Properties

Label 731.2.m.b.87.5
Level $731$
Weight $2$
Character 731.87
Analytic conductor $5.837$
Analytic rank $0$
Dimension $116$
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] = [731,2,Mod(87,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.87");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.m (of order \(8\), 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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(116\)
Relative dimension: \(29\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.5
Character \(\chi\) \(=\) 731.87
Dual form 731.2.m.b.689.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.60811 - 1.60811i) q^{2} +(-0.921811 + 0.381827i) q^{3} +3.17206i q^{4} +(0.244536 + 0.590361i) q^{5} +(2.09640 + 0.868356i) q^{6} +(-1.44759 + 3.49480i) q^{7} +(1.88481 - 1.88481i) q^{8} +(-1.41738 + 1.41738i) q^{9} +O(q^{10})\) \(q+(-1.60811 - 1.60811i) q^{2} +(-0.921811 + 0.381827i) q^{3} +3.17206i q^{4} +(0.244536 + 0.590361i) q^{5} +(2.09640 + 0.868356i) q^{6} +(-1.44759 + 3.49480i) q^{7} +(1.88481 - 1.88481i) q^{8} +(-1.41738 + 1.41738i) q^{9} +(0.556127 - 1.34261i) q^{10} +(-2.51124 - 1.04019i) q^{11} +(-1.21118 - 2.92404i) q^{12} +2.56367i q^{13} +(7.94793 - 3.29214i) q^{14} +(-0.450831 - 0.450831i) q^{15} +0.282148 q^{16} +(-3.76350 + 1.68406i) q^{17} +4.55861 q^{18} +(-0.728044 - 0.728044i) q^{19} +(-1.87266 + 0.775682i) q^{20} -3.77427i q^{21} +(2.36562 + 5.71111i) q^{22} +(-3.10552 - 1.28635i) q^{23} +(-1.01777 + 2.45711i) q^{24} +(3.24681 - 3.24681i) q^{25} +(4.12268 - 4.12268i) q^{26} +(1.91084 - 4.61318i) q^{27} +(-11.0857 - 4.59186i) q^{28} +(-3.02073 - 7.29268i) q^{29} +1.44998i q^{30} +(6.15759 - 2.55056i) q^{31} +(-4.22334 - 4.22334i) q^{32} +2.71206 q^{33} +(8.76030 + 3.34399i) q^{34} -2.41718 q^{35} +(-4.49601 - 4.49601i) q^{36} +(5.47045 - 2.26594i) q^{37} +2.34155i q^{38} +(-0.978879 - 2.36322i) q^{39} +(1.57362 + 0.651815i) q^{40} +(0.304574 - 0.735308i) q^{41} +(-6.06946 + 6.06946i) q^{42} +(0.707107 - 0.707107i) q^{43} +(3.29955 - 7.96582i) q^{44} +(-1.18336 - 0.490165i) q^{45} +(2.92544 + 7.06263i) q^{46} -7.44664i q^{47} +(-0.260087 + 0.107732i) q^{48} +(-5.16835 - 5.16835i) q^{49} -10.4425 q^{50} +(2.82622 - 2.98939i) q^{51} -8.13213 q^{52} +(6.28294 + 6.28294i) q^{53} +(-10.4914 + 4.34567i) q^{54} -1.73690i q^{55} +(3.85859 + 9.31547i) q^{56} +(0.949105 + 0.393132i) q^{57} +(-6.86979 + 16.5851i) q^{58} +(-4.97677 + 4.97677i) q^{59} +(1.43006 - 1.43006i) q^{60} +(-1.82194 + 4.39855i) q^{61} +(-14.0037 - 5.80052i) q^{62} +(-2.90166 - 7.00523i) q^{63} +13.0189i q^{64} +(-1.51349 + 0.626909i) q^{65} +(-4.36131 - 4.36131i) q^{66} -8.56149 q^{67} +(-5.34193 - 11.9381i) q^{68} +3.35387 q^{69} +(3.88710 + 3.88710i) q^{70} +(5.75355 - 2.38320i) q^{71} +5.34297i q^{72} +(0.737399 + 1.78024i) q^{73} +(-12.4410 - 5.15323i) q^{74} +(-1.75322 + 4.23266i) q^{75} +(2.30940 - 2.30940i) q^{76} +(7.27052 - 7.27052i) q^{77} +(-2.22618 + 5.37448i) q^{78} +(-11.0682 - 4.58460i) q^{79} +(0.0689952 + 0.166569i) q^{80} -1.03133i q^{81} +(-1.67225 + 0.692668i) q^{82} +(3.45906 + 3.45906i) q^{83} +11.9722 q^{84} +(-1.91451 - 1.81001i) q^{85} -2.27422 q^{86} +(5.56908 + 5.56908i) q^{87} +(-6.69378 + 2.77265i) q^{88} -0.0263658i q^{89} +(1.11474 + 2.69122i) q^{90} +(-8.95953 - 3.71116i) q^{91} +(4.08038 - 9.85091i) q^{92} +(-4.70226 + 4.70226i) q^{93} +(-11.9750 + 11.9750i) q^{94} +(0.251776 - 0.607841i) q^{95} +(5.50571 + 2.28054i) q^{96} +(2.91669 + 7.04152i) q^{97} +16.6226i q^{98} +(5.03372 - 2.08504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 116 q - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.60811 1.60811i −1.13711 1.13711i −0.988966 0.148142i \(-0.952671\pi\)
−0.148142 0.988966i \(-0.547329\pi\)
\(3\) −0.921811 + 0.381827i −0.532208 + 0.220448i −0.632570 0.774503i \(-0.718000\pi\)
0.100362 + 0.994951i \(0.468000\pi\)
\(4\) 3.17206i 1.58603i
\(5\) 0.244536 + 0.590361i 0.109360 + 0.264017i 0.969080 0.246748i \(-0.0793620\pi\)
−0.859720 + 0.510766i \(0.829362\pi\)
\(6\) 2.09640 + 0.868356i 0.855851 + 0.354505i
\(7\) −1.44759 + 3.49480i −0.547139 + 1.32091i 0.372459 + 0.928049i \(0.378515\pi\)
−0.919598 + 0.392861i \(0.871485\pi\)
\(8\) 1.88481 1.88481i 0.666381 0.666381i
\(9\) −1.41738 + 1.41738i −0.472459 + 0.472459i
\(10\) 0.556127 1.34261i 0.175863 0.424570i
\(11\) −2.51124 1.04019i −0.757169 0.313630i −0.0295059 0.999565i \(-0.509393\pi\)
−0.727663 + 0.685935i \(0.759393\pi\)
\(12\) −1.21118 2.92404i −0.349637 0.844098i
\(13\) 2.56367i 0.711035i 0.934670 + 0.355518i \(0.115695\pi\)
−0.934670 + 0.355518i \(0.884305\pi\)
\(14\) 7.94793 3.29214i 2.12417 0.879862i
\(15\) −0.450831 0.450831i −0.116404 0.116404i
\(16\) 0.282148 0.0705370
\(17\) −3.76350 + 1.68406i −0.912783 + 0.408444i
\(18\) 4.55861 1.07447
\(19\) −0.728044 0.728044i −0.167025 0.167025i 0.618646 0.785670i \(-0.287682\pi\)
−0.785670 + 0.618646i \(0.787682\pi\)
\(20\) −1.87266 + 0.775682i −0.418740 + 0.173448i
\(21\) 3.77427i 0.823614i
\(22\) 2.36562 + 5.71111i 0.504352 + 1.21761i
\(23\) −3.10552 1.28635i −0.647546 0.268222i 0.0346412 0.999400i \(-0.488971\pi\)
−0.682187 + 0.731177i \(0.738971\pi\)
\(24\) −1.01777 + 2.45711i −0.207751 + 0.501555i
\(25\) 3.24681 3.24681i 0.649361 0.649361i
\(26\) 4.12268 4.12268i 0.808524 0.808524i
\(27\) 1.91084 4.61318i 0.367741 0.887806i
\(28\) −11.0857 4.59186i −2.09500 0.867779i
\(29\) −3.02073 7.29268i −0.560935 1.35422i −0.909019 0.416754i \(-0.863168\pi\)
0.348084 0.937463i \(-0.386832\pi\)
\(30\) 1.44998i 0.264728i
\(31\) 6.15759 2.55056i 1.10594 0.458094i 0.246400 0.969168i \(-0.420752\pi\)
0.859536 + 0.511075i \(0.170752\pi\)
\(32\) −4.22334 4.22334i −0.746589 0.746589i
\(33\) 2.71206 0.472110
\(34\) 8.76030 + 3.34399i 1.50238 + 0.573489i
\(35\) −2.41718 −0.408578
\(36\) −4.49601 4.49601i −0.749334 0.749334i
\(37\) 5.47045 2.26594i 0.899337 0.372517i 0.115372 0.993322i \(-0.463194\pi\)
0.783965 + 0.620805i \(0.213194\pi\)
\(38\) 2.34155i 0.379850i
\(39\) −0.978879 2.36322i −0.156746 0.378418i
\(40\) 1.57362 + 0.651815i 0.248811 + 0.103061i
\(41\) 0.304574 0.735308i 0.0475665 0.114836i −0.898310 0.439362i \(-0.855205\pi\)
0.945877 + 0.324526i \(0.105205\pi\)
\(42\) −6.06946 + 6.06946i −0.936538 + 0.936538i
\(43\) 0.707107 0.707107i 0.107833 0.107833i
\(44\) 3.29955 7.96582i 0.497426 1.20089i
\(45\) −1.18336 0.490165i −0.176405 0.0730695i
\(46\) 2.92544 + 7.06263i 0.431332 + 1.04133i
\(47\) 7.44664i 1.08620i −0.839667 0.543102i \(-0.817250\pi\)
0.839667 0.543102i \(-0.182750\pi\)
\(48\) −0.260087 + 0.107732i −0.0375403 + 0.0155497i
\(49\) −5.16835 5.16835i −0.738336 0.738336i
\(50\) −10.4425 −1.47679
\(51\) 2.82622 2.98939i 0.395750 0.418598i
\(52\) −8.13213 −1.12772
\(53\) 6.28294 + 6.28294i 0.863028 + 0.863028i 0.991689 0.128660i \(-0.0410677\pi\)
−0.128660 + 0.991689i \(0.541068\pi\)
\(54\) −10.4914 + 4.34567i −1.42769 + 0.591370i
\(55\) 1.73690i 0.234204i
\(56\) 3.85859 + 9.31547i 0.515626 + 1.24483i
\(57\) 0.949105 + 0.393132i 0.125712 + 0.0520716i
\(58\) −6.86979 + 16.5851i −0.902048 + 2.17774i
\(59\) −4.97677 + 4.97677i −0.647920 + 0.647920i −0.952490 0.304570i \(-0.901487\pi\)
0.304570 + 0.952490i \(0.401487\pi\)
\(60\) 1.43006 1.43006i 0.184620 0.184620i
\(61\) −1.82194 + 4.39855i −0.233276 + 0.563177i −0.996559 0.0828868i \(-0.973586\pi\)
0.763283 + 0.646064i \(0.223586\pi\)
\(62\) −14.0037 5.80052i −1.77847 0.736667i
