Properties

Label 360.2.bk.a.229.16
Level $360$
Weight $2$
Character 360.229
Analytic conductor $2.875$
Analytic rank $0$
Dimension $136$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(229,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.229");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bk (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(68\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 229.16
Character \(\chi\) \(=\) 360.229
Dual form 360.2.bk.a.349.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.04987 - 0.947511i) q^{2} +(-1.58768 + 0.692297i) q^{3} +(0.204446 + 1.98952i) q^{4} +(0.371573 + 2.20498i) q^{5} +(2.32281 + 0.777522i) q^{6} +(1.08980 - 0.629197i) q^{7} +(1.67045 - 2.28245i) q^{8} +(2.04145 - 2.19829i) q^{9} +O(q^{10})\) \(q+(-1.04987 - 0.947511i) q^{2} +(-1.58768 + 0.692297i) q^{3} +(0.204446 + 1.98952i) q^{4} +(0.371573 + 2.20498i) q^{5} +(2.32281 + 0.777522i) q^{6} +(1.08980 - 0.629197i) q^{7} +(1.67045 - 2.28245i) q^{8} +(2.04145 - 2.19829i) q^{9} +(1.69914 - 2.66701i) q^{10} +(-3.87308 + 2.23612i) q^{11} +(-1.70194 - 3.01719i) q^{12} +(0.185906 - 0.321998i) q^{13} +(-1.74032 - 0.372025i) q^{14} +(-2.11644 - 3.24356i) q^{15} +(-3.91640 + 0.813500i) q^{16} +6.15264i q^{17} +(-4.22616 + 0.373622i) q^{18} -2.88248i q^{19} +(-4.31089 + 1.19005i) q^{20} +(-1.29466 + 1.75343i) q^{21} +(6.18497 + 1.32215i) q^{22} +(-3.76390 - 2.17309i) q^{23} +(-1.07201 + 4.78025i) q^{24} +(-4.72387 + 1.63862i) q^{25} +(-0.500273 + 0.161908i) q^{26} +(-1.71929 + 4.90347i) q^{27} +(1.47461 + 2.03955i) q^{28} +(-6.05317 + 3.49480i) q^{29} +(-0.851325 + 5.41066i) q^{30} +(-3.69538 + 6.40059i) q^{31} +(4.88251 + 2.85677i) q^{32} +(4.60114 - 6.23156i) q^{33} +(5.82970 - 6.45946i) q^{34} +(1.79231 + 2.16920i) q^{35} +(4.79092 + 3.61208i) q^{36} +6.86426 q^{37} +(-2.73118 + 3.02622i) q^{38} +(-0.0722400 + 0.639931i) q^{39} +(5.65345 + 2.83522i) q^{40} +(3.78603 - 6.55760i) q^{41} +(3.02062 - 0.614162i) q^{42} +(-0.759922 - 1.31622i) q^{43} +(-5.24065 - 7.24841i) q^{44} +(5.60574 + 3.68452i) q^{45} +(1.89257 + 5.84780i) q^{46} +(-7.58643 + 4.38003i) q^{47} +(5.65481 - 4.00289i) q^{48} +(-2.70822 + 4.69078i) q^{49} +(6.51205 + 2.75558i) q^{50} +(-4.25946 - 9.76842i) q^{51} +(0.678630 + 0.304032i) q^{52} -7.26213 q^{53} +(6.45112 - 3.51895i) q^{54} +(-6.36973 - 7.70917i) q^{55} +(0.384350 - 3.53846i) q^{56} +(1.99553 + 4.57645i) q^{57} +(9.66638 + 2.06637i) q^{58} +(-0.700805 - 0.404610i) q^{59} +(6.02044 - 4.87384i) q^{60} +(-4.18952 + 2.41882i) q^{61} +(9.94429 - 3.21836i) q^{62} +(0.841614 - 3.68017i) q^{63} +(-2.41917 - 7.62546i) q^{64} +(0.779076 + 0.290272i) q^{65} +(-10.7351 + 2.18269i) q^{66} +(5.20696 - 9.01872i) q^{67} +(-12.2408 + 1.25788i) q^{68} +(7.48029 + 0.844429i) q^{69} +(0.173650 - 3.97560i) q^{70} -6.36723 q^{71} +(-1.60735 - 8.33165i) q^{72} +7.70836i q^{73} +(-7.20656 - 6.50396i) q^{74} +(6.36557 - 5.87193i) q^{75} +(5.73476 - 0.589311i) q^{76} +(-2.81392 + 4.87386i) q^{77} +(0.682184 - 0.603395i) q^{78} +(1.17778 + 2.03998i) q^{79} +(-3.24898 - 8.33331i) q^{80} +(-0.664975 - 8.97540i) q^{81} +(-10.1882 + 3.29731i) q^{82} +(2.73857 + 4.74334i) q^{83} +(-3.75318 - 2.21728i) q^{84} +(-13.5665 + 2.28616i) q^{85} +(-0.449319 + 2.10190i) q^{86} +(7.19105 - 9.73921i) q^{87} +(-1.36595 + 12.5754i) q^{88} +17.0757 q^{89} +(-2.39416 - 9.17976i) q^{90} -0.467885i q^{91} +(3.55390 - 7.93265i) q^{92} +(1.43597 - 12.7204i) q^{93} +(12.1149 + 2.58977i) q^{94} +(6.35580 - 1.07105i) q^{95} +(-9.72959 - 1.15548i) q^{96} +(4.19011 - 2.41916i) q^{97} +(7.28784 - 2.35863i) q^{98} +(-2.99104 + 13.0791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04987 0.947511i −0.742369 0.669991i
\(3\) −1.58768 + 0.692297i −0.916647 + 0.399698i
\(4\) 0.204446 + 1.98952i 0.102223 + 0.994762i
\(5\) 0.371573 + 2.20498i 0.166173 + 0.986097i
\(6\) 2.32281 + 0.777522i 0.948284 + 0.317422i
\(7\) 1.08980 0.629197i 0.411906 0.237814i −0.279702 0.960087i \(-0.590236\pi\)
0.691608 + 0.722273i \(0.256902\pi\)
\(8\) 1.67045 2.28245i 0.590594 0.806968i
\(9\) 2.04145 2.19829i 0.680483 0.732764i
\(10\) 1.69914 2.66701i 0.537315 0.843382i
\(11\) −3.87308 + 2.23612i −1.16778 + 0.674216i −0.953155 0.302481i \(-0.902185\pi\)
−0.214621 + 0.976697i \(0.568852\pi\)
\(12\) −1.70194 3.01719i −0.491307 0.870987i
\(13\) 0.185906 0.321998i 0.0515609 0.0893061i −0.839093 0.543988i \(-0.816914\pi\)
0.890654 + 0.454682i \(0.150247\pi\)
\(14\) −1.74032 0.372025i −0.465120 0.0994278i
\(15\) −2.11644 3.24356i −0.546463 0.837483i
\(16\) −3.91640 + 0.813500i −0.979101 + 0.203375i
\(17\) 6.15264i 1.49224i 0.665814 + 0.746118i \(0.268084\pi\)
−0.665814 + 0.746118i \(0.731916\pi\)
\(18\) −4.22616 + 0.373622i −0.996115 + 0.0880635i
\(19\) 2.88248i 0.661286i −0.943756 0.330643i \(-0.892734\pi\)
0.943756 0.330643i \(-0.107266\pi\)
\(20\) −4.31089 + 1.19005i −0.963944 + 0.266104i
\(21\) −1.29466 + 1.75343i −0.282519 + 0.382630i
\(22\) 6.18497 + 1.32215i 1.31864 + 0.281883i
\(23\) −3.76390 2.17309i −0.784828 0.453121i 0.0533108 0.998578i \(-0.483023\pi\)
−0.838139 + 0.545457i \(0.816356\pi\)
\(24\) −1.07201 + 4.78025i −0.218823 + 0.975765i
\(25\) −4.72387 + 1.63862i −0.944773 + 0.327725i
\(26\) −0.500273 + 0.161908i −0.0981115 + 0.0317527i
\(27\) −1.71929 + 4.90347i −0.330878 + 0.943673i
\(28\) 1.47461 + 2.03955i 0.278675 + 0.385438i
\(29\) −6.05317 + 3.49480i −1.12404 + 0.648968i −0.942430 0.334402i \(-0.891466\pi\)
−0.181614 + 0.983370i \(0.558132\pi\)
\(30\) −0.851325 + 5.41066i −0.155430 + 0.987847i
\(31\) −3.69538 + 6.40059i −0.663710 + 1.14958i 0.315923 + 0.948785i \(0.397686\pi\)
−0.979633 + 0.200795i \(0.935647\pi\)
\(32\) 4.88251 + 2.85677i 0.863114 + 0.505010i
\(33\) 4.60114 6.23156i 0.800956 1.08478i
\(34\) 5.82970 6.45946i 0.999785 1.10779i
\(35\) 1.79231 + 2.16920i 0.302955 + 0.366661i
\(36\) 4.79092 + 3.61208i 0.798486 + 0.602013i
\(37\) 6.86426 1.12848 0.564238 0.825612i \(-0.309170\pi\)
0.564238 + 0.825612i \(0.309170\pi\)
\(38\) −2.73118 + 3.02622i −0.443056 + 0.490918i
\(39\) −0.0722400 + 0.639931i −0.0115677 + 0.102471i
\(40\) 5.65345 + 2.83522i 0.893890 + 0.448287i
\(41\) 3.78603 6.55760i 0.591279 1.02413i −0.402781 0.915296i \(-0.631957\pi\)
0.994060 0.108829i \(-0.0347101\pi\)
\(42\) 3.02062 0.614162i 0.466092 0.0947673i
\(43\) −0.759922 1.31622i −0.115887 0.200722i 0.802247 0.596992i \(-0.203638\pi\)
−0.918134 + 0.396270i \(0.870304\pi\)
\(44\) −5.24065 7.24841i −0.790058 1.09274i
\(45\) 5.60574 + 3.68452i 0.835654 + 0.549257i
\(46\) 1.89257 + 5.84780i 0.279045 + 0.862210i
\(47\) −7.58643 + 4.38003i −1.10659 + 0.638893i −0.937945 0.346784i \(-0.887274\pi\)
−0.168649 + 0.985676i \(0.553941\pi\)
\(48\) 5.65481 4.00289i 0.816201 0.577768i
\(49\) −2.70822 + 4.69078i −0.386889 + 0.670111i
\(50\) 6.51205 + 2.75558i 0.920943 + 0.389697i
\(51\) −4.25946 9.76842i −0.596444 1.36785i
\(52\) 0.678630 + 0.304032i 0.0941090 + 0.0421617i
\(53\) −7.26213 −0.997530 −0.498765 0.866737i \(-0.666213\pi\)
−0.498765 + 0.866737i \(0.666213\pi\)
\(54\) 6.45112 3.51895i 0.877887 0.478868i
\(55\) −6.36973 7.70917i −0.858895 1.03950i
\(56\) 0.384350 3.53846i 0.0513610 0.472847i
\(57\) 1.99553 + 4.57645i 0.264315 + 0.606165i
\(58\) 9.66638 + 2.06637i 1.26926 + 0.271327i
\(59\) −0.700805 0.404610i −0.0912370 0.0526757i 0.453687 0.891161i \(-0.350108\pi\)
−0.544924 + 0.838485i \(0.683442\pi\)
\(60\) 6.02044 4.87384i 0.777235 0.629210i
\(61\) −4.18952 + 2.41882i −0.536413 + 0.309698i −0.743624 0.668598i \(-0.766895\pi\)
0.207211 + 0.978296i \(0.433561\pi\)
\(62\) 9.94429 3.21836i 1.26293 0.408732i
\(63\) 0.841614 3.68017i 0.106033 0.463658i
\(64\) −2.41917 7.62546i −0.302396 0.953182i
\(65\) 0.779076 + 0.290272i 0.0966325 + 0.0360038i
\(66\) −10.7351 + 2.18269i −1.32140 + 0.268670i
\(67\) 5.20696 9.01872i 0.636131 1.10181i −0.350143 0.936696i \(-0.613867\pi\)
