Properties

Label 336.2.bo.a.5.14
Level $336$
Weight $2$
Character 336.5
Analytic conductor $2.683$
Analytic rank $0$
Dimension $240$
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] = [336,2,Mod(5,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bo (of order \(12\), 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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(60\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 5.14
Character \(\chi\) \(=\) 336.5
Dual form 336.2.bo.a.269.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.05796 - 0.938469i) q^{2} +(-1.55615 - 0.760516i) q^{3} +(0.238553 + 1.98572i) q^{4} +(-0.772302 + 0.206938i) q^{5} +(0.932627 + 2.26500i) q^{6} +(1.91339 - 1.82728i) q^{7} +(1.61116 - 2.32469i) q^{8} +(1.84323 + 2.36696i) q^{9} +O(q^{10})\) \(q+(-1.05796 - 0.938469i) q^{2} +(-1.55615 - 0.760516i) q^{3} +(0.238553 + 1.98572i) q^{4} +(-0.772302 + 0.206938i) q^{5} +(0.932627 + 2.26500i) q^{6} +(1.91339 - 1.82728i) q^{7} +(1.61116 - 2.32469i) q^{8} +(1.84323 + 2.36696i) q^{9} +(1.01127 + 0.505849i) q^{10} +(3.96651 + 1.06282i) q^{11} +(1.13895 - 3.27151i) q^{12} +(-4.84304 - 4.84304i) q^{13} +(-3.73913 + 0.137532i) q^{14} +(1.35920 + 0.265321i) q^{15} +(-3.88618 + 0.947402i) q^{16} +(-1.28146 - 2.21956i) q^{17} +(0.271254 - 4.23396i) q^{18} +(-2.65990 + 0.712717i) q^{19} +(-0.595156 - 1.48421i) q^{20} +(-4.36720 + 1.38837i) q^{21} +(-3.19898 - 4.84687i) q^{22} +(1.87046 - 3.23974i) q^{23} +(-4.27517 + 2.39226i) q^{24} +(-3.77650 + 2.18036i) q^{25} +(0.578696 + 9.66879i) q^{26} +(-1.06824 - 5.08516i) q^{27} +(4.08491 + 3.36355i) q^{28} +(-3.81398 - 3.81398i) q^{29} +(-1.18898 - 1.55626i) q^{30} +(3.73448 - 2.15610i) q^{31} +(5.00053 + 2.64475i) q^{32} +(-5.36421 - 4.67051i) q^{33} +(-0.727251 + 3.55081i) q^{34} +(-1.09958 + 1.80716i) q^{35} +(-4.26041 + 4.22479i) q^{36} +(0.311632 - 0.0835015i) q^{37} +(3.48292 + 1.74220i) q^{38} +(3.85331 + 11.2197i) q^{39} +(-0.763235 + 2.12877i) q^{40} -5.77477i q^{41} +(5.92326 + 2.62965i) q^{42} +(-5.64901 - 5.64901i) q^{43} +(-1.16425 + 8.12993i) q^{44} +(-1.91334 - 1.44657i) q^{45} +(-5.01927 + 1.67214i) q^{46} +(-1.69030 + 2.92769i) q^{47} +(6.76802 + 1.48120i) q^{48} +(0.322103 - 6.99259i) q^{49} +(6.04158 + 1.23739i) q^{50} +(0.306144 + 4.42855i) q^{51} +(8.46161 - 10.7723i) q^{52} +(-6.21901 - 1.66638i) q^{53} +(-3.64211 + 6.38240i) q^{54} -3.28328 q^{55} +(-1.16508 - 7.39206i) q^{56} +(4.68124 + 0.913796i) q^{57} +(0.455733 + 7.61434i) q^{58} +(0.0299734 - 0.111862i) q^{59} +(-0.202611 + 2.76229i) q^{60} +(11.4397 - 3.06526i) q^{61} +(-5.97436 - 1.22362i) q^{62} +(7.85191 + 1.16081i) q^{63} +(-2.80834 - 7.49088i) q^{64} +(4.74250 + 2.73808i) q^{65} +(1.29198 + 9.97535i) q^{66} +(-0.567353 - 0.152022i) q^{67} +(4.10173 - 3.07411i) q^{68} +(-5.37460 + 3.61902i) q^{69} +(2.85927 - 0.879982i) q^{70} +9.98237 q^{71} +(8.47218 - 0.471391i) q^{72} +(4.62974 + 8.01895i) q^{73} +(-0.408057 - 0.204116i) q^{74} +(7.53502 - 0.520894i) q^{75} +(-2.04979 - 5.11180i) q^{76} +(9.53154 - 5.21433i) q^{77} +(6.45272 - 15.4862i) q^{78} +(6.10009 - 10.5657i) q^{79} +(2.80525 - 1.53588i) q^{80} +(-2.20499 + 8.72571i) q^{81} +(-5.41944 + 6.10946i) q^{82} +(2.68177 - 2.68177i) q^{83} +(-3.79872 - 8.34085i) q^{84} +(1.44898 + 1.44898i) q^{85} +(0.675001 + 11.2778i) q^{86} +(3.03455 + 8.83573i) q^{87} +(8.86140 - 7.50852i) q^{88} +(-11.2991 - 6.52354i) q^{89} +(0.666676 + 3.32603i) q^{90} +(-18.1162 - 0.417027i) q^{91} +(6.87943 + 2.94137i) q^{92} +(-7.45117 + 0.515098i) q^{93} +(4.53581 - 1.51108i) q^{94} +(1.90675 - 1.10087i) q^{95} +(-5.77022 - 7.91862i) q^{96} +15.2445i q^{97} +(-6.90309 + 7.09558i) q^{98} +(4.79554 + 11.3476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.05796 0.938469i −0.748090 0.663597i
\(3\) −1.55615 0.760516i −0.898446 0.439084i
\(4\) 0.238553 + 1.98572i 0.119277 + 0.992861i
\(5\) −0.772302 + 0.206938i −0.345384 + 0.0925453i −0.427341 0.904091i \(-0.640550\pi\)
0.0819572 + 0.996636i \(0.473883\pi\)
\(6\) 0.932627 + 2.26500i 0.380743 + 0.924681i
\(7\) 1.91339 1.82728i 0.723192 0.690647i
\(8\) 1.61116 2.32469i 0.569630 0.821901i
\(9\) 1.84323 + 2.36696i 0.614411 + 0.788986i
\(10\) 1.01127 + 0.505849i 0.319791 + 0.159964i
\(11\) 3.96651 + 1.06282i 1.19595 + 0.320453i 0.801234 0.598351i \(-0.204177\pi\)
0.394714 + 0.918804i \(0.370844\pi\)
\(12\) 1.13895 3.27151i 0.328786 0.944405i
\(13\) −4.84304 4.84304i −1.34322 1.34322i −0.892835 0.450384i \(-0.851287\pi\)
−0.450384 0.892835i \(-0.648713\pi\)
\(14\) −3.73913 + 0.137532i −0.999324 + 0.0367569i
\(15\) 1.35920 + 0.265321i 0.350944 + 0.0685055i
\(16\) −3.88618 + 0.947402i −0.971546 + 0.236850i
\(17\) −1.28146 2.21956i −0.310800 0.538322i 0.667736 0.744398i \(-0.267264\pi\)
−0.978536 + 0.206077i \(0.933930\pi\)
\(18\) 0.271254 4.23396i 0.0639351 0.997954i
\(19\) −2.65990 + 0.712717i −0.610222 + 0.163509i −0.550679 0.834717i \(-0.685631\pi\)
−0.0595434 + 0.998226i \(0.518964\pi\)
\(20\) −0.595156 1.48421i −0.133081 0.331880i
\(21\) −4.36720 + 1.38837i −0.953001 + 0.302966i
\(22\) −3.19898 4.84687i −0.682024 1.03336i
\(23\) 1.87046 3.23974i 0.390019 0.675533i −0.602433 0.798170i \(-0.705802\pi\)
0.992452 + 0.122637i \(0.0391351\pi\)
\(24\) −4.27517 + 2.39226i −0.872666 + 0.488318i
\(25\) −3.77650 + 2.18036i −0.755300 + 0.436073i
\(26\) 0.578696 + 9.66879i 0.113492 + 1.89620i
\(27\) −1.06824 5.08516i −0.205584 0.978640i
\(28\) 4.08491 + 3.36355i 0.771976 + 0.635652i
\(29\) −3.81398 3.81398i −0.708238 0.708238i 0.257926 0.966165i \(-0.416961\pi\)
−0.966165 + 0.257926i \(0.916961\pi\)
\(30\) −1.18898 1.55626i −0.217077 0.284134i
\(31\) 3.73448 2.15610i 0.670732 0.387247i −0.125622 0.992078i \(-0.540093\pi\)
0.796354 + 0.604831i \(0.206759\pi\)
\(32\) 5.00053 + 2.64475i 0.883977 + 0.467530i
\(33\) −5.36421 4.67051i −0.933789 0.813031i
\(34\) −0.727251 + 3.55081i −0.124722 + 0.608959i
\(35\) −1.09958 + 1.80716i −0.185863 + 0.305466i
\(36\) −4.26041 + 4.22479i −0.710069 + 0.704132i
\(37\) 0.311632 0.0835015i 0.0512320 0.0137276i −0.233112 0.972450i \(-0.574891\pi\)
0.284344 + 0.958722i \(0.408224\pi\)
\(38\) 3.48292 + 1.74220i 0.565005 + 0.282623i
\(39\) 3.85331 + 11.2197i 0.617024 + 1.79660i
\(40\) −0.763235 + 2.12877i −0.120678 + 0.336588i
\(41\) 5.77477i 0.901867i −0.892558 0.450933i \(-0.851091\pi\)
0.892558 0.450933i \(-0.148909\pi\)
\(42\) 5.92326 + 2.62965i 0.913978 + 0.405763i
\(43\) −5.64901 5.64901i −0.861466 0.861466i 0.130042 0.991508i \(-0.458489\pi\)
−0.991508 + 0.130042i \(0.958489\pi\)
\(44\) −1.16425 + 8.12993i −0.175517 + 1.22563i
\(45\) −1.91334 1.44657i −0.285224 0.215642i
\(46\) −5.01927 + 1.67214i −0.740051 + 0.246543i
\(47\) −1.69030 + 2.92769i −0.246556 + 0.427047i −0.962568 0.271041i \(-0.912632\pi\)
0.716012 + 0.698088i \(0.245966\pi\)
\(48\) 6.76802 + 1.48120i 0.976879 + 0.213793i
\(49\) 0.322103 6.99259i 0.0460147 0.998941i
\(50\) 6.04158 + 1.23739i 0.854409 + 0.174994i
\(51\) 0.306144 + 4.42855i 0.0428688 + 0.620120i
\(52\) 8.46161 10.7723i 1.17341 1.49384i
\(53\) −6.21901 1.66638i −0.854247 0.228895i −0.194983 0.980807i \(-0.562465\pi\)
−0.659264 + 0.751912i \(0.729132\pi\)
\(54\) −3.64211 + 6.38240i −0.495628 + 0.868535i
\(55\) −3.28328 −0.442717
\(56\) −1.16508 7.39206i −0.155691 0.987806i
\(57\) 4.68124 + 0.913796i 0.620046 + 0.121035i
\(58\) 0.455733 + 7.61434i 0.0598407 + 0.999811i
\(59\) 0.0299734 0.111862i 0.00390220 0.0145632i −0.963947 0.266093i \(-0.914267\pi\)
0.967849 + 0.251530i \(0.0809337\pi\)
\(60\) −0.202611 + 2.76229i −0.0261570 + 0.356610i
\(61\) 11.4397 3.06526i 1.46470 0.392466i 0.563591 0.826054i \(-0.309419\pi\)
0.901111 + 0.433588i \(0.142753\pi\)
\(62\) −5.97436 1.22362i −0.758744 0.155400i
\(63\) 7.85191 + 1.16081i 0.989248 + 0.146248i
\(64\) −2.80834 7.49088i −0.351042 0.936360i
\(65\) 4.74250 + 2.73808i 0.588234 + 0.339617i
\(66\) 1.29198 + 9.97535i 0.159032 + 1.22788i
\(67\) −0.567353 0.152022i −0.0693133 0.0185724i 0.223996 0.974590i \(-0.428090\pi\)
