Properties

Label 216.2.t.a.85.24
Level $216$
Weight $2$
Character 216.85
Analytic conductor $1.725$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [216,2,Mod(13,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.t (of order \(18\), 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: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 85.24
Character \(\chi\) \(=\) 216.85
Dual form 216.2.t.a.61.24

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.531223 - 1.31065i) q^{2} +(0.346028 - 1.69713i) q^{3} +(-1.43560 - 1.39250i) q^{4} +(3.12086 + 0.550291i) q^{5} +(-2.04053 - 1.35508i) q^{6} +(0.272184 - 0.228389i) q^{7} +(-2.58770 + 1.14185i) q^{8} +(-2.76053 - 1.17451i) q^{9} +O(q^{10})\) \(q+(0.531223 - 1.31065i) q^{2} +(0.346028 - 1.69713i) q^{3} +(-1.43560 - 1.39250i) q^{4} +(3.12086 + 0.550291i) q^{5} +(-2.04053 - 1.35508i) q^{6} +(0.272184 - 0.228389i) q^{7} +(-2.58770 + 1.14185i) q^{8} +(-2.76053 - 1.17451i) q^{9} +(2.37911 - 3.79802i) q^{10} +(0.752218 - 0.132636i) q^{11} +(-2.86001 + 1.95457i) q^{12} +(1.01726 + 2.79490i) q^{13} +(-0.154748 - 0.478063i) q^{14} +(2.01382 - 5.10609i) q^{15} +(0.121915 + 3.99814i) q^{16} +(-3.30776 + 5.72921i) q^{17} +(-3.00583 + 2.99416i) q^{18} +(-0.123806 + 0.0714795i) q^{19} +(-3.71403 - 5.13578i) q^{20} +(-0.293424 - 0.540962i) q^{21} +(0.225756 - 1.05635i) q^{22} +(-5.43289 - 4.55874i) q^{23} +(1.04245 + 4.78678i) q^{24} +(4.73845 + 1.72466i) q^{25} +(4.20352 + 0.151444i) q^{26} +(-2.94853 + 4.27857i) q^{27} +(-0.708779 - 0.0511381i) q^{28} +(2.23558 - 6.14220i) q^{29} +(-5.62251 - 5.35189i) q^{30} +(2.36944 + 1.98819i) q^{31} +(5.30493 + 1.96412i) q^{32} +(0.0351870 - 1.32251i) q^{33} +(5.75182 + 7.37880i) q^{34} +(0.975127 - 0.562990i) q^{35} +(2.32752 + 5.53016i) q^{36} +(7.84495 + 4.52928i) q^{37} +(0.0279159 + 0.200238i) q^{38} +(5.09532 - 0.759313i) q^{39} +(-8.70418 + 2.13955i) q^{40} +(-3.14214 + 1.14364i) q^{41} +(-0.864885 + 0.0972046i) q^{42} +(7.77365 - 1.37070i) q^{43} +(-1.26458 - 0.857046i) q^{44} +(-7.96889 - 5.18458i) q^{45} +(-8.86099 + 4.69891i) q^{46} +(5.24581 - 4.40176i) q^{47} +(6.82757 + 1.17656i) q^{48} +(-1.19361 + 6.76933i) q^{49} +(4.77760 - 5.29427i) q^{50} +(8.57866 + 7.59618i) q^{51} +(2.43150 - 5.42890i) q^{52} -2.40651i q^{53} +(4.04138 + 6.13736i) q^{54} +2.42055 q^{55} +(-0.443544 + 0.901795i) q^{56} +(0.0784699 + 0.234850i) q^{57} +(-6.86268 - 6.19294i) q^{58} +(-10.8039 - 1.90501i) q^{59} +(-10.0013 + 4.52609i) q^{60} +(-4.68886 - 5.58797i) q^{61} +(3.86453 - 2.04933i) q^{62} +(-1.01962 + 0.310792i) q^{63} +(5.39237 - 5.90951i) q^{64} +(1.63671 + 9.28226i) q^{65} +(-1.71465 - 0.748666i) q^{66} +(-3.33686 - 9.16794i) q^{67} +(12.7265 - 3.61883i) q^{68} +(-9.61673 + 7.64290i) q^{69} +(-0.219872 - 1.57712i) q^{70} +(-6.07535 + 10.5228i) q^{71} +(8.48453 - 0.112817i) q^{72} +(-1.95917 - 3.39339i) q^{73} +(10.1037 - 7.87591i) q^{74} +(4.56661 - 7.44501i) q^{75} +(0.277271 + 0.0697832i) q^{76} +(0.174449 - 0.207900i) q^{77} +(1.71156 - 7.08154i) q^{78} +(0.515393 + 0.187588i) q^{79} +(-1.81966 + 12.5447i) q^{80} +(6.24104 + 6.48455i) q^{81} +(-0.170260 + 4.72577i) q^{82} +(-4.63970 + 12.7475i) q^{83} +(-0.332046 + 1.18520i) q^{84} +(-13.4758 + 16.0598i) q^{85} +(2.33303 - 10.9167i) q^{86} +(-9.65056 - 5.91945i) q^{87} +(-1.79506 + 1.20214i) q^{88} +(-6.70489 - 11.6132i) q^{89} +(-11.0284 + 7.69025i) q^{90} +(0.915207 + 0.528395i) q^{91} +(1.45146 + 14.1098i) q^{92} +(4.19412 - 3.33328i) q^{93} +(-2.98246 - 9.21374i) q^{94} +(-0.425716 + 0.154948i) q^{95} +(5.16903 - 8.32353i) q^{96} +(2.03404 + 11.5356i) q^{97} +(8.23814 + 5.16043i) q^{98} +(-2.23230 - 0.517343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.531223 1.31065i 0.375632 0.926769i
\(3\) 0.346028 1.69713i 0.199779 0.979841i
\(4\) −1.43560 1.39250i −0.717802 0.696248i
\(5\) 3.12086 + 0.550291i 1.39569 + 0.246098i 0.820371 0.571832i \(-0.193767\pi\)
0.575318 + 0.817930i \(0.304878\pi\)
\(6\) −2.04053 1.35508i −0.833043 0.553209i
\(7\) 0.272184 0.228389i 0.102876 0.0863231i −0.589899 0.807477i \(-0.700832\pi\)
0.692775 + 0.721154i \(0.256388\pi\)
\(8\) −2.58770 + 1.14185i −0.914890 + 0.403704i
\(9\) −2.76053 1.17451i −0.920176 0.391504i
\(10\) 2.37911 3.79802i 0.752341 1.20104i
\(11\) 0.752218 0.132636i 0.226802 0.0399913i −0.0590920 0.998253i \(-0.518821\pi\)
0.285894 + 0.958261i \(0.407709\pi\)
\(12\) −2.86001 + 1.95457i −0.825614 + 0.564236i
\(13\) 1.01726 + 2.79490i 0.282137 + 0.775165i 0.997107 + 0.0760102i \(0.0242182\pi\)
−0.714970 + 0.699155i \(0.753560\pi\)
\(14\) −0.154748 0.478063i −0.0413581 0.127768i
\(15\) 2.01382 5.10609i 0.519966 1.31839i
\(16\) 0.121915 + 3.99814i 0.0304787 + 0.999535i
\(17\) −3.30776 + 5.72921i −0.802250 + 1.38954i 0.115883 + 0.993263i \(0.463030\pi\)
−0.918132 + 0.396274i \(0.870303\pi\)
\(18\) −3.00583 + 2.99416i −0.708481 + 0.705730i
\(19\) −0.123806 + 0.0714795i −0.0284031 + 0.0163985i −0.514134 0.857710i \(-0.671887\pi\)
0.485731 + 0.874108i \(0.338553\pi\)
\(20\) −3.71403 5.13578i −0.830483 1.14839i
\(21\) −0.293424 0.540962i −0.0640304 0.118047i
\(22\) 0.225756 1.05635i 0.0481313 0.225215i
\(23\) −5.43289 4.55874i −1.13284 0.950563i −0.133656 0.991028i \(-0.542672\pi\)
−0.999181 + 0.0404648i \(0.987116\pi\)
\(24\) 1.04245 + 4.78678i 0.212789 + 0.977098i
\(25\) 4.73845 + 1.72466i 0.947691 + 0.344931i
\(26\) 4.20352 + 0.151444i 0.824379 + 0.0297007i
\(27\) −2.94853 + 4.27857i −0.567444 + 0.823412i
\(28\) −0.708779 0.0511381i −0.133947 0.00966419i
\(29\) 2.23558 6.14220i 0.415136 1.14058i −0.539287 0.842122i \(-0.681306\pi\)
0.954424 0.298456i \(-0.0964715\pi\)
\(30\) −5.62251 5.35189i −1.02653 0.977117i
\(31\) 2.36944 + 1.98819i 0.425564 + 0.357090i 0.830275 0.557354i \(-0.188184\pi\)
−0.404711 + 0.914445i \(0.632628\pi\)
\(32\) 5.30493 + 1.96412i 0.937787 + 0.347210i
\(33\) 0.0351870 1.32251i 0.00612526 0.230219i
\(34\) 5.75182 + 7.37880i 0.986430 + 1.26545i
\(35\) 0.975127 0.562990i 0.164827 0.0951626i
\(36\) 2.32752 + 5.53016i 0.387920 + 0.921693i
\(37\) 7.84495 + 4.52928i 1.28970 + 0.744609i 0.978601 0.205768i \(-0.0659691\pi\)
0.311100 + 0.950377i \(0.399302\pi\)
\(38\) 0.0279159 + 0.200238i 0.00452855 + 0.0324829i
\(39\) 5.09532 0.759313i 0.815904 0.121587i
\(40\) −8.70418 + 2.13955i −1.37625 + 0.338293i
\(41\) −3.14214 + 1.14364i −0.490719 + 0.178607i −0.575515 0.817791i \(-0.695198\pi\)
0.0847958 + 0.996398i \(0.472976\pi\)
\(42\) −0.864885 + 0.0972046i −0.133455 + 0.0149990i
\(43\) 7.77365 1.37070i 1.18547 0.209031i 0.454062 0.890970i \(-0.349974\pi\)
0.731409 + 0.681939i \(0.238863\pi\)
\(44\) −1.26458 0.857046i −0.190643 0.129205i
\(45\) −7.96889 5.18458i −1.18793 0.772871i
\(46\) −8.86099 + 4.69891i −1.30648 + 0.692817i
\(47\) 5.24581 4.40176i 0.765180 0.642062i −0.174289 0.984694i \(-0.555763\pi\)
0.939470 + 0.342632i \(0.111318\pi\)
\(48\) 6.82757 + 1.17656i 0.985475 + 0.169822i
\(49\) −1.19361 + 6.76933i −0.170516 + 0.967047i
\(50\) 4.77760 5.29427i 0.675654 0.748723i
\(51\) 8.57866 + 7.59618i 1.20125 + 1.06368i
\(52\) 2.43150 5.42890i 0.337188 0.752852i
\(53\) 2.40651i 0.330559i −0.986247 0.165279i \(-0.947147\pi\)
0.986247 0.165279i \(-0.0528526\pi\)
\(54\) 4.04138 + 6.13736i 0.549963 + 0.835189i
\(55\) 2.42055 0.326387
\(56\) −0.443544 + 0.901795i −0.0592711 + 0.120507i
\(57\) 0.0784699 + 0.234850i 0.0103936 + 0.0311066i
\(58\) −6.86268 6.19294i −0.901114 0.813172i
\(59\) −10.8039 1.90501i −1.40654 0.248012i −0.581714 0.813393i \(-0.697618\pi\)
−0.824829 + 0.565382i \(0.808729\pi\)
\(60\) −10.0013 + 4.52609i −1.29116 + 0.584316i
\(61\) −4.68886 5.58797i −0.600347 0.715466i 0.377212 0.926127i \(-0.376883\pi\)
−0.977559 + 0.210661i \(0.932438\pi\)
\(62\) 3.86453 2.04933i 0.490795 0.260265i
\(63\) −1.01962 + 0.310792i −0.128460 + 0.0391561i
\(64\) 5.39237 5.90951i 0.674046 0.738689i
\(65\) 1.63671 + 9.28226i 0.203009 + 1.15132i
\(66\) −1.71465 0.748666i −0.211059 0.0921544i
\(67\) −3.33686 9.16794i −0.407662 1.12004i −0.958416 0.285374i \(-0.907882\pi\)
0.550754 0.834667i \(-0.314340\pi\)