\(63\) −2.90166 7.00523i −0.365575 0.882576i
\(64\) 13.0189i 1.62737i
\(65\) −1.51349 + 0.626909i −0.187726 + 0.0777585i
\(66\) −4.36131 4.36131i −0.536840 0.536840i
\(67\) −8.56149 −1.04595 −0.522976 0.852347i \(-0.675178\pi\)
−0.522976 + 0.852347i \(0.675178\pi\)
\(68\) −5.34193 11.9381i −0.647805 1.44770i
\(69\) 3.35387 0.403758
\(70\) 3.88710 + 3.88710i 0.464598 + 0.464598i
\(71\) 5.75355 2.38320i 0.682821 0.282834i −0.0141845 0.999899i \(-0.504515\pi\)
0.697006 + 0.717066i \(0.254515\pi\)
\(72\) 5.34297i 0.629675i
\(73\) 0.737399 + 1.78024i 0.0863060 + 0.208361i 0.961140 0.276062i \(-0.0890295\pi\)
−0.874834 + 0.484423i \(0.839030\pi\)
\(74\) −12.4410 5.15323i −1.44624 0.599051i
\(75\) −1.75322 + 4.23266i −0.202445 + 0.488745i
\(76\) 2.30940 2.30940i 0.264906 0.264906i
\(77\) 7.27052 7.27052i 0.828553 0.828553i
\(78\) −2.22618 + 5.37448i −0.252066 + 0.608540i
\(79\) −11.0682 4.58460i −1.24527 0.515807i −0.339912 0.940457i \(-0.610397\pi\)
−0.905358 + 0.424650i \(0.860397\pi\)
\(80\) 0.0689952 + 0.166569i 0.00771389 + 0.0186230i
\(81\) 1.03133i 0.114593i
\(82\) −1.67225 + 0.692668i −0.184669 + 0.0764924i
\(83\) 3.45906 + 3.45906i 0.379681 + 0.379681i 0.870987 0.491306i \(-0.163480\pi\)
−0.491306 + 0.870987i \(0.663480\pi\)
\(84\) 11.9722 1.30628
\(85\) −1.91451 1.81001i −0.207658 0.196323i
\(86\) −2.27422 −0.245235
\(87\) 5.56908 + 5.56908i 0.597068 + 0.597068i
\(88\) −6.69378 + 2.77265i −0.713559 + 0.295566i
\(89\) 0.0263658i 0.00279477i −0.999999 0.00139739i \(-0.999555\pi\)
0.999999 0.00139739i \(-0.000444802\pi\)
\(90\) 1.11474 + 2.69122i 0.117504 + 0.283680i
\(91\) −8.95953 3.71116i −0.939214 0.389035i
\(92\) 4.08038 9.85091i 0.425409 1.02703i
\(93\) −4.70226 + 4.70226i −0.487602 + 0.487602i
\(94\) −11.9750 + 11.9750i −1.23513 + 1.23513i
\(95\) 0.251776 0.607841i 0.0258317 0.0623632i
\(96\) 5.50571 + 2.28054i 0.561924 + 0.232757i
\(97\) 2.91669 + 7.04152i 0.296145 + 0.714958i 0.999989 + 0.00460334i \(0.00146529\pi\)
−0.703844 + 0.710354i \(0.748535\pi\)
\(98\) 16.6226i 1.67914i
\(99\) 5.03372 2.08504i 0.505908 0.209554i
\(100\) 10.2991 + 10.2991i 1.02991 + 1.02991i
\(101\) 1.68427 0.167591 0.0837955 0.996483i \(-0.473296\pi\)
0.0837955 + 0.996483i \(0.473296\pi\)
\(102\) −9.35216 + 0.262392i −0.926002 + 0.0259807i
\(103\) −9.88441 −0.973940 −0.486970 0.873419i \(-0.661898\pi\)
−0.486970 + 0.873419i \(0.661898\pi\)
\(104\) 4.83204 + 4.83204i 0.473820 + 0.473820i
\(105\) 2.22818 0.922944i 0.217448 0.0900701i
\(106\) 20.2074i 1.96271i
\(107\) 3.49227 + 8.43108i 0.337610 + 0.815063i 0.997944 + 0.0640911i \(0.0204148\pi\)
−0.660334 + 0.750972i \(0.729585\pi\)
\(108\) 14.6333 + 6.06130i 1.40809 + 0.583249i
\(109\) 1.35759 3.27750i 0.130033 0.313928i −0.845432 0.534084i \(-0.820657\pi\)
0.975465 + 0.220156i \(0.0706567\pi\)
\(110\) −2.79314 + 2.79314i −0.266315 + 0.266315i
\(111\) −4.17753 + 4.17753i −0.396513 + 0.396513i
\(112\) −0.408435 + 0.986050i −0.0385935 + 0.0931730i
\(113\) 7.42308 + 3.07474i 0.698304 + 0.289247i 0.703455 0.710740i \(-0.251640\pi\)
−0.00515084 + 0.999987i \(0.501640\pi\)
\(114\) −0.894067 2.15847i −0.0837371 0.202159i
\(115\) 2.14794i 0.200296i
\(116\) 23.1328 9.58194i 2.14783 0.889660i
\(117\) −3.63369 3.63369i −0.335935 0.335935i
\(118\) 16.0064 1.47351
\(119\) −0.437421 15.5905i −0.0400983 1.42918i
\(120\) −1.69946 −0.155139
\(121\) −2.55382 2.55382i −0.232166 0.232166i
\(122\) 10.0033 4.14349i 0.905653 0.375134i
\(123\) 0.794109i 0.0716024i
\(124\) 8.09053 + 19.5323i 0.726551 + 1.75405i
\(125\) 5.66255 + 2.34551i 0.506474 + 0.209788i
\(126\) −6.59901 + 15.9314i −0.587886 + 1.41928i
\(127\) −13.1824 + 13.1824i −1.16975 + 1.16975i −0.187485 + 0.982267i \(0.560034\pi\)
−0.982267 + 0.187485i \(0.939966\pi\)
\(128\) 12.4893 12.4893i 1.10390 1.10390i
\(129\) −0.381827 + 0.921811i −0.0336179 + 0.0811609i
\(130\) 3.44201 + 1.42573i 0.301884 + 0.125045i
\(131\) −8.20703 19.8135i −0.717052 1.73112i −0.681578 0.731746i \(-0.738706\pi\)
−0.0354744 0.999371i \(-0.511294\pi\)
\(132\) 8.60284i 0.748781i
\(133\) 3.59828 1.49046i 0.312010 0.129239i
\(134\) 13.7678 + 13.7678i 1.18936 + 1.18936i
\(135\) 3.19071 0.274612
\(136\) −3.91936 + 10.2676i −0.336082 + 0.880440i
\(137\) −11.0348 −0.942764 −0.471382 0.881929i \(-0.656245\pi\)
−0.471382 + 0.881929i \(0.656245\pi\)
\(138\) −5.39340 5.39340i −0.459117 0.459117i
\(139\) 17.7840 7.36636i 1.50842 0.624806i 0.533185 0.845998i \(-0.320995\pi\)
0.975230 + 0.221192i \(0.0709949\pi\)
\(140\) 7.66745i 0.648018i
\(141\) 2.84332 + 6.86439i 0.239451 + 0.578086i
\(142\) −13.0848 5.41991i −1.09805 0.454829i
\(143\) 2.66671 6.43801i 0.223002 0.538374i
\(144\) −0.399910 + 0.399910i −0.0333258 + 0.0333258i
\(145\) 3.56664 3.56664i 0.296193 0.296193i
\(146\) 1.67701 4.04865i 0.138790 0.335069i
\(147\) 6.73765 + 2.79083i 0.555712 + 0.230184i
\(148\) 7.18769 + 17.3526i 0.590824 + 1.42638i
\(149\) 21.7288i 1.78009i −0.455869 0.890047i \(-0.650672\pi\)
0.455869 0.890047i \(-0.349328\pi\)
\(150\) 9.62598 3.98721i 0.785958 0.325554i
\(151\) −9.72489 9.72489i −0.791400 0.791400i 0.190321 0.981722i \(-0.439047\pi\)
−0.981722 + 0.190321i \(0.939047\pi\)
\(152\) −2.74445 −0.222604
\(153\) 2.94736 7.72124i 0.238280 0.624226i
\(154\) −23.3837 −1.88431
\(155\) 3.01150 + 3.01150i 0.241889 + 0.241889i
\(156\) 7.49629 3.10506i 0.600183 0.248604i
\(157\) 21.0078i 1.67661i 0.545205 + 0.838303i \(0.316452\pi\)
−0.545205 + 0.838303i \(0.683548\pi\)
\(158\) 10.4264 + 25.1715i 0.829477 + 2.00254i
\(159\) −8.19068 3.39269i −0.649563 0.269058i
\(160\) 1.46054 3.52605i 0.115466 0.278759i
\(161\) 8.99107 8.99107i 0.708595 0.708595i
\(162\) −1.65850 + 1.65850i −0.130304 + 0.130304i
\(163\) 6.45944 15.5945i 0.505942 1.22145i −0.440258 0.897871i \(-0.645113\pi\)
0.946200 0.323582i \(-0.104887\pi\)
\(164\) 2.33244 + 0.966129i 0.182133 + 0.0754420i
\(165\) 0.663196 + 1.60110i 0.0516297 + 0.124645i
\(166\) 11.1251i 0.863477i
\(167\) −1.37713 + 0.570426i −0.106565 + 0.0441409i −0.435329 0.900271i \(-0.643368\pi\)
0.328764 + 0.944412i \(0.393368\pi\)
\(168\) −7.11378 7.11378i −0.548840 0.548840i
\(169\) 6.42757 0.494429
\(170\) 0.168045 + 5.98946i 0.0128885 + 0.459371i
\(171\) 2.06382 0.157825
\(172\) 2.24299 + 2.24299i 0.171026 + 0.171026i
\(173\) 3.92812 1.62708i 0.298650 0.123705i −0.228327 0.973585i \(-0.573326\pi\)
0.526977 + 0.849880i \(0.323326\pi\)
\(174\) 17.9114i 1.35786i
\(175\) 6.64688 + 16.0470i 0.502457 + 1.21304i
\(176\) −0.708542 0.293488i −0.0534084 0.0221225i
\(177\) 2.68738 6.48790i 0.201996 0.487660i
\(178\) −0.0423992 + 0.0423992i −0.00317796 + 0.00317796i
\(179\) −7.95969 + 7.95969i −0.594935 + 0.594935i −0.938960 0.344026i \(-0.888209\pi\)
0.344026 + 0.938960i \(0.388209\pi\)
\(180\) 1.55483 3.75370i 0.115890 0.279784i
\(181\) 1.21431 + 0.502982i 0.0902586 + 0.0373863i 0.427356 0.904083i \(-0.359445\pi\)
−0.337097 + 0.941470i \(0.609445\pi\)
\(182\) 8.43998 + 20.3759i 0.625613 + 1.51036i
\(183\) 4.75030i 0.351152i
\(184\) −8.27784 + 3.42879i −0.610250 + 0.252774i
\(185\) 2.67544 + 2.67544i 0.196702 + 0.196702i
\(186\) 15.1236 1.10891
\(187\) 11.2028 0.314316i 0.819231 0.0229850i
\(188\) 23.6212 1.72275
\(189\) 13.3560 + 13.3560i 0.971507 + 0.971507i
\(190\) −1.38236 + 0.572593i −0.100287 + 0.0415403i
\(191\) 18.6821i 1.35179i −0.737000 0.675893i \(-0.763758\pi\)
0.737000 0.675893i \(-0.236242\pi\)