−0.293309 + 0.956018i \(0.594756\pi\)
\(68\) 4.10173 3.07411i 0.497407 0.372791i
\(69\) −5.37460 + 3.61902i −0.647026 + 0.435678i
\(70\) 2.85927 0.879982i 0.341749 0.105178i
\(71\) 9.98237 1.18469 0.592344 0.805685i \(-0.298202\pi\)
0.592344 + 0.805685i \(0.298202\pi\)
\(72\) 8.47218 0.471391i 0.998456 0.0555540i
\(73\) 4.62974 + 8.01895i 0.541871 + 0.938547i 0.998797 + 0.0490427i \(0.0156170\pi\)
−0.456926 + 0.889505i \(0.651050\pi\)
\(74\) −0.408057 0.204116i −0.0474357 0.0237280i
\(75\) 7.53502 0.520894i 0.870069 0.0601477i
\(76\) −2.04979 5.11180i −0.235127 0.586363i
\(77\) 9.53154 5.21433i 1.08622 0.594228i
\(78\) 6.45272 15.4862i 0.730627 1.75347i
\(79\) 6.10009 10.5657i 0.686314 1.18873i −0.286708 0.958018i \(-0.592561\pi\)
0.973022 0.230713i \(-0.0741057\pi\)
\(80\) 2.80525 1.53588i 0.313637 0.171716i
\(81\) −2.20499 + 8.72571i −0.244999 + 0.969523i
\(82\) −5.41944 + 6.10946i −0.598477 + 0.674677i
\(83\) 2.68177 2.68177i 0.294362 0.294362i −0.544439 0.838801i \(-0.683257\pi\)
0.838801 + 0.544439i \(0.183257\pi\)
\(84\) −3.79872 8.34085i −0.414474 0.910061i
\(85\) 1.44898 + 1.44898i 0.157164 + 0.157164i
\(86\) 0.675001 + 11.2778i 0.0727873 + 1.21612i
\(87\) 3.03455 + 8.83573i 0.325338 + 0.947290i
\(88\) 8.86140 7.50852i 0.944629 0.800411i
\(89\) −11.2991 6.52354i −1.19770 0.691494i −0.237660 0.971348i \(-0.576380\pi\)
−0.960042 + 0.279855i \(0.909714\pi\)
\(90\) 0.666676 + 3.32603i 0.0702738 + 0.350594i
\(91\) −18.1162 0.417027i −1.89910 0.0437163i
\(92\) 6.87943 + 2.94137i 0.717230 + 0.306659i
\(93\) −7.45117 + 0.515098i −0.772651 + 0.0534132i
\(94\) 4.53581 1.51108i 0.467833 0.155856i
\(95\) 1.90675 1.10087i 0.195629 0.112946i
\(96\) −5.77022 7.91862i −0.588921 0.808191i
\(97\) 15.2445i 1.54784i 0.633283 + 0.773921i \(0.281707\pi\)
−0.633283 + 0.773921i \(0.718293\pi\)
\(98\) −6.90309 + 7.09558i −0.697318 + 0.716762i
\(99\) 4.79554 + 11.3476i 0.481970 + 1.14048i
\(100\) −5.23049 6.97895i −0.523049 0.697895i
\(101\) −4.52681 + 16.8943i −0.450435 + 1.68105i 0.250739 + 0.968055i \(0.419327\pi\)
−0.701173 + 0.712991i \(0.747340\pi\)
\(102\) 3.83216 4.97252i 0.379441 0.492353i
\(103\) 4.12459 7.14401i 0.406408 0.703920i −0.588076 0.808806i \(-0.700114\pi\)
0.994484 + 0.104886i \(0.0334477\pi\)
\(104\) −19.0615 + 3.45565i −1.86913 + 0.338855i
\(105\) 3.08549 1.97598i 0.301113 0.192835i
\(106\) 5.01561 + 7.59931i 0.487159 + 0.738110i
\(107\) 3.55532 + 13.2686i 0.343706 + 1.28273i 0.894117 + 0.447834i \(0.147804\pi\)
−0.550411 + 0.834894i \(0.685529\pi\)
\(108\) 9.84288 3.33432i 0.947132 0.320845i
\(109\) 0.472606 + 0.126634i 0.0452675 + 0.0121294i 0.281382 0.959596i \(-0.409207\pi\)
−0.236114 + 0.971725i \(0.575874\pi\)
\(110\) 3.47357 + 3.08125i 0.331192 + 0.293786i
\(111\) −0.548452 0.107060i −0.0520567 0.0101617i
\(112\) −5.70461 + 8.91389i −0.539035 + 0.842283i
\(113\) 7.82950i 0.736537i −0.929719 0.368269i \(-0.879951\pi\)
0.929719 0.368269i \(-0.120049\pi\)
\(114\) −4.09499 5.35996i −0.383531 0.502006i
\(115\) −0.774139 + 2.88913i −0.0721888 + 0.269412i
\(116\) 6.66367 8.48334i 0.618706 0.787659i
\(117\) 2.53644 20.3901i 0.234494 1.88507i
\(118\) −0.136690 + 0.0902165i −0.0125833 + 0.00830510i
\(119\) −6.50768 1.90528i −0.596558 0.174657i
\(120\) 2.80667 2.73224i 0.256213 0.249418i
\(121\) 5.07733 + 2.93140i 0.461575 + 0.266490i
\(122\) −14.9794 7.49288i −1.35617 0.678373i
\(123\) −4.39180 + 8.98643i −0.395995 + 0.810279i
\(124\) 5.17229 + 6.90129i 0.464486 + 0.619754i
\(125\) 5.29222 5.29222i 0.473350 0.473350i
\(126\) −7.21761 8.59686i −0.642996 0.765869i
\(127\) −2.26444 −0.200936 −0.100468 0.994940i \(-0.532034\pi\)
−0.100468 + 0.994940i \(0.532034\pi\)
\(128\) −4.05885 + 10.5606i −0.358755 + 0.933432i
\(129\) 4.49457 + 13.0869i 0.395725 + 1.15224i
\(130\) −2.44776 7.34746i −0.214683 0.644415i
\(131\) −0.177292 0.661664i −0.0154901 0.0578099i 0.957748 0.287608i \(-0.0928600\pi\)
−0.973238 + 0.229798i \(0.926193\pi\)
\(132\) 7.99468 11.7660i 0.695848 1.02410i
\(133\) −3.78708 + 6.22408i −0.328382 + 0.539696i
\(134\) 0.457569 + 0.693276i 0.0395279 + 0.0598899i
\(135\) 1.87732 + 3.70622i 0.161574 + 0.318980i
\(136\) −7.22441 0.597060i −0.619488 0.0511974i
\(137\) 4.89004 + 8.46980i 0.417784 + 0.723624i 0.995716 0.0924613i \(-0.0294735\pi\)
−0.577932 + 0.816085i \(0.696140\pi\)
\(138\) 9.08244 + 1.21513i 0.773149 + 0.103438i
\(139\) 4.78683 4.78683i 0.406014 0.406014i −0.474332 0.880346i \(-0.657310\pi\)
0.880346 + 0.474332i \(0.157310\pi\)
\(140\) −3.85083 1.75235i −0.325455 0.148101i
\(141\) 4.85692 3.27043i 0.409027 0.275420i
\(142\) −10.5609 9.36814i −0.886254 0.786157i
\(143\) −14.0627 24.3573i −1.17598 2.03686i
\(144\) −9.40560 7.45216i −0.783800 0.621013i
\(145\) 3.73480 + 2.15629i 0.310158 + 0.179070i
\(146\) 2.62746 12.8286i 0.217450 1.06170i
\(147\) −5.81921 + 10.6366i −0.479961 + 0.877290i
\(148\) 0.240152 + 0.598895i 0.0197404 + 0.0492289i
\(149\) −2.24500 8.37845i −0.183918 0.686389i −0.994860 0.101263i \(-0.967712\pi\)
0.810942 0.585126i \(-0.198955\pi\)
\(150\) −8.46058 6.52029i −0.690804 0.532380i
\(151\) −5.04431 + 2.91233i −0.410500 + 0.237002i −0.691005 0.722850i \(-0.742832\pi\)
0.280505 + 0.959853i \(0.409498\pi\)
\(152\) −2.62867 + 7.33173i −0.213213 + 0.594682i
\(153\) 2.89157 7.12433i 0.233770 0.575968i
\(154\) −14.9775 3.42851i −1.20692 0.276277i
\(155\) −2.43797 + 2.43797i −0.195822 + 0.195822i
\(156\) −21.3601 + 10.3281i −1.71017 + 0.826911i
\(157\) 0.401938 1.50005i 0.0320781 0.119717i −0.948030 0.318180i \(-0.896928\pi\)
0.980108 + 0.198463i \(0.0635950\pi\)
\(158\) −16.3692 + 5.45330i −1.30226 + 0.433841i
\(159\) 8.41043 + 7.32280i 0.666991 + 0.580736i
\(160\) −4.40921 1.00775i −0.348579 0.0796694i
\(161\) −2.34099 9.61674i −0.184495 0.757905i
\(162\) 10.5216 7.16212i 0.826655 0.562710i
\(163\) 5.59801 + 20.8920i 0.438470 + 1.63639i 0.732624 + 0.680633i \(0.238295\pi\)
−0.294155 + 0.955758i \(0.595038\pi\)
\(164\) 11.4671 1.37759i 0.895429 0.107572i
\(165\) 5.10929 + 2.49699i 0.397758 + 0.194390i
\(166\) −5.35395 + 0.320445i −0.415547 + 0.0248713i
\(167\) 7.60648i 0.588607i −0.955712 0.294304i \(-0.904912\pi\)
0.955712 0.294304i \(-0.0950877\pi\)
\(168\) −3.80873 + 12.3893i −0.293850 + 0.955852i
\(169\) 33.9101i 2.60847i
\(170\) −0.173139 2.89279i −0.0132792 0.221867i
\(171\) −6.58978 4.98217i −0.503933 0.380996i
\(172\) 9.86977 12.5650i 0.752563 0.958069i
\(173\) −0.681956 2.54509i −0.0518482 0.193500i 0.935144 0.354267i \(-0.115270\pi\)
−0.986992 + 0.160767i \(0.948603\pi\)
\(174\) 5.08163 12.1957i 0.385237 0.924552i
\(175\) −3.24178 + 11.0726i −0.245055 + 0.837010i
\(176\) −16.4215 0.372449i −1.23782 0.0280744i
\(177\) −0.131716 + 0.151280i −0.00990039 + 0.0113709i
\(178\) 5.83185 + 17.5055i 0.437115 + 1.31209i
\(179\) 2.18209 8.14366i 0.163097 0.608686i −0.835178 0.549979i \(-0.814636\pi\)
0.998275 0.0587066i \(-0.0186976\pi\)
\(180\) 2.41606 4.14445i 0.180082 0.308909i
\(181\) −7.66335 + 7.66335i −0.569612 + 0.569612i −0.932020 0.362407i \(-0.881955\pi\)
0.362407 + 0.932020i \(0.381955\pi\)
\(182\) 18.7748 + 17.4427i 1.39168 + 1.29294i
\(183\) −20.1331 3.93005i −1.48828 0.290518i
\(184\) −4.51777 9.56798i −0.333054 0.705361i
\(185\) −0.223394 + 0.128977i −0.0164243 + 0.00948256i
\(186\) 8.36644 + 6.44774i 0.613457 + 0.472771i
\(187\) −2.72393 10.1659i −0.199194 0.743401i
\(188\) −6.21680 2.65806i −0.453407 0.193859i
\(189\) −11.3360 7.77790i −0.824570 0.565759i
\(190\) −3.05040 0.624759i −0.221299 0.0453248i
\(191\) 15.0326 + 8.67905i 1.08772 + 0.627994i 0.932968 0.359960i \(-0.117210\pi\)
0.154750 + 0.987954i \(0.450543\pi\)
\(192\) −1.32672 + 13.7927i −0.0957478 + 0.995406i
\(193\) −3.11155 5.38937i −0.223974 0.387935i 0.732037 0.681265i \(-0.238570\pi\)
−0.956011 + 0.293330i \(0.905237\pi\)
\(194\) 14.3065 16.1280i 1.02714 1.15792i
\(195\) −5.29770 7.86762i −0.379376 0.563412i
\(196\) 13.9622 1.02850i 0.997298 0.0734642i
\(197\) 18.4497 18.4497i 1.31449 1.31449i 0.396415 0.918072i \(-0.370254\pi\)