\(68\) 12.7265 3.61883i 1.54332 0.438848i
\(69\) −9.61673 + 7.64290i −1.15772 + 0.920097i
\(70\) −0.219872 1.57712i −0.0262797 0.188502i
\(71\) −6.07535 + 10.5228i −0.721012 + 1.24883i 0.239583 + 0.970876i \(0.422989\pi\)
−0.960595 + 0.277953i \(0.910344\pi\)
\(72\) 8.48453 0.112817i 0.999912 0.0132956i
\(73\) −1.95917 3.39339i −0.229304 0.397166i 0.728298 0.685261i \(-0.240312\pi\)
−0.957602 + 0.288094i \(0.906978\pi\)
\(74\) 10.1037 7.87591i 1.17453 0.915556i
\(75\) 4.56661 7.44501i 0.527307 0.859676i
\(76\) 0.277271 + 0.0697832i 0.0318052 + 0.00800468i
\(77\) 0.174449 0.207900i 0.0198803 0.0236924i
\(78\) 1.71156 7.08154i 0.193796 0.801827i
\(79\) 0.515393 + 0.187588i 0.0579863 + 0.0211053i 0.370850 0.928693i \(-0.379066\pi\)
−0.312864 + 0.949798i \(0.601288\pi\)
\(80\) −1.81966 + 12.5447i −0.203444 + 1.40254i
\(81\) 6.24104 + 6.48455i 0.693449 + 0.720506i
\(82\) −0.170260 + 4.72577i −0.0188020 + 0.521874i
\(83\) −4.63970 + 12.7475i −0.509273 + 1.39922i 0.372716 + 0.927945i \(0.378426\pi\)
−0.881989 + 0.471270i \(0.843796\pi\)
\(84\) −0.332046 + 1.18520i −0.0362292 + 0.129316i
\(85\) −13.4758 + 16.0598i −1.46165 + 1.74193i
\(86\) 2.33303 10.9167i 0.251577 1.17718i
\(87\) −9.65056 5.91945i −1.03465 0.634631i
\(88\) −1.79506 + 1.20214i −0.191354 + 0.128149i
\(89\) −6.70489 11.6132i −0.710717 1.23100i −0.964588 0.263760i \(-0.915037\pi\)
0.253871 0.967238i \(-0.418296\pi\)
\(90\) −11.0284 + 7.69025i −1.16250 + 0.810623i
\(91\) 0.915207 + 0.528395i 0.0959397 + 0.0553908i
\(92\) 1.45146 + 14.1098i 0.151325 + 1.47105i
\(93\) 4.19412 3.33328i 0.434910 0.345645i
\(94\) −2.98246 9.21374i −0.307618 0.950324i
\(95\) −0.425716 + 0.154948i −0.0436775 + 0.0158973i
\(96\) 5.16903 8.32353i 0.527562 0.849517i
\(97\) 2.03404 + 11.5356i 0.206525 + 1.17126i 0.895021 + 0.446023i \(0.147160\pi\)
−0.688496 + 0.725240i \(0.741729\pi\)
\(98\) 8.23814 + 5.16043i 0.832178 + 0.521283i
\(99\) −2.23230 0.517343i −0.224355 0.0519949i
\(100\) −4.40097 9.07420i −0.440097 0.907420i
\(101\) 4.43650 + 5.28722i 0.441448 + 0.526098i 0.940189 0.340654i \(-0.110648\pi\)
−0.498741 + 0.866751i \(0.666204\pi\)
\(102\) 14.5131 7.20834i 1.43701 0.713732i
\(103\) 1.10708 6.27854i 0.109083 0.618643i −0.880427 0.474182i \(-0.842744\pi\)
0.989510 0.144461i \(-0.0461449\pi\)
\(104\) −5.82371 6.07080i −0.571062 0.595291i
\(105\) −0.618048 1.84973i −0.0603153 0.180515i
\(106\) −3.15408 1.27839i −0.306352 0.124168i
\(107\) 7.48200i 0.723312i −0.932312 0.361656i \(-0.882211\pi\)
0.932312 0.361656i \(-0.117789\pi\)
\(108\) 10.1908 2.03653i 0.980611 0.195965i
\(109\) 0.944408i 0.0904579i 0.998977 + 0.0452290i \(0.0144017\pi\)
−0.998977 + 0.0452290i \(0.985598\pi\)
\(110\) 1.28585 3.17249i 0.122601 0.302485i
\(111\) 10.4014 11.7467i 0.987255 1.11494i
\(112\) 0.946316 + 1.06039i 0.0894185 + 0.100197i
\(113\) 3.06382 17.3758i 0.288220 1.63458i −0.405331 0.914170i \(-0.632844\pi\)
0.693551 0.720408i \(-0.256045\pi\)
\(114\) 0.349490 + 0.0219110i 0.0327328 + 0.00205216i
\(115\) −14.4466 17.2168i −1.34716 1.60548i
\(116\) −11.7624 + 5.70473i −1.09211 + 0.529671i
\(117\) 0.474468 8.91018i 0.0438646 0.823747i
\(118\) −8.23607 + 13.1481i −0.758192 + 1.21038i
\(119\) 0.408171 + 2.31485i 0.0374170 + 0.212202i
\(120\) 0.619214 + 15.5125i 0.0565262 + 1.41609i
\(121\) −9.78838 + 3.56268i −0.889853 + 0.323880i
\(122\) −9.81470 + 3.17699i −0.888581 + 0.287632i
\(123\) 0.853650 + 5.72836i 0.0769710 + 0.516509i
\(124\) −0.633022 6.15369i −0.0568471 0.552618i
\(125\) 0.116794 + 0.0674311i 0.0104464 + 0.00603122i
\(126\) −0.134305 + 1.50146i −0.0119649 + 0.133761i
\(127\) 3.86113 + 6.68768i 0.342620 + 0.593435i 0.984918 0.173019i \(-0.0553523\pi\)
−0.642298 + 0.766455i \(0.722019\pi\)
\(128\) −4.88074 10.2068i −0.431401 0.902160i
\(129\) 0.363633 13.6672i 0.0320161 1.20333i
\(130\) 13.0353 + 2.78580i 1.14327 + 0.244331i
\(131\) −12.3669 + 14.7383i −1.08050 + 1.28769i −0.125176 + 0.992134i \(0.539950\pi\)
−0.955325 + 0.295557i \(0.904495\pi\)
\(132\) −1.89210 + 1.84960i −0.164686 + 0.160987i
\(133\) −0.0173729 + 0.0477316i −0.00150642 + 0.00413885i
\(134\) −13.7886 0.496774i −1.19115 0.0429147i
\(135\) −11.5564 + 11.7303i −0.994615 + 1.00958i
\(136\) 2.01761 18.6024i 0.173008 1.59514i
\(137\) −5.35030 1.94735i −0.457107 0.166373i 0.103196 0.994661i \(-0.467093\pi\)
−0.560303 + 0.828288i \(0.689315\pi\)
\(138\) 4.90853 + 16.6642i 0.417842 + 1.41855i
\(139\) −5.15895 + 6.14819i −0.437576 + 0.521483i −0.939092 0.343665i \(-0.888331\pi\)
0.501516 + 0.865148i \(0.332776\pi\)
\(140\) −2.18386 0.549629i −0.184570 0.0464522i
\(141\) −5.65518 10.4260i −0.476252 0.878026i
\(142\) 10.5644 + 13.5526i 0.886541 + 1.13731i
\(143\) 1.13591 + 1.96745i 0.0949892 + 0.164526i
\(144\) 4.35932 11.1802i 0.363277 0.931681i
\(145\) 10.3569 17.9387i 0.860094 1.48973i
\(146\) −5.48830 + 0.765143i −0.454215 + 0.0633237i
\(147\) 11.0754 + 4.36810i 0.913486 + 0.360275i
\(148\) −4.95523 17.4263i −0.407317 1.43243i
\(149\) 0.818135 + 2.24781i 0.0670243 + 0.184148i 0.968683 0.248301i \(-0.0798721\pi\)
−0.901659 + 0.432448i \(0.857650\pi\)
\(150\) −7.33191 9.94019i −0.598648 0.811613i
\(151\) −0.149554 0.848164i −0.0121705 0.0690226i 0.978118 0.208053i \(-0.0667126\pi\)
−0.990288 + 0.139030i \(0.955601\pi\)
\(152\) 0.238754 0.326335i 0.0193655 0.0264693i
\(153\) 15.8602 11.9306i 1.28222 0.964535i
\(154\) −0.179813 0.339082i −0.0144897 0.0273240i
\(155\) 6.30059 + 7.50875i 0.506075 + 0.603117i
\(156\) −8.37220 6.00513i −0.670312 0.480796i
\(157\) 9.45013 + 1.66631i 0.754202 + 0.132986i 0.537514 0.843255i \(-0.319363\pi\)
0.216688 + 0.976241i \(0.430475\pi\)
\(158\) 0.519651 0.575849i 0.0413412 0.0458121i
\(159\) −4.08416 0.832719i −0.323895 0.0660389i
\(160\) 15.4751 + 9.04898i 1.22341 + 0.715385i
\(161\) −2.51991 −0.198597
\(162\) 11.8144 4.73507i 0.928224 0.372022i
\(163\) 11.1701i 0.874908i −0.899241 0.437454i \(-0.855880\pi\)
0.899241 0.437454i \(-0.144120\pi\)
\(164\) 6.10338 + 2.73359i 0.476594 + 0.213458i
\(165\) 0.837579 4.10800i 0.0652054 0.319807i
\(166\) 14.2427 + 12.8528i 1.10545 + 0.997568i
\(167\) −3.33218 + 18.8977i −0.257852 + 1.46235i 0.530794 + 0.847501i \(0.321894\pi\)
−0.788645 + 0.614848i \(0.789217\pi\)
\(168\) 1.37699 + 1.06480i 0.106237 + 0.0821511i
\(169\) 3.18194 2.66996i 0.244764 0.205382i
\(170\) 13.8901 + 26.1934i 1.06532 + 2.00894i
\(171\) 0.425724 0.0519094i 0.0325559 0.00396961i
\(172\) −13.0686 8.85698i −0.996470 0.675339i
\(173\) 18.5858 3.27717i 1.41305 0.249159i 0.585555 0.810633i \(-0.300877\pi\)
0.827494 + 0.561474i \(0.189766\pi\)
\(174\) −12.8849 + 9.50395i −0.976803 + 0.720493i
\(175\) 1.68362 0.612789i 0.127270 0.0463225i
\(176\) 0.622005 + 2.99130i 0.0468854 + 0.225478i
\(177\) −6.97151 + 17.6764i −0.524010 + 1.32864i
\(178\) −18.7826 + 2.61855i −1.40782 + 0.196269i
\(179\) −5.34027 3.08320i −0.399150 0.230449i 0.286967 0.957940i \(-0.407353\pi\)
−0.686117 + 0.727491i \(0.740686\pi\)
\(180\) 4.22066 + 18.5396i 0.314590 + 1.38186i
\(181\) 7.72285 4.45879i 0.574035 0.331419i −0.184724 0.982790i \(-0.559139\pi\)
0.758759 + 0.651371i \(0.225806\pi\)
\(182\) 1.17872 0.918819i 0.0873725 0.0681074i
\(183\) −11.1060 + 6.02403i −0.820980 + 0.445309i
\(184\) 19.2641 + 5.59311i 1.42017 + 0.412330i
\(185\) 21.9905 + 18.4522i 1.61678 + 1.35664i
\(186\) −2.14075 7.26774i −0.156967 0.532897i
\(187\) −1.72825 + 4.74834i −0.126382 + 0.347233i
\(188\) −13.6603 0.985587i −0.996282 0.0718813i
\(189\) 0.174639 + 1.83797i 0.0127032 + 0.133693i
\(190\) −0.0230678 + 0.640276i −0.00167352 + 0.0464505i
\(191\) −4.67810 1.70269i −0.338496 0.123202i 0.167179 0.985927i \(-0.446534\pi\)
−0.505675 + 0.862724i \(0.668756\pi\)
\(192\) −8.16332 11.1964i −0.589137 0.808033i
\(193\) −11.3867 9.55454i −0.819630 0.687751i 0.133256 0.991082i \(-0.457457\pi\)
−0.952885 + 0.303331i \(0.901901\pi\)
\(194\) 16.1997 + 3.46207i 1.16307 + 0.248562i
\(195\) 16.3196 + 0.434202i 1.16867 + 0.0310939i
\(196\) 11.1398 8.05597i 0.795701 0.575426i
\(197\) 14.0946 8.13754i 1.00420 0.579776i 0.0947127 0.995505i \(-0.469807\pi\)
