Properties

Label 150.2.g.a.91.1
Level $150$
Weight $2$
Character 150.91
Analytic conductor $1.198$
Analytic rank $0$
Dimension $4$
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] = [150,2,Mod(31,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.g (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.19775603032\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 150.91
Dual form 150.2.g.a.61.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.309017 + 0.951057i) q^{6} +2.61803 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.309017 + 0.951057i) q^{6} +2.61803 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.690983 - 2.12663i) q^{10} +(-2.92705 - 2.12663i) q^{11} +(0.809017 - 0.587785i) q^{12} +(5.23607 - 3.80423i) q^{13} +(-2.11803 - 1.53884i) q^{14} +(0.690983 - 2.12663i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.381966 - 1.17557i) q^{17} +1.00000 q^{18} +(-1.76393 + 5.42882i) q^{19} +(-0.690983 + 2.12663i) q^{20} +(-0.809017 - 2.48990i) q^{21} +(1.11803 + 3.44095i) q^{22} +(-3.61803 - 2.62866i) q^{23} -1.00000 q^{24} +(1.54508 + 4.75528i) q^{25} -6.47214 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 2.48990i) q^{28} +(2.61803 + 8.05748i) q^{29} +(-1.80902 + 1.31433i) q^{30} +(2.04508 - 6.29412i) q^{31} +1.00000 q^{32} +(-1.11803 + 3.44095i) q^{33} +(-1.00000 + 0.726543i) q^{34} +(4.73607 + 3.44095i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(-6.47214 + 4.70228i) q^{37} +(4.61803 - 3.35520i) q^{38} +(-5.23607 - 3.80423i) q^{39} +(1.80902 - 1.31433i) q^{40} +(-4.61803 + 3.35520i) q^{41} +(-0.809017 + 2.48990i) q^{42} -7.70820 q^{43} +(1.11803 - 3.44095i) q^{44} -2.23607 q^{45} +(1.38197 + 4.25325i) q^{46} +(0.527864 + 1.62460i) q^{47} +(0.809017 + 0.587785i) q^{48} -0.145898 q^{49} +(1.54508 - 4.75528i) q^{50} -1.23607 q^{51} +(5.23607 + 3.80423i) q^{52} +(-0.645898 - 1.98787i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-2.50000 - 7.69421i) q^{55} +(0.809017 - 2.48990i) q^{56} +5.70820 q^{57} +(2.61803 - 8.05748i) q^{58} +(2.92705 - 2.12663i) q^{59} +2.23607 q^{60} +(-2.23607 - 1.62460i) q^{61} +(-5.35410 + 3.88998i) q^{62} +(-2.11803 + 1.53884i) q^{63} +(-0.809017 - 0.587785i) q^{64} +14.4721 q^{65} +(2.92705 - 2.12663i) q^{66} +(-0.472136 + 1.45309i) q^{67} +1.23607 q^{68} +(-1.38197 + 4.25325i) q^{69} +(-1.80902 - 5.56758i) q^{70} +(1.70820 + 5.25731i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-2.85410 - 2.07363i) q^{73} +8.00000 q^{74} +(4.04508 - 2.93893i) q^{75} -5.70820 q^{76} +(-7.66312 - 5.56758i) q^{77} +(2.00000 + 6.15537i) q^{78} +(-1.73607 - 5.34307i) q^{79} -2.23607 q^{80} +(0.309017 - 0.951057i) q^{81} +5.70820 q^{82} +(0.663119 - 2.04087i) q^{83} +(2.11803 - 1.53884i) q^{84} +(2.23607 - 1.62460i) q^{85} +(6.23607 + 4.53077i) q^{86} +(6.85410 - 4.97980i) q^{87} +(-2.92705 + 2.12663i) q^{88} +(-2.85410 - 2.07363i) q^{89} +(1.80902 + 1.31433i) q^{90} +(13.7082 - 9.95959i) q^{91} +(1.38197 - 4.25325i) q^{92} -6.61803 q^{93} +(0.527864 - 1.62460i) q^{94} +(-10.3262 + 7.50245i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-1.04508 - 3.21644i) q^{97} +(0.118034 + 0.0857567i) q^{98} +3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + q^{3} - q^{4} + 5 q^{5} + q^{6} + 6 q^{7} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + q^{3} - q^{4} + 5 q^{5} + q^{6} + 6 q^{7} - q^{8} - q^{9} - 5 q^{10} - 5 q^{11} + q^{12} + 12 q^{13} - 4 q^{14} + 5 q^{15} - q^{16} + 6 q^{17} + 4 q^{18} - 16 q^{19} - 5 q^{20} - q^{21} - 10 q^{23} - 4 q^{24} - 5 q^{25} - 8 q^{26} + q^{27} + q^{28} + 6 q^{29} - 5 q^{30} - 3 q^{31} + 4 q^{32} - 4 q^{34} + 10 q^{35} - q^{36} - 8 q^{37} + 14 q^{38} - 12 q^{39} + 5 q^{40} - 14 q^{41} - q^{42} - 4 q^{43} + 10 q^{46} + 20 q^{47} + q^{48} - 14 q^{49} - 5 q^{50} + 4 q^{51} + 12 q^{52} - 16 q^{53} + q^{54} - 10 q^{55} + q^{56} - 4 q^{57} + 6 q^{58} + 5 q^{59} - 8 q^{62} - 4 q^{63} - q^{64} + 40 q^{65} + 5 q^{66} + 16 q^{67} - 4 q^{68} - 10 q^{69} - 5 q^{70} - 20 q^{71} - q^{72} + 2 q^{73} + 32 q^{74} + 5 q^{75} + 4 q^{76} - 15 q^{77} + 8 q^{78} + 2 q^{79} - q^{81} - 4 q^{82} - 13 q^{83} + 4 q^{84} + 16 q^{86} + 14 q^{87} - 5 q^{88} + 2 q^{89} + 5 q^{90} + 28 q^{91} + 10 q^{92} - 22 q^{93} + 20 q^{94} - 10 q^{95} + q^{96} + 7 q^{97} - 4 q^{98} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 0.587785i −0.572061 0.415627i
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) 1.80902 + 1.31433i 0.809017 + 0.587785i
\(6\) −0.309017 + 0.951057i −0.126156 + 0.388267i
\(7\) 2.61803 0.989524 0.494762 0.869029i \(-0.335255\pi\)
0.494762 + 0.869029i \(0.335255\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −0.690983 2.12663i −0.218508 0.672499i
\(11\) −2.92705 2.12663i −0.882539 0.641202i 0.0513829 0.998679i \(-0.483637\pi\)
−0.933922 + 0.357477i \(0.883637\pi\)
\(12\) 0.809017 0.587785i 0.233543 0.169679i
\(13\) 5.23607 3.80423i 1.45222 1.05510i 0.466919 0.884300i \(-0.345364\pi\)
0.985305 0.170802i \(-0.0546359\pi\)
\(14\) −2.11803 1.53884i −0.566068 0.411273i
\(15\) 0.690983 2.12663i 0.178411 0.549093i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 0.381966 1.17557i 0.0926404 0.285118i −0.893991 0.448085i \(-0.852106\pi\)
0.986632 + 0.162967i \(0.0521064\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.76393 + 5.42882i −0.404674 + 1.24546i 0.516494 + 0.856291i \(0.327237\pi\)
−0.921167 + 0.389167i \(0.872763\pi\)
\(20\) −0.690983 + 2.12663i −0.154508 + 0.475528i
\(21\) −0.809017 2.48990i −0.176542 0.543340i
\(22\) 1.11803 + 3.44095i 0.238366 + 0.733614i
\(23\) −3.61803 2.62866i −0.754412 0.548113i 0.142779 0.989755i \(-0.454396\pi\)
−0.897191 + 0.441642i \(0.854396\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.54508 + 4.75528i 0.309017 + 0.951057i
\(26\) −6.47214 −1.26929
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 0.809017 + 2.48990i 0.152890 + 0.470547i
\(29\) 2.61803 + 8.05748i 0.486157 + 1.49624i 0.830299 + 0.557319i \(0.188170\pi\)
−0.344142 + 0.938918i \(0.611830\pi\)
\(30\) −1.80902 + 1.31433i −0.330280 + 0.239962i
\(31\) 2.04508 6.29412i 0.367308 1.13046i −0.581215 0.813750i \(-0.697422\pi\)
0.948523 0.316708i \(-0.102578\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.11803 + 3.44095i −0.194625 + 0.598993i
\(34\) −1.00000 + 0.726543i −0.171499 + 0.124601i
\(35\) 4.73607 + 3.44095i 0.800542 + 0.581628i
\(36\) −0.809017 0.587785i −0.134836 0.0979642i
\(37\) −6.47214 + 4.70228i −1.06401 + 0.773050i −0.974827 0.222965i \(-0.928427\pi\)
−0.0891861 + 0.996015i \(0.528427\pi\)
\(38\) 4.61803 3.35520i 0.749144 0.544285i
\(39\) −5.23607 3.80423i −0.838442 0.609164i
\(40\) 1.80902 1.31433i 0.286031 0.207813i
\(41\) −4.61803 + 3.35520i −0.721216 + 0.523994i −0.886772 0.462206i \(-0.847058\pi\)
0.165557 + 0.986200i \(0.447058\pi\)
\(42\) −0.809017 + 2.48990i −0.124834 + 0.384200i
\(43\) −7.70820 −1.17549 −0.587745 0.809046i \(-0.699984\pi\)
−0.587745 + 0.809046i \(0.699984\pi\)
\(44\) 1.11803 3.44095i 0.168550 0.518743i
\(45\) −2.23607 −0.333333
\(46\) 1.38197 + 4.25325i 0.203760 + 0.627108i
\(47\) 0.527864 + 1.62460i 0.0769969 + 0.236972i 0.982145 0.188123i \(-0.0602405\pi\)
−0.905149 + 0.425096i \(0.860241\pi\)
\(48\) 0.809017 + 0.587785i 0.116772 + 0.0848395i
\(49\) −0.145898 −0.0208426
\(50\) 1.54508 4.75528i 0.218508 0.672499i
\(51\) −1.23607 −0.173084
\(52\) 5.23607 + 3.80423i 0.726112 + 0.527551i
\(53\) −0.645898 1.98787i −0.0887209 0.273055i 0.896846 0.442344i \(-0.145853\pi\)
−0.985566 + 0.169289i \(0.945853\pi\)
\(54\) −0.309017 0.951057i −0.0420519 0.129422i
\(55\) −2.50000 7.69421i −0.337100 1.03749i
\(56\) 0.809017 2.48990i 0.108109 0.332727i