0.918072 0.396415i \(-0.129746\pi\)
\(198\) 5.57588 16.5058i 0.396261 1.17301i
\(199\) 0.589818 + 1.02159i 0.0418111 + 0.0724189i 0.886174 0.463353i \(-0.153354\pi\)
−0.844363 + 0.535772i \(0.820021\pi\)
\(200\) −1.01588 + 12.2921i −0.0718333 + 0.869182i
\(201\) 0.767274 + 0.668051i 0.0541194 + 0.0471207i
\(202\) 20.6440 13.6252i 1.45250 0.958666i
\(203\) −14.2668 0.328416i −1.00134 0.0230503i
\(204\) −8.72083 + 1.66436i −0.610580 + 0.116529i
\(205\) 1.19502 + 4.45986i 0.0834635 + 0.311490i
\(206\) −11.0681 + 3.68726i −0.771150 + 0.256904i
\(207\) 11.1160 1.54428i 0.772618 0.107335i
\(208\) 23.4093 + 14.2327i 1.62314 + 0.986857i
\(209\) −11.3080 −0.782191
\(210\) −5.11871 0.805135i −0.353225 0.0555596i
\(211\) 7.21278 7.21278i 0.496548 0.496548i −0.413813 0.910362i \(-0.635803\pi\)
0.910362 + 0.413813i \(0.135803\pi\)
\(212\) 1.82540 12.7467i 0.125369 0.875450i
\(213\) −15.5341 7.59175i −1.06438 0.520178i
\(214\) 8.69082 17.3742i 0.594092 1.18768i
\(215\) 5.53173 + 3.19375i 0.377261 + 0.217812i
\(216\) −13.5425 5.70967i −0.921451 0.388494i
\(217\) 3.20570 10.9494i 0.217617 0.743293i
\(218\) −0.381156 0.577500i −0.0258151 0.0391133i
\(219\) −1.10606 15.9997i −0.0747404 1.08116i
\(220\) −0.783238 6.51968i −0.0528059 0.439557i
\(221\) −4.54324 + 16.9556i −0.305611 + 1.14056i
\(222\) 0.479767 + 0.627970i 0.0321999 + 0.0421466i
\(223\) 6.01995i 0.403126i 0.979476 + 0.201563i \(0.0646021\pi\)
−0.979476 + 0.201563i \(0.935398\pi\)
\(224\) 14.4006 4.07693i 0.962184 0.272401i
\(225\) −12.1218 4.91991i −0.808120 0.327994i
\(226\) −7.34774 + 8.28329i −0.488764 + 0.550996i
\(227\) 11.3007 + 3.02802i 0.750055 + 0.200977i 0.613542 0.789662i \(-0.289744\pi\)
0.136512 + 0.990638i \(0.456411\pi\)
\(228\) −0.697817 + 9.51364i −0.0462141 + 0.630056i
\(229\) −1.95196 7.28481i −0.128989 0.481394i 0.870961 0.491352i \(-0.163497\pi\)
−0.999950 + 0.00995758i \(0.996830\pi\)
\(230\) 3.53036 2.33007i 0.232785 0.153640i
\(231\) −18.7981 + 0.865409i −1.23683 + 0.0569397i
\(232\) −15.0112 + 2.72139i −0.985536 + 0.178668i
\(233\) −8.48448 + 14.6956i −0.555837 + 0.962738i 0.442001 + 0.897015i \(0.354269\pi\)
−0.997838 + 0.0657233i \(0.979065\pi\)
\(234\) −21.8190 + 19.1916i −1.42635 + 1.25459i
\(235\) 0.699574 2.61085i 0.0456352 0.170313i
\(236\) 0.229278 + 0.0328337i 0.0149247 + 0.00213729i
\(237\) −17.5280 + 11.8026i −1.13857 + 0.766661i
\(238\) 5.09681 + 8.12297i 0.330377 + 0.526534i
\(239\) 1.11687i 0.0722444i −0.999347 0.0361222i \(-0.988499\pi\)
0.999347 0.0361222i \(-0.0115005\pi\)
\(240\) −5.53347 + 0.256623i −0.357184 + 0.0165649i
\(241\) 4.92310 2.84235i 0.317125 0.183092i −0.332986 0.942932i \(-0.608056\pi\)
0.650110 + 0.759840i \(0.274723\pi\)
\(242\) −2.62058 7.86621i −0.168457 0.505659i
\(243\) 10.0673 11.9016i 0.645821 0.763489i
\(244\) 8.81572 + 21.9848i 0.564369 + 1.40743i
\(245\) 1.19827 + 5.46704i 0.0765545 + 0.349276i
\(246\) 13.0798 5.38570i 0.833939 0.343380i
\(247\) 16.3337 + 9.43028i 1.03929 + 0.600034i
\(248\) 1.00457 12.1553i 0.0637904 0.771863i
\(249\) −6.21277 + 2.13372i −0.393718 + 0.135219i
\(250\) −10.5655 + 0.632368i −0.668223 + 0.0399945i
\(251\) 3.82022 + 3.82022i 0.241130 + 0.241130i 0.817318 0.576187i \(-0.195460\pi\)
−0.576187 + 0.817318i \(0.695460\pi\)
\(252\) −0.431948 + 15.8686i −0.0272102 + 0.999630i
\(253\) 10.8625 10.8625i 0.682919 0.682919i
\(254\) 2.39568 + 2.12510i 0.150318 + 0.133341i
\(255\) −1.15287 3.35682i −0.0721954 0.210212i
\(256\) 14.2049 7.36356i 0.887804 0.460222i
\(257\) −10.9742 + 19.0078i −0.684549 + 1.18567i 0.289029 + 0.957320i \(0.406667\pi\)
−0.973578 + 0.228353i \(0.926666\pi\)
\(258\) 7.52657 18.0634i 0.468584 1.12458i
\(259\) 0.443692 0.729209i 0.0275697 0.0453109i
\(260\) −4.30573 + 10.0705i −0.267030 + 0.624544i
\(261\) 1.99749 16.0576i 0.123641 0.993940i
\(262\) −0.433383 + 0.866396i −0.0267745 + 0.0535262i
\(263\) −9.95172 17.2369i −0.613649 1.06287i −0.990620 0.136647i \(-0.956368\pi\)
0.376971 0.926225i \(-0.376966\pi\)
\(264\) −19.5001 + 4.94517i −1.20015 + 0.304354i
\(265\) 5.14779 0.316226
\(266\) 9.84768 3.03076i 0.603800 0.185828i
\(267\) 12.6219 + 18.7448i 0.772447 + 1.14716i
\(268\) 0.166529 1.16287i 0.0101724 0.0710337i
\(269\) 25.5554 + 6.84756i 1.55814 + 0.417503i 0.932075 0.362266i \(-0.117997\pi\)
0.626067 + 0.779769i \(0.284664\pi\)
\(270\) 1.49205 5.68283i 0.0908030 0.345846i
\(271\) −0.253863 0.146568i −0.0154211 0.00890337i 0.492270 0.870443i \(-0.336167\pi\)
−0.507691 + 0.861539i \(0.669501\pi\)
\(272\) 7.08281 + 7.41155i 0.429458 + 0.449391i
\(273\) 27.8745 + 14.4266i 1.68704 + 0.873139i
\(274\) 2.77518 13.5498i 0.167655 0.818576i
\(275\) −17.2969 + 4.63468i −1.04304 + 0.279482i
\(276\) −8.46849 9.80914i −0.509743 0.590441i
\(277\) 0.985453 3.67776i 0.0592102 0.220975i −0.929981 0.367608i \(-0.880177\pi\)
0.989191 + 0.146633i \(0.0468435\pi\)
\(278\) −9.55657 + 0.571980i −0.573165 + 0.0343051i
\(279\) 11.9869 + 4.86516i 0.717638 + 0.291270i
\(280\) 2.42949 + 5.46780i 0.145190 + 0.326764i
\(281\) 16.9432 1.01075 0.505373 0.862901i \(-0.331355\pi\)
0.505373 + 0.862901i \(0.331355\pi\)
\(282\) −8.20762 1.09809i −0.488757 0.0653901i
\(283\) −6.46182 1.73144i −0.384115 0.102923i 0.0615938 0.998101i \(-0.480382\pi\)
−0.445709 + 0.895178i \(0.647048\pi\)
\(284\) 2.38133 + 19.8222i 0.141306 + 1.17623i
\(285\) −3.80443 + 0.262999i −0.225355 + 0.0155787i
\(286\) −7.98080 + 38.9664i −0.471915 + 2.30413i
\(287\) −10.5521 11.0494i −0.622871 0.652223i
\(288\) 2.95712 + 16.7109i 0.174250 + 0.984701i
\(289\) 5.21571 9.03388i 0.306807 0.531404i
\(290\) −1.92766 5.78625i −0.113196 0.339781i
\(291\) 11.5937 23.7227i 0.679632 1.39065i
\(292\) −14.8190 + 11.1063i −0.867215 + 0.649949i
\(293\) 18.4200 + 18.4200i 1.07611 + 1.07611i 0.996854 + 0.0792562i \(0.0252545\pi\)
0.0792562 + 0.996854i \(0.474745\pi\)
\(294\) 16.1386 5.79191i 0.941221 0.337791i
\(295\) 0.0925940i 0.00539103i
\(296\) 0.307973 0.858981i 0.0179006 0.0499273i
\(297\) 1.16743 21.3057i 0.0677411 1.23628i
\(298\) −5.48780 + 10.9709i −0.317900 + 0.635528i
\(299\) −24.7489 + 6.63146i −1.43127 + 0.383507i
\(300\) 2.83186 + 14.8382i 0.163497 + 0.856683i
\(301\) −21.1311 0.486427i −1.21797 0.0280372i
\(302\) 8.06980 + 1.65280i 0.464365 + 0.0951078i
\(303\) 19.8928 22.8474i 1.14281 1.31255i
\(304\) 9.66162 5.28974i 0.554132 0.303388i
\(305\) −8.20057 + 4.73460i −0.469564 + 0.271103i
\(306\) −9.74512 + 4.82360i −0.557091 + 0.275747i
\(307\) −8.09356 8.09356i −0.461924 0.461924i 0.437362 0.899286i \(-0.355913\pi\)
−0.899286 + 0.437362i \(0.855913\pi\)
\(308\) 12.6280 + 17.6831i 0.719546 + 1.00759i
\(309\) −11.8516 + 7.98036i −0.674216 + 0.453987i
\(310\) 4.86722 0.291313i 0.276440 0.0165455i
\(311\) −7.30697 + 4.21868i −0.414340 + 0.239219i −0.692653 0.721271i \(-0.743558\pi\)
0.278313 + 0.960491i \(0.410225\pi\)
\(312\) 32.2907 + 9.11902i 1.82810 + 0.516263i
\(313\) 5.95658 10.3171i 0.336686 0.583157i −0.647121 0.762387i \(-0.724027\pi\)
0.983807 + 0.179230i \(0.0573607\pi\)
\(314\) −1.83299 + 1.20979i −0.103441 + 0.0682723i
\(315\) −6.30426 + 0.728359i −0.355205 + 0.0410384i
\(316\) 22.4357 + 9.59261i 1.26211 + 0.539627i
\(317\) 21.2135 5.68415i 1.19147 0.319253i 0.392003 0.919964i \(-0.371782\pi\)
0.799467 + 0.600710i \(0.205116\pi\)
\(318\) −2.02568 15.6401i −0.113594 0.877056i
\(319\) −11.0746 19.1818i −0.620059 1.07397i
\(320\) 3.71903 + 5.20406i 0.207900 + 0.290916i
\(321\) 4.55838 23.3519i 0.254424 1.30338i
\(322\) −6.54834 + 12.3711i −0.364925 + 0.689412i
\(323\) 4.99047 + 4.99047i 0.277677 + 0.277677i
\(324\) −17.8528 2.29696i −0.991825 0.127609i
\(325\) 28.8494 + 7.73016i 1.60027 + 0.428792i
\(326\) 13.6841 27.3565i 0.757890 1.51513i
\(327\) −0.639141 0.556487i −0.0353446 0.0307738i
\(328\) −13.4245 9.30406i −0.741245 0.513731i
\(329\) 2.11550 + 8.69046i 0.116631 + 0.479120i
\(330\) −3.06207 7.43662i −0.168562 0.409372i
\(331\) −13.2817 + 3.55882i −0.730028 + 0.195610i −0.604642 0.796497i \(-0.706684\pi\)
