Properties

Label 378.2.u.c.169.1
Level $378$
Weight $2$
Character 378.169
Analytic conductor $3.018$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,2,Mod(43,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.u (of order \(9\), degree \(6\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 169.1
Character \(\chi\) \(=\) 378.169
Dual form 378.2.u.c.85.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 - 0.342020i) q^{2} +(-1.33338 + 1.10549i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.412508 - 2.33945i) q^{5} +(-0.874866 + 1.49486i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.555794 - 2.94807i) q^{9} +O(q^{10})\) \(q+(0.939693 - 0.342020i) q^{2} +(-1.33338 + 1.10549i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.412508 - 2.33945i) q^{5} +(-0.874866 + 1.49486i) q^{6} +(-0.766044 - 0.642788i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.555794 - 2.94807i) q^{9} +(-1.18777 - 2.05728i) q^{10} +(0.330918 - 1.87673i) q^{11} +(-0.310833 + 1.70393i) q^{12} +(-0.325226 - 0.118372i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(3.13626 + 2.66335i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.98208 - 3.43306i) q^{17} +(-0.486023 - 2.96037i) q^{18} +(0.954309 - 1.65291i) q^{19} +(-1.81977 - 1.52697i) q^{20} +(1.73202 + 0.0102262i) q^{21} +(-0.330918 - 1.87673i) q^{22} +(1.91185 - 1.60423i) q^{23} +(0.290691 + 1.70748i) q^{24} +(-0.604396 + 0.219982i) q^{25} -0.346098 q^{26} +(2.51797 + 4.54531i) q^{27} -1.00000 q^{28} +(7.53184 - 2.74137i) q^{29} +(3.85804 + 1.43006i) q^{30} +(-3.82464 + 3.20925i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(1.63346 + 2.86821i) q^{33} +(-3.03672 - 2.54811i) q^{34} +(-1.18777 + 2.05728i) q^{35} +(-1.46922 - 2.61561i) q^{36} +(-0.898531 - 1.55630i) q^{37} +(0.331428 - 1.87962i) q^{38} +(0.564508 - 0.201698i) q^{39} +(-2.23228 - 0.812482i) q^{40} +(-8.54001 - 3.10831i) q^{41} +(1.63106 - 0.582776i) q^{42} +(-1.74449 + 9.89349i) q^{43} +(-0.952839 - 1.65037i) q^{44} +(-7.12612 - 0.0841508i) q^{45} +(1.24787 - 2.16137i) q^{46} +(9.88005 + 8.29035i) q^{47} +(0.857154 + 1.50509i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-0.492708 + 0.413431i) q^{50} +(6.43807 + 2.38640i) q^{51} +(-0.325226 + 0.118372i) q^{52} -2.36703 q^{53} +(3.92070 + 3.41000i) q^{54} -4.52701 q^{55} +(-0.939693 + 0.342020i) q^{56} +(0.554819 + 3.25893i) q^{57} +(6.14001 - 5.15208i) q^{58} +(0.541789 + 3.07264i) q^{59} +(4.11448 + 0.0242927i) q^{60} +(-2.82647 - 2.37169i) q^{61} +(-2.49636 + 4.32382i) q^{62} +(-2.32074 + 1.90109i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.142768 + 0.809678i) q^{65} +(2.51594 + 2.13656i) q^{66} +(3.72631 + 1.35627i) q^{67} +(-3.72509 - 1.35582i) q^{68} +(-0.775758 + 4.25257i) q^{69} +(-0.412508 + 2.33945i) q^{70} +(-0.671111 - 1.16240i) q^{71} +(-2.27520 - 1.95536i) q^{72} +(-4.74972 + 8.22676i) q^{73} +(-1.37663 - 1.15513i) q^{74} +(0.562701 - 0.961472i) q^{75} +(-0.331428 - 1.87962i) q^{76} +(-1.45983 + 1.22495i) q^{77} +(0.461479 - 0.382607i) q^{78} +(-3.98400 + 1.45006i) q^{79} -2.37554 q^{80} +(-8.38219 - 3.27703i) q^{81} -9.08809 q^{82} +(7.30158 - 2.65756i) q^{83} +(1.33338 - 1.10549i) q^{84} +(-7.21385 + 6.05314i) q^{85} +(1.74449 + 9.89349i) q^{86} +(-7.01225 + 11.9816i) q^{87} +(-1.45983 - 1.22495i) q^{88} +(7.20467 - 12.4789i) q^{89} +(-6.72514 + 2.35820i) q^{90} +(0.173049 + 0.299730i) q^{91} +(0.433380 - 2.45782i) q^{92} +(1.55190 - 8.50724i) q^{93} +(12.1197 + 4.41120i) q^{94} +(-4.26056 - 1.55072i) q^{95} +(1.32023 + 1.12116i) q^{96} +(-2.51966 + 14.2897i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-5.34879 - 2.01864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 0.342020i 0.664463 0.241845i
\(3\) −1.33338 + 1.10549i −0.769826 + 0.638254i
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) −0.412508 2.33945i −0.184479 1.04623i −0.926623 0.375992i \(-0.877302\pi\)
0.742144 0.670241i \(-0.233809\pi\)
\(6\) −0.874866 + 1.49486i −0.357163 + 0.610274i
\(7\) −0.766044 0.642788i −0.289538 0.242951i
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) 0.555794 2.94807i 0.185265 0.982689i
\(10\) −1.18777 2.05728i −0.375606 0.650568i
\(11\) 0.330918 1.87673i 0.0997754 0.565854i −0.893404 0.449255i \(-0.851690\pi\)
0.993179 0.116599i \(-0.0371994\pi\)
\(12\) −0.310833 + 1.70393i −0.0897298 + 0.491883i
\(13\) −0.325226 0.118372i −0.0902014 0.0328306i 0.296525 0.955025i \(-0.404172\pi\)
−0.386727 + 0.922194i \(0.626394\pi\)
\(14\) −0.939693 0.342020i −0.251143 0.0914087i
\(15\) 3.13626 + 2.66335i 0.809779 + 0.687673i
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) −1.98208 3.43306i −0.480725 0.832640i 0.519031 0.854756i \(-0.326293\pi\)
−0.999755 + 0.0221160i \(0.992960\pi\)
\(18\) −0.486023 2.96037i −0.114557 0.697766i
\(19\) 0.954309 1.65291i 0.218934 0.379204i −0.735549 0.677472i \(-0.763076\pi\)
0.954482 + 0.298268i \(0.0964089\pi\)
\(20\) −1.81977 1.52697i −0.406913 0.341440i
\(21\) 1.73202 + 0.0102262i 0.377958 + 0.00223153i
\(22\) −0.330918 1.87673i −0.0705519 0.400119i
\(23\) 1.91185 1.60423i 0.398647 0.334505i −0.421323 0.906911i \(-0.638434\pi\)
0.819971 + 0.572406i \(0.193990\pi\)
\(24\) 0.290691 + 1.70748i 0.0593371 + 0.348539i
\(25\) −0.604396 + 0.219982i −0.120879 + 0.0439964i
\(26\) −0.346098 −0.0678754
\(27\) 2.51797 + 4.54531i 0.484583 + 0.874745i
\(28\) −1.00000 −0.188982
\(29\) 7.53184 2.74137i 1.39863 0.509059i 0.470857 0.882209i \(-0.343945\pi\)
0.927771 + 0.373150i \(0.121722\pi\)
\(30\) 3.85804 + 1.43006i 0.704379 + 0.261093i
\(31\) −3.82464 + 3.20925i −0.686926 + 0.576399i −0.918021 0.396532i \(-0.870214\pi\)
0.231095 + 0.972931i \(0.425769\pi\)
\(32\) −0.173648 0.984808i −0.0306970 0.174091i
\(33\) 1.63346 + 2.86821i 0.284349 + 0.499292i
\(34\) −3.03672 2.54811i −0.520793 0.436997i
\(35\) −1.18777 + 2.05728i −0.200770 + 0.347743i
\(36\) −1.46922 2.61561i −0.244870 0.435935i
\(37\) −0.898531 1.55630i −0.147718 0.255854i 0.782666 0.622442i \(-0.213859\pi\)
−0.930384 + 0.366588i \(0.880526\pi\)
\(38\) 0.331428 1.87962i 0.0537647 0.304915i
\(39\) 0.564508 0.201698i 0.0903936 0.0322975i
\(40\) −2.23228 0.812482i −0.352954 0.128465i
\(41\) −8.54001 3.10831i −1.33373 0.485436i −0.425894 0.904773i \(-0.640041\pi\)
−0.907831 + 0.419337i \(0.862263\pi\)
\(42\) 1.63106 0.582776i 0.251679 0.0899244i
\(43\) −1.74449 + 9.89349i −0.266032 + 1.50874i 0.500048 + 0.865998i \(0.333316\pi\)
−0.766080 + 0.642745i \(0.777795\pi\)
\(44\) −0.952839 1.65037i −0.143646 0.248802i
\(45\) −7.12612 0.0841508i −1.06230 0.0125445i
\(46\) 1.24787 2.16137i 0.183988 0.318677i
\(47\) 9.88005 + 8.29035i 1.44115 + 1.20927i 0.938732 + 0.344648i \(0.112002\pi\)
0.502421 + 0.864623i \(0.332443\pi\)
\(48\) 0.857154 + 1.50509i 0.123720 + 0.217241i
\(49\) 0.173648 + 0.984808i 0.0248069 + 0.140687i
\(50\) −0.492708 + 0.413431i −0.0696795 + 0.0584680i
\(51\) 6.43807 + 2.38640i 0.901510 + 0.334163i
\(52\) −0.325226 + 0.118372i −0.0451007 + 0.0164153i
\(53\) −2.36703 −0.325136 −0.162568 0.986697i \(-0.551978\pi\)
−0.162568 + 0.986697i \(0.551978\pi\)
\(54\) 3.92070 + 3.41000i 0.533540 + 0.464042i
\(55\) −4.52701 −0.610422
\(56\) −0.939693 + 0.342020i −0.125572 + 0.0457044i
\(57\) 0.554819 + 3.25893i 0.0734876 + 0.431656i
\(58\) 6.14001 5.15208i 0.806223 0.676502i
\(59\) 0.541789 + 3.07264i 0.0705349 + 0.400023i 0.999550 + 0.0299826i \(0.00954518\pi\)
−0.929016 + 0.370041i \(0.879344\pi\)
\(60\) 4.11448 + 0.0242927i 0.531177 + 0.00313617i
\(61\) −2.82647 2.37169i −0.361892 0.303664i 0.443652 0.896199i \(-0.353683\pi\)
−0.805544 + 0.592535i \(0.798127\pi\)
\(62\) −2.49636 + 4.32382i −0.317038 + 0.549125i
\(63\) −2.32074 + 1.90109i −0.292386 + 0.239515i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −0.142768 + 0.809678i −0.0177082 + 0.100428i
\(66\) 2.51594 + 2.13656i 0.309690 + 0.262992i
\(67\) 3.72631 + 1.35627i 0.455242 + 0.165694i 0.559455 0.828861i \(-0.311010\pi\)