\(57\) 5.70820 0.756070
\(58\) 2.61803 8.05748i 0.343765 1.05800i
\(59\) 2.92705 2.12663i 0.381070 0.276863i −0.380717 0.924692i \(-0.624323\pi\)
0.761786 + 0.647829i \(0.224323\pi\)
\(60\) 2.23607 0.288675
\(61\) −2.23607 1.62460i −0.286299 0.208009i 0.435361 0.900256i \(-0.356621\pi\)
−0.721660 + 0.692247i \(0.756621\pi\)
\(62\) −5.35410 + 3.88998i −0.679972 + 0.494028i
\(63\) −2.11803 + 1.53884i −0.266847 + 0.193876i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 14.4721 1.79505
\(66\) 2.92705 2.12663i 0.360295 0.261770i
\(67\) −0.472136 + 1.45309i −0.0576806 + 0.177523i −0.975746 0.218907i \(-0.929751\pi\)
0.918065 + 0.396430i \(0.129751\pi\)
\(68\) 1.23607 0.149895
\(69\) −1.38197 + 4.25325i −0.166369 + 0.512032i
\(70\) −1.80902 5.56758i −0.216219 0.665453i
\(71\) 1.70820 + 5.25731i 0.202727 + 0.623928i 0.999799 + 0.0200445i \(0.00638080\pi\)
−0.797073 + 0.603884i \(0.793619\pi\)
\(72\) 0.309017 + 0.951057i 0.0364180 + 0.112083i
\(73\) −2.85410 2.07363i −0.334047 0.242700i 0.408099 0.912938i \(-0.366192\pi\)
−0.742146 + 0.670238i \(0.766192\pi\)
\(74\) 8.00000 0.929981
\(75\) 4.04508 2.93893i 0.467086 0.339358i
\(76\) −5.70820 −0.654776
\(77\) −7.66312 5.56758i −0.873293 0.634485i
\(78\) 2.00000 + 6.15537i 0.226455 + 0.696958i
\(79\) −1.73607 5.34307i −0.195323 0.601142i −0.999973 0.00739236i \(-0.997647\pi\)
0.804650 0.593750i \(-0.202353\pi\)
\(80\) −2.23607 −0.250000
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 5.70820 0.630366
\(83\) 0.663119 2.04087i 0.0727868 0.224015i −0.908044 0.418874i \(-0.862425\pi\)
0.980831 + 0.194859i \(0.0624250\pi\)
\(84\) 2.11803 1.53884i 0.231096 0.167901i
\(85\) 2.23607 1.62460i 0.242536 0.176212i
\(86\) 6.23607 + 4.53077i 0.672453 + 0.488565i
\(87\) 6.85410 4.97980i 0.734837 0.533890i
\(88\) −2.92705 + 2.12663i −0.312025 + 0.226699i
\(89\) −2.85410 2.07363i −0.302534 0.219804i 0.426152 0.904651i \(-0.359869\pi\)
−0.728686 + 0.684848i \(0.759869\pi\)
\(90\) 1.80902 + 1.31433i 0.190687 + 0.138542i
\(91\) 13.7082 9.95959i 1.43701 1.04405i
\(92\) 1.38197 4.25325i 0.144080 0.443432i
\(93\) −6.61803 −0.686258
\(94\) 0.527864 1.62460i 0.0544450 0.167565i
\(95\) −10.3262 + 7.50245i −1.05945 + 0.769735i
\(96\) −0.309017 0.951057i −0.0315389 0.0970668i
\(97\) −1.04508 3.21644i −0.106112 0.326580i 0.883878 0.467718i \(-0.154924\pi\)
−0.989990 + 0.141138i \(0.954924\pi\)
\(98\) 0.118034 + 0.0857567i 0.0119232 + 0.00866274i
\(99\) 3.61803 0.363626
\(100\) −4.04508 + 2.93893i −0.404508 + 0.293893i
\(101\) 4.38197 0.436022 0.218011 0.975946i \(-0.430043\pi\)
0.218011 + 0.975946i \(0.430043\pi\)
\(102\) 1.00000 + 0.726543i 0.0990148 + 0.0719384i
\(103\) 4.42705 + 13.6251i 0.436210 + 1.34252i 0.891841 + 0.452348i \(0.149414\pi\)
−0.455631 + 0.890169i \(0.650586\pi\)
\(104\) −2.00000 6.15537i −0.196116 0.603583i
\(105\) 1.80902 5.56758i 0.176542 0.543340i
\(106\) −0.645898 + 1.98787i −0.0627352 + 0.193079i
\(107\) −11.6180 −1.12316 −0.561579 0.827423i \(-0.689806\pi\)
−0.561579 + 0.827423i \(0.689806\pi\)
\(108\) −0.309017 + 0.951057i −0.0297352 + 0.0915155i
\(109\) −13.9443 + 10.1311i −1.33562 + 0.970384i −0.336026 + 0.941853i \(0.609083\pi\)
−0.999593 + 0.0285313i \(0.990917\pi\)
\(110\) −2.50000 + 7.69421i −0.238366 + 0.733614i
\(111\) 6.47214 + 4.70228i 0.614308 + 0.446321i
\(112\) −2.11803 + 1.53884i −0.200135 + 0.145407i
\(113\) 15.5623 11.3067i 1.46398 1.06364i 0.481674 0.876350i \(-0.340029\pi\)
0.982304 0.187292i \(-0.0599712\pi\)
\(114\) −4.61803 3.35520i −0.432519 0.314243i
\(115\) −3.09017 9.51057i −0.288160 0.886865i
\(116\) −6.85410 + 4.97980i −0.636387 + 0.462363i
\(117\) −2.00000 + 6.15537i −0.184900 + 0.569064i
\(118\) −3.61803 −0.333067
\(119\) 1.00000 3.07768i 0.0916698 0.282131i
\(120\) −1.80902 1.31433i −0.165140 0.119981i
\(121\) 0.645898 + 1.98787i 0.0587180 + 0.180715i
\(122\) 0.854102 + 2.62866i 0.0773268 + 0.237987i
\(123\) 4.61803 + 3.35520i 0.416394 + 0.302528i
\(124\) 6.61803 0.594317
\(125\) −3.45492 + 10.6331i −0.309017 + 0.951057i
\(126\) 2.61803 0.233233
\(127\) −11.0172 8.00448i −0.977620 0.710283i −0.0204448 0.999791i \(-0.506508\pi\)
−0.957176 + 0.289508i \(0.906508\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) 2.38197 + 7.33094i 0.209720 + 0.645453i
\(130\) −11.7082 8.50651i −1.02688 0.746070i
\(131\) −5.52786 + 17.0130i −0.482972 + 1.48643i 0.351925 + 0.936028i \(0.385527\pi\)
−0.834897 + 0.550406i \(0.814473\pi\)
\(132\) −3.61803 −0.314909
\(133\) −4.61803 + 14.2128i −0.400434 + 1.23241i
\(134\) 1.23607 0.898056i 0.106780 0.0775802i
\(135\) 0.690983 + 2.12663i 0.0594703 + 0.183031i
\(136\) −1.00000 0.726543i −0.0857493 0.0623005i
\(137\) 9.85410 7.15942i 0.841893 0.611671i −0.0810060 0.996714i \(-0.525813\pi\)
0.922899 + 0.385043i \(0.125813\pi\)
\(138\) 3.61803 2.62866i 0.307988 0.223766i
\(139\) −8.47214 6.15537i −0.718597 0.522091i 0.167339 0.985899i \(-0.446483\pi\)
−0.885936 + 0.463808i \(0.846483\pi\)
\(140\) −1.80902 + 5.56758i −0.152890 + 0.470547i
\(141\) 1.38197 1.00406i 0.116383 0.0845569i
\(142\) 1.70820 5.25731i 0.143349 0.441184i
\(143\) −23.4164 −1.95818
\(144\) 0.309017 0.951057i 0.0257514 0.0792547i
\(145\) −5.85410 + 18.0171i −0.486157 + 1.49624i
\(146\) 1.09017 + 3.35520i 0.0902231 + 0.277678i
\(147\) 0.0450850 + 0.138757i 0.00371855 + 0.0114445i
\(148\) −6.47214 4.70228i −0.532006 0.386525i
\(149\) 22.0902 1.80970 0.904849 0.425733i \(-0.139984\pi\)
0.904849 + 0.425733i \(0.139984\pi\)
\(150\) −5.00000 −0.408248
\(151\) 18.3262 1.49137 0.745684 0.666300i \(-0.232123\pi\)
0.745684 + 0.666300i \(0.232123\pi\)
\(152\) 4.61803 + 3.35520i 0.374572 + 0.272143i
\(153\) 0.381966 + 1.17557i 0.0308801 + 0.0950392i
\(154\) 2.92705 + 9.00854i 0.235868 + 0.725929i
\(155\) 11.9721 8.69827i 0.961625 0.698662i
\(156\) 2.00000 6.15537i 0.160128 0.492824i
\(157\) 8.65248 0.690543 0.345271 0.938503i \(-0.387787\pi\)
0.345271 + 0.938503i \(0.387787\pi\)
\(158\) −1.73607 + 5.34307i −0.138114 + 0.425072i
\(159\) −1.69098 + 1.22857i −0.134104 + 0.0974320i
\(160\) 1.80902 + 1.31433i 0.143015 + 0.103907i
\(161\) −9.47214 6.88191i −0.746509 0.542370i
\(162\) −0.809017 + 0.587785i −0.0635624 + 0.0461808i
\(163\) 0.381966 0.277515i 0.0299179 0.0217366i −0.572726 0.819747i \(-0.694114\pi\)
0.602644 + 0.798010i \(0.294114\pi\)
\(164\) −4.61803 3.35520i −0.360608 0.261997i
\(165\) −6.54508 + 4.75528i −0.509534 + 0.370198i
\(166\) −1.73607 + 1.26133i −0.134745 + 0.0978980i
\(167\) 3.61803 11.1352i 0.279972 0.861665i −0.707889 0.706324i \(-0.750352\pi\)
0.987861 0.155341i \(-0.0496477\pi\)
\(168\) −2.61803 −0.201986
\(169\) 8.92705 27.4746i 0.686696 2.11343i
\(170\) −2.76393 −0.211984
\(171\) −1.76393 5.42882i −0.134891 0.415153i
\(172\) −2.38197 7.33094i −0.181623 0.558979i
\(173\) −4.11803 2.99193i −0.313088 0.227472i 0.420132 0.907463i \(-0.361984\pi\)
−0.733221 + 0.679991i \(0.761984\pi\)
\(174\) −8.47214 −0.642271
\(175\) 4.04508 + 12.4495i 0.305780 + 0.941093i
\(176\) 3.61803 0.272720
\(177\) −2.92705 2.12663i −0.220011 0.159847i
\(178\) 1.09017 + 3.35520i 0.0817117 + 0.251483i
\(179\) 3.04508 + 9.37181i 0.227600 + 0.700482i 0.998017 + 0.0629414i \(0.0200481\pi\)
−0.770417 + 0.637540i \(0.779952\pi\)
\(180\) −0.690983 2.12663i −0.0515028 0.158509i
\(181\) −2.05573 + 6.32688i −0.152801 + 0.470273i −0.997931 0.0642869i \(-0.979523\pi\)
0.845130 + 0.534560i \(0.179523\pi\)
\(182\) −16.9443 −1.25599
\(183\) −0.854102 + 2.62866i −0.0631370 + 0.194316i
\(184\) −3.61803 + 2.62866i −0.266725 + 0.193787i
\(185\) −17.8885 −1.31519
\(186\) 5.35410 + 3.88998i 0.392582 + 0.285227i
\(187\) −3.61803 + 2.62866i −0.264577 + 0.192226i