−0.125386 + 0.992108i \(0.540017\pi\)
\(332\) 5.96499 + 4.68550i 0.327371 + 0.257150i
\(333\) 0.772055 + 0.583708i 0.0423083 + 0.0319870i
\(334\) −7.13845 + 8.04735i −0.390598 + 0.440331i
\(335\) 0.469627 0.0256585
\(336\) 15.6564 9.53294i 0.854127 0.520065i
\(337\) 10.3141 0.561845 0.280923 0.959730i \(-0.409360\pi\)
0.280923 + 0.959730i \(0.409360\pi\)
\(338\) 31.8236 35.8755i 1.73098 1.95137i
\(339\) −5.95446 + 12.1839i −0.323402 + 0.661739i
\(340\) −2.53162 + 3.22294i −0.137296 + 0.174789i
\(341\) 17.1044 4.58311i 0.926255 0.248189i
\(342\) 2.29611 + 11.4552i 0.124159 + 0.619428i
\(343\) −12.1611 13.9681i −0.656638 0.754206i
\(344\) −22.2336 + 4.03073i −1.19876 + 0.217323i
\(345\) 3.40190 3.90718i 0.183152 0.210356i
\(346\) −1.66701 + 3.33260i −0.0896190 + 0.179162i
\(347\) 33.8322 + 9.06531i 1.81621 + 0.486652i 0.996308 0.0858542i \(-0.0273619\pi\)
0.819901 + 0.572506i \(0.194029\pi\)
\(348\) −16.8214 + 8.13357i −0.901722 + 0.436005i
\(349\) −0.391705 0.391705i −0.0209675 0.0209675i 0.696545 0.717513i \(-0.254720\pi\)
−0.717513 + 0.696545i \(0.754720\pi\)
\(350\) 13.8210 8.67205i 0.738761 0.463541i
\(351\) −19.4541 + 29.8012i −1.03838 + 1.59067i
\(352\) 17.0237 + 15.8051i 0.907369 + 0.842415i
\(353\) 3.10916 + 5.38523i 0.165484 + 0.286627i 0.936827 0.349793i \(-0.113748\pi\)
−0.771343 + 0.636420i \(0.780415\pi\)
\(354\) 0.281321 0.0364361i 0.0149521 0.00193656i
\(355\) −7.70940 + 2.06573i −0.409172 + 0.109637i
\(356\) 10.2585 23.9931i 0.543699 1.27163i
\(357\) 8.67796 + 7.91411i 0.459286 + 0.418859i
\(358\) −9.95113 + 6.56784i −0.525933 + 0.347121i
\(359\) 9.73161 16.8556i 0.513615 0.889607i −0.486261 0.873814i \(-0.661639\pi\)
0.999875 0.0157929i \(-0.00502725\pi\)
\(360\) −6.44553 + 2.11727i −0.339709 + 0.111590i
\(361\) −9.88739 + 5.70849i −0.520389 + 0.300447i
\(362\) 15.2993 0.915695i 0.804114 0.0481279i
\(363\) −5.67173 8.42309i −0.297689 0.442098i
\(364\) −3.49359 36.0732i −0.183114 1.89075i
\(365\) −5.23498 5.23498i −0.274011 0.274011i
\(366\) 17.6118 + 23.0521i 0.920581 + 1.20495i
\(367\) 5.88381 3.39702i 0.307133 0.177323i −0.338510 0.940963i \(-0.609923\pi\)
0.645643 + 0.763640i \(0.276590\pi\)
\(368\) −4.19964 + 14.3623i −0.218921 + 0.748687i
\(369\) 13.6686 10.6442i 0.711561 0.554117i
\(370\) 0.357383 + 0.0731964i 0.0185794 + 0.00380530i
\(371\) −14.9443 + 8.17544i −0.775870 + 0.424448i
\(372\) −2.80034 14.6731i −0.145191 0.760764i
\(373\) 11.7034 3.13591i 0.605978 0.162371i 0.0572328 0.998361i \(-0.481772\pi\)
0.548745 + 0.835989i \(0.315106\pi\)
\(374\) −6.65853 + 13.3114i −0.344304 + 0.688316i
\(375\) −12.2603 + 4.21069i −0.633120 + 0.217439i
\(376\) 4.08262 + 8.64639i 0.210545 + 0.445904i
\(377\) 36.9426i 1.90264i
\(378\) 4.69367 + 18.8672i 0.241416 + 0.970422i
\(379\) 24.4697 + 24.4697i 1.25693 + 1.25693i 0.952553 + 0.304372i \(0.0984465\pi\)
0.304372 + 0.952553i \(0.401553\pi\)
\(380\) 2.64088 + 3.52367i 0.135474 + 0.180760i
\(381\) 3.52381 + 1.72214i 0.180530 + 0.0882279i
\(382\) −7.75881 23.2897i −0.396975 1.19160i
\(383\) −14.6633 + 25.3976i −0.749260 + 1.29776i 0.198919 + 0.980016i \(0.436257\pi\)
−0.948178 + 0.317740i \(0.897076\pi\)
\(384\) 14.3477 13.3471i 0.732177 0.681115i
\(385\) −6.28219 + 5.99947i −0.320170 + 0.305761i
\(386\) −1.76586 + 8.62182i −0.0898798 + 0.438839i
\(387\) 2.95854 23.7834i 0.150391 1.20898i
\(388\) −30.2713 + 3.63662i −1.53679 + 0.184621i
\(389\) −25.3345 6.78837i −1.28451 0.344184i −0.448939 0.893562i \(-0.648198\pi\)
−0.835574 + 0.549378i \(0.814865\pi\)
\(390\) −1.77876 + 13.2953i −0.0900713 + 0.673236i
\(391\) −9.58772 −0.484872
\(392\) −15.7366 12.0149i −0.794819 0.606847i
\(393\) −0.227312 + 1.16448i −0.0114664 + 0.0587405i
\(394\) −36.8335 + 2.20456i −1.85564 + 0.111064i
\(395\) −2.52468 + 9.42222i −0.127030 + 0.474083i
\(396\) −21.3892 + 12.2296i −1.07485 + 0.614561i
\(397\) −6.00652 + 1.60944i −0.301459 + 0.0807756i −0.406378 0.913705i \(-0.633208\pi\)
0.104919 + 0.994481i \(0.466542\pi\)
\(398\) 0.334731 1.63433i 0.0167786 0.0819216i
\(399\) 10.6268 6.80549i 0.532005 0.340701i
\(400\) 12.6105 12.0512i 0.630525 0.602558i
\(401\) −27.5972 15.9333i −1.37814 0.795670i −0.386205 0.922413i \(-0.626214\pi\)
−0.991936 + 0.126743i \(0.959548\pi\)
\(402\) −0.184800 1.42683i −0.00921699 0.0711640i
\(403\) −28.5283 7.64415i −1.42110 0.380782i
\(404\) −34.6273 4.95880i −1.72277 0.246710i
\(405\) −0.102758 7.19517i −0.00510607 0.357531i
\(406\) 14.7855 + 13.7364i 0.733793 + 0.681727i
\(407\) 1.32484 0.0656698
\(408\) 10.7882 + 6.42340i 0.534097 + 0.318006i
\(409\) −11.4370 19.8094i −0.565522 0.979512i −0.997001 0.0773894i \(-0.975342\pi\)
0.431479 0.902123i \(-0.357992\pi\)
\(410\) 2.92116 5.83983i 0.144266 0.288409i
\(411\) −1.16824 16.8993i −0.0576251 0.833579i
\(412\) 15.1700 + 6.48607i 0.747370 + 0.319546i
\(413\) −0.147053 0.268805i −0.00723599 0.0132271i
\(414\) −13.2096 8.79827i −0.649215 0.432411i
\(415\) −1.51617 + 2.62609i −0.0744261 + 0.128910i
\(416\) −11.4091 37.0264i −0.559379 1.81537i
\(417\) −11.0895 + 3.80859i −0.543056 + 0.186507i
\(418\) 11.9634 + 10.6122i 0.585149 + 0.519060i
\(419\) −3.03969 + 3.03969i −0.148498 + 0.148498i −0.777447 0.628949i \(-0.783486\pi\)
0.628949 + 0.777447i \(0.283486\pi\)
\(420\) 4.65979 + 5.65555i 0.227375 + 0.275963i
\(421\) −8.07074 8.07074i −0.393344 0.393344i 0.482534 0.875877i \(-0.339717\pi\)
−0.875877 + 0.482534i \(0.839717\pi\)
\(422\) −14.3998 + 0.861856i −0.700971 + 0.0419545i
\(423\) −10.0453 + 1.39553i −0.488421 + 0.0678531i
\(424\) −13.8936 + 11.7725i −0.674734 + 0.571721i
\(425\) 9.67888 + 5.58811i 0.469495 + 0.271063i
\(426\) 9.30982 + 22.6100i 0.451062 + 1.09546i
\(427\) 16.2875 26.7685i 0.788207 1.29542i
\(428\) −25.4997 + 10.2252i −1.23257 + 0.494252i
\(429\) 3.35961 + 48.5986i 0.162203 + 2.34636i
\(430\) −2.85511 8.57021i −0.137686 0.413292i
\(431\) −0.978915 + 0.565177i −0.0471527 + 0.0272236i −0.523391 0.852093i \(-0.675333\pi\)
0.476238 + 0.879316i \(0.342000\pi\)
\(432\) 8.96908 + 18.7498i 0.431525 + 0.902101i
\(433\) 5.35407i 0.257300i 0.991690 + 0.128650i \(0.0410644\pi\)
−0.991690 + 0.128650i \(0.958936\pi\)
\(434\) −13.6672 + 8.57555i −0.656045 + 0.411640i
\(435\) −4.17203 6.19589i −0.200034 0.297070i
\(436\) −0.138719 + 0.968674i −0.00664344 + 0.0463911i
\(437\) −2.66623 + 9.95049i −0.127543 + 0.475996i
\(438\) −13.8451 + 17.9650i −0.661543 + 0.858403i
\(439\) 1.00125 1.73421i 0.0477869 0.0827693i −0.841143 0.540813i \(-0.818117\pi\)
0.888929 + 0.458044i \(0.151450\pi\)
\(440\) −5.28988 + 7.63260i −0.252185 + 0.363870i
\(441\) 17.1449 12.1266i 0.816423 0.577455i
\(442\) 20.7188 13.6746i 0.985495 0.650436i
\(443\) −0.415854 1.55199i −0.0197578 0.0737372i 0.955343 0.295499i \(-0.0954859\pi\)
−0.975101 + 0.221762i \(0.928819\pi\)
\(444\) 0.0817559 1.11461i 0.00387996 0.0528972i
\(445\) 10.0763 + 2.69993i 0.477661 + 0.127989i
\(446\) 5.64954 6.36886i 0.267513 0.301574i
\(447\) −2.87838 + 14.7455i −0.136143 + 0.697439i
\(448\) −19.0614 9.20133i −0.900565 0.434722i
\(449\) 33.4703i 1.57956i −0.613388 0.789782i \(-0.710194\pi\)
0.613388 0.789782i \(-0.289806\pi\)
\(450\) 8.20718 + 16.5810i 0.386890 + 0.781635i
\(451\) 6.13755 22.9057i 0.289006 1.07859i
\(452\) 15.5472 1.86775i 0.731279 0.0878517i
\(453\) 10.0646 0.695763i 0.472876 0.0326898i
\(454\) −9.11399 13.8089i −0.427741 0.648083i
\(455\) 14.0775 3.42685i 0.659962 0.160653i
\(456\) 9.66651 9.41016i 0.452676 0.440671i
\(457\) −15.6355 9.02716i −0.731398 0.422273i 0.0875356 0.996161i \(-0.472101\pi\)
−0.818933 + 0.573889i \(0.805434\pi\)
\(458\) −4.77148 + 9.53889i −0.222956 + 0.445723i
\(459\) −9.91789 + 8.88747i −0.462928 + 0.414831i
\(460\) −5.92167 0.848014i −0.276099 0.0395388i
\(461\) −10.0127 + 10.0127i −0.466340 + 0.466340i −0.900727 0.434387i \(-0.856965\pi\)
0.434387 + 0.900727i \(0.356965\pi\)
\(462\) 20.6998 + 16.7259i 0.963042 + 0.778159i
\(463\) −35.1541 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(464\) 18.4352 + 11.2085i 0.855833 + 0.520340i
