Properties

Label 380.2.bj.a.327.46
Level $380$
Weight $2$
Character 380.327
Analytic conductor $3.034$
Analytic rank $0$
Dimension $672$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(23,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 27, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.bj (of order \(36\), degree \(12\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(672\)
Relative dimension: \(56\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 327.46
Character \(\chi\) \(=\) 380.327
Dual form 380.2.bj.a.43.46

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.09496 - 0.895026i) q^{2} +(0.235285 - 0.336022i) q^{3} +(0.397856 - 1.96003i) q^{4} +(2.06687 - 0.853251i) q^{5} +(-0.0431218 - 0.578516i) q^{6} +(-0.371598 - 1.38682i) q^{7} +(-1.31864 - 2.50224i) q^{8} +(0.968509 + 2.66096i) q^{9} +O(q^{10})\) \(q+(1.09496 - 0.895026i) q^{2} +(0.235285 - 0.336022i) q^{3} +(0.397856 - 1.96003i) q^{4} +(2.06687 - 0.853251i) q^{5} +(-0.0431218 - 0.578516i) q^{6} +(-0.371598 - 1.38682i) q^{7} +(-1.31864 - 2.50224i) q^{8} +(0.968509 + 2.66096i) q^{9} +(1.49945 - 2.78418i) q^{10} +(-1.39727 + 0.806716i) q^{11} +(-0.565003 - 0.594854i) q^{12} +(-1.24316 - 1.77542i) q^{13} +(-1.64813 - 1.18592i) q^{14} +(0.199593 - 0.895272i) q^{15} +(-3.68342 - 1.55962i) q^{16} +(1.48460 + 3.18374i) q^{17} +(3.44210 + 2.04679i) q^{18} +(0.135064 + 4.35681i) q^{19} +(-0.850079 - 4.39060i) q^{20} +(-0.553435 - 0.201434i) q^{21} +(-0.807920 + 2.13391i) q^{22} +(-0.283597 - 3.24152i) q^{23} +(-1.15106 - 0.145646i) q^{24} +(3.54393 - 3.52712i) q^{25} +(-2.95025 - 0.831341i) q^{26} +(2.31071 + 0.619152i) q^{27} +(-2.86606 + 0.176587i) q^{28} +(0.834461 + 2.29266i) q^{29} +(-0.582746 - 1.15892i) q^{30} +(-5.96207 - 3.44220i) q^{31} +(-5.42908 + 1.58905i) q^{32} +(-0.0576833 + 0.659323i) q^{33} +(4.47510 + 2.15729i) q^{34} +(-1.95136 - 2.54932i) q^{35} +(5.60088 - 0.839628i) q^{36} +(2.32134 + 2.32134i) q^{37} +(4.04735 + 4.64962i) q^{38} -0.889076 q^{39} +(-4.86050 - 4.04667i) q^{40} +(0.909979 + 5.16075i) q^{41} +(-0.786276 + 0.274778i) q^{42} +(1.51832 + 0.132836i) q^{43} +(1.02527 + 3.05965i) q^{44} +(4.27225 + 4.67348i) q^{45} +(-3.21178 - 3.29550i) q^{46} +(-0.338802 + 0.726562i) q^{47} +(-1.39072 + 0.870756i) q^{48} +(4.27698 - 2.46932i) q^{49} +(0.723574 - 7.03395i) q^{50} +(1.41911 + 0.250228i) q^{51} +(-3.97446 + 1.73027i) q^{52} +(-1.43407 + 0.125465i) q^{53} +(3.08428 - 1.39020i) q^{54} +(-2.19965 + 2.85960i) q^{55} +(-2.98016 + 2.75855i) q^{56} +(1.49576 + 0.979708i) q^{57} +(2.96569 + 1.76350i) q^{58} +(0.719010 + 0.261698i) q^{59} +(-1.67535 - 0.747398i) q^{60} +(0.724227 + 0.607699i) q^{61} +(-9.60906 + 1.56715i) q^{62} +(3.33038 - 2.33196i) q^{63} +(-4.52236 + 6.59911i) q^{64} +(-4.08433 - 2.60883i) q^{65} +(0.526951 + 0.773557i) q^{66} +(-6.15398 + 13.1973i) q^{67} +(6.83087 - 1.64319i) q^{68} +(-1.15595 - 0.667388i) q^{69} +(-4.41836 - 1.04488i) q^{70} +(1.97078 + 2.34868i) q^{71} +(5.38122 - 5.93229i) q^{72} +(0.596943 + 0.417984i) q^{73} +(4.61943 + 0.464104i) q^{74} +(-0.351358 - 2.02072i) q^{75} +(8.59320 + 1.46865i) q^{76} +(1.63800 + 1.63800i) q^{77} +(-0.973499 + 0.795746i) q^{78} +(1.90246 + 10.7894i) q^{79} +(-8.94391 - 0.0806463i) q^{80} +(-5.75597 + 4.82983i) q^{81} +(5.61539 + 4.83633i) q^{82} +(12.3265 - 3.30287i) q^{83} +(-0.615004 + 1.00461i) q^{84} +(5.78501 + 5.31364i) q^{85} +(1.78138 - 1.21349i) q^{86} +(0.966722 + 0.259032i) q^{87} +(3.86110 + 2.43254i) q^{88} +(-17.2986 - 3.05022i) q^{89} +(8.86081 + 1.29347i) q^{90} +(-2.00023 + 2.38379i) q^{91} +(-6.46631 - 0.733802i) q^{92} +(-2.55944 + 1.19349i) q^{93} +(0.279320 + 1.09879i) q^{94} +(3.99661 + 8.88972i) q^{95} +(-0.743428 + 2.19817i) q^{96} +(-0.691299 - 1.48250i) q^{97} +(2.47300 - 6.53180i) q^{98} +(-3.49991 - 2.93677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09496 0.895026i 0.774251 0.632879i
\(3\) 0.235285 0.336022i 0.135842 0.194002i −0.745467 0.666542i \(-0.767774\pi\)
0.881309 + 0.472540i \(0.156663\pi\)
\(4\) 0.397856 1.96003i 0.198928 0.980014i
\(5\) 2.06687 0.853251i 0.924334 0.381585i
\(6\) −0.0431218 0.578516i −0.0176044 0.236178i
\(7\) −0.371598 1.38682i −0.140451 0.524170i −0.999916 0.0129754i \(-0.995870\pi\)
0.859465 0.511195i \(-0.170797\pi\)
\(8\) −1.31864 2.50224i −0.466211 0.884674i
\(9\) 0.968509 + 2.66096i 0.322836 + 0.886985i
\(10\) 1.49945 2.78418i 0.474168 0.880434i
\(11\) −1.39727 + 0.806716i −0.421294 + 0.243234i −0.695631 0.718400i \(-0.744875\pi\)
0.274337 + 0.961634i \(0.411542\pi\)
\(12\) −0.565003 0.594854i −0.163102 0.171720i
\(13\) −1.24316 1.77542i −0.344790 0.492412i 0.608881 0.793261i \(-0.291619\pi\)
−0.953672 + 0.300850i \(0.902730\pi\)
\(14\) −1.64813 1.18592i −0.440481 0.316951i
\(15\) 0.199593 0.895272i 0.0515348 0.231158i
\(16\) −3.68342 1.55962i −0.920855 0.389904i
\(17\) 1.48460 + 3.18374i 0.360069 + 0.772170i 0.999993 + 0.00373178i \(0.00118787\pi\)
−0.639924 + 0.768438i \(0.721034\pi\)
\(18\) 3.44210 + 2.04679i 0.811311 + 0.482432i
\(19\) 0.135064 + 4.35681i 0.0309859 + 0.999520i
\(20\) −0.850079 4.39060i −0.190083 0.981768i
\(21\) −0.553435 0.201434i −0.120769 0.0439565i
\(22\) −0.807920 + 2.13391i −0.172249 + 0.454952i
\(23\) −0.283597 3.24152i −0.0591340 0.675905i −0.966686 0.255965i \(-0.917607\pi\)
0.907552 0.419940i \(-0.137949\pi\)
\(24\) −1.15106 0.145646i −0.234960 0.0297299i
\(25\) 3.54393 3.52712i 0.708785 0.705424i
\(26\) −2.95025 0.831341i −0.578591 0.163039i
\(27\) 2.31071 + 0.619152i 0.444695 + 0.119156i
\(28\) −2.86606 + 0.176587i −0.541634 + 0.0333719i
\(29\) 0.834461 + 2.29266i 0.154956 + 0.425737i 0.992742 0.120261i \(-0.0383730\pi\)
−0.837787 + 0.545998i \(0.816151\pi\)
\(30\) −0.582746 1.15892i −0.106394 0.211590i
\(31\) −5.96207 3.44220i −1.07082 0.618238i −0.142414 0.989807i \(-0.545486\pi\)
−0.928405 + 0.371569i \(0.878820\pi\)
\(32\) −5.42908 + 1.58905i −0.959735 + 0.280907i
\(33\) −0.0576833 + 0.659323i −0.0100414 + 0.114773i
\(34\) 4.47510 + 2.15729i 0.767473 + 0.369973i
\(35\) −1.95136 2.54932i −0.329839 0.430914i
\(36\) 5.60088 0.839628i 0.933479 0.139938i
\(37\) 2.32134 + 2.32134i 0.381626 + 0.381626i 0.871688 0.490062i \(-0.163026\pi\)
−0.490062 + 0.871688i \(0.663026\pi\)
\(38\) 4.04735 + 4.64962i 0.656566 + 0.754268i
\(39\) −0.889076 −0.142366
\(40\) −4.86050 4.04667i −0.768513 0.639835i
\(41\) 0.909979 + 5.16075i 0.142115 + 0.805973i 0.969639 + 0.244542i \(0.0786377\pi\)
−0.827524 + 0.561431i \(0.810251\pi\)
\(42\) −0.786276 + 0.274778i −0.121325 + 0.0423992i
\(43\) 1.51832 + 0.132836i 0.231541 + 0.0202572i 0.202336 0.979316i \(-0.435147\pi\)
0.0292055 + 0.999573i \(0.490702\pi\)
\(44\) 1.02527 + 3.05965i 0.154566 + 0.461260i
\(45\) 4.27225 + 4.67348i 0.636869 + 0.696681i
\(46\) −3.21178 3.29550i −0.473550 0.485895i
\(47\) −0.338802 + 0.726562i −0.0494193 + 0.105980i −0.929467 0.368905i \(-0.879733\pi\)
0.880048 + 0.474885i \(0.157510\pi\)
\(48\) −1.39072 + 0.870756i −0.200733 + 0.125683i
\(49\) 4.27698 2.46932i 0.610997 0.352759i
\(50\) 0.723574 7.03395i 0.102329 0.994751i
\(51\) 1.41911 + 0.250228i 0.198715 + 0.0350389i
\(52\) −3.97446 + 1.73027i −0.551159 + 0.239945i
\(53\) −1.43407 + 0.125465i −0.196985 + 0.0172339i −0.185221 0.982697i \(-0.559300\pi\)
−0.0117637 + 0.999931i \(0.503745\pi\)
\(54\) 3.08428 1.39020i 0.419717 0.189182i
\(55\) −2.19965 + 2.85960i −0.296601 + 0.385589i
\(56\) −2.98016 + 2.75855i −0.398240 + 0.368627i
\(57\) 1.49576 + 0.979708i 0.198119 + 0.129765i
\(58\) 2.96569 + 1.76350i 0.389414 + 0.231559i
\(59\) 0.719010 + 0.261698i 0.0936071 + 0.0340702i 0.388399 0.921491i \(-0.373028\pi\)
−0.294792 + 0.955561i \(0.595250\pi\)
\(60\) −1.67535 0.747398i −0.216287 0.0964887i
\(61\) 0.724227 + 0.607699i 0.0927277 + 0.0778078i 0.687973 0.725736i \(-0.258501\pi\)
−0.595245 + 0.803544i \(0.702945\pi\)
\(62\) −9.60906 + 1.56715i −1.22035 + 0.199028i
\(63\) 3.33038 2.33196i 0.419589 0.293799i
\(64\) −4.52236 + 6.59911i −0.565295 + 0.824889i
\(65\) −4.08433 2.60883i −0.506598 0.323586i
\(66\) 0.526951 + 0.773557i 0.0648632 + 0.0952183i