\(188\) −1.38197 + 1.00406i −0.100790 + 0.0732284i
\(189\) 2.11803 + 1.53884i 0.154064 + 0.111934i
\(190\) 12.7639 0.925993
\(191\) −3.47214 + 2.52265i −0.251235 + 0.182533i −0.706274 0.707939i \(-0.749625\pi\)
0.455039 + 0.890472i \(0.349625\pi\)
\(192\) −0.309017 + 0.951057i −0.0223014 + 0.0686366i
\(193\) 17.8541 1.28517 0.642583 0.766216i \(-0.277863\pi\)
0.642583 + 0.766216i \(0.277863\pi\)
\(194\) −1.04508 + 3.21644i −0.0750327 + 0.230927i
\(195\) −4.47214 13.7638i −0.320256 0.985648i
\(196\) −0.0450850 0.138757i −0.00322036 0.00991123i
\(197\) −5.28115 16.2537i −0.376267 1.15803i −0.942620 0.333867i \(-0.891646\pi\)
0.566354 0.824162i \(-0.308354\pi\)
\(198\) −2.92705 2.12663i −0.208016 0.151133i
\(199\) 19.5066 1.38278 0.691392 0.722480i \(-0.256998\pi\)
0.691392 + 0.722480i \(0.256998\pi\)
\(200\) 5.00000 0.353553
\(201\) 1.52786 0.107767
\(202\) −3.54508 2.57565i −0.249431 0.181222i
\(203\) 6.85410 + 21.0948i 0.481064 + 1.48056i
\(204\) −0.381966 1.17557i −0.0267430 0.0823064i
\(205\) −12.7639 −0.891472
\(206\) 4.42705 13.6251i 0.308447 0.949303i
\(207\) 4.47214 0.310835
\(208\) −2.00000 + 6.15537i −0.138675 + 0.426798i
\(209\) 16.7082 12.1392i 1.15573 0.839687i
\(210\) −4.73607 + 3.44095i −0.326820 + 0.237448i
\(211\) 2.76393 + 2.00811i 0.190277 + 0.138244i 0.678845 0.734281i \(-0.262481\pi\)
−0.488568 + 0.872526i \(0.662481\pi\)
\(212\) 1.69098 1.22857i 0.116137 0.0843786i
\(213\) 4.47214 3.24920i 0.306426 0.222631i
\(214\) 9.39919 + 6.82891i 0.642515 + 0.466815i
\(215\) −13.9443 10.1311i −0.950991 0.690936i
\(216\) 0.809017 0.587785i 0.0550466 0.0399937i
\(217\) 5.35410 16.4782i 0.363460 1.11862i
\(218\) 17.2361 1.16737
\(219\) −1.09017 + 3.35520i −0.0736669 + 0.226723i
\(220\) 6.54508 4.75528i 0.441270 0.320601i
\(221\) −2.47214 7.60845i −0.166294 0.511800i
\(222\) −2.47214 7.60845i −0.165919 0.510646i
\(223\) 6.54508 + 4.75528i 0.438291 + 0.318437i 0.784956 0.619552i \(-0.212686\pi\)
−0.346664 + 0.937989i \(0.612686\pi\)
\(224\) 2.61803 0.174925
\(225\) −4.04508 2.93893i −0.269672 0.195928i
\(226\) −19.2361 −1.27956
\(227\) 18.0172 + 13.0903i 1.19584 + 0.868832i 0.993870 0.110558i \(-0.0352639\pi\)
0.201975 + 0.979391i \(0.435264\pi\)
\(228\) 1.76393 + 5.42882i 0.116819 + 0.359533i
\(229\) −1.70820 5.25731i −0.112881 0.347413i 0.878618 0.477525i \(-0.158466\pi\)
−0.991499 + 0.130113i \(0.958466\pi\)
\(230\) −3.09017 + 9.51057i −0.203760 + 0.627108i
\(231\) −2.92705 + 9.00854i −0.192586 + 0.592718i
\(232\) 8.47214 0.556223
\(233\) 5.76393 17.7396i 0.377608 1.16216i −0.564095 0.825710i \(-0.690775\pi\)
0.941702 0.336447i \(-0.109225\pi\)
\(234\) 5.23607 3.80423i 0.342292 0.248690i
\(235\) −1.18034 + 3.63271i −0.0769969 + 0.236972i
\(236\) 2.92705 + 2.12663i 0.190535 + 0.138432i
\(237\) −4.54508 + 3.30220i −0.295235 + 0.214501i
\(238\) −2.61803 + 1.90211i −0.169702 + 0.123296i
\(239\) −9.94427 7.22494i −0.643241 0.467342i 0.217721 0.976011i \(-0.430138\pi\)
−0.860962 + 0.508669i \(0.830138\pi\)
\(240\) 0.690983 + 2.12663i 0.0446028 + 0.137273i
\(241\) −7.73607 + 5.62058i −0.498324 + 0.362054i −0.808376 0.588666i \(-0.799653\pi\)
0.310052 + 0.950719i \(0.399653\pi\)
\(242\) 0.645898 1.98787i 0.0415199 0.127785i
\(243\) −1.00000 −0.0641500
\(244\) 0.854102 2.62866i 0.0546783 0.168282i
\(245\) −0.263932 0.191758i −0.0168620 0.0122510i
\(246\) −1.76393 5.42882i −0.112464 0.346129i
\(247\) 11.4164 + 35.1361i 0.726409 + 2.23566i
\(248\) −5.35410 3.88998i −0.339986 0.247014i
\(249\) −2.14590 −0.135991
\(250\) 9.04508 6.57164i 0.572061 0.415627i
\(251\) 13.5623 0.856045 0.428023 0.903768i \(-0.359210\pi\)
0.428023 + 0.903768i \(0.359210\pi\)
\(252\) −2.11803 1.53884i −0.133424 0.0969379i
\(253\) 5.00000 + 15.3884i 0.314347 + 0.967462i
\(254\) 4.20820 + 12.9515i 0.264046 + 0.812651i
\(255\) −2.23607 1.62460i −0.140028 0.101736i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) −22.0000 −1.37232 −0.686161 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) 2.38197 7.33094i 0.148295 0.456404i
\(259\) −16.9443 + 12.3107i −1.05287 + 0.764952i
\(260\) 4.47214 + 13.7638i 0.277350 + 0.853596i
\(261\) −6.85410 4.97980i −0.424258 0.308242i
\(262\) 14.4721 10.5146i 0.894092 0.649596i
\(263\) 9.47214 6.88191i 0.584077 0.424357i −0.256115 0.966646i \(-0.582442\pi\)
0.840192 + 0.542290i \(0.182442\pi\)
\(264\) 2.92705 + 2.12663i 0.180148 + 0.130885i
\(265\) 1.44427 4.44501i 0.0887209 0.273055i
\(266\) 12.0902 8.78402i 0.741296 0.538583i
\(267\) −1.09017 + 3.35520i −0.0667173 + 0.205335i
\(268\) −1.52786 −0.0933292
\(269\) −2.80902 + 8.64527i −0.171269 + 0.527111i −0.999443 0.0333590i \(-0.989380\pi\)
0.828175 + 0.560470i \(0.189380\pi\)
\(270\) 0.690983 2.12663i 0.0420519 0.129422i
\(271\) −5.57295 17.1518i −0.338533 1.04190i −0.964956 0.262413i \(-0.915482\pi\)
0.626423 0.779483i \(-0.284518\pi\)
\(272\) 0.381966 + 1.17557i 0.0231601 + 0.0712794i
\(273\) −13.7082 9.95959i −0.829658 0.602782i
\(274\) −12.1803 −0.735841
\(275\) 5.59017 17.2048i 0.337100 1.03749i
\(276\) −4.47214 −0.269191
\(277\) −13.7082 9.95959i −0.823646 0.598414i 0.0941084 0.995562i \(-0.470000\pi\)
−0.917755 + 0.397148i \(0.870000\pi\)
\(278\) 3.23607 + 9.95959i 0.194086 + 0.597337i
\(279\) 2.04508 + 6.29412i 0.122436 + 0.376819i
\(280\) 4.73607 3.44095i 0.283034 0.205636i
\(281\) 1.81966 5.60034i 0.108552 0.334088i −0.881996 0.471257i \(-0.843800\pi\)
0.990548 + 0.137169i \(0.0438004\pi\)
\(282\) −1.70820 −0.101722
\(283\) 1.41641 4.35926i 0.0841967 0.259131i −0.900091 0.435701i \(-0.856500\pi\)
0.984288 + 0.176571i \(0.0565004\pi\)
\(284\) −4.47214 + 3.24920i −0.265372 + 0.192804i
\(285\) 10.3262 + 7.50245i 0.611674 + 0.444407i
\(286\) 18.9443 + 13.7638i 1.12020 + 0.813872i
\(287\) −12.0902 + 8.78402i −0.713660 + 0.518504i
\(288\) −0.809017 + 0.587785i −0.0476718 + 0.0346356i
\(289\) 12.5172 + 9.09429i 0.736307 + 0.534958i
\(290\) 15.3262 11.1352i 0.899988 0.653879i
\(291\) −2.73607 + 1.98787i −0.160391 + 0.116531i
\(292\) 1.09017 3.35520i 0.0637974 0.196348i
\(293\) −22.0902 −1.29052 −0.645261 0.763962i \(-0.723251\pi\)
−0.645261 + 0.763962i \(0.723251\pi\)
\(294\) 0.0450850 0.138757i 0.00262941 0.00809249i
\(295\) 8.09017 0.471028
\(296\) 2.47214 + 7.60845i 0.143690 + 0.442232i
\(297\) −1.11803 3.44095i −0.0648749 0.199664i
\(298\) −17.8713 12.9843i −1.03526 0.752159i
\(299\) −28.9443 −1.67389
\(300\) 4.04508 + 2.93893i 0.233543 + 0.169679i
\(301\) −20.1803 −1.16318
\(302\) −14.8262 10.7719i −0.853154 0.619853i
\(303\) −1.35410 4.16750i −0.0777911 0.239416i
\(304\) −1.76393 5.42882i −0.101168 0.311364i
\(305\) −1.90983 5.87785i −0.109357 0.336565i
\(306\) 0.381966 1.17557i 0.0218355 0.0672029i
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 2.92705 9.00854i 0.166784 0.513309i
\(309\) 11.5902 8.42075i 0.659342 0.479040i
\(310\) −14.7984 −0.840491
\(311\) 0.854102 + 0.620541i 0.0484317 + 0.0351877i 0.611738 0.791061i \(-0.290471\pi\)
−0.563306 + 0.826248i \(0.690471\pi\)
\(312\) −5.23607 + 3.80423i −0.296434 + 0.215372i
\(313\) 13.1631 9.56357i 0.744023 0.540565i −0.149945 0.988694i \(-0.547910\pi\)
0.893969 + 0.448130i \(0.147910\pi\)
\(314\) −7.00000 5.08580i −0.395033 0.287008i
\(315\) −5.85410 −0.329841
\(316\) 4.54508 3.30220i 0.255681 0.185763i
\(317\) −6.35410 + 19.5559i −0.356882 + 1.09837i 0.598028 + 0.801475i \(0.295951\pi\)
−0.954910 + 0.296895i \(0.904049\pi\)
\(318\) 2.09017 0.117211
\(319\) 9.47214 29.1522i 0.530338 1.63221i
\(320\) −0.690983 2.12663i −0.0386271 0.118882i
\(321\) 3.59017 + 11.0494i 0.200384 + 0.616718i
\(322\) 3.61803 + 11.1352i 0.201625 + 0.620538i
\(323\) 5.70820 + 4.14725i 0.317613 + 0.230759i