0.909489 + 0.415729i \(0.136473\pi\)
\(198\) −1.86391 + 2.65094i −0.132462 + 0.188394i
\(199\) −3.09691 + 5.36400i −0.219534 + 0.380244i −0.954666 0.297680i \(-0.903787\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(200\) −14.2310 + 0.947698i −1.00628 + 0.0670124i
\(201\) −16.7139 + 2.49073i −1.17891 + 0.175682i
\(202\) 9.28646 3.00600i 0.653393 0.211502i
\(203\) −0.794324 2.18239i −0.0557506 0.153174i
\(204\) −1.73791 22.8508i −0.121678 1.59988i
\(205\) −10.4355 + 1.84006i −0.728846 + 0.128515i
\(206\) −7.64086 4.78630i −0.532364 0.333477i
\(207\) 9.64337 + 18.9655i 0.670260 + 1.31820i
\(208\) −11.0504 + 4.40789i −0.766206 + 0.305632i
\(209\) −0.0836484 + 0.0701893i −0.00578608 + 0.00485510i
\(210\) −2.75267 0.172577i −0.189952 0.0119089i
\(211\) 10.3455 + 1.82419i 0.712214 + 0.125582i 0.518005 0.855378i \(-0.326675\pi\)
0.194209 + 0.980960i \(0.437786\pi\)
\(212\) −3.35105 + 3.45479i −0.230151 + 0.237276i
\(213\) 15.7564 + 13.9519i 1.07961 + 0.955967i
\(214\) −9.80628 3.97461i −0.670343 0.271699i
\(215\) 25.0147 1.70599
\(216\) 2.74442 14.4384i 0.186734 0.982410i
\(217\) 1.09900 0.0746053
\(218\) 1.23779 + 0.501692i 0.0838336 + 0.0339789i
\(219\) −6.43697 + 2.15077i −0.434970 + 0.145336i
\(220\) −3.47495 3.37060i −0.234281 0.227246i
\(221\) −19.3774 3.41676i −1.30347 0.229836i
\(222\) −9.87031 19.8727i −0.662452 1.33377i
\(223\) −13.7805 + 11.5632i −0.922810 + 0.774329i −0.974512 0.224333i \(-0.927980\pi\)
0.0517029 + 0.998663i \(0.483535\pi\)
\(224\) 1.89250 0.676987i 0.126448 0.0452331i
\(225\) −11.0550 10.3263i −0.737001 0.688422i
\(226\) −21.1460 13.2460i −1.40661 0.881113i
\(227\) 2.19805 0.387576i 0.145890 0.0257243i −0.100226 0.994965i \(-0.531957\pi\)
0.246116 + 0.969240i \(0.420846\pi\)
\(228\) 0.214375 0.446420i 0.0141973 0.0295649i
\(229\) 0.332100 + 0.912438i 0.0219458 + 0.0602956i 0.950182 0.311696i \(-0.100897\pi\)
−0.928236 + 0.371992i \(0.878675\pi\)
\(230\) −30.2396 + 9.78850i −1.99394 + 0.645434i
\(231\) −0.292470 0.368002i −0.0192431 0.0242128i
\(232\) 1.22845 + 18.4468i 0.0806516 + 1.21109i
\(233\) 4.97785 8.62190i 0.326110 0.564839i −0.655626 0.755086i \(-0.727595\pi\)
0.981736 + 0.190246i \(0.0609287\pi\)
\(234\) −11.4261 5.35516i −0.746946 0.350078i
\(235\) 18.7937 10.8505i 1.22596 0.707810i
\(236\) 12.8573 + 17.7792i 0.836942 + 1.15733i
\(237\) 0.496702 0.809781i 0.0322643 0.0526009i
\(238\) 3.25079 + 0.694735i 0.210718 + 0.0450330i
\(239\) −17.3351 14.5459i −1.12131 0.940893i −0.122642 0.992451i \(-0.539137\pi\)
−0.998670 + 0.0515580i \(0.983581\pi\)
\(240\) 20.6604 + 7.42903i 1.33362 + 0.479542i
\(241\) 15.4358 + 5.61819i 0.994310 + 0.361899i 0.787388 0.616458i \(-0.211433\pi\)
0.206923 + 0.978357i \(0.433655\pi\)
\(242\) −0.530393 + 14.7217i −0.0340950 + 0.946348i
\(243\) 13.1647 8.34805i 0.844518 0.535527i
\(244\) −1.04987 + 14.5513i −0.0672111 + 0.931553i
\(245\) −7.45020 + 20.4693i −0.475976 + 1.30773i
\(246\) 7.96135 + 1.92420i 0.507597 + 0.122683i
\(247\) −0.325721 0.273312i −0.0207251 0.0173904i
\(248\) −8.40160 2.43931i −0.533502 0.154897i
\(249\) 20.0287 + 12.2852i 1.26927 + 0.778541i
\(250\) 0.150422 0.117255i 0.00951354 0.00741587i
\(251\) 1.91128 1.10348i 0.120639 0.0696507i −0.438466 0.898748i \(-0.644478\pi\)
0.559105 + 0.829097i \(0.311145\pi\)
\(252\) 1.89654 + 0.973638i 0.119471 + 0.0613334i
\(253\) −4.69137 2.70857i −0.294944 0.170286i
\(254\) 10.8163 1.50794i 0.678676 0.0946166i
\(255\) 22.5926 + 28.4273i 1.41481 + 1.78019i
\(256\) −15.9703 + 0.974866i −0.998142 + 0.0609291i
\(257\) 9.84464 3.58316i 0.614092 0.223511i −0.0162007 0.999869i \(-0.505157\pi\)
0.630293 + 0.776358i \(0.282935\pi\)
\(258\) −17.7198 7.73695i −1.10319 0.481681i
\(259\) 3.16971 0.558905i 0.196956 0.0347287i
\(260\) 10.5758 15.6048i 0.655885 0.967766i
\(261\) −13.3855 + 14.3300i −0.828539 + 0.887005i
\(262\) 12.7472 + 24.0380i 0.787522 + 1.48507i
\(263\) 17.2300 14.4577i 1.06245 0.891500i 0.0681012 0.997678i \(-0.478306\pi\)
0.994347 + 0.106178i \(0.0338615\pi\)
\(264\) 1.41905 + 3.46244i 0.0873365 + 0.213098i
\(265\) 1.32428 7.51035i 0.0813498 0.461357i
\(266\) 0.0533305 + 0.0481259i 0.00326990 + 0.00295079i
\(267\) −22.0293 + 7.36060i −1.34817 + 0.450461i
\(268\) −7.97591 + 17.8081i −0.487206 + 1.08780i
\(269\) 26.3984i 1.60954i −0.593588 0.804769i \(-0.702289\pi\)
0.593588 0.804769i \(-0.297711\pi\)
\(270\) 9.23524 + 21.3778i 0.562039 + 1.30101i
\(271\) −9.83986 −0.597729 −0.298865 0.954296i \(-0.596608\pi\)
−0.298865 + 0.954296i \(0.596608\pi\)
\(272\) −23.3095 12.5264i −1.41334 0.759526i
\(273\) 1.21344 1.37039i 0.0734410 0.0829397i
\(274\) −5.39450 + 5.97789i −0.325894 + 0.361138i
\(275\) 3.79310 + 0.668826i 0.228733 + 0.0403317i
\(276\) 24.4485 + 2.41907i 1.47163 + 0.145611i
\(277\) 11.4107 + 13.5987i 0.685602 + 0.817069i 0.990816 0.135215i \(-0.0431725\pi\)
−0.305214 + 0.952284i \(0.598728\pi\)
\(278\) 5.31757 + 10.0276i 0.318927 + 0.601417i
\(279\) −4.20574 8.27140i −0.251791 0.495196i
\(280\) −1.88049 + 2.57029i −0.112381 + 0.153604i
\(281\) 1.76754 + 10.0242i 0.105443 + 0.597995i 0.991043 + 0.133546i \(0.0426364\pi\)
−0.885600 + 0.464449i \(0.846252\pi\)
\(282\) −16.6690 + 1.87343i −0.992622 + 0.111561i
\(283\) 3.69352 + 10.1479i 0.219557 + 0.603227i 0.999751 0.0223098i \(-0.00710203\pi\)
−0.780194 + 0.625537i \(0.784880\pi\)
\(284\) 23.3748 6.64670i 1.38704 0.394409i
\(285\) 0.115658 + 0.776113i 0.00685096 + 0.0459729i
\(286\) 3.18205 0.443621i 0.188159 0.0262318i
\(287\) −0.594043 + 1.02891i −0.0350652 + 0.0607347i
\(288\) −12.3375 11.6527i −0.726995 0.686642i
\(289\) −13.3826 23.1793i −0.787209 1.36349i
\(290\) −18.0095 23.1037i −1.05755 1.35670i
\(291\) 20.2813 + 0.539609i 1.18891 + 0.0316324i
\(292\) −1.91268 + 7.59970i −0.111931 + 0.444739i
\(293\) −2.51213 + 2.99384i −0.146760 + 0.174902i −0.834417 0.551134i \(-0.814195\pi\)
0.687656 + 0.726036i \(0.258640\pi\)
\(294\) 11.6086 12.1956i 0.677026 0.711260i
\(295\) −32.6690 11.8905i −1.90206 0.692294i
\(296\) −25.4721 2.76269i −1.48054 0.160578i
\(297\) −1.65044 + 3.60950i −0.0957682 + 0.209444i
\(298\) 3.38070 + 0.121800i 0.195839 + 0.00705567i
\(299\) 7.21455 19.8218i 0.417228 1.14633i
\(300\) −16.9230 + 4.32910i −0.977049 + 0.249941i
\(301\) 1.80281 2.14850i 0.103912 0.123838i
\(302\) −1.19109 0.254551i −0.0685397 0.0146478i
\(303\) 10.5083 5.69981i 0.603684 0.327446i
\(304\) −0.300879 0.486280i −0.0172566 0.0278901i
\(305\) −11.5582 20.0195i −0.661823 1.14631i
\(306\) −7.21158 27.1250i −0.412259 1.55063i
\(307\) 10.0125 + 5.78071i 0.571443 + 0.329923i 0.757725 0.652574i \(-0.226311\pi\)
−0.186283 + 0.982496i \(0.559644\pi\)
\(308\) −0.539939 + 0.0555428i −0.0307659 + 0.00316485i
\(309\) −10.2724 4.05141i −0.584379 0.230477i
\(310\) 13.1884 4.26904i 0.749048 0.242465i
\(311\) 4.64349 1.69009i 0.263308 0.0958363i −0.206993 0.978342i \(-0.566368\pi\)
0.470301 + 0.882506i \(0.344145\pi\)
\(312\) −12.3181 + 7.78295i −0.697377 + 0.440623i
\(313\) −2.17391 12.3289i −0.122877 0.696869i −0.982546 0.186018i \(-0.940442\pi\)
0.859669 0.510851i \(-0.170669\pi\)
\(314\) 7.20408 11.5006i 0.406550 0.649017i
\(315\) −3.35310 + 0.408851i −0.188926 + 0.0230361i
\(316\) −0.478685 0.986984i −0.0269281 0.0555222i
\(317\) 3.52049 + 4.19555i 0.197730 + 0.235646i 0.855794 0.517316i \(-0.173069\pi\)
−0.658064 + 0.752962i \(0.728624\pi\)
\(318\) −3.26100 + 4.91055i −0.182868 + 0.275370i
\(319\) 0.866962 4.91679i 0.0485406 0.275287i
\(320\) 20.0808 15.4754i 1.12255 0.865099i
\(321\) −12.6980 2.58898i −0.708731 0.144503i
\(322\) −1.33864 + 3.30272i −0.0745993 + 0.184054i
\(323\) 0.945748i 0.0526228i
\(324\) 0.0700470 17.9999i 0.00389150 0.999992i
\(325\) 14.9979i 0.831935i
\(326\) −14.6401 5.93380i −0.810837 0.328643i
\(327\) 1.60279 + 0.326792i 0.0886344 + 0.0180716i
\(328\) 6.82504 6.54725i 0.376850 0.361511i
\(329\) 0.422510 2.39617i 0.0232937 0.132105i
\(330\) −4.93920 3.28004i −0.271894 0.180560i
\(331\) −10.4571 12.4623i −0.574776 0.684991i 0.397828 0.917460i \(-0.369764\pi\)
−0.972604 + 0.232469i \(0.925320\pi\)
