Properties

Label 65.2.e.a.61.1
Level $65$
Weight $2$
Character 65.61
Analytic conductor $0.519$
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] = [65,2,Mod(16,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 61.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 65.61
Dual form 65.2.e.a.16.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 + 1.40126i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-0.309017 - 0.535233i) q^{4} +1.00000 q^{5} +(1.80902 + 3.13331i) q^{6} +(0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 1.40126i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-0.309017 - 0.535233i) q^{4} +1.00000 q^{5} +(1.80902 + 3.13331i) q^{6} +(0.118034 + 0.204441i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.809017 + 1.40126i) q^{10} +(-2.11803 + 3.66854i) q^{11} -1.38197 q^{12} +(-1.00000 - 3.46410i) q^{13} -0.381966 q^{14} +(1.11803 - 1.93649i) q^{15} +(2.42705 - 4.20378i) q^{16} +(-2.73607 - 4.73901i) q^{17} +3.23607 q^{18} +(0.118034 + 0.204441i) q^{19} +(-0.309017 - 0.535233i) q^{20} +0.527864 q^{21} +(-3.42705 - 5.93583i) q^{22} +(-4.11803 + 7.13264i) q^{23} +(-2.50000 + 4.33013i) q^{24} +1.00000 q^{25} +(5.66312 + 1.40126i) q^{26} +2.23607 q^{27} +(0.0729490 - 0.126351i) q^{28} +(-0.736068 + 1.27491i) q^{29} +(1.80902 + 3.13331i) q^{30} +(1.69098 + 2.92887i) q^{32} +(4.73607 + 8.20311i) q^{33} +8.85410 q^{34} +(0.118034 + 0.204441i) q^{35} +(-0.618034 + 1.07047i) q^{36} +(-1.50000 + 2.59808i) q^{37} -0.381966 q^{38} +(-7.82624 - 1.93649i) q^{39} -2.23607 q^{40} +(2.97214 - 5.14789i) q^{41} +(-0.427051 + 0.739674i) q^{42} +(0.881966 + 1.52761i) q^{43} +2.61803 q^{44} +(-1.00000 - 1.73205i) q^{45} +(-6.66312 - 11.5409i) q^{46} +12.9443 q^{47} +(-5.42705 - 9.39993i) q^{48} +(3.47214 - 6.01392i) q^{49} +(-0.809017 + 1.40126i) q^{50} -12.2361 q^{51} +(-1.54508 + 1.60570i) q^{52} +6.00000 q^{53} +(-1.80902 + 3.13331i) q^{54} +(-2.11803 + 3.66854i) q^{55} +(-0.263932 - 0.457144i) q^{56} +0.527864 q^{57} +(-1.19098 - 2.06284i) q^{58} +(-6.35410 - 11.0056i) q^{59} -1.38197 q^{60} +(6.20820 + 10.7529i) q^{61} +(0.236068 - 0.408882i) q^{63} +4.23607 q^{64} +(-1.00000 - 3.46410i) q^{65} -15.3262 q^{66} +(-5.35410 + 9.27358i) q^{67} +(-1.69098 + 2.92887i) q^{68} +(9.20820 + 15.9491i) q^{69} -0.381966 q^{70} +(0.881966 + 1.52761i) q^{71} +(2.23607 + 3.87298i) q^{72} -6.00000 q^{73} +(-2.42705 - 4.20378i) q^{74} +(1.11803 - 1.93649i) q^{75} +(0.0729490 - 0.126351i) q^{76} -1.00000 q^{77} +(9.04508 - 9.39993i) q^{78} +(2.42705 - 4.20378i) q^{80} +(5.50000 - 9.52628i) q^{81} +(4.80902 + 8.32946i) q^{82} -8.94427 q^{83} +(-0.163119 - 0.282530i) q^{84} +(-2.73607 - 4.73901i) q^{85} -2.85410 q^{86} +(1.64590 + 2.85078i) q^{87} +(4.73607 - 8.20311i) q^{88} +(4.50000 - 7.79423i) q^{89} +3.23607 q^{90} +(0.590170 - 0.613323i) q^{91} +5.09017 q^{92} +(-10.4721 + 18.1383i) q^{94} +(0.118034 + 0.204441i) q^{95} +7.56231 q^{96} +(-2.73607 - 4.73901i) q^{97} +(5.61803 + 9.73072i) q^{98} +8.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + q^{4} + 4 q^{5} + 5 q^{6} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + q^{4} + 4 q^{5} + 5 q^{6} - 4 q^{7} - 4 q^{9} - q^{10} - 4 q^{11} - 10 q^{12} - 4 q^{13} - 6 q^{14} + 3 q^{16} - 2 q^{17} + 4 q^{18} - 4 q^{19} + q^{20} + 20 q^{21} - 7 q^{22} - 12 q^{23} - 10 q^{24} + 4 q^{25} + 7 q^{26} + 7 q^{28} + 6 q^{29} + 5 q^{30} + 9 q^{32} + 10 q^{33} + 22 q^{34} - 4 q^{35} + 2 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{41} + 5 q^{42} + 8 q^{43} + 6 q^{44} - 4 q^{45} - 11 q^{46} + 16 q^{47} - 15 q^{48} - 4 q^{49} - q^{50} - 40 q^{51} + 5 q^{52} + 24 q^{53} - 5 q^{54} - 4 q^{55} - 10 q^{56} + 20 q^{57} - 7 q^{58} - 12 q^{59} - 10 q^{60} - 2 q^{61} - 8 q^{63} + 8 q^{64} - 4 q^{65} - 30 q^{66} - 8 q^{67} - 9 q^{68} + 10 q^{69} - 6 q^{70} + 8 q^{71} - 24 q^{73} - 3 q^{74} + 7 q^{76} - 4 q^{77} + 25 q^{78} + 3 q^{80} + 22 q^{81} + 17 q^{82} + 15 q^{84} - 2 q^{85} + 2 q^{86} + 20 q^{87} + 10 q^{88} + 18 q^{89} + 4 q^{90} - 20 q^{91} - 2 q^{92} - 24 q^{94} - 4 q^{95} - 10 q^{96} - 2 q^{97} + 18 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 1.40126i −0.572061 + 0.990839i 0.424293 + 0.905525i \(0.360523\pi\)
−0.996354 + 0.0853143i \(0.972811\pi\)
\(3\) 1.11803 1.93649i 0.645497 1.11803i −0.338689 0.940898i \(-0.609984\pi\)
0.984186 0.177136i \(-0.0566831\pi\)
\(4\) −0.309017 0.535233i −0.154508 0.267617i
\(5\) 1.00000 0.447214
\(6\) 1.80902 + 3.13331i 0.738528 + 1.27917i
\(7\) 0.118034 + 0.204441i 0.0446127 + 0.0772714i 0.887469 0.460866i \(-0.152461\pi\)
−0.842857 + 0.538138i \(0.819128\pi\)
\(8\) −2.23607 −0.790569
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) −0.809017 + 1.40126i −0.255834 + 0.443117i
\(11\) −2.11803 + 3.66854i −0.638611 + 1.10611i 0.347126 + 0.937818i \(0.387157\pi\)
−0.985738 + 0.168289i \(0.946176\pi\)
\(12\) −1.38197 −0.398939
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) −0.381966 −0.102085
\(15\) 1.11803 1.93649i 0.288675 0.500000i
\(16\) 2.42705 4.20378i 0.606763 1.05094i
\(17\) −2.73607 4.73901i −0.663594 1.14938i −0.979664 0.200643i \(-0.935697\pi\)
0.316071 0.948736i \(-0.397636\pi\)
\(18\) 3.23607 0.762749
\(19\) 0.118034 + 0.204441i 0.0270789 + 0.0469020i 0.879247 0.476366i \(-0.158046\pi\)
−0.852168 + 0.523268i \(0.824713\pi\)
\(20\) −0.309017 0.535233i −0.0690983 0.119682i
\(21\) 0.527864 0.115189
\(22\) −3.42705 5.93583i −0.730650 1.26552i
\(23\) −4.11803 + 7.13264i −0.858669 + 1.48726i 0.0145291 + 0.999894i \(0.495375\pi\)
−0.873199 + 0.487365i \(0.837958\pi\)
\(24\) −2.50000 + 4.33013i −0.510310 + 0.883883i
\(25\) 1.00000 0.200000
\(26\) 5.66312 + 1.40126i 1.11063 + 0.274809i
\(27\) 2.23607 0.430331
\(28\) 0.0729490 0.126351i 0.0137861 0.0238782i
\(29\) −0.736068 + 1.27491i −0.136684 + 0.236744i −0.926240 0.376935i \(-0.876978\pi\)
0.789555 + 0.613679i \(0.210311\pi\)
\(30\) 1.80902 + 3.13331i 0.330280 + 0.572061i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.69098 + 2.92887i 0.298926 + 0.517756i
\(33\) 4.73607 + 8.20311i 0.824444 + 1.42798i
\(34\) 8.85410 1.51847
\(35\) 0.118034 + 0.204441i 0.0199514 + 0.0345568i
\(36\) −0.618034 + 1.07047i −0.103006 + 0.178411i
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −0.381966 −0.0619631
\(39\) −7.82624 1.93649i −1.25320 0.310087i
\(40\) −2.23607 −0.353553
\(41\) 2.97214 5.14789i 0.464170 0.803965i −0.534994 0.844856i \(-0.679686\pi\)
0.999164 + 0.0408904i \(0.0130195\pi\)
\(42\) −0.427051 + 0.739674i −0.0658954 + 0.114134i
\(43\) 0.881966 + 1.52761i 0.134499 + 0.232958i 0.925406 0.378978i \(-0.123724\pi\)
−0.790907 + 0.611936i \(0.790391\pi\)
\(44\) 2.61803 0.394683
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) −6.66312 11.5409i −0.982423 1.70161i
\(47\) 12.9443 1.88812 0.944058 0.329779i \(-0.106974\pi\)
0.944058 + 0.329779i \(0.106974\pi\)
\(48\) −5.42705 9.39993i −0.783327 1.35676i
\(49\) 3.47214 6.01392i 0.496019 0.859131i
\(50\) −0.809017 + 1.40126i −0.114412 + 0.198168i
\(51\) −12.2361 −1.71339
\(52\) −1.54508 + 1.60570i −0.214265 + 0.222670i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.80902 + 3.13331i −0.246176 + 0.426389i
\(55\) −2.11803 + 3.66854i −0.285596 + 0.494666i