\(67\) −6.15398 + 13.1973i −0.751828 + 1.61230i 0.0382301 + 0.999269i \(0.487828\pi\)
−0.790058 + 0.613032i \(0.789950\pi\)
\(68\) 6.83087 1.64319i 0.828365 0.199266i
\(69\) −1.15595 0.667388i −0.139160 0.0803441i
\(70\) −4.41836 1.04488i −0.528095 0.124887i
\(71\) 1.97078 + 2.34868i 0.233889 + 0.278738i 0.870204 0.492691i \(-0.163987\pi\)
−0.636316 + 0.771429i \(0.719542\pi\)
\(72\) 5.38122 5.93229i 0.634183 0.699127i
\(73\) 0.596943 + 0.417984i 0.0698669 + 0.0489213i 0.607988 0.793946i \(-0.291977\pi\)
−0.538121 + 0.842867i \(0.680866\pi\)
\(74\) 4.61943 + 0.464104i 0.536998 + 0.0539510i
\(75\) −0.351358 2.02072i −0.0405713 0.233332i
\(76\) 8.59320 + 1.46865i 0.985708 + 0.168466i
\(77\) 1.63800 + 1.63800i 0.186667 + 0.186667i
\(78\) −0.973499 + 0.795746i −0.110227 + 0.0901005i
\(79\) 1.90246 + 10.7894i 0.214044 + 1.21390i 0.882558 + 0.470203i \(0.155819\pi\)
−0.668514 + 0.743699i \(0.733069\pi\)
\(80\) −8.94391 0.0806463i −0.999959 0.00901653i
\(81\) −5.75597 + 4.82983i −0.639552 + 0.536648i
\(82\) 5.61539 + 4.83633i 0.620116 + 0.534084i
\(83\) 12.3265 3.30287i 1.35301 0.362537i 0.491763 0.870729i \(-0.336353\pi\)
0.861244 + 0.508192i \(0.169686\pi\)
\(84\) −0.615004 + 1.00461i −0.0671024 + 0.109612i
\(85\) 5.78501 + 5.31364i 0.627472 + 0.576345i
\(86\) 1.78138 1.21349i 0.192091 0.130854i
\(87\) 0.966722 + 0.259032i 0.103644 + 0.0277712i
\(88\) 3.86110 + 2.43254i 0.411594 + 0.259309i
\(89\) −17.2986 3.05022i −1.83365 0.323323i −0.853428 0.521210i \(-0.825481\pi\)
−0.980225 + 0.197887i \(0.936592\pi\)
\(90\) 8.86081 + 1.29347i 0.934011 + 0.136344i
\(91\) −2.00023 + 2.38379i −0.209681 + 0.249889i
\(92\) −6.46631 0.733802i −0.674159 0.0765041i
\(93\) −2.55944 + 1.19349i −0.265402 + 0.123759i
\(94\) 0.279320 + 1.09879i 0.0288096 + 0.113332i
\(95\) 3.99661 + 8.88972i 0.410043 + 0.912066i
\(96\) −0.743428 + 2.19817i −0.0758758 + 0.224350i
\(97\) −0.691299 1.48250i −0.0701908 0.150525i 0.868082 0.496421i \(-0.165353\pi\)
−0.938273 + 0.345896i \(0.887575\pi\)
\(98\) 2.47300 6.53180i 0.249811 0.659812i
\(99\) −3.49991 2.93677i −0.351754 0.295156i
\(100\) −5.50329 8.34948i −0.550329 0.834948i
\(101\) −0.382754 + 2.17071i −0.0380854 + 0.215993i −0.997911 0.0646042i \(-0.979421\pi\)
0.959826 + 0.280598i \(0.0905326\pi\)
\(102\) 1.77782 0.996154i 0.176031 0.0986339i
\(103\) 3.09641 11.5559i 0.305098 1.13864i −0.627763 0.778404i \(-0.716029\pi\)
0.932861 0.360236i \(-0.117304\pi\)
\(104\) −2.80322 + 5.45182i −0.274879 + 0.534594i
\(105\) −1.31575 + 0.0558809i −0.128404 + 0.00545341i
\(106\) −1.45795 + 1.42091i −0.141609 + 0.138011i
\(107\) −2.25334 8.40956i −0.217838 0.812983i −0.985148 0.171707i \(-0.945072\pi\)
0.767310 0.641276i \(-0.221595\pi\)
\(108\) 2.13288 4.28272i 0.205237 0.412104i
\(109\) −10.5856 12.6155i −1.01392 1.20834i −0.977918 0.208990i \(-0.932982\pi\)
−0.0360013 0.999352i \(-0.511462\pi\)
\(110\) 0.150897 + 5.09989i 0.0143875 + 0.486255i
\(111\) 1.32620 0.233845i 0.125877 0.0221956i
\(112\) −0.794161 + 5.68781i −0.0750412 + 0.537448i
\(113\) 8.91841 8.91841i 0.838974 0.838974i −0.149750 0.988724i \(-0.547847\pi\)
0.988724 + 0.149750i \(0.0478469\pi\)
\(114\) 2.51466 0.266010i 0.235519 0.0249141i
\(115\) −3.35199 6.45784i −0.312575 0.602197i
\(116\) 4.82568 0.723418i 0.448053 0.0671677i
\(117\) 3.52029 5.02750i 0.325451 0.464792i
\(118\) 1.02151 0.356985i 0.0940377 0.0328631i
\(119\) 3.86361 3.24195i 0.354176 0.297189i
\(120\) −2.50337 + 0.681115i −0.228526 + 0.0621770i
\(121\) −4.19842 + 7.27188i −0.381674 + 0.661080i
\(122\) 1.33690 + 0.0172008i 0.121037 + 0.00155729i
\(123\) 1.94823 + 0.908474i 0.175666 + 0.0819144i
\(124\) −9.11886 + 10.3163i −0.818898 + 0.926433i
\(125\) 4.31532 10.3140i 0.385974 0.922510i
\(126\) 1.55946 5.53417i 0.138927 0.493023i
\(127\) 6.54726 + 9.35046i 0.580975 + 0.829719i 0.996817 0.0797180i \(-0.0254020\pi\)
−0.415842 + 0.909437i \(0.636513\pi\)
\(128\) 0.954588 + 11.2734i 0.0843744 + 0.996434i
\(129\) 0.401874 0.478934i 0.0353830 0.0421678i
\(130\) −6.80713 + 0.799026i −0.597025 + 0.0700792i
\(131\) −2.15852 + 5.93049i −0.188591 + 0.518149i −0.997569 0.0696901i \(-0.977799\pi\)
0.808978 + 0.587839i \(0.200021\pi\)
\(132\) 1.26934 + 0.375376i 0.110482 + 0.0326723i
\(133\) 5.99193 1.80629i 0.519567 0.156625i
\(134\) 5.07355 + 19.9584i 0.438288 + 1.72414i
\(135\) 5.30423 0.691904i 0.456515 0.0595496i
\(136\) 6.00880 7.91303i 0.515250 0.678537i
\(137\) −1.36009 15.5458i −0.116200 1.32817i −0.800659 0.599120i \(-0.795517\pi\)
0.684459 0.729051i \(-0.260038\pi\)
\(138\) −1.86304 + 0.303845i −0.158593 + 0.0258650i
\(139\) −0.562759 + 3.19157i −0.0477326 + 0.270705i −0.999328 0.0366477i \(-0.988332\pi\)
0.951596 + 0.307353i \(0.0994432\pi\)
\(140\) −5.77310 + 2.81045i −0.487916 + 0.237526i
\(141\) 0.164426 + 0.284794i 0.0138472 + 0.0239840i
\(142\) 4.26005 + 0.807805i 0.357496 + 0.0677895i
\(143\) 3.16929 + 1.47786i 0.265029 + 0.123585i
\(144\) 0.582646 11.3119i 0.0485538 0.942660i
\(145\) 3.68094 + 4.02664i 0.305686 + 0.334394i
\(146\) 1.02773 0.0766057i 0.0850557 0.00633994i
\(147\) 0.176566 2.01815i 0.0145629 0.166455i
\(148\) 5.47346 3.62634i 0.449915 0.298083i
\(149\) −8.95006 + 1.57814i −0.733218 + 0.129286i −0.527776 0.849383i \(-0.676974\pi\)
−0.205441 + 0.978669i \(0.565863\pi\)
\(150\) −2.19332 1.89812i −0.179084 0.154981i
\(151\) 17.5950i 1.43186i −0.698174 0.715928i \(-0.746004\pi\)
0.698174 0.715928i \(-0.253996\pi\)
\(152\) 10.7237 6.08303i 0.869803 0.493399i
\(153\) −7.03393 + 7.03393i −0.568660 + 0.568660i
\(154\) 3.25959 + 0.327484i 0.262665 + 0.0263894i
\(155\) −15.2599 2.02745i −1.22570 0.162849i
\(156\) −0.353724 + 1.74261i −0.0283206 + 0.139521i
\(157\) −19.9144 1.74229i −1.58935 0.139050i −0.742114 0.670274i \(-0.766177\pi\)
−0.847231 + 0.531224i \(0.821732\pi\)
\(158\) 11.7399 + 10.1112i 0.933977 + 0.804401i
\(159\) −0.295257 + 0.511400i −0.0234154 + 0.0405566i
\(160\) −9.86536 + 7.91673i −0.779925 + 0.625872i
\(161\) −4.39004 + 1.59784i −0.345984 + 0.125928i
\(162\) −1.97970 + 10.4402i −0.155540 + 0.820259i
\(163\) −5.86459 + 21.8870i −0.459350 + 1.71432i 0.215623 + 0.976477i \(0.430822\pi\)
−0.674973 + 0.737842i \(0.735845\pi\)
\(164\) 10.4772 + 0.269648i 0.818136 + 0.0210560i
\(165\) 0.443344 + 1.41195i 0.0345143 + 0.109921i
\(166\) 10.5408 14.6490i 0.818124 1.13698i
\(167\) 9.85429 0.862139i 0.762548 0.0667143i 0.300754 0.953702i \(-0.402762\pi\)
0.461794 + 0.886987i \(0.347206\pi\)
\(168\) 0.225748 + 1.65044i 0.0174168 + 0.127335i
\(169\) 2.83961 7.80176i 0.218431 0.600135i
\(170\) 11.0902 + 0.640467i 0.850578 + 0.0491216i
\(171\) −11.4625 + 4.57900i −0.876556 + 0.350165i
\(172\) 0.864433 2.92310i 0.0659124 0.222884i
\(173\) 10.7685 5.02145i 0.818717 0.381774i 0.0323065 0.999478i \(-0.489715\pi\)
0.786411 + 0.617704i \(0.211937\pi\)
\(174\) 1.29036 0.581613i 0.0978218 0.0440920i
\(175\) −6.20842 3.60413i −0.469312 0.272447i
\(176\) 6.40491 0.792264i 0.482788 0.0597192i
\(177\) 0.257109 0.180030i 0.0193255 0.0135318i
\(178\) −21.6713 + 12.1429i −1.62433 + 0.910148i
\(179\) −8.38118 14.5166i −0.626439 1.08502i −0.988261 0.152776i \(-0.951179\pi\)
0.361822 0.932247i \(-0.382155\pi\)
\(180\) 10.8599 6.51436i 0.809448 0.485551i
\(181\) −21.5464 + 7.84226i −1.60153 + 0.582910i −0.979741 0.200271i \(-0.935818\pi\)
−0.621793 + 0.783182i \(0.713595\pi\)
\(182\) −0.0566162 + 4.40040i −0.00419667 + 0.326179i
\(183\) 0.374600 0.100374i 0.0276912 0.00741984i
\(184\) −7.73709 + 4.98404i −0.570386 + 0.367428i
\(185\) 6.77861 + 2.81723i 0.498373 + 0.207127i
\(186\) −1.73427 + 3.59759i −0.127163 + 0.263788i
\(187\) −4.64276 3.25090i −0.339512 0.237729i
\(188\) 1.28929 + 0.953128i 0.0940310 + 0.0695140i
\(189\) 3.43462i 0.249832i
\(190\) 12.3326 + 6.15678i 0.894704 + 0.446660i
\(191\) 21.9821i 1.59057i −0.606236 0.795285i \(-0.707321\pi\)
0.606236 0.795285i \(-0.292679\pi\)
\(192\) 1.15340 + 3.07229i 0.0832396 + 0.221723i
\(193\) −19.4924 13.6487i −1.40309 0.982455i −0.997663 0.0683286i \(-0.978233\pi\)
−0.405429 0.914127i \(-0.632878\pi\)
\(194\) −2.08381 1.00454i −0.149609 0.0721215i