\(332\) 24.4115 11.8395i 1.33976 0.649779i
\(333\) −16.3365 21.7172i −0.895235 1.19010i
\(334\) 22.9982 + 14.4062i 1.25840 + 0.788274i
\(335\) −5.36881 30.4480i −0.293330 1.66355i
\(336\) 2.12707 1.23910i 0.116041 0.0675986i
\(337\) −15.8064 + 5.75306i −0.861030 + 0.313389i −0.734529 0.678577i \(-0.762597\pi\)
−0.126501 + 0.991967i \(0.540375\pi\)
\(338\) −1.80907 5.58875i −0.0984002 0.303988i
\(339\) −28.4289 11.2122i −1.54405 0.608965i
\(340\) 41.7091 4.29056i 2.26199 0.232688i
\(341\) 2.04604 + 1.18128i 0.110799 + 0.0639700i
\(342\) 0.158120 0.585550i 0.00855012 0.0316629i
\(343\) 2.46475 + 4.26907i 0.133084 + 0.230508i
\(344\) −18.5507 + 12.4233i −1.00019 + 0.669819i
\(345\) −34.2182 + 18.5604i −1.84225 + 0.999257i
\(346\) 5.57797 26.1003i 0.299873 1.40316i
\(347\) 9.25688 11.0319i 0.496936 0.592225i −0.458032 0.888936i \(-0.651445\pi\)
0.954967 + 0.296711i \(0.0958898\pi\)
\(348\) 5.61158 + 21.9363i 0.300812 + 1.17591i
\(349\) 9.44754 25.9569i 0.505715 1.38944i −0.379903 0.925026i \(-0.624043\pi\)
0.885618 0.464414i \(-0.153735\pi\)
\(350\) 0.0912288 2.53217i 0.00487638 0.135350i
\(351\) −14.9576 3.88841i −0.798377 0.207548i
\(352\) 4.25097 + 0.773819i 0.226578 + 0.0412447i
\(353\) 9.87864 + 3.59553i 0.525787 + 0.191371i 0.591256 0.806484i \(-0.298632\pi\)
−0.0654692 + 0.997855i \(0.520854\pi\)
\(354\) 19.4642 + 18.5273i 1.03451 + 0.984716i
\(355\) −24.7509 + 29.4970i −1.31364 + 1.56554i
\(356\) −6.54577 + 26.0085i −0.346925 + 1.37845i
\(357\) 4.06986 + 0.108283i 0.215400 + 0.00573097i
\(358\) −6.87787 + 5.36135i −0.363507 + 0.283356i
\(359\) 3.54540 + 6.14081i 0.187119 + 0.324100i 0.944289 0.329119i \(-0.106752\pi\)
−0.757169 + 0.653218i \(0.773418\pi\)
\(360\) 26.5411 + 4.31688i 1.39884 + 0.227519i
\(361\) −9.48978 + 16.4368i −0.499462 + 0.865094i
\(362\) −1.74135 12.4906i −0.0915234 0.656489i
\(363\) 2.65929 + 17.8450i 0.139576 + 0.936619i
\(364\) −0.578087 2.03299i −0.0303000 0.106557i
\(365\) −4.24695 11.6684i −0.222295 0.610752i
\(366\) 1.99562 + 17.7562i 0.104313 + 0.928131i
\(367\) −5.75192 32.6208i −0.300248 1.70279i −0.645071 0.764123i \(-0.723172\pi\)
0.344823 0.938668i \(-0.387939\pi\)
\(368\) 17.5641 22.2773i 0.915594 1.16128i
\(369\) 10.0172 + 0.533416i 0.521474 + 0.0277685i
\(370\) 35.8663 19.0196i 1.86460 0.988782i
\(371\) −0.549620 0.655012i −0.0285349 0.0340065i
\(372\) −10.6627 1.05503i −0.552834 0.0547006i
\(373\) 3.52760 + 0.622010i 0.182652 + 0.0322065i 0.264226 0.964461i \(-0.414884\pi\)
−0.0815739 + 0.996667i \(0.525995\pi\)
\(374\) 5.30532 + 4.78756i 0.274332 + 0.247559i
\(375\) 0.154854 0.174882i 0.00799661 0.00903088i
\(376\) −8.54845 + 17.3803i −0.440852 + 0.896322i
\(377\) 19.4410 1.00126
\(378\) 2.50171 + 0.747482i 0.128674 + 0.0384463i
\(379\) 24.5400i 1.26053i 0.776378 + 0.630267i \(0.217055\pi\)
−0.776378 + 0.630267i \(0.782945\pi\)
\(380\) 0.826923 + 0.370363i 0.0424202 + 0.0189992i
\(381\) 12.6859 4.23873i 0.649921 0.217157i
\(382\) −4.71675 + 5.22684i −0.241330 + 0.267429i
\(383\) −1.42138 + 8.06103i −0.0726290 + 0.411899i 0.926718 + 0.375758i \(0.122618\pi\)
−0.999347 + 0.0361411i \(0.988493\pi\)
\(384\) −19.0111 + 4.75145i −0.970159 + 0.242471i
\(385\) 0.658835 0.552828i 0.0335773 0.0281747i
\(386\) −18.5715 + 9.84832i −0.945265 + 0.501266i
\(387\) −23.0693 5.34638i −1.17268 0.271772i
\(388\) 13.1432 19.3930i 0.667245 0.984528i
\(389\) −10.8773 + 1.91796i −0.551500 + 0.0972443i −0.442452 0.896792i \(-0.645891\pi\)
−0.109048 + 0.994036i \(0.534780\pi\)
\(390\) 9.23844 21.1586i 0.467806 1.07141i
\(391\) 44.0887 16.0470i 2.22966 0.811530i
\(392\) −4.64082 18.8799i −0.234397 0.953579i
\(393\) 20.7336 + 26.0882i 1.04587 + 1.31597i
\(394\) −3.17806 22.7960i −0.160109 1.14844i
\(395\) 1.50524 + 0.869051i 0.0757368 + 0.0437267i
\(396\) 2.48430 + 3.85117i 0.124841 + 0.193528i
\(397\) −9.59600 + 5.54025i −0.481609 + 0.278057i −0.721087 0.692845i \(-0.756357\pi\)
0.239478 + 0.970902i \(0.423024\pi\)
\(398\) 5.38518 + 6.90844i 0.269934 + 0.346289i
\(399\) 0.0749954 + 0.0460006i 0.00375446 + 0.00230291i
\(400\) −6.31773 + 19.1553i −0.315887 + 0.957763i
\(401\) 3.52648 + 2.95907i 0.176104 + 0.147769i 0.726579 0.687083i \(-0.241109\pi\)
−0.550475 + 0.834852i \(0.685553\pi\)
\(402\) −5.61432 + 23.2292i −0.280017 + 1.15856i
\(403\) −3.14647 + 8.64485i −0.156737 + 0.430631i
\(404\) 0.993366 13.7682i 0.0494218 0.684991i
\(405\) 15.9090 + 23.6717i 0.790524 + 1.17626i
\(406\) −3.28231 0.118255i −0.162898 0.00586889i
\(407\) 6.50185 + 2.36648i 0.322285 + 0.117302i
\(408\) −30.8727 9.86111i −1.52842 0.488198i
\(409\) 24.2977 + 20.3882i 1.20145 + 1.00813i 0.999588 + 0.0287174i \(0.00914229\pi\)
0.201858 + 0.979415i \(0.435302\pi\)
\(410\) −3.13190 + 14.6548i −0.154674 + 0.723747i
\(411\) −5.15627 + 8.40634i −0.254340 + 0.414654i
\(412\) −10.3322 + 7.47190i −0.509029 + 0.368114i
\(413\) −3.37572 + 1.94897i −0.166108 + 0.0959027i
\(414\) 29.9800 2.56414i 1.47343 0.126020i
\(415\) −21.4946 + 37.2298i −1.05513 + 1.82754i
\(416\) −0.0930240 + 16.8247i −0.00456087 + 0.824901i
\(417\) 8.64917 + 10.8829i 0.423552 + 0.532936i
\(418\) 0.0475576 + 0.146920i 0.00232612 + 0.00718609i
\(419\) 1.62113 + 4.45403i 0.0791976 + 0.217594i 0.972972 0.230923i \(-0.0741746\pi\)
−0.893774 + 0.448517i \(0.851952\pi\)
\(420\) −1.68847 + 3.51611i −0.0823889 + 0.171569i
\(421\) −22.8626 + 4.03129i −1.11425 + 0.196473i −0.700316 0.713833i \(-0.746958\pi\)
−0.413937 + 0.910306i \(0.635847\pi\)
\(422\) 7.88665 12.5903i 0.383916 0.612885i
\(423\) −19.6511 + 5.98991i −0.955471 + 0.291239i
\(424\) 2.74786 + 6.22731i 0.133448 + 0.302425i
\(425\) −25.5546 + 21.4428i −1.23958 + 1.04013i
\(426\) 26.6562 13.2395i 1.29150 0.641458i
\(427\) −2.55246 0.450068i −0.123522 0.0217803i
\(428\) −10.4186 + 10.7412i −0.503604 + 0.519195i
\(429\) 3.73208 1.24699i 0.180186 0.0602054i
\(430\) 13.2884 32.7855i 0.640824 1.58106i
\(431\) 21.0838 1.01557 0.507786 0.861483i \(-0.330464\pi\)
0.507786 + 0.861483i \(0.330464\pi\)
\(432\) −17.4658 11.2670i −0.840324 0.542084i
\(433\) −7.94589 −0.381855 −0.190928 0.981604i \(-0.561150\pi\)
−0.190928 + 0.981604i \(0.561150\pi\)
\(434\) 0.583817 1.44041i 0.0280241 0.0691419i
\(435\) −26.8606 23.7844i −1.28787 1.14037i
\(436\) 1.31508 1.35580i 0.0629811 0.0649309i
\(437\) 0.998482 + 0.176059i 0.0477639 + 0.00842206i
\(438\) −0.600557 + 9.57915i −0.0286957 + 0.457709i
\(439\) 27.8547 23.3729i 1.32943 1.11553i 0.345222 0.938521i \(-0.387804\pi\)
0.984210 0.177005i \(-0.0566409\pi\)
\(440\) −6.26366 + 2.76390i −0.298608 + 0.131764i
\(441\) 11.2457 17.2850i 0.535508 0.823096i
\(442\) −14.7719 + 23.5819i −0.702628 + 1.12168i
\(443\) −9.24722 + 1.63053i −0.439349 + 0.0774690i −0.388947 0.921260i \(-0.627161\pi\)
−0.0504013 + 0.998729i \(0.516050\pi\)
\(444\) −31.2894 + 2.37970i −1.48493 + 0.112935i
\(445\) −14.5343 39.9328i −0.688994 1.89300i
\(446\) 7.83479 + 24.2040i 0.370988 + 1.14609i
\(447\) 4.09793 0.610680i 0.193825 0.0288842i
\(448\) 0.118047 2.84003i 0.00557718 0.134179i
\(449\) −14.1729 + 24.5482i −0.668861 + 1.15850i 0.309362 + 0.950944i \(0.399884\pi\)
−0.978223 + 0.207557i \(0.933449\pi\)
\(450\) −19.4069 + 9.00365i −0.914849 + 0.424436i
\(451\) −2.21188 + 1.27703i −0.104153 + 0.0601330i
\(452\) −28.5942 + 20.6784i −1.34496 + 0.972630i
\(453\) −1.49120 0.0396751i −0.0700626 0.00186410i
\(454\) 0.659681 3.08677i 0.0309604 0.144869i
\(455\) 2.56546 + 2.15267i 0.120270 + 0.100919i
\(456\) −0.471219 0.518119i −0.0220668 0.0242632i
\(457\) −21.2745 7.74327i −0.995177 0.362215i −0.207454 0.978245i \(-0.566518\pi\)
−0.787723 + 0.616030i \(0.788740\pi\)
\(458\) 1.37231 + 0.0494413i 0.0641236 + 0.00231024i
\(459\) −14.7598 31.0452i −0.688930 1.44907i
\(460\) −3.23471 + 44.8334i −0.150819 + 2.09037i
\(461\) 0.00327106 0.00898717i 0.000152348 0.000418574i −0.939616 0.342229i \(-0.888818\pi\)
0.939769 + 0.341811i \(0.111040\pi\)
\(462\) −0.637689 + 0.187834i −0.0296680 + 0.00873883i
\(463\) 11.6431 + 9.76976i 0.541103 + 0.454039i 0.871915 0.489658i \(-0.162878\pi\)
−0.330812 + 0.943697i \(0.607323\pi\)