\(192\) −4.97098 12.0010i −0.358749 0.866098i
\(193\) −1.51912 0.629239i −0.109348 0.0452936i 0.327339 0.944907i \(-0.393848\pi\)
−0.436687 + 0.899614i \(0.643848\pi\)
\(194\) 6.63319 16.0139i 0.476235 1.14973i
\(195\) 1.15578 1.15578i 0.0827674 0.0827674i
\(196\) 16.3943 16.3943i 1.17102 1.17102i
\(197\) −2.56550 + 6.19366i −0.182784 + 0.441280i −0.988538 0.150970i \(-0.951760\pi\)
0.805754 + 0.592250i \(0.201760\pi\)
\(198\) −11.4478 4.74182i −0.813558 0.336987i
\(199\) −5.78492 13.9660i −0.410082 0.990026i −0.985115 0.171896i \(-0.945011\pi\)
0.575033 0.818130i \(-0.304989\pi\)
\(200\) 12.2392i 0.865443i
\(201\) 7.89207 3.26900i 0.556664 0.230578i
\(202\) −2.70850 2.70850i −0.190569 0.190569i
\(203\) 29.8592 2.09571
\(204\) 9.48252 + 8.96494i 0.663909 + 0.627672i
\(205\) 0.508576 0.0355205
\(206\) 15.8953 + 15.8953i 1.10748 + 1.10748i
\(207\) 6.22494 2.57845i 0.432663 0.179215i
\(208\) 0.723335i 0.0501543i
\(209\) 1.07099 + 2.58560i 0.0740820 + 0.178850i
\(210\) −5.06737 2.09897i −0.349682 0.144843i
\(211\) 2.43340 5.87474i 0.167522 0.404433i −0.817717 0.575621i \(-0.804760\pi\)
0.985238 + 0.171187i \(0.0547604\pi\)
\(212\) −19.9299 + 19.9299i −1.36879 + 1.36879i
\(213\) −4.39372 + 4.39372i −0.301053 + 0.301053i
\(214\) 7.94217 19.1741i 0.542916 1.31071i
\(215\) 0.590361 + 0.244536i 0.0402623 + 0.0166772i
\(216\) −5.09339 12.2965i −0.346561 0.836673i
\(217\) 25.2117i 1.71148i
\(218\) −7.45375 + 3.08744i −0.504831 + 0.209108i
\(219\) −1.35948 1.35948i −0.0918655 0.0918655i
\(220\) 5.50957 0.371455
\(221\) −4.31737 9.64839i −0.290418 0.649021i
\(222\) 13.4359 0.901757
\(223\) −7.32182 7.32182i −0.490305 0.490305i 0.418097 0.908402i \(-0.362697\pi\)
−0.908402 + 0.418097i \(0.862697\pi\)
\(224\) 20.8734 8.64606i 1.39466 0.577689i
\(225\) 9.20389i 0.613593i
\(226\) −6.99262 16.8817i −0.465142 1.12295i
\(227\) −21.7596 9.01311i −1.44423 0.598221i −0.483413 0.875393i \(-0.660603\pi\)
−0.960820 + 0.277171i \(0.910603\pi\)
\(228\) −1.24704 + 3.01062i −0.0825872 + 0.199383i
\(229\) −12.6749 + 12.6749i −0.837583 + 0.837583i −0.988540 0.150957i \(-0.951764\pi\)
0.150957 + 0.988540i \(0.451764\pi\)
\(230\) −3.45413 + 3.45413i −0.227758 + 0.227758i
\(231\) −3.92597 + 9.47812i −0.258310 + 0.623615i
\(232\) −19.4388 8.05182i −1.27622 0.528628i
\(233\) 6.57072 + 15.8631i 0.430462 + 1.03923i 0.979139 + 0.203193i \(0.0651320\pi\)
−0.548676 + 0.836035i \(0.684868\pi\)
\(234\) 11.6868i 0.763989i
\(235\) 4.39621 1.82097i 0.286777 0.118787i
\(236\) −15.7866 15.7866i −1.02762 1.02762i
\(237\) 11.9533 0.776450
\(238\) −24.3679 + 25.7748i −1.57954 + 1.67073i
\(239\) −25.8798 −1.67402 −0.837012 0.547185i \(-0.815700\pi\)
−0.837012 + 0.547185i \(0.815700\pi\)
\(240\) −0.127201 0.127201i −0.00821079 0.00821079i
\(241\) 5.64562 2.33849i 0.363666 0.150636i −0.193365 0.981127i \(-0.561940\pi\)
0.557032 + 0.830491i \(0.311940\pi\)
\(242\) 8.21368i 0.527996i
\(243\) 6.12631 + 14.7902i 0.393003 + 0.948794i
\(244\) −13.9525 5.77931i −0.893216 0.369982i
\(245\) 1.78735 4.31504i 0.114189 0.275678i
\(246\) 1.27702 1.27702i 0.0814197 0.0814197i
\(247\) 1.86647 1.86647i 0.118760 0.118760i
\(248\) 6.79857 16.4132i 0.431710 1.04224i
\(249\) −4.50936 1.86784i −0.285769 0.118369i
\(250\) −5.33419 12.8779i −0.337364 0.814468i
\(251\) 11.4766i 0.724394i 0.932102 + 0.362197i \(0.117973\pi\)
−0.932102 + 0.362197i \(0.882027\pi\)
\(252\) 22.2210 9.20425i 1.39979 0.579813i
\(253\) 6.46068 + 6.46068i 0.406179 + 0.406179i
\(254\) 42.3977 2.66027
\(255\) 2.45593 + 0.937478i 0.153796 + 0.0587072i
\(256\) −14.1304 −0.883151
\(257\) −21.8515 21.8515i −1.36306 1.36306i −0.869994 0.493062i \(-0.835878\pi\)
−0.493062 0.869994i \(-0.664122\pi\)
\(258\) 2.09640 0.868356i 0.130516 0.0540615i
\(259\) 22.3983i 1.39176i
\(260\) −1.98860 4.80089i −0.123327 0.297739i
\(261\) 14.6180 + 6.05497i 0.904831 + 0.374793i
\(262\) −18.6646 + 45.0603i −1.15310 + 2.78383i
\(263\) 16.8536 16.8536i 1.03924 1.03924i 0.0400425 0.999198i \(-0.487251\pi\)
0.999198 0.0400425i \(-0.0127493\pi\)
\(264\) 5.11172 5.11172i 0.314605 0.314605i
\(265\) −2.17280 + 5.24561i −0.133474 + 0.322235i
\(266\) −8.18326 3.38962i −0.501748 0.207831i
\(267\) 0.0100672 + 0.0243043i 0.000616101 + 0.00148740i
\(268\) 27.1576i 1.65891i
\(269\) 12.9790 5.37607i 0.791343 0.327785i 0.0498597 0.998756i \(-0.484123\pi\)
0.741483 + 0.670971i \(0.234123\pi\)
\(270\) −5.13102 5.13102i −0.312264 0.312264i
\(271\) −12.8469 −0.780393 −0.390197 0.920732i \(-0.627593\pi\)
−0.390197 + 0.920732i \(0.627593\pi\)
\(272\) −1.06186 + 0.475153i −0.0643850 + 0.0288104i
\(273\) 9.67601 0.585619
\(274\) 17.7452 + 17.7452i 1.07202 + 1.07202i
\(275\) −11.5308 + 4.77622i −0.695335 + 0.288017i
\(276\) 10.6387i 0.640373i
\(277\) −11.5754 27.9456i −0.695501 1.67909i −0.733393 0.679805i \(-0.762064\pi\)
0.0378920 0.999282i \(-0.487936\pi\)
\(278\) −40.4446 16.7527i −2.42570 1.00476i
\(279\) −5.11253 + 12.3427i −0.306079 + 0.738940i
\(280\) −4.55592 + 4.55592i −0.272269 + 0.272269i
\(281\) −14.2480 + 14.2480i −0.849963 + 0.849963i −0.990128 0.140165i \(-0.955237\pi\)
0.140165 + 0.990128i \(0.455237\pi\)
\(282\) 6.46634 15.6111i 0.385065 0.929629i
\(283\) −10.9050 4.51699i −0.648233 0.268507i 0.0342443 0.999413i \(-0.489098\pi\)
−0.682478 + 0.730906i \(0.739098\pi\)
\(284\) 7.55966 + 18.2506i 0.448583 + 1.08298i
\(285\) 0.656449i 0.0388847i
\(286\) −14.6414 + 6.06468i −0.865766 + 0.358612i
\(287\) 2.12885 + 2.12885i 0.125662 + 0.125662i
\(288\) 11.9721 0.705465
\(289\) 11.3279 12.6759i 0.666347 0.745642i
\(290\) −11.4711 −0.673608
\(291\) −5.37728 5.37728i −0.315221 0.315221i
\(292\) −5.64703 + 2.33908i −0.330467 + 0.136884i
\(293\) 16.8522i 0.984518i 0.870449 + 0.492259i \(0.163829\pi\)
−0.870449 + 0.492259i \(0.836171\pi\)
\(294\) −6.34695 15.3229i −0.370161 0.893649i
\(295\) −4.15509 1.72109i −0.241918 0.100206i
\(296\) 6.03990 14.5816i 0.351062 0.847539i
\(297\) −9.59718 + 9.59718i −0.556885 + 0.556885i
\(298\) −34.9424 + 34.9424i −2.02416 + 2.02416i
\(299\) 3.29778 7.96155i 0.190716 0.460428i
\(300\) −13.4262 5.56133i −0.775165 0.321084i
\(301\) 1.44759 + 3.49480i 0.0834379 + 0.201437i
\(302\) 31.2775i 1.79982i
\(303\) −1.55258 + 0.643098i −0.0891932 + 0.0369450i
\(304\) −0.205416 0.205416i −0.0117814 0.0117814i
\(305\) −3.04226 −0.174199
\(306\) −17.1563 + 7.67695i −0.980762 + 0.438862i
\(307\) −8.60388 −0.491049 −0.245525 0.969390i \(-0.578960\pi\)
−0.245525 + 0.969390i \(0.578960\pi\)
\(308\) 23.0625 + 23.0625i 1.31411 + 1.31411i
\(309\) 9.11156 3.77413i 0.518338 0.214703i
\(310\) 9.68567i 0.550109i
\(311\) 9.76657 + 23.5786i 0.553811 + 1.33702i 0.914596 + 0.404370i \(0.132509\pi\)
−0.360784 + 0.932649i \(0.617491\pi\)
\(312\) −6.29922 2.60922i −0.356623 0.147718i
\(313\) −4.33786 + 10.4725i −0.245191 + 0.591942i −0.997784 0.0665436i \(-0.978803\pi\)
0.752593 + 0.658486i \(0.228803\pi\)
\(314\) 33.7829 33.7829i 1.90648 1.90648i
\(315\) 3.42606 3.42606i 0.193036 0.193036i
\(316\) 14.5426 35.1090i 0.818087 1.97504i
\(317\) 1.84590 + 0.764596i 0.103676 + 0.0429440i 0.433919 0.900952i \(-0.357131\pi\)
−0.330243 + 0.943896i \(0.607131\pi\)
\(318\) 7.71571 + 18.6274i 0.432676 + 1.04457i
\(319\) 21.4558i 1.20130i
\(320\) −7.68587 + 3.18359i −0.429653 + 0.177968i
\(321\) −6.43842 6.43842i −0.359358 0.359358i
\(322\) −28.9173 −1.61150
\(323\) 3.96606 + 1.51393i 0.220678 + 0.0842371i
\(324\) 3.27146 0.181748