\(465\) 5.64796 1.93974i 0.261918 0.0899532i
\(466\) 22.7676 7.58487i 1.05469 0.351362i
\(467\) −6.23032 23.2519i −0.288305 1.07597i −0.946390 0.323025i \(-0.895300\pi\)
0.658086 0.752943i \(-0.271366\pi\)
\(468\) 41.0942 + 0.172518i 1.89958 + 0.00797464i
\(469\) −1.36335 + 0.745836i −0.0629538 + 0.0344395i
\(470\) −3.19032 + 2.10564i −0.147158 + 0.0971259i
\(471\) −1.76629 + 2.02863i −0.0813864 + 0.0934745i
\(472\) −0.211753 0.249906i −0.00974671 0.0115029i
\(473\) −16.4030 28.4108i −0.754209 1.30633i
\(474\) 29.6203 + 3.96286i 1.36051 + 0.182020i
\(475\) 8.49112 8.49112i 0.389599 0.389599i
\(476\) 2.23093 13.3770i 0.102255 0.613132i
\(477\) −7.51883 17.7917i −0.344264 0.814625i
\(478\) −1.04815 + 1.18160i −0.0479412 + 0.0540453i
\(479\) −3.73185 6.46375i −0.170513 0.295336i 0.768087 0.640346i \(-0.221209\pi\)
−0.938599 + 0.345010i \(0.887876\pi\)
\(480\) 6.09501 + 4.92149i 0.278198 + 0.224634i
\(481\) −1.91365 1.10485i −0.0872549 0.0503766i
\(482\) −7.87589 1.61308i −0.358737 0.0734738i
\(483\) −3.67075 + 16.7455i −0.167025 + 0.761946i
\(484\) −4.60972 + 10.7815i −0.209533 + 0.490066i
\(485\) −3.15465 11.7733i −0.143245 0.534599i
\(486\) −21.8201 + 3.14353i −0.989781 + 0.142593i
\(487\) 16.6305 9.60162i 0.753599 0.435091i −0.0733936 0.997303i \(-0.523383\pi\)
0.826993 + 0.562212i \(0.190050\pi\)
\(488\) 11.3054 31.5323i 0.511771 1.42740i
\(489\) 7.17737 36.7686i 0.324572 1.66273i
\(490\) 3.86293 6.90844i 0.174509 0.312091i
\(491\) −12.3610 + 12.3610i −0.557845 + 0.557845i −0.928694 0.370848i \(-0.879067\pi\)
0.370848 + 0.928694i \(0.379067\pi\)
\(492\) −18.8922 6.57715i −0.851727 0.296521i
\(493\) −3.57788 + 13.3528i −0.161139 + 0.601381i
\(494\) −8.43038 25.3055i −0.379301 1.13855i
\(495\) −6.05185 7.77139i −0.272010 0.349298i
\(496\) −12.4702 + 11.9171i −0.559928 + 0.535092i
\(497\) 19.1001 18.2406i 0.856758 0.818201i
\(498\) 8.57528 + 3.57310i 0.384267 + 0.160115i
\(499\) 4.68841 + 17.4974i 0.209882 + 0.783290i 0.987906 + 0.155055i \(0.0495556\pi\)
−0.778024 + 0.628235i \(0.783778\pi\)
\(500\) 11.7714 + 9.24640i 0.526431 + 0.413511i
\(501\) −5.78485 + 11.8369i −0.258448 + 0.528832i
\(502\) −0.456479 7.62680i −0.0203737 0.340401i
\(503\) 27.5591i 1.22880i 0.788995 + 0.614400i \(0.210602\pi\)
−0.788995 + 0.614400i \(0.789398\pi\)
\(504\) 15.3492 16.3830i 0.683707 0.729756i
\(505\) 13.9843i 0.622291i
\(506\) −21.6862 + 1.29796i −0.964068 + 0.0577014i
\(507\) 25.7892 52.7694i 1.14534 2.34357i
\(508\) −0.540189 4.49654i −0.0239670 0.199502i
\(509\) 0.931585 + 3.47672i 0.0412918 + 0.154103i 0.983494 0.180943i \(-0.0579149\pi\)
−0.942202 + 0.335046i \(0.891248\pi\)
\(510\) −1.93058 + 4.63331i −0.0854876 + 0.205166i
\(511\) 23.5114 + 6.88353i 1.04008 + 0.304509i
\(512\) −21.9386 5.54048i −0.969559 0.244857i
\(513\) 6.46570 + 12.7646i 0.285468 + 0.563573i
\(514\) 29.4484 9.81056i 1.29891 0.432725i
\(515\) −1.70707 + 6.37086i −0.0752224 + 0.280734i
\(516\) −24.9147 + 12.0469i −1.09681 + 0.530335i
\(517\) −9.81621 + 9.81621i −0.431717 + 0.431717i
\(518\) −1.15375 + 0.355082i −0.0506928 + 0.0156014i
\(519\) −0.874356 + 4.47920i −0.0383800 + 0.196615i
\(520\) 14.0061 6.61334i 0.614208 0.290014i
\(521\) 14.5793 8.41736i 0.638731 0.368771i −0.145395 0.989374i \(-0.546445\pi\)
0.784125 + 0.620602i \(0.213112\pi\)
\(522\) −17.1828 + 15.1137i −0.752071 + 0.661508i
\(523\) 9.64668 + 36.0019i 0.421820 + 1.57425i 0.770771 + 0.637112i \(0.219871\pi\)
−0.348951 + 0.937141i \(0.613462\pi\)
\(524\) 1.27159 0.509896i 0.0555495 0.0222749i
\(525\) 13.4656 14.7653i 0.587687 0.644408i
\(526\) −5.64777 + 27.5753i −0.246254 + 1.20234i
\(527\) −9.57118 5.52593i −0.416927 0.240713i
\(528\) 25.2711 + 13.0684i 1.09979 + 0.568729i
\(529\) 4.50272 + 7.79894i 0.195771 + 0.339085i
\(530\) −5.44615 4.83104i −0.236566 0.209847i
\(531\) 0.320021 0.135242i 0.0138877 0.00586901i
\(532\) −13.2627 6.03531i −0.575012 0.261664i
\(533\) −27.9674 + 27.9674i −1.21140 + 1.21140i
\(534\) 4.23794 31.6764i 0.183394 1.37077i
\(535\) −5.49156 9.51166i −0.237421 0.411225i
\(536\) −1.26750 + 1.07399i −0.0547476 + 0.0463892i
\(537\) −9.58904 + 11.0133i −0.413798 + 0.475258i
\(538\) −20.6104 31.2274i −0.888576 1.34631i
\(539\) 8.70950 27.3938i 0.375145 1.17994i
\(540\) −6.91168 + 4.61196i −0.297431 + 0.198467i
\(541\) 1.83812 + 6.85996i 0.0790270 + 0.294933i 0.994116 0.108319i \(-0.0345467\pi\)
−0.915089 + 0.403251i \(0.867880\pi\)
\(542\) 0.131027 + 0.393306i 0.00562811 + 0.0168939i
\(543\) 17.7534 6.09726i 0.761873 0.261658i
\(544\) −0.537814 14.4881i −0.0230586 0.621173i
\(545\) −0.391200 −0.0167572
\(546\) −15.9511 41.4221i −0.682644 1.77270i
\(547\) 25.8698 25.8698i 1.10611 1.10611i 0.112457 0.993657i \(-0.464128\pi\)
0.993657 0.112457i \(-0.0358719\pi\)
\(548\) −15.6521 + 11.7308i −0.668626 + 0.501113i
\(549\) 28.3413 + 21.4273i 1.20958 + 0.914495i
\(550\) 22.6489 + 11.3293i 0.965751 + 0.483081i
\(551\) 12.8631 + 7.42651i 0.547986 + 0.316380i
\(552\) −0.246256 + 18.3251i −0.0104813 + 0.779967i
\(553\) −7.63459 31.3628i −0.324656 1.33368i
\(554\) −4.49403 + 2.96610i −0.190933 + 0.126018i
\(555\) 0.445725 0.0308129i 0.0189200 0.00130793i
\(556\) 10.6472 + 8.36341i 0.451543 + 0.354687i
\(557\) −2.44214 + 9.11418i −0.103477 + 0.386180i −0.998168 0.0605049i \(-0.980729\pi\)
0.894691 + 0.446685i \(0.147396\pi\)
\(558\) −8.11586 16.3965i −0.343572 0.694119i
\(559\) 54.7168i 2.31427i
\(560\) 2.56106 8.06471i 0.108225 0.340796i
\(561\) −3.49244 + 17.8912i −0.147451 + 0.755369i
\(562\) −17.9252 15.9006i −0.756128 0.670728i
\(563\) −30.9965 8.30549i −1.30635 0.350035i −0.462500 0.886619i \(-0.653048\pi\)
−0.843847 + 0.536585i \(0.819714\pi\)
\(564\) 7.65281 + 8.86433i 0.322241 + 0.373255i
\(565\) 1.62022 + 6.04673i 0.0681631 + 0.254388i
\(566\) 5.21143 + 7.89600i 0.219053 + 0.331894i
\(567\) 11.7253 + 20.7248i 0.492416 + 0.870360i
\(568\) 16.0832 23.2059i 0.674835 0.973697i
\(569\) −8.58044 + 14.8618i −0.359711 + 0.623037i −0.987912 0.155013i \(-0.950458\pi\)
0.628202 + 0.778051i \(0.283791\pi\)
\(570\) 4.27175 + 3.29210i 0.178924 + 0.137891i
\(571\) −1.07584 + 4.01510i −0.0450226 + 0.168027i −0.984777 0.173825i \(-0.944387\pi\)
0.939754 + 0.341852i \(0.111054\pi\)
\(572\) 45.0121 33.7351i 1.88205 1.41053i
\(573\) −16.7924 24.9384i −0.701514 1.04182i
\(574\) 0.794214 + 21.5926i 0.0331499 + 0.901258i
\(575\) 16.3132i 0.680306i
\(576\) 12.5542 20.4546i 0.523091 0.852277i
\(577\) −9.69166 + 5.59548i −0.403469 + 0.232943i −0.687980 0.725730i \(-0.741502\pi\)
0.284511 + 0.958673i \(0.408169\pi\)
\(578\) −13.9960 + 4.66269i −0.582158 + 0.193942i
\(579\) 0.743357 + 10.7531i 0.0308929 + 0.446882i
\(580\) −3.39084 + 7.93066i −0.140797 + 0.329303i
\(581\) 0.230923 10.0316i 0.00958028 0.416181i
\(582\) −34.5287 + 14.2174i −1.43126 + 0.589330i
\(583\) −22.8967 13.2194i −0.948285 0.547492i
\(584\) 26.1008 + 2.15709i 1.08006 + 0.0892612i
\(585\) 2.26059 + 16.2722i 0.0934640 + 0.672774i
\(586\) −2.20101 36.7743i −0.0909231 1.51913i
\(587\) 30.0034 + 30.0034i 1.23837 + 1.23837i 0.960666 + 0.277707i \(0.0895746\pi\)
0.277707 + 0.960666i \(0.410425\pi\)
\(588\) −22.5095 9.01795i −0.928275 0.371894i
\(589\) −8.39664 + 8.39664i −0.345977 + 0.345977i
\(590\) 0.0868965 0.0979606i 0.00357747 0.00403297i
\(591\) −42.7418 + 14.6793i −1.75816 + 0.603825i
\(592\) −1.13195 + 0.619743i −0.0465229 + 0.0254713i
\(593\) 4.85090 8.40201i 0.199203 0.345029i −0.749067 0.662494i \(-0.769498\pi\)
0.948270 + 0.317465i \(0.102831\pi\)
\(594\) −21.2298 + 21.4449i −0.871070 + 0.879897i
\(595\) 5.42017 + 0.124770i 0.222205 + 0.00511506i
\(596\) 16.1017 6.45665i 0.659552 0.264475i
\(597\) −0.140909 2.03832i −0.00576702 0.0834230i
\(598\) 32.4068 + 16.2103i 1.32521 + 0.662888i
\(599\) 0.529267 + 0.916718i 0.0216253 + 0.0374561i 0.876636 0.481155i \(-0.159783\pi\)
−0.855010 + 0.518611i \(0.826449\pi\)
\(600\) 10.9292 18.3558i 0.446182 0.749372i
\(601\) 33.7798 1.37791 0.688953 0.724806i \(-0.258071\pi\)
