696\) 5.76593 6.18819i 0.218557 0.234563i
\(697\) 12.9734 22.4706i 0.491402 0.851133i
\(698\) 5.17619 8.96543i 0.195922 0.339346i
\(699\) 5.77203 1.76723i 0.218318 0.0668427i
\(700\) −11.2238 + 3.11461i −0.424219 + 0.117721i
\(701\) 0.299896i 0.0113269i 0.999984 + 0.00566346i \(0.00180274\pi\)
−0.999984 + 0.00566346i \(0.998197\pi\)
\(702\) 3.12108 18.4732i 0.117797 0.697226i
\(703\) 18.4818 + 10.6705i 0.697055 + 0.402445i
\(704\) −2.34039 + 1.35122i −0.0882066 + 0.0509261i
\(705\) −4.80693 + 5.15896i −0.181040 + 0.194298i
\(706\) 25.8963 14.9512i 0.974621 0.562698i
\(707\) 6.73076 26.0435i 0.253136 0.979468i
\(708\) −18.9455 4.36587i −0.712014 0.164080i
\(709\) 17.7350 30.7179i 0.666052 1.15364i −0.312946 0.949771i \(-0.601316\pi\)
0.978999 0.203866i \(-0.0653507\pi\)
\(710\) −4.33413 + 7.50694i −0.162657 + 0.281730i
\(711\) 2.17875 + 30.8013i 0.0817095 + 1.15514i
\(712\) 10.3497i 0.387871i
\(713\) −10.0796 + 17.4584i −0.377485 + 0.653824i
\(714\) −10.2288 + 6.52464i −0.382805 + 0.244179i
\(715\) 7.53131 + 0.0866035i 0.281655 + 0.00323879i
\(716\) 11.8611 6.84801i 0.443270 0.255922i
\(717\) −4.27847 + 18.5662i −0.159782 + 0.693366i
\(718\) 2.97641 + 5.15529i 0.111079 + 0.192394i
\(719\) 22.6978 39.3138i 0.846487 1.46616i −0.0378368 0.999284i \(-0.512047\pi\)
0.884324 0.466874i \(-0.154620\pi\)
\(720\) −0.163624 2.31317i −0.00609789 0.0862069i
\(721\) 23.7097 + 6.12760i 0.882996 + 0.228204i
\(722\) 2.44478 1.41150i 0.0909854 0.0525305i
\(723\) 0.899185 3.90196i 0.0334411 0.145116i
\(724\) 13.0400i 0.484628i
\(725\) 18.6184 10.7493i 0.691470 0.399220i
\(726\) −4.68463 4.36497i −0.173863 0.161999i
\(727\) 11.4955i 0.426346i 0.977014 + 0.213173i \(0.0683798\pi\)
−0.977014 + 0.213173i \(0.931620\pi\)
\(728\) 2.49300 9.20787i 0.0923967 0.341267i
\(729\) 5.67736 + 26.3964i 0.210273 + 0.977643i
\(730\) −8.02964 −0.297190
\(731\) −14.9902 25.9638i −0.554433 0.960307i
\(732\) 16.4960 + 15.3704i 0.609709 + 0.568104i
\(733\) 3.91444 2.26000i 0.144583 0.0834751i −0.425963 0.904740i \(-0.640065\pi\)
0.570546 + 0.821265i \(0.306731\pi\)
\(734\) 8.53079 + 14.7758i 0.314877 + 0.545383i
\(735\) −8.91113 + 2.90260i −0.328692 + 0.107064i
\(736\) −5.38541 −0.198509
\(737\) 16.2455 + 9.37933i 0.598410 + 0.345492i
\(738\) −16.4604 24.3612i −0.605914 0.896747i
\(739\) −3.98629 6.90445i −0.146638 0.253984i 0.783345 0.621587i \(-0.213512\pi\)
−0.929983 + 0.367603i \(0.880179\pi\)
\(740\) 1.76562 + 3.05815i 0.0649055 + 0.112420i