\(325\) 8.32375 + 8.32375i 0.461719 + 0.461719i
\(326\) −35.4652 + 14.6902i −1.96424 + 0.813613i
\(327\) 3.53960i 0.195740i
\(328\) −0.811850 1.95998i −0.0448269 0.108222i
\(329\) 26.0245 + 10.7797i 1.43478 + 0.594304i
\(330\) 1.50825 3.64124i 0.0830265 0.200444i
\(331\) −9.54746 + 9.54746i −0.524776 + 0.524776i −0.919010 0.394234i \(-0.871010\pi\)
0.394234 + 0.919010i \(0.371010\pi\)
\(332\) −10.9723 + 10.9723i −0.602186 + 0.602186i
\(333\) −4.54201 + 10.9654i −0.248900 + 0.600899i
\(334\) 3.13189 + 1.29727i 0.171369 + 0.0709835i
\(335\) −2.09359 5.05437i −0.114385 0.276150i
\(336\) 1.06490i 0.0580952i
\(337\) 12.2510 5.07453i 0.667354 0.276427i −0.0231752 0.999731i \(-0.507378\pi\)
0.690530 + 0.723304i \(0.257378\pi\)
\(338\) −10.3363 10.3363i −0.562219 0.562219i
\(339\) −8.01669 −0.435407
\(340\) 5.74147 6.07295i 0.311375 0.329352i
\(341\) −18.1163 −0.981052
\(342\) −3.31886 3.31886i −0.179464 0.179464i
\(343\) 1.08041 0.447522i 0.0583369 0.0241639i
\(344\) 2.66552i 0.143715i
\(345\) 0.820139 + 1.97999i 0.0441548 + 0.106599i
\(346\) −8.93341 3.70034i −0.480263 0.198931i
\(347\) −6.73450 + 16.2585i −0.361527 + 0.872803i 0.633550 + 0.773701i \(0.281597\pi\)
−0.995077 + 0.0991019i \(0.968403\pi\)
\(348\) −17.6655 + 17.6655i −0.946968 + 0.946968i
\(349\) −9.30407 + 9.30407i −0.498035 + 0.498035i −0.910826 0.412791i \(-0.864554\pi\)
0.412791 + 0.910826i \(0.364554\pi\)
\(350\) 15.1164 36.4943i 0.808008 1.95070i
\(351\) 11.8267 + 4.89877i 0.631262 + 0.261477i
\(352\) 6.21276 + 14.9989i 0.331141 + 0.799446i
\(353\) 4.00210i 0.213010i −0.994312 0.106505i \(-0.966034\pi\)
0.994312 0.106505i \(-0.0339661\pi\)
\(354\) −14.7549 + 6.11168i −0.784214 + 0.324832i
\(355\) 2.81390 + 2.81390i 0.149346 + 0.149346i
\(356\) 0.0836340 0.00443259
\(357\) 6.35609 + 14.2045i 0.336400 + 0.751781i
\(358\) 25.6002 1.35301
\(359\) −6.63651 6.63651i −0.350262 0.350262i 0.509945 0.860207i \(-0.329666\pi\)
−0.860207 + 0.509945i \(0.829666\pi\)
\(360\) −3.15428 + 1.30655i −0.166245 + 0.0688610i
\(361\) 17.9399i 0.944206i
\(362\) −1.14389 2.76159i −0.0601215 0.145146i
\(363\) 3.32926 + 1.37903i 0.174741 + 0.0723800i
\(364\) 11.7720 28.4202i 0.617022 1.48962i
\(365\) −0.870663 + 0.870663i −0.0455726 + 0.0455726i
\(366\) −7.63902 + 7.63902i −0.399298 + 0.399298i
\(367\) 13.2786 32.0574i 0.693138 1.67338i −0.0452223 0.998977i \(-0.514400\pi\)
0.738360 0.674406i \(-0.235600\pi\)
\(368\) −0.876216 0.362941i −0.0456759 0.0189196i
\(369\) 0.610511 + 1.47390i 0.0317820 + 0.0767284i
\(370\) 8.60482i 0.447343i
\(371\) −31.0528 + 12.8625i −1.61218 + 0.667786i
\(372\) −14.9159 14.9159i −0.773352 0.773352i
\(373\) −1.29148 −0.0668701 −0.0334351 0.999441i \(-0.510645\pi\)
−0.0334351 + 0.999441i \(0.510645\pi\)
\(374\) −18.5209 17.5100i −0.957691 0.905418i
\(375\) −6.11538 −0.315797
\(376\) −14.0355 14.0355i −0.723825 0.723825i
\(377\) 18.6961 7.74416i 0.962896 0.398845i
\(378\) 42.9560i 2.20942i
\(379\) −0.192321 0.464305i −0.00987888 0.0238497i 0.918863 0.394576i \(-0.129109\pi\)
−0.928742 + 0.370727i \(0.879109\pi\)
\(380\) 1.92811 + 0.798649i 0.0989099 + 0.0409698i
\(381\) 7.11831 17.1851i 0.364682 0.880420i
\(382\) −30.0429 + 30.0429i −1.53713 + 1.53713i
\(383\) −6.15263 + 6.15263i −0.314385 + 0.314385i −0.846606 0.532221i \(-0.821358\pi\)
0.532221 + 0.846606i \(0.321358\pi\)
\(384\) −6.74400 + 16.2815i −0.344153 + 0.830860i
\(385\) 6.07013 + 2.51433i 0.309363 + 0.128142i
\(386\) 1.43103 + 3.45480i 0.0728373 + 0.175845i
\(387\) 2.00447i 0.101893i
\(388\) −22.3361 + 9.25193i −1.13394 + 0.469695i
\(389\) −20.8363 20.8363i −1.05644 1.05644i −0.998309 0.0581362i \(-0.981484\pi\)
−0.0581362 0.998309i \(-0.518516\pi\)
\(390\) −3.71726 −0.188231
\(391\) 13.8539 0.388697i 0.700623 0.0196573i
\(392\) −19.4827 −0.984025
\(393\) 15.1307 + 15.1307i 0.763241 + 0.763241i
\(394\) 14.0857 5.83450i 0.709629 0.293938i
\(395\) 7.65533i 0.385181i
\(396\) 6.61386 + 15.9673i 0.332359 + 0.802386i
\(397\) −22.3405 9.25372i −1.12124 0.464431i −0.256443 0.966559i \(-0.582551\pi\)
−0.864793 + 0.502128i \(0.832551\pi\)
\(398\) −13.1562 + 31.7618i −0.659459 + 1.59207i
\(399\) −2.74783 + 2.74783i −0.137564 + 0.137564i
\(400\) 0.916079 0.916079i 0.0458040 0.0458040i
\(401\) 7.10666 17.1570i 0.354890 0.856780i −0.641112 0.767447i \(-0.721527\pi\)
0.996002 0.0893324i \(-0.0284734\pi\)
\(402\) −17.9483 7.43442i −0.895179 0.370795i
\(403\) 6.53880 + 15.7861i 0.325721 + 0.786360i
\(404\) 5.34260i 0.265804i
\(405\) 0.608860 0.252198i 0.0302545 0.0125318i
\(406\) −48.0171 48.0171i −2.38305 2.38305i
\(407\) −16.0946 −0.797782
\(408\) −0.307540 10.9613i −0.0152255 0.542666i
\(409\) 5.79719 0.286652 0.143326 0.989675i \(-0.454220\pi\)
0.143326 + 0.989675i \(0.454220\pi\)
\(410\) −0.817849 0.817849i −0.0403907 0.0403907i
\(411\) 10.1720 4.21337i 0.501746 0.207830i
\(412\) 31.3540i 1.54470i
\(413\) −10.1885 24.5971i −0.501342 1.21035i
\(414\) −14.1569 5.86396i −0.695771 0.288198i
\(415\) −1.19623 + 2.88796i −0.0587206 + 0.141764i
\(416\) 10.8273 10.8273i 0.530851 0.530851i
\(417\) −13.5808 + 13.5808i −0.665053 + 0.665053i
\(418\) 2.43566 5.88021i 0.119132 0.287611i
\(419\) 24.3903 + 10.1028i 1.19154 + 0.493553i 0.888257 0.459347i \(-0.151917\pi\)
0.303285 + 0.952900i \(0.401917\pi\)
\(420\) 2.92763 + 7.06794i 0.142854 + 0.344880i
\(421\) 8.05999i 0.392820i −0.980522 0.196410i \(-0.937072\pi\)
0.980522 0.196410i \(-0.0629283\pi\)
\(422\) −13.3604 + 5.53407i −0.650375 + 0.269394i
\(423\) 10.5547 + 10.5547i 0.513187 + 0.513187i
\(424\) 23.6843 1.15021
\(425\) −6.75155 + 17.6872i −0.327499 + 0.857954i
\(426\) 14.1312 0.684659
\(427\) −12.7346 12.7346i −0.616272 0.616272i
\(428\) −26.7439 + 11.0777i −1.29272 + 0.535460i
\(429\) 6.95285i 0.335687i
\(430\) −0.556127 1.34261i −0.0268188 0.0647463i
\(431\) 12.9800 + 5.37650i 0.625225 + 0.258977i 0.672723 0.739895i \(-0.265125\pi\)
−0.0474977 + 0.998871i \(0.515125\pi\)
\(432\) 0.539140 1.30160i 0.0259394 0.0626232i
\(433\) 19.5323 19.5323i 0.938662 0.938662i −0.0595629 0.998225i \(-0.518971\pi\)
0.998225 + 0.0595629i \(0.0189707\pi\)
\(434\) 40.5433 40.5433i 1.94614 1.94614i
\(435\) −1.92593 + 4.64960i −0.0923412 + 0.222931i
\(436\) 10.3964 + 4.30634i 0.497899 + 0.206236i
\(437\) 1.32444 + 3.19747i 0.0633564 + 0.152956i
\(438\) 4.37241i 0.208922i
\(439\) −29.5258 + 12.2300i −1.40919 + 0.583705i −0.952119 0.305727i \(-0.901101\pi\)
−0.457069 + 0.889431i \(0.651101\pi\)
\(440\) −3.27373 3.27373i −0.156069 0.156069i
\(441\) 14.6510 0.697666
\(442\) −8.57289 + 22.4585i −0.407771 + 1.06824i
\(443\) −12.6819 −0.602534 −0.301267 0.953540i \(-0.597410\pi\)
−0.301267 + 0.953540i \(0.597410\pi\)
\(444\) −13.2514 13.2514i −0.628882 0.628882i
\(445\) 0.0155653 0.00644738i 0.000737868 0.000305635i
\(446\) 23.5486i 1.11506i
\(447\) 8.29664 + 20.0298i 0.392417 + 0.947379i
\(448\) −45.4986 18.8461i −2.14961 0.890396i
\(449\) 3.27292 7.90153i 0.154459 0.372896i −0.827641 0.561258i \(-0.810318\pi\)
0.982100 + 0.188362i \(0.0603177\pi\)
\(450\) 14.8009 14.8009i 0.697722 0.697722i
\(451\) −1.52972 + 1.52972i −0.0720318 + 0.0720318i
\(452\) −9.75326 + 23.5465i −0.458755 + 1.10753i
\(453\) 12.6777 + 5.25129i 0.595652 + 0.246727i
\(454\) 20.4978 + 49.4860i 0.962008 + 2.32249i
\(455\) 6.19687i 0.290514i
\(456\) 2.52986 1.04790i 0.118472 0.0490725i
\(457\) 23.8166 + 23.8166i 1.11409 + 1.11409i 0.992591 + 0.121503i \(0.0387714\pi\)