0.986274 0.165116i \(-0.0527997\pi\)
\(68\) −12.2408 + 1.25788i −1.48442 + 0.152541i
\(69\) 7.48029 + 0.844429i 0.900521 + 0.101657i
\(70\) 0.173650 3.97560i 0.0207552 0.475175i
\(71\) −6.36723 −0.755652 −0.377826 0.925877i \(-0.623328\pi\)
−0.377826 + 0.925877i \(0.623328\pi\)
\(72\) −1.60735 8.33165i −0.189428 0.981895i
\(73\) 7.70836i 0.902196i 0.892474 + 0.451098i \(0.148967\pi\)
−0.892474 + 0.451098i \(0.851033\pi\)
\(74\) −7.20656 6.50396i −0.837746 0.756070i
\(75\) 6.36557 5.87193i 0.735032 0.678032i
\(76\) 5.73476 0.589311i 0.657822 0.0675986i
\(77\) −2.81392 + 4.87386i −0.320676 + 0.555427i
\(78\) 0.682184 0.603395i 0.0772421 0.0683210i
\(79\) 1.17778 + 2.03998i 0.132511 + 0.229516i 0.924644 0.380833i \(-0.124363\pi\)
−0.792133 + 0.610349i \(0.791029\pi\)
\(80\) −3.24898 8.33331i −0.363247 0.931693i
\(81\) −0.664975 8.97540i −0.0738861 0.997267i
\(82\) −10.1882 + 3.29731i −1.12510 + 0.364127i
\(83\) 2.73857 + 4.74334i 0.300597 + 0.520649i 0.976271 0.216551i \(-0.0694808\pi\)
−0.675674 + 0.737200i \(0.736147\pi\)
\(84\) −3.75318 2.21728i −0.409505 0.241925i
\(85\) −13.5665 + 2.28616i −1.47149 + 0.247969i
\(86\) −0.449319 + 2.10190i −0.0484513 + 0.226653i
\(87\) 7.19105 9.73921i 0.770961 1.04415i
\(88\) −1.36595 + 12.5754i −0.145611 + 1.34055i
\(89\) 17.0757 1.81002 0.905009 0.425392i \(-0.139864\pi\)
0.905009 + 0.425392i \(0.139864\pi\)
\(90\) −2.39416 9.17976i −0.252366 0.967632i
\(91\) 0.467885i 0.0490476i
\(92\) 3.55390 7.93265i 0.370519 0.827036i
\(93\) 1.43597 12.7204i 0.148903 1.31904i
\(94\) 12.1149 + 2.58977i 1.24955 + 0.267115i
\(95\) 6.35580 1.07105i 0.652092 0.109888i
\(96\) −9.72959 1.15548i −0.993022 0.117931i
\(97\) 4.19011 2.41916i 0.425441 0.245628i −0.271962 0.962308i \(-0.587672\pi\)
0.697403 + 0.716680i \(0.254339\pi\)
\(98\) 7.28784 2.35863i 0.736183 0.238257i
\(99\) −2.99104 + 13.0791i −0.300611 + 1.31450i
\(100\) −4.22586 9.06323i −0.422586 0.906323i
\(101\) 12.1808 7.03257i 1.21203 0.699767i 0.248831 0.968547i \(-0.419954\pi\)
0.963202 + 0.268780i \(0.0866204\pi\)
\(102\) −4.78382 + 14.2914i −0.473668 + 1.41506i
\(103\) −4.62270 2.66892i −0.455489 0.262976i 0.254657 0.967031i \(-0.418037\pi\)
−0.710145 + 0.704055i \(0.751371\pi\)
\(104\) −0.424398 0.962203i −0.0416156 0.0943517i
\(105\) −4.34734 2.20318i −0.424257 0.215008i
\(106\) 7.62428 + 6.88094i 0.740535 + 0.668336i
\(107\) 12.7259 1.23026 0.615128 0.788427i \(-0.289104\pi\)
0.615128 + 0.788427i \(0.289104\pi\)
\(108\) −10.1071 2.41808i −0.972553 0.232680i
\(109\) 9.13001i 0.874496i 0.899341 + 0.437248i \(0.144047\pi\)
−0.899341 + 0.437248i \(0.855953\pi\)
\(110\) −0.617141 + 14.1290i −0.0588421 + 1.34715i
\(111\) −10.8982 + 4.75211i −1.03441 + 0.451050i
\(112\) −3.75625 + 3.35074i −0.354932 + 0.316615i
\(113\) −0.767993 0.443401i −0.0722467 0.0417116i 0.463442 0.886128i \(-0.346614\pi\)
−0.535688 + 0.844416i \(0.679948\pi\)
\(114\) 2.24119 6.69546i 0.209907 0.627087i
\(115\) 3.39305 9.10679i 0.316404 0.849212i
\(116\) −8.19052 11.3284i −0.760471 1.05182i
\(117\) −0.328329 1.06602i −0.0303540 0.0985533i
\(118\) 0.352380 + 1.08881i 0.0324392 + 0.100233i
\(119\) 3.87122 + 6.70516i 0.354875 + 0.614661i
\(120\) −10.9387 0.587542i −0.998561 0.0536350i
\(121\) 4.50048 7.79506i 0.409134 0.708642i
\(122\) 6.69030 + 1.43017i 0.605711 + 0.129482i
\(123\) −1.47119 + 13.0324i −0.132653 + 1.17509i
\(124\) −13.4896 6.04347i −1.21140 0.542720i
\(125\) −5.36839 9.80716i −0.480164 0.877179i
\(126\) −4.37059 + 3.06626i −0.389363 + 0.273164i
\(127\) 5.93133i 0.526320i 0.964752 + 0.263160i \(0.0847648\pi\)
−0.964752 + 0.263160i \(0.915235\pi\)
\(128\) −4.68540 + 10.2979i −0.414134 + 0.910216i
\(129\) 2.11773 + 1.56365i 0.186456 + 0.137672i
\(130\) −0.542891 1.04293i −0.0476147 0.0914710i
\(131\) 15.7751 + 9.10776i 1.37828 + 0.795749i 0.991952 0.126613i \(-0.0404108\pi\)
0.386326 + 0.922362i \(0.373744\pi\)
\(132\) 13.3385 + 7.88006i 1.16097 + 0.685871i
\(133\) −1.81365 3.14133i −0.157263 0.272388i
\(134\) −14.0120 + 4.53481i −1.21045 + 0.391748i
\(135\) −11.4509 1.96901i −0.985536 0.169465i
\(136\) 14.0431 + 10.2777i 1.20419 + 0.881306i
\(137\) 2.58698 1.49359i 0.221020 0.127606i −0.385402 0.922749i \(-0.625937\pi\)
0.606423 + 0.795143i \(0.292604\pi\)
\(138\) −7.05321 7.97420i −0.600409 0.678809i
\(139\) −0.501453 0.289514i −0.0425327 0.0245563i 0.478583 0.878042i \(-0.341151\pi\)
−0.521116 + 0.853486i \(0.674484\pi\)
\(140\) −3.94923 + 4.00932i −0.333771 + 0.338849i
\(141\) 9.01253 12.2061i 0.758992 1.02794i
\(142\) 6.68476 + 6.03302i 0.560972 + 0.506280i
\(143\) 1.66283i 0.139053i
\(144\) −6.20683 + 10.2701i −0.517236 + 0.855843i
\(145\) −9.95515 12.0485i −0.826730 1.00058i
\(146\) 7.30376 8.09277i 0.604463 0.669762i
\(147\) 1.05237 9.32235i 0.0867983 0.768894i
\(148\) 1.40337 + 13.6566i 0.115356 + 1.12257i
\(149\) −3.14600 1.81634i −0.257730 0.148801i 0.365568 0.930784i \(-0.380875\pi\)
−0.623299 + 0.781984i \(0.714208\pi\)
\(150\) −12.2467 + 0.133305i −0.999941 + 0.0108843i
\(151\) 3.91539 + 6.78166i 0.318630 + 0.551884i 0.980202 0.197998i \(-0.0634439\pi\)
−0.661572 + 0.749881i \(0.730111\pi\)
\(152\) −6.57911 4.81504i −0.533637 0.390552i
\(153\) 13.5253 + 12.5603i 1.09346 + 1.01544i
\(154\) 7.57228 2.45068i 0.610192 0.197482i
\(155\) −15.4863 5.76995i −1.24389 0.463454i
\(156\) −1.28793 0.0128918i −0.103117 0.00103217i
\(157\) −0.820511 + 1.42117i −0.0654839 + 0.113422i −0.896909 0.442216i \(-0.854192\pi\)
0.831425 + 0.555638i \(0.187526\pi\)
\(158\) 0.696387 3.25767i 0.0554016 0.259167i
\(159\) 11.5299 5.02755i 0.914383 0.398711i
\(160\) −4.48490 + 11.8273i −0.354563 + 0.935032i
\(161\) −5.46921 −0.431034
\(162\) −7.80615 + 10.0531i −0.613309 + 0.789843i
\(163\) 3.98567 0.312182 0.156091 0.987743i \(-0.450111\pi\)
0.156091 + 0.987743i \(0.450111\pi\)
\(164\) 13.8205 + 6.19172i 1.07920 + 0.483492i
\(165\) 15.4501 + 7.82993i 1.20279 + 0.609560i
\(166\) 1.61923 7.57470i 0.125677 0.587911i
\(167\) 21.1866 + 12.2321i 1.63947 + 0.946549i 0.981016 + 0.193928i \(0.0621228\pi\)
0.658454 + 0.752621i \(0.271211\pi\)
\(168\) 1.83944 + 5.88403i 0.141916 + 0.453963i
\(169\) 6.43088 + 11.1386i 0.494683 + 0.856816i
\(170\) 16.4091 + 10.4542i 1.25852 + 0.801800i
\(171\) −6.33653 5.88443i −0.484566 0.449994i
\(172\) 2.46330 1.78098i 0.187825 0.135798i
\(173\) −10.3193 17.8735i −0.784559 1.35890i −0.929262 0.369421i \(-0.879556\pi\)
0.144703 0.989475i \(-0.453777\pi\)
\(174\) −16.7777 + 3.41129i −1.27191 + 0.258609i
\(175\) −4.11706 + 4.75802i −0.311220 + 0.359672i
\(176\) 13.3494 11.9083i 1.00625 0.897622i
\(177\) 1.39276 + 0.157225i 0.104686 + 0.0118178i
\(178\) −17.9272 16.1794i −1.34370 1.21270i
\(179\) 19.6649i 1.46982i 0.678163 + 0.734911i \(0.262776\pi\)
−0.678163 + 0.734911i \(0.737224\pi\)
\(180\) −6.18438 + 11.9060i −0.460956 + 0.887423i
\(181\) 11.1512i 0.828863i 0.910081 + 0.414431i \(0.136019\pi\)
−0.910081 + 0.414431i \(0.863981\pi\)
\(182\) −0.443326 + 0.491217i −0.0328615 + 0.0364114i
\(183\) 4.97707 6.74070i 0.367915 0.498287i
\(184\) −11.2474 + 4.96088i −0.829169 + 0.365721i
\(185\) 2.55058 + 15.1355i 0.187522 + 1.11279i
\(186\) −13.5603 + 11.9941i −0.994288 + 0.879452i
\(187\) −13.7581 23.8297i −1.00609 1.74260i
\(188\) −10.2652 14.1979i −0.748665 1.03549i
\(189\) 1.21156 + 6.42558i 0.0881281 + 0.467392i
\(190\) −7.68759 4.89773i −0.557716 0.355319i
\(191\) 3.18969 + 5.52471i 0.230798 + 0.399754i 0.958043 0.286624i \(-0.0925330\pi\)
−0.727245 + 0.686378i \(0.759200\pi\)
\(192\) 9.11995 + 10.4320i 0.658176 + 0.752864i
\(193\) −12.7936 7.38640i −0.920906 0.531685i −0.0369817 0.999316i \(-0.511774\pi\)
−0.883924 + 0.467631i \(0.845108\pi\)
\(194\) −6.69124 1.43037i −0.480403 0.102695i
\(195\) −1.43788 + 0.0784936i −0.102969 + 0.00562105i
\(196\) −9.88610 4.42906i −0.706150 0.316361i