−0.104214 + 0.994555i \(0.533233\pi\)
\(68\) −3.72509 1.35582i −0.451733 0.164418i
\(69\) −0.775758 + 4.25257i −0.0933902 + 0.511949i
\(70\) −0.412508 + 2.33945i −0.0493041 + 0.279618i
\(71\) −0.671111 1.16240i −0.0796462 0.137951i 0.823451 0.567387i \(-0.192046\pi\)
−0.903097 + 0.429436i \(0.858712\pi\)
\(72\) −2.27520 1.95536i −0.268135 0.230442i
\(73\) −4.74972 + 8.22676i −0.555913 + 0.962869i 0.441919 + 0.897055i \(0.354298\pi\)
−0.997832 + 0.0658142i \(0.979036\pi\)
\(74\) −1.37663 1.15513i −0.160030 0.134281i
\(75\) 0.562701 0.961472i 0.0649751 0.111021i
\(76\) −0.331428 1.87962i −0.0380174 0.215607i
\(77\) −1.45983 + 1.22495i −0.166364 + 0.139596i
\(78\) 0.461479 0.382607i 0.0522522 0.0433217i
\(79\) −3.98400 + 1.45006i −0.448235 + 0.163144i −0.556268 0.831003i \(-0.687767\pi\)
0.108033 + 0.994147i \(0.465545\pi\)
\(80\) −2.37554 −0.265593
\(81\) −8.38219 3.27703i −0.931354 0.364115i
\(82\) −9.08809 −1.00361
\(83\) 7.30158 2.65756i 0.801452 0.291705i 0.0913640 0.995818i \(-0.470877\pi\)
0.710088 + 0.704113i \(0.248655\pi\)
\(84\) 1.33338 1.10549i 0.145483 0.120619i
\(85\) −7.21385 + 6.05314i −0.782452 + 0.656555i
\(86\) 1.74449 + 9.89349i 0.188113 + 1.06684i
\(87\) −7.01225 + 11.9816i −0.751792 + 1.28457i
\(88\) −1.45983 1.22495i −0.155619 0.130580i
\(89\) 7.20467 12.4789i 0.763694 1.32276i −0.177241 0.984168i \(-0.556717\pi\)
0.940934 0.338589i \(-0.109950\pi\)
\(90\) −6.72514 + 2.35820i −0.708892 + 0.248576i
\(91\) 0.173049 + 0.299730i 0.0181405 + 0.0314202i
\(92\) 0.433380 2.45782i 0.0451830 0.256246i
\(93\) 1.55190 8.50724i 0.160925 0.882160i
\(94\) 12.1197 + 4.41120i 1.25005 + 0.454981i
\(95\) −4.26056 1.55072i −0.437125 0.159100i
\(96\) 1.32023 + 1.12116i 0.134746 + 0.114427i
\(97\) −2.51966 + 14.2897i −0.255833 + 1.45090i 0.538092 + 0.842886i \(0.319145\pi\)
−0.793925 + 0.608015i \(0.791966\pi\)
\(98\) 0.500000 + 0.866025i 0.0505076 + 0.0874818i
\(99\) −5.34879 2.01864i −0.537574 0.202881i
\(100\) −0.321593 + 0.557015i −0.0321593 + 0.0557015i
\(101\) 10.4929 + 8.80459i 1.04408 + 0.876090i 0.992459 0.122577i \(-0.0391158\pi\)
0.0516241 + 0.998667i \(0.483560\pi\)
\(102\) 6.86600 + 0.0405381i 0.679836 + 0.00401387i
\(103\) −2.31687 13.1396i −0.228288 1.29469i −0.856299 0.516481i \(-0.827242\pi\)
0.628011 0.778205i \(-0.283869\pi\)
\(104\) −0.265126 + 0.222467i −0.0259978 + 0.0218147i
\(105\) −0.690549 4.05619i −0.0673907 0.395844i
\(106\) −2.22428 + 0.809570i −0.216041 + 0.0786324i
\(107\) 10.1212 0.978454 0.489227 0.872156i \(-0.337279\pi\)
0.489227 + 0.872156i \(0.337279\pi\)
\(108\) 4.85054 + 1.86339i 0.466744 + 0.179305i
\(109\) 16.8796 1.61677 0.808384 0.588656i \(-0.200343\pi\)
0.808384 + 0.588656i \(0.200343\pi\)
\(110\) −4.25400 + 1.54833i −0.405603 + 0.147627i
\(111\) 2.91855 + 1.08182i 0.277017 + 0.102682i
\(112\) −0.766044 + 0.642788i −0.0723844 + 0.0607377i
\(113\) −1.14830 6.51235i −0.108023 0.612631i −0.989970 0.141281i \(-0.954878\pi\)
0.881946 0.471350i \(-0.156233\pi\)
\(114\) 1.63598 + 2.87264i 0.153224 + 0.269047i
\(115\) −4.54166 3.81091i −0.423512 0.355369i
\(116\) 4.00761 6.94138i 0.372097 0.644491i
\(117\) −0.529728 + 0.892996i −0.0489734 + 0.0825575i
\(118\) 1.56002 + 2.70203i 0.143611 + 0.248742i
\(119\) −0.688369 + 3.90393i −0.0631027 + 0.357873i
\(120\) 3.87466 1.38441i 0.353706 0.126379i
\(121\) 6.92402 + 2.52014i 0.629457 + 0.229103i
\(122\) −3.46718 1.26195i −0.313903 0.114252i
\(123\) 14.8233 5.29632i 1.33657 0.477553i
\(124\) −0.866976 + 4.91686i −0.0778567 + 0.441547i
\(125\) −5.17489 8.96318i −0.462856 0.801691i
\(126\) −1.53057 + 2.58018i −0.136354 + 0.229861i
\(127\) −2.99602 + 5.18927i −0.265854 + 0.460473i −0.967787 0.251770i \(-0.918987\pi\)
0.701933 + 0.712243i \(0.252321\pi\)
\(128\) −0.766044 0.642788i −0.0677094 0.0568149i
\(129\) −8.61106 15.1203i −0.758162 1.33127i
\(130\) 0.142768 + 0.809678i 0.0125216 + 0.0710135i
\(131\) 10.5773 8.87545i 0.924147 0.775451i −0.0506103 0.998718i \(-0.516117\pi\)
0.974757 + 0.223267i \(0.0716722\pi\)
\(132\) 3.09495 + 1.14721i 0.269381 + 0.0998518i
\(133\) −1.79351 + 0.652786i −0.155517 + 0.0566037i
\(134\) 3.96546 0.342564
\(135\) 9.59484 7.76563i 0.825792 0.668359i
\(136\) −3.96416 −0.339924
\(137\) 7.22521 2.62976i 0.617291 0.224676i −0.0143993 0.999896i \(-0.504584\pi\)
0.631690 + 0.775221i \(0.282361\pi\)
\(138\) 0.725489 + 4.26143i 0.0617578 + 0.362757i
\(139\) 17.1807 14.4164i 1.45725 1.22278i 0.530185 0.847882i \(-0.322123\pi\)
0.927067 0.374897i \(-0.122322\pi\)
\(140\) 0.412508 + 2.33945i 0.0348633 + 0.197720i
\(141\) −22.3387 0.131892i −1.88126 0.0111073i
\(142\) −1.02820 0.862763i −0.0862847 0.0724015i
\(143\) −0.329776 + 0.571188i −0.0275772 + 0.0477652i
\(144\) −2.80677 1.05928i −0.233897 0.0882730i
\(145\) −9.52023 16.4895i −0.790612 1.36938i
\(146\) −1.64956 + 9.35512i −0.136519 + 0.774236i
\(147\) −1.32023 1.12116i −0.108891 0.0924713i
\(148\) −1.68868 0.614631i −0.138809 0.0505224i
\(149\) 3.00996 + 1.09554i 0.246585 + 0.0897498i 0.462356 0.886694i \(-0.347004\pi\)
−0.215771 + 0.976444i \(0.569226\pi\)
\(150\) 0.199923 1.09594i 0.0163237 0.0894834i
\(151\) −2.30734 + 13.0856i −0.187768 + 1.06489i 0.734578 + 0.678524i \(0.237380\pi\)
−0.922347 + 0.386363i \(0.873731\pi\)
\(152\) −0.954309 1.65291i −0.0774047 0.134069i
\(153\) −11.2225 + 3.93522i −0.907287 + 0.318144i
\(154\) −0.952839 + 1.65037i −0.0767820 + 0.132990i
\(155\) 9.08558 + 7.62371i 0.729772 + 0.612351i
\(156\) 0.302789 0.517368i 0.0242426 0.0414226i
\(157\) 1.87437 + 10.6301i 0.149591 + 0.848373i 0.963565 + 0.267473i \(0.0861885\pi\)
−0.813974 + 0.580901i \(0.802700\pi\)
\(158\) −3.24779 + 2.72522i −0.258380 + 0.216807i
\(159\) 3.15614 2.61672i 0.250298 0.207519i
\(160\) −2.23228 + 0.812482i −0.176477 + 0.0642324i
\(161\) −2.49574 −0.196692
\(162\) −8.99749 0.212528i −0.706910 0.0166978i
\(163\) −5.77576 −0.452392 −0.226196 0.974082i \(-0.572629\pi\)
−0.226196 + 0.974082i \(0.572629\pi\)
\(164\) −8.54001 + 3.10831i −0.666863 + 0.242718i
\(165\) 6.03622 5.00456i 0.469919 0.389604i
\(166\) 5.95230 4.99457i 0.461988 0.387654i
\(167\) −0.844377 4.78870i −0.0653399 0.370561i −0.999891 0.0147331i \(-0.995310\pi\)
0.934552 0.355828i \(-0.115801\pi\)
\(168\) 0.874866 1.49486i 0.0674974 0.115331i
\(169\) −9.86682 8.27924i −0.758986 0.636865i
\(170\) −4.70850 + 8.15537i −0.361126 + 0.625488i
\(171\) −4.34249 3.73204i −0.332079 0.285397i
\(172\) 5.02305 + 8.70019i 0.383004 + 0.663383i
\(173\) −0.283357 + 1.60699i −0.0215432 + 0.122178i −0.993683 0.112225i \(-0.964202\pi\)
0.972140 + 0.234403i \(0.0753134\pi\)
\(174\) −2.49140 + 13.6574i −0.188872 + 1.03536i
\(175\) 0.604396 + 0.219982i 0.0456881 + 0.0166291i
\(176\) −1.79075 0.651780i −0.134983 0.0491298i
\(177\) −4.11917 3.49805i −0.309616 0.262929i
\(178\) 2.50216 14.1904i 0.187545 1.06362i
\(179\) −6.07571 10.5234i −0.454120 0.786559i 0.544517 0.838750i \(-0.316713\pi\)
−0.998637 + 0.0521910i \(0.983380\pi\)
\(180\) −5.51302 + 4.51612i −0.410916 + 0.336612i
\(181\) 4.29724 7.44303i 0.319411 0.553236i −0.660954 0.750426i \(-0.729848\pi\)
0.980365 + 0.197190i \(0.0631816\pi\)
\(182\) 0.265126 + 0.222467i 0.0196525 + 0.0164904i
\(183\) 6.39062 + 0.0377314i 0.472409 + 0.00278919i
\(184\) −0.433380 2.45782i −0.0319492 0.181193i
\(185\) −3.27023 + 2.74405i −0.240432 + 0.201747i
\(186\) −1.45134 8.52497i −0.106417 0.625081i
\(187\) −7.09882 + 2.58376i −0.519117 + 0.188943i
\(188\) 12.8975 0.940646
\(189\) 0.992794 5.10043i 0.0722151 0.371002i
\(190\) −4.53400 −0.328931
\(191\) −20.3794 + 7.41749i −1.47460 + 0.536711i −0.949346 0.314233i \(-0.898253\pi\)
−0.525256 + 0.850944i \(0.676030\pi\)
\(192\) 1.62407 + 0.601995i 0.117207 + 0.0434453i
\(193\) 5.55729 4.66312i 0.400023 0.335659i −0.420480 0.907302i \(-0.638138\pi\)
0.820502 + 0.571643i \(0.193694\pi\)
\(194\) 2.51966 + 14.2897i 0.180901 + 1.02594i