0.688953 + 0.724806i \(0.258071\pi\)
\(602\) 21.8993 + 20.3455i 0.892549 + 0.829219i
\(603\) −0.685934 1.62311i −0.0279334 0.0660983i
\(604\) −6.98642 9.32185i −0.284273 0.379301i
\(605\) −4.52784 1.21323i −0.184083 0.0493249i
\(606\) −42.4874 + 5.50286i −1.72593 + 0.223539i
\(607\) −25.8950 14.9505i −1.05105 0.606822i −0.128104 0.991761i \(-0.540889\pi\)
−0.922942 + 0.384939i \(0.874223\pi\)
\(608\) −15.1859 3.47080i −0.615868 0.140760i
\(609\) 21.9516 + 11.3612i 0.889525 + 0.460380i
\(610\) 13.1191 + 2.68697i 0.531179 + 0.108792i
\(611\) 22.3651 5.99272i 0.904796 0.242439i
\(612\) 14.8367 + 4.04232i 0.599739 + 0.163401i
\(613\) −3.23477 + 12.0723i −0.130651 + 0.487596i −0.999978 0.00664139i \(-0.997886\pi\)
0.869327 + 0.494237i \(0.164553\pi\)
\(614\) 0.967101 + 16.1582i 0.0390290 + 0.652092i
\(615\) 1.53216 7.84906i 0.0617828 0.316505i
\(616\) 3.23514 30.5590i 0.130348 1.23126i
\(617\) −33.1658 −1.33521 −0.667603 0.744517i \(-0.732680\pi\)
−0.667603 + 0.744517i \(0.732680\pi\)
\(618\) 20.0279 + 2.67950i 0.805639 + 0.107785i
\(619\) 17.6747 + 4.73593i 0.710407 + 0.190353i 0.595887 0.803068i \(-0.296801\pi\)
0.114519 + 0.993421i \(0.463467\pi\)
\(620\) −5.42271 4.25954i −0.217781 0.171067i
\(621\) −18.4727 6.05078i −0.741284 0.242810i
\(622\) 11.6896 + 2.39417i 0.468709 + 0.0959975i
\(623\) −33.5399 + 8.16455i −1.34375 + 0.327106i
\(624\) −25.6043 39.9513i −1.02499 1.59933i
\(625\) 7.90979 13.7002i 0.316392 0.548006i
\(626\) −15.9841 + 5.32500i −0.638853 + 0.212830i
\(627\) 17.5970 + 8.59991i 0.702756 + 0.343447i
\(628\) 3.07457 + 0.440294i 0.122689 + 0.0175697i
\(629\) −0.584681 0.584681i −0.0233128 0.0233128i
\(630\) 7.35319 + 5.14578i 0.292958 + 0.205013i
\(631\) 12.6471i 0.503472i 0.967796 + 0.251736i \(0.0810014\pi\)
−0.967796 + 0.251736i \(0.918999\pi\)
\(632\) −14.7337 31.2038i −0.586074 1.24122i
\(633\) −16.7096 + 5.73877i −0.664148 + 0.228095i
\(634\) −27.7774 13.8946i −1.10318 0.551826i
\(635\) 1.74883 0.468597i 0.0694001 0.0185957i
\(636\) −12.5347 + 18.4477i −0.497033 + 0.731497i
\(637\) −35.4254 + 32.3054i −1.40360 + 1.27999i
\(638\) −6.28502 + 30.6867i −0.248826 + 1.21490i
\(639\) 18.3998 + 23.6279i 0.727885 + 0.934704i
\(640\) 0.949272 8.99588i 0.0375233 0.355593i
\(641\) −18.3872 + 10.6158i −0.726250 + 0.419301i −0.817049 0.576569i \(-0.804391\pi\)
0.0907987 + 0.995869i \(0.471058\pi\)
\(642\) −26.7376 + 20.4275i −1.05525 + 0.806208i
\(643\) −11.2326 11.2326i −0.442972 0.442972i 0.450038 0.893010i \(-0.351411\pi\)
−0.893010 + 0.450038i \(0.851411\pi\)
\(644\) 18.5377 6.94265i 0.730489 0.273579i
\(645\) −6.17933 9.17693i −0.243311 0.361341i
\(646\) −0.596313 9.96312i −0.0234616 0.391994i
\(647\) 36.4667 21.0540i 1.43365 0.827720i 0.436256 0.899823i \(-0.356304\pi\)
0.997397 + 0.0721029i \(0.0229710\pi\)
\(648\) 16.7320 + 19.1844i 0.657293 + 0.753635i
\(649\) 0.237779 0.411846i 0.00933366 0.0161664i
\(650\) −23.2669 35.2524i −0.912603 1.38271i
\(651\) −13.3158 + 14.6010i −0.521886 + 0.572257i
\(652\) −40.1504 + 16.1000i −1.57241 + 0.630523i
\(653\) 6.37257 1.70752i 0.249378 0.0668206i −0.131965 0.991254i \(-0.542129\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(654\) 0.153939 + 1.18855i 0.00601948 + 0.0464761i
\(655\) 0.273846 + 0.474316i 0.0107001 + 0.0185330i
\(656\) 5.47102 + 22.4418i 0.213608 + 0.876205i
\(657\) −10.4468 + 25.7392i −0.407570 + 1.00418i
\(658\) 5.91761 11.1795i 0.230692 0.435821i
\(659\) 1.14982 + 1.14982i 0.0447907 + 0.0447907i 0.729147 0.684357i \(-0.239917\pi\)
−0.684357 + 0.729147i \(0.739917\pi\)
\(660\) −3.73948 + 10.7413i −0.145559 + 0.418104i
\(661\) 14.9738 + 4.01223i 0.582414 + 0.156057i 0.537984 0.842955i \(-0.319186\pi\)
0.0444303 + 0.999012i \(0.485853\pi\)
\(662\) 17.3913 + 8.69937i 0.675933 + 0.338111i
\(663\) 19.9650 22.9303i 0.775375 0.890539i
\(664\) −1.91352 10.5550i −0.0742589 0.409614i
\(665\) 1.63677 5.59056i 0.0634713 0.216792i
\(666\) −0.269011 1.34209i −0.0104240 0.0520048i
\(667\) −19.4902 + 5.22239i −0.754664 + 0.202212i
\(668\) 15.1044 1.81455i 0.584405 0.0702072i
\(669\) 4.57827 9.36797i 0.177006 0.362187i
\(670\) −0.496846 0.440730i −0.0191948 0.0170269i
\(671\) 48.6335 1.87747
\(672\) −25.5102 4.60758i −0.984077 0.177741i
\(673\) −32.7518 −1.26249 −0.631244 0.775584i \(-0.717456\pi\)
−0.631244 + 0.775584i \(0.717456\pi\)
\(674\) −10.9119 9.67947i −0.420311 0.372839i
\(675\) 15.1217 + 16.8750i 0.582035 + 0.649517i
\(676\) −67.3361 + 8.08938i −2.58985 + 0.311130i
\(677\) −18.6656 + 5.00142i −0.717376 + 0.192220i −0.599001 0.800749i \(-0.704435\pi\)
−0.118375 + 0.992969i \(0.537769\pi\)
\(678\) 17.7338 7.30200i 0.681062 0.280432i
\(679\) 27.8559 + 29.1686i 1.06901 + 1.11939i
\(680\) 5.70298 1.03389i 0.218699 0.0396480i
\(681\) −15.2828 13.3064i −0.585638 0.509903i
\(682\) −22.3969 11.2032i −0.857620 0.428993i
\(683\) 8.09880 + 2.17007i 0.309892 + 0.0830353i 0.410413 0.911900i \(-0.365384\pi\)
−0.100521 + 0.994935i \(0.532051\pi\)
\(684\) 8.32118 14.2740i 0.318168 0.545779i
\(685\) −5.52930 5.52930i −0.211264 0.211264i
\(686\) −0.242680 + 26.1905i −0.00926558 + 0.999957i
\(687\) −2.50266 + 12.8208i −0.0954826 + 0.489144i
\(688\) 27.3050 + 16.6012i 1.04099 + 0.632915i
\(689\) 22.0486 + 38.1893i 0.839985 + 1.45490i
\(690\) −7.26584 + 0.941055i −0.276606 + 0.0358253i
\(691\) 25.9533 6.95418i 0.987312 0.264549i 0.271191 0.962526i \(-0.412583\pi\)
0.716121 + 0.697976i \(0.245916\pi\)
\(692\) 4.89117 1.96132i 0.185934 0.0745581i
\(693\) 29.9109 + 12.9496i 1.13622 + 0.491913i
\(694\) −27.2856 41.3412i −1.03575 1.56929i
\(695\) −2.70630 + 4.68745i −0.102656 + 0.177805i
\(696\) 25.4295 + 7.18139i 0.963901 + 0.272210i
\(697\) −12.8174 + 7.40014i −0.485495 + 0.280300i
\(698\) 0.0468049 + 0.782010i 0.00177159 + 0.0295995i
\(699\) 24.3794 16.4160i 0.922112 0.620909i
\(700\) −22.7604 3.79586i −0.860264 0.143470i
\(701\) −1.73634 1.73634i −0.0655806 0.0655806i 0.673556 0.739136i \(-0.264766\pi\)
−0.739136 + 0.673556i \(0.764766\pi\)
\(702\) 48.5491 13.2714i 1.83237 0.500896i
\(703\) −0.769396 + 0.444211i −0.0290183 + 0.0167537i
\(704\) −3.17783 32.6974i −0.119769 1.23233i
\(705\) −3.07423 + 3.53084i −0.115782 + 0.132979i
\(706\) 1.76450 8.61520i 0.0664079 0.324237i
\(707\) 22.2091 + 40.5971i 0.835257 + 1.52681i
\(708\) −0.331821 0.225463i −0.0124706 0.00847344i
\(709\) −2.11854 + 0.567661i −0.0795634 + 0.0213190i −0.298381 0.954447i \(-0.596447\pi\)
0.218818 + 0.975766i \(0.429780\pi\)
\(710\) 10.0948 + 5.04957i 0.378853 + 0.189507i
\(711\) 36.2524 5.03631i 1.35957 0.188876i
\(712\) −33.3698 + 15.7564i −1.25059 + 0.590497i
\(713\) 16.1317i 0.604135i
\(714\) −1.75378 16.5168i −0.0656335 0.618126i
\(715\) 15.9011 + 15.9011i 0.594666 + 0.594666i
\(716\) 16.6916 + 2.39032i 0.623794 + 0.0893305i
\(717\) −0.849398 + 1.73802i −0.0317213 + 0.0649077i
\(718\) −26.1141 + 8.69976i −0.974571 + 0.324672i
\(719\) 4.98414 8.63278i 0.185877 0.321948i −0.757995 0.652261i \(-0.773821\pi\)
0.943872 + 0.330312i \(0.107154\pi\)
\(720\) 8.80609 + 3.80894i 0.328184 + 0.141951i
\(721\) −5.16215 21.2060i −0.192248 0.789754i
\(722\) 15.8177 + 3.23966i 0.588674 + 0.120568i
\(723\) −9.82275 + 0.679045i −0.365312 + 0.0252539i
\(724\) −17.0454 13.3892i −0.633487 0.497604i
\(725\) 22.7194 + 6.08764i 0.843776 + 0.226089i
\(726\) −1.90435 + 14.2340i −0.0706770 + 0.528274i
\(727\) −29.3459 −1.08838 −0.544190 0.838962i \(-0.683163\pi\)
−0.544190 + 0.838962i \(0.683163\pi\)
\(728\) −30.1575 + 41.4426i −1.11771 + 1.53597i
\(729\) −24.7177 + 10.8644i −0.915471 + 0.402384i
\(730\) 0.625529 + 10.4513i 0.0231519 + 0.386818i
\(731\) −5.29931 + 19.7773i −0.196002 + 0.731490i
\(732\) 3.00117 40.9163i 0.110927 1.51231i
\(733\) 29.5310 7.91280i 1.09075 0.292266i 0.331758 0.943365i \(-0.392358\pi\)
0.758993 + 0.651099i \(0.225692\pi\)
\(734\) −9.41283 1.92787i −0.347434 0.0711588i
\(735\) 2.29308 9.41886i 0.0845815 0.347420i
\(736\) 17.9216 11.2535i 0.660600 0.414810i
\(737\) −2.08884 1.20599i −0.0769434 0.0444233i