\(197\) −6.08190 −0.433318 −0.216659 0.976247i \(-0.569516\pi\)
−0.216659 + 0.976247i \(0.569516\pi\)
\(198\) 15.5328 10.8973i 1.10387 0.774435i
\(199\) 9.59861 0.680428 0.340214 0.940348i \(-0.389501\pi\)
0.340214 + 0.940348i \(0.389501\pi\)
\(200\) −4.15092 + 13.5192i −0.293514 + 0.955955i
\(201\) −2.02334 + 17.9236i −0.142716 + 1.26423i
\(202\) −19.4516 4.15814i −1.36861 0.292566i
\(203\) −4.39783 + 7.61727i −0.308667 + 0.534627i
\(204\) 18.5637 10.4714i 1.29972 0.733145i
\(205\) 15.8662 + 5.91149i 1.10814 + 0.412877i
\(206\) 2.32440 + 7.18208i 0.161949 + 0.500399i
\(207\) −12.4609 + 3.83790i −0.866092 + 0.266753i
\(208\) −0.466136 + 1.41231i −0.0323207 + 0.0979259i
\(209\) 6.44557 + 11.1641i 0.445849 + 0.772234i
\(210\) 2.47660 + 6.43219i 0.170901 + 0.443864i
\(211\) 6.40284 + 3.69668i 0.440790 + 0.254490i 0.703932 0.710267i \(-0.251426\pi\)
−0.263143 + 0.964757i \(0.584759\pi\)
\(212\) −1.48471 14.4482i −0.101971 0.992304i
\(213\) 10.1091 4.40802i 0.692666 0.302033i
\(214\) −13.3605 12.0579i −0.913304 0.824262i
\(215\) 2.61988 2.16469i 0.178674 0.147630i
\(216\) 8.31994 + 12.1152i 0.566100 + 0.824337i
\(217\) 9.30049i 0.631359i
\(218\) 8.65078 9.58530i 0.585905 0.649199i
\(219\) −5.33648 12.2384i −0.360606 0.826995i
\(220\) 14.0353 14.2488i 0.946260 0.960657i
\(221\) 1.98114 + 1.14381i 0.133266 + 0.0769410i
\(222\) 15.9444 + 5.33711i 1.07012 + 0.358203i
\(223\) −1.26177 + 0.728481i −0.0844941 + 0.0487827i −0.541652 0.840603i \(-0.682201\pi\)
0.457158 + 0.889386i \(0.348868\pi\)
\(224\) 7.11843 + 0.0412495i 0.475620 + 0.00275610i
\(225\) −6.04136 + 13.7296i −0.402757 + 0.915307i
\(226\) 0.386164 + 1.19319i 0.0256872 + 0.0793701i
\(227\) 2.56490 + 4.44253i 0.170238 + 0.294861i 0.938503 0.345271i \(-0.112213\pi\)
−0.768265 + 0.640132i \(0.778880\pi\)
\(228\) −8.69697 + 4.90579i −0.575971 + 0.324894i
\(229\) −23.0734 13.3215i −1.52474 0.880307i −0.999570 0.0293064i \(-0.990670\pi\)
−0.525165 0.851000i \(-0.675997\pi\)
\(230\) −12.1910 + 6.34597i −0.803853 + 0.418441i
\(231\) 1.09345 9.68619i 0.0719435 0.637304i
\(232\) −2.13483 + 19.6540i −0.140158 + 1.29035i
\(233\) 7.99994i 0.524094i −0.965055 0.262047i \(-0.915602\pi\)
0.965055 0.262047i \(-0.0843975\pi\)
\(234\) −0.665361 + 1.43027i −0.0434960 + 0.0934998i
\(235\) −12.4768 15.1004i −0.813896 0.985043i
\(236\) 0.661704 1.47699i 0.0430732 0.0961437i
\(237\) −3.28222 2.42346i −0.213203 0.157421i
\(238\) 2.28893 10.7076i 0.148370 0.694068i
\(239\) 0.466877 0.808654i 0.0301997 0.0523075i −0.850531 0.525926i \(-0.823719\pi\)
0.880730 + 0.473618i \(0.157052\pi\)
\(240\) 10.9275 + 10.9814i 0.705365 + 0.708844i
\(241\) −2.80281 4.85460i −0.180545 0.312712i 0.761522 0.648140i \(-0.224453\pi\)
−0.942066 + 0.335427i \(0.891119\pi\)
\(242\) −12.1108 + 3.91953i −0.778513 + 0.251957i
\(243\) 7.26941 + 13.7897i 0.466333 + 0.884609i
\(244\) −5.66883 7.84062i −0.362909 0.501944i
\(245\) −11.3494 4.22861i −0.725085 0.270156i
\(246\) 13.8929 12.2884i 0.885781 0.783477i
\(247\) −0.928151 0.535868i −0.0590569 0.0340965i
\(248\) 8.43607 + 19.1264i 0.535691 + 1.21453i
\(249\) −7.63177 5.63500i −0.483644 0.357103i
\(250\) −3.65628 + 15.3828i −0.231244 + 0.972896i
\(251\) 19.2296i 1.21376i −0.794792 0.606882i \(-0.792420\pi\)
0.794792 0.606882i \(-0.207580\pi\)
\(252\) 7.49386 + 0.922014i 0.472069 + 0.0580814i
\(253\) 19.4372 1.22200
\(254\) 5.62000 6.22711i 0.352630 0.390724i
\(255\) 19.9565 13.0217i 1.24972 0.815451i
\(256\) 14.6764 6.37199i 0.917277 0.398249i
\(257\) −26.4381 15.2641i −1.64916 0.952145i −0.977405 0.211376i \(-0.932206\pi\)
−0.671759 0.740769i \(-0.734461\pi\)
\(258\) −0.741764 3.64820i −0.0461802 0.227127i
\(259\) 7.48067 4.31897i 0.464826 0.268368i
\(260\) −0.418224 + 1.60933i −0.0259371 + 0.0998067i
\(261\) −4.67464 + 20.4411i −0.289353 + 1.26527i
\(262\) −7.93208 24.5090i −0.490045 1.51417i
\(263\) −9.92751 + 5.73165i −0.612156 + 0.353429i −0.773809 0.633419i \(-0.781651\pi\)
0.161653 + 0.986848i \(0.448318\pi\)
\(264\) −6.53725 20.9114i −0.402340 1.28701i
\(265\) −2.69841 16.0128i −0.165762 0.983661i
\(266\) −1.07235 + 5.01643i −0.0657502 + 0.307577i
\(267\) −27.1107 + 11.8214i −1.65915 + 0.723461i
\(268\) 19.0075 + 8.51553i 1.16107 + 0.520169i
\(269\) 9.32956i 0.568834i 0.958701 + 0.284417i \(0.0917999\pi\)
−0.958701 + 0.284417i \(0.908200\pi\)
\(270\) 10.1563 + 12.9170i 0.618091 + 0.786106i
\(271\) 1.90948 0.115993 0.0579963 0.998317i \(-0.481529\pi\)
0.0579963 + 0.998317i \(0.481529\pi\)
\(272\) −5.00518 24.0962i −0.303483 1.46105i
\(273\) 0.323915 + 0.742851i 0.0196042 + 0.0449594i
\(274\) −4.13118 0.883114i −0.249574 0.0533509i
\(275\) 14.6317 16.9097i 0.882327 1.01969i
\(276\) −0.150696 + 15.0549i −0.00907081 + 0.906196i
\(277\) 6.14089 + 10.6363i 0.368971 + 0.639076i 0.989405 0.145183i \(-0.0463770\pi\)
−0.620434 + 0.784258i \(0.713044\pi\)
\(278\) 0.252142 + 0.779084i 0.0151225 + 0.0467264i
\(279\) 6.52643 + 21.1900i 0.390727 + 1.26861i
\(280\) 7.94505 0.467314i 0.474808 0.0279274i
\(281\) −7.18088 12.4376i −0.428375 0.741968i 0.568354 0.822784i \(-0.307581\pi\)
−0.996729 + 0.0808166i \(0.974247\pi\)
\(282\) −21.0274 + 4.27537i −1.25216 + 0.254594i
\(283\) −15.7086 + 27.2080i −0.933777 + 1.61735i −0.156978 + 0.987602i \(0.550175\pi\)
−0.776800 + 0.629748i \(0.783158\pi\)
\(284\) −1.30176 12.6678i −0.0772450 0.751693i
\(285\) −9.34949 + 6.10059i −0.553816 + 0.361368i
\(286\) 1.57555 1.74575i 0.0931642 0.103228i
\(287\) 9.52864i 0.562458i
\(288\) 16.2474 4.90123i 0.957387 0.288808i
\(289\) −20.8550 −1.22677
\(290\) −0.964520 + 22.0820i −0.0566386 + 1.29670i
\(291\) −4.97777 + 6.74165i −0.291802 + 0.395203i
\(292\) −15.3360 + 1.57594i −0.897470 + 0.0922252i
\(293\) 5.33082 9.23325i 0.311430 0.539412i −0.667242 0.744841i \(-0.732525\pi\)
0.978672 + 0.205428i \(0.0658588\pi\)
\(294\) −9.93788 + 8.79010i −0.579589 + 0.512649i
\(295\) 0.631756 1.69560i 0.0367822 0.0987218i
\(296\) 11.4664 15.6673i 0.666472 0.910645i
\(297\) −4.30580 22.8361i −0.249848 1.32508i
\(298\) 1.58188 + 4.88779i 0.0916359 + 0.283142i
\(299\) −1.39946 + 0.807979i −0.0809329 + 0.0467266i
\(300\) 12.9838 + 11.4640i 0.749617 + 0.661872i
\(301\) −1.65633 0.956282i −0.0954692 0.0551192i
\(302\) 2.31505 10.8297i 0.133216 0.623181i
\(303\) −14.4705 + 19.5982i −0.831310 + 1.12589i
\(304\) 2.34490 + 11.2889i 0.134489 + 0.647465i
\(305\) −6.89016 8.33903i −0.394529 0.477491i
\(306\) −2.29876 26.0020i −0.131411 1.48644i
\(307\) 16.5867 0.946653 0.473326 0.880887i \(-0.343053\pi\)
0.473326 + 0.880887i \(0.343053\pi\)
\(308\) −10.2719 4.60192i −0.585298 0.262219i
\(309\) 9.18706 + 1.03710i 0.522633 + 0.0589986i
\(310\) 10.7915 + 20.7311i 0.612913 + 1.17745i
\(311\) 15.6786 27.1562i 0.889055 1.53989i 0.0480600 0.998844i \(-0.484696\pi\)
0.840995 0.541043i \(-0.181971\pi\)
\(312\) 1.33994 + 1.23386i 0.0758590 + 0.0698535i
\(313\) 9.96330 5.75231i 0.563159 0.325140i −0.191253 0.981541i \(-0.561255\pi\)
0.754412 + 0.656401i \(0.227922\pi\)
\(314\) 2.20800 0.714595i 0.124605 0.0403269i
\(315\) 8.42743 + 0.488287i 0.474832 + 0.0275118i
\(316\) −3.81780 + 2.76029i −0.214768 + 0.155279i
\(317\) 12.1655 + 21.0713i 0.683283 + 1.18348i 0.973973 + 0.226664i \(0.0727819\pi\)
−0.290690 + 0.956817i \(0.593885\pi\)
\(318\) −16.8686 5.64646i −0.945942 0.316638i
\(319\) 15.6296 27.0712i 0.875089 1.51570i
\(320\) 15.9151 8.16764i 0.889680 0.456585i
\(321\) −20.2046 + 8.81009i −1.12771 + 0.491731i
\(322\) 5.74194 + 5.18213i 0.319986 + 0.288789i
\(323\) 17.7349 0.986794
\(324\) 17.7208 3.15797i 0.984490 0.175443i
\(325\) −0.350560 + 1.82570i −0.0194455 + 0.101272i
\(326\) −4.18443 3.77647i −0.231754 0.209159i
\(327\) −6.32068 14.4955i −0.349534 0.801604i
\(328\) −8.64302 19.5956i −0.477231 1.08199i
\(329\) −5.51180 + 9.54672i −0.303875 + 0.526327i
\(330\) −8.80165 22.8596i −0.484515 1.25838i