\(195\) −0.704726 1.23744i −0.0504664 0.0886146i
\(196\) 0.766044 + 0.642788i 0.0547175 + 0.0459134i
\(197\) −10.3102 + 17.8577i −0.734569 + 1.27231i 0.220343 + 0.975423i \(0.429282\pi\)
−0.954912 + 0.296889i \(0.904051\pi\)
\(198\) −5.71664 0.0675065i −0.406264 0.00479748i
\(199\) −0.981724 1.70040i −0.0695925 0.120538i 0.829129 0.559057i \(-0.188837\pi\)
−0.898722 + 0.438519i \(0.855503\pi\)
\(200\) −0.111688 + 0.633414i −0.00789753 + 0.0447891i
\(201\) −6.46792 + 2.31098i −0.456212 + 0.163004i
\(202\) 12.8715 + 4.68483i 0.905632 + 0.329623i
\(203\) −7.53184 2.74137i −0.528632 0.192406i
\(204\) 6.46580 2.31022i 0.452696 0.161748i
\(205\) −3.74891 + 21.2611i −0.261835 + 1.48494i
\(206\) −6.67116 11.5548i −0.464802 0.805061i
\(207\) −3.66678 6.52787i −0.254859 0.453718i
\(208\) −0.173049 + 0.299730i −0.0119988 + 0.0207825i
\(209\) −2.78627 2.33796i −0.192730 0.161720i
\(210\) −2.03620 3.57539i −0.140511 0.246726i
\(211\) −1.25721 7.13000i −0.0865500 0.490850i −0.997011 0.0772554i \(-0.975384\pi\)
0.910461 0.413594i \(-0.135727\pi\)
\(212\) −1.81325 + 1.52149i −0.124534 + 0.104497i
\(213\) 2.17986 + 0.808011i 0.149362 + 0.0553640i
\(214\) 9.51083 3.46166i 0.650147 0.236634i
\(215\) 23.8649 1.62757
\(216\) 5.19534 + 0.0920312i 0.353498 + 0.00626193i
\(217\) 4.99271 0.338927
\(218\) 15.8616 5.77315i 1.07428 0.391007i
\(219\) −2.76141 16.2201i −0.186599 1.09606i
\(220\) −3.46789 + 2.90991i −0.233805 + 0.196186i
\(221\) 0.238243 + 1.35114i 0.0160260 + 0.0908877i
\(222\) 3.11255 + 0.0183770i 0.208900 + 0.00123339i
\(223\) 6.01701 + 5.04887i 0.402929 + 0.338097i 0.821624 0.570029i \(-0.193068\pi\)
−0.418696 + 0.908127i \(0.637513\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 0.312602 + 1.90406i 0.0208402 + 0.126938i
\(226\) −3.30641 5.72687i −0.219939 0.380946i
\(227\) −3.82272 + 21.6797i −0.253723 + 1.43894i 0.545606 + 0.838042i \(0.316300\pi\)
−0.799329 + 0.600894i \(0.794812\pi\)
\(228\) 2.51982 + 2.13986i 0.166879 + 0.141716i
\(229\) −1.14034 0.415051i −0.0753560 0.0274273i 0.304067 0.952651i \(-0.401655\pi\)
−0.379423 + 0.925223i \(0.623878\pi\)
\(230\) −5.57118 2.02774i −0.367352 0.133705i
\(231\) 0.592348 3.24715i 0.0389736 0.213646i
\(232\) 1.39183 7.89345i 0.0913780 0.518230i
\(233\) −9.05240 15.6792i −0.593042 1.02718i −0.993820 0.111004i \(-0.964593\pi\)
0.400778 0.916175i \(-0.368740\pi\)
\(234\) −0.192359 + 1.02032i −0.0125749 + 0.0667004i
\(235\) 15.3192 26.5337i 0.999317 1.73087i
\(236\) 2.39009 + 2.00552i 0.155581 + 0.130548i
\(237\) 3.70916 6.33774i 0.240936 0.411680i
\(238\) 0.688369 + 3.90393i 0.0446203 + 0.253054i
\(239\) −23.3668 + 19.6071i −1.51147 + 1.26828i −0.650642 + 0.759384i \(0.725500\pi\)
−0.860830 + 0.508892i \(0.830055\pi\)
\(240\) 3.16749 2.62613i 0.204461 0.169516i
\(241\) 23.4053 8.51882i 1.50767 0.548746i 0.549634 0.835406i \(-0.314767\pi\)
0.958032 + 0.286660i \(0.0925450\pi\)
\(242\) 7.36839 0.473658
\(243\) 14.7993 4.89688i 0.949378 0.314135i
\(244\) −3.68969 −0.236208
\(245\) 2.23228 0.812482i 0.142615 0.0519076i
\(246\) 12.1179 10.0468i 0.772606 0.640559i
\(247\) −0.506025 + 0.424605i −0.0321976 + 0.0270170i
\(248\) 0.866976 + 4.91686i 0.0550530 + 0.312221i
\(249\) −6.79786 + 11.6153i −0.430797 + 0.736092i
\(250\) −7.92839 6.65271i −0.501436 0.420754i
\(251\) −1.91165 + 3.31107i −0.120662 + 0.208993i −0.920029 0.391850i \(-0.871835\pi\)
0.799367 + 0.600843i \(0.205168\pi\)
\(252\) −0.555794 + 2.94807i −0.0350117 + 0.185711i
\(253\) −2.37804 4.11888i −0.149506 0.258952i
\(254\) −1.04051 + 5.90102i −0.0652873 + 0.370263i
\(255\) 2.92712 16.0459i 0.183303 1.00484i
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) 7.75754 + 2.82351i 0.483902 + 0.176126i 0.572440 0.819947i \(-0.305997\pi\)
−0.0885375 + 0.996073i \(0.528219\pi\)
\(258\) −13.2632 11.2632i −0.825730 0.701219i
\(259\) −0.312056 + 1.76976i −0.0193902 + 0.109968i
\(260\) 0.411085 + 0.712019i 0.0254944 + 0.0441576i
\(261\) −3.89558 23.7280i −0.241130 1.46873i
\(262\) 6.90387 11.9579i 0.426523 0.738759i
\(263\) −9.10090 7.63657i −0.561186 0.470891i 0.317522 0.948251i \(-0.397149\pi\)
−0.878708 + 0.477360i \(0.841594\pi\)
\(264\) 3.30067 + 0.0194878i 0.203142 + 0.00119939i
\(265\) 0.976417 + 5.53754i 0.0599808 + 0.340168i
\(266\) −1.46209 + 1.22684i −0.0896463 + 0.0752222i
\(267\) 4.18867 + 24.6037i 0.256343 + 1.50572i
\(268\) 3.72631 1.35627i 0.227621 0.0828472i
\(269\) −22.1411 −1.34997 −0.674983 0.737833i \(-0.735849\pi\)
−0.674983 + 0.737833i \(0.735849\pi\)
\(270\) 6.36020 10.5789i 0.387069 0.643814i
\(271\) −3.53856 −0.214952 −0.107476 0.994208i \(-0.534277\pi\)
−0.107476 + 0.994208i \(0.534277\pi\)
\(272\) −3.72509 + 1.35582i −0.225867 + 0.0822088i
\(273\) −0.562087 0.208349i −0.0340191 0.0126099i
\(274\) 5.89004 4.94233i 0.355830 0.298577i
\(275\) 0.212841 + 1.20708i 0.0128348 + 0.0727898i
\(276\) 2.13923 + 3.75630i 0.128767 + 0.226103i
\(277\) 21.1442 + 17.7421i 1.27043 + 1.06602i 0.994489 + 0.104844i \(0.0334344\pi\)
0.275943 + 0.961174i \(0.411010\pi\)
\(278\) 11.2139 19.4231i 0.672567 1.16492i
\(279\) 7.33538 + 13.0590i 0.439158 + 0.781820i
\(280\) 1.18777 + 2.05728i 0.0709828 + 0.122946i
\(281\) 2.61384 14.8238i 0.155929 0.884316i −0.802003 0.597320i \(-0.796232\pi\)
0.957932 0.286996i \(-0.0926567\pi\)
\(282\) −21.0366 + 7.51635i −1.25271 + 0.447592i
\(283\) 21.6254 + 7.87101i 1.28550 + 0.467883i 0.892247 0.451548i \(-0.149128\pi\)
0.393251 + 0.919431i \(0.371350\pi\)
\(284\) −1.26128 0.459067i −0.0748429 0.0272406i
\(285\) 7.39524 2.64231i 0.438056 0.156517i
\(286\) −0.114530 + 0.649531i −0.00677229 + 0.0384076i
\(287\) 4.54404 + 7.87052i 0.268226 + 0.464582i
\(288\) −2.99979 0.0354239i −0.176764 0.00208737i
\(289\) 0.642729 1.11324i 0.0378076 0.0654846i
\(290\) −14.5858 12.2390i −0.856510 0.718697i
\(291\) −12.4374 21.8391i −0.729096 1.28023i
\(292\) 1.64956 + 9.35512i 0.0965332 + 0.547467i
\(293\) 0.560993 0.470729i 0.0327736 0.0275003i −0.626254 0.779619i \(-0.715413\pi\)
0.659027 + 0.752119i \(0.270968\pi\)
\(294\) −1.62407 0.601995i −0.0947177 0.0351091i
\(295\) 6.96479 2.53498i 0.405506 0.147592i
\(296\) −1.79706 −0.104452
\(297\) 9.36354 3.22141i 0.543328 0.186925i
\(298\) 3.20313 0.185552
\(299\) −0.811678 + 0.295427i −0.0469405 + 0.0170850i
\(300\) −0.186968 1.09823i −0.0107946 0.0634062i
\(301\) 7.69577 6.45751i 0.443577 0.372205i
\(302\) 2.30734 + 13.0856i 0.132772 + 0.752989i
\(303\) −23.7244 0.140073i −1.36293 0.00804699i
\(304\) −1.46209 1.22684i −0.0838564 0.0703639i
\(305\) −4.38250 + 7.59072i −0.250941 + 0.434643i
\(306\) −9.19979 + 7.53623i −0.525917 + 0.430817i
\(307\) −7.14798 12.3807i −0.407957 0.706602i 0.586704 0.809801i \(-0.300425\pi\)
−0.994661 + 0.103200i \(0.967092\pi\)
\(308\) −0.330918 + 1.87673i −0.0188558 + 0.106936i
\(309\) 17.6150 + 14.9588i 1.00208 + 0.850977i
\(310\) 11.1451 + 4.05649i 0.633000 + 0.230393i
\(311\) 5.73618 + 2.08780i 0.325269 + 0.118388i 0.499493 0.866318i \(-0.333520\pi\)
−0.174224 + 0.984706i \(0.555742\pi\)
\(312\) 0.107579 0.589727i 0.00609044 0.0333867i
\(313\) −2.37172 + 13.4507i −0.134057 + 0.760277i 0.841454 + 0.540328i \(0.181700\pi\)
−0.975512 + 0.219948i \(0.929411\pi\)
\(314\) 5.39704 + 9.34794i 0.304572 + 0.527535i
\(315\) 5.40483 + 4.64504i 0.304528 + 0.261719i
\(316\) −2.11984 + 3.67167i −0.119250 + 0.206548i
\(317\) 0.0486763 + 0.0408443i 0.00273394 + 0.00229404i 0.644154 0.764896i \(-0.277210\pi\)
−0.641420 + 0.767190i \(0.721654\pi\)
\(318\) 2.07083 3.53837i 0.116126 0.198422i
\(319\) −2.65238 15.0424i −0.148505 0.842211i
\(320\) −1.81977 + 1.52697i −0.101728 + 0.0853600i
\(321\) −13.4954 + 11.1889i −0.753240 + 0.624502i
\(322\) −2.34523 + 0.853592i −0.130694 + 0.0475688i
\(323\) −7.56606 −0.420987
\(324\) −8.52756 + 2.87761i −0.473754 + 0.159867i
\(325\) 0.222605 0.0123479
\(326\) −5.42743 + 1.97542i −0.300598 + 0.109409i
\(327\) −22.5068 + 18.6601i −1.24463 + 1.03191i