\(195\) −1.83761 + 0.758605i −0.131594 + 0.0543248i
\(196\) −3.13831 9.36544i −0.224165 0.668960i
\(197\) 10.7798 2.88843i 0.768027 0.205792i 0.146527 0.989207i \(-0.453190\pi\)
0.621500 + 0.783414i \(0.286524\pi\)
\(198\) −6.46073 0.0831247i −0.459144 0.00590741i
\(199\) 9.94967 3.62138i 0.705313 0.256713i 0.0356354 0.999365i \(-0.488654\pi\)
0.669678 + 0.742652i \(0.266432\pi\)
\(200\) −13.4989 4.21672i −0.954514 0.298167i
\(201\) 2.98663 + 5.17299i 0.210661 + 0.364875i
\(202\) 1.52374 + 2.71940i 0.107210 + 0.191336i
\(203\) 2.86944 2.00920i 0.201395 0.141018i
\(204\) 1.05505 2.68194i 0.0738686 0.187774i
\(205\) 6.28422 + 9.89016i 0.438909 + 0.690759i
\(206\) −6.95245 15.4246i −0.484400 1.07468i
\(207\) 8.35089 3.89408i 0.580427 0.270657i
\(208\) 1.81011 + 8.47846i 0.125509 + 0.587875i
\(209\) −3.70343 5.97869i −0.256171 0.413554i
\(210\) −1.39068 + 1.23882i −0.0959659 + 0.0854868i
\(211\) 2.36724 6.50393i 0.162967 0.447749i −0.831151 0.556046i \(-0.812318\pi\)
0.994119 + 0.108297i \(0.0345399\pi\)
\(212\) −0.324638 + 2.86074i −0.0222963 + 0.196476i
\(213\) 1.25291 0.109615i 0.0858477 0.00751070i
\(214\) −9.99408 7.19130i −0.683182 0.491587i
\(215\) 3.25151 1.02095i 0.221751 0.0696284i
\(216\) −1.49773 6.59837i −0.101908 0.448962i
\(217\) −2.55823 + 9.54746i −0.173664 + 0.648124i
\(218\) −22.8820 4.33895i −1.54976 0.293871i
\(219\) 0.280904 0.102241i 0.0189817 0.00690878i
\(220\) 4.72976 + 5.44909i 0.318880 + 0.367378i
\(221\) 3.80686 6.59368i 0.256077 0.443539i
\(222\) 1.24283 1.44303i 0.0834135 0.0968501i
\(223\) −27.3785 2.39531i −1.83340 0.160402i −0.882584 0.470155i \(-0.844198\pi\)
−0.950817 + 0.309753i \(0.899754\pi\)
\(224\) 4.22117 + 6.93869i 0.282039 + 0.463611i
\(225\) 12.8178 + 6.01418i 0.854523 + 0.400945i
\(226\) 1.78305 17.7475i 0.118607 1.18055i
\(227\) −1.38313 + 1.38313i −0.0918017 + 0.0918017i −0.751516 0.659715i \(-0.770677\pi\)
0.659715 + 0.751516i \(0.270677\pi\)
\(228\) 2.51535 2.54195i 0.166583 0.168345i
\(229\) 15.1394i 1.00044i 0.865898 + 0.500220i \(0.166747\pi\)
−0.865898 + 0.500220i \(0.833253\pi\)
\(230\) −9.45022 4.07093i −0.623129 0.268429i
\(231\) 0.935800 0.165007i 0.0615711 0.0108567i
\(232\) 4.63643 5.11122i 0.304396 0.335568i
\(233\) 2.34209 26.7702i 0.153435 1.75377i −0.396013 0.918245i \(-0.629606\pi\)
0.549448 0.835528i \(-0.314838\pi\)
\(234\) −0.645179 8.65564i −0.0421767 0.565837i
\(235\) −0.0803197 + 1.79079i −0.00523948 + 0.116819i
\(236\) 0.798998 1.30516i 0.0520103 0.0849588i
\(237\) 4.07310 + 1.89932i 0.264576 + 0.123374i
\(238\) 1.32885 7.00783i 0.0861364 0.454250i
\(239\) 1.15362 + 1.99812i 0.0746213 + 0.129248i 0.900922 0.433982i \(-0.142892\pi\)
−0.826300 + 0.563230i \(0.809559\pi\)
\(240\) −2.13147 + 2.98638i −0.137586 + 0.192770i
\(241\) −0.173516 + 0.984061i −0.0111772 + 0.0633889i −0.989886 0.141864i \(-0.954691\pi\)
0.978709 + 0.205253i \(0.0658016\pi\)
\(242\) 1.91144 + 11.7201i 0.122872 + 0.753395i
\(243\) 0.894123 + 10.2199i 0.0573580 + 0.655605i
\(244\) 1.47924 1.17773i 0.0946989 0.0753964i
\(245\) 6.73303 8.75310i 0.430157 0.559215i
\(246\) 2.94633 0.748978i 0.187851 0.0477531i
\(247\) 7.56723 5.65600i 0.481492 0.359883i
\(248\) −0.751362 + 19.4575i −0.0477116 + 1.23555i
\(249\) 1.79040 4.91909i 0.113462 0.311734i
\(250\) −4.50619 15.1557i −0.284996 0.958529i
\(251\) −10.7026 + 12.7549i −0.675545 + 0.805083i −0.989527 0.144346i \(-0.953892\pi\)
0.313983 + 0.949429i \(0.398337\pi\)
\(252\) −3.24569 7.45543i −0.204459 0.469648i
\(253\) 3.01125 + 4.30051i 0.189316 + 0.270371i
\(254\) 15.5379 + 4.37836i 0.974932 + 0.274723i
\(255\) 3.14663 0.693669i 0.197050 0.0434393i
\(256\) 11.1352 + 11.4895i 0.695949 + 0.718091i
\(257\) 17.6007 + 8.20736i 1.09790 + 0.511961i 0.885226 0.465162i \(-0.154004\pi\)
0.212678 + 0.977122i \(0.431782\pi\)
\(258\) 0.0113749 0.884099i 0.000708173 0.0550416i
\(259\) 2.35669 4.08190i 0.146437 0.253637i
\(260\) −6.73835 + 6.96746i −0.417895 + 0.432103i
\(261\) −5.29249 + 4.44093i −0.327597 + 0.274887i
\(262\) 2.94446 + 8.42555i 0.181909 + 0.520532i
\(263\) 16.9617 24.2239i 1.04591 1.49371i 0.186474 0.982460i \(-0.440294\pi\)
0.859433 0.511249i \(-0.170817\pi\)
\(264\) 1.72584 0.725074i 0.106218 0.0446252i
\(265\) −2.85699 + 1.48294i −0.175503 + 0.0910964i
\(266\) 4.94422 7.34075i 0.303150 0.450090i
\(267\) −5.09506 + 5.09506i −0.311813 + 0.311813i
\(268\) 23.4186 + 17.3126i 1.43052 + 1.05753i
\(269\) −10.8886 + 1.91996i −0.663891 + 0.117062i −0.495432 0.868647i \(-0.664990\pi\)
−0.168459 + 0.985709i \(0.553879\pi\)
\(270\) 5.18862 5.50503i 0.315769 0.335025i
\(271\) 13.7629 + 16.4020i 0.836035 + 0.996348i 0.999951 + 0.00987376i \(0.00314297\pi\)
−0.163916 + 0.986474i \(0.552413\pi\)
\(272\) −0.503001 14.0425i −0.0304989 0.851449i
\(273\) 0.330379 + 1.23299i 0.0199955 + 0.0746241i
\(274\) −15.4032 15.8047i −0.930540 0.954797i
\(275\) −2.10644 + 7.78729i −0.127023 + 0.469591i
\(276\) −1.76800 + 2.00017i −0.106421 + 0.120396i
\(277\) 1.44092 5.37759i 0.0865765 0.323108i −0.909032 0.416727i \(-0.863177\pi\)
0.995608 + 0.0936194i \(0.0298437\pi\)
\(278\) 2.24034 + 3.99831i 0.134367 + 0.239803i
\(279\) 3.38523 19.1986i 0.202669 1.14939i
\(280\) −3.80586 + 8.24440i −0.227444 + 0.492697i
\(281\) −0.767149 0.643714i −0.0457642 0.0384008i 0.619619 0.784903i \(-0.287287\pi\)
−0.665383 + 0.746502i \(0.731732\pi\)
\(282\) 0.434938 + 0.164671i 0.0259002 + 0.00980604i
\(283\) 5.33804 + 11.4475i 0.317314 + 0.680482i 0.998675 0.0514659i \(-0.0163893\pi\)
−0.681361 + 0.731948i \(0.738612\pi\)
\(284\) 5.38757 2.92835i 0.319694 0.173765i
\(285\) 3.92749 + 0.748670i 0.232644 + 0.0443474i
\(286\) 4.79296 1.21840i 0.283413 0.0720456i
\(287\) 6.81890 3.17971i 0.402507 0.187692i
\(288\) −9.48650 12.9075i −0.558997 0.760584i
\(289\) 2.99525 3.56960i 0.176191 0.209976i
\(290\) 7.63442 + 1.11445i 0.448308 + 0.0654428i
\(291\) −0.660804 0.116518i −0.0387370 0.00683038i
\(292\) 1.05676 1.00373i 0.0618420 0.0587387i
\(293\) −10.1438 2.71801i −0.592605 0.158788i −0.0499614 0.998751i \(-0.515910\pi\)
−0.542643 + 0.839963i \(0.682576\pi\)
\(294\) −1.61297 2.36782i −0.0940703 0.138094i
\(295\) 1.70940 0.0725991i 0.0995249 0.00422688i
\(296\) 2.74752 8.86957i 0.159697 0.515533i
\(297\) −3.72817 + 0.998959i −0.216330 + 0.0579655i
\(298\) −8.38745 + 9.73853i −0.485872 + 0.564138i
\(299\) −5.40250 + 4.53323i −0.312434 + 0.262164i
\(300\) −4.10045 0.115282i −0.236740 0.00665583i
\(301\) −0.379985 2.15500i −0.0219020 0.124212i
\(302\) −15.7479 19.2657i −0.906192 1.10862i
\(303\) 0.639349 + 0.639349i 0.0367296 + 0.0367296i
\(304\) 6.29745 16.2586i 0.361184 0.932495i
\(305\) 2.01540 + 0.638088i 0.115402 + 0.0365368i
\(306\) −1.40629 + 13.9974i −0.0803922 + 0.800178i
\(307\) −5.64988 3.95609i −0.322456 0.225786i 0.401129 0.916022i \(-0.368618\pi\)
−0.723585 + 0.690236i \(0.757507\pi\)
\(308\) 3.86221 2.55883i 0.220070 0.145803i
\(309\) −3.15451 3.75940i −0.179454 0.213865i
\(310\) −18.5235 + 11.4380i −1.05207 + 0.649637i
\(311\) 26.3244 + 15.1984i 1.49272 + 0.861822i 0.999965 0.00834562i \(-0.00265652\pi\)
0.492755 + 0.870168i \(0.335990\pi\)
\(312\) 1.17237 + 2.22468i 0.0663726 + 0.125948i
\(313\) −6.83128 + 14.6497i −0.386127 + 0.828051i 0.613148 + 0.789968i \(0.289903\pi\)
−0.999275 + 0.0380832i \(0.987875\pi\)
\(314\) −23.3648 + 15.9162i −1.31855 + 0.898204i
\(315\) 4.89373 7.66151i 0.275730 0.431677i
\(316\) 21.9044 + 0.563745i 1.23222 + 0.0317131i
\(317\) 4.25232 2.97751i 0.238834 0.167233i −0.448032 0.894018i \(-0.647875\pi\)
0.686866 + 0.726784i \(0.258986\pi\)
\(318\) 0.134423 + 0.824222i 0.00753808 + 0.0462201i
\(319\) −3.01550 2.53030i −0.168835 0.141670i
\(320\) −3.71645 + 17.4982i −0.207756 + 0.978181i
\(321\) −3.35598 1.22148i −0.187312 0.0681761i
\(322\) −3.37679 + 5.67877i −0.188181 + 0.316466i
\(323\) −13.6704 + 6.89813i −0.760642 + 0.383822i
\(324\) 7.17656 + 13.2034i 0.398698 + 0.733524i
\(325\) −10.6678 1.90716i −0.591741 0.105790i
\(326\) 13.1679 + 29.2142i 0.729304 + 1.61803i
\(327\) −6.72972 + 0.588774i −0.372154 + 0.0325593i
\(328\) 11.7135 9.08216i 0.646768 0.501478i