\(331\) 8.74389 5.04829i 0.480608 0.277479i −0.240062 0.970758i \(-0.577168\pi\)
0.720670 + 0.693279i \(0.243834\pi\)
\(332\) −8.87709 + 6.41820i −0.487194 + 0.352245i
\(333\) 14.0130 15.0896i 0.767909 0.826907i
\(334\) −10.6531 32.9167i −0.582912 1.80112i
\(335\) 21.8209 + 8.13012i 1.19220 + 0.444196i
\(336\) 3.64401 7.92034i 0.198797 0.432090i
\(337\) 2.47105 + 1.42666i 0.134607 + 0.0777152i 0.565791 0.824549i \(-0.308571\pi\)
−0.431184 + 0.902264i \(0.641904\pi\)
\(338\) 3.80238 17.7874i 0.206822 0.967507i
\(339\) 1.52629 + 0.172299i 0.0828968 + 0.00935798i
\(340\) −7.32197 26.5234i −0.397090 1.43843i
\(341\) 33.0533i 1.78994i
\(342\) 1.07696 + 12.1818i 0.0582351 + 0.658716i
\(343\) 15.6248i 0.843659i
\(344\) −4.27363 0.464205i −0.230419 0.0250283i
\(345\) 0.917529 + 16.8077i 0.0493981 + 0.904894i
\(346\) −6.10146 + 28.5424i −0.328017 + 1.53445i
\(347\) −8.86869 + 15.3610i −0.476096 + 0.824622i −0.999625 0.0273854i \(-0.991282\pi\)
0.523529 + 0.852008i \(0.324615\pi\)
\(348\) 20.8466 + 12.3156i 1.11749 + 0.660186i
\(349\) −5.68659 + 3.28316i −0.304396 + 0.175743i −0.644416 0.764675i \(-0.722900\pi\)
0.340020 + 0.940418i \(0.389566\pi\)
\(350\) 8.83064 1.09433i 0.472018 0.0584945i
\(351\) 1.25928 + 1.46519i 0.0672154 + 0.0782061i
\(352\) −25.2984 0.146598i −1.34841 0.00781369i
\(353\) 18.0366 10.4134i 0.959992 0.554251i 0.0638212 0.997961i \(-0.479671\pi\)
0.896170 + 0.443710i \(0.146338\pi\)
\(354\) −1.31325 1.48472i −0.0697982 0.0789122i
\(355\) −2.36590 14.0396i −0.125569 0.745146i
\(356\) 3.49105 + 33.9724i 0.185025 + 1.80054i
\(357\) −10.7882 7.96560i −0.570973 0.421584i
\(358\) 18.6327 20.6455i 0.984769 1.09115i
\(359\) −32.0447 −1.69125 −0.845627 0.533774i \(-0.820773\pi\)
−0.845627 + 0.533774i \(0.820773\pi\)
\(360\) 17.7739 6.63999i 0.936765 0.349958i
\(361\) 10.6913 0.562701
\(362\) 10.5659 11.7073i 0.555331 0.615322i
\(363\) −1.74882 + 15.4917i −0.0917891 + 0.813104i
\(364\) 0.930867 0.0956572i 0.0487907 0.00501380i
\(365\) −16.9968 + 2.86422i −0.889652 + 0.149920i
\(366\) −11.6121 + 2.36102i −0.606977 + 0.123413i
\(367\) 29.0554 16.7752i 1.51668 0.875656i 0.516873 0.856062i \(-0.327096\pi\)
0.999808 0.0195943i \(-0.00623747\pi\)
\(368\) 16.5088 + 5.44876i 0.860579 + 0.284036i
\(369\) −6.68653 21.7098i −0.348087 1.13017i
\(370\) 11.6633 18.3070i 0.606347 0.951737i
\(371\) −7.91427 + 4.56931i −0.410889 + 0.237227i
\(372\) 25.6011 + 0.256261i 1.32735 + 0.0132865i
\(373\) −12.2073 + 21.1436i −0.632069 + 1.09478i 0.355059 + 0.934844i \(0.384461\pi\)
−0.987128 + 0.159932i \(0.948873\pi\)
\(374\) −8.13471 + 38.0539i −0.420636 + 1.96772i
\(375\) 15.3128 + 11.8541i 0.790747 + 0.612143i
\(376\) −2.67558 + 24.6323i −0.137982 + 1.27031i
\(377\) 2.59881i 0.133845i
\(378\) 4.81633 7.89398i 0.247725 0.406023i
\(379\) 17.5073i 0.899290i 0.893207 + 0.449645i \(0.148450\pi\)
−0.893207 + 0.449645i \(0.851550\pi\)
\(380\) 3.43030 + 12.4260i 0.175971 + 0.637443i
\(381\) −4.10624 9.41705i −0.210369 0.482450i
\(382\) 1.88597 8.82248i 0.0964944 0.451397i
\(383\) 12.3525 + 7.13170i 0.631181 + 0.364413i 0.781209 0.624269i \(-0.214603\pi\)
−0.150028 + 0.988682i \(0.547936\pi\)
\(384\) 0.309683 19.5935i 0.0158035 0.999875i
\(385\) −11.7923 4.39364i −0.600993 0.223921i
\(386\) 6.43292 + 19.8769i 0.327427 + 1.01171i
\(387\) −4.44479 1.01647i −0.225941 0.0516702i
\(388\) 5.66963 + 7.84173i 0.287832 + 0.398103i
\(389\) 25.6906 14.8325i 1.30256 0.752036i 0.321721 0.946834i \(-0.395739\pi\)
0.980843 + 0.194798i \(0.0624053\pi\)
\(390\) 1.58395 + 1.28000i 0.0802067 + 0.0648151i
\(391\) 13.3702 23.1579i 0.676162 1.17115i
\(392\) 6.18252 + 14.0171i 0.312264 + 0.707971i
\(393\) −31.3511 3.53914i −1.58145 0.178526i
\(394\) 6.38520 + 5.76267i 0.321682 + 0.290319i
\(395\) −4.06048 + 3.35499i −0.204305 + 0.168808i
\(396\) −26.6326 3.27677i −1.33834 0.164664i
\(397\) −3.18698 −0.159950 −0.0799749 0.996797i \(-0.525484\pi\)
−0.0799749 + 0.996797i \(0.525484\pi\)
\(398\) −10.0773 9.09479i −0.505128 0.455881i
\(399\) 5.05422 + 3.73184i 0.253027 + 0.186825i
\(400\) 17.1675 10.2604i 0.858377 0.513019i
\(401\) −9.31236 + 16.1295i −0.465037 + 0.805468i −0.999203 0.0399115i \(-0.987292\pi\)
0.534166 + 0.845380i \(0.320626\pi\)
\(402\) 19.1070 16.9003i 0.952973 0.842909i
\(403\) 1.37398 + 2.37981i 0.0684430 + 0.118547i
\(404\) 16.4818 + 22.7962i 0.819999 + 1.13415i
\(405\) 19.5435 4.80128i 0.971123 0.238577i
\(406\) 11.8346 3.83013i 0.587341 0.190086i
\(407\) −26.5858 + 15.3493i −1.31781 + 0.760837i
\(408\) −29.4112 6.59569i −1.45607 0.326535i
\(409\) −3.97421 + 6.88353i −0.196512 + 0.340369i −0.947395 0.320066i \(-0.896295\pi\)
0.750883 + 0.660435i \(0.229628\pi\)
\(410\) −11.0562 21.2397i −0.546026 1.04895i
\(411\) −3.07328 + 4.16230i −0.151594 + 0.205311i
\(412\) 4.36478 9.74263i 0.215037 0.479985i
\(413\) −1.01832 −0.0501081
\(414\) 16.7188 + 7.77754i 0.821682 + 0.382245i
\(415\) −9.44139 + 7.80099i −0.463459 + 0.382935i
\(416\) 1.82756 1.04107i 0.0896034 0.0510425i
\(417\) 0.996577 + 0.112501i 0.0488026 + 0.00550919i
\(418\) 3.81107 17.8280i 0.186405 0.871998i
\(419\) −15.5863 8.99874i −0.761439 0.439617i 0.0683730 0.997660i \(-0.478219\pi\)
−0.829812 + 0.558043i \(0.811553\pi\)
\(420\) 3.49447 9.09956i 0.170513 0.444013i
\(421\) −7.92781 + 4.57712i −0.386378 + 0.223075i −0.680590 0.732665i \(-0.738276\pi\)
0.294212 + 0.955740i \(0.404943\pi\)
\(422\) −3.21949 9.94779i −0.156722 0.484251i
\(423\) −5.85873 + 25.6188i −0.284861 + 1.24563i
\(424\) −12.1310 + 16.5755i −0.589136 + 0.804975i
\(425\) −10.0819 29.0643i −0.489042 1.40982i
\(426\) −14.7899 4.95067i −0.716573 0.239861i
\(427\) −3.04383 + 5.27206i −0.147301 + 0.255133i
\(428\) 2.60175 + 25.3184i 0.125761 + 1.22381i
\(429\) −1.15117 2.64004i −0.0555791 0.127462i
\(430\) −4.80159 0.209729i −0.231553 0.0101140i
\(431\) −17.5146 −0.843647 −0.421824 0.906678i \(-0.638610\pi\)
−0.421824 + 0.906678i \(0.638610\pi\)
\(432\) 2.74447 20.6026i 0.132043 0.991244i
\(433\) 5.31270i 0.255312i 0.991819 + 0.127656i \(0.0407454\pi\)
−0.991819 + 0.127656i \(0.959255\pi\)
\(434\) 8.81232 9.76429i 0.423005 0.468701i
\(435\) 24.1467 + 12.2373i 1.15775 + 0.586732i
\(436\) −18.1644 + 1.86659i −0.869915 + 0.0893936i
\(437\) −6.26388 + 10.8494i −0.299642 + 0.518995i
\(438\) −5.99342 + 17.9051i −0.286377 + 0.855538i
\(439\) −1.80194 3.12106i −0.0860020 0.148960i 0.819816 0.572627i \(-0.194076\pi\)
−0.905818 + 0.423668i \(0.860742\pi\)
\(440\) −28.2361 + 1.66080i −1.34611 + 0.0791756i
\(441\) 4.78300 + 15.5294i 0.227762 + 0.739498i
\(442\) −0.996160 3.07800i −0.0473825 0.146406i
\(443\) 5.89373 + 10.2082i 0.280020 + 0.485008i 0.971389 0.237493i \(-0.0763256\pi\)
−0.691370 + 0.722501i \(0.742992\pi\)
\(444\) −11.6825 20.7107i −0.554428 0.982888i
\(445\) 6.34487 + 37.6515i 0.300776 + 1.78485i
\(446\) 2.01493 + 0.430728i 0.0954097 + 0.0203956i
\(447\) 6.25229 + 0.705804i 0.295723 + 0.0333834i
\(448\) −7.43433 6.78810i −0.351239 0.320707i
\(449\) 40.0680 1.89093 0.945464 0.325727i \(-0.105609\pi\)
0.945464 + 0.325727i \(0.105609\pi\)
\(450\) 19.3516 8.69002i 0.912242 0.409651i
\(451\) 33.8641i 1.59460i
\(452\) 0.725143 1.61859i 0.0341079 0.0761321i
\(453\) −10.9113 8.05648i −0.512658 0.378526i
\(454\) 1.51654 7.09434i 0.0711749 0.332954i
\(455\) 1.03168 0.173854i 0.0483657 0.00815038i
\(456\) 13.7790 + 3.09004i 0.645259 + 0.144704i
\(457\) −4.72025 + 2.72524i −0.220804 + 0.127481i −0.606323 0.795219i \(-0.707356\pi\)
0.385518 + 0.922700i \(0.374023\pi\)
\(458\) 11.6018 + 35.8481i 0.542118 + 1.67507i
\(459\) −30.1693 10.5782i −1.40818 0.493748i
\(460\) 18.8119 + 4.88871i 0.877107 + 0.227937i
\(461\) −12.7630 + 7.36870i −0.594430 + 0.343195i −0.766847 0.641830i \(-0.778176\pi\)
0.172417 + 0.985024i \(0.444842\pi\)
\(462\) −10.3257 + 9.13317i −0.480397 + 0.424913i
\(463\) −12.5702 7.25740i −0.584186 0.337280i 0.178609 0.983920i \(-0.442840\pi\)