\(741\) 28.3513 + 6.87763i 1.04151 + 0.252656i
\(742\) 9.31000 2.58353i 0.341781 0.0948445i
\(743\) −18.4735 10.6657i −0.677726 0.391285i 0.121272 0.992619i \(-0.461303\pi\)
−0.798998 + 0.601334i \(0.794636\pi\)
\(744\) −4.41990 + 4.74359i −0.162041 + 0.173908i
\(745\) 0.308927i 0.0113182i
\(746\) 20.4954 + 11.8330i 0.750388 + 0.433237i
\(747\) −44.1406 21.4849i −1.61502 0.786090i
\(748\) −6.19630 + 3.57744i −0.226559 + 0.130804i
\(749\) 2.24660 2.28690i 0.0820888 0.0835616i
\(750\) 2.82686 12.2670i 0.103222 0.447928i
\(751\) −37.6651 −1.37442 −0.687209 0.726460i \(-0.741164\pi\)
−0.687209 + 0.726460i \(0.741164\pi\)
\(752\) 2.63336 + 4.56112i 0.0960289 + 0.166327i
\(753\) 4.25731 + 13.9050i 0.155145 + 0.506727i
\(754\) −0.202451 + 17.6058i −0.00737284 + 0.641165i
\(755\) −5.56752 −0.202623
\(756\) 1.57501 + 13.6572i 0.0572827 + 0.496708i
\(757\) −16.7324 + 28.9814i −0.608150 + 1.05335i 0.383395 + 0.923584i \(0.374755\pi\)
−0.991545 + 0.129762i \(0.958579\pi\)
\(758\) −23.0303 13.2966i −0.836498 0.482953i
\(759\) 7.37977 + 24.1035i 0.267869 + 0.874900i
\(760\) 3.61100 0.130985
\(761\) 5.12883 8.88340i 0.185920 0.322023i −0.757966 0.652294i \(-0.773807\pi\)
0.943886 + 0.330271i \(0.107140\pi\)
\(762\) −9.20139 8.57352i −0.333331 0.310586i
\(763\) −19.5306 + 5.41976i −0.707054 + 0.196208i
\(764\) −1.68042 0.970190i −0.0607954 0.0351002i
\(765\) −0.433202 6.12425i −0.0156625 0.221423i
\(766\) −13.5406 7.81768i −0.489242 0.282464i
\(767\) 35.2799 19.8315i 1.27388 0.716074i
\(768\) −1.68782 0.388948i −0.0609038 0.0140349i
\(769\) −23.6054 13.6286i −0.851232 0.491459i 0.00983428 0.999952i \(-0.496870\pi\)
−0.861066 + 0.508493i \(0.830203\pi\)
\(770\) −5.32559 + 1.47786i −0.191921 + 0.0532582i
\(771\) 41.5912 + 9.58446i 1.49787 + 0.345176i
\(772\) 5.02278 + 8.69971i 0.180774 + 0.313109i
\(773\) 39.5055 1.42091 0.710457 0.703741i \(-0.248488\pi\)
0.710457 + 0.703741i \(0.248488\pi\)
\(774\) −33.8868 + 2.39700i −1.21804 + 0.0861585i
\(775\) −14.2720 + 8.23996i −0.512666 + 0.295988i
\(776\) −3.96597 6.86925i −0.142370 0.246592i
\(777\) −11.2582 17.6498i −0.403885 0.633182i
\(778\) 2.68276 4.64668i 0.0961817 0.166592i
\(779\) 39.6485 22.8910i 1.42055 0.820157i
\(780\) 3.49371 + 3.33117i 0.125095 + 0.119275i
\(781\) 15.1526 26.2451i 0.542204 0.939125i
\(782\) −14.2582 −0.509871
\(783\) −9.12193 23.6780i −0.325991 0.846182i
\(784\) 0.124461 + 6.99889i 0.00444504 + 0.249960i
\(785\) 9.34981i 0.333709i
\(786\) 18.1577 5.55937i 0.647665 0.198296i