\(329\) 1.13351 + 0.199869i 0.0624926 + 0.0110191i
\(330\) 1.74918 + 1.14922i 0.0962891 + 0.0632627i
\(331\) −20.6139 + 11.9014i −1.13304 + 0.654162i −0.944698 0.327941i \(-0.893645\pi\)
−0.188344 + 0.982103i \(0.560312\pi\)
\(332\) −1.56956 25.4743i −0.0861407 1.39808i
\(333\) −3.92875 + 8.42523i −0.215294 + 0.461700i
\(334\) 10.0184 9.76385i 0.548181 0.534254i
\(335\) −1.45892 + 32.5279i −0.0797095 + 1.77719i
\(336\) 1.72438 + 1.60511i 0.0940724 + 0.0875661i
\(337\) 7.50056 + 0.656214i 0.408582 + 0.0357463i 0.289594 0.957149i \(-0.406480\pi\)
0.118987 + 0.992896i \(0.462035\pi\)
\(338\) −3.87353 11.0841i −0.210692 0.602896i
\(339\) −0.898414 5.09516i −0.0487951 0.276731i
\(340\) 12.7165 9.22472i 0.689648 0.500280i
\(341\) 11.1075 0.601506
\(342\) −8.45255 + 15.2730i −0.457062 + 0.825870i
\(343\) −12.1204 12.1204i −0.654441 0.654441i
\(344\) −1.66973 3.97435i −0.0900260 0.214283i
\(345\) −2.95865 0.393091i −0.159288 0.0211633i
\(346\) 7.29674 15.1364i 0.392275 0.813738i
\(347\) −0.693008 + 7.92112i −0.0372026 + 0.425228i 0.954640 + 0.297761i \(0.0962400\pi\)
−0.991843 + 0.127466i \(0.959316\pi\)
\(348\) 0.892327 1.79175i 0.0478337 0.0960476i
\(349\) 23.9478 + 13.8262i 1.28189 + 0.740102i 0.977194 0.212347i \(-0.0681107\pi\)
0.304699 + 0.952449i \(0.401444\pi\)
\(350\) −10.0237 + 1.61034i −0.535791 + 0.0860760i
\(351\) −1.77332 4.87217i −0.0946530 0.260057i
\(352\) 6.30400 6.60006i 0.336004 0.351784i
\(353\) 2.90773 + 0.779123i 0.154763 + 0.0414685i 0.335368 0.942087i \(-0.391139\pi\)
−0.180606 + 0.983556i \(0.557806\pi\)
\(354\) 0.120392 0.427244i 0.00639874 0.0227077i
\(355\) 6.07737 + 3.17286i 0.322553 + 0.168398i
\(356\) −12.8609 + 32.6923i −0.681625 + 1.73269i
\(357\) −0.180318 2.06104i −0.00954343 0.109082i
\(358\) −22.1698 8.39368i −1.17171 0.443620i
\(359\) 26.0214 + 9.47103i 1.37336 + 0.499862i 0.920158 0.391547i \(-0.128060\pi\)
0.453201 + 0.891409i \(0.350282\pi\)
\(360\) 6.06057 16.8528i 0.319420 0.888221i
\(361\) −18.9635 + 1.17690i −0.998080 + 0.0619420i
\(362\) −16.5734 + 27.8715i −0.871076 + 1.46490i
\(363\) 1.45569 + 3.12173i 0.0764037 + 0.163848i
\(364\) 3.87648 + 4.86892i 0.203183 + 0.255201i
\(365\) 1.59045 + 0.354577i 0.0832479 + 0.0185594i
\(366\) 0.320333 0.445182i 0.0167441 0.0232700i
\(367\) 3.47346 + 4.96061i 0.181313 + 0.258942i 0.899512 0.436896i \(-0.143922\pi\)
−0.718199 + 0.695838i \(0.755033\pi\)
\(368\) −4.01093 + 12.3822i −0.209084 + 0.645467i
\(369\) −12.8512 + 7.41964i −0.669006 + 0.386251i
\(370\) 9.94377 2.98229i 0.516952 0.155042i
\(371\) 0.706896 + 1.94218i 0.0367002 + 0.100833i
\(372\) 1.32098 + 5.49142i 0.0684897 + 0.284717i
\(373\) −2.44427 9.12213i −0.126559 0.472326i 0.873331 0.487127i \(-0.161955\pi\)
−0.999890 + 0.0148012i \(0.995288\pi\)
\(374\) −7.99326 + 0.595806i −0.413322 + 0.0308084i
\(375\) −2.45039 3.87677i −0.126538 0.200195i
\(376\) 2.26479 0.110315i 0.116798 0.00568905i
\(377\) 3.03306 4.33166i 0.156211 0.223092i
\(378\) −3.07407 3.76075i −0.158113 0.193432i
\(379\) −15.1673 −0.779093 −0.389546 0.921007i \(-0.627368\pi\)
−0.389546 + 0.921007i \(0.627368\pi\)
\(380\) 19.0142 4.29664i 0.975407 0.220413i
\(381\) 4.68243 0.239888
\(382\) −19.6746 24.0694i −1.00664 1.23150i
\(383\) −6.32794 + 9.03723i −0.323342 + 0.461781i −0.947610 0.319430i \(-0.896509\pi\)
0.624267 + 0.781211i \(0.285398\pi\)
\(384\) 4.01270 + 2.33169i 0.204772 + 0.118989i
\(385\) 4.78315 + 1.98791i 0.243772 + 0.101313i
\(386\) −33.5592 + 2.50146i −1.70812 + 0.127321i
\(387\) 1.11703 + 4.16883i 0.0567821 + 0.211914i
\(388\) −3.18077 + 0.765146i −0.161479 + 0.0388444i
\(389\) −4.92394 13.5284i −0.249654 0.685918i −0.999699 0.0245316i \(-0.992191\pi\)
0.750045 0.661386i \(-0.230032\pi\)
\(390\) −1.33313 + 2.47535i −0.0675055 + 0.125344i
\(391\) 9.89913 5.71527i 0.500621 0.289033i
\(392\) −11.8186 7.44587i −0.596930 0.376073i
\(393\) 1.48491 + 2.12067i 0.0749037 + 0.106974i
\(394\) 9.21815 12.8109i 0.464404 0.645403i
\(395\) 13.1382 + 20.6770i 0.661055 + 1.04037i
\(396\) −7.14861 + 5.69150i −0.359231 + 0.286009i
\(397\) 5.64748 + 12.1111i 0.283439 + 0.607837i 0.995550 0.0942297i \(-0.0300388\pi\)
−0.712112 + 0.702066i \(0.752261\pi\)
\(398\) 7.65321 12.8705i 0.383621 0.645138i
\(399\) 0.802860 2.43842i 0.0401932 0.122074i
\(400\) −18.5547 + 7.46471i −0.927737 + 0.373236i
\(401\) 26.8970 + 9.78970i 1.34317 + 0.488874i 0.910810 0.412826i \(-0.135458\pi\)
0.432361 + 0.901701i \(0.357681\pi\)
\(402\) 7.90019 + 2.99109i 0.394026 + 0.149182i
\(403\) 1.30046 + 14.8644i 0.0647807 + 0.740446i
\(404\) 4.10236 + 1.61384i 0.204100 + 0.0802914i
\(405\) −7.77580 + 14.8939i −0.386382 + 0.740086i
\(406\) 1.34362 4.76821i 0.0666826 0.236642i
\(407\) −5.11621 1.37088i −0.253601 0.0679522i
\(408\) −1.24517 3.88091i −0.0616452 0.192134i
\(409\) 9.58204 + 26.3264i 0.473801 + 1.30176i 0.914675 + 0.404189i \(0.132446\pi\)
−0.440874 + 0.897569i \(0.645331\pi\)
\(410\) 15.7329 + 5.20475i 0.776993 + 0.257044i
\(411\) −5.54376 3.20069i −0.273453 0.157878i
\(412\) −21.4181 10.6666i −1.05519 0.525508i
\(413\) 0.0957465 1.09439i 0.00471138 0.0538513i
\(414\) 5.65854 11.7381i 0.278102 0.576897i
\(415\) 22.6591 17.3442i 1.11229 0.851393i
\(416\) 9.57043 + 7.66344i 0.469229 + 0.375731i
\(417\) 0.940028 + 0.940028i 0.0460334 + 0.0460334i
\(418\) −9.40617 3.23173i −0.460071 0.158069i
\(419\) −26.3188 −1.28576 −0.642878 0.765969i \(-0.722260\pi\)
−0.642878 + 0.765969i \(0.722260\pi\)
\(420\) −0.413952 + 2.60115i −0.0201988 + 0.126923i
\(421\) 3.95002 + 22.4017i 0.192512 + 1.09179i 0.915917 + 0.401367i \(0.131465\pi\)
−0.723405 + 0.690424i \(0.757424\pi\)
\(422\) −3.22917 9.24025i −0.157193 0.449809i
\(423\) −2.26148 0.197854i −0.109957 0.00961999i
\(424\) 2.20497 + 3.42294i 0.107083 + 0.166233i
\(425\) 16.4907 + 6.04656i 0.799919 + 0.293301i
\(426\) 1.27377 1.24141i 0.0617142 0.0601464i
\(427\) 0.573649 1.23020i 0.0277608 0.0595333i
\(428\) −17.3795 + 1.07081i −0.840069 + 0.0517595i
\(429\) 1.24228 0.717232i 0.0599779 0.0346283i
\(430\) 2.64648 4.02809i 0.127625 0.194252i
\(431\) 1.21244 + 0.213787i 0.0584014 + 0.0102977i 0.202773 0.979226i \(-0.435005\pi\)
−0.144371 + 0.989524i \(0.546116\pi\)
\(432\) −7.54566 5.88441i −0.363041 0.283114i
\(433\) 7.80478 0.682830i 0.375074 0.0328147i 0.101939 0.994791i \(-0.467495\pi\)
0.273134 + 0.961976i \(0.411940\pi\)
\(434\) 5.74408 + 12.7437i 0.275724 + 0.611719i
\(435\) 2.21911 0.289470i 0.106398 0.0138790i
\(436\) −28.9382 + 15.7290i −1.38589 + 0.753282i
\(437\) 14.0844 1.67339i 0.673748 0.0800491i
\(438\) 0.216069 0.363365i 0.0103242 0.0173623i
\(439\) −26.1519 9.51853i −1.24816 0.454295i −0.368383 0.929674i \(-0.620089\pi\)
−0.879781 + 0.475379i \(0.842311\pi\)
\(440\) 10.0560 + 1.73326i 0.479399 + 0.0826298i
\(441\) 10.7130 + 8.98930i 0.510145 + 0.428062i
\(442\) −1.73317 10.6270i −0.0824385 0.505476i
\(443\) 8.96026 6.27404i 0.425715 0.298089i −0.341016 0.940057i \(-0.610771\pi\)
0.766731 + 0.641969i \(0.221882\pi\)
\(444\) 0.0692938 2.69243i 0.00328854 0.127777i
\(445\) −38.3567 + 8.45568i −1.81828 + 0.400838i
\(446\) −32.1221 + 21.8817i −1.52103 + 1.03613i
\(447\) −1.57553 + 3.37873i −0.0745199 + 0.159809i
\(448\) 10.8323 + 3.81951i 0.511778 + 0.180455i
\(449\) 12.9742 + 7.49064i 0.612289 + 0.353505i 0.773861 0.633356i \(-0.218323\pi\)
−0.161572 + 0.986861i \(0.551656\pi\)
\(450\) 19.4178 4.88704i 0.915365 0.230377i
\(451\) −5.43474 6.47687i −0.255912 0.304984i
\(452\) −13.9321 21.0286i −0.655311 0.989102i
\(453\) −5.91229 4.13983i −0.277784 0.194506i
\(454\) −0.276529 + 2.75241i −0.0129781 + 0.129177i
\(455\) −2.10026 + 6.63368i −0.0984617 + 0.310992i
\(456\) 0.479084 5.03463i 0.0224351 0.235768i
\(457\) 4.27441 + 4.27441i 0.199949 + 0.199949i 0.799978 0.600029i \(-0.204844\pi\)
−0.600029 + 0.799978i \(0.704844\pi\)
\(458\) 13.5502 + 16.5770i 0.633157 + 0.774591i
\(459\) 1.45926 + 8.27587i 0.0681124 + 0.386285i
\(460\) −13.9912 + 4.00071i −0.652341 + 0.186534i
\(461\) 10.5629 8.86332i 0.491963 0.412806i −0.362766 0.931880i \(-0.618168\pi\)
0.854729 + 0.519074i \(0.173723\pi\)
\(462\) 0.876974 1.01824i 0.0408005 0.0473729i