\(324\) 1.00000 0.0555556
\(325\) 26.1803 + 19.0211i 1.45222 + 1.05510i
\(326\) −0.472136 −0.0261492
\(327\) 13.9443 + 10.1311i 0.771120 + 0.560251i
\(328\) 1.76393 + 5.42882i 0.0973969 + 0.299757i
\(329\) 1.38197 + 4.25325i 0.0761903 + 0.234489i
\(330\) 8.09017 0.445349
\(331\) −5.56231 + 17.1190i −0.305732 + 0.940946i 0.673671 + 0.739031i \(0.264716\pi\)
−0.979403 + 0.201915i \(0.935284\pi\)
\(332\) 2.14590 0.117771
\(333\) 2.47214 7.60845i 0.135472 0.416941i
\(334\) −9.47214 + 6.88191i −0.518292 + 0.376561i
\(335\) −2.76393 + 2.00811i −0.151010 + 0.109715i
\(336\) 2.11803 + 1.53884i 0.115548 + 0.0839507i
\(337\) −0.736068 + 0.534785i −0.0400962 + 0.0291316i −0.607653 0.794203i \(-0.707889\pi\)
0.567557 + 0.823334i \(0.307889\pi\)
\(338\) −23.3713 + 16.9803i −1.27123 + 0.923604i
\(339\) −15.5623 11.3067i −0.845228 0.614094i
\(340\) 2.23607 + 1.62460i 0.121268 + 0.0881062i
\(341\) −19.3713 + 14.0741i −1.04902 + 0.762155i
\(342\) −1.76393 + 5.42882i −0.0953825 + 0.293557i
\(343\) −18.7082 −1.01015
\(344\) −2.38197 + 7.33094i −0.128427 + 0.395258i
\(345\) −8.09017 + 5.87785i −0.435560 + 0.316453i
\(346\) 1.57295 + 4.84104i 0.0845623 + 0.260256i
\(347\) 6.35410 + 19.5559i 0.341106 + 1.04982i 0.963636 + 0.267220i \(0.0861051\pi\)
−0.622529 + 0.782596i \(0.713895\pi\)
\(348\) 6.85410 + 4.97980i 0.367418 + 0.266945i
\(349\) −27.8885 −1.49284 −0.746420 0.665475i \(-0.768229\pi\)
−0.746420 + 0.665475i \(0.768229\pi\)
\(350\) 4.04508 12.4495i 0.216219 0.665453i
\(351\) 6.47214 0.345457
\(352\) −2.92705 2.12663i −0.156012 0.113350i
\(353\) −4.09017 12.5882i −0.217698 0.670005i −0.998951 0.0457907i \(-0.985419\pi\)
0.781253 0.624214i \(-0.214581\pi\)
\(354\) 1.11803 + 3.44095i 0.0594228 + 0.182885i
\(355\) −3.81966 + 11.7557i −0.202727 + 0.623928i
\(356\) 1.09017 3.35520i 0.0577789 0.177825i
\(357\) −3.23607 −0.171271
\(358\) 3.04508 9.37181i 0.160938 0.495315i
\(359\) −17.9443 + 13.0373i −0.947062 + 0.688081i −0.950110 0.311914i \(-0.899030\pi\)
0.00304782 + 0.999995i \(0.499030\pi\)
\(360\) −0.690983 + 2.12663i −0.0364180 + 0.112083i
\(361\) −10.9894 7.98424i −0.578387 0.420223i
\(362\) 5.38197 3.91023i 0.282870 0.205517i
\(363\) 1.69098 1.22857i 0.0887536 0.0644833i
\(364\) 13.7082 + 9.95959i 0.718505 + 0.522025i
\(365\) −2.43769 7.50245i −0.127595 0.392696i
\(366\) 2.23607 1.62460i 0.116881 0.0849191i
\(367\) −9.46149 + 29.1195i −0.493886 + 1.52002i 0.324800 + 0.945783i \(0.394703\pi\)
−0.818686 + 0.574242i \(0.805297\pi\)
\(368\) 4.47214 0.233126
\(369\) 1.76393 5.42882i 0.0918266 0.282613i
\(370\) 14.4721 + 10.5146i 0.752371 + 0.546629i
\(371\) −1.69098 5.20431i −0.0877915 0.270194i
\(372\) −2.04508 6.29412i −0.106033 0.326335i
\(373\) 9.32624 + 6.77591i 0.482894 + 0.350843i 0.802445 0.596726i \(-0.203532\pi\)
−0.319551 + 0.947569i \(0.603532\pi\)
\(374\) 4.47214 0.231249
\(375\) 11.1803 0.577350
\(376\) 1.70820 0.0880939
\(377\) 44.3607 + 32.2299i 2.28469 + 1.65993i
\(378\) −0.809017 2.48990i −0.0416113 0.128067i
\(379\) −6.23607 19.1926i −0.320325 0.985860i −0.973507 0.228658i \(-0.926566\pi\)
0.653181 0.757201i \(-0.273434\pi\)
\(380\) −10.3262 7.50245i −0.529725 0.384868i
\(381\) −4.20820 + 12.9515i −0.215593 + 0.663526i
\(382\) 4.29180 0.219587
\(383\) −6.18034 + 19.0211i −0.315801 + 0.971934i 0.659623 + 0.751597i \(0.270716\pi\)
−0.975424 + 0.220338i \(0.929284\pi\)
\(384\) 0.809017 0.587785i 0.0412850 0.0299953i
\(385\) −6.54508 20.1437i −0.333568 1.02662i
\(386\) −14.4443 10.4944i −0.735194 0.534150i
\(387\) 6.23607 4.53077i 0.316997 0.230312i
\(388\) 2.73607 1.98787i 0.138903 0.100919i
\(389\) 10.0172 + 7.27794i 0.507893 + 0.369006i 0.812024 0.583624i \(-0.198366\pi\)
−0.304131 + 0.952630i \(0.598366\pi\)
\(390\) −4.47214 + 13.7638i −0.226455 + 0.696958i
\(391\) −4.47214 + 3.24920i −0.226166 + 0.164319i
\(392\) −0.0450850 + 0.138757i −0.00227713 + 0.00700830i
\(393\) 17.8885 0.902358
\(394\) −5.28115 + 16.2537i −0.266061 + 0.818850i
\(395\) 3.88197 11.9475i 0.195323 0.601142i
\(396\) 1.11803 + 3.44095i 0.0561833 + 0.172914i
\(397\) −9.50658 29.2582i −0.477121 1.46843i −0.843075 0.537796i \(-0.819257\pi\)
0.365954 0.930633i \(-0.380743\pi\)
\(398\) −15.7812 11.4657i −0.791038 0.574723i
\(399\) 14.9443 0.748149
\(400\) −4.04508 2.93893i −0.202254 0.146946i
\(401\) 25.7082 1.28381 0.641903 0.766786i \(-0.278145\pi\)
0.641903 + 0.766786i \(0.278145\pi\)
\(402\) −1.23607 0.898056i −0.0616495 0.0447910i
\(403\) −13.2361 40.7364i −0.659336 2.02923i
\(404\) 1.35410 + 4.16750i 0.0673691 + 0.207341i
\(405\) 1.80902 1.31433i 0.0898908 0.0653095i
\(406\) 6.85410 21.0948i 0.340163 1.04692i
\(407\) 28.9443 1.43471
\(408\) −0.381966 + 1.17557i −0.0189101 + 0.0581994i
\(409\) −4.69098 + 3.40820i −0.231954 + 0.168525i −0.697691 0.716399i \(-0.745789\pi\)
0.465737 + 0.884923i \(0.345789\pi\)
\(410\) 10.3262 + 7.50245i 0.509977 + 0.370520i
\(411\) −9.85410 7.15942i −0.486067 0.353148i
\(412\) −11.5902 + 8.42075i −0.571007 + 0.414861i
\(413\) 7.66312 5.56758i 0.377077 0.273963i
\(414\) −3.61803 2.62866i −0.177817 0.129191i
\(415\) 3.88197 2.82041i 0.190558 0.138449i
\(416\) 5.23607 3.80423i 0.256719 0.186518i
\(417\) −3.23607 + 9.95959i −0.158471 + 0.487723i
\(418\) −20.6525 −1.01015
\(419\) −0.954915 + 2.93893i −0.0466507 + 0.143576i −0.971669 0.236347i \(-0.924050\pi\)
0.925018 + 0.379923i \(0.124050\pi\)
\(420\) 5.85410 0.285651
\(421\) −7.03444 21.6498i −0.342838 1.05515i −0.962731 0.270460i \(-0.912824\pi\)
0.619893 0.784686i \(-0.287176\pi\)
\(422\) −1.05573 3.24920i −0.0513920 0.158168i
\(423\) −1.38197 1.00406i −0.0671935 0.0488189i
\(424\) −2.09017 −0.101508
\(425\) 6.18034 0.299791
\(426\) −5.52786 −0.267826
\(427\) −5.85410 4.25325i −0.283300 0.205829i
\(428\) −3.59017 11.0494i −0.173537 0.534093i
\(429\) 7.23607 + 22.2703i 0.349361 + 1.07522i
\(430\) 5.32624 + 16.3925i 0.256854 + 0.790515i
\(431\) 5.20163 16.0090i 0.250554 0.771124i −0.744120 0.668046i \(-0.767131\pi\)
0.994673 0.103078i \(-0.0328692\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 4.79180 14.7476i 0.230279 0.708726i −0.767434 0.641128i \(-0.778467\pi\)
0.997713 0.0675976i \(-0.0215334\pi\)
\(434\) −14.0172 + 10.1841i −0.672848 + 0.488853i
\(435\) 18.9443 0.908308
\(436\) −13.9443 10.1311i −0.667810 0.485192i
\(437\) 20.6525 15.0049i 0.987942 0.717782i
\(438\) 2.85410 2.07363i 0.136374 0.0990817i
\(439\) 19.0172 + 13.8168i 0.907642 + 0.659441i 0.940418 0.340022i \(-0.110434\pi\)
−0.0327751 + 0.999463i \(0.510434\pi\)
\(440\) −8.09017 −0.385684
\(441\) 0.118034 0.0857567i 0.00562067 0.00408365i
\(442\) −2.47214 + 7.60845i −0.117588 + 0.361897i
\(443\) 16.6180 0.789547 0.394773 0.918779i \(-0.370823\pi\)
0.394773 + 0.918779i \(0.370823\pi\)
\(444\) −2.47214 + 7.60845i −0.117322 + 0.361081i
\(445\) −2.43769 7.50245i −0.115558 0.355650i
\(446\) −2.50000 7.69421i −0.118378 0.364331i
\(447\) −6.82624 21.0090i −0.322870 0.993692i
\(448\) −2.11803 1.53884i −0.100068 0.0727034i
\(449\) −27.7082 −1.30763 −0.653815 0.756654i \(-0.726833\pi\)
−0.653815 + 0.756654i \(0.726833\pi\)
\(450\) 1.54508 + 4.75528i 0.0728360 + 0.224166i
\(451\) 20.6525 0.972487
\(452\) 15.5623 + 11.3067i 0.731989 + 0.531821i
\(453\) −5.66312 17.4293i −0.266077 0.818899i
\(454\) −6.88197 21.1805i −0.322987 0.994051i
\(455\) 37.8885 1.77624
\(456\) 1.76393 5.42882i 0.0826037 0.254228i
\(457\) −4.09017 −0.191330 −0.0956650 0.995414i \(-0.530498\pi\)
−0.0956650 + 0.995414i \(0.530498\pi\)
\(458\) −1.70820 + 5.25731i −0.0798191 + 0.245658i
\(459\) 1.00000 0.726543i 0.0466760 0.0339121i
\(460\) 8.09017 5.87785i 0.377206 0.274056i