\(56\) −0.263932 0.457144i −0.0352694 0.0610884i
\(57\) 0.527864 0.0699173
\(58\) −1.19098 2.06284i −0.156384 0.270865i
\(59\) −6.35410 11.0056i −0.827234 1.43281i −0.900200 0.435476i \(-0.856580\pi\)
0.0729666 0.997334i \(-0.476753\pi\)
\(60\) −1.38197 −0.178411
\(61\) 6.20820 + 10.7529i 0.794879 + 1.37677i 0.922916 + 0.385002i \(0.125799\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0.236068 0.408882i 0.0297418 0.0515143i
\(64\) 4.23607 0.529508
\(65\) −1.00000 3.46410i −0.124035 0.429669i
\(66\) −15.3262 −1.88653
\(67\) −5.35410 + 9.27358i −0.654108 + 1.13295i 0.328009 + 0.944675i \(0.393622\pi\)
−0.982117 + 0.188273i \(0.939711\pi\)
\(68\) −1.69098 + 2.92887i −0.205062 + 0.355177i
\(69\) 9.20820 + 15.9491i 1.10854 + 1.92004i
\(70\) −0.381966 −0.0456537
\(71\) 0.881966 + 1.52761i 0.104670 + 0.181294i 0.913603 0.406607i \(-0.133288\pi\)
−0.808933 + 0.587900i \(0.799955\pi\)
\(72\) 2.23607 + 3.87298i 0.263523 + 0.456435i
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.42705 4.20378i −0.282139 0.488679i
\(75\) 1.11803 1.93649i 0.129099 0.223607i
\(76\) 0.0729490 0.126351i 0.00836783 0.0144935i
\(77\) −1.00000 −0.113961
\(78\) 9.04508 9.39993i 1.02415 1.06433i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 2.42705 4.20378i 0.271353 0.469996i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 4.80902 + 8.32946i 0.531067 + 0.919835i
\(83\) −8.94427 −0.981761 −0.490881 0.871227i \(-0.663325\pi\)
−0.490881 + 0.871227i \(0.663325\pi\)
\(84\) −0.163119 0.282530i −0.0177977 0.0308266i
\(85\) −2.73607 4.73901i −0.296768 0.514018i
\(86\) −2.85410 −0.307766
\(87\) 1.64590 + 2.85078i 0.176459 + 0.305636i
\(88\) 4.73607 8.20311i 0.504867 0.874455i
\(89\) 4.50000 7.79423i 0.476999 0.826187i −0.522654 0.852545i \(-0.675058\pi\)
0.999653 + 0.0263586i \(0.00839118\pi\)
\(90\) 3.23607 0.341112
\(91\) 0.590170 0.613323i 0.0618666 0.0642937i
\(92\) 5.09017 0.530687
\(93\) 0 0
\(94\) −10.4721 + 18.1383i −1.08012 + 1.87082i
\(95\) 0.118034 + 0.204441i 0.0121100 + 0.0209752i
\(96\) 7.56231 0.771825
\(97\) −2.73607 4.73901i −0.277806 0.481173i 0.693034 0.720905i \(-0.256274\pi\)
−0.970839 + 0.239732i \(0.922940\pi\)
\(98\) 5.61803 + 9.73072i 0.567507 + 0.982951i
\(99\) 8.47214 0.851482
\(100\) −0.309017 0.535233i −0.0309017 0.0535233i
\(101\) −4.73607 + 8.20311i −0.471256 + 0.816240i −0.999459 0.0328781i \(-0.989533\pi\)
0.528203 + 0.849118i \(0.322866\pi\)
\(102\) 9.89919 17.1459i 0.980166 1.69770i
\(103\) −4.94427 −0.487174 −0.243587 0.969879i \(-0.578324\pi\)
−0.243587 + 0.969879i \(0.578324\pi\)
\(104\) 2.23607 + 7.74597i 0.219265 + 0.759555i
\(105\) 0.527864 0.0515143
\(106\) −4.85410 + 8.40755i −0.471472 + 0.816614i
\(107\) 5.11803 8.86469i 0.494779 0.856982i −0.505203 0.863001i \(-0.668582\pi\)
0.999982 + 0.00601821i \(0.00191567\pi\)
\(108\) −0.690983 1.19682i −0.0664899 0.115164i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −3.42705 5.93583i −0.326756 0.565959i
\(111\) 3.35410 + 5.80948i 0.318357 + 0.551411i
\(112\) 1.14590 0.108277
\(113\) 3.73607 + 6.47106i 0.351460 + 0.608746i 0.986505 0.163728i \(-0.0523521\pi\)
−0.635046 + 0.772475i \(0.719019\pi\)
\(114\) −0.427051 + 0.739674i −0.0399970 + 0.0692768i
\(115\) −4.11803 + 7.13264i −0.384009 + 0.665122i
\(116\) 0.909830 0.0844756
\(117\) −5.00000 + 5.19615i −0.462250 + 0.480384i
\(118\) 20.5623 1.89291
\(119\) 0.645898 1.11873i 0.0592094 0.102554i
\(120\) −2.50000 + 4.33013i −0.228218 + 0.395285i
\(121\) −3.47214 6.01392i −0.315649 0.546720i
\(122\) −20.0902 −1.81888
\(123\) −6.64590 11.5110i −0.599240 1.03791i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0.381966 + 0.661585i 0.0340282 + 0.0589386i
\(127\) −0.118034 + 0.204441i −0.0104738 + 0.0181412i −0.871215 0.490902i \(-0.836667\pi\)
0.860741 + 0.509043i \(0.170001\pi\)
\(128\) −6.80902 + 11.7936i −0.601838 + 1.04241i
\(129\) 3.94427 0.347274
\(130\) 5.66312 + 1.40126i 0.496688 + 0.122899i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 2.92705 5.06980i 0.254767 0.441270i
\(133\) −0.0278640 + 0.0482619i −0.00241612 + 0.00418484i
\(134\) −8.66312 15.0050i −0.748379 1.29623i
\(135\) 2.23607 0.192450
\(136\) 6.11803 + 10.5967i 0.524617 + 0.908663i
\(137\) 3.73607 + 6.47106i 0.319194 + 0.552860i 0.980320 0.197415i \(-0.0632546\pi\)
−0.661126 + 0.750275i \(0.729921\pi\)
\(138\) −29.7984 −2.53661
\(139\) 1.64590 + 2.85078i 0.139603 + 0.241800i 0.927346 0.374204i \(-0.122084\pi\)
−0.787743 + 0.616004i \(0.788751\pi\)
\(140\) 0.0729490 0.126351i 0.00616532 0.0106786i
\(141\) 14.4721 25.0665i 1.21877 2.11098i
\(142\) −2.85410 −0.239511
\(143\) 14.8262 + 3.66854i 1.23983 + 0.306779i
\(144\) −9.70820 −0.809017
\(145\) −0.736068 + 1.27491i −0.0611271 + 0.105875i
\(146\) 4.85410 8.40755i 0.401728 0.695814i
\(147\) −7.76393 13.4475i −0.640358 1.10913i
\(148\) 1.85410 0.152406
\(149\) −6.73607 11.6672i −0.551840 0.955815i −0.998142 0.0609327i \(-0.980593\pi\)
0.446302 0.894883i \(-0.352741\pi\)
\(150\) 1.80902 + 3.13331i 0.147706 + 0.255834i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −0.263932 0.457144i −0.0214077 0.0370792i
\(153\) −5.47214 + 9.47802i −0.442396 + 0.766252i
\(154\) 0.809017 1.40126i 0.0651924 0.112917i
\(155\) 0 0
\(156\) 1.38197 + 4.78727i 0.110646 + 0.383288i
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 0 0
\(159\) 6.70820 11.6190i 0.531995 0.921443i
\(160\) 1.69098 + 2.92887i 0.133684 + 0.231547i
\(161\) −1.94427 −0.153230
\(162\) 8.89919 + 15.4138i 0.699186 + 1.21103i
\(163\) −0.645898 1.11873i −0.0505906 0.0876256i 0.839621 0.543173i \(-0.182777\pi\)
−0.890212 + 0.455547i \(0.849444\pi\)
\(164\) −3.67376 −0.286873
\(165\) 4.73607 + 8.20311i 0.368702 + 0.638611i
\(166\) 7.23607 12.5332i 0.561628 0.972768i
\(167\) −2.59017 + 4.48631i −0.200433 + 0.347161i −0.948668 0.316273i \(-0.897568\pi\)
0.748235 + 0.663434i \(0.230902\pi\)
\(168\) −1.18034 −0.0910652
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 8.85410 0.679079
\(171\) 0.236068 0.408882i 0.0180526 0.0312680i
\(172\) 0.545085 0.944115i 0.0415623 0.0719881i
\(173\) −8.44427 14.6259i −0.642006 1.11199i −0.984984 0.172644i \(-0.944769\pi\)
0.342978 0.939343i \(-0.388564\pi\)
\(174\) −5.32624 −0.403781
\(175\) 0.118034 + 0.204441i 0.00892253 + 0.0154543i
\(176\) 10.2812 + 17.8075i 0.774971 + 1.34229i
\(177\) −28.4164 −2.13591
\(178\) 7.28115 + 12.6113i 0.545745 + 0.945259i
\(179\) 1.88197 3.25966i 0.140665 0.243638i −0.787082 0.616848i \(-0.788409\pi\)
0.927747 + 0.373209i \(0.121743\pi\)
\(180\) −0.618034 + 1.07047i −0.0460655 + 0.0797878i
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0.381966 + 1.32317i 0.0283132 + 0.0980798i
\(183\) 27.7639 2.05237
\(184\) 9.20820 15.9491i 0.678838 1.17578i
\(185\) −1.50000 + 2.59808i −0.110282 + 0.191014i
\(186\) 0 0
\(187\) 23.1803 1.69511
\(188\) −4.00000 6.92820i −0.291730 0.505291i
\(189\) 0.263932 + 0.457144i 0.0191982 + 0.0332523i
\(190\) −0.381966 −0.0277107
\(191\) 2.40983 + 4.17395i 0.174369 + 0.302016i 0.939943 0.341332i \(-0.110878\pi\)
−0.765574 + 0.643348i \(0.777545\pi\)
\(192\) 4.73607 8.20311i 0.341796 0.592008i
\(193\) −2.73607 + 4.73901i −0.196946 + 0.341121i −0.947537 0.319646i \(-0.896436\pi\)