\(463\) −16.9826 + 4.55047i −0.789248 + 0.211478i −0.630858 0.775898i \(-0.717297\pi\)
−0.158390 + 0.987377i \(0.550630\pi\)
\(464\) 0.502004 9.74629i 0.0233050 0.452460i
\(465\) −4.27170 + 4.65064i −0.198095 + 0.215668i
\(466\) −21.3955 31.4084i −0.991129 1.45497i
\(467\) −36.1165 9.67738i −1.67127 0.447816i −0.705818 0.708393i \(-0.749420\pi\)
−0.965453 + 0.260577i \(0.916087\pi\)
\(468\) −8.45347 8.90009i −0.390762 0.411407i
\(469\) 20.5891 + 3.63041i 0.950715 + 0.167637i
\(470\) 1.51486 + 2.03273i 0.0698754 + 0.0937628i
\(471\) −5.27102 + 6.28176i −0.242876 + 0.289448i
\(472\) −0.293287 2.14422i −0.0134996 0.0986957i
\(473\) −2.22866 + 1.03924i −0.102474 + 0.0477845i
\(474\) 6.15980 1.56586i 0.282929 0.0719225i
\(475\) 15.8456 + 14.9638i 0.727048 + 0.686587i
\(476\) −4.81716 8.86261i −0.220794 0.406217i
\(477\) −1.72277 3.69448i −0.0788801 0.169159i
\(478\) 3.05153 + 1.15534i 0.139574 + 0.0528440i
\(479\) 31.0398 + 26.0455i 1.41825 + 1.19005i 0.952271 + 0.305253i \(0.0987410\pi\)
0.465976 + 0.884798i \(0.345703\pi\)
\(480\) 0.339022 + 5.17767i 0.0154742 + 0.236327i
\(481\) 1.23555 7.00714i 0.0563362 0.319498i
\(482\) 0.690767 + 1.23280i 0.0314636 + 0.0561527i
\(483\) −0.496001 + 1.85110i −0.0225688 + 0.0842280i
\(484\) 12.5827 + 11.1222i 0.571942 + 0.505554i
\(485\) −2.69377 2.47428i −0.122318 0.112351i
\(486\) 10.1261 + 10.3900i 0.459328 + 0.471302i
\(487\) −3.84310 14.3426i −0.174147 0.649927i −0.996695 0.0812309i \(-0.974115\pi\)
0.822548 0.568696i \(-0.192552\pi\)
\(488\) 0.565608 2.61352i 0.0256039 0.118309i
\(489\) 5.97465 + 7.12031i 0.270183 + 0.321992i
\(490\) −0.461888 15.6105i −0.0208660 0.705210i
\(491\) 34.5960 6.10021i 1.56130 0.275299i 0.674788 0.738012i \(-0.264235\pi\)
0.886508 + 0.462713i \(0.153124\pi\)
\(492\) 2.55575 3.45714i 0.115222 0.155860i
\(493\) −6.06040 + 6.06040i −0.272946 + 0.272946i
\(494\) 3.22352 12.9659i 0.145033 0.583365i
\(495\) −9.73966 3.08363i −0.437765 0.138599i
\(496\) 16.5923 + 21.9776i 0.745016 + 0.986825i
\(497\) 2.52487 3.60589i 0.113256 0.161746i
\(498\) −2.44230 6.98864i −0.109442 0.313168i
\(499\) 17.7092 14.8598i 0.792771 0.665214i −0.153658 0.988124i \(-0.549106\pi\)
0.946430 + 0.322910i \(0.104661\pi\)
\(500\) −18.4988 12.5616i −0.827291 0.561773i
\(501\) 2.02887 3.51411i 0.0906433 0.156999i
\(502\) −0.302936 + 23.5452i −0.0135207 + 1.05087i
\(503\) −24.9368 11.6282i −1.11188 0.518477i −0.222171 0.975008i \(-0.571314\pi\)
−0.889708 + 0.456530i \(0.849092\pi\)
\(504\) −10.2267 5.25838i −0.455533 0.234227i
\(505\) 1.06105 + 4.81316i 0.0472162 + 0.214183i
\(506\) 7.14626 + 2.01372i 0.317690 + 0.0895208i
\(507\) −1.95345 2.78981i −0.0867556 0.123900i
\(508\) 20.9320 9.11268i 0.928708 0.404310i
\(509\) −0.760612 + 0.906462i −0.0337135 + 0.0401782i −0.782638 0.622477i \(-0.786126\pi\)
0.748924 + 0.662656i \(0.230571\pi\)
\(510\) 2.82457 3.57585i 0.125074 0.158341i
\(511\) 0.357847 0.983177i 0.0158302 0.0434932i
\(512\) 22.4759 + 2.61415i 0.993304 + 0.115530i
\(513\) −2.38543 + 10.1509i −0.105319 + 0.448174i
\(514\) 26.6178 6.76643i 1.17406 0.298454i
\(515\) −3.46024 26.5267i −0.152477 1.16890i
\(516\) −0.778837 0.978230i −0.0342864 0.0430642i
\(517\) −0.112731 1.28852i −0.00495791 0.0566691i
\(518\) −1.07294 6.57880i −0.0471423 0.289056i
\(519\) 0.846360 4.79994i 0.0371511 0.210694i
\(520\) −1.14214 + 13.6601i −0.0500862 + 0.599033i
\(521\) −5.85745 10.1454i −0.256620 0.444478i 0.708714 0.705495i \(-0.249275\pi\)
−0.965334 + 0.261017i \(0.915942\pi\)
\(522\) −1.82030 + 9.59954i −0.0796722 + 0.420160i
\(523\) 27.4921 + 12.8198i 1.20214 + 0.560569i 0.917374 0.398027i \(-0.130305\pi\)
0.284770 + 0.958596i \(0.408083\pi\)
\(524\) 10.7651 + 6.59024i 0.470277 + 0.287896i
\(525\) −2.67182 + 1.23817i −0.116608 + 0.0540381i
\(526\) −3.10866 41.7053i −0.135544 1.81844i
\(527\) 2.10777 24.0920i 0.0918161 1.04946i
\(528\) 1.24076 2.33860i 0.0539973 0.101775i
\(529\) 12.2235 2.15534i 0.531458 0.0937103i
\(530\) −1.80100 + 4.18084i −0.0782306 + 0.181604i
\(531\) 2.16671i 0.0940272i
\(532\) −1.15646 12.4630i −0.0501389 0.540340i
\(533\) 8.03122 8.03122i 0.347871 0.347871i
\(534\) −1.01865 + 10.1391i −0.0440814 + 0.438761i
\(535\) −11.8328 15.4588i −0.511578 0.668344i
\(536\) 41.1375 2.00375i 1.77687 0.0865489i
\(537\) −6.84987 0.599286i −0.295594 0.0258611i
\(538\) −10.2041 + 11.8479i −0.439932 + 0.510798i
\(539\) −3.98407 + 6.90062i −0.171606 + 0.297231i
\(540\) 0.754165 10.6717i 0.0324541 0.459237i
\(541\) 6.07646 2.21165i 0.261247 0.0950862i −0.208076 0.978113i \(-0.566720\pi\)
0.469323 + 0.883026i \(0.344498\pi\)
\(542\) 29.7499 + 5.64128i 1.27787 + 0.242314i
\(543\) −2.43438 + 9.08525i −0.104469 + 0.389885i
\(544\) −13.1191 14.9257i −0.562478 0.639933i
\(545\) −32.6433 17.0423i −1.39829 0.730014i
\(546\) 1.46531 + 1.05437i 0.0627095 + 0.0451230i
\(547\) −17.7638 + 1.55413i −0.759526 + 0.0664499i −0.460337 0.887744i \(-0.652272\pi\)
−0.299189 + 0.954194i \(0.596716\pi\)
\(548\) −31.0114 3.51920i −1.32474 0.150333i
\(549\) −0.915639 + 2.51570i −0.0390785 + 0.107367i
\(550\) 4.66337 + 10.4121i 0.198847 + 0.443972i
\(551\) −9.87598 + 3.94524i −0.420731 + 0.168073i
\(552\) −0.145677 + 3.77251i −0.00620043 + 0.160569i
\(553\) 14.2561 6.64771i 0.606229 0.282689i
\(554\) −3.23534 7.17788i −0.137456 0.304959i
\(555\) 2.54156 1.61491i 0.107883 0.0685491i
\(556\) 6.03166 + 2.37281i 0.255800 + 0.100629i
\(557\) 6.35217 4.44784i 0.269150 0.188461i −0.431208 0.902253i \(-0.641913\pi\)
0.700358 + 0.713792i \(0.253024\pi\)
\(558\) −13.4766 24.0515i −0.570509 1.01818i
\(559\) −1.65167 2.86078i −0.0698583 0.120998i
\(560\) 3.21170 + 12.4336i 0.135719 + 0.525415i
\(561\) −2.18475 + 0.795183i −0.0922401 + 0.0335727i
\(562\) −1.41613 0.0182202i −0.0597360 0.000768573i
\(563\) 19.2062 5.14628i 0.809444 0.216890i 0.169718 0.985493i \(-0.445714\pi\)
0.639726 + 0.768603i \(0.279048\pi\)
\(564\) 0.623623 0.208973i 0.0262593 0.00879934i
\(565\) 10.8236 26.0429i 0.455351 1.09563i
\(566\) 16.0907 + 7.75679i 0.676343 + 0.326042i
\(567\) 8.83704 + 6.18776i 0.371121 + 0.259861i
\(568\) 3.27821 8.02843i 0.137550 0.336865i
\(569\) 24.0585i 1.00859i −0.863533 0.504293i \(-0.831753\pi\)
0.863533 0.504293i \(-0.168247\pi\)
\(570\) 4.97050 2.69544i 0.208191 0.112900i
\(571\) 41.3229i 1.72931i −0.502366 0.864655i \(-0.667537\pi\)
0.502366 0.864655i \(-0.332463\pi\)
\(572\) 4.15757 5.62392i 0.173837 0.235148i
\(573\) −7.38647 5.17207i −0.308574 0.216066i
\(574\) 4.62047 9.58473i 0.192855 0.400059i
\(575\) −12.4383 10.4874i −0.518713 0.437357i
\(576\) −21.9399 5.64252i −0.914162 0.235105i
\(577\) −35.3229 + 9.46473i −1.47051 + 0.394022i −0.903106 0.429417i \(-0.858719\pi\)
−0.567404 + 0.823439i \(0.692052\pi\)
\(578\) 0.0847799 6.58938i 0.00352638 0.274082i
\(579\) −9.17253 + 3.33853i −0.381198 + 0.138745i
\(580\) 9.35681 5.61273i 0.388520 0.233056i
\(581\) −9.16100 15.8673i −0.380062 0.658287i
\(582\) −0.827837 + 0.463855i −0.0343150 + 0.0192274i
\(583\) 1.90257 1.33220i 0.0787965 0.0551739i
\(584\) 0.258740 2.04486i 0.0107067 0.0846170i
\(585\) 2.98628 13.3949i 0.123467 0.553810i
\(586\) −13.5397 + 6.10283i −0.559318 + 0.252106i
\(587\) −17.4504 + 8.13725i −0.720255 + 0.335860i −0.747949 0.663756i \(-0.768961\pi\)
0.0276944 + 0.999616i \(0.491183\pi\)
\(588\) −3.88539 1.14901i −0.160231 0.0473843i
\(589\) 14.1917 26.4405i 0.584761 1.08946i
\(590\) 1.80673 1.60945i 0.0743821 0.0662599i
\(591\) 1.56575 4.30185i 0.0644061 0.176954i
\(592\) −4.93008 12.1709i −0.202625 0.500220i
\(593\) −28.7332 + 2.51383i −1.17993 + 0.103231i −0.660194 0.751095i \(-0.729526\pi\)
−0.519737 + 0.854326i \(0.673970\pi\)
\(594\) −3.18808 + 4.43062i −0.130809 + 0.181791i
\(595\) 5.21939 9.99733i 0.213974 0.409851i
\(596\) −0.467639 + 18.1702i −0.0191553 + 0.744282i
\(597\) 1.12415 4.19537i 0.0460082 0.171705i
\(598\) −1.85813 + 9.79907i −0.0759846 + 0.400714i
\(599\) 17.1652 6.24762i 0.701351 0.255271i 0.0333634 0.999443i \(-0.489378\pi\)
0.667988 + 0.744172i \(0.267156\pi\)
\(600\) −4.59300 + 3.54378i −0.187508 + 0.144674i
\(601\) 12.6291 21.8742i 0.515152 0.892269i −0.484694 0.874684i \(-0.661069\pi\)