\(787\) 26.2020i 0.934002i −0.884257 0.467001i \(-0.845334\pi\)
0.884257 0.467001i \(-0.154666\pi\)
\(788\) 2.55609 + 1.47576i 0.0910568 + 0.0525717i
\(789\) 37.7766 11.5661i 1.34488 0.411764i
\(790\) −6.89023 3.97807i −0.245143 0.141534i
\(791\) 26.3014 + 6.79741i 0.935170 + 0.241688i
\(792\) 0.572048 + 8.08713i 0.0203268 + 0.287364i
\(793\) −46.9321 0.539678i −1.66661 0.0191645i
\(794\) 2.90825 5.03723i 0.103210 0.178765i
\(795\) −1.09792 + 4.76437i −0.0389393 + 0.168975i
\(796\) 2.80034i 0.0992553i
\(797\) 19.9610 + 34.5734i 0.707054 + 1.22465i 0.965945 + 0.258747i \(0.0833096\pi\)
−0.258891 + 0.965906i \(0.583357\pi\)
\(798\) −21.3866 + 0.945895i −0.757079 + 0.0334843i
\(799\) 6.97197 + 12.0758i 0.246651 + 0.427211i
\(800\) −3.81267 2.20125i −0.134798 0.0778259i
\(801\) 27.9176 + 13.5885i 0.986421 + 0.480127i
\(802\) 8.68621 0.306721
\(803\) 28.0726 0.990660
\(804\) 3.51975 + 11.4960i 0.124132 + 0.405434i
\(805\) −10.6635 2.75590i −0.375838 0.0971326i
\(806\) 0.155190 13.4958i 0.00546634 0.475370i
\(807\) 3.08683 + 0.711343i 0.108662 + 0.0250405i
\(808\) 8.80484 5.08348i 0.309753 0.178836i
\(809\) 47.7092 27.5449i 1.67736 0.968427i 0.714034 0.700111i \(-0.246866\pi\)
0.963331 0.268316i \(-0.0864672\pi\)
\(810\) −6.45447 2.59570i −0.226787 0.0912036i
\(811\) 7.30412i 0.256482i −0.991743 0.128241i \(-0.959067\pi\)
0.991743 0.128241i \(-0.0409331\pi\)
\(812\) −3.45475 12.4495i −0.121238 0.436892i
\(813\) −2.83889 + 12.3192i −0.0995643 + 0.432054i
\(814\) −6.17282 10.6916i −0.216357 0.374742i
\(815\) −7.30060 −0.255729
\(816\) −4.46858 1.02976i −0.156432 0.0360488i
\(817\) 52.8994i 1.85071i
\(818\) 10.0665 0.351968
\(819\) −21.5645 18.8141i −0.753525 0.657419i
\(820\) 7.57546 0.264547
\(821\) 29.3769i 1.02526i −0.858610 0.512630i \(-0.828671\pi\)
0.858610 0.512630i \(-0.171329\pi\)
\(822\) 8.41779 + 1.93983i 0.293604 + 0.0676595i
\(823\) −12.2245 −0.426120 −0.213060 0.977039i \(-0.568343\pi\)
−0.213060 + 0.977039i \(0.568343\pi\)
\(824\) 4.62793 + 8.01582i 0.161222 + 0.279244i
\(825\) −4.62751 + 20.0808i −0.161109 + 0.699123i
\(826\) −20.8122 + 21.1856i −0.724150 + 0.737142i
\(827\) 30.9380i 1.07582i 0.843003 + 0.537910i \(0.180786\pi\)
−0.843003 + 0.537910i \(0.819214\pi\)
\(828\) −7.07074 + 14.5268i −0.245725 + 0.504842i
\(829\) 42.5213 24.5497i 1.47682 0.852645i 0.477167 0.878812i \(-0.341664\pi\)
0.999658 + 0.0261672i \(0.00833022\pi\)
\(830\) 10.9544 6.32452i 0.380232 0.219527i
\(831\) 28.5549 + 6.58032i 0.990559 + 0.228269i