0.750590 + 0.660768i \(0.229769\pi\)
\(194\) 8.85410 0.635687
\(195\) −7.82624 1.93649i −0.560449 0.138675i
\(196\) −4.29180 −0.306557
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) −6.85410 + 11.8717i −0.487100 + 0.843682i
\(199\) 7.35410 + 12.7377i 0.521318 + 0.902950i 0.999693 + 0.0247939i \(0.00789296\pi\)
−0.478374 + 0.878156i \(0.658774\pi\)
\(200\) −2.23607 −0.158114
\(201\) 11.9721 + 20.7363i 0.844449 + 1.46263i
\(202\) −7.66312 13.2729i −0.539175 0.933879i
\(203\) −0.347524 −0.0243914
\(204\) 3.78115 + 6.54915i 0.264734 + 0.458532i
\(205\) 2.97214 5.14789i 0.207583 0.359544i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 16.4721 1.14489
\(208\) −16.9894 4.20378i −1.17800 0.291479i
\(209\) −1.00000 −0.0691714
\(210\) −0.427051 + 0.739674i −0.0294693 + 0.0510424i
\(211\) −4.59017 + 7.95041i −0.316000 + 0.547329i −0.979650 0.200715i \(-0.935673\pi\)
0.663649 + 0.748044i \(0.269007\pi\)
\(212\) −1.85410 3.21140i −0.127340 0.220560i
\(213\) 3.94427 0.270257
\(214\) 8.28115 + 14.3434i 0.566088 + 0.980493i
\(215\) 0.881966 + 1.52761i 0.0601496 + 0.104182i
\(216\) −5.00000 −0.340207
\(217\) 0 0
\(218\) 1.61803 2.80252i 0.109587 0.189810i
\(219\) −6.70820 + 11.6190i −0.453298 + 0.785136i
\(220\) 2.61803 0.176508
\(221\) −13.6803 + 14.2170i −0.920239 + 0.956341i
\(222\) −10.8541 −0.728480
\(223\) 6.35410 11.0056i 0.425502 0.736991i −0.570965 0.820974i \(-0.693431\pi\)
0.996467 + 0.0839830i \(0.0267642\pi\)
\(224\) −0.399187 + 0.691412i −0.0266718 + 0.0461969i
\(225\) −1.00000 1.73205i −0.0666667 0.115470i
\(226\) −12.0902 −0.804226
\(227\) 0.881966 + 1.52761i 0.0585381 + 0.101391i 0.893809 0.448447i \(-0.148023\pi\)
−0.835271 + 0.549838i \(0.814689\pi\)
\(228\) −0.163119 0.282530i −0.0108028 0.0187110i
\(229\) −19.8885 −1.31427 −0.657136 0.753772i \(-0.728232\pi\)
−0.657136 + 0.753772i \(0.728232\pi\)
\(230\) −6.66312 11.5409i −0.439353 0.760982i
\(231\) −1.11803 + 1.93649i −0.0735612 + 0.127412i
\(232\) 1.64590 2.85078i 0.108058 0.187163i
\(233\) 19.8885 1.30294 0.651471 0.758674i \(-0.274152\pi\)
0.651471 + 0.758674i \(0.274152\pi\)
\(234\) −3.23607 11.2101i −0.211548 0.732825i
\(235\) 12.9443 0.844391
\(236\) −3.92705 + 6.80185i −0.255629 + 0.442763i
\(237\) 0 0
\(238\) 1.04508 + 1.81014i 0.0677428 + 0.117334i
\(239\) 9.88854 0.639637 0.319818 0.947479i \(-0.396378\pi\)
0.319818 + 0.947479i \(0.396378\pi\)
\(240\) −5.42705 9.39993i −0.350315 0.606763i
\(241\) −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i \(-0.327162\pi\)
−0.999812 + 0.0193858i \(0.993829\pi\)
\(242\) 11.2361 0.722282
\(243\) −8.94427 15.4919i −0.573775 0.993808i
\(244\) 3.83688 6.64567i 0.245631 0.425446i
\(245\) 3.47214 6.01392i 0.221827 0.384215i
\(246\) 21.5066 1.37121
\(247\) 0.590170 0.613323i 0.0375516 0.0390248i
\(248\) 0 0
\(249\) −10.0000 + 17.3205i −0.633724 + 1.09764i
\(250\) −0.809017 + 1.40126i −0.0511667 + 0.0886234i
\(251\) −7.88197 13.6520i −0.497505 0.861704i 0.502491 0.864583i \(-0.332417\pi\)
−0.999996 + 0.00287826i \(0.999084\pi\)
\(252\) −0.291796 −0.0183814
\(253\) −17.4443 30.2144i −1.09671 1.89956i
\(254\) −0.190983 0.330792i −0.0119833 0.0207558i
\(255\) −12.2361 −0.766252
\(256\) −6.78115 11.7453i −0.423822 0.734081i
\(257\) −4.26393 + 7.38535i −0.265977 + 0.460685i −0.967819 0.251647i \(-0.919028\pi\)
0.701842 + 0.712332i \(0.252361\pi\)
\(258\) −3.19098 + 5.52694i −0.198662 + 0.344093i
\(259\) −0.708204 −0.0440057
\(260\) −1.54508 + 1.60570i −0.0958221 + 0.0995812i
\(261\) 2.94427 0.182246
\(262\) 9.70820 16.8151i 0.599775 1.03884i
\(263\) −4.11803 + 7.13264i −0.253929 + 0.439818i −0.964604 0.263703i \(-0.915056\pi\)
0.710675 + 0.703520i \(0.248390\pi\)
\(264\) −10.5902 18.3427i −0.651780 1.12892i
\(265\) 6.00000 0.368577
\(266\) −0.0450850 0.0780895i −0.00276434 0.00478797i
\(267\) −10.0623 17.4284i −0.615803 1.06660i
\(268\) 6.61803 0.404261
\(269\) 7.73607 + 13.3993i 0.471676 + 0.816967i 0.999475 0.0324021i \(-0.0103157\pi\)
−0.527799 + 0.849370i \(0.676982\pi\)
\(270\) −1.80902 + 3.13331i −0.110093 + 0.190687i
\(271\) −7.35410 + 12.7377i −0.446730 + 0.773759i −0.998171 0.0604550i \(-0.980745\pi\)
0.551441 + 0.834214i \(0.314078\pi\)
\(272\) −26.5623 −1.61058
\(273\) −0.527864 1.82857i −0.0319478 0.110670i
\(274\) −12.0902 −0.730394
\(275\) −2.11803 + 3.66854i −0.127722 + 0.221221i
\(276\) 5.69098 9.85707i 0.342557 0.593326i
\(277\) 9.44427 + 16.3580i 0.567451 + 0.982854i 0.996817 + 0.0797238i \(0.0254038\pi\)
−0.429366 + 0.903131i \(0.641263\pi\)
\(278\) −5.32624 −0.319447
\(279\) 0 0
\(280\) −0.263932 0.457144i −0.0157730 0.0273196i
\(281\) 19.8885 1.18645 0.593226 0.805036i \(-0.297854\pi\)
0.593226 + 0.805036i \(0.297854\pi\)
\(282\) 23.4164 + 40.5584i 1.39443 + 2.41522i
\(283\) −1.35410 + 2.34537i −0.0804930 + 0.139418i −0.903462 0.428669i \(-0.858983\pi\)
0.822969 + 0.568087i \(0.192316\pi\)
\(284\) 0.545085 0.944115i 0.0323448 0.0560229i
\(285\) 0.527864 0.0312680
\(286\) −17.1353 + 17.8075i −1.01323 + 1.05298i
\(287\) 1.40325 0.0828314
\(288\) 3.38197 5.85774i 0.199284 0.345170i
\(289\) −6.47214 + 11.2101i −0.380714 + 0.659416i
\(290\) −1.19098 2.06284i −0.0699369 0.121134i
\(291\) −12.2361 −0.717291
\(292\) 1.85410 + 3.21140i 0.108503 + 0.187933i
\(293\) 6.02786 + 10.4406i 0.352152 + 0.609944i 0.986626 0.162999i \(-0.0521168\pi\)
−0.634475 + 0.772944i \(0.718783\pi\)
\(294\) 25.1246 1.46530
\(295\) −6.35410 11.0056i −0.369950 0.640772i
\(296\) 3.35410 5.80948i 0.194953 0.337669i
\(297\) −4.73607 + 8.20311i −0.274815 + 0.475993i
\(298\) 21.7984 1.26275
\(299\) 28.8262 + 7.13264i 1.66706 + 0.412491i
\(300\) −1.38197 −0.0797878
\(301\) −0.208204 + 0.360620i −0.0120007 + 0.0207858i
\(302\) −6.47214 + 11.2101i −0.372430 + 0.645067i
\(303\) 10.5902 + 18.3427i 0.608389 + 1.05376i
\(304\) 1.14590 0.0657218
\(305\) 6.20820 + 10.7529i 0.355481 + 0.615711i
\(306\) −8.85410 15.3358i −0.506155 0.876687i
\(307\) 7.05573 0.402692 0.201346 0.979520i \(-0.435468\pi\)
0.201346 + 0.979520i \(0.435468\pi\)
\(308\) 0.309017 + 0.535233i 0.0176079 + 0.0304977i
\(309\) −5.52786 + 9.57454i −0.314469 + 0.544677i
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 17.5000 + 4.33013i 0.990742 + 0.245145i
\(313\) −31.8885 −1.80245 −0.901224 0.433355i \(-0.857330\pi\)
−0.901224 + 0.433355i \(0.857330\pi\)
\(314\) 14.5623 25.2227i 0.821798 1.42340i
\(315\) 0.236068 0.408882i 0.0133009 0.0230379i
\(316\) 0 0
\(317\) 23.8885 1.34171 0.670857 0.741587i \(-0.265926\pi\)
0.670857 + 0.741587i \(0.265926\pi\)
\(318\) 10.8541 + 18.7999i 0.608668 + 1.05424i
\(319\) −3.11803 5.40059i −0.174576 0.302375i
\(320\) 4.23607 0.236803
\(321\) −11.4443 19.8221i −0.638757 1.10636i
\(322\) 1.57295 2.72443i 0.0876570 0.151826i
\(323\) 0.645898 1.11873i 0.0359387 0.0622477i
\(324\) −6.79837 −0.377687
\(325\) −1.00000 3.46410i −0.0554700 0.192154i
\(326\) 2.09017 0.115764
\(327\) −2.23607 + 3.87298i −0.123655 + 0.214176i
\(328\) −6.64590 + 11.5110i −0.366958 + 0.635590i
\(329\) 1.52786 + 2.64634i 0.0842339 + 0.145897i
\(330\) −15.3262 −0.843682
\(331\) −12.8262 22.2157i −0.704994 1.22109i −0.966694 0.255936i \(-0.917616\pi\)
0.261700 0.965149i \(-0.415717\pi\)