0.121503 + 0.992591i \(0.461229\pi\)
\(458\) 40.7655 1.90485
\(459\) 0.577400 + 20.5797i 0.0269507 + 0.960577i
\(460\) 6.81339 0.317676
\(461\) 2.21754 + 2.21754i 0.103281 + 0.103281i 0.756859 0.653578i \(-0.226733\pi\)
−0.653578 + 0.756859i \(0.726733\pi\)
\(462\) 21.5553 8.92850i 1.00284 0.415391i
\(463\) 29.1181i 1.35323i −0.736336 0.676617i \(-0.763445\pi\)
0.736336 0.676617i \(-0.236555\pi\)
\(464\) −0.852292 2.05761i −0.0395667 0.0955224i
\(465\) −3.92590 1.62616i −0.182059 0.0754115i
\(466\) 14.9432 36.0762i 0.692233 1.67120i
\(467\) 18.2843 18.2843i 0.846095 0.846095i −0.143548 0.989643i \(-0.545851\pi\)
0.989643 + 0.143548i \(0.0458512\pi\)
\(468\) 11.5263 11.5263i 0.532803 0.532803i
\(469\) 12.3936 29.9207i 0.572281 1.38161i
\(470\) −9.99792 4.14128i −0.461170 0.191023i
\(471\) −8.02134 19.3652i −0.369604 0.892302i
\(472\) 18.7605i 0.863523i
\(473\) −2.51124 + 1.04019i −0.115467 + 0.0478281i
\(474\) −19.2223 19.2223i −0.882908 0.882908i
\(475\) −4.72763 −0.216919
\(476\) 49.4541 1.38753i 2.26672 0.0635971i
\(477\) −17.8106 −0.815491
\(478\) 41.6176 + 41.6176i 1.90355 + 1.90355i
\(479\) 10.0704 4.17129i 0.460128 0.190591i −0.140564 0.990072i \(-0.544892\pi\)
0.600692 + 0.799480i \(0.294892\pi\)
\(480\) 3.80803i 0.173812i
\(481\) 5.80912 + 14.0245i 0.264873 + 0.639460i
\(482\) −12.8394 5.31824i −0.584817 0.242239i
\(483\) −4.85503 + 11.7211i −0.220912 + 0.533328i
\(484\) 8.10089 8.10089i 0.368222 0.368222i
\(485\) −3.44380 + 3.44380i −0.156375 + 0.156375i
\(486\) 13.9326 33.6362i 0.631994 1.52577i
\(487\) −8.04076 3.33059i −0.364362 0.150924i 0.192989 0.981201i \(-0.438182\pi\)
−0.557350 + 0.830277i \(0.688182\pi\)
\(488\) 4.85642 + 11.7244i 0.219840 + 0.530741i
\(489\) 16.8415i 0.761601i
\(490\) −9.81333 + 4.06481i −0.443321 + 0.183630i
\(491\) −1.03090 1.03090i −0.0465239 0.0465239i 0.683462 0.729986i \(-0.260473\pi\)
−0.729986 + 0.683462i \(0.760473\pi\)
\(492\) −2.51896 −0.113564
\(493\) 23.6498 + 22.3590i 1.06513 + 1.00700i
\(494\) −6.00298 −0.270087
\(495\) 2.46185 + 2.46185i 0.110652 + 0.110652i
\(496\) 1.73735 0.719634i 0.0780094 0.0323125i
\(497\) 23.5574i 1.05669i
\(498\) 4.24787 + 10.2553i 0.190351 + 0.459549i
\(499\) −17.2153 7.13082i −0.770663 0.319219i −0.0375222 0.999296i \(-0.511946\pi\)
−0.733141 + 0.680077i \(0.761946\pi\)
\(500\) −7.44009 + 17.9620i −0.332731 + 0.803283i
\(501\) 1.05165 1.05165i 0.0469842 0.0469842i
\(502\) 18.4556 18.4556i 0.823714 0.823714i
\(503\) −0.199984 + 0.482804i −0.00891684 + 0.0215272i −0.928275 0.371894i \(-0.878709\pi\)
0.919358 + 0.393421i \(0.128709\pi\)
\(504\) −18.6726 7.73445i −0.831744 0.344520i
\(505\) 0.411863 + 0.994326i 0.0183277 + 0.0442469i
\(506\) 20.7790i 0.923739i
\(507\) −5.92501 + 2.45422i −0.263139 + 0.108996i
\(508\) −41.8155 41.8155i −1.85526 1.85526i
\(509\) 9.12190 0.404321 0.202160 0.979352i \(-0.435204\pi\)
0.202160 + 0.979352i \(0.435204\pi\)
\(510\) −2.44184 5.45699i −0.108127 0.241639i
\(511\) −7.28903 −0.322448
\(512\) −2.25520 2.25520i −0.0996666 0.0996666i
\(513\) −4.74977 + 1.96742i −0.209707 + 0.0868637i
\(514\) 70.2793i 3.09989i
\(515\) −2.41709 5.83537i −0.106510 0.257137i
\(516\) −2.92404 1.21118i −0.128724 0.0533191i
\(517\) −7.74593 + 18.7003i −0.340666 + 0.822440i
\(518\) 36.0190 36.0190i 1.58258 1.58258i
\(519\) −2.99972 + 2.99972i −0.131673 + 0.131673i
\(520\) −1.67104 + 4.03425i −0.0732800 + 0.176914i
\(521\) −7.65588 3.17117i −0.335410 0.138931i 0.208621 0.977997i \(-0.433103\pi\)
−0.544031 + 0.839065i \(0.683103\pi\)
\(522\) −13.7703 33.2445i −0.602710 1.45507i
\(523\) 2.41846i 0.105752i 0.998601 + 0.0528760i \(0.0168388\pi\)
−0.998601 + 0.0528760i \(0.983161\pi\)
\(524\) 62.8498 26.0332i 2.74560 1.13727i
\(525\) −12.2543 12.2543i −0.534823 0.534823i
\(526\) −54.2052 −2.36346
\(527\) −18.8788 + 19.9688i −0.822375 + 0.869853i
\(528\) 0.765203 0.0333012
\(529\) −8.27388 8.27388i −0.359734 0.359734i
\(530\) 11.9296 4.94142i 0.518191 0.214642i
\(531\) 14.1079i 0.612231i
\(532\) 4.72782 + 11.4140i 0.204977 + 0.494858i
\(533\) 1.88509 + 0.780830i 0.0816523 + 0.0338215i
\(534\) 0.0228949 0.0552732i 0.000990760 0.00239191i
\(535\) −4.12340 + 4.12340i −0.178270 + 0.178270i
\(536\) −16.1368 + 16.1368i −0.697002 + 0.697002i
\(537\) 4.29810 10.3765i 0.185477 0.447781i
\(538\) −29.5170 12.2264i −1.27257 0.527116i
\(539\) 7.60291 + 18.3551i 0.327481 + 0.790608i
\(540\) 10.1211i 0.435544i
\(541\) 24.6940 10.2286i 1.06168 0.439762i 0.217632 0.976031i \(-0.430167\pi\)
0.844047 + 0.536269i \(0.180167\pi\)
\(542\) 20.6593 + 20.6593i 0.887391 + 0.887391i
\(543\) −1.31141 −0.0562781
\(544\) 23.0069 + 8.78221i 0.986413 + 0.376534i
\(545\) 2.26689 0.0971027
\(546\) −15.5601 15.5601i −0.665912 0.665912i
\(547\) −14.8693 + 6.15907i −0.635766 + 0.263343i −0.677201 0.735798i \(-0.736807\pi\)
0.0414349 + 0.999141i \(0.486807\pi\)
\(548\) 35.0030i 1.49525i
\(549\) −3.65203 8.81678i −0.155865 0.376291i
\(550\) 26.2236 + 10.8622i 1.11818 + 0.463164i
\(551\) −3.11017 + 7.50861i −0.132498 + 0.319878i
\(552\) 6.32140 6.32140i 0.269057 0.269057i
\(553\) 32.0445 32.0445i 1.36267 1.36267i
\(554\) −26.3251 + 63.5543i −1.11844 + 2.70016i
\(555\) −3.48780 1.44470i −0.148049 0.0613239i
\(556\) 23.3665 + 56.4118i 0.990962 + 2.39239i
\(557\) 11.2120i 0.475069i 0.971379 + 0.237535i \(0.0763394\pi\)
−0.971379 + 0.237535i \(0.923661\pi\)
\(558\) 28.0700 11.6270i 1.18830 0.492210i
\(559\) 1.81279 + 1.81279i 0.0766729 + 0.0766729i
\(560\) −0.682002 −0.0288199
\(561\) −10.2069 + 4.56727i −0.430934 + 0.192830i
\(562\) 45.8247 1.93300
\(563\) −9.55205 9.55205i −0.402571 0.402571i 0.476567 0.879138i \(-0.341881\pi\)
−0.879138 + 0.476567i \(0.841881\pi\)
\(564\) −21.7743 + 9.01920i −0.916863 + 0.379777i
\(565\) 5.13418i 0.215996i
\(566\) 10.2726 + 24.8003i 0.431790 + 1.04243i
\(567\) 3.60431 + 1.49295i 0.151367 + 0.0626981i
\(568\) 6.35247 15.3362i 0.266544 0.643494i
\(569\) −5.68110 + 5.68110i −0.238164 + 0.238164i −0.816089 0.577926i \(-0.803862\pi\)
0.577926 + 0.816089i \(0.303862\pi\)
\(570\) 1.05564 1.05564i 0.0442161 0.0442161i
\(571\) −1.52567 + 3.68330i −0.0638475 + 0.154142i −0.952583 0.304279i \(-0.901585\pi\)
0.888736 + 0.458420i \(0.151585\pi\)
\(572\) 20.4218 + 8.45898i 0.853877 + 0.353688i
\(573\) 7.13331 + 17.2213i 0.297998 + 0.719431i
\(574\) 6.84688i 0.285783i
\(575\) −14.2596 + 5.90650i −0.594664 + 0.246318i
\(576\) −18.4527 18.4527i −0.768864 0.768864i
\(577\) −7.59744 −0.316286 −0.158143 0.987416i \(-0.550551\pi\)
−0.158143 + 0.987416i \(0.550551\pi\)
\(578\) −38.6009 + 2.16774i −1.60558 + 0.0901662i
\(579\) 1.64060 0.0681809
\(580\) 11.3136 + 11.3136i 0.469772 + 0.469772i
\(581\) −17.0960 + 7.08140i −0.709263 + 0.293786i
\(582\) 17.2945i 0.716882i
\(583\) −9.24254 22.3135i −0.382787 0.924129i
\(584\) 4.74527 + 1.96555i 0.196361 + 0.0813352i
\(585\) 1.25662 3.03376i 0.0519550 0.125430i
\(586\) 27.1003 27.1003i 1.11950 1.11950i
\(587\) −23.2523 + 23.2523i −0.959725 + 0.959725i −0.999220 0.0394943i \(-0.987425\pi\)
0.0394943 + 0.999220i \(0.487425\pi\)
\(588\) −8.85268 + 21.3722i −0.365078 + 0.881377i
\(589\) −6.33991 2.62608i −0.261231 0.108206i
\(590\) 3.91414 + 9.44957i 0.161143 + 0.389032i
\(591\) 6.68896i 0.275147i
\(592\) 1.54348 0.639329i 0.0634365 0.0262763i
\(593\) −21.0995 21.0995i −0.866454 0.866454i 0.125624 0.992078i \(-0.459907\pi\)
−0.992078 + 0.125624i \(0.959907\pi\)
\(594\) 30.8667 1.26648