\(832\) 3.14302 1.76675i 0.108965 0.0612511i
\(833\) 0.329518 + 18.5299i 0.0114171 + 0.642025i
\(834\) 0.143430 + 0.468465i 0.00496658 + 0.0162216i
\(835\) 14.5765 0.504439
\(836\) −12.6245 −0.436627
\(837\) 6.99247 + 18.1505i 0.241695 + 0.627372i
\(838\) 11.9228 + 6.88362i 0.411866 + 0.237791i
\(839\) −8.62928 14.9464i −0.297916 0.516005i 0.677743 0.735299i \(-0.262958\pi\)
−0.975659 + 0.219293i \(0.929625\pi\)
\(840\) −3.14295 1.63385i −0.108442 0.0563733i
\(841\) −2.57674 4.46304i −0.0888530 0.153898i
\(842\) 5.26092i 0.181303i
\(843\) 12.2991 53.3710i 0.423602 1.83820i
\(844\) 6.57341 11.3855i 0.226266 0.391904i
\(845\) −10.0461 0.231074i −0.345598 0.00794919i
\(846\) 15.7608 1.11485i 0.541868 0.0383293i
\(847\) −9.42463 + 2.61534i −0.323834 + 0.0898643i
\(848\) 3.16257 + 1.82591i 0.108603 + 0.0627021i
\(849\) −1.12972 + 0.345888i −0.0387720 + 0.0118708i
\(850\) −10.0943 5.82792i −0.346230 0.199896i
\(851\) 24.6023i 0.843356i
\(852\) 18.5723 5.68628i 0.636275 0.194809i
\(853\) 1.10853i 0.0379553i −0.999820 0.0189776i \(-0.993959\pi\)
0.999820 0.0189776i \(-0.00604113\pi\)
\(854\) 33.1869 9.20941i 1.13563 0.315139i
\(855\) 4.74104 9.74046i 0.162140 0.333117i
\(856\) 1.21168 0.0414142
\(857\) 17.4478 30.2204i 0.596005 1.03231i −0.397399 0.917646i \(-0.630087\pi\)
0.993404 0.114665i \(-0.0365794\pi\)
\(858\) −12.2144 11.6462i −0.416993 0.397594i
\(859\) −17.5635 + 10.1403i −0.599259 + 0.345982i −0.768750 0.639550i \(-0.779121\pi\)
0.169491 + 0.985532i \(0.445788\pi\)
\(860\) 4.37657 7.58044i 0.149240 0.258491i
\(861\) −44.8667 + 1.98438i −1.52905 + 0.0676274i
\(862\) 11.0492 + 19.1377i 0.376336 + 0.651833i
\(863\) 36.5693 21.1133i 1.24484 0.718706i 0.274760 0.961513i \(-0.411401\pi\)
0.970075 + 0.242807i \(0.0780681\pi\)
\(864\) −3.26517 + 4.04211i −0.111083 + 0.137515i
\(865\) 9.28983 0.315864
\(866\) 0.403262 + 0.698470i 0.0137034 + 0.0237350i
\(867\) 16.8621 + 3.88577i 0.572665 + 0.131968i
\(868\) 2.64826 + 9.54324i 0.0898878 + 0.323919i
\(869\) 24.0891 + 13.9078i 0.817165 + 0.471791i
\(870\) 6.37101 + 1.46816i 0.215997 + 0.0497754i
\(871\) −21.5291 12.7621i −0.729485 0.432428i
\(872\) −6.63447 3.83041i −0.224671 0.129714i
\(873\) −23.7365 + 1.67901i −0.803358 + 0.0568260i
\(874\) −21.7875 12.5790i −0.736972 0.425491i
\(875\) −13.7175 13.4757i −0.463736 0.455563i
\(876\) 13.1637 + 12.2654i 0.444759 + 0.414410i
\(877\) −9.82427 + 17.0161i −0.331742 + 0.574594i −0.982853 0.184388i \(-0.940970\pi\)