\(738\) −24.4501 1.56643i −0.900022 0.0576610i
\(739\) 35.8845 + 9.61523i 1.32003 + 0.353702i 0.848991 0.528408i \(-0.177211\pi\)
0.471043 + 0.882110i \(0.343878\pi\)
\(740\) −0.309403 0.412831i −0.0113739 0.0151760i
\(741\) −18.2459 27.0970i −0.670280 0.995434i
\(742\) 23.4829 + 5.37549i 0.862083 + 0.197341i
\(743\) 16.7999 0.616330 0.308165 0.951333i \(-0.400285\pi\)
0.308165 + 0.951333i \(0.400285\pi\)
\(744\) −10.8076 + 18.1516i −0.396225 + 0.665468i
\(745\) 3.46763 + 6.00612i 0.127044 + 0.220047i
\(746\) −15.3247 7.66559i −0.561075 0.280657i
\(747\) 11.2907 + 1.40451i 0.413107 + 0.0513885i
\(748\) 19.5368 7.83408i 0.714335 0.286442i
\(749\) 31.0482 + 18.8915i 1.13448 + 0.690280i
\(750\) 16.9225 + 7.05119i 0.617923 + 0.257473i
\(751\) 0.792234 1.37219i 0.0289090 0.0500719i −0.851209 0.524827i \(-0.824130\pi\)
0.880118 + 0.474755i \(0.157463\pi\)
\(752\) 3.79513 12.9789i 0.138394 0.473293i
\(753\) −3.03952 8.85019i −0.110766 0.322519i
\(754\) 34.6694 39.0837i 1.26259 1.42334i
\(755\) 3.29306 3.29306i 0.119847 0.119847i
\(756\) 12.7405 24.3655i 0.463368 0.886166i
\(757\) −26.3149 26.3149i −0.956430 0.956430i 0.0426596 0.999090i \(-0.486417\pi\)
−0.999090 + 0.0426596i \(0.986417\pi\)
\(758\) −2.92389 48.8520i −0.106201 1.77439i
\(759\) −25.1648 + 8.64261i −0.913424 + 0.313707i
\(760\) 0.512916 6.20628i 0.0186054 0.225125i
\(761\) −24.1624 13.9502i −0.875887 0.505694i −0.00658710 0.999978i \(-0.502097\pi\)
−0.869300 + 0.494285i \(0.835430\pi\)
\(762\) −2.11188 5.12894i −0.0765052 0.185802i
\(763\) 1.13568 0.621283i 0.0411142 0.0224919i
\(764\) −13.6481 + 31.9209i −0.493772 + 1.15486i
\(765\) −0.758873 + 6.10050i −0.0274371 + 0.220564i
\(766\) 39.3480 13.1085i 1.42170 0.473631i
\(767\) −0.686916 + 0.396591i −0.0248031 + 0.0143201i
\(768\) −27.7051 + 0.655809i −0.999720 + 0.0236645i
\(769\) 6.53834i 0.235779i −0.993027 0.117889i \(-0.962387\pi\)
0.993027 0.117889i \(-0.0376128\pi\)
\(770\) 12.2766 0.451556i 0.442418 0.0162729i
\(771\) 31.5332 21.2330i 1.13564 0.764689i
\(772\) 9.95952 7.46433i 0.358451 0.268647i
\(773\) −0.725416 + 2.70729i −0.0260914 + 0.0973744i −0.977744 0.209803i \(-0.932718\pi\)
0.951652 + 0.307177i \(0.0993845\pi\)
\(774\) −25.4500 + 22.3854i −0.914781 + 0.804626i
\(775\) −9.40217 + 16.2850i −0.337736 + 0.584976i
\(776\) 35.4386 + 24.5612i 1.27217 + 0.881697i
\(777\) −1.24503 + 0.797328i −0.0446652 + 0.0286040i
\(778\) 20.4322 + 30.9575i 0.732531 + 1.10988i
\(779\) 4.11578 + 15.3603i 0.147463 + 0.550339i
\(780\) 14.3591 12.3966i 0.514139 0.443870i
\(781\) 39.5952 + 10.6095i 1.41683 + 0.379637i
\(782\) 10.1434 + 8.99777i 0.362728 + 0.321760i
\(783\) −15.3204 + 23.4690i −0.547508 + 0.838712i
\(784\) 5.37304 + 27.4796i 0.191894 + 0.981416i
\(785\) 1.24167i 0.0443171i
\(786\) 1.33332 1.01865i 0.0475579 0.0363341i
\(787\) −7.34751 + 27.4213i −0.261911 + 0.977464i 0.702204 + 0.711976i \(0.252200\pi\)
−0.964114 + 0.265488i \(0.914467\pi\)
\(788\) 41.0372 + 32.2347i 1.46189 + 1.14831i
\(789\) 2.37749 + 34.3917i 0.0846409 + 1.22438i
\(790\) 11.5135 7.59899i 0.409631 0.270360i
\(791\) −14.3067 14.9809i −0.508687 0.532658i
\(792\) 34.1060 + 7.13465i 1.21190 + 0.253519i
\(793\) −70.2481 40.5578i −2.49458 1.44025i
\(794\) 7.86506 + 3.93421i 0.279121 + 0.139620i
\(795\) −8.01075 3.91497i −0.284112 0.138850i
\(796\) −1.88790 + 1.41492i −0.0669148 + 0.0501505i
\(797\) 30.0823 30.0823i 1.06557 1.06557i 0.0678778 0.997694i \(-0.478377\pi\)
0.997694 0.0678778i \(-0.0216228\pi\)
\(798\) −17.6294 2.77298i −0.624076 0.0981624i
\(799\) 8.66423 0.306518
\(800\) −24.6510 + 0.915072i −0.871545 + 0.0323527i
\(801\) −5.38591 38.7689i −0.190302 1.36983i
\(802\) 14.2439 + 42.7559i 0.502968 + 1.50976i
\(803\) 9.84120 + 36.7278i 0.347288 + 1.29610i
\(804\) −1.14353 + 1.68296i −0.0403291 + 0.0593534i
\(805\) 3.79801 + 6.94258i 0.133862 + 0.244694i
\(806\) 23.0080 + 34.8601i 0.810423 + 1.22790i
\(807\) −34.5605 30.0912i −1.21659 1.05926i
\(808\) 31.9805 + 37.7428i 1.12507 + 1.32779i
\(809\) 1.08417 + 1.87783i 0.0381173 + 0.0660211i 0.884455 0.466626i \(-0.154531\pi\)
−0.846337 + 0.532647i \(0.821197\pi\)
\(810\) −6.64373 + 7.70863i −0.233437 + 0.270854i
\(811\) 24.6635 24.6635i 0.866053 0.866053i −0.125980 0.992033i \(-0.540208\pi\)
0.992033 + 0.125980i \(0.0402075\pi\)
\(812\) −2.75126 28.4083i −0.0965503 0.996936i
\(813\) 0.283583 + 0.421149i 0.00994569 + 0.0147704i
\(814\) −1.40162 1.24332i −0.0491269 0.0435783i
\(815\) −8.64670 14.9765i −0.302881 0.524605i
\(816\) −5.38534 16.9201i −0.188525 0.592322i
\(817\) 19.0519 + 10.9996i 0.666543 + 0.384829i
\(818\) −6.49067 + 31.6908i −0.226941 + 1.10804i
\(819\) −32.4053 43.6490i −1.13233 1.52522i
\(820\) −8.57097 + 3.43689i −0.299311 + 0.120021i
\(821\) −5.27434 19.6841i −0.184076 0.686980i −0.994826 0.101589i \(-0.967607\pi\)
0.810751 0.585392i \(-0.199059\pi\)
\(822\) −14.6235 + 18.9751i −0.510052 + 0.661832i
\(823\) −0.798483 + 0.461005i −0.0278334 + 0.0160696i −0.513852 0.857879i \(-0.671782\pi\)
0.486019 + 0.873948i \(0.338449\pi\)
\(824\) −9.96221 21.0985i −0.347050 0.735002i
\(825\) 30.4413 + 5.94226i 1.05983 + 0.206883i
\(826\) −0.0966897 + 0.422390i −0.00336427 + 0.0146968i
\(827\) 33.1087 33.1087i 1.15130 1.15130i 0.165010 0.986292i \(-0.447234\pi\)
0.986292 0.165010i \(-0.0527657\pi\)
\(828\) 5.71827 + 21.7050i 0.198724 + 0.754300i
\(829\) −10.6698 + 39.8202i −0.370577 + 1.38301i 0.489123 + 0.872215i \(0.337317\pi\)
−0.859701 + 0.510798i \(0.829350\pi\)
\(830\) 4.06855 1.35541i 0.141222 0.0470471i
\(831\) −4.33051 + 4.97371i −0.150224 + 0.172536i
\(832\) −22.6777 + 49.8796i −0.786209 + 1.72926i
\(833\) −15.9332 + 8.24581i −0.552053 + 0.285700i
\(834\) 15.3065 + 6.37783i 0.530020 + 0.220846i
\(835\) 1.57407 + 5.87450i 0.0544728 + 0.203295i
\(836\) −2.69756 22.4545i −0.0932972 0.776607i
\(837\) −14.9535 16.6872i −0.516867 0.576793i
\(838\) 6.06851 0.363213i 0.209633 0.0125470i
\(839\) 17.9010i 0.618011i 0.951060 + 0.309006i \(0.0999962\pi\)
−0.951060 + 0.309006i \(0.900004\pi\)
\(840\) 0.377688 10.3564i 0.0130315 0.357330i
\(841\) 0.0929014i 0.00320350i
\(842\) 0.964374 + 16.1127i 0.0332345 + 0.555279i
\(843\) −26.3662 12.8855i −0.908100 0.443802i
\(844\) 16.0432 + 12.6019i 0.552230 + 0.433777i
\(845\) −7.01728 26.1889i −0.241402 0.900924i
\(846\) 11.9372 + 7.95082i 0.410410 + 0.273355i
\(847\) 15.0714 3.66880i 0.517858 0.126061i
\(848\) 25.7470 + 0.583955i 0.884154 + 0.0200531i
\(849\) 8.73880 + 7.60870i 0.299915 + 0.261130i
\(850\) −4.99560 14.9953i −0.171348 0.514335i
\(851\) 0.312373 1.16579i 0.0107080 0.0399629i
\(852\) 11.3694 32.6574i 0.389509 1.11883i
\(853\) 16.1682 16.1682i 0.553590 0.553590i −0.373885 0.927475i \(-0.621975\pi\)
0.927475 + 0.373885i \(0.121975\pi\)
\(854\) −42.3529 + 13.0347i −1.44929 + 0.446039i
\(855\) 6.12030 + 2.48406i 0.209310 + 0.0849531i
\(856\) 36.5736 + 13.1129i 1.25006 + 0.448188i
\(857\) −24.5006 + 14.1455i −0.836926 + 0.483200i −0.856218 0.516614i \(-0.827192\pi\)
0.0192920 + 0.999814i \(0.493859\pi\)
\(858\) 42.0539 54.5682i 1.43570 1.86293i
\(859\) 2.85106 + 10.6403i 0.0972770 + 0.363043i 0.997355 0.0726865i \(-0.0231572\pi\)
−0.900078 + 0.435729i \(0.856491\pi\)
\(860\) −5.02228 + 11.7464i −0.171258 + 0.400548i
\(861\) 8.01749 + 25.2196i 0.273235 + 0.859480i
\(862\) 1.56605 + 0.320747i 0.0533399 + 0.0109247i
\(863\) −14.2102 8.20426i −0.483721 0.279276i 0.238245 0.971205i \(-0.423428\pi\)
−0.721966 + 0.691929i \(0.756761\pi\)
\(864\) 8.10720 28.2537i 0.275812 0.961211i
\(865\) 1.05335 + 1.82446i 0.0358150 + 0.0620334i
\(866\) 5.02463 5.66439i 0.170744 0.192484i
\(867\) −14.9869 + 10.0915i −0.508980 + 0.342724i
\(868\) 22.5072 + 3.75362i 0.763944 + 0.127406i
\(869\) 35.4255 35.4255i 1.20173 1.20173i
\(870\) −1.40081 + 10.4703i −0.0474918 + 0.354977i
\(871\) 2.01147 + 3.48397i 0.0681560 + 0.118050i
\(872\) 1.05583 0.894634i 0.0357549 0.0302961i
\(873\) −36.0830 + 28.0991i −1.22123 + 0.951010i
\(874\) 12.1590 8.02504i 0.411284 0.271451i