\(332\) 2.76393 + 4.78727i 0.151690 + 0.262736i
\(333\) 6.00000 0.328798
\(334\) −4.19098 7.25900i −0.229320 0.397195i
\(335\) −5.35410 + 9.27358i −0.292526 + 0.506670i
\(336\) 1.28115 2.21902i 0.0698926 0.121058i
\(337\) 27.8885 1.51919 0.759593 0.650399i \(-0.225398\pi\)
0.759593 + 0.650399i \(0.225398\pi\)
\(338\) −0.809017 21.0189i −0.0440047 1.14328i
\(339\) 16.7082 0.907465
\(340\) −1.69098 + 2.92887i −0.0917064 + 0.158840i
\(341\) 0 0
\(342\) 0.381966 + 0.661585i 0.0206544 + 0.0357744i
\(343\) 3.29180 0.177740
\(344\) −1.97214 3.41584i −0.106330 0.184170i
\(345\) 9.20820 + 15.9491i 0.495753 + 0.858669i
\(346\) 27.3262 1.46907
\(347\) −8.64590 14.9751i −0.464136 0.803907i 0.535026 0.844836i \(-0.320302\pi\)
−0.999162 + 0.0409283i \(0.986968\pi\)
\(348\) 1.01722 1.76188i 0.0545288 0.0944466i
\(349\) 12.2082 21.1452i 0.653490 1.13188i −0.328780 0.944407i \(-0.606637\pi\)
0.982270 0.187472i \(-0.0600293\pi\)
\(350\) −0.381966 −0.0204169
\(351\) −2.23607 7.74597i −0.119352 0.413449i
\(352\) −14.3262 −0.763591
\(353\) 5.26393 9.11740i 0.280171 0.485270i −0.691256 0.722610i \(-0.742942\pi\)
0.971427 + 0.237340i \(0.0762756\pi\)
\(354\) 22.9894 39.8187i 1.22187 2.11634i
\(355\) 0.881966 + 1.52761i 0.0468099 + 0.0810771i
\(356\) −5.56231 −0.294802
\(357\) −1.44427 2.50155i −0.0764390 0.132396i
\(358\) 3.04508 + 5.27424i 0.160938 + 0.278752i
\(359\) −17.8885 −0.944121 −0.472061 0.881566i \(-0.656490\pi\)
−0.472061 + 0.881566i \(0.656490\pi\)
\(360\) 2.23607 + 3.87298i 0.117851 + 0.204124i
\(361\) 9.47214 16.4062i 0.498533 0.863485i
\(362\) −4.85410 + 8.40755i −0.255126 + 0.441891i
\(363\) −15.5279 −0.815001
\(364\) −0.510643 0.126351i −0.0267650 0.00662261i
\(365\) −6.00000 −0.314054
\(366\) −22.4615 + 38.9044i −1.17408 + 2.03357i
\(367\) 12.8262 22.2157i 0.669524 1.15965i −0.308513 0.951220i \(-0.599831\pi\)
0.978037 0.208430i \(-0.0668353\pi\)
\(368\) 19.9894 + 34.6226i 1.04202 + 1.80483i
\(369\) −11.8885 −0.618893
\(370\) −2.42705 4.20378i −0.126176 0.218544i
\(371\) 0.708204 + 1.22665i 0.0367681 + 0.0636842i
\(372\) 0 0
\(373\) −5.02786 8.70852i −0.260333 0.450910i 0.705997 0.708214i \(-0.250499\pi\)
−0.966330 + 0.257305i \(0.917166\pi\)
\(374\) −18.7533 + 32.4816i −0.969709 + 1.67959i
\(375\) 1.11803 1.93649i 0.0577350 0.100000i
\(376\) −28.9443 −1.49269
\(377\) 5.15248 + 1.27491i 0.265366 + 0.0656611i
\(378\) −0.854102 −0.0439303
\(379\) −16.5902 + 28.7350i −0.852180 + 1.47602i 0.0270571 + 0.999634i \(0.491386\pi\)
−0.879237 + 0.476385i \(0.841947\pi\)
\(380\) 0.0729490 0.126351i 0.00374221 0.00648169i
\(381\) 0.263932 + 0.457144i 0.0135216 + 0.0234202i
\(382\) −7.79837 −0.399000
\(383\) 0.118034 + 0.204441i 0.00603126 + 0.0104464i 0.869025 0.494768i \(-0.164747\pi\)
−0.862994 + 0.505214i \(0.831414\pi\)
\(384\) 15.2254 + 26.3712i 0.776969 + 1.34575i
\(385\) −1.00000 −0.0509647
\(386\) −4.42705 7.66788i −0.225331 0.390285i
\(387\) 1.76393 3.05522i 0.0896657 0.155306i
\(388\) −1.69098 + 2.92887i −0.0858467 + 0.148691i
\(389\) −35.8885 −1.81962 −0.909811 0.415023i \(-0.863773\pi\)
−0.909811 + 0.415023i \(0.863773\pi\)
\(390\) 9.04508 9.39993i 0.458016 0.475984i
\(391\) 45.0689 2.27923
\(392\) −7.76393 + 13.4475i −0.392138 + 0.679203i
\(393\) −13.4164 + 23.2379i −0.676768 + 1.17220i
\(394\) −2.42705 4.20378i −0.122273 0.211783i
\(395\) 0 0
\(396\) −2.61803 4.53457i −0.131561 0.227871i
\(397\) −5.02786 8.70852i −0.252341 0.437068i 0.711829 0.702353i \(-0.247867\pi\)
−0.964170 + 0.265285i \(0.914534\pi\)
\(398\) −23.7984 −1.19290
\(399\) 0.0623059 + 0.107917i 0.00311920 + 0.00540261i
\(400\) 2.42705 4.20378i 0.121353 0.210189i
\(401\) 13.4443 23.2862i 0.671375 1.16286i −0.306139 0.951987i \(-0.599037\pi\)
0.977514 0.210869i \(-0.0676293\pi\)
\(402\) −38.7426 −1.93231
\(403\) 0 0
\(404\) 5.85410 0.291252
\(405\) 5.50000 9.52628i 0.273297 0.473365i
\(406\) 0.281153 0.486971i 0.0139534 0.0241680i
\(407\) −6.35410 11.0056i −0.314961 0.545529i
\(408\) 27.3607 1.35456
\(409\) 5.44427 + 9.42976i 0.269202 + 0.466271i 0.968656 0.248406i \(-0.0799068\pi\)
−0.699454 + 0.714678i \(0.746573\pi\)
\(410\) 4.80902 + 8.32946i 0.237500 + 0.411363i
\(411\) 16.7082 0.824155
\(412\) 1.52786 + 2.64634i 0.0752725 + 0.130376i
\(413\) 1.50000 2.59808i 0.0738102 0.127843i
\(414\) −13.3262 + 23.0817i −0.654949 + 1.13440i
\(415\) −8.94427 −0.439057
\(416\) 8.45492 8.78661i 0.414536 0.430799i
\(417\) 7.36068 0.360454
\(418\) 0.809017 1.40126i 0.0395703 0.0685378i
\(419\) 6.82624 11.8234i 0.333484 0.577610i −0.649709 0.760183i \(-0.725109\pi\)
0.983192 + 0.182573i \(0.0584425\pi\)
\(420\) −0.163119 0.282530i −0.00795939 0.0137861i
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) −7.42705 12.8640i −0.361543 0.626211i
\(423\) −12.9443 22.4201i −0.629372 1.09010i
\(424\) −13.4164 −0.651558
\(425\) −2.73607 4.73901i −0.132719 0.229876i
\(426\) −3.19098 + 5.52694i −0.154604 + 0.267781i
\(427\) −1.46556 + 2.53842i −0.0709233 + 0.122843i
\(428\) −6.32624 −0.305790
\(429\) 23.6803 24.6093i 1.14330 1.18815i
\(430\) −2.85410 −0.137637
\(431\) −2.40983 + 4.17395i −0.116077 + 0.201052i −0.918210 0.396094i \(-0.870365\pi\)
0.802133 + 0.597146i \(0.203699\pi\)
\(432\) 5.42705 9.39993i 0.261109 0.452254i
\(433\) 11.7361 + 20.3275i 0.563999 + 0.976876i 0.997142 + 0.0755503i \(0.0240713\pi\)
−0.433143 + 0.901325i \(0.642595\pi\)
\(434\) 0 0
\(435\) 1.64590 + 2.85078i 0.0789148 + 0.136684i
\(436\) 0.618034 + 1.07047i 0.0295985 + 0.0512660i
\(437\) −1.94427 −0.0930071
\(438\) −10.8541 18.7999i −0.518629 0.898292i
\(439\) 4.64590 8.04693i 0.221737 0.384059i −0.733599 0.679583i \(-0.762161\pi\)
0.955335 + 0.295524i \(0.0954941\pi\)
\(440\) 4.73607 8.20311i 0.225783 0.391068i
\(441\) −13.8885 −0.661359
\(442\) −8.85410 30.6715i −0.421147 1.45889i
\(443\) −16.9443 −0.805047 −0.402523 0.915410i \(-0.631867\pi\)
−0.402523 + 0.915410i \(0.631867\pi\)
\(444\) 2.07295 3.59045i 0.0983778 0.170395i
\(445\) 4.50000 7.79423i 0.213320 0.369482i
\(446\) 10.2812 + 17.8075i 0.486827 + 0.843209i
\(447\) −30.1246 −1.42485
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) 6.97214 + 12.0761i 0.329035 + 0.569906i 0.982321 0.187206i \(-0.0599431\pi\)
−0.653285 + 0.757112i \(0.726610\pi\)
\(450\) 3.23607 0.152550
\(451\) 12.5902 + 21.8068i 0.592848 + 1.02684i
\(452\) 2.30902 3.99933i 0.108607 0.188113i
\(453\) 8.94427 15.4919i 0.420239 0.727875i
\(454\) −2.85410 −0.133950
\(455\) 0.590170 0.613323i 0.0276676 0.0287530i
\(456\) −1.18034 −0.0552745
\(457\) 14.2082 24.6093i 0.664632 1.15118i −0.314753 0.949174i \(-0.601922\pi\)
0.979385 0.202002i \(-0.0647449\pi\)
\(458\) 16.0902 27.8690i 0.751844 1.30223i
\(459\) −6.11803 10.5967i −0.285565 0.494614i
\(460\) 5.09017 0.237330
\(461\) 14.2082 + 24.6093i 0.661742 + 1.14617i 0.980158 + 0.198220i \(0.0635159\pi\)
−0.318416 + 0.947951i \(0.603151\pi\)
\(462\) −1.80902 3.13331i −0.0841631 0.145775i
\(463\) 28.9443 1.34515 0.672577 0.740027i \(-0.265187\pi\)
0.672577 + 0.740027i \(0.265187\pi\)
\(464\) 3.57295 + 6.18853i 0.165870 + 0.287295i
\(465\) 0 0
\(466\) −16.0902 + 27.8690i −0.745363 + 1.29101i
\(467\) −8.94427 −0.413892 −0.206946 0.978352i \(-0.566352\pi\)