\(328\) −6.96188 + 5.84171i −0.384405 + 0.322554i
\(329\) −2.23963 12.7015i −0.123475 0.700259i
\(330\) 3.96053 6.76725i 0.218020 0.372525i
\(331\) 10.6680 + 8.95154i 0.586368 + 0.492021i 0.887031 0.461709i \(-0.152764\pi\)
−0.300663 + 0.953730i \(0.597208\pi\)
\(332\) 3.88509 6.72917i 0.213222 0.369311i
\(333\) −5.08747 + 1.78394i −0.278792 + 0.0977596i
\(334\) −2.43129 4.21111i −0.133034 0.230422i
\(335\) 1.63578 9.27699i 0.0893724 0.506856i
\(336\) 0.310833 1.70393i 0.0169573 0.0929571i
\(337\) −21.5054 7.82734i −1.17148 0.426382i −0.318292 0.947993i \(-0.603109\pi\)
−0.853184 + 0.521611i \(0.825331\pi\)
\(338\) −12.1034 4.40529i −0.658341 0.239616i
\(339\) 8.73045 + 7.41399i 0.474173 + 0.402673i
\(340\) −1.63525 + 9.27394i −0.0886837 + 0.502950i
\(341\) 4.75725 + 8.23980i 0.257620 + 0.446210i
\(342\) −5.35704 2.02175i −0.289676 0.109324i
\(343\) 0.500000 0.866025i 0.0269975 0.0467610i
\(344\) 7.69577 + 6.45751i 0.414928 + 0.348166i
\(345\) 10.2687 + 0.0606281i 0.552846 + 0.00326411i
\(346\) 0.283357 + 1.60699i 0.0152333 + 0.0863926i
\(347\) −27.7911 + 23.3195i −1.49191 + 1.25186i −0.599704 + 0.800222i \(0.704715\pi\)
−0.892202 + 0.451636i \(0.850841\pi\)
\(348\) 2.32996 + 13.6859i 0.124899 + 0.733639i
\(349\) 21.3201 7.75987i 1.14124 0.415376i 0.298877 0.954292i \(-0.403388\pi\)
0.842360 + 0.538916i \(0.181166\pi\)
\(350\) 0.643185 0.0343797
\(351\) −0.280868 1.77631i −0.0149916 0.0948124i
\(352\) −1.90568 −0.101573
\(353\) 25.4215 9.25267i 1.35305 0.492470i 0.439151 0.898413i \(-0.355279\pi\)
0.913898 + 0.405943i \(0.133057\pi\)
\(354\) −5.06716 1.87825i −0.269316 0.0998278i
\(355\) −2.44253 + 2.04953i −0.129636 + 0.108778i
\(356\) −2.50216 14.1904i −0.132614 0.752091i
\(357\) −3.39789 5.96640i −0.179836 0.315775i
\(358\) −9.30853 7.81078i −0.491971 0.412813i
\(359\) −16.7778 + 29.0600i −0.885497 + 1.53373i −0.0403540 + 0.999185i \(0.512849\pi\)
−0.845143 + 0.534540i \(0.820485\pi\)
\(360\) −3.63594 + 6.12933i −0.191631 + 0.323044i
\(361\) 7.67859 + 13.2997i 0.404136 + 0.699984i
\(362\) 1.49241 8.46390i 0.0784396 0.444853i
\(363\) −12.0183 + 4.29412i −0.630798 + 0.225383i
\(364\) 0.325226 + 0.118372i 0.0170465 + 0.00620440i
\(365\) 21.2054 + 7.71813i 1.10994 + 0.403985i
\(366\) 6.01813 2.15027i 0.314573 0.112396i
\(367\) −2.72278 + 15.4417i −0.142128 + 0.806048i 0.827500 + 0.561465i \(0.189762\pi\)
−0.969628 + 0.244583i \(0.921349\pi\)
\(368\) −1.24787 2.16137i −0.0650497 0.112669i
\(369\) −13.9100 + 23.4489i −0.724125 + 1.22070i
\(370\) −2.13449 + 3.69705i −0.110967 + 0.192201i
\(371\) 1.81325 + 1.52149i 0.0941391 + 0.0789921i
\(372\) −4.27953 7.51447i −0.221883 0.389607i
\(373\) 4.18598 + 23.7399i 0.216742 + 1.22921i 0.877858 + 0.478921i \(0.158972\pi\)
−0.661116 + 0.750284i \(0.729917\pi\)
\(374\) −5.78701 + 4.85588i −0.299239 + 0.251092i
\(375\) 16.8088 + 6.23052i 0.868001 + 0.321743i
\(376\) 12.1197 4.41120i 0.625024 0.227490i
\(377\) −2.77405 −0.142871
\(378\) −0.811528 5.13239i −0.0417405 0.263982i
\(379\) 19.2429 0.988441 0.494220 0.869337i \(-0.335454\pi\)
0.494220 + 0.869337i \(0.335454\pi\)
\(380\) −4.26056 + 1.55072i −0.218562 + 0.0795502i
\(381\) −1.74184 10.2313i −0.0892370 0.524166i
\(382\) −16.6134 + 13.9403i −0.850017 + 0.713249i
\(383\) −3.22526 18.2914i −0.164803 0.934645i −0.949267 0.314471i \(-0.898173\pi\)
0.784464 0.620175i \(-0.212938\pi\)
\(384\) 1.73202 + 0.0102262i 0.0883868 + 0.000521852i
\(385\) 3.46789 + 2.90991i 0.176740 + 0.148303i
\(386\) 3.62727 6.28261i 0.184623 0.319776i
\(387\) 28.1971 + 10.6416i 1.43334 + 0.540943i
\(388\) 7.25508 + 12.5662i 0.368321 + 0.637950i
\(389\) −4.11924 + 23.3614i −0.208854 + 1.18447i 0.682406 + 0.730974i \(0.260934\pi\)
−0.891259 + 0.453494i \(0.850177\pi\)
\(390\) −1.08545 0.921779i −0.0549641 0.0466761i
\(391\) −9.29684 3.38377i −0.470162 0.171125i
\(392\) 0.939693 + 0.342020i 0.0474616 + 0.0172746i
\(393\) −4.29190 + 23.5275i −0.216498 + 1.18680i
\(394\) −3.58069 + 20.3071i −0.180392 + 1.02306i
\(395\) 5.03577 + 8.72220i 0.253377 + 0.438862i
\(396\) −5.39497 + 1.89177i −0.271107 + 0.0950650i
\(397\) 0.946796 1.63990i 0.0475183 0.0823042i −0.841288 0.540587i \(-0.818202\pi\)
0.888806 + 0.458283i \(0.151535\pi\)
\(398\) −1.50409 1.26208i −0.0753931 0.0632623i
\(399\) 1.66979 2.85312i 0.0835939 0.142835i
\(400\) 0.111688 + 0.633414i 0.00558440 + 0.0316707i
\(401\) 3.05690 2.56504i 0.152654 0.128092i −0.563262 0.826278i \(-0.690454\pi\)
0.715916 + 0.698186i \(0.246009\pi\)
\(402\) −5.28746 + 4.38377i −0.263714 + 0.218642i
\(403\) 1.62376 0.591000i 0.0808852 0.0294398i
\(404\) 13.6975 0.681477
\(405\) −4.20874 + 20.9615i −0.209134 + 1.04159i
\(406\) −8.01522 −0.397789
\(407\) −3.21809 + 1.17129i −0.159515 + 0.0580586i
\(408\) 5.28572 4.38233i 0.261682 0.216958i
\(409\) −22.8598 + 19.1816i −1.13034 + 0.948471i −0.999080 0.0428763i \(-0.986348\pi\)
−0.131264 + 0.991348i \(0.541903\pi\)
\(410\) 3.74891 + 21.2611i 0.185145 + 1.05001i
\(411\) −6.72676 + 11.4938i −0.331807 + 0.566949i
\(412\) −10.2208 8.57628i −0.503543 0.422523i
\(413\) 1.56002 2.70203i 0.0767635 0.132958i
\(414\) −5.67831 4.88008i −0.279074 0.239843i
\(415\) −9.22918 15.9854i −0.453042 0.784692i
\(416\) −0.0600993 + 0.340840i −0.00294661 + 0.0167111i
\(417\) −6.97132 + 38.2155i −0.341387 + 1.87142i
\(418\) −3.41786 1.24400i −0.167173 0.0608460i
\(419\) 3.86429 + 1.40649i 0.188783 + 0.0687114i 0.434682 0.900584i \(-0.356861\pi\)
−0.245899 + 0.969296i \(0.579083\pi\)
\(420\) −3.13626 2.66335i −0.153034 0.129958i
\(421\) 5.64475 32.0129i 0.275108 1.56022i −0.463510 0.886092i \(-0.653410\pi\)
0.738618 0.674124i \(-0.235479\pi\)
\(422\) −3.62000 6.27002i −0.176219 0.305220i
\(423\) 29.9318 24.5193i 1.45533 1.19217i
\(424\) −1.18351 + 2.04990i −0.0574765 + 0.0995521i
\(425\) 1.95317 + 1.63891i 0.0947428 + 0.0794987i
\(426\) 2.32475 + 0.0137258i 0.112635 + 0.000665016i
\(427\) 0.640708 + 3.63364i 0.0310061 + 0.175844i
\(428\) 7.75330 6.50579i 0.374770 0.314469i
\(429\) −0.191726 1.12617i −0.00925661 0.0543721i
\(430\) 22.4257 8.16228i 1.08146 0.393620i
\(431\) −20.1814 −0.972106 −0.486053 0.873929i \(-0.661564\pi\)
−0.486053 + 0.873929i \(0.661564\pi\)
\(432\) 4.91350 1.69043i 0.236401 0.0813308i
\(433\) −36.2474 −1.74194 −0.870969 0.491337i \(-0.836508\pi\)
−0.870969 + 0.491337i \(0.836508\pi\)
\(434\) 4.69162 1.70761i 0.225205 0.0819678i
\(435\) 30.9230 + 11.4623i 1.48265 + 0.549574i
\(436\) 12.9305 10.8500i 0.619258 0.519619i
\(437\) −0.827158 4.69104i −0.0395683 0.224403i
\(438\) −8.14249 14.2975i −0.389063 0.683160i
\(439\) −23.1787 19.4492i −1.10626 0.928261i −0.108429 0.994104i \(-0.534582\pi\)
−0.997830 + 0.0658431i \(0.979026\pi\)
\(440\) −2.26351 + 3.92051i −0.107908 + 0.186903i
\(441\) 2.99979 + 0.0354239i 0.142847 + 0.00168685i
\(442\) 0.685993 + 1.18818i 0.0326294 + 0.0565157i
\(443\) −1.83115 + 10.3850i −0.0870005 + 0.493404i 0.909906 + 0.414813i \(0.136153\pi\)
−0.996907 + 0.0785908i \(0.974958\pi\)
\(444\) 2.93112 1.04728i 0.139105 0.0497019i
\(445\) −32.1656 11.7073i −1.52480 0.554981i
\(446\) 7.38095 + 2.68645i 0.349498 + 0.127207i
\(447\) −5.22451 + 1.86671i −0.247111 + 0.0882923i
\(448\) −0.173648 + 0.984808i −0.00820411 + 0.0465278i
\(449\) −7.92163 13.7207i −0.373845 0.647518i 0.616309 0.787505i \(-0.288627\pi\)
−0.990153 + 0.139987i \(0.955294\pi\)
\(450\) 0.944979 + 1.68232i 0.0445467 + 0.0793053i
\(451\) −8.65949 + 14.9987i −0.407759 + 0.706260i
\(452\) −5.06571 4.25064i −0.238271 0.199933i
\(453\) −11.3894 19.9987i −0.535119 0.939622i
\(454\) 3.82272 + 21.6797i 0.179409 + 1.01748i
\(455\) 0.629818 0.528480i 0.0295263 0.0247755i
\(456\) 3.09973 + 1.14898i 0.145158 + 0.0538059i
\(457\) 33.5281 12.2032i 1.56838 0.570844i 0.595744 0.803175i \(-0.296857\pi\)
0.972637 + 0.232331i \(0.0746352\pi\)
\(458\) −1.21353 −0.0567044
\(459\) 10.6135 17.6535i 0.495396 0.823995i
\(460\) −5.92872 −0.276428