\(461\) −6.11803 4.44501i −0.284945 0.207025i 0.436126 0.899885i \(-0.356350\pi\)
−0.721072 + 0.692861i \(0.756350\pi\)
\(462\) 7.66312 5.56758i 0.356521 0.259027i
\(463\) 18.4721 13.4208i 0.858473 0.623717i −0.0689961 0.997617i \(-0.521980\pi\)
0.927469 + 0.373900i \(0.121980\pi\)
\(464\) −6.85410 4.97980i −0.318194 0.231181i
\(465\) −11.9721 8.69827i −0.555195 0.403372i
\(466\) −15.0902 + 10.9637i −0.699039 + 0.507881i
\(467\) 3.29837 10.1514i 0.152631 0.469749i −0.845283 0.534320i \(-0.820568\pi\)
0.997913 + 0.0645710i \(0.0205679\pi\)
\(468\) −6.47214 −0.299175
\(469\) −1.23607 + 3.80423i −0.0570763 + 0.175663i
\(470\) 3.09017 2.24514i 0.142539 0.103561i
\(471\) −2.67376 8.22899i −0.123200 0.379172i
\(472\) −1.11803 3.44095i −0.0514617 0.158383i
\(473\) 22.5623 + 16.3925i 1.03742 + 0.753727i
\(474\) 5.61803 0.258045
\(475\) −28.5410 −1.30955
\(476\) 3.23607 0.148325
\(477\) 1.69098 + 1.22857i 0.0774248 + 0.0562524i
\(478\) 3.79837 + 11.6902i 0.173734 + 0.534697i
\(479\) −9.00000 27.6992i −0.411220 1.26561i −0.915588 0.402117i \(-0.868274\pi\)
0.504368 0.863489i \(-0.331726\pi\)
\(480\) 0.690983 2.12663i 0.0315389 0.0970668i
\(481\) −16.0000 + 49.2429i −0.729537 + 2.24528i
\(482\) 9.56231 0.435551
\(483\) −3.61803 + 11.1352i −0.164626 + 0.506667i
\(484\) −1.69098 + 1.22857i −0.0768629 + 0.0558441i
\(485\) 2.33688 7.19218i 0.106112 0.326580i
\(486\) 0.809017 + 0.587785i 0.0366978 + 0.0266625i
\(487\) −14.3992 + 10.4616i −0.652489 + 0.474061i −0.864118 0.503289i \(-0.832123\pi\)
0.211629 + 0.977350i \(0.432123\pi\)
\(488\) −2.23607 + 1.62460i −0.101222 + 0.0735421i
\(489\) −0.381966 0.277515i −0.0172731 0.0125496i
\(490\) 0.100813 + 0.310271i 0.00455427 + 0.0140166i
\(491\) 20.4443 14.8536i 0.922637 0.670335i −0.0215419 0.999768i \(-0.506858\pi\)
0.944179 + 0.329433i \(0.106858\pi\)
\(492\) −1.76393 + 5.42882i −0.0795242 + 0.244750i
\(493\) 10.4721 0.471641
\(494\) 11.4164 35.1361i 0.513648 1.58085i
\(495\) 6.54508 + 4.75528i 0.294180 + 0.213734i
\(496\) 2.04508 + 6.29412i 0.0918270 + 0.282615i
\(497\) 4.47214 + 13.7638i 0.200603 + 0.617392i
\(498\) 1.73607 + 1.26133i 0.0777951 + 0.0565214i
\(499\) 35.5967 1.59353 0.796765 0.604290i \(-0.206543\pi\)
0.796765 + 0.604290i \(0.206543\pi\)
\(500\) −11.1803 −0.500000
\(501\) −11.7082 −0.523084
\(502\) −10.9721 7.97172i −0.489710 0.355795i
\(503\) 7.38197 + 22.7194i 0.329146 + 1.01301i 0.969534 + 0.244955i \(0.0787732\pi\)
−0.640389 + 0.768051i \(0.721227\pi\)
\(504\) 0.809017 + 2.48990i 0.0360365 + 0.110909i
\(505\) 7.92705 + 5.75934i 0.352749 + 0.256287i
\(506\) 5.00000 15.3884i 0.222277 0.684099i
\(507\) −28.8885 −1.28299
\(508\) 4.20820 12.9515i 0.186709 0.574631i
\(509\) 14.1631 10.2901i 0.627769 0.456101i −0.227857 0.973694i \(-0.573172\pi\)
0.855627 + 0.517593i \(0.173172\pi\)
\(510\) 0.854102 + 2.62866i 0.0378203 + 0.116399i
\(511\) −7.47214 5.42882i −0.330548 0.240157i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) −4.61803 + 3.35520i −0.203891 + 0.148136i
\(514\) 17.7984 + 12.9313i 0.785053 + 0.570374i
\(515\) −9.89919 + 30.4666i −0.436210 + 1.34252i
\(516\) −6.23607 + 4.53077i −0.274528 + 0.199456i
\(517\) 1.90983 5.87785i 0.0839942 0.258508i
\(518\) 20.9443 0.920238
\(519\) −1.57295 + 4.84104i −0.0690448 + 0.212498i
\(520\) 4.47214 13.7638i 0.196116 0.603583i
\(521\) 4.38197 + 13.4863i 0.191977 + 0.590846i 0.999999 + 0.00169226i \(0.000538663\pi\)
−0.808021 + 0.589153i \(0.799461\pi\)
\(522\) 2.61803 + 8.05748i 0.114588 + 0.352666i
\(523\) −8.94427 6.49839i −0.391106 0.284155i 0.374803 0.927105i \(-0.377710\pi\)
−0.765908 + 0.642950i \(0.777710\pi\)
\(524\) −17.8885 −0.781465
\(525\) 10.5902 7.69421i 0.462193 0.335803i
\(526\) −11.7082 −0.510502
\(527\) −6.61803 4.80828i −0.288286 0.209452i
\(528\) −1.11803 3.44095i −0.0486562 0.149748i
\(529\) −0.927051 2.85317i −0.0403066 0.124051i
\(530\) −3.78115 + 2.74717i −0.164243 + 0.119329i
\(531\) −1.11803 + 3.44095i −0.0485185 + 0.149325i
\(532\) −14.9443 −0.647916
\(533\) −11.4164 + 35.1361i −0.494500 + 1.52191i
\(534\) 2.85410 2.07363i 0.123509 0.0897346i
\(535\) −21.0172 15.2699i −0.908654 0.660176i
\(536\) 1.23607 + 0.898056i 0.0533900 + 0.0387901i
\(537\) 7.97214 5.79210i 0.344023 0.249947i
\(538\) 7.35410 5.34307i 0.317058 0.230356i
\(539\) 0.427051 + 0.310271i 0.0183944 + 0.0133643i
\(540\) −1.80902 + 1.31433i −0.0778477 + 0.0565597i
\(541\) 21.1803 15.3884i 0.910614 0.661600i −0.0305561 0.999533i \(-0.509728\pi\)
0.941170 + 0.337933i \(0.109728\pi\)
\(542\) −5.57295 + 17.1518i −0.239379 + 0.736732i
\(543\) 6.65248 0.285485
\(544\) 0.381966 1.17557i 0.0163767 0.0504022i
\(545\) −38.5410 −1.65092
\(546\) 5.23607 + 16.1150i 0.224083 + 0.689657i
\(547\) 3.00000 + 9.23305i 0.128271 + 0.394777i 0.994483 0.104900i \(-0.0334522\pi\)
−0.866212 + 0.499677i \(0.833452\pi\)
\(548\) 9.85410 + 7.15942i 0.420946 + 0.305835i
\(549\) 2.76393 0.117962
\(550\) −14.6353 + 10.6331i −0.624049 + 0.453398i
\(551\) −48.3607 −2.06023
\(552\) 3.61803 + 2.62866i 0.153994 + 0.111883i
\(553\) −4.54508 13.9883i −0.193277 0.594844i
\(554\) 5.23607 + 16.1150i 0.222459 + 0.684659i
\(555\) 5.52786 + 17.0130i 0.234645 + 0.722162i
\(556\) 3.23607 9.95959i 0.137240 0.422381i
\(557\) −18.3262 −0.776508 −0.388254 0.921552i \(-0.626922\pi\)
−0.388254 + 0.921552i \(0.626922\pi\)
\(558\) 2.04508 6.29412i 0.0865754 0.266452i
\(559\) −40.3607 + 29.3238i −1.70707 + 1.24026i
\(560\) −5.85410 −0.247381
\(561\) 3.61803 + 2.62866i 0.152754 + 0.110982i
\(562\) −4.76393 + 3.46120i −0.200954 + 0.146002i
\(563\) −17.2082 + 12.5025i −0.725239 + 0.526917i −0.888054 0.459739i \(-0.847943\pi\)
0.162815 + 0.986657i \(0.447943\pi\)
\(564\) 1.38197 + 1.00406i 0.0581913 + 0.0422784i
\(565\) 43.0132 1.80958
\(566\) −3.70820 + 2.69417i −0.155867 + 0.113244i
\(567\) 0.809017 2.48990i 0.0339755 0.104566i
\(568\) 5.52786 0.231944
\(569\) −8.58359 + 26.4176i −0.359843 + 1.10748i 0.593305 + 0.804978i \(0.297823\pi\)
−0.953148 + 0.302505i \(0.902177\pi\)
\(570\) −3.94427 12.1392i −0.165207 0.508456i
\(571\) 2.43769 + 7.50245i 0.102014 + 0.313968i 0.989018 0.147794i \(-0.0472174\pi\)
−0.887004 + 0.461762i \(0.847217\pi\)
\(572\) −7.23607 22.2703i −0.302555 0.931169i
\(573\) 3.47214 + 2.52265i 0.145051 + 0.105385i
\(574\) 14.9443 0.623762
\(575\) 6.90983 21.2663i 0.288160 0.886865i
\(576\) 1.00000 0.0416667
\(577\) −7.26393 5.27756i −0.302401 0.219708i 0.426228 0.904616i \(-0.359842\pi\)
−0.728629 + 0.684908i \(0.759842\pi\)
\(578\) −4.78115 14.7149i −0.198870 0.612058i
\(579\) −5.51722 16.9803i −0.229288 0.705676i
\(580\) −18.9443 −0.786618
\(581\) 1.73607 5.34307i 0.0720242 0.221668i
\(582\) 3.38197 0.140187
\(583\) −2.33688 + 7.19218i −0.0967837 + 0.297870i
\(584\) −2.85410 + 2.07363i −0.118104 + 0.0858073i
\(585\) −11.7082 + 8.50651i −0.484075 + 0.351701i
\(586\) 17.8713 + 12.9843i 0.738258 + 0.536376i
\(587\) 0.781153 0.567541i 0.0322416 0.0234249i −0.571548 0.820569i \(-0.693657\pi\)
0.603789 + 0.797144i \(0.293657\pi\)
\(588\) −0.118034 + 0.0857567i −0.00486764 + 0.00353655i
\(589\) 30.5623 + 22.2048i 1.25930 + 0.914933i
\(590\) −6.54508 4.75528i −0.269457 0.195772i
\(591\) −13.8262 + 10.0453i −0.568735 + 0.413210i
\(592\) 2.47214 7.60845i 0.101604 0.312705i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) −1.11803 + 3.44095i −0.0458735 + 0.141184i
\(595\) 5.85410 4.25325i 0.239995 0.174366i
\(596\) 6.82624 + 21.0090i 0.279614 + 0.860562i
\(597\) −6.02786 18.5519i −0.246704 0.759277i
\(598\) 23.4164 + 17.0130i 0.957568 + 0.695714i
\(599\) 0.472136 0.0192910 0.00964548 0.999953i \(-0.496930\pi\)
0.00964548 + 0.999953i \(0.496930\pi\)
\(600\) −1.54508 4.75528i −0.0630778 0.194134i