\(595\) 9.09707 4.07067i 0.372943 0.166881i
\(596\) 68.9251 2.82328
\(597\) 10.6652 + 10.6652i 0.436498 + 0.436498i
\(598\) −18.1063 + 7.49987i −0.740421 + 0.306692i
\(599\) 44.9954i 1.83846i 0.393719 + 0.919231i \(0.371188\pi\)
−0.393719 + 0.919231i \(0.628812\pi\)
\(600\) 4.67326 + 11.2822i 0.190785 + 0.460596i
\(601\) 20.5131 + 8.49680i 0.836747 + 0.346592i 0.759570 0.650426i \(-0.225409\pi\)
0.0771768 + 0.997017i \(0.475409\pi\)
\(602\) 3.29214 7.94793i 0.134178 0.323933i
\(603\) 12.1349 12.1349i 0.494169 0.494169i
\(604\) 30.8480 30.8480i 1.25519 1.25519i
\(605\) 0.883178 2.13218i 0.0359063 0.0866854i
\(606\) 3.53090 + 1.46255i 0.143433 + 0.0594118i
\(607\) −6.64544 16.0435i −0.269730 0.651186i 0.729740 0.683724i \(-0.239641\pi\)
−0.999470 + 0.0325384i \(0.989641\pi\)
\(608\) 6.14956i 0.249397i
\(609\) −27.5246 + 11.4011i −1.11535 + 0.461994i
\(610\) 4.89231 + 4.89231i 0.198084 + 0.198084i
\(611\) 19.0908 0.772330
\(612\) 24.4923 + 9.34920i 0.990041 + 0.377919i
\(613\) −31.6201 −1.27712 −0.638561 0.769571i \(-0.720470\pi\)
−0.638561 + 0.769571i \(0.720470\pi\)
\(614\) 13.8360 + 13.8360i 0.558376 + 0.558376i
\(615\) −0.468811 + 0.194188i −0.0189043 + 0.00783041i
\(616\) 27.4071i 1.10426i
\(617\) −6.13476 14.8106i −0.246976 0.596253i 0.750968 0.660338i \(-0.229587\pi\)
−0.997944 + 0.0640854i \(0.979587\pi\)
\(618\) −20.7217 8.58319i −0.833547 0.345267i
\(619\) −8.95319 + 21.6149i −0.359859 + 0.868777i 0.635460 + 0.772134i \(0.280811\pi\)
−0.995319 + 0.0966432i \(0.969189\pi\)
\(620\) −9.55266 + 9.55266i −0.383644 + 0.383644i
\(621\) −11.8683 + 11.8683i −0.476259 + 0.476259i
\(622\) 22.2113 53.6228i 0.890592 2.15008i
\(623\) 0.0921432 + 0.0381670i 0.00369164 + 0.00152913i
\(624\) −0.276189 0.666778i −0.0110564 0.0266925i
\(625\) 19.0419i 0.761675i
\(626\) 23.8168 9.86524i 0.951911 0.394294i
\(627\) −1.97450 1.97450i −0.0788540 0.0788540i
\(628\) −66.6381 −2.65915
\(629\) −16.7721 + 17.7404i −0.668747 + 0.707356i
\(630\) −11.0190 −0.439007
\(631\) 16.8505 + 16.8505i 0.670808 + 0.670808i 0.957902 0.287094i \(-0.0926892\pi\)
−0.287094 + 0.957902i \(0.592689\pi\)
\(632\) −29.5025 + 12.2203i −1.17355 + 0.486099i
\(633\) 6.34453i 0.252172i
\(634\) −1.73886 4.19797i −0.0690588 0.166723i
\(635\) −11.0060 4.55882i −0.436759 0.180911i
\(636\) 10.7618 25.9813i 0.426734 1.03023i
\(637\) 13.2500 13.2500i 0.524983 0.524983i
\(638\) 34.5034 34.5034i 1.36600 1.36600i
\(639\) −4.77706 + 11.5328i −0.188978 + 0.456232i
\(640\) 10.4272 + 4.31910i 0.412173 + 0.170728i
\(641\) −7.82656 18.8950i −0.309131 0.746307i −0.999734 0.0230734i \(-0.992655\pi\)
0.690603 0.723234i \(-0.257345\pi\)
\(642\) 20.7074i 0.817257i
\(643\) 36.8114 15.2478i 1.45170 0.601314i 0.489098 0.872229i \(-0.337326\pi\)
0.962603 + 0.270915i \(0.0873262\pi\)
\(644\) 28.5202 + 28.5202i 1.12385 + 1.12385i
\(645\) −0.637571 −0.0251043
\(646\) −3.94331 8.81244i −0.155147 0.346721i
\(647\) 14.7545 0.580061 0.290031 0.957017i \(-0.406335\pi\)
0.290031 + 0.957017i \(0.406335\pi\)
\(648\) −1.94387 1.94387i −0.0763624 0.0763624i
\(649\) 17.6747 7.32109i 0.693791 0.287378i
\(650\) 26.7711i 1.05005i
\(651\) −9.62650 23.2404i −0.377292 0.910864i
\(652\) 49.4666 + 20.4897i 1.93726 + 0.802440i
\(653\) −7.28654 + 17.5913i −0.285144 + 0.688399i −0.999940 0.0109339i \(-0.996520\pi\)
0.714796 + 0.699333i \(0.246520\pi\)
\(654\) 5.69208 5.69208i 0.222578 0.222578i
\(655\) 9.69023 9.69023i 0.378628 0.378628i
\(656\) 0.0859350 0.207465i 0.00335520 0.00810017i
\(657\) −3.56844 1.47810i −0.139218 0.0576661i
\(658\) −24.5154 59.1854i −0.955709 2.30729i
\(659\) 19.7181i 0.768108i −0.923311 0.384054i \(-0.874528\pi\)
0.923311 0.384054i \(-0.125472\pi\)
\(660\) −5.07878 + 2.10370i −0.197691 + 0.0818864i
\(661\) 21.3612 + 21.3612i 0.830853 + 0.830853i 0.987634 0.156780i \(-0.0501115\pi\)
−0.156780 + 0.987634i \(0.550111\pi\)
\(662\) 30.7068 1.19345
\(663\) 7.66381 + 7.24551i 0.297638 + 0.281392i
\(664\) 13.0393 0.506024
\(665\) 1.75981 + 1.75981i 0.0682426 + 0.0682426i
\(666\) 24.9376 10.3295i 0.966314 0.400260i
\(667\) 26.5333i 1.02737i
\(668\) −1.80943 4.36834i −0.0700088 0.169016i
\(669\) 9.54500 + 3.95367i 0.369031 + 0.152858i
\(670\) −4.76127 + 11.4947i −0.183944 + 0.444080i
\(671\) 9.15067 9.15067i 0.353258 0.353258i
\(672\) −15.9401 + 15.9401i −0.614901 + 0.614901i
\(673\) 14.5841 35.2091i 0.562176 1.35721i −0.345847 0.938291i \(-0.612408\pi\)
0.908022 0.418922i \(-0.137592\pi\)
\(674\) −27.8614 11.5406i −1.07318 0.444526i
\(675\) −8.77396 21.1822i −0.337710 0.815304i
\(676\) 20.3887i 0.784179i
\(677\) −0.635991 + 0.263436i −0.0244431 + 0.0101247i −0.394872 0.918736i \(-0.629211\pi\)
0.370428 + 0.928861i \(0.379211\pi\)
\(678\) 12.8918 + 12.8918i 0.495105 + 0.495105i
\(679\) −28.8309 −1.10643
\(680\) −7.02002 + 0.196959i −0.269205 + 0.00755305i
\(681\) 23.4996 0.900508
\(682\) 29.1331 + 29.1331i 1.11556 + 1.11556i
\(683\) −35.9530 + 14.8922i −1.37570 + 0.569835i −0.943329 0.331860i \(-0.892324\pi\)
−0.432374 + 0.901694i \(0.642324\pi\)
\(684\) 6.54658i 0.250315i
\(685\) −2.69839 6.51450i −0.103100 0.248906i
\(686\) −2.45710 1.01776i −0.0938124 0.0388584i
\(687\) 6.84427 16.5235i 0.261125 0.630412i
\(688\) 0.199509 0.199509i 0.00760620 0.00760620i
\(689\) −16.1074 + 16.1074i −0.613644 + 0.613644i
\(690\) 1.86517 4.50293i 0.0710060 0.171424i
\(691\) 1.98209 + 0.821007i 0.0754021 + 0.0312326i 0.420066 0.907494i \(-0.362007\pi\)
−0.344664 + 0.938726i \(0.612007\pi\)
\(692\) 5.16121 + 12.4603i 0.196200 + 0.473668i
\(693\) 20.6101i 0.782914i
\(694\) 36.9754 15.3157i 1.40357 0.581377i
\(695\) 8.69762 + 8.69762i 0.329919 + 0.329919i
\(696\) 20.9933 0.795749
\(697\) 0.0920335 + 3.28025i 0.00348602 + 0.124248i
\(698\) 29.9240 1.13264
\(699\) −12.1139 12.1139i −0.458191 0.458191i
\(700\) −50.9020 + 21.0843i −1.92392 + 0.796912i
\(701\) 19.8333i 0.749095i 0.927208 + 0.374548i \(0.122202\pi\)
−0.927208 + 0.374548i \(0.877798\pi\)
\(702\) −11.1409 26.8964i −0.420485 1.01514i
\(703\) −5.63243 2.33303i −0.212431 0.0879918i
\(704\) 13.5422 32.6937i 0.510391 1.23219i
\(705\) −3.35718 + 3.35718i −0.126439 + 0.126439i
\(706\) −6.43584 + 6.43584i −0.242216 + 0.242216i
\(707\) −2.43814 + 5.88618i −0.0916955 + 0.221373i
\(708\) 20.5800 + 8.52452i 0.773444 + 0.320371i
\(709\) 5.25475 + 12.6861i 0.197346 + 0.476436i 0.991313 0.131526i \(-0.0419875\pi\)
−0.793967 + 0.607961i \(0.791988\pi\)
\(710\) 9.05013i 0.339645i
\(711\) 22.1859 9.18970i 0.832036 0.344641i
\(712\) −0.0496945 0.0496945i −0.00186238 0.00186238i
\(713\) −22.4034 −0.839016
\(714\) 12.6211 33.0638i 0.472333 1.23738i
\(715\) 4.45286 0.166527
\(716\) −25.2486 25.2486i −0.943585 0.943585i
\(717\) 23.8563 9.88159i 0.890928 0.369035i
\(718\) 21.3445i 0.796571i
\(719\) −20.0609 48.4313i −0.748145 1.80618i −0.568959 0.822366i \(-0.692654\pi\)
−0.179186 0.983815i \(-0.557346\pi\)
\(720\) −0.333883 0.138299i −0.0124431 0.00515410i
\(721\) 14.3086 34.5440i 0.532880 1.28649i
\(722\) −28.8494 + 28.8494i −1.07366 + 1.07366i
\(723\) −4.31129 + 4.31129i −0.160339 + 0.160339i
\(724\) −1.59549 + 3.85185i −0.0592959 + 0.143153i
\(725\) −33.4856 13.8702i −1.24363 0.515127i
\(726\) −3.13620 7.57146i −0.116395 0.281003i
\(727\) 24.8956i 0.923325i −0.887056 0.461663i \(-0.847253\pi\)
0.887056 0.461663i \(-0.152747\pi\)
\(728\) −23.8818 + 9.89217i −0.885119 + 0.366628i
\(729\) −9.10681 9.10681i −0.337289 0.337289i