\(464\) 24.8299 + 8.18933i 1.15270 + 0.380180i
\(465\) 14.9235 8.09470i 0.692062 0.375383i
\(466\) −8.65593 11.1044i −0.400978 0.514400i
\(467\) −9.14473 + 5.27971i −0.423168 + 0.244316i −0.696432 0.717623i \(-0.745230\pi\)
0.273264 + 0.961939i \(0.411897\pi\)
\(468\) −13.0885 + 12.1308i −0.605018 + 0.560746i
\(469\) −3.00210 1.73326i −0.138624 0.0800346i
\(470\) −4.23760 30.3960i −0.195466 1.40206i
\(471\) 6.09797 15.4615i 0.280979 0.712430i
\(472\) 30.1324 7.40676i 1.38696 0.340924i
\(473\) 5.66567 2.06214i 0.260508 0.0948171i
\(474\) −0.797479 1.08118i −0.0366294 0.0496601i
\(475\) −0.709927 + 0.125179i −0.0325737 + 0.00574362i
\(476\) 2.63745 3.89159i 0.120887 0.178371i
\(477\) −2.82647 + 6.64323i −0.129415 + 0.304173i
\(478\) −28.2733 + 14.9931i −1.29319 + 0.685769i
\(479\) −6.31972 + 5.30287i −0.288755 + 0.242294i −0.775646 0.631169i \(-0.782576\pi\)
0.486890 + 0.873463i \(0.338131\pi\)
\(480\) 20.7121 23.1321i 0.945376 1.05583i
\(481\) −4.67853 + 26.5333i −0.213323 + 1.20981i
\(482\) 15.5634 17.2465i 0.708892 0.785555i
\(483\) −0.871961 + 4.27663i −0.0396756 + 0.194593i
\(484\) 19.0132 + 8.51568i 0.864238 + 0.387076i
\(485\) 37.1203i 1.68555i
\(486\) −3.94795 21.6890i −0.179083 0.983834i
\(487\) 8.73787 0.395951 0.197975 0.980207i \(-0.436563\pi\)
0.197975 + 0.980207i \(0.436563\pi\)
\(488\) 18.5140 + 9.10601i 0.838088 + 0.412210i
\(489\) −18.9571 3.86516i −0.857270 0.174789i
\(490\) 22.8703 + 20.6383i 1.03317 + 0.932345i
\(491\) 23.0393 + 4.06246i 1.03975 + 0.183336i 0.667357 0.744738i \(-0.267426\pi\)
0.372395 + 0.928074i \(0.378537\pi\)
\(492\) 6.75121 9.41236i 0.304368 0.424342i
\(493\) 27.7952 + 33.1250i 1.25183 + 1.49187i
\(494\) −0.531247 + 0.281716i −0.0239019 + 0.0126750i
\(495\) −6.68200 2.84297i −0.300334 0.127782i
\(496\) −7.66021 + 9.71574i −0.343954 + 0.436249i
\(497\) 0.749687 + 4.25169i 0.0336281 + 0.190714i
\(498\) 26.7412 19.7244i 1.19830 0.883872i
\(499\) −6.03120 16.5706i −0.269994 0.741801i −0.998394 0.0566496i \(-0.981958\pi\)
0.728401 0.685152i \(-0.240264\pi\)
\(500\) −0.0737725 0.259440i −0.00329921 0.0116025i
\(501\) 30.9189 + 12.1943i 1.38136 + 0.544801i
\(502\) −0.430955 3.09120i −0.0192345 0.137967i
\(503\) −16.2955 + 28.2247i −0.726581 + 1.25848i 0.231739 + 0.972778i \(0.425559\pi\)
−0.958320 + 0.285697i \(0.907775\pi\)
\(504\) 2.28359 1.96848i 0.101719 0.0876832i
\(505\) 10.9362 + 18.9420i 0.486653 + 0.842908i
\(506\) −6.04215 + 4.70989i −0.268606 + 0.209380i
\(507\) −3.43024 6.32406i −0.152342 0.280861i
\(508\) 3.76950 14.9775i 0.167245 0.664517i
\(509\) −13.0562 + 15.5598i −0.578706 + 0.689675i −0.973393 0.229140i \(-0.926409\pi\)
0.394687 + 0.918816i \(0.370853\pi\)
\(510\) 49.2600 14.5098i 2.18127 0.642503i
\(511\) −1.30827 0.476171i −0.0578744 0.0210646i
\(512\) −7.20608 + 21.4493i −0.318467 + 0.947934i
\(513\) 0.0592153 0.740473i 0.00261442 0.0326927i
\(514\) 0.533442 14.8063i 0.0235291 0.653079i
\(515\) 6.91005 18.9852i 0.304493 0.836588i
\(516\) −19.5536 + 19.1144i −0.860799 + 0.841463i
\(517\) 3.36216 4.00686i 0.147868 0.176222i
\(518\) 0.951294 4.45128i 0.0417975 0.195578i
\(519\) 0.869398 32.6765i 0.0381623 1.43434i
\(520\) −14.8342 22.1508i −0.650525 0.971378i
\(521\) −20.1680 34.9320i −0.883576 1.53040i −0.847337 0.531056i \(-0.821795\pi\)
−0.0362395 0.999343i \(-0.511538\pi\)
\(522\) 11.6709 + 25.1561i 0.510823 + 1.10105i
\(523\) −3.36053 1.94020i −0.146946 0.0848391i 0.424724 0.905323i \(-0.360371\pi\)
−0.571670 + 0.820484i \(0.693704\pi\)
\(524\) 38.2770 3.93751i 1.67214 0.172011i
\(525\) −0.457404 3.06938i −0.0199627 0.133959i
\(526\) −9.79599 30.2628i −0.427125 1.31952i
\(527\) −19.2283 + 6.99853i −0.837598 + 0.304861i
\(528\) 5.29187 0.0205512i 0.230299 0.000894374i
\(529\) 4.74033 + 26.8837i 0.206101 + 1.16886i
\(530\) −9.13995 5.72534i −0.397014 0.248693i
\(531\) 27.5869 + 17.9481i 1.19717 + 0.778882i
\(532\) 0.0914065 0.0443320i 0.00396297 0.00192203i
\(533\) −6.39274 7.61857i −0.276900 0.329997i
\(534\) −2.05529 + 32.7828i −0.0889411 + 1.41865i
\(535\) 4.11728 23.3502i 0.178005 1.00952i
\(536\) 19.1032 + 19.9137i 0.825131 + 0.860140i
\(537\) −7.08049 + 7.99627i −0.305546 + 0.345065i
\(538\) −34.5990 14.0234i −1.49167 0.604593i
\(539\) 5.25032i 0.226147i
\(540\) 32.9247 0.747797i 1.41685 0.0321800i
\(541\) 35.6307i 1.53189i −0.642909 0.765943i \(-0.722273\pi\)
0.642909 0.765943i \(-0.277727\pi\)
\(542\) −5.22716 + 12.8966i −0.224526 + 0.553957i
\(543\) −4.89484 14.6496i −0.210058 0.628674i
\(544\) −28.8003 + 23.8962i −1.23480 + 1.02454i
\(545\) −0.519699 + 2.94736i −0.0222615 + 0.126251i
\(546\) −1.15149 2.31838i −0.0492792 0.0992176i
\(547\) 13.5809 + 16.1851i 0.580679 + 0.692027i 0.973786 0.227466i \(-0.0730441\pi\)
−0.393107 + 0.919493i \(0.628600\pi\)
\(548\) 4.96924 + 10.2459i 0.212275 + 0.437683i
\(549\) 6.38060 + 20.9329i 0.272317 + 0.893393i
\(550\) 2.89158 4.61613i 0.123297 0.196832i
\(551\) 0.162263 + 0.920240i 0.00691264 + 0.0392035i
\(552\) 16.1582 30.7584i 0.687738 1.30916i
\(553\) 0.183125 0.0666519i 0.00778726 0.00283433i
\(554\) 23.8848 7.73145i 1.01477 0.328478i
\(555\) 38.9253 30.9359i 1.65229 1.31315i
\(556\) 15.9675 1.64256i 0.677174 0.0696600i
\(557\) −14.1822 8.18809i −0.600919 0.346940i 0.168484 0.985704i \(-0.446113\pi\)
−0.769403 + 0.638764i \(0.779446\pi\)
\(558\) −13.0751 + 1.11829i −0.553513 + 0.0473410i
\(559\) 11.7388 + 20.3322i 0.496499 + 0.859961i
\(560\) 2.36980 + 3.83006i 0.100142 + 0.161850i
\(561\) 7.46055 + 4.57614i 0.314984 + 0.193205i
\(562\) 14.0772 + 3.00847i 0.593811 + 0.126905i
\(563\) 18.0449 21.5051i 0.760504 0.906333i −0.237376 0.971418i \(-0.576287\pi\)
0.997880 + 0.0650846i \(0.0207317\pi\)
\(564\) −6.39953 + 22.8424i −0.269469 + 0.961837i
\(565\) 19.1235 52.5414i 0.804531 2.21043i
\(566\) 15.2624 + 0.549872i 0.641525 + 0.0231128i
\(567\) 3.17971 + 0.339603i 0.133535 + 0.0142620i
\(568\) 3.70574 34.1670i 0.155489 1.43362i
\(569\) −19.6797 7.16282i −0.825015 0.300281i −0.105204 0.994451i \(-0.533549\pi\)
−0.719811 + 0.694170i \(0.755772\pi\)
\(570\) 1.07865 + 0.260703i 0.0451797 + 0.0109196i
\(571\) 19.7767 23.5689i 0.827627 0.986328i −0.172372 0.985032i \(-0.555143\pi\)
0.999999 0.00129565i \(-0.000412417\pi\)
\(572\) 1.10895 4.40622i 0.0463675 0.184233i
\(573\) −4.50845 + 7.35019i −0.188343 + 0.307059i
\(574\) 1.03297 + 1.32516i 0.0431155 + 0.0553113i
\(575\) −17.8813 30.9713i −0.745700 1.29159i
\(576\) −21.8266 + 9.97997i −0.909441 + 0.415832i
\(577\) 10.8548 18.8011i 0.451892 0.782701i −0.546611 0.837387i \(-0.684082\pi\)
0.998504 + 0.0546859i \(0.0174158\pi\)
\(578\) −37.4890 + 5.22647i −1.55934 + 0.217392i
\(579\) −20.1554 + 16.0186i −0.837632 + 0.665708i
\(580\) −39.8479 + 11.3309i −1.65460 + 0.470490i
\(581\) 1.64853 + 4.52931i 0.0683927 + 0.187907i
\(582\) 11.4811 26.2950i 0.475909 1.08996i
\(583\) −0.319190 1.81022i −0.0132195 0.0749715i
\(584\) 8.94448 + 6.54399i 0.370125 + 0.270792i
\(585\) 6.38394 27.5463i 0.263943 1.13890i
\(586\) 2.58937 + 4.88292i 0.106966 + 0.201712i
\(587\) −11.8328 14.1017i −0.488390 0.582040i 0.464417 0.885617i \(-0.346264\pi\)
−0.952807 + 0.303576i \(0.901819\pi\)
\(588\) −9.81737 21.6933i −0.404861 0.894619i
\(589\) −0.435466 0.0767844i −0.0179431 0.00316385i
\(590\) −32.9389 + 36.5011i −1.35607 + 1.50272i
\(591\) −8.93336 26.7363i −0.367469 1.09978i
\(592\) −17.1523 + 31.9174i −0.704955 + 1.31180i
\(593\) 8.34484 0.342681 0.171341 0.985212i \(-0.445190\pi\)
0.171341 + 0.985212i \(0.445190\pi\)
\(594\) 3.85404 + 4.08060i 0.158133 + 0.167429i
\(595\) 7.44894i 0.305377i
\(596\) 1.95554 4.36621i 0.0801022 0.178847i
\(597\) 8.03181 + 7.11196i 0.328720 + 0.291073i
\(598\) −22.1469 19.9856i −0.905655 0.817270i
\(599\) −0.217739 + 1.23486i −0.00889658 + 0.0504550i −0.988933 0.148364i \(-0.952599\pi\)
0.980036 + 0.198819i \(0.0637105\pi\)
\(600\) −3.31595 + 24.4798i −0.135373 + 0.999384i
\(601\) 10.6016 8.89580i 0.432448 0.362867i −0.400426 0.916329i \(-0.631138\pi\)
0.832875 + 0.553462i \(0.186693\pi\)
\(602\) −1.85824 3.50418i −0.0757362 0.142820i