0.651112 + 0.758982i \(0.274303\pi\)
\(878\) 22.1127 0.746268
\(879\) 3.95521 + 12.9183i 0.133406 + 0.435724i
\(880\) −1.80908 1.04447i −0.0609842 0.0352092i
\(881\) −3.68778 + 6.38743i −0.124245 + 0.215198i −0.921437 0.388527i \(-0.872984\pi\)
0.797193 + 0.603725i \(0.206317\pi\)
\(882\) 19.0425 + 8.85342i 0.641194 + 0.298110i
\(883\) 40.9675 1.37867 0.689333 0.724445i \(-0.257904\pi\)
0.689333 + 0.724445i \(0.257904\pi\)
\(884\) 8.32132 4.67757i 0.279876 0.157324i
\(885\) −4.39965 14.3699i −0.147893 0.483040i
\(886\) 13.2558 + 22.9597i 0.445336 + 0.771345i
\(887\) −22.2164 −0.745953 −0.372976 0.927841i \(-0.621663\pi\)
−0.372976 + 0.927841i \(0.621663\pi\)
\(888\) 1.77684 7.71048i 0.0596268 0.258747i
\(889\) −18.5115 + 5.13697i −0.620857 + 0.172288i
\(890\) −6.92833 + 4.00007i −0.232238 + 0.134083i
\(891\) 22.5656 + 9.07488i 0.755976 + 0.304020i
\(892\) 2.33020 + 1.34534i 0.0780209 + 0.0450454i
\(893\) 24.6036i 0.823327i
\(894\) 0.471891 0.506450i 0.0157824 0.0169382i
\(895\) 9.16845 + 5.29341i 0.306467 + 0.176939i
\(896\) −1.85412 + 1.88739i −0.0619419 + 0.0630532i
\(897\) −9.47553 32.2695i −0.316379 1.07745i
\(898\) 18.8011 + 32.5645i 0.627401 + 1.08669i
\(899\) −9.13984 15.8307i −0.304831 0.527982i
\(900\) −10.9436 + 7.39434i −0.364785 + 0.246478i
\(901\) 8.37308 + 4.83420i 0.278948 + 0.161051i
\(902\) −26.4847 −0.881845
\(903\) −23.9351 + 46.0426i −0.796511 + 1.53220i
\(904\) 5.13381 + 8.89202i 0.170748 + 0.295744i
\(905\) 8.72930 5.03986i 0.290172 0.167531i
\(906\) 9.12730 + 8.50448i 0.303234 + 0.282543i
\(907\) 21.0951 + 36.5378i 0.700452 + 1.21322i 0.968308 + 0.249759i \(0.0803514\pi\)
−0.267856 + 0.963459i \(0.586315\pi\)
\(908\) 5.28026 0.175232
\(909\) −2.15212 30.4249i −0.0713813 1.00913i
\(910\) 7.12750 1.88990i 0.236274 0.0626495i
\(911\) 22.5763i 0.747985i 0.927432 + 0.373992i \(0.122011\pi\)
−0.927432 + 0.373992i \(0.877989\pi\)
\(912\) −5.91981 5.51587i −0.196025 0.182649i
\(913\) −38.2979 + 22.1113i −1.26747 + 0.731777i
\(914\) 19.1061i 0.631973i
\(915\) −3.91371 + 16.9833i −0.129383 + 0.561452i
\(916\) −22.9130 + 13.2288i −0.757068 + 0.437093i
\(917\) 7.25824 28.0845i 0.239688 0.927433i
\(918\) −8.64471 + 10.7017i −0.285318 + 0.353209i
\(919\) −5.03819 + 8.72641i −0.166195 + 0.287858i −0.937079 0.349118i \(-0.886481\pi\)
0.770884 + 0.636975i \(0.219815\pi\)
\(920\) −2.08142 3.60512i −0.0686224 0.118857i
\(921\) −0.631289 + 2.73944i −0.0208017 + 0.0902677i
\(922\) 3.71257 2.14345i 0.122267 0.0705909i