\(730\) 2.80025 0.103642
\(731\) −1.47039 + 3.85201i −0.0543843 + 0.142472i
\(732\) 15.0682 0.556938
\(733\) 24.5184 + 24.5184i 0.905606 + 0.905606i 0.995914 0.0903077i \(-0.0287851\pi\)
−0.0903077 + 0.995914i \(0.528785\pi\)
\(734\) −72.9055 + 30.1984i −2.69099 + 1.11465i
\(735\) 4.66010i 0.171890i
\(736\) 7.68299 + 18.5484i 0.283199 + 0.683702i
\(737\) 21.5000 + 8.90558i 0.791962 + 0.328041i
\(738\) 1.38844 3.35198i 0.0511090 0.123388i
\(739\) 8.63027 8.63027i 0.317470 0.317470i −0.530325 0.847795i \(-0.677930\pi\)
0.847795 + 0.530325i \(0.177930\pi\)
\(740\) −8.48666 + 8.48666i −0.311976 + 0.311976i
\(741\) −1.00786 + 2.43320i −0.0370248 + 0.0893857i
\(742\) 70.6207 + 29.2521i 2.59257 + 1.07388i
\(743\) −4.20321 10.1475i −0.154201 0.372274i 0.827834 0.560973i \(-0.189573\pi\)
−0.982035 + 0.188699i \(0.939573\pi\)
\(744\) 17.7257i 0.649857i
\(745\) 12.8278 5.31347i 0.469976 0.194670i
\(746\) 2.07684 + 2.07684i 0.0760386 + 0.0760386i
\(747\) −9.80558 −0.358767
\(748\) 0.997028 + 35.5360i 0.0364550 + 1.29933i
\(749\) −34.5203 −1.26134
\(750\) 9.83422 + 9.83422i 0.359095 + 0.359095i
\(751\) −5.00906 + 2.07482i −0.182783 + 0.0757113i −0.472198 0.881492i \(-0.656539\pi\)
0.289415 + 0.957204i \(0.406539\pi\)
\(752\) 2.10105i 0.0766175i
\(753\) −4.38205 10.5792i −0.159691 0.385528i
\(754\) −42.5189 17.6119i −1.54845 0.641388i
\(755\) 3.36311 8.11928i 0.122396 0.295491i
\(756\) −42.3661 + 42.3661i −1.54084 + 1.54084i
\(757\) −2.23033 + 2.23033i −0.0810626 + 0.0810626i −0.746476 0.665413i \(-0.768256\pi\)
0.665413 + 0.746476i \(0.268256\pi\)
\(758\) −0.437380 + 1.05593i −0.0158864 + 0.0383531i
\(759\) −8.42238 3.48866i −0.305713 0.126630i
\(760\) −0.671114 1.62021i −0.0243439 0.0587713i
\(761\) 9.22097i 0.334260i −0.985935 0.167130i \(-0.946550\pi\)
0.985935 0.167130i \(-0.0534500\pi\)
\(762\) −39.0827 + 16.1886i −1.41582 + 0.586450i
\(763\) 9.48898 + 9.48898i 0.343524 + 0.343524i
\(764\) 59.2607 2.14398
\(765\) 5.27906 0.148114i 0.190865 0.00535506i
\(766\) 19.7883 0.714979
\(767\) −12.7588 12.7588i −0.460694 0.460694i
\(768\) 13.0256 5.39537i 0.470020 0.194688i
\(769\) 20.5337i 0.740464i 0.928939 + 0.370232i \(0.120722\pi\)
−0.928939 + 0.370232i \(0.879278\pi\)
\(770\) −5.71813 13.8048i −0.206067 0.497490i
\(771\) 28.4864 + 11.7994i 1.02591 + 0.424946i
\(772\) 1.99598 4.81873i 0.0718370 0.173430i
\(773\) −5.41911 + 5.41911i −0.194912 + 0.194912i −0.797815 0.602903i \(-0.794011\pi\)
0.602903 + 0.797815i \(0.294011\pi\)
\(774\) 3.22342 3.22342i 0.115864 0.115864i
\(775\) 11.7113 28.2737i 0.420684 1.01562i
\(776\) 18.7693 + 7.77451i 0.673779 + 0.279089i
\(777\) −8.55226 20.6470i −0.306811 0.740706i
\(778\) 67.0145i 2.40258i
\(779\) −0.757079 + 0.313593i −0.0271252 + 0.0112356i
\(780\) 3.66622 + 3.66622i 0.131272 + 0.131272i
\(781\) −16.9276 −0.605716
\(782\) −22.9038 21.6536i −0.819037 0.774332i
\(783\) −39.4146 −1.40856
\(784\) −1.45824 1.45824i −0.0520799 0.0520799i
\(785\) −12.4022 + 5.13715i −0.442653 + 0.183353i
\(786\) 48.6637i 1.73578i
\(787\) 4.86879 + 11.7543i 0.173554 + 0.418995i 0.986590 0.163217i \(-0.0521871\pi\)
−0.813037 + 0.582213i \(0.802187\pi\)
\(788\) −19.6467 8.13792i −0.699884 0.289901i
\(789\) −9.10070 + 21.9710i −0.323994 + 0.782190i
\(790\) −12.3106 + 12.3106i −0.437993 + 0.437993i
\(791\) −21.4912 + 21.4912i −0.764139 + 0.764139i
\(792\) 5.55771 13.4175i 0.197485 0.476770i
\(793\) −11.2765 4.67086i −0.400439 0.165867i
\(794\) 21.0450 + 50.8071i 0.746858 + 1.80308i
\(795\) 5.66509i 0.200920i
\(796\) 44.3011 18.3501i 1.57021 0.650403i
\(797\) 29.4157 + 29.4157i 1.04196 + 1.04196i 0.999080 + 0.0428772i \(0.0136524\pi\)
0.0428772 + 0.999080i \(0.486348\pi\)
\(798\) 8.83766 0.312850
\(799\) 12.5406 + 28.0255i 0.443653 + 0.991469i
\(800\) −27.4248 −0.969611
\(801\) 0.0373703 + 0.0373703i 0.00132041 + 0.00132041i
\(802\) −39.0187 + 16.1621i −1.37780 + 0.570703i
\(803\) 5.23765i 0.184833i
\(804\) 10.3695 + 25.0341i 0.365703 + 0.882886i
\(805\) 7.50661 + 3.10934i 0.264573 + 0.109590i
\(806\) 14.8706 35.9009i 0.523796 1.26456i
\(807\) −9.91145 + 9.91145i −0.348899 + 0.348899i
\(808\) 3.17452 3.17452i 0.111679 0.111679i
\(809\) −5.49174 + 13.2582i −0.193079 + 0.466134i −0.990538 0.137239i \(-0.956177\pi\)
0.797459 + 0.603373i \(0.206177\pi\)
\(810\) −1.38468 0.573553i −0.0486527 0.0201526i
\(811\) −18.7407 45.2441i −0.658076 1.58874i −0.800772 0.598970i \(-0.795577\pi\)
0.142696 0.989767i \(-0.454423\pi\)
\(812\) 94.7154i 3.32386i
\(813\) 11.8424 4.90528i 0.415331 0.172036i
\(814\) 25.8820 + 25.8820i 0.907165 + 0.907165i
\(815\) 10.7859 0.377815
\(816\) 0.797412 0.843449i 0.0279150 0.0295266i
\(817\) −1.02961 −0.0360215
\(818\) −9.32254 9.32254i −0.325955 0.325955i
\(819\) 17.9591 7.43892i 0.627543 0.259937i
\(820\) 1.61324i 0.0563366i
\(821\) 12.1394 + 29.3070i 0.423666 + 1.02282i 0.981257 + 0.192705i \(0.0617259\pi\)
−0.557591 + 0.830116i \(0.688274\pi\)
\(822\) −23.1333 9.58211i −0.806865 0.334214i
\(823\) 10.0406 24.2401i 0.349992 0.844956i −0.646628 0.762806i \(-0.723821\pi\)
0.996620 0.0821504i \(-0.0261788\pi\)
\(824\) −18.6302 + 18.6302i −0.649015 + 0.649015i
\(825\) 8.80555 8.80555i 0.306570 0.306570i
\(826\) −23.1708 + 55.9392i −0.806215 + 1.94637i
\(827\) 21.8165 + 9.03671i 0.758636 + 0.314237i 0.728260 0.685301i \(-0.240330\pi\)
0.0303760 + 0.999539i \(0.490330\pi\)
\(828\) 8.17901 + 19.7459i 0.284240 + 0.686217i
\(829\) 23.9642i 0.832311i 0.909294 + 0.416155i \(0.136623\pi\)
−0.909294 + 0.416155i \(0.863377\pi\)
\(830\) 6.56784 2.72049i 0.227973 0.0944295i
\(831\) 21.3407 + 21.3407i 0.740302 + 0.740302i
\(832\) −33.3763 −1.15712
\(833\) 28.1549 + 10.7473i 0.975509 + 0.372372i
\(834\) 43.6789 1.51248
\(835\) −0.673514 0.673514i −0.0233079 0.0233079i
\(836\) −8.20168 + 3.39725i −0.283661 + 0.117496i
\(837\) 33.2798i 1.15032i
\(838\) −22.9759 55.4687i −0.793689 1.91613i
\(839\) 31.1030 + 12.8833i 1.07380 + 0.444781i 0.848329 0.529470i \(-0.177609\pi\)
0.225467 + 0.974251i \(0.427609\pi\)
\(840\) 2.46013 5.93927i 0.0848825 0.204924i
\(841\) −23.5523 + 23.5523i −0.812149 + 0.812149i
\(842\) −12.9614 + 12.9614i −0.446679 + 0.446679i
\(843\) 7.69368 18.5742i 0.264984 0.639729i
\(844\) 18.6350 + 7.71888i 0.641444 + 0.265695i
\(845\) 1.57177 + 3.79459i 0.0540705 + 0.130538i
\(846\) 33.9463i 1.16710i
\(847\) 12.6220 5.22821i 0.433697 0.179643i
\(848\) 1.77272 + 1.77272i 0.0608754 + 0.0608754i
\(849\) 11.7770 0.404187
\(850\) 39.3003 17.5857i 1.34799 0.603185i
\(851\) −19.9034 −0.682280
\(852\) −13.9371 13.9371i −0.477479 0.477479i
\(853\) −30.4294 + 12.6043i −1.04188 + 0.431563i −0.836988 0.547221i \(-0.815686\pi\)
−0.204896 + 0.978784i \(0.565686\pi\)
\(854\) 40.9575i 1.40154i
\(855\) 0.504678 + 1.21840i 0.0172596 + 0.0416684i
\(856\) 22.4732 + 9.30872i 0.768119 + 0.318165i
\(857\) −0.711156 + 1.71688i −0.0242926 + 0.0586476i −0.935560 0.353167i \(-0.885105\pi\)
0.911268 + 0.411814i \(0.135105\pi\)
\(858\) 11.1810 11.1810i 0.381712 0.381712i
\(859\) −31.0170 + 31.0170i −1.05829 + 1.05829i −0.0600938 + 0.998193i \(0.519140\pi\)
−0.998193 + 0.0600938i \(0.980860\pi\)
\(860\) −0.775682 + 1.87266i −0.0264505 + 0.0638572i
\(861\) −2.77525 1.14955i −0.0945803 0.0391765i
\(862\) −12.2273 29.5194i −0.416464 1.00543i
\(863\) 11.1194i 0.378509i 0.981928 + 0.189255i \(0.0606072\pi\)
−0.981928 + 0.189255i \(0.939393\pi\)
\(864\) −27.5532 + 11.4129i −0.937378 + 0.388275i