\(603\) −1.55637 + 29.2275i −0.0633802 + 1.19024i
\(604\) −0.966364 + 1.42588i −0.0393208 + 0.0580183i
\(605\) −32.5086 + 5.73215i −1.32166 + 0.233045i
\(606\) −1.88822 16.8005i −0.0767035 0.682475i
\(607\) −3.28186 + 1.19450i −0.133207 + 0.0484832i −0.407763 0.913088i \(-0.633691\pi\)
0.274557 + 0.961571i \(0.411469\pi\)
\(608\) −0.797177 + 0.136024i −0.0323298 + 0.00551648i
\(609\) −3.97866 + 0.592907i −0.161224 + 0.0240258i
\(610\) −32.3785 + 4.51400i −1.31097 + 0.182766i
\(611\) 17.6388 + 10.1838i 0.713590 + 0.411992i
\(612\) −39.3823 4.95757i −1.59194 0.200398i
\(613\) 2.83466 1.63659i 0.114491 0.0661013i −0.441661 0.897182i \(-0.645611\pi\)
0.556152 + 0.831081i \(0.312277\pi\)
\(614\) 12.8953 10.0520i 0.520414 0.405666i
\(615\) −0.488148 + 18.3471i −0.0196840 + 0.739828i
\(616\) −0.214031 + 0.737176i −0.00862355 + 0.0297017i
\(617\) 9.15508 + 7.68203i 0.368570 + 0.309267i 0.808195 0.588914i \(-0.200444\pi\)
−0.439626 + 0.898181i \(0.644889\pi\)
\(618\) −10.7669 + 11.3114i −0.433110 + 0.455010i
\(619\) −9.55647 + 26.2562i −0.384107 + 1.05533i 0.585503 + 0.810670i \(0.300897\pi\)
−0.969610 + 0.244655i \(0.921325\pi\)
\(620\) 1.41075 19.5531i 0.0566570 0.785272i
\(621\) 35.5239 9.80348i 1.42553 0.393400i
\(622\) 0.251612 6.98380i 0.0100887 0.280025i
\(623\) −4.47730 1.62960i −0.179379 0.0652886i
\(624\) 3.65704 + 20.2792i 0.146399 + 0.811819i
\(625\) −18.9867 15.9318i −0.759469 0.637270i
\(626\) −17.3137 3.70015i −0.691993 0.147888i
\(627\) 0.0901760 + 0.166250i 0.00360128 + 0.00663938i
\(628\) −11.2463 15.5514i −0.448776 0.620569i
\(629\) −51.8984 + 29.9636i −2.06932 + 1.19473i
\(630\) −1.24539 + 4.61194i −0.0496174 + 0.183744i
\(631\) 17.2806 29.9309i 0.687931 1.19153i −0.284575 0.958654i \(-0.591853\pi\)
0.972506 0.232877i \(-0.0748140\pi\)
\(632\) −1.54788 + 0.103079i −0.0615713 + 0.00410028i
\(633\) 6.67573 16.9265i 0.265337 0.672767i
\(634\) 7.36906 2.38535i 0.292663 0.0947342i
\(635\) 8.36986 + 22.9960i 0.332148 + 0.912569i
\(636\) 4.70368 + 6.88263i 0.186513 + 0.272914i
\(637\) −20.1338 + 3.55013i −0.797730 + 0.140661i
\(638\) −5.98363 3.74820i −0.236894 0.148392i
\(639\) 29.1304 21.9130i 1.15238 0.866864i
\(640\) −9.61540 34.5397i −0.380082 1.36530i
\(641\) −13.4082 + 11.2508i −0.529591 + 0.444379i −0.867960 0.496634i \(-0.834569\pi\)
0.338369 + 0.941013i \(0.390125\pi\)
\(642\) −10.1387 + 15.2672i −0.400142 + 0.602550i
\(643\) 23.1589 + 4.08353i 0.913297 + 0.161039i 0.610500 0.792016i \(-0.290969\pi\)
0.302797 + 0.953055i \(0.402080\pi\)
\(644\) 3.61760 + 3.50897i 0.142553 + 0.138273i
\(645\) 8.65580 42.4534i 0.340822 1.67160i
\(646\) −1.23954 0.502403i −0.0487692 0.0197668i
\(647\) 43.1602 1.69680 0.848401 0.529355i \(-0.177566\pi\)
0.848401 + 0.529355i \(0.177566\pi\)
\(648\) −23.5543 9.65375i −0.925300 0.379235i
\(649\) −8.37953 −0.328925
\(650\) 19.6570 + 7.96725i 0.771012 + 0.312501i
\(651\) 0.380287 1.86516i 0.0149046 0.0731013i
\(652\) −15.5543 + 16.0358i −0.609152 + 0.628010i
\(653\) 28.5513 + 5.03436i 1.11730 + 0.197010i 0.701654 0.712518i \(-0.252445\pi\)
0.415644 + 0.909527i \(0.363556\pi\)
\(654\) 1.27975 1.92709i 0.0500421 0.0753553i
\(655\) −46.7057 + 39.1907i −1.82494 + 1.53131i
\(656\) −4.95552 12.4233i −0.193481 0.485048i
\(657\) 1.42278 + 11.6686i 0.0555079 + 0.455236i
\(658\) −2.91610 1.82667i −0.113681 0.0712109i
\(659\) 24.9915 4.40668i 0.973532 0.171660i 0.335813 0.941929i \(-0.390989\pi\)
0.637719 + 0.770269i \(0.279878\pi\)
\(660\) −6.92280 + 4.73113i −0.269470 + 0.184159i
\(661\) 2.29708 + 6.31116i 0.0893459 + 0.245476i 0.976315 0.216352i \(-0.0694160\pi\)
−0.886969 + 0.461828i \(0.847194\pi\)
\(662\) −21.8888 + 7.08535i −0.850732 + 0.275380i
\(663\) −12.5038 + 31.7038i −0.485609 + 1.23127i
\(664\) −2.54951 38.2844i −0.0989402 1.48572i
\(665\) −0.0804844 + 0.139403i −0.00312105 + 0.00540582i
\(666\) −37.1420 + 9.87474i −1.43922 + 0.382639i
\(667\) −40.1463 + 23.1785i −1.55447 + 0.897475i
\(668\) 31.0987 22.4896i 1.20324 0.870149i
\(669\) 14.8559 + 27.3885i 0.574361 + 1.05890i
\(670\) −42.7588 9.13808i −1.65191 0.353035i
\(671\) −4.26821 3.58145i −0.164772 0.138260i
\(672\) −0.494080 3.44608i −0.0190596 0.132935i
\(673\) 43.9840 + 16.0089i 1.69546 + 0.617097i 0.995296 0.0968855i \(-0.0308881\pi\)
0.700164 + 0.713982i \(0.253110\pi\)
\(674\) −0.856486 + 23.7728i −0.0329906 + 0.915695i
\(675\) −21.3505 + 15.1886i −0.821782 + 0.584611i
\(676\) −8.28591 0.597825i −0.318689 0.0229933i
\(677\) 10.3174 28.3468i 0.396529 1.08946i −0.567434 0.823419i \(-0.692064\pi\)
0.963963 0.266036i \(-0.0857141\pi\)
\(678\) −29.7974 + 31.3041i −1.14436 + 1.20223i
\(679\) 3.18824 + 2.67525i 0.122354 + 0.102667i
\(680\) 16.5334 56.9452i 0.634027 2.18375i
\(681\) 0.102820 3.86451i 0.00394006 0.148088i
\(682\) 2.63515 2.05412i 0.100905 0.0786561i
\(683\) 14.3697 8.29634i 0.549840 0.317451i −0.199217 0.979955i \(-0.563840\pi\)
0.749058 + 0.662505i \(0.230507\pi\)
\(684\) −0.683454 0.518297i −0.0261325 0.0198176i
\(685\) −15.6259 9.02162i −0.597035 0.344699i
\(686\) 6.90458 0.962591i 0.263618 0.0367519i
\(687\) 1.66345 0.247889i 0.0634644 0.00945757i
\(688\) 6.42800 + 30.9131i 0.245065 + 1.17855i
\(689\) 6.72594 2.44804i 0.256238 0.0932630i
\(690\) 6.14863 + 54.7078i 0.234074 + 2.08269i
\(691\) 34.2813 6.04471i 1.30412 0.229952i 0.521929 0.852989i \(-0.325213\pi\)
0.782192 + 0.623038i \(0.214102\pi\)
\(692\) −31.2452 21.1759i −1.18777 0.804986i
\(693\) −0.725752 + 0.369021i −0.0275690 + 0.0140180i
\(694\) −9.54151 17.9929i −0.362191 0.683003i
\(695\) −19.4836 + 16.3487i −0.739056 + 0.620141i
\(696\) 31.7318 + 4.29829i 1.20279 + 0.162926i
\(697\) 3.84126 21.7849i 0.145498 0.825160i
\(698\) −29.0016 26.1713i −1.09773 0.990599i
\(699\) −12.9100 11.4315i −0.488302 0.432379i
\(700\) −3.27032 1.46472i −0.123607 0.0553610i
\(701\) 11.1860i 0.422491i 0.977433 + 0.211245i \(0.0677519\pi\)
−0.977433 + 0.211245i \(0.932248\pi\)
\(702\) −13.0422 + 17.5386i −0.492245 + 0.661950i
\(703\) −1.29500 −0.0488420
\(704\) 3.27242 5.16046i 0.123334 0.194492i
\(705\) −11.9117 35.6500i −0.448619 1.34266i
\(706\) 9.96025 11.0374i 0.374859 0.415398i
\(707\) 2.41509 + 0.425845i 0.0908287 + 0.0160156i
\(708\) 34.6226 15.6685i 1.30120 0.588860i
\(709\) −2.86983 3.42012i −0.107779 0.128445i 0.709458 0.704747i \(-0.248940\pi\)
−0.817237 + 0.576302i \(0.804495\pi\)
\(710\) 25.5119 + 48.1093i 0.957446 + 1.80551i
\(711\) −1.20243 1.12318i −0.0450948 0.0421224i
\(712\) 30.6107 + 22.3955i 1.14719 + 0.839308i
\(713\) −3.80924 21.6033i −0.142657 0.809050i
\(714\) 2.30393 5.27663i 0.0862222 0.197473i
\(715\) 2.46233 + 6.76519i 0.0920859 + 0.253004i
\(716\) 3.37316 + 11.8626i 0.126061 + 0.443324i
\(717\) −30.6847 + 24.3867i −1.14594 + 0.910737i
\(718\) 9.93185 1.38463i 0.370653 0.0516741i
\(719\) −9.80642 + 16.9852i −0.365718 + 0.633441i −0.988891 0.148642i \(-0.952510\pi\)
0.623173 + 0.782084i \(0.285843\pi\)
\(720\) 19.7572 32.4928i 0.736306 1.21094i
\(721\) −1.13262 1.96176i −0.0421811 0.0730598i
\(722\) 16.5017 + 21.1694i 0.614128 + 0.787843i
\(723\) 14.8761 24.2527i 0.553247 0.901966i
\(724\) −17.2958 4.35298i −0.642793 0.161777i
\(725\) 21.1864 25.2489i 0.786841 0.937721i
\(726\) 24.8012 + 5.99428i 0.920459 + 0.222468i
\(727\) 13.4924 + 4.91083i 0.500405 + 0.182133i 0.579876 0.814705i \(-0.303101\pi\)
−0.0794709 + 0.996837i \(0.525323\pi\)
\(728\) −2.97163 0.322301i −0.110136 0.0119453i
\(729\) −9.61239 25.2310i −0.356014 0.934481i
\(730\) −17.5492 0.632263i −0.649527 0.0234011i
\(731\) −17.8603 + 49.0708i −0.660588 + 1.81495i
\(732\) 24.3323 + 6.81694i 0.899346 + 0.251961i
\(733\) 14.6154 17.4180i 0.539833 0.643348i −0.425317 0.905044i \(-0.639838\pi\)
0.965150 + 0.261697i \(0.0842820\pi\)
\(734\) −45.8100 9.79016i −1.69088 0.361362i
\(735\) 32.1611 + 19.7269i 1.18628 + 0.727639i
\(736\) −19.8672 34.8546i −0.732315 1.28476i
\(737\) −3.72604 6.45370i −0.137251 0.237725i
\(738\) 6.02048 12.8457i 0.221617 0.472855i
\(739\) −8.29627 4.78985i −0.305183 0.176198i 0.339586 0.940575i \(-0.389713\pi\)
−0.644769 + 0.764377i \(0.723046\pi\)