\(461\) 10.1946 3.71052i 0.474808 0.172816i −0.0935209 0.995617i \(-0.529812\pi\)
0.568329 + 0.822801i \(0.307590\pi\)
\(462\) −0.553964 3.25391i −0.0257728 0.151386i
\(463\) −28.9146 + 24.2622i −1.34378 + 1.12756i −0.363136 + 0.931736i \(0.618294\pi\)
−0.980639 + 0.195825i \(0.937261\pi\)
\(464\) −1.39183 7.89345i −0.0646140 0.366444i
\(465\) −20.5424 0.121286i −0.952632 0.00562452i
\(466\) −13.8691 11.6375i −0.642473 0.539099i
\(467\) 5.57777 9.66099i 0.258109 0.447057i −0.707627 0.706587i \(-0.750234\pi\)
0.965735 + 0.259529i \(0.0835674\pi\)
\(468\) 0.168211 + 1.02458i 0.00777557 + 0.0473611i
\(469\) −1.98273 3.43419i −0.0915540 0.158576i
\(470\) 5.32032 30.1730i 0.245408 1.39178i
\(471\) −14.2507 12.1018i −0.656636 0.557623i
\(472\) 2.93188 + 1.06712i 0.134951 + 0.0491180i
\(473\) 17.9901 + 6.54786i 0.827185 + 0.301071i
\(474\) 1.31783 7.22413i 0.0605301 0.331815i
\(475\) −0.213170 + 1.20894i −0.00978089 + 0.0554702i
\(476\) 1.98208 + 3.43306i 0.0908484 + 0.157354i
\(477\) −1.31558 + 6.97815i −0.0602362 + 0.319507i
\(478\) −15.2516 + 26.4165i −0.697592 + 1.20826i
\(479\) −10.6748 8.95725i −0.487746 0.409267i 0.365472 0.930822i \(-0.380908\pi\)
−0.853218 + 0.521555i \(0.825352\pi\)
\(480\) 2.07828 3.55110i 0.0948600 0.162085i
\(481\) 0.108002 + 0.612510i 0.00492447 + 0.0279281i
\(482\) 19.0802 16.0101i 0.869077 0.729242i
\(483\) 3.32776 2.75901i 0.151418 0.125539i
\(484\) 6.92402 2.52014i 0.314728 0.114552i
\(485\) 34.4694 1.56518
\(486\) 12.2320 9.66323i 0.554855 0.438333i
\(487\) 14.8303 0.672027 0.336013 0.941857i \(-0.390921\pi\)
0.336013 + 0.941857i \(0.390921\pi\)
\(488\) −3.46718 + 1.26195i −0.156952 + 0.0571258i
\(489\) 7.70127 6.38503i 0.348263 0.288741i
\(490\) 1.81977 1.52697i 0.0822088 0.0689813i
\(491\) 1.38168 + 7.83587i 0.0623542 + 0.353628i 0.999982 + 0.00598757i \(0.00190592\pi\)
−0.937628 + 0.347640i \(0.886983\pi\)
\(492\) 7.95086 13.5854i 0.358453 0.612478i
\(493\) −24.3400 20.4237i −1.09622 0.919836i
\(494\) −0.330284 + 0.572069i −0.0148602 + 0.0257386i
\(495\) −2.51609 + 13.3459i −0.113090 + 0.599855i
\(496\) 2.49636 + 4.32382i 0.112090 + 0.194145i
\(497\) −0.233074 + 1.32183i −0.0104548 + 0.0592922i
\(498\) −2.41523 + 13.2398i −0.108229 + 0.593292i
\(499\) −5.29141 1.92592i −0.236876 0.0862158i 0.220855 0.975307i \(-0.429115\pi\)
−0.457731 + 0.889091i \(0.651338\pi\)
\(500\) −9.72562 3.53983i −0.434943 0.158306i
\(501\) 6.41972 + 5.45170i 0.286812 + 0.243564i
\(502\) −0.663908 + 3.76521i −0.0296317 + 0.168050i
\(503\) 5.38397 + 9.32531i 0.240059 + 0.415795i 0.960731 0.277481i \(-0.0894997\pi\)
−0.720672 + 0.693277i \(0.756166\pi\)
\(504\) 0.486023 + 2.96037i 0.0216492 + 0.131865i
\(505\) 16.2695 28.1796i 0.723983 1.25398i
\(506\) −3.64336 3.05714i −0.161967 0.135907i
\(507\) 22.3088 + 0.131715i 0.990769 + 0.00584968i
\(508\) 1.04051 + 5.90102i 0.0461651 + 0.261815i
\(509\) 11.4608 9.61673i 0.507990 0.426254i −0.352431 0.935838i \(-0.614645\pi\)
0.860421 + 0.509584i \(0.170201\pi\)
\(510\) −2.73744 16.0794i −0.121216 0.712007i
\(511\) 8.92655 3.24900i 0.394888 0.143727i
\(512\) −1.00000 −0.0441942
\(513\) 9.91592 + 0.175652i 0.437798 + 0.00775525i
\(514\) 8.25540 0.364130
\(515\) −29.7838 + 10.8404i −1.31243 + 0.477685i
\(516\) −16.3156 6.04771i −0.718253 0.266236i
\(517\) 18.8282 15.7987i 0.828063 0.694827i
\(518\) 0.312056 + 1.76976i 0.0137110 + 0.0777588i
\(519\) −1.39869 2.45598i −0.0613957 0.107806i
\(520\) 0.629818 + 0.528480i 0.0276193 + 0.0231754i
\(521\) 5.66431 9.81087i 0.248158 0.429822i −0.714857 0.699271i \(-0.753508\pi\)
0.963015 + 0.269449i \(0.0868415\pi\)
\(522\) −11.7761 20.9647i −0.515426 0.917598i
\(523\) −5.74177 9.94503i −0.251070 0.434866i 0.712751 0.701417i \(-0.247449\pi\)
−0.963821 + 0.266552i \(0.914116\pi\)
\(524\) 2.39769 13.5980i 0.104744 0.594030i
\(525\) −1.04908 + 0.374833i −0.0457854 + 0.0163591i
\(526\) −11.1639 4.06333i −0.486770 0.177170i
\(527\) 18.5983 + 6.76923i 0.810155 + 0.294872i
\(528\) 3.10828 1.11058i 0.135271 0.0483320i
\(529\) −2.91230 + 16.5165i −0.126622 + 0.718109i
\(530\) 2.81148 + 4.86963i 0.122123 + 0.211523i
\(531\) 9.35946 + 0.110524i 0.406166 + 0.00479633i
\(532\) −0.954309 + 1.65291i −0.0413745 + 0.0716628i
\(533\) 2.40949 + 2.02180i 0.104367 + 0.0875740i
\(534\) 12.3510 + 21.6873i 0.534481 + 0.938502i
\(535\) −4.17508 23.6781i −0.180504 1.02369i
\(536\) 3.03772 2.54895i 0.131209 0.110098i
\(537\) 19.7347 + 7.31510i 0.851617 + 0.315670i
\(538\) −20.8058 + 7.57270i −0.897003 + 0.326482i
\(539\) 1.90568 0.0820834
\(540\) 2.35842 12.1163i 0.101490 0.521401i
\(541\) 1.23159 0.0529501 0.0264751 0.999649i \(-0.491572\pi\)
0.0264751 + 0.999649i \(0.491572\pi\)
\(542\) −3.32516 + 1.21026i −0.142828 + 0.0519850i
\(543\) 2.49834 + 14.6749i 0.107214 + 0.629761i
\(544\) −3.03672 + 2.54811i −0.130198 + 0.109249i
\(545\) −6.96295 39.4889i −0.298260 1.69152i
\(546\) −0.599449 0.00353926i −0.0256540 0.000151466i
\(547\) −30.0680 25.2300i −1.28561 1.07876i −0.992444 0.122697i \(-0.960846\pi\)
−0.293169 0.956061i \(-0.594710\pi\)
\(548\) 3.84445 6.65879i 0.164227 0.284449i
\(549\) −8.56283 + 7.01445i −0.365453 + 0.299369i
\(550\) 0.612852 + 1.06149i 0.0261321 + 0.0452621i
\(551\) 2.65647 15.0656i 0.113169 0.641815i
\(552\) 3.29495 + 2.79811i 0.140242 + 0.119095i
\(553\) 3.98400 + 1.45006i 0.169417 + 0.0616627i
\(554\) 25.9372 + 9.44036i 1.10197 + 0.401083i
\(555\) 1.32694 7.27406i 0.0563256 0.308767i
\(556\) 3.89456 22.0871i 0.165166 0.936703i
\(557\) −1.24983 2.16478i −0.0529572 0.0917245i 0.838332 0.545161i \(-0.183531\pi\)
−0.891289 + 0.453436i \(0.850198\pi\)
\(558\) 11.3594 + 9.76258i 0.480883 + 0.413283i
\(559\) 1.73847 3.01112i 0.0735294 0.127357i
\(560\) 1.81977 + 1.52697i 0.0768992 + 0.0645261i
\(561\) 6.60910 11.2928i 0.279036 0.476782i
\(562\) −2.61384 14.8238i −0.110258 0.625306i
\(563\) −3.85341 + 3.23340i −0.162402 + 0.136271i −0.720367 0.693593i \(-0.756027\pi\)
0.557965 + 0.829864i \(0.311582\pi\)
\(564\) −17.1972 + 14.2580i −0.724134 + 0.600371i
\(565\) −14.7616 + 5.37280i −0.621027 + 0.226035i
\(566\) 23.0133 0.967321
\(567\) 4.31469 + 7.89832i 0.181200 + 0.331698i
\(568\) −1.34222 −0.0563183
\(569\) −5.78120 + 2.10419i −0.242361 + 0.0882120i −0.460345 0.887740i \(-0.652274\pi\)
0.217984 + 0.975952i \(0.430052\pi\)
\(570\) 6.04553 5.01228i 0.253219 0.209941i
\(571\) 8.53072 7.15812i 0.356999 0.299558i −0.446594 0.894737i \(-0.647363\pi\)
0.803593 + 0.595179i \(0.202919\pi\)
\(572\) 0.114530 + 0.649531i 0.00478873 + 0.0271583i
\(573\) 18.9735 32.4195i 0.792629 1.35434i
\(574\) 6.96188 + 5.84171i 0.290583 + 0.243828i
\(575\) −0.802611 + 1.39016i −0.0334712 + 0.0579738i
\(576\) −2.83100 + 0.992701i −0.117958 + 0.0413626i
\(577\) 19.4406 + 33.6721i 0.809322 + 1.40179i 0.913334 + 0.407210i \(0.133498\pi\)
−0.104013 + 0.994576i \(0.533168\pi\)
\(578\) 0.223217 1.26593i 0.00928462 0.0526557i
\(579\) −2.25495 + 12.3612i −0.0937124 + 0.513715i
\(580\) −17.8922 6.51222i −0.742933 0.270405i
\(581\) −7.30158 2.65756i −0.302920 0.110254i
\(582\) −19.1568 16.2681i −0.794074 0.674336i
\(583\) −0.783290 + 4.44226i −0.0324406 + 0.183980i
\(584\) 4.74972 + 8.22676i 0.196545 + 0.340426i
\(585\) 2.30764 + 0.870904i 0.0954090 + 0.0360075i
\(586\) 0.366162 0.634211i 0.0151260 0.0261990i
\(587\) 15.4533 + 12.9668i 0.637825 + 0.535199i 0.903349 0.428906i \(-0.141101\pi\)
−0.265525 + 0.964104i \(0.585545\pi\)
\(588\) −1.73202 0.0102262i −0.0714273 0.000421720i
\(589\) 1.65473 + 9.38441i 0.0681818 + 0.386678i
\(590\) 5.67775 4.76420i 0.233749 0.196139i
\(591\) −5.99416 35.2089i −0.246567 1.44830i
\(592\) −1.68868 + 0.614631i −0.0694045 + 0.0252612i
\(593\) −4.64427 −0.190718 −0.0953588 0.995443i \(-0.530400\pi\)
−0.0953588 + 0.995443i \(0.530400\pi\)
\(594\) 7.69706 6.22966i 0.315814 0.255606i
\(595\) 9.41701 0.386060
\(596\) 3.00996 1.09554i 0.123293 0.0448749i