\(923\) −20.6176 + 34.7810i −0.678638 + 1.14483i
\(924\) 10.9881 + 5.71215i 0.361483 + 0.187916i
\(925\) 10.0560 17.4175i 0.330640 0.572685i
\(926\) 30.5605i 1.00428i
\(927\) 27.6984 1.95926i 0.909735 0.0643506i
\(928\) 2.44165 4.22905i 0.0801509 0.138825i
\(929\) 3.78399 6.55406i 0.124149 0.215032i −0.797251 0.603648i \(-0.793713\pi\)
0.921400 + 0.388616i \(0.127047\pi\)
\(930\) −4.88373 1.12543i −0.160144 0.0369043i
\(931\) −15.8442 + 28.6057i −0.519272 + 0.937516i
\(932\) 3.01825 1.74259i 0.0988662 0.0570804i
\(933\) −35.8920 + 38.5205i −1.17505 + 1.26110i
\(934\) −16.7199 + 9.65321i −0.547090 + 0.315863i
\(935\) −4.78964 2.76530i −0.156638 0.0904350i
\(936\) −0.639100 10.7978i −0.0208897 0.352936i
\(937\) 47.8920i 1.56456i −0.622925 0.782282i \(-0.714056\pi\)
0.622925 0.782282i \(-0.285944\pi\)
\(938\) 17.7809 + 4.59535i 0.580567 + 0.150043i
\(939\) −8.22306 + 2.51766i −0.268349 + 0.0821607i
\(940\) −2.03555 + 3.52567i −0.0663923 + 0.114995i
\(941\) 7.73208 13.3924i 0.252059 0.436578i −0.712034 0.702145i \(-0.752226\pi\)
0.964092 + 0.265567i \(0.0855591\pi\)
\(942\) 14.2820 15.3279i 0.465332 0.499410i
\(943\) −45.7076 26.3893i −1.48844 0.859353i
\(944\) −11.2248 −0.365337
\(945\) −8.53373 + 6.33276i −0.277602 + 0.206005i
\(946\) −15.3010 + 26.5021i −0.497479 + 0.861659i
\(947\) 4.59259i 0.149239i 0.997212 + 0.0746196i \(0.0237742\pi\)
−0.997212 + 0.0746196i \(0.976226\pi\)
\(948\) 5.21914 + 17.0465i 0.169510 + 0.553645i
\(949\) −37.4514 0.430659i −1.21572 0.0139798i
\(950\) −10.2831 17.8109i −0.333629 0.577863i
\(951\) −22.1626 + 6.78554i −0.718672 + 0.220036i
\(952\) −4.90889 + 4.99696i −0.159098 + 0.161952i
\(953\) −45.1678 + 26.0776i −1.46313 + 0.844737i −0.999155 0.0411118i \(-0.986910\pi\)
−0.463973 + 0.885849i \(0.653577\pi\)
\(954\) 9.07756 6.13353i 0.293897 0.198580i
\(955\) 1.49988i 0.0485351i
\(956\) 11.0001i 0.355769i
\(957\) −22.2738 5.13287i −0.720010 0.165922i
\(958\) 32.5686 18.8035i 1.05224 0.607512i
\(959\) 9.24723 9.41314i 0.298609 0.303966i
\(960\) −0.391956 1.28019i −0.0126503 0.0413179i
\(961\) −8.49380 14.7117i −0.273994 0.474571i
\(962\) 8.07110 + 14.3583i 0.260223 + 0.462931i
\(963\) 1.59086 3.26842i 0.0512648 0.105323i
\(964\) 2.31184i 0.0744594i
\(965\) −3.88253 + 6.72474i −0.124983 + 0.216477i
\(966\) 13.2718 + 20.8066i 0.427014 + 0.669441i
\(967\) 54.0463 1.73801 0.869006 0.494802i \(-0.164759\pi\)
0.869006 + 0.494802i \(0.164759\pi\)
\(968\) −3.20151 1.84839i −0.102900 0.0594096i