−0.206946 + 0.978352i \(0.566352\pi\)
\(468\) 4.32624 + 1.07047i 0.199980 + 0.0494823i
\(469\) −2.52786 −0.116726
\(470\) −10.4721 + 18.1383i −0.483044 + 0.836656i
\(471\) −20.1246 + 34.8569i −0.927293 + 1.60612i
\(472\) 14.2082 + 24.6093i 0.653986 + 1.13274i
\(473\) −7.47214 −0.343569
\(474\) 0 0
\(475\) 0.118034 + 0.204441i 0.00541577 + 0.00938039i
\(476\) −0.798374 −0.0365934
\(477\) −6.00000 10.3923i −0.274721 0.475831i
\(478\) −8.00000 + 13.8564i −0.365911 + 0.633777i
\(479\) 4.06231 7.03612i 0.185611 0.321489i −0.758171 0.652056i \(-0.773907\pi\)
0.943782 + 0.330567i \(0.107240\pi\)
\(480\) 7.56231 0.345170
\(481\) 10.5000 + 2.59808i 0.478759 + 0.118462i
\(482\) 24.2705 1.10549
\(483\) −2.17376 + 3.76507i −0.0989096 + 0.171316i
\(484\) −2.14590 + 3.71680i −0.0975408 + 0.168946i
\(485\) −2.73607 4.73901i −0.124238 0.215187i
\(486\) 28.9443 1.31294
\(487\) 13.0623 + 22.6246i 0.591910 + 1.02522i 0.993975 + 0.109607i \(0.0349591\pi\)
−0.402065 + 0.915611i \(0.631708\pi\)
\(488\) −13.8820 24.0443i −0.628407 1.08843i
\(489\) −2.88854 −0.130624
\(490\) 5.61803 + 9.73072i 0.253797 + 0.439589i
\(491\) −2.11803 + 3.66854i −0.0955855 + 0.165559i −0.909853 0.414931i \(-0.863806\pi\)
0.814267 + 0.580490i \(0.197139\pi\)
\(492\) −4.10739 + 7.11421i −0.185175 + 0.320733i
\(493\) 8.05573 0.362812
\(494\) 0.381966 + 1.32317i 0.0171855 + 0.0595322i
\(495\) 8.47214 0.380794
\(496\) 0 0
\(497\) −0.208204 + 0.360620i −0.00933922 + 0.0161760i
\(498\) −16.1803 28.0252i −0.725058 1.25584i
\(499\) 13.8885 0.621737 0.310868 0.950453i \(-0.399380\pi\)
0.310868 + 0.950453i \(0.399380\pi\)
\(500\) −0.309017 0.535233i −0.0138197 0.0239364i
\(501\) 5.79180 + 10.0317i 0.258758 + 0.448183i
\(502\) 25.5066 1.13841
\(503\) 6.59017 + 11.4145i 0.293841 + 0.508948i 0.974715 0.223453i \(-0.0717330\pi\)
−0.680873 + 0.732401i \(0.738400\pi\)
\(504\) −0.527864 + 0.914287i −0.0235129 + 0.0407256i
\(505\) −4.73607 + 8.20311i −0.210752 + 0.365034i
\(506\) 56.4508 2.50955
\(507\) 1.11803 + 29.0474i 0.0496536 + 1.29004i
\(508\) 0.145898 0.00647318
\(509\) −5.68034 + 9.83864i −0.251777 + 0.436090i −0.964015 0.265848i \(-0.914348\pi\)
0.712238 + 0.701938i \(0.247681\pi\)
\(510\) 9.89919 17.1459i 0.438343 0.759233i
\(511\) −0.708204 1.22665i −0.0313291 0.0542636i
\(512\) −5.29180 −0.233867
\(513\) 0.263932 + 0.457144i 0.0116529 + 0.0201834i
\(514\) −6.89919 11.9497i −0.304310 0.527081i
\(515\) −4.94427 −0.217871
\(516\) −1.21885 2.11111i −0.0536567 0.0929362i
\(517\) −27.4164 + 47.4866i −1.20577 + 2.08846i
\(518\) 0.572949 0.992377i 0.0251739 0.0436025i
\(519\) −37.7639 −1.65765
\(520\) 2.23607 + 7.74597i 0.0980581 + 0.339683i
\(521\) −41.7771 −1.83029 −0.915144 0.403128i \(-0.867923\pi\)
−0.915144 + 0.403128i \(0.867923\pi\)
\(522\) −2.38197 + 4.12569i −0.104256 + 0.180576i
\(523\) −9.35410 + 16.2018i −0.409026 + 0.708454i −0.994781 0.102034i \(-0.967465\pi\)
0.585755 + 0.810488i \(0.300798\pi\)
\(524\) 3.70820 + 6.42280i 0.161994 + 0.280581i
\(525\) 0.527864 0.0230379
\(526\) −6.66312 11.5409i −0.290526 0.503205i
\(527\) 0 0
\(528\) 45.9787 2.00097
\(529\) −22.4164 38.8264i −0.974626 1.68810i
\(530\) −4.85410 + 8.40755i −0.210849 + 0.365201i
\(531\) −12.7082 + 22.0113i −0.551489 + 0.955207i
\(532\) 0.0344419 0.00149324
\(533\) −20.8050 5.14789i −0.901162 0.222980i
\(534\) 32.5623 1.40911
\(535\) 5.11803 8.86469i 0.221272 0.383254i
\(536\) 11.9721 20.7363i 0.517118 0.895674i
\(537\) −4.20820 7.28882i −0.181597 0.314536i
\(538\) −25.0344 −1.07931
\(539\) 14.7082 + 25.4754i 0.633527 + 1.09730i
\(540\) −0.690983 1.19682i −0.0297352 0.0515028i
\(541\) 7.88854 0.339155 0.169577 0.985517i \(-0.445760\pi\)
0.169577 + 0.985517i \(0.445760\pi\)
\(542\) −11.8992 20.6100i −0.511114 0.885275i
\(543\) 6.70820 11.6190i 0.287877 0.498617i
\(544\) 9.25329 16.0272i 0.396731 0.687159i
\(545\) −2.00000 −0.0856706
\(546\) 2.98936 + 0.739674i 0.127933 + 0.0316551i
\(547\) −34.8328 −1.48934 −0.744672 0.667431i \(-0.767394\pi\)
−0.744672 + 0.667431i \(0.767394\pi\)
\(548\) 2.30902 3.99933i 0.0986363 0.170843i
\(549\) 12.4164 21.5058i 0.529919 0.917847i
\(550\) −3.42705 5.93583i −0.146130 0.253104i
\(551\) −0.347524 −0.0148050
\(552\) −20.5902 35.6632i −0.876376 1.51793i
\(553\) 0 0
\(554\) −30.5623 −1.29847
\(555\) 3.35410 + 5.80948i 0.142374 + 0.246598i
\(556\) 1.01722 1.76188i 0.0431398 0.0747203i
\(557\) −3.97214 + 6.87994i −0.168305 + 0.291512i −0.937824 0.347111i \(-0.887163\pi\)
0.769519 + 0.638624i \(0.220496\pi\)
\(558\) 0 0
\(559\) 4.40983 4.58283i 0.186516 0.193833i
\(560\) 1.14590 0.0484230
\(561\) 25.9164 44.8885i 1.09419 1.89520i
\(562\) −16.0902 + 27.8690i −0.678723 + 1.17558i
\(563\) −8.64590 14.9751i −0.364381 0.631127i 0.624295 0.781188i \(-0.285386\pi\)
−0.988677 + 0.150062i \(0.952053\pi\)
\(564\) −17.8885 −0.753244
\(565\) 3.73607 + 6.47106i 0.157178 + 0.272240i
\(566\) −2.19098 3.79489i −0.0920939 0.159511i
\(567\) 2.59675 0.109053
\(568\) −1.97214 3.41584i −0.0827490 0.143325i
\(569\) 9.44427 16.3580i 0.395924 0.685761i −0.597294 0.802022i \(-0.703758\pi\)
0.993219 + 0.116261i \(0.0370909\pi\)
\(570\) −0.427051 + 0.739674i −0.0178872 + 0.0309815i
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) −2.61803 9.06914i −0.109466 0.379200i
\(573\) 10.7771 0.450219
\(574\) −1.13525 + 1.96632i −0.0473846 + 0.0820726i
\(575\) −4.11803 + 7.13264i −0.171734 + 0.297452i
\(576\) −4.23607 7.33708i −0.176503 0.305712i
\(577\) −7.88854 −0.328404 −0.164202 0.986427i \(-0.552505\pi\)
−0.164202 + 0.986427i \(0.552505\pi\)
\(578\) −10.4721 18.1383i −0.435583 0.754453i
\(579\) 6.11803 + 10.5967i 0.254257 + 0.440386i
\(580\) 0.909830 0.0377786
\(581\) −1.05573 1.82857i −0.0437990 0.0758621i
\(582\) 9.89919 17.1459i 0.410335 0.710720i
\(583\) −12.7082 + 22.0113i −0.526320 + 0.911613i
\(584\) 13.4164 0.555175
\(585\) −5.00000 + 5.19615i −0.206725 + 0.214834i
\(586\) −19.5066 −0.805809
\(587\) −2.88197 + 4.99171i −0.118951 + 0.206030i −0.919352 0.393435i \(-0.871287\pi\)
0.800401 + 0.599465i \(0.204620\pi\)
\(588\) −4.79837 + 8.31103i −0.197882 + 0.342741i
\(589\) 0 0
\(590\) 20.5623 0.846537
\(591\) 3.35410 + 5.80948i 0.137969 + 0.238970i
\(592\) 7.28115 + 12.6113i 0.299254 + 0.518322i
\(593\) 27.8885 1.14525 0.572623 0.819819i \(-0.305926\pi\)
0.572623 + 0.819819i \(0.305926\pi\)
\(594\) −7.66312 13.2729i −0.314422 0.544594i
\(595\) 0.645898 1.11873i 0.0264792 0.0458634i
\(596\) −4.16312 + 7.21073i −0.170528 + 0.295363i
\(597\) 32.8885 1.34604
\(598\) −33.3156 + 34.6226i −1.36238 + 1.41582i
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −2.50000 + 4.33013i −0.102062 + 0.176777i
\(601\) −13.0279 + 22.5649i −0.531418 + 0.920442i 0.467910 + 0.883776i \(0.345007\pi\)
−0.999328 + 0.0366662i \(0.988326\pi\)
\(602\) −0.336881 0.583495i −0.0137302 0.0237815i
\(603\) 21.4164 0.872144
\(604\) −2.47214 4.28187i −0.100590 0.174227i
\(605\) −3.47214 6.01392i −0.141162 0.244500i
\(606\) −34.2705 −1.39214
\(607\) −6.35410 11.0056i −0.257905 0.446705i 0.707775 0.706437i \(-0.249699\pi\)
−0.965681 + 0.259733i \(0.916366\pi\)
\(608\) −0.399187 + 0.691412i −0.0161892 + 0.0280405i
\(609\) −0.388544 + 0.672978i −0.0157446 + 0.0272704i