0.999845 0.0175849i \(-0.00559774\pi\)
\(602\) −2.34485 2.01953i −0.0955690 0.0823101i
\(603\) −41.0775 3.59381i −1.67280 0.146351i
\(604\) −34.4866 7.00025i −1.40324 0.284836i
\(605\) −2.47286 + 18.6123i −0.100536 + 0.756700i
\(606\) 1.27229 + 0.127825i 0.0516834 + 0.00519252i
\(607\) 17.0786 17.0786i 0.693198 0.693198i −0.269736 0.962934i \(-0.586937\pi\)
0.962934 + 0.269736i \(0.0869366\pi\)
\(608\) −7.65645 23.4388i −0.310510 0.950570i
\(609\) 1.43693i 0.0582273i
\(610\) 2.77788 1.10516i 0.112473 0.0447467i
\(611\) 1.71113 0.301719i 0.0692251 0.0122062i
\(612\) 10.9882 + 16.5852i 0.444172 + 0.670417i
\(613\) 0.655881 7.49676i 0.0264908 0.302791i −0.971378 0.237539i \(-0.923659\pi\)
0.997869 0.0652522i \(-0.0207852\pi\)
\(614\) −9.72717 + 0.725050i −0.392557 + 0.0292606i
\(615\) 4.80190 + 0.215372i 0.193631 + 0.00868464i
\(616\) 1.93872 6.25859i 0.0781133 0.252166i
\(617\) 4.71744 + 2.19978i 0.189917 + 0.0885598i 0.515251 0.857040i \(-0.327699\pi\)
−0.325334 + 0.945599i \(0.605477\pi\)
\(618\) −6.81882 1.29301i −0.274293 0.0520124i
\(619\) 17.6557 + 30.5807i 0.709644 + 1.22914i 0.964989 + 0.262290i \(0.0844777\pi\)
−0.255345 + 0.966850i \(0.582189\pi\)
\(620\) −10.0451 + 29.1032i −0.403421 + 1.16881i
\(621\) 1.35169 7.66580i 0.0542413 0.307618i
\(622\) 42.4270 6.91946i 1.70117 0.277445i
\(623\) 2.19803 + 25.1236i 0.0880624 + 1.00656i
\(624\) 3.27484 + 1.38662i 0.131099 + 0.0555091i
\(625\) 0.118814 24.9997i 0.00475255 0.999989i
\(626\) 5.63194 + 22.1550i 0.225098 + 0.885491i
\(627\) −2.88033 0.162264i −0.115029 0.00648020i
\(628\) −11.3380 + 38.3397i −0.452436 + 1.52992i
\(629\) −3.94428 + 10.8368i −0.157269 + 0.432092i
\(630\) −1.49884 12.7690i −0.0597152 0.508730i
\(631\) −9.02797 + 10.7591i −0.359398 + 0.428313i −0.915199 0.403001i \(-0.867967\pi\)
0.555802 + 0.831315i \(0.312411\pi\)
\(632\) 24.4890 18.9878i 0.974118 0.755293i
\(633\) −1.62849 2.32572i −0.0647266 0.0924392i
\(634\) 1.99116 7.06618i 0.0790789 0.280634i
\(635\) 21.5106 + 13.7397i 0.853624 + 0.545245i
\(636\) 0.884888 + 0.782175i 0.0350881 + 0.0310152i
\(637\) −9.70103 4.52367i −0.384369 0.179234i
\(638\) −5.56652 0.0716197i −0.220381 0.00283545i
\(639\) −4.34103 + 7.51888i −0.171728 + 0.297442i
\(640\) 11.5920 + 22.4861i 0.458215 + 0.888841i
\(641\) −10.2710 + 8.61842i −0.405681 + 0.340407i −0.822685 0.568498i \(-0.807525\pi\)
0.417003 + 0.908905i \(0.363080\pi\)
\(642\) −4.76790 + 1.66623i −0.188174 + 0.0657607i
\(643\) 24.4754 34.9545i 0.965216 1.37847i 0.0399290 0.999203i \(-0.487287\pi\)
0.925287 0.379268i \(-0.123824\pi\)
\(644\) 1.38522 + 9.24032i 0.0545852 + 0.364119i
\(645\) 0.421970 1.33280i 0.0166151 0.0524788i
\(646\) −8.79448 + 19.7885i −0.346014 + 0.778569i
\(647\) 1.41944 1.41944i 0.0558038 0.0558038i −0.678654 0.734458i \(-0.737436\pi\)
0.734458 + 0.678654i \(0.237436\pi\)
\(648\) 19.6754 + 8.03397i 0.772924 + 0.315604i
\(649\) −1.21577 + 0.214373i −0.0477231 + 0.00841487i
\(650\) −13.3877 + 7.45968i −0.525109 + 0.292593i
\(651\) 2.60624 + 3.10600i 0.102147 + 0.121734i
\(652\) 40.5658 + 20.2026i 1.58868 + 0.791196i
\(653\) 2.89127 + 10.7904i 0.113144 + 0.422260i 0.999141 0.0414306i \(-0.0131916\pi\)
−0.885997 + 0.463691i \(0.846525\pi\)
\(654\) −6.84177 + 6.66795i −0.267534 + 0.260738i
\(655\) 0.598807 + 14.0993i 0.0233973 + 0.550906i
\(656\) 4.69695 20.4284i 0.183385 0.797596i
\(657\) −0.534092 + 1.99326i −0.0208369 + 0.0777644i
\(658\) 1.42003 0.795676i 0.0553587 0.0310187i
\(659\) 6.00184 34.0381i 0.233799 1.32594i −0.611330 0.791375i \(-0.709365\pi\)
0.845129 0.534562i \(-0.179524\pi\)
\(660\) 2.94386 0.307212i 0.114590 0.0119582i
\(661\) −6.02515 5.05570i −0.234351 0.196644i 0.518048 0.855352i \(-0.326659\pi\)
−0.752399 + 0.658708i \(0.771103\pi\)
\(662\) −11.9192 + 31.4815i −0.463253 + 1.22356i
\(663\) −1.31992 2.83058i −0.0512616 0.109931i
\(664\) −24.5188 26.4884i −0.951513 1.02795i
\(665\) 10.8433 8.84600i 0.420487 0.343033i
\(666\) 3.23900 + 12.7416i 0.125509 + 0.493726i
\(667\) 7.19507 3.35512i 0.278594 0.129911i
\(668\) 2.23077 19.6577i 0.0863111 0.760579i
\(669\) −7.24664 + 8.63621i −0.280171 + 0.333895i
\(670\) 27.5159 + 36.9224i 1.06303 + 1.42644i
\(671\) −1.50218 0.264875i −0.0579911 0.0102254i
\(672\) 3.32473 + 0.214166i 0.128254 + 0.00826164i
\(673\) 39.4757 + 10.5775i 1.52168 + 0.407732i 0.920293 0.391230i \(-0.127950\pi\)
0.601382 + 0.798961i \(0.294617\pi\)
\(674\) 8.80011 5.99468i 0.338968 0.230906i
\(675\) 10.3728 5.95591i 0.399249 0.229243i
\(676\) −14.1619 8.66968i −0.544689 0.333449i
\(677\) −41.4191 + 11.0982i −1.59186 + 0.426539i −0.942573 0.334000i \(-0.891601\pi\)
−0.649292 + 0.760539i \(0.724935\pi\)
\(678\) −5.54402 4.77487i −0.212917 0.183378i
\(679\) −1.79908 + 1.50960i −0.0690422 + 0.0579333i
\(680\) 5.66762 21.4822i 0.217343 0.823807i
\(681\) 0.139332 + 0.790194i 0.00533923 + 0.0302803i
\(682\) 12.1622 9.94152i 0.465716 0.380680i
\(683\) 1.37971 + 1.37971i 0.0527929 + 0.0527929i 0.733010 0.680217i \(-0.238115\pi\)
−0.680217 + 0.733010i \(0.738115\pi\)
\(684\) 4.41457 + 24.2885i 0.168795 + 0.928695i
\(685\) −16.0756 30.9708i −0.614218 1.18333i
\(686\) −24.1194 2.42322i −0.920883 0.0925192i
\(687\) 5.08717 + 3.56208i 0.194088 + 0.135902i
\(688\) −5.38543 2.85728i −0.205318 0.108933i
\(689\) 2.00553 + 2.39010i 0.0764046 + 0.0910555i
\(690\) −3.59142 + 2.21765i −0.136723 + 0.0844247i
\(691\) −0.893161 0.515667i −0.0339774 0.0196169i 0.482915 0.875667i \(-0.339578\pi\)
−0.516893 + 0.856050i \(0.672911\pi\)
\(692\) −5.55787 23.1045i −0.211278 0.878300i
\(693\) −2.77222 + 5.94505i −0.105308 + 0.225834i
\(694\) 6.33079 + 9.29353i 0.240314 + 0.352778i
\(695\) 1.56006 + 7.07674i 0.0591763 + 0.268436i
\(696\) −0.626601 2.76054i −0.0237512 0.104638i
\(697\) −15.0795 + 10.5588i −0.571177 + 0.399942i
\(698\) 38.5966 6.29475i 1.46090 0.238260i
\(699\) −8.44432 7.08562i −0.319393 0.268003i
\(700\) −9.53425 + 10.7347i −0.360361 + 0.405735i
\(701\) −15.2061 5.53457i −0.574327 0.209038i 0.0384952 0.999259i \(-0.487744\pi\)
−0.612822 + 0.790221i \(0.709966\pi\)
\(702\) −6.30243 3.74763i −0.237870 0.141445i
\(703\) −9.80011 + 10.4272i −0.369618 + 0.393268i
\(704\) 0.995371 12.8690i 0.0375144 0.485019i
\(705\) 0.582849 + 0.448337i 0.0219514 + 0.0168853i
\(706\) 3.88117 1.74939i 0.146070 0.0658390i
\(707\) 3.15262 0.275818i 0.118566 0.0103732i
\(708\) −0.250571 0.575566i −0.00941703 0.0216311i
\(709\) 42.2175 + 7.44408i 1.58551 + 0.279568i 0.895780 0.444498i \(-0.146618\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(710\) 9.49424 1.96526i 0.356313 0.0737550i
\(711\) −26.8676 + 15.5120i −1.00761 + 0.581745i
\(712\) 15.1784 + 47.3074i 0.568833 + 1.77292i
\(713\) −9.46716 + 20.3024i −0.354548 + 0.760331i
\(714\) −2.04213 2.09536i −0.0764247 0.0784169i
\(715\) 7.81150 + 0.350357i 0.292134 + 0.0131026i
\(716\) −31.7875 + 10.6518i −1.18795 + 0.398077i
\(717\) 0.942843 + 0.0824881i 0.0352111 + 0.00308057i
\(718\) 36.9691 12.9195i 1.37968 0.482152i
\(719\) 2.49948 + 14.1753i 0.0932150 + 0.528649i 0.995280 + 0.0970478i \(0.0309400\pi\)
−0.902065 + 0.431601i \(0.857949\pi\)
\(720\) −8.44766 23.8775i −0.314826 0.889860i
\(721\) −17.1767 −0.639693
\(722\) −19.7109 + 18.2615i −0.733562 + 0.679622i
\(723\) 0.289840 + 0.289840i 0.0107793 + 0.0107793i
\(724\) 6.79868 + 45.3517i 0.252671 + 1.68548i
\(725\) 11.0438 + 5.18178i 0.410155 + 0.192447i
\(726\) 4.38794 + 2.11528i 0.162852 + 0.0785053i
\(727\) 2.57770 29.4632i 0.0956015 1.09273i −0.785199 0.619243i \(-0.787439\pi\)
0.880801 0.473487i \(-0.157005\pi\)
\(728\) 8.60238 + 1.86169i 0.318826 + 0.0689990i
\(729\) −15.8772 9.16669i −0.588043 0.339507i
\(730\) 2.05883 1.03525i 0.0762006 0.0383162i
\(731\) 1.83118 + 5.03113i 0.0677287 + 0.186083i
\(732\) −0.0476987 0.774161i −0.00176299 0.0286138i
\(733\) 19.0542 + 5.10556i 0.703784 + 0.188578i 0.592925 0.805258i \(-0.297973\pi\)
0.110859 + 0.993836i \(0.464640\pi\)
\(734\) 8.24316 + 2.32281i 0.304261 + 0.0857366i
\(735\) −1.35705 4.32192i −0.0500557 0.159417i
\(736\) 6.69061 + 17.1479i 0.246619 + 0.632078i