−0.762795 + 0.646640i \(0.776174\pi\)
\(464\) 20.8636 18.6113i 0.968569 0.864007i
\(465\) 28.5818 1.56028i 1.32545 0.0723561i
\(466\) −7.58003 + 8.39889i −0.351138 + 0.389071i
\(467\) 16.2530 0.752100 0.376050 0.926599i \(-0.377282\pi\)
0.376050 + 0.926599i \(0.377282\pi\)
\(468\) 2.05374 0.871160i 0.0949341 0.0402694i
\(469\) 13.1048i 0.605124i
\(470\) −1.20883 + 27.6753i −0.0557593 + 1.27657i
\(471\) 0.318838 2.82440i 0.0146913 0.130141i
\(472\) −2.09416 + 0.923671i −0.0963917 + 0.0425154i
\(473\) 5.88648 + 3.39856i 0.270660 + 0.156266i
\(474\) 1.14964 + 5.65425i 0.0528047 + 0.259708i
\(475\) 4.72330 + 13.6164i 0.216720 + 0.624765i
\(476\) −12.5486 + 9.07273i −0.575165 + 0.415848i
\(477\) −14.8253 + 15.9643i −0.678802 + 0.730954i
\(478\) −1.25637 + 0.406609i −0.0574649 + 0.0185979i
\(479\) −14.8226 25.6735i −0.677262 1.17305i −0.975802 0.218655i \(-0.929833\pi\)
0.298540 0.954397i \(-0.403500\pi\)
\(480\) −1.06744 21.8829i −0.0487219 0.998812i
\(481\) 1.27610 2.21028i 0.0581853 0.100780i
\(482\) −1.65721 + 7.75238i −0.0754839 + 0.353111i
\(483\) 8.68334 3.78632i 0.395106 0.172283i
\(484\) 16.4286 + 7.36014i 0.746752 + 0.334552i
\(485\) 6.89113 + 8.34020i 0.312910 + 0.378709i
\(486\) 5.43396 21.3652i 0.246489 0.969145i
\(487\) 17.1523i 0.777245i 0.921397 + 0.388622i \(0.127049\pi\)
−0.921397 + 0.388622i \(0.872951\pi\)
\(488\) −1.47756 + 13.6029i −0.0668858 + 0.615774i
\(489\) −6.32797 + 2.75927i −0.286160 + 0.124778i
\(490\) 7.90870 + 15.1931i 0.357278 + 0.686356i
\(491\) 15.2612 + 8.81107i 0.688729 + 0.397638i 0.803136 0.595796i \(-0.203163\pi\)
−0.114406 + 0.993434i \(0.536497\pi\)
\(492\) −26.2291 0.262547i −1.18250 0.0118365i
\(493\) −21.5022 37.2430i −0.968412 1.67734i
\(494\) 0.466695 + 1.44202i 0.0209976 + 0.0648798i
\(495\) −29.9505 1.73534i −1.34617 0.0779976i
\(496\) 9.26573 28.0735i 0.416043 1.26054i
\(497\) −6.93902 + 4.00624i −0.311258 + 0.179705i
\(498\) 2.67313 + 13.1472i 0.119786 + 0.589140i
\(499\) 23.8310 + 13.7588i 1.06682 + 0.615929i 0.927311 0.374291i \(-0.122114\pi\)
0.139510 + 0.990221i \(0.455447\pi\)
\(500\) 18.4140 12.6856i 0.823500 0.567316i
\(501\) −42.1058 4.75321i −1.88115 0.212358i
\(502\) −18.2203 + 20.1886i −0.813211 + 0.901060i
\(503\) 22.1392i 0.987140i −0.869706 0.493570i \(-0.835692\pi\)
0.869706 0.493570i \(-0.164308\pi\)
\(504\) −6.99394 8.06850i −0.311535 0.359400i
\(505\) 20.0327 + 24.2452i 0.891445 + 1.07890i
\(506\) −20.4065 18.4169i −0.907178 0.818732i
\(507\) −17.9214 13.2325i −0.795917 0.587674i
\(508\) −11.8005 + 1.21264i −0.523563 + 0.0538021i
\(509\) −19.1461 11.0540i −0.848634 0.489959i 0.0115557 0.999933i \(-0.496322\pi\)
−0.860190 + 0.509974i \(0.829655\pi\)
\(510\) −33.2899 5.23790i −1.47410 0.231938i
\(511\) 4.85008 + 8.40058i 0.214555 + 0.371620i
\(512\) −21.4459 7.21633i −0.947782 0.318920i
\(513\) 14.1341 + 4.95582i 0.624038 + 0.218805i
\(514\) 13.2937 + 41.0756i 0.586359 + 1.81177i
\(515\) 4.16724 11.1847i 0.183630 0.492855i
\(516\) −2.67795 + 4.53296i −0.117890 + 0.199552i
\(517\) 19.5885 33.9284i 0.861503 1.49217i
\(518\) −11.9460 2.55367i −0.524877 0.112202i
\(519\) 28.7574 + 21.2334i 1.26231 + 0.932041i
\(520\) 1.96394 1.29332i 0.0861245 0.0567157i
\(521\) −24.6602 −1.08039 −0.540193 0.841541i \(-0.681649\pi\)
−0.540193 + 0.841541i \(0.681649\pi\)
\(522\) 24.2759 17.0312i 1.06253 0.745433i
\(523\) −1.28881 −0.0563557 −0.0281778 0.999603i \(-0.508970\pi\)
−0.0281778 + 0.999603i \(0.508970\pi\)
\(524\) −14.8949 + 33.2470i −0.650689 + 1.45240i
\(525\) 3.24260 10.4044i 0.141519 0.454087i
\(526\) 15.8534 + 3.38895i 0.691240 + 0.147765i
\(527\) −39.3805 22.7364i −1.71544 0.990412i
\(528\) −12.9505 + 28.1483i −0.563600 + 1.22500i
\(529\) −2.05536 3.55999i −0.0893636 0.154782i
\(530\) −12.3394 + 19.3681i −0.535988 + 0.841298i
\(531\) −2.32011 + 0.714583i −0.100684 + 0.0310103i
\(532\) 5.87895 4.25052i 0.254885 0.184283i
\(533\) −1.40769 2.43819i −0.0609738 0.105610i
\(534\) 39.6636 + 13.2767i 1.71641 + 0.574540i
\(535\) 4.72860 + 28.0603i 0.204435 + 1.21315i
\(536\) −11.8868 26.9500i −0.513432 1.16406i
\(537\) −13.6140 31.2215i −0.587485 1.34731i
\(538\) 8.83986 9.79481i 0.381114 0.422284i
\(539\) 24.2237i 1.04339i
\(540\) 1.57629 23.1844i 0.0678328 0.997697i
\(541\) 8.60519i 0.369966i 0.982742 + 0.184983i \(0.0592230\pi\)
−0.982742 + 0.184983i \(0.940777\pi\)
\(542\) −2.00470 1.80925i −0.0861092 0.0777140i
\(543\) −7.71995 17.7045i −0.331295 0.759774i
\(544\) −17.5767 + 30.0403i −0.753594 + 1.28797i
\(545\) −20.1315 + 3.39247i −0.862338 + 0.145317i
\(546\) 0.363791 1.08681i 0.0155688 0.0465111i
\(547\) −5.68349 9.84409i −0.243008 0.420903i 0.718561 0.695464i \(-0.244801\pi\)
−0.961570 + 0.274561i \(0.911468\pi\)
\(548\) 3.50043 + 4.84149i 0.149531 + 0.206818i
\(549\) −3.23541 + 14.1477i −0.138084 + 0.603808i
\(550\) −31.3835 + 3.88918i −1.33820 + 0.165835i
\(551\) 10.0737 + 17.4481i 0.429153 + 0.743315i
\(552\) 14.4228 15.6628i 0.613877 0.666654i
\(553\) 2.56710 + 1.48212i 0.109164 + 0.0630260i
\(554\) 3.63092 16.9853i 0.154263 0.721637i
\(555\) −14.5278 22.2646i −0.616670 0.945081i
\(556\) 0.473475 1.05684i 0.0200798 0.0448201i
\(557\) 8.27867 0.350778 0.175389 0.984499i \(-0.443882\pi\)
0.175389 + 0.984499i \(0.443882\pi\)
\(558\) 13.2259 28.4306i 0.559896 1.20356i
\(559\) −0.565095 −0.0239010
\(560\) −8.78404 7.03740i −0.371193 0.297385i
\(561\) 38.3406 + 28.3092i 1.61874 + 1.19521i
\(562\) −4.24583 + 19.8618i −0.179100 + 0.837821i
\(563\) 1.88888 3.27164i 0.0796070 0.137883i −0.823473 0.567355i \(-0.807967\pi\)
0.903080 + 0.429471i \(0.141300\pi\)
\(564\) 26.1270 + 15.4351i 1.10014 + 0.649937i
\(565\) 0.692324 1.85816i 0.0291263 0.0781735i
\(566\) 42.2718 13.6808i 1.77682 0.575047i
\(567\) −6.37198 9.36300i −0.267598 0.393209i
\(568\) −10.6362 + 14.5329i −0.446284 + 0.609787i
\(569\) −21.5011 37.2409i −0.901372 1.56122i −0.825715 0.564088i \(-0.809228\pi\)
−0.0756567 0.997134i \(-0.524105\pi\)
\(570\) 15.5961 + 2.45392i 0.653249 + 0.102784i
\(571\) −37.5876 21.7012i −1.57299 0.908169i −0.995799 0.0915621i \(-0.970814\pi\)
−0.577195 0.816607i \(-0.695853\pi\)
\(572\) −3.30824 + 0.339959i −0.138324 + 0.0142144i
\(573\) −8.88895 6.56325i −0.371341 0.274184i
\(574\) −9.02849 + 10.0038i −0.376842 + 0.417551i
\(575\) 21.3410 + 4.09777i 0.889983 + 0.170889i
\(576\) −21.7016 10.2489i −0.904233 0.427039i
\(577\) 3.43161i 0.142860i −0.997446 0.0714299i \(-0.977244\pi\)
0.997446 0.0714299i \(-0.0227562\pi\)
\(578\) 21.8950 + 19.7604i 0.910713 + 0.821923i
\(579\) 25.4258 + 2.87024i 1.05666 + 0.119283i
\(580\) 21.9355 22.2693i 0.910824 0.924681i
\(581\) 5.96899 + 3.44620i 0.247635 + 0.142972i
\(582\) 11.6138 2.36135i 0.481407 0.0978813i
\(583\) 28.1268 16.2390i 1.16489 0.672551i
\(584\) 17.5940 + 12.8765i 0.728044 + 0.532832i
\(585\) 2.22855 1.12006i 0.0921390 0.0463088i
\(586\) −14.3453 + 4.64269i −0.592597 + 0.191788i
\(587\) 7.33310 + 12.7013i 0.302669 + 0.524238i 0.976740 0.214429i \(-0.0687889\pi\)
−0.674070 + 0.738667i \(0.735456\pi\)
\(588\) 18.7622 + 0.187805i 0.773739 + 0.00774495i
\(589\) 18.4496 + 10.6519i 0.760201 + 0.438902i
\(590\) −2.26986 + 1.18156i −0.0934487 + 0.0486442i
\(591\) 9.65611 4.21049i 0.397199 0.173196i
\(592\) −26.8832 + 5.58407i −1.10489 + 0.229504i
\(593\) 36.7833i 1.51051i 0.655431 + 0.755255i \(0.272487\pi\)
−0.655431 + 0.755255i \(0.727513\pi\)
\(594\) −17.1169 + 28.0547i −0.702315 + 1.15110i
\(595\) −13.3463 + 11.0274i −0.547144 + 0.452080i
\(596\) 2.97047 6.63039i 0.121675 0.271591i
\(597\) −15.2395 + 6.64509i −0.623712 + 0.271966i
\(598\) 2.23482 + 0.477733i 0.0913885 + 0.0195359i
\(599\) −14.9416 + 25.8797i −0.610499 + 1.05742i 0.380657 + 0.924716i \(0.375698\pi\)
−0.991156 + 0.132699i \(0.957635\pi\)
\(600\) −2.76901 24.3379i −0.113044 0.993590i