\(610\) −20.0902 −0.813427
\(611\) −12.9443 44.8403i −0.523669 1.81404i
\(612\) 6.76393 0.273416
\(613\) −11.0279 + 19.1008i −0.445411 + 0.771475i −0.998081 0.0619256i \(-0.980276\pi\)
0.552670 + 0.833400i \(0.313609\pi\)
\(614\) −5.70820 + 9.88690i −0.230364 + 0.399003i
\(615\) −6.64590 11.5110i −0.267988 0.464170i
\(616\) 2.23607 0.0900937
\(617\) 6.79180 + 11.7637i 0.273427 + 0.473590i 0.969737 0.244151i \(-0.0785093\pi\)
−0.696310 + 0.717741i \(0.745176\pi\)
\(618\) −8.94427 15.4919i −0.359791 0.623177i
\(619\) 12.0000 0.482321 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(620\) 0 0
\(621\) −9.20820 + 15.9491i −0.369512 + 0.640014i
\(622\) 19.4164 33.6302i 0.778527 1.34845i
\(623\) 2.12461 0.0851208
\(624\) −27.1353 + 28.1998i −1.08628 + 1.12889i
\(625\) 1.00000 0.0400000
\(626\) 25.7984 44.6841i 1.03111 1.78594i
\(627\) −1.11803 + 1.93649i −0.0446500 + 0.0773360i
\(628\) 5.56231 + 9.63420i 0.221960 + 0.384446i
\(629\) 16.4164 0.654565
\(630\) 0.381966 + 0.661585i 0.0152179 + 0.0263582i
\(631\) −12.0623 20.8925i −0.480193 0.831718i 0.519549 0.854441i \(-0.326100\pi\)
−0.999742 + 0.0227223i \(0.992767\pi\)
\(632\) 0 0
\(633\) 10.2639 + 17.7777i 0.407955 + 0.706598i
\(634\) −19.3262 + 33.4740i −0.767543 + 1.32942i
\(635\) −0.118034 + 0.204441i −0.00468404 + 0.00811299i
\(636\) −8.29180 −0.328791
\(637\) −24.3050 6.01392i −0.962997 0.238280i
\(638\) 10.0902 0.399474
\(639\) 1.76393 3.05522i 0.0697801 0.120863i
\(640\) −6.80902 + 11.7936i −0.269150 + 0.466182i
\(641\) 13.4443 + 23.2862i 0.531017 + 0.919748i 0.999345 + 0.0361934i \(0.0115232\pi\)
−0.468328 + 0.883555i \(0.655143\pi\)
\(642\) 37.0344 1.46163
\(643\) 15.3541 + 26.5941i 0.605507 + 1.04877i 0.991971 + 0.126464i \(0.0403628\pi\)
−0.386465 + 0.922304i \(0.626304\pi\)
\(644\) 0.600813 + 1.04064i 0.0236754 + 0.0410069i
\(645\) 3.94427 0.155306
\(646\) 1.04508 + 1.81014i 0.0411183 + 0.0712190i
\(647\) 23.2984 40.3540i 0.915954 1.58648i 0.110454 0.993881i \(-0.464769\pi\)
0.805499 0.592597i \(-0.201897\pi\)
\(648\) −12.2984 + 21.3014i −0.483126 + 0.836798i
\(649\) 53.8328 2.11312
\(650\) 5.66312 + 1.40126i 0.222126 + 0.0549619i
\(651\) 0 0
\(652\) −0.399187 + 0.691412i −0.0156334 + 0.0270778i
\(653\) 10.5000 18.1865i 0.410897 0.711694i −0.584091 0.811688i \(-0.698549\pi\)
0.994988 + 0.0999939i \(0.0318823\pi\)
\(654\) −3.61803 6.26662i −0.141476 0.245044i
\(655\) −12.0000 −0.468879
\(656\) −14.4271 24.9884i −0.563282 0.975633i
\(657\) 6.00000 + 10.3923i 0.234082 + 0.405442i
\(658\) −4.94427 −0.192748
\(659\) 24.1180 + 41.7737i 0.939505 + 1.62727i 0.766396 + 0.642368i \(0.222048\pi\)
0.173109 + 0.984903i \(0.444619\pi\)
\(660\) 2.92705 5.06980i 0.113935 0.197342i
\(661\) −1.68034 + 2.91043i −0.0653576 + 0.113203i −0.896853 0.442330i \(-0.854152\pi\)
0.831495 + 0.555532i \(0.187485\pi\)
\(662\) 41.5066 1.61320
\(663\) 12.2361 + 42.3870i 0.475210 + 1.64617i
\(664\) 20.0000 0.776151
\(665\) −0.0278640 + 0.0482619i −0.00108052 + 0.00187152i
\(666\) −4.85410 + 8.40755i −0.188093 + 0.325786i
\(667\) −6.06231 10.5002i −0.234733 0.406570i
\(668\) 3.20163 0.123875
\(669\) −14.2082 24.6093i −0.549321 0.951452i
\(670\) −8.66312 15.0050i −0.334685 0.579692i
\(671\) −52.5967 −2.03047
\(672\) 0.892609 + 1.54604i 0.0344331 + 0.0596400i
\(673\) 18.2082 31.5375i 0.701875 1.21568i −0.265933 0.963992i \(-0.585680\pi\)
0.967808 0.251691i \(-0.0809867\pi\)
\(674\) −22.5623 + 39.0791i −0.869068 + 1.50527i
\(675\) 2.23607 0.0860663
\(676\) 7.10739 + 3.74663i 0.273361 + 0.144101i
\(677\) 47.8885 1.84051 0.920253 0.391324i \(-0.127983\pi\)
0.920253 + 0.391324i \(0.127983\pi\)
\(678\) −13.5172 + 23.4125i −0.519126 + 0.899152i
\(679\) 0.645898 1.11873i 0.0247873 0.0429328i
\(680\) 6.11803 + 10.5967i 0.234616 + 0.406367i
\(681\) 3.94427 0.151145
\(682\) 0 0
\(683\) −15.1180 26.1852i −0.578475 1.00195i −0.995654 0.0931246i \(-0.970315\pi\)
0.417179 0.908824i \(-0.363019\pi\)
\(684\) −0.291796 −0.0111571
\(685\) 3.73607 + 6.47106i 0.142748 + 0.247246i
\(686\) −2.66312 + 4.61266i −0.101678 + 0.176112i
\(687\) −22.2361 + 38.5140i −0.848359 + 1.46940i
\(688\) 8.56231 0.326435
\(689\) −6.00000 20.7846i −0.228582 0.791831i
\(690\) −29.7984 −1.13440
\(691\) 5.29837 9.17705i 0.201560 0.349112i −0.747471 0.664294i \(-0.768732\pi\)
0.949031 + 0.315182i \(0.102066\pi\)
\(692\) −5.21885 + 9.03931i −0.198391 + 0.343623i
\(693\) 1.00000 + 1.73205i 0.0379869 + 0.0657952i
\(694\) 27.9787 1.06206
\(695\) 1.64590 + 2.85078i 0.0624325 + 0.108136i
\(696\) −3.68034 6.37454i −0.139503 0.241626i
\(697\) −32.5279 −1.23208
\(698\) 19.7533 + 34.2137i 0.747673 + 1.29501i
\(699\) 22.2361 38.5140i 0.841045 1.45673i
\(700\) 0.0729490 0.126351i 0.00275721 0.00477563i
\(701\) −27.8885 −1.05334 −0.526668 0.850071i \(-0.676559\pi\)
−0.526668 + 0.850071i \(0.676559\pi\)
\(702\) 12.6631 + 3.13331i 0.477939 + 0.118259i
\(703\) −0.708204 −0.0267104
\(704\) −8.97214 + 15.5402i −0.338150 + 0.585693i
\(705\) 14.4721 25.0665i 0.545052 0.944058i
\(706\) 8.51722 + 14.7523i 0.320550 + 0.555209i
\(707\) −2.23607 −0.0840960
\(708\) 8.78115 + 15.2094i 0.330016 + 0.571604i
\(709\) 19.1525 + 33.1731i 0.719286 + 1.24584i 0.961283 + 0.275563i \(0.0888644\pi\)
−0.241997 + 0.970277i \(0.577802\pi\)
\(710\) −2.85410 −0.107113
\(711\) 0 0
\(712\) −10.0623 + 17.4284i −0.377101 + 0.653158i
\(713\) 0 0
\(714\) 4.67376 0.174911
\(715\) 14.8262 + 3.66854i 0.554470 + 0.137196i
\(716\) −2.32624 −0.0869356
\(717\) 11.0557 19.1491i 0.412884 0.715136i
\(718\) 14.4721 25.0665i 0.540095 0.935473i
\(719\) −4.06231 7.03612i −0.151498 0.262403i 0.780280 0.625430i \(-0.215077\pi\)
−0.931779 + 0.363027i \(0.881743\pi\)
\(720\) −9.70820 −0.361803
\(721\) −0.583592 1.01081i −0.0217341 0.0376446i
\(722\) 15.3262 + 26.5458i 0.570384 + 0.987933i
\(723\) −33.5410 −1.24740
\(724\) −1.85410 3.21140i −0.0689072 0.119351i
\(725\) −0.736068 + 1.27491i −0.0273369 + 0.0473489i
\(726\) 12.5623 21.7586i 0.466231 0.807536i
\(727\) 11.0557 0.410034 0.205017 0.978758i \(-0.434275\pi\)
0.205017 + 0.978758i \(0.434275\pi\)
\(728\) −1.31966 + 1.37143i −0.0489099 + 0.0508286i
\(729\) −7.00000 −0.259259
\(730\) 4.85410 8.40755i 0.179658 0.311177i
\(731\) 4.82624 8.35929i 0.178505 0.309179i
\(732\) −8.57953 14.8602i −0.317108 0.549248i
\(733\) −8.11146 −0.299603 −0.149802 0.988716i \(-0.547864\pi\)
−0.149802 + 0.988716i \(0.547864\pi\)
\(734\) 20.7533 + 35.9458i 0.766018 + 1.32678i
\(735\) −7.76393 13.4475i −0.286377 0.496019i
\(736\) −27.8541 −1.02672
\(737\) −22.6803 39.2835i −0.835441 1.44703i
\(738\) 9.61803 16.6589i 0.354045 0.613223i
\(739\) 19.7705 34.2435i 0.727270 1.25967i −0.230763 0.973010i \(-0.574122\pi\)
0.958033 0.286659i \(-0.0925445\pi\)
\(740\) 1.85410 0.0681581
\(741\) −0.527864 1.82857i −0.0193916 0.0671744i
\(742\) −2.29180 −0.0841345
\(743\) −1.06231 + 1.83997i −0.0389722 + 0.0675019i −0.884854 0.465869i \(-0.845742\pi\)
0.845881 + 0.533371i \(0.179075\pi\)
\(744\) 0 0
\(745\) −6.73607 11.6672i −0.246790 0.427454i
\(746\) 16.2705 0.595706
\(747\) 8.94427 + 15.4919i 0.327254 + 0.566820i
\(748\) −7.16312 12.4069i −0.261910 0.453641i
\(749\) 2.41641 0.0882936
\(750\) 1.80902 + 3.13331i 0.0660560 + 0.114412i