\(601\) −7.72949 −0.315292 −0.157646 0.987496i \(-0.550391\pi\)
−0.157646 + 0.987496i \(0.550391\pi\)
\(602\) 16.3262 + 11.8617i 0.665408 + 0.483447i
\(603\) −0.472136 1.45309i −0.0192269 0.0591742i
\(604\) 5.66312 + 17.4293i 0.230429 + 0.709188i
\(605\) −1.44427 + 4.44501i −0.0587180 + 0.180715i
\(606\) −1.35410 + 4.16750i −0.0550066 + 0.169293i
\(607\) 6.56231 0.266356 0.133178 0.991092i \(-0.457482\pi\)
0.133178 + 0.991092i \(0.457482\pi\)
\(608\) −1.76393 + 5.42882i −0.0715369 + 0.220168i
\(609\) 17.9443 13.0373i 0.727139 0.528297i
\(610\) −1.90983 + 5.87785i −0.0773268 + 0.237987i
\(611\) 8.94427 + 6.49839i 0.361847 + 0.262897i
\(612\) −1.00000 + 0.726543i −0.0404226 + 0.0293687i
\(613\) −39.0344 + 28.3602i −1.57659 + 1.14546i −0.656105 + 0.754669i \(0.727797\pi\)
−0.920481 + 0.390788i \(0.872203\pi\)
\(614\) −8.09017 5.87785i −0.326493 0.237211i
\(615\) 3.94427 + 12.1392i 0.159048 + 0.489501i
\(616\) −7.66312 + 5.56758i −0.308756 + 0.224324i
\(617\) 0.652476 2.00811i 0.0262677 0.0808436i −0.937063 0.349160i \(-0.886467\pi\)
0.963331 + 0.268316i \(0.0864671\pi\)
\(618\) −14.3262 −0.576286
\(619\) −2.90983 + 8.95554i −0.116956 + 0.359953i −0.992350 0.123457i \(-0.960602\pi\)
0.875394 + 0.483410i \(0.160602\pi\)
\(620\) 11.9721 + 8.69827i 0.480813 + 0.349331i
\(621\) −1.38197 4.25325i −0.0554564 0.170677i
\(622\) −0.326238 1.00406i −0.0130809 0.0402590i
\(623\) −7.47214 5.42882i −0.299365 0.217501i
\(624\) 6.47214 0.259093
\(625\) −20.2254 + 14.6946i −0.809017 + 0.587785i
\(626\) −16.2705 −0.650300
\(627\) −16.7082 12.1392i −0.667261 0.484794i
\(628\) 2.67376 + 8.22899i 0.106695 + 0.328373i
\(629\) 3.05573 + 9.40456i 0.121840 + 0.374985i
\(630\) 4.73607 + 3.44095i 0.188689 + 0.137091i
\(631\) 14.3607 44.1976i 0.571690 1.75948i −0.0754947 0.997146i \(-0.524054\pi\)
0.647184 0.762334i \(-0.275946\pi\)
\(632\) −5.61803 −0.223473
\(633\) 1.05573 3.24920i 0.0419614 0.129144i
\(634\) 16.6353 12.0862i 0.660670 0.480005i
\(635\) −9.40983 28.9605i −0.373418 1.14926i
\(636\) −1.69098 1.22857i −0.0670518 0.0487160i
\(637\) −0.763932 + 0.555029i −0.0302681 + 0.0219911i
\(638\) −24.7984 + 18.0171i −0.981777 + 0.713303i
\(639\) −4.47214 3.24920i −0.176915 0.128536i
\(640\) −0.690983 + 2.12663i −0.0273135 + 0.0840623i
\(641\) 11.1803 8.12299i 0.441597 0.320839i −0.344672 0.938723i \(-0.612010\pi\)
0.786269 + 0.617884i \(0.212010\pi\)
\(642\) 3.59017 11.0494i 0.141693 0.436085i
\(643\) 21.8885 0.863200 0.431600 0.902065i \(-0.357949\pi\)
0.431600 + 0.902065i \(0.357949\pi\)
\(644\) 3.61803 11.1352i 0.142571 0.438787i
\(645\) −5.32624 + 16.3925i −0.209720 + 0.645453i
\(646\) −2.18034 6.71040i −0.0857843 0.264017i
\(647\) −7.09017 21.8213i −0.278743 0.857884i −0.988205 0.153139i \(-0.951062\pi\)
0.709461 0.704744i \(-0.248938\pi\)
\(648\) −0.809017 0.587785i −0.0317812 0.0230904i
\(649\) −13.0902 −0.513834
\(650\) −10.0000 30.7768i −0.392232 1.20717i
\(651\) −17.3262 −0.679069
\(652\) 0.381966 + 0.277515i 0.0149589 + 0.0108683i
\(653\) −1.19098 3.66547i −0.0466068 0.143441i 0.925045 0.379858i \(-0.124027\pi\)
−0.971652 + 0.236417i \(0.924027\pi\)
\(654\) −5.32624 16.3925i −0.208272 0.640996i
\(655\) −32.3607 + 23.5114i −1.26444 + 0.918667i
\(656\) 1.76393 5.42882i 0.0688700 0.211960i
\(657\) 3.52786 0.137635
\(658\) 1.38197 4.25325i 0.0538746 0.165809i
\(659\) 16.6803 12.1190i 0.649774 0.472088i −0.213420 0.976960i \(-0.568460\pi\)
0.863194 + 0.504872i \(0.168460\pi\)
\(660\) −6.54508 4.75528i −0.254767 0.185099i
\(661\) 24.6525 + 17.9111i 0.958870 + 0.696660i 0.952888 0.303322i \(-0.0980958\pi\)
0.00598211 + 0.999982i \(0.498096\pi\)
\(662\) 14.5623 10.5801i 0.565980 0.411209i
\(663\) −6.47214 + 4.70228i −0.251357 + 0.182622i
\(664\) −1.73607 1.26133i −0.0673725 0.0489490i
\(665\) −27.0344 + 19.6417i −1.04835 + 0.761671i
\(666\) −6.47214 + 4.70228i −0.250790 + 0.182210i
\(667\) 11.7082 36.0341i 0.453343 1.39525i
\(668\) 11.7082 0.453004
\(669\) 2.50000 7.69421i 0.0966556 0.297475i
\(670\) 3.41641 0.131987
\(671\) 3.09017 + 9.51057i 0.119295 + 0.367151i
\(672\) −0.809017 2.48990i −0.0312085 0.0960499i
\(673\) 25.4443 + 18.4863i 0.980805 + 0.712596i 0.957888 0.287141i \(-0.0927049\pi\)
0.0229163 + 0.999737i \(0.492705\pi\)
\(674\) 0.909830 0.0350453
\(675\) −1.54508 + 4.75528i −0.0594703 + 0.183031i
\(676\) 28.8885 1.11110
\(677\) −23.5344 17.0988i −0.904502 0.657159i 0.0351163 0.999383i \(-0.488820\pi\)
−0.939618 + 0.342224i \(0.888820\pi\)
\(678\) 5.94427 + 18.2946i 0.228288 + 0.702599i
\(679\) −2.73607 8.42075i −0.105001 0.323159i
\(680\) −0.854102 2.62866i −0.0327533 0.100804i
\(681\) 6.88197 21.1805i 0.263718 0.811639i
\(682\) 23.9443 0.916874
\(683\) 10.3541 31.8666i 0.396189 1.21934i −0.531843 0.846843i \(-0.678500\pi\)
0.928032 0.372501i \(-0.121500\pi\)
\(684\) 4.61803 3.35520i 0.176575 0.128289i
\(685\) 27.2361 1.04064
\(686\) 15.1353 + 10.9964i 0.577867 + 0.419845i
\(687\) −4.47214 + 3.24920i −0.170623 + 0.123965i
\(688\) 6.23607 4.53077i 0.237748 0.172734i
\(689\) −10.9443 7.95148i −0.416944 0.302927i
\(690\) 10.0000 0.380693
\(691\) −9.09017 + 6.60440i −0.345806 + 0.251243i −0.747108 0.664703i \(-0.768558\pi\)
0.401301 + 0.915946i \(0.368558\pi\)
\(692\) 1.57295 4.84104i 0.0597945 0.184029i
\(693\) 9.47214 0.359817
\(694\) 6.35410 19.5559i 0.241198 0.742332i
\(695\) −7.23607 22.2703i −0.274480 0.844762i
\(696\) −2.61803 8.05748i −0.0992363 0.305418i
\(697\) 2.18034 + 6.71040i 0.0825863 + 0.254174i
\(698\) 22.5623 + 16.3925i 0.853996 + 0.620464i
\(699\) −18.6525 −0.705501
\(700\) −10.5902 + 7.69421i −0.400271 + 0.290814i
\(701\) 40.8328 1.54223 0.771117 0.636693i \(-0.219698\pi\)
0.771117 + 0.636693i \(0.219698\pi\)
\(702\) −5.23607 3.80423i −0.197623 0.143581i
\(703\) −14.1115 43.4306i −0.532224 1.63802i
\(704\) 1.11803 + 3.44095i 0.0421375 + 0.129686i
\(705\) 3.81966 0.143857
\(706\) −4.09017 + 12.5882i −0.153936 + 0.473765i
\(707\) 11.4721 0.431454
\(708\) 1.11803 3.44095i 0.0420183 0.129319i
\(709\) 35.3607 25.6910i 1.32800 0.964847i 0.328203 0.944607i \(-0.393557\pi\)
0.999795 0.0202400i \(-0.00644302\pi\)
\(710\) 10.0000 7.26543i 0.375293 0.272667i
\(711\) 4.54508 + 3.30220i 0.170454 + 0.123842i
\(712\) −2.85410 + 2.07363i −0.106962 + 0.0777124i
\(713\) −23.9443 + 17.3965i −0.896720 + 0.651505i
\(714\) 2.61803 + 1.90211i 0.0979775 + 0.0711848i
\(715\) −42.3607 30.7768i −1.58420 1.15099i
\(716\) −7.97214 + 5.79210i −0.297933 + 0.216461i
\(717\) −3.79837 + 11.6902i −0.141853 + 0.436578i
\(718\) 22.1803 0.827763
\(719\) −5.12461 + 15.7719i −0.191116 + 0.588194i 0.808884 + 0.587968i \(0.200072\pi\)
−1.00000 0.000225882i \(0.999928\pi\)
\(720\) 1.80902 1.31433i 0.0674181 0.0489821i
\(721\) 11.5902 + 35.6709i 0.431640 + 1.32845i
\(722\) 4.19756 + 12.9188i 0.156217 + 0.480787i
\(723\) 7.73607 + 5.62058i 0.287707 + 0.209032i
\(724\) −6.65248 −0.247237
\(725\) −34.2705 + 24.8990i −1.27277 + 0.924725i
\(726\) −2.09017 −0.0775735
\(727\) 6.94427 + 5.04531i 0.257549 + 0.187120i 0.709066 0.705142i \(-0.249117\pi\)
−0.451517 + 0.892263i \(0.649117\pi\)
\(728\) −5.23607 16.1150i −0.194062 0.597260i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −2.43769 + 7.50245i −0.0902231 + 0.277678i
\(731\) −2.94427 + 9.06154i −0.108898 + 0.335153i
\(732\) −2.76393 −0.102158
\(733\) −11.0902 + 34.1320i −0.409625 + 1.26070i 0.507346 + 0.861742i \(0.330626\pi\)
−0.916971 + 0.398953i \(0.869374\pi\)
\(734\) 24.7705 17.9968i 0.914296 0.664275i
\(735\) −0.100813 + 0.310271i −0.00371855 + 0.0114445i
\(736\) −3.61803 2.62866i −0.133363 0.0968935i
\(737\) 4.47214 3.24920i 0.164733 0.119686i
\(738\) −4.61803 + 3.35520i −0.169992 + 0.123507i