\(601\) 9.00456 + 15.5963i 0.367303 + 0.636188i 0.989143 0.146956i \(-0.0469477\pi\)
−0.621839 + 0.783145i \(0.713614\pi\)
\(602\) 0.832839 + 2.57336i 0.0339440 + 0.104882i
\(603\) −9.19604 29.8577i −0.374492 1.21590i
\(604\) −12.6918 + 9.17625i −0.516421 + 0.373376i
\(605\) 18.8602 + 7.02703i 0.766776 + 0.285689i
\(606\) 33.7616 6.86453i 1.37147 0.278852i
\(607\) 31.0617 + 17.9335i 1.26075 + 0.727897i 0.973220 0.229874i \(-0.0738314\pi\)
0.287534 + 0.957771i \(0.407165\pi\)
\(608\) 8.23457 14.0737i 0.333956 0.570765i
\(609\) 1.70893 15.1384i 0.0692493 0.613438i
\(610\) −0.667564 + 15.2834i −0.0270289 + 0.618806i
\(611\) 3.25708i 0.131768i
\(612\) −22.2238 + 29.4768i −0.898345 + 1.19153i
\(613\) −8.74067 −0.353032 −0.176516 0.984298i \(-0.556483\pi\)
−0.176516 + 0.984298i \(0.556483\pi\)
\(614\) −17.4138 15.7161i −0.702766 0.634249i
\(615\) −29.2829 + 1.59855i −1.18080 + 0.0644598i
\(616\) 6.42381 + 14.5642i 0.258823 + 0.586808i
\(617\) −4.05942 2.34371i −0.163426 0.0943542i 0.416056 0.909339i \(-0.363412\pi\)
−0.579482 + 0.814985i \(0.696745\pi\)
\(618\) −8.66253 9.79366i −0.348458 0.393959i
\(619\) 28.0606 16.2008i 1.12785 0.651164i 0.184457 0.982841i \(-0.440947\pi\)
0.943393 + 0.331676i \(0.107614\pi\)
\(620\) 8.31334 31.9899i 0.333872 1.28475i
\(621\) 17.1269 14.7200i 0.687280 0.590693i
\(622\) −42.1913 + 13.6548i −1.69172 + 0.547506i
\(623\) 18.6091 10.7440i 0.745557 0.430448i
\(624\) −0.237663 2.56500i −0.00951413 0.102682i
\(625\) 19.6298 15.4813i 0.785193 0.619251i
\(626\) −15.9105 3.40116i −0.635913 0.135938i
\(627\) −17.9623 13.2627i −0.717347 0.529661i
\(628\) −2.99520 1.34187i −0.119521 0.0535466i
\(629\) 42.2333i 1.68395i
\(630\) −8.38503 8.49772i −0.334068 0.338557i
\(631\) −17.7843 −0.707981 −0.353991 0.935249i \(-0.615176\pi\)
−0.353991 + 0.935249i \(0.615176\pi\)
\(632\) 6.62359 + 0.719460i 0.263472 + 0.0286186i
\(633\) −12.7249 1.43647i −0.505768 0.0570947i
\(634\) 7.19309 33.6490i 0.285674 1.33637i
\(635\) −13.0785 + 2.20392i −0.519003 + 0.0874601i
\(636\) 12.3597 + 21.9112i 0.490093 + 0.868835i
\(637\) 1.00695 + 1.74408i 0.0398967 + 0.0691031i
\(638\) −42.0593 + 13.6120i −1.66514 + 0.538905i
\(639\) −12.9984 + 13.9970i −0.514208 + 0.553714i
\(640\) −24.4477 6.50477i −0.966379 0.257123i
\(641\) 2.56554 + 4.44364i 0.101333 + 0.175513i 0.912234 0.409670i \(-0.134356\pi\)
−0.810901 + 0.585183i \(0.801023\pi\)
\(642\) 29.5598 + 9.89465i 1.16663 + 0.390511i
\(643\) −3.59767 + 6.23134i −0.141878 + 0.245740i −0.928204 0.372072i \(-0.878647\pi\)
0.786326 + 0.617812i \(0.211981\pi\)
\(644\) −1.11816 10.8811i −0.0440616 0.428776i
\(645\) −2.66092 + 5.25056i −0.104774 + 0.206741i
\(646\) −18.6193 16.8040i −0.732565 0.661143i
\(647\) 16.1680i 0.635631i −0.948153 0.317816i \(-0.897051\pi\)
0.948153 0.317816i \(-0.102949\pi\)
\(648\) −21.5967 13.4752i −0.848400 0.529356i
\(649\) 3.61903 0.142059
\(650\) 2.09792 1.58459i 0.0822870 0.0621527i
\(651\) −6.43871 14.7662i −0.252353 0.578733i
\(652\) 0.814855 + 7.92958i 0.0319122 + 0.310546i
\(653\) 22.1523 38.3690i 0.866888 1.50149i 0.00172690 0.999999i \(-0.499450\pi\)
0.865161 0.501495i \(-0.167216\pi\)
\(654\) −7.09878 + 21.2073i −0.277584 + 0.829271i
\(655\) −14.2208 + 38.1680i −0.555653 + 1.49135i
\(656\) −9.49302 + 28.7622i −0.370640 + 1.12297i
\(657\) 16.9452 + 15.7362i 0.661097 + 0.613929i
\(658\) 14.8323 4.80030i 0.578222 0.187135i
\(659\) 17.4430 10.0707i 0.679482 0.392299i −0.120178 0.992752i \(-0.538346\pi\)
0.799660 + 0.600453i \(0.205013\pi\)
\(660\) −12.4191 + 32.3392i −0.483413 + 1.25880i
\(661\) 34.8999 + 20.1494i 1.35745 + 0.783723i 0.989279 0.146036i \(-0.0466517\pi\)
0.368168 + 0.929759i \(0.379985\pi\)
\(662\) −13.9632 2.98490i −0.542697 0.116011i
\(663\) −3.93727 0.444467i −0.152911 0.0172617i
\(664\) 15.4011 + 1.67288i 0.597678 + 0.0649203i
\(665\) 6.25266 5.16629i 0.242468 0.200340i
\(666\) −29.0094 + 2.56463i −1.12409 + 0.0993776i
\(667\) 30.3780 1.17624
\(668\) −20.0045 + 44.6521i −0.773999 + 1.72764i
\(669\) 1.49895 2.03011i 0.0579529 0.0784886i
\(670\) −15.2056 29.2111i −0.587445 1.12852i
\(671\) 10.8175 18.7365i 0.417607 0.723316i
\(672\) −11.3303 + 4.86258i −0.437077 + 0.187578i
\(673\) 34.3878 19.8538i 1.32555 0.765308i 0.340944 0.940084i \(-0.389253\pi\)
0.984608 + 0.174775i \(0.0559200\pi\)
\(674\) −1.24250 3.83916i −0.0478593 0.147879i
\(675\) 0.0867669 25.9806i 0.00333966 0.999994i
\(676\) −20.8457 + 15.0716i −0.801760 + 0.579678i
\(677\) 19.9651 + 34.5806i 0.767323 + 1.32904i 0.939010 + 0.343890i \(0.111745\pi\)
−0.171687 + 0.985151i \(0.554922\pi\)
\(678\) −1.43915 1.62707i −0.0552702 0.0624872i
\(679\) 3.04426 5.27281i 0.116828 0.202352i
\(680\) −17.4441 + 34.7837i −0.668950 + 1.33389i
\(681\) −7.14778 5.27764i −0.273904 0.202240i
\(682\) −31.3184 + 34.7016i −1.19924 + 1.32879i
\(683\) −35.7856 −1.36930 −0.684649 0.728873i \(-0.740044\pi\)
−0.684649 + 0.728873i \(0.740044\pi\)
\(684\) 10.4117 13.8097i 0.398102 0.528028i
\(685\) 4.25459 + 5.14925i 0.162560 + 0.196743i
\(686\) 14.8046 16.4040i 0.565244 0.626306i
\(687\) 45.8556 + 5.17651i 1.74950 + 0.197496i
\(688\) 4.04691 + 4.53667i 0.154287 + 0.172959i
\(689\) −1.35007 + 2.33839i −0.0514335 + 0.0890855i
\(690\) 14.9622 18.5152i 0.569599 0.704861i
\(691\) 10.5688 6.10193i 0.402058 0.232128i −0.285314 0.958434i \(-0.592098\pi\)
0.687372 + 0.726306i \(0.258764\pi\)
\(692\) 33.4500 24.1846i 1.27158 0.919360i
\(693\) 4.96968 + 16.1355i 0.188783 + 0.612939i
\(694\) 23.8657 7.72386i 0.905929 0.293194i
\(695\) 0.452046 1.21327i 0.0171471 0.0460219i
\(696\) −10.2170 32.6821i −0.387273 1.23881i
\(697\) 40.3466 + 23.2941i 1.52824 + 0.882327i
\(698\) 9.08100 + 1.94123i 0.343721 + 0.0734766i
\(699\) 5.53834 + 12.7013i 0.209479 + 0.480409i
\(700\) −10.3079 7.21822i −0.389602 0.272823i
\(701\) 23.5648i 0.890029i 0.895523 + 0.445015i \(0.146802\pi\)
−0.895523 + 0.445015i \(0.853198\pi\)
\(702\) 0.0662056 2.73144i 0.00249877 0.103092i
\(703\) 19.7861i 0.746246i
\(704\) 26.4211 + 24.1244i 0.995782 + 0.909223i
\(705\) 30.2631 + 15.3370i 1.13977 + 0.577624i
\(706\) −28.8029 6.15714i −1.08401 0.231727i
\(707\) 8.84975 15.3282i 0.332829 0.576477i
\(708\) −0.0280582 + 2.80308i −0.00105449 + 0.105346i
\(709\) 11.5103 6.64548i 0.432279 0.249576i −0.268038 0.963408i \(-0.586375\pi\)
0.700317 + 0.713832i \(0.253042\pi\)
\(710\) −10.8188 + 16.9815i −0.406023 + 0.637303i
\(711\) 6.88886 + 1.57540i 0.258352 + 0.0590823i
\(712\) 28.5241 38.9744i 1.06899 1.46063i
\(713\) 27.8181 16.0608i 1.04180 0.601481i
\(714\) 3.77872 + 18.5848i 0.141415 + 0.695518i
\(715\) −3.66650 + 0.617863i −0.137119 + 0.0231068i
\(716\) −39.1237 + 4.02041i −1.46212 + 0.150250i
\(717\) −0.181421 + 1.60710i −0.00677530 + 0.0600183i
\(718\) 33.6427 + 30.3627i 1.25553 + 1.13313i
\(719\) −44.7322 −1.66823 −0.834115 0.551591i \(-0.814021\pi\)
−0.834115 + 0.551591i \(0.814021\pi\)
\(720\) −24.9517 9.86982i −0.929894 0.367826i
\(721\) −6.71710 −0.250158
\(722\) −11.2245 10.1301i −0.417732 0.377005i
\(723\) 7.81078 + 5.76717i 0.290486 + 0.214484i
\(724\) −22.1856 + 2.27982i −0.824521 + 0.0847288i
\(725\) 22.8677 26.4278i 0.849285 0.981504i
\(726\) 16.5146 14.6072i 0.612914 0.542126i
\(727\) −39.3588 + 22.7238i −1.45974 + 0.842780i −0.998998 0.0447553i \(-0.985749\pi\)
−0.460740 + 0.887535i \(0.652416\pi\)
\(728\) −1.06792 0.781580i −0.0395799 0.0289673i
\(729\) −21.0881 16.8610i −0.781039 0.624482i
\(730\) 20.5583 + 13.0976i 0.760895 + 0.484763i
\(731\) 8.09826 4.67553i 0.299525 0.172931i
\(732\) 14.4283 + 8.52388i 0.533286 + 0.315052i
\(733\) 3.53846 6.12880i 0.130696 0.226372i −0.793249 0.608897i \(-0.791612\pi\)
0.923945 + 0.382525i \(0.124945\pi\)
\(734\) −46.3990 9.91863i −1.71262 0.366103i
\(735\) 20.9466 1.14347i 0.772627 0.0421777i
\(736\) −12.1693 21.3627i −0.448565 0.787440i
\(737\) 46.5736i 1.71556i
\(738\) −13.5503 + 29.1280i −0.498794 + 1.07222i