\(865\) 1.92113 + 1.92113i 0.0653204 + 0.0653204i
\(866\) −62.8203 −2.13472
\(867\) −5.60219 + 16.0101i −0.190260 + 0.543731i
\(868\) −79.9731 −2.71446
\(869\) 23.0261 + 23.0261i 0.781106 + 0.781106i
\(870\) 10.5742 4.37998i 0.358499 0.148495i
\(871\) 21.9489i 0.743709i
\(872\) −3.61867 8.73625i −0.122544 0.295847i
\(873\) −14.1145 5.84643i −0.477705 0.197872i
\(874\) 3.01206 7.27175i 0.101884 0.245971i
\(875\) −16.3941 + 16.3941i −0.554223 + 0.554223i
\(876\) 4.31237 4.31237i 0.145701 0.145701i
\(877\) −17.3611 + 41.9135i −0.586243 + 1.41532i 0.300825 + 0.953679i \(0.402738\pi\)
−0.887069 + 0.461638i \(0.847262\pi\)
\(878\) 67.1480 + 27.8136i 2.26614 + 0.938664i
\(879\) −6.43463 15.5346i −0.217035 0.523968i
\(880\) 0.490064i 0.0165200i
\(881\) 23.0013 9.52747i 0.774935 0.320989i 0.0400655 0.999197i \(-0.487243\pi\)
0.734870 + 0.678208i \(0.237243\pi\)
\(882\) −23.5605 23.5605i −0.793322 0.793322i
\(883\) 1.59743 0.0537578 0.0268789 0.999639i \(-0.491443\pi\)
0.0268789 + 0.999639i \(0.491443\pi\)
\(884\) 30.6053 13.6950i 1.02937 0.460612i
\(885\) 4.48736 0.150841
\(886\) 20.3939 + 20.3939i 0.685146 + 0.685146i
\(887\) −45.2950 + 18.7618i −1.52086 + 0.629959i −0.977763 0.209713i \(-0.932747\pi\)
−0.543093 + 0.839672i \(0.682747\pi\)
\(888\) 15.7477i 0.528458i
\(889\) −26.9872 65.1528i −0.905121 2.18515i
\(890\) −0.0353990 0.0146627i −0.00118658 0.000491496i
\(891\) −1.07279 + 2.58993i −0.0359397 + 0.0867660i
\(892\) 23.2253 23.2253i 0.777639 0.777639i
\(893\) −5.42148 + 5.42148i −0.181423 + 0.181423i
\(894\) 18.8683 45.5522i 0.631052 1.52349i
\(895\) −6.64551 2.75266i −0.222135 0.0920113i
\(896\) 25.5681 + 61.7268i 0.854170 + 2.06215i
\(897\) 8.59822i 0.287086i
\(898\) −17.9698 + 7.44333i −0.599660 + 0.248387i
\(899\) −37.2008 37.2008i −1.24072 1.24072i
\(900\) −29.1953 −0.973177
\(901\) −34.2267 13.0650i −1.14026 0.435259i
\(902\) 4.91993 0.163816
\(903\) −2.66881 2.66881i −0.0888126 0.0888126i
\(904\) 19.7864 8.19579i 0.658085 0.272588i
\(905\) 0.839875i 0.0279184i
\(906\) −11.9426 28.8319i −0.396765 0.957876i
\(907\) −43.3406 17.9523i −1.43910 0.596096i −0.479522 0.877530i \(-0.659190\pi\)
−0.959580 + 0.281434i \(0.909190\pi\)
\(908\) 28.5901 69.0227i 0.948797 2.29060i
\(909\) −2.38724 + 2.38724i −0.0791799 + 0.0791799i
\(910\) −9.96527 + 9.96527i −0.330345 + 0.330345i
\(911\) 3.07887 7.43305i 0.102007 0.246268i −0.864633 0.502403i \(-0.832449\pi\)
0.966641 + 0.256135i \(0.0824493\pi\)
\(912\) 0.267788 + 0.110921i 0.00886734 + 0.00367297i
\(913\) −5.08846 12.2846i −0.168403 0.406562i
\(914\) 76.5996i 2.53369i
\(915\) 2.80439 1.16162i 0.0927103 0.0384019i
\(916\) −40.2057 40.2057i −1.32843 1.32843i
\(917\) 81.1248 2.67898
\(918\) 32.1659 34.0230i 1.06163 1.12293i
\(919\) 1.37930 0.0454989 0.0227494 0.999741i \(-0.492758\pi\)
0.0227494 + 0.999741i \(0.492758\pi\)
\(920\) −4.04845 4.04845i −0.133473 0.133473i
\(921\) 7.93115 3.28519i 0.261340 0.108251i
\(922\) 7.13211i 0.234883i
\(923\) 6.10975 + 14.7502i 0.201105 + 0.485510i
\(924\) −30.0652 12.4534i −0.989072 0.409687i
\(925\) 10.4044 25.1185i 0.342096 0.825893i
\(926\) −46.8252 + 46.8252i −1.53877 + 1.53877i
\(927\) 14.0099 14.0099i 0.460147 0.460147i
\(928\) −18.0419 + 43.5571i −0.592255 + 1.42983i
\(929\) −10.9036 4.51642i −0.357736 0.148179i 0.196575 0.980489i \(-0.437018\pi\)
−0.554311 + 0.832310i \(0.687018\pi\)
\(930\) 3.69825 + 8.92835i 0.121270 + 0.292772i
\(931\) 7.52557i 0.246640i
\(932\) −50.3188 + 20.8427i −1.64825 + 0.682727i
\(933\) −18.0059 18.0059i −0.589485 0.589485i
\(934\) −58.8064 −1.92420
\(935\) 2.92505 + 6.53684i 0.0956592 + 0.213778i
\(936\) −13.6976 −0.447721
\(937\) 5.07802 + 5.07802i 0.165892 + 0.165892i 0.785171 0.619279i \(-0.212575\pi\)
−0.619279 + 0.785171i \(0.712575\pi\)
\(938\) −68.0461 + 28.1856i −2.22178 + 0.920293i
\(939\) 11.3100i 0.369088i
\(940\) 5.77622 + 13.9450i 0.188400 + 0.454837i
\(941\) −45.5441 18.8650i −1.48469 0.614980i −0.514539 0.857467i \(-0.672037\pi\)
−0.970155 + 0.242487i \(0.922037\pi\)
\(942\) −18.2423 + 44.0407i −0.594365 + 1.43492i
\(943\) −1.89173 + 1.89173i −0.0616030 + 0.0616030i
\(944\) −1.40418 + 1.40418i −0.0457023 + 0.0457023i
\(945\) −4.61885 + 11.1509i −0.150251 + 0.362738i
\(946\) 5.71111 + 2.36562i 0.185684 + 0.0769130i
\(947\) 13.3751 + 32.2903i 0.434632 + 1.04929i 0.977775 + 0.209655i \(0.0672340\pi\)
−0.543143 + 0.839640i \(0.682766\pi\)
\(948\) 37.9166i 1.23147i
\(949\) −4.56395 + 1.89045i −0.148152 + 0.0613666i
\(950\) 7.60257 + 7.60257i 0.246660 + 0.246660i
\(951\) −1.99351 −0.0646440
\(952\) −30.2096 28.5607i −0.979099 0.925657i
\(953\) −19.0277 −0.616367 −0.308184 0.951327i \(-0.599721\pi\)
−0.308184 + 0.951327i \(0.599721\pi\)
\(954\) 28.6415 + 28.6415i 0.927301 + 0.927301i
\(955\) 11.0292 4.56843i 0.356895 0.147831i
\(956\) 82.0923i 2.65505i
\(957\) −8.19241 19.7782i −0.264823 0.639339i
\(958\) −22.9023 9.48642i −0.739938 0.306492i
\(959\) 15.9739 38.5643i 0.515823 1.24531i
\(960\) 5.86934 5.86934i 0.189432 0.189432i
\(961\) 9.49028 9.49028i 0.306138 0.306138i
\(962\) 13.2112 31.8947i 0.425946 1.02832i
\(963\) −16.8999 7.00016i −0.544591 0.225577i
\(964\) 7.41784 + 17.9083i 0.238913 + 0.576786i
\(965\) 1.05070i 0.0338232i
\(966\) 26.6563 11.0414i 0.857652 0.355251i
\(967\) 32.8397 + 32.8397i 1.05605 + 1.05605i 0.998333 + 0.0577200i \(0.0183831\pi\)
0.0577200 + 0.998333i \(0.481617\pi\)
\(968\) −9.62694 −0.309422
\(969\) −4.23401 + 0.118793i −0.136016 + 0.00381618i
\(970\) 11.0761 0.355631
\(971\) −13.4294 13.4294i −0.430969 0.430969i 0.457989 0.888958i \(-0.348570\pi\)
−0.888958 + 0.457989i \(0.848570\pi\)
\(972\) −46.9155 + 19.4330i −1.50482 + 0.623315i
\(973\) 72.8148i 2.33434i
\(974\) 7.57449 + 18.2864i 0.242702 + 0.585935i
\(975\) −10.8512 4.49469i −0.347515 0.143945i
\(976\) −0.514057 + 1.24104i −0.0164545 + 0.0397248i
\(977\) 17.3442 17.3442i 0.554890 0.554890i −0.372958 0.927848i \(-0.621657\pi\)
0.927848 + 0.372958i \(0.121657\pi\)
\(978\) 27.0831 27.0831i 0.866022 0.866022i
\(979\) −0.0274255 + 0.0662110i −0.000876523 + 0.00211611i
\(980\) 13.6876 + 5.66957i 0.437233 + 0.181108i
\(981\) 2.72124 + 6.56966i 0.0868826 + 0.209753i
\(982\) 3.31561i 0.105805i
\(983\) 19.4688 8.06426i 0.620959 0.257210i −0.0499470 0.998752i \(-0.515905\pi\)
0.670906 + 0.741542i \(0.265905\pi\)
\(984\) 1.49674 + 1.49674i 0.0477145 + 0.0477145i
\(985\) −4.28385 −0.136495
\(986\) −2.07585 73.9873i −0.0661086 2.35624i
\(987\) −28.1057 −0.894613
\(988\) 5.92055 + 5.92055i 0.188358 + 0.188358i
\(989\) −3.10552 + 1.28635i −0.0987499 + 0.0409035i
\(990\) 7.91786i 0.251646i
\(991\) 4.17804 + 10.0867i 0.132720 + 0.320414i 0.976243 0.216679i \(-0.0695225\pi\)
−0.843523 + 0.537093i \(0.819522\pi\)
\(992\) −36.7775 15.2337i −1.16769 0.483672i
\(993\) 5.15548 12.4464i 0.163604 0.394976i
\(994\) 37.8830 37.8830i 1.20158 1.20158i
\(995\) 6.83038 6.83038i 0.216538 0.216538i
\(996\) 5.92489 14.3040i 0.187737 0.453238i
\(997\) 25.9821 + 10.7621i 0.822861 + 0.340840i 0.754073 0.656791i \(-0.228087\pi\)
0.0687883 + 0.997631i \(0.478087\pi\)
\(998\) 16.2170 + 39.1513i 0.513341 + 1.23931i
\(999\) 29.5660i 0.935427i
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 731.2.m.b.87.5 116
17.9 even 8 inner 731.2.m.b.689.5 yes 116
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.m.b.87.5 116 1.1 even 1 trivial
731.2.m.b.689.5 yes 116 17.9 even 8 inner