\(969\) −15.6730 14.6035i −0.503490 0.469134i
\(970\) 3.06563 5.30983i 0.0984314 0.170488i
\(971\) −19.1393 + 33.1502i −0.614209 + 1.06384i 0.376314 + 0.926492i \(0.377191\pi\)
−0.990523 + 0.137349i \(0.956142\pi\)
\(972\) 6.61638 + 14.1147i 0.212220 + 0.452728i
\(973\) 0.724574 + 0.187261i 0.0232288 + 0.00600330i
\(974\) 35.0418i 1.12281i
\(975\) 6.48158 26.7186i 0.207577 0.855681i
\(976\) 11.2735 + 6.50875i 0.360855 + 0.208340i
\(977\) −42.1551 + 24.3383i −1.34866 + 0.778651i −0.988060 0.154069i \(-0.950762\pi\)
−0.360602 + 0.932720i \(0.617429\pi\)
\(978\) 11.9685 + 11.1518i 0.382709 + 0.356595i
\(979\) 24.2223 13.9847i 0.774147 0.446954i
\(980\) −4.63712 + 2.78834i −0.148128 + 0.0890701i
\(981\) −19.0430 + 12.8670i −0.607995 + 0.410810i
\(982\) 12.2429 21.2054i 0.390688 0.676691i
\(983\) 10.2329 17.7240i 0.326380 0.565307i −0.655411 0.755273i \(-0.727504\pi\)
0.981791 + 0.189966i \(0.0608378\pi\)
\(984\) −12.4191 11.5716i −0.395906 0.368891i
\(985\) 2.28148i 0.0726938i
\(986\) 6.46439 11.1966i 0.205868 0.356574i
\(987\) 11.1323 21.4145i 0.354344 0.681630i
\(988\) 16.8423 + 0.193671i 0.535823 + 0.00616150i
\(989\) −52.8132 + 30.4917i −1.67936 + 0.969581i
\(990\) −5.19263 + 3.50856i −0.165033 + 0.111509i
\(991\) 19.3399 + 33.4977i 0.614352 + 1.06409i 0.990498 + 0.137529i \(0.0439160\pi\)
−0.376145 + 0.926561i \(0.622751\pi\)
\(992\) −1.87166 + 3.24180i −0.0594252 + 0.102927i
\(993\) −34.8497 + 37.4019i −1.10592 + 1.18691i
\(994\) 7.42394 28.7257i 0.235473 0.911123i
\(995\) 1.87461 1.08231i 0.0594292 0.0343115i
\(996\) −27.6192 6.36470i −0.875149 0.201673i
\(997\) 2.83228i 0.0896993i 0.998994 + 0.0448497i \(0.0142809\pi\)
−0.998994 + 0.0448497i \(0.985719\pi\)
\(998\) 17.2311 9.94836i 0.545440 0.314910i
\(999\) −18.4657 14.9163i −0.584228 0.471932i
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 546.2.bb.a.269.1 yes 76
3.2 odd 2 inner 546.2.bb.a.269.27 yes 76
7.5 odd 6 546.2.u.a.425.6 yes 76
13.3 even 3 546.2.u.a.185.33 yes 76
21.5 even 6 546.2.u.a.425.33 yes 76
39.29 odd 6 546.2.u.a.185.6 76
91.68 odd 6 inner 546.2.bb.a.341.8 yes 76
273.68 even 6 inner 546.2.bb.a.341.20 yes 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.u.a.185.6 76 39.29 odd 6
546.2.u.a.185.33 yes 76 13.3 even 3
546.2.u.a.425.6 yes 76 7.5 odd 6
546.2.u.a.425.33 yes 76 21.5 even 6
546.2.bb.a.269.1 yes 76 1.1 even 1 trivial
546.2.bb.a.269.27 yes 76 3.2 odd 2 inner
546.2.bb.a.341.8 yes 76 91.68 odd 6 inner
546.2.bb.a.341.20 yes 76 273.68 even 6 inner