\(739\) 10.1856i 0.374682i −0.982295 0.187341i \(-0.940013\pi\)
0.982295 0.187341i \(-0.0599869\pi\)
\(740\) −29.5911 + 8.16883i −1.08779 + 0.300292i
\(741\) 1.84459 + 0.208230i 0.0677626 + 0.00764953i
\(742\) 12.6384 + 2.70169i 0.463971 + 0.0991822i
\(743\) 16.3550 + 9.44258i 0.600008 + 0.346415i 0.769045 0.639195i \(-0.220732\pi\)
−0.169037 + 0.985610i \(0.554066\pi\)
\(744\) −26.6349 24.5263i −0.976484 0.899179i
\(745\) 2.83603 7.61177i 0.103904 0.278874i
\(746\) 32.8499 10.6315i 1.20272 0.389246i
\(747\) 16.0179 + 3.66311i 0.586064 + 0.134026i
\(748\) 44.5969 32.2439i 1.63062 1.17895i
\(749\) 13.8687 8.00708i 0.506750 0.292572i
\(750\) −4.84449 26.9542i −0.176896 0.984230i
\(751\) −13.5515 + 23.4719i −0.494501 + 0.856501i −0.999980 0.00633801i \(-0.997983\pi\)
0.505479 + 0.862839i \(0.331316\pi\)
\(752\) 26.1484 23.3255i 0.953533 0.850594i
\(753\) 13.3126 + 30.5305i 0.485139 + 1.11259i
\(754\) 2.46240 2.72841i 0.0896753 0.0993627i
\(755\) −13.4986 + 11.1532i −0.491263 + 0.405908i
\(756\) −12.5361 + 3.72411i −0.455935 + 0.135445i
\(757\) −14.6015 −0.530700 −0.265350 0.964152i \(-0.585488\pi\)
−0.265350 + 0.964152i \(0.585488\pi\)
\(758\) 16.5884 18.3804i 0.602517 0.667605i
\(759\) −30.8600 + 13.4563i −1.12015 + 0.488433i
\(760\) 8.17245 16.2960i 0.296446 0.591116i
\(761\) −0.938494 + 1.62552i −0.0340204 + 0.0589250i −0.882534 0.470248i \(-0.844164\pi\)
0.848514 + 0.529173i \(0.177498\pi\)
\(762\) −4.61174 + 13.7774i −0.167066 + 0.499101i
\(763\) 5.74457 + 9.94989i 0.207967 + 0.360210i
\(764\) −10.3394 + 7.47547i −0.374067 + 0.270453i
\(765\) −22.6696 + 34.4901i −0.819620 + 1.24699i
\(766\) −6.21109 19.1914i −0.224416 0.693415i
\(767\) −0.260567 + 0.150438i −0.00940853 + 0.00543202i
\(768\) −18.8902 + 20.2771i −0.681640 + 0.731688i
\(769\) −22.2231 + 38.4915i −0.801385 + 1.38804i 0.117319 + 0.993094i \(0.462570\pi\)
−0.918705 + 0.394946i \(0.870763\pi\)
\(770\) 8.21736 + 15.7861i 0.296133 + 0.568892i
\(771\) 52.5425 + 5.93138i 1.89227 + 0.213613i
\(772\) 12.0798 26.9633i 0.434762 0.970432i
\(773\) −6.05291 −0.217708 −0.108854 0.994058i \(-0.534718\pi\)
−0.108854 + 0.994058i \(0.534718\pi\)
\(774\) 3.70332 + 5.27865i 0.133113 + 0.189737i
\(775\) 6.96833 36.2909i 0.250310 1.30361i
\(776\) 1.47776 13.6048i 0.0530487 0.488384i
\(777\) −8.88690 + 12.0360i −0.318816 + 0.431789i
\(778\) −41.0257 8.76998i −1.47084 0.314419i
\(779\) −18.9021 10.9132i −0.677239 0.391004i
\(780\) −0.450133 2.84464i −0.0161174 0.101855i
\(781\) 24.6608 14.2379i 0.882432 0.509472i
\(782\) −35.9794 + 11.6443i −1.28662 + 0.416401i
\(783\) −6.72947 35.6901i −0.240492 1.27546i
\(784\) 6.79054 20.5741i 0.242519 0.734790i
\(785\) −3.43853 1.28114i −0.122726 0.0457259i
\(786\) 29.5611 + 33.4211i 1.05441 + 1.19209i
\(787\) 9.63082 16.6811i 0.343302 0.594616i −0.641742 0.766921i \(-0.721788\pi\)
0.985044 + 0.172305i \(0.0551213\pi\)
\(788\) −1.24342 12.1001i −0.0442950 0.431048i
\(789\) 11.7937 15.9728i 0.419866 0.568647i
\(790\) 7.44186 + 0.325053i 0.264770 + 0.0115649i
\(791\) −1.11595 −0.0396785
\(792\) 24.8560 + 28.6749i 0.883219 + 1.01892i
\(793\) 1.79869i 0.0638732i
\(794\) 3.34591 + 3.01970i 0.118742 + 0.107165i
\(795\) 15.3699 + 23.5551i 0.545113 + 0.835415i
\(796\) 1.96240 + 19.0967i 0.0695554 + 0.676863i
\(797\) 4.55380 7.88741i 0.161304 0.279387i −0.774033 0.633146i \(-0.781763\pi\)
0.935337 + 0.353759i \(0.115097\pi\)
\(798\) −1.77031 8.70686i −0.0626682 0.308220i
\(799\) −26.9487 46.6766i −0.953378 1.65130i
\(800\) −27.7455 5.49440i −0.980951 0.194256i
\(801\) 34.8591 37.5373i 1.23169 1.32632i
\(802\) 25.0596 8.11027i 0.884886 0.286383i
\(803\) −17.2368 29.8551i −0.608275 1.05356i
\(804\) −36.0731 0.361083i −1.27220 0.0127344i
\(805\) −2.03221 12.0595i −0.0716261 0.425041i
\(806\) 0.812394 3.80035i 0.0286154 0.133862i
\(807\) −6.45883 14.8124i −0.227362 0.521419i
\(808\) 4.29591 39.5496i 0.151130 1.39135i
\(809\) 27.7682 0.976279 0.488140 0.872766i \(-0.337676\pi\)
0.488140 + 0.872766i \(0.337676\pi\)
\(810\) −25.0673 13.4770i −0.880777 0.473532i
\(811\) 12.9219i 0.453748i −0.973924 0.226874i \(-0.927149\pi\)
0.973924 0.226874i \(-0.0728505\pi\)
\(812\) −16.0538 7.19227i −0.563380 0.252399i
\(813\) −3.03164 + 1.32193i −0.106324 + 0.0463620i
\(814\) 42.4552 + 9.07557i 1.48805 + 0.318099i
\(815\) 1.48097 + 8.78832i 0.0518761 + 0.307841i
\(816\) 24.6284 + 34.7920i 0.862166 + 1.21796i
\(817\) −3.79399 + 2.19046i −0.132735 + 0.0766345i
\(818\) 10.6946 3.46119i 0.373928 0.121018i
\(819\) −1.02855 0.955163i −0.0359403 0.0333761i
\(820\) −8.51728 + 32.7747i −0.297436 + 1.14454i
\(821\) −23.5459 + 13.5943i −0.821759 + 0.474443i −0.851023 0.525129i \(-0.824017\pi\)
0.0292636 + 0.999572i \(0.490684\pi\)
\(822\) 7.17036 1.45790i 0.250095 0.0508502i
\(823\) −38.1352 22.0174i −1.32931 0.767478i −0.344118 0.938926i \(-0.611822\pi\)
−0.985193 + 0.171448i \(0.945155\pi\)
\(824\) −13.8137 + 6.09279i −0.481223 + 0.212253i
\(825\) −11.5240 + 36.9766i −0.401214 + 1.28736i
\(826\) 1.06910 + 0.964866i 0.0371987 + 0.0335720i
\(827\) −34.9371 −1.21488 −0.607441 0.794365i \(-0.707804\pi\)
−0.607441 + 0.794365i \(0.707804\pi\)
\(828\) −10.1832 24.0066i −0.353890 0.834287i
\(829\) 38.0705i 1.32224i −0.750279 0.661121i \(-0.770081\pi\)
0.750279 0.661121i \(-0.229919\pi\)
\(830\) 17.3037 + 0.755810i 0.600621 + 0.0262346i
\(831\) −17.1133 12.6358i −0.593653 0.438330i
\(832\) −2.90512 0.638647i −0.100717 0.0221411i
\(833\) −28.8607 16.6627i −0.999964 0.577329i
\(834\) −0.939678 1.06238i −0.0325384 0.0367871i
\(835\) −19.0991 + 51.2612i −0.660953 + 1.77397i
\(836\) −20.8934 + 15.1061i −0.722612 + 0.522454i
\(837\) −25.0317 29.1247i −0.865221 1.00670i
\(838\) 7.83713 + 24.2157i 0.270729 + 0.836516i
\(839\) −5.06506 8.77295i −0.174865 0.302876i 0.765249 0.643734i \(-0.222616\pi\)
−0.940115 + 0.340858i \(0.889282\pi\)
\(840\) −12.2907 + 6.24228i −0.424068 + 0.215379i
\(841\) 9.92721 17.1944i 0.342318 0.592912i
\(842\) 12.6600 + 2.70631i 0.436293 + 0.0932656i
\(843\) 20.0115 + 14.7757i 0.689232 + 0.508902i
\(844\) −6.04560 + 13.4944i −0.208098 + 0.464495i
\(845\) −22.1709 + 18.3188i −0.762701 + 0.630185i
\(846\) 30.4250 21.3451i 1.04603 0.733861i
\(847\) 11.3268i 0.389192i
\(848\) 28.4414 5.90774i 0.976682 0.202873i
\(849\) 6.10411 54.0726i 0.209492 1.85577i
\(850\) −16.9541 + 40.0663i −0.581520 + 1.37426i
\(851\) −25.8364 14.9166i −0.885660 0.511336i
\(852\) 10.8366 + 19.2111i 0.371257 + 0.658163i
\(853\) 0.859119 + 1.48804i 0.0294157 + 0.0509495i 0.880358 0.474309i \(-0.157302\pi\)
−0.850943 + 0.525258i \(0.823969\pi\)
\(854\) 8.19095 2.65091i 0.280289 0.0907123i
\(855\) 10.6206 16.1584i 0.363215 0.552606i
\(856\) 21.2580 29.0462i 0.726583 0.992779i
\(857\) 19.1841 11.0759i 0.655315 0.378346i −0.135175 0.990822i \(-0.543160\pi\)
0.790490 + 0.612475i \(0.209826\pi\)
\(858\) −1.29289 + 3.86244i −0.0441384 + 0.131862i
\(859\) −33.1304 19.1279i −1.13040 0.652634i −0.186361 0.982481i \(-0.559669\pi\)
−0.944034 + 0.329847i \(0.893003\pi\)
\(860\) 4.84232 + 4.76975i 0.165122 + 0.162647i
\(861\) 6.59665 + 15.1284i 0.224813 + 0.515575i
\(862\) 18.3880 + 16.5953i 0.626298 + 0.565237i
\(863\) 19.0063i 0.646981i 0.946231 + 0.323491i \(0.104856\pi\)
−0.946231 + 0.323491i \(0.895144\pi\)
\(864\) −22.4025 + 19.0296i −0.762150 + 0.647401i
\(865\) 35.5763 29.3951i 1.20963 0.999463i
\(866\) 5.03384 5.57763i 0.171057 0.189536i
\(867\) 33.1111 14.4379i 1.12451 0.490336i
\(868\) −18.5035 + 1.90145i −0.628051 + 0.0645394i
\(869\) −9.12329 5.26734i −0.309487 0.178682i
\(870\) −13.7560 35.7268i −0.466370 1.21125i
\(871\) −1.93601 3.35326i −0.0655990 0.113621i
\(872\) 20.8388 + 15.2513i 0.705691 + 0.516473i
\(873\) 3.23587 14.1497i 0.109518 0.478894i
\(874\) 16.8561 5.45530i 0.570167 0.184528i
\(875\) −12.0211 7.31007i −0.406388 0.247126i