\(597\) 3.18877 + 1.18199i 0.130508 + 0.0483755i
\(598\) −0.661686 + 0.555220i −0.0270583 + 0.0227046i
\(599\) 0.0810987 + 0.459934i 0.00331360 + 0.0187924i 0.986420 0.164244i \(-0.0525185\pi\)
−0.983106 + 0.183036i \(0.941407\pi\)
\(600\) −0.551309 0.968049i −0.0225071 0.0395205i
\(601\) −8.97886 7.53416i −0.366255 0.307325i 0.441023 0.897496i \(-0.354616\pi\)
−0.807278 + 0.590171i \(0.799060\pi\)
\(602\) 5.02305 8.70019i 0.204724 0.354593i
\(603\) 6.06943 10.2316i 0.247166 0.416664i
\(604\) 6.64371 + 11.5072i 0.270329 + 0.468223i
\(605\) 3.03952 17.2380i 0.123574 0.700823i
\(606\) −22.3415 + 7.98259i −0.907563 + 0.324271i
\(607\) −34.3390 12.4984i −1.39378 0.507294i −0.467453 0.884018i \(-0.654828\pi\)
−0.926326 + 0.376724i \(0.877051\pi\)
\(608\) −1.79351 0.652786i −0.0727366 0.0264740i
\(609\) 13.0733 4.67108i 0.529758 0.189282i
\(610\) −1.52203 + 8.63185i −0.0616251 + 0.349493i
\(611\) −2.23190 3.86576i −0.0902929 0.156392i
\(612\) −6.06743 + 10.2283i −0.245261 + 0.413453i
\(613\) −19.6703 + 34.0699i −0.794475 + 1.37607i 0.128697 + 0.991684i \(0.458920\pi\)
−0.923172 + 0.384387i \(0.874413\pi\)
\(614\) −10.9513 9.18926i −0.441960 0.370848i
\(615\) −18.5052 32.4935i −0.746201 1.31026i
\(616\) 0.330918 + 1.87673i 0.0133330 + 0.0756155i
\(617\) 26.4702 22.2112i 1.06565 0.894188i 0.0710004 0.997476i \(-0.477381\pi\)
0.994651 + 0.103288i \(0.0329364\pi\)
\(618\) 21.6689 + 8.03202i 0.871649 + 0.323095i
\(619\) −16.3927 + 5.96644i −0.658877 + 0.239811i −0.649751 0.760147i \(-0.725127\pi\)
−0.00912534 + 0.999958i \(0.502905\pi\)
\(620\) 11.8604 0.476325
\(621\) 12.1057 + 4.65053i 0.485784 + 0.186620i
\(622\) 6.10431 0.244761
\(623\) −13.5404 + 4.92829i −0.542483 + 0.197448i
\(624\) −0.100608 0.590956i −0.00402753 0.0236572i
\(625\) −21.2978 + 17.8709i −0.851910 + 0.714837i
\(626\) 2.37172 + 13.4507i 0.0947928 + 0.537597i
\(627\) 6.29973 + 0.0371947i 0.251587 + 0.00148541i
\(628\) 8.26874 + 6.93830i 0.329959 + 0.276868i
\(629\) −3.56192 + 6.16942i −0.142023 + 0.245991i
\(630\) 6.66758 + 2.51635i 0.265643 + 0.100254i
\(631\) 18.9580 + 32.8363i 0.754708 + 1.30719i 0.945520 + 0.325565i \(0.105555\pi\)
−0.190812 + 0.981627i \(0.561112\pi\)
\(632\) −0.736213 + 4.17527i −0.0292850 + 0.166083i
\(633\) 9.55847 + 8.11716i 0.379915 + 0.322628i
\(634\) 0.0597104 + 0.0217328i 0.00237140 + 0.000863120i
\(635\) 13.3759 + 4.86843i 0.530807 + 0.193198i
\(636\) 0.735750 4.03325i 0.0291744 0.159929i
\(637\) 0.0600993 0.340840i 0.00238122 0.0135046i
\(638\) −7.63721 13.2280i −0.302360 0.523703i
\(639\) −3.79982 + 1.33242i −0.150319 + 0.0527099i
\(640\) −1.18777 + 2.05728i −0.0469507 + 0.0813210i
\(641\) −13.8270 11.6022i −0.546134 0.458261i 0.327496 0.944853i \(-0.393795\pi\)
−0.873629 + 0.486592i \(0.838240\pi\)
\(642\) −8.85471 + 15.1298i −0.349467 + 0.597126i
\(643\) −2.88880 16.3832i −0.113923 0.646091i −0.987278 0.159006i \(-0.949171\pi\)
0.873354 0.487085i \(-0.161940\pi\)
\(644\) −1.91185 + 1.60423i −0.0753373 + 0.0632155i
\(645\) −31.8210 + 26.3824i −1.25295 + 1.03881i
\(646\) −7.10977 + 2.58775i −0.279730 + 0.101814i
\(647\) −31.4385 −1.23597 −0.617987 0.786188i \(-0.712052\pi\)
−0.617987 + 0.786188i \(0.712052\pi\)
\(648\) −7.02909 + 5.62067i −0.276129 + 0.220801i
\(649\) 5.94579 0.233393
\(650\) 0.209180 0.0761354i 0.00820473 0.00298628i
\(651\) −6.65717 + 5.51938i −0.260915 + 0.216322i
\(652\) −4.42449 + 3.71258i −0.173276 + 0.145396i
\(653\) −2.43255 13.7957i −0.0951930 0.539866i −0.994688 0.102935i \(-0.967176\pi\)
0.899495 0.436931i \(-0.143935\pi\)
\(654\) −14.7674 + 25.2326i −0.577449 + 0.986672i
\(655\) −25.1269 21.0840i −0.981789 0.823819i
\(656\) −4.54404 + 7.87052i −0.177415 + 0.307292i
\(657\) 21.6132 + 18.5749i 0.843210 + 0.724675i
\(658\) −6.44874 11.1696i −0.251398 0.435434i
\(659\) 8.57069 48.6068i 0.333867 1.89345i −0.104280 0.994548i \(-0.533254\pi\)
0.438146 0.898904i \(-0.355635\pi\)
\(660\) 1.40715 7.71372i 0.0547730 0.300256i
\(661\) −11.1971 4.07541i −0.435517 0.158515i 0.114952 0.993371i \(-0.463329\pi\)
−0.550469 + 0.834856i \(0.685551\pi\)
\(662\) 13.0863 + 4.76301i 0.508613 + 0.185120i
\(663\) −1.81134 1.53821i −0.0703466 0.0597391i
\(664\) 1.34928 7.65213i 0.0523621 0.296960i
\(665\) 2.26700 + 3.92656i 0.0879104 + 0.152265i
\(666\) −4.17052 + 3.41638i −0.161604 + 0.132382i
\(667\) 10.0019 17.3239i 0.387277 0.670783i
\(668\) −3.72495 3.12560i −0.144123 0.120933i
\(669\) −13.6044 0.0803229i −0.525977 0.00310546i
\(670\) −1.63578 9.27699i −0.0631959 0.358401i
\(671\) −5.38634 + 4.51968i −0.207937 + 0.174480i
\(672\) −0.290691 1.70748i −0.0112137 0.0658676i
\(673\) 41.4523 15.0874i 1.59787 0.581577i 0.618880 0.785485i \(-0.287587\pi\)
0.978990 + 0.203908i \(0.0653644\pi\)
\(674\) −22.8856 −0.881520
\(675\) −2.52174 2.19326i −0.0970617 0.0844186i
\(676\) −12.8802 −0.495393
\(677\) −37.9511 + 13.8131i −1.45858 + 0.530879i −0.944973 0.327147i \(-0.893913\pi\)
−0.513605 + 0.858027i \(0.671690\pi\)
\(678\) 10.7397 + 3.98088i 0.412455 + 0.152885i
\(679\) 11.1154 9.32695i 0.426571 0.357936i
\(680\) 1.63525 + 9.27394i 0.0627088 + 0.355640i
\(681\) −18.8696 33.1333i −0.723083 1.26967i
\(682\) 7.28853 + 6.11581i 0.279092 + 0.234186i
\(683\) 14.6084 25.3026i 0.558977 0.968176i −0.438606 0.898680i \(-0.644527\pi\)
0.997582 0.0694962i \(-0.0221392\pi\)
\(684\) −5.72546 0.0676106i −0.218918 0.00258516i
\(685\) −9.13265 15.8182i −0.348940 0.604383i
\(686\) 0.173648 0.984808i 0.00662992 0.0376001i
\(687\) 1.97934 0.707216i 0.0755166 0.0269820i
\(688\) 9.44026 + 3.43597i 0.359906 + 0.130995i
\(689\) 0.769817 + 0.280191i 0.0293277 + 0.0106744i
\(690\) 9.67013 3.45512i 0.368135 0.131534i
\(691\) −7.15437 + 40.5745i −0.272165 + 1.54352i 0.475660 + 0.879629i \(0.342209\pi\)
−0.747825 + 0.663896i \(0.768902\pi\)
\(692\) 0.815893 + 1.41317i 0.0310156 + 0.0537206i
\(693\) 2.79986 + 4.98451i 0.106358 + 0.189346i
\(694\) −18.1394 + 31.4183i −0.688561 + 1.19262i
\(695\) −40.8135 34.2466i −1.54814 1.29905i
\(696\) 6.87028 + 12.0636i 0.260417 + 0.457270i
\(697\) 6.25596 + 35.4793i 0.236961 + 1.34387i
\(698\) 17.3803 14.5838i 0.657853 0.552004i
\(699\) 29.4034 + 10.8990i 1.11214 + 0.412238i
\(700\) 0.604396 0.219982i 0.0228440 0.00831455i
\(701\) −24.7627 −0.935276 −0.467638 0.883920i \(-0.654895\pi\)
−0.467638 + 0.883920i \(0.654895\pi\)
\(702\) −0.871463 1.57312i −0.0328913 0.0593737i
\(703\) −3.42990 −0.129361
\(704\) −1.79075 + 0.651780i −0.0674915 + 0.0245649i
\(705\) 8.90634 + 52.3147i 0.335432 + 1.97029i
\(706\) 20.7238 17.3893i 0.779950 0.654456i
\(707\) −2.37855 13.4894i −0.0894545 0.507322i
\(708\) −5.40397 0.0319060i −0.203094 0.00119910i
\(709\) 2.40825 + 2.02076i 0.0904437 + 0.0758913i 0.686888 0.726763i \(-0.258976\pi\)
−0.596445 + 0.802654i \(0.703421\pi\)
\(710\) −1.59425 + 2.76132i −0.0598311 + 0.103631i
\(711\) 2.06058 + 12.5510i 0.0772778 + 0.470700i
\(712\) −7.20467 12.4789i −0.270006 0.467665i
\(713\) −2.16374 + 12.2712i −0.0810328 + 0.459560i
\(714\) −5.23361 4.44444i −0.195863 0.166329i
\(715\) 1.47230 + 0.535874i 0.0550609 + 0.0200405i
\(716\) −11.4186 4.15603i −0.426733 0.155318i
\(717\) 9.48140 51.9754i 0.354089 1.94106i
\(718\) −5.82686 + 33.0458i −0.217456 + 1.23326i
\(719\) 9.48235 + 16.4239i 0.353632 + 0.612508i 0.986883 0.161438i \(-0.0516132\pi\)
−0.633251 + 0.773947i \(0.718280\pi\)
\(720\) −1.32031 + 7.00325i −0.0492051 + 0.260996i
\(721\) −6.67116 + 11.5548i −0.248447 + 0.430323i
\(722\) 11.7643 + 9.87140i 0.437821 + 0.367376i
\(723\) −21.7906 + 37.2331i −0.810402 + 1.38471i
\(724\) −1.49241 8.46390i −0.0554651 0.314558i
\(725\) −3.94917 + 3.31374i −0.146668 + 0.123069i
\(726\) −9.82485 + 8.14566i −0.364634 + 0.302314i
\(727\) 21.1969 7.71503i 0.786148 0.286135i 0.0824143 0.996598i \(-0.473737\pi\)
0.703734 + 0.710464i \(0.251515\pi\)
\(728\) 0.346098 0.0128272
\(729\) −14.3197 + 22.8899i −0.530359 + 0.847773i
\(730\) 22.5663 0.835216