\(875\) 0.455704 19.7964i 0.0154056 0.669241i
\(876\) 31.5071 6.01311i 1.06453 0.203164i
\(877\) −9.30456 34.7251i −0.314193 1.17258i −0.924739 0.380602i \(-0.875717\pi\)
0.610546 0.791981i \(-0.290950\pi\)
\(878\) −2.68678 + 0.895084i −0.0906744 + 0.0302076i
\(879\) −14.6557 42.6732i −0.494324 1.43933i
\(880\) 12.7594 3.11058i 0.430120 0.104858i
\(881\) 17.0174 0.573331 0.286666 0.958031i \(-0.407453\pi\)
0.286666 + 0.958031i \(0.407453\pi\)
\(882\) −29.5190 3.26054i −0.993955 0.109788i
\(883\) −1.71357 + 1.71357i −0.0576662 + 0.0576662i −0.735352 0.677686i \(-0.762983\pi\)
0.677686 + 0.735352i \(0.262983\pi\)
\(884\) −34.7529 4.97679i −1.16887 0.167388i
\(885\) 0.0704192 0.144091i 0.00236711 0.00484355i
\(886\) −1.01654 + 2.03221i −0.0341512 + 0.0682733i
\(887\) −45.7410 26.4086i −1.53583 0.886714i −0.999076 0.0429779i \(-0.986316\pi\)
−0.536758 0.843736i \(-0.680351\pi\)
\(888\) −1.13252 + 1.10249i −0.0380050 + 0.0369971i
\(889\) −4.33275 + 4.13776i −0.145316 + 0.138776i
\(890\) −8.12649 12.3127i −0.272400 0.412722i
\(891\) −18.0200 + 32.2671i −0.603693 + 1.08099i
\(892\) −11.9540 + 1.43608i −0.400248 + 0.0480835i
\(893\) 2.40941 8.99206i 0.0806280 0.300908i
\(894\) 16.8834 12.8989i 0.564666 0.431403i
\(895\) 6.74092i 0.225324i
\(896\) 11.5310 + 27.6231i 0.385223 + 0.922824i
\(897\) 43.5565 + 8.50239i 1.45431 + 0.283886i
\(898\) −31.4109 + 35.4102i −1.04819 + 1.18166i
\(899\) −22.4666 6.01990i −0.749302 0.200775i
\(900\) 6.87787 25.2442i 0.229262 0.841473i
\(901\) 4.27080 + 15.9389i 0.142281 + 0.531000i
\(902\) −27.9895 + 18.4733i −0.931949 + 0.615095i
\(903\) 32.5133 + 16.8275i 1.08197 + 0.559983i
\(904\) −18.2011 12.6146i −0.605361 0.419554i
\(905\) 4.33258 7.50425i 0.144020 0.249450i
\(906\) −11.3009 8.70922i −0.375447 0.289344i
\(907\) −5.29094 + 19.7461i −0.175683 + 0.655657i 0.820752 + 0.571285i \(0.193555\pi\)
−0.996434 + 0.0843718i \(0.973112\pi\)
\(908\) −3.31698 + 23.1624i −0.110078 + 0.768672i
\(909\) −48.3321 + 20.4253i −1.60307 + 0.677465i
\(910\) −18.1094 9.58580i −0.600320 0.317766i
\(911\) 40.9626i 1.35715i −0.734530 0.678576i \(-0.762597\pi\)
0.734530 0.678576i \(-0.237403\pi\)
\(912\) −19.0579 + 0.883840i −0.631070 + 0.0292669i
\(913\) 13.4875 7.78701i 0.446371 0.257712i
\(914\) 8.07001 + 24.2238i 0.266932 + 0.801251i
\(915\) 16.3621 1.13111i 0.540914 0.0373933i
\(916\) 14.0000 5.61387i 0.462572 0.185487i
\(917\) −1.54827 0.942057i −0.0511285 0.0311095i
\(918\) 18.8333 0.0949435i 0.621592 0.00313360i
\(919\) 49.2908 + 28.4581i 1.62595 + 0.938745i 0.985283 + 0.170928i \(0.0546766\pi\)
0.640670 + 0.767816i \(0.278657\pi\)
\(920\) 5.46905 + 6.45447i 0.180309 + 0.212798i
\(921\) 6.43955 + 18.7501i 0.212190 + 0.617837i
\(922\) 19.9897 1.19642i 0.658326 0.0394021i
\(923\) −48.3450 48.3450i −1.59130 1.59130i
\(924\) −6.20282 37.1214i −0.204058 1.22120i
\(925\) −0.994815 + 0.994815i −0.0327093 + 0.0327093i
\(926\) 37.1916 + 32.9910i 1.22219 + 1.08415i
\(927\) 24.5122 3.40531i 0.805085 0.111845i
\(928\) −8.98490 29.1590i −0.294944 0.957189i
\(929\) 12.9239 22.3849i 0.424020 0.734424i −0.572309 0.820038i \(-0.693952\pi\)
0.996328 + 0.0856147i \(0.0272854\pi\)
\(930\) −7.79569 3.24827i −0.255631 0.106515i
\(931\) 4.12698 + 18.8291i 0.135256 + 0.617100i
\(932\) −31.2053 13.3421i −1.02216 0.437037i
\(933\) 14.5791 1.00785i 0.477300 0.0329956i
\(934\) −15.2297 + 30.4465i −0.498332 + 0.996239i
\(935\) 4.20740 + 7.28743i 0.137597 + 0.238324i
\(936\) −43.3141 38.7482i −1.41577 1.26652i
\(937\) 52.1716 1.70437 0.852186 0.523240i \(-0.175277\pi\)
0.852186 + 0.523240i \(0.175277\pi\)
\(938\) 2.14232 + 0.490400i 0.0699491 + 0.0160121i
\(939\) −17.1157 + 11.5249i −0.558549 + 0.376102i
\(940\) 5.35130 + 0.766333i 0.174540 + 0.0249950i
\(941\) −21.6584 5.80336i −0.706044 0.189184i −0.112108 0.993696i \(-0.535760\pi\)
−0.593936 + 0.804512i \(0.702427\pi\)
\(942\) 3.77247 0.488602i 0.122914 0.0159195i
\(943\) −18.7087 10.8015i −0.609240 0.351745i
\(944\) −0.0105037 + 0.463114i −0.000341865 + 0.0150731i
\(945\) 10.3643 + 3.66105i 0.337152 + 0.119094i
\(946\) −9.30895 + 45.4511i −0.302660 + 1.47774i
\(947\) 12.7223 3.40893i 0.413419 0.110775i −0.0461133 0.998936i \(-0.514684\pi\)
0.459533 + 0.888161i \(0.348017\pi\)
\(948\) −27.6180 31.9903i −0.896993 1.03900i
\(949\) 16.4141 61.2582i 0.532824 1.98853i
\(950\) −16.9519 + 1.01461i −0.549992 + 0.0329181i
\(951\) −37.3344 7.28781i −1.21065 0.236323i
\(952\) −14.9141 + 12.0586i −0.483369 + 0.390822i
\(953\) 45.5719 1.47622 0.738109 0.674682i \(-0.235719\pi\)
0.738109 + 0.674682i \(0.235719\pi\)
\(954\) −8.74231 + 25.8790i −0.283043 + 0.837865i
\(955\) −13.4057 3.59204i −0.433798 0.116236i
\(956\) 2.21779 0.266433i 0.0717286 0.00861707i
\(957\) 2.64575 + 38.2722i 0.0855249 + 1.23717i
\(958\) −2.11789 + 10.3406i −0.0684258 + 0.334090i
\(959\) 24.8332 + 7.27054i 0.801907 + 0.234778i
\(960\) −1.82961 10.9267i −0.0590504 0.352658i
\(961\) −6.20245 + 10.7430i −0.200079 + 0.346547i
\(962\) 0.987699 + 2.96478i 0.0318447 + 0.0955884i
\(963\) −24.8530 + 32.8725i −0.800878 + 1.05930i
\(964\) 6.81854 + 9.09785i 0.219610 + 0.293022i
\(965\) 3.51832 + 3.51832i 0.113259 + 0.113259i
\(966\) 19.5986 14.2712i 0.630575 0.459167i
\(967\) 40.2001i 1.29275i −0.763020 0.646374i \(-0.776284\pi\)
0.763020 0.646374i \(-0.223716\pi\)
\(968\) 14.9950 7.08025i 0.481956 0.227568i
\(969\) −3.97061 11.5613i −0.127554 0.371402i
\(970\) −7.71140 + 15.4162i −0.247598 + 0.494985i
\(971\) 20.4364 5.47591i 0.655834 0.175730i 0.0844688 0.996426i \(-0.473081\pi\)
0.571365 + 0.820696i \(0.306414\pi\)
\(972\) 26.0349 + 17.1518i 0.835070 + 0.550144i
\(973\) 0.412187 17.9059i 0.0132141 0.574038i
\(974\) −26.6052 5.44908i −0.852485 0.174600i
\(975\) −39.0151 33.9697i −1.24948 1.08790i
\(976\) −41.5527 + 22.7501i −1.33007 + 0.728214i
\(977\) −21.5127 + 12.4204i −0.688252 + 0.397362i −0.802957 0.596037i \(-0.796741\pi\)
0.114705 + 0.993400i \(0.463408\pi\)
\(978\) −42.0995 + 32.1639i −1.34620 + 1.02849i
\(979\) −37.8846 37.8846i −1.21080 1.21080i
\(980\) −10.5702 + 3.68361i −0.337652 + 0.117669i
\(981\) 0.571384 + 1.35206i 0.0182429 + 0.0431678i
\(982\) 24.6779 1.47702i 0.787503 0.0471336i
\(983\) −7.48665 + 4.32242i −0.238787 + 0.137864i −0.614619 0.788824i \(-0.710690\pi\)
0.375832 + 0.926688i \(0.377357\pi\)
\(984\) 13.8147 + 24.6881i 0.440398 + 0.787028i
\(985\) −10.4308 + 18.0667i −0.332353 + 0.575652i
\(986\) 16.3164 10.7690i 0.519622 0.342955i
\(987\) 3.31718 15.1326i 0.105587 0.481675i
\(988\) −14.8294 + 34.6839i −0.471788 + 1.10344i
\(989\) −28.8676 + 7.73505i −0.917936 + 0.245960i
\(990\) −0.890602 + 13.9013i −0.0283052 + 0.441812i
\(991\) −17.7772 30.7911i −0.564713 0.978111i −0.997076 0.0764118i \(-0.975654\pi\)
0.432364 0.901699i \(-0.357680\pi\)
\(992\) 24.3767 0.904890i 0.773962 0.0287303i
\(993\) 23.3749 + 4.56287i 0.741780 + 0.144798i
\(994\) −37.3254 + 1.37289i −1.18389 + 0.0435455i
\(995\) −0.666923 0.666923i −0.0211429 0.0211429i
\(996\) −5.71905 11.8278i −0.181215 0.374779i
\(997\) −60.4741 16.2040i −1.91523 0.513185i −0.991492 0.130170i \(-0.958448\pi\)
−0.923742 0.383015i \(-0.874886\pi\)
\(998\) 11.4606 22.9114i 0.362779 0.725248i
\(999\) −0.757518 1.49550i −0.0239668 0.0473155i
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 336.2.bo.a.5.14 240
3.2 odd 2 inner 336.2.bo.a.5.47 yes 240
7.3 odd 6 inner 336.2.bo.a.101.55 yes 240
16.13 even 4 inner 336.2.bo.a.173.6 yes 240
21.17 even 6 inner 336.2.bo.a.101.6 yes 240
48.29 odd 4 inner 336.2.bo.a.173.55 yes 240
112.45 odd 12 inner 336.2.bo.a.269.47 yes 240
336.269 even 12 inner 336.2.bo.a.269.14 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bo.a.5.14 240 1.1 even 1 trivial
336.2.bo.a.5.47 yes 240 3.2 odd 2 inner
336.2.bo.a.101.6 yes 240 21.17 even 6 inner
336.2.bo.a.101.55 yes 240 7.3 odd 6 inner
336.2.bo.a.173.6 yes 240 16.13 even 4 inner
336.2.bo.a.173.55 yes 240 48.29 odd 4 inner
336.2.bo.a.269.14 yes 240 336.269 even 12 inner
336.2.bo.a.269.47 yes 240 112.45 odd 12 inner