\(737\) −2.04764 23.4047i −0.0754259 0.862122i
\(738\) −7.43071 + 19.6263i −0.273528 + 0.722455i
\(739\) −31.1961 11.3545i −1.14757 0.417680i −0.302926 0.953014i \(-0.597964\pi\)
−0.844641 + 0.535334i \(0.820186\pi\)
\(740\) 8.21876 12.1654i 0.302128 0.447209i
\(741\) −0.120082 3.87353i −0.00441134 0.142298i
\(742\) 2.51232 + 1.49391i 0.0922303 + 0.0548432i
\(743\) −14.9358 32.0299i −0.547940 1.17506i −0.964044 0.265744i \(-0.914382\pi\)
0.416103 0.909317i \(-0.363395\pi\)
\(744\) 6.36138 + 4.83055i 0.233220 + 0.177096i
\(745\) −17.1521 + 10.8985i −0.628404 + 0.399289i
\(746\) −10.8409 7.80064i −0.396914 0.285602i
\(747\) 20.7271 + 29.6014i 0.758365 + 1.08306i
\(748\) −8.21900 + 7.80656i −0.300516 + 0.285436i
\(749\) −10.8253 + 6.24996i −0.395546 + 0.228369i
\(750\) −6.15288 2.05173i −0.224671 0.0749184i
\(751\) 13.9080 + 38.2118i 0.507509 + 1.39437i 0.883799 + 0.467867i \(0.154977\pi\)
−0.376290 + 0.926502i \(0.622801\pi\)
\(752\) 2.38111 2.14783i 0.0868301 0.0783235i
\(753\) 1.76776 + 6.59737i 0.0644207 + 0.240421i
\(754\) −0.555883 7.45765i −0.0202441 0.271591i
\(755\) −15.0129 36.3665i −0.546376 1.32351i
\(756\) −6.73195 1.36648i −0.244839 0.0496985i
\(757\) −28.2375 + 40.3273i −1.02631 + 1.46572i −0.147194 + 0.989108i \(0.547024\pi\)
−0.879114 + 0.476612i \(0.841865\pi\)
\(758\) −16.6075 + 13.5751i −0.603213 + 0.493072i
\(759\) 2.15357 0.0781696
\(760\) 16.9741 21.7228i 0.615714 0.787970i
\(761\) 23.2191 0.841693 0.420847 0.907132i \(-0.361733\pi\)
0.420847 + 0.907132i \(0.361733\pi\)
\(762\) 5.12706 4.19090i 0.185734 0.151820i
\(763\) −13.5618 + 19.3683i −0.490971 + 0.701179i
\(764\) −43.0855 8.74571i −1.55878 0.316409i
\(765\) −8.53653 + 20.5400i −0.308639 + 0.742624i
\(766\) 1.15975 + 15.5590i 0.0419034 + 0.562171i
\(767\) −0.429221 1.60187i −0.0154983 0.0578403i
\(768\) 6.48066 1.03837i 0.233851 0.0374690i
\(769\) −0.971250 2.66849i −0.0350242 0.0962281i 0.920948 0.389686i \(-0.127416\pi\)
−0.955972 + 0.293457i \(0.905194\pi\)
\(770\) 7.01657 2.10438i 0.252860 0.0758365i
\(771\) 6.89905 3.98317i 0.248463 0.143450i
\(772\) −34.5070 + 32.7754i −1.24193 + 1.17961i
\(773\) 10.3901 + 14.8387i 0.373707 + 0.533710i 0.961320 0.275433i \(-0.0888211\pi\)
−0.587613 + 0.809142i \(0.699932\pi\)
\(774\) 4.95432 + 3.56491i 0.178079 + 0.128138i
\(775\) −33.2702 + 8.83004i −1.19510 + 0.317184i
\(776\) −2.79798 + 3.68467i −0.100442 + 0.132272i
\(777\) −0.817116 1.75231i −0.0293139 0.0628638i
\(778\) −17.4998 10.4060i −0.627398 0.373072i
\(779\) −22.3615 + 4.66163i −0.801183 + 0.167020i
\(780\) 0.755785 + 3.90358i 0.0270614 + 0.139770i
\(781\) −4.64844 1.69189i −0.166334 0.0605407i
\(782\) 5.72380 15.1179i 0.204683 0.540617i
\(783\) 0.508688 + 5.81433i 0.0181790 + 0.207787i
\(784\) −19.6051 + 2.42508i −0.700183 + 0.0866100i
\(785\) −42.6472 + 13.3909i −1.52214 + 0.477943i
\(786\) 3.52396 + 0.993005i 0.125695 + 0.0354193i
\(787\) 31.2109 + 8.36294i 1.11255 + 0.298107i 0.767865 0.640612i \(-0.221319\pi\)
0.344684 + 0.938719i \(0.387986\pi\)
\(788\) −1.37261 22.2778i −0.0488973 0.793615i
\(789\) −4.14891 11.3990i −0.147705 0.405817i
\(790\) 32.8923 + 10.8814i 1.17025 + 0.387143i
\(791\) −15.6823 9.05421i −0.557600 0.321930i
\(792\) −2.73336 + 12.6301i −0.0971259 + 0.448792i
\(793\) 0.178588 2.04127i 0.00634184 0.0724876i
\(794\) 17.0235 + 8.20643i 0.604140 + 0.291235i
\(795\) −0.173906 + 1.30893i −0.00616780 + 0.0464228i
\(796\) −3.13948 20.9424i −0.111276 0.742284i
\(797\) −6.03551 6.03551i −0.213789 0.213789i 0.592086 0.805875i \(-0.298305\pi\)
−0.805875 + 0.592086i \(0.798305\pi\)
\(798\) −1.30335 3.38854i −0.0461382 0.119953i
\(799\) −2.81617 −0.0996289
\(800\) −13.6355 + 24.7805i −0.482087 + 0.876123i
\(801\) −8.63740 48.9851i −0.305187 1.73080i
\(802\) 38.2130 13.3542i 1.34935 0.471554i
\(803\) −1.17129 0.102474i −0.0413338 0.00361624i
\(804\) 11.3275 3.79577i 0.399489 0.133867i
\(805\) −7.71029 + 7.04835i −0.271752 + 0.248422i
\(806\) 14.7279 + 15.1119i 0.518770 + 0.532293i
\(807\) −1.91678 + 4.11055i −0.0674740 + 0.144698i
\(808\) 5.93633 1.90464i 0.208839 0.0670052i
\(809\) −27.1152 + 15.6549i −0.953319 + 0.550399i −0.894110 0.447847i \(-0.852191\pi\)
−0.0592083 + 0.998246i \(0.518858\pi\)
\(810\) 4.81631 + 23.2677i 0.169228 + 0.817545i
\(811\) 15.3524 + 2.70704i 0.539095 + 0.0950569i 0.436564 0.899673i \(-0.356195\pi\)
0.102530 + 0.994730i \(0.467306\pi\)
\(812\) −2.79647 6.42355i −0.0981368 0.225422i
\(813\) 8.74962 0.765493i 0.306863 0.0268470i
\(814\) −6.82900 + 3.07809i −0.239356 + 0.107887i
\(815\) 6.55370 + 50.2415i 0.229566 + 1.75988i
\(816\) −4.83692 3.13496i −0.169326 0.109746i
\(817\) −0.373669 + 6.63296i −0.0130730 + 0.232058i
\(818\) 34.0548 + 20.2501i 1.19070 + 0.708028i
\(819\) −8.28039 3.01382i −0.289340 0.105311i
\(820\) 21.8852 8.38239i 0.764265 0.292726i
\(821\) 12.0645 + 10.1233i 0.421055 + 0.353307i 0.828564 0.559894i \(-0.189158\pi\)
−0.407509 + 0.913201i \(0.633603\pi\)
\(822\) −8.93487 + 1.45720i −0.311639 + 0.0508255i
\(823\) 30.4333 21.3096i 1.06084 0.742806i 0.0933264 0.995636i \(-0.470250\pi\)
0.967511 + 0.252829i \(0.0813611\pi\)
\(824\) −32.9987 + 7.49022i −1.14957 + 0.260934i
\(825\) 2.12109 + 2.54005i 0.0738468 + 0.0884331i
\(826\) −0.874667 1.28400i −0.0304336 0.0446761i
\(827\) −11.3226 + 24.2814i −0.393725 + 0.844346i 0.605112 + 0.796140i \(0.293128\pi\)
−0.998837 + 0.0482062i \(0.984650\pi\)
\(828\) −4.31006 17.9173i −0.149785 0.622668i
\(829\) 1.82415 + 1.05318i 0.0633555 + 0.0365783i 0.531343 0.847157i \(-0.321687\pi\)
−0.467988 + 0.883735i \(0.655021\pi\)
\(830\) 9.28718 39.2716i 0.322363 1.36314i
\(831\) −1.46796 1.74945i −0.0509230 0.0606877i
\(832\) 17.3382 0.174668i 0.601093 0.00605552i
\(833\) 14.2113 + 9.95083i 0.492391 + 0.344776i
\(834\) 1.87064 + 0.187939i 0.0647749 + 0.00650780i
\(835\) 19.6319 10.1901i 0.679391 0.352643i
\(836\) −13.1918 + 4.88016i −0.456249 + 0.168784i
\(837\) −11.6453 11.6453i −0.402522 0.402522i
\(838\) −28.8179 + 23.5560i −0.995497 + 0.813728i
\(839\) 1.12548 + 6.38292i 0.0388559 + 0.220363i 0.998053 0.0623765i \(-0.0198680\pi\)
−0.959197 + 0.282739i \(0.908757\pi\)
\(840\) 1.87484 + 3.21864i 0.0646880 + 0.111054i
\(841\) 17.6553 14.8146i 0.608804 0.510847i
\(842\) 24.3752 + 20.9935i 0.840024 + 0.723482i
\(843\) −0.396801 + 0.106322i −0.0136666 + 0.00366194i
\(844\) −11.8061 7.22748i −0.406382 0.248780i
\(845\) −0.787750 18.5481i −0.0270994 0.638075i
\(846\) −2.65331 + 1.80744i −0.0912226 + 0.0621412i
\(847\) 11.6449 + 3.12025i 0.400125 + 0.107213i
\(848\) 5.47796 + 1.77446i 0.188114 + 0.0609352i
\(849\) 5.10257 + 0.899721i 0.175120 + 0.0308783i
\(850\) 23.4685 8.13894i 0.804962 0.279163i
\(851\) 6.86636 8.18301i 0.235376 0.280510i
\(852\) 0.283627 2.49934i 0.00971690 0.0856260i
\(853\) −34.5133 + 16.0938i −1.18171 + 0.551041i −0.911316 0.411708i \(-0.864932\pi\)
−0.270396 + 0.962749i \(0.587155\pi\)
\(854\) −0.472936 1.86044i −0.0161836 0.0636630i
\(855\) −19.7844 + 19.2446i −0.676612 + 0.658150i
\(856\) −18.0714 + 16.7276i −0.617667 + 0.571737i
\(857\) −17.4489 37.4194i −0.596044 1.27822i −0.940620 0.339463i \(-0.889755\pi\)
0.344575 0.938759i \(-0.388023\pi\)
\(858\) 0.718302 1.89721i 0.0245224 0.0647697i
\(859\) 43.7495 + 36.7102i 1.49271 + 1.25253i 0.891151 + 0.453708i \(0.149899\pi\)
0.601562 + 0.798826i \(0.294545\pi\)
\(860\) −0.707462 6.77925i −0.0241243 0.231170i
\(861\) 0.535935 3.03944i 0.0182646 0.103584i
\(862\) 1.51892 0.851083i 0.0517346 0.0289880i
\(863\) −0.793731 + 2.96224i −0.0270189 + 0.100836i −0.978119 0.208048i \(-0.933289\pi\)
0.951100 + 0.308884i \(0.0999556\pi\)
\(864\) −13.5289 + 0.310397i −0.460262 + 0.0105599i
\(865\) 17.9726 19.5670i 0.611088 0.665297i
\(866\) 7.93474 7.73315i 0.269633 0.262783i
\(867\) −0.494726 1.84634i −0.0168018 0.0627051i
\(868\) 17.6955 + 8.81272i 0.600624 + 0.299123i
\(869\) −11.3622 13.5410i −0.385438 0.459347i
\(870\) 2.17075 2.30312i 0.0735952 0.0780831i
\(871\) 31.0810 5.48041i 1.05314 0.185697i
\(872\) −17.6082 + 43.1230i −0.596288 + 1.46033i
\(873\) 3.27533 3.27533i 0.110853 0.110853i
\(874\) 13.9241 14.4382i 0.470988 0.488379i