\(740\) −5.87502 57.1118i −0.215970 2.09947i
\(741\) −0.576556 + 0.458218i −0.0211803 + 0.0168331i
\(742\) −1.15046 + 0.372402i −0.0422348 + 0.0136713i
\(743\) −37.3636 + 13.5993i −1.37074 + 0.498908i −0.919358 0.393423i \(-0.871291\pi\)
−0.451381 + 0.892331i \(0.649069\pi\)
\(744\) −7.04703 + 13.4146i −0.258357 + 0.491802i
\(745\) 1.31633 + 7.46530i 0.0482267 + 0.273507i
\(746\) 2.68918 4.29302i 0.0984579 0.157178i
\(747\) 27.7801 29.7403i 1.01642 1.08814i
\(748\) 9.09313 4.41015i 0.332478 0.161251i
\(749\) −1.70881 2.03648i −0.0624385 0.0744113i
\(750\) −0.146947 0.295860i −0.00536576 0.0108033i
\(751\) −7.36297 + 41.7575i −0.268679 + 1.52375i 0.489673 + 0.871906i \(0.337116\pi\)
−0.758351 + 0.651846i \(0.773995\pi\)
\(752\) 18.2384 + 20.4369i 0.665086 + 0.745255i
\(753\) −1.21139 3.62552i −0.0441455 0.132121i
\(754\) 10.3275 25.4803i 0.376105 0.927938i
\(755\) 2.72930i 0.0993292i
\(756\) 2.30865 2.88178i 0.0839649 0.104809i
\(757\) 0.480515i 0.0174646i 0.999962 + 0.00873230i \(0.00277961\pi\)
−0.999962 + 0.00873230i \(0.997220\pi\)
\(758\) 32.1633 + 13.0362i 1.16822 + 0.473497i
\(759\) −6.22015 + 7.02465i −0.225777 + 0.254979i
\(760\) 0.924697 0.887060i 0.0335423 0.0321771i
\(761\) −6.56885 + 37.2538i −0.238121 + 1.35045i 0.597820 + 0.801630i \(0.296034\pi\)
−0.835941 + 0.548819i \(0.815078\pi\)
\(762\) 1.18358 18.8785i 0.0428764 0.683897i
\(763\) 0.215693 + 0.257053i 0.00780860 + 0.00930593i
\(764\) 4.34491 + 8.95862i 0.157193 + 0.324112i
\(765\) 56.0627 28.5061i 2.02695 1.03064i
\(766\) 9.81011 + 6.14513i 0.354454 + 0.222033i
\(767\) −5.66602 32.1336i −0.204588 1.16028i
\(768\) −3.87169 + 27.4410i −0.139707 + 0.990193i
\(769\) −12.1347 + 4.41665i −0.437587 + 0.159269i −0.551414 0.834232i \(-0.685911\pi\)
0.113827 + 0.993501i \(0.463689\pi\)
\(770\) −0.374575 1.15718i −0.0134988 0.0417017i
\(771\) −2.67457 17.9476i −0.0963225 0.646365i
\(772\) 3.04208 + 29.5724i 0.109487 + 1.06433i
\(773\) 33.4525 + 19.3138i 1.20320 + 0.694670i 0.961266 0.275622i \(-0.0888839\pi\)
0.241937 + 0.970292i \(0.422217\pi\)
\(774\) −19.2622 + 27.3956i −0.692365 + 0.984716i
\(775\) 7.79852 + 13.5074i 0.280131 + 0.485201i
\(776\) −18.4354 27.5281i −0.661792 0.988202i
\(777\) 0.148271 5.57281i 0.00531921 0.199924i
\(778\) −3.26449 + 15.2752i −0.117038 + 0.547641i
\(779\) 0.307269 0.366189i 0.0110090 0.0131201i
\(780\) −22.8238 23.3483i −0.817225 0.836003i
\(781\) −3.17428 + 8.72126i −0.113585 + 0.312071i
\(782\) 2.38899 66.3093i 0.0854301 2.37122i
\(783\) 19.6882 + 27.6755i 0.703598 + 0.989042i
\(784\) −27.2102 3.94696i −0.971794 0.140963i
\(785\) 28.5755 + 10.4006i 1.01990 + 0.371215i
\(786\) 45.2066 13.3158i 1.61247 0.474959i
\(787\) 9.35099 11.1441i 0.333327 0.397243i −0.573184 0.819427i \(-0.694292\pi\)
0.906510 + 0.422184i \(0.138736\pi\)
\(788\) −31.5658 7.94443i −1.12449 0.283009i
\(789\) −18.5746 34.2444i −0.661273 1.21913i
\(790\) 1.93864 1.51118i 0.0689737 0.0537654i
\(791\) −3.13452 5.42916i −0.111451 0.193039i
\(792\) 6.36725 1.21022i 0.226250 0.0430033i
\(793\) 10.8480 18.7893i 0.385224 0.667228i
\(794\) 2.16371 + 15.5201i 0.0767872 + 0.550788i
\(795\) −12.2878 4.84627i −0.435805 0.171880i
\(796\) 11.9153 3.38815i 0.422326 0.120090i
\(797\) 10.2867 + 28.2624i 0.364372 + 1.00110i 0.977466 + 0.211094i \(0.0677026\pi\)
−0.613094 + 0.790010i \(0.710075\pi\)
\(798\) 0.100130 0.0738561i 0.00354456 0.00261448i
\(799\) 7.86671 + 44.6143i 0.278304 + 1.57834i
\(800\) 21.7497 + 18.4561i 0.768969 + 0.652520i
\(801\) 4.86918 + 39.9336i 0.172044 + 1.41098i
\(802\) 5.75165 3.05005i 0.203098 0.107701i
\(803\) −1.92381 2.29271i −0.0678898 0.0809080i
\(804\) 27.4628 + 19.6983i 0.968539 + 0.694705i
\(805\) −7.86429 1.38669i −0.277180 0.0488742i
\(806\) 9.65889 + 8.71626i 0.340220 + 0.307017i
\(807\) −44.8016 9.13459i −1.57709 0.321553i
\(808\) −17.5175 8.61592i −0.616264 0.303107i
\(809\) 9.40912 0.330807 0.165403 0.986226i \(-0.447107\pi\)
0.165403 + 0.986226i \(0.447107\pi\)
\(810\) 39.4766 8.27613i 1.38707 0.290794i
\(811\) 30.9245i 1.08591i −0.839763 0.542953i \(-0.817306\pi\)
0.839763 0.542953i \(-0.182694\pi\)
\(812\) −1.89863 + 4.23914i −0.0666289 + 0.148765i
\(813\) −3.40487 + 16.6996i −0.119414 + 0.585679i
\(814\) 6.55556 7.26452i 0.229772 0.254621i
\(815\) 6.14679 34.8602i 0.215313 1.22110i
\(816\) −29.3247 + 35.2248i −1.02657 + 1.23311i
\(817\) −0.864449 + 0.725358i −0.0302432 + 0.0253771i
\(818\) 39.6293 21.0151i 1.38561 0.734776i
\(819\) −1.90585 2.53357i −0.0665957 0.0885301i
\(820\) 17.5435 + 11.8898i 0.612646 + 0.415209i
\(821\) −22.1555 + 3.90662i −0.773234 + 0.136342i −0.546324 0.837574i \(-0.683973\pi\)
−0.226910 + 0.973916i \(0.572862\pi\)
\(822\) 8.27864 + 11.2237i 0.288751 + 0.391472i
\(823\) −36.4000 + 13.2485i −1.26882 + 0.461814i −0.886721 0.462306i \(-0.847022\pi\)
−0.382103 + 0.924120i \(0.624800\pi\)
\(824\) 4.30435 + 17.5111i 0.149949 + 0.610027i
\(825\) 2.44761 6.20597i 0.0852147 0.216064i
\(826\) 0.761159 + 5.45973i 0.0264841 + 0.189968i
\(827\) 3.08888 + 1.78336i 0.107411 + 0.0620137i 0.552743 0.833352i \(-0.313581\pi\)
−0.445332 + 0.895365i \(0.646914\pi\)
\(828\) 12.5654 40.6553i 0.436677 1.41287i
\(829\) −0.534957 + 0.308858i −0.0185798 + 0.0107271i −0.509261 0.860612i \(-0.670081\pi\)
0.490681 + 0.871339i \(0.336748\pi\)
\(830\) 37.3767 + 47.9493i 1.29737 + 1.66434i
\(831\) 27.0273 14.6599i 0.937567 0.508547i
\(832\) 22.0019 + 9.05962i 0.762780 + 0.314086i
\(833\) −34.8347 29.2298i −1.20695 1.01275i
\(834\) 18.8583 5.55479i 0.653008 0.192347i
\(835\) −20.7985 + 57.1434i −0.719761 + 1.97753i
\(836\) 0.217824 + 0.0157159i 0.00753361 + 0.000543546i
\(837\) −15.4930 + 4.27557i −0.535516 + 0.147785i
\(838\) 6.69885 + 0.241346i 0.231408 + 0.00833716i
\(839\) 7.10517 + 2.58607i 0.245298 + 0.0892811i 0.461743 0.887014i \(-0.347224\pi\)
−0.216446 + 0.976295i \(0.569446\pi\)
\(840\) 3.71143 + 4.08083i 0.128057 + 0.140802i
\(841\) −10.5135 8.82187i −0.362534 0.304202i
\(842\) −6.86152 + 32.1063i −0.236464 + 1.10646i
\(843\) 17.6241 + 0.468909i 0.607005 + 0.0161501i
\(844\) −12.3119 17.0249i −0.423792 0.586020i
\(845\) 11.3996 6.58157i 0.392159 0.226413i
\(846\) −2.58847 + 28.9377i −0.0889934 + 0.994900i
\(847\) −1.85056 + 3.20527i −0.0635860 + 0.110134i
\(848\) 9.62155 0.293389i 0.330405 0.0100750i
\(849\) 18.5003 2.75695i 0.634930 0.0946183i
\(850\) 14.5289 + 44.8840i 0.498336 + 1.53951i
\(851\) −21.9730 60.3702i −0.753223 2.06946i
\(852\) −3.19201 41.9701i −0.109356 1.43787i
\(853\) −31.1657 + 5.49535i −1.06709 + 0.188157i −0.679501 0.733674i \(-0.737804\pi\)
−0.387591 + 0.921832i \(0.626693\pi\)
\(854\) −1.94581 + 3.10630i −0.0665843 + 0.106295i
\(855\) 1.35719 + 0.0722704i 0.0464149 + 0.00247160i
\(856\) 8.54330 + 19.3612i 0.292004 + 0.661751i
\(857\) −2.64400 + 2.21858i −0.0903172 + 0.0757851i −0.686828 0.726820i \(-0.740998\pi\)
0.596511 + 0.802605i \(0.296553\pi\)
\(858\) 0.348196 5.55387i 0.0118872 0.189606i
\(859\) −44.1188 7.77933i −1.50531 0.265427i −0.640671 0.767816i \(-0.721344\pi\)
−0.864642 + 0.502388i \(0.832455\pi\)
\(860\) −35.9112 34.8329i −1.22456 1.18779i
\(861\) 1.54065 + 1.36420i 0.0525051 + 0.0464919i
\(862\) 11.2002 27.6335i 0.381481 0.941201i
\(863\) −30.0515 −1.02297 −0.511483 0.859294i \(-0.670904\pi\)
−0.511483 + 0.859294i \(0.670904\pi\)
\(864\) −24.0453 + 16.9063i −0.818039 + 0.575163i
\(865\) 59.8069 2.03349
\(866\) −4.22104 + 10.4143i −0.143437 + 0.353892i
\(867\) −43.9691 + 14.6913i −1.49327 + 0.498943i
\(868\) −1.57774 1.53036i −0.0535518 0.0519438i
\(869\) 0.412569 + 0.0727470i 0.0139954 + 0.00246777i
\(870\) −45.4419 + 22.5700i −1.54063 + 0.765195i
\(871\) 22.2290 18.6524i 0.753201 0.632011i
\(872\) −1.07837 2.44384i −0.0365182 0.0827590i
\(873\) 7.93369 34.2334i 0.268515 1.15862i
\(874\) 0.761169 1.21513i 0.0257469 0.0411025i
\(875\) 0.0471900 0.00832087i 0.00159531 0.000281297i
\(876\) 12.2359 + 5.87579i 0.413412 + 0.198524i
\(877\) 9.66967 + 26.5672i 0.326522 + 0.897111i 0.988985 + 0.148016i \(0.0472888\pi\)
−0.662463 + 0.749094i \(0.730489\pi\)