\(739\) 38.9787 + 28.3197i 1.43386 + 1.04176i 0.989283 + 0.146014i \(0.0466444\pi\)
0.444573 + 0.895743i \(0.353356\pi\)
\(740\) −5.52786 17.0130i −0.203208 0.625411i
\(741\) 29.8885 21.7153i 1.09798 0.797731i
\(742\) −1.69098 + 5.20431i −0.0620779 + 0.191056i
\(743\) −39.0132 −1.43125 −0.715627 0.698483i \(-0.753859\pi\)
−0.715627 + 0.698483i \(0.753859\pi\)
\(744\) −2.04508 + 6.29412i −0.0749765 + 0.230754i
\(745\) 39.9615 + 29.0337i 1.46408 + 1.06371i
\(746\) −3.56231 10.9637i −0.130425 0.401408i
\(747\) 0.663119 + 2.04087i 0.0242623 + 0.0746715i
\(748\) −3.61803 2.62866i −0.132288 0.0961132i
\(749\) −30.4164 −1.11139
\(750\) −9.04508 6.57164i −0.330280 0.239962i
\(751\) 24.7984 0.904906 0.452453 0.891788i \(-0.350549\pi\)
0.452453 + 0.891788i \(0.350549\pi\)
\(752\) −1.38197 1.00406i −0.0503951 0.0366142i
\(753\) −4.19098 12.8985i −0.152728 0.470048i
\(754\) −16.9443 52.1491i −0.617074 1.89916i
\(755\) 33.1525 + 24.0867i 1.20654 + 0.876604i
\(756\) −0.809017 + 2.48990i −0.0294237 + 0.0905567i
\(757\) −17.1246 −0.622405 −0.311202 0.950344i \(-0.600732\pi\)
−0.311202 + 0.950344i \(0.600732\pi\)
\(758\) −6.23607 + 19.1926i −0.226504 + 0.697108i
\(759\) 13.0902 9.51057i 0.475143 0.345212i
\(760\) 3.94427 + 12.1392i 0.143074 + 0.440336i
\(761\) −1.14590 0.832544i −0.0415388 0.0301797i 0.566822 0.823840i \(-0.308173\pi\)
−0.608361 + 0.793661i \(0.708173\pi\)
\(762\) 11.0172 8.00448i 0.399112 0.289972i
\(763\) −36.5066 + 26.5236i −1.32163 + 0.960218i
\(764\) −3.47214 2.52265i −0.125617 0.0912664i
\(765\) −0.854102 + 2.62866i −0.0308801 + 0.0950392i
\(766\) 16.1803 11.7557i 0.584619 0.424751i
\(767\) 7.23607 22.2703i 0.261279 0.804135i
\(768\) −1.00000 −0.0360844
\(769\) 7.62868 23.4787i 0.275097 0.846662i −0.714097 0.700047i \(-0.753162\pi\)
0.989194 0.146615i \(-0.0468377\pi\)
\(770\) −6.54508 + 20.1437i −0.235868 + 0.725929i
\(771\) 6.79837 + 20.9232i 0.244837 + 0.753532i
\(772\) 5.51722 + 16.9803i 0.198569 + 0.611133i
\(773\) 0.927051 + 0.673542i 0.0333437 + 0.0242256i 0.604332 0.796732i \(-0.293440\pi\)
−0.570989 + 0.820958i \(0.693440\pi\)
\(774\) −7.70820 −0.277066
\(775\) 33.0902 1.18863
\(776\) −3.38197 −0.121406
\(777\) 16.9443 + 12.3107i 0.607872 + 0.441645i
\(778\) −3.82624 11.7759i −0.137177 0.422188i
\(779\) −10.0689 30.9888i −0.360755 1.11029i
\(780\) 11.7082 8.50651i 0.419221 0.304582i
\(781\) 6.18034 19.0211i 0.221150 0.680630i
\(782\) 5.52786 0.197676
\(783\) −2.61803 + 8.05748i −0.0935609 + 0.287951i
\(784\) 0.118034 0.0857567i 0.00421550 0.00306274i
\(785\) 15.6525 + 11.3722i 0.558661 + 0.405891i
\(786\) −14.4721 10.5146i −0.516204 0.375044i
\(787\) −22.7082 + 16.4985i −0.809460 + 0.588107i −0.913674 0.406448i \(-0.866767\pi\)
0.104214 + 0.994555i \(0.466767\pi\)
\(788\) 13.8262 10.0453i 0.492539 0.357851i
\(789\) −9.47214 6.88191i −0.337217 0.245002i
\(790\) −10.1631 + 7.38394i −0.361588 + 0.262709i
\(791\) 40.7426 29.6013i 1.44864 1.05250i
\(792\) 1.11803 3.44095i 0.0397276 0.122269i
\(793\) −17.8885 −0.635241
\(794\) −9.50658 + 29.2582i −0.337376 + 1.03834i
\(795\) −4.67376 −0.165761
\(796\) 6.02786 + 18.5519i 0.213652 + 0.657553i
\(797\) 0.465558 + 1.43284i 0.0164909 + 0.0507538i 0.958963 0.283530i \(-0.0915056\pi\)
−0.942472 + 0.334284i \(0.891506\pi\)
\(798\) −12.0902 8.78402i −0.427987 0.310951i
\(799\) 2.11146 0.0746979
\(800\) 1.54508 + 4.75528i 0.0546270 + 0.168125i
\(801\) 3.52786 0.124651
\(802\) −20.7984 15.1109i −0.734416 0.533585i
\(803\) 3.94427 + 12.1392i 0.139190 + 0.428384i
\(804\) 0.472136 + 1.45309i 0.0166510 + 0.0512464i
\(805\) −8.09017 24.8990i −0.285141 0.877574i
\(806\) −13.2361 + 40.7364i −0.466221 + 1.43488i
\(807\) 9.09017 0.319989
\(808\) 1.35410 4.16750i 0.0476371 0.146612i
\(809\) 24.9443 18.1231i 0.876994 0.637173i −0.0554606 0.998461i \(-0.517663\pi\)
0.932454 + 0.361288i \(0.117663\pi\)
\(810\) −2.23607 −0.0785674
\(811\) 4.61803 + 3.35520i 0.162161 + 0.117817i 0.665906 0.746035i \(-0.268045\pi\)
−0.503745 + 0.863852i \(0.668045\pi\)
\(812\) −17.9443 + 13.0373i −0.629720 + 0.457519i
\(813\) −14.5902 + 10.6004i −0.511700 + 0.371772i
\(814\) −23.4164 17.0130i −0.820745 0.596306i
\(815\) 1.05573 0.0369805
\(816\) 1.00000 0.726543i 0.0350070 0.0254341i
\(817\) 13.5967 41.8465i 0.475690 1.46402i
\(818\) 5.79837 0.202735
\(819\) −5.23607 + 16.1150i −0.182963 + 0.563102i
\(820\) −3.94427 12.1392i −0.137740 0.423920i
\(821\) −13.9336 42.8833i −0.486287 1.49664i −0.830108 0.557602i \(-0.811721\pi\)
0.343821 0.939035i \(-0.388279\pi\)
\(822\) 3.76393 + 11.5842i 0.131282 + 0.404045i
\(823\) −2.39919 1.74311i −0.0836304 0.0607610i 0.545184 0.838316i \(-0.316460\pi\)
−0.628815 + 0.777555i \(0.716460\pi\)
\(824\) 14.3262 0.499078
\(825\) −18.0902 −0.629819
\(826\) −9.47214 −0.329578
\(827\) −35.6803 25.9233i −1.24073 0.901441i −0.243080 0.970006i \(-0.578158\pi\)
−0.997647 + 0.0685652i \(0.978158\pi\)
\(828\) 1.38197 + 4.25325i 0.0480266 + 0.147811i
\(829\) 8.00000 + 24.6215i 0.277851 + 0.855139i 0.988451 + 0.151542i \(0.0484239\pi\)
−0.710599 + 0.703597i \(0.751576\pi\)
\(830\) −4.79837 −0.166554
\(831\) −5.23607 + 16.1150i −0.181637 + 0.559022i
\(832\) −6.47214 −0.224381
\(833\) −0.0557281 + 0.171513i −0.00193086 + 0.00594259i
\(834\) 8.47214 6.15537i 0.293366 0.213143i
\(835\) 21.1803 15.3884i 0.732976 0.532538i
\(836\) 16.7082 + 12.1392i 0.577865 + 0.419844i
\(837\) 5.35410 3.88998i 0.185065 0.134457i
\(838\) 2.50000 1.81636i 0.0863611 0.0627450i
\(839\) −5.14590 3.73871i −0.177656 0.129075i 0.495403 0.868663i \(-0.335020\pi\)
−0.673060 + 0.739588i \(0.735020\pi\)
\(840\) −4.73607 3.44095i −0.163410 0.118724i
\(841\) −34.6074 + 25.1437i −1.19336 + 0.867026i
\(842\) −7.03444 + 21.6498i −0.242423 + 0.746101i
\(843\) −5.88854 −0.202812
\(844\) −1.05573 + 3.24920i −0.0363397 + 0.111842i
\(845\) 52.2599 37.9690i 1.79779 1.30617i
\(846\) 0.527864 + 1.62460i 0.0181483 + 0.0558548i
\(847\) 1.69098 + 5.20431i 0.0581029 + 0.178822i
\(848\) 1.69098 + 1.22857i 0.0580686 + 0.0421893i
\(849\) −4.58359 −0.157308
\(850\) −5.00000 3.63271i −0.171499 0.124601i
\(851\) 35.7771 1.22642
\(852\) 4.47214 + 3.24920i 0.153213 + 0.111316i
\(853\) −13.4721 41.4630i −0.461277 1.41967i −0.863605 0.504169i \(-0.831799\pi\)
0.402328 0.915496i \(-0.368201\pi\)
\(854\) 2.23607 + 6.88191i 0.0765167 + 0.235494i
\(855\) 3.94427 12.1392i 0.134891 0.415153i
\(856\) −3.59017 + 11.0494i −0.122709 + 0.377661i
\(857\) −16.0689 −0.548903 −0.274451 0.961601i \(-0.588496\pi\)
−0.274451 + 0.961601i \(0.588496\pi\)
\(858\) 7.23607 22.2703i 0.247035 0.760296i
\(859\) 1.85410 1.34708i 0.0632611 0.0459619i −0.555705 0.831379i \(-0.687552\pi\)
0.618966 + 0.785417i \(0.287552\pi\)
\(860\) 5.32624 16.3925i 0.181623 0.558979i
\(861\) 12.0902 + 8.78402i 0.412032 + 0.299359i
\(862\) −13.6180 + 9.89408i −0.463832 + 0.336994i
\(863\) 8.23607 5.98385i 0.280359 0.203693i −0.438715 0.898626i \(-0.644566\pi\)
0.719074 + 0.694934i \(0.244566\pi\)
\(864\) 0.809017 + 0.587785i 0.0275233 + 0.0199969i
\(865\) −3.51722 10.8249i −0.119589 0.368057i
\(866\) −12.5451 + 9.11454i −0.426299 + 0.309725i
\(867\) 4.78115 14.7149i 0.162376 0.499743i
\(868\) 17.3262 0.588091
\(869\) −6.28115 + 19.3314i −0.213074 + 0.655773i
\(870\) −15.3262 11.1352i −0.519608 0.377517i
\(871\) 3.05573 + 9.40456i 0.103539 + 0.318661i
\(872\) 5.32624 + 16.3925i 0.180369 + 0.555119i
\(873\) 2.73607 + 1.98787i 0.0926019 + 0.0672792i
\(874\) −25.5279 −0.863493
\(875\) −9.04508 + 27.8379i −0.305780 + 0.941093i
\(876\) −3.52786 −0.119195
\(877\) 30.0344 + 21.8213i 1.01419 + 0.736853i 0.965084 0.261941i \(-0.0843625\pi\)