\(751\) 8.64590 14.9751i 0.315493 0.546450i −0.664049 0.747689i \(-0.731163\pi\)
0.979542 + 0.201239i \(0.0644967\pi\)
\(752\) 31.4164 54.4148i 1.14564 1.98430i
\(753\) −35.2492 −1.28455
\(754\) −5.95492 + 6.18853i −0.216865 + 0.225373i
\(755\) 8.00000 0.291150
\(756\) 0.163119 0.282530i 0.00593258 0.0102755i
\(757\) −14.4443 + 25.0182i −0.524986 + 0.909302i 0.474591 + 0.880207i \(0.342596\pi\)
−0.999577 + 0.0290958i \(0.990737\pi\)
\(758\) −26.8435 46.4942i −0.974998 1.68875i
\(759\) −78.0132 −2.83170
\(760\) −0.263932 0.457144i −0.00957382 0.0165823i
\(761\) 10.0279 + 17.3688i 0.363510 + 0.629617i 0.988536 0.150986i \(-0.0482450\pi\)
−0.625026 + 0.780604i \(0.714912\pi\)
\(762\) −0.854102 −0.0309408
\(763\) −0.236068 0.408882i −0.00854623 0.0148025i
\(764\) 1.48936 2.57964i 0.0538830 0.0933282i
\(765\) −5.47214 + 9.47802i −0.197845 + 0.342678i
\(766\) −0.381966 −0.0138010
\(767\) −31.7705 + 33.0169i −1.14717 + 1.19217i
\(768\) −30.3262 −1.09430
\(769\) 11.9164 20.6398i 0.429717 0.744291i −0.567131 0.823627i \(-0.691947\pi\)
0.996848 + 0.0793363i \(0.0252801\pi\)
\(770\) 0.809017 1.40126i 0.0291549 0.0504979i
\(771\) 9.53444 + 16.5141i 0.343375 + 0.594742i
\(772\) 3.38197 0.121720
\(773\) 18.9721 + 32.8607i 0.682380 + 1.18192i 0.974252 + 0.225460i \(0.0723885\pi\)
−0.291872 + 0.956457i \(0.594278\pi\)
\(774\) 2.85410 + 4.94345i 0.102589 + 0.177689i
\(775\) 0 0
\(776\) 6.11803 + 10.5967i 0.219625 + 0.380401i
\(777\) −0.791796 + 1.37143i −0.0284055 + 0.0491998i
\(778\) 29.0344 50.2891i 1.04094 1.80295i
\(779\) 1.40325 0.0502767
\(780\) 1.38197 + 4.78727i 0.0494823 + 0.171412i
\(781\) −7.47214 −0.267374
\(782\) −36.4615 + 63.1532i −1.30386 + 2.25835i
\(783\) −1.64590 + 2.85078i −0.0588196 + 0.101879i
\(784\) −16.8541 29.1922i −0.601932 1.04258i
\(785\) −18.0000 −0.642448
\(786\) −21.7082 37.5997i −0.774306 1.34114i
\(787\) 18.7705 + 32.5115i 0.669096 + 1.15891i 0.978157 + 0.207867i \(0.0666520\pi\)
−0.309061 + 0.951042i \(0.600015\pi\)
\(788\) 1.85410 0.0660496
\(789\) 9.20820 + 15.9491i 0.327821 + 0.567802i
\(790\) 0 0
\(791\) −0.881966 + 1.52761i −0.0313591 + 0.0543156i
\(792\) −18.9443 −0.673155
\(793\) 31.0410 32.2588i 1.10230 1.14554i
\(794\) 16.2705 0.577419
\(795\) 6.70820 11.6190i 0.237915 0.412082i
\(796\) 4.54508 7.87232i 0.161096 0.279027i
\(797\) −0.0835921 0.144786i −0.00296099 0.00512858i 0.864541 0.502562i \(-0.167609\pi\)
−0.867502 + 0.497434i \(0.834276\pi\)
\(798\) −0.201626 −0.00713749
\(799\) −35.4164 61.3430i −1.25294 2.17016i
\(800\) 1.69098 + 2.92887i 0.0597853 + 0.103551i
\(801\) −18.0000 −0.635999
\(802\) 21.7533 + 37.6778i 0.768135 + 1.33045i
\(803\) 12.7082 22.0113i 0.448463 0.776760i
\(804\) 7.39919 12.8158i 0.260949 0.451977i
\(805\) −1.94427 −0.0685266
\(806\) 0 0
\(807\) 34.5967 1.21786
\(808\) 10.5902 18.3427i 0.372561 0.645294i
\(809\) −16.4443 + 28.4823i −0.578150 + 1.00138i 0.417542 + 0.908658i \(0.362892\pi\)
−0.995692 + 0.0927271i \(0.970442\pi\)
\(810\) 8.89919 + 15.4138i 0.312686 + 0.541587i
\(811\) −39.7771 −1.39676 −0.698381 0.715726i \(-0.746096\pi\)
−0.698381 + 0.715726i \(0.746096\pi\)
\(812\) 0.107391 + 0.186006i 0.00376868 + 0.00652755i
\(813\) 16.4443 + 28.4823i 0.576726 + 0.998918i
\(814\) 20.5623 0.720708
\(815\) −0.645898 1.11873i −0.0226248 0.0391873i
\(816\) −29.6976 + 51.4377i −1.03962 + 1.80068i
\(817\) −0.208204 + 0.360620i −0.00728413 + 0.0126165i
\(818\) −17.6180 −0.616000
\(819\) −1.65248 0.408882i −0.0577422 0.0142875i
\(820\) −3.67376 −0.128293
\(821\) −9.68034 + 16.7668i −0.337846 + 0.585167i −0.984027 0.178017i \(-0.943032\pi\)
0.646181 + 0.763184i \(0.276365\pi\)
\(822\) −13.5172 + 23.4125i −0.471467 + 0.816605i
\(823\) −11.2984 19.5694i −0.393837 0.682145i 0.599115 0.800663i \(-0.295519\pi\)
−0.992952 + 0.118518i \(0.962186\pi\)
\(824\) 11.0557 0.385145
\(825\) 4.73607 + 8.20311i 0.164889 + 0.285596i
\(826\) 2.42705 + 4.20378i 0.0844479 + 0.146268i
\(827\) 8.94427 0.311023 0.155511 0.987834i \(-0.450297\pi\)
0.155511 + 0.987834i \(0.450297\pi\)
\(828\) −5.09017 8.81643i −0.176896 0.306392i
\(829\) −18.6246 + 32.2588i −0.646860 + 1.12039i 0.337009 + 0.941501i \(0.390585\pi\)
−0.983869 + 0.178892i \(0.942749\pi\)
\(830\) 7.23607 12.5332i 0.251168 0.435035i
\(831\) 42.2361 1.46515
\(832\) −4.23607 14.6742i −0.146859 0.508735i
\(833\) −38.0000 −1.31662
\(834\) −5.95492 + 10.3142i −0.206202 + 0.357152i
\(835\) −2.59017 + 4.48631i −0.0896365 + 0.155255i
\(836\) 0.309017 + 0.535233i 0.0106876 + 0.0185114i
\(837\) 0 0
\(838\) 11.0451 + 19.1306i 0.381546 + 0.660857i
\(839\) −8.64590 14.9751i −0.298490 0.516999i 0.677301 0.735706i \(-0.263149\pi\)
−0.975791 + 0.218707i \(0.929816\pi\)
\(840\) −1.18034 −0.0407256
\(841\) 13.4164 + 23.2379i 0.462635 + 0.801307i
\(842\) −4.85410 + 8.40755i −0.167283 + 0.289743i
\(843\) 22.2361 38.5140i 0.765851 1.32649i
\(844\) 5.67376 0.195299
\(845\) −11.0000 + 6.92820i −0.378412 + 0.238337i
\(846\) 41.8885 1.44016
\(847\) 0.819660 1.41969i 0.0281639 0.0487812i
\(848\) 14.5623 25.2227i 0.500072 0.866149i
\(849\) 3.02786 + 5.24441i 0.103916 + 0.179988i
\(850\) 8.85410 0.303693
\(851\) −12.3541 21.3979i −0.423493 0.733512i
\(852\) −1.21885 2.11111i −0.0417570 0.0723253i
\(853\) 6.00000 0.205436 0.102718 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) −2.37132 4.10725i −0.0811450 0.140547i
\(855\) 0.236068 0.408882i 0.00807335 0.0139835i
\(856\) −11.4443 + 19.8221i −0.391157 + 0.677504i
\(857\) 0.111456 0.00380727 0.00190364 0.999998i \(-0.499394\pi\)
0.00190364 + 0.999998i \(0.499394\pi\)
\(858\) 15.3262 + 53.0916i 0.523229 + 1.81252i
\(859\) −13.8885 −0.473871 −0.236935 0.971525i \(-0.576143\pi\)
−0.236935 + 0.971525i \(0.576143\pi\)
\(860\) 0.545085 0.944115i 0.0185872 0.0321940i
\(861\) 1.56888 2.71739i 0.0534674 0.0926083i
\(862\) −3.89919 6.75359i −0.132807 0.230028i
\(863\) −38.8328 −1.32188 −0.660942 0.750437i \(-0.729843\pi\)
−0.660942 + 0.750437i \(0.729843\pi\)
\(864\) 3.78115 + 6.54915i 0.128637 + 0.222807i
\(865\) −8.44427 14.6259i −0.287114 0.497296i
\(866\) −37.9787 −1.29057
\(867\) 14.4721 + 25.0665i 0.491500 + 0.851302i
\(868\) 0 0
\(869\) 0 0
\(870\) −5.32624 −0.180576
\(871\) 37.4787 + 9.27358i 1.26992 + 0.314223i
\(872\) 4.47214 0.151446
\(873\) −5.47214 + 9.47802i −0.185204 + 0.320782i
\(874\) 1.57295 2.72443i 0.0532058 0.0921551i
\(875\) 0.118034 + 0.204441i 0.00399028 + 0.00691136i
\(876\) 8.29180 0.280154
\(877\) −27.8607 48.2561i −0.940788 1.62949i −0.763972 0.645249i \(-0.776754\pi\)
−0.176816 0.984244i \(-0.556580\pi\)
\(878\) 7.51722 + 13.0202i 0.253694 + 0.439411i
\(879\) 26.9574 0.909251
\(880\) 10.2812 + 17.8075i 0.346578 + 0.600290i
\(881\) −7.50000 + 12.9904i −0.252681 + 0.437657i −0.964263 0.264946i \(-0.914646\pi\)
0.711582 + 0.702603i \(0.247979\pi\)
\(882\) 11.2361 19.4614i 0.378338 0.655301i
\(883\) 10.8328 0.364553 0.182277 0.983247i \(-0.441653\pi\)
0.182277 + 0.983247i \(0.441653\pi\)
\(884\) 11.8369 + 2.92887i 0.398117 + 0.0985085i
\(885\) −28.4164 −0.955207
\(886\) 13.7082 23.7433i 0.460536 0.797672i
\(887\) 20.2426 35.0613i 0.679682 1.17724i −0.295395 0.955375i \(-0.595451\pi\)
0.975077 0.221868i \(-0.0712153\pi\)
\(888\) −7.50000 12.9904i −0.251684 0.435929i