\(731\) 37.4227 13.6207i 1.38413 0.503781i
\(732\) 4.91976 4.07891i 0.181839 0.150761i
\(733\) −0.275415 + 0.231101i −0.0101727 + 0.00853590i −0.647860 0.761760i \(-0.724336\pi\)
0.637687 + 0.770296i \(0.279891\pi\)
\(734\) 2.72278 + 15.4417i 0.100500 + 0.569962i
\(735\) −2.07828 + 3.55110i −0.0766585 + 0.130984i
\(736\) −1.91185 1.60423i −0.0704716 0.0591327i
\(737\) 3.77845 6.54446i 0.139181 0.241068i
\(738\) −5.05110 + 26.7923i −0.185934 + 0.986238i
\(739\) 15.7925 + 27.3534i 0.580936 + 1.00621i 0.995369 + 0.0961312i \(0.0306468\pi\)
−0.414432 + 0.910080i \(0.636020\pi\)
\(740\) −0.741302 + 4.20413i −0.0272508 + 0.154547i
\(741\) 0.205327 1.12556i 0.00754286 0.0413486i
\(742\) 2.22428 + 0.809570i 0.0816557 + 0.0297203i
\(743\) −0.349432 0.127183i −0.0128194 0.00466589i 0.335602 0.942004i \(-0.391060\pi\)
−0.348422 + 0.937338i \(0.613282\pi\)
\(744\) −6.59154 5.59761i −0.241657 0.205218i
\(745\) 1.32132 7.49356i 0.0484093 0.274543i
\(746\) 12.0531 + 20.8765i 0.441294 + 0.764344i
\(747\) −3.77648 23.0026i −0.138174 0.841620i
\(748\) −3.77720 + 6.54231i −0.138108 + 0.239211i
\(749\) −7.75330 6.50579i −0.283299 0.237716i
\(750\) 17.9260 + 0.105839i 0.654566 + 0.00386468i
\(751\) −6.54925 37.1426i −0.238985 1.35535i −0.834056 0.551680i \(-0.813987\pi\)
0.595070 0.803674i \(-0.297124\pi\)
\(752\) 9.88005 8.29035i 0.360288 0.302318i
\(753\) −1.11140 6.52821i −0.0405016 0.237901i
\(754\) −2.60675 + 0.948781i −0.0949324 + 0.0345526i
\(755\) 31.5648 1.14876
\(756\) −2.51797 4.54531i −0.0915776 0.165311i
\(757\) 24.6362 0.895416 0.447708 0.894180i \(-0.352240\pi\)
0.447708 + 0.894180i \(0.352240\pi\)
\(758\) 18.0824 6.58145i 0.656782 0.239049i
\(759\) 7.72419 + 2.86313i 0.280370 + 0.103925i
\(760\) −3.47324 + 2.91440i −0.125988 + 0.105716i
\(761\) −6.85593 38.8819i −0.248527 1.40947i −0.812156 0.583440i \(-0.801706\pi\)
0.563629 0.826028i \(-0.309405\pi\)
\(762\) −5.13611 9.01855i −0.186062 0.326708i
\(763\) −12.9305 10.8500i −0.468115 0.392795i
\(764\) −10.8437 + 18.7818i −0.392310 + 0.679500i
\(765\) 13.8356 + 24.6312i 0.500228 + 0.890543i
\(766\) −9.28677 16.0852i −0.335545 0.581181i
\(767\) 0.187512 1.06343i 0.00677067 0.0383984i
\(768\) 1.63106 0.582776i 0.0588560 0.0210291i
\(769\) 32.2229 + 11.7282i 1.16199 + 0.422929i 0.849807 0.527094i \(-0.176718\pi\)
0.312180 + 0.950023i \(0.398941\pi\)
\(770\) 4.25400 + 1.54833i 0.153304 + 0.0557979i
\(771\) −13.4651 + 4.81105i −0.484933 + 0.173266i
\(772\) 1.25974 7.14432i 0.0453389 0.257130i
\(773\) 10.8230 + 18.7459i 0.389275 + 0.674244i 0.992352 0.123439i \(-0.0393922\pi\)
−0.603077 + 0.797683i \(0.706059\pi\)
\(774\) 30.1362 + 0.355872i 1.08322 + 0.0127916i
\(775\) 1.60562 2.78101i 0.0576755 0.0998970i
\(776\) 11.1154 + 9.32695i 0.399021 + 0.334818i
\(777\) −1.54036 2.70473i −0.0552600 0.0970318i
\(778\) 4.11924 + 23.3614i 0.147682 + 0.837545i
\(779\) −13.2876 + 11.1496i −0.476077 + 0.399476i
\(780\) −1.33526 0.494942i −0.0478100 0.0177218i
\(781\) −2.40358 + 0.874833i −0.0860070 + 0.0313040i
\(782\) −9.89350 −0.353791
\(783\) 31.4253 + 27.3319i 1.12305 + 0.976762i
\(784\) 1.00000 0.0357143
\(785\) 24.0954 8.76999i 0.860000 0.313014i
\(786\) 4.01379 + 23.5765i 0.143167 + 0.840946i
\(787\) −13.6152 + 11.4245i −0.485330 + 0.407240i −0.852349 0.522973i \(-0.824823\pi\)
0.367019 + 0.930213i \(0.380378\pi\)
\(788\) 3.58069 + 20.3071i 0.127557 + 0.723410i
\(789\) 20.5771 + 0.121491i 0.732563 + 0.00432519i
\(790\) 7.71524 + 6.47386i 0.274496 + 0.230329i
\(791\) −3.30641 + 5.72687i −0.117562 + 0.203624i
\(792\) −4.42259 + 3.62287i −0.157150 + 0.128733i
\(793\) 0.638497 + 1.10591i 0.0226737 + 0.0392720i
\(794\) 0.328819 1.86482i 0.0116693 0.0661801i
\(795\) −7.42361 6.30421i −0.263288 0.223587i
\(796\) −1.84504 0.671538i −0.0653956 0.0238021i
\(797\) 28.1483 + 10.2451i 0.997064 + 0.362902i 0.788452 0.615097i \(-0.210883\pi\)
0.208612 + 0.977998i \(0.433105\pi\)
\(798\) 0.593262 3.25216i 0.0210012 0.115125i
\(799\) 8.87823 50.3509i 0.314089 1.78129i
\(800\) 0.321593 + 0.557015i 0.0113700 + 0.0196934i
\(801\) −32.7842 28.1755i −1.15837 0.995533i
\(802\) 1.99525 3.45587i 0.0704546 0.122031i
\(803\) 13.8676 + 11.6363i 0.489377 + 0.410636i
\(804\) −3.46925 + 5.92781i −0.122351 + 0.209058i
\(805\) 1.02951 + 5.83865i 0.0362855 + 0.205785i
\(806\) 1.32370 1.11072i 0.0466253 0.0391233i
\(807\) 29.5225 24.4767i 1.03924 0.861621i
\(808\) 12.8715 4.68483i 0.452816 0.164812i
\(809\) −45.0164 −1.58269 −0.791346 0.611369i \(-0.790619\pi\)
−0.791346 + 0.611369i \(0.790619\pi\)
\(810\) 3.21434 + 21.1368i 0.112940 + 0.742673i
\(811\) −18.1317 −0.636689 −0.318344 0.947975i \(-0.603127\pi\)
−0.318344 + 0.947975i \(0.603127\pi\)
\(812\) −7.53184 + 2.74137i −0.264316 + 0.0962031i
\(813\) 4.71824 3.91183i 0.165476 0.137194i
\(814\) −2.62341 + 2.20130i −0.0919505 + 0.0771556i
\(815\) 2.38255 + 13.5121i 0.0834569 + 0.473308i
\(816\) 3.46811 5.92586i 0.121408 0.207447i
\(817\) 14.6883 + 12.3249i 0.513878 + 0.431195i
\(818\) −14.9207 + 25.8434i −0.521689 + 0.903592i
\(819\) 0.979802 0.343572i 0.0342371 0.0120054i
\(820\) 10.7946 + 18.6967i 0.376962 + 0.652918i
\(821\) −9.79649 + 55.5586i −0.341900 + 1.93901i 0.00198540 + 0.999998i \(0.499368\pi\)
−0.343885 + 0.939012i \(0.611743\pi\)
\(822\) −2.38997 + 13.1014i −0.0833596 + 0.456963i
\(823\) −45.8486 16.6875i −1.59818 0.581690i −0.619127 0.785291i \(-0.712513\pi\)
−0.979054 + 0.203601i \(0.934736\pi\)
\(824\) −12.5377 4.56334i −0.436771 0.158972i
\(825\) −1.61821 1.37420i −0.0563389 0.0478436i
\(826\) 0.541789 3.07264i 0.0188512 0.106911i
\(827\) −15.0924 26.1409i −0.524816 0.909008i −0.999582 0.0288959i \(-0.990801\pi\)
0.474767 0.880112i \(-0.342532\pi\)
\(828\) −7.00495 2.64368i −0.243439 0.0918741i
\(829\) 1.07321 1.85885i 0.0372740 0.0645605i −0.846787 0.531933i \(-0.821466\pi\)
0.884061 + 0.467372i \(0.154799\pi\)
\(830\) −14.1399 11.8648i −0.490804 0.411833i
\(831\) −47.8068 0.282260i −1.65840 0.00979151i
\(832\) 0.0600993 + 0.340840i 0.00208357 + 0.0118165i
\(833\) 3.03672 2.54811i 0.105216 0.0882868i
\(834\) 6.51959 + 38.2952i 0.225755 + 1.32605i
\(835\) −10.8546 + 3.95075i −0.375639 + 0.136721i
\(836\) −3.63721 −0.125796
\(837\) −24.2174 9.30338i −0.837075 0.321572i
\(838\) 4.11229 0.142057
\(839\) −38.5535 + 14.0323i −1.33101 + 0.484450i −0.906971 0.421192i \(-0.861612\pi\)
−0.424043 + 0.905642i \(0.639390\pi\)
\(840\) −3.85804 1.43006i −0.133115 0.0493419i
\(841\) 26.9983 22.6542i 0.930975 0.781181i
\(842\) −5.64475 32.0129i −0.194531 1.10324i
\(843\) 12.9023 + 22.6554i 0.444380 + 0.780292i
\(844\) −5.54616 4.65378i −0.190907 0.160190i
\(845\) −15.2987 + 26.4982i −0.526292 + 0.911565i
\(846\) 19.7406 33.2779i 0.678694 1.14412i
\(847\) −3.68420 6.38121i −0.126590 0.219261i
\(848\) −0.411030 + 2.33106i −0.0141148 + 0.0800491i
\(849\) −37.5362 + 13.4116i −1.28824 + 0.460285i
\(850\) 2.39592 + 0.872044i 0.0821794 + 0.0299109i
\(851\) −4.21451 1.53396i −0.144472 0.0525834i
\(852\) 2.18925 0.782215i 0.0750024 0.0267982i
\(853\) −1.93661 + 10.9831i −0.0663084 + 0.376054i 0.933537 + 0.358481i \(0.116705\pi\)
−0.999846 + 0.0175731i \(0.994406\pi\)
\(854\) 1.84485 + 3.19537i 0.0631293 + 0.109343i
\(855\) −6.93962 + 11.6985i −0.237330 + 0.400082i
\(856\) 5.06060 8.76522i 0.172968 0.299589i
\(857\) 32.4176 + 27.2016i 1.10736 + 0.929188i 0.997898 0.0648031i \(-0.0206419\pi\)
0.109465 + 0.993991i \(0.465086\pi\)
\(858\) −0.565337 0.992682i −0.0193003 0.0338896i
\(859\) −6.03469 34.2244i −0.205901 1.16772i −0.896016 0.444022i \(-0.853551\pi\)
0.690115 0.723700i \(-0.257560\pi\)
\(860\) 18.2816 15.3401i 0.623397 0.523092i
\(861\) −14.7597 5.47099i −0.503009 0.186451i
\(862\) −18.9644 + 6.90246i −0.645928 + 0.235099i
\(863\) 45.3907 1.54512 0.772558 0.634944i \(-0.218977\pi\)
0.772558 + 0.634944i \(0.218977\pi\)
\(864\) 4.03902 3.26900i 0.137410 0.111214i
\(865\) 3.87637 0.131801