0.0491070 + 0.998794i \(0.484362\pi\)
\(878\) −7.26393 22.3561i −0.245146 0.754481i
\(879\) 6.82624 + 21.0090i 0.230243 + 0.708616i
\(880\) 6.54508 + 4.75528i 0.220635 + 0.160301i
\(881\) −7.29180 + 22.4418i −0.245667 + 0.756085i 0.749859 + 0.661597i \(0.230121\pi\)
−0.995526 + 0.0944874i \(0.969879\pi\)
\(882\) −0.145898 −0.00491264
\(883\) −9.29180 + 28.5972i −0.312694 + 0.962373i 0.663999 + 0.747733i \(0.268858\pi\)
−0.976693 + 0.214640i \(0.931142\pi\)
\(884\) 6.47214 4.70228i 0.217681 0.158155i
\(885\) −2.50000 7.69421i −0.0840366 0.258638i
\(886\) −13.4443 9.76784i −0.451669 0.328157i
\(887\) −18.9443 + 13.7638i −0.636086 + 0.462144i −0.858503 0.512808i \(-0.828605\pi\)
0.222417 + 0.974952i \(0.428605\pi\)
\(888\) 6.47214 4.70228i 0.217191 0.157798i
\(889\) −28.8435 20.9560i −0.967379 0.702842i
\(890\) −2.43769 + 7.50245i −0.0817117 + 0.251483i
\(891\) −2.92705 + 2.12663i −0.0980599 + 0.0712447i
\(892\) −2.50000 + 7.69421i −0.0837062 + 0.257621i
\(893\) −9.75078 −0.326297
\(894\) −6.82624 + 21.0090i −0.228304 + 0.702646i
\(895\) −6.80902 + 20.9560i −0.227600 + 0.700482i
\(896\) 0.809017 + 2.48990i 0.0270274 + 0.0831817i
\(897\) 8.94427 + 27.5276i 0.298641 + 0.919121i
\(898\) 22.4164 + 16.2865i 0.748045 + 0.543487i
\(899\) 56.0689 1.87000
\(900\) 1.54508 4.75528i 0.0515028 0.158509i
\(901\) −2.58359 −0.0860719
\(902\) −16.7082 12.1392i −0.556322 0.404192i
\(903\) 6.23607 + 19.1926i 0.207523 + 0.638691i
\(904\) −5.94427 18.2946i −0.197704 0.608469i
\(905\) −12.0344 + 8.74353i −0.400038 + 0.290645i
\(906\) −5.66312 + 17.4293i −0.188145 + 0.579049i
\(907\) 30.4721 1.01181 0.505905 0.862589i \(-0.331159\pi\)
0.505905 + 0.862589i \(0.331159\pi\)
\(908\) −6.88197 + 21.1805i −0.228386 + 0.702900i
\(909\) −3.54508 + 2.57565i −0.117583 + 0.0854291i
\(910\) −30.6525 22.2703i −1.01612 0.738254i
\(911\) −14.7082 10.6861i −0.487305 0.354047i 0.316842 0.948478i \(-0.397377\pi\)
−0.804147 + 0.594431i \(0.797377\pi\)
\(912\) −4.61803 + 3.35520i −0.152918 + 0.111102i
\(913\) −6.28115 + 4.56352i −0.207876 + 0.151031i
\(914\) 3.30902 + 2.40414i 0.109453 + 0.0795219i
\(915\) −5.00000 + 3.63271i −0.165295 + 0.120094i
\(916\) 4.47214 3.24920i 0.147764 0.107356i
\(917\) −14.4721 + 44.5407i −0.477912 + 1.47086i
\(918\) −1.23607 −0.0407963
\(919\) −12.5836 + 38.7283i −0.415094 + 1.27753i 0.497072 + 0.867709i \(0.334408\pi\)
−0.912166 + 0.409820i \(0.865592\pi\)
\(920\) −10.0000 −0.329690
\(921\) −3.09017 9.51057i −0.101825 0.313384i
\(922\) 2.33688 + 7.19218i 0.0769611 + 0.236862i
\(923\) 28.9443 + 21.0292i 0.952712 + 0.692186i
\(924\) −9.47214 −0.311610
\(925\) −32.3607 23.5114i −1.06401 0.773050i
\(926\) −22.8328 −0.750333
\(927\) −11.5902 8.42075i −0.380671 0.276574i
\(928\) 2.61803 + 8.05748i 0.0859412 + 0.264500i
\(929\) −5.87539 18.0826i −0.192765 0.593270i −0.999995 0.00303360i \(-0.999034\pi\)
0.807230 0.590237i \(-0.200966\pi\)
\(930\) 4.57295 + 14.0741i 0.149953 + 0.461508i
\(931\) 0.257354 0.792055i 0.00843444 0.0259585i
\(932\) 18.6525 0.610982
\(933\) 0.326238 1.00406i 0.0106806 0.0328714i
\(934\) −8.63525 + 6.27388i −0.282554 + 0.205288i
\(935\) −10.0000 −0.327035
\(936\) 5.23607 + 3.80423i 0.171146 + 0.124345i
\(937\) 7.02786 5.10604i 0.229590 0.166807i −0.467043 0.884235i \(-0.654681\pi\)
0.696633 + 0.717428i \(0.254681\pi\)
\(938\) 3.23607 2.35114i 0.105661 0.0767675i
\(939\) −13.1631 9.56357i −0.429562 0.312095i
\(940\) −3.81966 −0.124584
\(941\) 3.59017 2.60841i 0.117036 0.0850318i −0.527728 0.849414i \(-0.676956\pi\)
0.644764 + 0.764382i \(0.276956\pi\)
\(942\) −2.67376 + 8.22899i −0.0871159 + 0.268115i
\(943\) 25.5279 0.831302
\(944\) −1.11803 + 3.44095i −0.0363889 + 0.111994i
\(945\) 1.80902 + 5.56758i 0.0588473 + 0.181113i
\(946\) −8.61803 26.5236i −0.280196 0.862356i
\(947\) −10.3713 31.9196i −0.337023 1.03725i −0.965717 0.259597i \(-0.916410\pi\)
0.628694 0.777652i \(-0.283590\pi\)
\(948\) −4.54508 3.30220i −0.147617 0.107250i
\(949\) −22.8328 −0.741185
\(950\) 23.0902 + 16.7760i 0.749144 + 0.544285i
\(951\) 20.5623 0.666778
\(952\) −2.61803 1.90211i −0.0848510 0.0616478i
\(953\) 1.63932 + 5.04531i 0.0531028 + 0.163434i 0.974091 0.226157i \(-0.0726164\pi\)
−0.920988 + 0.389591i \(0.872616\pi\)
\(954\) −0.645898 1.98787i −0.0209117 0.0643597i
\(955\) −9.59675 −0.310543
\(956\) 3.79837 11.6902i 0.122848 0.378088i
\(957\) −30.6525 −0.990854
\(958\) −9.00000 + 27.6992i −0.290777 + 0.894919i
\(959\) 25.7984 18.7436i 0.833073 0.605263i
\(960\) −1.80902 + 1.31433i −0.0583858 + 0.0424197i
\(961\) −10.3541 7.52270i −0.334003 0.242668i
\(962\) 41.8885 30.4338i 1.35054 0.981225i
\(963\) 9.39919 6.82891i 0.302885 0.220059i
\(964\) −7.73607 5.62058i −0.249162 0.181027i
\(965\) 32.2984 + 23.4661i 1.03972 + 0.755402i
\(966\) 9.47214 6.88191i 0.304761 0.221422i
\(967\) 3.37132 10.3759i 0.108414 0.333665i −0.882102 0.471058i \(-0.843872\pi\)
0.990517 + 0.137393i \(0.0438722\pi\)
\(968\) 2.09017 0.0671806
\(969\) 2.18034 6.71040i 0.0700426 0.215569i
\(970\) −6.11803 + 4.44501i −0.196438 + 0.142721i
\(971\) −4.39261 13.5191i −0.140966 0.433847i 0.855505 0.517795i \(-0.173247\pi\)
−0.996470 + 0.0839479i \(0.973247\pi\)
\(972\) −0.309017 0.951057i −0.00991172 0.0305052i
\(973\) −22.1803 16.1150i −0.711069 0.516622i
\(974\) 17.7984 0.570297
\(975\) 10.0000 30.7768i 0.320256 0.985648i
\(976\) 2.76393 0.0884713
\(977\) 0.618034 + 0.449028i 0.0197727 + 0.0143657i 0.597628 0.801774i \(-0.296110\pi\)
−0.577855 + 0.816139i \(0.696110\pi\)
\(978\) 0.145898 + 0.449028i 0.00466530 + 0.0143583i
\(979\) 3.94427 + 12.1392i 0.126059 + 0.387971i
\(980\) 0.100813 0.310271i 0.00322036 0.00991123i
\(981\) 5.32624 16.3925i 0.170054 0.523371i
\(982\) −25.2705 −0.806414
\(983\) 12.4164 38.2138i 0.396022 1.21883i −0.532141 0.846656i \(-0.678612\pi\)
0.928163 0.372174i \(-0.121388\pi\)
\(984\) 4.61803 3.35520i 0.147218 0.106960i
\(985\) 11.8090 36.3444i 0.376267 1.15803i
\(986\) −8.47214 6.15537i −0.269808 0.196027i
\(987\) 3.61803 2.62866i 0.115163 0.0836710i
\(988\) −29.8885 + 21.7153i −0.950881 + 0.690856i
\(989\) 27.8885 + 20.2622i 0.886804 + 0.644301i
\(990\) −2.50000 7.69421i −0.0794552 0.244538i
\(991\) −23.8262 + 17.3108i −0.756865 + 0.549895i −0.897947 0.440103i \(-0.854942\pi\)
0.141082 + 0.989998i \(0.454942\pi\)
\(992\) 2.04508 6.29412i 0.0649315 0.199839i
\(993\) 18.0000 0.571213
\(994\) 4.47214 13.7638i 0.141848 0.436562i
\(995\) 35.2877 + 25.6380i 1.11870 + 0.812780i
\(996\) −0.663119 2.04087i −0.0210117 0.0646675i
\(997\) −1.72949 5.32282i −0.0547735 0.168576i 0.919927 0.392089i \(-0.128247\pi\)
−0.974701 + 0.223513i \(0.928247\pi\)
\(998\) −28.7984 20.9232i −0.911597 0.662314i
\(999\) −8.00000 −0.253109
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 150.2.g.a.91.1 yes 4
3.2 odd 2 450.2.h.c.91.1 4
5.2 odd 4 750.2.h.b.49.2 8
5.3 odd 4 750.2.h.b.49.1 8
5.4 even 2 750.2.g.b.451.1 4
25.2 odd 20 750.2.h.b.199.1 8
25.6 even 5 3750.2.a.f.1.2 2
25.8 odd 20 3750.2.c.b.1249.1 4
25.11 even 5 inner 150.2.g.a.61.1 4
25.14 even 10 750.2.g.b.301.1 4
25.17 odd 20 3750.2.c.b.1249.4 4
25.19 even 10 3750.2.a.d.1.1 2
25.23 odd 20 750.2.h.b.199.2 8
75.11 odd 10 450.2.h.c.361.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.g.a.61.1 4 25.11 even 5 inner
150.2.g.a.91.1 yes 4 1.1 even 1 trivial
450.2.h.c.91.1 4 3.2 odd 2
450.2.h.c.361.1 4 75.11 odd 10
750.2.g.b.301.1 4 25.14 even 10
750.2.g.b.451.1 4 5.4 even 2
750.2.h.b.49.1 8 5.3 odd 4
750.2.h.b.49.2 8 5.2 odd 4
750.2.h.b.199.1 8 25.2 odd 20
750.2.h.b.199.2 8 25.23 odd 20
3750.2.a.d.1.1 2 25.19 even 10
3750.2.a.f.1.2 2 25.6 even 5
3750.2.c.b.1249.1 4 25.8 odd 20
3750.2.c.b.1249.4 4 25.17 odd 20