\(875\) −15.9072 2.15194i −0.537763 0.0727488i
\(876\) −0.0886353 0.591256i −0.00299471 0.0199767i
\(877\) 4.52838 6.46719i 0.152912 0.218382i −0.735386 0.677649i \(-0.762999\pi\)
0.888298 + 0.459267i \(0.151888\pi\)
\(878\) −37.1546 + 12.9843i −1.25391 + 0.438199i
\(879\) −3.29999 + 2.76902i −0.111306 + 0.0933967i
\(880\) 12.5621 7.10251i 0.423470 0.239425i
\(881\) 8.27276 14.3288i 0.278716 0.482751i −0.692350 0.721562i \(-0.743424\pi\)
0.971066 + 0.238811i \(0.0767577\pi\)
\(882\) 19.7760 + 0.254440i 0.665891 + 0.00856745i
\(883\) 27.2272 + 12.6962i 0.916267 + 0.427263i 0.822781 0.568358i \(-0.192421\pi\)
0.0934861 + 0.995621i \(0.470199\pi\)
\(884\) −11.4092 10.0849i −0.383733 0.339191i
\(885\) 0.377801 0.591477i 0.0126996 0.0198823i
\(886\) 4.19565 14.8895i 0.140956 0.500221i
\(887\) 6.19964 + 8.85400i 0.208163 + 0.297288i 0.909634 0.415410i \(-0.136362\pi\)
−0.701471 + 0.712698i \(0.747473\pi\)
\(888\) −2.33392 3.01011i −0.0783212 0.101013i
\(889\) 10.5345 12.5545i 0.353315 0.421065i
\(890\) −34.4308 + 43.5889i −1.15412 + 1.46110i
\(891\) 4.14636 11.3920i 0.138908 0.381647i
\(892\) −15.5876 + 52.7097i −0.521911 + 1.76485i
\(893\) −3.21125 1.37796i −0.107460 0.0461117i
\(894\) 1.29892 + 5.10970i 0.0434424 + 0.170894i
\(895\) −29.7091 22.8528i −0.993067 0.763884i
\(896\) 15.2795 5.51301i 0.510451 0.184177i
\(897\) 0.252139 + 2.88196i 0.00841867 + 0.0962259i
\(898\) 20.9105 3.41031i 0.697791 0.113803i
\(899\) 2.91670 16.5414i 0.0972773 0.551687i
\(900\) 16.8876 22.7306i 0.562920 0.757685i
\(901\) −2.52847 4.37944i −0.0842356 0.145900i
\(902\) −11.7478 2.22765i −0.391158 0.0741727i
\(903\) −0.813533 0.379357i −0.0270727 0.0126242i
\(904\) −34.0762 10.5558i −1.13336 0.351080i
\(905\) −37.8423 + 34.5935i −1.25792 + 1.14993i
\(906\) −10.1790 + 0.758726i −0.338173 + 0.0252070i
\(907\) −4.05138 + 46.3075i −0.134524 + 1.53762i 0.566251 + 0.824233i \(0.308393\pi\)
−0.700775 + 0.713383i \(0.747162\pi\)
\(908\) 2.16069 + 3.26126i 0.0717050 + 0.108229i
\(909\) −6.14685 + 1.08386i −0.203878 + 0.0359492i
\(910\) 3.63763 + 9.14337i 0.120586 + 0.303100i
\(911\) 14.0582i 0.465770i 0.972504 + 0.232885i \(0.0748166\pi\)
−0.972504 + 0.232885i \(0.925183\pi\)
\(912\) −3.98155 5.94149i −0.131842 0.196742i
\(913\) −14.5590 + 14.5590i −0.481832 + 0.481832i
\(914\) 8.50600 + 0.854580i 0.281353 + 0.0282670i
\(915\) 0.688607 0.527088i 0.0227646 0.0174250i
\(916\) 29.6736 + 6.02330i 0.980445 + 0.199015i
\(917\) 9.02665 + 0.789729i 0.298086 + 0.0260792i
\(918\) 9.00495 + 7.75564i 0.297208 + 0.255974i
\(919\) 11.6714 20.2155i 0.385005 0.666848i −0.606765 0.794881i \(-0.707533\pi\)
0.991770 + 0.128033i \(0.0408665\pi\)
\(920\) −11.7390 + 16.9031i −0.387022 + 0.557277i
\(921\) −2.65867 + 0.967675i −0.0876060 + 0.0318860i
\(922\) 3.63299 19.1590i 0.119646 0.630968i
\(923\) 1.71990 6.41874i 0.0566111 0.211275i
\(924\) 0.0488954 1.89984i 0.00160854 0.0625003i
\(925\) 16.4143 + 0.0390052i 0.539700 + 0.00128248i
\(926\) −14.5224 + 20.1824i −0.477235 + 0.663236i
\(927\) 33.7487 2.95263i 1.10845 0.0969772i
\(928\) −8.17351 11.1211i −0.268309 0.365067i
\(929\) 1.86991 5.13755i 0.0613499 0.168557i −0.905231 0.424920i \(-0.860302\pi\)
0.966581 + 0.256363i \(0.0825243\pi\)
\(930\) −0.514879 + 8.91552i −0.0168836 + 0.292352i
\(931\) 11.3360 + 18.3005i 0.371522 + 0.599773i
\(932\) −51.5385 15.2412i −1.68820 0.499243i
\(933\) 11.3007 5.26962i 0.369970 0.172520i
\(934\) −48.2074 + 21.7289i −1.57740 + 0.710991i
\(935\) −12.3698 2.75775i −0.404537 0.0901880i
\(936\) −17.2220 2.17913i −0.562918 0.0712270i
\(937\) 14.3956 10.0799i 0.470285 0.329297i −0.314294 0.949326i \(-0.601768\pi\)
0.784579 + 0.620028i \(0.212879\pi\)
\(938\) 25.7934 14.4526i 0.842186 0.471895i
\(939\) 3.31533 + 5.74233i 0.108192 + 0.187394i
\(940\) 3.47805 + 0.869907i 0.113442 + 0.0283732i
\(941\) 12.4278 4.52334i 0.405134 0.147457i −0.131412 0.991328i \(-0.541951\pi\)
0.536546 + 0.843871i \(0.319729\pi\)
\(942\) −0.149195 + 11.5960i −0.00486104 + 0.377816i
\(943\) 16.4706 4.41329i 0.536357 0.143716i
\(944\) −2.24027 2.08532i −0.0729145 0.0678715i
\(945\) −2.93059 7.09892i −0.0953322 0.230928i
\(946\) −1.51014 + 3.13264i −0.0490989 + 0.101851i
\(947\) −31.6519 22.1629i −1.02855 0.720198i −0.0678237 0.997697i \(-0.521606\pi\)
−0.960726 + 0.277499i \(0.910494\pi\)
\(948\) 5.34322 7.22774i 0.173540 0.234746i
\(949\) 1.57944i 0.0512708i
\(950\) 30.7433 + 2.20243i 0.997444 + 0.0714564i
\(951\) 2.12944i 0.0690518i
\(952\) −13.2068 5.39268i −0.428036 0.174778i
\(953\) 27.0637 + 18.9502i 0.876681 + 0.613859i 0.922886 0.385073i \(-0.125824\pi\)
−0.0462051 + 0.998932i \(0.514713\pi\)
\(954\) −5.19301 2.50338i −0.168130 0.0810498i
\(955\) −18.7563 45.4342i −0.606938 1.47022i
\(956\) 4.37535 1.46616i 0.141509 0.0474189i
\(957\) −1.55974 + 0.417931i −0.0504192 + 0.0135098i
\(958\) 57.2987 + 0.737213i 1.85124 + 0.0238183i
\(959\) −21.0540 + 7.66301i −0.679868 + 0.247452i
\(960\) 5.00537 + 5.36589i 0.161547 + 0.173183i
\(961\) 8.19752 + 14.1985i 0.264436 + 0.458017i
\(962\) −4.91871 8.77836i −0.158586 0.283026i
\(963\) 20.1951 14.1408i 0.650778 0.455680i
\(964\) 1.85975 + 0.731611i 0.0598986 + 0.0235636i
\(965\) −51.9340 11.5782i −1.67182 0.372717i
\(966\) 1.11368 + 2.47081i 0.0358322 + 0.0794969i
\(967\) −33.2632 + 15.5109i −1.06967 + 0.498797i −0.876021 0.482273i \(-0.839811\pi\)
−0.193653 + 0.981070i \(0.562033\pi\)
\(968\) 23.7322 + 0.916429i 0.762780 + 0.0294551i
\(969\) −0.898522 + 6.21659i −0.0288647 + 0.199706i
\(970\) −5.16410 0.298231i −0.165809 0.00957563i
\(971\) 11.1782 30.7119i 0.358726 0.985590i −0.620747 0.784011i \(-0.713170\pi\)
0.979472 0.201579i \(-0.0646073\pi\)
\(972\) 20.3870 + 2.31353i 0.653912 + 0.0742064i
\(973\) 4.63526 0.405533i 0.148600 0.0130008i
\(974\) −17.0451 12.2649i −0.546159 0.392992i
\(975\) −3.15082 + 3.13588i −0.100907 + 0.100429i
\(976\) −1.71986 3.36793i −0.0550513 0.107805i
\(977\) 7.75798 28.9532i 0.248200 0.926294i −0.723548 0.690274i \(-0.757490\pi\)
0.971748 0.236020i \(-0.0758432\pi\)
\(978\) 12.9148 + 2.44896i 0.412971 + 0.0783090i
\(979\) 26.6316 9.69311i 0.851149 0.309793i
\(980\) −14.4776 16.6794i −0.462468 0.532804i
\(981\) 23.3169 40.3861i 0.744451 1.28943i
\(982\) 32.4212 37.6438i 1.03460 1.20126i
\(983\) −0.227564 0.0199093i −0.00725817 0.000635008i 0.0835261 0.996506i \(-0.473382\pi\)
−0.0907843 + 0.995871i \(0.528937\pi\)
\(984\) −0.295802 6.07288i −0.00942981 0.193596i
\(985\) 19.8159 15.1679i 0.631386 0.483289i
\(986\) −1.21165 + 12.0601i −0.0385868 + 0.384071i
\(987\) 0.333859 0.333859i 0.0106269 0.0106269i
\(988\) −8.07525 17.0823i −0.256908 0.543459i
\(989\) 4.95934i 0.157698i
\(990\) −13.4244 + 5.34081i −0.426656 + 0.169742i
\(991\) −29.1673 + 5.14299i −0.926531 + 0.163372i −0.616501 0.787354i \(-0.711450\pi\)
−0.310030 + 0.950727i \(0.600339\pi\)
\(992\) 37.8384 + 9.21398i 1.20137 + 0.292544i
\(993\) −0.850998 + 9.72695i −0.0270056 + 0.308676i
\(994\) −0.462745 6.20812i −0.0146774 0.196910i
\(995\) 17.4747 15.9745i 0.553987 0.506426i
\(996\) −8.92923 5.46632i −0.282933 0.173207i
\(997\) 18.5717 + 8.66013i 0.588172 + 0.274269i 0.693836 0.720133i \(-0.255919\pi\)
−0.105664 + 0.994402i \(0.533697\pi\)
\(998\) 6.09088 32.1209i 0.192803 1.01677i
\(999\) 3.92668 + 6.80120i 0.124235 + 0.215180i
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 380.2.bj.a.327.46 yes 672
4.3 odd 2 inner 380.2.bj.a.327.4 yes 672
5.3 odd 4 inner 380.2.bj.a.23.18 672
19.5 even 9 inner 380.2.bj.a.347.33 yes 672
20.3 even 4 inner 380.2.bj.a.23.33 yes 672
76.43 odd 18 inner 380.2.bj.a.347.18 yes 672
95.43 odd 36 inner 380.2.bj.a.43.4 yes 672
380.43 even 36 inner 380.2.bj.a.43.46 yes 672
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.bj.a.23.18 672 5.3 odd 4 inner
380.2.bj.a.23.33 yes 672 20.3 even 4 inner
380.2.bj.a.43.4 yes 672 95.43 odd 36 inner
380.2.bj.a.43.46 yes 672 380.43 even 36 inner
380.2.bj.a.327.4 yes 672 4.3 odd 2 inner
380.2.bj.a.327.46 yes 672 1.1 even 1 trivial
380.2.bj.a.347.18 yes 672 76.43 odd 18 inner
380.2.bj.a.347.33 yes 672 19.5 even 9 inner