\(878\) −15.8366 48.9240i −0.534458 1.65110i
\(879\) 4.21168 + 5.29938i 0.142057 + 0.178744i
\(880\) 0.295101 + 9.67770i 0.00994785 + 0.326235i
\(881\) −11.0974 + 19.2212i −0.373880 + 0.647579i −0.990159 0.139949i \(-0.955306\pi\)
0.616279 + 0.787528i \(0.288639\pi\)
\(882\) −16.6806 23.9213i −0.561666 0.805473i
\(883\) −24.4063 + 14.0910i −0.821337 + 0.474199i −0.850877 0.525365i \(-0.823929\pi\)
0.0295406 + 0.999564i \(0.490596\pi\)
\(884\) 23.0605 + 31.8881i 0.775607 + 1.07251i
\(885\) −31.4842 + 51.3292i −1.05833 + 1.72541i
\(886\) −2.77528 + 12.9860i −0.0932373 + 0.436274i
\(887\) 42.2633 + 35.4631i 1.41906 + 1.19073i 0.951840 + 0.306594i \(0.0991894\pi\)
0.467221 + 0.884140i \(0.345255\pi\)
\(888\) −13.5027 + 42.2736i −0.453122 + 1.41861i
\(889\) 2.57833 + 0.938436i 0.0864744 + 0.0314741i
\(890\) −60.0589 2.16380i −2.01318 0.0725307i
\(891\) 5.55471 + 4.05001i 0.186090 + 0.135680i
\(892\) 35.8850 + 2.58909i 1.20152 + 0.0866891i
\(893\) −0.334828 + 0.919933i −0.0112046 + 0.0307844i
\(894\) 1.37653 5.69536i 0.0460380 0.190481i
\(895\) −14.9695 12.5609i −0.500376 0.419866i
\(896\) −3.65958 1.66341i −0.122258 0.0555706i
\(897\) −31.1438 19.1030i −1.03986 0.637829i
\(898\) 24.6451 + 31.6163i 0.822417 + 1.05505i
\(899\) 17.5089 10.1088i 0.583956 0.337147i
\(900\) 1.49124 + 30.2186i 0.0497079 + 1.00729i
\(901\) 13.7874 + 7.96014i 0.459324 + 0.265191i
\(902\) 0.498736 + 3.57739i 0.0166061 + 0.119114i
\(903\) −3.02248 3.80305i −0.100582 0.126558i
\(904\) 11.9123 + 48.4618i 0.396196 + 1.61181i
\(905\) 26.5555 9.66542i 0.882736 0.321290i
\(906\) −0.844159 + 1.93336i −0.0280453 + 0.0642316i
\(907\) 48.8333 8.61062i 1.62148 0.285911i 0.712164 0.702013i \(-0.247715\pi\)
0.909318 + 0.416102i \(0.136604\pi\)
\(908\) −3.69523 2.50437i −0.122631 0.0831106i
\(909\) −6.03719 19.8062i −0.200241 0.656931i
\(910\) 4.18423 2.21886i 0.138706 0.0735546i
\(911\) −6.56378 + 5.50767i −0.217468 + 0.182477i −0.745013 0.667050i \(-0.767557\pi\)
0.527545 + 0.849527i \(0.323112\pi\)
\(912\) −0.929395 + 0.342365i −0.0307753 + 0.0113369i
\(913\) −1.79929 + 10.2043i −0.0595476 + 0.337711i
\(914\) −21.4502 + 23.7699i −0.709509 + 0.786240i
\(915\) −37.9752 + 12.6886i −1.25542 + 0.419472i
\(916\) 0.793801 1.77235i 0.0262279 0.0585600i
\(917\) 6.83600i 0.225745i
\(918\) −48.5302 + 2.85301i −1.60173 + 0.0941633i
\(919\) 1.83837 0.0606424 0.0303212 0.999540i \(-0.490347\pi\)
0.0303212 + 0.999540i \(0.490347\pi\)
\(920\) 57.0426 + 28.0561i 1.88064 + 0.924984i
\(921\) 13.2752 14.9922i 0.437434 0.494011i
\(922\) −0.0100414 0.00906141i −0.000330695 0.000298422i
\(923\) −35.5904 6.27555i −1.17147 0.206562i
\(924\) −0.0925704 + 0.935568i −0.00304534 + 0.0307779i
\(925\) 29.3615 + 34.9916i 0.965399 + 1.15052i
\(926\) 18.9898 10.0702i 0.624045 0.330926i
\(927\) −10.4303 + 16.0318i −0.342577 + 0.526554i
\(928\) 23.9236 28.1930i 0.785330 0.925479i
\(929\) 1.61499 + 9.15907i 0.0529861 + 0.300499i 0.999772 0.0213656i \(-0.00680140\pi\)
−0.946786 + 0.321865i \(0.895690\pi\)
\(930\) −2.68159 23.8596i −0.0879327 0.782387i
\(931\) −0.336091 0.923403i −0.0110149 0.0302633i
\(932\) −19.1522 + 5.44599i −0.627350 + 0.178389i
\(933\) −1.26153 8.46544i −0.0413008 0.277146i
\(934\) 2.06196 + 14.7902i 0.0674693 + 0.483951i
\(935\) −8.00660 + 13.8678i −0.261844 + 0.453527i
\(936\) 8.94628 + 23.5986i 0.292418 + 0.771346i
\(937\) −14.0107 24.2672i −0.457710 0.792776i 0.541130 0.840939i \(-0.317997\pi\)
−0.998839 + 0.0481628i \(0.984663\pi\)
\(938\) −3.86648 + 3.01395i −0.126245 + 0.0984089i
\(939\) −21.6760 0.576715i −0.707369 0.0188204i
\(940\) −42.0896 10.5930i −1.37281 0.345507i
\(941\) 1.46274 1.74323i 0.0476840 0.0568276i −0.741675 0.670759i \(-0.765968\pi\)
0.789359 + 0.613931i \(0.210413\pi\)
\(942\) −17.0253 16.2058i −0.554714 0.528014i
\(943\) 22.2845 + 8.11089i 0.725682 + 0.264127i
\(944\) 6.29936 43.4276i 0.205027 1.41345i
\(945\) −0.466394 + 5.83214i −0.0151718 + 0.189720i
\(946\) 0.307000 8.52117i 0.00998143 0.277047i
\(947\) 7.38132 20.2800i 0.239861 0.659011i −0.760097 0.649809i \(-0.774849\pi\)
0.999958 0.00920194i \(-0.00292911\pi\)
\(948\) −1.84068 + 0.470869i −0.0597826 + 0.0152931i
\(949\) 7.49119 8.92765i 0.243174 0.289804i
\(950\) −0.213064 + 0.996964i −0.00691270 + 0.0323458i
\(951\) 8.33860 4.52296i 0.270398 0.146667i
\(952\) −3.69943 5.52408i −0.119899 0.179036i
\(953\) 12.7377 + 22.0623i 0.412613 + 0.714667i 0.995175 0.0981199i \(-0.0312829\pi\)
−0.582562 + 0.812787i \(0.697950\pi\)
\(954\) 7.20546 + 7.23355i 0.233285 + 0.234195i
\(955\) −13.6627 7.88817i −0.442115 0.255255i
\(956\) 4.63126 + 45.0211i 0.149786 + 1.45609i
\(957\) −8.04445 3.17270i −0.260040 0.102559i
\(958\) 3.59302 + 11.0999i 0.116085 + 0.358623i
\(959\) −1.90102 + 0.691915i −0.0613871 + 0.0223431i
\(960\) −19.3152 39.4347i −0.623397 1.27275i
\(961\) −3.72178 21.1072i −0.120057 0.680879i
\(962\) 32.2905 + 20.2270i 1.04109 + 0.652145i
\(963\) −8.78770 + 20.6543i −0.283180 + 0.665575i
\(964\) −14.3365 29.5598i −0.461746 0.952058i
\(965\) −30.2783 36.0843i −0.974694 1.16160i
\(966\) 5.14196 + 3.41468i 0.165440 + 0.109866i
\(967\) 5.80797 32.9387i 0.186772 1.05924i −0.736886 0.676017i \(-0.763704\pi\)
0.923658 0.383219i \(-0.125184\pi\)
\(968\) 21.2613 20.3960i 0.683366 0.655551i
\(969\) −1.60506 0.327256i −0.0515620 0.0105130i
\(970\) 48.6517 + 19.7192i 1.56211 + 0.633144i
\(971\) 15.7949i 0.506881i 0.967351 + 0.253441i \(0.0815622\pi\)
−0.967351 + 0.253441i \(0.918438\pi\)
\(972\) −30.5239 6.34734i −0.979056 0.203591i
\(973\) 2.85169i 0.0914209i
\(974\) 4.64176 11.4523i 0.148732 0.366955i
\(975\) 25.4535 + 5.18970i 0.815164 + 0.166204i
\(976\) 21.7698 19.4280i 0.696836 0.621875i
\(977\) 4.73244 26.8390i 0.151404 0.858655i −0.810596 0.585606i \(-0.800857\pi\)
0.962000 0.273049i \(-0.0880322\pi\)
\(978\) −15.1363 + 22.7929i −0.484007 + 0.728836i
\(979\) −6.58387 7.84635i −0.210421 0.250770i
\(980\) 39.1989 19.0114i 1.25216 0.607296i
\(981\) 1.10922 2.60707i 0.0354147 0.0832372i
\(982\) 17.5635 28.0384i 0.560474 0.894742i
\(983\) 10.5208 + 59.6663i 0.335561 + 1.90306i 0.421626 + 0.906770i \(0.361460\pi\)
−0.0860648 + 0.996290i \(0.527429\pi\)
\(984\) −8.74990 13.8485i −0.278937 0.441475i
\(985\) 48.4653 17.6399i 1.54423 0.562055i
\(986\) 58.1807 18.8330i 1.85285 0.599763i
\(987\) −3.92043 1.54620i −0.124789 0.0492161i
\(988\) 0.0870201 + 0.845933i 0.00276848 + 0.0269127i
\(989\) −48.4821 27.9912i −1.54164 0.890067i
\(990\) −7.27577 + 7.24751i −0.231239 + 0.230341i
\(991\) −17.4648 30.2498i −0.554786 0.960918i −0.997920 0.0644624i \(-0.979467\pi\)
0.443134 0.896455i \(-0.353867\pi\)
\(992\) 8.66464 + 15.2011i 0.275103 + 0.482635i
\(993\) −24.7687 + 13.4348i −0.786010 + 0.426342i
\(994\) 5.97072 + 1.27602i 0.189380 + 0.0404729i
\(995\) −12.6168 + 15.0361i −0.399978 + 0.476676i
\(996\) −11.6462 45.5265i −0.369024 1.44256i
\(997\) 3.61162 9.92284i 0.114381 0.314259i −0.869272 0.494334i \(-0.835412\pi\)
0.983653 + 0.180075i \(0.0576340\pi\)
\(998\) −24.9221 0.897893i −0.788896 0.0284223i
\(999\) −42.5099 + 20.2105i −1.34495 + 0.639431i
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 216.2.t.a.85.24 yes 204
3.2 odd 2 648.2.t.a.469.11 204
4.3 odd 2 864.2.bf.a.625.15 204
8.3 odd 2 864.2.bf.a.625.20 204
8.5 even 2 inner 216.2.t.a.85.15 yes 204
24.5 odd 2 648.2.t.a.469.20 204
27.7 even 9 inner 216.2.t.a.61.15 204
27.20 odd 18 648.2.t.a.181.20 204
108.7 odd 18 864.2.bf.a.817.20 204
216.61 even 18 inner 216.2.t.a.61.24 yes 204
216.101 odd 18 648.2.t.a.181.11 204
216.115 odd 18 864.2.bf.a.817.15 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.t.a.61.15 204 27.7 even 9 inner
216.2.t.a.61.24 yes 204 216.61 even 18 inner
216.2.t.a.85.15 yes 204 8.5 even 2 inner
216.2.t.a.85.24 yes 204 1.1 even 1 trivial
648.2.t.a.181.11 204 216.101 odd 18
648.2.t.a.181.20 204 27.20 odd 18
648.2.t.a.469.11 204 3.2 odd 2
648.2.t.a.469.20 204 24.5 odd 2
864.2.bf.a.625.15 204 4.3 odd 2
864.2.bf.a.625.20 204 8.3 odd 2
864.2.bf.a.817.15 204 216.115 odd 18
864.2.bf.a.817.20 204 108.7 odd 18