\(866\) −34.0614 + 12.3973i −1.15745 + 0.421279i
\(867\) 0.373671 + 2.19490i 0.0126905 + 0.0745426i
\(868\) 3.82464 3.20925i 0.129817 0.108929i
\(869\) 1.40299 + 7.95673i 0.0475930 + 0.269913i
\(870\) 32.9785 + 0.194711i 1.11808 + 0.00660132i
\(871\) −1.05135 0.882186i −0.0356236 0.0298917i
\(872\) 8.43978 14.6181i 0.285807 0.495032i
\(873\) 40.7266 + 15.3703i 1.37839 + 0.520205i
\(874\) −2.38171 4.12523i −0.0805624 0.139538i
\(875\) −1.79722 + 10.1925i −0.0607572 + 0.344571i
\(876\) −12.5415 10.6503i −0.423737 0.359842i
\(877\) 15.1181 + 5.50254i 0.510502 + 0.185807i 0.584411 0.811457i \(-0.301325\pi\)
−0.0739096 + 0.997265i \(0.523548\pi\)
\(878\) −28.4329 10.3487i −0.959563 0.349252i
\(879\) −0.227631 + 1.24783i −0.00767779 + 0.0420883i
\(880\) −0.786108 + 4.45824i −0.0264997 + 0.150287i
\(881\) 14.5982 + 25.2849i 0.491827 + 0.851869i 0.999956 0.00941223i \(-0.00299605\pi\)
−0.508129 + 0.861281i \(0.669663\pi\)
\(882\) 2.83100 0.992701i 0.0953246 0.0334260i
\(883\) −25.1723 + 43.5998i −0.847117 + 1.46725i 0.0366530 + 0.999328i \(0.488330\pi\)
−0.883770 + 0.467922i \(0.845003\pi\)
\(884\) 1.05100 + 0.881896i 0.0353490 + 0.0296614i
\(885\) −6.48431 + 11.0796i −0.217968 + 0.372436i
\(886\) 1.83115 + 10.3850i 0.0615186 + 0.348889i
\(887\) −9.07886 + 7.61807i −0.304838 + 0.255790i −0.782355 0.622833i \(-0.785982\pi\)
0.477516 + 0.878623i \(0.341537\pi\)
\(888\) 2.39616 1.98663i 0.0804099 0.0666669i
\(889\) 5.63068 2.04940i 0.188847 0.0687347i
\(890\) −34.2300 −1.14739
\(891\) −8.92391 + 14.6466i −0.298962 + 0.490681i
\(892\) 7.85464 0.262993
\(893\) 23.1318 8.41930i 0.774077 0.281741i
\(894\) −4.27098 + 3.54102i −0.142843 + 0.118429i
\(895\) −22.1128 + 18.5548i −0.739148 + 0.620219i
\(896\) 0.173648 + 0.984808i 0.00580118 + 0.0329001i
\(897\) 0.755683 1.29122i 0.0252315 0.0431124i
\(898\) −12.1366 10.1838i −0.405005 0.339839i
\(899\) −20.0088 + 34.6563i −0.667332 + 1.15585i
\(900\) 1.46338 + 1.25766i 0.0487792 + 0.0419220i
\(901\) 4.69163 + 8.12614i 0.156301 + 0.270721i
\(902\) −3.00741 + 17.0559i −0.100136 + 0.567898i
\(903\) −3.12266 + 17.1179i −0.103916 + 0.569647i
\(904\) −6.21401 2.26172i −0.206675 0.0752236i
\(905\) −19.1852 6.98286i −0.637739 0.232118i
\(906\) −17.5425 14.8973i −0.582809 0.494928i
\(907\) 9.23628 52.3816i 0.306686 1.73930i −0.308776 0.951135i \(-0.599919\pi\)
0.615462 0.788167i \(-0.288969\pi\)
\(908\) 11.0071 + 19.0648i 0.365283 + 0.632689i
\(909\) 31.7884 26.0402i 1.05436 0.863700i
\(910\) 0.411085 0.712019i 0.0136273 0.0236032i
\(911\) −11.4308 9.59156i −0.378719 0.317783i 0.433481 0.901163i \(-0.357285\pi\)
−0.812199 + 0.583380i \(0.801730\pi\)
\(912\) 3.30577 + 0.0195179i 0.109465 + 0.000646301i
\(913\) −2.57129 14.5825i −0.0850972 0.482610i
\(914\) 27.3324 22.9346i 0.904075 0.758609i
\(915\) −2.54791 14.9661i −0.0842314 0.494764i
\(916\) −1.14034 + 0.415051i −0.0376780 + 0.0137137i
\(917\) −13.8077 −0.455972
\(918\) 3.93559 20.2189i 0.129894 0.667323i
\(919\) 9.99424 0.329679 0.164840 0.986320i \(-0.447289\pi\)
0.164840 + 0.986320i \(0.447289\pi\)
\(920\) −5.57118 + 2.02774i −0.183676 + 0.0668527i
\(921\) 23.2176 + 8.60610i 0.765047 + 0.283581i
\(922\) 8.31069 6.97350i 0.273698 0.229660i
\(923\) 0.0806665 + 0.457482i 0.00265517 + 0.0150582i
\(924\) −1.63346 2.86821i −0.0537369 0.0943572i
\(925\) 0.885427 + 0.742961i 0.0291127 + 0.0244284i
\(926\) −18.8727 + 32.6884i −0.620194 + 1.07421i
\(927\) −40.0242 0.472637i −1.31457 0.0155234i
\(928\) −4.00761 6.94138i −0.131556 0.227862i
\(929\) −0.663361 + 3.76211i −0.0217642 + 0.123431i −0.993754 0.111592i \(-0.964405\pi\)
0.971990 + 0.235022i \(0.0755163\pi\)
\(930\) −19.3451 + 6.91195i −0.634349 + 0.226652i
\(931\) 1.79351 + 0.652786i 0.0587801 + 0.0213942i
\(932\) −17.0129 6.19221i −0.557278 0.202832i
\(933\) −9.95652 + 3.55745i −0.325962 + 0.116466i
\(934\) 1.93714 10.9861i 0.0633852 0.359475i
\(935\) 8.97290 + 15.5415i 0.293445 + 0.508262i
\(936\) 0.508493 + 0.905256i 0.0166206 + 0.0295892i
\(937\) 12.0054 20.7939i 0.392198 0.679307i −0.600541 0.799594i \(-0.705048\pi\)
0.992739 + 0.120287i \(0.0383815\pi\)
\(938\) −3.03772 2.54895i −0.0991850 0.0832261i
\(939\) −11.7072 20.5567i −0.382049 0.670843i
\(940\) −5.32032 30.1730i −0.173530 0.984135i
\(941\) 26.0360 21.8468i 0.848749 0.712185i −0.110765 0.993847i \(-0.535330\pi\)
0.959514 + 0.281662i \(0.0908857\pi\)
\(942\) −17.5303 6.49798i −0.571169 0.211716i
\(943\) −21.3136 + 7.75752i −0.694067 + 0.252620i
\(944\) 3.12004 0.101549
\(945\) −12.3417 0.218624i −0.401476 0.00711183i
\(946\) 19.1447 0.622446
\(947\) 11.9760 4.35889i 0.389167 0.141645i −0.140024 0.990148i \(-0.544718\pi\)
0.529190 + 0.848503i \(0.322496\pi\)
\(948\) −1.23244 7.23919i −0.0400278 0.235118i
\(949\) 2.51855 2.11332i 0.0817557 0.0686012i
\(950\) 0.213170 + 1.20894i 0.00691613 + 0.0392234i
\(951\) −0.110057 0.000649796i −0.00356884 2.10711e-5i
\(952\) 3.03672 + 2.54811i 0.0984207 + 0.0825848i
\(953\) −3.76136 + 6.51486i −0.121842 + 0.211037i −0.920494 0.390756i \(-0.872214\pi\)
0.798652 + 0.601793i \(0.205547\pi\)
\(954\) 1.15043 + 7.00727i 0.0372465 + 0.226869i
\(955\) 25.7595 + 44.6168i 0.833558 + 1.44377i
\(956\) −5.29682 + 30.0398i −0.171312 + 0.971556i
\(957\) 20.1658 + 17.1250i 0.651867 + 0.553573i
\(958\) −13.0946 4.76606i −0.423068 0.153984i
\(959\) −7.22521 2.62976i −0.233314 0.0849194i
\(960\) 0.738396 4.04776i 0.0238316 0.130641i
\(961\) −1.05453 + 5.98055i −0.0340172 + 0.192921i
\(962\) 0.310980 + 0.538632i 0.0100264 + 0.0173662i
\(963\) 5.62531 29.8380i 0.181273 0.961516i
\(964\) 12.4537 21.5704i 0.401106 0.694736i
\(965\) −13.2016 11.0774i −0.424973 0.356595i
\(966\) 2.18344 3.73078i 0.0702509 0.120036i
\(967\) 8.05753 + 45.6965i 0.259113 + 1.46950i 0.785291 + 0.619127i \(0.212514\pi\)
−0.526178 + 0.850375i \(0.676375\pi\)
\(968\) 5.64451 4.73631i 0.181422 0.152231i
\(969\) 10.0884 8.36419i 0.324087 0.268696i
\(970\) 32.3907 11.7892i 1.04000 0.378530i
\(971\) 1.49732 0.0480514 0.0240257 0.999711i \(-0.492352\pi\)
0.0240257 + 0.999711i \(0.492352\pi\)
\(972\) 8.18930 13.2641i 0.262672 0.425445i
\(973\) −22.4279 −0.719004
\(974\) 13.9360 5.07227i 0.446537 0.162526i
\(975\) −0.296817 + 0.246087i −0.00950574 + 0.00788109i
\(976\) −2.82647 + 2.37169i −0.0904731 + 0.0759159i
\(977\) 3.63782 + 20.6311i 0.116384 + 0.660048i 0.986056 + 0.166417i \(0.0532197\pi\)
−0.869671 + 0.493631i \(0.835669\pi\)
\(978\) 5.05301 8.63395i 0.161578 0.276083i
\(979\) −21.0353 17.6507i −0.672290 0.564118i
\(980\) 1.18777 2.05728i 0.0379419 0.0657173i
\(981\) 9.38155 49.7620i 0.299530 1.58878i
\(982\) 3.97838 + 6.89075i 0.126955 + 0.219893i
\(983\) 10.7482 60.9561i 0.342815 1.94420i 0.0137080 0.999906i \(-0.495636\pi\)
0.329107 0.944293i \(-0.393252\pi\)
\(984\) 2.82488 15.4855i 0.0900538 0.493659i
\(985\) 46.0303 + 16.7537i 1.46665 + 0.533816i
\(986\) −29.8574 10.8672i −0.950854 0.346082i
\(987\) 17.0277 + 14.4601i 0.541997 + 0.460270i
\(988\) −0.114707 + 0.650533i −0.00364930 + 0.0206962i
\(989\) 12.5362 + 21.7134i 0.398629 + 0.690445i
\(990\) 2.20023 + 13.4016i 0.0699279 + 0.425932i
\(991\) 11.3070 19.5844i 0.359180 0.622118i −0.628644 0.777693i \(-0.716390\pi\)
0.987824 + 0.155575i \(0.0497232\pi\)
\(992\) 3.82464 + 3.20925i 0.121432 + 0.101894i
\(993\) −24.1203 0.142411i −0.765436 0.00451927i
\(994\) 0.233074 + 1.32183i 0.00739267 + 0.0419259i
\(995\) −3.57302 + 2.99812i −0.113272 + 0.0950468i
\(996\) 2.25872 + 13.2674i 0.0715704 + 0.420395i
\(997\) −13.3333 + 4.85291i −0.422269 + 0.153693i −0.544410 0.838819i \(-0.683246\pi\)
0.122141 + 0.992513i \(0.461024\pi\)
\(998\) −5.63100 −0.178246
\(999\) 4.81140 8.00281i 0.152226 0.253198i
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 378.2.u.c.169.1 yes 24
27.4 even 9 inner 378.2.u.c.85.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.u.c.85.1 24 27.4 even 9 inner
378.2.u.c.169.1 yes 24 1.1 even 1 trivial