\(876\) 23.2576 13.1191i 0.785800 0.443255i
\(877\) 16.1696 28.0065i 0.546008 0.945713i −0.452535 0.891747i \(-0.649480\pi\)
0.998543 0.0539665i \(-0.0171864\pi\)
\(878\) −1.06543 + 4.98406i −0.0359566 + 0.168204i
\(879\) −2.07147 + 18.3500i −0.0698691 + 0.618928i
\(880\) 31.2179 + 25.0104i 1.05235 + 0.843102i
\(881\) 28.4065 0.957040 0.478520 0.878077i \(-0.341173\pi\)
0.478520 + 0.878077i \(0.341173\pi\)
\(882\) 9.69280 20.8358i 0.326373 0.701579i
\(883\) 0.119595 0.00402468 0.00201234 0.999998i \(-0.499359\pi\)
0.00201234 + 0.999998i \(0.499359\pi\)
\(884\) −1.87060 + 4.17537i −0.0629151 + 0.140433i
\(885\) 0.170836 + 3.12943i 0.00574258 + 0.105195i
\(886\) 3.48478 16.3017i 0.117074 0.547666i
\(887\) 24.6042 + 14.2052i 0.826128 + 0.476965i 0.852525 0.522686i \(-0.175070\pi\)
−0.0263972 + 0.999652i \(0.508403\pi\)
\(888\) −7.35854 + 32.8129i −0.246936 + 1.10113i
\(889\) 3.73197 + 6.46397i 0.125166 + 0.216795i
\(890\) 29.0139 45.5410i 0.972550 1.52654i
\(891\) 22.6456 + 33.2754i 0.758656 + 1.11477i
\(892\) −1.70729 2.36138i −0.0571644 0.0790647i
\(893\) 12.6253 + 21.8677i 0.422490 + 0.731775i
\(894\) −5.89532 6.66512i −0.197169 0.222915i
\(895\) −43.3607 + 7.30695i −1.44939 + 0.244244i
\(896\) 1.37327 + 14.1707i 0.0458777 + 0.473410i
\(897\) 1.66253 2.25165i 0.0555103 0.0751805i
\(898\) −42.0662 37.9649i −1.40377 1.26691i
\(899\) 51.6584i 1.72291i
\(900\) −28.5505 9.21246i −0.951683 0.307082i
\(901\) 44.6813i 1.48855i
\(902\) 32.0866 35.5529i 1.06837 1.18378i
\(903\) 3.29175 + 0.371596i 0.109543 + 0.0123660i
\(904\) −2.29494 + 1.01223i −0.0763285 + 0.0336661i
\(905\) −24.5882 + 4.14349i −0.817339 + 0.137734i
\(906\) 3.82183 + 18.7968i 0.126972 + 0.624483i
\(907\) 8.25667 + 14.3010i 0.274158 + 0.474856i 0.969922 0.243414i \(-0.0782675\pi\)
−0.695764 + 0.718270i \(0.744934\pi\)
\(908\) −8.31413 + 6.01118i −0.275914 + 0.199488i
\(909\) 9.40678 41.1335i 0.312003 1.36431i
\(910\) −1.24785 0.795001i −0.0413659 0.0263540i
\(911\) 28.9308 + 50.1096i 0.958519 + 1.66020i 0.726101 + 0.687588i \(0.241330\pi\)
0.232418 + 0.972616i \(0.425336\pi\)
\(912\) −11.5382 16.2999i −0.382070 0.539742i
\(913\) −21.2134 12.2475i −0.702060 0.405335i
\(914\) 7.53784 + 1.61135i 0.249329 + 0.0532987i
\(915\) 16.7124 + 8.46966i 0.552496 + 0.279998i
\(916\) 21.7861 48.6287i 0.719832 1.60674i
\(917\) 22.9223 0.756961
\(918\) 21.6508 + 39.6915i 0.714584 + 1.31001i
\(919\) 11.5750 0.381823 0.190911 0.981607i \(-0.438856\pi\)
0.190911 + 0.981607i \(0.438856\pi\)
\(920\) −15.1179 22.9569i −0.498421 0.756868i
\(921\) −26.3343 + 11.4829i −0.867746 + 0.378375i
\(922\) 20.3813 + 4.35688i 0.671224 + 0.143486i
\(923\) −1.18370 + 2.05024i −0.0389621 + 0.0674843i
\(924\) 19.4944 + 0.195135i 0.641320 + 0.00641947i
\(925\) −32.4258 + 11.2479i −1.06615 + 0.369830i
\(926\) 6.32057 + 19.5297i 0.207707 + 0.641786i
\(927\) −15.3041 + 4.71359i −0.502652 + 0.154815i
\(928\) −39.5385 0.229115i −1.29791 0.00752107i
\(929\) 15.7361 + 27.2557i 0.516285 + 0.894232i 0.999821 + 0.0189077i \(0.00601887\pi\)
−0.483536 + 0.875324i \(0.660648\pi\)
\(930\) −31.4854 25.4434i −1.03245 0.834323i
\(931\) 13.5211 + 7.80639i 0.443135 + 0.255844i
\(932\) 15.9161 1.63556i 0.521348 0.0535744i
\(933\) −6.09248 + 53.9696i −0.199459 + 1.76689i
\(934\) −17.0635 15.3999i −0.558336 0.503900i
\(935\) 47.4318 39.1907i 1.55118 1.28167i
\(936\) −2.98159 1.03134i −0.0974563 0.0337103i
\(937\) 10.8895i 0.355744i −0.984054 0.177872i \(-0.943079\pi\)
0.984054 0.177872i \(-0.0569214\pi\)
\(938\) −12.4170 + 13.7583i −0.405428 + 0.449225i
\(939\) −11.8362 + 16.0304i −0.386260 + 0.523132i
\(940\) 27.4918 27.9101i 0.896684 0.910326i
\(941\) 19.1338 + 11.0469i 0.623744 + 0.360119i 0.778325 0.627861i \(-0.216069\pi\)
−0.154581 + 0.987980i \(0.549403\pi\)
\(942\) −3.01088 + 2.66314i −0.0980999 + 0.0867698i
\(943\) −28.5005 + 16.4548i −0.928104 + 0.535841i
\(944\) 3.07378 + 1.01451i 0.100043 + 0.0330195i
\(945\) −13.7181 + 5.05904i −0.446250 + 0.164571i
\(946\) −2.95985 9.14554i −0.0962331 0.297347i
\(947\) 5.65034 + 9.78667i 0.183611 + 0.318024i 0.943108 0.332487i \(-0.107888\pi\)
−0.759496 + 0.650512i \(0.774555\pi\)
\(948\) 4.15049 7.02551i 0.134802 0.228178i
\(949\) 2.48208 + 1.43303i 0.0805716 + 0.0465180i
\(950\) 7.94289 18.7708i 0.257701 0.609006i
\(951\) −33.9025 25.0323i −1.09936 0.811727i
\(952\) 21.7709 + 2.36477i 0.705599 + 0.0766427i
\(953\) 9.62101i 0.311655i −0.987784 0.155828i \(-0.950196\pi\)
0.987784 0.155828i \(-0.0498044\pi\)
\(954\) 30.6909 2.71329i 0.993654 0.0878459i
\(955\) −10.9967 + 9.08604i −0.355844 + 0.294017i
\(956\) 1.70429 + 0.763536i 0.0551206 + 0.0246945i
\(957\) −6.07342 + 53.8007i −0.196326 + 1.73913i
\(958\) −8.76415 + 40.9984i −0.283157 + 1.32460i
\(959\) 1.87953 3.25544i 0.0606931 0.105123i
\(960\) −19.6136 + 23.9856i −0.633026 + 0.774130i
\(961\) −11.8117 20.4585i −0.381023 0.659951i
\(962\) −3.43400 + 1.11138i −0.110717 + 0.0358322i
\(963\) 25.9792 27.9752i 0.837169 0.901488i
\(964\) 9.08532 6.56875i 0.292618 0.211565i
\(965\) 11.5331 30.9543i 0.371263 0.996453i
\(966\) −12.7039 4.25243i −0.408743 0.136820i
\(967\) 6.34293 + 3.66209i 0.203975 + 0.117765i 0.598508 0.801117i \(-0.295760\pi\)
−0.394533 + 0.918882i \(0.629094\pi\)
\(968\) −10.2740 23.2934i −0.330219 0.748679i
\(969\) −28.1573 + 12.2778i −0.904541 + 0.394420i
\(970\) 0.667658 15.2855i 0.0214372 0.490789i
\(971\) 16.5617i 0.531490i 0.964043 + 0.265745i \(0.0856179\pi\)
−0.964043 + 0.265745i \(0.914382\pi\)
\(972\) −25.9487 + 17.2819i −0.832305 + 0.554318i
\(973\) −0.728646 −0.0233593
\(974\) 16.2520 18.0077i 0.520747 0.577002i
\(975\) −0.707354 3.14132i −0.0226535 0.100603i
\(976\) 14.4401 12.8812i 0.462217 0.412319i
\(977\) 20.3148 + 11.7287i 0.649928 + 0.375236i 0.788428 0.615126i \(-0.210895\pi\)
−0.138501 + 0.990362i \(0.544228\pi\)
\(978\) 9.25797 + 3.09895i 0.296037 + 0.0990934i
\(979\) −66.1354 + 38.1833i −2.11370 + 1.22034i
\(980\) 6.09257 23.4444i 0.194620 0.748903i
\(981\) 20.0704 + 18.6384i 0.640799 + 0.595080i
\(982\) −7.67368 23.7106i −0.244877 0.756637i
\(983\) −22.8468 + 13.1906i −0.728699 + 0.420715i −0.817946 0.575295i \(-0.804887\pi\)
0.0892468 + 0.996010i \(0.471554\pi\)
\(984\) 27.2883 + 25.1280i 0.869920 + 0.801051i
\(985\) −2.25987 13.4105i −0.0720056 0.427293i
\(986\) −12.7136 + 59.4738i −0.404884 + 1.89403i
\(987\) 2.14180 18.9729i 0.0681743 0.603915i
\(988\) 0.876366 1.95613i 0.0278809 0.0622329i
\(989\) 6.60552i 0.210043i
\(990\) 29.7998 + 30.2003i 0.947100 + 0.959828i
\(991\) −5.70203 −0.181131 −0.0905655 0.995890i \(-0.528867\pi\)
−0.0905655 + 0.995890i \(0.528867\pi\)
\(992\) −36.3277 + 20.6941i −1.15341 + 0.657038i
\(993\) −10.3876 + 14.0684i −0.329640 + 0.446448i
\(994\) 11.0810 + 2.36877i 0.351468 + 0.0751328i
\(995\) 3.56659 + 21.1647i 0.113069 + 0.670967i
\(996\) 9.65067 16.3356i 0.305793 0.517614i
\(997\) −1.96192 3.39814i −0.0621346 0.107620i 0.833285 0.552844i \(-0.186457\pi\)
−0.895419 + 0.445224i \(0.853124\pi\)
\(998\) −11.9827 37.0251i −0.379307 1.17201i
\(999\) −11.8017 + 33.6587i −0.373388 + 1.06491i
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 360.2.bk.a.229.16 136
5.4 even 2 inner 360.2.bk.a.229.53 yes 136
8.5 even 2 inner 360.2.bk.a.229.39 yes 136
9.7 even 3 inner 360.2.bk.a.349.30 yes 136
40.29 even 2 inner 360.2.bk.a.229.30 yes 136
45.34 even 6 inner 360.2.bk.a.349.39 yes 136
72.61 even 6 inner 360.2.bk.a.349.53 yes 136
360.349 even 6 inner 360.2.bk.a.349.16 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bk.a.229.16 136 1.1 even 1 trivial
360.2.bk.a.229.30 yes 136 40.29 even 2 inner
360.2.bk.a.229.39 yes 136 8.5 even 2 inner
360.2.bk.a.229.53 yes 136 5.4 even 2 inner
360.2.bk.a.349.16 yes 136 360.349 even 6 inner
360.2.bk.a.349.30 yes 136 9.7 even 3 inner
360.2.bk.a.349.39 yes 136 45.34 even 6 inner
360.2.bk.a.349.53 yes 136 72.61 even 6 inner