\(889\) −0.0557281 −0.00186906
\(890\) 7.28115 + 12.6113i 0.244065 + 0.422733i
\(891\) 23.2984 + 40.3540i 0.780525 + 1.35191i
\(892\) −7.85410 −0.262975
\(893\) 1.52786 + 2.64634i 0.0511280 + 0.0885563i
\(894\) 24.3713 42.2124i 0.815099 1.41179i
\(895\) 1.88197 3.25966i 0.0629072 0.108958i
\(896\) −3.21478 −0.107398
\(897\) 46.0410 47.8472i 1.53726 1.59757i
\(898\) −22.5623 −0.752914
\(899\) 0 0
\(900\) −0.618034 + 1.07047i −0.0206011 + 0.0356822i
\(901\) −16.4164 28.4341i −0.546910 0.947276i
\(902\) −40.7426 −1.35658
\(903\) 0.465558 + 0.806370i 0.0154928 + 0.0268343i
\(904\) −8.35410 14.4697i −0.277853 0.481256i
\(905\) 6.00000 0.199447
\(906\) 14.4721 + 25.0665i 0.480805 + 0.832778i
\(907\) 10.0623 17.4284i 0.334113 0.578701i −0.649201 0.760617i \(-0.724896\pi\)
0.983314 + 0.181916i \(0.0582298\pi\)
\(908\) 0.545085 0.944115i 0.0180893 0.0313316i
\(909\) 18.9443 0.628342
\(910\) 0.381966 + 1.32317i 0.0126620 + 0.0438626i
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 1.28115 2.21902i 0.0424232 0.0734792i
\(913\) 18.9443 32.8124i 0.626964 1.08593i
\(914\) 22.9894 + 39.8187i 0.760420 + 1.31709i
\(915\) 27.7639 0.917847
\(916\) 6.14590 + 10.6450i 0.203066 + 0.351721i
\(917\) −1.41641 2.45329i −0.0467739 0.0810148i
\(918\) 19.7984 0.653444
\(919\) −16.6459 28.8315i −0.549098 0.951065i −0.998337 0.0576532i \(-0.981638\pi\)
0.449239 0.893412i \(-0.351695\pi\)
\(920\) 9.20820 15.9491i 0.303585 0.525825i
\(921\) 7.88854 13.6634i 0.259936 0.450223i
\(922\) −45.9787 −1.51423
\(923\) 4.40983 4.58283i 0.145151 0.150846i
\(924\) 1.38197 0.0454633
\(925\) −1.50000 + 2.59808i −0.0493197 + 0.0854242i
\(926\) −23.4164 + 40.5584i −0.769511 + 1.33283i
\(927\) 4.94427 + 8.56373i 0.162391 + 0.281270i
\(928\) −4.97871 −0.163434
\(929\) −1.02786 1.78031i −0.0337231 0.0584102i 0.848671 0.528921i \(-0.177403\pi\)
−0.882394 + 0.470511i \(0.844070\pi\)
\(930\) 0 0
\(931\) 1.63932 0.0537266
\(932\) −6.14590 10.6450i −0.201316 0.348689i
\(933\) −26.8328 + 46.4758i −0.878467 + 1.52155i
\(934\) 7.23607 12.5332i 0.236771 0.410100i
\(935\) 23.1803 0.758078
\(936\) 11.1803 11.6190i 0.365441 0.379777i
\(937\) −6.00000 −0.196011 −0.0980057 0.995186i \(-0.531246\pi\)
−0.0980057 + 0.995186i \(0.531246\pi\)
\(938\) 2.04508 3.54219i 0.0667744 0.115657i
\(939\) −35.6525 + 61.7519i −1.16347 + 2.01520i
\(940\) −4.00000 6.92820i −0.130466 0.225973i
\(941\) 23.8885 0.778744 0.389372 0.921081i \(-0.372692\pi\)
0.389372 + 0.921081i \(0.372692\pi\)
\(942\) −32.5623 56.3996i −1.06094 1.83760i
\(943\) 24.4787 + 42.3984i 0.797137 + 1.38068i
\(944\) −61.6869 −2.00774
\(945\) 0.263932 + 0.457144i 0.00858571 + 0.0148709i
\(946\) 6.04508 10.4704i 0.196543 0.340422i
\(947\) −8.40983 + 14.5663i −0.273283 + 0.473340i −0.969700 0.244297i \(-0.921443\pi\)
0.696418 + 0.717637i \(0.254776\pi\)
\(948\) 0 0
\(949\) 6.00000 + 20.7846i 0.194768 + 0.674697i
\(950\) −0.381966 −0.0123926
\(951\) 26.7082 46.2600i 0.866073 1.50008i
\(952\) −1.44427 + 2.50155i −0.0468091 + 0.0810758i
\(953\) 28.0967 + 48.6650i 0.910143 + 1.57641i 0.813861 + 0.581060i \(0.197362\pi\)
0.0962820 + 0.995354i \(0.469305\pi\)
\(954\) 19.4164 0.628629
\(955\) 2.40983 + 4.17395i 0.0779803 + 0.135066i
\(956\) −3.05573 5.29268i −0.0988293 0.171177i
\(957\) −13.9443 −0.450754
\(958\) 6.57295 + 11.3847i 0.212362 + 0.367822i
\(959\) −0.881966 + 1.52761i −0.0284802 + 0.0493291i
\(960\) 4.73607 8.20311i 0.152856 0.264754i
\(961\) −31.0000 −1.00000
\(962\) −12.1353 + 12.6113i −0.391256 + 0.406605i
\(963\) −20.4721 −0.659705
\(964\) −4.63525 + 8.02850i −0.149292 + 0.258580i
\(965\) −2.73607 + 4.73901i −0.0880771 + 0.152554i
\(966\) −3.51722 6.09201i −0.113165 0.196007i
\(967\) −1.16718 −0.0375341 −0.0187671 0.999824i \(-0.505974\pi\)
−0.0187671 + 0.999824i \(0.505974\pi\)
\(968\) 7.76393 + 13.4475i 0.249542 + 0.432220i
\(969\) −1.44427 2.50155i −0.0463967 0.0803614i
\(970\) 8.85410 0.284288
\(971\) 8.11803 + 14.0608i 0.260520 + 0.451234i 0.966380 0.257117i \(-0.0827726\pi\)
−0.705860 + 0.708351i \(0.749439\pi\)
\(972\) −5.52786 + 9.57454i −0.177306 + 0.307104i
\(973\) −0.388544 + 0.672978i −0.0124561 + 0.0215747i
\(974\) −42.2705 −1.35443
\(975\) −7.82624 1.93649i −0.250640 0.0620174i
\(976\) 60.2705 1.92921
\(977\) −17.2082 + 29.8055i −0.550539 + 0.953562i 0.447696 + 0.894186i \(0.352245\pi\)
−0.998236 + 0.0593763i \(0.981089\pi\)
\(978\) 2.33688 4.04760i 0.0747252 0.129428i
\(979\) 19.0623 + 33.0169i 0.609234 + 1.05522i
\(980\) −4.29180 −0.137096
\(981\) 2.00000 + 3.46410i 0.0638551 + 0.110600i
\(982\) −3.42705 5.93583i −0.109362 0.189420i
\(983\) −14.8328 −0.473093 −0.236547 0.971620i \(-0.576016\pi\)
−0.236547 + 0.971620i \(0.576016\pi\)
\(984\) 14.8607 + 25.7395i 0.473741 + 0.820544i
\(985\) −1.50000 + 2.59808i −0.0477940 + 0.0827816i
\(986\) −6.51722 + 11.2882i −0.207551 + 0.359488i
\(987\) 6.83282 0.217491
\(988\) −0.510643 0.126351i −0.0162457 0.00401977i
\(989\) −14.5279 −0.461959
\(990\) −6.85410 + 11.8717i −0.217838 + 0.377306i
\(991\) 16.6459 28.8315i 0.528774 0.915864i −0.470663 0.882313i \(-0.655985\pi\)
0.999437 0.0335508i \(-0.0106816\pi\)
\(992\) 0 0
\(993\) −57.3607 −1.82029
\(994\) −0.336881 0.583495i −0.0106852 0.0185073i
\(995\) 7.35410 + 12.7377i 0.233141 + 0.403812i
\(996\) 12.3607 0.391663
\(997\) −8.44427 14.6259i −0.267433 0.463207i 0.700765 0.713392i \(-0.252842\pi\)
−0.968198 + 0.250185i \(0.919509\pi\)
\(998\) −11.2361 + 19.4614i −0.355672 + 0.616041i
\(999\) −3.35410 + 5.80948i −0.106119 + 0.183804i
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 65.2.e.a.61.1 yes 4
3.2 odd 2 585.2.j.e.451.2 4
4.3 odd 2 1040.2.q.n.321.1 4
5.2 odd 4 325.2.o.a.74.1 8
5.3 odd 4 325.2.o.a.74.4 8
5.4 even 2 325.2.e.b.126.2 4
13.2 odd 12 845.2.m.e.361.1 8
13.3 even 3 inner 65.2.e.a.16.1 4
13.4 even 6 845.2.a.b.1.1 2
13.5 odd 4 845.2.m.e.316.4 8
13.6 odd 12 845.2.c.c.506.1 4
13.7 odd 12 845.2.c.c.506.4 4
13.8 odd 4 845.2.m.e.316.1 8
13.9 even 3 845.2.a.e.1.2 2
13.10 even 6 845.2.e.g.146.2 4
13.11 odd 12 845.2.m.e.361.4 8
13.12 even 2 845.2.e.g.191.2 4
39.17 odd 6 7605.2.a.bf.1.2 2
39.29 odd 6 585.2.j.e.406.2 4
39.35 odd 6 7605.2.a.ba.1.1 2
52.3 odd 6 1040.2.q.n.81.1 4
65.3 odd 12 325.2.o.a.224.1 8
65.4 even 6 4225.2.a.y.1.2 2
65.9 even 6 4225.2.a.u.1.1 2
65.29 even 6 325.2.e.b.276.2 4
65.42 odd 12 325.2.o.a.224.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.e.a.16.1 4 13.3 even 3 inner
65.2.e.a.61.1 yes 4 1.1 even 1 trivial
325.2.e.b.126.2 4 5.4 even 2
325.2.e.b.276.2 4 65.29 even 6
325.2.o.a.74.1 8 5.2 odd 4
325.2.o.a.74.4 8 5.3 odd 4
325.2.o.a.224.1 8 65.3 odd 12
325.2.o.a.224.4 8 65.42 odd 12
585.2.j.e.406.2 4 39.29 odd 6
585.2.j.e.451.2 4 3.2 odd 2
845.2.a.b.1.1 2 13.4 even 6
845.2.a.e.1.2 2 13.9 even 3
845.2.c.c.506.1 4 13.6 odd 12
845.2.c.c.506.4 4 13.7 odd 12
845.2.e.g.146.2 4 13.10 even 6
845.2.e.g.191.2 4 13.12 even 2
845.2.m.e.316.1 8 13.8 odd 4
845.2.m.e.316.4 8 13.5 odd 4
845.2.m.e.361.1 8 13.2 odd 12
845.2.m.e.361.4 8 13.11 odd 12
1040.2.q.n.81.1 4 52.3 odd 6
1040.2.q.n.321.1 4 4.3 odd 2
4225.2.a.u.1.1 2 65.9 even 6
4225.2.a.y.1.2 2 65.4 even 6
7605.2.a.ba.1.1 2 39.35 odd 6
7605.2.a.bf.1.2 2 39.17 odd 6